Estimating Evapotranspiration from t h e Amazon
Basin using the Atmospheric Water Balance
by
Hanan Nadim Karam
B. S., Environment a1 Engineering, Yale University (2003)
Submitted to the Department of Civil and Environmental Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Civil and Environmental Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2006
@ Massachusetts Institute of Technology 2006. All rights reserved.
Author . . . . . . . ..; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-. . . . . . . . . . . . . . . . . . . . .
Department of Civil and Environmental Engineering
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4
Certified by ......
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-
May 12, 2006
.-. . . .-. . . . . . . . . . . . . . . . . . . . . . . . . .
Rafael L. Bras
Edward A. Abdun-Nur Professor of Civil
and Environmental Engineering
Accepted b y . . . . . . . . . . . . . . . . . . . . . . . . . . . . .'. .LM M .v::. :.w.\ . I . , .....
Andrew Whittle
Professor of Civil and Environmental Engineering
Chairman, Department Committee on Graduate Students
T.
MASSACHUSRTS I N S m E ,
OF TECHNOLOGY
I
LIBRARIES
I
Estimating Evapotranspiration from the Amazon Basin using the
Atmospheric Water Balance
Hanan Nadim Karam
Submitted to the Department of Civil and Environmental Engineering
on May 12,2006 in Partial Fulfillment of the Requirements for the
Degree of Master of Science in Civil and Environmental Engineering
ABSTRACT
The spatio-temporal patterns of evapotranspiration (ET) in the Amazon basin are still poorly
understood. Field studies in the Amazonian forest have shown that at some sites, deep roots
allow trees to sustain elevated transpiration during several months of minimal rainfall, whereas at
others, trees experience evident dry season water limitation. However, the few sites investigated
are inadequate to characterize the conditions of transpiration throughout the basin. As a result of
this uncertainty in modeling trees' access to deep soil moisture, land surface models cannot
provide reliable estimates of transpiration in the region. From a basin-averaged perspective, it
remains uncertain whether transpiration is water-limited, peaking during the basin's wet season,
or energy-limited, peaking during the dry season when clearer skies allow for higher surface
radiation. In this work, we investigate an approach to deriving a spatially-averaged ET estimate
for the Amazon basin, which avoids modeling the forest's terrestrial hydrology. ET is computed
as a residual of the atmospheric water balance, using basin-averaged convergence of atmospheric
water vapor flux [ q , precipitation [PI, and tendency of total atmospheric water vapor [dwldt] as
inputs. As our resulting estimate of ET is only as good as the input estimates of the other
hydrologic components, we analyze multiple cutting-edge datasets that may be used to compute
these components. [PI data are obtained from GPCP and TRMM products. The three global
reanalyses, NCEPINCAR, NCEPIDOE and ECMWF ERA-40 provide data on atmospheric fields
to compute [CJand [dwldt]. The large discrepancies between [qestimates produced by the
different reanalyses, interpreted as uncertainty in these estimates, led to a thorough investigation
of data on this field over a time period dating back to 1980. Concurrent time series of
precipitation and Amazon river discharge are used to evaluate the accuracy of the various
reanalyses in simulating [CJ at the monthly and annual timescales. A measure of the random
error associated with [qestimates from each data source is derived, and used as a weighting
factor to combine information from the three reanalyses. The resulting estimates of monthly
basin-averaged ET are significantly lower in their long-term mean than estimates published in
the literature. The resulting climatological annual cycle of basin-averaged ET suggests a switch
between water and energy limited conditions for transpiration over a year's duration.
Thesis supervisor: Rafael L. Bras
Title: Edward A. Abdun-Nur Professor
Table of Contents
.........................m....................m.mm...m.....m......................................
2
Acknowledgements .....................................mmmm................................m............
6
Chapter 1. Background ...................................................................................7
Abstract
1.1. Goal and Motivation .................................................................................. 7
1.2. Global Water Budget Studies ....................................................................... -10
1.3. The Hydrologic Budget of the Amazon River Basin .............................................17
1.3.1. Precipitation ............................................................................... 18
1.3.2. Atmospheric water vaporflwr convergence ........................................... 22
1.3.3. Evapotranspiration ........................................................................ 25
1.3.4. River Discharge ........................................................................... 33
1.4. This Study's Contribution ...........................................................................34
.
....................m.............m..mm...............m.m.m..................
Chapter 2 Datasets
37
2.1. Atmospheric Water Vapor Flux Convergence. C ................................................ 37
2.2. Precipitable water tendency. dw/dt ................................................................ 39
2.3. Precipitation .......................................................................................... 40
2.4. Amazon Basin Boundaries .......................................................................... 41
2.5. Amazon River Discharge ............................................................................42
.
Chapter 3 Analysis of the Amazon's Atmospheric Water Budget
44
for the Period 1997-2001 ...................m...m..a............mm.mmmm.m...............
3.1. Atmospheric water vapor flux convergence over rectangular regions
of different areas within the Amazon Basin ....................................................... 45
3.2. Atmospheric moisture flux convergence over the Amazon Basin .............................. 55
3.3. Rainfall over the Amazon Basin .................................................................... 62
3.4. Monthly change in total atmospheric water vapor over the Amazon Basin .................. 65
3.5. Climatological atmospheric water budget for the Amazon basin. 1997-2001 ................ 67
.
Chapter 4 Analysis of Basin-Averaged Atmospheric Moisture Flux Convergence
70
Estimates for the Amazon over the Period 1980-2001
4.1. Basin-Averaged Atmospheric Moisture Flux Convergence over 1980-2001 ................ 70
4.2. Basin-Averaged Atmospheric Moisture Flux Convergence over 1988-2001 ................ 74
4.3. Estimation of Random Error in Amazon Basin [qby Comparison to River Discharge .... 78
4.4. A Comparison Between Time Series of Monthly [qand [PIfor the Amazon Basin ........ 80
.
..............................
Chapter 5 Amazonian Evapotranspiration Computed from the Atmospheric
Water Balance
85
5.1. Mean Annual [ET]...................................................................................... 89
5.2. Climatological Annual Cycle of [ET]................................................................ 91
...............................m...m..............................m............
.................................................................................. 88
References ................................................................................................... 90
Appendix A: An analysis of the relationship between time series of monthly
[CJ and [PIfor the Amazon Basin.....................m..................mm..mm.......
102
.
Chapter 6 Conclusions
Table of Figures
Figure 1.1. The atmospheric and terrestrial branches of the water budget model ................10
Figure 1.2. Mean annual cycle of the Amazonian hydrologic budget, 1970-1999,
copiedfrom Marengo (2005) ................................................................ 18
Figure 1.3. Spatial distribution of mean annual rainfall in the Amazon Basin,
copiedfrom Sombroek (2001) .............................................................. 19
Figure 1.4. Number of consecutive months with total rainfall less than 100 mm in the
Amazon Basin, copiedfrom Sombroek (2001). ......................................... 20
Figure 1.5. Mean seasonal rainfall for tropical South America based on CMAP data for
the period 1979-1999, copiedfrom Marengo (2005) ................................... 2 1
Figure 1.6. Spatially-distributed precipitation anomalies associated with El Nino events
in the Brazilian Amazon, copiedfrom Saleska (2003) .................................. 24
Figure 1.7. Annual variation of surface net radiation averaged over the Amazon from
various datasets, copiedfrom Werth and Avissar (2004) .............................. 26
Figure 1.8. Annual cycle of evapotranspiration averaged over the Amazon from various
land surface models, copiedfrom Werth and Avissar (2004). .......................... 27
Figure 1.9. Spatial distribution of mean annual rainfall in the Amazon Basin, copied from
Sombroek (2001), with the location of field study sites where data related to
Amazonian transpiration has been collected.. ............................................ 29
Figure 1.10. Spatial distribution of forests that rely on deep roots to maintain canopy
greenness during the dry season, copiedfrom Nepstad et a1 (1994) ................. 3 1
Figure 3.1. Monthly [qfor Region A, computed from ERA-40 data products using four
different algorithms, 1997-2001 .......................................................... 49
Figure 3.2. Absolute error associated with various methods for computing [qfor
Region A, from ERA-40 data products, 1997-2001 ................ .................... 49
Figure 3.3. Monthly [qfor Region A, based on R- 1, R-2 and ERA-40, 1997-2001 ............53
Figure 3.4. Climatology of monthly [qfor Region A, based on R-1, R-2 and ERA-40,
1997-2001..................................................................................... 53
Figure 3.5. Monthly [qfor the Amazon basin, based on R- 1, R-2 and ERA-40, 1997-2001... 56
Figure 3.6. Climatology of monthly [qfor the Amazon basin, based on R- 1, R-2
and ERA-40, 1997-2001...................................................................... 57
Figure 3.7. Error in monthly [qfor the Amazon basin computed based on a finite
difference approximation of the divergence operator, from ERA40
data products, 1997-2001 ................................................................... 59
Figure 3.8. Monthly anomalies of [CJfor the Amazon basin, based on R-1, R-2
and ERA-40, 1997-2001 ................................................................... 6 1
Figure 3.9. Monthly [PI and spatially-averaged absolute random error for the Amazon
basin, derived from TRMM and GPCP products, 1997-2001 ........................ 63
Figure 3.10. Rainfall rate vs. associated random error for grid cells within the Amazon
basin, based on TRMM and GPCP products, 1997-2001 ............................ 64
Figure 3.11. Monthly tendencies in total atmospheric column water vapor averaged
over the Amazon basin, based on R- 1, R-2, and ERA-40, 1997-2001 ............. 66
Figure 3.12. Climatology of monthly tendencies in total atmospheric column water
vapor averaged over the Amazon basin, based on R- 1, R-2, and
ERA-40, 1997-2001 ....................................................................... 66
Figure 3.13. Climatologies of basin-averaged atmospheric water balance components,
1997-2001. ................................................................................... 68
4
Figure 4.1. Monthly [ q for the Amazon basin, 1980-2001, based on R- 1, R-2,
and ERA-40.. .................................................................................. 70
Figure 4.2. Annual [ q and [R] for the Amazon basin, 1980-2001; [ q based on
R- 1, R-2, and ERA-40. ....................................................................... 7 1
Figure 4.3 (a-c). Annual [ q for the Amazon basin, based on R- 1, R-2, and ERA-40,
1980-2001............................................................................... 72
Figure 4.4. Annual [R] and bias-corrected [ q for the Amazon basin, the latter based
on R- 1, R-2, and ERA-40, 1988-2001..................................................... 76
Figure 4.5. Time-averaged [ q and [R] for the Amazon basin, over a moving
five-year window, 1988-2001; [ q estimates based on R- 1, R-2, and ERA-40.. ... 79
Figure 4.6 (a-c). Monthly anomalies of [CJ and [PI for the Amazon basin,
1988-2001; [ q based on R- 1, R-2, and ERA-40; [PI based on GPCP.. ........ 8 1
Figure 4.7 (a-d). Annual anomalies of [CJ and [PI for the Amazon basin,
1988-2001; [CJ based on R- 1, R-2, and ERA-40; [PI based on GPCP.. ....... 83
Figure 5.1. Bias-corrected monthly [ q from R- 1, R-2 and ERA-40, and best
estimate [ C 1, 1988-2001 .................................................................... 87
Figure 5.2. Monthly [ETJ for the Amazon basin, based on [qestimates from R-1,
R-2 and ERA-40, and best-estimate [ C 1, 1988-2001.. .................................. 88
Figure 5.3 (a-c). Monthly anomalies of [ETJ for the Amazon basin, based on [ q
estimates from R-1, R-2 and ERA-40, 1988-2001................................... 89
Figure 5.4. Climatological annual cycle of Amazonian [ET] based on [ q estimates
1, 1988-2001....................... 92
from R-1, R-2 and ERA-40, and best-estimate
Figure 5.5. Climatological annual cycle of Amazonian [PI from GPCP and [ q
from R-1, R-2 and ERA-40, 1988-2001.. ................................................. 92
A
A
[e
Acknowledgements
Professor Bras: I am very grateful to you for supporting my work on this thesis. Your infallible
readiness to discuss my research, share your ideas in relation to my methods and results, and to
revise my writing promptly and thoroughly were integral to the completion of this thesis. I am
also appreciative of your support in my other academic endeavors during my first years at MIT,
ranging from a number of fellowship applications to my first experience as a busy teaching
assistant.
Members of the Bras group: It was great to learn about your work and discuss it, and hear your
ideas on my work during group meetings, not to mention the philosophical discussions we had
and picture sharing we did during those meetings.
Jean: You were extremely helpful to me throughout my research for this project. Thank you for
sharing your ideas, knowledge, criticisms, motivation and kindness.
David: Thank you for helping with the math whenever I got stuck.
Family and Friends: Thank you for your inspiration, especially Samer, Zahi, Mamy and Papy,
Mamy Alieh, Aamme Linda, and Emma
Funding sources
Grant funding fi-om TRMMINASA supported me during work on this thesis. Additional support
was provided by the Department of Civil and Environmental Engineering at MIT.
Data sources
This thesis is based on data fi-om the following sources:
NCEPINCAR reanalysis data products produced by the National Center for
Environmental Prediction (NCEP) and the National Center for Atmospheric Research
(NCAR)
NCEPIDOE reanalysis data products produced by the National Center for Environmental
Prediction (NCEP) and the Department of Energy (DOE)
ECMWF ERA-40 reanalysis produced by the European Center for Medium-Range
Weather Forecasts (ECMWF)
TRMM and Other Sources Rainfall Product 3B43 produced by the Tropical Rainfall
Measuring Mission (TRMM)
Combined Precipitation dataset (Version 2) produced by the Global Precipitation
Climatology Project (GPCP)
Total Runoff Integrating Pathways (TRIP) dataset, produced by Oki and Sud (1998)
Annual Amazon River discharge at Obidos gauging station for the period 1980-2001
provided by Jacques Callede (Callede et a1 2002)
The Ferret program was used for all data analysis and graphics production in this work. Ferret is
a product of NOAA's Pacific Marine Environmental Laboratory. Information is available at
http://ferret.pmel.noaa.gov/Ferret/
Chapter 1- Background
1.1. Goal and Motivation
The hydrological cycle of the Amazon basin, both its atmospheric and terrestrial
branches, is of interest for many reasons. It is linked to regional and global hydrometeorological
dynamics. The Amazon basin is one of the major tropical heating centers; its large rain rates are
associated with latent heat release that fuels global atmospheric circulation (Costa and Foley
1999). Regional atmospheric circulation features link the Amazon's hydrology to that of
adjacent regions. For example, a low level jet east of the Andes transports atmospheric moisture
from the basin to higher latitudes in South America (Berbery and Barros 2002).
Rain over the Amazon basin sustains the largest tropical rainforest in the world. The
Amazon river is first globally in terms of its drainage area and discharge, with a mean annual
discharge for the period 1968-1999 of 170*103 m3Isec (Callede et al, 2002). It is thus an
important source of dissolved substances and suspended particles to the ocean. Note that the
mean annual discharge of the Congo river, which follows in second place, is four times smaller
at 40.6*103 m3Isec (Callede et al, 2002).
Deforestation in the Amazon basin, which started becoming important in 1976, has been
proceeding rapidly (Callede et al, 2002). In 1997, the deforested area of the basin was 546,000
krn2,90% of which had been converted to pasture. The effects of these transformations on the
basin's water cycle and possible repercussions at regional and global scales can only be
understood and predicted if the Amazon's water budget is well quantified.
Evapotranspiration (ET) is a key process in the water cycle and is one of the most
difficult to quantify at regional scales. It involves both a water and energy flux from the land
surface to the atmosphere. Our ability to quantify it accurately at the field and regional scales
7
and understand its dependence on land cover, soil moisture, and weather conditions (radiation,
winds, atmospheric humidity) is essential to successful water resource planning. Furthermore,
ET is a critical source of water vapor to the atmosphere over a region, which may be transported
elsewhere or may fall as precipitation over the same region (precipitation recycling). As
mentioned earlier, the Amazon basin contributes atmospheric moisture to central and southern
regions of the continent. At the same time, precipitation recycling in the basin is significant,
with the precipitation recycling ratio (the percentage of total precipitation over the basin
contributed by ET from the basin) estimated to reach -30% (Costa and Foley, 1999; Eltahir and
Bras, 1994). Accurate estimation of evaporation rates at large spatial scales is central to
understanding the hydrometeorology of the Amazon and coupled regions. Finally, transpiration
is inevitably coupled with photosynthesis. A sound understanding of transpiration patterns for a
given system improves our ability to model and predict carbon exchanges between its terrestrial
landscape and the atmosphere. The ET flux in the Amazon is expected to be particularly
affected by the rapid deforestation in the basin. Decreased ET rates are often associated with
deforestation and forest conversion to pasture, because of decreased infiltration of precipitation
and/or diminished access of grass roots, in comparison to tree roots, to deep soil moisture
(Callede et. al. 2002, Hodnett et a1 1995).
The estimation of regional scale evapotranspiration is an active area of research. The
most promising methods currently being developed are based on estimating spatially-distributed
ET as a residual of the energy balance computed at the pixel scale. Data from satellite-borne
infra-red and visible spectrum sensors are used to estimate spatially-distributed fields associated
with land surface conditions (albedo, surface temperature, fractional vegetation cover), which are
then used to derive estimates of the various energy balance components. These methods require
auxiliary ground-based data, particularly air temperature, as well as near-surface wind-speed and
vegetation height to estimate aerodynamic resistance (see review by Jiang and Islam, 2003). For
the Amazon basin, the sparseness of near-surface meteorological measurements and groundbased data on land cover renders unreasonable the use of such methods. Their application is
furthermore restricted to clear days, as satellite observations of the earth's surface in the visible
and infia-red spectra are obstructed by clouds.
An alternative method, proposed by Jiang and Islam (2003), which relies solely on
satellite observations of surface temperature and fractional vegetation cover, involves making
rough assumptions about the ability of vegetation to access soil moisture in different soil wetness
conditions.
Many estimates of ET for the region have been derived using land-surface models that
compute this flux fiom an estimate of evaporative demand based on near-surface meteorological
conditions, adjusted by a factor relating to soil water availability. Werth and Avissar (2004)
review estimates of spatially-averaged evaporation over the Amazon basin produced by different
models that use this general approach. They find that the resulting estimates of monthly
evaporation diverge in magnitude and seasonal cycles, due to differences between the models'
parameterizations of how soil water availability modulates ET. In vegetated regions, plants
control the movement of water between the soil and the atmosphere, and their ability to access
moisture fiom different soil layers determines the rate of ET. For the Amazon, the success in
estimating ET using soil moisture dependent procedures would depend on how we can model the
distributed soil moisture profile and vegetation access to this moisture (Werth and Avissar,
2004). Saleska et a1 (2003) demonstrate that two widely used ecosystem models fail to account
for trees' ability to access deep soil moisture for transpiration, and hence underestimate dry
season transpiration and photosynthesis in their study site, situated in an old-growth forest in the
eastern Amazon.
