HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-21-1849-2017Estimating annual water storage variations in medium-scale (2000–10 000 km2) basins using microwave-based soil moisture retrievalsCrowWade T.wade.crow@ars.usda.govhttps://orcid.org/0000-0002-8217-261XHanEunjinRyuDongryeolhttps://orcid.org/0000-0002-5335-6209HainChristopher R.AndersonMartha C.https://orcid.org/0000-0003-0748-5525USDA-ARS Hydrology and Remote Sensing Laboratory, Beltsville, MD, USAInternational Research Institute for Climate and Society, Columbia
University, NY, USAMelbourne School of Engineering, The University of Melbourne, Parkville, Victoria, AustraliaNASA Marshall Space Flight Center, Earth Science Branch,
Huntsville, AL, USAWade T. Crow (wade.crow@ars.usda.gov)29March2017213184918623November201621November201610February201716February2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://hess.copernicus.org/articles/21/1849/2017/hess-21-1849-2017.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/21/1849/2017/hess-21-1849-2017.pdf
Due to their shallow vertical support, remotely sensed
surface soil moisture retrievals are commonly regarded as being of limited
value for water budget applications requiring the characterization of
temporal variations in total terrestrial water storage (dS/ dt). However, advances
in our ability to estimate evapotranspiration remotely now allow for the
direct evaluation of approaches for quantifying dS/ dt via water budget closure
considerations. By applying an annual water budget analysis within a series
of medium-scale (2000–10 000 km2) basins within the United States, we
demonstrate that, despite their clear theoretical limitations, surface soil
moisture retrievals derived from passive microwave remote sensing contain
statistically significant information concerning dS/ dt. This suggests the
possibility of using (relatively) higher-resolution microwave remote sensing
products to enhance the spatial resolution of dS/ dt estimates acquired from
gravity remote sensing.
Introduction
Within the past decade, the analysis of data products from the Gravity
Recovery and Climate Experiment (GRACE) satellite mission (Tarpley et al.,
2004a, b) has led to an enhanced appreciation of the role played by
interannual variations of total terrestrial water storage (dS/ dt) within the
terrestrial water budget (Chen et al., 2009; Rodell et al., 2007; Syed et al., 2008). However, the application of GRACE storage retrievals is potentially
limited by their extremely coarse spatial resolution (∼ 200 000 km2). This has spurred interest in the development of spatial
downscaling techniques for GRACE-based dS/ dt. These approaches have generally
been based on the use of (relatively) higher-resolution water storage
predictions obtained from distributed land surface model predictions (Reager
et al., 2015; Wan et al., 2015) or a combination of land surface model
output and independent evapotranspiration (ET) and precipitation (P) flux
estimates (Ning et al., 2014). In contrast, microwave-based surface soil
moisture (θ) retrievals provide a direct assessment of soil water
storage that can be obtained at relatively finer resolutions (typically
∼ 1000 km2). However, such retrievals are hampered by
both shallow vertical support (reflecting soil moisture conditions only in
the top several centimeters of the soil column) and substantially reduced
accuracy for dense vegetative cover. As a result, they are generally assumed
to be of limited value for the examination of dS/ dt and are commonly neglected in
water budget studies. However, recent empirical work demonstrates that
microwave-based θ retrievals are generally well-correlated with
GRACE-based storage estimates (Abelen and Seitz, 2013; Abelen et al., 2015). This
suggests that θ retrievals retain some value for water-balance
studies – particularly at spatial scales finer than the resolution of GRACE
products.
Confirming such potential will require the availability of accurate
terrestrial water flux variables. Recent progress in the remote sensing of
dS/ dt and θ has been mirrored by the increased consideration of
satellite-derived ET retrievals in a water balance context (Senay et
al., 2011; Hain et al., 2015; Hendrickx et al., 2016; Wang-Erlandsson et
al., 2016). In particular, when combined with P and basin-outlet stream flow
(Q) measurements, satellite-derived ET estimates can be used to verify
estimates of dS/ dt obtained from independent sources (Han et al., 2015). This opens
up the possibility for the objective “top-down” evaluation of dS/ dt estimates
obtained from various remote sensing sources and the opportunity to
empirically confront “bottom-up” expectations for these products based
solely on theoretical considerations.
Here, we combine ET estimates acquired from thermal infrared (TIR)
remote sensing with ground-based Q and P measurements to evaluate the water
balance performance of passive microwave (PM) estimates of annual dS/ dt for a set
of medium-scale (2000–10 000 km2) river basins within the United
States. The analysis will focus on two primary tasks: (1) evaluating the
suitability of existing ET, Q, and P datasets to accurately estimate dS/ dt and
(2) empirically investigating the ability of interannual dS/ dt estimates acquired
from microwave remote sensing of soil moisture to close the interannual
terrestrial water balance. As discussed above, this particular application
of θ is arguably inconsistent with their known theoretical
limitations. Therefore, our focus will be on empirically evaluating their
ability to provide dS/ dt closure within an annual water budget analysis and
examining how these results fit with a priori theoretical expectations.
Section 2 describes the water balance datasets and study basins. Section 3
examines the ability of existing flux and storage products to close the
terrestrial water balance within a set of larger-scale
(150 000–1 000 000 km2) hydrologic basins where GRACE-based dS/ dt can be
directly utilized (see task #1 defined above). Based on verification
results in Sect. 3, Sect. 4 derives a technique for estimating dS/ dt from
microwave remote sensing and evaluates the ability of microwave-based dS/ dt to
close the terrestrial water balance within a second set of medium-scale
(2000–10 000 km2) basins (see task #2 defined above). Results are
discussed in Sect. 5 and conclusions summarized in Sect. 6.
Study basins and datasets
Within a closed hydrologic basin, the annual water budget equation can be
summarized as follows:
P-Q-ET=dS/dt,
where P, Q, and ET (mm yr-1) represent annual sums of fluxes, and
dS/ dt (mm yr-1) is the annual change in terrestrial water storage. Besides
Q, all other lateral water fluxes (into or out of the basin) are assumed to
be negligible. See Sect. 2.2 below for a description of data products used
to describe flux terms on the left-hand side of (1). Here, the storage
change term dS/ dt is independently obtained using both gravity-based (GR)
retrievals of total terrestrial water storage and PM-based retrievals of surface soil moisture content. In both cases, annual
change estimates are based on the differencing of temporally averaged
storage retrievals acquired at (or near) the end of each calendar year.
