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  • View in gallery

    (a) Time series of precipitation, (b) SMAP Level-2 soil moisture retrievals, and (c),(d) model-simulated near-surface soil moisture at a grid cell centered on the Little Washita watershed in southwestern Oklahoma. The model-simulated time series in (c) uses a value of 1 for the calibrated parameter α (the default value in GEOS systems), and the time series in (d) uses an α value of 0.01. For ease of comparison, model values are plotted only on the dates of SMAP retrievals.

  • View in gallery

    Optimal values of the studied model parameter α (dimensionless), as determined by optimization against SMAP retrieval time series. These are the values used in the OPT and OPT_DA simulations; in the BL and BL_DA simulations, α is set to 1 everywhere.

  • View in gallery

    Time series (February–July 2016) of daily-averaged soil moisture (m3 m−3) at the EASE-Grid cell containing the Prairie View SCAN measurement site located in Texas. The observations are shown as the heavy black curves in both panels. (top) The simulated time series from BL (blue) and BL_DA (red) and (bottom) the simulated time series from OPT (blue) and OPT_DA (red). For ease of comparison, the mean simulated bias for February–July 2016 was removed from all simulation results prior to plotting. The BL and BL_DA simulations used the default value of 1 for α, whereas the OPT and OPT_DA simulations used an α of 0.001, the optimized value for this location.

  • View in gallery

    (a) Spatial distribution of the ubRMSE of surface soil moisture estimation for the BL simulation. Circles refer to SCAN sites and triangles refer to USCRN sites. (b) Differences in ubRMSE: BL_DA minus BL. Blue shades indicate improved near-surface soil moisture estimation. (c) As in (b), but for OPT minus BL. (d) As in (b), but for OPT_DA minus BL. (e) Average ubRMSE across the CONUS sites for each simulation (see text for details).

  • View in gallery

    As in Fig. 4, but for the temporal correlation metric R. As in Fig. 4, the blue shading in (b)–(d) indicates improvement, though here the blue shading indicates a positive difference.

  • View in gallery

    As in Fig. 4, but for (a) bias and (b)–(d) differences in the absolute values of the biases. As in Fig. 4, the blue shading in (b)–(d) indicates improvement.

  • View in gallery

    (a) The BL simulation’s bias in long-term average runoff ratio (ratio of total 2-yr streamflow to total 2-yr precipitation) in multiple unregulated basins. Values are plotted at the centroids of the basins. (b) Differences in the absolute value of the bias: BL_DA minus BL. Blue shades indicate an improved estimation of runoff ratio. (c) As in (b), but for OPT minus BL. (d) As in (b), but for OPT_DA minus BL. (e) Average absolute bias across the unregulated basins (see text for details).

  • View in gallery

    As in Fig. 7, but for the temporal correlation R between observed and simulated 10-day streamflow totals in the warm season (April–September of 2015 and 2016) in multiple unregulated basins. The R values and R differences are plotted at the centroids of the basins. As in Fig. 4, the blue shading in (b)–(d) indicates improvement.

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Improved Hydrological Simulation Using SMAP Data: Relative Impacts of Model Calibration and Data Assimilation

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  • 1 Global Modeling and Assimilation Office, NASA GSFC, Greenbelt, Maryland
  • 2 Global Modeling and Assimilation Office, NASA GSFC, Greenbelt, and Science Systems and Applications, Inc., Lanham, Maryland
  • 3 Global Modeling and Assimilation Office, NASA GSFC, Greenbelt, Maryland
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Abstract

The assimilation of remotely sensed soil moisture information into a land surface model has been shown in past studies to contribute accuracy to the simulated hydrological variables. Remotely sensed data, however, can also be used to improve the model itself through the calibration of the model’s parameters, and this can also increase the accuracy of model products. Here, data provided by the Soil Moisture Active Passive (SMAP) satellite mission are applied to the land surface component of the NASA GEOS Earth system model using both data assimilation and model calibration in order to quantify the relative degrees to which each strategy improves the estimation of near-surface soil moisture and streamflow. The two approaches show significant complementarity in their ability to extract useful information from the SMAP data record. Data assimilation reduces the ubRMSE (the RMSE after removing the long-term bias) of soil moisture estimates and improves the timing of streamflow variations, whereas model calibration reduces the model biases in both soil moisture and streamflow. While both approaches lead to an improved timing of simulated soil moisture, these contributions are largely independent; joint use of both approaches provides the highest soil moisture simulation accuracy.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Randal Koster, randal.d.koster@nasa.gov

Abstract

The assimilation of remotely sensed soil moisture information into a land surface model has been shown in past studies to contribute accuracy to the simulated hydrological variables. Remotely sensed data, however, can also be used to improve the model itself through the calibration of the model’s parameters, and this can also increase the accuracy of model products. Here, data provided by the Soil Moisture Active Passive (SMAP) satellite mission are applied to the land surface component of the NASA GEOS Earth system model using both data assimilation and model calibration in order to quantify the relative degrees to which each strategy improves the estimation of near-surface soil moisture and streamflow. The two approaches show significant complementarity in their ability to extract useful information from the SMAP data record. Data assimilation reduces the ubRMSE (the RMSE after removing the long-term bias) of soil moisture estimates and improves the timing of streamflow variations, whereas model calibration reduces the model biases in both soil moisture and streamflow. While both approaches lead to an improved timing of simulated soil moisture, these contributions are largely independent; joint use of both approaches provides the highest soil moisture simulation accuracy.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Randal Koster, randal.d.koster@nasa.gov

1. Introduction

One of the flagship science data products of the National Aeronautics and Space Administration’s (NASA) Soil Moisture Active Passive (SMAP) satellite mission (Entekhabi et al. 2010a) is an extensive set of estimates (retrievals) of moisture content in the top several centimeters of soil. These retrievals, provided on a global ~36-km grid with a repeat time of 3 days or less, are derived from L-band measurements taken with a passive radiometer and feature significantly reduced errors from the radio frequency interference that can plague such datasets (Piepmeier et al. 2014, 2017; Kerr et al. 2016). Overall, SMAP soil moisture retrieval accuracy has been shown to be quite high (Chan et al. 2016a, 2018).

