scholarly journals Technical Note: Sequential ensemble data assimilation in convergent and divergent systems

2021 ◽  
Vol 25 (6) ◽  
pp. 3319-3329
Author(s):  
Hannes Helmut Bauser ◽  
Daniel Berg ◽  
Kurt Roth
Keyword(s):  
Data Assimilation ◽  
Water Movement ◽  
Measurement Data ◽  
Technical Note ◽  
Richards Equation ◽  
Model Errors ◽  
Parameter Uncertainties ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Abstract Data

Abstract. Data assimilation methods are used throughout the geosciences to combine information from uncertain models and uncertain measurement data. However, the characteristics of geophysical systems differ and may be distinguished between divergent and convergent systems. In divergent systems initially nearby states will drift apart, while they will coalesce in convergent systems. This difference has implications for the application of sequential ensemble data assimilation methods. This study explores these implications on two exemplary systems, i.e., the divergent Lorenz 96 model and the convergent description of soil water movement by the Richards equation. The results show that sequential ensemble data assimilation methods require a sufficient divergent component. This makes the transfer of the methods from divergent to convergent systems challenging. We demonstrate, through a set of case studies, that it is imperative to represent model errors adequately and incorporate parameter uncertainties in ensemble data assimilation in convergent systems.

scholarly journals Technical note: Sequential ensemble data assimilation in convergent and divergent systems

2021 ◽  
Author(s):  
Hannes Helmut Bauser ◽  
Daniel Berg ◽  
Kurt Roth
Keyword(s):  
Data Assimilation ◽  
Water Movement ◽  
Measurement Data ◽  
Technical Note ◽  
Richards Equation ◽  
Model Errors ◽  
Parameter Uncertainties ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Abstract Data

Abstract. Data assimilation methods are used throughout the geosciences to combine information from uncertain models and uncertain measurement data. However, the characteristics of geophysical systems differ and may be distinguished between divergent and convergent systems. In divergent systems initially nearby states will drift apart, while they will coalesce in convergent systems. This difference has implications for the application of sequential ensemble data assimilation methods. This study explores these implications on two exemplary systems: the divergent Lorenz-96 model and the convergent description of soil water movement by the Richards equation. The results show that sequential ensemble data assimilation methods require a sufficient divergent component. This makes the transfer of the methods from divergent to convergent systems challenging. We demonstrate through a set of case studies that it is imperative to represent model errors adequately and incorporate parameter uncertainties in ensemble data assimilation in convergent systems.

Ensemble Data Assimilation to Characterize Surface-Layer Errors in Numerical Weather Prediction Models

2013 ◽  
Vol 141 (6) ◽  
pp. 1804-1821 ◽  
Author(s):  
J. P. Hacker ◽  
W. M. Angevine
Keyword(s):  
Surface Layer ◽  
Data Assimilation ◽  
Atmospheric Surface Layer ◽  
Weather Prediction ◽  
Model Error ◽  
Time Of Day ◽  
Turbulent Heat ◽  
Model Errors ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Abstract Experiments with the single-column implementation of the Weather Research and Forecasting Model provide a basis for deducing land–atmosphere coupling errors in the model. Coupling occurs both through heat and moisture fluxes through the land–atmosphere interface and roughness sublayer, and turbulent heat, moisture, and momentum fluxes through the atmospheric surface layer. This work primarily addresses the turbulent fluxes, which are parameterized following the Monin–Obukhov similarity theory applied to the atmospheric surface layer. By combining ensemble data assimilation and parameter estimation, the model error can be characterized. Ensemble data assimilation of 2-m temperature and water vapor mixing ratio, and 10-m wind components, forces the model to follow observations during a month-long simulation for a column over the well-instrumented Atmospheric Radiation Measurement (ARM) Central Facility near Lamont, Oklahoma. One-hour errors in predicted observations are systematically small but nonzero, and the systematic errors measure bias as a function of local time of day. Analysis increments for state elements nearby (15 m AGL) can be too small or have the wrong sign, indicating systematically biased covariances and model error. Experiments using the ensemble filter to objectively estimate a parameter controlling the thermal land–atmosphere coupling show that the parameter adapts to offset the model errors, but that the errors cannot be eliminated. Results suggest either structural errors or further parametric errors that may be difficult to estimate. Experiments omitting atypical observations such as soil and flux measurements lead to qualitatively similar deductions, showing the potential for assimilating common in situ observations as an inexpensive framework for deducing and isolating model errors.

scholarly journals Model Error Representation Using the Stochastically Perturbed Hybrid Physical–Dynamical Tendencies in Ensemble Data Assimilation System