Based on constraints associated with the availability of various remote
sensing products, the analysis is conducted within a time period from 1 January 2003 to
31 December 2010. Additional methodological details are given
below.
Map of the 5 large-scale basins (color shading – see
Table 1) and 16 unregulated medium-scale basins (red outlines – see Table 2)
considered in the analysis.
Attributes of large-scale basins in Fig. 1.
River basinUSGS stationUSGS station nameBasin sizeAnnual PRunoff rationo.(km2)(mm)Q/PMissouri06934500Missouri River at Hermann, MO1 347 5565630.10Arkansas07263450Arkansas River at Little Rock, AR409 2017470.14Red07344370Red River at Spring Bank, AR153 9068500.13Upper Miss.07022000Mississippi River at Thebes, IL496 0168980.31Ohio03611500Ohio River at Metropolis, IL527 55711870.45Study basins
For the analysis, hydrologic basins are sought with the following: excellent ground-based
rain gauge coverage, the availability of good remotely sensed ET
products, and the relative absence of complex topography and/or dense
vegetation conditions known to reduce the accuracy of existing long-term,
satellite-based soil moisture products. In addition, arid areas are avoided
due to their known lack of interannual dS/ dt variability. The North American
Mississippi River system is one of only a handful of continental-scale river
basins that generally meets all of these criteria. Therefore, water budget
closure will be examined in two separate sets of basins within the
Mississippi River system. To start, a large-scale analysis will be conducted
on five major Mississippi River sub-basins: the Missouri, the Arkansas, the
Red, the Ohio and the Upper Mississippi – see Fig. 1 and Table 1. The
primary focus in these large-scale basins will be evaluating the ability of
existing P, Q, ET, and GRACE-based dS/ dt product to close the annual water
budget. The results of this water balance analysis will then be used to
refine the geographic focus and water flux processing approach applied in
the medium-scale analysis described below.
Attributes of medium-scale basins in Fig. 1.
BasinUSGS stationUSGS station NameBasin sizeAnnual PRunoff rationumberno.(km2)(mm)Q/P107144780Ninnescah River AB Cheney Re, KS20497680.08207144200Arkansas River at Valley Center, KS34028420.11307152000Chikaskia River near Blackwell, OK48918960.19407243500Deep Fork near Beggs, OK52109450.15507147800Walnut River at Winfield, KS48559800.31607177500Bird Creek Near Sperry, OK236010250.23706908000Blackwater River at Blue Lick, MS292411400.29807196500Illinois River near Tahlequah, OK249211750.29907019000Meramec River near Eureka, MO976611870.281007052500James River at Galena, MO256812550.311107186000Spring River near Wace, MO298012580.271207056000Buffalo River near St. Joe, AR214812380.371306933500Gasconade River at Jerome, MO735612930.241407067000Current River at Van Buren, MO435113090.311507068000Current River at Doniphan, MO532313140.361607290000Big Black River NR Bovina, MS722713680.37
Following this large-scale water balance analysis, the performance of a
microwave-based dS/ dt proxy is examined within 16 (smaller) medium-scale
(2000–10 000 km2) unregulated basins positioned along an east–west
transect across the United States Southern Great Plains (SGP) region (see Fig. 1 and Table 2). A complete justification of this geographic emphasis
is given in Sect. 3. However, in general, medium-scale basins were
selected following a screening analysis applied by the Model Parameter
Estimation Experiment project (Duan et al., 2006), which removed basins with
either inadequate rain gauge coverage or excessive human regulation of
stream flow. Moving from west to east, these basins exhibit progressively
higher mean P and annual runoff ratios (Q/P) (Fig. 1 and Table 2). Associated
with this climatic gradient is a gradual west–east increase in vegetation
biomass. Western basins are characterized by large fractions of rangeland,
grassland, and winter wheat land cover with relatively low biomass. In
contrast, basins located along the eastern edge of the transect contain
significant upland forest cover and intensive summer agricultural
cultivation in low-lying areas.
Data products and processing
A range of ground and remotely sensed datasets were acquired to
characterize components of the terrestrial water balance summarized in Eq. (1).
The acquisition and processing of these datasets is described below.
Thermal remote sensing of ET
Daily evapotranspiration estimates were obtained from the Atmosphere–Land
Exchange Inverse (ALEXI) algorithm. In particular, ALEXI exploits the
moisture signal conveyed by the mid-morning rise in satellite-observed land
surface temperature (LST) in order to capture water limitations on surface
energy fluxes (Anderson et al., 2007a, b; Hain et al., 2009, 2011). Based on
this principle, ALEXI produces estimates of daily evapotranspiration without
direct knowledge of antecedent precipitation or soil water balance
considerations (Anderson et al., 2011). This ensures that ALEXI
evapotranspiration estimates are independent of those derived via water
balance calculations.
ALEXI evapotranspiration has been evaluated using a spatial disaggregation
technique (DisALEXI) which uses high-resolution LST retrievals from Landsat
to downscale ALEXI fluxes to a 30 m pixel level (Anderson et al., 2004).
Typical accuracies obtained in comparison with eddy-covariance tower
observations are on the order of 5 to 15 % for daily to seasonal
evapotranspiration estimates during snow-free periods (Anderson et al.,
2012; Cammalleri et al., 2013, 2014a; Semmens et al., 2016).
Here, the ALEXI model was processed over CONUS at a spatial resolution of
4 km for the period 2003–2010 and forced with meteorological inputs from
the Climate Forecast System Reanalysis (CFSR; Saha et al., 2010), thermal infrared land
surface temperature from the Geostationary Operational Environmental
Satellites (GOES East and West), and leaf area index estimates obtained from
the 4-day 1 km Combined Aqua-Terra MODIS product (MCD15A3).
