Assessment of GRACE
satellites for groundwater
estimation in Australia
P. Tregoning, S. McClusky
Research School of Earth Sciences
the Australian National University
A.I.J.M. van Dijk, R.S. Crosbie,
J.L. Peña-Arancibia
CSIRO Water for a Healthy Country Flagship
Waterlines Report Series No 71, February 2012
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Waterlines
This paper is part of a series of works commissioned by the National Water Commission on
key water issues. This work has been undertaken by a consortium of scientists from The
Australian National University and CSIRO on behalf of the National Water Commission.
© Commonwealth of Australia 2012
This work is copyright.
Apart from any use as permitted under the Copyright Act 1968, no part may be reproduced by
any process without prior written permission.
Requests and enquiries concerning reproduction and rights should be addressed to the
Communications Director, National Water commission, 95 Northbourne Avenue, Canberra
ACT 2600 or email bookshop@nwc.gov.au.
Online/print: ISBN: 978-1-921853-54-8
Assessment of GRACE satellites for groundwater estimation in Australia, February 2012
Authors: P Tregoning, S McClusky, A.I.J.M. van Dijk, RS Crosbie and JL Peña-Arancibia
Published by the National Water Commission
95 Northbourne Avenue
Canberra ACT 2600
Tel: 02 6102 6000
Email: enquiries@nwc.gov.au
Date of publication: February 2012
Cover design by: Angelink
Front cover image courtesy of nasa.gov.au
An appropriate citation for this report is:
Tregoning P et al, 2012, Assessment of GRACE satellites for groundwater estimation in
Australia, Waterlines report, National Water Commission, Canberra
Disclaimer
This paper is presented by the National Water Commission for the purpose of informing
discussion and does not necessarily reflect the views or opinions of the Commission.
Contents
Executive summary ................................................................................................................... ix
1. Introduction ............................................................................................................................1
1.1 The earth’s gravity field and the GRACE mission ......................................................1
1.2 Why use GRACE to monitor groundwater? ...............................................................3
2. Review of existing studies applying GRACE to hydrology or groundwater estimation .........5
2.1 Hydrological studies using GRACE products .............................................................5
2.2 Review of applications of GRACE products for hydrological studies in
Australia ............................................................................................................................9
3. Assessment of the available GRACE gravity fields .............................................................12
3.1 GRACE products and their use ................................................................................12
3.2 Comparison and validation of EWH solutions ..........................................................20
4. Interpreting GRACE water storage estimates ......................................................................22
4.1 Introduction ...............................................................................................................22
4.2 Review ......................................................................................................................23
4.3 Soil moisture storage estimation uncertainty due to rainfall estimation
error ................................................................................................................................26
4.4 Soil storage estimation uncertainty due to model error ............................................31
5. Derivation and Assessment of Groundwater Variations .......................................................39
5.1 Point-scale groundwater level observations .............................................................39
5.2 Grid-scale groundwater level observations ..............................................................40
5.3 Time series comparison of groundwater level observations and
GRACE/AWRA ...............................................................................................................42
5.4
Assessment of the comparison in GWS between the GW data and
GRACE ...........................................................................................................................64
6. Known Errors and Estimates of Uncertainties of Remotely Sensed Groundwater ..............67
6.1 Quantification of GRACE errors ...............................................................................67
6.2 Quantification of modelled soil moisture errors ........................................................73
6.3 Groundwater uncertainty map for Australia ..............................................................73
7. Conclusions ..........................................................................................................................75
Bibliography ..............................................................................................................................77
Tables
Table 1: Average continental (including Tasmania) seasonal amplitude, trend and RMSD
when compared with AWRA-L for 2002–2010 ...............................................................36
Table 2: Details on the grid cells chosen for further investigation (shown in Figure 19d) ........42
Figures
Figure 1: The GRACE space gravity mission (nasa.gov.au) ......................................................2
Figure 2: The earth’s gravity field, showing a) the latitudinal variation caused by the equatorial
bulge, b) a snapshot of geophysical processes by computing anomalies at a single
epoch (i.e. residual signal about the mean value)..........................................................13
Figure 3: Rate of change (in terms of EWH) for the CSR GRACE solutions (2002–2011) using
Gaussian filtering with radii from 0 km to 700 km ..........................................................16
Figure 4: Rate of change (in terms of EWH) for the period 2002–2011 derived from the GRGS
and CSR solutions using coefficient rates that pass an f-test with statistical confidence
interval of 95%, 99%, 99.9% or 99.99%. ........................................................................19
Figure 5: Rate of change in the Australian region (in terms of EWH/year) derived from several
different GRACE solutions spanning 2002–2010...........................................................21
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Figure 6: (a) Standard difference between GRACE and AWRA-L TWS anomalies (b) GRACE
water storage retrieval error estimates (c) Coefficient of correlation between GRACE
and AWRA TWS anomalies (d) Colour composite showing the relative contribution of
the three signal components (seasonal cycle, eight-year trends, de-trended anomalies)
to the overall disagreement between GRACE and AWRA-L TWS (from Van Dijk et al.
2011) ..............................................................................................................................24
Figure 7: (a) Geographical distribution of active rain gauges (black dots) during 1998–2008
used in generating precipitation forcing data (b) Areas with >20 unreliable data (in blue)
during 1911–2010 (after BoM 2011) ..............................................................................26
Figure 8: Summary statistics for the three member ensemble precipitation data (SILO,
BAWAP and LSBLEND) for 1998–2008. .......................................................................28
Figure 9: Comparison of precipitation monthly correlation (r) and root mean squared
difference (RMSD) for all months in 1998–2008. ...........................................................29
Figure 10: Comparison of AWRA-L modelled soil moisture storage (SMS) trends with different
precipitation forcing for 1998–2008. ...............................................................................30
Figure 11: Comparison of AWRA modelled soil moisture correlation with different precipitation
forcing for 1998–2008. ...................................................................................................31
Figure 12: Modelled soil moisture seasonal amplitude for 2002–2010 ....................................33
Figure 13: Modelled SMS trend for 2002–2010 .......................................................................34
Figure 14: Root mean square difference (RMSD) in soil moisture storage (SMS) anomalies for
2002–2010, between the four GLDAS models and AWRA-L ........................................35
Figure 15: Averaged root mean square difference between soil moisture storage (SMS)
estimates from the four GLDAS models and AWRA ......................................................35
Figure 16: (a) Monthly uncertainty time series (in the form of standard deviation) from the
AWRA-L and GLDAS models evaluated in the Canning basin near Broome (E122.5º,
S17.5º) (b) Ensemble SMS change (blue line and dots) showing standard deviation
bars (grey) (c) Time series of SMS change from AWRA-L and GLDAS ........................37
Figure 17: (a) Monthly uncertainty time series (in the form of standard deviation) from the
AWRA-L and GLDAS models evaluated in the Condamine basin (E148.5º, S27.5º) (b)
Ensemble SMS change (blue line and dots) showing error bars (grey) (c) Time series of
SMS change from the AWRA-L and GLDAS .................................................................38
Figure 18: Trend in groundwater level at each monitoring bore that has at least five
measurements spread over at least two years in the period 1/7/2002 to 30/6/2010 .....39
Figure 19: Trends in groundwater level from monitoring bores aggregated to a grid scale .....41
Figure 20: Method used to create a time series of EWH from multiple observation bores within
a grid cell ........................................................................................................................44
Figure 21: Sources of uncertainty in the calculation of the combined time series at the Lachlan
grid cell ...........................................................................................................................45
Figure 22: Differences in the combined time series at Lachlan of assuming different values of
specific yield (note the different y-axis scales) ...............................................................45
Figure 23: Surface geology of the grid cell near Broome with the location and trend in the
observation bores ...........................................................................................................46
Figure 24: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Broome ........................................................47
Figure 25: Surface geology of the grid cell near Telfer with the location and trend in the
observation bores ...........................................................................................................48
Figure 26: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Telfer ...........................................................48
Figure 27: Surface geology of the grid cell in the Daly West with the location and trend in the
observation bores ...........................................................................................................49
Figure 28: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Daly West...................................................50
Figure 29: Surface geology of the grid cell in the Daly East with the location and trend in the
observation bores ...........................................................................................................51
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Figure 30: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Daly East....................................................51
Figure 31: Surface geology of the grid cell in the Fitzroy East with the location and trend in the
observation bores ...........................................................................................................52
Figure 32: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Fitzroy East ................................................53
Figure 33: Surface geology of the grid cell in the Fitzroy West with the location and trend in
the observation bores .....................................................................................................54
Figure 34: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Fitzroy West ...............................................54
Figure 35: Surface geology of the grid cell in the Brisbane Catchment with the location and
trend in the observation bores ........................................................................................55
Figure 36: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Brisbane Catchment ..................................56
Figure 37: Surface geology of the grid cell in the Condamine East with the location and trend
in the observation bores .................................................................................................57
Figure 38: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Condamine East ........................................57
Figure 39: Surface geology of the grid cell in the Condamine West with the location and trend
in the observation bores .................................................................................................58
Figure 40: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Condamine West .......................................59
Figure 41: Surface geology of the grid cell in the lower Lachlan with the location and trend in
the observation bores .....................................................................................................60
Figure 42: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the lower Lachlan .............................................60
Figure 43: Surface geology of the grid cell near Renmark with the location and trend in the
observation bores ...........................................................................................................61
Figure 44: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Renmark ......................................................62
Figure 45: Surface geology of the grid cell near Shepparton with the location and trend in the
observation bores ...........................................................................................................63
Figure 46: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Shepparton ..................................................63
Figure 47: Scatter plot of the GWS derived from GW data and GRACE (GRGS solution minus
AWRA-L) ........................................................................................................................65
Figure 48: a) Time series of EWH change (and formal uncertainties) from the GRGS GRACE
solutions evaluated at location E122º, S22º, b) Time series of the formal uncertainties
themselves, c) Histogram of the formal uncertainties ....................................................68
Figure 49: Histogram of uncertainties in GRACE EWH at 145ºE for latitudes 5ºS, 45ºS and
85ºS ................................................................................................................................69
Figure 50: Amplitude of S2 ocean tide errors in GRACE solutions, aliased to 161-day period
signal in EWH time series ..............................................................................................70
Figure 51: Amplitude of the annual variations in GRACE solutions .........................................71
Figure 52: Standard deviation (of a single observation about the mean) of the MOG2D-G
barotropic ocean model ..................................................................................................72
Figure 53: Estimated overall uncertainty in SMS estimates. ....................................................73
Figure 54: Map showing likely uncertainties in groundwater estimates derived from a
combination of GRACE TWS and SMS .........................................................................74
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Abbreviations and acronyms
AARR
Accumulated Annual Rainfall Record
AWRA
Australian Water Resources Assessment system
AWRA-L
AWRA Landscape hydrology model
BAWAP
Bureau of Meteorology Australian Water Availability Project
BoM
Bureau of Meteorology
C20
Degree 2, Order 0 spherical harmonic coefficient that describes the equatorial
bulge of the earth
CSR
Center for Space Research, University of Texas at Austin, USA
EWH
Equivalent Water Height
GFZ
GeoForschungsZentrum (German Research Centre for Geosciences)
GLDAS
Global Land Data Assimilation System
GRACE
Gravity Recovery and Climate Experiment
GRGS
Groupe de Recherche de Géodésie Spatiale (Space Geodesy Research
Group, France)
GWL
groundwater level
GWS
groundwater storage
IOD
Indian Ocean dipole
ITG
Institute of Geodesy and Geoinformation, University of Bonn, Germany
JPL
NASA Jet Propulsion Laboratory
LAGEOS
Laser Geodynamics Satellites
LSBLEND
blended satellite-gauge precipitation estimates (Li and Shao 2010)
MDB
Murray–Darling Basin
MOG2D-G
2-dimensional gravity waves barotropic model of Carrère and Lyard (2003)
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NOAH
N: National Centers for Environmental Prediction; O: Oregon State University
(Department of Atmospheric Sciences); A: Air force; H: Hydrologic Research
Lab
RMSD
Root Mean Square Difference
SILO
Specialised Information for Land Owners spatial precipitation estimates
SMS
Soil Moisture Storage
SWS
Surface Water Storage
TWS
Total Water Storage
WIRADA
Water Information Research and Development Alliance
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Executive summary
Groundwater management and GRACE
Groundwater is an important resource for many water users in Australia. Water managers
need information on the character, dynamics and current status of groundwater resources to
inform the planning and adjustment of groundwater management regimes. Ongoing
challenges in groundwater management include the expense and scarcity of groundwater
mapping and monitoring, the high spatial variability in groundwater system characteristics and
the complexity of groundwater storage dynamics. This combination means that local
measurements cannot be interpreted over larger areas without introducing large uncertainty.
The Gravity Recovery and Climate Experiment (GRACE) space gravity mission was launched
in 2002 with a planned 5-year lifetime. The mission, a scientific and technical success, is still
functioning today. GRACE mass variation estimates over Australia quantify changes in total
water storage expressed as an Equivalent Water Height (EWH). Estimating groundwater
changes then requires separating the total water storage changes into the components of
surface water, soil moisture, biomass and groundwater.
The reliability and accuracy of GRACE-derived groundwater storage changes depends upon
both the GRACE total water storage estimates and the soil moisture content estimates being
accurate and containing no systematic biases or trends. To estimate reliable large-scale
groundwater storage changes from discrete measurements in monitoring bores, the bore level
observations must be representative of the groundwater variations at larger scales and the
specific yield (or percentage of water per volume of subsurface material) must be known
accurately to enable the conversion from groundwater levels to groundwater volumes. These
requirements are critical to the resulting accuracy of each technique, and errors will degrade
the agreement in the comparison of groundwater estimates from the two techniques.
Errors in groundwater storage estimates derived from this process will be the summation of
the errors in the GRACE total water storage changes, the modelled soil moisture values and
the surface water estimates. Studies to date, and analysis in this report, show that the
greatest uncertainty originates from the separation between soil moisture and groundwater: in
other words, separating storage in the unsaturated and saturated zones. Careful
consideration of the assumptions and processes involved can lead to the generation of a map
that shows the accumulated uncertainty in groundwater storage estimates over Australia
derived from remote sensing observations.
The two most commonly used GRACE products are those of the Centre for Space Research
(CSR) at the University of Texas, Austin, and the French Groupe de Recherche de Géodésie
Spatiale (GRGS). The CSR fields must undergo filtering and scaling procedures before being
used to estimate water mass changes. The GRGS solutions undergo a regularisation during
the generation of the products, and hence, can be used directly without subsequent filtering.
We assessed the likely errors in the rate fields of both CSR and GRGS solutions and then
focused our error analysis on just the GRGS solutions, because they seem to provide the
best agreement with soil moisture and groundwater bore information across Australia.
Objective
The goal of this study is to evaluate the potential utility of GRACE observations for deriving
estimates of groundwater storage changes. Preconditions of such a use are (1) that estimates
of groundwater storage can reliably be derived from GRACE for at least some parts of
Australia, (2) that the estimation accuracy is sufficient (that is, the uncertainty sufficiently
small) to be useful for management, and (3) that estimates can be reconciled with
measurements in monitoring bores, where available.
In this report, we independently quantified the likely level and spatial and temporal variations
of error in each of the above assumptions. We also attempted to reconcile the two
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independent estimates of groundwater storage variations for 12 1°x1° grid cells where
groundwater level variations from a reasonably large number of bores could be obtained.
Results
GRACE total water storage estimates around Australia are affected by errors in modelled
ocean mass movement—both tidal and non-tidal. This is most problematic around the coast,
northern Australia and in the region of Gulf St Vincent. The formal uncertainties of the
GRACE estimates at any epoch increase from approximately 21 mm EWH in Tasmania to
26 mm EWH in Cape York, caused by changes in the spatial separation of the GRACE
