Ensemble Data Assimilation Using a Unified Representation of Model Error

2015 ◽  
Vol 144 (1) ◽  
pp. 213-224 ◽  
Author(s):  
Chiara Piccolo ◽  
Mike Cullen
Keyword(s):  
Data Assimilation ◽  
Covariance Structure ◽  
Model Error ◽  
Model Errors ◽  
Stochastic Forcing ◽  
Ensemble Forecasts ◽  
Verification Methods ◽  
Physically Based ◽  
Set Up ◽  
Initial Uncertainty

Abstract A natural way to set up an ensemble forecasting system is to use a model with additional stochastic forcing representing the model error and to derive the initial uncertainty by using an ensemble of analyses generated with this model. Current operational practice has tended to separate the problems of generating initial uncertainty and forecast uncertainty. Thus, in ensemble forecasts, it is normal to use physically based stochastic forcing terms to represent model errors, while in generating analysis uncertainties, artificial inflation methods are used to ensure that the analysis spread is sufficient given the observations. In this paper a more unified approach is tested that uses the same stochastic forcing in the analyses and forecasts and estimates the model error forcing from data assimilation diagnostics. This is shown to be successful if there are sufficient observations. Ensembles used in data assimilation have to be reliable in a broader sense than the usual forecast verification methods; in particular, they need to have the correct covariance structure, which is demonstrated.

Effect of inaccurate specification of time-correlated model error in an Ensemble Smoother

2020 ◽  
Author(s):  
Haonan Ren ◽  
Peter Jan Van Leeuwen ◽  
Javier Amezcua
Keyword(s):  
Data Assimilation ◽  
Time Scale ◽  
Correlation Time ◽  
Time Window ◽  
Model Error ◽  
Multiple Time ◽  
Model Errors ◽  
Time Step ◽  
Single Observation ◽  
Kalman Smoother

<p>Data assimilation has been often performed under the perfect model assumption known as the strong-constraint setting. There is an increasing number of researches accounting for the model errors, the weak-constrain setting, but often with different degrees of approximation or simplification without knowing their impact on the data assimilation results. We investigate what effect inaccurate model errors, in particular, the an inaccurate time correlation, can have on data assimilation results, with a Kalman Smoother and the Ensemble Kalman Smoother.<br>We choose a linear auto-regressive model for the experiment. We assume the true state of the system has the correct and fixed correlation time-scale ω<sub>r</sub> in the model errors, and the prior or the background generated by the model contains the model error with the fixed, guessed time-scale ω<sub>g</sub> which differs from the correct one and is also used in the data assimilation process. There are 10 variables in the system and we separate the simulation period into multiple time-windows. And we use a fairly large ensemble size (up to 200 ensemble members) to improve the accuracy of the data assimilation results. In order to evaluate the performance of the EnKS with auto-correlated model errors, we calculate the ratio of root-mean-square error over the spread of all ensemble members.<br>The results with a single observation at the end of the simulation time-window show that, using an underestimated correlation time-scale leads to overestimated spread of the ensemble, and with an overestimated time-scale, the results show underestimation in the ensemble spread. However, with very dense observation frequency, observing every time-step for instance, the results are completely opposite to the results with a single observation. In order to understand the results, we derive the expression for the true posterior state covariance and the posterior covariance using the incorrect decorrelation time-scale. We do this for a Kalman Smoother to avoid the sampling uncertainties. The results are richer than expected and highly dependent on the observation frequency. From the analytical solution of the analysis, we find that the RMSE is a function of both ω<sub>r</sub><sub> </sub>and ω<sub>g</sub>, and the spread or the variance only depends on ω<sub>g</sub>. We also find that the analyzed variance is not always a monotonically increasing function of ω<sub>g</sub>, and it also depends on the observation frequency. In general, the results show the effect of the correlated model error and the incorrect correlation time-scale on data assimilation result, which is also affected by the observation frequency.</p>

scholarly journals A Comparison of Model Error Representations in Mesoscale Ensemble Data Assimilation

2015 ◽  
Vol 143 (10) ◽  
pp. 3893-3911 ◽  
Author(s):  
Soyoung Ha ◽  
Judith Berner ◽  
Chris Snyder
Keyword(s):  
Data Assimilation ◽  
Numerical Models ◽  
Wrf Model ◽  
Forecast Model ◽  
Model Error ◽  
Ensemble Forecasts ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Independent Observations ◽  
Almost All