Daily, instantaneous, clear-sky latent heat fluxes retrieved from ALEXI were
upscaled to daytime-integrated evapotranspiration estimates assuming a
self-preservation of the ratio of latent heat flux and incoming shortwave
radiation (fSUN) during daytime hours (Cammalleri et al., 2014b). Hourly
CFSR incoming shortwave radiation inputs were integrated to produce daily
estimates (24 h) of insolation used in this temporal upscaling. Currently,
ALEXI is not executed over snow-covered surfaces. These periods were instead
gap-filled with a linear interpolation of fSUN and a snow albedo
correction to account for differences in surface net radiation over
snow-covered versus snow-free surfaces. Resulting 4 km ALEXI daily
evapotranspiration estimates were temporally summed within calendar
years to produce annual ET (mm yr-1) and spatially averaged within
each of the basins listed in Tables 1 and 2. Annual ALEXI ET estimates
acquired in this way have been successfully applied to verify interannual
evapotranspiration estimates acquired from land surface modeling (Han et al.,
2015).
Land surface model predictions of ET
For the purposes of cross-comparison with ALEXI ET results, annual
ET was also acquired from 0.125∘ resolution Noah v3.2
simulations (Chen et al., 2001; Chen and Dudhia, 2001; Ek et al., 2003)
generated as part of North American Land Data Assimilation Phase 2 (NLDAS-2)
activities (Xia et al., 2012). Hourly Noah predictions of (1) direct
evaporation from the surface soil, (2) direct evaporation of
canopy-intercepted precipitation, and (3) transpiration via plant root uptake
of soil water were aggregated to produce an hourly evapotranspiration
estimate. Annual ET averages were then obtained by summing these
estimates for the calendar years 2003 to 2010 and spatially averaging these
summations within the basins indicated in Fig. 1.
Ground-based observations of P and Q
Daily stream-flow magnitudes were obtained from United States Geologic
Survey (USGS) stream gauging stations located at the outlet of basins listed
in Tables 1 and 2. These values were aggregated into (calendar year) sums
and normalized by basin drainage area to obtain units of water depth per
year (mm yr-1). Annual total (liquid plus solid phase) precipitation
(P) (mm yr-1) was based on the temporal aggregation of rain gauge
observations acquired by the National Centers for Environmental Prediction
(NCEP)'s Climate Prediction Center (CPC) and re-sampled onto a
0.125∘ grid by the NLDSE-2 project (Xia et al., 2012). These
annual averages were then spatially averaged within each of the basins listed in
Tables 1 and 2.
Gravity remote sensing of dS/ dt
Monthly GRACE terrestrial water storage deviation (SGR) data
were obtained by separately applying the rescaling coefficients of Landerer
and Swenson (2012) to gridded 1∘ GRACE Level-3 terrestrial water
storage products provided by the GeoForschungsZentrum (GFZ; version
RL05.DSTvSCS1409), University of Texas Center for Space Research (CSR;
version RL05.DSTvSCS1409), and the NASA/Cal-Tech Jet Propulsion Laboratory
(JPL; version RL05.DSTvSCS1411). GRACE-based annual estimates of terrestrial
water storage variations (dSGR/ dt) were then derived via simple
linear averaging of the GFZ, CSR and JPL terrestrial storage product to
estimate SGR,Dec,i and SGR,Jan,i+1 (where i
is an annual index) and the subsequent application of year-over-year
differencing:
dSGR/dt,i=SGR,Dec,i+SGR,Jan,i+1/2-SGR,Dec,i-1+SGR,Jan,i/2.
Finally, gridded 1∘ dSGR/ dt (mm yr-1) products were
spatially averaged within all of the coarse-scale basins listed in Table 1.
Note that GRACE Level-3 values capture monthly deviations from a
long-term average datum (based on average 2004–2009 conditions) and not
absolute storage levels. However, the distinction is immaterial since our
focus lies solely on annual dSGR/ dt, which is insensitive to the presence or
absence of any such datum.
The primary application of dSGR/ dt retrievals will be to verify annual water
balance closure within the coarse-scale basins listed in Table 1. However,
we will also apply dSGR/ dt within the medium-scale basins to calibrate
microwave-based dS/ dt estimates (see Sect. 4.1) and as a baseline for
evaluating microwave-based dS/ dt as a source of downscaling information (see
Sect. 4.2). These applications will be approached with caution since the
spatial resolution of the dSGR/ dt retrievals (∼ 200 000 km2) is much coarser than the size of the medium-scale basins
considered here (2000–10 000 km2). The impacts of this significant
scale mismatch will be discussed below.
Passive microwave remote sensing of soil moisture
PM-based surface soil moisture retrievals were based on the
application of the Land Parameter Retrieval Model (LPRM; Owe et al., 2001) to
Advanced Microwave Scanning Radiometer – EOS (AMSR-E) C- and X-band
brightness temperature observations obtained from both ascending (13:30 LT) and descending (01:30 LT) orbits of the NASA Aqua satellite (Owe et
al., 2008). AMSR-E LPRM Level 3 soil moisture data products were downloaded
from the NASA Global Change Master Directory (http://gcmd.nasa.gov). The
Aqua satellite was launched in June 2002 and remained operational until
October 2011. Soil moisture datasets acquired from AMSR-E represent the
longest surface soil moisture data record currently available from a single
satellite sensor. The processing of these datasets into dS/ dt estimates is
discussed in Sect. 4.
Statistical approach
The temporal length of required remotely sensed datasets imposes a serious
challenge for this analysis. The primary limiting factor for this length is
the availability of a consistent microwave-based θ dataset. As noted
above, the data period utilized here (2003–2010) represents the longest
current period of (temporally consistent) microwave-based θ
retrievals available from any single sensor (AMSR-E). Nevertheless, it still
provides only eight annual values upon which to evaluate the annual closure
expressed in Eq. (1). Longer θ datasets based on the merger of
multi-sensor θ retrievals exist (Liu et al., 2011).
However, concerns about their temporal consistency currently limit their
value for analyses conducted at interannual timescales (Loew et al.,
2013).