The goal of this work is to estimate evapotranspiration from the Amazon basin as a
residual of the atmospheric water balance. The merit of the proposed atmospheric water balance
approach lies in its independence of any land surface model, or of our understanding of land
surface and vegetation properties. Furthermore, it relies on atmospheric data that has been
collected globally for decades, and hence it can be used to evaluate historical conditions, in
contrast to methods based on data from satellite-borne sensors that only became available
recently (Seneviratne et al, 2004). The availability of reanalysis systems, that assimilate
available observations into numerical atmospheric models to produce global atmospheric data
with high spatio-temporal resolution, makes the proposed approach even more promising.
Finally, the proposed approach provides an estimate of ET integrated over the entire Amazon
basin, smoothing the large spatial variability in the hydrologic budget within the basin.
1.2. Global Water Budget Studies
The water balance of a region can be perceived as having two branches, the atmospheric
and terrestrial branches, linked by the land-atmosphere moisture exchanges, precipitation and
evaporation, as shown in Figure 1.1 below.
Net convergence of
water vapor flux, c
C
Net runoff
across
boundaries, R
Figure 1.1. The atmospheric and terrestrial branches
of the water budget for a control volume.
The land surface water balance can be represented by the equation:
The square brackets indicate spatial averaging over the control region of interest. S is terrestrial
water storage, which includes soil moisture, groundwater, snow, and land ice; P is precipitation,
ET evapotranspiration, and R is net runoff out of the control region, including surface and
subsurface water flows. When the control region is a river basin, R is usually taken to be river
discharge at the basin's outlet, as subsurface flows across basin boundaries are relatively
negligible. If an average of the water budget is taken over several years, the net change in
terrestrial water storage is expected to be small, as seasonal and interannual variations cancel out.
The atmospheric branch of the water cycle has the equation:
[dwldt] = [c]+ [ET]-
[P]
[ 1-21
w is the water vapor content of the atmospheric column overlying the region of interest (also
known as total precipitable water) and [qis the net convergence of atmospheric water vapor
flux over the control region. The change in precipitable water (dwldt) is usually neglected for
averages of a month or more (e.g. Zeng 1999, Marengo 2005).
Equations 1.1 and 1.2 may be combined to yield the total water balance equation
[dwldt] - [C] = -[dS/ dt] + [R]
[I-31
For averages over several years, changes in water storage on land and in the atmosphere
can be neglected, and the equation relates the convergence of atmospheric moisture flux to
surface and groundwater runoff out of the control region.
Among the earliest and most widely referenced studies on regional atmospheric water
budgets are Rasmusson's investigations of regional water balances in North America
(Rasmusson 1967, 1968, 1971). He used twice-daily (00 GMT and 12 GMT) raw radiosonde
data to map the water vapor flux field over North America. After carrying out a monthly water
11
balance for the period May 1958-April 1963 over a large region encompassing the North
American Central Plains and the Eastern U.S. (area= 64*10' km2),he finds that the five-year
average net atmospheric moisture flux convergence over the region is underestimated by 0.35
c d m o or 2 1% in comparison to observed runoff out of the region (Rasmusson 1968). Note that
this negative bias is actually a result of some cancellation between biases of opposite signs over
the central plains and eastern regions (Rasmusson 1971). He attributes apparent errors in the
water vapor flux convergence field to inadequate spatial resolution of the radiosonde data to
capture fine-scale atmospheric features and inadequate temporal resolution to resolve large
diurnal variation in atmospheric flow patterns (Rasmusson 1968, 1971). Examining a map of
mean annual runoff for the Unites States, he notes that runoff variations occur over distances that
are not resolved by the available radiosonde network (Rasmusson 1971). These runoff features
would coincide with features of mean annual water vapor flux convergence that similarly cannot
be resolved. Smaller errors in atmospheric moisture flux convergence estimates are expected for
averages over larger regions due to canceling out of errors at smaller scales arising fiom
inadequate temporal and spatial sampling. He found that for areas of lo6km2 or greater the
water budget computations with the available aerological network were reasonable but became
much more erratic for areas of 5* 10' km2 or smaller. For example, water balance computations
for the Ohio Basin, with an area of 5.2*lo5km2revealed a negative bias in atmospheric moisture
flux convergence estimates of 3.47 cm/mo, equivalent to 9 1% of mean runoff (compare to a 2 1%
bias error in convergence estimates for the larger region described above) (Rasmusson 1971).
Rasmusson (1968) uses the derived estimates of monthly water vapor flux convergence
over the Central Plains and Eastern Regions for the period May 1958-April 1963, after adjusting
them by a uniform bias correction, to estimate monthly evapotranspiration based on Equation
1.1. He finds very good agreement with evapotranspiration estimates derived by other methods,
12
in both magnitudes and seasonal cycle.
More recent studies have come to rely on reanalyses to obtain data on wind speeds and
specific humidity that are needed to compute water vapor flux convergence. Reanalysis systems
assimilate archived observations into an operational forecast model, keeping both the
assimilation algorithm and the atmospheric circulation model constant, and thus avoiding the
introduction of artificial changes and trends associated with modifications to the model. Shortterm numerical weather forecasts are adjusted in the direction of available observations to
produce "analyses" of atmospheric fields such as upper-air temperature, winds, and humidity.
These in turn are used to initialize subsequent forecasts, and so forth. Thus, observations affect
the archived analyses of vertically resolved specific humidity and wind speeds by constraining
both the initial conditions of the short-term forecast and its result. Where observational data are
scarce, the analyzed fields become more dependent on the atmospheric model used. The
reanalyses rely on a large database of observations, including rawinsonde, aircraft, and surface
marine data, in addition to data from satellite-borne infi-ared and microwave sensors. These
observations are subject to complex quality control pre-processing before use in the assimilation
model. Among the reanalysis data products widely used in the community are those produced
by the NASAIGOES- 1 reanalysis, the NCEP/NCAR reanalysis, the NCEP/DOE reanalysis, and
the ECMWF ERA-40 reanalysis.
The reanalysis systems assimilate observations of different types and from different
sources, and the associated numerical weather models fill in gaps to produce gridded data at
regular time intervals. They can thus provide estimates of atmospheric fields at higher temporal
and spatial resolution than can be obtained from raw radiosondes. Reanalysis data products have
been used widely in recent years to evaluate regional water balances globally. Many studies
using these products have focused on evaluating the seasonal cycles, interannual variations, and
13
long-term trends in different water budget components for a specified region, particularly
atmospheric moisture flux convergence, precipitation, evaporation, and terrestrial water storage.
Three studies carried out in the Mississippi Basin in the United States, concur that the reanalysis
datasets successfully represent monthly and annual-scale variability in atmospheric water
budgets over regions with an area of -16 inn2,an order of magnitude less than the threshold area
identified by Rasmusson (1968) (Gutowski 1997, Yeh et a1 1998, Seneviratne 2004). These
studies will be discussed further below.
Gutowski et. al. (1997) used NCEPMCAR reanalysis data, with a T62 resolution (-250
krn grid spacing), to compute area-averages of atmospheric moisture flux convergence
(henceforth [ q ) for the Upper Mississippi and Ohio-Tennessee basins over the ten-year period
1984-1993. They identified a positive bias of 39% in the resulting [qestimates for the Upper
Mississippi basin, and a negative bias of 33% in those for the Ohio-Tennessee basin, by
comparing ten-year average [ q to ten-year average river discharge at the mouths of the
respective basins. Rasmusson (1971) obtained a much larger bias error, equivalent to 9 1% of
mean runoff, in the [qestimates for the Ohio-Tennessee basin that he derived from radiosonde
data. Gutowski et a1 (1997) attributed the bias error in their results to inaccuracies in the regional
atmospheric water vapor transport characterized by the reanalysis. The inadequacy of the four
analysis times per day in resolving higher frequency atmospheric features, such as a low-level jet
that transports substantial amounts of water from the Gulf of Mexico up the Mississippi River
Valley, may have contributed to this error (Gutowski et al. 1997). Yet, despite this bias,
Gutowski et a1 (1997) found that the temporal variations of the computed atmospheric water
vapor flux convergence at daily, seasonal and interannual scales are physically justifiable. They
concluded this by studying the time-lagged correlation between smoothed time series of daily
[CJand streamflow, and checking its consistency with the autocorrelation function of the
streamflow time series. Gutowski et al. (1997) interpret the autocorrelation function of the
streamflow record as an indicator of the importance of water storage in the basin, which should
also be reflected in the lag correlation function between [ q and discharge at the basin's mouth.
Seneviratne et. al. (2004) used atmospheric water vapor flux convergence data from the
ECMWF ERA-40 reanalysis with a TI59 model resolution (equivalent to -1 12 krn grid spacing)
and streamflow observations for the 10-year period 1987-1996 to compute the area-averaged
change in terrestrial water storage at a monthly timescale ([dS/dt]) for a domain covering the
state of Illinois, using Equation 1.3. They were able to investigate the accuracy of [ q estimates
for this domain obtained from ERA-40 by comparing the resulting [dS/dt] to estimates of this
field based on well-distributed ground observations of soil moisture and water table levels in
Illinois available for the same period. They concluded that monthly and interannual variability
in [dS/dt] computed from the water balance are well captured, despite a net negative bias of 13%
in long-term average [ q over this domain when compared to runoff. The 10-year climatological
annual cycle of [dS/dt] computed from the water balance matched that obtained from
observations in timing and amplitude.
Yeh et. al. (1998) carried out a similar study over Illinois, also making use of the ground
observations of groundwater and unsaturated-zone water available for this state. They compared
monthly evaporation estimates obtained from the atmospheric water balance to those from the
soil water balance over the period 1983-1994, using NCEPINCAR reanalysis products for
computing atmospheric water vapor flux convergence and monthly changes in precipitable water
and observation-based data for the other water budget components. They identified a small
negative bias in the 12-year average [qin comparison to runoff, equivalent to 6.4% of mean
runoff (Yeh et a1 1998). They found a very good agreement between the average annual cycles
of evapotranspiration derived from the atmospheric and terrestrial water balances. For individual
years, the two estimates agreed reasonably well in the timing and magnitude of the seasonal
pattern, and though for some months the two estimates of evaporation were significantly
different, they exhibited a high correlation of 0.785. Estimates of monthly evapotranspiration
derived fkom the soil water balance had evident errors in some months, such as a value of -72
mm/mo for October 1986. Such errors may have originated in the precipitation, runoff, soil
moisture, and/or water table data that constitute the estimate.
The studies described above (Gutowski et al. 1997, Yeh et a1 1998, Seneviratne et a1
2004) suggest that atmospheric data for the Mississippi basin region in North America produced
by the NCEPNCAR and ERA-40 reanalyses are quite reliable, and more so than data based
solely on available radiosonde observations. The studies agree that sub-annual and interannual
variations in atmospheric moisture flux convergence over this region are well captured by the
reanalyses, despite the existence of bias errors in reanalysis-derived estimates of this field. The
bias error is computed as the difference between the long-term averages of net atmospheric
moisture flux convergence over a domain and net runoff out of the domain, and is usually
corrected by summing a uniform correction factor to monthly [CJestimates.
Roads (2002) analyzed the water budgets of the GEWEX Continental Scale Experiment
(CSE) regions, which include major river basins (Amazon, Lena, Mackenzie, Mississippi), the
Baltic sea, and some large-scale regions distributed globally over a variety of climatic regimes.
He computes the 12-year mean (1988- 1999) [qover these regions using data fkom the
NCEPINCAR reanalysis and compares it to mean annual runoff for the regions derived from the
Global Runoff Data Center (GRDC) gridded runoff dataset. The imbalance in the water budgets
of the Mississippi and Lena river basins is relatively small (4% of total runoff for the Lena basin,
and -20% for the Mississippi basin), while that for the Mackenzie reaches 76% and for the
Amazon basin 46% (Roads 2002). The algorithm that produces GRDC runoff data ensures that
16
basin-integrated runoff estimates match available river discharge observations (Fekete et a1
2000). Hence, this runoff dataset can be safely used as a reference against which to determine
accuracies of the reanalysis-derived atmospheric moisture flux convergence estimates,
particularly for control regions constituting major river basins for which reliable river discharge
observations are likely available. Roads' (2002) comparison of water balance closure between
basins leads to the conclusion that the accuracy of reanalysis estimates of [qis not uniform from
one region to the next. This is expected, since the hydrometeorology of different regions is
characterized by different atmospheric processes, which are captured in the reanalysis circulation
models with varying success. Furthermore the quality and density of available observations that
may be assimilated into the atmospheric model varies between regions. In conclusion, the
accuracy of reanalysis-derived
[qestimates for a region must be carefully assessed before they
are used.
1.3. The hydrologic budget of the Amazon River Basin
The atmospheric circulation over the Amazon basin is influenced by the Pacific and
Atlantic oceans surrounding it, as well as by the Andes mountain range along its western
boundary (Satyamurty, Nobre and Silva Dias 1998). Large seasonal changes are seen in the
overall characteristics of the regional circulation over the basin (Satyamurty, Nobre and Silva
Dias 1998), producing a strong seasonal signature in its water budget, particularly in the annual
cycles of precipitation, moisture convergence and runoff (Zeng 1999, Marengo 2005). Figures
1.2 (a-c)are copies of the figures presented by Marengo (2005), showing mean annual cycles of
precipitation, runoff, evaporation and atmospheric moisture flux convergence spatially-averaged
over the Amazon basin, which he computed by averaging annual cycles over the period 19701999. Basin-averaged precipitation (P) and runoff (R) data were obtained from observations,
17
and basin-averaged atmospheric moisture flux convergence (C) and evaporation (E) estimates
were obtained from the NCEP/NCAR reanalysis.
Figure 1.2. Mean annual cycle of
Amazonian hydrologic budget for the
period 1970-1999. a) Entire Amazon
basin b) Northern basin c) Southern
basin. Spatially-averaged precipitation
(P) and runoff (R) are based on
observations. Spatially-averaged
atmospheric moisture flux convergence
(C) and evaporation (E) are derived
fkom the NCEP/NCAR reanalysis.
Vertical bars represent one standard
deviation from the mean.
Figure copiedporn Marengo (2005).
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1.3.1. Precipitation
Figure 1.2a shows that basin-averaged precipitation peaks in austral summer, particularly
in the months of January, February, March (Zeng 1999, Marengo 2005). Yet the basin,
extending between 5"N and 20°S, does not act as a single entity. Variation in the annual cycle of
solar radiation cycle over its extent, along with spatial variability in the regional atmospheric
circulation over the South American continent, produce significant spatial variability in the
hydrologic cycle over the basin (Rao et al, 1996, Marengo 2005).
Sombroek (200 1) presents the most detailed climatological rainfall map for the Amazon
based on rain gauge data, relying primarily on the pluviometric database of the Brazilian
National Agency of Electric Energy (ANEEL) (Figure 1.3). A trend of increasing wettness
westward is evident in this map. The southern regions of the basin are also shown to be
relatively dry.
I
C
Figure 1.3. Spatial distribution of mean annual rainfall (mmlyear) in the Amazon basin. Copiedfiom Sombroek (2001).
Figure 1.4, also taken fiom Sombroek (200 I), shows the large variability in the length of
the dry season across the Amazon basin. The dry season is defmed here to include months with
average precipitation less than 100 mm.
Marengo (2005) analyzed the seasonal cycle in the Amazon basin's hydrologic budget
and focused on resolving North-South variability in the basin. Using rainfall data fiom gauging
stations, he shows that the mean seasonal cycles of rainfall for the northern and southern
Amazon sub-basins, demarcated by the Amazon and Solimoes rivers, are out of phase with one
another (Figure 1.2 a-c). Spatially-averaged rainfall over the northern sub-basin (extending
mostly north of 5's) peaks in the months of April-May at 8.5 d d a y and is minimum in
August-September at 4 &day.
The southern sub-basin (extending mostly south of 5's) shows
a more pronounced dry season. The seasonal range spans 8.5 &day
to 1 &day,
with the
peak occurring in January-February and the minimum around July. As the southern basin has the
greater spatial extent, it dominates the seasonal signature of the whole basin (Figure 1.2a)
(Marengo 2005).
The phase shift between the seasonal cycles of the northern and southern portions of the
Amazon is also apparent in Figure 1.5 a-b (copied fiom Marengo 2005), which maps mean
rainfall in the Amazon region for two three-month periods: December-February and March-May.
The rainfall data is obtained fiom the Climate Prediction Center Merged Analysis Precipitation
(CMAP) dataset (Xie and Arkin 1997), which combines rain-gauge observations with satellite
data and precipitation estimates fiom the NCEPNCAR reanalysis to derive a final gridded
monthly rainfall dataset.
Figure 1.5. Mean seasonal raidall for tropical South America based on CMAP data for the period 19791999. a) December-February mean. b) March-May mean. Units are &day. Copiedfiom Marengo (2005).
Uncertainty exists in the estimates of precipitation for the Amazon basin. Marengo
(2005) compares estimates of mean basin-averaged precipitation derived fiom different
observation-based datasets. The climatological mean rainfall for 1970-1999 is 5.2 mmlday
according to the Global Precipitation Climatology Project (GPCP) Combined Precipitation
dataset, 5.6 &day
based on the CMAP dataset, and 6.0 mmlday according to the Climate
Research Unit (CRU) dataset. The datasets vary in their methodology for deriving gridded
precipitation estimates. GPCP (Huffman et a1 1997) combines rain-gauge observations with
satellite data to obtain an estimate of precipitation. As mentioned above, CMAP (Xie and Arkin
1997) additionally incorporates precipitation data from the NCEPNCAR reanalysis in deriving
the final estimate. CRU (New et al. 2000) is based solely on rain-gauge data, which are spatially
interpolated using Thiessen Polygons. Marengo's (2005) estimate of basin-averaged annual
rainfall, was derived from a weighted average of 164 gauging stations and is 5.8 mdday.