Abstract Mesoscale forecasts are strongly influenced by physical processes that are either poorly resolved or must be parameterized in numerical models. In part because of errors in these parameterizations, mesoscale ensemble data assimilation systems generally suffer from underdispersiveness, which can limit the quality of analyses. Two explicit representations of model error for mesoscale ensemble data assimilation are explored: a multiphysics ensemble in which each member’s forecast is based on a distinct suite of physical parameterization, and stochastic kinetic energy backscatter in which small noise terms are included in the forecast model equations. These two model error techniques are compared with a baseline experiment that includes spatially and temporally adaptive covariance inflation, in a domain over the continental United States using the Weather Research and Forecasting (WRF) Model for mesoscale ensemble forecasts and the Data Assimilation Research Testbed (DART) for the ensemble Kalman filter. Verification against independent observations and Rapid Update Cycle (RUC) 13-km analyses for the month of June 2008 showed that including the model error representation improved not only the analysis ensemble, but also short-range forecasts initialized from these analyses. Explicitly accounting for model uncertainty led to a better-tuned ensemble spread, a more skillful ensemble mean, and higher probabilistic scores, as well as significantly reducing the need for inflation. In particular, the stochastic backscatter scheme consistently outperformed both the multiphysics approach and the control run with adaptive inflation over almost all levels of the atmosphere both deterministically and probabilistically.

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.

A Comparison of Methods to Sample Model Errors for Convection-Allowing Ensemble Forecasts in the Setting of Multiscale Initial Conditions Produced by the GSI-Based EnVar Assimilation System

2020 ◽  
Vol 148 (3) ◽  
pp. 1177-1203 ◽  
Author(s):  
Nicholas A. Gasperoni ◽  
Xuguang Wang ◽  
Yongming Wang
Keyword(s):  
Initial Conditions ◽  
Heavy Precipitation ◽  
Model Error ◽  
Lead Times ◽  
Model Errors ◽  
Ensemble Forecasts ◽  
System A ◽  
Ensemble Mean ◽  
Statistical Interpolation ◽  
Stochastic Physics

Abstract A gridpoint statistical interpolation (GSI)-based hybrid ensemble–variational (EnVar) scheme was extended for convective scales—including radar reflectivity assimilation—and implemented in real-time spring forecasting experiments. This study compares methods to address model error during the forecast under the context of multiscale initial condition error sampling provided by the EnVar system. A total of 10 retrospective cases were used to explore the optimal design of convection-allowing ensemble forecasts. In addition to single-model single-physics (SMSP) configurations, ensemble forecast experiments compared multimodel (MM) and multiphysics (MP) approaches. Stochastic physics was also applied to MP for further comparison. Neighborhood-based verification of precipitation and composite reflectivity showed each of these model error techniques to be superior to SMSP configurations. Comparisons of MM and MP approaches had mixed findings. The MM approach had better overall skill in heavy-precipitation forecasts; however, MP ensembles had better skill for light (2.54 mm) precipitation and reduced ensemble mean error of other diagnostic fields, particularly near the surface. The MM experiment had the largest spread in precipitation, and for most hours in other fields; however, rank histograms and spaghetti contours showed significant clustering of the ensemble distribution. MP plus stochastic physics was able to significantly increase spread with time to be competitive with MM by the end of the forecast. The results generally suggest that an MM approach is best for early forecast lead times up to 6–12 h, while a combination of MP and stochastic physics approaches is preferred for forecasts beyond 6–12 h.

scholarly journals Accounting for model error in air-quality forecasts: an application of 4DEnVar to the assimilation of atmospheric composition using QG-Chem 1.0

2016 ◽  
Author(s):  
Emanuele Emili ◽  
Selime Gürol ◽  
Daniel Cariolle
Keyword(s):  
Air Quality ◽  
Data Assimilation ◽  
Atmospheric Chemistry ◽  
Transport Model ◽  
Model Error ◽  
Tropospheric Chemistry ◽  
Atmospheric Composition ◽  
Forecast Errors ◽  
Model Errors ◽  
Ensemble Size