The restriction of the annual analysis to only 8 years limits our ability to
robustly assess closure using temporal sampling alone. Therefore, whenever
possible, we will sample closure evaluation statistics across both space and
time to maximize the total degrees of freedom available for a statistical
analysis. However, due to significant amounts of both spatial and temporal
auto-correlation in P-Q-ET fields, considerations must be made for
oversampling (in both space and time) when calculating effective sample
sizes. To address this we applied the approach of Bretherton et al. (1999)
who recommended (for the case of sampling quadratic statistics) an effective
sampling size N∗ of
N∗=N(1-ρ2)/(1+ρ2),
where N is the original sample size and ρ the auto-correlation at
individual sampling points. In particular, we applied Eq. (3) separately in both
space and time, utilizing both temporal (separated in time, sampled over
time, and then averaged across various basins) and spatial (separated in space,
sampled over space, and then averaged over various years) samples of ρ
to obtain both spatial and temporal sample size reduction factors. Next, the
total sample size (i.e., total time samples × total space samples) was
multiplied by both reduction factors to estimate effective sample sizes in
both time and space. For example, in the large-scale basin analysis, we have
a total sample size of 40 annual values (5 basins over 8 years); however,
after accounting for over-sampling in both space and time, the effective
sample size was reduced to 9.7. Likewise, for the medium-scale basins
analysis, the total sample size of 128 annual values (16 basins over 8 years) was
reduced to an actual effective size of 48.4. These effective
sample sizes were then used to calculate effective degrees of freedom for
all statistical hypothesis tests.
Water balance closure within large-scale basins
All water storage and flux products described above contain significant
errors and biases. In addition, it is possible that non-resolved flux terms
in Eq. (1) may hinder closure versus observed storage changes. Therefore, before
deriving and evaluating an approach to estimate dS/ dt for medium-scale basins
using microwave-based remote sensing, we will first verify the ability of
water balance datasets introduced in Section 2 to close the terrestrial
water balance via Eq. (1). Due to the coarse spatial resolution of GRACE, a
direct closure analysis is possible only for the large-scale basins listed
in Table 1. Based on ET values derived from ALEXI, Fig. 2 plots annual
variations of P-Q-ET and (GRACE-based) dSGR/ dt for all five large-scale basins.
In all basins except the Missouri, annual values of P-Q-ET depart
significantly from zero – illustrating the general importance of annual
dS/ dt on the terrestrial water budget. Within the Missouri, P-Q is roughly balanced
by ET, and therefore, alone among other basins examined here, the annual
estimation of dSGR/ dt does not appear to be a requirement for closing the
annual water budget. This may be linked to the very large reservoir capacity
of the Missouri River Basin system and the active management of Q to minimize
interannual reservoir and channel level variability. This aggressive level
of management ensures that the Missouri River Basin exhibits the smallest
standard deviation of interannual P-Q-ET variability (∼ 30 mm yr-1- see Fig. 2) of any large basin considered in this analysis.
Annual time series of P-Q-ET (black) and gravity-based
dSGR/ dt (red) estimates for each of the large-scale basins listed in Table 1.
The best closure results in Fig. 2 are obtained in the Arkansas River and
Red River basins. In these two basins, GRACE-based dSGR/ dt closely matches
interannual variations in P-Q-ET. This suggests that in the United States
SGP region, both the assumptions underlying Eq. (1) and
the water flux datasets considered are sufficiently accurate to
characterize interannual variations in dS/ dt. In contrast, there is clear
evidence of a low bias in annual P-Q-ET relative to dSGR/ dt within both the
Upper Mississippi and Ohio River Basins. Given the frequency and extent of
wintertime snow cover in these basins, it seems reasonable to ascribe this
bias to known under-catch issues associated with the gauge-based measurement
of snowfall (Goodison et al., 1998). In addition, there exists a potential
for systematic error in cold-season ALEXI ET estimates (which are based
on a simple extrapolation approach).
Figure 3a shows annual P-Q-ET versus dSGR/ dt for all five large-scale basins.
The sampled correlation in Fig. 3a is marginal (0.37 [-]) but improves
considerably (0.52 [-]) when the 8-year mean of annual P-Q-ET is subtracted
from yearly P-Q-ET results for each basin (Fig. 3b). This is equivalent to
imposing closure of P-Q-ET within each basin over the entire 8-year time
period. In addition, replacing ALEXI ET with Noah-based ET reduces
the sampled correlations in both Fig. 3a and b (from 0.37 to 0.33 [-] and
from 0.52 to 0.33 [-], respectively). This implies that preference should be
given to the remote-sensing-based ALEXI ET product.
(a) Relationship between annual P-Q-ET and
gravity-based dSGR/ dt within each of the large-scale basins listed in Table 1. (b) Same,
except that annual P-Q-ET time series for each basin
have been closed (i.e., modified to sum to zero over the 8-year data
record). The blue line is a one-to-one line and red line is the
least-squares linear fit.
Due to the coarse spatial resolution of GRACE-based dSGR/ dt, a comparable
water balance analysis cannot be applied to the medium-scale basins listed
in Fig. 1 and Table 2. Instead we will cross-apply general tendencies
observed in the large-scale closure analysis (Figs. 2 and 3) to refine the
medium-scale analysis presented below. In particular, the medium-scale
basins listed in Table 2 are selected based on the principal of minimization
of both human regulation (to avoid the lack of annual P-Q-ET signal noted in
the Missouri Basin) and cold season impacts
(to avoid the low bias in
annual P-Q-ET observed in the Ohio and Upper Mississippi River basins).
Overall, these two considerations motivate our decision to utilize only
lightly regulated MOPEX basins within the SGP portion of the Mississippi
River system (see Fig. 1 and earlier discussion in Sect. 2.1). In
addition, based on annual water balance closure results presented in Figs. 2–3, ALEXI-based (as opposed to Noah-based) ET will be used and closure
will be imposed on 8-year P-Q-ET totals.
Microwave-based closure for medium-scale basins
As discussed above, the primary focus of this analysis is the utilization of
new ET remote sensing products to objectively evaluate the contribution
of microwave surface soil moisture retrievals towards describing
interannual P-Q-ET variations within medium-scale basins. To this end,
this section will describe the derivation of a new microwave-based proxy for
dS/ dt and its empirical evaluation within the specific set of medium-scale basins
listed in Table 2.