A unique feature of the core SMAP mission is the publication of an enhanced Level-4 Soil Moisture (L4_SM) product through the assimilation of the observed brightness temperatures into a land surface model (LSM). Through the assimilation process (Reichle et al. 2017a), the LSM combines the SMAP brightness temperatures with observation-based meteorological forcing to produce a soil moisture product that is superior to an “open loop” LSM-based product, that is, the LSM product generated without the assimilation of SMAP data. The development of the SMAP L4_SM product is based on an extensive body of research into soil moisture data assimilation (Reichle et al. 2002; Reichle 2008; Kumar et al. 2008; Drusch et al. 2009; Draper et al. 2012; de Rosnay et al. 2013; Carrera et al. 2015; De Lannoy and Reichle 2016a,b). The L4_SM product has already been evaluated successfully against a host of in situ soil moisture observations (Reichle et al. 2017a) and in the context of key assimilation diagnostics (Reichle et al. 2017b).

SMAP data, however, can potentially interface with an LSM in another useful way: through the calibration of model parameters. Calibration in this context involves identifying the values of targeted parameters (typically, parameters that cannot be easily quantified with direct measurements) that lead, in a model simulation, to the most accurate reproduction of the satellite-measured variable. Using similar L-band soil moisture retrievals from the Soil Moisture Ocean Salinity mission (Kerr et al. 2010), Shellito et al. (2016) calibrated an LSM’s soil hydraulic properties, improving its simulation of soil moisture; their study calls to mind earlier calibrations of LSM soil and vegetation parameters using satellite-based surface temperatures (e.g., Crow et al. 2003; Gutmann and Small 2010; Corbari and Mancini 2014).

L-band soil moisture retrievals indeed reveal important time scales of near-surface soil moisture dynamics (McColl et al. 2017)—time scales that could serve as targets for a model calibration exercise. To demonstrate the potential of calibration more clearly, we present here an example taken from the analysis performed later in this paper. Consider the time series plots shown in Fig. 1, obtained for a grid cell in the Little Washita watershed of southwestern Oklahoma (O’Neill et al. 2016) during the period May–September 2016. Figure 1a shows the gauge-based precipitation rates recorded there, and Fig. 1b shows the contemporaneous SMAP Level-2 (nonassimilated) soil moisture retrievals. The retrieved soil moisture increases as expected during precipitation events (e.g., on day 164), and it subsequently dries down with a time scale of a few days. Now consider the soil moisture time series in Fig. 1c, which was produced at the site by an LSM without the benefit of data assimilation but with the precipitation information contained in Fig. 1a. The LSM used here is the Catchment LSM of the NASA Global Earth Observing System (GEOS)—the LSM underlying the L4_SM product, as discussed in section 2b. The modeled soil moisture also increases as desired during precipitation events, but the time scale of dry-down is noticeably longer—the dry-down occurs over a span of 1–2 weeks. In this context, the model does not behave like nature, at least nature as represented by SMAP. This particular facet of Catchment LSM behavior was in fact heretofore never carefully examined.

Fig. 1.
Fig. 1.

(a) Time series of precipitation, (b) SMAP Level-2 soil moisture retrievals, and (c),(d) model-simulated near-surface soil moisture at a grid cell centered on the Little Washita watershed in southwestern Oklahoma. The model-simulated time series in (c) uses a value of 1 for the calibrated parameter α (the default value in GEOS systems), and the time series in (d) uses an α value of 0.01. For ease of comparison, model values are plotted only on the dates of SMAP retrievals.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

Now consider the soil moisture time series in Fig. 1d, which was produced by the same LSM after calibrating a particular parameter. (Details are provided below in section 2c.) While the model results still differ somewhat from the observations in terms of absolute magnitude, the time scale of the dry-down is more in line with that captured by the SMAP retrievals. We thus might expect the calibrated model results in Fig. 1d to be more realistic than the uncalibrated results in Fig. 1c—they might agree better with independent in situ soil moisture observations.

Data assimilation and model calibration are in fact expected to improve soil moisture estimation in different ways. Model calibration specifically addresses deficiencies in the model’s representations of physical processes, improvements that can manifest themselves at every simulation time step. Data assimilation corrects for such deficiencies “after the fact” and only at selected times and locations, depending on the availability of the satellite data; however, unlike calibration, data assimilation also corrects for potentially important deficiencies in the meteorological forcing. To some extent the contributions of the two approaches to improved soil moisture estimation are complementary. They may indeed build on each other, so that applying both approaches together may lead to soil moisture estimates of unprecedented accuracy.

We explore this potential complementarity in the present paper. We use the Catchment LSM to produce four sets of soil moisture estimates: 1) open-loop estimates with the default version of the LSM, 2) estimates obtained through the assimilation of SMAP data into the default LSM, 3) open-loop estimates obtained after the LSM has been calibrated with SMAP data, and 4) estimates obtained through the assimilation of SMAP data into the calibrated LSM. By evaluating the relative accuracies of the four sets of estimates against independent in situ data, we can isolate the contributions of data assimilation and model calibration to hydrological estimation as well as quantify their joint impact.

Section 2 below describes data used in the analysis as well as the LSM, the calibration procedure, and the data assimilation system. Section 3 presents the results, focusing on the accuracy of the simulated near-surface soil moisture and streamflow. Section 4 provides a summary and discussion.

2. Data and models used

a. SMAP soil moisture and brightness temperature data

Different components of the SMAP data suite are used in this study. For the calibration exercise (section 2c), we use version 4 of the SMAP Level-2 soil moisture retrievals (O’Neill et al. 2016), a set of retrievals derived from L-band radiometer measurements that represent volumetric soil moisture in roughly the top 5 cm of soil. We use the data associated with the descending overpasses, which correspond to a 0600 local collection time. The data are provided on the 36-km Equal-Area Scalable Earth Grid (EASE-Grid; Brodzik et al. 2012), with retrieval values provided at a given grid cell at least once every three days. We achieve extensive spatial and temporal coverage of soil moisture data for our analysis by utilizing the retrievals flagged as having “uncertain quality” along with those flagged as having “recommended quality.”