satellite ground tracks.
Errors in the precipitation models used to force the hydrological models induce variations in
soil moisture estimates of more than 30 mm/month where rainfall is high and seasonal, spatial
rainfall gradients are high and the density of gauges low. Most of this error is random, but we
found systematic differences in linear soil moisture trends of >5 mm per year. Differences in
model assumptions, structure and parameters cause large systematic differences in soil
moisture estimates between models, with the greatest monthly differences (>20 mm) in
regions with high rainfall and a strong seasonality. Strong differences in linear trends
(>10 mm per year) were found in northern Queensland and Tasmania, while differences in the
seasonal amplitude in soil moisture storage dominated elsewhere. The lack of accurate
knowledge about the maximum capacity of the soil to store and retain water affects, in
particular, the estimated seasonal amplitude in the models. This is caused by uncertainty in
depth to groundwater, active root zone depth, and soil hydraulic properties.
The error in the specific yield is very difficult to quantify and acts as a scale factor in the
conversion from groundwater level in boreholes to changes in EWH. The distribution of
monitored groundwater boreholes is not homogeneous and was commonly biased towards
certain areas or groundwater systems. Accounting for this sampling problem would require a
good understanding of local hydrogeology and the characteristics of the monitoring bores.
The comparison between groundwater storage changes derived from GRACE and model soil
moisture, and those derived from bore data produced mixed results. For a few regions, the
direction of bore levels and GRACE-inferred groundwater storage was opposite. In some
cases the bore estimates were also opposite to those estimated from rainfall patterns directly,
while in other cases there was no consistency in linear trend between individual bores within
the grid cell, with both increasing and decreasing trends observed. Generally, for regions with
a large number of bores (Lachlan, Renmark, Shepparton), there was better agreement
between GRACE- and bore-derived water storage.
In cases with strong seasonality in GRACE water storage (e.g. northern Australia), the
modelled soil moisture accounted for most of that variability, whereas the bore estimates
suggested that groundwater, too, had a strong seasonal cycle. This implies that shallow
groundwater changes have been included in the model parameterisation of soil storage
capacity.
In summary, our results indicate that three sources of uncertainty prevent us from making a
direct comparison between the two methods of groundwater storage estimation, namely, (1)
hydrological model assumptions required to estimate soil moisture dynamics, (2) the scarcity
and biased positioning of groundwater monitoring bores, and (3) specific yield assumptions
that need to be made to translate groundwater levels into storage.
Recommendations
For the few regions with sufficient bores to allow a good comparison (e.g. Shepparton,
Renmark), we found arguably reasonable agreement 1 in derived groundwater storage
1
The agreement (or otherwise) between the two techniques is detailed in Chapter 5.
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estimates. Nonetheless, some distinct differences were found and these lead to the following
recommendations.
1. A major source of uncertainty in deriving groundwater dynamics from GRACE is the need
to subtract estimated soil moisture storage. For most of the 12 regions investigated, it was
not possible to reliably infer seasonal cycles in groundwater storage from GRACE
because of uncertainty in the seasonal cycle of water storage in the unsaturated zone.
This uncertainty can be reduced by improving the soil moisture modelling using better
spatial information on depth to groundwater, subsurface hydraulic properties and
vegetation rooting depth, and improved representation of groundwater discharge
processes in the hydrological model used. This requires a combination of field
hydrological process knowledge and a sufficient number of observations of groundwater
and soil water behaviour in space and time. Such models may exist for certain regions.
On a continental scale, CSIRO and the Bureau of Meteorology are currently improving the
Australian Water Resources Assessment system along these lines.
Recommendation 1: To interpret GRACE observations of groundwater variations, it is first
necessary to identify or develop hydrological models that cover a sufficiently large area
and which are known to describe saturated and unsaturated dynamics (and their
coupling) reliably.
2. GRACE can add an overall constraint on a sufficiently reliable model, by providing the
total monthly water storage changes, each with an accuracy of approximately 25 mm
EWH. Moreover, there is no reason to assume the presence of systematic errors such as
long-term drift in the monthly GRACE solutions. Therefore, a particular strength of the
GRACE data is in providing valuable information on inter-annual changes in water
storage over large areas. Methods are required to constrain finer-resolution models with
these observations.
Recommendation 2: Research needs to be conducted into how to assimilate GRACE total
water storage into hydrological models in Australia.
3. There is potential for GRACE observations to help improve the translation of groundwater
level changes measured in bores into groundwater volumes. Comparisons of the two
independent groundwater estimates could be used to derive specific yield values on
broad scales, and these could be used to extrapolate estimates derived locally from bore
pumping tests.
Recommendation 3: A study should be undertaken of the feasibility and accuracy of
specific yield estimates from the comparison of GRACE, soil moisture and groundwater
levels from borehole measurements.
4. The utility of GRACE-derived water storage estimates and the ability to reconcile these
with bore measurements is limited by the coarse resolution of GRACE TWS estimates.
Recommendation 4: Improvements in the spatial resolution of GRACE products, tailored
for the Australian hydrological community, need to be made in order to make the GRACE
products more relevant for the Australian groundwater community.
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1. Introduction
Knowledge and understanding of groundwater systems is complicated by the fact that it is
difficult and expensive to make observations of groundwater levels. Traditional methods
involve the drilling and monitoring of groundwater bores, yet such approaches provide only
discrete sampling and limited knowledge on catchment and/or basin scales. Nonetheless, the
observations of groundwater levels at such bores have provided the only knowledge on the
changes in water resources in groundwater systems.
With the launch of the Gravity Recovery and Climate Experiment (GRACE) mission in 2002, a
new capability to observe total water storage (TWS) at broad spatial scales became available.
GRACE detects the integrated change in mass of all components of the hydrological cycle,
including groundwater, soil moisture and surface storage. Thus, there is the possibility of
deriving groundwater variation estimates if the hydrology signals other than groundwater can
be subtracted from GRACE TWS estimates.
This report investigates the potential of using the GRACE space gravity mission, in
conjunction with modelling of soil moisture storage (SMS), to derive estimates of broad-scale
groundwater changes. In this chapter we describe the GRACE mission and the potential it
offers for monitoring groundwater. Chapter 2 describes some of the pioneering hydrological
studies conducted using GRACE observations as well as applications in the Australian region.
Chapters 3 assesses some of the available GRACE products and explains how they should
be used and their known limitations. In Chapter 4 we describe methods to estimate the
influence of terrestrial mass changes other than groundwater, and in particular soil moisture
storage, and uncertainties in accounting for these influences. In Chapter 5 we derive
estimates of groundwater storage change for a number of regions in Australia where we can
compare these with groundwater storage change estimates derived from groundwater bore
measurements. An assessment of the known biases in the GRACE and soil moisture
estimation, including their spatial variability, is used to generate a groundwater uncertainty
map in Chapter 6. This can be used to assess where remotely sensed groundwater estimates
are likely to be more reliable. Conclusions and recommendations are made in Chapter 7.
1.1 The earth’s gravity field and the GRACE
mission
The Gravity Recovery and Climate Experiment (GRACE) space gravity mission is a joint
mission by NASA and the German Deutsche Forschungsanstalt für Luft und Raumfahrt (DLR)
mission. Launched in 2002 with a planned 5-year lifetime2, the single earth observing mission
has brought together a number of different disciplines, providing information at broad spatial
scales. There are well over 100 scientific publications each year that depend on GRACE data.
GRACE data has been used to study geophysical processes on earth including earthquake
deformation, melting of continental ice and oceanic and hydrologic processes. Temporal
estimates (monthly or 10-daily snapshots) of the earth’s gravity field are publicly available as
Level-2 products from the GRACE mission (described in Chapter 3). The GRACE mission is
expected to survive until (at best) 2014, while the replacement GRACE Follow-on mission is
not scheduled for launch until 2017.
Gravity is much weaker than other basic natural forces such as strong and weak nuclear
interaction and electromagnetism. But gravity’s effects are ubiquitous and dramatic. It plays a
significant role in controlling everything from the earth’s tides to the expansion of the universe.
2
The mission is still functioning today, although many components are now in critical status and
batteries are starting to fail. Unforseen failure of this mission would result in no such space-based
gravity observations of the Earth being available until the launch of the GRACE Follow-on mission,
currently scheduled for 2017.
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Gravity is a natural phenomenon by which physical bodies attract with a force that is
proportional to their mass. Mass refers to the amount of matter contained within a given
space and is directly related to the density of a material. As an example, a volume filled with
more dense material, like rock, has more mass than that same volume filled with water. Since
mass and density are directly related, there is also a direct relationship between density and
gravity. An increase in density results in an increase in mass, and an increase in mass results
in an increase in the gravitational force exerted by the volume. Mass fluctuations on the
surface of the earth, and within the earth’s interior, therefore, cause variations in the gravity
field. The branch of science that deals with obtaining precise measurements of the earth,
including its geometric shape and gravitational field, is known as geodesy.
Since the first artificial earth satellite was launched in 1957 (Sputnik), geodesists have used
observations of and from satellites to improve our knowledge of the earth's gravity field. While
these early gravity measurements described the large-scale features of earth's gravitational
field they could not resolve the finer-scale features or accurately describe the small month-tomonth variations associated with mass redistributions on and within the earth. To learn more
about the earths’ gravity, in particular its time variable nature, the twin GRACE satellites were
launched in 2002 with the primary goal to precisely measure the changing gravity field of the
earth.
Figure 1: The GRACE space gravity mission (nasa.gov.au)
GRACE is the first earth-monitoring mission in the history of space flight whose key
measurement is not derived from electromagnetic waves either reflected off, emitted by, or
transmitted through the earth's surface and/or atmosphere. Instead, the mission uses a
microwave ranging system to accurately measure changes in the speed and distance
between two identical spacecraft flying in a polar orbit about 220 kilometers apart, 500
kilometers above the earth (Figure 1). The ranging system is sensitive enough to detect
separation changes as small as 10 micrometres (approximately one-tenth the width of a
human hair) over a distance of 220 kilometers. ('GRACE Launch Press Kit'—
http://grace.jpl.nasa.gov/files/GRACE_Press_Kit.pdf).
Circling the globe every 90 minutes, the twin GRACE satellites sense infinitesimal variations
in earth's gravitational field. When the first satellite approaches a region of stronger gravity,
called a 'gravity anomaly', it is accelerated towards it. This causes the distance between the
two satellites to increase. The first spacecraft lingers over the anomaly because it is
decelerated by it. Meanwhile the following spacecraft is accelerated and will catch up to the
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first satellite, thus decreasing the distance between them. The first satellite will continue past
the anomaly while the second is still retarded by it and so the distance between the satellites
increases.
This continuous change in distance between the satellites is caused directly by the highs and
lows of the gravity field. By constantly measuring the changing distance between the two
satellites and combining that data with precise measurements of the GRACE satellites'
absolute positions from Global Positioning System (GPS) instruments onboard, we can
construct a detailed map of earth's gravity as a function of time.
The two satellites constantly maintain a two-way K/Ka-band microwave-ranging link3 between
them. Precise accelerometers located at the center of mass of each satellite are used to
distinguish (and correct for) accelerations caused by non-gravitational sources such as
atmospheric drag, solar radiation and satellite thruster firings. All of this information is
downloaded to ground stations. To maintain correct baseline separation and proper
orientation of each spacecraft, the satellites use star cameras, magnetometers, and GPS
observations. The GRACE vehicles also have optical corner reflectors to enable laser ranging
from ground stations, bridging the range between spacecraft positions and Doppler ranges.
('GRACE Mission Overview'—http://www.csr.utexas.edu/grace/overview.html).
Visit http://www.csr.utexas.edu/grace for additional information about the Gravity Recovery
and Climate Experiment.
1.2 Why use GRACE to monitor groundwater?
While in situ hydrologic measurements provide discrete sampling of soil, ground and surface
water, GRACE gravity observations provide a unique quantitative measurement of TWS
anomalies that are not available to hydrologists by any other practical means. GRACE gives
hydrologists the ability to close the terrestrial water storage budget by providing a quantitative
estimate of total integrated water mass change over time. With nearly 10 years of GRACE
observations, long-term trends in terrestrial TWS can now be reliably assessed and compared
with hydrological models and standard drought indices.
The combination of remotely sensed total water storage changes from GRACE and SMS
modelling and surface water estimates, offers the possibility to estimate groundwater changes
without the costly effort of drilling and instrumenting discrete groundwater bores. If shown to
be sufficiently accurate, this could provide a totally new spatial and temporal dataset for
groundwater monitoring, enabling observation of all the aspects of the hydrological cycle.
Until recently, one of the major factors limiting the usefulness of GRACE estimates in
hydrological models has been its relatively low native spatial resolution (about 350 km).
Recent progress, however, has been made in reducing this spatial resolution by customising
GRACE analysis for particular regions, catchments and drainage basins, and has enabled
GRACE to provide valuable information on fine-scale integrated mass redistribution. For
example, the work of Wouters et al. (2008) showed that using a forward modelling
('fingerprint') approach allowed for better spatial resolution of time variable masses changes
in Greenland to be derived than could be achieved using the original spherical harmonics
directly. Similarly, the paper by Kurtenbach et al. (2009) that applied a Kalman filter approach
to steer the spherical harmonic solutions was able to resolve spatially variable unloading rates
over different regions of the Greenland ice sheet. More recently, Longuevergne et al. (2010)
developed a mass concentration algorithm, called spatiospectral localisation, to study the US
High Plains aquifer, which optimises drainage basin shape descriptions, taking into account
GRACE’s limited spatial resolution and noise characteristics. This method appears to be
3
The K/Ka-band microwave link is the inter-satellite range measuring system that provides the
information that makes the GRACE mission unique at this time in being able to detect accurately the
temporal changes in the Earth’s gravity field. Changes in the separation distance of the two spacecraft
are related to the strength of the gravity field, which changes with both spatial location and time.
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particularly suited to retrieval of basin‐ scale TWS variations and is effective for basins as
small as 200,000 km2 (e.g. Longuevergne et al. 2010; Luthcke et al. 2006).
Since launch in 2002, GRACE has been proven reliable, and offers a great potential for water
storage budget closure on basin to regional scale (Swenson et al. 2006; Yeh et al. 2006).
GRACE data is available for virtually all river basins and can be used to estimate water
storage change in the thin layer at the surface of the earth (Brunner et al. 2006; Swenson et
al. 2006) with unprecedented accuracy (Tapley et al. 2005). GRACE is promising because no
other global network exists of hydrological observations with temporal and spatial resolutions
necessary to characterise storage on regional to continental scale (Swenson et al. 2006;
Klees et al. 2006; Chen et al. 2007).
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2. Review of existing studies applying
GRACE to hydrology or groundwater
estimation
In this chapter we assess how GRACE data has been used to study hydrological processes.
We begin in Section 2.1 with simulation studies that were used prior to the launch of the
GRACE satellites to demonstrate the likely capability of the mission and capacity to estimate
signals associated with groundwater, surface water and soil moisture. Some of the extreme
climate events over the past decade are described as seen by GRACE. We then look in detail
at some of the groundwater studies that have been undertaken and at some attempts to
validate, through in situ observations, the estimates of terrestrial water storage change from
GRACE. In Section 2.2 we focus on the applications of GRACE data to studies of Australian
hydrology.
2.1 Hydrological studies using GRACE products
Prelaunch assessments of the anticipated results from the GRACE mission showed that
monthly, seasonal and annual changes in water storage within drainage basins should be
detectable in basins of approximately 200 000 km2 (Rodell and Famiglietti 1999). The primary
controls on the detectability of the signals were thought to be driven by the GRACE
instrumental errors, atmospheric modelling errors in the region of the drainage basin and the
magnitude of the water storage changes themselves.
The first published results using data from the GRACE mission showed significant
improvement in the accuracy with which the earth’s gravity field could be measured (Tapley et
al. 2004) and yielded the first estimates of the amplitude of annual variations in the global
hydrological cycle. However, the results were about 40 times worse than the predicted
accuracy from prelaunch simulations (Wahr et al. 2004). Significant errors in a north–south
striping pattern were evident in the solutions, completely masking the hydrological and
oceanic signals that were being sought. The stripes were found to be related to unidentified
errors in the reduction of the raw observations and filtering techniques were employed to
reduce these errors (Tapley et al. 2004; Wahr et al. 2004).
Subsequently, hundreds of studies using GRACE have been undertaken to quantify
hydrologic, oceanic and climatic changes on the earth. These include the estimation of snow
mass (Frappart et al. 2006), the derivation of steric sea level variations4 (e.g. Lombard et al.
2007), the seasonal exchange of water between oceans and continents (Chambers et al.
2004), and glacial isostatic adjustment5 (e.g. Tamisiea et al. 2007; Tregoning et al. 2009a; Wu
et al. 2010; Ivins et al. 2011).
In this chapter, we review some of the original studies that demonstrated the capabilities of
the GRACE mission. We also provide examples of recent studies that show how improved
analysis techniques have led to greater accuracy in the estimation of mass changes. We
divide the discussion into studies of TWS changes, examples of extreme climate events
(droughts, floods, etc.), quantification of only groundwater variations and, finally, the validation
of GRACE estimates.
4
Steric sea level variations are the increases or decreases of sea surface heights through the
combination of thermal expansion/contraction and density changes related to salinity variations.
5 Glacial isostatic adjustment is the return to a state of isostatic (or buoyancy) equilibrium of the Earth’s
crust as a result of changes in the mass of the ice sheets on the continents since the Last Glacial
Maximum about 20 000 years ago.
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2.1.1 Total water storage (TWS) studies
Despite its importance, TWS at regional and continental scales remains poorly known
(Ramillien et al. 2008), largely because of a lack of systematic and comprehensive
observations (Lettenmaier and Famiglietti 2006). The prelaunch study of Rodell and
Famiglietti (1999) investigated the feasibility of detecting monthly, seasonal and trend signals
in drainage basins of different spatial scales, given a likely range of errors of the original
GRACE observations. They found that:

monthly changes in TWS should be detectable 50–91% of the time in 15 of 17 basins
larger than 200 000 km2

seasonal signals should be detectable 50–100% of the time in 17 of 18 basins larger than
184 000 km2

annual variations should be detectable in 13 of 17 basins larger than 200 000 km2.
When launched, the GRACE science team encountered difficulties in achieving the expected
level of accuracy and it took nearly two years before the data was released publicly. The
publication of Tapley et al. (2004) contains the first published results and shows clearly the
annual variations globally and, in particular, over the Amazon/Orinoco river systems. They
also provided the first attempts at estimating temporal trends, although the time series used
contains only 14 months of GRACE data.
Rodell et al. (2004) found that the GRACE TWS estimates lay roughly between estimates
derived from a water balance model and the Global Land Data Assimilation System (GLDAS)
model (Rodell et al. 2004) driving the NOAH land surface model (Ek et al. 2003). They also
found that the spatial scaling applied to the GRACE data affected the amplitude of the
variations in the GRACE estimates (see Section 3.1.2 for a detailed explanation of spatial
scaling processes and their effects).
Syed et al. (2005) used GRACE TWS estimates (which include changes in groundwater
storage—GWS) to estimate basin discharge, which they called ‘total basin discharge’ and
included the net of surface, groundwater and tidal inflows and/or outflows in addition to
streamflow. They found good correlation between streamflow and GRACE total basin flow,
although there were significant differences in magnitudes of low flows (Amazon) and annual
amplitudes (Mississippi). They attributed at least part of these differences to changes in
GWSs.
Schmidt et al. (2006) found that the hydrological signals of the world’s major river systems
were able to be recovered from GRACE data, with a background model uncertainty of around
35 mm EWH from one month to another.
Crowley et al. (2006) found significant seasonal variation and long-term loss of TWS in the
Congo Basin. Syed et al. (2008) found that GRACE-based storage changes were in good
agreement with those obtained from GLDAS simulations (e.g. 15 mm/month RMS between
the two estimates for the Mississippi River), whereas other authors have found significant
differences in amplitudes between GRACE and GLDAS (e.g. Tregoning et al. 2009a).
To put the TWS in perspective, the range of variation in TWS since the launch of GRACE in
2002 has been around ±300 mm in the Amazon Basin, while in the Murray–Darling Basin the
peak-to-peak changes are around 250–300 mm (Leblanc et al. 2009). Thus, a potential
uncertainty of approximately 30 mm represents around 10% of the anticipated changes in
TWS.
2.1.2 Extreme climate events: droughts and floods
Andersen et al. (2005) identified a significant mass loss over Europe that occurred during a
record-breaking heatwave in the summer of 2003. They estimated a loss of 78±10 mm EWH
from GRACE and confirmed this with GLDAS and a vertically integrated water balance
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estimate combined with a terrestrial water balance. Chen et al. (2009) provided quantitative
estimates of the extreme drought in the Amazon River Basin in 2005 using GRACE data. The
measurements were consistent with in situ water levels from river gauge stations and with
remotely sensed precipitation observations. However, they found that the land surface models
significantly underestimated the intensity of the drought.
Reager and Famiglietti (2009) used a combination of GRACE TWS and precipitation to derive
monthly storage deficit estimates and global maps of effective storage capacity from which
they derived a monthly global flood index. Effectively, they identified cases where the
drainage systems were near capacity but precipitation continued, and used the information to
try to identify occasions of high likelihood of flooding events. The aim of this work was to
present the information contained in GRACE data in a way that it may help to predict future
floods. Houborg et al. (2010) also found that GRACE-based drought indicators contained
valuable information on drought conditions in addition to those that rely heavily on
precipitation and do not account well for changes in SMS.
Steckler et al. (2010) found an additional 50 Gt6 of water storage in Bangladesh during
extreme flooding events, with GRACE estimates of the amount of floodwater agreeing within
statistical limits with observed daily river levels. Chen et al. (2010) found peak flood flow
anomalies of 624±32 Gt for the entire Amazon River Basin.
2.1.3 Groundwater studies
Rodell and Famiglietti (2002) showed that it was feasible to use GRACE to sense
groundwater changes in the High Plains aquifer of the central USA, since the uncertainty of
the GRACE estimates was around 8.7 mm compared with the observed periodic variations of
approximately 20–45 mm in GWS (note, however, that this does not include any uncertainty
in soil moisture storage). Post-launch studies found high correlations between GRACE TWS
and the sum of GWS+SMS (correlation coefficient r=0.82) and GRACE and measured
groundwater variations (r=0.58) (Strassberg et al. 2007).
Yeh et al. (2006) found that groundwater estimates from GRACE agreed ‘reasonably well’
with in situ observations in Illinois, USA; however, they noted that the estimates differed
substantially in month-to-month variations. In general, the seasonal cycles between the
estimated and measured groundwater changes agreed well (r=0.83, 36 observations). They
concluded that GRACE offered a means of estimating seasonal GWS changes at the basin
scale of 200,000 km2.
A similar study in the Mississippi River Basin found that it is possible to estimate variations in
TWS from GRACE, being the sum of GWS, SMS and snow mass (Rodell et al. 2006). This
study demonstrated how subtracting modelled estimates of snow and soil moisture (derived
from the GLDAS model) from the GRACE TWS estimates did yield groundwater estimates
that ‘compared favourably’ with well-based time series. However, the authors stated that the
results were better in basins larger than 900 000 km2 than in sub-basins smaller than
500 000 km2. Thus, the relevance of GRACE observations for smaller catchments remained
in question.
Leblanc et al. (2009) performed a study of the multi-year drought in the Murray–Darling Basin,
documenting the propagation of water deficits through the hydrological cycle. They found a
high correlation between the observed groundwater variations from boreholes and the
GRACE TWS estimates, at a time when the ongoing drought had reduced the available
surface water resources. The net loss of water over the period of GRACE observations
(2002–2007) was found to be about 200 km 3. In a similar study, Rodell et al. (2009) quantified
the depletion of groundwater in India through a comparison of GRACE and GLDAS
observations as 109 km 3 over the period August 2002 to October 2008 (or 4010 mm/year in
terms of EWH). These two studies provided information averaged over approximately
1 million km2 and 450 000 km2, respectively.
6
1 gigatonne (Gt) of water is equivalent to 1 km3 or 1000 GL
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Famiglietti et al. (2011) followed a similar analysis approach to estimate that groundwater was
being depleted at a rate of 20.4±3.9 mm/year (EWH) in the Central Valley, California,
amounting to around two-thirds of the total water loss. In this case, the basin has a size of
only about 52 000 km2. However, the authors computed the GRACE TWS over the entire
Sacramento and San Joaquin basin regions (about 154 000 km2) and then assumed that all
groundwater changes must have occurred only in the Central Valley region (since other parts
of the total region were mountainous and would have limited capacity to store groundwater).
Like Leblanc et al. (2009), they found that groundwater depletion correlated with times of
drought.
More recently, Sun et al. (2010) formulated a means of estimating aquifer storage parameters
from remotely sensed observations and modelled SMS estimates. They found that their
estimated aquifer storage parameters were consistent with previous results derived from in
situ calibrations, and concluded that GRACE data can be used to derive spatially variable
parameters for groundwater modelling.
2.1.4 Validation of GRACE through ground truth experiments
Because of the large spatial footprint of GRACE estimates of the earth’s gravity field (around
380 km for a degree 50 spherical harmonic model7), it is extremely difficult to validate GRACE
estimates with in situ observations. Put simply, the spatial averaging that occurs when
generating a GRACE estimate of mass change is nearly impossible to replicate with discrete,
point-wise measurements. Nonetheless, several authors have found innovative ways in which
to validate the broad spatial estimates from GRACE using a range of different geophysical
signals.
Davis et al. (2004) estimated the pattern of annual deformation of the surface of the earth
caused by annual variations in the global hydrological cycle. They compared the GRACEderived deformation with observed vertical surface movement at a GPS site at Brazilia in
South America and found very good agreement. Van Dam et al. (2007) undertook a similar
study over Europe and concluded that there were significant differences between GRACE
and GPS-derived deformations, while Tregoning et al. (2009b) found very high correlations in
a similar comparison over the same region. The improved agreement in the latter study was
due to an improvement in the analysis of the GPS observations rather than the identification
of any errors in the GRACE data.
Several authors have made comparisons of GRACE mass variation estimates and observed
ocean bottom pressure changes. For example, Rietbroek et al. (2006) found correlations of
0.7–0.8 between GRACE and ocean bottom pressure observations in the Crozet-Kerguelen
region, while more recently Siegismund et al. (2011) found globally averaged errors of 8.6,
11.1 and 5.7 mm EWH in a comparison of ocean bottom pressure variations and GRACE,
non-steric altimetry and a climate/ocean model, respectively. Tregoning et al. (2008)
compared sea surface height changes in the Gulf of Carpentaria estimated by GRACE with
tide gauge measurements and found excellent agreement in phase but small (<20%)
differences in amplitude. They also identified that the barotropic model8 used in the reduction
of the raw GRACE observations underestimated the non-tidal ocean mass movement
significantly in the Gulf of Carpentaria. Wouters and Chambers (2010) reached a similar
conclusion from a study of ocean bottom pressure changes in the Gulf of Thailand, even
though the barotropic model in their analysis was not the same model.
Lo et al. (2010) incorporated both GRACE TWS and estimated streamflow records to
constrain land surface model simulations and demonstrated the advantage of this coupled
7
Simplistically speaking, the summation of many sine and cosine terms with different amplitudes and
periods allows complicated shapes and surfaces on a sphere to be represented by just the amplitudes
of the periodic terms. Thus, a representation of the Earth’s gravity field—either a mean field or at a
particular epoch—can be reduced to just a set of coefficients, known as Stoke’s coefficients, that are
multiplied by cosine and sine terms. This is what is known as a 'spherical harmonic model'.
8
The barotropic ocean model, described in Section 6.1.3, accounts for the gravitational effects on the
satellites from the non-tidal ocean mass movement.
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approach. They calibrated their model parameters using two years of data, then validated the
results using simulations spanning different time periods.
2.2 Review of applications of GRACE products
for hydrological studies in Australia
Despite the great technical success of the GRACE mission and the many different scientific
results that have been generated internationally, there are surprisingly few examples of the
use of GRACE data in Australia. Below, we document (in chronological order) the published
studies that we are aware of, including research driven by both national and international
scientists.
Rodell and Famiglietti (1999) considered the Murray–Darling Basin in a prelaunch
assessment of what types of hydrological signals would be detectable by the GRACE
mission. They concluded that monthly changes in TWS should be detectable over 80% of the
time, that the mean uncertainty would be 25–50% of the mean change in storage and that
seasonal and annual trends would be detectable.
Ellett et al. (2005a) presented the first assessment of the potential of the use of GRACE to
contribute to hydrological studies of the Murray–Darling Basin. They considered the
combination of GRACE with hydrological modelling, data assimilation and ground-based
monitoring as a means of obtaining better resource management. Their initial results showed
the capability of GRACE to estimate statistically significant TWS changes on a basin scale,
and the potential for these estimates to improve model predictions in a data assimilation
framework. No actual GRACE results were presented (the data had not yet been made
publicly available); rather, the magnitudes of the hydrological signals were compared with the
expected errors of GRACE estimates based on prelaunch simulation studies. Ellett et al.
(2006) again proposed a framework by which GRACE observations could contribute to the
hydrological modelling of the Murray–Darling Basin but again did not use any GRACE data.
Ellett et al. (2005b) provided the first direct comparisons between actual GRACE estimates of
monthly TWS changes for the Murray–Darling Basin and those derived from two land surface
models and one rainfall/runoff model. They concluded from a comparison of data spanning
2002–2004 that the differences were significant, with the models under- and over-predicting
the monthly mean water storages. This was the first use of GRACE data in a study of
Australian hydrology.
No further studies were undertaken until Syed et al. (2008) used GRACE data (converted to
1º x 1º global EWH grids) spanning April 2002 to July 2004 to estimate a net depletion of 1.3
mm/month of TWS in Australia, with 1.1 mm/month of the total being lost from the Murray–
Darling Basin. This was the first quantification of water storage changes in Australia from
GRACE, albeit from only two years of data collected four years earlier.
Awange et al. (2009) compared GRACE TWS estimates to rainfall data over Australia and
concluded that GRACE could detect hydrological signals. However, they noted that the
relatively small hydrological signals over much of Australia were not detectable because of
errors in the GRACE data processing and the filtering methods that they had employed. They
indicated that an Australian-focused reprocessing of GRACE observations would be required
to reduce spectral leakage of ocean signals into continental estimates of TWS and to reach a
level of error smaller than the signals that are being sought.
Leblanc et al. (2009) conducted a detailed study of the multi-year drought and its effect on the
Murray–Darling Basin. This was a comprehensive study that incorporated GRACE
observations, groundwater bore observations and estimates of surface water changes to
assess the response of water resources to the drought and the assessment of its severity.
They found high correlations between TWS losses estimated by GRACE and depletion of
groundwater levels at a time when there was little change in modelled SMS and surface water
storage (the latter two had effectively reached low values by the time the GRACE mission
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was launched or shortly after). This study showed, for the first time in an Australian context,
how GRACE data could provide important, basin-scale information on changes in TWS and
how, through integration with soil moisture and surface water storage information,
groundwater variations could be sensed remotely.
Brown and Tregoning (2010) investigated the magnitude of spectral leakage into estimates of
TWS in the Murray–Darling Basin from near and far-field sources such as the Amazon Basin,
melting of Antarctica and Greenland and hydrological processes in Australia. They simulated
some of the world’s largest geophysical processes that have been detected by GRACE and
then assessed the amount of the simulated signal that appeared in integrated TWS estimates
for the Murray–Darling Basin. The leaked signals into the basin reached maximum values of
approximately 10 mm EWH, which is around 30% of the formal uncertainty of GRACE
estimates and only about 10% of the magnitude of changes in TWS that occur in the basin.
Leblanc et al. (2011) reduced the spatial extent to study groundwater changes in just the
Murray Basin (aproximately 300 000 km2, compared with approximately 1 000 000 km2 for the
entire Murray–Darling Basin) and found a change in the long-term dynamics of the water table
since the onset of the drought in 1997. Borehole data showed a regional increase in the water
table from 1980–1992, then a steady decline (around 17 cm/year) from 1997 to 2009. Over
the GRACE period, groundwater losses of 18±1.3 mm/year have occurred (derived from
GRACE TWS minus modelled soil moisture values), equating to about 45±3 km 3 integrated
over the basin. They argued that the drought (temporarily) reversed the impacts of past land
clearing in creating dry land and salinity problems.
Awange et al. (2011) investigated the use of 4°×4° resolution 'mascon' (mass concentration)
GRACE solutions (see Section 3.1.5 for more details) over Australia for monitoring
hydrological processes. They extracted from the mascon solutions the main spatial and
temporal components (rate, annual trend, etc.) but concluded that, when considering Australia
as a whole, the mascon approach (at least, at the 4°×4° resolution) did not contribute
significantly more information than the available spherical harmonic solutions.
Frappart et al. (2011) developed a series of solutions using an Independent Component
Analysis for the Murray–Darling Basin. They found that their solutions agreed better with the
in situ observations than the other spherical harmonic solutions that had undergone various
types of filtering and rescaling (see Section 3), with the maximum deviations between GRACE
and in situ observations decreasing by a factor of two to three. This shows the potential to
improve the accuracy of GRACE estimates through more appropriate statistical treatment of
the data.
García-García et al. (2011) analysed GRACE data from 2002 to 2010 and found that 60% of
the variance across the Australian continent could be accounted for with an annual periodic
signal. They found that phases of the Indian Ocean Dipole (IOD) were correlated with
precipitation in south-eastern Australia associated with changes in tropical moisture flux. They
noted, in particular, that the dry period of 2006–2008 coincided with three consecutive periods
of positive IOD events.
Van Dijk et al. (2011) compared the AWRA hydrological/land surface model with GRACE
estimates of TWS across the Australian continent. This is the most extensive comparison of
GRACE and hydrological models over Australia and is discussed further in Chapter 4.
2.1.4 Summary
The results and conclusions of the above studies demonstrate clearly the potential of GRACE
to contribute significant and unique information regarding changes in total water storage over
the Australian continent. While it has not been, and may never be, demonstrated that
estimates can be made at spatial scales as small as individual farms or basin subcatchments, the ability to provide over-arching constraints on the total water storage at the
200 000 km2 scale is feasible. Researchers have already shown how such information can be
used to study aspects of hydrology as diverse as the severity of droughts, constraining
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specific yield values, estimating groundwater storage changes, guiding the development and
improvements in hydrological models and even identifying surface deformation caused by
hydrological loading.
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3. Assessment of the available
GRACE gravity fields
Several international centres use the original GRACE satellite observations to derive temporal
estimates of the earth’s gravity field and provide these as products in the form of spherical
harmonic coefficients (defined below). The available products have different time intervals
(daily, 10-day and 30-day averages) and are generated using a range of different analysis
strategies. Consequently, the way in which the gravity fields generated by different
international groups should be used is also different. Incorrect use can result in wildly
incorrect estimates of hydrological variables. Additionally, some centres now provide global
grids of estimates of changes in mass in terms of EWH. The suite of available information can
be confusing for users not familiar with the technical details of the analysis processes.
To date, no comprehensive assessment of these different solutions has been made and it is
not well known to what extent the hydrological estimates across Australia would differ
between solutions; however, a preliminary analysis of only three of the available products
showed considerable differences in quality (Van Dijk et al. 2011). Below we provide a short
description of the analysis strategies of several available GRACE gravity fields, as well as
brief explanations of how each centre indicates that their GRACE products should be used. In
this report we use products provided by the French interagency Space Geodesy Research
Group (Groupe de Recherche de Géodésie Spatiale, GRGS) and the Center for Space
Research of the University of Texas at Austin (CSR). We discuss methods recommended for
reducing correlations between parameters of the spherical harmonic coefficients, reducing
leakage of ocean and land signals into other regions, application of spatial filtering to mitigate
high levels of noise in the higher degree spherical harmonic coefficients and, subsequently,
the rescaling of resulting solutions to mitigate the loss of signal from the filtering processes.
3.1 GRACE products and their use
The shape of the earth is commonly referenced to its gravitational equipotential surface called
the geoid. The geoid is a useful reference since it is the surface that the earth’s sea level
would describe in the absence of winds, ocean currents, and other non-self gravitational
disturbing forces. The geoid provides access to the local up/down direction and the horizontal
plane. In mathematical models, the earth's first order shape is conveniently described as an
ellipsoid, where the equatorial radius is about 21 km greater than the polar radius. Departures
of the earth’s topographic relief, and geoid, are represented as elevation above or below its
best-fitting reference ellipsoid. The earth’s geoid is up to 110 m below and 90 m above the
reference ellipsoid, while its topographic surface can be up to 11 000 m below and
approximately 9000 m above this reference ellipsoid.
The earth's gravity field is determined by how the material that makes up the earth is
distributed. Because gravity changes over the surface of the earth, the weight of an object
changes along with it. For convenience we represent the earth’s gravity field as the sum of a
smooth standard earth gravity model (Figure 2a), and gravity 'anomalies' (Figure 2b) which
describe how actual gravity deviates from the standard model. A map of gravity anomalies
(usually expressed in units of milliGals 9) tends to highlight short wavelength features better
than a map of the full geoid.
Historically, geodetic analysts have produced representations of the earth’s gravity field using
spherical harmonic models. These have been derived since the 1970s from the observations
of the motion of satellites orbiting the earth, with a trend of gradual increases in accuracy as
more observations became available. A quantum leap occurred with the GRACE mission
because, for the first time, inter-satellite range changes could be used to map changes in the
gravity field (Tapley et al. 2004). Today, gravity field estimates are available for both the mean
9
A Gal, short for Galileo, is a unit of measure of acceleration and is equal to 0.01 m/s².
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(or static) field and for means of particular time intervals of 1, 10 or 30 days duration (e.g.
Tapley et al. 2004; Kurtenbach et al. 2009; Bruinsma et al. 2010).
Figure 2: The earth’s gravity field, showing a) the latitudinal variation caused by the equatorial
bulge, b) a snapshot of geophysical processes by computing anomalies at a single epoch (i.e.
residual signal about the mean value)
The original approach of the GRACE science team was to develop spherical harmonic
models for 30-day epochs from the GRACE observations, and solutions by CSR, the German
Research Centre for Geosciences (GFZ) and Jet Propulsion Laboratory (JPL) are available.
Essentially the observations (the satellites’ positions/velocities and the changes in the intersatellite distance) are related to the parameters (the Stoke’s coefficients), and a linear
inversion yields estimates of the spherical harmonic model(s) of the gravity field(s).
Subsequently, the French GRGS developed spherical harmonic models as did the Institute of
Geodesy and Geoinformation, University of Bonn (ITG). Differences between the approaches
used to generate the models mean that the solutions are not exactly the same, as will be
explained below.
An alternate approach has been used to localise the changes in the gravity field into regions,
then estimate mass changes for each region (assuming a constant mass change across each
region). This 'mascon' approach was developed for studies of Venus and was first applied to
the analysis of GRACE data by Rowlands et al. (2005). Luthcke et al. (2006) used a similar
approach to study mass balance changes of Greenland and global mascon solutions of a 4º x
4º degree grid are now publicly available. Awange et al. (2011) assessed the feasibility of
using these grids for studying hydrological processes in Australia and found no significant
improvement over using the more conventional spherical harmonic fields.
3.1.1 Underlying model assumptions
The process of estimating mass changes on earth from the original GRACE observations is
complicated and involves many detailed steps. The motion of the satellites is governed by the
shape of the earth’s gravity field as well as the gravitational attractions of the sun, moon and
other planetary bodies, although the earth’s gravity field exerts the greatest force, since it is
the closest to the satellites. It is comprised of many different components:

the static (or constant) gravitational field caused by the mass of the earth (known as the
central body force)

the change in gravity caused by the deformation of the solid earth as a result of the
gravitational forces of the sun and the moon. This is often called the 'solid earth' or 'body'
tide
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
the temporal redistribution of mass in the so-called 'fluid envelope' of the earth. This
includes the ocean tides, non-tidal ocean movement and the variations in atmospheric
mass

hydrological processes (and associated crustal deformations) that cause redistribution of
water and the ongoing exchange of water mass between continents and oceans. Any
present-day melting or growing of glaciated continental regions can be considered as part
of this process

deformation of the earth caused by geophysical processes such as earthquakes and the
ongoing isostatic adjustment of the surface as a result of melting of major ice sheets over
the past 20 000 years.
The orbit of each GRACE satellite is affected by each of these components of the earth’s
gravity field. Some of them are well understood and can be modelled with sufficient accuracy
such that the remaining errors will not affect the results (e.g. the central body force, the solid
body tides and the sun/moon/planetary effects). Some are modelled using what are called
'background' or 'dealiasing' models (e.g. ocean and atmosphere effects). It is recognised that
accuracy limitations in these background models contribute to the errors in the estimates of
mass change from GRACE (see Chapter 6.1), but they are the best models available at this
time. The remaining components—the hydrological and deformational processes on earth—
are the signals that the GRACE mission was designed and launched to detect. The effect of
non-gravitational forces acting on the satellites (such as atmospheric drag, solar radiation
pressure and thrust manoeuvres) are measured by the tri-axial accelerometers onboard each
satellite. These observations are used in the determination of the spacecraft orbit.
The process of estimating the gravity field from GRACE data involves integrating a theoretical
trajectory of the spacecraft by modelling the effect of gravitational forces derived from an a
priori model of the above gravitational effects, modelling the effect of non-gravitational forces,
comparing the inter-satellite distance observations with the theoretically derived values, then
fitting (i.e. inverting) the model to solve for corrections to the hydrological (and deformational)
components of the earth’s gravity field needed to reproduce the measurements. By doing this
for successive periods, temporal snapshots and time series are derived. Adding these to the
background model for the earth’s gravity field yields an estimate of the gravity field for a
particular epoch.
There are many other effects, typically small in nature, that, if not accounted for correctly, can
degrade the accuracy with which the gravity field can be recovered. For example, small errors
can be induced in the estimated gravity fields from small errors in the modelling of the
orientation of the spacecraft (Howarth et al. 2010). Additionally, it is essential that the offset
between the centre of mass of each satellite and the centre of the accelerometer proof mass
be known to within a few micrometres; otherwise, errors in correcting for the non-gravitational
forces will be introduced. Interested readers are referred to http://op.gfzpotsdam.de/grace/payload/payload.html#CMT for further details.
3.1.2 CSR spherical harmonic fields
The CSR produces 30-day estimates of GRACE gravity fields and makes these publicly
available (ftp://podaac-ftp.jpl.nasa.gov/allData/grace/L2/CSR). The most recent release,
RL04, was used in this report. Tapley et al. (2004) published the first results of the GRACE
mission, which were derived from the spherical harmonic fields of the CSR solutions, and
showed that the GRACE mission had yielded a considerable improvement in the accuracy
and resolution of the estimate of the earth’s gravity field.
The degree 2, order 0 (known as C20) estimates of the spherical harmonic coefficients from
GRACE are not well determined (e.g. Tapley et al. 2004; Velicogna and Wahr 2006,
Chambers et al. 2004). This affects the CSR solutions and, as such, it is necessary to replace
the GRACE C20 coefficients with estimates determined by other means, typically from
analysis of satellite laser ranging observations (e.g. Tapley et al. 2004). This is an essential
step when using the CSR spherical harmonic models. While this is a highly technical issue,
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the practical implications are that not following it will result in substantial errors in estimates of
EWH changes.
The CSR spherical harmonic models contain considerable noise (Figure 3) and various
filtering techniques need to be employed before geophysical interpretations can be made.
The typical signature of the errors is a pattern of regions of alternating positive and negative
errors with a north–south orientation. This pattern is related to the near-polar orbit of the
satellites that results in the path of the satellites over the surface of the earth being nearly
north–south in alignment. Swenson and Wahr (2006) identified high correlations between
some of the Stoke’s coefficients and developed a 'de-striping' filter to mitigate the problem.
Several other authors have developed similar filters (e.g. Chambers 2006) and it has become
standard practice to 'de-stripe' the CSR solutions.
However, the de-striped gravity fields still contain significant errors caused by the large
amounts of 'noise' that are contained in the higher degree spherical harmonic coefficients 10.
To mitigate this noise, spatial filters are used, of which an isotropic Gaussian filter (reflecting a
symmetrical bell-shaped normal distribution) is probably the most common (e.g. Tapley et al.
2004; Velicogna and Wahr 2006). Essentially, the contribution of the higher degree
coefficients is reduced as the degree increases to the point that they do not contribute at all.
The radius of the filter affects the extent of noise removal. This is demonstrated in Figure 3,
where the filter radius is varied from 0 km to 700 km. It is clear that the north–south striped
pattern of error is reduced as the filter radius is increased. Thus, the noise is removed from
the system. However, the higher degree coefficients also contain some component of the
actual gravity field signal; therefore, reducing the contribution of these coefficients also
removes some of the signal itself. Several studies have been conducted to identify scaling
factors that need to be applied in order to 'upscale' the fields to restore the signal removed
during the filtering process (e.g. Velicogna and Wahr 2006).
Finally, the spherical harmonic expansion is a mathematical approximation of an infinite
series. Because of the truncation of the spherical harmonic fields to a maximum degree
(rather than an expansion to infinity), some smearing of actual signals may occur because the
spatial resolution of the GRACE fields is not sufficiently small to capture the processes
accurately. Several techniques have been developed (e.g. Baur et al. 2009) to reduce the socalled 'leakage' effects of continental hydrology signals into ocean regions and vice versa.
10
The higher degree spherical harmonic coefficients represent amplitudes of periodic functions with
smaller spatial extents, or smaller spatial footprints. Therefore, higher levels of noise in these
coefficients restrict the ability to increase the spatial resolution of GRACE results.
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Figure 3: Rate of change (in terms of EWH) for the CSR GRACE solutions (2002–2011) using
Gaussian filtering with radii from 0 km to 700 km
In summary, the following steps need to be undertaken before using the CSR spherical
harmonic gravity fields:
1. filter (de-stripe) the fields to remove correlations between coefficients
2. apply a spatial filter (e.g. Gaussian) to remove additional north–south error stripes
caused by noise contained in estimates of higher degree coefficients
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3. reduce leakage effects between continents and oceans using a suitable technique
4. upscale the remaining signals to restore the signal that has been removed during the
spatial filtering step.
There are two websites that offer CSR GRACE products for which these steps are already
performed, thus providing users with global grids of gravity anomalies in terms of EWH.
The NASA/JPL Tellus portal (http://grace.jpl.nasa.gov/data/) provides separate grids for land
and oceans where the spherical harmonic solutions have undergone de-striping, Gaussian
filtering (radius 300 km for land, 500 km for oceans) and reduction of leakage. Additionally, a
grid of values to upscale the land grid values is provided. These are the grids that were used
recently by Van Dijk et al. (2011) to study hydrological processes in Australia.
An interactive website at the University of Colorado
(http://geoid.colorado.edu/grace/grace.php) provides access to CSR de-striped fields where
the user can choose the radius of the Gaussian filter to be used. Figure 3 was generated from
numerical global grids of rate of change of EWH generated by this website. No upscaling or
leakage reduction is provided.
3.1.3 GRGS spherical harmonic fields
GRGS produce spherical harmonic models of the gravity field from a simultaneous
combination of GRACE observations and satellite laser ranging observations. Their analysis
is described in detail in Lemoine et al. (2007) and Bruinsma et al. (2010). The inclusion of
observations of the Laser Geodynamics Satellites (LAGEOS) in the inversion of the gravity
fields overcomes the errors in the C20 coefficient estimates that occur in the CSR approach
and obviates the need to replace the C20 coefficients in the GRGS products.
The major difference between the CSR and GRGS approach is that, in the latter, constraints
are applied in the estimation of the spherical harmonic coefficients11 in a process known as
'regularisation'. This is an alternative approach to the a posteriori filtering and no subsequent
filtering or scaling needs to be applied to the fields 12 (Bruinsma et al. 2010). The GRGS
spherical harmonic solutions are computed to degree 50 (spatial footprint of about 400 km)
and are available at http://grgs.obs-mip.fr/index.php/fre/Donnees-scientifiques/Champ-degravite/grace. Gridded fields of gravity change expressed in terms of EWH are also available
at this website.
3.1.4 ITG spherical harmonic fields
The Institute of Geodesy and Geoinformation, University of Bonn, Bonn, Germany (ITG),
produces daily and 30-day spherical harmonic solutions (known as ITG solutions, available
from ftp://skylab.itg.uni-bonn.de/ITG-Grace2010/monthly/ITG-Grace2010/) based on a
Kalman filter, as described in Kurtenbach et al. (2009). The principal difference between the
approach of ITG and CSR is that the former takes into account the temporal correlations in
the gravity field from one epoch to the next, thus providing additional constraints on the
estimates of the spherical harmonic coefficients. They introduced stochastical correlation
patterns of the WaterGAP Hydrological Model to provide the additional temporal information
(Döll et al. 2003). The authors claimed that daily snapshots of the earth’s gravity field could be
estimated using their technique.
11
Constraints are added to the diagonal of the normal equation matrices prior to inverting for the
parameters. Their first solutions (RL01—see Lemoine et al. 2007) applied constraints that were a
function of degree only, whereas the current solutions (RL02—see Bruinsma et al. 2010) apply a
different constraint per coefficient. The authors claim that their regularisation technique, when solving for
the gravity field coefficients, generates more accurate estimates than applying indiscriminately a spatial
filter, because the constraint acts strongly when the signal is weak (i.e. there is little contribution from
the observations) but has little effect when the signal is strong.
12
This has recently been disputed by Swenson and Wahr (2011) but the French team maintain their
view (R. Biancale, pers. comm. July 2011).
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3.1.5 Alternate uses of spherical harmonic fields
Several authors have published methods by which geophysical results can be obtained from
the available spherical harmonic fields via different approaches from the above. In some
cases, the aims of the methods are to extract higher spatial resolution from the original
spherical harmonic fields, while in other cases the motivation has been to try to minimise the
post-processing filtering steps required before the signals can be detected above the noise.
Two examples are discussed below.
Rather than trying to limit leakage and subsequently upscale the continental values derived
from the spherical harmonic solutions, Wouters et al. (2008) used an approach based on
finding small-scale mass change values that agreed in summation with the filtered GRACE
observations. They used forward modelling of higher resolution mass variations to find the
best-fitting mass variations and showed that this approach yielded higher spatial resolution in
a study of Greenland mass balance change. This method has not yet been applied to the
Australian continent; however, a project currently funded by the Australian Space Research
Project ('The GRACE Follow-on mission') includes research by The Australian National
University to develop software to enable this type of analysis to be applied to Australian
hydrological studies.
Davis et al. (2008) developed a statistical filter to derive a GRACE rate field through a
parameterised model for the temporal evolution of the spherical harmonic coefficients.
Essentially, they fit a linear trend and annual periodic signal to time series of each coefficient
and used a statistical f-test to determine whether the estimated trends and annual variations
were statistically significant. Using only the significant coefficients, they then produced a set
of spherical harmonic coefficients that represented the rate of change of gravity as observed
by GRACE.
Figure 4 shows the rate fields generated from the CSR and GRGS GRACE solutions using
their method for f-test probability distributions of 95%, 99%, 99.9% and 99.99%—the latter is
the value used by Davis et al. (2008). Clearly, increasing the confidence level has a major
impact on reducing the errors visible in a north–south striped pattern13 in the CSR rate fields,
although there is little difference in the GRGS fields. In particular, the signals visible over
continental regions are largely unaffected, indicating that such signals are real rather than
showing the presence of errors. Essentially, the pattern of geophysical trends only become
visible in the CSR solutions once only highly statistically significant coefficient rates are used,
indicating that there is significant noise in the unfiltered CSR spherical harmonic coefficients.
On the other hand, the rate fields using the GRGS coefficients are unaffected by this
statistical filtering approach.
13
The north–south stripes evident in Figure 4 have no physical meaning. This spatial pattern of error is
a consequence of the roughly north–south trajectory of the spacecraft in their near-polar orbit.
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Figure 4: Rate of change (in terms of EWH) for the period 2002–2011 derived from the GRGS
and CSR solutions using coefficient rates that pass an f-test with statistical confidence interval
of 95%, 99%, 99.9% or 99.99%.
No de-striping or spatial filtering is applied.
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3.2 Comparison and validation of EWH solutions
With such a variety of choice of GRACE solutions computed in different ways, it may be
challenging for a non-expert to appreciate the consequences of particular analysis choices
made by the international centres, or to decide which GRACE product is the most appropriate
for use in Australian hydrological studies. In fact, given the approximately 400 km footprint of
the GRACE spherical harmonic fields, it is very difficult even for experts to be able to validate
the estimates using ground measurements. A common way of quantifying the likely accuracy
of solutions is to assess the standard deviation for time series over regions where no signal is
expected (i.e. very arid regions in Africa and ocean basins) (e.g. Bruinsma et al. 2010;
Kurtenbach et al. 2009). Another approach is to compare sea surface height variations from
GRACE with those of satellite altimetry, tide gauges (e.g. Tregoning et al. 2008) or ocean
bottom pressure.
In Figure 5 we show estimates of the rate of change of gravity in the Australian region
expressed as a rate of EWH, as derived from the solutions of several different analysis
centres and following their recommended procedures.
There are some notable features in Figure 5:

the statistical filtering method of Davis et al. (2008) removes a considerable amount of the
north–south striping error (compare Figure 5a and Figure 4)

the level of ocean noise pattern (most likely 'noise') is fairly similar in the CSR (statistically
filtered), ITG and GRGS rate fields (Figure 5a,b,e,f)

the statistical filtering of the GRGS solutions has little effect on the rate field (cf. Figure 5e
and 5f)

the CSR solutions that have undergone de-striping display much less north–south
striping—particularly over the oceans (Figure 5c,d)

the solution with leakage corrections and upscaling (Figure 5d) seems to display the
cleanest continental hydrological signals (but see Section 4.2 for further discussion). It
also has the largest amplitudes of trends in NE Australia (positive trends) and NW
Australia (negative trends).
Of particular interest is the fact that there are many continental signals (±10 mm/year or
greater) that are visible in nearly all solutions: positive rates in the top end and eastern
Queensland, negative trends in SE Australia, negative trend in NW Australia. Only the destriped/upscaled CSR and GRGS solutions show the negative trend in SW Western Australia.
Discussion of the merits of these two GRACE solutions and their use for hydrological studies
in Australia are given in the conclusion of Chapter 5.
3.2.1 Conclusion
While many different GRACE solutions have been generated by international analysis centres
using different approaches, there is strong evidence that hydrological signals have been, and
will be, detected by GRACE. We find that the approach of the French GRGS group of
incorporating LAGEOS observations into the analysis of the GRACE observations, and the
regularisation of the spherical harmonic coefficient estimates, yields GRACE solutions that
contain hydrological signals seen in all other GRACE solutions, but with a smaller level of
noise. Additionally, the GRGS solutions are simple to use because they require no
subsequent filtering or scaling and provide TWS estimates accurate to approximately 25 mm
EWH over Australia (see Chapter 6) with a temporal resolution of 10 days and a spatial
resolution of around 400 km. We use these solutions in this report.
A full discussion and quantification of likely errors in the GRACE solutions, in conjunction with
errors in soil moisture modelling, and how the errors affect groundwater storage estimates is
given in Chapter 6.
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Figure 5: Rate of change in the Australian region (in terms of EWH/year) derived from several
different GRACE solutions spanning 2002–2010.
a) CSR using the statistical filtering approach of Davis et al. (2008) (no de-striping filtering), b)
ITG using the same filtering approach as a), c) CSR (de-striped, 300 km Gaussian filter), d)
CSR (de-striped, Gaussian filter—500km over oceans, 300 km over land—leakage accounted
for and upscaled, e) GRGS using the rate of change of all coefficients, f) GRGS using the
same filtering approach as a). Note that the colour scheme has been chosen to saturate at
high (white) and low (black) values so that the detail of the remaining small-amplitude error
pattern can be seen.
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4. Interpreting GRACE water storage
estimates
4.1 Introduction
Just as GRACE can sense the mass changes caused by changes in sea surface heights and
soil moisture, so it can detect changes in water stored in aquifers. Thus, there is potential to
use GRACE as a tool for observing GWS changes. However, it is not possible from GRACE
alone to identify whether water storage changes are occurring in groundwater, shallow soil
layers or surface waters, and the footprint of the observations represent relatively large areas
(>250 km across).
In order to derive estimates of groundwater variations, it is necessary to first remove from the
observed mass changes the contributions from all effects that are not related to groundwater.
In the Australian environment, the contributions from glacial melt, earthquake deformation and
crustal uplift/subsidence can be assumed to be negligible; however, variations in SMS and
surface water storage (in reservoirs, lakes, rivers, etc.) are known to occur and, in some
cases, may be of a similar or greater magnitude than GWS changes (e.g. Leblanc et al. 2009;
Van Dijk et al. 2011). Changes in biomass can also make a small contribution to changes in
mass as well as TWS (given most of biomass is water). Thus, GRACE provides an estimate
of changes in TWS over Australia, of which groundwater is only one component. These
limitations can be overcome by combining GRACE observations with estimates of surface,
soil, biomass and groundwater dynamics from hydrological models or measurements.
Broadly, two approaches can be taken to infer groundwater variations: (1) they are assumed
to equal the residual GRACE water storage signal after the signal from other storage terms
are removed, using estimates derived from models or observations, or (2) GWS variations are
estimated along with variations in the other stores and GRACE data is used to constrain the
estimation through some form of model-data fusion; for example, using statistical data
assimilation techniques.
The residual method requires that soil and surface water store dynamics are accurately
estimated, or errors will accumulate entirely in the estimated groundwater dynamics. The
model-data fusion approach relies on reasonable prior estimates of GWS from the model, and
reasonable estimates of the error in each of the terms.
Either way, the uncertainty in soil and surface water storage and biomass dynamics needs to
be estimated, as these affect the uncertainty in deriving the groundwater signal from GRACE
observations. In this section, we first review previous work on uncertainty in interpreting
GRACE observations over Australia, and address the likely magnitude of surface water and
biomass signals and the associated uncertainty. Subsequently, we focus on water storage in
the unsaturated term (i.e. SMS), being the largest or second largest term (after groundwater)
contributing to the GRACE signal. Spatially, soil moisture can only be observed for the top
few centimetres of soil using remote sensing, and therefore models are needed to estimate
TWS in the soil. This introduces errors and uncertainties. The two most important sources of
this are likely to be (1) rainfall estimation error, being the most uncertain dynamic model input
in many areas, and (2) model error in assumptions, structure and parameter values. The
impact of rainfall estimation uncertainty was analysed by using different rainfall products in
combination with the landscape hydrology model of the CSIRO/Bureau of Meteorology (BoM)
Australian Water Resources Assessment system (AWRA-L) (Van Dijk 2010a; Van Dijk and
Renzullo 2011). A tentative analysis of model error was carried out by comparing AWRA-L
SMS estimates to those from four models used in the Global Land Data Assimilation System
(GLDAS).
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4.2 Review
The AWRA-L model
The AWRA system (Van Dijk and Renzullo 2011; Van Dijk 2010a; Van Dijk et al. in press) is a
water balance monitoring system used by BoM to support the production of water accounts
and water resource assessments. The system combines a comprehensive spatial
hydrological model with meteorological forcing data and remotely sensed land surface
properties to produce estimates of water stored in the soil, surface water and groundwater.
The AWRA system includes a grid-based spatial landscape water balance model, AWRA-L
(version 0.5). Conceptual aspects of AWRA-L relevant here include the following:

