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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Comparison of high-resolution airborne soil moisture retrievals to SMAP soil moisture during the SMAP validation experiment 2016 (SMAPVEX16)

The NASA's Soil Moisture Active Passive (SMAP) mission conducted a field experiment with its partners over two 40-km agricultural domains in Iowa and Manitoba in the summer of 2016 to address concerns observed in SMAP soil moisture (SM) retrievals over agricultural areas. The experiment featured airborne Passive Active L-band System (PALS) flights over each domain with intensive ground measurements and dense networks of SM monitoring stations. With two intensive observation periods separated in time (May 28–June 20 and July 14–August 16), the flights captured both early-season/low vegetation and later-season/high-vegetation conditions. The comparison of the PALS brightness temperature (TB) measurements to the SMAP TB observed over the sites resulted in root mean square difference (RMSD) of 2.8 K and 4.0 K for vertical and horizontal polarizations, respectively. The subsequent SM analysis rescaled the PALS TB with the SMAP TB to allow equitable comparisons between the SM retrievals from the two instruments. The PALS SM retrieval algorithm used the SM sampled by the ground teams during the overpass days for tuning, and was parameterized by a high-resolution vegetation water content product calibrated using vegetation samples collected during the experiment. The tuning process was not able to find a satisfactory result with a temporally constant set of parameters in the single channel algorithm for the two intensive observation periods of the experiment. This result indicated that the rapid change in the vegetation structure during the growth stages and likely variation in the surface roughness conditions were not compatible with rigid parameterization over the entire period. However, using seasonally variable parameters we found that it was possible to retrieve soil moisture with satisfactory accuracy. Comparative analysis with the SMAP SM product included aggregation of the PALS SM to the SMAP pixel-scale. The RMSD between the PALS SM and the aggregated manual field samples was <0.04 m3/m3 with Pearson correlation >0.85 for both sites. The comparison between different in situ sources indicated that the soil moisture network measurements were not the source of the large biases observed for SMAP over the sites reported in earlier studies. Therefore, the results suggested the rapidly growing vegetation and the early-season surface condition changes not captured by the SMAP algorithm caused the SMAP retrieval errors. In addition, the significant deviations of the vegetation water content used by the SMAP product from the calibrated vegetation water content obtained during the experiment compounds the problem.

Andreas Colliander↗
NASA NTRS2016

Overview of the SMAP Applications and the SMAP Early Adopters Program - NASA's First Mission-Directed Outreach Effort

Satellite data provide global observations of many of the earths system processes and features. These data are valuable for developing scientific products that increase our understanding of how the earths systems are integrated. The water, energy and carbon cycle exchanges between the land and atmosphere are linked by soil moisture. NASAs Soil Moisture Active Passive (SMAP) mission provides soil moisture and freeze thaw measurements from space and allows scientists to link the water energy and carbon cycles. In order for SMAP data to be best integrated into decision support systems, the mission has engaged with the stakeholder community since 2009 and has attempted to scale the utility of the data to the thematic societal impacts of the satellite product applications. The SMAP Mission, which launched on January 31, 2015, has actively grown an Early Adopter (EA) community as part of its applications effort and worked with these EAs to demonstrate a scaled thematic impact of SMAP data product in societally relevant decision support applications. The SMAP mission provides global observations of the Earths surface soil moisture, providing high accuracy, resolution and continuous global coverage. Through the Early Adopters Program, the SMAP Applications Team will spend the next 2 years after launch documenting and evaluating the use of SMAP science products in applications related to weather forecasting, drought, agriculture productivity, floods, human health and national security.

SMAP↗
NASA NTRS2013

Assessment of Soil Moisture Data Requirements by the Potential SMAP Data User Community: Review of SMAP Mission User Community

NASA's Soil Moisture Active and Passive (SMAP) mission is planned for launch in October 2014 and will provide global measurements of soil moisture and freeze thaw state. The project is driven by both basic research and applied science goals. Understanding how application driven end-users will apply SMAP data, prior to the satellite's launch, is an important goal of NASA's applied science program and SMAP mission success. Because SMAP data are unique, there are no direct proxy data sets that can be used in research and operational studies to determine how the data will interact with existing processes. The objective of this study is to solicit data requirements, accuracy needs, and current understanding of the SMAP mission from the potential user community. This study showed that the data to be provided by the SMAP mission did substantially meet the user community needs. Although there was a broad distribution of requirements stated, the SMAP mission fit within these requirements.