For the data assimilation exercise (section 2d), we use version 3 of the 36-km resolution SMAP Level-1C brightness temperature (L1C_TB) observations (Chan et al. 2016b). The assimilated SMAP observations include horizontal-polarization and vertical-polarization brightness temperatures from ascending and descending half-orbits (after first averaging over fore- and aft-looking data).

b. Land surface modeling system

The LSM used for all simulations is the Catchment LSM (Koster et al. 2000; Ducharne et al. 2000), the LSM underlying the MERRA-2 reanalysis (Gelaro et al. 2017; Reichle et al. 2017c) and the SMAP L4_SM product (Reichle et al. 2017a). It solves the land surface energy and water balance at every simulation time step, partitioning precipitation inputs into runoff, evapotranspiration, and changes in water storage, and partitioning radiative energy inputs into latent heat, sensible heat, and changes in energy storage. A key feature of the LSM is its explicit treatment of spatial soil moisture heterogeneity (as determined from topographic conditions) and its effects on the surface water fluxes—evapotranspiration and runoff generation, for example, both occur more efficiently in the (dynamically varying) subcatchment areas characterized by wetter conditions.

The Catchment LSM follows a prognostic soil water variable representing the top 5 cm of soil, and the average soil moisture in the top 5 cm is a standard simulation output. This depth is consistent with the ostensible sensing depth of the SMAP radiometer (section 2a). Also standardly produced are surface runoff and baseflow fluxes, the sum of which are averaged here in space and time for comparison against streamflow measurements.

c. Land surface model calibration strategy

While the Catchment LSM’s performance has been evaluated in numerous venues (e.g., Bowling et al. 2003; Boone et al. 2004; Reichle et al. 2011), its treatment of near-surface moisture and how it relates to the root zone has never been properly calibrated. Indeed, one study (Kumar et al. 2009) suggests that the connection between the near-surface and deeper soil moisture in the model may be too strong—it is, in any case, stronger than that seen in some other models. This particular aspect of the LSM can thus be considered ripe for calibration.

The Catchment LSM’s formulation of near-surface soil moisture dynamics uses two independent processes to replenish drying soil via recharge from below [see Koster et al. (2000) for details]. First, replenishment occurs through changes in the equilibrium moisture state of the catchment; as this equilibrium water increases, some of the increase is deposited in the near-surface soil. Second, the upward flow of soil moisture between the root zone and the near-surface soil in nonequilibrium situations is determined through parameterized fits of detailed Richards equation calculations—in effect, as the near-surface soil dries, the increasing vertical gradient in matric potential overcomes gravity, allowing upward moisture flow.

Of relevance to the present study is the recent inclusion of a time-invariant parameter α into the formulation of the second process. In the new version of the formulation, any upward moisture flux in nonequilibrium situations is multiplied by α, where α lies between 0 and 1. The imposed reduction in upward flow can be considered a reflection of the fact that near-surface soils in nature are more heterogeneous than those tested in laboratories, making upward flow more difficult than laboratory-established soil parameters would suggest. This interpretation, however, is rather loose, since the equilibrium profile of soil moisture is not similarly adjusted; α is thus perhaps best considered here to be a simple tuning parameter. The value of α turns out to have a first-order impact on the character of the simulated soil moisture, as illustrated earlier in Fig. 1d. At this grid cell, replacing α’s default value of 1 with a value of 0.01 produced a better match (in terms of temporal variability and the speed of dry-down) of simulated soil moisture with the SMAP data.

In a calibration exercise, a number of open-loop (land model only) simulations, each utilizing a different value for α, generated soil moisture time series for 2015–16 across the continental United States (CONUS) and portions of Canada and Mexico. This region was chosen for study because it offers two key advantages: 1) high-quality precipitation measurements based on a dense rain gauge network and 2) a broad range of climates, with wetter conditions in the east and much drier conditions in the west. The forcing data applied in these simulations were derived from atmospheric analysis, with the analysis-generated precipitation corrected by gauge observations; the forcing data essentially match those used in the generation of the version 2 L4_SM product for 2015–17 and those used in the production of the corresponding 2000–14 model-only simulation for the SMAP project (Nature Run v4; Reichle et al. 2017a).

At a given SMAP grid cell, and for a given simulation, we evaluated the agreement (using the temporal correlation coefficient R) between the local time series of SMAP retrievals and the model-simulated surface soil moisture time series. We then repeated the process with data at that grid cell from each of the other simulations. By comparing the different R values, we were able to determine for the grid cell the single value of α that allows the best reproduction of the behavior of the SMAP retrievals. The spatial distribution of these optimized α values is shown in Fig. 2. The optimal values clearly vary in space, with smaller values in the east. Notice that the default value of 1 works best at only a handful of locations.

Fig. 2.
Fig. 2.

Optimal values of the studied model parameter α (dimensionless), as determined by optimization against SMAP retrieval time series. These are the values used in the OPT and OPT_DA simulations; in the BL and BL_DA simulations, α is set to 1 everywhere.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

d. Data assimilation system

The data assimilation system used in this study is essentially the same as that used to generate the SMAP L4_SM product (Reichle et al. 2017a,b). It uses an ensemble Kalman filter (Evensen 2003) and assimilates horizontally and vertically polarized SMAP brightness temperature observations from the version 3 SMAP L1C_TB product (Chan et al. 2016b) from both ascending and descending half-orbits. The observed brightness temperatures are differenced with corresponding brightness temperatures generated from the Catchment model’s soil moisture and temperature estimates, which are calculated using a zero-order “tau-omega” radiative transfer model (De Lannoy et al. 2013). The brightness temperature differences are then inverted into corrections of the model forecast soil moistures and surface temperatures based on the modeled error covariances, which are diagnosed from the ensemble. The analysis is bias-corrected by a rescaling—prior to assimilation—of the SMAP brightness temperature observations into the spatially and seasonally varying climatology of the modeled brightness temperature. Reichle et al. (2017a, see their section 2d) provide a detailed description of the different facets of the data assimilation system, including the model and observation error parameters.

