Evaluation of Surface Analyses and Forecasts with a Multiscale Ensemble Kalman Filter in Regions of Complex Terrain

2011 ◽  
Vol 139 (6) ◽  
pp. 2008-2024 ◽  
Author(s):  
Brian C. Ancell ◽  
Clifford F. Mass ◽  
Gregory J. Hakim
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Complex Terrain ◽  
Error Variance ◽  
Small Scale ◽  
Observation Error ◽  
Grid Spacing ◽  
Background Error

Abstract Previous research suggests that an ensemble Kalman filter (EnKF) data assimilation and modeling system can produce accurate atmospheric analyses and forecasts at 30–50-km grid spacing. This study examines the ability of a mesoscale EnKF system using multiscale (36/12 km) Weather Research and Forecasting (WRF) model simulations to produce high-resolution, accurate, regional surface analyses, and 6-h forecasts. This study takes place over the complex terrain of the Pacific Northwest, where the small-scale features of the near-surface flow field make the region particularly attractive for testing an EnKF and its flow-dependent background error covariances. A variety of EnKF experiments are performed over a 5-week period to test the impact of decreasing the grid spacing from 36 to 12 km and to evaluate new approaches for dealing with representativeness error, lack of surface background variance, and low-level bias. All verification in this study is performed with independent, unassimilated observations. Significant surface analysis and 6-h forecast improvements are found when EnKF grid spacing is reduced from 36 to 12 km. Forecast improvements appear to be a consequence of increased resolution during model integration, whereas analysis improvements also benefit from high-resolution ensemble covariances during data assimilation. On the 12-km domain, additional analysis improvements are found by reducing observation error variance in order to address representativeness error. Removing model surface biases prior to assimilation significantly enhances the analysis. Inflating surface wind and temperature background error variance has large impacts on analyses, but only produces small improvements in analysis RMS errors. Both surface and upper-air 6-h forecasts are nearly unchanged in the 12-km experiments. Last, 12-km WRF EnKF surface analyses and 6-h forecasts are shown to generally outperform those of the Global Forecast System (GFS), North American Model (NAM), and the Rapid Update Cycle (RUC) by about 10%–30%, although these improvements do not extend above the surface. Based on these results, future improvements in multiscale EnKF are suggested.

scholarly journals Assimilation of Stratospheric Temperature and Ozone with an Ensemble Kalman Filter in a Chemistry–Climate Model

2011 ◽  
Vol 139 (11) ◽  
pp. 3389-3404 ◽  
Author(s):  
Thomas Milewski ◽  
Michel S. Bourqui
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Climate Model ◽  
Observation Error ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Analysis Error

Abstract A new stratospheric chemical–dynamical data assimilation system was developed, based upon an ensemble Kalman filter coupled with a Chemistry–Climate Model [i.e., the intermediate-complexity general circulation model Fast Stratospheric Ozone Chemistry (IGCM-FASTOC)], with the aim to explore the potential of chemical–dynamical coupling in stratospheric data assimilation. The system is introduced here in a context of a perfect-model, Observing System Simulation Experiment. The system is found to be sensitive to localization parameters, and in the case of temperature (ozone), assimilation yields its best performance with horizontal and vertical decorrelation lengths of 14 000 km (5600 km) and 70 km (14 km). With these localization parameters, the observation space background-error covariance matrix is underinflated by only 5.9% (overinflated by 2.1%) and the observation-error covariance matrix by only 1.6% (0.5%), which makes artificial inflation unnecessary. Using optimal localization parameters, the skills of the system in constraining the ensemble-average analysis error with respect to the true state is tested when assimilating synthetic Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) retrievals of temperature alone and ozone alone. It is found that in most cases background-error covariances produced from ensemble statistics are able to usefully propagate information from the observed variable to other ones. Chemical–dynamical covariances, and in particular ozone–wind covariances, are essential in constraining the dynamical fields when assimilating ozone only, as the radiation in the stratosphere is too slow to transfer ozone analysis increments to the temperature field over the 24-h forecast window. Conversely, when assimilating temperature, the chemical–dynamical covariances are also found to help constrain the ozone field, though to a much lower extent. The uncertainty in forecast/analysis, as defined by the variability in the ensemble, is large compared to the analysis error, which likely indicates some amount of noise in the covariance terms, while also reducing the risk of filter divergence.