applications↗
NASA NTRS2021

The Contributions of Gauge-Based Precipitation and SMAP Brightness Temperature Observations to the Skill of the SMAP Level-4 Soil Moisture Product

Soil Moisture Active Passive (SMAP) mission L-band brightness temperature (Tb) observations are routinely assimilated into the Catchment land surface model to generate Level-4 Soil Moisture (L4_SM) estimates of global surface and root-zone soil moisture at 9-km, 3-hourly resolution with ~2.5-day latency. The Catchment model in the L4_SM algorithm is driven with ¼-degree, hourly surface meteorological forcing data from the Goddard Earth Observing System (GEOS). Outside of Africa and the high latitudes, GEOS precipitation is corrected using Climate Prediction Center Unified (CPCU) gauge-based, ½-degree, daily precipitation. L4_SM soil moisture was previously shown to improve over land model-only estimates that use CPCU precipitation but no Tb assimilation (CPCU_SIM). Here, we additionally examine the skill of model-only (CTRL) and Tb assimilation-only (SMAP_DA) estimates derived without CPCU precipitation. Soil moisture is assessed versus in situ measurements in well-instrumented regions and globally through the Instrumental Variable (IV) method using independent soil moisture retrievals from the Advanced Scatterometer. At the in situ locations, SMAP_DA and CPCU_SIM have comparable soil moisture skill improvements relative to CTRL for the unbiased root-mean-square error (surface and root-zone) and correlation metrics (root-zone only). In the global average, SMAP Tb assimilation increases the surface soil moisture anomaly correlation by 0.10-0.11 compared to an increase of 0.02-0.03 from the CPCU-based precipitation corrections. The contrast is particularly strong in central Australia, where CPCU is known to have errors and observation-minus-forecast Tb residuals are larger when CPCU precipitation is used. Validation versus streamflow measurements in the contiguous U.S. reveals that CPCU precipitation provides most of the skill gained in L4_SM runoff estimates over CTRL.

SMAP↗
NASA NTRS2016

Soil Moisture Active Passive (SMAP) Project Algorithm Theoretical Basis Document SMAP L1B Radiometer Data Product: L1B_TB

The purpose of the Soil Moisture Active Passive (SMAP) radiometer calibration algorithm is to convert Level 0 (L0) radiometer digital counts data into calibrated estimates of brightness temperatures referenced to the Earth's surface within the main beam. The algorithm theory in most respects is similar to what has been developed and implemented for decades for other satellite radiometers; however, SMAP includes two key features heretofore absent from most satellite borne radiometers: radio frequency interference (RFI) detection and mitigation, and measurement of the third and fourth Stokes parameters using digital correlation. The purpose of this document is to describe the SMAP radiometer and forward model, explain the SMAP calibration algorithm, including approximations, errors, and biases, provide all necessary equations for implementing the calibration algorithm and detail the RFI detection and mitigation process. Section 2 provides a summary of algorithm objectives and driving requirements. Section 3 is a description of the instrument and Section 4 covers the forward models, upon which the algorithm is based. Section 5 gives the retrieval algorithm and theory. Section 6 describes the orbit simulator, which implements the forward model and is the key for deriving antenna pattern correction coefficients and testing the overall algorithm.

microwave radiometers↗
NASA NTRS2019

Sensitvity analysis of SMAP-Reflectometry (SMAP-R) signals to vegetation water content

Global Navigation Satellite System – Reflectometry (GNSSR) techniques have proven successful to retrieve several geophysical parameters such as, ocean wind speed, soil moisture, altimetry, wetland dynamics, snow depth estimations. In this paper, the L2C GPS signals measured from the Soil Moisture Active Passive (SMAP) radar after its malfunction is used to investigate the effect of the vegetation water content on the electromagnetic signal. The SMAP Reflectometry (SMAP-R) measurements are obtained at V and H polarizations allowing for not only signal-to-noise ratio (SNR) analysis but also for polarimetric ratio (PR) studies.