e. Simulations performed

Results from four offline simulations with the Catchment LSM were evaluated for this study:

  1. A model-only “baseline” simulation (BL) with the default version of the Catchment LSM, that is, the version used to produce the version 2 L4_SM product (Reichle et al. 2017a). Note that in the default model, α is set to 1 everywhere.
  2. A data assimilation simulation (BL_DA) with the default version of the Catchment LSM that includes the assimilation of SMAP brightness temperatures, as outlined in section 2d above.
  3. A model-only simulation (OPT, for “optimized parameter”) with a version of the Catchment LSM that uses the spatial distribution of optimized α values illustrated in Fig. 2.
  4. A data assimilation simulation (OPT_DA) with both the use of the optimized α values from Fig. 2 and the assimilation of SMAP brightness temperatures.
All four simulations covered the period from April 2015 to March 2017 and were run across the CONUS on the SMAP 36-km EASE-Grid (section 2a). The BL and OPT simulations were spun up independently for 30 years. The BL_DA and OPT_DA simulations used the same perturbation and radiative transfer model parameters as used for the SMAP L4_SM product (Reichle et al. 2017a,b). The SMAP brightness temperatures were assimilated after removing their seasonally varying bias relative to the model forecast brightness temperatures. The rescaling parameters were constructed separately for the BL and OPT simulations using the (version 6) brightness temperature from the Soil Moisture Ocean Salinity mission (Kerr et al. 2016) for the period from July 2010 to June 2016 and the underlying Catchment LSM. Output diagnostics produced by each simulation include 3-hourly near-surface (top 5 cm) soil moistures and total runoff fluxes.

f. Validation data

For validating simulated near-surface soil moisture, we utilize a number of in situ soil moisture measurement sites encompassed by the USDA Natural Resources Conservation Service Soil Climate Analysis Network (SCAN; Schaefer et al. 2007) and the U.S. Climate Reference Network (USCRN; Diamond et al. 2013; Bell et al. 2013). Quality control was applied to the hourly in situ measurements at these sites; we eliminated measurements indicating volumetric soil moisture below 0 m3 m−3 or greater than 0.6 m3 m−3 as well as measurements taken when the contemporaneous soil temperature was below 4°C. We also filtered out obviously unphysical measurements associated with spikes, sudden dry-downs, or high-frequency oscillations. The quality-controlled hourly data were averaged into 3-hourly time series, on which we base the soil moisture–related evaluations in section 3a.

Some caveats regarding the use of such in situ observations for validation are worth noting. First, the site measurements are highly localized, whereas the soil moisture estimates produced by the simulations represent a large-scale spatial average. This leads to a potentially important spatial representativeness error—the local measurement may not properly represent the large-scale average. Second, the LSM’s near-surface soil moisture variable represents an average over the top 5 cm of soil, whereas the in situ measurements do not represent such a depth average; for the sites examined here, the surface soil moisture measurements instead represent conditions at a depth of about 5 cm. Time variability of soil moisture at a 5-cm depth can differ from that of the depth-averaged soil moisture above it (Shellito et al. 2016); presumably, time scales for the depth-averaged moisture will be shorter than those at 5-cm depth. The spatial representativeness error and the vertical mismatch between the in situ measurements and the modeled soil moisture variable will influence (and will presumably inflate inappropriately, though perhaps to only a small degree) the error metrics we compute for the simulations. We make the assumption here that these issues affect to some extent all four of our simulations, so that the relative magnitudes of the skill metrics across the simulations are still telling. In addition, we emphasize the key advantage of the SCAN and USCRN networks: they encompass the CONUS and thereby cover a broad range of soil textures and background climates (Reichle et al. 2017c).

For the validation of simulated streamflow, we examine a subset of the 573 unregulated CONUS hydrological basins analyzed by Kumar et al. (2014): the 240 basins that lie within the intermediate size range (2000–10 000 km2). Daily streamflow data for the 240 basins were obtained from the U.S. Geological Survey (USGS; http://nwis.waterdata.usgs.gov/nwis) for the period from 1980 through September 2017. For each basin, observed river discharges were normalized by basin area to convert the discharges to units of millimeters per day. Conversions between the irregular basin areas and the SMAP EASE-Grid cells were facilitated by EASE-Grid arrays containing the fractions of each basin held within each grid element.

g. Skill metrics

We evaluate model simulation skill against the in situ observations using three metrics: the unbiased root-mean-square error (ubRMSE), the bias, and the temporal correlation R. The bias, of course, is simply the long-term mean of the simulation variable minus the long-term mean of the corresponding set of observations. The ubRMSE at a given site can be computed from the bias and the traditional root-mean-square error (RMSE) via
e1
In essence, (1) recognizes the fact that the error characterized by the traditional RMSE stems both from a mean bias and from residual, time-varying errors that remain after the mean bias is removed from the time series. We represent the latter error contribution with the ubRMSE, using (1) (see Entekhabi et al. 2010b).

The final metric, the temporal correlation R (the traditional Pearson correlation coefficient), concerns itself with the timing and relative magnitudes of anomalies in a time series. For the near-surface soil moisture comparisons below, both R and ubRMSE are computed from time series of 3-hourly data. For the streamflow comparisons, R is computed from the smoothed time series obtained by applying a 10-day moving average window to the daily observed and simulated totals during warm season months (April–September of 2015 and 2016). We limit the streamflow R calculation to warm season months in order to avoid, for most of the CONUS, intense periods of snowmelt-dominated runoff generation. We use the 10-day moving window to minimize errors associated with streamflow routing times (the time it takes for locally generated runoff to reach a stream gauge observation site), given that a routing model is not employed in this analysis.