shallow and deep soil layers are assumed to be explored by all vegetation and deeprooted vegetation only, respectively

a linear reservoir groundwater model has a drainage characteristic estimated from
analysis of streamflow from several hundred small upland catchments (Van Dijk 2010b)

the only surface water storage considered is the stream network, which drains rapidly in
response to reduced inflows.
Meteorological forcing is derived by interpolation of station data on a regular 0.05°
(approximately 5 km) grid; model outputs have the same resolution. Full technical detail on
AWRA-L (version 0.5) can be found in Van Dijk (2010a) whereas the specific AWRA-L model
parameterisation used in this analysis is detailed in Van Dijk and Warren (2010).
AWRA-L water balance estimates have received fairly extensive evaluation for Australian
conditions, using streamflow and deep drainage observations from several hundred
catchments and sites, respectively, evapotranspiration measurements at seven flux tower
sites, radar and microwave remote sensing estimates of surface soil moisture content, and
vegetation canopy cover and density estimated from optical remote sensing (Liu et al. 2010;
Van Dijk and Warren 2010; Van Dijk et al. in press). The current AWRA system version
ignores diffuse lateral water transport between grid cells. Additional AWRA system
components describing deep groundwater systems and the lateral redistribution and
subsequent evapotranspiration of surface water are being developed (Van Dijk and Renzullo
2011) but are not yet implemented at the time of writing.
Earlier comparisons of AWRA and GRACE
Van Dijk et al. (2011) compared AWRA estimates of TWS (surface, soil, biomass and
groundwater) with terrestrial water storage retrieved from GRACE satellite mission (the CSR
product). The aim was to test whether differences could be attributed and used to identify
model deficiencies. Data for 2003–2010 was decomposed into the seasonal cycle, linear
trends and the remaining de-trended anomalies before comparing. The overall agreement
between GRACE (CSR) and AWRA-L TWS estimates is illustrated in Figure 6.
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Figure 6: (a) Standard difference between GRACE and AWRA-L TWS anomalies (b) GRACE
water storage retrieval error estimates (c) Coefficient of correlation between GRACE and
AWRA TWS anomalies (d) Colour composite showing the relative contribution of the three
signal components (seasonal cycle, eight-year trends, de-trended anomalies) to the overall
disagreement between GRACE and AWRA-L TWS (from Van Dijk et al. 2011)
The analysis of Van Dijk et al. (2011) highlighted some issues with the GRACE CSR product.
In particular, the recommended use of a scaling coefficient deteriorated the agreement
between AWRA-L and GRACE CSR TWS and suggested that scaling the coefficients may
have led to over-correction. This is also evident in the comparison of rates of change of TWS
between solutions of different GRACE analysis centres as shown in Figure 5. However, the
spatial pattern in the disagreement between AWRA and GRACE CSR was very similar, but of
smaller magnitude, to the GRACE CSR TWS estimates themselves (cf. Figure 6a and b),
suggesting that the broad-scale signals captured by both AWRA and GRACE are correlated.
The analysis also highlighted some likely issues with the AWRA-L model estimates. The
model appeared to underestimate the seasonal TWS amplitude, suggesting a tendency of the
modelled soil, groundwater and/or surface water systems to drain too quickly. The AWRA-L
model structure and parameterisation were developed using concepts and streamflow
observations that were probably biased towards small, well-defined upland catchments, often
with medium to high precipitation (cf. Van Dijk 2010b; Van Dijk 2010c). In contrast, most of
Australia is covered by extensive plains with often poorly developed drainage networks that
drain internally into aquifers, wetlands and (salt) lakes.
The study also indicated some likely errors in model forcing and model physics. The greatest
trend deviations (>15 mm/year) occurred in North Queensland, the Great Sandy Desert, and
the southern Murray Basin. The difference in trends for North Queensland were mainly
associated with cyclone Charlotte in 2009, and plausible explanations were that (1) the
precipitation gauge interpolation procedure for this event led to precipitation overestimation
or, probably more likely, (2) runoff to the ocean occurred faster and more effectively than
estimated by the model. Errors in the gauge interpolation could explain some of the difference
in GRACE and AWRA-L TWS trends for the Great Sandy Desert. In addition, the
disagreement found for the Great Sandy Desert, and also for the Murray Basin, suggested a
tendency for the model to underestimate diffuse groundwater discharge. This process is
described in the model, but is assumed negligible once groundwater level reaches the base of
the surface drainage network. In reality, groundwater discharge can continue after
connectivity with the surface water network has been lost, through deep root water uptake
and capillary rise—see Van Dijk et al. (2011) for more details.
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Uncertainty from surface water storage changes
Unaccounted changes in water stored in public reservoirs were considered in the study of
Van Dijk et al. (2011) but could not explain the difference: the change in total storage across
Australia between early 2003 and end 2009 was negligible, and during 2010 storage
increased by an equivalent TWS of <4 mm. These storage changes may account for a small
part of unexplained regional trends. For example, the linear trend contribution of public
storage declines for Victoria was estimated at –1.6 mm/year during 2003–2009. Similarly,
Leblanc et al. (2010) estimated the range between minimum and maximum water storage in
public reservoirs across the Murray–Darling Basin as less than 15 mm, compared with the
estimated ranges in groundwater and soil water storage of around 80 and 110 mm,
respectively. In most other regions of Australia there are fewer or no public storages, while
the volume of private storages is also negligible in these regions.
Uncertainty from biomass changes
Van Dijk et al. (2011) did produce estimates of vegetation biomass water but, because model
estimated changes were negligible, they were not discussed. The potential influence of
biomass change (including both dry biomass and water) can be estimated by considering the
most extreme example of biomass changes, i.e. removal or burning of forest stands. Keith et
al. (2010) estimated a mean living biomass stock of 289 t C/ha14 for south-east Australian
eucalypt forests, with maximum values of up to 1500 t C/ha in mountain ash forests in the
Victorian highlands. Converting to total mass by assuming a dry matter carbon content of
45% and a biomass water content of 40% (and considering that 1 kg per m 2 is equivalent in
mass to 1 mm EWH) yields numbers an average forest biomass equivalent to approximately
160 mm EWH and an average mountain ash biomass of approximately 840 mm EWH. In
2002–03 a total of approximately 2.8 million hectares of forest was burnt: equivalent to 0.36%
of the Australian continent. Combining this with the estimated mean biomass of forests
suggests a biomass loss equivalent to 0.6 mm EWH across the continent in 2002–03,
assuming all biomass was lost (which was not the case). However, forests burning may have
made a greater contribution to observed mass changes at regional scale. For example, if the
same loss of biomass is concentrated in an area of about 200 000 km2, equivalent to 20
GRACE grid cells or the size of Victoria) the associated mass change is in the order of 20 mm
EWH.
The living biomass of herbaceous vegetation such as grasslands and annual crop is typically
less than 20 t/ha of dry matter or 10 mm EWH of total biomass. This provides an estimate of
the influence of associated biomass changes on the annual cycle in biomass. An influence on
multi-annual trends is not to be expected, however. In summary, large-scale bushfires can
lead to small (<10 mm EWH) reductions in mass, and the seasonal cycle in biomass may be
expressed in small mass changes (<5 mm EWH).
Conclusions
Overall, the following conclusions may be drawn from earlier analyses:

there is fairly good agreement between AWRA and GRACE patterns of TWS in space
and time, but long-term trends do not agree everywhere

important model deficiencies are associated with rainfall uncertainty and the description of
groundwater dynamics in the AWRA-L model

biomass and surface water variations can be excluded as an important source of mass
variations over Australia, although they can each make a modest (<10 mm EWH)
contribution to regional scale mass variations

the apparent deficiency in groundwater process simulation suggests that assimilation of
GRACE TWS into AWRA-L is currently not a reliable procedure.
14
Tonnes of carbon per hectare
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Therefore the alternative approach of removing the SMS signal from the total GRACE TWS
signal appears the most promising one. This procedure, however, still requires that SMS
dynamics are correctly simulated. Unfortunately, there are no large-scale measurements of
total SMS in the unsaturated zone that can be used to assess the accuracy in SMS estimation
by the AWRA system.
In the remainder of this section, we follow two lines of analysis to assess the likely uncertainty
in AWRA-L estimated SMS. We assume the main sources of uncertainty in SMS estimation to
be, (1) error in rainfall estimates used as model inputs, (2) error in the model itself, e.g. in the
way that the soil is represented, that processes are described and in the estimates of soil and
vegetation properties used to drive the model.
4.3 Soil moisture storage estimation uncertainty
due to rainfall estimation error
Many parts of Australia have sparse rainfall gauging networks, leading to considerable
uncertainty in daily precipitation estimates (Figure 7a). This in turn may create a potentially
large uncertainty in estimating soil water storage variations. The uncertainty varies spatially
as a function of gauge density as well as precipitation type. Most rain gauges in Australia are
located in coastal regions in the south east and south west, with many areas in the interior
being relatively poorly covered. Gauges are also sparse in high-altitude mountainous areas,
where orographic-induced rainfall is typically higher than in low-lying areas.
Figure 7: (a) Geographical distribution of active rain gauges (black dots) during 1998–2008
used in generating precipitation forcing data (b) Areas with >20 unreliable data (in blue)
during 1911–2010 (after BoM 2011)
In this section we evaluate the impact of precipitation uncertainty on estimated soil water
storage. Three high-resolution daily rainfall data products are currently available for Australia:

the Specialised Information for Land Owners (SILO) spatial precipitation estimates
(Jeffrey et al. 2001) available from the Queensland Department of Environment and
Resource Management (QDERM) and the Queensland Climate Change Centre of
Excellence (QCCCE) (http://www.longpaddock.qld.gov.au/silo/)

the Bureau of Meteorology Australian Water Availability Project (BAWAP) spatial
precipitation estimates (Jones et al. 2009) available from the Bureau of Meteorology
(http://www.bom.gov.au/climate/data-services/)
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
the blended satellite-gauge precipitation product, developed by CSIRO and BoM through
WIRADA and currently being made operational as an experimental data service, referred
here as LSBLEND (Li and Shao 2010).
SILO, BAWAP and LSBLEND all provide continental 0.05° grids of gauge-based spatially
interpolated daily rainfall. Although all three datasets use largely the same gauging stations,
interpolation procedures and complex topography are accounted for differently—these
different methods have been explained previously in the published literature (Jeffrey et al.
2001; Jones et al. 2009; Li and Shao 2010) and will not be discussed here. A previous
comparative study by Beesley et al. (2009) against rainfall measured at gauging sites
concluded that error statistics were similar for both SILO and BAWAP across the continent,
with lower error statistics for SILO along the east coast of Australia. The addition of satellitebased gridded precipitation estimates in the LSBLEND improved rainfall estimates in areas
with gauge densities less than 4 per 10 000 km2, whereas results in areas with more than
1000 gauges showed no or only marginal improvements (Renzullo et al. 2011). It is noted that
the BAWAP interpolation scheme generates reliability indicators when interpolation fails as a
result of sparse gauged networks (BoM 2011). In case of interpolation failure, no precipitation
estimates are obtained for the corresponding grid cells. Areas considered to have greater
than 20% unreliable data during 1911–2010 are shown in Figure 7b. This unreliability also
affects the SILO estimates and, to a lesser extent, the LSBLEND estimates; however, in the
latter two products estimates are still provided.
To assist in the interpretation of precipitation forcing effects on SMS estimation we performed
a spatial comparison across Australia of mean annual and monthly precipitation estimates
from the aforementioned datasets for data spanning 1998–200815. The annual mean
precipitation, standard deviation of the mean and coefficient of variation (standard deviation
normalised by the mean) were computed for the three-member ensemble. Using SILO as
reference for comparison, the root mean square difference (RMSD) and the correlation
coefficient for monthly precipitation totals were computed for BAWAP and LSBLEND,
respectively. Linear trends were also computed to assess temporal changes. The RMSD is
defined as follows:
n
RMSD 
 (P
i 1
mod, i
 Pref ,i ) 2
(4–1)
n
where n is total number of months, Pmod,i is precipitation using BAWAP or LSBLEND forcing
at month i and Pref,i is precipitation using SILO forcing. Figure 8 shows the (a) mean, (b)
standard deviation and (c) normalised standard deviation of the three-member ensemble
precipitation. Standard deviations larger than 100 mm/year occur in areas with scarce gauge
density, for example the Great Sandy Desert, the coastline along Shark Bay, Barkly
Tablelands and the mountain ranges in central Queensland. High standard deviations are
also observed in the higher rainfall regions along the eastern and northern coastline, areas of
Cape York Peninsula and Arnhem Land. The convective nature of summer precipitation and
the influence of topography in some of these areas (e.g. mountain ranges in central
Queensland, eastern Tasmania, Victorian Alps and Snowy Mountains) are also indicative of
the differences observed in the precipitation datasets. The spatial pattern is also present in
the map of coefficient of variation (Figure 8c). Note that the high values in central northern
Australia (the Tanami Desert) are due to increased sensitivity of this statistical measure when
the ensemble mean is small. Standard deviations <35 mm/year and coefficients of variation
<0.1 are observed in lower latitude areas with fairly dense gauge coverage (inland southeastern and south-western Australia). These areas are associated with winter synoptic
precipitation systems, which are generally more densely gauged and tend to exhibit lower
spatial variability (Beesley et al. 2009). The spatial monthly correlation and RMSD (Figure 9)
corroborated the findings of the univariate statistics presented in Figure 8, with the lowest
correlations occurring in sparsely gauged areas, along complex topographical terrain and in
areas of high convective precipitation events.
15
2008 is currently the last year with readily available LSBLEND data.
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Figure 8: Summary statistics for the three member ensemble precipitation data (SILO,
BAWAP and LSBLEND) for 1998–2008.
(a) Average annual rainfall data (b) Standard deviation (c) Coefficient of variation (d) gauge
network (same as Figure 7a, for reference)
(d) gauge network
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Figure 9: Comparison of precipitation monthly correlation (r) and root mean squared
difference (RMSD) for all months in 1998–2008.
(a–b) Correlation of BAWAP and LSBLEND vs. SILO, respectively (c–d) RMSD of BAWAP
and LSBLEND vs. SILO, respectively
The relationship between error in precipitation forcing models and resulting error in computed
SMS dynamics has not been studied previously. To assess the impact of different
precipitation forcing on SMS, we used the AWRA-L, forced by the three precipitation datasets,
to derive SMS estimates. Daily continental simulations using SILO precipitation forcing were
conducted for 1998–2008, with initial SMS values initialised to those of 1 January 1998. The
other two precipitation forcing models were used to perform simulations for 1998–2008. The
resulting SMS estimates corresponding to the topsoil, shallow and deep soil moisture
storages were aggregated on a 1° grid.
Maps comparing the linear 11-year trend for the simulations with different model forcing are
shown in Figure 10. Comparisons of trends show reasonable agreement both spatially and in
magnitude across the continent, with positive trends of similar magnitude in Cape York
Peninsula, Arnhem Land and the eastern coast. Strong negative trends (>15 mm/year)
occurred in the Great Sandy Desert and in areas of the Tanami Desert and BAWAP showed
more negative trends in the arid and semi-arid areas of the interior. Tasmania also showed
negative trends in the three model runs. The trend differences between different model
forcings are highlighted in Figure 11(d–e), with BAWAP showing more positive trends than
SILO in northern and continental eastern Australia and more negative trends in the arid
interior. Whereas LSBLEND has generally more positive trends across the continent except
for areas in the Great Sandy Desert and the Tanami Desert. The period mean continental
trends for simulations was –0.88, –1.33 and –0.18 mm/year for SILO, BAWAP and LS
BLEND, respectively.
A feature of interest is that the satellite-informed LSBLEND product generates a considerably
stronger and spatially extensive negative trend in the Great Sandy Desert than does the SILO
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product (Figure 10e). This probably goes a long way to explain the difference between AWRA
(SILO) trends and GRACE (CSR) trends found by Van Dijk et al. (2011) for this region.
Maps comparing modelled SMS correlation (r) and RMSD between SILO and BAWAP and
SILO and LS BLEND, respectively, are show in Figure 11. Both comparisons show
reasonable agreement in areas where the precipitation was similar and vice versa, although
the correlation of SMS estimates is lower than that of precipitation in arid and semi-arid areas
in the continental interior. This result was expected: hydrological modelling in drier areas has
been shown to be more sensitive to small absolute perturbations in precipitation than in humid
areas (e.g. Farmer et al. 2003). SMS RMSD exhibits a similar spatial pattern as precipitation
RMSD.
Figure 10: Comparison of AWRA-L modelled soil moisture storage (SMS) trends with different
precipitation forcing for 1998–2008.
(a–c) SILO, BAWAP and LS BLEND, respectively (d–e) Biasof BAWAP and LS BLEND vs.
SILO, respectively (f) Standard deviation of the three member ensemble
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Figure 11: Comparison of AWRA modelled soil moisture correlation with different precipitation
forcing for 1998–2008.
(a–b) BAWAP and LSBLEND vs. SILO (c–d) Root mean squared difference (RMSD) of
BAWAP and LSBLEND vs. SILO, respectively
4.4 Soil storage estimation uncertainty due to
model error
In addition to uncertainty in precipitation, SMS estimates are also affected by errors in the
model structure and parameters. For example, different models and parameter sets reflect
different assumptions about the degree and depth of vegetation root access to soil water and,
in some cases, groundwater. Dynamic soil storage estimates from models can be used to
quantify apparent model assumptions about water extractable by vegetation. This can help to
provide an insight into the likely magnitude and nature of uncertainties due to model error.
However, just as the three rainfall products analysed in the previous section were derived by
interpolation techniques that are to some extent similar and therefore not fully independent,
so different models are also not independent. Different hydrological models are likely to share
identical or similar assumptions, concepts, equations and input data. Therefore, we can only
derive a tentative estimate of SMS uncertainty from comparing estimates from different
models.
In this study, total soil water storage estimates were obtained from a number of models,
including AWRA and four models included in NASA’s GLDAS system (Rodell et al. 2004): the
Community Land Model (CLM), Mosaic, NOAH, and the Variable Infiltration Capacity (VIC)
model. GLDAS model outputs can be downloaded as 1° resolution grids from the Goddard
Earth Sciences Data and Information Services Center (http://disc.sci.gsfc.nasa.gov). All four
GLDAS models use the same global rainfall input data, a combination of NOAA/GDAS
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atmospheric analysis fields and spatially and temporally disaggregated NOAA Climate
Prediction Center Merged Analysis of Precipitation (CMAP). Compared with the three
Australian datasets, these rainfall estimates have coarser resolution (1° vs. 0.05°) and are
constrained by a smaller number of rain gauges, and therefore can be assumed to have
greater rainfall estimation error over the Australian continent.
CLM, Mosaic and NOAH can be considered ‘conventional’ land surface schemes as used in
global climate models. That is, they model SMS dynamics by solving a layer-based
formulation of the standard diffusion and gravity equations for unsaturated flow (Kumar et al.
2009). In the VIC model, soil water movement is not modelled using vertical diffusion but by
gravity drainage, with the unsaturated hydraulic conductivity a function of the degree of
saturation of the soil (Nijssen et al. 1997). In contrast, AWRA-L uses a simplified diffusionbased equation. This equation is based on the results from off-line simulations of drainage
from a multi-layered soil using Richard’s equation of movement of water in unsaturated soils
(Richards 1931). Conceptually, the resulting function is arguably closest to the VIC soil water
movement formulation.
The soil column is described in each of the models as follows:

the blended satellite-gauge precipitation product, developed by CSIRO and BoM through
WIRADA and currently being made operational as an experimental data service, referred
here as LSBLEND (Li and Shao 2010)

in CLM, the soil column is discretised in 10 uneven layers with thicknesses of 1.75, 2.76,
4.55, 7.5, 12.36, 20.38, 33.60, 55.93, 91.33, and 113.7 cm, respectively (i.e. 344 cm in
total)

Mosaic has three soil layers of 2, 140 and 200 cm respectively (342 cm in total). NOAH
has four layers of 10, 30, 60 and 100 cm (200 cm in total)

VIC has three layers of 10, 150 and 40 cm respectively (200 cm in total)

in AWRA-L (version 0.5), soil layers are not represented by soil depth but by soil layer
storage capacity at field capacity, with a top, shallow and deep soil layer of 30, 200 and
1000 mm storage, respectively, in the parameterisation used here. To derive comparable
soil layer depths, soil hydraulic properties would need to be assumed. For example, for a
soil with 35% storage capacity, the three layers would have thicknesses 8, 57 and 143
cm, respectively, i.e. 351 cm in total. Total soil depth becomes 615 cm if a lower storage
capacity of 20% by volume is assumed.
To compare SMS from the different models, soil moisture depths in all stores were summed
over the period 2002–2010. The dynamic range of SMS between models and the amplitude of
the seasonal cycle was computed for each model. Results are shown in Figure 12. There is
reasonable spatial and magnitude agreement between models except for CLM, which shows
lower amplitude in northern Australia, the eastern and southwestern coast and Tasmania.
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Figure 12: Modelled soil moisture seasonal amplitude for 2002–2010
(a) AWRA-L (b) CLM (c) Mosaic (d) NOAH (e) VIC and (f) Standard deviation of the five
member ensemble
Maps comparing the nine-year trend are shown in Figure 13. All models but CLM show strong
positive trends (>10 mm/year) in Cape York Peninsula and north Queensland. Conversely,
the GLDAS models show a slight positive trend along areas in the west coast and Tasmania
whereas AWRA-L shows negative trends (<–1.5 mm/year). The trends in the NOAH model
are either systematically higher or lower than the other models, with strong negative trends
(<–10 mm/year) in the Great Sandy Desert, Tanami and Gibson Deserts.
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Figure 13: Modelled SMS trend for 2002–2010
(a) AWRA-L (b) CLM (c) Mosaic (d) NOAH (e) VIC (f) Standard deviation of the five member
ensemble
Finally, the disagreement between actual monthly SMS (anomalies) from the four GLDAS
models is shown in Figure 14, whereas the overall average deviation is shown in Figure 15.
When compared with AWRA-L, differences in monthly SMS increase from VIC (continental
mean RMSD 35 mm), MOSAIC (39 mm), NOAH (40 mm) and, considerably greater, CLM
(89 mm). However, the mean value masks the fact that NOAH agrees better with AWRA-L for
humid regions, whereas VIC agrees better for arid regions. The use of AWRA-L as a
reference is not to suggest that these estimates are more reliable than the others. In wellgauged areas the BAWAP rainfall information used in AWRA-L is likely to be of better quality
than the 1° global data used in GLDAS, but the reverse is true for the regions where the
BAWAP product does not provide interpolated values. Moreover, although AWRA-L was
developed for Australian conditions, there is no direct evidence that the model assumptions,
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equations and parameters are superior to that of the other models. Nonetheless, choosing
another model as the reference would result in similar spatial patterns.
Figure 14: Root mean square difference (RMSD) in soil moisture storage (SMS) anomalies for
2002–2010, between the four GLDAS models and AWRA-L
Figure 15: Averaged root mean square difference between soil moisture storage (SMS)
estimates from the four GLDAS models and AWRA
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Table 1: Average continental (including Tasmania) seasonal amplitude, trend and RMSD
when compared with AWRA-L for 2002–2010
Spatial mean of
ensemble standard
deviation
AWRA-L
CLM
Mos
aic
(350615)*
344
342
200
200
Average Seasonal
Amplitude (mm)
74.4
24.8
67.8
71.6
62.9
±25.3
Linear trend
(mm/year)
0.48
-0.26
0.43
0.75
1.76
±4.0
Soil depth (cm)
NOAH
VIC
* estimated because AWRA-L v0.5 does not make direct assumptions about soil depth (see text)
Average continental amplitudes, trends and RMSD estimates are summarised in Table 1. The
following conclusions can be drawn from this table and the preceding figures:

the continental mean seasonal amplitude in SMS varies from 25 mm (CLM) to 74 mm
(AWRA). This indicates large model uncertainty when estimating SMS dynamics,
although the range is reduced to 68–74 mm if CLM is not considered. The standard
deviation of the continental mean amplitude is 25 mm or 42% of the ensemble mean (if
CLM is not considered, the standard deviation of the continental mean amplitude is
reduced to 16 mm or 23% of the ensemble mean). The spatial mean of the ensemble
standard deviation for each grid cell is of similar magnitude, at 25 mm (Table 1)

as expected, all models show the greatest amplitude in seasonally wet regions and the
smallest amplitude in arid regions. In absolute terms, the amplitude (>50 mm) and
ensemble standard deviation (>75 mm) are greatest in northern Australia (Figure 12)

the different models show mean continental trends varying from –0.26 to +1.76 mm/year
for the period 2002–2010 (Table 1), with an average of 0.63±0.73 mm/year. The spatial
mean of ensemble standard deviation in trends is 4.0 mm per year. The latter value is
larger because both positive and negative trends occur for all models and lead to a
smaller mean continental trend and associated smaller standard deviation (Figure 10)

the greatest variation in estimated storage trends is in northern Queensland
(RMSD >10 mm/year), a region with the greatest increasing storage trends according to
most models (>2 mm/year). There is generally good agreement in estimated storage
trends for inland Australia, and lesser agreement in coastal regions.
The uncertainty in modelled SMS is not constant in time however. To illustrate this point, time
series of estimated SMS anomalies from the different models are compared in Figure 16 and
Figure 17. These figures clearly show a common feature, namely that the absolute
differences in SMS anomaly estimates are greatest for maximum and minimum values, and
least for transitional period. This is partly a result of the calculation of anomaly values.
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Figure 16: (a) Monthly uncertainty time series (in the form of standard deviation) from the
AWRA-L and GLDAS models evaluated in the Canning basin near Broome (E122.5º, S17.5º)
(b) Ensemble SMS change (blue line and dots) showing standard deviation bars (grey) (c)
Time series of SMS change from AWRA-L and GLDAS
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Figure 17: (a) Monthly uncertainty time series (in the form of standard deviation) from the
AWRA-L and GLDAS models evaluated in the Condamine basin (E148.5º, S27.5º) (b)
Ensemble SMS change (blue line and dots) showing error bars (grey) (c) Time series of SMS
change from the AWRA-L and GLDAS
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5. Derivation and Assessment of
Groundwater Variations
We use the TWS changes from GRACE and estimate variations in groundwater storage by
subtracting estimates of SMS changes derived from the hydrological models. The magnitude
and spatial variation of these groundwater storage variations is then assessed in terms of
credibility with respect to known behaviour of groundwater systems.
5.1 Point-scale groundwater level observations
There are tens of thousands of monitoring bores spread unevenly across Australia.
Individually, these monitoring bores provide a point-scale estimate of the change in GWS over
time. Collectively, it may be possible to use this data to assess the accuracy of the change in
groundwater storage estimated from GRACE.
The groundwater databases were obtained from the jurisdictions in each state. Groundwater
levels are usually measured manually at irregular intervals; there are few bores around the
country that are monitored automatically through the use of data loggers. The jurisdictions’
databases were queried for those bores that had at least five observations spread over at
least two years in the period 1/7/2002 and 30/6/2010. We chose these as the minimum data
requirements necessary to enable an estimation of a linear trend in groundwater levels.
We calculated the linear trend in groundwater levels for 28 070 bores (Figure 18). Of these,
3% do not have a statistically significant (p<0.05) trend, 28% have increasing trends and 69%
have decreasing trends.
Individual monitoring bores provide a very local observation of the trend in groundwater
levels. These point-scale measurements can be influenced by local effects such as pumping
causing a drawdown or recharge through irrigation. The point-scale trends were aggregated
to a 1° grid to enable a comparison with the GRACE-derived estimates at an appropriate
scale.
Figure 18: Trend in groundwater level at each monitoring bore that has at least five
measurements spread over at least two years in the period 1/7/2002 to 30/6/2010
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5.2 Grid-scale groundwater level observations
Figure 19a shows that most of the country does not have any groundwater monitoring bores
within a 1° grid cell, partly because we did not receive data from Western Australia or
Tasmania. However, there are some areas where there are more than 1000 bores within a
single grid cell. We categorised these cells into those showing increasing (rising groundwater)
trend, decreasing (falling) trend and no significant trend (Figure 19b). It can be seen that all of
Victoria, south-east South Australia and southern New South Wales is dominated by a
decreasing trend in the groundwater level observations. Coastal Queensland and the top end
of the Northern Territory have predominantly an increasing trend in groundwater levels, while
the remainder of the country has a mix of both increasing and decreasing trend in
groundwater levels. The pattern of the mean of the groundwater level trends (Figure 19c) is
similar to that of the mode of the groundwater level trends (Figure 19b), and shows that
groundwater level increases and decreases of >400 mm/year occur in several regions.
To convert groundwater level changes to GWS changes, knowledge is needed of specific
yield or storativity16. In an unconfined aquifer, it may also be called specific yield or drainable
porosity and can be defined as the change in GWS per unit groundwater level change (both in
mm). In confined aquifers, storativity can be defined in a similar way, being the change in
GWS per unit change in groundwater pressure. The storativity of confined aquifers is several
magnitudes smaller than specific yield (small storage changes can result in large pressure
changes). Unfortunately, specific yield itself is also highly variable, from a few per cent in
consolidated clay deposits and certain rock types, to more than 30 per cent in loosely packed
sand or gravel.
Groundwater level trends need to be multiplied by the specific yield to convert them into GWS
trends. Additionally, within a grid cell there may be multiple aquifers with differing specific
yields (or storativities). It is noted that monitoring bores are biased with respect to large area
average specific yield: they are usually concentrated in water yielding aquifers, which
normally have higher specific yields than surrounding groundwater systems from which water
is not readily extracted. This is an unavoidable problem encountered when trying to compare
groundwater levels with groundwater volume estimates, and needs to be addressed on a
regional basis through expert knowledge and, where necessary, additional data collection and
aquifer characterisation.
The different GRACE solutions for the trend in EWH (Figure 5) show similar patterns with an
increasing trend over the top end of NT and central Queensland and a decreasing trend over
the Canning Basin and Murray Basin. We chose these areas to investigate the time series of
GWS derived from bore observations and through the combination of GRACE and AWRA-L
(Figure19c; Table 2). There are no monitoring bores within the Canning Basin and so the
closest bores have been chosen from near Broome and Telfer, with five and six bores,
respectively17. Two sites have been chosen within the Daly catchment with the eastern site
having a mode of decreasing water levels but a small mean rate of increase. There were five
sites chosen in Queensland spread amongst the Fitzroy, Condamine and Brisbane
catchments. These sites show a mix of increasing and decreasing water levels. Three sites
were selected in the Murray Basin that all show an average decreasing trend in water levels,
the site selected near Shepparton has the highest number of observation bores in a single
grid cell (2868).
16
Specific yield is the volume of water released from storage per unit decline in hydraulic head in an
unconfined aquifer; storativity is a similar concept but applies to confined aquifers.
17 While the bores are at some distance from the Canning Basin and may not be located in the same
sediment types, they are the closest and best information available with which to compare to the
GRACE observations.
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Figure 19: Trends in groundwater level from monitoring bores aggregated to a grid scale
(a) The number of monitoring bores in each 1° grid cell (b) The mode (i.e. most common
direction) of the categorised trend in groundwater level (c) The mean of the trend in
groundwater level (d) Regions and sites chosen for more detailed analysis
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Table 2: Details on the grid cells chosen for further investigation (shown in Figure 19d)
Listed are the coordinates of the centre of the grid cell, the number of bores and the mean
and standard deviation of the trend in the grid cell.
Location
Long
Lat
No.
GWL Trend (m/yr)
bores
mean
Std
dev
Canning Basin (near Broome)
122.5
-17.5
5
-0.04
0.03
Canning Basin (near Telfer)
122.5
-21.5
6
0.58
0.03
Daly E
132.5
-14.5
47
0.04
0.55
Daly W
131.5
-14.5
25
0.40
0.76
Fitzroy E
150.5
-24.5
334
-0.10
0.53
Fitzroy W
148.5
-21.5
181
0.23
0.38
Brisbane
152.5
-27.5
790
0.22
0.84
Condamine E
151.5
-27.5
506
-0.11
0.75
Condamine W
148.5
-27.5
67
0.49
0.68
Murray Basin (lower Lachlan)
145.5
-33.5
131
-0.26
0.25
Murray Basin (near Renmark)
140.5
-34.5
411
-0.07
0.3
Murray Basin (near Shepparton)
145.5
-36.5
2686
-0.17
0.22
5.3 Time series comparison of groundwater
level observations and GRACE/AWRA
5.3.1 Method of creating an average time series from
observed groundwater levels at a grid cell scale
The observed time series of groundwater levels (GWL) from different bores within a grid cell
will seldom be identical. There are differences due to position in the landscape,
hydrogeological conditions and local effects such as pumping or influence from nearby
surface water features (e.g. rivers). Representative time series need to be created that can
then be used to compare with the GWS time series derived from GRACE.
The method used here is illustrated in Figure 20 using an example of a subset of five bores
from the lower Lachlan region. It can be seen (Figure 20a) that each of the five bores has a
decreasing trend in GWL through time, and also a seasonal cycle. However, the magnitude of
the trend is different for each bore and the amplitude of the seasonal cycle is also different.
The trend can be removed from each of the time series using:
DTi  SWLi  (ti  t0 )  ms
(5–1)
where DTi is the de-trended standing water level (SWL) at time ti subject to the observed
trend m for bore s. It then becomes clear that the period and phase of the seasonal cycles are
nearly the same in each of the five bores but that the amplitudes are different and that there is
an offset in the depth below ground level (Figure 20b). These effects are then removed
through normalising the de-trended time series:
NDTi 
DTi   s
s
(5–2)
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Where NDTi is the normalised and de-trended SWL at time i, s and s are the mean and
standard deviation of the DT time series. The five time series are now much more consistent,
with a much reduced scatter (Figure 20c). The time series of NDT at each bore is then
reduced to a monthly series by temporal averaging. The monthly series of NDT at each bore
is then averaged at the grid cell level to create a single time series for the grid cell (Figure
20d). This time series is then converted back to a GWL time series:
GWLi  NDT i    ti  t0  m
(5–3)
Where GWLi is the average GWL at time i, NDT i is the average NDT across all bores in
the grid cell at time i,  is the average standard deviation of the DT series of all bores in the
grid cell andm is the average trend in SWL across each bore. For the five bores used as an
example in the Lachlan region, the time series of
original time series of SWL (Figure 16e).
GWL is visually very similar to the five
The final stage is the conversion from GWL to a residual EWH where first the mean of the
time series is removed and then each value is multiplied by a specific yield (Sy).


