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NASA NTRSDate not supplied

A Generalized, Compactly-Supported Correlation Function for Data Assimilation Applications

Correlation functions play an essential role in modern data assimilation, where they are used to model covariances given a set of tunable parameters or applied as tapering functions to localize covariances in ensemble-based schemes. One of the most widely-used correlation functions in data assimilation is the Gaspari and Cohn (1999) piecewise-rational, compactly-supported parametric correlation function (hereafter referred to as GC99). The GC99 correlation function is useful due to its tunable cut-off parameter c and Gaussian-like shape achieved when the parameter a is set to one-half. These properties are attractive for tapering functions in data assimilation applications. However, the GC99 correlation function is homogeneous over Euclidean 3-space and isotropic when restricted to the sphere, properties that may be less than ideal for some geophysical applications. GC99 is also compactly-supported on a sphere of fixed radius, which requires tuning of the cut-off parameter c that can depend on the specific application. This work presents a generalization of the GC99 correlation function that allows the cut-off parameter c and shape parameter a to vary over space to gain more flexibility in shape while maintaining its compact support property. The function, which we call the Generalized Gaspari Cohn (GenGC) correlation function, introduces inhomogeneity in Euclidean 3-space and anisotropy when restricted to the sphere by allowing both parameters c and a to vary, as functions, over the spatial domain. The GC99 correlation function is a special case of GenGC where the functions c and a are held constant, as fixed parameters rather than functions. The GenGC correlation function also generalizes the follow-on to the work of Gaspari and Cohn (1999) presented in Gaspari et al. (2006), which allowed a to vary while keeping c fixed. We illustrate through simple one- and two-dimensional examples the variety of inhomogeneous and anisotropic correlation functions GenGC can produce by varying c and a over space, and suggest applications where they may be useful in data assimilation, such as covariance modeling or localization. In particular, we describe how the GenGC correlation function can be used to construct covariances using correlation length and variance fields derived from dynamics. For example, the correlation length field for advective dynamics is governed by a partial differential equation (PDE) in N spatial dimensions, where N is the number of space dimensions of the state. Correlation length fields can be determined from this PDE and used with GenGC to construct the corresponding correlations. We can then approximate the full covariance by rescaling by the variance, which also satisfies a PDE in N spatial dimensions for advective dynamics. Thus we can approximate the full covariance without solving the covariance PDE, which is in 2N spatial dimensions, by solving just two PDEs each in only N spatial dimensions. This approach to evolving the correlation length and variance fields, then reconstructing the correlations using GenGC, is suggested as an alternative to current methods of covariance modeling in data assimilation algorithms.

GC99↗

DOE OSTI2022

Simulated wind speed and initial conditions over the WFIP2 region: Cold-front (D01)

The purpose of this work is to assess the sensitivity of the forecast for turbine height wind speed to initial condition (IC) uncertainties over the Columbia River Gorge and Columbia River Basin for two typical weather phenomena: a local thermal gradient induced by a marine air intrusion and passage of a cold front. The Weather Research and Forecasting (WRF) model data assimilation system (WRFDA) was used to generate ensemble ICs from the North American Regional Analysis (NARR) for the WRF model initialization. The simulated turbine-height wind speeds were categorized into four types using the self-organizing map (SOM) technique. This work advances understanding of IC uncertainties impacts on wind speed forecasts and locates the high-impact regions.

17 WIND ENERGY↗

DOE OSTI2022

Simulated wind speed and initial conditions over the WFIP2 region: Cold-front (D02)

17 WIND ENERGY↗

DOE OSTI2022

Simulated wind speed and initial conditions over the WFIP2 region: Sea-breeze (D01)

17 WIND ENERGY↗

DOE OSTI2022

Simulated wind speed and initial conditions over the WFIP2 region: Sea-breeze (D02)

17 WIND ENERGY↗

DOE OSTI2025

A 1 km soil moisture dataset over eastern CONUS generated by assimilating SMAP data into the Noah-MP land surface model

