Water Resources Research
Supporting Information for
Identifying multiple time-scale rainfall controls on Mojave Desert ecohydrology
using an integrated data and modeling approach for Larrea tridentata
Gene-Hua Crystal Ng*,a ([email protected]), David R. Bedfordb ([email protected]),
David M. Millerc ([email protected])
*Corresponding author
of Minnesota – Twin Cities, Department of Earth Sciences, 310 Pillsbury Dr SE, Minneapolis, MN
55455-0231, 612-624-9243
bU.S. Geological Survey, 345 Middlefield Rd, Menlo Park, CA 94025, United States
Contents of this file
Text S1 to S7
Figures S1 to S6
This supplementary information section includes text detailing the model calibration
procedure, which includes some of the data-processing steps and uncertainty
parameterization (Text S1-S5). Supplementary Text S6 describes the method used for
the spectral analysis. Supplementary figures include site photos, comprehensive plots
of the calibration data, and exhaustive parameter estimates and site simulations. The
figures supplement the example parameters, site, and statistical results presented in the
main manuscript.
Text S1. EnKF Implementation
The following implementation specifications were chosen based on results found
by Ng et al. [2014] for various EnKF configurations. We use the mean-preserving square
root formulation with random orthogonal ensemble rotations by Sakov and Oke [2008],
and we apply a factor-of-two inflation to the observational error covariance in the update
equation. An assimilation cycle time of 30 days is used, with new data over that time
period assimilated in a batch fashion. An ensemble size of 100 is implemented based on
preliminary tests.
Text S2. Soil Moisture Data: Bias Correction
The problem of assimilating biased soil moisture observations with land-surface
models has been raised by others (e.g., De Lannoy et al. [2007], Reichle et al. [2004], and
Reichle and Koster [2004]). Our in-situ soil moisture data is susceptible to biases due to
extreme dry conditions and mechanical perturbation of high gravel content soils during
probe installation. It is usually difficult to quantify bias because observations typically
represent the best knowledge of the state. One solution is to assimilate normalized soil
moisture, where the time series has the mean removed and is scaled by the standard
deviation [Reichle et al. 2004]. We similarly scale and shift the raw soil moisture data
based on assumptions about physically reasonable desert soil moisture values, which we
know to span a large dynamic range from extremely low soil moisture levels during dry
periods, to fast wetting during heavy rain events. Specifically, for probes that measured
time series with an unrealistically low dynamic range of soil moisture substantially less
than about half of saturation (TB4 at 15 cm, TA1 at 35 cm), we applied a multiplicative
factor of two. The soil moisture records were also shifted (after scaling where
applicable) to ensure minimum values close to but greater than zero; this required adding
a small value around 0.02 to 0.06 to the record (TB5 15cm: 0.03, 35cm: 0.03; TB4 15cm:
0.03, 35cm: 0.03; TA3 15cm: 0.02, 35cm: 0.02; TA1 15cm: 0.03, 35cm: 0.06). Finally,
we also screened out occasional periods when soil moisture values appeared excessively
noisy, due to freezing temperatures or other factors. The adjusted soil moisture time
series that were assimilated into the model are shown in Figure (S2). Independent of the
actual scaling and shifting parameters, the relative dynamical information remains intact
and thus effective for conditioning simulations of plant water usage.
Text S3. MODIS Leaf-Area-Index Data: Validation with Field Data
MODIS LAI data (MOD 15) is a level 4 data product available at 1 km, 8-day
resolution. The data were freely downloaded from the LP DAAC data pool
(https://lpdaac.usgs.gov/get_data/data_pool). Data for days with ≤10% cloud cover at
our study area were used, which included about 80% of the dates. The MODIS data has a
reported standard deviation error of 0.1 for LAI. Although MODIS data is available
starting mid-2002, observations are assimilated with the model starting 2 July 2007, when
soil moisture observations became available at the study sites. Similar to findings by
Pauwels et al. [2007], preliminary results showed that assimilating both vegetation and
soil moisture observations is necessary for properly conditioning the coupled
ecohydrological model. We extracted from the MODIS data set the observed LAI values
for the pixels corresponding to our study sites (Figure (S2)). As validation, the typical
MODIS LAI value of 0.2 compared well with field measurements on 17 March 2011 for
Larrea tridentata and Ambrosia dumosa plants within a 195 m2 wash plot and 176 m2
interfluvial plot at the TB5 site. Using areal percent coverage observations over the two
plots (~16% Larrea tridentata and ~6% Ambrosia dumosa) and repeat plant-scale
measurements made with an AccuPAR model LP-80 PAR/LAI ceptometer (Decagon
Devices, Pullman, WA), we determined an area-average LAI of about 0.17 to 0.26.
