# Assessment of the SMAP Level-4 Surface and Root-Zone Soil Moisture Product Using In Situ Measurements

Rolf H. Reichle, Gabrielle J. M. de Lannoy, Qing Liu, Joseph V. Ardizzone,

Andreas Colliander, Austin Conaty, Wade Crow, Thomas J. Jackson, Lucas

A. Jones, John S. Kimball, et al.

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► To cite this version:

Rolf H. Reichle, Gabrielle J. M. de Lannoy, Qing Liu, Joseph V. Ardizzone, Andreas Colliander, et al. Assessment of the SMAP Level-4 Surface and Root-Zone Soil Moisture Product Using In Situ Measurements. Journal of Hydrometeorology, 2017, 18, pp.2621-2645. 10.1175/JHM-D-17-0063.1. insu-03668266

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# Assessment of the SMAP Level-4 Surface and Root-Zone Soil Moisture Product Using In Situ Measurements

ROLF H. REICHLE,ª GABRIELLE J. M. DE LANNoy,ᵇ QING LIU,ª,ᶜ JOSEPH V. ARDIZZONE,ª,ᶜ

ANDREAS COLLIANDER,ᵈ AUSTIN CONATY,ª,ᶜ WADE CROW,ᵉ THOMAS J. JACKSON,ᵉ

LUCAS A. JONES,ᵇ JOHN S. KIMBALL,ᵇ RANDAL D. KOSTER,ª SARITH P. MAHANAMA,ª,ᶜ

EDMOND B. SMITH,ª,ᶜ AARON BERG, g SIMONE BIRCHER,ʰ DAVID BOSCH,ᵢ TODD G. CALDWELL,ⱼ

MICHAEL COSH,ᶜ ÁNGEL GONZÁLEZ-ZAMORA,ᵏ CHANDRA D. HOLIFIELD COLLINS,<fnref n="1" />

KARSTEN H. JENSEN,ᵇ STAN LIVINGSTON,ⁿ ERNESTO LOPEZ-BAEZA,'o JOSÉ MARTÍNEZ-FERNÁNDEZ,ᵏ

HEATHER MCNAIRN,ᵇ MAHTA MOGHADDAM,q ANNA PACHECO,ᵇ THIERRY PELLARIN, r

JOHN PRUEGER,§ TRACY ROWLANDSON, g MARK SEYFRIED, t PATRICK STARKS, u ZHONGBO SU, v

MARC THIBEAULT,w ROGIER VAN DER VELDE,v JEFFREY WALKER,x XIAOLING WU,x AND YIJIAN ZENGv

(Manuscript received 10 April 2017, in final form 11 July 2017)

## ABSTRACT

The Soil Moisture Active Passive (SMAP) mission Level-4 Surface and Root-Zone Soil Moisture (L4_SM) data product is generated by assimilating SMAP L-band brightness temperature observations into the NASA Catchment land surface model. The L4_SM product is available from 31 March 2015 to present (within 3 days from real time) and provides 3-hourly, global, 9-km resolution estimates of surface (0–5 cm) and root-zone (0–100 cm) soil moisture and land surface conditions. This study presents an overview of the L4_SM algorithm, validation approach, and product assessment versus in situ measurements. Core validation sites provide spatially averaged surface (root zone) soil moisture measurements for 43 (17) “reference pixels” at 9- and 36-km gridcell scales located in 17 (7) distinct watersheds. Sparse networks provide point-scale measurements of surface (root zone) soil moisture at 406 (311) locations. Core validation site results indicate that the L4_SM product meets its soil moisture accuracy requirement, specified as an unbiased RMSE (ubRMSE, or standard deviation of the error) of 0.04 m³ m⁻³ or better. The ubRMSE for L4_SM surface (root zone) soil moisture is 0.038 m³ m⁻³ (0.030 m³ m⁻³) at the 9-km scale and 0.035 m³ m⁻³ (0.026 m³ m⁻³) at the 36-km scale. The L4_SM estimates improve (significantly at the 5% level for surface soil moisture) over model-only estimates, which do not benefit from the assimilation of SMAP brightness temperature observations and have a 9-km surface (root zone) ubRMSE of 0.042 m³ m⁻³ (0.032 m³ m⁻³). Time series correlations exhibit similar relative performance. The sparse network results corroborate these findings over a greater variety of climate and land cover conditions.

<footnote>ª NASA Goddard Space Flight Center, Greenbelt, Maryland</footnote>

<footnote>ᵇ KU Leuven, Heverlee, Belgium</footnote>

<footnote>ᶜ Science Systems and Applications, Inc., Lanham, Maryland</footnote>

<footnote>ᵈ Jet Propulsion Laboratory, Pasadena, California</footnote>

<footnote>ᵉ Hydrology and Remote Sensing Laboratory, Agricultural Research Service, USDA, Beltsville, Maryland</footnote>

<footnote>f University of Montana, Missoula, Montana</footnote>

<footnote>g Department of Geography, University of Guelph, Guelph, Ontario, Canada</footnote>

<footnote>h CESBIO, University of Toulouse, CNES/CNRS/IRD/UPS, Toulouse, France</footnote>

<footnote>i Southeast Watershed Research, Agricultural Research Service, USDA, Tifton, Georgia</footnote>

<footnote>j Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas</footnote>

<footnote>k University of Salamanca, Villamayor, Spain</footnote>

<footnote n="1">¹ Southwest Watershed Research Center, Agricultural Research Service, USDA, Tucson, Arizona</footnote>

<footnote>m Department of Geosciences and Natural Resource Management, University of Copenhagen, Copenhagen, Denmark</footnote>

<footnote>ⁿ National Soil Erosion Research Laboratory, Agricultural Research Service, USDA, West Lafayette, Indiana</footnote>

<footnote>o University of Valencia, Valencia, Spain</footnote>

<footnote>p Agriculture and Agri-Food Canada, Ottawa, Ontario, Canada</footnote>

<footnote>q University of Southern California, Los Angeles, California</footnote>

<footnote>r Université Grenoble Alpes, CNRS, IRD, Grenoble INP, IGE, Grenoble, France</footnote>

<footnote>s National Laboratory for Agriculture and the Environment, Agricultural Research Service, USDA, Ames, Iowa</footnote>

<footnote>t Northwest Watershed Research Center, Agricultural Research Service, USDA, Boise, Idaho</footnote>

<footnote>u Grazinglands Research Laboratory, Agricultural Research Service, USDA, El Reno, Oklahoma</footnote>

<footnote>v Faculty of Geo-Information Science and Earth Observations (ITC), University of Twente, Enschede, Netherlands</footnote>

<footnote>w Comisión Nacional de Actividades Espaciales, Buenos Aires, Argentina</footnote>

<footnote>x Monash University, Clayton, Victoria, Australia</footnote>
# 1. Introduction

The Soil Moisture Active Passive (SMAP) mission has been providing global observations of L-band (1.4 GHz) passive microwave brightness temperature since 31 March 2015 at about 40-km resolution from a 685-km, near-polar, sun-synchronous orbit (Entekhabi et al. 2010a; Piepmeier et al. 2017). These observations are highly sensitive to surface soil moisture and temperature, which impact the land surface water and energy balance through, for example, the partitioning of rainfall into runoff and infiltration, and the partitioning of net radiation into latent and sensible heat fluxes. Thus, SMAP observations can be used to enhance our understanding of processes that link the water, energy, and nutrient cycles and, ultimately, to extend the capabilities of current weather and climate prediction models (Entekhabi et al. 2014).

L-band brightness temperature observations and surface soil moisture retrievals similar to those from SMAP are also available from the Soil Moisture Ocean Salinity (SMOS) mission, launched in November 2009 (Kerr et al. 2010; De Lannoy et al. 2015). Moreover, surface soil moisture retrievals are available from a variety of past and current, active and passive satellite sensors, including the Advanced Microwave Scanning Radiometers (Mladenova et al. 2014; Parinussa et al. 2015) and the Advanced Scatterometer (Wagner et al. 2013). Because the latter instruments take measurements at C and/or X band (i.e., at frequencies higher than L band), they provide observations that have slightly higher spatial resolution but are more sensitive to vegetation and thus less sensitive to soil conditions than SMOS and SMAP, resulting in noisier and less accurate soil moisture retrievals (Kerr et al. 2016). In addition to satellite retrievals, global soil moisture data are also available from reanalysis products (Saha et al. 2010; Dee et al. 2011; Gelaro et al. 2017) and operational numerical weather prediction systems (de Rosnay et al. 2013; Lucchesi 2013a). Some of these model-based products assimilate surface observations to improve the quality of the soil moisture estimates. For example, the SM-DAS-2 product (Albergel et al. 2012) assimilates ASCAT surface soil moisture retrievals and screen-level air temperature and humidity measurements. Furthermore, precipitation observations are used in several reanalysis products, including the Climate Forecasting System Reanalysis (Saha et al. 2010), MERRA-Land (Reichle et al. 2011), ERA-Interim/Land (Balsamo et al. 2015), and MERRA-2 (Reichle et al. 2017a,b).

The SMAP Level-4 Surface and Root-Zone Soil Moisture (L4_SM) product is generated using a land

data assimilation system that combines the advantages of spaceborne L-band brightness temperature measurements, precipitation observations, and land surface modeling (section 2). The land model's key strength is its reliance on conservation principles for water (converting precipitation inputs into evaporation, runoff, and storage change) and energy (converting incident radiation into outgoing radiation, latent heat flux, sensible heat flux, storage change, and other miscellaneous terms). Given realistic forcing data, these conservation principles ensure at least some first-order reliability in the simulation products, which are then further corrected through the assimilation of SMAP brightness temperature observations.

The L4_SM assimilation system provides two major and invaluable benefits for soil moisture estimation. First, the system facilitates complete coverage in space and time (as opposed to just the times and locations of satellite overpasses). Second, the embedded land model provides a means for producing soil moisture estimates at levels below the ~0-5 cm surface layer that is directly sampled by the satellite instrument. By design, the L4_SM surface and deeper layer soil moisture estimates are consistent with the available SMAP satellite observations. That is, during the course of the data assimilation process, the subsurface transport formulations in the land model (along with the subsurface assimilation updates) effectively propagate the surface soil moisture and temperature information that is contained in the SMAP brightness temperatures into the deeper soil levels. The L4_SM product thus facilitates the use of SMAP data in applications that require complete spatiotemporal coverage and/or knowledge of deeper-layer soil moisture. The latter is particularly relevant for drought monitoring, water resource management, and subseasonal to seasonal climate forecasting.

The SMAP L4_SM product is available every 3 h on a global grid with 9-km spacing, thereby interpolating and extrapolating the coarser-scale (~40 km) SMAP observations in time and in space (both horizontally and vertically). The product is published within about 3 days from the time of observation, with the latency primarily dictated by the availability of the gauge-based precipitation product used to drive the land model (Reichle and Liu 2014).

The main objective of this study is to assess the quality of the L4_SM soil moisture and temperature estimates versus in situ measurements. In the following, we describe the L4_SM algorithm and product (section 2), discuss our validation approach (section 3), evaluate the L4_SM product against in situ measurements (section 4), and provide a
summary and conclusions (section 5). A companion paper (Reichle et al. 2017, manuscript submitted to *J. Hydrometeor.*.) assesses the internal diagnostics of the L4_SM algorithm, including the observation-minus-forecast residuals and the analysis increments. Their key findings, updated from Reichle et al. (2016a), confirm that the L4_SM analysis is unbiased and produces realistic soil moisture and soil temperature increments that result in spatially consistent soil moisture and temperature analysis fields.

## 2. L4_SM algorithm and data product

Reichle et al. (2014) and De Lannoy and Reichle (2016a,b) provide a detailed description of the Goddard Earth Observing System, version 5 (GEOS-5), land data assimilation system (LDAS), which forms the basis of the L4_SM algorithm. Here, we briefly summarize their discussion, highlight key features of the L4_SM system, and point out differences between the L4_SM algorithm and the SMOS assimilation described in (De Lannoy and Reichle 2016a,b).

### a. Overview

The L4_SM algorithm, shown schematically in Fig. 1, is a customized version of the ensemble-based GEOS-5 LDAS built around the GEOS-5 Catchment land surface model (hereinafter “Catchment model”; Koster et al. 2000; Ducharne et al. 2000). The primary drivers of this system are the SMAP L1C_TB brightness temperature observations (section 2d) and the surface meteorological forcing data from the GEOS-5 atmospheric assimilation system, corrected with precipitation observations (section 2b). The SMAP brightness temperature observations are merged with the model estimates using a spatially distributed ensemble Kalman filter (EnKF; section 2d). Briefly, the L4_SM algorithm interpolates and extrapolates the information from the SMAP observations and the model estimates in time and in space, taking into consideration the relative uncertainties of each; the L4_SM data product represents the merged information.

