scholarly journals A Comparison of the Hybrid and EnSRF Analysis Schemes in the Presence of Model Errors due to Unresolved Scales

2009 ◽  
Vol 137 (10) ◽  
pp. 3219-3232 ◽  
Author(s):  
Xuguang Wang ◽  
Thomas M. Hamill ◽  
Jeffrey S. Whitaker ◽  
Craig H. Bishop
Keyword(s):  
Model Comparison ◽  
Additive Noise ◽  
Initial Conditions ◽  
Random Noise ◽  
Model Error ◽  
Forecast Errors ◽  
Model Errors ◽  
Hybrid Analysis ◽  
Error Covariance ◽  
Analysis Scheme

Abstract A hybrid analysis scheme is compared with an ensemble square root filter (EnSRF) analysis scheme in the presence of model errors as a follow-up to a previous perfect-model comparison. In the hybrid scheme, the ensemble perturbations are updated by the ensemble transform Kalman filter (ETKF) and the ensemble mean is updated with a hybrid ensemble and static background-error covariance. The experiments were conducted with a two-layer primitive equation model. The true state was a T127 simulation. Data assimilation experiments were conducted at T31 resolution (3168 complex spectral coefficients), assimilating imperfect observations drawn from the T127 nature run. By design, the magnitude of the truncation error was large, which provided a test on the ability of both schemes to deal with model error. Additive noise was used to parameterize model errors in the background ensemble for both schemes. In the first set of experiments, additive noise was drawn from a large inventory of historical forecast errors; in the second set of experiments, additive noise was drawn from a large inventory of differences between forecasts and analyses. The static covariance was computed correspondingly from the two inventories. The hybrid analysis was statistically significantly more accurate than the EnSRF analysis. The improvement of the hybrid over the EnSRF was smaller when differences of forecasts and analyses were used to form the random noise and the static covariance. The EnSRF analysis was more sensitive to the size of the ensemble than the hybrid. A series of tests was conducted to understand why the EnSRF performed worse than the hybrid. It was shown that the inferior performance of the EnSRF was likely due to the sampling error in the estimation of the model-error covariance in the mean update and the less-balanced EnSRF initial conditions resulting from the extra localizations used in the EnSRF.

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.

The Geometry of Model Error

2008 ◽  
Vol 65 (6) ◽  
pp. 1749-1772 ◽  
Author(s):  
Kevin Judd ◽  
Carolyn A. Reynolds ◽  
Thomas E. Rosmond ◽  
Leonard A. Smith
Keyword(s):  
Weather Forecasting ◽  
Model Space ◽  
Forecast Model ◽  
Model Error ◽  
Forecast Errors ◽  
Model Errors ◽  
Direction Error ◽  
Forecasting System ◽  
Projection Error ◽  
Low Dimensional

Abstract This paper investigates the nature of model error in complex deterministic nonlinear systems such as weather forecasting models. Forecasting systems incorporate two components, a forecast model and a data assimilation method. The latter projects a collection of observations of reality into a model state. Key features of model error can be understood in terms of geometric properties of the data projection and a model attracting manifold. Model error can be resolved into two components: a projection error, which can be understood as the model’s attractor being in the wrong location given the data projection, and direction error, which can be understood as the trajectories of the model moving in the wrong direction compared to the projection of reality into model space. This investigation introduces some new tools and concepts, including the shadowing filter, causal and noncausal shadow analyses, and various geometric diagnostics. Various properties of forecast errors and model errors are described with reference to low-dimensional systems, like Lorenz’s equations; then, an operational weather forecasting system is shown to have the same predicted behavior. The concepts and tools introduced show promise for the diagnosis of model error and the improvement of ensemble forecasting systems.

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.

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.

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 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 A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 2: Optimization scheme and identical twin experiment of atmospheric CO<sub>2</sub> inversion

2017 ◽  
Vol 10 (6) ◽  
pp. 2201-2219 ◽  
Author(s):  
Yosuke Niwa ◽  
Yosuke Fujii ◽  
Yousuke Sawa ◽  
Yosuke Iida ◽  
Akihiko Ito ◽  
...  
Keyword(s):  
Transport Model ◽  
Surface Fluxes ◽  
Identical Twin ◽  
Inversion Problem ◽  
Model Errors ◽  
Optimization Scheme ◽  
Error Covariance ◽  
Optimal Setting ◽  
Source Sink ◽  
Quasi Newton

Abstract. A four-dimensional variational method (4D-Var) is a popular technique for source/sink inversions of atmospheric constituents, but it is not without problems. Using an icosahedral grid transport model and the 4D-Var method, a new atmospheric greenhouse gas (GHG) inversion system has been developed. The system combines offline forward and adjoint models with a quasi-Newton optimization scheme. The new approach is then used to conduct identical twin experiments to investigate optimal system settings for an atmospheric CO2 inversion problem, and to demonstrate the validity of the new inversion system. In this paper, the inversion problem is simplified by assuming the prior flux errors to be reasonably well known and by designing the prior error correlations with a simple function as a first step. It is found that a system of forward and adjoint models with smaller model errors but with nonlinearity has comparable optimization performance to that of another system that conserves linearity with an exact adjoint relationship. Furthermore, the effectiveness of the prior error correlations is demonstrated, as the global error is reduced by about 15 % by adding prior error correlations that are simply designed when 65 weekly flask sampling observations at ground-based stations are used. With the optimal setting, the new inversion system successfully reproduces the spatiotemporal variations of the surface fluxes, from regional (such as biomass burning) to global scales. The optimization algorithm introduced in the new system does not require decomposition of a matrix that establishes the correlation among the prior flux errors. This enables us to design the prior error covariance matrix more freely.

scholarly journals Rapid estimation of earthquake locations using waveform traveltimes

2019 ◽  
Vol 217 (3) ◽  
pp. 1727-1741 ◽  
Author(s):  
D W Vasco ◽  
Seiji Nakagawa ◽  
Petr Petrov ◽  
Greg Newman
Keyword(s):  
Standard Error ◽  
Random Noise ◽  
Grid Point ◽  
Synthetic Data ◽  
Velocity Model ◽  
Source Location ◽  
Model Errors ◽  
Average Deviation ◽  
Origin Time ◽  
Data Set

SUMMARY We introduce a new approach for locating earthquakes using arrival times derived from waveforms. The most costly computational step of the algorithm scales as the number of stations in the active seismographic network. In this approach, a variation on existing grid search methods, a series of full waveform simulations are conducted for all receiver locations, with sources positioned successively at each station. The traveltime field over the region of interest is calculated by applying a phase picking algorithm to the numerical wavefields produced from each simulation. An event is located by subtracting the stored traveltime field from the arrival time at each station. This provides a shifted and time-reversed traveltime field for each station. The shifted and time-reversed fields all approach the origin time of the event at the source location. The mean or median value at the source location thus approximates the event origin time. Measures of dispersion about this mean or median time at each grid point, such as the sample standard error and the average deviation, are minimized at the correct source position. Uncertainty in the event position is provided by the contours of standard error defined over the grid. An application of this technique to a synthetic data set indicates that the approach provides stable locations even when the traveltimes are contaminated by additive random noise containing a significant number of outliers and velocity model errors. It is found that the waveform-based method out-performs one based upon the eikonal equation for a velocity model with rapid spatial variations in properties due to layering. A comparison with conventional location algorithms in both a laboratory and field setting demonstrates that the technique performs at least as well as existing techniques.

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

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