1.3.2. Atmospheric water vapor flux convergence
Atmospheric moisture flux convergence in the Amazon region shows positive spatiotemporal correlation with precipitation, reflecting the mechanistic relationship between these two
components of the water cycle (Marengo 2005, Roads 2003, Rao et a1 1996). Monthly moisture
derived from either the
flux convergence spatially averaged over the Amazon basin ([q)
NCEPNCAR or the GOES- 1 reanalysis correlates strongly with monthly basin-averaged
precipitation. It exhibits the same seasonal cycle that peaks in austral summer, though with a
smaller range of variation (Marengo 2005, Zeng 1999) (Figure 1.2~).This correlation is also
evident when averages are taken over the northern and southern sub-basins separately (Marengo
2005) (Figure 1.2 a-c). Similarly, maps of moisture convergence computed from the
NCEPNCAR and NCEPIDOE reanalyses and precipitation obtained from the Tropical Rainfall
Measuring Mission (TRMM) data products show evident spatio-temporal correlation between
the two water cycle components throughout the global tropics (Roads, 2003). This relationship
between atmospheric water vapor flux convergence and rainfall in the Amazon was specifically
investigated by Rao el a1 (1996). Using once-daily ECMWF analyses of atmospheric moisture
and windspeeds, in addition to rainfall and surface dew-point temperature data for Brasilia
(15'5 1' S, 47O56' W, at the southeastern comer of the basin), they found that the onset of the
rainy season in Brasilia near the end of September is associated with an abrupt increase in
atmospheric humidity that is evident in surface dew-point temperature data. Furthermore, the
start of the summer rainy season is associated with an increase in precipitable water and
atmospheric water vapor flux convergence over central Brazil. These seasonal developments are
associated with a characteristic summer circulation that involves a dominant southeastward
transport of water vapor into central South America (Rao et a1 1996).
While different reanalyses seem to give synchronous seasonal cycles for Amazon basin
[ q , they give different absolute values. Roads (2003) emphasizes the uncertainty in reanalysisderived estimates of atmospheric moisture flux convergence for tropical regions. He finds large
differences between estimates of this field derived fi-om the NCEPNCAR and NCEPIDOE
reanalyses. He attributes these to the fact that observations in these regions are scarce, and hence
the estimates of atmospheric moisture and wind velocity are highly model dependent. The
modifications to model parameterizations in the NCEPIDOE reanalysis relative to its
predecessor, the NCEPNCAR model, apparently significantly impact the simulation of tropical
hydrometeorology (Roads 2003).
Furthermore, a large bias in reanalysis-derived moisture flux convergence has been
identified upon comparing long-term averages of [ q for the Amazon basin to river discharge at
its outlet. Zeng (1999) finds a negative bias of 2.2 m d d a y in [ q estimates derived fi-om the
GOES-1 reanalysis over the period 1985-1993, amounting to 73% of the mean annual river
discharge. Using NCEPNCAR reanalysis data, Marengo (2005) finds a negative bias in [ q of
1.5 &day
or 52% of the Amazon's mean annual discharge for the period 1970-1999. This is
close to the bias of 46% found by Roads (2002), using the same reanalysis for the period 19881999.
There has been much interest in understanding the sources of variability in the Amazon
basin's hydrologic cycle at interannual time scales, as well as identifying long-term trends in its
water budget (Costa and Foley 1999). The Amazon experiences strong interannual variability in
rainfall, influenced by ENSO, the strength of the North Atlantic high, the position of the
intertropical convergence zone (ITCZ) and sea surface temperatures in the tropical Atlantic
(Costa and Foley 1999, Marengo 2005). During El Nifio years, the basin experiences decreased
precipitation on average, though the spatial distribution of precipitation anomalies is complex
and varies fiom one ENS0 to the next (Figure 1.6, Saleska 2003).
Figure 1.6. Effect of El Niiio on precipitation
patterns in the Amazon basin north of 10" S (Brazil
only): percent anomaly relative to long-term
average during El Niiio years in (a)
1983, (b) 1987, and@) 1992. Gridded
precipitation derived fiom observation-based
datasets. CopiedJLornSaleska (2003).
Longitude
Examining a time series of annual basin-averaged rainfall over the period 1970-1999,
Marengo (2005) found strong negative anomalies associated with the El Nifio events of 19821983, 1986-1987, 1997-1998, and a strong positive anomaly associated with the La Niiia
occurrence of 1998-1999. These signals were stronger in the precipitation record of the northern
24
sub-basin relative to that of the southern sub-basin, indicating that the former is more strongly
influenced by ENS0 (Marengo, 2005). Marengo (2005) compares timeseries of annual [ q for
the Amazon basin and each of its sub-basins, derived from the NCEPNCAR reanalysis, to the
rainfall record and suggests that similar interannual variability can be identified by visual
inspection in the records of the two hydrologic components, though he does not quantify this
similarity.
Costa and Foley (1999) focused on investigating longer-scale trends in the basin's water
balance over the period 1976-1995. They analyzed time series of anomalies relative to 20-year
means for each of the water budget components spatially-averaged over the Amazon basin, [R],
[ET],[CJ and [PI,all of which they derived fiom the NCEPNCAR reanalysis. They found no
trend in the time series of [ q anomalies, but found that atmospheric moisture influx into the
basin was actually exhibiting a declining trend. As the same declining trend was present in the
moisture outflux from the basin, the net atmospheric moisture flux convergence for the basin was
stable in time. The declining moisture influx was associated with a decline in the strength of the
southeasterly trade winds, which carry water vapor from the Atlantic into the basin. While Costa
and Foley (1999) find no significant trends in basin-averaged evaporation, precipitation and
runoff, it is difficult to have much confidence in their conclusions. Estimates of these
components obtained from the NCEPNCAR reanalysis are associated with great uncertainties,
because they are completely model derived (Kalnay et a1 1996).
1.3.3. Evapotranspiration
The spatio-temporal patterns of evapotranspiration in the Amazon basin are still poorly
understood and highly uncertain. Unlike precipitation there is no regular well-distributed
network of stations measuring evaporative fluxes. Hence, the community has largely relied on
land surface models to estimate large-scale evapotranspiration in the basin. The seasonal cycles
of precipitation and solar radiation in the Amazon are out of phase with one another.
Precipitation is maximum in the austral summer (December-February) and minimum in the
austral winter (June-August) (Figure 1.2a), while spatial averages of solar radiation over the
basin peak in the austral spring (September-November) and are relatively lower in austral
summer due to cloudiness (Figure 1.7, Werth and Avissar 2004). Figure 1.7, copied from Werth
and Avissar (2004), shows that various data sources agree reasonably well in depicting the phase
and amplitude of the annual cycle in surface net radiation. The sources for the surface net
radiation data presented in this figure are the International Satellite Land Surface Climatology
Project (ISLSCP), the Goddard Institute for Space Studies (GISS) Model I1 GCM, and the
NCEP/NCAR and NASAIGOES- 1 reanalyses (Werth and Avissar 2004).
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Figure 1.7. Annual variation of surface net radiation averaged over the Amazon fiom
ISLSCP (dotted black line), simulated by the GISS GCM (solid gray line), and from the
NASAIGOES-1 reanalysis (dotted gray line) and the NCEPNCAR reanalysis (dashed
gray line). Copiedfiom Werth and Avissar (2004).
However, different models of evapotranspiration in the Amazon produce basin-averaged
ET cycles that are out of phase with one another (Figure 1.8). Different formulations produce an
ET cycle that is either energy-limited, and thus peaks along with maximum solar radiation, or
water-limited peaking during the rainy season. Figure 1.8, copied from Werth and Avissar
(2004), shows that the NCEP/NCAR and GOES-1 reanalyses model basin-averaged ET in the
Amazon to be water limited, peaking during the rainy season. The ET cycle modeled by the
GISS GCM also peaks during the rainy season, but exhibits a much larger seasonal range in
comparison to the other results and a more prolonged drop in ET during the dry season. A
comparison of rainfall simulated by the GOES-1 reanalysis and the GISS GCM shows that the
latter produces a more pronounced and longer dry season. In contrast to these results, the
Shuttleworth model yields a seasonal cycle in basin-averaged ET that is in phase with the annual
surface net radiation cycle, with its minimum in June and maximum in September (compare
figures 1.7 and 1.8). This latter model uses the Penman-Monteith-Rutter equation in which
latent heat flux is a function of net available radiation, stomata1and atmospheric resistances, and
near surface atmospheric saturation deficit (Werth and Avissar 2004). In the other three land
surface schemes, net surface radiation does not figure directly in the equation for
evapotranspiration; ET is modeled as a function of the near surface atmospheric moisture
gradient modified by a parameter relating to surface resistance.
Figure 1.8. Annual cycle of
evapotranspiration averaged over the
Amazon computed an ensemble mean of
six realizations of 8 years each with the
GISS GCM (solid gray line), calculated
using ISLSCP data with the model of
Shuttleworth (1 988) (dotted black line),
fiom the NASA/ GOES-1 reanalysis
(dotted gray line) and the NCEPNCAR
reanalysis (dashed gray line). Copied
porn Werth and Avissar (2004).
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Furthermore, a near-constant value of stomatal resistance is used in the Shuttleworth
model, whereas the other three land surface schemes parameterize canopy or stomatal resistance
as a more sensitive function of soil moisture, which is also simulated by these models (Werth
and Avissar 2004). It follows that another important parameter in these land surface schemes is
the depth of the soil layer fiom which water can be drawn by plants for transpiration (Werth and
Avissar 2004). The NCEP/NCAR land surface model uses a soil layer of lm, and the GISS
GCM soil layer is 3.6m deep (Werth and Avissar 2004). Yet, water extraction by mature trees in
an old-growth Amazonian forest has been found to be significant up to depths of at least 8m, and
deep extraction of soil water is hypothesized for forests covering half the basin (Nepstad et a1
1994, Werth and Avissar 2004). Hence, it appears the land surface models used in the NCEP
reanalysis and the GISS GCM likely underestimate the water available for plant transpiration in
the Amazonian dry season. (Werth and Avissar 2004). The net result of the model differences
described above is that the reanalyses and the GISS GCM simulate greater vegetation control on
ET during the Amazonian dry season compared to the Shuttleworth model (Werth and Avissar
2004).
Field measurements of evapotranspiration at various sites in the Amazon rainforest have
shown that the seasonal cycle of ET is highly variable over the extent of the Amazon (Figure 1.9
shows the locations of the sites for which field data are discussed below).
Figure 1.9. Annual midall (mmfyear)in the Amazon basin (Copiedpom Sombroek, 2001). The three red stars
indicate the sites were long-term eddy covariance rneasu~efllentsof above-canopy C02andH20fluxes have been
underway: Cuieiras forest reserve ( 6 W , 2.65); Tapajos National forest (54.9"W,2.9%); Caxiuana forest (5 1S0W,
1.75). The white star indicates a site near the town of Paragominas (48W, 3%), where Nepstad et a1 (1994)
measured soil water up to depths of 8 m.
Studies in Tapajos National Forest (54.g0W, 2.9's) (Da Rocha et a1 2004, Saleska et a1
2003) showed that ET at this site was not water-limited in the dry season and was thus greater
than wet season ET, which was limited by energy availability due to increased cloudiness. Da
Rocha et a1 (2004) complemented eddy covariance measurements of evaporative flux at their site
in Tapajos with soil moisture measurements up to a depth of 2.5m. They found that tree roots
extracted water for transpiration at 2m depth, and that the daily extraction of soil water at this
depth remained constant throughout the dry season, implying no water limitation. They
additionally documented the occurrence of hydraulic lift at their site, which redistributed soil
water, replenishing shallow dry soil from deep soil moisture. Climatological rainfall at this site
is 1920 mdyear and its dry season extends for 5 months (including months with 4 0 0 mm of
precipitation). According to these two criteria, this Tapajos site is drier than -70% of
Amazonian forests (Saleska 2003). Another study relying on eddy covariance measurements of
ET was carried out a site fbrther east in the Caxiuana forest (5 1SOW, 1.7's) (Carswell et a1
2002), characterized by a mean annual rainfall of 2000mm (Andreae et al. 2002). ET at this site
was also found to increase during the dry season. Nepstad et a1 (1994) similarly found that ET
was not water-limited during the dry season in a mature evergreen forest near the Brazilian town
of Paragominas (4g0W,3"S), where climatological rainfall is 1750 m d y r . Their conclusion is
based on soil moisture measurements up to a depth of 8m and observations of tree root
distributions with depth. The soil moisture measurements were taken during a severe 5.5-month
dry season in 1992, for which the total rainfall was only 95 mm. While average daily rainfall
during the dry season was only 0.6 mm, evapotranspiration was maintained at 3.6 mmlday. Plant
available water stored below 2m in the soil provided more than 75% of the transpired water
during this season. Roots in this forest were found to extend to depths of -1 8m. In an additional
analysis, Nepstad et a1 (1994) estimated the distribution of Amazonian forests that rely on deep
rooting systems by using satellite NDVI data and gauge rainfall data to identify areas of
evergreen forests that occur in climate regimes characterized by seasonal periods of significant
drought (rainfall less than 1.5 rnm/day during the driest three months). They concluded that
"half of Brazilian Amazonia's closed forests depend on deep root systems to maintain green
canopies during the dry season" (Figure 1.10)
Figure 1.10. Distribution of forests that rely on deep roots to maintain canopy greenness during the dry
season. Copiedfiom Nepstad et al(1994).
Water-limited dry season transpiration has also been observed in the Amazon. Malhi et
a1 (2002) found that evapotranspiration was water-limited during the dry season at an old-growth
forest site in the Cuieriras reserve, located -60 km north of Manaus. This site is generally wetter
than those discussed previously, with a mean annual rainfall of 243 lmm (Araujo et a1 2002).
Malhi et a1 (2002) analyzed eddy covariance measurements of water vapor fluxes above the
canopy for the period September 1995-August 1996. This year was characterized by total
rainfall of 2088 mrn and a 5-month dry season (P~lOOm/mo),which may have been significantly
more severe than mean dry season conditions for the site. While dry season solar radiation at the
site was greater than in the wet season, latent heat flux was reduced. However, Araujo et a1
(2002) found that the same forest site showed no dry season water-limitation during another
unusually wet year extending between July 1999 and June 2000, for which total rainfall was
2730mm. For this year, ET peaked during the dry-season along with surface radiation.
Many estimates of mean annual evapotranspiration for the basin have been derived.
Callede et al. (2002) estimate mean annual evapotranspiration as a residual of the mean
terrestrial water balance computed from rain-gauge and river discharge data for the period 19691992. The mean evapotranspiration over this period, when the average change in water storage
in the basin is taken to be negligible, is 3.27 &day.
The estimate of mean annual
evapotranspiration over the period 1970-1999 obtained fkom the NCEPNCAR reanalysis is 4.3
mmlday (Marengo 2005). Other estimates of ET over the basin derived by different methods
are presented in Table 1.1. All these estimates show the Amazon basin to act as a moisture sink
(P>ET) in its mean state. Both the NCEP/NCAR and GOES- 1 reanalysis simulate a
climatological mean annual cycle for basin-averaged ET in which monthly [ET] exceeds
precipitation during 2-3 months in the dry season, while mean annual [PI exceeds mean annual
[ET] (Zeng 1999, Marengo 2005)
ET annual
Source
Method and Data sources
Time period
estimate
(mmlday)
Rao et a1 (1996)
4.5
Atmospheric water balance;
atmospheric fields from once daily
ECMWF analyses; precipitation from
rain gauge data
Costa and Foley (1997)
Zeng (1999)
3.7
LSX land surface model;
Five
climatological mean climate data from
simulation
observation-based datasets
years
I Derived from NASA/GEOS-1
1 1985-1993
reanalysis gridded evaporation
Terrestrial water balance, neglecting
1976-1996
storage change; precipitation and
runoff derived from NCEP/NCAR
reanalysis
Terrestrial water balance; precipitation
1969-1992
from rain gauge data and runoff from
I gauged discharge at Obidos station,
Marengo (2005)
/
I
Derived from NCEP-NCAR reanalysis
gridded evaporation
Betts et a1 (2005)
Derived from ERA-40 reanalysis
I
I
Table 1.l.Spatially-averaged evaporation estimates for the Amazon basin. Estimates from earlier publications are
also provided in Costa and Foley (1999).
1.3.4. River Discharge
Callede et a1 (2004) found no significant autocorrelation in the record of annual discharge
of the Amazon River over the period 1903-1999, suggesting that change in water storage in the
basin at the interannual timescale is not important. This conclusion is corroborated by the high
correlation at the yearly timescale between annual rainfall and mean annual discharge, maximum
discharge, and minimum discharge (coefficients of linear correlation are 0.7 15,0.689, and 0.607
respectively).
Callede et a1 (2004) also identify a potential signal of the effect of deforestation on runoff
production in the basin. Time series of mean annual rainfall and mean annual discharge over the
period 1945-1998 reveal a steady increase in runoff coefficient starting in 1974. This implies an
associated long-term declining trend in evapotranspiration in the Amazon basin. However,
Callede et a1 (2004) conclude that since the variations are only a few percent, the signal cannot
be verified.
1.4. This Study's Contributions
The aim of this study is to derive the best possible estimate of large-scale
evapotranspirationin the basin by applying both the atmospheric and terrestrial water balances,
independently of land surface parameterizations used by previous researchers. The success of
this endeavor hinges on an accurate characterization of the water balance components for the
basin, [ q , [PIand [dw/dt], using available datasets. While other workers have investigated the
atmospheric water budget for the Amazon basin (Costa and Foley 1999, Zeng 1999, Marengo
2005), their work has been limited in some significant aspects. The most important of these is
that they relied on atmospheric humidity and wind velocity data &om one particular reanalysis to
compute [ q estimates for the basin, neglecting the large uncertainty in reanalysis-derived
atmospheric fields for our region, revealed by the discrepancies between [Cj estimates derived
fiom different reanalyses. Specifically, Roads (2003) showed that the NCEP/NCAR and
NCEP/DOE reanalyses produce significantly different spatio-temporal patterns of atmospheric
moisture convergence over the Amazon basin. The ERA-40 model differs significantly fiom the
34
models used in the two U.S. reanalyses, and would thus be expected to produce an even more
divergent characterization of the atmospheric water budget for the Amazon basin, as will be
shown below.
This work emphasizes the importance of characterizing and quantifying sources of
uncertainty in estimates of the Amazon's atmospheric water budget components. The specific
contributions of this work in this regard are listed below:
1)
Evaluation of the differences between estimates of [qcomputed by alternative
algorithms. Other workers rely on approximations in computing the basinaveraged atmospheric moisture flux convergence field from the original model
data of horizontally and vertically distributed atmospheric humidity and wind
velocity. Yet, they do not quantify the errors introduced to the basin-averaged
[qestimates by these approximations (Costa and Foley 1999, Zeng 1999,
Marengo 2005).
2)
Derivation of
[qestimates for the Amazon basin from each of three
reanalyses: ERA-40, NCEP/NCAR, and NCEPIDOE, and use of a weighted
average of these estimates in the water balance equation. These are the most
cutting-edge global reanalyses available today. This approach recognizes that
there are important differences between these reanalyses that affect modeled
atmospheric moisture transport. There is inadequate evidence to establish the
superiority of one model over another in relation to its accuracy in depicting
atmospheric moisture flux convergence over the Amazon basin. Other workers
rely on data from one reanalysis, neglecting information provided by the others
(Costa and Foley 1999, Zeng 1999, Marengo 2005).