The L4_SM data are generated and distributed on the global, cylindrical, 9-km Equal-Area Scalable Earth, version 2 (EASEv2) grid (Brodzik et al. 2012). The L4_SM outputs include soil moisture estimates for the “surface” (0–5 cm), “root zone” (0–100 cm) and “profile” (from 0 cm to depth of bedrock) layers. A single root-zone depth was chosen in the modeling system to make the SMAP product more straightforward; in nature, the depths tapped by roots vary with vegetation type, soil type, and other environmental

factors (Jackson et al. 1996). Along with soil moisture, a large number of related land surface variables are also available in the L4_SM product, including soil temperature, snow mass, land surface fluxes, surface meteorological forcing data, assimilation diagnostics, and land model parameters. L4_SM surface soil temperature estimates are for the 0–10-cm layer except for tropical (broadleaf evergreen) forests, which are not considered here. The L4_SM soil temperature and snow estimates can be used to screen or flag the L4_SM soil moisture output for times and locations with frozen or snow-covered ground.

The generation of the L4_SM product involves three basic time scales: 1) the land model computational time step of 7.5 min, 2) the 3-h EnKF analysis update time step, and 3) the 3-h reporting (or output) time step for the published instantaneous and time-average output fields. The available SMAP brightness temperature observations are assimilated in an EnKF analysis update step at the nearest 3-hourly analysis time (0000, 0300, ..., and 2100 UTC). The latest L4_SM data are generated operationally once per day by the NASA Global Modeling and Assimilation Office and then automatically delivered to the National Snow and Ice Data Center (NSIDC), where they become available to the public almost immediately.

Here, we use L4_SM version 2 data (Science Version ID: Vv2030) for the period from April 2015 to November 2016. Specifically, we use 3-hourly, instantaneous “analysis” soil moisture and soil temperature fields from the “analysis update” files (Reichle et al. 2016b) and time-invariant land model parameters (including soil porosity and wilting point) from the “land-model constants” file (Reichle et al. 2016c). Note that 3-hourly time-averaged soil moisture and many other land surface fields are provided in the “geophysical” files (Reichle et al. 2016d). See (Reichle et al. 2015a) and the NSIDC website (https://nsidc.org/data/smap/) for

<figure><img src="image_3.png" /><figcaption>FIG. 1. Schematic of the L4_SM algorithm and data product. See section 2 for details and abbreviations.</figcaption></figure>
complete lists of the available data fields and further
details about data product specifications.

b. *Modeling system*

In the Catchment model, the vertical character of soil
moisture for each grid cell is determined 1) by the spa-
tially varying equilibrium profile (defined by a balance
of gravity and capillary forces) from the surface to
the spatially (horizontally and vertically) varying water
table (related to the model's "catchment deficit" prog-
nostic variable) and 2) by two additional model prog-
nostic variables that describe the average deviations
from the equilibrium profiles in the 0-100-cm root-zone
layer (root-zone excess) and in the 0-5-cm surface layer
(surface excess). The volumetric soil moisture estimates
provided in the L4_SM product are diagnosed from
these three model prognostic variables.

The Catchment model differs from traditional, layer-
based models by including an explicit treatment of the
spatial variation of soil water and water table depth
within each 9-km grid cell based on the statistics of the
catchment topography. This spatial variation enters into
the calculation of moisture diffusion between the root
zone and deeper soil moisture storage. The treatment of
spatial heterogeneity also allows for the diagnostic
separation of each grid cell into “saturated,” “un-
saturated,” and “wilting” subgrid areas whose sizes vary
dynamically. The surface energy balance is computed
separately for each subgrid area using physics specific to
its corresponding hydrological regime. For example,
transpiration may be water limited in the “unsaturated”
subgrid area while it is energy limited in the “saturated”
subgrid area. This entails the monitoring of independent
prognostic surface (skin) temperature variables for each
subgrid area, which in turn interact with an underlying,
six-layer heat diffusion model for soil temperature that
is common to all three subgrid areas. A three-layer snow
model component describes the state of the snowpack in
terms of snow water equivalent, snow depth, and snow
heat content (Stieglitz et al. 2001).

The Catchment model version and parameters of the
(version 2) L4_SM system match those of MERRA-2
(Reichle et al. 2017b, their Table 2) except for the fol-
lowing four differences: 1) the L4_SM soil hydraulic
parameters are based on the pedotransfer functions of
Wösten et al. (2001) applied to soil textures from the
Harmonized World Soil Database (version 1.21) and the
State Soil Geographic (STATSGO2) project [labeled
"REV" in De Lannoy et al. (2014b)]; 2) the WEMIN
snow parameter, which governs the model's snow de-
pletion curve, is set to 13 kg m⁻² (Reichle et al. 2017b);
3) the leaf area index is based on a merger of data from
the Moderate Resolution Imaging Spectroradiometer

(MODIS) and the GEOLAND product (Mahanama
et al. 2015); and 4) the surface turbulence scheme is that
of Louis (1979). For further details, see De Lannoy and
Reichle (2016a, their section 2b).

The observation-minus-forecast brightness tempera-
ture residuals needed in the soil moisture analysis
 subsection 2d) are computed by converting the Catchment
model soil moisture and temperature estimates into
estimates of L-band brightness temperatures using
a zero-order "tau-omega" radiative transfer model
(RTM; De Lannoy et al. 2013). Select RTM input pa-
rameters, including the microwave surface roughness,
vegetation structure parameter, and scattering albedo,
were calibrated prior to the SMAP launch using multi-
angular L-band brightness temperature observations
from SMOS (De Lannoy et al. 2014a). This calibration
ensured that the long-term mean and variance of
the modeled brightness temperatures match those of
SMOS. Residual seasonal biases are addressed through
rescaling (section 2d).

The Catchment model is driven with surface meteo-
rological forcing data from the GEOS-5 forward-
processing (FP) system at 0.25° × 0.3125° (latitude ×
longitude) resolution (GEOS-5.13.0 prior to 1 May
2015, then GEOS-5.13.1 until 24 January 2017, and
GEOS-5.16 thereafter; Lucchesi 2013a). The GEOS-5
precipitation data are corrected with gauge-based pre-
cipitation observations from the NOAA Climate Pre-
diction Center Unified (CPCU; Xie et al. 2007; Chen
et al. 2008) product (Fig. 1). The CPCU data are scaled
to the climatology of the Global Precipitation Clima-
tology Project, version 2.2 (GPCPv2.2; Adler et al. 2003;
Huffman et al. 2009) pentad precipitation product. The
precipitation corrections are applied in full within 42.5°
latitude of the equator except in Africa, where no cor-
rections are applied because too few gauges are avail-
able there. Between 42.5° and 62.5° latitude (in the
Northern and Southern Hemispheres), the precipitation
corrections are linearly tapered between full corrections
(at 42.5° latitude) and no corrections (at 62.5° latitude).
Poleward of 62.5° latitude, the model is forced with the
uncorrected GEOS-5 FP precipitation. See Reichle and
Liu (2014) and Reichle et al. (2017a) for further details
on the precipitation correction algorithm.

c. *NRv4 simulation*

A longer-term, model-only simulation termed the
Nature Run, version 4 (NRv4), was conducted for
the period from 2001 through present. NRv4 is a
single-member, unperturbed simulation using the
Catchment model version of the L4_SM algorithm
on the same 9-km EASEv2 grid. Through 2013, the
model is driven with surface meteorological forcing
from the GEOS-5.9.1 forward-processing for instrument teams (FP-IT) product at 0.5° × 0.625° (latitude × longitude) resolution (Lucchesi 2013b). Thereafter, forcing is from the GEOS-5 FP product at 0.25° × 0.3125° resolution (GEOS-5.11.0 prior to 1 August 2014, as for L4_SM thereafter). The precipitation corrections used for NRv4 are the same as for the L4_SM product.

The NRv4 simulation plays three roles in this study. First, the NRv4 simulation provides initial conditions for the ensemble simulation required to estimate the brightness temperature rescaling parameters, which in turn provides the ensemble initial conditions for the L4_SM simulation starting 31 March 2015 at 0000 UTC. (NRv4 was itself spun up for 15 years.) Second, the NRv4 simulation provides the multiyear climatological information needed to 1) calibrate the L4_SM RTM parameters, 2) determine the parameters that convert L4_SM root-zone and profile soil moisture from volumetric to percentile units, and 3) calibrate the level-4 carbon algorithm (Jones et al. 2017). Third, the NRv4 outputs provide a model-only reference skill against which the impact of the SMAP observations on the skill of the L4_SM product can be measured (section 4).

### d. Assimilation of SMAP brightness temperature observations

The version 2 L4_SM algorithm assimilates horizontally (H) and vertically (V) polarized SMAP brightness temperature observations from the version 3 SMAP L1C_TB product (Chan et al. 2016a) after averaging the fore- and aft-looking measurements provided in the L1C_TB product on their native 36-km EASEv2 grid. Brightness temperatures from the ascending [~1800 local time (LT) equator crossing] and descending (~0600 LT equator crossing) half orbits are assimilated. The version 2 L4_SM algorithm does not assimilate data products that are based on the SMAP radar, which failed on 7 July 2015.

The ensemble-based L4_SM data assimilation algorithm is shown schematically in Fig. 1 of De Lannoy and Reichle (2016b), but note that for the L4_SM system discussed here the model is on the 9-km grid, and the assimilated SMAP observations are only available for a single, 40° incidence angle. The EnKF updates in the L4_SM algorithm are spatially distributed in the sense that all observations within a radius of 1.25° impact the analysis at a given 9-km grid cell (De Lannoy and Reichle 2016b, their section 3.1). The weight of an observation-minus-forecast residual toward the soil moisture (and temperature) increments at a given 9-km grid cell is proportional to the modeled error correlations between the brightness temperature at the

observation location and the soil moisture (and temperature) at the location of the increment. This correlation-based weight typically decays with increasing distance of the observation from the location of the increment. The L4_SM system uses 24 ensemble members. The perturbation parameters for the model forcing and prognostic variables match those of De Lannoy and Reichle (2016a, their Table 2), except that the spatial correlation scale for the model prognostics perturbations is set to 0.3° in the L4_SM system.

Seasonally varying bias in the modeled brightness temperatures is addressed prior to assimilation by converting the observations and model forecast brightness temperatures into anomalies from their respective long-term mean seasonal cycles. Since the brightness temperature is strongly impacted by the surface temperature and the RTM parameters, this is done separately for each 36-km grid cell, polarization, and orbit direction (i.e., time of day). For details, see De Lannoy and Reichle (2016a, their section 3b and Figs. 1 and 2). For the version 2 L4_SM system, the mean seasonal cycles for the assimilated SMAP brightness temperatures were estimated from SMOS (version 5) observations for the period from July 2010 to June 2014, after interpolating the SMOS data to the 40° SMAP incidence angle (De Lannoy et al. 2015). The mean seasonal cycles for the modeled brightness temperatures were computed from subsampled model output (at the times and locations of SMOS overpasses), generated with the ensemble L4_SM modeling system using surface meteorological forcing as for NRv4 (section 2c).

Only SMAP brightness temperature observations deemed to be of good quality are assimilated (i.e., the lowest bit of the L1C_TB quality flag must equal zero). Moreover, observations that fall outside the natural range between 100 and 320 K are excluded from the assimilation. Observations are further screened based on the modeled soil temperature (must be greater than 273.35 K) and snow mass (must be less than $10^{-4} \text{ kg m}^{-2}$) to exclude times and locations with frozen or snow-covered soil conditions, for which the RTM is not valid. Finally, the (hourly) precipitation rate at the observation time and location must be less than $2 \text{ mm h}^{-1}$ to minimize the detrimental impact of standing water on the analysis. These model-based conditions must be satisfied for all 9-km grid cells within a radius of 40 km from the center point of the observation.

The total brightness temperature observation error standard deviation is set to a constant value of 4 K. This error includes the instrument error (~1.3 K; Piepmeier et al. 2017) and the much larger representativeness error (~3.8 K). The latter consists of all errors associated with the observation operator, including errors in the
approximation of the footprint of the satellite observations as well as errors in the RTM-based conversion of the model state vector into brightness temperatures. Since for a given brightness temperature observation only about 50% of the signal originates from a circle with a radius of 20 km, we assume an isotropic spatial correlation length for the observation error of 0.25°. Observation errors of H- and V-polarization brightness temperatures are assumed to be uncorrelated, even though this assumption is likely wrong for the representativeness error component. The estimates for the observation and model error parameters used in the L4_SM system are similar to those of De Lannoy and Reichle (2016a,b) and are motivated by the positive results obtained with the assimilation of SMOS observations. Results presented below demonstrate that the assimilation of SMAP data with these error settings also produces skill enhancements. Further refinement of the error parameters may lead to additional skill improvements but is left for future work.