2020 ◽  
Vol 10 (24) ◽  
pp. 9010
Author(s):  
Sujeong Lim ◽  
Myung-Seo Koo ◽  
In-Hyuk Kwon ◽  
Seon Ki Park
Keyword(s):  
Data Assimilation ◽  
Weather Prediction ◽  
Stochastic Perturbation ◽  
Numerical Weather Prediction Model ◽  
Natural State ◽  
Model Errors ◽  
Background Error ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Stochastically Perturbed

Ensemble data assimilation systems generally suffer from underestimated background error covariance that leads to a filter divergence problem—the analysis diverges from the natural state by ignoring the observation influence due to the diminished estimation of model uncertainty. To alleviate this problem, we have developed and implemented the stochastically perturbed hybrid physical–dynamical tendencies to the local ensemble transform Kalman filter in a global numerical weather prediction model—the Korean Integrated Model (KIM). This approach accounts for the model errors associated with computational representations of underlying partial differential equations and the imperfect physical parameterizations. The new stochastic perturbation hybrid tendencies scheme generally improved the background error covariances in regions where the ensemble spread was not sufficiently expressed by the control experiment that used an additive inflation and the relaxation to prior spread method.

scholarly journals Accounting for the Error due to Unresolved Scales in Ensemble Data Assimilation: A Comparison of Different Approaches

2005 ◽  
Vol 133 (11) ◽  
pp. 3132-3147 ◽  
Author(s):  
Thomas M. Hamill ◽  
Jeffrey S. Whitaker
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Additive Model ◽  
Model Error ◽  
Ensemble Member ◽  
Model Errors ◽  
Ensemble Data Assimilation ◽  
Additive Error ◽  
Ensemble Data ◽  
Analysis Errors

Abstract Insufficient model resolution is one source of model error in numerical weather predictions. Methods for parameterizing this error in ensemble data assimilations are explored here. Experiments were conducted with a two-layer primitive equation model, where the assumed true state was a T127 forecast simulation. Ensemble data assimilations were performed with the same model at T31 resolution, assimilating imperfect observations drawn from the T127 forecast. By design, the magnitude of errors due to model truncation was much larger than the error growth due to initial condition uncertainty, making this a stringent test of the ability of an ensemble-based data assimilation to deal with model error. Two general methods, “covariance inflation” and “additive error,” were considered for parameterizing the model error at the resolved scales (T31 and larger) due to interaction with the unresolved scales (T32 to T127). Covariance inflation expanded the background forecast members’ deviations about the ensemble mean, while additive error added specially structured noise to each ensemble member forecast before the update step. The method of parameterizing this model error had a substantial effect on the accuracy of the ensemble data assimilation. Covariance inflation produced ensembles with analysis errors that were no lower than the analysis errors from three-dimensional variational (3D-Var) assimilation, and for the method to avoid filter divergence, the assimilations had to be periodically reseeded. Covariance inflation uniformly expanded the model spread; however, the actual growth of model errors depended on the dynamics, growing proportionally more in the midlatitudes. The inappropriately uniform inflation progressively degradated the capacity of the ensemble to span the actual forecast error. The most accurate model-error parameterization was an additive model-error parameterization, which reduced the error difference between 3D-Var and a near-perfect assimilation system by ∼40%. In the lowest-error simulations, additive errors were parameterized using samples of model error from a time series of differences between T63 and T31 forecasts. Scaled samples of differences between model forecast states separated by 24 h were also tested as additive error parameterizations, as well as scaled samples of the T31 model state’s anomaly from the T31 model climatology. The latter two methods produced analyses that were progressively less accurate. The decrease in accuracy was likely due to their inappropriately long spatial correlation length scales.

scholarly journals Model Error Estimation Employing an Ensemble Data Assimilation Approach

2006 ◽  
Vol 134 (5) ◽  
pp. 1337-1354 ◽  
Author(s):  
Dusanka Zupanski ◽  
Milija Zupanski
Keyword(s):  
Data Assimilation ◽  
Error Estimation ◽  
Forecast Error ◽  
Model Error ◽  
Model Errors ◽  
Model Bias ◽  
Model Framework ◽  
Ensemble Data Assimilation ◽  
Filter Performance ◽  
Ensemble Data

Abstract A methodology for model error estimation is proposed and examined in this study. It provides estimates of the dynamical model state, the bias, and the empirical parameters by combining three approaches: 1) ensemble data assimilation, 2) state augmentation, and 3) parameter and model bias estimation. Uncertainties of these estimates are also determined, in terms of the analysis and forecast error covariances, employing the same methodology. The model error estimation approach is evaluated in application to Korteweg–de Vries–Burgers (KdVB) numerical model within the framework of maximum likelihood ensemble filter (MLEF). Experimental results indicate improved filter performance due to model error estimation. The innovation statistics also indicate that the estimated uncertainties are reliable. On the other hand, neglecting model errors—either in the form of an incorrect model parameter, or a model bias—has detrimental effects on data assimilation, in some cases resulting in filter divergence. Although the method is examined in a simplified model framework, the results are encouraging. It remains to be seen how the methodology performs in applications to more complex models.