Microwave-based dS/ dt estimation
Any transition between surface soil moisture and terrestrial water storage
must account for relative
variations in the temporal scale and phase of both quantities. In
particular, the tendency for terrestrial water storage
to be temporally smoothed and lagged in time
with respect to corresponding surface soil moisture variations (Chagnon,
1987; Entekhabi et al., 1992; Swenson et al., 2008). Based on this
reasoning, instantaneous 0.25∘ LPRM surface soil moisture
retrievals (see Sect. 2.2) were averaged in time and space into a single
monthly value for each of the basins in Tables 1 and 2. Next monthly
(basin-scale) soil moisture averages for October, November, and December
(θPM,Oct, θPM,Nov, and θPM,Dec) were
merged into a single, end-of-calendar-year estimate of PM-based θPM:
θPM,i=WOctθPM,Oct,i+WNovθPM,Nov,i+WDecθPM,Dec,i,
where i is an annual index (here corresponding to calendar years between 2003
and 2010), and W are constant weighting factors (summing to unity) applied to
each month. Annual changes in θPM(dθPM/ dt) were
then derived from annual differencing of θPM,i with
θPM,i-1. This entire procedure was done separately for
LPRM retrievals acquired during both ascending and descending AMSR-E orbits.
Finalized values of dθPM/ dt were then obtained by averaging results
obtained from both orbits. Our decision to utilize a calendar year to
accumulate annual flux or storage change totals in Eq. (1) is largely arbitrary,
and the impact of utilizing other annual periods will be discussed below.
In addition to the specification of W, we also allowed for the application of
a single calibration factor KPM (mm) when converting volumetric
dθPM/ dt (m3 m-3 yr-1) variations into annual dS/ dt depth
changes (mm yr-1):
dSPM/dt=KPMdθPM/dt.
Our approach for obtaining KPM was based on scaling dθPM/ dt to match the sampled temporal variance of gravity-based
dSGR/ dt. Therefore, KPM was defined as the following ratio:
KPM=σdSGR/dt/σdθPM/dt,
where the σ operator indicates a standard deviation sampled across
all available years and medium-scale study basins.
Despite some evidence for significant large-scale correlation between
θ and S (Abelen and Seitz, 2013; Abelen et al., 2015), there are viable
reasons for scepticism regarding the application of Eqs. (4)–(6) to a water budget
application. First, due to the extremely shallow vertical support of PM-based surface soil moisture retrievals, it is uncertain if
dθPM/ dt actually provides an effective linear proxy for dS/ dt. Second,
even if such a linear relationship can be established, it is unclear if the
ratio σ(dSGR/ dt) /σ(dθPM/ dt) in Eq. (6) provides a
robust calibration coefficient to convert surface soil moisture variations
into annual variations in S. These theoretical concerns are addressed below.
Evaluation of proxy assumptions and calibration
Figure 4 plots (annual) variations of P-Q-ET and dSPM/ dt for all
16 medium-scale basins listed in Table 1. See Sect. 3 for the rationale
behind the selection of these particular basins. The large plotted
departures (from zero) seen for P-Q-ET confirm that interannual variations
in S play a significant role in the application of Eq. (1) at an annual timescale.
For the 16 medium-scale basins listed in Table 2, the
annual time series of raw P-Q-ET (solid black line) and P-Q-ET obtained by
assuming flux closure over the 8-year period of record (dashed red line).
Values of the microwave-based dSPM/ dt proxy are also plotted (solid blue
line).
In addition, consistently negative P-Q-ET estimates are observed
within several medium-scale basins (see, e.g., basins #5, #8, #9,
and #12 in Fig. 4). Because these basins cannot be directly resolved by
GRACE, it is difficult to confirm whether this tendency is real (i.e., a
decadal-scale trend in storage) or an artefact of the summed impact of multiple
long-term measurement biases in independent P,Q, and ET products. However,
based on the large-basin analysis presented in Sect. 3, the
latter appears more likely. Therefore, annual P-Q-ET values are de-biased by
subtracting out (on a basin-by-basin basis) the 8-year annual mean of
P-Q-ET (see dashed line in Fig. 4). The impact of this assumption on
subsequent results will be discussed below.
Our primary goal is to determine the potential for explaining observed annual
P-Q-ET variations in Fig. 4 using the microwave-based dSPM/ dt proxy
introduced above and empirically evaluating the assumptions – expressed in
Eqs. (4)–(6) – which underlie the proxy. The first issue is the degree to which the
appropriate temporal averaging of microwave-based soil moisture via Eq. (4) can
be used to obtain a robust linear proxy for P-Q-ET. Figure 5a addresses this
by plotting the average linear correlation for all the medium-scale basins
between annual P-Q-ET and dθPM/ dt obtained using all potential
combinations of WDec, WNov, and WOct
(where WDec+WNov+WOct=1.0). Plotted correlations in Fig. 5a are
generally greater than 0.50 [-]. In fact, even after realistically
accounting for the impact of over-sampling due to spatial and temporal
auto-correlation in the P-Q-ET fields (Sect. 2.3), sampled correlations
are statistically significant (one-tailed, 95 % confidence) for all
possible combinations of WDec, WNov, and WOct. Since these
correlations are based on annual values (where there is no potential for
obtaining spurious fitting due to the trivial representation of an obvious
seasonal cycle), and there is no credible reason to suspect cross-correlated
errors between the wholly independent P-Q-ET and dSPM/ dt fields, the
statistical significance of sampled correlation in Fig. 5a can be taken as
clear evidence of a robust linear underlying relationship between dθPM/ dt and P-Q-ET. As such, it provides empirical support for Eqs. (4)–(5).
The impact of monthly weighting factors in Eq. (4) on the
sampled correlation between (a)dθPM/ dt and P-Q-ET
and (b)dθPM/ dt and dSGR/ dt.
Nevertheless, the performance of the dθPM/ dt proxy does vary as a
function of WDec, WNov, and WOct in Fig. 5a and feasible
parameterization strategies will be required to fix their values. To this
end, Fig. 5b plots the sampled correlation between dθPM/ dt and
dSGR/ dt as a function of WDec, WNov, and WOct. Note that monthly
weighting values which maximize this correlation in Fig. 5b also tend to
maximize the correlation between dθPM/ dt and P-Q-ET in Fig. 5a.