### 3. Validation approach and measurements

The L4_SM product is primarily validated through comparison with independent in situ measurements (section 4). Suitable measurements fall into two main categories: 1) for a limited set of climate and land cover conditions, “core validation site” measurements provide accurate estimates of soil moisture at the 9- or 36-km scales of the model and satellite estimates (section 3b), and 2) for a much wider range of conditions, “sparse network” measurements provide soil moisture estimates at a single, point-scale location within a 9-km model grid cell (section 3c).

#### a. L4_SM accuracy requirement, validation metrics, and processing of in situ measurements

The accuracy requirement for the L4_SM surface and root-zone soil moisture estimates is that their average unbiased RMSE (ubRMSE) versus in situ measurements must be less than 0.04 m³ m⁻³ (excluding regions of snow and ice, frozen ground, mountainous topography, open water, urban areas, and vegetation with water content greater than 5 kg m⁻²). The ubRMSE is the RMSE computed after removing the long-term mean bias from the data, also referred to as the standard deviation of the error (Entekhabi et al. 2010b; Reichle et al. 2015b, their appendix A). The meeting of the requirement is verified by comparing the L4_SM estimates to the 9-km gridcell scale in situ measurements from the core validation sites (section 3b).

In addition to the ubRMSE, we also determine the time series correlation coefficient *R* and the bias. The

latter is computed as the mean of the differences between the L4_SM (or NRv4) estimates and the in situ measurements (i.e., estimates minus measurements). Metrics are computed wherever suitable in situ measurements are available, including for densely vegetated or topographically complex areas outside of the limited geographic region for which the 0.04 m³ m⁻³ validation criterion applies. Metrics are computed using 3-hourly data for the period from 1 April 2015 to 31 March 2017 if at least 480 data points are available. All in situ measurements used here are subjected to extensive automated and manual quality control procedures following Liu et al. (2011), De Lannoy et al. (2014b), Entekhabi et al. (2014), and Reichle et al. (2015b, their appendix C) to remove spikes, temporal inhomogeneities, oscillations, and other artifacts commonly seen in automated measurements. Moreover, we exclude times when the soil temperature is below 4°C or when the soil is partially or fully snow covered.

Surface soil moisture and temperature are validated against measurements from the uppermost sensor (typically at ~5 cm depth, see below). Root-zone soil moisture is validated against vertical averages of in situ measurements using weights that are proportional to the spacing of the sensor depths within the 0–100-cm layer (see below). In all cases, the deepest sensors used here are weighted most strongly. Vertical averages are only computed if all sensors within a given profile provide measurements that pass quality control.

For each statistic, we also computed 95% confidence intervals that take into account temporal autocorrelation in the time series (De Lannoy and Reichle 2016a, their section 4b). The metrics provided here are conservative skill estimates because they ignore errors in the in situ measurements. Triple collocation techniques could be used to correct for such errors (Chen et al. 2017) but are not considered here. In any case, the relative performance of the L4_SM and NRv4 estimates does not depend on the use of triple collocation approaches.

#### b. Core validation site measurements

Core validation sites have locally dense sensor networks that provide accurate soil moisture and soil temperature measurements at the gridcell scale of the L4_SM product. For any given core validation site, however, the spatial distribution of the in situ sensors is typically not aligned with the grid cells of the standard EASEv2 grid. Therefore, we defined custom “shifted” grid cells (or reference pixels) that better exploit the spatial coverage of the in situ measurements at each site, but that do not necessarily align with the standard EASEv2 grid (for examples, see Fig. 4 of Colliander et al. 2017). The
gridcell-scale measurements are then computed as the weighted average of the contributing sensor measurements using Thiessen polygons or, if available, custom upscaling functions derived from intensive field campaigns (Colliander et al. 2017, their Fig. 7).

A core validation site may provide in situ measurements for one or more 9-km and/or 36-km reference pixels. Core validation site reference pixels must satisfy a number of criteria, including verification through an intensive field campaign and provision of a minimum number and representative distribution of sensors within the reference pixel (Reichle et al. 2015b, their section 6.2; Colliander et al. 2017). For the comparison against the in situ measurements, the 9-km L4_SM estimates are interpolated bilinearly to the location of the 9-km reference pixels and are aggregated (using area-weighted averaging) for comparison to the 36-km reference pixel estimates. A repeat of the assessment using nearest-neighbor interpolation resulted in skill differences that were much smaller than the typical differences between the L4_SM and NRv4 skill metrics (not shown).

Table 1 lists the core validation sites and reference pixels used here consisting of a total of 43 reference pixels from 19 different core validation sites. Table 2 breaks down the number of core validation sites and reference pixels with suitable quantities of measurements by variable and by horizontal scale. Surface soil moisture measurements are available for all 43 reference pixels. Root-zone soil moisture measurements are available for only 17 reference pixels. Root-zone soil moisture measurements at the 9-km scale are available from only six different sites, all of which are in North America (Little Washita, Fort Cobb, Little River, South Fork, Kenaston, and TxSON). Surface soil temperature measurements at 0600 LT (1800 LT) are available for 35 (36) references pixels. Average metrics across all reference pixels of a given horizontal scale (9 or 36 km) are computed using the arithmetic average of the metrics at the individual reference pixels. The 95% confidence intervals are first averaged in the same way and then divided by the square root of the number of different core validation sites contributing to the metric (as listed in Table 2).

Table 1 also lists the depths of the shallowest sensors, which are used to validate the L4_SM surface soil moisture and surface soil temperature estimates. Moreover, Table 1 provides the depths of the deepest sensors that contribute to the in situ root-zone soil moisture measurements. At all reference pixels except Little River and Yanco, the deepest sensors are at 45 or 50 cm depth. At Little River, the deepest sensors are at 30 cm depth. At Yanco, the deepest sensors are installed

vertically and centered at depths of 45 and 75 cm, representing the 30–60-cm and 60–90-cm layers, respectively. For many sites, individual sensors tend to drop out temporarily, which leads to undesirable discontinuities in the reference pixel average soil moisture. To mitigate this effect, we require at least eight individual, complete sensor profiles (after quality control) to compute the reference pixel average, provided at least eight sensor profiles were in the ground. For the 17 reference pixels that are based on fewer than eight sensor profiles, we require data from all contributing sensor profiles (after quality control) to compute the reference pixel average. The time-averaged number of individual sensors that contribute to any given 36-km reference pixel average ranges between 6 and 33.2 for surface soil moisture (Table 1), with a mean value of 15.3 (not shown). At the 9-km scale, 14 of the 26 surface reference pixels are based on fewer than eight individual sensor profiles, while the rest of the 9-km reference pixels have eight or more sensor profiles each (Table 1), with a mean value of 7.4 across all 9-km reference pixels (not shown).

### c. Sparse network measurements

The defining feature of sparse network measurements is that there is usually just one sensor (or profile of sensors) located within a given 9-km EASEv2 grid cell. The sparse network measurements used here include data from the USDA Natural Resources Conservation Service Soil Climate Analysis Network (SCAN; Schaefer et al. 2007), the U.S. Climate Reference Network (USCRN; Bell et al. 2013; Diamond et al. 2013), the Oklahoma Mesonet (McPherson et al. 2007), and the OzNet in Australia's Murrumbidgee catchment (Smith et al. 2012). Note that for the Australian data, the core validation site and the sparse network results are not independent because about three-quarters of the OzNet sites also contributed to the gridcell-scale soil moisture measurements of the Yanco reference pixels.

