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All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Application of an Ensemble Smoother to Precipitation Assimilation

Assimilation of precipitation in a global modeling system poses a special challenge in that the observation operators for precipitation processes are highly nonlinear. In the variational approach, substantial development work and model simplifications are required to include precipitation-related physical processes in the tangent linear model and its adjoint. An ensemble based data assimilation algorithm "Maximum Likelihood Ensemble Smoother (MLES)" has been developed to explore the ensemble representation of the precipitation observation operator with nonlinear convection and large-scale moist physics. An ensemble assimilation system based on the NASA GEOS-5 GCM has been constructed to assimilate satellite precipitation data within the MLES framework. The configuration of the smoother takes the time dimension into account for the relationship between state variables and observable rainfall. The full nonlinear forward model ensembles are used to represent components involving the observation operator and its transpose. Several assimilation experiments using satellite precipitation observations have been carried out to investigate the effectiveness of the ensemble representation of the nonlinear observation operator and the data impact of assimilating rain retrievals from the TMI and SSM/I sensors. Preliminary results show that this ensemble assimilation approach is capable of extracting information from nonlinear observations to improve the analysis and forecast if ensemble size is adequate, and a suitable localization scheme is applied. In addition to a dynamically consistent precipitation analysis, the assimilation system produces a statistical estimate of the analysis uncertainty.

Zhang, Sara↗
NASA NTRS2006

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Monte Carlo↗
NASA NTRS2012

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↗
NASA NTRS1999

Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqui↗
NASA NTRS1999

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqiu↗
NASA NTRS2016

Assimilation of Gridded GRACE Terrestrial Water Storage Estimates in the North American Land Data Assimilation System

The objective of the North American Land Data Assimilation System (NLDAS) is to provide best available estimates of near-surface meteorological conditions and soil hydrological status for the continental United States. To support the ongoing efforts to develop data assimilation (DA) capabilities for NLDAS, the results of Gravity Recovery and Climate Experiment (GRACE) DA implemented in a manner consistent with NLDAS development are presented. Following previous work, GRACE terrestrial water storage (TWS) anomaly estimates are assimilated into the NASA Catchment land surface model using an ensemble smoother. In contrast to many earlier GRACE DA studies, a gridded GRACE TWS product is assimilated, spatially distributed GRACE error estimates are accounted for, and the impact that GRACE scaling factors have on assimilation is evaluated. Comparisons with quality-controlled in situ observations indicate that GRACE DA has a positive impact on the simulation of unconfined groundwater variability across the majority of the eastern United States and on the simulation of surface and root zone soil moisture across the country. Smaller improvements are seen in the simulation of snow depth, and the impact of GRACE DA on simulated river discharge and evapotranspiration is regionally variable. The use of GRACE scaling factors during assimilation improved DA results in the western United States but led to small degradations in the eastern United States. The study also found comparable performance between the use of gridded and basin averaged GRACE observations in assimilation. Finally, the evaluations presented in the paper indicate that GRACE DA can be helpful in improving the representation of droughts.

Kumar, Sujay V.↗
NASA NTRS2015

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↗
NASA NTRS2010

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↗
NASA NTRS2011

Using Enhanced Grace Water Storage Data to Improve Drought Detection by the U.S. and North American Drought Monitors

NASA's Gravity Recovery and Climate Experiment (GRACE) satellites measure time variations of the Earth's gravity field enabling reliable detection of spatio-temporal variations in total terrestrial water storage (TWS), including groundwater. The U.S. and North American Drought Monitors 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 by filling this observational gap. GRACE TWS data were assimilating into the Catchment Land Surface Model using an ensemble Kalman smoother enabling spatial and temporal downscaling and vertical decomposition into soil moisture and groundwater components. The Drought Monitors combine several short- and long-term drought indicators expressed in percentiles as a reference to their historical frequency of occurrence. To be consistent, we generated a climatology of estimated soil moisture and ground water based on a 60-year Catchment model simulation, which was used to convert seven years of GRACE assimilated fields into drought indicator percentiles. At this stage we provide a preliminary evaluation of the GRACE assimilated moisture and indicator fields.

