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.

scholarly journals Interpretation of Adaptive Observing Guidance for Atlantic Tropical Cyclones

2007 ◽  
Vol 135 (12) ◽  
pp. 4006-4029 ◽  
Author(s):  
C. A. Reynolds ◽  
M. S. Peng ◽  
S. J. Majumdar ◽  
S. D. Aberson ◽  
C. H. Bishop ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Total Energy ◽  
Tropical Cyclones ◽  
Error Variance ◽  
Naval Research ◽  
Error Statistics ◽  
Background Error ◽  
Analysis Error ◽  
The Impact ◽  
Perturbation Growth

Abstract Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.

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 Facilitating Strongly Coupled Ocean–Atmosphere Data Assimilation with an Interface Solver

2015 ◽  
Vol 144 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Sergey Frolov ◽  
Craig H. Bishop ◽  
Teddy Holt ◽  
James Cummings ◽  
David Kuhl
Keyword(s):  
Data Assimilation ◽  
Impact Analysis ◽  
Coupled Model ◽  
Deep Ocean ◽  
Accurate Solution ◽  
Fluid Interface ◽  
Strongly Coupled ◽  
Grid Points ◽  
Coupled Data Assimilation ◽  
Observation Vector

Abstract In a strongly coupled data assimilation (DA), a cross-fluid covariance is specified that allows measurements from a coupled fluid (e.g., atmosphere) to directly impact analysis increments in a target fluid (e.g., ocean). The exhaustive solution to this coupled DA problem calls for a covariance where all available measurements can influence all grid points in all fluids. Solution of such a large algebraic problem is computationally expensive, often calls for a substantial rewrite of existing fluid-specific DA systems, and, as shown in this paper, can be avoided. The proposed interface solver assumes that covariances between coupled measurements and target fluid are often close to null (e.g., between stratospheric observations and the deep ocean within a 6-h forecast cycle). In the interface solver, two separate DA solvers are run in parallel: one that produces an analysis solution in the atmosphere, and one in the ocean. Each system uses a coupled observation vector where in addition to resident measurements in the target fluid it also includes nonresident measurements in the coupled fluid that are likely to have significant influence on the analysis in the target fluid (interface measurements). An ensemble-based method is employed and a localization function for coupled ensembles is proposed. Using a coupled model for the Mediterranean Sea (in a twin setting), it is demonstrated that (i) the solution of the interface solver converges to the exhaustive solution and (ii) that in presence of poorly known error covariances, the interface solver can be configured to produce a more accurate solution than an exhaustive solver.

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.

Air-sea strongly coupled data assimilation for tropical cyclone prediction

2021 ◽  
Author(s):  
Xingchao Chen
Keyword(s):  
Tropical Cyclone ◽  
Data Assimilation ◽  
Forecast Error ◽  
Regional Scale ◽  
Forecast Errors ◽  
State Variables ◽  
Strongly Coupled ◽  
Weakly Coupled ◽  
Coupled Data Assimilation ◽  
Tc Prediction

<p>Air-sea interactions are critical to tropical cyclone (TC) energetics. However, oceanic state variables are still poorly initialized, and are inconsistent with atmospheric initial fields in most operational coupled TC forecast models. In this study, we first investigate the forecast error covariance across the oceanic and atmospheric domains during the rapid intensification of Hurricane Florence (2018) using a 200-member ensemble of convection-permitting forecasts from a coupled atmosphere-ocean regional model. Meaningful and dynamically consistent cross domain ensemble error correlations suggest that it is possible to use atmospheric and oceanic observations to simultaneously update model state variables associated with the coupled ocean-atmosphere prediction of TCs using strongly coupled data assimilation (DA). A regional-scale strongly coupled DA system based on the ensemble Kalman filter (EnKF) is then developed for TC prediction. The potential impacts of different atmospheric and oceanic observations on TC analysis and prediction are examined through observing system simulation experiments (OSSEs) of Hurricane Florence (2018). Results show that strongly coupled DA resulted in better analysis and forecast of both the oceanic and atmospheric variables than weakly coupled DA. Compared to weakly coupled DA in which the analysis update is performed separately for the atmospheric and oceanic domains, strongly coupled DA reduces the forecast errors of TC track and intensity. Results show promise in potential further improvement in TC prediction through assimilation of both atmospheric and oceanic observations using the ensemble-based strongly coupled DA system.</p>

Dynamical Structures of Cross-Domain Forecast Error Covariance of a Simulated Tropical Cyclone in a Convection-Permitting Coupled Atmosphere–Ocean Model

2021 ◽  
Vol 149 (1) ◽  
pp. 41-63
Author(s):  
Xingchao Chen ◽  
Robert G. Nystrom ◽  
Christopher A. Davis ◽  
Colin M. Zarzycki
Keyword(s):  
Tropical Cyclone ◽  
Data Assimilation ◽  
Forecast Error ◽  
State Variables ◽  
Ensemble Spread ◽  
Strongly Coupled ◽  
Error Covariance ◽  
Cross Domain ◽  
Forecast Lead Time ◽  
Coupled Data Assimilation

AbstractUnderstanding the dynamics of the flow-dependent forecast error covariance across the air–sea interface is beneficial toward revealing the potential influences of strongly coupled data assimilation on tropical cyclone (TC) initialization in coupled models, and the fundamental dynamics associated with TC air–sea interactions. A 200-member ensemble of convection-permitting forecasts from a coupled atmosphere–ocean regional model is used to investigate the forecast error covariance across the oceanic and atmospheric domains during the rapid intensification of Hurricane Florence (2018). Forecast uncertainties in both atmospheric and oceanic domains, from an Eulerian perspective, increase with forecast lead time, mainly from TC displacement errors. In a storm-relative framework, the ensemble forecast uncertainties in both domains are predominantly caused by differences in the simulated storm intensity and structure. The largest ensemble spread in the atmospheric pressure, temperature, and wind fields can be found within the TC inner-core region. Alternatively, the largest ensemble spread in the upper-ocean currents and temperature fields are located along the cold wake behind the storm. Cross-domain ensemble correlations between simulated atmospheric (oceanic) observations and oceanic (atmospheric) state variables in the storm-relative coordinates are highly anisotropic, variable dependent, and ultimately driven by the dynamics of TC air–sea interactions. Meaningful and dynamically consistent cross-domain ensemble correlations suggest that it is possible to use atmospheric and oceanic observations to simultaneously update state variables associated with the coupled ocean–atmosphere prediction of TCs using strongly coupled data assimilation. Sensitivity experiments demonstrate that at least 60–80 ensemble members are required to represent physically consistent cross-domain correlations and minimize sampling errors.

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 Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz ’96 system

2021 ◽  
Author(s):  
Zofia Stanley ◽  
Ian Grooms ◽  
William Kleiber
Keyword(s):  
Data Assimilation ◽  
Spatial Scales ◽  
Background Error ◽  
Strongly Coupled ◽  
Localization Function ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Coupled Data Assimilation ◽  
Lorenz 96 ◽  
The Impact

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari-Cohn localization function; the within-component localization functions are standard Gaspari-Cohn with different localization radii while the cross-localization function is newly constructed. The functions produce non-negative definite localization matrices, which are suitable for use in variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate analogs of all four functions in a simple experiment with the bivariate Lorenz '96 system. In our experiment the multivariate Gaspari-Cohn function leads to better performance than any of the other localization functions.

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.

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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