Table 3 lists the number of sparse network sites with sufficient data after quality control. Across all networks, 406 locations have surface and 311 have root-zone soil moisture measurements. Most of the sites are in the continental United States, including about 100 each in the USCRN and SCAN networks, and another 100 in Oklahoma from the Mesonet. OzNet contributes 42 sites with surface soil moisture measurements, 18 of which also provide root-zone measurements. Moreover, Table 3 lists the measurement depths used for computing root-zone measurements. For SCAN and USCRN sites, measurements at 50 cm (and occasionally 100 cm) depth are available. It is, however, very difficult to take and verify such deeper-layer measurements consistently
<table><caption>TABLE 1. Core validation sites and reference pixels. Information for 36-km reference pixels is shown in bold.</caption><thead><tr><th rowspan="2">Site name</th><th rowspan="2">Country</th><th rowspan="2">Climate regime</th><th rowspan="2">Land cover</th><th rowspan="2">ID</th><th rowspan="2">Lat (°)</th><th rowspan="2">Lon (°)</th><th rowspan="2">Horizontal scale (km)</th><th rowspan="2">Depth of deepest sensor (m)</th><th colspan="4">Reference pixel</th><th rowspan="2">Number of sensors (surface soil moisture)</th><th rowspan="2">Number of sensors (root-zone profiles)</th></tr><tr><th>Min</th><th>Mean</th><th>Max</th><th>Min</th><th>Mean</th><th>Max</th></tr></thead><tbody><tr><td rowspan="2">REMEDHUS</td><td rowspan="2">Spain</td><td rowspan="2">Temperate</td><td rowspan="2">Croplands</td><td>03013602</td><td>41.28</td><td>-5.41</td><td>36</td><td>0.05</td><td>8</td><td>14.6</td><td>17</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>03010903</td><td>41.42</td><td>-5.37</td><td>9</td><td>0.05</td><td>4</td><td>4.0</td><td>4</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Reynolds Creek</td><td rowspan="2">United States (Idaho)</td><td rowspan="2">Arid</td><td rowspan="2">Grasslands</td><td>03010908</td><td>41.32</td><td>-5.27</td><td>9</td><td>0.05</td><td>4</td><td>4.0</td><td>4</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>04013603</td><td>43.14</td><td>-116.76</td><td>36</td><td>0.05</td><td>8</td><td>9.5</td><td>11</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Yanco</td><td rowspan="2">Australia (New South Wales)</td><td rowspan="2">Arid</td><td rowspan="2">Cropland/natural mosaic</td><td>04010907</td><td>43.19</td><td>-116.72</td><td>9</td><td>0.05</td><td>4</td><td>4.0</td><td>4</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>04010910</td><td>43.09</td><td>-116.81</td><td>9</td><td>0.05</td><td>4</td><td>4.0</td><td>4</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Carman</td><td rowspan="2">Canada (Manitoba)</td><td rowspan="2">Cold</td><td rowspan="2">Croplands</td><td>07013601</td><td>-34.85</td><td>146.17</td><td>36</td><td>0.75</td><td>9</td><td>25.4</td><td>28</td><td>7</td><td>7.0</td><td>7</td></tr><tr><td>07010902</td><td>-34.72</td><td>146.13</td><td>9</td><td>0.05</td><td>8</td><td>10.2</td><td>11</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Ngari Walnut Gulch</td><td rowspan="2">China (Tibet) United States (Arizona)</td><td rowspan="2">Cold Arid</td><td rowspan="2">Barren/sparse Shrub open</td><td>07010916</td><td>-34.98</td><td>146.31</td><td>9</td><td>0.05</td><td>8</td><td>10.3</td><td>11</td><td>—</td><td>—</td><td>—</td></tr><tr><td>09010906</td><td>49.67</td><td>-97.98</td><td>9</td><td>0.05</td><td>8</td><td>10.1</td><td>11</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Little Washita</td><td rowspan="2">United States (Oklahoma)</td><td rowspan="2">Temperate</td><td rowspan="2">Grasslands</td><td>12033601</td><td>32.41</td><td>79.98</td><td>36</td><td>0.05</td><td>6</td><td>6.0</td><td>6</td><td>—</td><td>—</td><td>—</td></tr><tr><td>16010907</td><td>34.92</td><td>-98.04</td><td>9</td><td>0.45</td><td>8</td><td>10.6</td><td>12</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Fort Cobb</td><td rowspan="2">United States (Oklahoma)</td><td rowspan="2">Temperate</td><td rowspan="2">Grasslands</td><td>16023602</td><td>34.88</td><td>-98.09</td><td>36</td><td>0.45</td><td>8</td><td>15.5</td><td>18</td><td>8</td><td>13.4</td><td>17</td></tr><tr><td>16020907</td><td>34.92</td><td>-98.04</td><td>9</td><td>0.45</td><td>4</td><td>4.0</td><td>4</td><td>4.0</td><td>4.0</td><td>4</td></tr><tr><td rowspan="2">Little River</td><td rowspan="2">United States (Georgia)</td><td rowspan="2">Temperate</td><td rowspan="2">Cropland/natural mosaic</td><td>16033602</td><td>35.42</td><td>-98.62</td><td>36</td><td>0.45</td><td>8</td><td>12.3</td><td>13</td><td>8</td><td>11.1</td><td>13</td></tr><tr><td>16030911</td><td>35.38</td><td>-98.57</td><td>9</td><td>0.45</td><td>4</td><td>4.0</td><td>4</td><td>4.0</td><td>4.0</td><td>4</td></tr><tr><td rowspan="2">St Josephs South Fork</td><td rowspan="2">United States (Indiana) United States (Iowa)</td><td rowspan="2">Temperate Cold</td><td rowspan="2">Croplands</td><td>16043602</td><td>31.60</td><td>-83.59</td><td>36</td><td>0.30</td><td>8</td><td>19.8</td><td>23</td><td>8</td><td>18.6</td><td>22</td></tr><tr><td>16040901</td><td>31.72</td><td>-83.73</td><td>9</td><td>0.30</td><td>8</td><td>8.0</td><td>8</td><td>6</td><td>6.0</td><td>6</td></tr><tr><td rowspan="2">Monte Buey</td><td rowspan="2">Argentina</td><td rowspan="2">Temperate</td><td rowspan="2">Croplands</td><td>16060907</td><td>41.45</td><td>-84.97</td><td>9</td><td>0.05</td><td>8</td><td>8.2</td><td>9</td><td>—</td><td>—</td><td>—</td></tr><tr><td>16073602</td><td>42.47</td><td>-93.39</td><td>36</td><td>0.50</td><td>8</td><td>14.4</td><td>15</td><td>8</td><td>13.1</td><td>15</td></tr><tr><td rowspan="2">Tonzi Ranch</td><td rowspan="2">United States (California)</td><td rowspan="2">Temperate</td><td rowspan="2">Savannas woody</td><td>19023601</td><td>-32.96</td><td>-62.52</td><td>36</td><td>0.05</td><td>8</td><td>10.3</td><td>13</td><td>—</td><td>—</td><td>—</td></tr><tr><td>19020902</td><td>-33.01</td><td>-62.49</td><td>9</td><td>0.05</td><td>5</td><td>5.0</td><td>5</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Kenaston</td><td rowspan="2">Canada (Saskatchewan)</td><td rowspan="2">Cold</td><td rowspan="2">Croplands</td><td>25013601</td><td>38.47</td><td>-121.00</td><td>36</td><td>0.05</td><td>8</td><td>17.5</td><td>26</td><td>—</td><td>—</td><td>—</td></tr><tr><td>27013601</td><td>51.45</td><td>-106.46</td><td>36</td><td>0.50</td><td>8</td><td>25.7</td><td>28</td><td>8</td><td>23.1</td><td>28</td></tr><tr><td rowspan="2">Valencia Niger</td><td rowspan="2">Spain Niger</td><td rowspan="2">Cold Arid</td><td rowspan="2">Savannas woody Grassland</td><td>27010910</td><td>51.39</td><td>-106.51</td><td>9</td><td>0.05</td><td>8</td><td>8.0</td><td>8</td><td>—</td><td>—</td><td>—</td></tr><tr><td>27010911</td><td>51.39</td><td>-106.42</td><td>9</td><td>0.50</td><td>8</td><td>13.6</td><td>14</td><td>8</td><td>12.2</td><td>14</td></tr><tr><td rowspan="2">Valencia Niger</td><td rowspan="2">Spain Niger</td><td rowspan="2">Cold Arid</td><td rowspan="2">Savannas woody Grassland</td><td>41010906</td><td>39.57</td><td>-1.26</td><td>9</td><td>0.05</td><td>6</td><td>6.0</td><td>6</td><td>—</td><td>—</td><td>—</td></tr><tr><td>45010902</td><td>13.55</td><td>2.69</td><td>9</td><td>0.05</td><td>4</td><td>4.0</td><td>4</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>
<table><caption>TABLE 1. (Continued)</caption><thead><tr><th rowspan="2">Site name</th><th rowspan="2">Country</th><th rowspan="2">Climate regime</th><th rowspan="2">Land cover</th><th rowspan="2">ID</th><th rowspan="2">Lat (°)</th><th rowspan="2">Lon (°)</th><th rowspan="2">Horizontal scale (km)</th><th rowspan="2">Depth of deepest sensor (m)</th><th colspan="4">Reference pixel</th></tr><tr><th>Number of sensors (surface soil moisture)</th><th>Min</th><th>Mean</th><th>Max</th><th>Number of sensors (root-zone profiles)</th><th>Min</th><th>Mean</th><th>Max</th></tr></thead><tbody><tr><td>Benin</td><td>Benin</td><td>Tropical</td><td>Savannas</td><td>45023601</td><td>9.77</td><td>1.68</td><td>36</td><td>0.05</td><td>7</td><td>7.0</td><td>7</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="3">TxSON</td><td rowspan="3">United States (Texas)</td><td rowspan="3">Temperate</td><td rowspan="3">Grasslands</td><td>45020902</td><td>9.80</td><td>1.73</td><td>9</td><td>0.05</td><td>5</td><td>5.0</td><td>5</td><td>—</td><td>—</td><td>—</td></tr><tr><td>48013601</td><td>30.31</td><td>-98.78</td><td>36</td><td>0.50</td><td>10</td><td>33.2</td><td>35</td><td>10</td><td>26.3</td><td>28</td><td>—</td><td>—</td></tr><tr><td>48010902</td><td>30.43</td><td>-98.82</td><td>9</td><td>0.50</td><td>8</td><td>9.9</td><td>11</td><td>8</td><td>8.6</td><td>10</td><td>—</td><td>—</td></tr><tr><td rowspan="2">HOBE</td><td rowspan="2">Denmark</td><td rowspan="2">Temperate</td><td rowspan="2">Croplands</td><td>48010911</td><td>30.27</td><td>-98.73</td><td>9</td><td>0.50</td><td>8</td><td>14.4</td><td>15</td><td>8</td><td>13.7</td><td>14</td></tr><tr><td>67013601</td><td>55.97</td><td>9.10</td><td>36</td><td>0.05</td><td>8</td><td>15.1</td><td>21</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

over long periods of time. These measurements are therefore not of the quantity and quality required for L4_SM validation and are not used here. For OzNet, the measurements at the 45-cm depth are used as root-zone measurements.

The sparse network measurements are compared to the L4_SM and NRv4 data from the standard 9-km EASEv2 grid cell that includes the sensor location. Spatially averaged skill metrics are calculated by clustering sites geographically to keep densely sampled areas from dominating the validation metrics and to ensure realistic confidence intervals (De Lannoy and Reichle 2016a). The number of clusters is estimated a priori after prescribing an average cluster radius of 1.5°, which is similar to the 1.25° compact support length scale of the L4_SM analysis (section 2d). The 95% confidence intervals are first averaged in the same way and then divided by the square root of the number of clusters.

Sparse network results are grouped into locations with “favorable” or “unfavorable” conditions for soil moisture estimation from spaceborne brightness temperature observations. Favorable locations include all areas where the accuracy requirement (section 3a) applies. Unfavorable locations include areas where 1) the maximum climatological leaf area index exceeds 5 m² m⁻² (MODIS 2008), 2) the predominant land cover is forest, wetland, or urban according to the International Geosphere-Biosphere Programme (IGBP) DISCover (Loveland et al. 2000) vegetation classification, 3) the topography is complex (elevation standard deviation greater than 71 m), or 4) the elevation of the sensor location differs by more than 500 m from the mean elevation of the surrounding 36-km grid cell. The above grouping is determined using the land cover, vegetation, and topography parameters of the L4_SM modeling system (Mahanama et al. 2015).

## 4. Results

In this section, we present a detailed, quantitative analysis of the skill of the L4_SM soil moisture and temperature estimates in reproducing in situ measurements from the core validation sites (section 4a) and sparse networks (section 4b). Some of the text in this section is from two non-peer-reviewed project reports (Reichle et al. 2015b, 2016a) and has been updated to reflect the results obtained for the version 2 L4_SM product and the longer validation period used here.

### a. Core site validation

In this subsection, we present the validation results using core site measurements. We first discuss the soil moisture validation results for three representative
<table><caption>TABLE 2. Number of different core sites and number of reference pixels used in the soil moisture and temperature validation.</caption><thead><tr><th rowspan="2">Horizontal scale</th><th colspan="2">Surface soil moisture</th><th colspan="2">Root-zone soil moisture</th><th colspan="2">Surface soil temperature (0600 LT)</th><th colspan="2">Surface soil temperature (1800 LT)</th></tr><tr><th>36 km</th><th>9 km</th><th>36 km</th><th>9 km</th><th>36 km</th><th>9 km</th><th>36 km</th><th>9 km</th></tr></thead><tbody><tr><td>Number of different core sites</td><td>17</td><td>17</td><td>7</td><td>6</td><td>14</td><td>12</td><td>14</td><td>13</td></tr><tr><td>Number of reference pixels</td><td>17</td><td>26</td><td>7</td><td>9</td><td>14</td><td>21</td><td>14</td><td>22</td></tr></tbody></table>

reference pixels (Little Washita, Little River, and South Fork) that exemplify features of the L4_SM estimates and indicate aspects needing improvement. For reference, Table 4 lists the metrics for all 43 reference pixels. Thereafter, we present average soil moisture and temperature metrics across all reference pixels and demonstrate that the L4_SM product meets its accuracy requirement.

### 1) LITTLE WASHITA (OKLAHOMA)

The Little Washita, Oklahoma, site is situated in grasslands in a temperate, subhumid climate. Based on several field campaigns that addressed in situ sensor calibration and upscaling (Cosh et al. 2006), the confidence in the quality of the in situ estimates at this site is very high, and good product performance at this site is considered to be important. Figure 2 shows the L4_SM, NRv4, and in situ time series for the 36-km reference pixel. (The results for the 9-km reference pixel at Little Washita are qualitatively similar, but there are long gaps in the in situ measurements.) Soil moisture varies considerably during the validation period, owing to the exceptionally wet conditions during May 2015 and the very dry conditions in August and September of both years. The L4_SM and NRv4 estimates clearly capture the overall variability, as well as the timing of the major rainstorms. However, neither the NRv4 nor the L4_SM estimates fully capture the wet conditions starting in late October 2015 and lasting through the winter of 2015/16. Nevertheless, the time series correlation coefficients are very high, with *R* values of 0.81 for L4_SM surface soil moisture and 0.88 for L4_SM root-zone soil moisture, which is an improvement over the already high values of 0.73 and 0.87 for NRv4 surface and root-zone soil moisture, respectively (Table 4).

The improvement is also reflected in the ubRMSE metric, which decreases from 0.037 m³ m⁻³ for NRv4 surface soil moisture to 0.033 m³ m⁻³ for L4_SM, and from 0.029 m³ m⁻³ for NRv4 root-zone soil moisture to 0.024 m³ m⁻³ for L4_SM (Table 4). The improvements are mostly due to the increased dynamic range and the generally faster dry-downs of the L4_SM estimates resulting from the assimilation of the SMAP observations, which leads to a better match of the dry-downs indicated by the in situ measurements. Bias values are very low for

surface soil moisture (around −0.01 m³ m⁻³ for L4_SM and NRv4). Root-zone soil moisture, however, is generally too dry and somewhat more biased for L4_SM (−0.043 m³ m⁻³) than for NRv4 (−0.037 m³ m⁻³).

### 2) LITTLE RIVER (GEORGIA)

The Little River, Georgia, site is in a humid agricultural environment, includes a substantial amount of tree cover, and has sandy soils. The site is also subject to irrigation and located near ephemeral, forested wetlands that can flood following rain events, but neither irrigation nor wetland processes are considered in the L4_SM modeling system. As for the Little Washita site, we show time series for the 36-km reference pixel at Little River (Fig. 3) because of gaps in the in situ measurements at the 9-km reference pixel. All time series reflect a drop from somewhat wetter conditions in April and May of both years to drier summer conditions, with frequent yet typically modest rain events (Fig. 3). The frequent wetting and drying events shown in the in situ measurements are reasonably captured by the L4_SM and NRv4 estimates, but the exact timing and magnitude of the storms and dry-downs is less certain. Moreover, the tree cover, sandy soils, and irrigation at Little River complicate the modeling of soil moisture and brightness temperature, resulting in overall slightly lower skill values than for Little Washita.