scholarly journals Data Assimilation of the High-Resolution Sea Surface Temperature Obtained from the Aqua-Terra Satellites (MODIS-SST) Using an Ensemble Kalman Filter

2013 ◽  
Vol 5 (6) ◽  
pp. 3123-3139 ◽  
Author(s):  
Yasumasa Miyazawa ◽  
Hiroshi Murakami ◽  
Toru Miyama ◽  
Sergey Varlamov ◽  
Xinyu Guo ◽  
...  
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Ensemble Kalman Filter ◽  
Sea Surface

scholarly journals Verification of 24-h Quantitative Precipitation Forecasts over the Pacific Northwest from a High-Resolution Ensemble Kalman Filter System

2017 ◽  
Vol 32 (3) ◽  
pp. 1185-1208 ◽  
Author(s):  
Phillipa Cookson-Hills ◽  
Daniel J. Kirshbaum ◽  
Madalina Surcel ◽  
Jonathan G. Doyle ◽  
Luc Fillion ◽  
...  
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Pacific Northwest ◽  
Ensemble Kalman Filter ◽  
Ensemble Prediction ◽  
Forecast Errors ◽  
Ensemble Prediction System ◽  
The Pacific ◽  
Quantitative Precipitation Forecasts

Abstract Environment and Climate Change Canada (ECCC) has recently developed an experimental high-resolution EnKF (HREnKF) regional ensemble prediction system, which it tested over the Pacific Northwest of North America for the first half of February 2011. The HREnKF has 2.5-km horizontal grid spacing and assimilates surface and upper-air observations every hour. To determine the benefits of the HREnKF over less expensive alternatives, its 24-h quantitative precipitation forecasts are compared with those from a lower-resolution (15 km) regional ensemble Kalman filter (REnKF) system and to ensembles directly downscaled from the REnKF using the same grid as the HREnKF but with no additional data assimilation (DS). The forecasts are verified against rain gauge observations and gridded precipitation analyses, the latter of which are characterized by uncertainties of comparable magnitude to the model forecast errors. Nonetheless, both deterministic and probabilistic verification indicates robust improvements in forecast skill owing to the finer grids of the HREnKF and DS. The HREnKF exhibits a further improvement in performance over the DS in the first few forecast hours, suggesting a modest positive impact of data assimilation. However, this improvement is not statistically significant and may be attributable to other factors.

E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

2012 ◽  
Vol 140 (2) ◽  
pp. 587-600 ◽  
Author(s):  
Meng Zhang ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Prediction Model ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Coupled System ◽  
Limited Area ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Hybrid Data Assimilation

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

scholarly journals An Examination of the Incremental Balance in a Global Ensemble-Based 3D-Var Data Assimilation System

2010 ◽  
Vol 138 (10) ◽  
pp. 3946-3966 ◽  
Author(s):  
Jean-François Caron ◽  
Luc Fillion
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Variational Data Assimilation ◽  
Spatial Covariance ◽  
Background Error ◽  
Localization Technique ◽  
Vertical Localization

Abstract This study examines the modification to the balance properties of the analysis increments in a global three-dimensional variational data assimilation scheme when using flow-dependent background-error covariances derived from an operational ensemble Kalman filter instead of static homogenous and isotropic background-error covariances based on lagged forecast differences. It is shown that the degree of balance in the analysis increments is degraded when the former method is used. This change can be attributed in part to the reduced degree of rotational balance found in short-term ensemble Kalman filter perturbations as compared to lagged forecast differences based on longer-range forecasts. However, the use of a horizontal and vertical localization technique to increase the rank of the ensemble-based covariances are found to have a significant deleterious effect on the rotational balance with the largest detrimental impact coming from the vertical localization and affecting particularly the upper levels. The examination of the vertical motion part of the analysis increments revealed that the spatial covariance localization technique also produces unrealistic vertical structure of vertical motion increments with abnormally large increments near the surface. A comparison between the analysis increments from the ensemble Kalman filter and from the ensemble-based three-dimensional variational data assimilation (3D-Var) scheme showed that the balance characteristics of the analysis increments resulting from the two systems are very similar.

