2.1. Two-Layer Palmer Model
 Model estimates of surface and root-zone soil moisture are derived from the 2-Layer Palmer water balance model currently used operationally by USDA FAS. The model is based on a bucket-type modeling approach as described inPalmer . The available water capacity (AWC) of the top model layer is assumed to be 2.54 cm at field capacity, and the AWC of the second layer (i.e., root-zone layer) is calculated using soil texture, depth to bedrock, and soil type derived from the Food and Agriculture Organization (FAO) Digital Soil Map of the World available from the FAO athttp://www.fao.org/ag/agl/lwdms.stm#cd1. In this fashion, water holding capacity for both layers (incorporating near-surface soil moisture and groundwater) range between 2.54 cm to 30 cm according to soil texture and soil depth. Vertical coupling between the two model layers is calculated using a simple linear diffusion equation based on the soil moisture content of each layer and an assigned diffusion coefficient [Bolten et al., 2010]. A confining layer (i.e., bedrock) is assumed for the bottom of the second model layer and is treated as a “no flow” boundary. Evapotranspiration is calculated from the modified FAO Penman-Monteith [Allen et al., 1998] method and observations of daily min/max temperature. Further modeling details are available in Bolten et al. . Required daily rainfall accumulation and air temperature datasets are obtained from the U.S. Air Force Weather Agency (AFWA) Agriculture Meteorological (AGRMET) system (see http://www.mmm.ucar.edu/mm5/documents/DATA_FORMAT_HANDBOOK.pdf) which derives a daily rainfall accumulation product based on: microwave sensors on various polar-orbiting satellites, infrared sensors on geostationary satellites, a model-based cloud analysis, and World Meteorological Organization (WMO) surface gauge observations.
 Despite its continued operational use, the 2-Layer Palmer model is obviously less complex than many more modern land surface models. However, using the same evaluation system applied here,Crow et al. found that modern land surface models generally offered only marginal increases in agricultural drought monitoring skill relative to simplistic soil water accounting models - suggesting that the 2-Layer Palmer model remains a reasonable baseline for evaluating the added impact of assimilating new remote sensing products.
 All modeling is performed on a quasi-global (60°S to 60°N) domain and 0.25° resolution mesh using a daily time step between June 1, 2002 to December 31, 2010. Soil moisture conditions are initialized using climatologically-averaged values (2002 to 2010) for June 1, 2002 and spun-up until the start of the analysis on July 1, 2002. Soil moisture predictions obtained from the model alone will be referred to as open loop (OL) results.
2.2. Remotely-Sensed Soil Moisture
 Surface soil moisture retrievals are obtained from gridded 0.25° Land Parameter Retrieval Model (LPRM) products provided by VU University Amsterdam based on Advanced Microwave Scanning Radiometer-EOS (AMSR-E) brightness temperature products [Njoku et al, 2003] between June 2002 and December 2010 [de Jeu, 2003; Owe et al., 2008]. The effective measurement depth of LPRM surface soil moisture retrievals is estimated to be 1–2 cm. For the purposes of this analysis, we assume these retrievals reflect the equivalent soil moisture estimated in the surface layer of the 2-Layer Palmer model. Only descending (1:30 AM local time) overpasses are used since they appear to be more useful for soil moisture retrieval than ascending overpasses [de Jeu, 2003]. LPRM gridded products are screened to mask areas with frozen soil, snow cover, and/or excessive vegetation using a surface temperature algorithm based on 37 GHz AMSR-E brightness temperature observations and retrieved canopy optical depth [Owe et al., 2008].
2.3. The Ensemble Kalman Filter
 Prior to assimilation, systematic biases between modeled and observed soil moisture datasets must be removed [Kumar et al., 2012]. To eliminate these differences, raw LPRM surface soil moisture retrievals (θLPRM) are rescaled such that their inter-annual (2002 to 2010) mean (μ) and standard deviation (σ) obtained for a 31-day moving window centered on a given day-of-year (DOY) matches the mean and standard deviation sampled from the top-layer of an open-loop realization (OL1) of the model over the same time period:
Note that all soil moisture variables in (1) and below are given in volumetric units [m3 m−3].