Despite the above complications, NRv4 estimates have reasonable skill, and the assimilation of SMAP observations again results in skill improvement. Surface soil moisture has an *R* value of 0.68 for NRv4, which improves to 0.76 for L4_SM. The correlation for root-zone soil moisture is higher, with *R* values of 0.81

<table><caption>TABLE 3. Overview of sparse networks, with indication of the sensor depths and number of sites *N* used here.</caption><thead><tr><th rowspan="2">Network</th><th rowspan="2">Area</th><th rowspan="2">Sensor<br>depths<br>(cm)</th><th colspan="2">N</th></tr><tr><th>Surface soil<br>moisture</th><th>Root-zone<br>soil moisture</th></tr></thead><tbody><tr><td>SCAN</td><td>United States</td><td>5, 10, 20</td><td>135</td><td>129</td></tr><tr><td>USCRN</td><td>United States</td><td>5, 10, 20</td><td>111</td><td>87</td></tr><tr><td>OK Mesonet</td><td>Oklahoma</td><td>5, 25, 60</td><td>118</td><td>77</td></tr><tr><td>OzNet</td><td>Australia</td><td>4, 45</td><td>42</td><td>18</td></tr><tr><td>All networks</td><td></td><td></td><td>406</td><td>311</td></tr></tbody></table>
for NRv4 and 0.84 for L4_SM (Table 4). The assimilation also improves the ubRMSE values for surface soil moisture estimates from 0.044 m³ m⁻³ for NRv4 to 0.035 m³ m⁻³ for L4_SM and for root-zone soil moisture estimates from 0.033 m³ m⁻³ for NRv4 to 0.025 m³ m⁻³ for L4_SM. Bias values are relatively high at ~0.10 m³ m⁻³ for surface soil moisture and ~0.07 m³ m⁻³ for root-zone soil moisture. The SMAP and SMOS passive soil moisture retrievals also exhibit a wet bias (Chan et al. 2016b), which may be related to the ephemeral wetlands in the vicinity of the site. The wet bias in the NRv4 estimates, however, suggests that errors in the Catchment model parameters are the main reason for the wet bias in L4_SM.

Figure 3 also reveals residual minor issues with the in situ measurements. Between May 17 and 5 June 2015, for example, the reference pixel average root-zone soil moisture shows somewhat erratic behavior. In this particular case, bad data from one sensor passed the automated quality control, and sensors also dropped out repeatedly during the period in question. The impacts of these residual issues are very minor and do not alter our main conclusions.

### 3) SOUTH FORK (IOWA)

South Fork, Iowa, is in a cold climate agricultural region dominated by summer crops of corn and soybeans. Conditions in winter are mostly bare soil or stubble, followed by intensive tillage in early April that creates large surface roughness, which subsequently decreases again with additional soil treatments and rainfall, and as crops begin to cover the surface. Such variations in surface roughness are difficult to capture in the (climatological) microwave RTM parameters of the L4_SM algorithm and in soil moisture retrieval algorithms in general (Patton and Hornbuckle 2013). Moreover, at the 9- and 36-km scales considered here, the land cover is a mix of corn and soybeans, which usually rotate each year, although there has been a trend toward more corn in recent years. By early July, for example, corn typically has a high vegetation water content of ~3 kg m⁻² while that of soybeans is typically much smaller (around 0.3 kg m⁻²; Jackson et al. 2004). Finally, owing to the high clay content of the soils in this region, the agricultural fields are equipped with tiles to improve drainage. This local feature is not captured in the global-scale Catchment model of the L4_SM algorithm.

Figure 4 shows soil moisture time series for a 9-km reference pixel at South Fork. Soil moisture conditions during the warm season are dominated by approximately weekly rain events with subsequent dry-downs. The L4_SM surface soil moisture estimates capture this pattern and present a clear improvement over NRv4,

especially in 2016. This is reflected in the ubRMSE values, which decrease from 0.070 m³ m⁻³ for NRv4 to 0.053 m³ m⁻³ for L4_SM (Table 4). The surface soil moisture *R* value increases considerably from 0.08 for NRv4 to 0.62 for L4_SM. Root-zone metrics show similar improvements for L4_SM over NRv4, with ubRMSE values decreasing from 0.044 m³ m⁻³ for NRv4 to 0.031 m³ m⁻³ for L4_SM and *R* values increasing considerably from 0.03 for NRv4 to 0.58 for L4_SM. Generally, however, the L4_SM estimates, and even more so the NRv4 estimates, do not capture the larger dynamic range of the in situ observations, which may be a reflection of the tile drainage. Bias values range from 0.075 m³ m⁻³ for NRv4 surface soil moisture to -0.014 m³ m⁻³ for L4_SM root-zone soil moisture.

### 4) SOIL MOISTURE SUMMARY METRICS

We now discuss the average soil moisture metrics across all reference pixels (section 3b), shown separately for the 9- and 36-km reference pixels in Fig. 5 (with numerical values listed in the bottom two rows of Table 4). The most important result is that the average ubRMSE values for L4_SM surface soil moisture (0.038 m³ m⁻³) and root-zone soil moisture (0.030 m³ m⁻³) at the 9-km scale meet the accuracy requirement of 0.04 m³ m⁻³.

For a more in-depth analysis, we first compare the skill of the L4_SM and NRv4 estimates. For the ubRMSE and *R* metrics and at the 9- and 36-km scales, the surface soil moisture skill of L4_SM exceeds that of NRv4 by a statistically significant margin (as indicated by the nonoverlapping confidence intervals; Fig. 5). For example, the 9-km ubRMSE for L4_SM surface soil moisture is 0.038 m³ m⁻³, compared to 0.042 m³ m⁻³ for NRv4. The corresponding *R* values are 0.67 for L4_SM and 0.58 for NRv4. The average bias is slightly (but not significantly) worse for L4_SM (0.046 m³ m⁻³) than NRv4 (0.043 m³ m⁻³). The results are similar for root-zone soil moisture, except here the differences between the L4_SM and NRv4 estimates are not significant (Fig. 5). The 9-km ubRMSE for L4_SM root-zone soil moisture (0.030 m³ m⁻³) is slightly lower than that of NRv4 (0.032 m³ m⁻³), and the *R* value for L4_SM (0.70) is higher than that of NRv4 (0.56). The average root-zone soil moisture bias is remarkably small and slightly better for L4_SM (0.009 m³ m⁻³) than NRv4 (0.019 m³ m⁻³).