Ambrosia dumosa contributed an area-average LAI of about 0.07. Because this is below
the MODIS error limit, and to avoid under-representation of root-uptake in our
calibration to soil moisture measurements, we attribute the full MODIS measurement to
the dominant shrub type Larrea tridentata in this study.
Text S4. Meteorological Time Series Compilation Procedure
Meteorological data was gathered at our study sites starting 1 July 2007. The
record before 1 July 2007 was filled using data from other locations. For the time period
of 1 January 2004 to 2 July 2007, available meteorological data from one of our other
nearby monitoring sites “Kel-Met” (located at 648 m elevation about 6 km to the south)
were included. For earlier periods, hourly meteorological data at Las Vegas (elevation
664.5 m) are available from the NCDC Solar and Meteorological Surface Observation
Network dataset (for 1961-1990) and the National Solar Radiation Database (after 1990).
We filled periods of missing data (only 4 months and some partial months) using a
simple hourly disaggregation of daily NCDC precipitation data from Barstow, CA
(elevation 676.7 m). Monthly rainfall for Las Vegas compared well with our Kelso
Valley study area over the common 2004-2010 observation period, and we elected to
directly include rainfall data from Las Vegas to avoid adjustments that may compromise
realistic temporal structures in rainfall that could be ecologically important. Minor
average differences in hourly temperature, humidity, pressure, and wind calculated
between Las Vegas and our study area were used to generate additive adjustments to Las
Vegas measurements to fill our meteorological record.
Text S5. Soil Parameter Uncertainty Model
Similar to Ng et al. [2009], soil texture measurement uncertainty was assumed to
follow a Gaussian first-order autoregressive process with depth. Following the relatively
homogeneous properties observed for Holocene soils found at our study sites [Nimmo et
al., 2009], the deepest soil texture measurement (5-10 cm) were extended as the nominal
value to lower soil layers. Standard deviation values of 10 percent sand content and 5
percent clay content were based on the range of nearby measurements on Holocene soils.
Starting with the vertical length-scale parameter value of 0.996 calculated in Ng et al.
[2009] as a basis, we apply a lower length scale parameter of 0.95 (with a 1-cm depth
resolution) to account for greater uncertainty due to a lack of detailed vertical data.
Uncertainty measures for the pedotransfer functions were based on average differences
between the original CLM pedotransfer function results and observed soil properties
(water retention relationships and hydraulic conductivity), which resulted in additive
Gaussian error perturbations with the following standard deviations: σ(B)=0.5, σ(ψsat)=10
mm, σ(θsat)=0.05, correlation-of-variation(ln(Ksat))=2. Perturbed B were also
constrained to ≥ 2.3 to avoid numerical problems. In contrast to the AR-1 perturbations
with depth for soil texture, we assume a constant correlation of 0.7 over all depths for the
hydraulic parameter perturbations, in order to represent consistent errors in the
pedotransfer scheme rather than spatial variability. Finally, we averaged soil parameter
values over the bottom 7 computational soil layers, covering the interval of 9.1-380 cm,
in order to facilitate parameter-conditioning and maintain estimates that were consistent
with homogeneous conditions observed for Holocene soils in the Kelso Valley area
[Nimmo et al., 2009].
Text S6. Spectral Analysis
Employing the window-closing method (see e.g., textbook by Jenkins and Watts
[1969]), smoothed spectral results were calculated using the Bartlett window with a
truncation point of 64 months. This truncation point corresponds to a sampling frequency
of 0.0031 mon-1, or once per ~27 years. Note that this sampling frequency is about the
PDO time scale of 20-30 years, which makes it difficult to detect the presence of PDO.
Spectral analysis results are shown in Figure (S6).
Text S7. References for Supplementary Text
De Lannoy, G. J., Reichle, R. H., Houser, P. R., Pauwels, V., & Verhoest, N. E. (2007).