 The assimilation of θ*LPRM from (1)into the USDA FAS 2-Layer Palmer model is based on an Ensemble Kalman Filter (EnKF). A 30-member ensemble of two-element soil moisture state vectorsθjcontaining model surface and root-zone predictions is created via the direct perturbation of model soil-water balance calculations. These additive, mean-zero Gaussian perturbations are applied during each daily time step of the model and have covariance:
where αis the ratio of surface layer AWC to root-zone AWC. Upon acquisition ofθ*LPRM at time i via the rescaling step in (1), each ensemble replicate θj is updated following:
where the observation operator H = [1 0]; εis mean-zero, Gaussian noise with varianceR [m6 m−6]; and j is an ensemble number index. The Kalman gain vector K in (3) is:
with P representing the 2 × 2 state covariance matrix sampled directly from the θij− ensemble (created, in part, by the introduction of noise with covariance Q) and R the scalar error variance of θ*LPRM retrievals. While θ*LPRM is assumed to directly reflect surface layer conditions, the covariance information in Pis used to update both surface and root-zone forecasts contained inθij−. After updating, each θij+replicate is propagated in time by the Palmer 2-Layer Model (and further perturbed viaQ) until the next-availableθ*LPRM observation, at which point (3)is re-applied using a newly sampledP. Daily EnKF state predictions for the surface and root-zone layers,θEnKF1 and θEnKF2 respectively, are then obtained by averaging across the resulting θij+ ensemble.
 The parameter R represents the error variance in θ*LPRM retrievals for a given land surface type. The skill of retrieved soil moisture decreases significantly over areas of dense vegetation [Njoku and Chan, 2006]. Therefore, following Bolten et al. , we calculate R as:
where φis the AMSR-E incidence angle;b [m2 kg−1] is a vegetation structure coefficient (set equal to 0.30 for wooded grasslands and shrubs, grasslands, and croplands and 0.28 for closed bushlands, open shrublands, and bare soil); ωc [kg m−2] is canopy vegetation water content; and Ro is a constant set equal to 0.152 m6 m−6. A monthly climatology of Advanced Very High Resolution Radiometer-derived Normalized Difference Vegetation Index (NDVI) retrievals is used to estimateωc following Bindlish et al. . While (5) has already been applied successfully for use in a similar data assimilation system [Bolten et al., 2010], it should be noted that more complex error estimates for θLPRM retrievals are also available [Parinussa et al., 2011].
 Likewise, Qcaptures the added uncertainty incurred when the 2-Layer Palmer advances soil moisture estimates ahead by a one day. Here we assumeQis driven primarily by the accuracy of daily rainfall accumulation products used to force the model. Since this accuracy is known to vary geographically according to the density of available rain gauges for the correction of satellite-based rainfall estimates [Gebremichael et al., 2003], Q is specified as a function of the average distance D[km] to the three-closest WMO rain gauges:
For the case D > = 200 km: Q = 0.082 m6 m−6 and R = 0.
2.4. MODIS NDVI and Land Cover Data
 Monthly NDVI products for evaluation are obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS) MOD13C2 product [NASA Land Processes Distributed Active Archive Center, 2011]. Monthly NDVI composite products categorized as “fully reliable” in the MOD13C2 reliability flag file are aggregated from their native 0.05° resolution to match the 0.25° resolution modeling grid. In order to focus on water-limited ecosystems, sub-grid fractions of barren, tundra, forest cover, and open water surfaces from the MODIS MCD12C1 land cover classification [NASA Land Processes Distributed Active Archive Center, 2010] are summed within each global 0.25° pixel, and pixels where the sum of these areas constitutes more than a 50% areal fraction are masked.