Houborg, Rasmus↗
NASA NTRS2011

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.↗
NASA NTRS2012

Assimilation of GRACE Terrestrial Water Storage into a Land Surface Model: Evaluation 1 and Potential Value for Drought Monitoring in Western and Central Europe

A land surface model s ability to simulate states (e.g., soil moisture) and fluxes (e.g., runoff) is limited by uncertainties in meteorological forcing and parameter inputs as well as inadequacies in model physics. In this study, anomalies of terrestrial water storage (TWS) observed by the Gravity Recovery and Climate Experiment (GRACE) satellite mission were assimilated into the NASA Catchment land surface model in western and central Europe for a 7-year period, using a previously developed ensemble Kalman smoother. GRACE data assimilation led to improved runoff correlations with gauge data in 17 out of 18 hydrological basins, even in basins smaller than the effective resolution of GRACE. Improvements in root zone soil moisture were less conclusive, partly due to the shortness of the in situ data record. In addition to improving temporal correlations, GRACE data assimilation also reduced increasing trends in simulated monthly TWS and runoff associated with increasing rates of precipitation. GRACE assimilated root zone soil moisture and TWS fields exhibited significant changes in their dryness rankings relative to those without data assimilation, suggesting that GRACE data assimilation could have a substantial impact on drought monitoring. Signals of drought in GRACE TWS correlated well with MODIS Normalized Difference Vegetation Index (NDVI) data in most areas. Although they detected the same droughts during warm seasons, drought signatures in GRACE derived TWS exhibited greater persistence than those in NDVI throughout all seasons, in part due to limitations associated with the seasonality of vegetation.

Li, Bailing↗
NASA NTRS2020

SWOT Applications in Alaska

Use of SWOT for model calibration and assimilation are encouraging, but further work is needed: account for uncertainty in meteorological forcing (calibration) and apply ensemble Kalman Smoother (data assimilation). Lessons learned can inform development of operational NOAA National Water Model Alaskan domain and other SWOT applications.

SWOT↗
NASA NTRS2024

Synergistic Retrievals of Ice in High Clouds From Elastic Backscatter Lidar, Ku-band Radar and Submillimeter Wave Radiometer Observations

In this study, we investigate the synergy of elastic backscatter lidar, Ku-band radar, and sub-millimeter-wave radiometer measurements in the retrieval of ice from satellite observations. The synergy is analyzed through the generation of a large dataset of IceWater Content (IWC) profiles and simulated lidar, radar and radiometer observations. The characteristics of the instruments e.g. frequencies, sensitivities, etc. are set based on the expected characteristics of instruments of the Atmosphere Observing System (AOS) mission. A hold-out validation methodology is used to assess the accuracy of the IWC profiles retrieved from various combinations of observations from the three instruments. Specifically, the IWC and associated observations are randomly divided into two datasets, one for training and the other for evaluation. The training dataset is used to train the retrieval algorithm, while the evaluation dataset is used to assess the retrieval performance. The dataset of IWC profiles is derived from CloudSat reflectivity and CALIOP lidar observations. The retrieval of the ice water content IWC profiles from the computed observations is achieved in two steps. In the first step, a class, out of 18 potential classes characterized by different vertical distribution of IWC, is estimated from the observations. The 18 classes are predetermined based on the k-Means clustering algorithm. In the second step, the IWC profile is estimated using an Ensemble Kalman Smoother (EKS) algorithm that uses the estimated class as a priori information. The results of the study show that the synergy of lidar, radar, and radiometer observations is significant in the retrieval of the IWC profiles. Nevertheless, it should be mentioned that this synergy was found under idealized conditions, and additional work might be required to materialize it in practice. The inclusion of the lidar backscatter observations in the retrieval process has a larger impact on the retrieval performance than the inclusion of the radar observations. As ice clouds have a significant impact on atmospheric radiative processes, this work is relevant to ongoing efforts to reduce uncertainties in climate analyses and projections.

Mircea Grecu↗
NASA NTRS2018

The Next-Generation Goddard Convective-Stratiform Heating Algorithm: New Tropical and Warm-Season Retrievals for GPM

The Goddard convective-stratiform heating (CSH) algorithm, used to estimate cloud heating in support of the Tropical Rainfall Measuring Mission (TRMM), is upgraded in support of the Global Precipitation Measurement (GPM) mission. The algorithm's lookup tables (LUTs) are revised using new and additional cloud-resolving model (CRM) simulations from the Goddard Cumulus Ensemble (GCE) model, producing smoother heating patterns that span a wider range of intensities because of the increased sampling and finer GPM product grid. Low-level stratiform cooling rates are reduced in the land LUTs for a given rain intensity because of the rain evaporation correction in the new four-class ice (4ICE) scheme. Additional criteria, namely, echo-top heights and low-level reflectivity gradients, are tested for the selection of heating profiles. Those resulting LUTs show greater and more precise variation in their depth of heating as well as a tendency for stronger cooling and heating rates when low-level dBZ values decrease toward the surface. Comparisons versus TRMM for a 3-month period show much more low-level heating in the GPM retrievals because of increased detection of shallow convection, while upper-level heating patterns remain similar. The use of echo tops and low-level reflectivity gradients greatly reduces midlevel heating from ~2 to 5 km in the mean GPM heating profile, resulting in a more top-heavy profile like TRMM versus a more bottom-heavy profile with much more midlevel heating. Integrated latent heating rates are much better balanced versus surface rainfall for the GPM retrievals using the additional selection criteria with an overall bias of +4.3%.