A closer look at the metrics for the individual reference pixels (Table 4) reveals that the ubRMSE and *R* metrics are worse for L4_SM than NRv4 at some sites, including Carman and HOBE. There could be several reasons why the L4_SM analysis degrades the model-only skill, including site-specific errors in the radiative transfer modeling. For example, the L4_SM system does
<table><caption>TABLE 4. Soil moisture metrics at individual reference pixels and averaged over 36- and 9-km reference pixels (bottom two rows). Information for 36-km reference pixels is shown in bold. Italics indicate L4_SM metrics.</caption><thead><tr><th rowspan="3">Site name</th><th rowspan="3">ID</th><th rowspan="3">Horiz. scale (km)</th><th colspan="2">Reference pixel</th><th colspan="2">Surface soil moisture</th><th colspan="2">Root-zone soil moisture</th><th rowspan="3">R</th><th rowspan="3">95% Conf.</th></tr><tr><th>ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th>95% Conf.</th><th>Bias (m<sup>3</sup> m<sup>-3</sup>)</th><th>95% Conf.</th><th>ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th>Bias (m<sup>3</sup> m<sup>-3</sup>)</th></tr><tr><th>NRv4 L4_SM Interval</th><th>NRv4 L4_SM Interval</th><th>NRv4 L4_SM Interval</th><th>NRv4 L4_SM Interval</th><th>NRv4 L4_SM Interval</th><th>NRv4 L4_SM Interval</th><th>NRv4 L4_SM Interval</th></tr></thead><tbody><tr><td rowspan="2">REMEDHUS</td><td><strong>03013602</strong></td><td>36</td><td><strong>0.027</strong></td><td><strong>0.028</strong></td><td><strong>±0.005</strong></td><td><strong>0.068</strong></td><td><strong>0.072</strong></td><td><strong>±0.007</strong></td><td><strong>0.78</strong></td><td><strong>0.77</strong></td><td><strong>±0.08</strong></td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>03010903</td><td>9</td><td>0.024</td><td>0.029</td><td>±0.005</td><td>0.142</td><td>0.150</td><td>±0.007</td><td>0.52</td><td>0.46</td><td>±0.14</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Reynolds Creek</td><td>03010908</td><td>9</td><td>0.035</td><td>0.038</td><td>±0.007</td><td>0.013</td><td>0.015</td><td>±0.009</td><td>0.68</td><td>0.63</td><td>±0.10</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td><strong>04013603</strong></td><td>36</td><td><strong>0.032</strong></td><td><strong>0.027</strong></td><td><strong>±0.008</strong></td><td><strong>0.025</strong></td><td><strong>0.033</strong></td><td><strong>±0.011</strong></td><td><strong>0.65</strong></td><td><strong>0.78</strong></td><td><strong>±0.18</strong></td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Yanco</td><td>04010907</td><td>9</td><td>0.032</td><td>0.031</td><td>±0.010</td><td>—0.005</td><td>—0.001</td><td>±0.013</td><td>0.33</td><td>0.45</td><td>±0.26</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>04010910</td><td>9</td><td>0.036</td><td>0.029</td><td>±0.018</td><td>0.042</td><td>0.039</td><td>±0.022</td><td>0.62</td><td>0.76</td><td>±0.22</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Carman</td><td><strong>07013601</strong></td><td>36</td><td><strong>0.065</strong></td><td><strong>0.038</strong></td><td><strong>±0.019</strong></td><td><strong>0.005</strong></td><td><strong>0.036</strong></td><td><strong>±0.025</strong></td><td><strong>0.83</strong></td><td><strong>0.93</strong></td><td><strong>±0.08</strong></td><td><strong>0.017</strong></td><td><strong>0.020</strong></td><td><strong>±0.010</strong></td><td><strong>-0.100</strong></td><td><strong>-0.079</strong></td><td><strong>±0.012</strong></td><td><strong>0.89</strong></td><td><strong>0.95</strong></td><td><strong>±0.17</strong></td></tr><tr><td>07010902</td><td>9</td><td>0.084</td><td>0.057</td><td>±0.017</td><td>-0.017</td><td>0.010</td><td>±0.023</td><td>0.83</td><td>0.91</td><td>±0.07</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Ngari Walnut Gulch</td><td>07010916</td><td>9</td><td>0.068</td><td>0.043</td><td>±0.019</td><td>0.028</td><td>0.068</td><td>±0.025</td><td>0.77</td><td>0.91</td><td>±0.10</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td><strong>09013610</strong></td><td>36</td><td><strong>0.025</strong></td><td><strong>0.038</strong></td><td><strong>±0.004</strong></td><td><strong>-0.080</strong></td><td><strong>-0.066</strong></td><td><strong>±0.005</strong></td><td><strong>0.60</strong></td><td><strong>0.45</strong></td><td><strong>±0.10</strong></td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Little Washita</td><td>09010906</td><td>9</td><td>0.031</td><td>0.050</td><td>±0.005</td><td>0.043</td><td>0.080</td><td>±0.007</td><td>0.53</td><td>0.26</td><td>±0.14</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>16010907</td><td>9</td><td>0.036</td><td>0.034</td><td>±0.006</td><td>0.075</td><td>0.081</td><td>±0.009</td><td>0.60</td><td>0.65</td><td>±0.15</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Fort Cobb</td><td>16010913</td><td>9</td><td>0.036</td><td>0.034</td><td>±0.006</td><td>—0.004</td><td>-0.015</td><td><strong>±0.006</strong></td><td><strong>0.73</strong></td><td><strong>0.81</strong></td><td><strong>±0.05</strong></td><td><strong>0.029</strong></td><td><strong>0.024</strong></td><td><strong>±0.005</strong></td><td><strong>-0.037</strong></td><td><strong>-0.043</strong></td><td><strong>±0.007</strong></td><td><strong>0.87</strong></td><td><strong>0.88</strong></td><td><strong>±0.09</strong></td></tr><tr><td>16020907</td><td>9</td><td>0.037</td><td>0.034</td><td>±0.006</td><td>-0.015</td><td>-0.026</td><td>±0.009</td><td>0.71</td><td>0.78</td><td>±0.07</td><td>0.030</td><td>0.030</td><td>±0.009</td><td>-0.039</td><td>-0.043</td><td>±0.012</td><td>0.82</td><td>0.76</td><td>±0.16</td></tr><tr><td rowspan="2">Little River</td><td>16033602</td><td>36</td><td><strong>0.038</strong></td><td><strong>0.034</strong></td><td><strong>±0.004</strong></td><td><strong>0.027</strong></td><td><strong>0.028</strong></td><td><strong>±0.005</strong></td><td><strong>0.70</strong></td><td><strong>0.78</strong></td><td><strong>±0.06</strong></td><td><strong>0.024</strong></td><td><strong>0.025</strong></td><td><strong>±0.004</strong></td><td><strong>0.020</strong></td><td><strong>0.025</strong></td><td><strong>±0.005</strong></td><td><strong>0.76</strong></td><td><strong>0.79</strong></td><td><strong>±0.12</strong></td></tr><tr><td>16030911</td><td>9</td><td>0.043</td><td>0.038</td><td>±0.006</td><td>0.027</td><td>0.033</td><td>±0.008</td><td>0.71</td><td>0.77</td><td>±0.07</td><td>0.029</td><td>0.032</td><td>±0.007</td><td>0.020</td><td>0.031</td><td>±0.009</td><td>0.69</td><td>0.74</td><td>±0.18</td></tr><tr><td rowspan="2">St. Josephs South Fork</td><td>16060907</td><td>9</td><td>0.053</td><td>0.050</td><td>±0.012</td><td>0.111</td><td>0.094</td><td>±0.017</td><td>0.43</td><td>0.60</td><td>±0.25</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td><strong>16073602</strong></td><td>36</td><td><strong>0.058</strong></td><td><strong>0.044</strong></td><td><strong>±0.008</strong></td><td><strong>0.077</strong></td><td><strong>0.045</strong></td><td><strong>±0.011</strong></td><td><strong>0.23</strong></td><td><strong>0.65</strong></td><td><strong>±0.11</strong></td><td><strong>0.040</strong></td><td><strong>0.031</strong></td><td><strong>±0.006</strong></td><td><strong>0.024</strong></td><td><strong>0.012</strong></td><td><strong>±0.009</strong></td><td><strong>0.11</strong></td><td><strong>0.56</strong></td><td><strong>±0.26</strong></td></tr><tr><td rowspan="2">Monte Buey</td><td>16070909</td><td>9</td><td>0.064</td><td>0.043</td><td>±0.008</td><td>0.029</td><td>-0.009</td><td>±0.011</td><td>0.11</td><td>0.71</td><td>±0.12</td><td>0.045</td><td>0.029</td><td>±0.007</td><td>-0.035</td><td>-0.081</td><td>±0.010</td><td>0.06</td><td>0.70</td><td>±0.25</td></tr><tr><td>16070911</td><td>9</td><td>0.070</td><td>0.053</td><td>±0.010</td><td>0.075</td><td>0.039</td><td>±0.013</td><td>0.08</td><td>0.62</td><td>±0.12</td><td>0.044</td><td>0.031</td><td>±0.008</td><td>0.028</td><td>-0.014</td><td>±0.010</td><td>0.03</td><td>0.58</td><td>±0.29</td></tr><tr><td rowspan="2">Tonzi Ranch</td><td>19023601</td><td>36</td><td><strong>0.044</strong></td><td><strong>0.034</strong></td><td><strong>±0.010</strong></td><td><strong>-0.043</strong></td><td><strong>-0.035</strong></td><td><strong>±0.014</strong></td><td><strong>0.65</strong></td><td><strong>0.79</strong></td><td><strong>±0.07</strong></td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>19020902</td><td>9</td><td>0.037</td><td>0.029</td><td>±0.009</td><td>-0.038</td><td>-0.025</td><td>±0.012</td><td>0.60</td><td>0.83</td><td>±0.09</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="2">Kenaston</td><td>25013601</td><td>36</td><td><strong>0.042</strong></td><td><strong>0.032</strong></td><td><strong>±0.010</strong></td><td><strong>0.029</strong></td><td><strong>0.047</strong></td><td><strong>±0.014</strong></td><td><strong>0.92</strong></td><td><strong>0.95</strong></td><td><strong>±0.06</strong></td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>27013601</td><td>36</td><td><strong>0.038</strong></td><td><strong>0.034</strong></td><td><strong>±0.005</strong></td><td><strong>0.010</strong></td><td><strong>0.012</strong></td><td><strong>±0.007</strong></td><td><strong>0.51</strong></td><td><strong>0.63</strong></td><td><strong>±0.09</strong></td><td><strong>0.020</strong></td><td><strong>0.023</strong></td><td><strong>±0.005</strong></td><td><strong>-0.043</strong></td><td><strong>-0.041</strong></td><td><strong>±0.007</strong></td><td><strong>0.53</strong></td><td><strong>0.63</strong></td><td><strong>±0.27</strong></td></tr><tr><td rowspan="2">27010910</td><td>27010911</td><td>9</td><td>0.034</td><td>0.035</td><td>±0.009</td><td>0.009</td><td>0.016</td><td>±0.012</td><td>0.61</td><td>0.61</td><td>±0.12</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>27010911</td><td>9</td><td>0.040</td><td>0.040</td><td>±0.008</td><td>-0.020</td><td>-0.021</td><td>±0.011</td><td>0.56</td><td>0.54</td><td>±0.11</td><td>0.018</td><td>0.023</td><td>±0.003</td><td>-0.069</td><td>-0.070</td><td>±0.004</td><td>0.63</td><td>0.63</td><td>±0.18</td></tr></tbody></table>
<table><caption>TABLE 4. (Continued)</caption><thead><tr><th rowspan="3">Reference pixel</th><th colspan="6">Surface soil moisture</th><th colspan="6">Root-zone soil moisture</th></tr><tr><th colspan="3">ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th colspan="3">Bias (m<sup>3</sup> m<sup>-3</sup>)</th><th colspan="3">ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th colspan="3">Bias (m<sup>3</sup> m<sup>-3</sup>)</th></tr><tr><th>Horiz. scale (km)</th><th>NRv4</th><th>L4_SM</th><th>Interval</th><th>NRv4</th><th>95% Conf.</th><th>95% Conf.</th><th>NRv4</th><th>95% Conf.</th><th>NRv4</th><th>95% Conf.</th><th>NRv4</th><th>95% Conf.</th></tr></thead><tbody><tr><td>Site name</td><td>ID</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Valencia</td><td>41010906</td><td>9</td><td>0.025</td><td>0.023</td><td>±0.005</td><td>0.104</td><td>0.109</td><td>±0.007</td><td>0.44</td><td>0.51</td><td>±0.16</td><td>—</td><td>—</td></tr><tr><td>Niger</td><td>45013601</td><td>36</td><td>0.030</td><td>0.030</td><td>±0.005</td><td>-0.001</td><td>0.022</td><td>±0.007</td><td>0.40</td><td>0.62</td><td>±0.20</td><td>—</td><td>—</td></tr><tr><td></td><td>45010902</td><td>9</td><td>0.032</td><td>0.033</td><td>±0.004</td><td>0.006</td><td>0.030</td><td>±0.006</td><td>0.31</td><td>0.52</td><td>±0.17</td><td>—</td><td>—</td></tr><tr><td>Benin</td><td>45023601</td><td>36</td><td>0.050</td><td>0.048</td><td>±0.016</td><td>0.059</td><td>0.037</td><td>±0.021</td><td>0.62</td><td>0.66</td><td>±0.20</td><td>—</td><td>—</td></tr><tr><td></td><td>45020902</td><td>9</td><td>0.050</td><td>0.047</td><td>±0.016</td><td>0.053</td><td>0.036</td><td>±0.021</td><td>0.68</td><td>0.72</td><td>±0.17</td><td>—</td><td>—</td></tr><tr><td>TxSON</td><td>48013601</td><td>36</td><td>0.041</td><td>0.036</td><td>±0.008</td><td>0.084</td><td>0.086</td><td>±0.010</td><td>0.82</td><td>0.87</td><td>±0.08</td><td>0.036</td><td>0.033</td></tr><tr><td></td><td>48010902</td><td>9</td><td>0.039</td><td>0.037</td><td>±0.005</td><td>0.120</td><td>0.121</td><td>±0.007</td><td>0.73</td><td>0.80</td><td>±0.08</td><td>0.032</td><td>0.029</td></tr><tr><td>HOBE</td><td>48010911</td><td>9</td><td>0.049</td><td>0.044</td><td>±0.008</td><td>0.124</td><td>0.127</td><td>±0.011</td><td>0.76</td><td>0.83</td><td>±0.10</td><td>0.028</td><td>0.029</td></tr><tr><td></td><td>67013601</td><td>36</td><td>0.030</td><td>0.035</td><td>±0.008</td><td>0.011</td><td>-0.004</td><td>±0.010</td><td>0.78</td><td>0.71</td><td>±0.13</td><td>—</td><td>—</td></tr><tr><td>All sites</td><td>Average</td><td>36</td><td>0.040</td><td>0.035</td><td>±0.002</td><td>0.023</td><td>0.026</td><td>±0.003</td><td>0.66</td><td>0.74</td><td>±0.03</td><td>0.028</td><td>0.026</td></tr><tr><td></td><td>Average</td><td>9</td><td>0.042</td><td>0.038</td><td>±0.002</td><td>0.043</td><td>0.046</td><td>±0.003</td><td>0.58</td><td>0.67</td><td>±0.03</td><td>0.032</td><td>0.030</td></tr></tbody></table>

not account for the heavy dewfall and the variety of different crops at Carman. At HOBE, the SMOS-based brightness temperature climatology used for rescaling might be impacted by radio-frequency interference or by the effect of the land-sea contrast in the interferometric processing (Al Bitar et al. 2012). Nevertheless, the L4_SM product has, on balance, higher skill than NRv4. The L4_SM root-zone ubRMSE is below the 0.04 m³ m⁻³ threshold at all 16 (9 and 36 km) reference pixels, while the NRv4 ubRMSE exceeds 0.04 m³ m⁻³ at two of the three South Fork reference pixels. Surface soil moisture estimates from NRv4 fail to meet the 0.04 m³ m⁻³ threshold at 18 of the 43 reference pixels. By contrast, L4_SM surface soil moisture estimates fail to meet the threshold at only 10 of the 43 reference pixels, including 9-km pixels at Yanco, Carman, St. Josephs, South Fork, Benin, and TxSON. This result further illustrates the key role played by the assimilation of SMAP observations in meeting the L4_SM accuracy requirement (which applies to the average ubRMSE across all 9-km reference pixels; section 3a).

Next, we compare the skill values at 9-km reference pixels to those at the 36-km scale. Generally, the L4_SM and NRv4 skill at 36 km is better for all three metrics than that at 9 km (Fig. 5), which is consistent with the fact that the model forcing data and the assimilated SMAP brightness temperature observations are all at resolutions of about 30 km or greater. The information used to downscale the assimilated information stems only from the land model parameters, which are at the finer, 9-km resolution. It is therefore not surprising that the L4_SM (and NRv4) estimates are more skillful (i.e., contain less random error) when averaged to the 36-km scale than at the 9-km scale. Perhaps the biggest difference between the 36- and 9-km reference pixel skills is for the surface soil moisture bias (Fig. 5b). The smaller bias at the 36-km scale is likely also related to the fact that the gridcell scale in situ measurements for 36-km reference pixels are typically based on more individual sensor locations than those for 9-km reference pixels, resulting in more robust in situ estimates of the true long-term mean conditions at the 36-km scale.

Finally, we compare the skill of the surface soil moisture estimates to that of the root-zone estimates. Across all scales and metrics and for the L4_SM and NRv4 estimates, the skill of the root-zone soil moisture estimates is always better than that of the surface estimates (Fig. 5). This result makes sense because there is much more variability in surface soil moisture.

## 5) SOIL TEMPERATURE SUMMARY METRICS

Since the focus of the L4_SM product is on soil moisture, there is no predefined accuracy target for the
<figure><img src="image_4.png" /><figcaption>FIG. 2. (a) Surface soil moisture from L4_SM (black solid line), NRv4 (light blue solid line), and in situ measurements (red dots) at the 36-km Little Washita reference pixel 16023602. (b) As in (a), but for root-zone soil moisture. See Table 4 for performance metrics.</figcaption></figure>

L4_SM surface soil temperature estimates. It is nevertheless instructive to assess their skill (Fig. 6; Table 5), especially given the importance of soil temperature for biophysical processes and the use of L4_SM soil temperature estimates as inputs to the SMAP level-4 carbon product (Jones et al. 2017). The average surface soil temperature metrics for L4_SM and NRv4 are fairly similar across all categories, with average ubRMSE values ranging from 1.6 to 1.8 K (Fig. 6a) and average *R* values of ~0.97 (Fig. 6c) for 9- and 36-km estimates at

0600 and 1800 LT. At 0600 LT, surface soil temperature estimates from L4_SM have a slightly lower ubRMSE than NRv4 (by ~0.1 K) and a slightly higher *R* value than NRv4 (by ~0.005), but the differences are not significant. At 1800 LT, the L4_SM and NRv4 ubRMSE and *R* values are essentially identical.