An improved fine-scale soil moisture (SM) dataset at 1 km grid spacing, covering much of the eastern continental US, was generated by assimilating 9 km Soil Moisture Active Passive (SMAP) SM data into the v4.0.1 Noah-MP land surface model. With 12 ensemble members, the assimilation was carried out using the ensemble Kalman filter algorithm within NASA's Land Information System. The SM analysis for 2016 was fully validated against in situ observations from four different networks and compared with four other existing datasets. Results indicate that this SM analysis surpasses other datasets in top-layer SM distribution, including a machine-learning-based product, despite all SM estimates being less heterogeneous than observed. The analysis of anomalous errors suggests that large similarity in intrinsic errors is likely due to overlapping data sources among the selected SM datasets. More detailed evaluations were performed over two geographic areas. The observations collected by the Atmospheric Radiation Measurement facility in Oklahoma suggest that soil temperature and surface heat fluxes are concurrently simulated with good accuracy. Investigation into the 2016 southeastern US drought response further indicates drier conditions and higher evapotranspiration estimates compared to GLEAMv4.1. Notably, large errors are associated with grids having clay soil textures, underscoring the need for refined model treatments for specific soil types to further improve SM estimates. The dataset is publicly available on Zenodo at https://doi.org/10.5281/zenodo.14370563 (Tai et al., 2024).

Tai, Sheng-Lun [Pacific Northwest National Laborat↗

DOE OSTI2023

An ensemble of 48 physically perturbed model estimates of the 1/8° terrestrial water budget over the conterminous United States, 1980–2015

Terrestrial water budget (TWB) data over large domains are of high interest for various hydrological applications. Spatiotemporally continuous and physically consistent estimations of TWB rely on land surface models (LSMs). As an augmentation of the operational North American Land Data Assimilation System Phase 2 (NLDAS-2) four-LSM ensemble, this paper describes a dataset simulated from an ensemble of 48 physics configurations of the Noah LSM with multi-physics options (Noah-MP). The 48 Noah-MP physics configurations are selected to give a representative cross-section of commonly used LSMs for parameterizing runoff, atmospheric surface layer turbulence, soil moisture limitation on photosynthesis, and stomatal conductance. The dataset spans from 1980 to 2015 over the conterminous United States (CONUS) at a monthly temporal resolution and a 1/8° spatial resolution. The dataset variables include total evapotranspiration and its constituents (canopy evaporation, soil evaporation, and transpiration), runoff (the surface and subsurface components), as well as terrestrial water storage (snow water equivalent, four-layer soil water content from the surface down to 2 m, and the groundwater storage anomaly). The dataset is available at https://doi.org/10.5281/zenodo.7109816. Evaluations carried out in this study and previous investigations show that the ensemble per forms well in reproducing the observed terrestrial water storage, snow water equivalent, soil moisture, and runoff. Noah-MP complements the NLDAS models well, and adding Noah-MP consistently improves the NLDAS es timations of the above variables in most areas of CONUS. Besides, the perturbed-physics ensemble facilitates the identification of model deficiencies. The parameterizations of shallow snow, spatially varying groundwater dynamics, and near-surface atmospheric turbulence should be improved in future model versions.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2013

Simultaneous Estimation of Model State Variables and Observation and Forecast Biases Using a Two-Stage Hybrid Kalman Filter

In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

Data Assimilation↗

NASA NTRS2016

Benefit of Modeling the Observation Error in a Data Assimilation Framework Using Vegetation Information Obtained From Passive Based Microwave Data

A primary operational goal of the United States Department of Agriculture (USDA) is to improve foreign market access for U.S. agricultural products. A large fraction of this crop condition assessment is based on satellite imagery and ground data analysis. The baseline soil moisture estimates that are currently used for this analysis are based on output from the modified Palmer two-layer soil moisture model, updated to assimilate near-real time observations derived from the Soil Moisture Ocean Salinity (SMOS) satellite. The current data assimilation system is based on a 1-D Ensemble Kalman Filter approach, where the observation error is modeled as a function of vegetation density. This allows for offsetting errors in the soil moisture retrievals. The observation error is currently adjusted using Normalized Difference Vegetation Index (NDVI) climatology. In this paper we explore the possibility of utilizing microwave-based vegetation optical depth instead.