Correcting for forecast bias in soil moisture assimilation with the ensemble Kalman
filter. Water Resources Research, 43(9).
Jenkins, G.M. and D.G. Watts (1969), Spectral Analysis and Its Applications, Holden Day,
San Francisco, CA.
Ng, G.-H. C., D. McLaughlin, D. Entekhabi, and B. Scanlon (2009), Using data
assimilation to identify diffuse recharge mechanisms from chemical and physical
data in the unsaturated zone, Water Resour. Res., 45, W09409,
Ng, G.-H. C., D. R. Bedford, and D. M. Miller (2014), A mechanistic modeling and data
assimilation framework for Mojave Desert ecohydrology, Water Resour. Res., 50,
Nimmo, J. R., K. S. Perkins, K. M. Schmidt, J. D. Stock, D. M. Miller, and K. Singha
(2009), Hydrologic characterization of desert soils with varying degrees of
pedogenesis. 1: Field experiments evaluating plant-relevant soil water behavior,
Vadose Zone J., 8, 480–496.
Pauwels, V. R. N., N. E. C. Verhoest, G. J. M. De Lannoy, V. Guissard, C. Lucau, and P.
Defourny (2007), Optimization of a coupled hydrology- crop growth model through
the assimilation of observed soil moisture and leaf area index values using an
ensemble Kalman filter, Water Resour. Res., 43, W04421,
Reichle, R. H., & Koster, R. D. (2004). Bias reduction in short records of satellite soil
moisture. Geophysical Research Letters, 31(19).
Reichle, R. H., Koster, R. D., Dong, J., & Berg, A. A. (2004). Global soil moisture from
satellite observations, land surface models, and ground data: Implications for data
assimilation. Journal of Hydrometeorology, 5(3), 430-442.
Sakov, P. and Oke, P. R. 2008a. Implications of the form of the ensemble transformation
in the ensemble square root filter. Mon. Wea. Rev. 136, 1042–1053.
Figure (SI1)
Study area: Kelso Valley Watershed in Mojave National Preserve, southeastern
California. Observations from the indicated sites (TB5, TB4, TA3, and TA1) are used in
this data assimilation study. Reproduced from Ng et al. [2014].
Figure (SI2)
Data for the four study sites (dark blue: TB5, light blue: TB4, green: TA3, red: TA1).
Daily soil moisture moisture data from EC-2O probes at a) 15 cm and b) 35 cm depths
from the 4 study sites. c) 8-day MODIS LAI data for pixels corresponding to each of the
study sites. EC-2O soil moisture probes have volumetric soil moisture measurement
error of sqrt(R) = 0.04 m3/m3. MODIS has LAI measurement error of sqrt(R) = 0.1.
Note that integer years on the x-axis correspond to the start of the year (e.g. 2008.0 is 1
January 2008).
Figure (SI3)
All plant parameter estimates over cumulative assimilation time. 25, 50, 75th percentiles
shown in dark blue and black.
Figure (SI4)
Boxplots of prior (red) and data-conditioned (light blue) distributions for all soil
parameters for all sites.
Figure (SI5.1)
b) and c) Correlations for conditioned simulations for TB5 closely follow results for TA1
in Figure (7)b-c in main text.
Figure (SI5.2)
b) and c) Correlations for conditioned simulations for TB4 closely follow results for TA1
in Figure (7)b-c in main text.
Figure (SI5.3)
b) and c) Correlations for conditioned simulations for TA3 closely follow results for TA1
in Figure (7)b-c in main text.
Figure (SI6)
a)-c) Smoothed auto-spectra of 50-year monthly rainfall time series (solid blue line),
simulated ensemble median of LAI for TA1 (dash-dotted blue line), and simulated
ensemble median for soil moisture in the a) 2nd layer, b) 5th layer, and c) 8th layer
(dashed blue line), with the 80% confidence interval (light blue) shown for a log scale.
d)-f) After aligning the time series according to peak cross-correlation lags, spectral
coherency of rainfall, LAI, and soil moisture at the same three soil layers as a)-c), with
the 95% confidence interval shown for a transformed arctanh axis. The circled asterisk
indicates the maximum cross-correlation. Note that results for rain and LAI are repeated
in a)-c) and d)-f) to facilitate visual comparisons for soil moisture results at the different