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Analyzing the Impact of CryoSat-2 Ice Thickness Initialization on Seasonal Arctic Sea Ice Prediction

Twin 5-month seasonal forecast experiments are performed to predict the September 2018 minimum ice extent using the fully coupled Navy Earth System Prediction Capability (ESPC). In the control run, ensemble forecasts are initialized from the operational US Navy Global Ocean Forecasting System (GOFS) 3.1 for the ocean and sea ice but do not assimilate ice thickness data. Another set of forecasts are initialized from the same GOFS 3.1 fields but with sea ice thickness derived from CryoSat-2 (CS2). The Navy ESPC ensemble mean September 2018 minimum sea ice extent initialized with GOFS 3.1 ice thickness was over-predicted by 0.68 M sq.km (5.27 M sq.km) versus the ensemble set of forecasts initialized with CS2 ice thickness that had an error of 0.40 M sq.km (4.99 M sq.km), a 56% reduction in error. The September mean Integrated Ice Edge Error (IIEE) shows a 19% improvement for the entire Arctic with the CS2 data versus the control run. Comparison against Upward Looking Sonar (ULS) ice thickness in the Beaufort Sea reveals a lower bias and RMSE with the CS2 forecasts at all three moorings. Ice concentration at these locations is also improved, but neither set of experiments show ice free conditions as observed at moorings A and D.

time-lagged ensembles↗

File Specification for M2AMIP Products: Version Number - 1.0

The Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) is an atmospheric reanalysis computed with the Goddard Earth Observing (EOS) System, Version 5.12.4 (GEOS) data assimilation system (Gelaro et al., 2017). To supplement the reanalysis, the GEOS General Circulation Model (GCM) used in MERRA-2 has been used to generate a 10-member ensemble of simulations, configured following the convention of the Atmospheric Model Intercomparison Project (AMIP; Gates et al., 1992). Each ensemble member was initialized using meteorological fields from a different date in November 1979. The AMIP simulations used the sea-surface temperature (SST) and sea-ice boundary conditions that were used in MERRA-2 (Bosilovich et al., 2016). This 10-member ensemble of AMIP simulations, denoted M2AMIP, is available for download in a group of self-describing files, which are documented in this office note. All data collections are provided on the same horizontal grid as MERRA-2. This grid has 576 points in the longitudinal direction and 361 points in the latitudinal direction, corresponding to a resolution of 0.625 degrees by 0.5 degrees. Although data collections are available at this grid, all fields are computed on a cubed-sphere grid with an approximate resolution of 50 km by 50 km and are then spatially interpolated to the latitude-longitude grid. There are no changes in the vertical grids used: variables are provided on either the native vertical grid of 72 model layers, or interpolated to 42 standard pressure levels. Unlike MERRA, no data collections are available at the vertical layer edges. More details on the grid are provided in Section 4. MERRA-2 introduced observation-based precipitation forcing for the land surface parameterization and the corresponding variable PRECTOTCORR in the MERRA-2 FLX (surface turbulent fluxes and related quantities) and LFO (land-surface forcing) collections (see Section 6; Reichle et al., 2017). While this variable is still available for M2AMIP, there was no observation-based forcing, making the value identical to the model derived precipitation, PRECTOT. Similarly, without data assimilation, the values for the analysis increments, D*DTANA, in the tendency and vertically integrated file collections are zero. The M2AMIP data are available for download online through the NASA Center for Climate Simulation (NCCS) DataPortal (https://portal.nccs.nasa.gov/datashare/gmao_m2amip/). Data are arranged in subdirectories based on ensemble member, followed by year and month. Control files that are compatible with the Grid Analysis and Display System (GrADS) are available in the ctl_daily and ctl_monthly directories for the hourly, three hourly, and monthly mean data. Control files for the monthly mean diurnal cycle can be found in the ctl_diurnal subdirectory within the directory for each individual ensemble member.

