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 Representation of Model Error in Convective‐Scale Data Assimilation: Additive Noise Based on Model Truncation Error

2019 ◽  
Vol 11 (3) ◽  
pp. 752-770 ◽  
Author(s):  
Yuefei Zeng ◽  
Tijana Janjić ◽  
Matthias Sommer ◽  
Alberto Lozar ◽  
Ulrich Blahak ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Truncation Error ◽  
Additive Noise ◽  
Model Error ◽  
Convective Scale ◽  
Scale Data

scholarly journals Representation of Model Error in Convective‐Scale Data Assimilation: Additive Noise, Relaxation Methods, and Combinations

2018 ◽  
Vol 10 (11) ◽  
pp. 2889-2911 ◽  
Author(s):  
Yuefei Zeng ◽  
Tijana Janjić ◽  
Alberto Lozar ◽  
Ulrich Blahak ◽  
Hendrik Reich ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Additive Noise ◽  
Model Error ◽  
Relaxation Methods ◽  
Convective Scale ◽  
Scale Data

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.

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.

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>

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.

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