Model forecast error correction based on the Local Dynamical Analog method: an example application to the ENSO forecast

2020 ◽  
Author(s):  
Zhaolu Hou ◽  
Bin Zuo ◽  
Shaoqing Zhang ◽  
Fei Huang ◽  
Ruiqiang Ding ◽  
...  
Keyword(s):  
Error Correction ◽  
Forecast Error ◽  
Forecast Errors ◽  
Model Errors ◽  
Model Forecast ◽  
New Approach ◽  
Correct Model ◽  
State Dependent ◽  
Dependent Model ◽  
Scalar Time Series

<p>Numerical forecasts always have associated errors. Analogue correction methods combine numerical simulations with statistical analyses to reduce model forecast errors. However, identifying appropriate analogues remains a challenging task. Here, we use the Local Dynamical Analog (LDA) method to locate analogues and correct model forecast errors. As an example, an ENSO model forecast error correction experiment confirms that the LDA method locates more dynamical analogues of states of interest and better corrects forecast errors than do other methods. This is because the LDA method ensures similarity of the initial states and the evolution of both states. In addition, the LDA method can be applied using a scalar time series, which reduces the complexity of the dynamical system. Model forecast error correction using the LDA method provides a new approach to correcting state-dependent model errors and can be readily integrated with other advanced models.</p>

scholarly journals Model error in weather forecasting

2001 ◽  
Vol 8 (6) ◽  
pp. 357-371 ◽  
Author(s):  
D. Orrell ◽  
L. Smith ◽  
J. Barkmeijer ◽  
T. N. Palmer
Keyword(s):  
Prediction Models ◽  
Weather Forecasting ◽  
Initial Conditions ◽  
Forecast Error ◽  
Weather Prediction ◽  
Model Error ◽  
Local Model ◽  
State Dependent ◽  
Rapid Divergence ◽  
Dependent Model

Abstract. Operational forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. Interest in chaos has fuelled much work on the first of these two issues; this paper focuses on the second. A new approach to quantifying state-dependent model error, the local model drift, is derived and deployed both in examples and in operational numerical weather prediction models. A simple law is derived to relate model error to likely shadowing performance (how long the model can stay close to the observations). Imperfect model experiments are used to contrast the performance of truncated models relative to a high resolution run, and the operational model relative to the analysis. In both cases the component of forecast error due to state-dependent model error tends to grow as the square-root of forecast time, and provides a major source of error out to three days. These initial results suggest that model error plays a major role and calls for further research in quantifying both the local model drift and expected shadowing times.

scholarly journals An Examination of Background Error Correlations between Mass and Rotational Wind over Precipitation Regions

2010 ◽  
Vol 138 (2) ◽  
pp. 563-578 ◽  
Author(s):  
Jean-François Caron ◽  
Luc Fillion
Keyword(s):  
Linear Regression ◽  
Data Assimilation ◽  
Traditional Approach ◽  
Forecast Error ◽  
Lower Atmosphere ◽  
Forecast Errors ◽  
Background Error ◽  
New Approach ◽  
Geostrophic Balance ◽  
Analysis System

Abstract The differences in the balance characteristics between dry and precipitation areas in estimated short-term forecast error fields are investigated. The motivation is to see if dry and precipitation areas need to be treated differently in atmospheric data assimilation systems. Using an ensemble of lagged forecast differences, it is shown that perturbations are, on average, farther away from geostrophic balance over precipitation areas than over dry areas and that the deviation from geostrophic balance is proportional to the intensity of precipitation. Following these results, the authors investigate whether some improvements in the coupling between mass and rotational wind increments over precipitation areas can be achieved by using only the precipitation points within an ensemble of estimated forecast errors to construct a so-called diabatic balance operator by linear regression. Comparisons with a traditional approach to construct balance operators by linear regression show that the new approach leads to a gradually significant improvement (related to the intensity of the diabatic processes) of the accuracy of the coupling over precipitation areas as judged from an ensemble of lagged forecast differences. Results from a series of simplified data assimilation experiments show that the new balance operators can produce analysis increments that are substantially different from those associated with the traditional balance operator, particularly for observations located in the lower atmosphere. Issues concerning the implementation of this new approach in a full-fledged analysis system are briefly discussed but their investigations are left for a following study.