M2AMIP↗

Assimilation of Terrestrial Water Storage from GRACE in a Snow-Dominated Basin

Terrestrial water storage (TWS) information derived from Gravity Recovery and Climate Experiment (GRACE) measurements is assimilated into a land surface model over the Mackenzie River basin located in northwest Canada. Assimilation is conducted using an ensemble Kalman smoother (EnKS). Model estimates with and without assimilation are compared against independent observational data sets of snow water equivalent (SWE) and runoff. For SWE, modest improvements in mean difference (MD) and root mean squared difference (RMSD) are achieved as a result of the assimilation. No significant differences in temporal correlations of SWE resulted. Runoff statistics of MD remain relatively unchanged while RMSD statistics, in general, are improved in most of the sub-basins. Temporal correlations are degraded within the most upstream sub-basin, but are, in general, improved at the downstream locations, which are more representative of an integrated basin response. GRACE assimilation using an EnKS offers improvements in hydrologic state/flux estimation, though comparisons with observed runoff would be enhanced by the use of river routing and lake storage routines within the prognostic land surface model. Further, GRACE hydrology products would benefit from the inclusion of better constrained models of post-glacial rebound, which significantly affects GRACE estimates of interannual hydrologic variability in the Mackenzie River basin.

Forman, Barton A.↗

Design and Implementation of a Parallel Multivariate Ensemble Kalman Filter for the Poseidon Ocean General Circulation Model

A multivariate ensemble Kalman filter (MvEnKF) implemented on a massively parallel computer architecture has been implemented for the Poseidon ocean circulation model and tested with a Pacific Basin model configuration. There are about two million prognostic state-vector variables. Parallelism for the data assimilation step is achieved by regionalization of the background-error covariances that are calculated from the phase-space distribution of the ensemble. Each processing element (PE) collects elements of a matrix measurement functional from nearby PEs. To avoid the introduction of spurious long-range covariances associated with finite ensemble sizes, the background-error covariances are given compact support by means of a Hadamard (element by element) product with a three-dimensional canonical correlation function. The methodology and the MvEnKF configuration are discussed. It is shown that the regionalization of the background covariances; has a negligible impact on the quality of the analyses. The parallel algorithm is very efficient for large numbers of observations but does not scale well beyond 100 PEs at the current model resolution. On a platform with distributed memory, memory rather than speed is the limiting factor.

Keppenne, Christian L.↗

GeoThermalCloud: Cloud Fusion of Big Data and Multi-Physics Models using Machine Learning for Discovery, Exploration, and Development of Hidden Geothermal Resources

The primary goals of this project are identifying hidden geothermal resources in the USA and designing profitable enhanced geothermal systems (EGS). Many non-obvious processes and parameters could characterize geothermal resources and could control the ultimate energy potential of geothermal fields. Diverse datasets (e.g., geology, geochemistry, geophysics, satellite, airborne geophysics) are available to help characterize geothermal resources, but this data is sparse and multi-scale that has hindered attempts to leverage the datasets for geothermal exploration and profitable EGS design. Recent advancements in machine learning (ML) give promise to overcome these issues. Modern ML methods and tools can (1) analyze large datasets, (2) assimilate model ensembles that include a multitude of inputs and outputs, (3) process sparse datasets, (4) perform transfer learning between sites with different data quality, (5) extract hidden geothermal signatures from field and simulation data, (6) label geothermal resources and processes, (7) identify highvalue data acquisition targets, and (8) guide geothermal exploration and production by selecting optimal exploration, production, and drilling strategies.

58 GEOSCIENCES↗

Cloud Fusion of Big Data and Multi-Physics Models using Machine Learning for Discovery, Exploration, and Development of Hidden Geothermal Resources

The primary goals of this project are identifying hidden geothermal resources in the USA and designing profitable enhanced geothermal systems (EGS). Many non-obvious processes and parameters could characterize geothermal resources and could control the ultimate energy potential of geothermal fields. Diverse datasets (e.g., geology, geochemistry, geophysics, satellite, airborne geophysics) are available to help characterize geothermal resources, but this data is sparse and multi-scale. This has hindered attempts to leverage the datasets for geothermal exploration and profitable EGS design. Recent advancements in machine learning (ML) give promise to overcome these issues. Modern ML methods and tools can (1) analyze large datasets, (2) assimilate model ensembles that include a multitude of inputs and outputs, (3) process sparse datasets, (4) perform transfer learning between sites with different data quality, (5) extract hidden geothermal signatures from field and simulation data, (6) label geothermal resources and processes, (7) identify high-value data acquisition targets, and (8) guide geothermal exploration and production by selecting optimal exploration, production, and drilling strategies. In this work, we implement ML-based geothermal exploration and an enhanced geothermal systems (EGS) design tool to achieve the above goals. Our exploration tool is GeoThermalCloud (GTC) EGS design tool is GeoDT-ML. GTC (github.com/SmartTensors/GeoThermalCloud.jl) utilizes a LANL unsupervised ML platform called SmartTensors (https://tensors.lanl.gov/) to automate data analyses and interpretations by extracting hidden signatures to identify geothermal prospects. It enables the identification of critical measurements needed to identify geothermal resource signatures. GeoDT-ML (github.com/SmartTensors/GeoThermalCloud.jl/tree/master/) adds coupling to GeoDT (https://github.com/GeoDesignTool/GeoDT.git) for stochastic EGS design optimization and performance prediction. GeoDT-ML leverages recent advances in deep learning and high-performance computing. Contributors to this effort include LANL, PNNL, Google, Stanford, and Julia Computing.

