Ensemble Square Root Filter Research Articles

Modeling and assimilation of root zone soil moisture using remote sensing observations in Walnut Gulch Watershed during SMEX04

Soil moisture status in the root zone is an important component of the water cycle at all spatial scales ( e.g., point, field, catchment, watershed, and region). In this study, the spatio-temporal evolution of root zone soil moisture of the Walnut Gulch Experimental Watershed (WGEW) in Arizona was investigated during the Soil Moisture Experiment 2004 (SMEX04). Root zone soil moisture was estimated via assimilation of aircraft-based remotely sensed surface soil moisture into a distributed Soil–Water–Atmosphere–Plant (SWAP) model. An ensemble square root filter (EnSRF) based on a Kalman filtering scheme was used for assimilating the aircraft-based soil moisture observations at a spatial resolution of 800 m × 800 m. The SWAP model inputs were derived from the SSURGO soil database, LAI (Leaf Area Index) data from SMEX04 database, and data from meteorological stations/rain gauges at the WGEW. Model predictions are presented in terms of temporal evolution of soil moisture probability density function at various depths across the WGEW. The assimilation of the remotely sensed surface soil moisture observations had limited influence on the profile soil moisture. More specifically, root zone soil moisture depended mostly on the soil type. Modeled soil moisture profile estimates were compared to field measurements made periodically during the experiment at the ground based soil moisture stations in the watershed. Comparisons showed that the ground-based soil moisture observations at various depths were within ± 1 standard deviation of the modeled profile soil moisture. Density plots of root zone soil moisture at various depths in the WGEW exhibited multi-modal variations due to the uneven distribution of precipitation and the heterogeneity of soil types and soil layers across the watershed.

A Comparison of Hybrid Ensemble Transform Kalman Filter–Optimum Interpolation and Ensemble Square Root Filter Analysis Schemes

Abstract A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A two-layer primitive equation model was used under perfect-model assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static background-error covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF background-error covariance was estimated fully from the ensemble. For 50-member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20-member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity wave activity than the EnSRF, especially when the ensemble size was small. Maximal growth in the ETKF ensemble perturbation space exceeded that in the EnSRF ensemble perturbation space. The relationship of the ETKF ensemble variance to the analysis error variance, a measure of a spread–skill relationship, was similar to that of the EnSRF ensemble. The hybrid scheme can be implemented in a reasonably straightforward manner in the operational variational frameworks, and the computational cost of the hybrid is expected to be much less than the EnSRF in the operational settings.

Southern High-Latitude Ensemble Data Assimilation in the Antarctic Mesoscale Prediction System

Abstract Ensemble data assimilation systems incorporate observations into numerical models via solution of the Kalman filter update equations, and estimates of forecast error covariances derived from ensembles of model integrations. In this paper, a particular algorithm, the ensemble square root filter (EnSRF), is tested in a limited-area, polar numerical weather prediction (NWP) model: the Antarctic Mesoscale Prediction System (AMPS). For application in the real-time AMPS, the number of model integrations that can be run to provide forecast error covariances is limited, resulting in an ensemble sampling error that degrades the analysis fit to observations. In this work, multivariate, climatologically plausible forecast error covariances are specified via averaged forecast difference statistics. Ensemble representations of the “true” forecast errors, created using randomized control variables of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) three-dimensional variational (3DVAR) data assimilation system, are then used to assess the dependence of sampling error on ensemble size, data density, and localization of covariances using simulated observation networks. Results highlight the detrimental impact of ensemble sampling error on the analysis increment structure of correlated, but unobserved fields—an issue not addressed by the spatial covariance localization techniques used to date. A 12-hourly cycling EnSRF/AMPS assimilation/forecast system is tested for a two-week period in December 2002 using real, conventional (surface, rawinsonde, satellite retrieval) observations. The dependence of forecast scores on methods used to maintain ensemble spread and the inclusion of perturbations to lateral boundary conditions are studied.

The impact of ensemble filter definition on the assimilation of temperature profiles in the tropical Pacific

AbstractThe traditional analysis scheme in the Ensemble Kalman Filter (EnKF) uses a stochastic perturbation or randomization of the measurements which ensures a correct variance in the updated ensemble. An alternative so‐called deterministic analysis algorithm is based on a square‐root formulation where the perturbation of measurements is avoided. Experiments with simple models have indicated that ensemble collapse is likely to occur when deterministic filters are applied to nonlinear problems. In this paper the properties of stochastic and deterministic ensemble analysis algorithms are evaluated in an identical‐twin experiment using an ocean general‐circulation model. In particular, the implications of the use of deterministic Ensemble Square‐Root Filters (EnSRF) for ensemble distribution are investigated. An explanation is presented for the observed collapse, and a simple solution based on randomization of the analysis ensemble anomalies is examined. A one‐year assimilation run with this improved EnSRF is found to produce Gaussian distributions, similar to the EnKF. Copyright © 2005 Royal Meteorological Society

Assimilation of along‐track altimeter data in the tropical Pacific region of a global OGCM ensemble

AbstractIdentical‐twin experiments are performed with an ocean general‐circulation model ensemble to investigate the potential for correction of subsurface ocean model states through assimilation of altimetric sea level observations with the Ensemble Kalman Filter (EnKF). The EnKF provides a convenient extension to existing ensemble prediction systems. Observations are simulated for the tropical Pacific by sampling a truth run at 10‐day intervals at the TOPEX/POSEIDON along‐track measurement points and adding realistic instrument and orbit errors. Ensemble spread is generated by perturbing the best‐guess forcing fields. The perturbations are based on a multivariate EOF decomposition of differences between two reanalysis products. The effectiveness of the assimilation is investigated by comparison of the forecasts and analyses with a control run and with the truth. Time series of subsurface state variables along the equator show that the analyses are closer to the truth than the control in all cases, indicating a significant potential for improved ENSO forecast initialization. A second assimilation run with an Ensemble Square‐Root Filter (ESRF) shows that the analyses are very similar to those from the EnKF. However, ensemble spread in the subsurface state variables is found to be a poor proxy for the true analysis error in this experiment, in particular in the case of the ESRF. While the sea level analyses remain close to the truth, persistent offsets are introduced in the subsurface state, suggesting a role for bias correction schemes in ensemble methods. Copyright © 2005 Royal Meteorological Society

Reanalysis without Radiosondes Using Ensemble Data Assimilation

Abstract Studies using idealized ensemble data assimilation systems have shown that flow-dependent background-error covariances are most beneficial when the observing network is sparse. The computational cost of recently proposed ensemble data assimilation algorithms is directly proportional to the number of observations being assimilated. Therefore, ensemble-based data assimilation should both be more computationally feasible and provide the greatest benefit over current operational schemes in situations when observations are sparse. Reanalysis before the radiosonde era (pre-1931) is just such a situation. The feasibility of reanalysis before radiosondes using an ensemble square root filter (EnSRF) is examined. Real surface pressure observations for 2001 are used, subsampled to resemble the density of observations we estimate to be available for 1915. Analysis errors are defined relative to a three-dimensional variational data assimilation (3DVAR) analysis using several orders of magnitude more observati...