Initiation of ensemble data assimilation

2006 ◽  
Author(s):  
M. Zupanski ◽  
S. J. Fletcher ◽  
I. M. Navon ◽  
B. Uzunoglu ◽  
R. P. Heikes ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Using a machine learning proxy for localization in ensemble data assimilation

2021 ◽  
Vol 25 (3) ◽  
pp. 931-944
Author(s):  
Johann M. Lacerda ◽  
Alexandre A. Emerick ◽  
Adolfo P. Pires
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Maximum Likelihood Ensemble Filter: Theoretical Aspects

2005 ◽  
Vol 133 (6) ◽  
pp. 1710-1726 ◽  
Author(s):  
Milija Zupanski
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

Abstract A new ensemble-based data assimilation method, named the maximum likelihood ensemble filter (MLEF), is presented. The analysis solution maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function that depends on a general nonlinear observation operator. The MLEF belongs to the class of deterministic ensemble filters, since no perturbed observations are employed. As in variational and ensemble data assimilation methods, the cost function is derived using a Gaussian probability density function framework. Like other ensemble data assimilation algorithms, the MLEF produces an estimate of the analysis uncertainty (e.g., analysis error covariance). In addition to the common use of ensembles in calculation of the forecast error covariance, the ensembles in MLEF are exploited to efficiently calculate the Hessian preconditioning and the gradient of the cost function. A sufficient number of iterative minimization steps is 2–3, because of superior Hessian preconditioning. The MLEF method is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization. The consistent treatment of nonlinear observation operators through optimization is an advantage of the MLEF over other ensemble data assimilation algorithms. The cost of MLEF is comparable to the cost of existing ensemble Kalman filter algorithms. The method is directly applicable to most complex forecast models and observation operators. In this paper, the MLEF method is applied to data assimilation with the one-dimensional Korteweg–de Vries–Burgers equation. The tested observation operator is quadratic, in order to make the assimilation problem more challenging. The results illustrate the stability of the MLEF performance, as well as the benefit of the cost function minimization. The improvement is noted in terms of the rms error, as well as the analysis error covariance. The statistics of innovation vectors (observation minus forecast) also indicate a stable performance of the MLEF algorithm. Additional experiments suggest the amplified benefit of targeted observations in ensemble data assimilation.

scholarly journals Convection-Permitting Forecasts Initialized with Continuously Cycling Limited-Area 3DVAR, Ensemble Kalman Filter, and “Hybrid” Variational–Ensemble Data Assimilation Systems

2014 ◽  
Vol 142 (2) ◽  
pp. 716-738 ◽  
Author(s):  
Craig S. Schwartz ◽  
Zhiquan Liu
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Three Dimensional ◽  
Skill Score ◽  
Limited Area ◽  
Computational Domain ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Precipitation Characteristics ◽  
High Precipitation

Abstract Analyses with 20-km horizontal grid spacing were produced from parallel continuously cycling three-dimensional variational (3DVAR), ensemble square root Kalman filter (EnSRF), and “hybrid” variational–ensemble data assimilation (DA) systems between 0000 UTC 6 May and 0000 UTC 21 June 2011 over a domain spanning the contiguous United States. Beginning 9 May, the 0000 UTC analyses initialized 36-h Weather Research and Forecasting Model (WRF) forecasts containing a large convection-permitting 4-km nest. These 4-km 3DVAR-, EnSRF-, and hybrid-initialized forecasts were compared to benchmark WRF forecasts initialized by interpolating 0000 UTC Global Forecast System (GFS) analyses onto the computational domain. While important differences regarding mean state characteristics of the 20-km DA systems were noted, verification efforts focused on the 4-km precipitation forecasts. The 3DVAR-, hybrid-, and EnSRF-initialized 4-km precipitation forecasts performed similarly regarding general precipitation characteristics, such as timing of the diurnal cycle, and all three forecast sets had high precipitation biases at heavier rainfall rates. However, meaningful differences emerged regarding precipitation placement as quantified by the fractions skill score. For most forecast hours, the hybrid-initialized 4-km precipitation forecasts were better than the EnSRF-, 3DVAR-, and GFS-initialized forecasts, and the improvement was often statistically significant at the 95th percentile. These results demonstrate the potential of limited-area continuously cycling hybrid DA configurations and suggest additional hybrid development is warranted.

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