15 GEOTHERMAL ENERGY↗

Simulation of Continental Shallow Cumulus Populations Using an Observation-Constrained Cloud-System Resolving Model

Continental shallow cumulus (ShCu) clouds observed on 30 August 2016 during the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems (HI-SCALE) field campaign are simulated by using an observation-constrained cloud-system resolving model. On this day, ShCu forms over Oklahoma and southern Kansas and some of these clouds transition to deeper, precipitating convection during the afternoon. We apply a four-dimensional ensemble-variational (4DEnVar) hybrid technique in the Community Gridpoint Statistical Interpolation (GSI) system to assimilate operational data sets and unique boundary layer measurements including a Raman lidar, radar wind profilers, radiosondes, and surface stations collected by the U.S. Department of Energy's (DOE) Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) atmospheric observatory into the Weather Research and Forecasting (WRF) model to ascertain how improved environmental conditions can influence forecasts of ShCu populations and the transition to deeper convection. Independent observations from aircraft, satellite, as well as ARM's remote sensors are used to evaluate model performance in different aspects. Several model experiments are conducted to identify the impact of data assimilation (DA) on the prediction of clouds evolution. The analyses indicate that ShCu populations are more accurately reproduced after DA in terms of cloud initiation time and cloud base height, which can be attributed to an improved representation of the ambient meteorological conditions and the convective boundary layer. Extending the assimilation to 18 UTC (local noon) also improved the simulation of shallow-to-deep transitions of convective clouds.

54 ENVIRONMENTAL SCIENCES↗

Integrating Enhanced Grace Terrestrial Water Storage Data Into the U.S. and North American Drought Monitors

NASA's Gravity Recovery and Climate Experiment (GRACE) satellites measure time variations nf the Earth's gravity field enabling reliable detection of spatio-temporal variations in total terrestrial water storage (TWS), including ground water. The U.S. and North American Drought Monitors are two of the premier drought monitoring products available to decision-makers for assessing and minimizing drought impacts, but they rely heavily on precipitation indices and do not currently incorporate systematic observations of deep soil moisture and groundwater storage conditions. Thus GRACE has great potential to improve the Drought Monitors hy filling this observational gap. Horizontal, vertical and temporal disaggregation of the coarse-resolution GRACE TWS data has been accomplished by assimilating GRACE TWS anomalies into the Catchment Land Surface Model using ensemble Kalman smoother. The Drought Monitors combine several short-term and long-term drought indices and indicators expressed in percentiles as a reference to their historical frequency of occurrence for the location and time of year in question. To be consistent, we are in the process of generating a climatology of estimated soil moisture and ground water based on m 60-year Catchment model simulation which will subsequently be used to convert seven years of GRACE assimilated fields into soil moisture and groundwater percentiles. for systematic incorporation into the objective blends that constitute Drought Monitor baselines. At this stage we provide a preliminary evaluation of GRACE assimilated Catchment model output against independent datasets including soil moisture observations from Aqua AMSR-E and groundwater level observations from the U.S. Geological Survey's Groundwater Climate Response Network.

Housborg, Rasmus↗

Multi-Scale Hydrometeorological Modeling, Land Data Assimilation and Parameter Estimation with the Land Information System