Based on Fig. 5b, the maximum correlation between dθPM/ dt and
dSGR/ dt is found at WOct= 0.4 [-], WNov= 0.5 [-], and
WDec= 0.1 [-]. These (spatially and seasonally fixed) weighting
values will be used for all subsequent calculations of dθPM/ dt via
Eq. (4). The relative lack of weight applied to December surface soil moisture
retrievals is likely reflective of frozen soil moisture conditions at this
time and the need for dS/ dt anomalies to be lagged in time with respect to
superficial surface soil moisture variations. Adding monthly-averaged
θ retrievals from September (θPM,Sep) into Eq. (4) – so that end-of-year θPM was calculated using a 4-month
weighted-average product – produced essentially no change to Fig. 5.
The parameterization of WOct, WNov, and WDec alone is sufficient
if dθPM/ dt is to be interpreted solely as a linear proxy for
relative interannual variations in dS/ dt; however, interpretation of
dθPM/ dt as an absolute measure requires the additional
parameterization of KPM (mm) in Eq. (5) to transform dθPM/ dt into a
dS/ dt estimates with units of (mm yr-1) (i.e., dSPM/ dt). Figure 6 shows the
impact of KPM in Eq. (5) on the root-mean-square difference (RMSD) between
dSPM/ dt and P-Q-ET. Results are obtained by lumping annual results for all
years within all medium-scale basins listed in Table 2, and the assumption
that KPM is fixed in both space and time. The plotted horizontal line
plots the interannual standard deviation of P-Q-ET – which is equivalent to
the RMSD accuracy achievable by assuming dS/ dt= 0 in Eq. (1). This baseline is
improved upon by a wide range of KPM values. However, the absolute
accuracy of the dSPM/ dt proxy is maximized near KPM= 900 mm.
The impact of KPM in Eq. (5) on the RMSD between
dSPM/ dt and P-Q-ET. Also plotted is the standard deviation of P-Q-ET (i.e.,
the RMSD incurred by neglecting annual dS/ dt) and the value of KPM defined by
the variance matching approach in Eq. (6).
The KPM estimation approach in Eq. (6) is based on the assumption that this
optimal value can be obtained via a simple variance matching approach
applied to dθPM/ dt and dSPM/ dt. Applying Eq. (6) (in a lumped manner to
all years and all medium-scale basins in Table 2) leads to a value of
KPM= 1150 mm, which is reasonably close to the optimal value
of KPM (900 mm). It is also well within the broad range of KPM
which improves upon a baseline of neglecting dS/ dt entirely (see Fig. 6).
It should be noted that the parameterization strategies presented above
involve direct comparison between (relatively) high-resolution θ
products obtained from microwave remote sensing with lower-resolution
GRACE-based dSGR/ dt retrievals (which have been trivially re-sampled to
capture a basin-scale mean). Despite the inability of GRACE retrievals to
spatially resolve the medium-scale basins considered here, Figs. 5 and 6
suggest these comparisons are still able to yield useful calibration
information. However, it is possible that resolution inconsistencies between
GRACE and AMSR-E may have a degrading impact on results. One strategy for
resolving this scale inconsistency is to first degrade the spatial
resolution of the AMSR-E θ field to match the ∼ 200 000 km2 GRACE resolution prior to applying the calibration approach
outlined in Figs. 5a and 6. However, attempts to do this (via smoothing of
the AMSR-E θ fields using a 2-dimensional Gaussian filter) actually
led to a small decrease in the quality of the WOct, WNov, WDec, and
KPM calibration. This implies that, despite their resolution
differences, direct comparisons between AMSR-E and GRACE products appear to
offer the most viable calibration approach.
Microwave-based closure evaluation
Utilizing the calibrated W and KPM derived in Sect. 4.2 leads to the
dSPM/ dt values plotted in Fig. 7. Each point in the scatter plot
represents one annual value within a single medium-scale basin. Our
microwave-based dSPM/ dt proxy product has a linear correlation with
independently acquired P-Q-ET values of 0.71 [-], which is
statistically significant (one-tailed, at 99 % confidence) even after
allowances have been made for over-sampling in both time and space (see
Sect. 2.3). Note that all calibrated parameters (W and KPM) are
constant in both space and time and therefore cannot provide a spurious
source of skill for dSPM/ dt temporal variations. In addition, all
calibration is against GRACE-based dSGR/ dt and P-Q-ET fields are used
solely for the purpose of independent verification.
Relationship between annual P-Q-ET (closed over the
9-year time series) and the microwave-based dSPM/ dt proxy within each of the
16 medium-scale basins listed in Table 1. The blue line is a one-to-one line
and red line is the least-squares linear fit.
While P-Q-ET derived in medium-scale basins cannot be directly validated
against GRACE-based dSGR/ dt retrievals (due to the ground resolution of
GRACE being much coarser than the size of the medium-scale basins), the
significant correlation in Fig. 7 strongly suggests that they are
adequately representing the net annual flux of water into and out of the
medium-scale basins. A slight reduction in correlation (from 0.71 to 0.62
[-]) is found when P-Q-ET is not corrected to close water balance over the
8-year study period. Likewise, replacing ALEXI ET with NOAH-based
ET leads to another (very) slight reduction in correlation in Fig. 7
(from 0.71 to 0.69 [-]). However, it should be stressed that, in all cases,
the correlation between dSGR/ dt and plotted P-Q-ET remains statistically
significant (one-tailed, at 95 % confidence). See Fig. 4 for
dSPM/ dt time series results within individual medium-scale basins.
Downscaling evaluation
An important follow-on question is the degree to which the skill
demonstrated in Fig. 7 enhances our ability to track dS/ dt in medium-scale
basins above and beyond existing GRACE products. To this end, Fig. 8a
plots annual GRACE-based dSGR/ dt versus P-Q-ET for all medium-scale basins.