Somewhat bigger differences between the various estimates occur for the average bias in surface soil temperature (Fig. 6b). At 0600 LT, both L4_SM and NRv4 are biased cold, with NRv4 having a larger

<figure><img src="image_5.png" /><figcaption>FIG. 3. As in Fig. 2, but for the 36-km Little River reference pixel 16043602.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>FIG. 4. As in Fig. 2, but for the 9-km South Fork reference pixel 16070911.</figcaption></figure>

(negative) bias of around -2.5 K compared to about -1.8 K for L4_SM (at both the 9- and 36-km scales). This 0600 LT cold bias is consistent with a known nighttime cold bias in the GEOS-5 modeling system (Chan et al. 2016b). At 1800 LT, the average bias at the 9-km scale nearly vanishes for NRv4 (0.1 K), whereas L4_SM still exhibits a distinct cold bias (-1.1 K). Note that some of the bias at individual sites might also be caused by instrumentation details such as the vertical or horizontal installation of the sensors, which impacts the exact depths where the sensors' thermistors are located.

The 36-km average bias shown in Fig. 6b includes the extreme values at the Ngari reference pixel in western Tibet, where the 1800 LT bias in surface soil temperature is -9.1 K for NRv4 and -12.5 K for L4_SM (Table 5). The L4_SM bias at Ngari is not unique for a global modeling system. In their Table 3, Su et al. (2013) report a diurnal mean bias of -6.9 K at Naqu (in central Tibet) for surface soil temperature estimates from the operational system of the European Centre for Medium-Range Weather Forecasts. The reasons for the extreme bias in Tibet are complex. Most importantly, there is a bias in the GEOS-5 radiation and air temperature forcing data used in the L4_SM system compared to the observation-based data of Chen et al. (2011) (not shown). This forcing bias is likely compounded by errors in the L4_SM soil texture inputs, soil thermal parameters, and surface turbulence parameterization (Van der Velde et al. 2009; Zeng et al. 2012; Zheng et al. 2015). If Ngari is excluded from the 36-km reference pixel average, the 1800 LT bias values change from -0.5 to 0.2 K for NRv4 and from -1.7 to -0.9 K for L4_SM. More generally, the increase in the

(absolute) bias in the L4_SM estimates compared to NRv4 is likely the result of using imperfect brightness temperature rescaling parameters (section 2d), but this requires further investigation and is left for future study.

The relatively minor differences between the L4_SM and NRv4 soil temperature metrics (Fig. 6) are not surprising. The L4_SM brightness temperature analysis has been calibrated primarily for updating the model forecast soil moisture estimates; soil temperature increments are relatively small by design (De Lannoy and Reichle 2016a). This strategy mirrors the approach taken by the SMAP and SMOS (passive) soil moisture retrieval algorithms, which rely on ancillary soil temperature information that is assumed to be sufficiently accurate to invert brightness temperature observations into soil moisture estimates.

b. Sparse network validation

Figure 7 illustrates the ubRMSE values for the L4_SM estimates at the sparse network sites. The gray background shading in the figure also indicates whether a site is within the mask of the formal accuracy requirement (section 3a). The resulting delineation (Fig. 7) suggests, for example, that sites in the more topographically complex western United States mountain areas and in the more densely vegetated portions of the eastern United States fall, as expected, outside the mask. Overall, ubRMSE values range from 0.02 to 0.07 m³ m⁻³, with generally lower error values for root-zone soil moisture than for surface soil moisture (Fig. 7). Errors are generally lowest in dry and mountainous areas in the western United States, where the soil moisture variability is typically low, thus naturally limiting the
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>FIG. 5. (a) ubRMSE (m³ m⁻³), (b) bias (m³ m⁻³), and (c) R (dimensionless) for L4_SM and NRv4 surface and root-zone soil moisture vs core validation site measurements, averaged across all 9- and 36-km reference pixels. Error bars indicate 95% confidence intervals. The thick horizontal line in (a) represents the L4_SM accuracy requirement of ubRMSE ≤ 0.04 m³ m⁻³.</figcaption></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>FIG. 6. As in Fig. 5, but for surface soil temperature (K) at 0600 LT and 1800 LT.</figcaption></figure>
ubRMSE values. The ubRMSE values at the Australian sites are relatively high both inside and outside the mask (on average, $0.063 \text{ m}^3 \text{ m}^{-3}$ for surface and $0.056 \text{ m}^3 \text{ m}^{-3}$ for root-zone soil moisture), owing primarily to the large variability in soil moisture in this region. The *R* values for the sparse network sites, shown in Fig. 8, range from 0.3 to 0.9, with generally similar correlations for surface and root-zone soil moisture. There is no obvious spatial pattern across the U.S. networks or the Australian sites, although the latter exhibit generally high *R* values.

Figure 9 shows the average L4_SM metrics versus sparse network measurements, broken down by the exclusion mask of the accuracy requirement (as indicated by the gray shading in Figs. 7, 8). The figure confirms that the L4_SM ubRMSE values are lower at the sites outside the mask, with values of $0.049 \text{ m}^3 \text{ m}^{-3}$ for surface soil moisture and $0.040 \text{ m}^3 \text{ m}^{-3}$ for root-zone soil moisture (Fig. 9b, Table 6), compared to 0.054 and $0.044 \text{ m}^3 \text{ m}^{-3}$ for surface and root-zone soil moisture, respectively, at sites within the mask (Fig. 9a). Again, this result is related to the much lower variability of soil moisture in the arid regions of the western United States, which also happen to lie largely in mountainous terrain. The result is reversed for the average bias. Inside the mask, average bias values are $0.028 \text{ m}^3 \text{ m}^{-3}$ for surface soil moisture and $-0.003 \text{ m}^3 \text{ m}^{-3}$ for root-zone soil moisture (Fig. 9c), compared to $0.078 \text{ m}^3 \text{ m}^{-3}$ for surface soil moisture and $0.042 \text{ m}^3 \text{ m}^{-3}$ for root-zone soil moisture, respectively, outside the mask (Fig. 9d). This relative performance is at least partly due to the increased topographical complexity near many of the sites outside of the mask, which are generally even less representative of the gridcell average conditions than are sparse network sites within the mask. The values for the time series correlation coefficients generally range between 0.6 and 0.7 and are more similar inside and outside the mask (Figs. 9e,f). This is expected because the *R* values are, by construction, insensitive to bias and to errors in variability.

Figure 9 also shows the skill of the NRv4 estimates. The surface soil moisture skill in terms of *R* is significantly higher (at the 5% level) for L4_SM than for NRv4, reflecting the additional information contributed by the assimilation of the SMAP brightness temperature observations in the L4_SM system both inside and outside of the exclusion mask. For root-zone soil moisture, the skill values are very similar for L4_SM and NRv4. As for the core validation sites, the typically small differences between L4_SM and NRv4 estimates reflect the fact that the sparse network measurements are located in areas where the surface meteorological forcing takes advantage of high-quality, gauge-based precipitation measurements. Larger improvements from the

assimilation of SMAP observations can be expected in areas where the precipitation forcing inputs are not as well informed by gauge measurements, as demonstrated by Bolten and Crow (2012) for the assimilation of AMSR-E soil moisture retrievals.

Table 6 further provides average skill metrics broken down by the IGBP land cover classes (section 3c). The ubRMSE and *R* skill of the L4_SM surface and root-zone soil moisture estimates is better than that of NRv4 for all IGBP classes except for root-zone soil moisture in grasslands and urban areas, where NRv4 is better than L4_SM (but not significantly). The bias values listed in Table 6 suggest that the mean soil moisture from the L4_SM estimates is biased high (i.e., wet) for all land cover classes, with similar mean bias values for NRv4. This is particularly true for the forest class, because in situ measurement sites are typically on grassy areas, regardless of the surrounding land cover. For the forest class, Table 6 shows that the L4_SM and NRv4 estimates have the highest bias values, ~0.1 $\text{ m}^3 \text{ m}^{-3}$ for surface soil moisture and $0.055 \text{ m}^3 \text{ m}^{-3}$ for root-zone soil moisture (not considering the higher average root-zone bias at the three sites in the urban class).

## 5. Summary and conclusions

This study provides a brief overview of the SMAP L4_SM algorithm and focuses on the validation of the L4_SM product using in situ soil moisture and temperature measurements from core validation sites and sparse networks. Based on the core validation site results, the L4_SM estimates of surface and root-zone soil moisture meet the accuracy requirement (ubRMSE ≤ 0.04 $\text{ m}^3 \text{ m}^{-3}$). For surface soil moisture, the ubRMSE is $0.038 \text{ m}^3 \text{ m}^{-3}$ at the 9-km scale and $0.035 \text{ m}^3 \text{ m}^{-3}$ at the 36-km scale. For root-zone soil moisture, the ubRMSE is $0.030 \text{ m}^3 \text{ m}^{-3}$ at the 9-km scale and $0.026 \text{ m}^3 \text{ m}^{-3}$ at the 36-km scale (Fig. 5). Through the assimilation of SMAP brightness temperatures, the L4_SM surface soil moisture estimates are improved significantly (at the 5% level) compared to model-only NRv4 estimates. The latter have an ubRMSE of $0.042 \text{ m}^3 \text{ m}^{-3}$ at the 9-km scale and do not meet the L4_SM accuracy requirement. L4_SM root-zone soil moisture estimates are also better (but not significantly) than those of NRv4, which have an ubRMSE of $0.032 \text{ m}^3 \text{ m}^{-3}$ at the 9-km scale. Similar qualitative results are obtained for the *R* metric.

Surface soil temperature ubRMSE values versus core validation site measurements range between 1.6 and 1.8 K for 0600 and 1800 LT estimates from L4_SM and NRv4 at the 9- and 36-km scales (Fig. 6). The L4_SM estimates show only minor improvements (not significant) of ~0.1 K for 0600 LT (compared to NRv4), with
<table><caption>TABLE 5. (Continued)</caption><thead><tr><th rowspan="3">Site name</th><th rowspan="3">ID</th><th colspan="10">Reference pixel</th></tr><tr><th colspan="5">Surface soil temperature (0600 LT)</th><th colspan="5">Surface soil temperature (1800 LT)</th></tr><tr><th>Horiz. Scale (km)</th><th>NRv4</th><th>ubRMSE (K)</th><th>95% Conf.</th><th>Bias (K)</th><th>95% Conf.</th><th>R</th><th>ubRMSE (K)</th><th>95% Conf.</th><th>Bias (K)</th><th>R</th></tr></thead><tbody><tr><td>Benin</td><td>45023601</td><td>36</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>TxSON</td><td>48013601</td><td>36</td><td>1.1</td><td>±0.3</td><td>-2.0</td><td>-1.4</td><td>±0.4</td><td>0.99</td><td>0.99</td><td>±0.01</td><td>1.6</td><td>1.5</td></tr><tr><td></td><td>48010902</td><td>9</td><td>1.3</td><td>±0.4</td><td>-2.7</td><td>-2.2</td><td>±0.5</td><td>0.98</td><td>0.99</td><td>±0.01</td><td>1.8</td><td>1.7</td></tr><tr><td></td><td>48010911</td><td>9</td><td>1.3</td><td>±0.4</td><td>-2.3</td><td>-1.8</td><td>±0.5</td><td>0.98</td><td>0.99</td><td>±0.01</td><td>2.1</td><td>2.1</td></tr><tr><td>HOBE</td><td>67013601</td><td>36</td><td>1.0</td><td>±0.5</td><td>-1.1</td><td>-0.4</td><td>±0.7</td><td>0.98</td><td>0.98</td><td>±0.02</td><td>1.1</td><td>1.2</td></tr><tr><td>All sites</td><td>Average</td><td>36</td><td>1.6</td><td>±0.2</td><td>-2.5</td><td>-1.7</td><td>±0.3</td><td>0.97</td><td>0.97</td><td>±0.01</td><td>1.8</td><td>1.7</td></tr><tr><td></td><td>Average</td><td>9</td><td>1.7</td><td>±0.3</td><td>-2.5</td><td>-1.8</td><td>±0.3</td><td>0.98</td><td>0.98</td><td>±0.01</td><td>1.8</td><td>1.7</td></tr></tbody></table>

nearly identical 1800 LT skill values for L4_SM and NRv4. The *R* values for surface soil temperature estimates are ~0.97, suggesting that the modeled soil temperatures adequately capture synoptic and seasonal variations. The L4_SM product is biased cold by about -2 K at 0600 LT, which is consistent with a known cold bias in current GEOS-5 products. In the arid, high-elevation environment at Ngari in western Tibet, however, errors in the L4_SM forcing data and modeling system result in a much larger cold bias of -12.5 K for surface soil temperature at 1800 LT.