EWH i  GWLi  GWL  S y
(5–4)
It is this time series of EWH (Figure 20f) that can then be compared to the EWH time series
derived from GRACE and AWRA-L. The specific yield has been assumed to be 0.1
everywhere for this study and is acknowledged as a substantial source of uncertainty. The
consequences of this assumption are to make the amplitude of the GWS estimates uncertain,
but it is expected that the pattern of temporal variability will be correct.
The uncertainty in the calculation of the average time series at a grid cell scale is due to
several sources—measurement error, averaging error and error introduced due to the specific
yield. The uncertainty introduced due to measurement error is small. The standing water
levels are recorded at worst to the nearest centimetre (often to the nearest millimetre
suggesting that the measurement error will be no more than half of this (i.e. 5 mm of SWL).
When multiplied by the specific yield (assumed to be 0.1), this error becomes 0.5 mm EWH.
Uncertainty in the averaging of individual bore time series to create a grid cell average can
occur during three steps—when averaging of NDT, adding the trend, and adding variance
back into the time series. In addition, there is uncertainty associated with the assumption that
the observation bores are a representative sample of the actual groundwater levels in the grid
cell. This uncertainty cannot be adequately quantified.
We approximate the uncertainty of a single monthly NDT as being the 95% confidence
interval of the mean monthly NDT (Figure 21a). The standard deviation is proportional to the
inverse of the square root of the number of observations. Therefore, the months with more
GWL observations generally have lower uncertainty about the mean than those that have
fewer observations. For the Lachlan example there are 131 observation bores in total and, for
an individual month, the minimum and maximum number of bores with at least one
observation is 3 and 126, respectively.
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Figure 20: Method used to create a time series of EWH from multiple observation bores within
a grid cell
-30
(a) Measured groundwater levels
-30
-32
-32
-34
-34
-36
-36
-40
2004
2006
2008
2010
DT SWL (m b gl)
SWL (m b gl)
-38
6
(b) Detrended
-38
-40
2004
2008
2010
2006
2008
2010
2008
2010
6
(d) Average NDT
(c) Normalised and Detrended
4
4
2
2
0
0
NDT (-)
NDT (-)
2006
-2
-4
-2
-4
2004
2006
2008
2010
2004
2
200
(e) Variance and trend added back in
(f) Equivalent Water Height
1
100
0
-1
0
EWH (mm)
GWL (m)
-2
-3
-4
2004
2006
2008
2010
-100
-200
2004
2006
When the trend is added back into the time series an uncertainty is also added. For the
Lachlan example the average trend across the 131 bores is –0.265 m/year with the range of
two standard errors being between –0.308 and –0.222 m/year. When this uncertainty is
propagated through to the EWH calculation it can be seen that the uncertainty is greatest at
either end of the time series and decreases to near zero in the middle due to the time series
being centred (Figure 21b).
The mean of the standard deviation from each of the de-trended time series is used to recreate the variance in the time series. For the Lachlan example, the mean standard deviation
is 0.402 m/year and the range of two standard errors either side of the mean is between
0.305 and 0.500 m/year. When this is propagated through the calculations to EWH it can be
seen that uncertainty increases in magnitude as EWH gets further from zero (Figure 21c).
If these three sources of uncertainty are assumed to be linear and independent then they can
be added (Figure 21d). (A more precise answer could be generated through boot-strapping,
but not within the time constraints of this study.) It can be seen that, at worst, the uncertainty
in the combined Lachlan time series is approximately one third of the range of the GWS
estimates. This relative uncertainty would scale linearly with the uncertainty in the specific
yield (which is not quantified here). A sensitivity analysis of the assumed specific yield is
shown in Figure 22. This demonstrates that the specific yield modifies the magnitude of the
time series of EWH but not the pattern.
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Figure 21: Sources of uncertainty in the calculation of the combined time series at the Lachlan
grid cell
150
150
(b) Uncertainty due to trend
(a) Uncertainty due to Av NDT
100
100
50
50
0
0
-50
-100
GW Data EWH (mm)
GW Data EWH (mm)
-50
-100
-150
2004
2006
2008
2010
150
(c) Uncertainty due to variance
-150
2004
50
0
0
-50
-50
-100
-100
GW Data EWH (mm)
GW Data EWH (mm)
50
2006
2008
2010
2010
2008
2010
(d) Combined uncertianty
100
2004
2008
150
100
-150
2006
-150
2004
2006
Sy=0.03
20
0
-20
-40
Sy=0.1
100
50
0
-50
-100
-150
2004
2006
2008
2010
2004
2006
2008
GW Data EWH (mm)
150
40
GW Data EWH (mm)
GW Data EWH (mm)
Figure 22: Differences in the combined time series at Lachlan of assuming different values of
specific yield (note the different y-axis scales)
400
Sy=0.3
200
0
-200
-400
2010
2004
2006
2008
2010
5.3.2 Precipitation time series as a predictor of groundwater
level
Precipitation has been shown to be a good predictor of GWL in some circumstances. One
measure of rainfall that has found wide application is the Accumulative Annual Residual
Rainfall (AARR) (Ferdowsian et al. 2001):
t 
A
AARRt    M i  
12 
i l 
(5–5)
where Mi is the precipitation in month i and A is the annual average rainfall.
For each of the sites selected (Figure 15d) the rainfall time series was downloaded from SILO
(Jeffrey et al. 2001) and the AARR was constructed using an average annual rainfall from
1900 to 2010. The AARR is then compared with the GWS time series derived from GRACE
and the GW data as a very simple model of the expected changes in GWS over time.
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5.3.3 Results from near Broome
In the grid cell selected near Broome there are five observation bores and all are located in a
sand dune system (Figure 22). There is a poor spatial representation of observation bores
within the grid cell.
All five of the bores have a decreasing trend in GWL with a mean of –0.04 m/year. The lack of
data at this site makes a comparison with the GRACE data difficult and very little can be
concluded from the results (Figure 23).
Figure 23: Surface geology of the grid cell near Broome with the location and trend in the
observation bores
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Figure 24: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Broome
5.3.4 Results from near Telfer
In the grid cell selected near Telfer there are six observation bores and all are located in a
sand dune system (Figure 25). There is a poor spatial representation of observation bores
within the grid cell.
All six of the bores have an increasing trend in GWL with a mean of 0.58 m/year. This
increase in GWL is consistent with the above average rainfall experienced during the period
of investigation (Figure 26). However, the four examples of the GWS estimated from GRACE
all show a decreasing trend in GWS. Possible reasons for this are discussed in Section 5.4.
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Figure 25: Surface geology of the grid cell near Telfer with the location and trend in the
observation bores
Figure 26: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Telfer
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5.3.5 Results from Daly Catchment West
In the grid cell selected in the Daly West there are 25 observation bores spread through the
north and east of the grid cell. They are located in the surface geology types of sand,
sandstone and alluvium but are probably drilled into the limestone beneath (Figure 27). Of the
25 bores, 18 have an increasing trend and the average across all bores is an increase of 0.40
m/year.
The CRS GRACE data has noticeably larger seasonal amplitude than the GRGS data and
provides a better match between the GRACE-SM signal and the GW data signal than the
GRGS GRACE data (Figure 28). The seasonal amplitude of both SM models is too large to fit
the GW data for the GRGS GRACE data; this could in part be due to the model
conceptualisation. In this environment the groundwater fills to near the ground surface during
the wet season. At such times, the saturated zone is within the soil of the hydrological models
and so the water is being counted twice, once as soil moisture and again as saturated
groundwater.
Figure 27: Surface geology of the grid cell in the Daly West with the location and trend in the
observation bores
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Figure 28: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Daly West
5.3.6 Results from Daly Catchment East
In the Daly East grid cell there are 47 bores with bores in either limestone or sand surface
geology types (Figure 29). Of the 47 bores, 26 have a decreasing trend and most of these are
located in the limestone aquifer. Overall the average trend for the grid cell is a small increase
in GWL (0.04 m/year) despite more bores having a decrease than an increase (the large
amplitude increases in some bores result in a difference between the average rate and the
mode rate in this location).
The time series of GWS (Figure 30: ) is similar to that of the Daly West site; there is a strong
seasonal cycle present in the GRACE, GRACE-SM, rainfall and GW data signals. The SMS in
AWRA-L appears to be too great because it is removing the seasonal cycle from GRACE that
is present in the GW data (Figure 30, the peak in 2004 red curve). Visually, the CSR-GLDAS
result provides a good fit to the GW data for this site.
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Figure 29: Surface geology of the grid cell in the Daly East with the location and trend in the
observation bores
Figure 30: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Daly East
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5.3.7 Results from Fitzroy Catchment East
In the Fitzroy East grid cell there are 331 bores and nearly all of them are located in the
alluvium along the river (Figure 31). Of these bores, 84% have a decreasing trend in GWL
with an average for the grid cell of –0.10 m/year.
There is a strong seasonal cycle in the GRACE time series at this site that is not removed by
the SM from the hydrological models to match the signal from the GW data (Figure 32). The
signal from the GW data is following the rainfall signal, neither of which matches any of the
four GRACE-SM signals. This is discussed in Section 5.4.
Figure 31: Surface geology of the grid cell in the Fitzroy East with the location and trend in the
observation bores
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Figure 32: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Fitzroy East
5.3.8 Results from Fitzroy Catchment West
In the Fitzroy West grid cell there are 181 bores that are in two clusters in the north east and
south east of the grid cell (Figure 33). Overall, 75% of bores show an increase in GWL for an
average across the grid cell of 0.23 m/year. Ninety-five per cent of bores in the north-east
cluster have an increasing trend, with an average of 0.30 m/year, while in the south-eastern
cluster 51% of bores have an increasing trend, with an average of 0.14 m/year.
The GRGS and GW data show similar trends (Figure 34) but the AWRA-L soil moisture is
removing too much signal to match the GW data and, after removing the GLDAS ensemble
soil moisture, the groundwater dynamics are not being reproduced. The CSR GRACE data
has too strong a seasonal signal that is not being removed by the hydrological models to
match the GW data, whereas the GRGS GRACE seasonal variations are much smaller in
amplitude.
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Figure 33: Surface geology of the grid cell in the Fitzroy West with the location and trend in
the observation bores
Figure 34: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Fitzroy West
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5.3.9 Results from Brisbane Catchment
In the Brisbane River Catchment grid cell there are 790 bores with the vast majority of them in
the alluvium along the river (Figure 35). Overall, 60% of the bores have an increasing trend in
GWL, with an average of 0.22 m/year.
The time series of GW data shows a steep rise after 2008 that is not reflected in the rainfall
signal (Figure 36). This is an artefact of the process used to create a single time series for the
grid cell. The distribution of trends in the individual bores is highly skewed (skewness = 0.90)
such that the mean (0.22 m/year) is much greater than the median (0.04 m/year). If the GW
data signal was to be recalculated using the median trend rather than the mean trend it would
have the effect of rotating the time series clockwise in the plot such that it would better mimic
the AARR signal. The break in slope around 2008 that is not present in any of the GRACE or
GRACE-SM signals would still remain but that is also present in the AARR signal. Note that
reducing the specific yield would also significantly reduce the misfit in amplitude between the
GWS and GRACE estimates.
Figure 35: Surface geology of the grid cell in the Brisbane Catchment with the location and
trend in the observation bores
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Figure 36: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Brisbane Catchment
5.3.10
Results from Condamine Catchment East
In the Condamine East grid cell there are 506 bores mainly drilled in the alluvium and basalt
(Figure 37). Overall, 75% of bores have a decreasing trend for an average of –0.11 m/year.
Both GRACE signals have too strong a seasonal cycle when compared with the GW data
time series and neither SM signal is able to damp the GRACE signal sufficiently (Figure 38).
There are times where the GRACE-SM and GW data are out of phase with each other in all
four cases.
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Figure 37: Surface geology of the grid cell in the Condamine East with the location and trend
in the observation bores
Figure 38: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Condamine East
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5.3.11
Results from Condamine Catchment West
In the Condamine West grid cell there are 67 bores that are either in alluvial sediments or
sand. Of these, 69% have an increasing trend for an average of 0.48 m/year. However, these
bores are not spread uniformly through the grid cell with the northern two-thirds of the grid cell
only having 14 bores (50% increasing) (Figure 39).
The time series of the GW data does not follow the trends from any of the GRACE-SM signals
(Figure 40). The representativeness (and accuracy) of the GW data signal has to be
questioned at this site as it appears to be out of phase with the AARR signal, whereas the
GRACE estimates appear to be in phase with AARR. The difference in GW trend is not
related to the methodology used for sampling the GW signal but may reflect local
anthropogenic influences such as pumping.
Figure 39: Surface geology of the grid cell in the Condamine West with the location and trend
in the observation bores
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Figure 40: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the Condamine West
5.3.12
Results from Murray Basin (lower Lachlan)
In the grid cell located in the lower Lachlan there are 131 bores in the alluvium, sand and clay
(Figure 41). Of these 131 bores, 95% have a decreasing trend for an average of –0.26
m/year.
The GRGS GRACE data is reproducing the trend seen in the GW data with the GLDAS
ensemble providing a better representation of the groundwater dynamics than AWRA-L
(Figure 42). The CRS GRACE data is not capturing the trend seen in the GW data. We do not
have an explanation for this.
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Figure 41: Surface geology of the grid cell in the lower Lachlan with the location and trend in
the observation bores
Figure 42: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell in the lower Lachlan
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5.3.13
Results from Murray Basin near Renmark
The grid cell located near Renmark has 411 bores spread amongst all the surface geology
types present in the grid cell (Figure 43). Of these 411 bores, 74% have a decreasing trend in
GWL for an average of –0.07 m/year.
Both GRACE solutions are able to capture the trend in the GW data at this site (Figure 44).
However, neither soil moisture source is able to reproduce the dynamics of the GW data
when subtracted from the GRGS GRACE signal. The seasonal amplitude of the CRS GRACE
data is too large when compared with the GW data but the GRGS GRACE data agrees well.
Figure 43: Surface geology of the grid cell near Renmark with the location and trend in the
observation bores
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Figure 44: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Renmark
5.3.14
Results from Murray Basin near Shepparton
The grid cell located near Shepparton has the most observation bores of any 1° grid cell in
the country with 2868. These are spread throughout all the surface geology types except for
the granite in the south of the grid cell (Figure 45). Of these observation bores, 79% have a
decreasing GWL with an average of –0.17 m/year.
The GW data signal appears to be controlled by the rainfall signal (Figure 46). The GRGS
GRACE signal captures the trend in the GW data well, with the AWRA-L SM data better
capturing the dynamics when compared with the GLDAS ensemble. Again, the amplitude of
the seasonal signal is over-estimated by the CRS GRACE data when compared with the GW
data.
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Figure 45: Surface geology of the grid cell near Shepparton with the location and trend in the
observation bores
Figure 46: A comparison of the change in groundwater storage derived from observation
bores and GRACE from the grid cell near Shepparton
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5.4 Assessment of the comparison in GWS
between the GW data and GRACE
In the previous sections, we compared GRACE-derived GWS estimates with those from
monitoring bores for 12 GRACE grid cells (1°x1°, ca. 10 000 km2 surface area each). The
following caveats need to be made about the method used to derive GWS from monitoring
bores:

in several grid cells, there was no consistency in linear trend between bores, with both
increasing and decreasing trends observed. This may be due to hydrogeological
conditions or extraction, and indicates that a very large number of bores may be needed
to reliably estimate large-area groundwater patterns. Similarly, for some of the areas
investigated the distribution of bores was clearly not homogenous. This needs to be
considered in interpretation