The Land Information System (LIS; http://lis.gsfc.nasa.gov; Kumar et al., 2006; Peters- Lidard et al.,2007) is a flexible land surface modeling framework that has been developed with the goal of integrating satellite- and ground-based observational data products and advanced land surface modeling techniques to produce optimal fields of land surface states and fluxes. As such, LIS represents a step towards the next generation land component of an integrated Earth system model. In recognition of LIS object-oriented software design, use and impact in the land surface and hydrometeorological modeling community, the LIS software was selected ase co-winner of NASA's 2005 Software of the Year award. LIS facilitates the integration of observations from Earth-observing systems and predictions and forecasts from Earth System and Earth science models into the decision-making processes of partnering agency and national organizations. Due to its flexible software design, LIS can serve both as a Problem Solving Environment (PSE) for hydrologic research to enable accurate global water and energy cycle predictions, and as a Decision Support System (DSS) to generate useful information for application areas including disaster management, water resources management, agricultural management, numerical weather prediction, air quality and military mobility assessment. LIS has evolved from two earlier efforts North American Land Data Assimilation System (NLDAS; Mitchell et al. 2004) and Global Land Data Assimilation System (GLDAS; Rodell al. 2004) that focused primarily on improving numerical weather prediction skills by improving the characterization of the land surface conditions. Both of GLDAS and NLDAS now use specific configurations of the LIS software in their current implementations. In addition, LIS was recently transitioned into operations at the US Air Force Weather Agency (AFWA) to ultimately replace their Agricultural Meteorology (AGRMET) system, and is also used routinely by NOAA's National Centers for Environmental Prediction (NCEP)/Environmental Modeling Center (EMC) for their land data assimilation systems to support weather and climate modeling. LIS not only consolidates the capabilities of these two systems, but also enables a much larger variety of configurations with respect to horizontal spatial resolution, input datasets and choice of land surface model through "plugins,". As described in Kumar et al., 2007, and demonstrated in Case et al., 2008, and Santanello et al., 2009, LIS has been coupled to the Weather Research and Forecasting (WRF) model to support studies of land-atmosphere coupling the enabling ensembles of land surface states to be tested against multiple representations of the atmospheric boundary layer. LIS has also been demonstrated for parameter estimation as described in Peters-Lidard et al. (2008) and Santanello et al. (2007), who showed that the use of sequential remotely sensed soil moisture products can be used to derive soil hydraulic and texture properties given a sufficient dynamic range in the soil moisture retrievals and accurate precipitation inputs. LIS has also recently been demonstrated for multi-model data assimilation (Kumar et al., 2008) using an Ensemble Kalman Filter for sequential assimilation of soil moisture, snow, and temperature. Ongoing work has demonstrated the value of bias correction as part of the filter, and also that of joint calibration and assimilation. Examples and case studies demonstrating the capabilities and impacts of LIS for hydrometeoroogical modeling, assimilation and parameter estimation will be presented as advancements towards the next generation of integrated observation and modeling systems.

Peters-Lidard, Christa D.↗

Combined assimilation of hydrography and TOPEX data into an Indian Ocean GCM using the adjoint method

To study seasonal circulation and meridional heat transport of the Indian Ocean by synthesizing dynamics with data, climatological monthly temperatures and salinities, surface heat and freshewater fluxes, and wind stresses, together with monthly ensembles of three years (93-95) of TOPEX-derived surface geostrophic velocity anomalies, are assimilated into an Indian Ocean GCM.

Hydrography Indian Ocean TOPEX meridional heat tra↗

Solar Activity Modeling: From Subgranular Dynamical Scales to the Solar Cycles

Dynamical effects of solar magnetoconvection span a wide range spatial and temporal scales that extends from the interior to the corona and from fast turbulent motions to the global-Sun magnetic activity. To study the solar activity on short temporal scales (from minutes to hours), we use 3D radiative MHD simulations that allow us to investigate complex turbulent interactions that drive various phenomena, such as plasma eruptions, spontaneous formation of magnetic structures, funnel-like structures and magnetic loops in the corona, and others. In particular, we focus on multi-scale processes of energy exchange across the different layers, which contribute to the corona heating and eruptive dynamics, as well as interlinks between different layers of the solar interior and atmosphere. For modeling the global-scale activity we use the data assimilation approach that has demonstrated great potential for building reliable long-term forecasts of solar activity. In particular, it has been shown that the Ensemble Kalman Filter (EnKF) method applied to the Parker-Kleeorin-Ruzmakin dynamo model is capable of predicting solar activity up to one sunspot cycle ahead in time, as well as estimating the properties of the next cycle a few years before it begins. In this presentation, using the available magnetogram data, we discuss development of the methodology and forecast quality criteria (including forecast uncertainties and sources of errors). We demonstrate the influence of observational limitation on the prediction accuracy. We present the EnKF predictions of the upcoming Solar Cycle 25 based on both the sunspot number series and observed magnetic fields, and discuss the uncertainties and potential of the data assimilation approach for modeling and forecasting the solar activity.