For both near-surface soil moisture and streamflow, when averaging the skill metrics across the CONUS, we account for spatial correlations in the site values, so that clusters of nearby similar measurements do not contribute excessively to the computed averages (Reichle et al. 2017a). For soil moisture, we also compute 95% confidence intervals for the averages using the approach in Reichle et al. (2017a), indicating these uncertainty estimates with lines (or “error bars”) in the histograms showing average skill across the CONUS. Note that the estimation of these uncertainty estimates is far from perfect. The estimation approach assumes that the errors in the simulation products are completely random, which is not the case for a model that, for example, always produces an overly extended dry-down period after a storm event (as the Catchment LSM appears to do in Fig. 1). Because presumably not all of the simulation errors examined here are random, the estimated uncertainty levels provided here are probably overestimated, perhaps significantly so. As for streamflow, we avoid assigning uncertainty estimates due to the small sample size of the temporal data relative to that for soil moisture—again, for the streamflow R metric, we are considering 10-day averages during the warm season of two years. We instead qualitatively address the relevance of any streamflow simulation improvements in terms of “field significance,” that is, the preponderance of sites that show improvement over those that show degradation.

3. Results

a. Near-surface soil moisture

1) Time series comparison at a representative site

A representative comparison of the soil moisture time series produced in the four simulations is shown in Fig. 3. The Prairie View site (30.08°N, 95.98°W), a SCAN site located west of Houston, Texas, provides subdiurnal soil moisture measurements at multiple depths throughout the SMAP period. The site measurements at the 5-cm depth, averaged over each day during February–July 2016, are plotted in both panels of the figure as a heavy black curve. The daily-averaged simulated soil moistures at the corresponding grid cell are also plotted, with BL and BL_DA included in Fig. 3a and OPT and OPT_DA in Fig. 3b. For ease of considering the ubRMSE and R metrics, the mean bias of each simulated time series computed over the February–July 2016 period was removed. These biases at this location and for this time period amount to 0.18 m3 m−3 for BL, 0.072 m3 m−3 for OPT, 0.15 m3 m−3 for BL_DA, and 0.066 m3 m−3 for OPT_DA.

Fig. 3.
Fig. 3.

Time series (February–July 2016) of daily-averaged soil moisture (m3 m−3) at the EASE-Grid cell containing the Prairie View SCAN measurement site located in Texas. The observations are shown as the heavy black curves in both panels. (top) The simulated time series from BL (blue) and BL_DA (red) and (bottom) the simulated time series from OPT (blue) and OPT_DA (red). For ease of comparison, the mean simulated bias for February–July 2016 was removed from all simulation results prior to plotting. The BL and BL_DA simulations used the default value of 1 for α, whereas the OPT and OPT_DA simulations used an α of 0.001, the optimized value for this location.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

The BL is seen to follow the ups and downs of the observations fairly well, indicating that the applied rainfall forcing for the period—the timing of the storms and interstorm periods—is reasonably accurate. As already suggested in Fig. 1, however, the time scale of poststorm dry-downs is excessive in the model; the simulated soil moisture in BL (blue curve in Fig. 3a) takes about a month to dry following the storm occurring just prior to mid-March, whereas significant dry-down for the in situ measurements occurs within a week. The assimilation of SMAP brightness temperatures into the baseline model (BL_DA) leads to more realistic amplitudes of soil moisture variation (particularly in June and July) and a somewhat more accurate dry-down time scale, with a faster dry-down, for example, in late June and early July.

Using the calibrated α parameter in OPT clearly leads to faster, and thus generally more realistic, dry-downs (Fig. 3b). For example, unlike BL and BL_DA, both OPT and OPT_DA produce reasonable dry-downs in late March. While the large June dry-down is simulated better in OPT than in either BL or BL_DA, OPT_DA performs better still. Also, note that while the plots appear to suggest that OPT and OPT_DA are wetter than BL and BL_DA following rainfall events in late February and mid-March, the soil moisture maxima achieved then by the four simulations are in fact roughly the same—a significantly larger bias (by about 0.1 m3 m−3) had been subtracted from the BL and BL_DA results prior to plotting (see above). The soil moisture minima for the four simulations are accordingly very different, with significantly lower minima obtained for OPT and OPT_DA. The precipitation event in late February had a larger impact on soil moisture in OPT than in BL presumably because the prestorm soil in the former was much drier.

The ubRMSE for BL, BL_DA, OPT, and OPT_DA over the particular time period shown in Fig. 3 are 0.066, 0.053, 0.069, and 0.052, respectively. Thus, according to the ubRMSE metric, and for this particular site and time period, only data assimilation produces an improved simulation of soil moisture—the excessive amplitude of variation (relative to observations) produced in the OPT simulation apparently counteracts the effects of the improved dry-down time scale. The temporal correlation metric R, which focuses less on such amplitudes, tells a different story: R for BL, BL_DA, OPT, and OPT_DA is 0.73, 0.82, 0.85, and 0.85, respectively. According to the R metric, both model calibration and data assimilation contribute accuracy to simulated soil moisture at this site.

Regarding the somewhat excessive amplitude seen in the OPT results and its apparent effect on the ubRMSE metric, it is worth remembering (section 2f) that the depth of the in situ measurements is inconsistent with the depth represented by the land model and of the SMAP signal used in the calibration, which ostensibly corresponds to average soil moisture conditions within the top 5 cm. An SMAP-calibrated model might indeed be expected to produce such higher amplitudes—because soil moisture variations tend to decrease with increasing depth into the soil, the variations at 5-cm depth (where the in situ measurements are taken) should show a reduced amplitude relative to those in the soil above. This may artificially increase the estimated ubRMSE.

2) Results across the CONUS

The results in Fig. 3 for the Prairie View site are in fact typical, as indicated in Fig. 4. Figure 4a first shows the distribution of ubRMSE across the USCRN and SCAN sites within the CONUS over the period from April 2015 to March 2017. Some large errors appear in the Southeast and up through the Mississippi Valley. The smallest errors are seen in the Southwest, perhaps reflecting the drier soils there and the associated lower temporal variability.