Morris, Mary↗
NASA NTRS2022

Analysis of the Smap Roughness Parameter and the Smap Vegetation Optical Depth

The SMAP product provides the soil moisture (SM) computed using three different retrieval algorithms: the single channel H and V algorithms (SCA-H and SCA-V), and the dual-channel algorithm (DCA) which in addition provides the vegetation optical depth (VOD). The roughness model and the roughness parameters play an important role in the determination of the soil moisture and the VOD. In this regard, the SMAP SCA and DCA utilize different approaches to incorporate the effect of roughness. In this work we will summarize those approaches and we will evaluate the effect of the DCA approach on the retrieval of VOD. We will compare the SMAP DCA roughness parameter h with topographic parameters such as DEM height, DEM slope, DEM height standard deviation and DEM slope standard deviation.

Mousavi, M.↗
NASA NTRS2019

Characterization of the land surface freeze/thaw state with SMAP-Reflectometry (SMAP-R)

The use of the Soil Moisture Active Passive (SMAP) radar in received mode has allowed for a new dataset of Global Navigation Satellite System – Reflectometry (GNSS-R) measurements. GNSS-R techniques have been used for more than two decades and have proven successful perform altimetry studies and to retrieve ocean wind speed and soil moisture, monitor wetland dynamics, estimate snow depth, detect sea ice and determine sea ice types. In this paper, the SMAP-Reflectometry measurements are used to classify freeze/thaw (F/T) state over Alaska, studying the differences in the SNR signal at both V and H polarizations.

Podest, Erika↗
NASA NTRS2018

An Initial Assessment of a SMAP Soil Moisture Disaggregation Scheme Using TIR Surface Evaporation Data over the Continental United States

The Soil Moisture Active Passive (SMAP) mission is dedicated toward global soil moisture mapping. Typically, an L-band microwave radiometer has spatial resolution on the order of 36-40 km, which is too coarse for many specific hydro-meteorological and agricultural applications. With the failure of the SMAP active radar within three months of becoming operational, an intermediate (9-km) and finer (3-km) scale soil moisture product solely from the SMAP mission is no longer possible. Therefore, the focus of this study is a disaggregation of the 36-km resolution SMAP passive-only surface soil moisture (SSM) using the Soil Evaporative Efficiency (SEE) approach to spatial scales of 3-km and 9-km. The SEE was computed using thermal-infrared (TIR) estimation of surface evaporation over Continental U.S. (CONUS). The disaggregation results were compared with the 3 months of SMAP-Active (SMAP-A) and Active/Passive (AP) products, while comparisons with SMAP-Enhanced (SMAP-E), SMAP-Passive (SMAP-P), as well as with more than 180 Soil Climate Analysis Network (SCAN) stations across CONUS were performed for a 19 month period. At the 9-km spatial scale, the TIR-Downscaled data correlated strongly with the SMAP-E SSM both spatially (r = 0.90) and temporally (r = 0.87). In comparison with SCAN observations, overall correlations of 0.49 and 0.47; bias of −0.022 and −0.019 and unbiased RMSD of 0.105 and 0.100 were found for SMAP-E and TIR-Downscaled SSM across the Continental U.S., respectively. At 3-km scale, TIR-Downscaled and SMAP-A had a mean temporal correlation of only 0.27. In terms of gain statistics, the highest percentage of SCAN sites with positive gains (>55%) was observed with the TIR-Downscaled SSM at 9-km. Overall, the TIR-based downscaled SSM showed strong correspondence with SMAP-E; compared to SCAN, and overall both SMAP-E and TIR-Downscaled performed similarly, however, gain statistics show that TIR-Downscaled SSM slightly outperformed SMAP-E.

Disaggregation↗
NASA NTRSDate not supplied

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗
NASA NTRSDate not supplied

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗
NASA NTRS2017

Evaluating Soil Moisture Retrievals from ESA's SMOS and NASA's SMAP Brightness Temperature Datasets