Vegetation↗

NASA NTRS2017

GEOS S2S-2_1: GMAO's New High Resolution Seasonal Prediction System

A new version of the modeling and analysis system used to produce sub-seasonal to seasonal forecasts has just been released by the NASA Goddard Global Modeling and Assimilation Office. The new version runs at higher atmospheric resolution (approximately 12 degree globally), contains a substantially improved model description of the cryosphere, and includes additional interactive earth system model components (aerosol model). In addition, the Ocean data assimilation system has been replaced with a Local Ensemble Transform Kalman Filter. Here will describe the new system, along with the plans for the future (GEOS S2S-3_0) which will include a higher resolution ocean model and more interactive earth system model components (interactive vegetation, biomass burning from fires). We will also present results from a free-running coupled simulation with the new system and results from a series of retrospective seasonal forecasts. Results from retrospective forecasts show significant improvements in surface temperatures over much of the northern hemisphere and a much improved prediction of sea ice extent in both hemispheres. The precipitation forecast skill is comparable to previous S2S systems, and the only trade off is an increased double ITCZ, which is expected as we go to higher atmospheric resolution.

Molod, Andrea↗

NASA NTRS2018

Sub-Seasonal Forecasting of the Stratospheric Wave Events, Sudden Stratospheric Warmings, and Their Influence on the Troposphere

Stratospheric wave events and major sudden stratospheric warming (SSW) events are well captured in high-resolution global forecasts out to 10 days. Tropospheric influences of SSW include statistically significant shifts in the storm tracks and associated surface temperature and precipitation pattern changes. Since these events can in turn influence the troposphere on time scales of 30-60 days the ability to predict these events and the subsequent long-term response on time scales beyond 10 days is of interest. Here we examine the prediction of stratospheric wave events and their evolution using the NASA GMAO (Global Modeling and Assimilation Office) Sub-Seasonal to Seasonal (S2S) system. This is a recently released subseasonal to seasonal forecast system, GEOS-S2S version 2.1. Compared to GMAO's previous system, the new version runs at higher atmospheric resolution (approximately 1/2 degree globally), contains a substantially improved model of the cryosphere, includes additional interactive aerosol model components, and the ocean data assimilation system has been replaced with a Local Ensemble Transform Kalman Filter. Results are based on a comprehensive series of hindcasts starting from the year 2000. They show that while the S2S system is not as accurate at 10 days in forecasting major SSW events as the NASA GMAO Forward Processing system, it can usefully predict stratospheric anomalies out to 20 days and the subsequent stratospheric/tropospheric evolution beyond 30 days.

Coy, L.↗

NASA NTRS2018

GEOS S2S-2_1: The GMAO High Resolution Seasonal Prediction System

A new version of the coupled modeling and analysis system used to produce near real time subseasonal to seasonal forecasts was recently released by the NASA/Goddard Global Modeling and Assimilation Office. The new version runs at higher atmospheric resolution than the previous, (approximately 1/2 degree globally), contains a substantially improved model description of the cryosphere, and includes additional interactive earth system model components (aerosol model). In addition, the Ocean data assimilation system has been replaced with a Local Ensemble Transform Kalman Filter, and now includes the assimilation of along-track sea surface height. Here will describe the new system, along with the plans for the future (GEOS S2S-3_0) which will include a higher resolution ocean model and more interactive earth system model components (interactive vegetation, biomass burning from fires). We will also present results from a series of retrospective seasonal forecasts. Results show significant improvements in surface temperatures over much of the northern hemisphere and a much improved prediction of sea ice extent in both hemispheres. Analysis of the ensemble spread shows improvements relative to the previous system, including generally better reliability. The precipitation forecast skill is comparable to previous S2S systems, and the only tradeoff is an increased "double ITCZ", which is expected as we go to higher atmospheric resolution.

Molod, Andrea↗

NASA NTRS2020

Impact of Satellite Microwave Radiance Data Assimilation on GEOS Atmospheric Analysis and Forecasts in Tropics

The NASA Global Modeling and Assimilation Office (GMAO) has developed a system to assimilate all-sky microwave radiance data in the Goddard Earth Observing System (GEOS). The system provides additional constraints on the analysis process near the storm regions and adjusts the geophysical parameters such as precipitation, cloud, moisture, surface pressure, and wind by combining information from microwave radiance measurements and model forecasts in an optimal manner. The system proved that assimilating the all-sky microwave radiance data improve the GEOS atmospheric analyses and forecasts. This all-sky data framework has been included in the GEOS Forward Processing (FP) system and currently assimilating all-sky GMI data in real-time for GEOS global analysis and forecast production at the GMAO. This presentation describes the methodologies to assimilate cloud- and precipitation-affected microwave radiances in GEOS data assimilation system based on hybrid four-dimensional ensemble-variational (4D-EnVar) configuration. In the current operational GEOS-FP system, the addition of all-sky GMI radiances has the largest impact in the Tropics. Specific humidity is significantly improved in the short term (0-72 hours) forecasts. Similar improvements are seen in the Tropical and lower tropospheric temperature and winds. More detailed results on all-sky microwave radiance data impact on GEOS analysis and forecasts are discussed in this presentation.