Fig. 4.
Fig. 4.

(a) Spatial distribution of the ubRMSE of surface soil moisture estimation for the BL simulation. Circles refer to SCAN sites and triangles refer to USCRN sites. (b) Differences in ubRMSE: BL_DA minus BL. Blue shades indicate improved near-surface soil moisture estimation. (c) As in (b), but for OPT minus BL. (d) As in (b), but for OPT_DA minus BL. (e) Average ubRMSE across the CONUS sites for each simulation (see text for details).

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

Figures 4b–d then show, respectively, the changes in ubRMSE obtained in the BL_DA, OPT, and OPT_DA experiments with respect to the BL simulation. Warm colors (yellow to red) indicate an increase in ubRMSE and thus a degradation in simulation skill compared to BL, whereas blue shading indicates a reduction in ubRMSE and a more accurate simulation. Each map shows a mix of improvements and degradations. Note that we can expect some degradation even for the OPT_DA simulation simply because the in situ validation data are themselves imperfect; the in situ data are subject, for example, to spatial and vertical representativeness errors (section 2f). As noted above, vertical representativeness issues are particularly relevant to the ubRMSE calculation and can complicate skill comparisons between the simulations. Spot checks of ubRMSE degradations seen for OPT_DA, for example, show that the amplitudes of soil moisture variations in OPT_DA can be greater than those for BL, which look more like those of the in situ measurements. Again, this does not necessarily imply a reduction in true skill relative to BL, given that the model data effectively (and properly) represent soil moisture at a depth shallower than 5 cm, which should indeed vary somewhat more than the in situ values. Some of the degradations seen in the maps, however, are suggestive for other reasons. The higher ubRMSE for the OPT experiment along the Mississippi–Arkansas border (Fig. 4c), for example, may reflect difficulties in calibrating the model in such regions of extensive irrigation (Kumar et al. 2015), given that irrigation is not explicitly treated in the model.

Such issues aside, the maps show that, overall, reductions outweigh increases in ubRMSE, particularly for BL_DA and OPT_DA. This implies that SMAP data indeed contribute to improved soil moisture estimation through both data assimilation and (to a lesser extent) the optimization of the model parameters.

This result is summarized in Fig. 4e, which shows the average ubRMSE across the CONUS validation points for each of the four simulations. While all three experiment simulations (BL_DA, OPT, and OPT_DA) on average perform better than the baseline run, the improvement seen with OPT is very small; the improvements are clearly larger when data assimilation is employed. Note that the improvements obtained with data assimilation are likely to be more significant than suggested by the overlapping 95% uncertainty ranges, given that these ranges are themselves likely to be overestimated (section 2g).

The temporal correlation metric R is examined in Fig. 5. Curiously, despite the baseline simulation’s relatively poor performance in the Southeast according to the ubRMSE metric (Fig. 4a), the R values produced there are high (Fig. 5a). We also see that for the R metric, all three experiment simulations show a general improvement (Figs. 5b–d) over the baseline simulation, with the increases in R overwhelming the handful of decreases.

Fig. 5.
Fig. 5.

As in Fig. 4, but for the temporal correlation metric R. As in Fig. 4, the blue shading in (b)–(d) indicates improvement, though here the blue shading indicates a positive difference.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

The CONUS-wide averages of R shown in Fig. 5e are especially telling. First, the average R values for all three experiment simulations (BL_DA, OPT, and OPT_DA) lie significantly above that for BL (as indicated by the nonoverlapping 95% confidence intervals, which, again, are likely to be overestimated anyway). Second, the contributions of data assimilation and parameter calibration to the average R values in Fig. 5e appear largely complementary; the increase in R from data assimilation (BL_DA minus BL) added to that obtained from parameter estimation (OPT minus BL) roughly equals the increase obtained when data assimilation and parameter calibration are employed together (OPT_DA minus BL). Such complementarity speaks to the value of considering multiple facets of SMAP data together when attempting to maximize the data’s usefulness.

Results for bias are shown in Fig. 6. Data assimilation is seen to have little impact on the bias (Fig. 6b). In contrast, model calibration has a large impact, sometimes increasing the absolute value of the bias and sometimes decreasing it (Fig. 6c). Generally, though, the calibration leads to an improvement, as indicated by the averages in Fig. 6e.

Fig. 6.
Fig. 6.

As in Fig. 4, but for (a) bias and (b)–(d) differences in the absolute values of the biases. As in Fig. 4, the blue shading in (b)–(d) indicates improvement.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

The relative impacts of data assimilation and model calibration on model bias in Fig. 6 are not unexpected. By design, our data assimilation procedure ingests SMAP data after transforming the data to be consistent with the host model’s climatology, so that data assimilation by itself should have minimal impact on bias. The calibration of the model parameters, on the other hand, has a first-order impact on the model’s physics and thus on any biases generated. The bias reductions found for OPT and OPT_DA indicate that this overall impact is, on average, positive.

b. Streamflow in small, unregulated basins

The above analysis shows that SMAP soil moisture retrievals and associated brightness temperatures have a positive impact on soil moisture simulation, with complementary contributions from data assimilation and model calibration. To what extent, though, do the different strategies for using SMAP data lead to improvements in overall hydrological simulation—in the partitioning, for example, of incident precipitation into streamflow, evapotranspiration, and changes in storage? In this section we focus specifically on the simulation of streamflow (given the wealth of available streamflow data relative to large-scale evapotranspiration data); we compare the abilities of the baseline simulation and the three experiment simulations to reproduce streamflow characteristics observed across the CONUS.