the method to combine data from different bores and the conversion of level to storage
estimates required assumptions about specific yield with high uncertainty. Therefore, a
difference in magnitude (as opposed to temporal pattern) between bore and
GRACE-derived groundwater volume estimates alone is not necessarily surprising.
A scatter plot of the two estimates of groundwater storage at each grid cell shows a generally
poor correlation, with the grid cell near Shepparton being clearly the best correlation (Figure
47).
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Figure 47: Scatter plot of the GWS derived from GW data and GRACE (GRGS solution minus
AWRA-L)
300
150
300
nr Broome
nr Telfer
Daly W
100
200
200
50
100
100
0
0
0
-50
-100
-100
-100
-200
-200
-50
0
50
100
150
GW Data EWH (mm)
400
Daly E
200
-300
-300
-200
-100
0
100
200
300
GW Data EWH (mm)
100
Fitzroy E
GR GS - AWR A EWH (mm)
-150 -100
GR GS - AWR A EWH (mm)
GR GS - AWR A EWH (mm)
-150
-300
-300 -200
-100
0
100
200
300
GW Data EWH (mm)
FitzroyW
200
50
100
0
0
-200
-50
0
200
400
GW Data EWH (mm)
300
Brisbane
-100
-100
-100
-50
0
50
100
GW Data EWH (mm)
100
Condamine E
GR GS - AWR A EWH (mm)
-200
GR GS - AWR A EWH (mm)
GR GS - AWR A EWH (mm)
-400
-400
0
-200
-200
-100
0
100
200
GW Data EWH (mm)
200
Condamine W
200
50
100
0
0
-50
-100
100
0
-100
-200
0
100
200
300
GW Data EWH (mm)
150
Lachlan
-100
-100
-50
0
50
100
GW Data EWH (mm)
100
nr Renmark
GR GS - AWR A EWH (mm)
-300 -200 -100
GR GS - AWR A EWH (mm)
GR GS - AWR A EWH (mm)
-300
-200
-200
-100
0
100
200
100
200
GW Data EWH (mm)
200
nr Shepparton
100
50
100
0
0
-50
-100
50
0
-50
-100
0
50
GW Data EWH (mm)
100
150
-100
-100
-50
0
GW Data EWH (mm)
50
100
GR GS - AWR A EWH (mm)
-50
GR GS - AWR A EWH (mm)
GR GS - AWR A EWH (mm)
-150
-150 -100
-200
-200
-100
0
GW Data EWH (mm)
The comparison produced mixed results. Overall the groundwater storages calculated from
observation bores and derived from GRACE at the 12 chosen grid cells do not match each
other well. The 12 regions were chosen in areas with the most available groundwater bores,
in locations where there were clear trends identified in the GRACE solutions (see Figure 5).
While other locations may have had better spatial coverage of groundwater bores, we
deliberately chose a sample of regions with strong trends and both strong and poor
groundwater bore coverage in order to assess whether sparse discrete sampling of
groundwater levels would match the spatially averaged GRACE estimates.
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The variation between the GRACE and GRACE-SMS time series is often small when
compared with the temporal variations in the GRACE time series themselves, yet the
uncertainties introduced into the GWS time series through the inclusion of the SMS
component are considerable. However, one cannot assume that GRACE is sensing only
GWS and, therefore, it is essential that a model for the SMS is included. This highlights the
dependence of the remotely sensed GWS estimates on the accuracy of the SMS modelling.
For six of the 12 regions (Broome, Condamine East, Lower Lachlan, Fitzroy West, Renmark,
Shepparton), the GRGS-based GWS estimate was closer to patterns estimated from bore
data than the best CSR-based estimate. The reverse was true for three regions (Daly
Catchment West and East, Brisbane). There was poor agreement in either case for the
remaining three regions (Telfer, Fitzroy East, Condamine West).
For three of the 12 regions, the small number of available bores or the clustering of bores
within a small region or specific groundwater unit, precluded strong conclusions from being
drawn. For two of these regions (Broome, Condamine West), GRACE-derived GWS
estimates agreed better with bore estimates than did the simple rainfall residual based
estimates, while the reverse was true for one region (Telfer).
For the remaining eight regions with seemingly sufficient bore data, inter-annual trend in GWS
estimated from bores was reproduced well for six regions by at least one of the
GRACE-derived GWS estimates. For two regions there was poor agreement between GWS
and any of the GRACE-derived estimates—for Fitzroy East, the rainfall residual based
method appeared to produce a better estimate of GWS suggesting a problem with the
GRACE-derived estimate. For Brisbane, a small sample and possible bias in bore data for the
first half of the period may have contributed to the differences.
The agreement in seasonal patterns (Daly Catchment West and East) and, sometimes, also
inter-annual trends (Fitzroy Catchment West, Renmark) appeared sensitive to the choice of
SMS estimates, reflecting uncertainty due to model assumptions. In cases with strong
seasonality in GRACE water storage (e.g. northern Australia) the modelled soil moisture
accounted for most of the observed variability, whereas the bore estimates suggested that
groundwater, too, had a strong seasonal cycle. This suggests erroneous assumptions in the
model, e.g. about soil storage capacity.
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6. Known Errors and Estimates of
Uncertainties of Remotely Sensed
Groundwater
We identify regions where known modelling errors of ocean signals cause spurious signals on
the Australian continent. Specifically, we develop a means of increasing the uncertainties on
the estimates of groundwater variations to account for these model errors that do not appear
in the formal estimate uncertainties. A similar approach is undertaken for the hydrological
models, identifying regions of high and low confidence. These two uncertainty maps are then
combined, leading to a more realistic uncertainty map for remotely sensed groundwater over
Australia.
6.1 Quantification of GRACE errors
The estimation of spherical harmonic coefficients through an inversion by least squares
produces a so-called 'formal uncertainty' of each parameter. This is a quantity that reflects the
level of agreement (or otherwise) of the observations and the mathematical equations used to
represent the observed quantity as well as the weights (or uncertainties) assigned a priori to
the observations. The assumption is made that there are no systematic biases in any
observations and that the misfit (or residuals) of the model and the observations are Gaussian
in nature. Typically, the residuals will not be Gaussian, nor will it be correct to assume that
there are no systematic biases; therefore, the formal uncertainties of the parameter estimates
will not represent the true level of uncertainty (or error) in the estimated parameters.
In this section we quantify the GRACE errors through an assessment of the formal errors and
through consideration of some of the known systematic errors in the GRACE analysis18.
6.1.4 Formal uncertainty estimates
The formal uncertainties of the GRGS spherical harmonic fields are provided along with the
coefficients themselves. Thus, through a conventional propagation of variances, it is possible
to estimate the formal uncertainties of the derived EWH estimates. These vary temporally with
a range from approximately 20 mm to 90 mm (Figure 48). They are greater for the first year
after launch.
There is also a systematic variation with latitude caused by the fact that the lateral distance
between subsequent satellite overpass tracks is smaller near the poles than at the equator.
As a result, there is a detectable increase in uncertainty from south to north across the
Australian continent (Figure 49).
18
Shortcomings in some of the background models used in the reduction of the GRACE observations
have been identified already. This allows the magnitude of the error of the systematic biases to be
quantified. While it may seem logical to just fix the problems, it is proving to be challenging to the
international community to improve the background models and hence remove the identified systematic
biases.
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Figure 48: a) Time series of EWH change (and formal uncertainties) from the GRGS GRACE
solutions evaluated at location E122º, S22º, b) Time series of the formal uncertainties
themselves, c) Histogram of the formal uncertainties
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Figure 49: Histogram of uncertainties in GRACE EWH at 145ºE for latitudes 5ºS, 45ºS and
85ºS
6.1.2 Ocean tide errors
As noted in Section 3.1.1, the gravitational effects on the GRACE satellites of water mass
movement related to the ocean tides are modelled during the reduction of the GRACE
observations, using the FES2004 ocean tide model19 (Lyard et al. 2006). Any errors in the
tidal models propagate into the orbit estimates of the GRACE satellites and, therefore, appear
as errors in the estimates of surface mass changes. It is therefore of importance to know, to
the extent possible, the magnitude and spatial variation of these errors.
Poor modelling of the influence of ocean tides affects the GRACE water storage estimates.
The degree to which this occurs depends on a combination of characteristics of the GRACE
orbit and the temporal characteristics of the tide (Ray and Luthcke 2006). The distortion is
visible as a temporally repeating bias pattern on top of the water storage estimates. For the
semi-diurnal ocean tide (the S2 tide), the tidal errors actually appear in GRACE time series as
a signal with a repeat period of 161 days. Melachroinos et al. (2009) identified from an
analysis of the GRGS Release 01 GRACE solutions the presence of a significant error in the
modelling of the S2 tide in the FES2004 model off the north-west coast of Australia. It is, in
fact, the region with the greatest amplitude S2 tidal error globally.
We generated time series of EWH on a 1º grid using the GRGS RL02 solutions, then
estimated the amplitude of the 161-day period signal in each time series (Figure 49). The
dominant signal reaches an amplitude of >100 mm NW of Broome but there are also regions
with errors evident near Darwin (NT), off the coast of northern Queensland and also centred
on Gulf St Vincent (SA).
The effect of these tide model errors is to introduce into time series of EWH, spurious periodic
variations that are not related to mass variations of hydrological origins. Certain regions of
continental Australia are more affected than others, with amplitudes exceeding 15 mm (see
Figure 8):
19
Ocean tide models are a mathematical representation of cyclic variations of ocean height that occur at
a number of different frequencies. Each tidal signal is modelled as a sine curve with a particular
amplitude, period and phase, where the phase can be thought of as a time offset relative to Greenwich
Mean Time. The contribution to sea level of each periodic component of the ensemble of tides at any
epoch is found by evaluating the sinusoidal model. The sum of the evaluated heights from all tidal
constituents (or components) gives the sea surface height for that instant.
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69

the Northern Territory and Western Australia, south to latitude 20ºS

the east coast of Queensland from Rockhampton to Townsville

the southern coastline of Australia from Geelong to Ceduna, stretching approximately 200
km inland.
Figure 50: Amplitude of S2 ocean tide errors in GRACE solutions, aliased to 161-day period
signal in EWH time series
We can incorporate a component of this tidal modelling error into the uncertainty of a single
epoch estimate of EWH. Alternatively, a band pass filter could be used to remove any power
at this frequency. Naturally, the best approach would be to improve the accuracy of the 12hour ocean tide model and therefore remove the error. New ocean tide models that
incorporate GRACE observations of tidal errors have been developed (Savcenco and Bosch
2008; Savcenko and Bosch 2010), but are not yet being used by the international centres that
are generating the GRACE solutions. It is emphasised that these tidal errors introduce a
cyclical error but do not affect inter-annual trends.
6.1.3 Non-tidal ocean mass variation errors
In addition to the consideration of the ocean tides, the influences of non-tidal ocean mass
movement on the GRACE satellite orbits are modelled. These include the influence of ocean
currents and wind-driven changes in the distribution of ocean mass. Importantly for northern
Australia, during the wet monsoon period, air currents drive ocean mass towards the north
Australian shores and increase water levels and mass to the north of the continent.
For the GRGS solutions, a non-tidal ocean model, MOG2D-G (Carrère and Lyard 2003) is
used, whereas a different model was used for the CSR solutions (Flechtner 2007; Bettadpur
2007). Non-tidal ocean variations occur at many frequencies and can also be non-stationary
in nature.
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If both the tidal and non-tidal models used in the reduction of the GRACE observations were
perfect then there would be no remaining signal of mass variations over the oceans. This is
not the case. For example, Tregoning et al. (2008) showed that the MOG2D-G model
removes only around 50% of the non-tidal signals in the Gulf of Carpentaria.
Because of the mathematical presentation of the GRACE products using spherical harmonics,
leakage of these unmodelled, higher spatial resolution signals from the oceans will influence
or 'leak' onto the coastal regions. This introduces apparent signal on the continental regions
where, in fact, no mass variations may have occurred. The spatial distribution and magnitude
of the errors will depend on the errors in the non-tidal ocean model used.
To assess the potential impact of the known frequency of the strong non-tidal signal in the
Gulf of Carpentaria, we calculated the amplitude of annual variations of ocean mass changes
in the Australian region from the GRGS EWH data (Figure 50). The residual non-tidal signal in
the gulf is clearly visible; however, the maximum amplitude of >150 mm at this frequency
occurs in the Daly River region south of Darwin.
Figure 51: Amplitude of the annual variations in GRACE solutions
A large part of the amplitude shown over northern Australia is certainly a real hydrological
signal. Therefore, it is difficult to identify what component of the annual variations on the
continent is related to leakage of the non-tidal ocean signal, and what part represents the
actual hydrological variations. It is likely, however, that at least some of the annual variations
of hydrological signals around the coastline of the Gulf of Carpentaria are over-estimated in
Figure 51 because of the leakage of the unmodelled non-tidal signals in the gulf.
Unfortunately the true non-tidal variations are not known, and therefore this source of error
cannot be removed. The true accuracy of the non-tidal models is not readily quantifiable.
Nonetheless, we can make a tentative assessment by evaluating the MOG2D-G barotropic
model20 to generate time series of non-tidal variations on a 1° grid, and then calculating the
standard deviation of a single observation about the mean of each time series. Over the
The MOG2D-G model is provided as a set of dimensionless spherical harmonic Stoke’s coefficients
(up to degree 50), averaged over the 10-day periods of the GRGS GRACE solutions. We expand the
spherical harmonic series and convert to EWH.
20
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continents—where there should be no mass change because there are no oceans—we find
that leakage of the barotropic model causes variations some distance inland (Figure 52).
In particular, it can be observed that:

because of the small spatial extent of Tasmania, a standard deviation of >30 mm is found
across the entire state

the spatial pattern of the leakage of the residual annual variations in the Gulf of
Carpentaria can now be identified

the distance to which the leakage propagates on the continent varies from virtually zero
(e.g. near Broome, Brisbane) to around 200 km (e.g. near Albany, Mallacoota).
Figure 52: Standard deviation (of a single observation about the mean) of the MOG2D-G
barotropic ocean model
The colour scale is saturated at high values (black) so that the detail of the spatial variability
at lower values remains visible.
One approach to mitigate the errors in modelling of the non-tidal ocean mass movement is to
calculate the value of the model at the location of interest in Australia and apply it as a
correction to the estimated EWH value. However, given that the accuracy of the non-tidal
models is neither well known nor easily quantifiable, this may or may not remove the leakage
errors accurately. The conservative approach taken here is to consider that the standard
deviations shown in Figure 10 represent the level of possible error in the non-tidal models;
hence, the level of uncertainty that needs to be added to the GRACE EWH estimates over
Australia.
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6.2 Quantification of modelled soil moisture
errors
In Section 4 the uncertainty associated with estimating mass changes associated with
biomass and surface water were estimated, and the influence of rainfall estimates and model
choices on soil moisture estimation uncertainty were analysed.
It was concluded that biomass and suface water storage changes can have a measurable
influence, but that these are small when compared with soil and groundwater signals (except,
perhaps, during flood events). The uncertainty in soil moisture content due to precipitation
and model choices can be quantified by combining the respective estimates of RMSD by
assuming that these errors are independent and hence can be added as:
RMSDSM = [ RMSDprecip2 + RMSDmodel2 ] ½
(6–1)
The result is shown in Figure 53. Comparing that figure with Figures 11(c–d) and Figure 15
makes it clear that the choice of model represents the greatest source of uncertainty. Both
rainfall and model uncertainty are greatest (in absolute terms) in more humid areas, and
hence this pattern reappears. The overall uncertainty in soil moisture estimates increases
from <15 mm in arid regions to >90 mm in humid parts of northern Australia and Tasmania.
Figure 53: Estimated overall uncertainty in SMS estimates.
6.3 Groundwater uncertainty map for Australia
The sum of the uncertainties described in Chapter 6 provides a quantitative measure of the
magnitude and spatial variation in the likely uncertainty of GWS estimates across Australia
derived from GRACE and SMS. As described above, we have attempted to quantify the
errors associated with GRACE and SMS estimates even though there is insufficient
information to do this in a complete and rigorous manner. We now make the assumption that
each of the error sources (formal GRACE errors, tidal and non-tidal ocean errors, soil
moisture model design, precipitation model errors) are independent and add together the
variances of each. Figure 53 shows the resulting uncertainty field, providing a first
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73
assessment of the likely accuracy with which GWS changes can be estimated from remote
sensing data.
Figure 54: Map showing likely uncertainties in groundwater estimates derived from a
combination of GRACE TWS and SMS
The majority of the continent has an uncertainty in the range of 20–40 mm EWH for any
monthly estimate. This value increases significantly in northern Australia where the pattern is
dominated by the uncertainty in the SMS modelling and by the errors in the modelling of the
non-tidal ocean mass movement used in processing the original GRACE observations. On
the other hand, being able to estimate GWS with a likely accuracy of about 20–40 mm across
inland Australia offers a substantial improvement in water resource monitoring where no
groundwater bore monitoring currently exists.
The uncertainties presented in Figure 54 consider only the errors in GRACE TWS and SMS
derived from the soil moisture models. As shown in Section 5, the remotely sensed GWS
changes did not always agree with GWS derived from GW bores. We consider that the
uncertainties in Figure 54 are realistic estimates of how well GWS changes can be estimated,
and suggest that much of the disagreement between remotely sensed GWS changes and
those from GW bores lies in the poor spatial sampling of the GW bores and local pumping
effects (see Section 5.4). Thus, in such sparsely sampled regions, the remotely sensed GWS
estimates offer the possibility of GW information to infill data voids in the GW bore network.
This is particularly relevant in regions where the saturated and unsaturated zones are not
connected, that is, where the soil moisture models are likely valid.
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7. Conclusions
The aim of this study was to assess to what extent the combination of remotely sensed total
water storage (from GRACE) and modelled soil moisture could be used to derive estimates of
changes in groundwater. The formal error estimates were assessed for the GRACE solutions
and the variations of an ensemble of soil moisture models was used to quantify the likely
errors in the derived groundwater values. Additionally, we attempted to quantify the
magnitude and spatial variability of some of the systematic errors and biases in both GRACE
and soil moisture estimates through an investigation of known errors in background models
(for GRACE—ocean mass movement) and forcing models (for soil moisture—precipitation
fields).
A major source of uncertainty in deriving groundwater dynamics from GRACE is the need to
subtract estimated soil moisture storage. For most of the 12 case study regions investigated it
was not possible to reliably infer seasonal cycles in groundwater storage from GRACE with
the approach because of uncertainty in the seasonal cycle of water storage in the unsaturated
zone. This can be improved upon using better spatial information on depth to groundwater,
subsurface hydraulic properties and vegetation rooting depth, and better representation of
groundwater discharge processes in the hydrological model used. This requires a
combination of field hydrological process knowledge and a sufficient number of observations
of groundwater and soil water behaviour in space and time. Such models may exist for certain
regions. On a continental scale, CSIRO and the Bureau of Meteorology are currently
improving the Australian Water Resources Assessment system along these lines.
Recommendation 1: To interpret GRACE observations of groundwater variations, it is first
necessary to identify or develop hydrological models that cover a sufficiently large area
and which are known to describe saturated and unsaturated dynamics (and their
coupling) reliably.
GRACE can add an overall constraint on a sufficiently reliable model by providing the total
water storage changes with an accuracy of approximately 25 mm EWH for monthly values.
Moreover, there is no reason to assume a systematic error such as long-term drift and,
therefore, a particular strength of the GRACE data is in providing valuable information on
inter-annual changes in water storage over large areas. Methods are required to constrain
finer resolution models with these observations.
Recommendation 2: Research needs to be conducted into how to assimilate GRACE total
water storage into hydrological models for Australia.
There is potential for GRACE observations to help improve the translation of groundwater
level changes into groundwater volumes. Comparisons of the two independent groundwater
estimates could be used to derive specific yield values on broad scales, which could be used
to extrapolate estimates derived locally from bore pumping tests.
Recommendation 3: A study should be undertaken of the feasibility and accuracy of
specific yield estimates from the comparison of GRACE, soil moisture and groundwater
levels from borehole measurements.
The GRACE TWS estimates are currently limited to a spatial resolution of around 400 km.
The benefits of incorporating the estimates into groundwater management systems would be
much more aparent if the spatial resolution was higher. Further research into strategies for
analysing the GRACE observations is required to minimise the errors inherent in the current
analysis in order to extract both more accurate estimates and greater spatial resolution.
Recommendation 4: Improvements in the spatial resolution of GRACE products, tailored
for the Australian hydrological community, need to be made in order to make the GRACE
products more relevant for the Australian groundwater community.
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Estimates of EWH changes derived from GRACE-SMS and boreholes do not agree well on
the majority of sites and it is difficult to ascertain in which of these three measurements the
majority of the error lies. Overall, our results indicate that four sources of uncertainty make it
very difficult to make a direct comparison between the two methods of groundwater storage
estimation—(1) hydrological model assumptions required to estimate soil moisture dynamics,
(2) the scarcity and biased positioning of groundwater monitoring bores, (3) specific yield
assumptions that need to be made to translate groundwater level into storage (4) the coarse
resolution of GRACE TWS estimates. The inclusion of GRACE TWS estimates into
hydrological models that have not been conceived to use them as input observables, poses a
great challenge; however, the benefits of doing so are expected to be significant.
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76
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