Two satellites are currently monitoring surface soil moisture (SM) using L-band observations: SMOS (Soil Moisture and Ocean Salinity), a joint ESA (European Space Agency), CNES (Centre national d'tudes spatiales), and CDTI (the Spanish government agency with responsibility for space) satellite launched on November 2, 2009 and SMAP (Soil Moisture Active Passive), a National Aeronautics and Space Administration (NASA) satellite successfully launched in January 2015. In this study, we used a multilinear regression approach to retrieve SM from SMAP data to create a global dataset of SM, which is consistent with SM data retrieved from SMOS. This was achieved by calibrating coefficients of the regression model using the CATDS (Centre Aval de Traitement des Donnes) SMOS Level 3 SM and the horizontally and vertically polarized brightness temperatures (TB) at 40 deg incidence angle, over the 2013 - 2014 period. Next, this model was applied to SMAP L3 TB data from Apr 2015 to Jul 2016. The retrieved SM from SMAP (referred to here as SMAP_Reg) was compared to: (i) the operational SMAP L3 SM (SMAP_SCA), retrieved using the baseline Single Channel retrieval Algorithm (SCA); and (ii) the operational SMOSL3 SM, derived from the multiangular inversion of the L-MEB model (L-MEB algorithm) (SMOSL3). This inter-comparison was made against in situ soil moisture measurements from more than 400 sites spread over the globe, which are used here as a reference soil moisture dataset. The in situ observations were obtained from the International Soil Moisture Network (ISMN; https:ismn.geo.tuwien.ac.at) in North of America (PBO_H2O, SCAN, SNOTEL, iRON, and USCRN), in Australia (Oznet), Africa (DAHRA), and in Europe (REMEDHUS, SMOSMANIA, FMI, and RSMN). The agreement was analyzed in terms of four classical statistical criteria: Root Mean Squared Error (RMSE),Bias, Unbiased RMSE (UnbRMSE), and correlation coefficient (R). Results of the comparison of these various products with in situ observations show that the performance of both SMAP products i.e. SMAP_SCA and SMAP_Reg is 48 similar and marginally better to that of the SMOSL3 product particularly over the PBO_H2O, SCAN, and USCRN sites. However, SMOSL3 SM was closer to the in situ observations over the DAHRA and Oznet sites. We found that the correlation between all three datasets and in situ measurements is best (R 0.80) over the Oznet sites and worst (R 0.58) over the SNOTEL sites for SMAP_SCA and over the DAHRA and SMOSMANIA sites (R 0.51 and R 0.45 for SMAP_Reg and SMOSL3, respectively). The Bias values showed that all products are generally dry, except over RSMN, DAHRA, and Oznet (and FMI for SMAP_SCA). Finally, our analysis provided interesting insights that can be useful to improve the consistency between SMAP and SMOS datasets.

SMOS↗
NASA NTRS2010

The SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) Product

The Soil Moisture Active and Passive (SMAP) mission is being developed by NASA for launch in 2013 as one of four first-tier missions recommended by the U.S. National Research Council Committee on Earth Science and Applications from Space in 2007. The primary science objectives of SMAP are to enhance understanding of land surface controls on the water, energy and carbon cycles, and to determine their linkages. Moreover, the high resolution soil moisture mapping provided by SMAP has practical applications in weather and seasonal climate prediction, agriculture, human health, drought and flood decision support. In this paper we describe the assimilation of SMAP observations for the generation of the planned SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) product. The SMAP mission makes simultaneous active (radar) and passive (radiometer) measurements in the 1.26-1.43 GHz range (L-band) from a sun-synchronous low-earth orbit. Measurements will be obtained across a 1000 km wide swath using conical scanning at a constant incidence angle (40 deg). The radar resolution varies from 1-3 km over the outer 70% of the swath to about 30 km near the center of the swath. The radiometer resolution is 40 km across the entire swath. The radiometer measurements will allow high-accuracy but coarse resolution (40 km) measurements. The radar measurements will add significantly higher resolution information. The radar is however very sensitive to surface roughness and vegetation structure. The combination of the two measurements allows optimal blending of the advantages of each instrument. SMAP directly observes only surface soil moisture (in the top 5 cm of the soil column). Several of the key applications targeted by SMAP, however, require knowledge of root zone soil moisture (approximately top 1 m of the soil column), which is not directly measured by SMAP. The foremost objective of the SMAP L4_SM product is to fill this gap and provide estimates of root zone soil moisture that are informed by and consistent with SMAP observations. Such estimates are obtained by merging SMAP observations with estimates from a land surface model in a soil moisture data assimilation system. The land surface model component of the assimilation system is driven with observations-based surface meteorological forcing data, including precipitation, which is the most important driver for soil moisture. The model also encapsulates knowledge of key land surface processes, including the vertical transfer of soil moisture between the surface and root zone reservoirs. Finally, the model interpolates and extrapolates SMAP observations in time and in space. The L4_SM product thus provides a comprehensive and consistent picture of land surface hydrological conditions based on SMAP observations and complementary information from a variety of sources. The assimilation algorithm considers the respective uncertainties of each component and yields a product that is superior to satellite or model data alone. Error estimates for the L4_SM product are generated as a by-product of the data assimilation system.

Reichle, Rolf↗