3)
Evaluation of the error in the [qestimates derived from each of the three
sources at the monthly and annual timescales by comparing them to concurrent
time series of precipitation and river discharge, which are less uncertain.
4)
Computation of estimates of basin-averaged [dwldt] at the monthly scale and
evaluation of its importance in the basin's water budget. Other workers neglect
this budget component without providing adequatejustification (Costa and
Foley 1999, Zeng 1999, Marengo 2005). Rao et a1 (1996) show its importance
in marking the transition to the rainy season in the Amazon basin.
An estimate of mean annual evapotranspiration, spatially-averaged over the
Amazon basin is derived. This estimate is very reliable, as it is based on the terrestrial
water balance for the Amazon basin and relies on widely used precipitation and river
discharge data. However, the resulting estimate is lower than most others published in
the literature, which are usually based on land surface models. Hence, the results of this
work encourage a re-evaluation of our understanding of the magnitude of Amazonian
evapotranspiration at the basin-averaged scale.
While application of the terrestrial water balance ensures that an unbiased
estimate of Amazonian ET is obtained, the atmospheric water balance is necessary for
obtaining monthly-scale information on ET. By applying the atmospheric water balance,
we derive the climatological annual cycle of areally-averaged ET for the Amazon basin.
A comparison of the resulting ET cycle with the annual evolution of basin-averaged
rainfall and surface net radiation allows us to infer whether water or energy availability
limit ET during different periods of the year.
The next chapter describes the different datasets used to characterize the Amazon
basin's water budget.
Chapter 2- Datasets
The datasets used for the estimation of the various components of the Amazon basin's
water budget are described below.
2.1. Atmospheric water vapor flux convergence, C
Atmospheric water vapor flux convergence (C) is computed from the divergence of the
vertically-integrated atmospheric water vapor flux vector field (Q).
C=-V-Q
-
L2.1I
Q = (Q,,Q,)
-
P.21
Qx refers to the vertically-integrated atmospheric moisture flux in the zonal direction, while Qy
refers to the flux in the meridional direction.
Data products from three global reanalyses are used for information on atmospheric fields
over the Amazon basin: the NCEPMCAR reanalysis (henceforth R-1), the NCEP/DOE
reanalysis (henceforth R-2), and the ECMWF ERA-40 reanalysis. Specific humidity, wind
velocity and surface pressure are provided as horizontally distributed fields on each reanalysis
model's global Gaussian grid. Specific humidity and wind velocity are also vertically resolved
on the models' vertical levels. Table 2.1 presents the horizontal and vertical resolutions of each
reanalysis model. The three reanalyses also provide these fields on a coarser, regular 2.5"
latitude-longitude grid, as well as vertically interpolated to coarser resolution pressure levels.
Many researchers use these interpolated fields to reduce data volumes, and because they are
available in more accessible digital formats (e.g. Costa and Foley 1999). In this work, the fields
distributed on the original Gaussian grid and vertical levels of each model are used, in order to
37
take advantage of each model's maximum horizontal and vertical resolution. Furthermore, by
working with data at the original vertical resolution, we avoid potentially important errors in the
interpolated pressure-level fields, which are introduced by the algorithms that interpolate fkom
the original levels to the pre-specified pressure levels (Trenberth et a1 2002).
R-1 and R-2
ERA-40
Horizontal resolution Vertical resolution
28 model levels
T62 -2 10 km at equator
(sigma levels)
(Gaussian grid)
60 model levels
TI59 -125 km (reduced
1 Gaussian grid) I (hybrid levels)
Table 2.1. Horizontal and vertical resolutions of R-1,R-2and ERA-40
In the case of R-1 and R-2, vertically-integrated atmospheric moisture fluxes in the zonal
and meridional directions are computed fi-omthe q, 3 and P,fields, according to Equation 2.3.
P,is surface pressure; g is gravity; q is specific humidity; is wind velocity with zonal and
meridional components. The original model vertical levels are terrain following coordinates
called sigma levels, such that
At the land surface, o = 1 and at the top of the atmosphere, o = 0.
Vertical integration is done numerically by multiplying (qv)at each sigma level by the
thickness of the sigma layer (delta sigma), and adding over all sigma layers. The sigma levels
and associated sigma layers are defined in Kalnay et al. (1996).
The divergence of this flux field is then computed by a centered difference algorithm,
which is further explained in Chapter 3.
In the case of ERA-40, vertically-integrated atmospheric moisture fluxes, computed on
38
the original model coordinates, are provided in the publicly available datasets. Note that ERA40 uses hybrid levels in the vertical, which are terrain-following up to a certain altitude, and then
are replaced by fixed-pressure levels to resolve the rest of the atmospheric column.
Q field computed in the model's spectral space. This is the
ERA-40 also provides the V .most accurate method of computing V Q from the model's spatially discretized moisture flux
field (Seneviratne et a1 2004).
All three models provide analyses of atmospheric fields for four time points per day, at
0000,0600, 1200, and 1800 UTC. These fields must be averaged over a temporal interval, such
as a month, to characterize the Amazon's atmospheric water budget at a coarser timescale. In the
case of R-1 and R-2 data, the vertical integration used to compute total column atmospheric
moisture fluxes, as in Equation 2.3, must be carried out for each time point, prior to temporal
averaging. This is particularly important since the pressure at the sigma levels is time-varying,
depending on surface pressure. Consequently, significant errors are introduced by taking time
averages of (q.d at each sigma level and then carrying out the vertical integration assuming a
constant surface pressure (Trenberth et a1 2002).
2.2. Precipitable water tendency, dwldt
For R-1 and R-2 data, total precipitable water or total column atmospheric water vapor
(w) is calculated from vertically resolved specific humidity as in Equation 2.5. Vertical
integration is carried out numerically, as was done for computing vertically integrated horizontal
water vapor fluxes.
In the case of ERA-40, vertically integrated atmospheric water vapor, which is provided
as one of the data products distributed on the horizontal grid, is used directly.
The tendency in w is computed over a month's duration as
N is the number of days in a given month. wris w at the end of the month, and wi is w at the
beginning of the month. wf is computed by averaging w for the 1800 UTC analysis time of the
last day of that month and the 0000 UTC analysis time of the frst day of the following month.
wi is similarly computed by averaging w for the 0000 UTC analysis time of the first day of that
month and the 1800 UTC analysis time of the last day of the preceding month.
2.3. Precipitation
The precipitation datasets utilized are the Global Precipitation Climatology Project
(GPCP) Combined Precipitation dataset (Version 2) (Huffban et a1 1997) and the Tropical
Rainfall Measuring Mission TRMM and Other Sources Rainfall Product 3B43 (Version 5)
(Adler et a1 2000, Kummerow et a1 2000). Both products consist of monthly-averaged surface
rainfall on a regular latitude-longitude grid. The GPCP data is global, with a uniform 2.5"
resolution, while the TRMM product is provided for the global tropics 40"s-40°N,with a 1'
resolution. While the GPCP dataset extends back to January 1979 and through the present,
TRMM data is only available starting December 1997, as the TRMM satellite was launched on
27 November 1997 (Kummerow et a1 2000).
Both products are created via a combination of data from multiple satellite-borne sensors
and from rain gauges. The GPCP product combines precipitation estimates based on infrared
data from Geostationary satellites with microwave precipitation estimates based on the Special
Sensor MicrowavelImage (SSMII) data from satellites that fly in sun-synchronous low-earth
orbits (Huffman et a1 1997). While the IR data has high temporal resolution (an image every 3
hours) that is capable of resolving diurnal cycles in rainfall, the relation between IR radiance and
instantaneous precipitation is relatively weak (Huffman et a1 1997). On the other hand, SSMII
radiances have strong physically-based connections with surface rainfall but low temporal
resolution (averaging 1.2 imagedday). Hence, they are used to calibrate the higher resolution IR
data. This multi-satellite estimate is subsequently combined with rain gauge data, which is
assembled and analyzed by the Global Precipitation Climatology Center (GPCC) of Deutscher
Wetterdienst (Huffian 1997).
The TRMM 3B43 is produced in a similar manner, with the primary difference being that
it incorporates rainfall estimates from the satellite-borne precipitation radar (Alder et a1 2000).
The TRMM satellite carries the TRMM passive Microwave Imager (TMI), which has slightly
different channels than SSMII and a higher spatial resolution, as well as the precipitation radar
(PR) (Kummerow 2000). It has an average visitation frequency of about 0.5 imageslday. A
surface rainfall estimate produced fiom a combination of TMI and PR data is used to adjust
rainfall rates inferred fiom Geostationary satellite IR observations to yield rainfall estimates with
high temporal resolution, which would be impossible using TRMM data alone. As in the GPCP
Combined Precipitation product, the resulting multi-satellite estimate is combined with GPCC
rain gauge data (Alder et a1 2000, Kummerow 2000).
The GPCP and TRMM products are based on similar algorithms for combining
precipitation estimates fkom different data sources, in which each input estimate is weighted by
the inverse of its square error (Alder et a1 2000, Huffinan et a1 1997, Huffian 1997). As the
statistical information required for a detailed estimation of the space and time-varying error
associated with each input dataset is unavailable, Huffinan (1997) derives a functional form for
41
the root mean square error, parameterizing its dependence on the estimated rainfall rate and on
the number of samples used in each space and time averaged rain estimate.
2.4. Amazon basin boundaries
The Amazon basin boundaries are obtained fiom the Total Runoff Integrating Pathways
(TRIP) dataset at 0.5 degree resolution (Oki and Sud 1998). This dataset was produced based
on the ETOPO5 global DEM, which has 5' x 5' horizontal resolution. Since the river discharge
data used in this work is measured at the Obidos gauging station (1°56'S, 55'30'W) (see section
2.5), the subset of the Amazon basin that discharges at Obidos is actually utilized (see Figure
2.1). For simplicity this sub-basin is henceforth referred to as the Amazon basin. The area of
this basin obtained fiom the TRIP dataset (4.784* lo6km2) compares well with the area cited in
Callede et a1 (2002) of 4.676* lo6km2.
Figure 2.1. Outline of the Amazonian sub-basin, which outlets at the Obidos gauging station.
Copiedfiom Callede et a1 (2002)
2.5. Amazon river discharge
Annual-averages of Amazon river discharge at the Obidos gauging station for the period
1980-2001 were kindly provided by Jacques Callede, who is affiliated with the Hydrology and
Geochemistry of the Amazon (HyBAm) project through the French "Institut de Recherches pour
le D6veloppement9'(IRD) (Callede et a1 2002). The Obidos gauging station is -800 km from the
Atlantic Ocean and is the furthest downstream gauging station on the Amazon river. Work by
Callede and others (2001,2002) improved the state-discharge relationship for this station based
on detailed and long-term discharge measurements using an Acoustic Doppler Current Profiler.
The resulting relationship reduced the mean dispersion between stage-derived discharge and
measured discharge to 2.9%.
Chapter 3 - Analysis of the Amazon's Atmospheric Water Budget for the
Period 1997-2001
The atmospheric water balance equation, from which evapotranspirationmay be
estimated, was presented in Chapter 1 and is repeated below.
We apply this equation for temporal and spatial averages, such that
The overbar indicates temporal averaging, and the square brackets indicate spatial
averaging over a specified region.
In this chapter, the five-year period 1997-2001 is studied to gain insight into the relative
magnitudes of the Amazon basin's water budget components, their annual cycles, and the
differences between estimates of these components obtained from different data sources. The
smallest time unit considered is a month. Hence, data available at higher temporal resolutions
are averaged to obtain monthly time series. In the following chapter, a longer time period is
studied to gain further understanding of the uncertainties associated with time series of monthly
atmospheric moisture flux convergence computed for the Amazon from the three reanalyses.
Finally, in Chapter 5, the climatological annual cycle of basin-averaged evapotranspiration for
the Amazon is derived using data for the period 1988-2001.
The water balance components studied in this chapter for the time period 1997-2001 are:
1) vertically-integrated atmospheric water vapor flux convergence (C)
2) precipitation (P)
3) the rate of change in total atmospheric column water vapor, also referred to as total
precipitable water (dwldt).
The computation of C and dwldt was explained in Chapter 2. C, P, and w are distributed
on horizontal latitude-longitude grids (see also Chapter 2). They are integrated over the
specified region of interest and divided by the region's area to obtain a spatial average of the
field for that region. Areal integration over the region of interest is carried out numerically by
multiplying the value at each grid point within the region by the area of its associated grid box
and summing over all grid boxes within the region. Temporal averaging over the time unit of
interest is carried out on the spatially-averaged fields. For the vertically integrated fields of C
and cjwldt, the operations of temporal and horizontal spatial averaging are interchangeable.
Other unit conversions are also applied so that all values of the water balance components
presented are in units of mmlday.
3.1. Atmospheric water vapor flux convergence over rectangular regions of different areas
within the Amazon Basin
Initially, estimates of [qderived from R- 1, R-2, and ERA40 for three rectangular
regions of different size that lie within the Amazon basin are analyzed (Table 3.1 describes the
locations and areas of these regions). The literature review presented in Chapter 1 leads to the
expectation of significant differences between estimates of this field for the Amazon region
obtained from different reanalyses. The aim in this section is to study and understand the
characteristics of these differences and their dependence on the size of the region over which C is
averaged. Yet, because [qcan be computed using a variety of algorithms, we begin by
investigating the effect of using different algorithms on the resulting [qestimate, keeping the
data source constant. The effect of the computation algorithm must be quantified so as to
separate it from differences in [qthat originate in the discrepancies between the q, v, and Ps
fields simulated by the different reanalyses. This is particularly important in this work, since it
45
is advantageous to use a different algorithm in computing C fiom ERA-40 data than that used
with R-1 or R-2 data, as explained below. Furthermore, in any investigation of the error in
reanalysis-derived [Cj estimates, it is important to understand the error contributed by the
computation algorithm employed, which is essentially a post-processing operation applied to the
original reanalysis data.
The ERA-40 data products include the field of vertically-integrated atmospheric water
vapor flux divergence (V Q = -C; Q is the vertically-integrated atmospheric water vapor flux
vector with zonal and meridional components), horizontally distributed on the model's Gaussian
grid. The spatial derivatives for this ERA-40 field have been computed in the model's spectral
space rather than on the Gaussian grid (see Chapter 2).
In the case of the U.S. reanalyses, R-1 and R-2, the divergence of atmospheric water
vapor flux is not provided as a data product, and hence this field must be computed fiom the
available fields of specific humidity and wind velocity, distributed horizontally on the models'
Gaussian grid and vertically on their terrain-following sigma levels, in addition to the
horizontally-distributed surface pressure field. First, vertically-integrated zonal and meridional
water vapor fluxes are computed on the model grid according to Equation 2.3, as described in
Chapter 2. V Q is then approximated by a center difference.
This finite difference approximation introduces an error in the resulting divergence field
relative to the computation of divergence in spectral space. The latter is more accurate, because
it replaces the derivative operator by a multiplication operation in spectral space. In the
following, ERA-40 data products are used to quantify the error introduced to [qestimates by the
center difference algorithm, as well as by another widely used algorithm that involves summing
46
atmospheric water vapor flows across the boundary of the region of interest.
[qestimates based
on the most accurate spectral computation of the ERA-40 divergence field are used as reference,
against which results fiom alternative approaches are compared. This analysis is carried out for
the three rectangular regions in the Amazon basin (Table 3. I), to investigate if the accuracy of a
particular algorithm for computing [qis dependent on region size. The various computational
methods are listed below, with an explanation of the steps involved. Method 1 is the reference
(spectral) against which the performance of the other methods is compared.
1) The field of V Q computed in spectral space, provided by ERA-40 on its Gaussian grid,
is integrated over the region of interest and divided by the region's area to obtain a spatial
average [V .Q 1. Convergence is the opposite of divergence: [ q = - [V Q 1.
2) The center difference algorithm (equation 3.3) is used to compute V Q fiom vertically
integrated zonal and meridional atmospheric water vapor fluxes. Two variations of this
method are tested:
a) Center differences are computed on the original ERA40 Gaussian grid, with a grid
point spacing of -1.175 degrees in latitude and longitude.
b) Vertically-integrated zonal and meridional atmospheric moisture flux fields are
bilinearly interpolated onto a 0.5" x 0.5" latitude-longitude grid, to test whether the
higher grid resolution improves the accuracy of the center difference computation.
3) In a third method, Gauss's theorem is used to transform the area integral of the
divergence field over the region of interest (R) into a line integral around the region's
boundary.
For a rectangular region (ABCD) on the horizontal latitude-longitude grid, the total
atmospheric moisture flux convergence becomes:
CTo, is divided by the region area to obtain a spatial average [q.
The definite integrals
along each border are approximated numerically by multiplying the value of each grid
point along the border by the length of its associated grid box and summing over all grid
boxes overlying the border.
Using these three methods, we compute monthly spatially-averaged atmospheric moisture
flux convergence [q,
starting from ERA-40 data products, for three rectangular regions within
the Amazon basin, over the time period 1997-2001. The corner coordinates and areas of the
three regions are listed in Table 3.1.
Region A
Longitudinal 64W-60W
extent
12.5s-8.5s
Latitudinal
extent
Area (krn2) 1.945* 10'
Region B
Region C
64W-56W
72W-56W
-
12.5s-4.5s
14.5s-1.5N
-
7.820* lo3
3.135*106
4.784* lo6
Amazon
Basin$
Table 3.1. Regions studied. *Outlet at Obidos gauging station (refer to Chapter 2).
Figure 3.1 presents the results for region A. Figure 3.2 plots the absolute error of
monthly [qestimates for region A computed by each of methods 2a, 2b, and 3. This
"algorithm-produced" absolute error is calculated relative to the results of Method 1, i.e. based
on the V .Q field computed in spectral space, by taking the absolute value of the difference
between the [CJestimate obtained by one of these methods and that obtained by Method 1.
1.0
Figure 3.1. Monthly [q
for Region A, computed
from ERA-40 data
products using four
alternative methods.
Black: v .Q is computed in
spectral space (Method 1reference). Red: v .Qis
computed by centered
difference on the original
Gaussian grid (Method 2a).
Green: centered difference
is done on a 0.5x0.5 degree
lat-lon grid (Method 2b).
Blue: CToral
is computed by
linear integration of normal
fluxes at the region
boundary. (Method 3).
Negative values indicate
net divergence
6.0
4.0
g '"
\
E
0.0
-2.0
-4.0
-6.0
I
I " " " " " '
. . . . . . . . . . .I " . . . . . . . . .
J F M A M J J A S O N D J F M A M J J A S O N D J F M A M JJ A ~ ~ N D J F U A N JJA S O N D J F M A M J J A S O N D '
1997
I
I
I
I
1
1
I
l
I
I
I
I
1
1
1
1
I
I
1
2000
1999
1998
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
I
0.40 -
0.30
B
2001
-
-
-
-
-
I
\
E
E 0.20-
-.