Kitiashvili, I. N.↗

Solar Activity Modeling: From Subgranular Dynamical Scales to the Solar Cycles

The dynamical effects of solar magnetoconvection span a wide range spatial and temporal scales that extend from the interior to the corona and from fast turbulent motions to global magnetic activity. To study the solar activity on short temporal scales (from minutes to hours), we use 3D radiative MHD simulations that allow us to investigate complex turbulent interactions that drive various phenomena, such as plasma eruptions, spontaneous formation of magnetic structures, funnel-like structures and magnetic loops in the corona, and others. In particular, we focus on multi-scale processes of energy exchange across layers of the solar interior and atmosphere, which contribute to coronal heating and eruptive dynamics. For modeling global-scale activity, we use a data assimilation approach that has demonstrated great potential for building reliable long-term forecasts of solar activity. In particular, it has been shown that the Ensemble Kalman Filter (EnKF) method applied to the Parker-Kleeorin-Ruzmakin dynamo model is capable of predicting solar activity up to one sunspot cycle ahead in time, as well as estimating the properties of the next cycle a few years before it begins. In this presentation, using the available magnetogram data, we discuss development of the methodology and forecast quality criteria (including forecast uncertainties and sources of errors). We demonstrate the influence of observational limitations on prediction accuracy, and we present the EnKF predictions of the upcoming Solar Cycle (25) based on both the sunspot number series and observed magnetic fields and discuss the uncertainties and potential of the data assimilation approach for modeling and forecasting solar activity.

Kitiashvili, I. N.↗

Assimilation of Satellite Soil Moisture for Improved Atmospheric Reanalyses

Satellite soil moisture observations are assimilated into NASA's Global Earth Observing System using a weakly coupled land/atmosphere data assimilation system. Specifically, Advanced Scatterometer and Soil Moisture Ocean Salinity soil moisture retrievals are assimilated with an Ensemble Kalman Filter into a system that uses the same model, atmospheric assimilation system (3DVar), and atmospheric observations as the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). The first set of experiments investigate the impact of the soil moisture assimilation on the model states and fluxes within the cycling DA system. Comparison to independent ground-based observations from global networks of soil moisture, latent and sensible heating, and 2m temperature and specific humidity showed small, but positive, improvements in the global mean statistics. Additionally, in some regions, the soil moisture assimilation induced more substantial improvements. For all variables evaluated, the soil moisture assimilation improved the model at monthly to seasonal, rather than daily, time scales. Based on the above experiments, it is recommended that satellite soil moisture be assimilated into future reanalyses, including the follow-on to MERRA-2.

Draper, Clara↗

Vertical transport by convective clouds: Comparisons of three modeling approaches

A preliminary comparison of the GEOS-1 (Goddard Earth Observing System) data assimilation system convective cloud mass fluxes with fluxes from a cloud-resolving model (the Goddard Cumulus Ensemble Model, GCE) is reported. A squall line case study (10-11 June 1985 Oklahoma PRESTORM episode) is the basis of the comparison. Regional (central U. S.) monthly total convective mass flux for June 1985 from GEOS-1 compares favorably with estimates from a statistical/dynamical approach using GCE simulations and satellite-derived cloud observations. The GEOS-1 convective mass fluxes produce reasonable estimates of monthly-averaged regional convective venting of CO from the boundary layer at least in an urban-influenced continental region, suggesting that they can be used in tracer transport simulations.

Pickering, Kenneth E.↗

Improving Simulated Soil Moisture Fields Through Assimilation of AMSR-E Soil Moisture Retrievals with an Ensemble Kalman Filter and a Mass Conservation Constraint

Model simulated soil moisture fields are often biased due to errors in input parameters and deficiencies in model physics. Satellite derived soil moisture estimates, if retrieved appropriately, represent the spatial mean of soil moisture in a footprint area, and can be used to reduce model bias (at locations near the surface) through data assimilation techniques. While assimilating the retrievals can reduce model bias, it can also destroy the mass balance enforced by the model governing equation because water is removed from or added to the soil by the assimilation algorithm. In addition, studies have shown that assimilation of surface observations can adversely impact soil moisture estimates in the lower soil layers due to imperfect model physics, even though the bias near the surface is decreased. In this study, an ensemble Kalman filter (EnKF) with a mass conservation updating scheme was developed to assimilate the actual value of Advanced Microwave Scanning Radiometer (AMSR-E) soil moisture retrievals to improve the mean of simulated soil moisture fields by the Noah land surface model. Assimilation results using the conventional and the mass conservation updating scheme in the Little Washita watershed of Oklahoma showed that, while both updating schemes reduced the bias in the shallow root zone, the mass conservation scheme provided better estimates in the deeper profile. The mass conservation scheme also yielded physically consistent estimates of fluxes and maintained the water budget. Impacts of model physics on the assimilation results are discussed.