Since the ground resolution of GRACE is significantly coarser than the size
of these basins, it is unfair to evaluate dSGR/ dt based on these
comparisons. However, despite this severe resolution penalty,
dSGR/ dt still manages to correlate relatively well (i.e., a linear
correlation of 0.66 [-]) with independently acquired estimates of annual
P-Q-ET. The tendency for skill in GRACE-based dSGR/ dt to persist even at
these (sub-resolution) scales implies that annual dS/ dt fields in this region
contain spatial auto-correlation at length scales finer than the GRACE
spatial resolution. However, it should be stressed that the use of
GRACE-based dSGR/ dt fields at these spatial resolutions is not recommended
and applied here only to define a baseline upon which to evaluate the
benefits of subsequent downscaling using microwave-based dSPM/ dt estimates.
(a) Relationship between annual P-Q-ET (with 8-year closure) and gravity-based dSGR/ dt estimates within
each of the 16 medium-scale basins listed in Table 1. Part (b) is the same as (a) except
for correlation against the simple average of dSPM/ dt and
dSGR/ dt. The blue line is a one-to-one line and red line is the least-squares
linear fit.
To this end, Fig. 8b plots the relationship between annual P-Q-ET and
dS/ dt estimates obtained via a simple downscaling strategy based on the direct
averaging of annual dSGR/ dt and dSPM/ dt estimates for each medium-scale
basin. Relative to GRACE-only results presented in Fig. 8a, this simple
downscaling strategy leads to a significant improvement in the degree of
correlation with independent P-Q-ET values. Specifically, this
correlation is increased from 0.66 [-] for the GRACE-only dSGR/ dt case in Fig. 8a to 0.77 [-]
for the case of averaging dSGR/ dt and dSPM/ dt in Fig. 8b.
Application of a Fisher z-transformation and the effective degree
sample size calculation presented in Sect. 2.3 confirms that this increase
in correlation is statistically significant (two-tailed, at 95 %
confidence).
In order to further examine geographic trends in results, Fig. 9 evaluates
dSPM/ dt, dSGR/ dt, and downscaling results (based on the simple linear
averaging of dSPM/ dt and dSGR/ dt) obtained individually for each
medium-scale basin in Table 2. Results are shown for both the linear
correlation and absolute RMSD match with annual P-Q-ET variations. It is
reasonable to expect that the accuracy of microwave-based θ
retrievals, and thus their value as the basis of dSPM/ dt estimates, should
progressively degrade for higher-numbered study basins (which generally have
wetter climates and denser vegetation coverage – see Fig. 1). Therefore,
it is somewhat surprising that no clear trend between basin land cover and
the relative performance of the microwave-based dSPM/ dt proxy is discernible
in Fig. 9. However, dSPM/ dt results demonstrate relatively poor accuracy
for the furthest northern (and most heavily cultivated) basin (i.e., basin
#7) and for the wettest basin (i.e., basin #16). The downscaled
results (based on the simple averaging of dSPM/ dt and dSGR/ dt) generally
produce results which are superior to the isolated application of either
dSPM/ dt or dSGR/ dt; however, basin-to-basin variations are large and metric
values for individual basins are impacted by considerable sampling errors.
For the 16 medium-scale basins listed in Table 1: (a) the
linear correlation between annual P-Q-ET and various annual dS/ dt estimates
and (b) the RMSD between P-Q-ET and various dS/ dt estimates. Basins are ordered from
drier to wetter (from left to right) and basin numbering corresponds to
listing in Fig. 2.
It is possible to replicate the dSPM/ dt approach applied to the medium-scale
basins for the larger-scale basins listed in Table 1. However, large-scale
dSPM/ dt proxies calculated in this way (not shown) are significantly less
accurate than GRACE-based dSGR/ dt results, and there is no indication that a
microwave-based dSPM/ dt proxy can consistently improve upon the relative
accuracy of annual dS/ dt in large basins beyond what is already possible via the
utilization of existing GRACE-based dSGR/ dt. As a result, the added benefits
of a microwave-based dSPM/ dt proxy appear to be limited to basins which cannot be
directly resolved by GRACE.
Discussion
PM-based estimates of surface soil moisture capture only soil
water storage variations occurring within the couple of centimeters of the
vertical soil column and cannot directly detect storage dynamics occurring
in deeper layers of the unsaturated zone – to say nothing of even deeper
variations in groundwater storage or reservoir storage. However, despite
this severe theoretical limitation, PM surface soil moisture
retrievals (θ) appear to retain significant value as an indicator of
relative interannual variations in P-Q-ET (see e.g., Fig. 7). This
implies that, at least at an annual timescale and for certain conditions,
unobserved components of dS/ dt are sufficiently correlated with observable trends in
surface soil moisture such that θ retrievals may serve as a
potential proxy for variations in total terrestrial water storage. Given the difference of 2 orders of magnitude
in the spatial resolution of microwave-based θ (1000 km2) versus gravity-based (200 000 km2) dS/ dt estimates, the
microwave-based proxy appears to enhance our existing ability to close
the
terrestrial water budget within the medium scale (2000–10 000 km2)
basins listed in Table 2 (Fig. 8).
Intuitively, the ability of surface θ retrievals to capture (much
deeper) dS/ dt variations is likely due to the tendency for (non-anthropogenic)
variations in dS/ dt to be forced, in a “top-down manner”, by
atmospherically driven anomalies in P and ET. In this simple conceptual
model, variations in surface soil moisture provide a leading indicator of
these anomalies as they are propagated downward into deeper hydrologic
storage units (Chagnon, 1987; Entekhabi et al., 1992; Swenson et al., 2008).
However, it must be stressed that this conceptual model is likely to break
down for a number of cases. For example, storage variations due to direct
groundwater pumping (Rodell et al., 2009), particularly when associated
with increased surface soil moisture via irrigation, will almost certainly
confound the ability of θ retrievals to effectively capture dS/ dt.
Likewise, it is difficult to imagine microwave-based θ providing an
effective representation of dS/ dt due to large changes in reservoir storage
and/or river system management. Finally, even in cases lacking significant
anthropogenic modifications of the hydrologic cycle, the relationship
between soil moisture and groundwater memory is known to vary significantly
as a function of climate (Lo and Famiglietti, 2010). Some modes of soil
moisture–groundwater interactions are almost certainly inconsistent with the
application of Eqs. (4)–(6). Therefore, additional study is required to better
understand the geographic limitations of dθPM/ dt as a credible
dS/ dt proxy.