Figure 7a shows, for the baseline simulation, the error in the runoff ratio at each of the unregulated, medium-sized basins described in section 2f. For both the simulation and the observations, we divide a given basin’s total streamflow Q from September 2015 through August 2017 by the total precipitation P in that basin over the same period (computed directly from the gridded precipitation data used in the four simulations). We then plot in Fig. 7a the difference between the modeled and observed ratios, with the dots positioned on the centroid of the basin. Because the Catchment LSM tends to underestimate streamflow, the raw errors in Fig. 7a tend to be negative. [This problem is discussed in more detail, along with a potential solution, by Koster and Mahanama (2012).] The runoff ratio errors for BL are especially large in parts of the Northwest, in the upper Midwest, and in Appalachia.

Fig. 7.
Fig. 7.

(a) The BL simulation’s bias in long-term average runoff ratio (ratio of total 2-yr streamflow to total 2-yr precipitation) in multiple unregulated basins. Values are plotted at the centroids of the basins. (b) Differences in the absolute value of the bias: BL_DA minus BL. Blue shades indicate an improved estimation of runoff ratio. (c) As in (b), but for OPT minus BL. (d) As in (b), but for OPT_DA minus BL. (e) Average absolute bias across the unregulated basins (see text for details).

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

Figures 7b–d show, respectively, the changes in the absolute runoff ratio error (compared to BL) for simulations BL_DA, OPT, and OPT_DA, with the color of the dots indicating an improvement (blue shading) or degradation (yellow to red shading) in the simulated runoff ratio. Averages (section 2g) across the basins for the different simulations are provided in Fig. 7e. The averages indicate an improvement in runoff ratio estimation stemming from the use of the calibrated model parameters—an improvement that appears significant, given the preponderance of blue dots in Fig. 7c and (to a lesser extent) Fig. 7d. Data assimilation by itself is seen to have little impact on Q/P accuracy and even seems, for this metric, to reduce slightly the ability of model calibration to have a positive impact, as seen by the higher average error for OPT_DA relative to OPT.

Figure 8 shows results for an alternative measure of runoff simulation skill: the temporal correlation R between observed and simulated runoff totals. For the warm period (April–September) of both 2015 and 2016, time series of observed 10-day basin streamflows were correlated against the corresponding streamflows simulated in BL. The resulting R value for each basin is plotted at the basin’s centroid in Fig. 8a; correlations are seen to be reasonably high, particularly in the east (except in Florida and Maine) and the Pacific Northwest.

Fig. 8.
Fig. 8.

As in Fig. 7, but for the temporal correlation R between observed and simulated 10-day streamflow totals in the warm season (April–September of 2015 and 2016) in multiple unregulated basins. The R values and R differences are plotted at the centroids of the basins. As in Fig. 4, the blue shading in (b)–(d) indicates improvement.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0228.1

Figures 8b–d show, respectively, the change in R obtained in simulations BL_DA, OPT, and OPT_DA. Improvements strongly overwhelm degradations for BL_DA (Fig. 8b). The average of R for all four simulations is provided in Fig. 8e. For this metric, model calibration has little impact, whereas the impact of data assimilation is relatively strong. This is presumably because only data assimilation corrects for errors in the timing of precipitation, which necessarily has a first-order impact on the timing of streamflow volumes.

Note that using both data assimilation and model calibration together (simulation OPT_DA) leads to an increase in R relative to the BL and OPT simulations, but not to the extent seen in simulation BL_DA. For this particular evaluation, the effects of the two data utilization strategies do not appear independent and additive. Potential “destructive interference” of the two approaches in the generation of higher-level fields such as runoff may be a fundamental characteristic of their joint application.

Alternatively, we can speculate that the apparent nonadditivity in Fig. 8e reflects an insufficient tuning of the data assimilation system underlying the OPT_DA simulation. Unlike the system underlying BL_DA, which underwent extensive development and testing for the generation of the SMAP L4_SM product, the system underlying OPT_DA has only been exercised in the present study. The system underlying OPT_DA lacks, for example, a proper tuning of model and observation error settings. Moreover, recalibration of the parameters underlying the radiative transfer model would bring the modeled brightness temperatures closer to the observations in a climatological sense and lessen the work left to the rescaling process, which might further improve the assimilation estimates. Further investigation of these potential improvements is left for future work.

4. Summary and discussion

In the present study, two different approaches are used to integrate SMAP data into a land surface model’s representation of near-surface soil moisture and hydrological fluxes. These approaches are distinct and largely complementary. In a standard open-loop land modeling exercise, a land model driven with observation-based meteorological forcing (rainfall, air temperature, etc.) produces, as a matter of course, estimates for hydrological states (e.g., soil moisture) and fluxes (e.g., evapotranspiration and runoff). Data assimilation, the first approach toward integrating SMAP data into these estimates, operates as a “course correction” to the evolving states, intermittently adjusting the states toward measured values and thereby correcting for errors that stem from inadequate model parameterizations and uncertainty in the meteorological forcing. The second approach, model calibration, utilizes the SMAP data to improve the performance of the land model itself by increasing the realism of its underlying parameterizations.

Our four simulations quantify the skill of reproducing both observed near-surface soil moisture and observed streamflow when 1) neither approach is used (simulation BL), 2) SMAP data are assimilated into the system (simulation BL_DA), 3) SMAP data are used to calibrate a particularly relevant model parameter (simulation OPT), and 4) SMAP data are used for both model calibration and assimilation (simulation OPT_DA). The results indeed demonstrate some complementarity in the contributions of the two approaches to simulation accuracy. For near-surface soil moisture, data assimilation produces the largest reductions in ubRMSE (Fig. 4), but model calibration produces the greatest reduction in bias (Fig. 6). Both data assimilation and model calibration produce significant improvements in the temporal correlation R, and these improvements appear independent; the sum of these improvements, as obtained from simulations BL_DA and OPT, roughly equals the improvement obtained in OPT_DA, the simulation that combines the two approaches (Fig. 5e). The two approaches appear particularly complementary in their contributions to the simulation of streamflow. Model calibration with SMAP data leads to improvements in the simulation of the long-term runoff ratio (Fig. 7) but has little impact on the timing of streamflow (Fig. 8). In contrast, data assimilation has little impact on simulated runoff ratio but a positive impact on streamflow timing.