0.00
1
1
1
1
1
1
1
1
1
1
1
1
.
1
1
.
.
1
1
,
.
1
1
,
,
1
,
1
1
1
1
1
1
1
1
1
.
1
1
1
1 . 1 ,
1
1
,
.
1
1
1
,
1
,
1
JFMAMJJASOND'J F M A U J JASOND'JFMAMJ JASOND'J F M A M J JASOND'JFMAMJ JASOND-
1997
1998
1999
2000
2001
Figure 3.2. Absolute
error associated with
various methods of
computing [C] for
Region A, from ERA40
data products. Method 1
is used as reference.
Red: Method 2a.
Green:Method 2b.
Black: Method 3.
Table 3.2 lists the average absolute error and the bias error of [qestimates computed by
the various methods, again relative to the results of the reference method. The average absolute
error is obtained by averaging the monthly absolute error (Figure 3.2) over the 60-month time
series covering 1997-2001.
Average absolute error (mdday)
Method 2a
Bias (mdday)
Method 2b
Method 3
Method 2a
Method 2b Method 3
RegionA 0.10
0.1 1
0.06
-0.06
-0.10
0.05
RegionB 0.10
0.09
0.02
-0.10
-0.08
0.01
I Region
0.12
1 0.02
1 -OJ2
I -OJ0
1 O-O1
Table 3.2. Average absolute error and bias associated with alternative methods of computing [qfor regions A, B,
and C. Average absolute error is computed by averaging the absolute error for each month over the five-year period
1997-2001. The data products used are fiom ERA-40. Method 1 provides the reference [qestimates against which
errors are measured. Methods 1,2a, 2b, and 3 are explained in the text.
Results summarized in Table 3.2 show that the boundary integral method (Method 3) is
the most accurate: the average absolute error and bias error associated with this method are an
order of magnitude smaller than those associated with methods 2a and 2b, in which the finite
difference approximation of V .Q is employed. Those latter methods (2a and 2b) have an
average absolute error of -0.1 mmlday, which appears to be independent of the size of the
region. The resolution of the grid over which the center difference approximation is carried out
has only a small effect on the resulting error. It is also apparent that the finite difference
approximation results in a consistent negative bias independent of region size, of about -0.1
mrn/day, nearly equal in magnitude to the average absolute error associated with this algorithm.
it is
While the boundary integral approach produces the most accurate estimate of [q,
difficult to apply to regions with highly irregular boundaries such as a river basin, for which the
50
areal integration of V .Q is more suited; hence our interest in using the finite difference
algorithm for R-1 and R-2 data products. The question remains: How does the effect of the
computation algorithm on [qestimates, quantified above, compare in magnitude to
discrepancies between monthly [qestimates based on different reanalyses originating from
differences in the reanalyses' models? "Reanalysis model" is used here to encompass the
atmospheric model, the assimilation algorithm, and the observations assimilated, all of which
affect the resulting data. Since the superiority of one reanalysis model over the others in
simulating [qin the Amazon region has not been established, the discrepancies between
monthly [qestimates produced by different reanalyses can be interpreted as a measure of the
uncertainty associated with these estimates. The preceding question can hence be reformulated
as: Is the error introduced to monthly [qestimates by the center difference approximation of
divergence of concern in comparison to the original, "model-associated" uncertainty in these
reanalysis estimates?
A variable, a,, which may be interpreted qualitatively as the mean "spread" in monthly
[qestimates produced by R- 1, R-2 and ERA-40, is defined as a quantifiable proxy to this
model-associated uncertainty. Mathematically, the standard deviation (a,) of the three different
estimates of [qis computed for each month, and then an average of a, is taken over the time
period of interest to obtain a, (Equations 3.6 a-c).
The index m refers to the month for which the variance in [CJ estimates is computed; i
indicates the reanalysis fiom which the [qestimate is obtained (i= R1,R2 or ERA40); and
E([q,)is the expected value, or average, of the [qestimates for a given month obtained fiom
the three reanalyses. For the time period investigated in this section, encompassing the 60
months between January 1997 and December 2001, a, becomes:
While om is not statistically significant because of the small number of estimates from
which it is obtained, it is used as an appropriate measure of the "spread" of [qestimates for a
given month derived from different sources. Moreover, om is well suited for comparison with
the average absolute error of monthly [qestimated by the center difference approximation of
V Q (Table 3.2).
Comparisons are made of monthly estimates of [qobtained fiom ERA-40, R-1 and R-2
for the period 1997-2001, for each of regions A, B, and C. The dependence of a,,on the size of
the averaging area is thus investigated. For this analysis, [qis computed using the boundary
integral method. This method, which was proven accurate, is used here to avoid conhsing
computation errors with the model-associated spread in the estimates from the different
reanalyses.
The time series of monthly [qproduced for Region A by the three reanalyses is shown
in Figure 3.3. Figure 3.4 shows the climatology of [qfor this region computed for the 5-year
period 1997-2001, based on each of the three reanalyses.
Figure 33. Monthly [Cj
for Region A, computed by
the boundary integral
method, using data fiom the
three reanalyses.
Black: ERA-40.
Red: NCEPBCAR
reanalysis (R- 1).
Green: NCEPDOE
reanalysis (R-2). Negative
. values indicate net
divergence.
I
1 1 1 " 1 1 " " ' 1 ' 1 1 " " 1 1 ' 1 l ' 1 1 1 a 1 1 " w ' 1 1 ' 1 1 1 1 1 1 1 1 w 1 ' 1 ' 1 " 1 " "
JFMAMJJASONDJFMAMJJASONDJFMAMJJASONDJFUANJJASONDJFMAMJJASONI
1997
1
1999
1998
I
I
I
1
I
2000
I
2001
I
I
1
-
I
-
-
-
-
I
J&l
1
FEB
MAR
APR
I
1
M Y
JW
JUL
MJ6
I
SEP
1
OCT
1
NW
DEC
Figure 3.4. Climatology
of [C'j for Region A,
derived from monthly
values for the period
1997-2001.
Black: ERA-40.
Red: NCEPINCAR
reanalysis (R- 1).
Green: NCEPIDOE
reanalysis (R-2).Negative
values indicate net
divergence.
Data presented in Table 3.3 show that the average "spread" in estimates of monthly [q
from different reanalyses, measured by o,,, decreases with region size, suggesting that the errors
associated with the distributed C fields derived from the reanalyses cancel out with spatial
averaging. Rasmusson (197 1) similarly found that estimates of spatially-averaged atmospheric
moisture convergence derived from radiosonde data were more reliable for larger regions.
1.45
0.29
-0.18
1.35
0.07
1.17
1.69
0.44
Region A
1.20
-0.55
Region B
0.95
Region C
0.77
I
I
I
I
I
Table 3.3. Summary statistics for timeseries of monthly [CJ for regions A, B, and C, computed from the three
reanalyses over the period 1997-2001.
For region C, whose area is of the same order of magnitude as that of the Amazon basin,
a,, is 0.8 d d a y , compared to an average absolute error of 0.1 d d a y associated with the
center difference approximation of V Q (Table 3.2). This implies that the model-related
uncertainty in the atmospheric moisture flux convergence field for the Amazon region produced
by today's reanalyses overwhelms the error introduced by the center difference approximation of
the divergence operator.
Table 3.4 shows that the correlation between the monthly time series of [qderived from
the different reanalyses increases with increasing region area. This supports the preceding
conclusion that the agreement between the various reanalyses in depicting Amazon [qat the
monthly timescale increases as averaging is carried over a larger area, probably because spatial
averaging allows for the cancellation of errors associated with the distributed C field.
Correlation between
ERA-40 and R-2 [CJ
Correlation between
R-1 and R-2 [q
Region A 0.66
0.78
0.76
Region B 0.84
0.88
0.8 1
Correlation between
ERA-40 and R-1 [q
I
I
I
I
Table 3.4. Correlations between timeseries of monthly [qcomputed from different reanalyses. The timeseries
extend between 1997-2001.
Table 3.3 also presents the five-year average [ q for each region according to three
reanalyses, showing the large differences between results. For example: for region A, the ERA40 data products yield a net divergence of 0.55 mm/day, while R-1 yields a net convergence of
1.45 rnmlday. As expected, the agreement between the reanalyses improves as the size of the
region for which [ q is computed increases.
3.2. Atmospheric moisture flux convergence over the Amazon Basin
While the preceding analysis for rectangular regions in the Amazon basin was useful to
characterize the properties of the uncertainty in reanalysis estimates of monthly [Cj and the
magnitude of the errors introduced by alternative computation algorithms for [ q , our interest
ultimately lies in deriving a best estimate of [qfor the Amazon basin. Hence, in what follows
we analyze the magnitude and uncertainty of estimates of monthly atmospheric moisture flux
convergence spatially-averaged over this basin. In all subsequent estimates of basin [ q , the
Q computed in spectral space provided by ERA-40 on its Gaussian grid is used. As
field of V -
this field isn't available in the R-1 and R-2 data products, the center difference of verticallyintegrated zonal and meridional atmospheric water vapor fluxes is used to compute divergence
based on these two reanalyses. For all three data sources, we integrate V Q over all grid boxes
within the Amazon basin, and divide by the basin's area to obtain average divergence over the
region. Convergence is the opposite of divergence.
Figure 3.5 shows monthly basin-averaged atmospheric moisture flux convergence [q
derived fiom the three reanalyses. Also plotted in this figure is the monthly [CJ derived from
ERA-40 using the center difference algorithm, to compare to estimates of [qfrom the same
reanalysis but in which V Q is computed in spectral space. The climatology of [CJ for the
period 1997-2001 according to the different data sources is shown in Figure 3.6. The
climatological seasonal signatures of [CJ derived from all three reanalyses are similar. Note,
however that peak [CJ occurs a month earlier in R-1relative to R-2 and ERA-40.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Figure 3.5. Monthly [C)
for the Amazon basin,
Black: derived fiom ERA40, using the V .Qfield
computed in spectral space.
- B1ue:derived fiom ERA-40,
using the finite difference
- computation of V .Q. Red:
NCEP/NCAR reanalysis
(R- 1). Green: NCEPIDOE
- reanalysis (R-2). Negative
- values indicate net
divergence.
-
-
1
11
3:
-
Figure 3.6. Climatology of [CJ
for the Amazon basin, for the
' period 1997-2001.
Black: ERA-40, using the V .Q
- field computed in spectral space.
Red: NCEPNCAR reanalysis
- (R-1). Green: NCEPIDOE
reanalysis (R-2). Negative
- values indicate net divergence.
'
JM
FEB
M4R
APR
MAY
JW
JUL
5-year average [q om(mmlday)
(mmlda~)
data source
R-1
1.51
R-2
0.68
ERA-40
(spectral space)
ERA-40
(finite difference)
1.72
1.59
5-year average
absolute error
(mmlday)
0.13
A
Table 3.5. Statistics for timeseries of monthly [CJ
for the Amazon basin computed fiom the three reanalyses. [q
estimates derived by two alternative methods from ERA-40 data products are also compared. Timeseries extends
between January 1997 and December 200 1.
Table 3.5 shows that ,
0 (0.66 &day),
which is the average model-associated spread in
monthly [qestimates produced by the three reanalyses (Equations 3.6a-c), significantly exceeds
the average absolute error in [CJ estimates introduced by employing the fmite difference
approximation of
V Q (0.13 mmlday). Figure 3.6 shows that the range of monthly Amazon [q
over a climatological annual cycle, according to either of the three reanalyses, is about 5
&day.
Hence, ,
0 is more than 13% of this range. Note that the ,
a value computed for the
Amazon basin is consistent with previous results: it is smaller than the om computed for Region
C (0.77 &day),
which has a smaller area than the basin. This supports the earlier conclusion
that as spatial averaging is carried out over larger areas, the uncertainty in the resulting [ q
estimates decreases.
Table 3.5 also lists the five-year averages of [qfor the basin derived from the three
reanalyses, showing that they differ significantly. Five-year averages of [CJ derived from ERA40 using both the spectral space and finite difference computations of V .Q are included: the
bias error (i.e. the error in the 5-year average [C]) introduced by the finite difference
approximation relative to the spectral computation of V Q is shown to be 0.13 &day
(1.72 -
1.59 rnmlday). Thus, the bias error associated with the center difference computation of C is
nearly equal in magnitude to the average absolute error associated with this computation. This
occurs because the error introduced in Amazon [ q at the monthly timescale by the numerical
approximation of divergence is consistently negative with an average of -0.13, as shown in
Figure 3.7. Hence, the spatial discretization of V .Q leads, consistently, to an underestimation
of monthly [ q by 0.13 &day
on average.
Figure 3.7. Error in
monthly [Cj for the
Amazon basin computed
based on a finite difference
approximation of V .Q,
relative to its computation
in spectral space. The
green line is drawn at 0.13
mm/day, which is the
- average absolute error in
monthly [CJcomputed by the
finite difference algorithm
Positive values indicate
- underestimation by the finite
- difference algorithm.
-
02a
024
0.20
0.1 6
2
-o
1
: :1
0.04
-
n M
-0.04
yv
. . . . . . . . . . . I . . . . . . . . . . . . . . . . . . . . . . .
I
.,,,,,,,,,,
I
,,,,,,,,,..
I
JFMAMJJASONDJFMAUJJASONDJFMAMJJASONDJFUAMJJASONDJFMAMJJASOND
1997
1 998
1999
2000
2001
The consistent underestimation of monthly [qby the fmite difference approximation of
V Q suggests that a bias correction applied to [qbased on an independent estimate of its longterm average (such as river discharge) will result in a reduction of the absolute error in monthly
[qintroduced through this approximation by about half, to an average of -0.06
mmlday. This
error would then be an order of magnitude smaller than the model-associated uncertainty of [q
estimates (am=0.66mm/day),and would thus be relatively negligible.
The bias in the reanalysis [qestimates for the Amazon basin can be estimated by
comparing their multi-year average to that of river discharge at the basin outlet (R). As
explained in Chapter 1, averages of monthly changes in terrestrial water storage over several
years approach zero, as do averages of monthly changes in total atmospheric water vapor. Thus,
for multi-year averages
- [C]= R I A
[3-71
[C] is the multi-year average of basin-averaged atmospheric moisture flux convergence; R is the
multi-year average of river discharge at the basin outlet; A is the basin area. Discharge is
divided by the basin area to yield average runoff in the basin in units of rnrn/day.
In this work, the atmospheric water budget is computed for the portion of the Amazon
basin that outlets at the Obidos gauging station (55"30'W,1°56'S), as explained in Chapter 2.
For this basin, the change in terrestrial water storage over several years is expected to be
negligible. This can be deduced fiom the lack of any significant autocorrelation in the time
series of annual river discharge at Obidos over the period 1903-1999, analyzed by Callede et a1
(2004). Hence, we expect equation 3.7 to apply for averages of [qover the five-year period
1997-2001.
Table 3.6 lists five-year averages of basin [qderived from the different data sources and
their bias errors, computed by comparison to the five-year average discharge at Obidos.
ERA-40 [Cj
Discharge at Obidos (R)
Five-year average, 19972001 (mdday)
1.72
Bias error in [Cj
(mdday)
-1.36
3.08
Table 3.6. Five-year averages and bias errors of atmospheric moisture flux convergence averaged over the Amazon
derived fiom the three reanalyses. Also, fiie-year average discharge at Obidos. The averaging period is
basin
1997-2001. A negative bias error indicates an underestimation of convergence by the reanalysis, deduced by
comparison to time-averaged discharge at Obidos.
([a,
The bias error in [qestimates for the Amazon basin is significant for all three reanalyses,
with a magnitude close to, and in the case of R-2 exceeding, that of mean [q.Due to the high
confidence of river discharge observations (see Chapter 2), we conclude that all three reanalyses
underestimate net atmospheric water vapor convergence over the basin, with R-2 showing the
greatest bias error.
The correlation between time series of monthly [CJ for the Amazon basin derived from
the different data sources is presented in Table 3.7. These correlations are also computed for
60
time series of monthly anomalies of [ q , which are derived by subtracting the climatology of
monthly [Cj for the five-year period fiom the original timeseries (Table 3.7 and Figure 3.8).
Correlation between two time series is a good measure of how closely they agree once the effect
of differences in their long-term means is removed.
Correlation between
ERA-40 and R-1 [Cj
Original timeseries of
monthly [cj
Timeseries of monthly
[qanomalies
Correlation between
ERA40 and R-2 [Cj
Correlation between
R-1 and R-2 [Cj
0.85
0.9 1
0.95
0.56
0.53
0.89
Table 3.7. Correlations between timeseries of monthly [qand [qanomalies for the Amazon basin derived from
different reanalyses over the period 1997-2001.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l 1 ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3.0
Figure 3.8. Monthly
I
2.0
-
h
- anomalies of [qfor the
Amazon basin, derived by
- subtracting the five-year
- climatology of monthly [ C j
from the original timeseries
- of monthly [q,
for each
J
data source. Black: [q
- computed from ERA40 data
-
-
products. Red: R-1. Green:
R-2. A positive value
indicates the amount by
which [qfor that particular
month (e.g. March 1998)
exceeds the 5-year average
[CJfor the month of March.
It is evident that there is large uncertainty in the reanalysis [qestimates at the monthly
and annual timescales (Table 3.7 and Figure 3.8), beyond their bias errors. Table 3.7 shows that
while the correlation between monthly [qtime series derived fiom different reanalyses is high
(ranging between 0.85 and 0.95), it is much weaker when the correlation is computed for the
time series of monthly [qanomalies. This suggests that the high correlation between different
reanalyses' monthly [qestimates is produced by the strong seasonal signal in the time series
derived fiom all three data sources (Figure 3.6). The correlation for the monthly anomalies of
[qremains strong between R-1 and R-2, but decreases to -0.5
between ERA-40 and each of the
two U.S. reanalyses, indicating their poor agreement in depicting monthly-scale interannual
anomalies obtained fiom R-1
variability. The stronger correlation between the time series of [CJ
and R-2 is expected because of the greater similarity between their underlying models.
From the preceding investigation of reanalysis-derived estimates of [ C j for the Amazon
basin over the limited period of 1997-2001, we conclude that these [qestimates exhibit
important bias errors, as well as significant uncertainty at the monthly and interannual timescales
beyond these bias errors. The model-associated uncertainty in monthly reanalysis [qestimates
Q ,particularly after a
overwhelms the errors introduced by finite difference approximation ofV .bias correction to the [qtime series reduces the magnitude of these latter errors by half. Longer
time series of Amazon basin [qderived fiom each reanalysis must be analyzed to enable us to
assign to each a random error estimate based on comparison to independent, more reliable data.