Weather Forecasts by the WRF-ARW Model with the GSI Data Assimilation System in the Complex Terrain Areas of Southwest Asia

2009 ◽  
Vol 24 (4) ◽  
pp. 987-1008 ◽  
Author(s):  
J. Xu ◽  
S. Rugg ◽  
L. Byerle ◽  
Z. Liu
Keyword(s):  
Data Assimilation ◽  
Satellite Data ◽  
Diurnal Cycle ◽  
Complex Terrain ◽  
Initial Conditions ◽  
Forecast Errors ◽  
Model Errors ◽  
Southwest Asia ◽  
Model Forecast ◽  
Near Surface

Abstract This paper will first describe the forecasting errors encountered from running the National Center for Atmospheric Research (NCAR) mesoscale model (the Advanced Research Weather Research and Forecasting model; ARW) in the complex terrain of southwest Asia from 1 to 31 May 2006. The subsequent statistical evaluation is designed to assess the model’s surface and upper-air forecast accuracy. Results show that the model biases caused by inadequate parameterization of physical processes are relatively small, except for the 2-m temperature, as compared to the nonsystematic errors resulting in part from the uncertainty in the initial conditions. The total model forecast errors at the surface show a substantial spatial heterogeneity; the errors are relatively larger in higher mountain areas. The performance of 2-m temperature forecasts is different from the other surface variables’ forecasts; the model forecast errors in 2-m temperature forecasts are closely related to the terrain configuration. The diurnal cycle variation of these near-surface temperature forecasts from the model is much smaller than what is observed. Second, in order to understand the role of the initial conditions in relation to the accuracy of the model forecasts, this study assimilated a form of satellite radiance data into this model through the Joint Center for Satellite Data Assimilation (JCSDA) analysis system called the Gridpoint Statistical Interpolation (GSI). The results indicate that on average over a 30-day experiment for the 24- and 48-h (second 24 h) forecasts, the satellite data provide beneficial information for improving the initial conditions and the model errors are reduced to some degree over some of the study locations. The diurnal cycle for some forecasting variables can be improved after satellite data assimilation; however, the improvement is very limited.

scholarly journals Growth of Forecast Errors from Covariances Modeled by 4DVAR and ETKF Methods

2011 ◽  
Vol 139 (5) ◽  
pp. 1505-1518 ◽  
Author(s):  
Chiara Piccolo
Keyword(s):  
Weather Forecasting ◽  
Initial Conditions ◽  
Forecast Error ◽  
Forecast Errors ◽  
Model Errors ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Numerical Weather Forecasting ◽  
Ensemble Transform Kalman Filter

Numerical weather forecasting errors grow with time. Error growth results from the amplification of small perturbations due to atmospheric instability or from model deficiencies during model integration. In current NWP systems, the dimension of the forecast error covariance matrices is far too large for these matrices to be represented explicitly. They must be approximated. This paper focuses on comparing the growth of forecast error from covariances modeled by the Met Office operational four-dimensional variational data assimilation (4DVAR) and ensemble transform Kalman filter (ETKF) methods over a period of 24 h. The growth of forecast errors implied by 4DVAR is estimated by drawing a random sample of initial conditions from a Gaussian distribution with the standard deviations given by the background error covariance matrix and then evolving the sample forward in time using linearized dynamics. The growth of the forecast error modeled by the ETKF is estimated by propagating the full nonlinear model in time starting from initial conditions generated by an ETKF. This method includes model errors in two ways: by using an inflation factor and by adding model perturbations through a stochastic physics scheme. Finally, these results are compared with a benchmark of the climatological error. The forecast error predicted by the implicit evolution of 4DVAR does not grow, regardless of the dataset used to generate the static background error covariance statistics. The forecast error predicted by the ETKF grows more rapidly because the ETKF selects balanced initial perturbations, which project onto rapidly growing modes. Finally, in both cases it is not possible to disentangle the contribution of the initial condition error from the model error.

Accounting for Model Errors in Ensemble Data Assimilation

2009 ◽  
Vol 137 (10) ◽  
pp. 3407-3419 ◽  
Author(s):  
Hong Li ◽  
Eugenia Kalnay ◽  
Takemasa Miyoshi ◽  
Christopher M. Danforth
Keyword(s):  
Kalman Filter ◽  
Forecast Errors ◽  
Random Errors ◽  
Model Errors ◽  
State Dependent ◽  
Constant Bias ◽  
Perfect Model ◽  
Ensemble Transform Kalman Filter ◽  
Low Dimensional ◽  
Bias Removal