Abstract. Model errors play a significant role in air-quality forecasts. Accounting for them in the data assimilation (DA) procedures is decisive to obtain improved forecasts. We address this issue using a reduced-order chemical transport model based on quasi-geostrophic dynamics and a detailed tropospheric chemistry mechanism, which we name QG-Chem. This model has been coupled to a generic software library for data assimilation and used to assess the potential of the 4DEnVar algorithm for air-quality analyses and forecasts. Among the assets of 4DEnVar, we reckon the possibility to deal with multivariate aspects of atmospheric chemistry and to account for model errors of generic type. A simple diagnostic procedure for detecting model errors is proposed, based on the 4DEnVar analysis and one additional model forecast. A large number of idealized data assimilation experiments are shown for several chemical species of relevance for air-quality forecasts (O3, NOx, CO and CO2), with very different atmospheric life-times and chemical couplings. Experiments are done both under a perfect model hypothesis and including model error through perturbation of surface chemical emissions, for two meteorological and chemical regimes. Some key elements of the 4DEnVar algorithm such as the ensemble size and localization are also discussed. A comparison with results of 3D-Var, widely used in operational centers, shows that, for some species, analyses and next day forecast errors can be halved when model error is taken in account. This result was obtained using a small ensemble size, which remain affordable for most operational centers. We conclude that 4DEnVar has a promising potential for operational air-quality models. We finally highlight areas that deserve further research for applying 4DEnVar to large scale chemistry models, i.e. localization techniques, propagation of analysis covariance between DA cycles and treatment for chemical non-linearities. QG-Chem provides a useful tool in this regard.

Representation of model error in convective scale data assimilation

2020 ◽  
Author(s):  
Tijana Janjic ◽  
Yuefei Zeng ◽  
Alberto de Lozar ◽  
Yvonne Ruckstuhl ◽  
Ulrich Blahak ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Additive Noise ◽  
Model Error ◽  
Ensemble Member ◽  
Radar Reflectivity ◽  
Model Errors ◽  
Estimation Of Parameters ◽  
Convective Scale ◽  
Reflectivity Data ◽  
Scale Data

<p>Model error is one of major contributors to forecast uncertainty. In addition, statistical representations of possible model errors substantially affect the data assimilation results. We investigate variety of methods of taking into account model error in ensemble based convective scale data assimilation. This is done using the operational convection-permitting COSMO model and data assimilation system KENDA of German weather service, for a two-week convective period in May 2016 over Germany. Conventional and radar reflectivity observations are assimilated hourly by the LETKF. For example, to take into account the model error due to unresolved scales and processes, we use the additive noise with samples coming from the difference between high-resolution model run and low-resolution experiment. We compare this technique for assimilation of radar reflectivity data to other methods such as RTPS, warm bubble initialization, stochastic boundary layer perturbation and estimation of parameters. To further improve on additive noise technique, which consists of perturbing each ensemble member with a sample from a given distribution, we propose a more flexible approach in which the model error samples are treated as additional synthetic ensemble members that are used in the update step of data assimilation but are not forecasted. In this way, the rank of the model error covariance matrix can be chosen independently of the ensemble. This altered additive noise method is analyzed as well.</p>

scholarly journals Precision variational approximations in statistical data assimilation

2014 ◽  
Vol 1 (2) ◽  
pp. 1603-1620 ◽  
Author(s):  
J. Ye ◽  
N. Kadakia ◽  
P. J. Rozdeba ◽  
H. D. I. Abarbanel ◽  
J. C. Quinn
Keyword(s):  
Data Assimilation ◽  
Statistical Data ◽  
State Variables ◽  
Model Errors ◽  
Initial State ◽  
Observation Window ◽  
Variational Approximations ◽  
Physically Based ◽  
Expected Values ◽  
Higher Order Corrections

Abstract. Data assimilation transfers information from observations of a complex system to physically-based system models with state variables x(t). Typically, the observations are noisy, the model has errors, and the initial state of the model is uncertain, so the data assimilation is statistical. One can thus ask questions about expected values of functions ⟨G(X)⟩ on the path X = {x(t0), ..., x(tm)} of the model as it moves through an observation window where measurements are made at times {t0, ..., tm}. The probability distribution on the path P(X) = exp[−A0(X)] determines these expected values. Variational methods seeking extrema of the "action" A0(X), widely known as 4DVar (Talagrand and Courtier, 1987; Evensen, 2009),, are widespread for estimating ⟨G(X) ⟩ in many fields of science. In a path integral formulation of statistical data assimilation, we consider variational approximations in a standard realization of the action where measurement and model errors are Gaussian. We (a) discuss an annealing method for locating the path X0 giving a consistent global minimum of the action A0(X0), (b) consider the explicit role of the number of measurements at each measurement time in determining A0(X0), and (c) identify a parameter regime for the scale of model errors which allows X0 to give a precise estimate of ⟨G(X0)⟩ with computable, small higher order corrections.