Kim, Min-Jeong↗

NASA NTRS2019

Soil Moisture Data Assimilation

Accurate knowledge of soil moisture at the continental scale is important for improving predictions of weather, agricultural productivity and natural hazards, but observations of soil moisture at such scales are limited to indirect measurements, either obtained through satellite remote sensing or from meteorological networks. Land surface models simulate soil moisture processes, using observation-based meteorological forcing data, and auxiliary information about soil, terrain and vegetation characteristics. Enhanced estimates of soil moisture and other land surface variables, along with their uncertainty, can be obtained by assimilating observations of soil moisture into land surface models. These assimilation results are of direct relevance for the initialization of hydro-meteorological ensemble forecasting systems. The success of the assimilation depends on the choice of the assimilation technique, the nature of the model and the assimilated observations, and, most importantly, the characterization of model and observation error. Systematic differences between satellite-based microwave observations or satellite-retrieved soil moisture and their simulated counterparts require special attention. Other challenges include inferring root-zone soil moisture information from observations that pertain to a shallow surface soil layer, propagating information to unobserved areas and downscaling of coarse information to finer-scale soil moisture estimates. This chapter summarizes state-of-the-art solutions to these issues with conceptual data assimilation examples, using techniques ranging from simplified optimal interpolation to spatial ensemble Kalman filtering. In addition, operational soil moisture assimilation systems are discussed that support numerical weather prediction at ECMWF and provide value-added soil moisture products for the NASA Soil Moisture Active Passive mission.

radar backscatter↗

NASA NTRS2011

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) 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 as a 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 e volved from two earlier efforts -- North American Land Data Assimilation System (NLDAS) and Global Land Data Assimilation System (GLDAS) 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". LIS has been coupled to the Weather Research and Forecasting (WRF) model to support studies of land-atmosphere coupling be 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, 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 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 hydrometeorological modeling, assimilation and parameter estimation will be presented as advancements towards the next generation of integrated observation and modeling systems

Peters-Lidard, Christa D.↗

NASA NTRS2013

Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms

Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.

EnKR↗

DOE OSTI2020

A Novel Modeling Framework for Computationally Efficient and Accurate Real-Time Ensemble Flood Forecasting With Uncertainty Quantification

A novel modeling framework that simultaneously improves accuracy, predictability, and computational efficiency is presented. It embraces the benefits of three modeling techniques integrated together for the first time: surrogate modeling, parameter inference, and data assimilation. The use of polynomial chaos expansion (PCE) surrogates significantly decreases computational time. Parameter inference allows for model faster convergence, reduced uncertainty, and superior accuracy of simulated results. Ensemble Kalman filters assimilate errors that occur during forecasting. To examine the applicability and effectiveness of the integrated framework, we developed 18 approaches according to how surrogate models are constructed, what type of parameter distributions are used as model inputs, and whether model parameters are updated during the data assimilation procedure. We conclude that (1) PCE must be built over various forcing and flow conditions, and in contrast to previous studies, it does not need to be rebuilt at each time step; (2) model parameter specification that relies on constrained, posterior information of parameters (so-called Selected specification) can significantly improve forecasting performance and reduce uncertainty bounds compared to Random specification using prior information of parameters; and (3) no substantial differences in results exist between single and dual ensemble Kalman filters, but the latter better simulates flood peaks. The use of PCE effectively compensates for the computational load added by the parameter inference and data assimilation (up to ~80 times faster). Therefore, the presented approach contributes to a shift in modeling paradigm arguing that complex, high-fidelity hydrologic and hydraulic models should be increasingly adopted for real-time and ensemble flood forecasting.

54 ENVIRONMENTAL SCIENCES↗

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↗