The sparse network results corroborate the core validation site findings for a greater variety of climate and land cover conditions (Fig. 9). It is important to keep in mind that the sparse network skill metrics presented here underestimate the true skill because these metrics are based on a direct comparison of the L4_SM product against in situ measurements that are subject to upscaling and other errors. The same is true, to a lesser extent, for the metrics versus core validation site measurements, and Chen et al. (2017) quantified the impact of such errors on the *R* skill of soil moisture retrievals. Therefore, the sparse network ubRMSE values suggest that the L4_SM estimates would meet the formal accuracy requirement across a very wide variety of surface conditions, beyond those that are covered by the few core validation sites that have been available to date for formal verification of the accuracy requirement. The sparse network results thus provide additional confidence in the conclusions drawn from the core validation site comparisons.

The core validation site and sparse network results both suggest that the L4_SM surface soil moisture is still biased wet (by 0.02–0.05 m³ m⁻³, on average), while the root-zone soil moisture bias is smaller (less than 0.01 m³ m⁻³ for the core sites, and 0.016 m³ m⁻³ for the sparse network sites). The wet bias in surface soil moisture is consistent with the findings of De Lannoy et al. (2014b), who introduced the revised soil texture and soil hydraulic parameters used here to address the even stronger bias in earlier versions of the GEOS-5 modeling system (such as those used in the MERRA-Land and MERRA-2 reanalysis products). The development of the L4_SM product played an important role in mitigating the bias of GEOS-5 soil moisture estimates, and work is ongoing to further reduce the remaining bias.

The skill of the model-only NRv4 estimates (section 2c) rests, to a large degree, on the accuracy of the precipitation forcing, which relies on the daily, 0.5°, gauge-based CPCU product (except in Africa and the high latitudes). For the most part, the soil moisture validation against in situ measurements is limited to regions that
<figure><img src="image_13.png" /><figcaption>FIG. 7. The ubRMSE (m³ m⁻³) vs sparse network measurements for L4_SM (a), (b) surface and (c), (d) root-zone soil moisture. (left) United States sites include SCAN (circles), USCRN (inverted triangles), and Oklahoma Mesonet (squares). (right) Australian sites from OzNet. Gray shading indicates areas with low or modest vegetation cover and topographic complexity that are within the mask of the SMAP accuracy requirement (section 3c).</figcaption></figure>

also have relatively accurate precipitation inputs, which implies that the model-only (NRv4) skill is already relatively high, thereby limiting the potential improvements that can be obtained from the assimilation of

SMAP observations. In regions with poor precipitation data, the impact of the SMAP observations should be larger, but the precise benefit remains unknown in those regions because they also lack soil moisture in situ

<figure><img src="image_14.png" /><figcaption>FIG. 8. As in Fig. 7 but for the time series correlation coefficient R (dimensionless).</figcaption></figure>
Average across sites *not* located in
mountainous topography, urban
areas, and dense vegetation

Average across sites located in
mountainous topography, urban
areas, or dense vegetation

<figure><img src="image_15.png" /></figure>

FIG. 9. (a),(b) ubRMSE (m³ m⁻³); (c),(d) bias (m³ m⁻³); and (e),(f) *R* (dimensionless) for L4_SM and NRv4 surface and root-zone soil moisture vs sparse network measurements, averaged across sites (left) within the mask and (right) outside the mask shown by the gray shading in Figs. 7 and 8. Averages are based on a clustering algorithm (section 3c). Error bars indicate 95% confidence intervals.
<table><caption>TABLE 6. Sparse network metrics by land cover (IGBP class) and by the mask of the L4_SM core validation site accuracy requirement (section 3c). Italics indicate L4_SM metrics. Averages are based on a clustering algorithm (section 3c).</caption><thead><tr><th rowspan="3">Sparse network subset</th><th colspan="4">Surface soil moisture</th><th colspan="6">Root-zone soil moisture</th></tr><tr><th colspan="2">ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th colspan="2">Bias (m<sup>3</sup> m<sup>-3</sup>)</th><th rowspan="2">R</th><th rowspan="2">95% Conf. of NRv4</th><th rowspan="2">ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th rowspan="2">Bias (m<sup>3</sup> m<sup>-3</sup>)</th><th rowspan="2">R</th><th rowspan="2">95% Conf. of NRv4</th><th rowspan="2">ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th rowspan="2">Bias (m<sup>3</sup> m<sup>-3</sup>)</th></tr><tr><th>No. of sites</th><th>NRv4</th><th>ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th>NRv4</th><th>ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th>NRv4</th><th>ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th>NRv4</th><th>ubRMSE (m<sup>3</sup> m<sup>-3</sup>)</th><th>NRv4</th></tr></thead><tbody><tr><td>Forests (IGBP 1-5)</td><td>41</td><td>0.056</td><td>0.054</td><td>±0.005</td><td>0.104</td><td>0.103</td><td>±0.004</td><td>0.64</td><td>0.65</td><td>±0.03</td><td>34</td><td>0.047</td><td>0.045</td><td>±0.005</td><td>0.055</td><td>±0.005</td><td>0.62</td><td>0.64</td><td>±0.08</td></tr><tr><td>Open shrublands (IGBP 7)</td><td>27</td><td>0.037</td><td>0.034</td><td>±0.003</td><td>0.016</td><td>0.030</td><td>±0.003</td><td>0.66</td><td>0.71</td><td>±0.03</td><td>20</td><td>0.028</td><td>0.026</td><td>±0.005</td><td>-0.008</td><td>0.006</td><td>±0.004</td><td>0.66</td><td>0.63</td><td>±0.09</td></tr><tr><td>Woody savannas (IGBP 8)</td><td>28</td><td>0.065</td><td>0.059</td><td>±0.008</td><td>0.069</td><td>0.060</td><td>±0.006</td><td>0.65</td><td>0.70</td><td>±0.05</td><td>23</td><td>0.054</td><td>0.048</td><td>±0.010</td><td>0.037</td><td>0.025</td><td>±0.013</td><td>0.68</td><td>0.70</td><td>±0.13</td></tr><tr><td>Grasslands (IGBP 10)</td><td>177</td><td>0.053</td><td>0.051</td><td>±0.003</td><td>0.026</td><td>0.031</td><td>±0.003</td><td>0.65</td><td>0.69</td><td>±0.02</td><td>130</td><td>0.041</td><td>0.042</td><td>±0.006</td><td>-0.014</td><td>-0.007</td><td>±0.007</td><td>0.72</td><td>0.69</td><td>±0.07</td></tr><tr><td>Croplands (IGBP 12)</td><td>83</td><td>0.060</td><td>0.057</td><td>±0.003</td><td>0.026</td><td>0.022</td><td>±0.004</td><td>0.60</td><td>0.64</td><td>±0.03</td><td>60</td><td>0.046</td><td>0.046</td><td>±0.005</td><td>0.007</td><td>0.004</td><td>±0.005</td><td>0.65</td><td>0.65</td><td>±0.07</td></tr><tr><td>Urban/built up (IGBP 13)</td><td>4</td><td>0.080</td><td>0.071</td><td>±0.017</td><td>0.027</td><td>0.006</td><td>±0.015</td><td>0.49</td><td>0.62</td><td>±0.11</td><td>3</td><td>0.047</td><td>0.049</td><td>±0.020</td><td>0.046</td><td>±0.032</td><td>±0.019</td><td>0.64</td><td>0.63</td><td>±0.32</td></tr><tr><td>Crop/natural (IGBP 14)</td><td>39</td><td>0.060</td><td>0.057</td><td>±0.003</td><td>0.033</td><td>0.027</td><td>±0.003</td><td>0.66</td><td>0.70</td><td>±0.02</td><td>36</td><td>0.048</td><td>0.045</td><td>±0.003</td><td>0.008</td><td>0.002</td><td>±0.004</td><td>0.66</td><td>0.69</td><td>±0.06</td></tr><tr><td>Barren/sparse (IGBP 16)</td><td>2</td><td>0.033</td><td>0.026</td><td>±0.005</td><td>0.004</td><td>0.016</td><td>±0.004</td><td>0.61</td><td>0.70</td><td>±0.08</td><td>1</td><td>0.016</td><td>0.017</td><td>±0.020</td><td>-0.028</td><td>-0.031</td><td>±0.014</td><td>0.95</td><td>0.92</td><td>±0.35</td></tr><tr><td>Inside mask</td><td>279</td><td>0.056</td><td>0.054</td><td>±0.002</td><td>0.030</td><td>0.028</td><td>±0.002</td><td>0.64</td><td>0.67</td><td>±0.02</td><td>206</td><td>0.045</td><td>0.044</td><td>±0.003</td><td>-0.001</td><td>-0.003</td><td>±0.003</td><td>0.66</td><td>0.66</td><td>±0.04</td></tr><tr><td>Outside mask</td><td>127</td><td>0.052</td><td>0.049</td><td>±0.003</td><td>0.074</td><td>0.078</td><td>±0.002</td><td>0.64</td><td>0.67</td><td>±0.02</td><td>105</td><td>0.041</td><td>0.040</td><td>±0.004</td><td>0.040</td><td>0.042</td><td>±0.004</td><td>0.65</td><td>0.65</td><td>±0.05</td></tr><tr><td>Average (all sites)</td><td>406</td><td>0.054</td><td>0.052</td><td>±0.002</td><td>0.050</td><td>0.051</td><td>±0.002</td><td>0.64</td><td>0.67</td><td>±0.01</td><td>311</td><td>0.044</td><td>0.042</td><td>±0.002</td><td>0.016</td><td>0.016</td><td>±0.003</td><td>0.66</td><td>0.66</td><td>±0.03</td></tr></tbody></table>

measurements suitable for validation. In future work, we plan to quantify the skill improvement against model-only estimates that do not benefit from the use of gauge-based precipitation data.

The NRv4 and L4_SM estimates differ in that the NRv4 estimates are from a single-member model run without perturbations, whereas the L4_SM estimates are based on an ensemble of model realizations that experiences perturbations to its model forcing and prognostic variables. An undesirable, yet at this time unavoidable, side effect of the perturbations regime is that it leads to biases between the ensemble mean estimates and the estimates from the unperturbed NRv4 model integration. This is particularly acute in very arid regions, where the perturbations in soil moisture are, by construction, biased wet because the unperturbed, single-member model run often remains at the lowest possible soil moisture value, thereby making negative (i.e., drying) perturbations unphysical. Some of the differences between the NRv4 and L4_SM estimates will therefore partly reflect the impact of the perturbations regime rather than the use of SMAP observations. We plan to investigate this issue further by generating a model-only ensemble run with the same perturbations regime as the L4_SM product but without SMAP assimilation. Preliminary results based on a small domain suggest that the relative performance of the L4_SM estimates and the revised model-only estimates is quite similar to that of L4_SM and NRv4.

Our assessment of the version 2 L4_SM data is still quite limited by the period of record. The two years of data that were available for this study do not yet cover a representative range of interannual variability. As the SMAP observatory and in situ networks continue to provide additional measurements, the reliability of future assessments will increase. Moreover, enhancements in the GEOS-5 modeling system and in the L-band brightness temperature climatology needed for bias correction are expected to improve the quality of the L4_SM product. In particular, the L-band brightness temperature climatology will eventually be based on SMAP (as opposed to SMOS) observations. This will improve the brightness temperature bias correction and permit the use of SMAP data in regions where SMOS observations are contaminated by radio-frequency interference.

Finally, the validation of the L4_SM product against in situ measurements must be viewed in conjunction with other assessments. For example, Crow et al. (2017) demonstrated for the south-central United States that L4_SM soil moisture estimates have significantly improved utility for forecasting the streamflow response to future rainfall events (relative to that of soil moisture
retrievals from L-band and higher-frequency brightness temperature observations). Moreover, Reichle et al. (2016a, 2017, manuscript submitted to *J. Hydrometeor.*.) evaluate the statistics of the observation-minus-forecast residuals and the analysis increments from the L4_SM algorithm, which are available wherever and whenever SMAP observations are assimilated, thereby providing a more global perspective of the algorithm's performance.

*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, dissemination, and validation of the L4_SM product possible, including SMAP team members at JPL, GSFC, and NSIDC and staff at NOAA/CPC, NOAA/NCEI, USDA-ARS, USDA-NRCS, the Oklahoma Climatological Survey, and Monash University. Erica Tetlock is acknowledged for her help with the Kenaston network, for which funding was provided by the Canadian Space Agency and by Environment and Climate Change Canada. We thank three anonymous reviewers for their helpful comments.

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