scholarly journals A New Data Assimilation Scheme: The Space-Expanded Ensemble Localization Kalman Filter

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongze Leng ◽  
Junqiang Song ◽  
Fengshun Lu ◽  
Xiaoqun Cao
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Forecast Error ◽  
Three Dimensional ◽  
Full Rank ◽  
Observation Error ◽  
Model Framework ◽  
Background Error ◽  
Error Covariance ◽  
Expanded Ensemble

This study considers a new hybrid three-dimensional variational (3D-Var) and ensemble Kalman filter (EnKF) data assimilation (DA) method in a non-perfect-model framework, named space-expanded ensemble localization Kalman filter (SELKF). In this method, the localization operation is directly applied to the ensemble anomalies with a Schur Product, rather than to the full error covariance of the state in the EnKF. Meanwhile, the correction space of analysis increment is expanded to a space with larger dimension, and the rank of the forecast error covariance is significantly increased. This scheme can reduce the spurious correlations in the covariance and approximate the full-rank background error covariance well. Furthermore, a deterministic scheme is used to generate the analysis anomalies. The results show that the SELKF outperforms the perturbed EnKF given a relatively small ensemble size, especially when the length scale is relatively long or the observation error covariance is relatively small.

scholarly journals Do surface lateral flows matter for data assimilation of soil moisture observations into hyperresolution land models?

2020 ◽  
Author(s):  
Yohei Sawada
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Pressure Head ◽  
Surface Flow ◽  
State Variables ◽  
Background Error ◽  
Water Flows

Abstract. It is expected that hyperresolution land modeling substantially innovates the simulation of terrestrial water, energy, and carbon cycles. The major advantage of hyperresolution land models against conventional one-dimensional land surface models is that hyperresolution land models can explicitly simulate lateral water flows. Despite many efforts on data assimilation of hydrological observations into those hyperresolution land models, how surface water flows driven by local topography matter for data assimilation of soil moisture observations has not been fully clarified. Here I perform two minimalist synthetic experiments where soil moisture observations are assimilated into an integrated surface-groundwater land model by an ensemble Kalman filter. I discuss how differently the ensemble Kalman filter works when surface lateral flows are switched on and off. A horizontal background error covariance provided by overland flows is important to adjust the unobserved state variables (pressure head and soil moisture) and parameters (saturated hydraulic conductivity). However, the non-Gaussianity of the background error provided by the nonlinearity of a topography-driven surface flow harms the performance of data assimilation. It is difficult to efficiently constrain model states at the edge of the area where the topography-driven surface flow reaches by linear-Gaussian filters. It brings the new challenge in land data assimilation for hyperresolution land models. This study highlights the importance of surface lateral flows in hydrological data assimilation.

scholarly journals Do surface lateral flows matter for data assimilation of soil moisture observations into hyperresolution land models?

2020 ◽  
Vol 24 (8) ◽  
pp. 3881-3898
Author(s):  
Yohei Sawada
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Pressure Head ◽  
Surface Flow ◽  
State Variables ◽  
Background Error ◽  
Water Flows