This random error estimate will subsequently be used to weight [qestimates from each
reanalysis, prior to averaging across data sources to derive a best estimate of [qfor the Amazon
basin. This analysis is left for the Chapter 4. The following sections will investigate other
components of the atmospheric water balance over the Amazon basin: rainfall and monthly
changes in total atmospheric water vapor.
3.3. Rainfall over the Amazon Basin
The TRMMand Other Sources RainfaN Product, 3B43 (Version 5), and the GPCP
Version 2 Combined Precipitation datasets are used to compute spatially-averaged monthly
62
rainfall over the Amazon basin ([PI)for the period 1997-2001. These datasets are described in
more detail in Chapter 2. Figure 3.9 shows basin averages of the two fields provided by each of
these datasets: monthly-averaged precipitation rate and its associated absolute random error.
Figure 3.9. Monthly [PIand
spatially-averagedabsolute
random error for the
Amazon basin, derived from
TRMM 3B43 (Version 5)
and GPCP Combined
Precipitation (Version 2)
products. Black: GPCP rain
rate. Blue: GPCP random
error. Red: TRMM rain rate.
Green: TRMM random error.
TRMM products are only
available starting December
1997 and are plotted here
starting January 1998.
The TRMM and GPCP products used here provide monthly rainfall rates distributed on
regular latitude-longitude grids. Basin-averaged precipitation and random error are obtained by
averaging each field over all grid boxes included within the Amazon basin. As shown in Figure
3.10 (green and white dots), the relationship between basin-averaged random error and basinaveraged rainfall follows that between rain rate and random error at the grid point scale.
Figure 3.10 presents a scatter plot of monthly precipitation rate vs. random error for all
grid boxes lying within the Amazon basin and for the 60 months in the period 1997-2001,
derived from the TRMM and GPCP datasets (red and black dots respectively). Both datasets
show a strong correlation between the grid-distributed fields of rainfall rate and its random error.
This arises from the parameterization of random error for the input datasets that make up the
TRMM and GPCP combined-source precipitation estimates (microwave, infiared and gauge, in
addition to radar in the case of TRMM). For all these input datasets, the mean square error
associated with the rainfall estimate is modeled as a monotonic increasing h c t i o n of the rainfall
rate (Huffinan 1997, Alder et a1 2000).
Figure 3.10 also shows that for a given rainfall rate, the random error values assigned to
the TRMM product are significantly higher than those assigned to the GPCP product. The
parameterization of TRMM random error produces these elevated values, because it attempts to
take into account the fact that TRMM radar products are relatively recent (since December 1997)
and have not yet been extensively used and tested.
I
8.0
I
I
I
I
I
1
I
I
Figure 3.10. Rainfall rate vs.
random error from TRMM 3B43
and GPCP Combined
Precipitation
products. Black:
I
-
"
P
ad;.-
=
6.0
"
-
h
-
It
6
9
g -
-
4.0
V
Yq, "
-
&
8
-*.-pz
*= "
-
A
*
-
2.0 7
K**-&
I
4.0
I
I
I
I
10
12.0
rainfall (mm/da y)
I
1
16.0
GPCP monthly rainfall and random
error for all grid boxes lying within
the Amazon basin and for 60
months 1997-2001. Red: TRMM
monthly rainfall and random error
for all grid boxes lying within the
Amazon basin and for 60 months
1998-2001. White: GPCP
monthly basin-averaged rainfall vs.
basin-averaged random error for 60
months 1997-2001. Green:
TRMM monthly basin-averaged
rainfall vs. basin-averaged random
error for 60 months 1998-2001.
,
I
Figure 3.9 shows that the TRMM and GPCP estimates of monthly basin-averaged
precipitation for the Amazon basin agree well. In fact, both datasets combine rain-gauge data,
assembled and analyzed by the Global Precipitation Climatology Center (GPCC), with satellite-
derived estimates of surface rainfall (Huffman et a1 1997, Alder et a1 2000). This is done by fxst
applying a bias correction to the satellite-derived monthly estimates of rainfall to match those
fiom rain gauges for large-scale spatial averages (12 . 5 12.5
~ degree boxes) ( H u f h n et a1 1997,
Alder et a1 2000). This minimizes the bias in the resulting combined-source estimates but
preserves the local detail made possible by the satellite-derived information (Huffman et a1
1997). Since we are averaging the precipitation products over an even larger area encompassing
the Amazon basin, the gauge data dominates our results from both the TRMM and GPCP
datasets.
Hence, for large-scale averages of surface rainfall in the Amazon basin, the TRMM
dataset adds little value to the GPCP dataset, which extends much further back in time.
Therefore, we will rely solely on the GPCP dataset in our subsequent analysis of the Amazon's
atmospheric water budget for the 14-year period 1988-2001 (Chapter 4) and in computing basinaveraged evaporation from the water balance equation (Chapter 5).
3.4. Monthly change in total atmospheric water vapor over the Amazon Basin
Rao et a1 (1996) observed an increase in near-surface atmospheric humidity and vertically
integrated atmospheric water vapor in central Brazil, associated with the beginning of the rainy
season around the end of September. However, the magnitude of monthly precipitable water
changes over the Amazon basin has not yet been quantified, and their importance in the basin's
water budget has not been adequately characterized. Figure 3.11 presents monthly column water
vapor changes spatially averaged over the Amazon basin, derived from the three reanalyses for
the period 1997-2001. The climatologies derived from these timeseries are presented in Figure
3.12. The computation of dwldt on the horizontal grid fiom the vertically-distributed specific
humidity field and surface pressure is explained in Chapter 2.
Figure 3.1 1. Monthly
tendencies in total
atmospheric column water
vapor spatially averaged
over the Amazon basin,
computed from the three
reanalyses. Black ERA-40.
Red R- 1. Green: R-2.
I
I
I
I
I
I
I
I
I
n
I
I
I Figure 3.12. Climatology
of monthly tendencies in
total atmospheric column
water vapor spatially
averaged over the Amazon
basin, derived from the
monthly timeseries for 1997200 1. Black ERA-40. Red
R- 1. Green: R-2.
'
-
-
A
-
-
The preceding two figures show that estimates of monthly changes in total atmospheric
66
water vapor over the Amazon basin agree more closely among the different data sources in
comparison to estimates of [ q . The average standard deviation for estimates of monthly [dw/dt]
from the different reanalyses (
a
,
)
is 0.036 (Table 3.8). This is less than 10% of the range of
monthly [dw/dt] derived from any given data source (about 0.5 rnmlday). The magnitudes of
monthy [dw/dt] are evidently much smaller than those of [qand [PI (compare Figures 3.5, 3.8
and 3.10). Table 3.8 shows that the multi-year average of [dwldt] is close to zero, as expected.
ERA-40
Five-year average dwldt
(mdday)
0.00 1
R-1
0.00 1
R-2
0.002
5-year average standard
deviation (mdday)
0.036
Table 3.8. Statistics of the timeseries of monthly [dwldt] for the Amazon basin, over the period
1997-2001.
Correlation between
ERA-40 and R-1
Monthly [dwldt]
0.8 1
Correlation between
ERA-40 and R-2
0.75
Correlation between
R-1 and R-2
0.84
Table 3.9. Correlationsbetween timeseries of monthly [dwldt] for the Amazon basin derived from different
reanalyses. Timeseries extend over the period 1997-2001.
The correlations between time series of monthly [dwldt] derived from different reanalyses
are weaker than those for basin-averaged atmospheric moisture flux convergence [ q (Tables 3.7
and 3.9). This is probably because of the less evident seasonal signal in [dwldt] (Figures 3.6 and
3.12). Figure 3.I 2 shows that monthly [dwldt] becomes positive in August and turns negative
again in March. The maximum positive [dwldt] occurs in October.
3.5. Climatological atmospheric water budget for the Amazon basin, 1997-2001
For each component of the atmospheric water balance, a timeseries of monthly basin67
averaged values for 1997-2001 is derived by averaging different estimates of that component
obtained fiom the various data sources utilized in our analysis. The resulting time series for [q
and [dw/dt] are created by averaging estimates of the monthly fields derived from the three
reanalyses, ERA-40, R-1 and R-2. Similarly monthly [PIvalues derived fiom TRMM and
GPCP are averaged when both are available (1998-2001), and the GPCP estimate is used over
1997. The climatologies of the water balance components over this 5-year period are derived
fiom these 'average' timeseries. They are plotted in Figure 3.13 and listed in Table 3.10.
Figure 3.13. Climatologies of the
basin-averaged atmospheric
water balance components
derived from time series over
1997-2001, as explained in the text.
Black: Precipitation. Red:
Atmospheric moisture flux
convergence. Green: Monthly
change in total precipitable water.
January
February
March
April
May
June
July
August
September
October
November
December
[PI (mmlday)
7.3
7.7
7.5
6.7
5.6
3.8
3.O
2.5
3.6
.
4.1
5.1
6.1
[C] (mmlday)
3.O
3.4
3.1
2.5
1.6
0.3
-0.9
-1.5
-0.3
0.4
1.8
2.2
[dwldt] (mmlday)
0.04
0.05
-0.1 1
0.00
-0.12
-0.06
-0.09
0.05
0.05
0.16
0.0 1
0.04
(I [dwldt] 11 [PI)*100%
0.5
0.6
1.5
0
2.1
1.6
3
2
1.4
3.9
0.2
0.7
Table 3.10. Climatologies of the basin-averaged atmospheric water balance components derived from timeseries
over 1997-2001, as exgained in the text. he first three columns list the values plotted in Figure 12.
,
t
The strong seasonal signals in basin-averaged
[qand [PI are evident in Figure 3.13. It is
also clear that the annual cycles of these two components are well-aligned. Minimum average
precipitation over the basin occurs in August, as does minimum atmospheric moisture flux
convergence, which is actually a maximum net divergence of atmospheric water vapor. The
rainy season appears to begin in September following this minimum. However, [dwldt] values
indicate that the transition to the rainy season begins in August with a net increase in total
atmospheric water vapor during that month. This increase in total column water vapor over a
month's duration persists through February, peaking in October. Maximum basin-averaged
rainfall and atmospheric moisture convergence coincide in February. The transition to the dry
season appears to begin in March, during which the net change in total column water vapor is
negative.
Table 3.4 also lists the ratio of the magnitude of monthly column water vapor change to
that of precipitation, month by month for the climatological averages. Note that in October,
when [dwldt] is at its maximum, its magnitude remains less than 0.2 &day
on average, 4% that
of precipitation. Given the uncertainties in the other components of the water balance for the
it is then reasonable to neglect the contribution of [dwldt] to the
Amazon basin, particularly [q,
basin's monthly water budget, as it is overwhelmed by the errors in the available estimates of the
other fields.
Chapter 4 - Analysis of Basin-Averaged Atmospheric Moisture Flux
Convergence Estimates for the Amazon over the Period 1980-2001
4.1. Basin-averaged atmospheric moisture flux convergence over 1980-2001
Estimates of monthly atmospheric water vapor flux convergence spatially-averaged over
derived fiom the three reanalyses, ERA-40, R-1 and R-2, are studied for
the Amazon basin ([q)
the 22-year period 1980-2001 (Figure 4.1). The goal is to gain a better understanding of the bias
and random errors associated with estimates of this field derived fiom the various data sources.
l
1
1
1
l
1
1
1
l
1
l
1
l
l
l
l
l
l
1
1
1
Figure 4.1. Monthly [ C j
fo; the Amazon basin,
January 1980 December
2001. Black: ERA-40. Red:
R-1. Green: R-2.
-
Figure 4.2, below, presents annual averages of [CJ over the 22-year period derived from
the three sources, along with annual averages of surface runoff [R]. [R] is computed by dividing
annual discharge observed at the Obidos gauging station by the basin area. The bias errors in the
[ q estimates fiom all three reanalyses are evident. For multi-year averages, basin-averaged
atmospheric moisture flux convergence and runoff should equal each other. Table 4.1 lists the
bias error associated with each reanalysis, derived by subtracting 22-year average [R] fiom the
average [qover that period.
1
4.0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3.0
-
-
-
-
3 2-o -
'.
E
E
fl-
-/
1.0
0.0
-
Figure 4.2. Annual
averages [qand [R] for
the Amazon basin, 19802001. Black: ERA-40 [ q .
Red: R-1 [ q . Green: R-2
[ q . Blue: [R] computed
from discharge observations
at Obidos.
,
\/
'
L-
-
-
-
l
1980
.
,
I
,
.
.
1985
l
1990
"
"
19.95
22-year averages
(mdda~)
Bias error in [Cj
estimates (mmlday)
ERA-40 [ q
1.41
-1.63
[Rl
3.04
l
'
2000
Standard deviation of 22-year
timeseries of annual [Cj and [R]
estimates (mdday)
0.40
0.28
Table 4.1. Summary statistics of the timeseries of annual [CJ and [R] for the Amazon basin (outlet at Obidos), over
the period 1980-2001.
Table 4.1 also presents the standard deviations of the 22-year time series of annual [R]
and [qfiom all three sources. The standard deviations of the annual [CJ time series derived
fiom ERA-40 and R- 1 are comparable, while R-2 shows a greater variability in annual [q.
The
annual variability of discharge is smaller than that of [q(0.3 for [R] vs. 0.4 mmlday for [C'l
fiom R-1 and ERA-40). This is anticipated because of the capacity of terrestrial water storage to
smooth out variability in surface runoff.
Figures 4.3 a-c allow a closer look at the timeseries of annual [qderived fiom the three
reanalyses. There is a clear change in the record derived fiom ERA-40 between the years of
1987 and 1988 (Figure 4.34.It appears that the annual [qvalues following that point have a
positive bias relative to those preceding it. A similar transition in behavior is not apparent in the
R- 1 and R-2 data.
1
1
1
1
1
1
1
1
1
1
1
1
1
-
1
1
-
2.2~
1
1
ma -
-
Figure 4.3a. Annual
[qfor the Amazon
basin derived from
ERA-40 over 19802001 (Black),and its
22-year average
(Red).
-
1980
1985
1990
Figure 4.3b. Same as 4.3a, but for [q
derived from R-1.
1995
2000
Figure 43c. Same as 4.3a, but for [q
derived from R-2.
Such a transition in the late 1980s in atmospheric moisture flux convergence estimates
fiom ERA-40 has not been explicitly described in the literature. However, it coincides with the
time when Special Sensor Microwave Imager (SSMII) data became available (starting June
1987) for assimilation in the ECMWF reanalysis. Although reanalysis models are frozen, the
data assimilated changes over the years as new sources of data become available, which has a
major impact on the resulting analyses (Betts et a1 2005). SSMII radiances are assimilated for
the analysis of total column water vapor over the ocean. They present an important addition to
the assimilated satellite data, which was previously limited to Television and Infrared
Observational Satellite Operational Vertical Sounder (TOVS) data, relating to atmospheric
humidity and temperature profiles, and Cloud Motion Winds data from Geostationary satellites
(Betts et a1 2005, ECMWF 2005a). Note that R-1 and R-2 models similarly rely on TOVS and
Cloud Motion Winds data but do not assimilate SSMII data, potentially explaining why a similar
transition is absent in [qestimates from these reanalyses.
Betts et a1 (2005) found that ERA-40 exhibits large analysis incrementsr for total
precipitable water (TPW, equivalent to total atmospheric column water vapor) over the Amazon
basin during the period 1973-1987, resulting in large positive biases in model forecasts of
precipitation over the basin when this additional atmospheric moisture is rained out. This
phenomenon does not persist beyond 1988, possibly an indication of the influence of assimilated
SSMn data on the TPW field. Betts et a1 (2005) do not explicitly state the connection between
the assimilation of S S M radiances and the observed shift in the pattern of TPW analysis
increments. Nevertheless, their results support the observations presented previously to suggest
an important influence of SSWI data assimilation on ERA-40 analyses relating to atmospheric
moisture transport over the Amazon basin.
analysis increments are the adjustments to model forecasts towards assimilated observations.
Sudradjat et a1 (2005) carry out a global comparison of monthly averages of TPW derived
from ERA-40, R-1 and R-2, amongst each other and to estimates produced by the NVAP dataset,
over the period January 1988- December 1999. They conclude that the assimilation of SSWI
data by ERA-40 has a significant effect on the long-term mean of the TPW analysis over the
tropical oceans as well as on its variability at the monthly/seasonal and interannual timescales.
As atmospheric water vapor is transported into the Amazon basin from the tropical Atlantic
(Costa and Foley 1999), the TPW analyses over the ocean are expected to have an important
influence on the magnitude of atmospheric moisture flux convergence over the basin. They also
conclude that the negative bias in TOVS-based estimates of TPW in deep convective regions
(TOVS is unable to perform retrievals over thick cloud regions) likely leads to the
underprediction of TPW in tropical atmospheric convergence zones by analyses that depend on
TOVS data. This may explain the negative bias in ERA-40 [CJ estimates for the Amazon basin
for the period 1980-1987, for which only TOVS data were available, relative to those estimates
for subsequent years when SSWI data is assimilated to derive the TPW field.
The effect of the introduction of SSMA data on the ERA-40 analyses of upper air fields,
both on their long-term means and their variabilities at higher temporal resolutions, has not been
quantified. Hence, it is difficult to formulate an adequate correction that assures continuity in the
ERA-40 estimates of [qover the 1980-2001 time period. For this reason, our subsequent
investigation is limited to the period 1988-2001 to avoid the artificial discontinuity in ERA-40
[qdata for the Amazon basin, likely related to the start of assimilation of SSMA radiances in
TPW analyses.
4.2. Basin-averaged atmospheric moisture flux convergence over 1988-2001
Figure 4.2 shows the bias in [qestimates for the Amazon basin derived from the three
74
reanalyses, ERA-40, R-1, R2. For timeseries of monthly basin-averaged [qover the period
1988-2001, the bias can be corrected by adjusting the multi-year average of this field to match
that of discharge at the basin's outlet. This approach to correcting biases in multi-year timeseries
of [qfor river basins has been adopted by many workers. It is assumed that the bias error is
uniformly distributed throughout the year and between years. Thus, a constant bias error is
subtracted from the original monthly estimates of [q(e.g. Rasmusson 1971, Marengo 2005).
The 14-year averages of [qestimates derived from the various reanalyses for the period 19882001 and their bias errors are listed in Table 4.2. The bias-corrected estimates of annual basinaveraged [qfrom the three reanalyses, along with annual discharge at Obidos, for 1988-2001
are presented in Figure 4.4.
I
I
ERA-40 [Cj
I
14-year averages
(mdday)
1.63
I
Bias error in [Cj
estimates (mdday)
-1.46
I
I
Table 4.2. Average of [CJ for the Amazon basin over the period
1988-2001 and associated bias error derived by subtracting average
discharge at Obidos fiom average [CJ.
I
I
4.20
3.40
Figure 4.4. Annual [R] and
bias-corrected [C) for the
Amazon basin for 19882001. Black: ERA-40 [q.