Lang, Stephen E.↗
NASA NTRS2008

Assimilation of GRACE Terrestrial Water Storage Data into a Land Surface Model

The NASA Gravity Recovery and Climate Experiment (GRACE) system of satellites provides observations of large-scale, monthly terrestrial water storage (TWS) changes. In. this presentation we describe a land data assimilation system that ingests GRACE observations and show that the assimilation improves estimates of water storage and fluxes, as evaluated against independent measurements. The ensemble-based land data assimilation system uses a Kalman smoother approach along with the NASA Catchment Land Surface Model (CLSM). We assimilated GRACE-derived TWS anomalies for each of the four major sub-basins of the Mississippi into the Catchment Land Surface Model (CLSM). Compared with the open-loop (no assimilation) CLSM simulation, assimilation estimates of groundwater variability exhibited enhanced skill with respect to measured groundwater. Assimilation also significantly increased the correlation between simulated TWS and gauged river flow for all four sub-basins and for the Mississippi River basin itself. In addition, model performance was evaluated for watersheds smaller than the scale of GRACE observations, in the majority of cases, GRACE assimilation led to increased correlation between TWS estimates and gauged river flow, indicating that data assimilation has considerable potential to downscale GRACE data for hydrological applications. We will also describe how the output from the GRACE land data assimilation system is now being prepared for use in the North American Drought Monitor.

Reichle, Rolf H.↗
NASA NTRS1993

Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength

Rigorously light scattering by size-shape distributions of randomly oriented axially symmetric particles are calculated by the T-matrix method, as extended to randomly oriented scatterers. The computational scheme is described along with a newly developed convergence procedure that makes it possible to substantially reduce computer time and storage requirements. The elements of the Stokes scattering matrix for a power-law size distribution of randomly oriented moderately aspherical spheroids are shown to be much smoother than and differ substantially from those of equivalent monodisperse spheroids; averaging over orientations does not eliminate the necessity of averaging over particle sizes. The angular-scattering behavior of the ensembles of nonspherical particles is found to be significantly different from that of the equivalent polydisperse spheres.

Mishchenko, Michael I.↗
NASA NTRS2015

Adaptive Shape Control for Aerodynamic Design

We present an approach to aerodynamic optimization in which the shape control is adaptively parameterized. Starting from a coarse set of design variables, a sequence of higher-dimensional nested search spaces is automatically generated. Refinement can be either uniform or adaptive, in which case only the most important shape control is added. The relative importance of candidate design variables is determined by comparing objective and constraint gradients, computed at low cost via adjoint solutions. A search procedure for finding an effective ensemble of shape parameters is also given. We first demonstrate this system on a multipoint drag miminization problem in 2D with many constraints, showing that an adaptive parameterization approach consistently achieves smoother, more robust, and faster design improvement than fixed parameterizations. We also establish a 3D shape- matching benchmark, where we demonstrate that our approach automatically discovers the necessary parameters to match a target shape. By largely automating shape parameterization, this work also aims to remove a time-consuming aspect of shape optimization.

Aerodynamic Design↗
NASA NTRS2011

Modelling the Huge, Herschel-Resolved Debris Ring around HD 207129

Debris disks, which are inferred from the observed infrared excess to be ensembles of dust, rocks. and probably planetesimals, arc common features of stellar systems. As the mechanisms of their fonnation and evolution are linked to those of planetary bodies, they provide valuable infonnation. The few well-resolved debris disks are even more valuable because they can serve as modelling benchmarks and help resolve degeneracies in modelling aspects such as typical grain sizes and distances. Here, we present an analysis of the HD 207129 debris disk, based on its well-covered spectral energy distribution and Herschel/PACS images obtained in the framework of the DUNES (DUst around NEarby Stars) programme. We use an empirical power-law approach to the distribution of dust and we then model the production and removal of dust by means of collisions, direct radiation pressure, and drag forces. The resulting best-fit model contains a total of nearly 10(sup -2) Earth masses in dust, with typical grain sizes in the planetesimal beh ranging from 4 to 7 micrometers. We constrain the dynamical excitation to be low, which results in very long collisional lifetimes and a drag that notably fills the inner gap, especially at 70 micrometers. The radial distribution stretches from well within 100 AU in an unusual, outward-riSing slope towards a rather sharp outer edge at about 170-190 AU. The inner edge is therefore smoother than that reported for Fomalhaut, but the contribution from the extended halo of barely bound grains is similarly small. Both slowly self-stirring and planetary perturbations could potentially have formed and shaped this disk.

Lohne, T.↗