Li, Bailing↗

An Improved Analysis of Forest Carbon Dynamics using Data Assimilation

There are two broad approaches to quantifying landscape C dynamics - by measuring changes in C stocks over time, or by measuring fluxes of C directly. However, these data may be patchy, and have gaps or biases. An alternative approach to generating C budgets has been to use process-based models, constructed to simulate the key processes involved in C exchange. However, the process of model building is arguably subjective, and parameters may be poorly defined. This paper demonstrates why data assimilation (DA) techniques - which combine stock and flux observations with a dynamic model - improve estimates of, and provide insights into, ecosystem carbon (C) exchanges. We use an ensemble Kalman filter (EnKF) to link a series of measurements with a simple box model of C transformations. Measurements were collected at a young ponderosa pine stand in central Oregon over a 3-year period, and include eddy flux and soil C02 efflux data, litterfall collections, stem surveys, root and soil cores, and leaf area index data. The simple C model is a mass balance model with nine unknown parameters, tracking changes in C storage among five pools; foliar, wood and fine root pools in vegetation, and also fresh litter and soil organic matter (SOM) plus coarse woody debris pools. We nested the EnKF within an optimization routine to generate estimates from the data of the unknown parameters and the five initial conditions for the pools. The efficacy of the DA process can be judged by comparing the probability distributions of estimates produced with the EnKF analysis vs. those produced with reduced data or model alone. Using the model alone, estimated net ecosystem exchange of C (NEE)= -251 f 197g Cm-2 over the 3 years, compared with an estimate of -419 f 29gCm-2 when all observations were assimilated into the model. The uncertainty on daily measurements of NEE via eddy fluxes was estimated at 0.5gCm-2 day-1, but the uncertainty on assimilated estimates averaged 0.47 g Cm-2 day-1, and only exceeded 0.5gC m-2 day-1 on days where neither eddy flux nor soil efflux data were available. In generating C budgets, the assimilation process reduced the uncertainties associated with using data or model alone and the forecasts of NEE were statistically unbiased estimates. The results of the analysis emphasize the importance of time series as constraints. Occasional, rare measurements of stocks have limited use in constraining the estimates of other components of the C cycle. Long time series are particularly crucial for improving the analysis of pools with long time constants, such as SOM, woody biomass, and woody debris. Long-running forest stem surveys, and tree ring data, offer a rich resource that could be assimilated to provide an important constraint on C cycling of slow pools. For extending estimates of NEE across regions, DA can play a further important role, by assimilating remote-sensing data into the analysis of C cycles. We show, via sensitivity analysis, how assimilating an estimate of photosynthesis - which might be provided indirectly by remotely sensed data - improves the analysis of NEE.

Williams, Mathew↗

A Particle Batch Smoother Approach to Snow Water Equivalent Estimation

This paper presents a newly proposed data assimilation method for historical snow water equivalent SWE estimation using remotely sensed fractional snow-covered area fSCA. The newly proposed approach consists of a particle batch smoother (PBS), which is compared to a previously applied Kalman-based ensemble batch smoother (EnBS) approach. The methods were applied over the 27-yr Landsat 5 record at snow pillow and snow course in situ verification sites in the American River basin in the Sierra Nevada (United States). This basin is more densely vegetated and thus more challenging for SWE estimation than the previous applications of the EnBS. Both data assimilation methods provided significant improvement over the prior (modeling only) estimates, with both able to significantly reduce prior SWE biases. The prior RMSE values at the snow pillow and snow course sites were reduced by 68%-82% and 60%-68%, respectively, when applying the data assimilation methods. This result is encouraging for a basin like the American where the moderate to high forest cover will necessarily obscure more of the snow-covered ground surface than in previously examined, less-vegetated basins. The PBS generally outperformed the EnBS: for snow pillows the PBSRMSE was approx.54%of that seen in the EnBS, while for snow courses the PBSRMSE was approx.79%of the EnBS. Sensitivity tests show relative insensitivity for both the PBS and EnBS results to ensemble size and fSCA measurement error, but a higher sensitivity for the EnBS to the mean prior precipitation input, especially in the case where significant prior biases exist.

EnBS↗

A Localized Ensemble Kalman Smoother

Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.

recursive estimation↗