Red: R- 1 [q.Green: R-2
[q.
Blue: Surface runoff
computed from discharge
observations at Obidos.
47 3.m
-.-.
E
E
2.00
Figure 4.4 shows that following bias correction, the agreement between estimates of [CJ
for the Amazon basin derived from different reanalyses remains poor, even for annual means of
this field. This is not unexpected. The availability of radiosonde observations of atmospheric
fields is poor in the Amazon region, and thus these "conventional" observations only weakly
constrain the numerical weather prediction (NWP) models of the reanalyses (Marengo 2005,
Roads 2003). Furthermore, there are important differences in the types of satellite data related to
upper air fields assimilated by the different reanalyses, as well as in the methods of assimilation
employed. While ERA-40 assimilates both TOVS and SSM/I radiances, the U.S. reanalyses do
not utilize the SSM/I data (Kalnay et a1 1996, Betts et a1 2005, Sudradjat et a1 2005). Moreover,
the U.S. reanalyses do not utilize TOVS-derived water vapor information and only assimilate the
vertical temperature soundings retrieved from TOVS sensors (Kistler et a1 1999, Trenberth and
Guillemot 1998), while ERA-40 uses three-dimensional'variational data assimilation to directly
assimilate TOVS radiances (Hernandez et al., Sudradjat et a1 2005). As TOVS radiances depend
strongly on both atmospheric temperature and humidity, the analysis of both variables is affected
(Andersson et al. 1995). Other important differences between the U.S. reanalyses and ERA-40
are related to their NWP models. Differences in their vertical and horizontal resolutions have
important effects on modeled upper-air fields (Sudradjat et a1 2005). Moreover, the three
reanalyses differ in the physical parameterizations they employ, including their convective and
boundary layer parameterizations, which affect moisture transport in the models. R-2 uses
different boundary layer, short wave radiation and convective parameterizations from those used
in R-1,and thus shows important differences in its atmospheric humidity and moisture transport
patterns (Sudjarat et a1 2005, Roads 2003, Kanamitsu et a1 2002).
The reanalysis-derived estimates of [qduring the time period of interest, 1988-2001,
may also be affected by the eruption of Mt Pinatubo in June 1991. The aerosols produced by this
eruption absorb in the infrared spectrum affecting observed radiances fiom HIRS (High
Resolution Infrared Radiation Sounder) one of the TOVS suite of instruments (ECMWF 2005b,
Sudradjat et a1 2005). Sudradjat et a1 (2005) relate this effect to a considerable positive bias in
ERA-40 analyses of TPW over the tropical oceans relative to those from R-1 and R-2 between
1992 and 1999. In our study, the rapid drop in R- 1 and R-2
[qin 1991, which persists as a large
negative bias in [qestimates from these sources through 1997, may also be associated with the
effects of aerosols produced by this eruption on TOVS-derived data (Figure 4.4, this bias is even
more evident in Figure 4.5).
In conclusion, errors in model parameterizations and in the assimilated observations (both
conventional and satellite based) produce errors in the [qestimates derived fiom available
reanalysis datasets. These errors cannot be estimated by tracking the errors associated with the
atmospheric humidity and wind speed fields that constitute C, as there are no adequate
independent observations of these fields, particularly in the Amazon basin. They must thus be
estimated by relating the resulting [ q estimates to other data that are less uncertain, particularly
river discharge at the basin outlet and precipitation.
4.3. Estimation of random error in Amazon basin [ C j by comparison to river discharge
Callede et a1 (2004) show that there is no significant autocorrelation in the annual river
discharge record at Obidos gauging station over the period 1903- 1999. This implies that net
terrestrial water storage changes at the interannual timescale averaged over the contributing
basin's area are minimal. Thus, over any given five-year period, the total atmospheric water
vapor convergence over the Amazon basin should equal the discharge at its outlet.
Random error in the bias-correctedtime series of basin-averaged [ q derived from a
given reanalysis can be estimated by moving a five-year window over the 14-year record of [q
and the concurrent record of [R], and computing the difference between time-averaged [ q and
[R] for the period corresponding to each position of that window. The five-year window begins
at 1988, covering the period 1988-1992, then shifts by one year to cover 1989-1993, and so on.
It thus covers ten five-year periods, the last one being 1997-2001. The root mean square error of
the [ q time series can then be estimated as the square root of the average random error
associated with these ten temporal intervals.
Figure 4.5. Time-averaged [ C j
and [R] for the Amazon basin
over a moving five-year window.
The x-axis lists the initial year of
each five-year interval, i.e. the [q
estimate associated with 1988 is an
average over the period 1988-1992.
Black: ERA-40 [q.
Red: R-1 [q.
Green: R-2 [q.
Blue: Surface
runoff computed fiom discharge
observations at Obidos.
Table 4.3 presents the root means square errors computed using this method for each of
R- 1, R-2 and ERA-40.
ERA-40 [Cj
RMSE (mmlday)
0.09
LC1
0.35
R-2
Table 4.3. RMSE of [qfor the Amazon
basin over the period 1988-2001,computed
by comparison to river discharge at Obidos.
(see text)
Because of the overlap between the consecutive five-year intervals, this mean error can
be associated with annual averages of Amazon basin [qestimated by each reanalysis.
However, the preceding comparison of [qestimates to river discharge yields no information
about the former's accuracy at the sub-annual time scale.
4.4. A comparison between time series of monthly [CJ and [PIfor the Amazon Basin
The preceding comparison of multi-year averages of atmospheric moisture convergence
to river discharge for the Amazon basin allows us to quantify the magnitude of the random error
in [CJ at the near-annual timescale. However, it does not provide us with any information about
how successful the various reanalyses are at representing the variability in [ q for the basin at
higher temporal resolutions. In the atmospheric water budget, surface rainfall is undeniably the
hydrologic component for which observations are most available, and which can be most
confidently quantified by available observational datasets. Hence, if a relationship can be
established between [PI and [CJ, data on the former can be used to determine the confidence of
reanalysis-derived [CJ estimates. Appendix A presents a derivation of a relationship between the
two water budget components, which can theoretically be used to test the reliability of [ q time
series at the monthly scale. However, the proposed test was unsuccessful at identifying any
difference in the accuracy of [CJ estimates simulated by the various reanalyses, and hence its
results and their discussion are confined to Appendix A.
Though the precipitation record was not successllly used for deriving a quantitative
measure of the error in reanalysis-derived [CJ at the monthly time scale, a qualitative comparison
of the [PI and [ q time series remains informative.
Figures 4.8 (a-c) present monthly anomalies of basin-averaged atmospheric moisture flux
convergence ([CJ') and precipitation ([PI'), for [CJ estimates derived fiom each of the three
reanalyses and [PI derived fkom the GPCP dataset. Figures 4.9 (a-d) present anomalies in
annual-averages of [CJ and [PI relative to their 14-year means.
Water years are used instead of calendar years to define the annual cycle, so as not to split
the rainy season over the basin in two. A water year for the Amazon basin extends between
September 1" and August 3 1" of the following year (refer to Figure 3.13; this is also the water
80
year for the Amazon basin defined by Marengo 2005 and Betts et a1 2005). Thus the 14-year
time series of monthly [CJ and [PI used in this investigation begin in September 1987 and end in
August 2001.
Figure 4.6a. Monthly anomalies of [ C j and [PIfor the Amazon basin. Black:
[PIanomaly, derived from GPCP dataset. Red: [qanomaly, derived from ERA-40.
September 1987-August 200 1.
1988
1990
1992
1994
1996
2000
1998
Figure 4.6b. Same as 4.8a;except Red [Cj anomalies derived from R-1.
I
I
1988
I
I
1990
I
I
1992
I
I
1994
I
I
1996
I
I
1998
I
I
2000
Figure 4.6~. Same as 4.8a; except Red [qanomalies derived from R-2.
-
Figure 4.7a. Annual anomalies of [ C j and [PI
from their 14-year mean. Black: [PI' from
:
GPCP. Red: [q'from ERA4O. ~ k n[q'
fiom R- 1. Blue: [CJ' from R-2. Water years,
September 1987-August 200 1. A datapoint
plotted in the beginning of 1988 is associated
with the water year Sept 1987-Aug 1988.
Figure 4.7b. Same as Figure 4.9a.Black:
[PI' from GPCP. Red: [ C j ' from ERA-40.
-1
m
19W
1 995
2000
Figure 4.7~.Same as Figure 4.9a. Black:
[PI' from GPCP. Red: [Cj' from R-1.
.za
=
I
1
]
1
1990
1
1
1
1
1
1
1995
1
1
~
t
2000
Figure 4.7d. Same as Figure 4.9a. Black:
[PI' from GPCP. Red: [Cj' from R-2.
The timeseries of [Planomalies for the Amazon basin at both the monthly and annual
timescales (Figures 4.8 and 4.9) show the characteristic signatures of El Niao and La Niaa
events. In this basin, El Niao events are associated with negative anomalies in [PI, while the
reverse is observed for La Niaa events (Marengo 2005). The El Niao events of 1991- 1992,
1992-1993, 1994-1995, and 1997-1998 (Null 2004) show up in the Amazon basin's water budget
as negative anomalies in annual [PI.The El Niao event of 1987-1988 is not reflected in the
rainfall timeseries (see possible explanation below). The events rated as strong El Niaos
1
occurring in 1991-1992, 1997-1998 (Null 2004) do in fact show up as the strongest negative
anomalies in the [PI' timeseries. The La Niiia events of 1988-1989, 1998-1999 and 2000-2001
are also reflected in the monthly and annual [PI'time series as positive anomalies. The
precipitation anomalies associated with the El Nifio events (negative anomalies) and La Nifia
events (positive anomalies) are most evident in the monthly time series around the month of
January, at the peak of the Amazonian rainy season (see Figures 4.8 a-c). During the period in
which this study is concerned, five El N 3 o events occurred in total, two of which were labeled
as strong, in comparison to three La Niiia events. Hence, we conclude that this time period may
be too short, given the unbalanced occurrences of El Niiio and La N3a events, to give a truly
representative climatological average precipitation rate at either the monthly or annual
timescales, instead producing negatively biased climatologies relative to more long-term means.
The various El Niiio and La Nifia events are reflected to different extents in the three [CJ'
time series. Figures 4.9 a-d plotting the annual anomalies of [CJ emphasize the large negative
bias that R- 1 and R-2 estimates of [CJ exhibit between 1992 and 1998 (see also Figures 4.4 and
4.5). The excessive negative anomalies in [CJ estimates from the U.S. reanalyses during this
period are neither paralleled in the precipitation timeseries nor in the river discharge record
(Figures 4.9 c-d, 4.4 and 4.5). This corroborates the conclusion that these anomalies are
artificial and possibly produced by the effects of the Mt Pinatubo eruption in June 1991 on the
U.S. reanalyses.
The root mean square errors in Amazon basin [qestimates produced by R-1, R-2, and
ERA-40, derived in section 4.3 by using discharge at the basin outlet as reference (Table 4.3),
remain the only available reliable quantitative measure of the accuracy of [qsimulated by each
reanalysis. However, they describe the accuracy of annual [CJ estimates, and provide no
information on their sub-annual accuracy. Nevertheless, we use the root mean square error
associated with each reanalysis as a general indicator of the relative reliability of [qestimates
produced by that reanalysis, regardless of temporal scale. Hence, in the following chapter, the
inverse mean square errors are used as weighting factors for the time series of monthly [q
estimated by each reanalysis, to derive a best estimate of Amazon basin [qwith monthly
resolution.
Chapter 5 -Amazonian Evapotranspiration Computed from the Atmospheric
Water Balance
Even after bias correction, the three reanalyses yield very different estimates of spatiallyaveraged atmospheric moisture flux convergence for the Amazon basin over the time period
considered, 1988-2001 (Figure 5.1). The annual-scale random error associated with [CJ
estimates produced by each reanalysis was estimated by comparing the [ q time series with data
on Amazon River discharge (Table 4.3). For lack of additional information, we assume that this
error is uniformly distributed over the year and is an adequate measure of the relative accuracy of
monthly [ q estimates produced by each reanalysis. A "best estimate" of basin-averaged
atmospheric moisture flux convergence ([el ) is then obtained by combining the bias-corrected
[ q time series fiom the three reanalyses after weighting each one by the inverse of its square
error. The weights ultimately assigned to [ q estimates fiom each reanalysis are listed in Table
0.14
0.05
0.8 1
Weight assigned to
[ q estimates
Table 5.1. Weights assigned to monthly [qestimates produced by each reanalysis to
derived the best-estimate [el. Weights are derived from the random error associated with
each reanalysis' [qestimates at the annual time-scale, obtained by comparison to Amazon
river discharge.
As expected, the best-estimate [ e l follows most closely the monthly [ q record obtained
fiom ERA-40 with a small shift toward estimates obtained fiom R- 1 (Figure 5.1)
Figure 5.1. Bias-corrected monthly [Cj derived from ERA-40(red), R-1 (blue) and R-2(green).
In black: the best-estimate [el derived as a weighted combination of [qtime series from the
three reanalyses.
Using GPCP precipitation rate and the various time series of [q(from R-1, R-2, ERA-40
and the best estimate [ e l ), basin-averaged evapotranspiration is computed at the monthly time
scale as a residual of the atmospheric water balance.
[ETI = [PI - [Cl
Figure 5.2 shows the resulting [ETJ time series, based on the various estimates of
atmospheric moisture flux convergence.
-1
.o
'
1988
1990
1992
1994
1996
1998
2000
Figure 5.2. [ E a for the Amazon basin, derived based on monthly [Cj estimates from ERA-40
(red), R-1 (blue), R-2 (green), and the best-estimate
[el (black).
It is clear from Figure 5.2 that relying on different reanalyses to obtain monthly [q
estimates for the Amazon basin results in very different evapotranspirationpatterns for the basin.
The monthly anomalies of [ET]relative to climatology for each of the resulting time series are
presented in Figures 5.3(a-c). The drop in [qestimates derived from R-1 and R-2 in the early to
mid nineties, which was discussed in Chapter 4 and highlighted in Figures 4.6 and 4.7, appears
as a positive bias in monthly [ET] estimates based on R-1 (Figure 5.36) and R-2 (Figure 5.34
during that period. As discussed in Chapter 4, this consistent bias in the early to mid nineties
appears artificial, as it does not show up in either the precipitation record (Figures 4.6 and 4.7) or
the river discharge data (Figure 4.4). The monthly anomalies of [ET]derived using [qestimates
88
fkom ERA-40 are more randomly distributed over the period investigated (1988-2001).
20
1.0
Figure 5.3a. Monthly
anomalies of Amazon basin
[ETj based on [CJ data derived
from ERA-40. Units are
mmlday. The anomaly for each
month is computed as the
diffkrence between [ET]for that
month and climatological [ETJ
for that month, over the period
1988-2001.
(10
-1.0
same as Figure 5.3a, but [ E q is based on [CJ
estimates derived from R-1.
same as Figure 5.3a, but [ETJis based on [CJ
estimates derived from R-2.
Figure 5.2 shows that the [ET]time series based on the best-estimate
[el follows closely
that based on ERA-40-derived [CJ, with a small shift towards [ET] estimates based on R-1 data.
5.1. Mean Annual [ETj
For all four time series of [ET]that were derived (Figure 5.2), the 14-year average [ET]is
2.1 mm/day. This average value is completely determined by the river discharge and rainfall
data used, since the time series of [qderived fiom all three reanalyses were bias-corrected to the
river discharge data (see Chapter 4, section 4.2). Hence, the estimate of mean annual [ET]
obtained is actually the result of a terrestrial water balance computation for the Amazon basin, in
which the change in terrestrial water storage is neglected. This is justified, because over a long
time period (14 years in this study) the net change in terrestrially stored water (such as soil
moisture, groundwater, snow and ice) is expected to be small relative to other components of the
basin's water budget. Mean [PI over our 14-year time period is 5.2 mdday, based on the GPCP
dataset, and mean runoff is 3.1 mdday, based on the record of river discharge at Obidos (see
Chapter 4, Table 4.2). The difference between these two fields yields our [ET] estimate.
The river discharge data used in this work is from Callede et a1 (2004) and is the most
accurate available for the Amazon River (refer to Chapter 2, section 2.5). Furthermore, the mean
annual runoff we computed for the basin agrees with estimates of this field computed by other
authors using different data sources and methods. Zeng (1999) and Marengo (2005) use a runoff
rate of 2.9 mmlday for the basin, which they derive by extrapolating measured discharge at
Obidos to estimate flow at the Amazon River's mouth. Roads (2002) used a mean runoff rate of
3.2 mrn/day, derived fiom the gridded global runoff dataset produced by Fekete et a1 (1999).
However, the rainfall data used in our water balance are not as certain as the runoff data.
The GPCP estimates of basin-averaged, monthly rainfall are dominated by rain-gauge data that is
assembled and analyzed by the Global Precipitation Climatology Center (GPCC) (refer to
Chapter 3, section 3.3). They fall at the lower end of estimates derived from various datasets by
Marengo (2005) (reviewed in Chapter 1, section 1.3.1). The mean annual [PIhe computes for
the period 1970-1999 based on GPCP data is 5.2 rnmlday, equivalent to that calculated here for
1988-2001. In comparison, Marengo (2005) finds that the CMAP dataset yields an estimate of
90
mean annual [PI for the same period (1970- 1999) of 5.6 &day;
the CRU dataset yields an
estimate of 6.0 mmlday; and Marengo's own estimate is 5.8 &day,
based on the rainfall
records of 164 gauging stations distributed over the basin. Hence, the GPCP precipitation data
used in this work may be negatively biased, resulting in estimates of Amazonian
evapotranspiration that are also characterized by this bias.
The value of mean annual [ET] for the Amazon basin computed in this work is
significantly lower than estimates published in the literature. However, most published estimates
were based on land surface models and are therefore less reliable than estimates based on a water
balance analysis. An exception is Callede et al's (2002) computation of evapotranspiration from
the terrestrial water balance of the Amazonian sub-basin that outlets at Obidos. Their analysis is
carried out for the period 1970-1992, using as inputs measured river discharge at Obidos and
rainfall estimated from 46 gauging stations distributed over the basin. They use the same river
discharge data that we rely upon, and compute mean runoff to be 3.2 &day.
However the
rainfall estimate they use is 6.5 mdday, much higher than that derived here based on GPCP
data. This estimate may be biased upwards, however, because of the small number of gauges
relied upon. Their ultimate estimate of mean annual [ET]is 3.3 &day.
Note that using a higher estimate for mean Amazonian precipitation of 6 &day
(such
as the estimate produced by the CRU dataset) would yield a mean annual [ET]rate of 2.9
mdday, which would still be lower than estimates of this field published in the literature.