We emphasize again that this complementarity is not surprising. The data assimilation strategy employed here (which in fact underlies the generation of the SMAP L4_SM product) transforms the SMAP brightness temperatures into values consistent with the climatology of the model before ingesting them into the model. Assimilating the SMAP data will thus have relatively small impacts on the climatology of the model products, as represented here by biases in both the near-surface soil moisture and the runoff ratio. The assimilation will, however, have important impacts on the timing of the variables produced, since it corrects for errors in the meteorological forcing data that drive the model. Correcting forcing-related errors should improve both ubRMSE and R.

In contrast, model calibration directly affects the climatology of the model, and thus associated improvements can be seen in the model biases. Model calibration also improves the R metric for near-surface soil moisture (computed from 3-hourly values), presumably through its improvement of dry-down behavior (Fig. 3). This, however, does not translate here into an improvement in R for 10-day streamflow totals (Fig. 8c); the 10-day runoff averaging period, necessitated by the comparisons against the stream gauge measurements, may have precluded this benefit. In any case, unlike data assimilation, model calibration cannot correct for errors in the precipitation forcing.

It is important to note that the data assimilation and model calibration exercises performed and compared here utilized different subsets of the SMAP data product, subsets specific to the needs of the given procedure. For example, as noted above, the model calibration exercise utilized soil moisture retrievals flagged as having “uncertain quality” as well as “recommended quality.” This was necessary to extend spatially the areas in which calibration could be performed; by allowing the additional data, calibrations could be performed for this study, for better or worse, across the CONUS. (Note that in Figs. 57, the OPT experiment does show improvements over the baseline experiment even in the far eastern part of the CONUS, where almost all of the data are flagged as “uncertain.”) The data assimilation procedure used here, however, follows that of the SMAP Level-4 system and therefore only assimilates brightness temperatures flagged as having “recommended quality.” While the different flag criteria across the experiments may appear inconsistent, note that ensuring flag consistency is somewhat inappropriate given that the flags for soil moisture retrievals and brightness temperatures are themselves different—SMAP brightness temperature measurements are often flagged as “recommended” even when the soil moisture retrievals themselves are flagged as “uncertain.” Given the varying degrees to which even recommended quality brightness temperatures are allowed to affect soil moisture in a data assimilation system, perfect consistency in this regard is presumably unattainable.

Another SMAP data subsetting difference involves the use of only descending (0600 LT) passes for the model calibration experiments versus the use of both descending and ascending (0600 and 1800 LT) passes in the data assimilation experiments. Here again this difference reflects the specific needs of the two procedures; we used what we felt to be optimal for each. The 0600 LT data on their own have an acceptable revisit interval (typically less than 3 days) to address the time-scale calibration problem, and these data have slightly better error characteristics (Chan et al. 2018) than the 1800 LT data, making them desirable for capturing second-order properties such as dry-down time scales. Data assimilation, on the other hand, does not focus on such second-order properties, considering both the 0600 and 1800 LT data as appropriate inputs to guide the model states.

Also worth mentioning here are a number of limitations associated with the two approaches, particularly when applied on the global scale. It is not possible to extract soil moisture information from the SMAP data where the observed brightness temperatures are not sensitive to soil moisture or have limited quality, such as in regions with dense vegetation or strong radio frequency interference (e.g., Japan). Model calibration, as employed in this study, further requires suitably accurate meteorological forcing data (particularly precipitation information) during the calibration period, and because the quality of meteorological information is poor in many regions of the globe, calibration in these areas may prove difficult or even impossible. The veracity of the dry-down time scales implied by the SMAP retrievals (Fig. 1), upon which the model calibration relies, may also be impacted by errors in the radiative transfer model underlying the retrieval algorithm. More work is indeed needed to determine the impact of errors in the SMAP retrievals on the effectiveness of model calibration.

Also worth pointing out is the seemingly small ubRMSE improvement in soil moisture estimation obtained here with the two approaches—the largest improvement in Fig. 4e is associated with data assimilation, but this improvement amounts to only about 0.003 m3 m−3. Presumably this reflects to some degree the nature of the in situ data networks examined. The SMAP core validation sites (Reichle et al. 2017a), for example, have the relative advantage of providing careful, spatially distributed measurements that are more relevant to the spatial scales of SMAP data. Reichle et al. (2017a) show that when the impacts of data assimilation (using the same systems as used here) are quantified at the SMAP core validation sites rather than at sparse network sites, the improvements in ubRMSE increase by a factor of about 2; furthermore, quantified improvements in temporal correlation R are about twice as large for the core sites as they are for sparse network sites. The core validation sites, however, have the distinct disadvantage of being far fewer in number, leading to greater noise in the multisite skill metrics. Applying our analyses to the core sites instead (not shown) produces similar results that are nevertheless affected by the smaller sample size. Here, for our joint analysis of data assimilation and model calibration, we take advantage of the broader range of conditions covered by the much more numerous SCAN and USCRN sites, accepting the disadvantage of the point-scale nature of the measurements at these sites.

The results of the present study—in particular the demonstrated complementarity of the data assimilation and model calibration approaches—have important implications for maximizing the effective utilization of SMAP data in hydrological simulation. For maximum simulation accuracy, the use of both approaches should be considered, since they each effectively access independent information contained within the SMAP data. Indeed, the two approaches together underline the wealth of hydrological information inherent in these data. The full hydrological information content of the SMAP data record—accessed through these two approaches or through other approaches not described here—will undoubtedly be easier to ascertain as the data record grows with time.

Acknowledgments

Funding for this work was provided by the NASA SMAP mission. Computational resources were provided by the NASA High-End Computing program through the NASA Center for Climate Simulation. We are grateful for the datasets and data archiving centers that supported this work and appreciate those who make the generation and dissemination of the SMAP data products and various validation datasets possible, including SMAP team members at JPL, GSFC, and NSIDC and staff at NOAA CPC, NOAA NCEI, USDA NRCS, and USGS.

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