Abstract. It is expected that hyperresolution land modeling substantially innovates the simulation of terrestrial water, energy, and carbon cycles. The major advantage of hyperresolution land models against conventional 1-D land surface models is that hyperresolution land models can explicitly simulate lateral water flows. Despite many efforts on data assimilation of hydrological observations into those hyperresolution land models, how surface water flows driven by local topography matter for data assimilation of soil moisture observations has not been fully clarified. Here I perform two minimalist synthetic experiments where soil moisture observations are assimilated into an integrated surface–groundwater land model by an ensemble Kalman filter. I discuss how differently the ensemble Kalman filter works when surface lateral flows are switched on and off. A horizontal background error covariance provided by overland flows is important for adjusting the unobserved state variables (pressure head and soil moisture) and parameters (saturated hydraulic conductivity). However, the non-Gaussianity of the background error provided by the nonlinearity of a topography-driven surface flow harms the performance of data assimilation. It is difficult to efficiently constrain model states at the edge of the area where the topography-driven surface flow reaches by linear-Gaussian filters. It brings the new challenge in land data assimilation for hyperresolution land models. This study highlights the importance of surface lateral flows in hydrological data assimilation.

scholarly journals Correlation-Cutoff Method for Covariance Localization in Strongly Coupled Data Assimilation

2018 ◽  
Vol 146 (9) ◽  
pp. 2881-2889 ◽  
Author(s):  
Takuma Yoshida ◽  
Eugenia Kalnay
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Coupled Model ◽  
Error Variance ◽  
State Variables ◽  
Background Error ◽  
Strongly Coupled ◽  
Error Correlation ◽  
Analysis Error ◽  
Coupled Data Assimilation

Abstract Strongly coupled data assimilation (SCDA), where observations of one component of a coupled model are allowed to directly impact the analysis of other components, sometimes fails to improve the analysis accuracy with an ensemble Kalman filter (EnKF) as compared with weakly coupled data assimilation (WCDA). It is well known that an observation’s area of influence should be localized in EnKFs since the assimilation of distant observations often degrades the analysis because of spurious correlations. This study derives a method to estimate the reduction of the analysis error variance by using estimates of the cross covariances between the background errors of the state variables in an idealized situation. It is shown that the reduction of analysis error variance is proportional to the squared background error correlation between the analyzed and observed variables. From this, the authors propose an offline method to systematically select which observations should be assimilated into which model state variable by cutting off the assimilation of observations when the squared background error correlation between the observed and analyzed variables is small. The proposed method is tested with the local ensemble transform Kalman filter (LETKF) and a nine-variable coupled model, in which three Lorenz models with different time scales are coupled with each other. The covariance localization with the correlation-cutoff method achieves an analysis more accurate than either the full SCDA or the WCDA methods, especially with smaller ensemble sizes.

A Model-Based Observation-Thinning Scheme for the Assimilation of High-Resolution SST in the Shelf and Coastal Seas around China

2010 ◽  
Vol 27 (6) ◽  
pp. 1044-1058 ◽  
Author(s):  
Xichen Li ◽  
Jiang Zhu ◽  
Yiguo Xiao ◽  
Ruiwen Wang
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Model Simulation ◽  
Error Variance ◽  
Global Ocean ◽  
Background Error ◽  
Full Dataset ◽  
Ocean Data Assimilation ◽  
Estimation Function ◽  
Analysis Error

Abstract The use of high-density remote sensing buoys and ship-based observations play an increasingly crucial role in the operational assimilation and forecast of oceans. With the recent release of several high-resolution observation datasets, such as the Global Ocean Data Assimilation Experiment (GODAE) high-resolution SST (GHRSST) datasets, the development of observation-thinning schemes becomes important in the process of data assimilation because the huge quantity and dense spatial–temporal distributions of these datasets might make it expensive to assimilate the full dataset into ocean models or even decay the assimilation result. In this paper, an objective model simulation ensemble-based observation-thinning scheme is proposed and applied to a Chinese shelf–coastal seas eddy-resolving model. A successful thinning scheme should select a subset of observations yielding a small analysis error variance (AEV) while keeping the number of observations to as few as possible. In this study, the background error covariance (BEC) is estimated using the historical ensemble and then the subset of observations to minimize the AEV is selected, which is estimated from the Kalman theory. The authors used this method in the GHRSST product to cover the shelf and coastal seas around China and then verified the result with an estimation function and assimilation–forecast systems.

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