The geographic scope of this study was limited by two considerations. First,
the evaluation analysis required access to sufficiently accurate annual
P-Q-ET time series to serve as an independent benchmark for microwave-based
dSPM/ dt estimates. As discussed in Sect. 2, this requirement restricts the
geographic domain over which the analysis can currently be conducted.
Second, the long-term AMSR-E LPRM soil moisture dataset utilized in the
analysis has known limitations within areas of moderate and/or dense
vegetation cover. Datasets based on lower-frequency L-band observations are
currently being produced but will require 2 or 3 more years (beyond 2017) to
match the temporal length of the existing AMSR-E data record. However, once
longer-term L-band datasets become available, they will enable the
expansion of this analysis into more densely vegetated areas.
Our decision to calculate annual flux quantities using a calendar year
(i.e., 1 January to 31 December) approach is admittedly arbitrary. This
choice may impact the accuracy of dSPM/ dt proxy estimates due to seasonal
variations in the availability and accuracy of remotely sensed soil moisture
retrievals acquired from PM remote sensing (due to, e.g.,
vegetation phenology and/or the presence of snow or frozen soils). In order
to directly examine this issue, results in Fig. 8 were re-generated using
a 1 September to 31 August annual time period. Relative to earlier 1 January to 31 December results, this new annual definition resulted in less skill
for both estimates of interannual storage change (i.e., a reduction in correlation from 0.66 to 0.39
(-)
for dSGR/ dt results in Fig. 8a and from 0.77 to 0.54 (-) for the simple
average of dSPM/ dt and dSGR/ dt in Fig. 8b). However, the relative
improvement seen when incorporating
dSPM/ dt
remained statistically significant (two-tailed, at 95 % confidence). The reason for
the reduction in performance is unclear; however, the added value of the
microwave-based dSPM/ dt retrievals appears to be robust
regardless of whether the fixed annual period is defined to end during the
summer (31 August) or the winter (31 December). A more detailed sensitivity
analysis involving a more continuous range of annual end dates is possible;
however, it is complicated by the relatively small number of annual cycles
currently available for this analysis and thus the tendency to significantly
change temporal sampling supports when accommodating changes in the
definition of an annual period.
The targeting of annual variations in S is motivated by the need to address
important questions surrounding interannual variations in the hydrologic
cycle. However, a natural extension of this work is the application of
dSPM/ dt at a finer timescale. In theory this is possible; however, a
seasonally varying W and/or KPM parameterization would likely be required
for dSPM/ dt to accurately capture monthly variations in total water storage. Given that monthly
dSPM/ dt variations are commonly dominated by a fixed seasonal cycle, it is
then challenging to discern whether any apparent skill in monthly
dSPM/ dt variations is real or simply an artefact of over-fitting a
seasonally varying parameterization. As a result, the objective validation
of a monthly dSPM/ dt proxy will require the availability of longer
dSPM/ dt and P-Q-ET datasets capable of supporting mutually exclusive
calibration and validation time periods.
Conclusions
Advances in the remote sensing of ET currently afford an opportunity to
independently verify other annual components of the terrestrial water budget
– including changes in terrestrial water storage (dS/ dt). Confirming recent work
with GRACE, results demonstrate the importance of dS/ dt for closing the annual
water budget. In particular, GRACE-based dSGR/ dt estimates appear to provide
a reliable source of such information within large-scale river basins with
relatively low annual snowfall totals and anthropogenic management (Figs. 2–3). In addition, for basins smaller than the 200 000 km2 GRACE
spatial resolution, estimates of dSPM/ dt derived from PM
remote sensing and Eqs. (4)–(6) also demonstrate clear value for providing annual
closure information (Fig. 7). Given that PM-based soil
moisture retrievals are available at substantially finer spatial resolution
than gravity-based retrievals of dS/ dt, this opens up the strong possibility of
using microwave-based surface soil moisture retrievals to downscale
gravity-based dS/ dt retrievals (Fig. 8).
The retrieval of the microwave-based dSPM/ dt proxy is based on two –
somewhat ad hoc – assumptions expressed in Eqs. (4)–(6) which claim that (1) dθPM/ dt obtained via Eq. (4) has a linear underlying relationship with dS/ dt and
(2) the constant of proportionality in the relationship can be derived via
variance matching between microwave- and gravity-based estimates of dS/ dt. These
assumptions are directly supported by empirical results presented in Figs. 5 and 6. Nevertheless, it should be stressed that theoretical support for
Eqs. (4)–(6) is still quite weak, and it is relatively easy to imagine cases in
which these assumptions would be expected to fail (see Sect. 5).
Therefore, additional validation work over a wider variety of conditions is
certainly required. Likewise, an objective intercomparison between this
approach and earlier downscaling approaches based on higher-resolution land
surface model output (e.g., Reager et al., 2015; Wan et al., 2015) is
warranted.
In addition to isolating potential value in microwave-based dSPM/ dt
estimates, water balance results presented here also provide confidence
regarding our ability to capture annual variations in dS/ dt via Eq. (1) and flux
observations. In particular, both annual dSGR/ dt and dSPM/ dt estimates
exhibit a statistically significant correlation against independent annual
P-Q-ET values within the medium-scale basins examined here (Fig. 7).
Terrestrial ET, in particular, is commonly perceived to represent a weak
link in the characterization of Eq. (1). However, based on results presented
here, it appears that ALEXI-based ET products over CONUS are now
sufficiently accurate (at least in a relative interannual sense) for annual
ET estimates to be used as a viable constraint to infer the accuracy of
other water budget components. This is a marked improvement over the
calculation of ET as a balance residual and opens the door to the fuller
use of Eq. (1) as a diagnostic tool for various water balance products.
All yearly, basin-averaged data
products used in this analysis are available upon request from the corresponding author.
The authors declare that they have no conflict of interest.
Acknowledgements
The research was partially supported by a grant from the
NASA Applied Sciences Water Resources Program (award number: NNX12AK90G).
Edited by: R. Greco
Reviewed by: two anonymous referees
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