5.2. Climatological annual cycle of [ETj
While the terrestrial water balance can be reliably used to estimate long-term mean
annual [ET] for the Amazon basin, it cannot be applied at the monthly or even annual time scale.
At these smaller time scales the change in terrestrial water storage in the basin would be a
91
significant component of the water balance, and data is not available to adequately estimate this
term. For this reason, the atmospheric water balance is applied to obtain estimates of Amazonian
[ET]at the monthly scale.
The climatological annual cycles of [ET]derived using [qdata fkom each of the three
reanalyses are very different (Figure 5.4). As expected, [ E q estimates that are based on the best
estimate [el follow closely those based on [qestimates produced by ERA-40. To clarify the
source of the differences between the various annual cycles of [ETJ,Figure 5.5 presents the
climatological annual cycles of basin-averaged rainfall and atmospheric moisture flux
convergence computed from the three reanalyses. Remember that [ET] is computed as the
difference between [PI and [q(Equation 5.1).
Figure 5.4.
CIimatological annual
cycles of Amazonian
[Eg,based on [q
estimates derived from
ERA-40(red),R-1
(blue), R-2(green),
and based on the best
estimate [el(black).
Climatological averages
are taken over the
period 1988-2001.
r
1
JAN
FEB
I
MAR
I
I
ABR
MY
1
I
JUN
JUL
I
1
AUC
S€P
I
I
I
OCT
liKW
DEC
Figure 5.5.
Climatological annual
cycles of Amazonian
[PIbased on the GPCP
dataset (black), and
[ C j derived from ERA40 (red), R-1 (blue), R2 (green).
Climatological averages
are taken over the
period 1988-200 1.
0.0
f
I
JAN
M4R
I
I
I
I
FEB
APR
W
I
JUN
I
JUL
SOP
OCT
1
I
1
1
I
AUC
W
DEC
Basin-averaged evapotranspiration computed based on R- 1 estimates of [qhas a very
pronounced seasonal cycle with a range of -3 mmlday, which follows closely the cycle of basinaveraged precipitation (refer to Figure 5.5). It peaks in the months of February-April, and
reaches its minimum in the months of August-September. This large seasonal variation in [ET]
actually results fiom the relatively small seasonal variation in Amazonian [qproduced by R-1
(see Figure 5.5). The annual cycle of [qproduced by R-1 has a range of variation of about 2.2
&day,
whereas that produced by R-2 has a range of -5 &day,
and by ERA-40, a range of
-4.2 mmlday. The difference between monthly [PIand monthly [CJ derived fiom R- 1 data
becomes smallest during the Amazonian dry season (June-September), producing the dry-season
minimum in the resulting [ET]cycle. The range of variation in the annual cycles of [ETJ
computed using [CJ estimates fiom R-2 and ERA-40 is much smaller: 1.3 &day
estimates from ERA-40 and 1 &day
using [q
using R-2 data. While the [ETJcycle based on R-1 data
would suggest water-limited transpiration in the Amazon, that based on R-2 does not, since it
93
peaks in the heart of the basin's dry season (August-September).
The annual cycle of [ET]based on [qestimates produced by ERA-40 is different fiom
the annual cycles computed using R-1 and R-2 data, and is closely followed by the [ET]cycle
based on the best estimate
[el.As our error analysis led us to have most confidence in [q
estimates produced by ERA-40, we are naturally most confident in the [ET]time series based on
these. The resulting annual cycle of [ET] has a very small range of variation, of -1.3 mmlday,
compared to a range of 4.75 mmlday for Amazonian [PIand 4.2 &day
for Amazonian [q.
ERA-40-based [ET]is out of phase with the precipitation cycle: its climatological minimum
occurs in June, leading the minimum in [PIthat occurs in August. This minimum [ET]instead
coincides with the minimum basin-averaged surface net radiation (refer to Figure 1.7),
suggesting energy-limited transpiration during the austral winter. Energy-limited transpiration
appears to persist in July and August, as [ET]increases in parallel to surface net radiation,
despite the concurrent decrease in precipitation. The derived [ E q cycle suggests a switch to
water-limited transpiration in the early months of austral summer. While surface net radiation
reaches its maximum in September and October, [ET] continues to rise along with increasing
rainfall, and it reaches its maximum in January when precipitation is near its peak.
In summary, our results based on ERA-40 suggest that on a basin-averaged scale,
Amazonian forests are not water-limited during the driest months of the year, and that their
minimum transpiration is forced by a lack of energy availability rather than water availability.
The very small seasonal variation in basin-averaged [ET]supports the idea that the forests, on
average, are buffered from the large seasonal variation in rainfall, most likely through moisture
storage in the soil.
The ERA-40 based [ET] cycle differs fiom those produced by the land surface schemes of
the NCEPNCAR and NASAIGOES-1 reanalyses, both of which are in phase with the annual
94
precipitation cycle (Zeng 1999, Werth and Avissar 2004, Marengo 2005). Furthermore, our
results show that the Amazon Basin, as a whole, acts as a moisture sink throughout the year, with
[PI > [ET]. This result contradicts the conclusions of Zeng (1999) and Marengo (2005), which
rely on the land surface models of the NASAIGOES-1 and NCEPINCAR reanalyses,
respectively, to obtain estimates of Amazonian evapotranspiration. They both find that while the
-
-
Amazon basin is a moisture sink on average [PI > [ET], it is a source of moisture to the
atmosphere during its dry season, particularly in the months of July and August when
evaporation from the basin exceeds precipitation over it. The reason for this difference is that
the estimates of Amazonian [ET]that they use are higher than ours, with means of 4.3 m d d a y
(Marengo 2005) and 4.6 d d a y (Zeng 1999) in comparison to our derived value of 2.1 mmld.
Note that the mean annual cycles of precipitation for the Amazon basin that have been
published in the literature agree closely with the annual cycle of [PI computed here based on
GPCP data. Marengo (2005) estimates precipitation over the basin from the records of 164
gauging stations. The climatological annual cycle of [PI that he computes is exactly in phase
with the one derived from the GPCP dataset, except that the wettest month has a higher
precipitation rate of 8 m d d a y compared to the 7.4 d d a y obtained here. In both his results
and ours, the minima in the [PI cycles occur at -2.5 mdday. Similarly, the CMAP dataset
produces an annual cycle of [PI that closely follows that based on GPCP data, except that it
reaches a higher peak rain rate of -8 m d d a y (Zeng 1999).
We can thus conclude that using a different data source to obtain estimates of monthly
basin-averaged rainfall for the Amazon would probably not have a large effect on the
climatological annual cycle of [ET] obtained. Nevertheless, it would be interesting to further
study the effect of using different rainfall datasets in the atmospheric water balance computation
of Amazonian [ET].
Chapter 6 - Conclusions
Spatially averaged ET over the Amazon basin was computed as the residual of the
atmospheric water balance for the basin, using estimates of basin-averaged atmospheric moisture
flux convergence fiom each of R- 1, R-2 and ERA-40, and of precipitation from the GPCP
dataset.
The mean basin-averaged ET over this period was found to be 2.1 mm/day, significantly
lower than published estimates of mean annual ET for the basin (Table 1. I ) . As discussed in
Chapter 5, this estimate is actually a result of a terrestrial water balance computation for the
basin, since the long-term means of [ q estimates fiom all three reanalyses were adjusted to
match mean Amazonian runoff. Mean precipitation over the basin is highly uncertain and is the
main source of uncertainty in the derived estimate of mean Amazonian ET. Nevertheless, using
mean annual rainfall estimates derived fiom other global precipitation datasets in the terrestrial
water balance computation would still yield a value for mean annual ET, areally-averaged over
the Amazon basin, which is lower than published estimates.
Estimates of Amazonian [ q produced by ERA-40 were found to be significantly more
accurate at the annual time scale than those produced by R-1 and R-2. Thus, they dominate the
derived "best estimate"
[el,which was computed as a weighted average of the [C'l time series
produced by the three reanalyses. Even at the monthly time scale, qualitative comparison with
rainfall time series suggests that ERA-40 estimates of [qare superior to those from R-1 and R2. The time series of Amazonian [ETJ that is based on ERA-40 estimates of [ q is thus assumed
to be the most reliable. The associated climatological annual cycle of [ET] was analyzed by
comparison to the cycles of rainfall and surface net radiation to deduce the conditions of
transpiration in the Amazon.
The precise features of this [ E q cycle are very uncertain. Since it is produced by the
difference between the [PIand [qcycles and its variability is small (on the order of 1 mm/day),
it is easily affected by errors in the monthly [PIand [ q estimates. Spatial averaging (over the
Amazon basin) and temporal averaging (over the 14 year period) does increase the confidence in
our results, as it allows for cancellation of random errors. Perhaps the most certain feature of the
ET cycle is its minimal variability compared to the seasonal variation of rainfall in the Amazon.
This in itself is interesting and points to the importance of terrestrial control on transpiration in
the Amazonian forests.
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Appendix A: An analysis of the relationship between time series of monthly [ C j and [Pj
for the Amazon Basin
The comparison of multi-year averages of atmospheric moisture convergence to river
discharge for the Amazon Basin allows us to quantify the magnitude of the random error in [q
at the near-annual timescale. However, it does not provide us with any information about how
successful the various reanalyses are at representing the variability in [ q for the basin at higher
temporal resolutions. In the atmospheric water budget, surface rainfall is undeniably the
hydrologic component for which observations are most available and which can be most
confidently quantified by available observational datasets. Hence, if a relationship can be
established between [PIand [q,data on the former can be used to determine the confidence of
reanalysis-derived [Cj estimates. The relationship between the two components will be
elaborated below and used to evaluate the various reanalyses' ability to replicate the "true"
monthly-scale variability in [ q for the Amazon basin.
The atmospheric water balance equation at the monthly timescale can be written as
[c],= [PI
z. - [ET]i
+[ h l d t ]
,
[All
i is an index indicating the month for which the balance is applied. For every month, each
component of the water budget can be separated into its climatology and its anomaly, which is
the difference between its value for that particular month and that month's climatological value
(the average for that month over several years).
[C], [C]:= [PI, [PI: - [ET],- [ET]: [dwldt], [ d ~ / d t ] :
+
+
+
+
The overbar indicates the climatological value of the water budget component for a
particular month, and the apostrophe indicates its anomaly for month (i). The water balance
applies to both the climatologies and anomalies. Hence, for any given month (0, we can write
We can assume that the magnitudes of the monthly anomalies of precipitable water
tendency [dwldt] are negligible relative to those of atmospheric moisture convergence and
precipitation. This assumption is reasonable, since the magnitude of [dwldt] itself is negligible
relative to that of [PI, and hence its anomaly can be similarly neglected. Thus, the following
equality holds:
The relationship between time series of [CJ' and [PI', which we seek, is thus modulated
by the sign and magnitude of the evapotranspiration anomalies, for which no reliable data is
available. Rasmusson (l968), in analyzing the error associated with the [ q estimates for the
U.S. Central Plains and Eastern Regions derived from radiosonde data, makes the assumption
that monthly evapotranspiration anomalies are negligible relative to precipitation anomalies, and
hence the variability of monthly [CJ and [PI time series should be equivalent. This bold
assumption is avoided in this analysis, because the controls on evapotranspiration in the Amazon
are still so poorly understood. We also cannot make any assumption concerning the relative
magnitudes of the precipitation and atmospheric moisture flux convergence anomalies, since the
sign of [ET]' can neither be determined based on available data nor based on our understanding
of the basin' s hydrology.
As discussed in Chapter 1, the energy versus water limitation of evapotranspirationin the
Amazon basin during different months of the year is not yet well understood and is variable
throughout the basin's extent, as shown by field data. Hence, the relative signs of the
precipitation and evapotranspiration anomalies are not known and are likely to vary between
months and seasons. For example, a positive precipitation anomaly during the dry season may
produce a positive anomaly in otherwise water-limited evapotranspiration. Yet, during the wet
season, when evapotranspiration is possibly energy limited and greater precipitation is associated
103
with increased cloudiness, a positive [PI' may produce a negative [ET]'.
An alternative assumption, which can be used to investigate the accuracy of the monthly
[qtime series, is that the magnitude of the precipitation anomaly [PI' in any month is greater
than that of the evaporation anomaly [ET]',though not necessarily so much greater that the latter
can be neglected. This assumption can be justified to a reasonable extent by referring to a
readily available dataset of field-measured monthly evapotranspiration and precipitation
collected over a year's duration, between September 1995 and August 1996, in an old-growth
forest site in the Cuieriras reserve, located 60 km north of Manaus (Malhi et a1 2002; this study is
also discussed in section 1.3.4) (Figures A1 and A2). The monthly ET data from this site reflects
two distinct environmental conditions: i) energy-limited ET during the wet season; ii) waterlimited ET during the dry season (Malhi et a1 2002). In both these conditions, it is evident that
month-to-month variability in ET is much more limited than that in P. During the wet season
(February-June), when evapotranspiration at this site is energy limited, variability in monthly
rainfall, which produces variability in net surface radiation, exceeds variability in monthly
evapotranspiration (Figure Al). Moreover, while monthly P varies over 200mm during the
studied year, the range of variation in monthly ET between the dry and wet seasons does not
exceed 25mm (Figure A2). Hence, the signal of the acute decline in rainfall is greatly dampened
in the ET record, even when the trees are shown to experience water limitation during the low
rainfall period. At other forest sites in the Amazon, where transpiration has been shown to
experience no water limitation during the dry season (Nepstad et a1 1994, Da Rocha et a1 2002,
Carswell et a1 2002), we expect even more terrestrial control on ET, further limiting its monthto-month variability. Additional field data, collected at other sites and over longer time periods
would be usehl in further supporting our assumption; however, it is not readily available at this
time.
Monthly P and ET for Cuieiras site
I -t Precipitation
Evapotranspiration I 1
Figure Al. Monthly precipitation and evapotranspiration for September 1995-August 1996,
measured in an old-growth forest in the Cuieiras reserve. Plotted fkom data presented in Malhi et a1
(2002).
Monthly E for Cuieiras site
60
55
50
E 45
1
+Evapotrans
piration
40
35
30
Month
Figure A2. Monthly evapotranspirationfor September 1995-August 1996, meamred in an old-growth
forest in the Cuieiras reserve (same evaporation time series as in Figure 4.6). Plotted fkom data
presented in Malhi et a1 (2002).
Following from the assumption that
I[P]~
> J [ E T ] [PI'
~ , and [CJ' must be of the same
sign. This criterion can be used to examine the validity of monthly [CJ estimates produced by
the various reanalyses.
The GPCP Combined Precipitation (Version 2) dataset is used to obtain estimates of
monthly basin-averaged rainfall for the period under investigation. Since the following analysis
is based on computing climatologies of the water budget components, water years are used
instead of calendar years to define the annual cycle, so as not to split the rainy season over the
basin in two. A water year for the Amazon basin extends between September 1'' and August 3 1''
of the following year (refer to Figure 3.13; this is also the water year for the Amazon basin
defined by Marengo 2005 and Betts et a1 2005). Thus the 14-year time series of monthly [Cj and
[PI investigated below begin in September 1987 and end in August 200 1.
Figures A3 (a-c) present the monthly anomalies of basin-averaged atmospheric moisture
flux convergence and precipitation, for [qestimates derived fkom each of the three reanalyses
and [PI derived fiom the GPCP dataset. Figures A4 (a-d)present anomalies in annual-averages
of [qand [PI relative to their 14-year means.
Figure A3a. Monthly anomalies of [ C j and [PIfor the Amazon basin. Black:
[PI anomaly, derived fiom GPCP dataset. Red: [qanomaly, derived fiom ERA-40.
September 1987-August 200 1.
1988
1990
1992
1994
1996
1998
2000
Figure A3b. Same as A3a; except Red [ C j anomalies derived from R-1.
Figure A3c. Same as A3a; except Red [ C j anomalies derived from R-2.
Figure A4a. Annual anomalies of [ C j and [PI
from their 14-year mean. Black: [PI' fiom
GPCP. Red: [ q ' fiom ERA-40. Green: [CJ' fiom
R- 1. Blue: [q' from R-2. Water years,
September 1987-August 2001. A datapoint
plotted in the beginning of 1988 is associated
with the water year Sept 1987-Aug 1988.
-Wb
1990
1993
2000
Figure A4c. Same as Figure 4 . 9 ~Black:
.
[PI' fiom GPCP. Red: [Cj' from R-1.
Figure A4b. Same as Figure 4 . 9 ~Black:
.
[PI' fiom GPCP. Red: [qtfrom ERA-40.
m
1990
1995
2000
Figure A4d. Same as Figure 4 . 9 ~Black:
.
[PI'from GPCP. Red: [ C j ' from R-2.
Table Al, below, lists the correlation between the timeseries [CJ'and [PI'for C estimates
derived fiom each of the three reanalyses. The second column lists the number of months in
each timeseries of [q'
(total number of monthsfor 1987-2001=168) for which the sign of the
anomaly [q' matches that of the basin-averaged precipitation anomaly.
Note that the correlation between monthly, basin-averaged [PI'and [CJ'is practically
equivalent for all three reanalyses. However, while the correlation between the two timeseries is
an interesting statistical property, we cannot assume that a higher correlation associated with a
particular data source for C is indicative of a more accurate reanalysis. Since we expect a change
in the relative magnitudes and relative signs of [PI' and [ET]'fiom month to month, we expect P'
and C' not to be perfectly correlated.
The test of the percentage of total months in the time series for which the monthly
precipitation anomalies are matched in sign by the concurrent convergence anomalies appears
unsuccessful at distinguishing between the three reanalyses in relation to their ability to capture
monthly-scale variability in [ q . According to this criterion, for all three data sources, 60% of
the 14-year time series of monthly [ q for the Amazon basin shows physical consistency with the
precipitation time series. Note, however, that in the case of R-1 and R-2, the large negative bias
in their [ q estimates between 1992-1999 may be rendering this test inadequate, because the
resulting climatological annual cycles of [ q are artificially negatively biased.
Correlation between # of months (out of
and [PI' 168) for which [q'
monthly [q'
and [PI1
match in
sign (mmlday)
0.49
106
Table Al. 1"' column: Correlation between timeseries of monthly [q'and [PI'
for the Amazon basin. 2"' column: Number of months in the timeseries
(total 168 months) for which [q'and [PI' match in sign (see text).
In conclusion, the relative accuracy of time series of monthly [ q for the Amazon basin
derived from R- 1, R-2, and ERA-40, could not be quantified by using a concurrent time series of
monthly basin-averaged precipitation as reference. Nevertheless, a comparison of time series of
monthly and annual anomalies of [CJ and [PI was very useful for qualitatively identifying
grossly inconsistent atmospheric water vapor flux convergence estimates, such as the negativelybiased R-1 and R-2 [CJ estimates in the 1990s.
109