scholarly journals Accounting for model error in air quality forecasts: an application of 4DEnVar to the assimilation of atmospheric composition using QG-Chem 1.0

2016 ◽  
Vol 9 (11) ◽  
pp. 3933-3959 ◽  
Author(s):  
Emanuele Emili ◽  
Selime Gürol ◽  
Daniel Cariolle
Keyword(s):  
Air Quality ◽  
Data Assimilation ◽  
Atmospheric Chemistry ◽  
Large Scale ◽  
Model Error ◽  
Tropospheric Chemistry ◽  
Atmospheric Composition ◽  
Forecast Errors ◽  
Model Errors ◽  
Ensemble Size

Abstract. Model errors play a significant role in air quality forecasts. Accounting for them in the data assimilation (DA) procedures is decisive to obtain improved forecasts. We address this issue using a reduced-order coupled chemistry–meteorology model based on quasi-geostrophic dynamics and a detailed tropospheric chemistry mechanism, which we name QG-Chem. This model has been coupled to the software library for the data assimilation Object Oriented Prediction System (OOPS) and used to assess the potential of the 4DEnVar algorithm for air quality analyses and forecasts. The assets of 4DEnVar include the possibility to deal with multivariate aspects of atmospheric chemistry and to account for model errors of a generic type. A simple diagnostic procedure for detecting model errors is proposed, based on the 4DEnVar analysis and one additional model forecast. A large number of idealized data assimilation experiments are shown for several chemical species of relevance for air quality forecasts (O3, NOx, CO and CO2) with very different atmospheric lifetimes and chemical couplings. Experiments are done both under a perfect model hypothesis and including model error through perturbation of surface chemical emissions. Some key elements of the 4DEnVar algorithm such as the ensemble size and localization are also discussed. A comparison with results of 3D-Var, widely used in operational centers, shows that, for some species, analysis and next-day forecast errors can be halved when model error is taken into account. This result was obtained using a small ensemble size, which remains affordable for most operational centers. We conclude that 4DEnVar has a promising potential for operational air quality models. We finally highlight areas that deserve further research for applying 4DEnVar to large-scale chemistry models, i.e., localization techniques, propagation of analysis covariance between DA cycles and treatment for chemical nonlinearities. QG-Chem can provide a useful tool in this regard.

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 Comparison of Methods Accounting for Subgrid-Scale Model Error in Convective-Scale Data Assimilation

2020 ◽  
Vol 148 (6) ◽  
pp. 2457-2477 ◽  
Author(s):  
Yuefei Zeng ◽  
Tijana Janjić ◽  
Alberto de Lozar ◽  
Stephan Rasp ◽  
Ulrich Blahak ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Additive Noise ◽  
Stochastic Perturbation ◽  
Model Error ◽  
Scale Model ◽  
Ensemble Spread ◽  
Physically Based ◽  
Convective Scale ◽  
Convective Cells ◽  
Scale Data

Abstract Different approaches for representing model error due to unresolved scales and processes are compared in convective-scale data assimilation, including the physically based stochastic perturbation (PSP) scheme for turbulence, an advanced warm bubble approach that automatically detects and triggers absent convective cells, and additive noise based on model truncation error. The analysis of kinetic energy spectrum guides the understanding of differences in precipitation forecasts. It is found that the PSP scheme results in more ensemble spread in assimilation cycles, but its effects on the root-mean-square error (RMSE) are neutral. This leads to positive impacts on precipitation forecasts that last up to three hours. The warm bubble technique does not create more spread, but is effective in reducing the RMSE, and improving precipitation forecasts for up to 3 h. The additive noise approach contributes greatly to ensemble spread, but it results in a larger RMSE during assimilation cycles. Nevertheless, it considerably improves the skill of precipitation forecasts up to 6 h. Combining the additive noise with either the PSP scheme or the warm bubble technique reduces the RMSE within cycles and improves the skill of the precipitation forecasts, with the latter being more beneficial.

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