Abstract This study addresses the issue of model errors with the ensemble Kalman filter. Observations generated from the NCEP–NCAR reanalysis fields are assimilated into a low-resolution AGCM. Without an effort to account for model errors, the performance of the local ensemble transform Kalman filter (LETKF) is seriously degraded when compared with the perfect-model scenario. Several methods to account for model errors, including model bias and system noise, are investigated. The results suggest that the two pure bias removal methods considered [Dee and Da Silva (DdSM) and low dimensional (LDM)] are not able to beat the multiplicative or additive inflation schemes used to account for the effects of total model errors. In contrast, when the bias removal methods are augmented by additive noise representing random errors (DdSM+ and LDM+), they outperform the pure inflation schemes. Of these augmented methods, the LDM+, where the constant bias, diurnal bias, and state-dependent errors are estimated from a large sample of 6-h forecast errors, gives the best results. The advantage of the LDM+ over other methods is larger in data-sparse regions than in data-dense regions.

scholarly journals Using Singular Value Decomposition to Parameterize State-Dependent Model Errors

2008 ◽  
Vol 65 (4) ◽  
pp. 1467-1478 ◽  
Author(s):  
Christopher M. Danforth ◽  
Eugenia Kalnay
Keyword(s):  
Singular Value Decomposition ◽  
Coupled System ◽  
Singular Value ◽  
Model Errors ◽  
Sampling Errors ◽  
Empirical Correction ◽  
State Dependent ◽  
Dependent Model ◽  
Value Decomposition ◽  
Lorenz 96

Abstract The purpose of the present study is to use a new method of empirical model error correction, developed by Danforth et al. in 2007, based on estimating the systematic component of the nonperiodic errors linearly dependent on the anomalous state. The method uses singular value decomposition (SVD) to generate a basis of model errors and states. It requires only a time series of errors to estimate covariances and uses negligible additional computation during a forecast integration. As a result, it should be suitable for operational use at a relatively small computational expense. The method is tested with the Lorenz ’96 coupled system as the truth and an uncoupled version of the same system as a model. The authors demonstrate that the SVD method explains a significant component of the effect that the model’s unresolved state has on the resolved state and shows that the results are better than those obtained with Leith’s empirical correction operator. The improvement is attributed to the fact that the SVD truncation effectively reduces sampling errors. Forecast improvements of up to 1000% are seen when compared with the original model. The improvements come at the expense of weakening ensemble spread.

scholarly journals Evolutionary modeling-based approach for model errors correction

2012 ◽  
Vol 19 (4) ◽  
pp. 439-447 ◽  
Author(s):  
S. Q. Wan ◽  
W. P. He ◽  
L. Wang ◽  
W. Jiang ◽  
W. Zhang
Keyword(s):  
Historical Data ◽  
Model Errors ◽  
Evolutionary Modeling ◽  
Research Topics ◽  
Dynamic Information ◽  
Lorenz Equation ◽  
New Approach ◽  
Numerical Tests ◽  
Correct Model ◽  
Self Learning

Abstract. The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model and the Lorenz equation with a periodic evolutionary function as an accurate representation of reality to generate "observational data." On the basis of the intelligent features of evolutionary modeling (EM), including self-organization, self-adaptive and self-learning, the dynamic information contained in the historical data can be identified and extracted by computer automatically. Thereby, a new approach is proposed to estimate model errors based on EM in the present paper. Numerical tests demonstrate the ability of the new approach to correct model structural errors. In fact, it can actualize the combination of the statistics and dynamics to certain extent.

scholarly journals Dynamical Properties of Model Output Statistics Forecasts

2008 ◽  
Vol 136 (2) ◽  
pp. 405-419 ◽  
Author(s):  
S. Vannitsem ◽  
C. Nicolis
Keyword(s):  
Space Velocity ◽  
Initial Condition ◽  
Model Output ◽  
Model Errors ◽  
State Dependent ◽  
Dependent Model ◽  
Dynamical Properties ◽  
Model Output Statistics ◽  
The Impact

Abstract The dynamical properties of forecasts corrected using model output statistics (MOS) schemes are explored, with emphasis on the respective role of model and initial condition uncertainties. Analytical and numerical investigations of low-order systems displaying chaos indicate that MOS schemes are able to partly correct the impact of both initial and model errors on model forecasting. Nevertheless the amplitude of the correction is much more sensitive to the presence of (state dependent) model errors, and if initial condition errors are much larger than model uncertainties then MOS schemes become less effective. Furthermore, the amplitude of the MOS correction depends strongly on the statistical properties of the phase space velocity difference between the model and reference systems, such as its mean and its covariance with the model predictors in the MOS scheme. Large corrections are expected when the predictors are closely related to the sources of model errors. The practical implications of these results are briefly discussed.

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