4D-Var Assimilation Method Research Articles

Application of multigrid NLS-4DVar in radar radial velocity data assimilation with WRF-ARW

The nonlinear least-squares four-dimensional variational assimilation (NLS-4DVar) method introduced here combines the merits of the ensemble Kalman filter and 4DVar assimilation methods. The multig...

Handling non-linearity in radar data assimilation using the non-linear least squares enhanced POD-4DVar

The Proper Orthogonal Decomposition (POD)-based ensemble four-dimensional variational (4DVar) assimilation method (POD4DEnVar) was proposed to combine the strengths of EnKF (i.e., the ensemble Kalman filter) and 4DVar assimilation methods. Recently, a POD4DEnVar-based radar data assimilation scheme (PRAS) was built and its effectiveness was demonstrated. POD4DEnVar is based on the assumption of a linear relationship between the model perturbations (MPs) and the observation perturbations (OPs); however, this assumption is likely to be destroyed by the highly non-linear forecast model or observation operator. To address this issue, using the Gauss-Newton iterative method, the nonlinear least squares enhanced POD4DEnVar algorithm (referred to as NLS-4DVar) was proposed. Naturally, the PRAS was upgraded to form the NLS-4DVar-based radar data assimilation scheme (NRAS). To evaluate the performance of NRAS against PRAS, observing system simulation experiments (OSSEs) were conducted to assimilate reflectivity and radial velocity individually, with one, two, and three iterations. The results demonstrated that the NRAS outperformed PRAS in improving the initial condition and the forecasting of model variables and rainfall. The NRAS, with a smaller number of iterations, can yield a convergent result. In contrast to the situation when assimilating radial velocity, the advantages of NRAS over PRAS were more obvious when assimilating reflectivity.

Estimation of Volcanic Ash Emissions Using Trajectory-Based 4D-Var Data Assimilation

Abstract Volcanic ash forecasting is a crucial tool in hazard assessment and operational volcano monitoring. Emission parameters such as plume height, total emission mass, and vertical distribution of the emission plume rate are essential and important in the implementation of volcanic ash models. Therefore, estimation of emission parameters using available observations through data assimilation could help to increase the accuracy of forecasts and provide reliable advisory information. This paper focuses on the use of satellite total-ash-column data in 4D-Var based assimilations. Experiments show that it is very difficult to estimate the vertical distribution of effective volcanic ash injection rates from satellite-observed ash columns using a standard 4D-Var assimilation approach. This paper addresses the ill-posed nature of the assimilation problem from the perspective of a spurious relationship. To reduce the influence of a spurious relationship created by a radiate observation operator, an adjoint-free trajectory-based 4D-Var assimilation method is proposed, which is more accurate to estimate the vertical profile of volcanic ash from volcanic eruptions. The method seeks the optimal vertical distribution of emission rates of a reformulated cost function that computes the total difference between simulated and observed ash columns. A 3D simplified aerosol transport model and synthetic satellite observations are used to compare the results of both the standard method and the new method.

PODEn4DVar-based radar data assimilation scheme: formulation and preliminary results from real-data experiments with advanced research WRF (ARW)

The Proper Orthogonal Decomposition (POD)-based ensemble four-dimensional variational (4DVar) assimilation method (referred to as PODEn4DVar) is a hybrid assimilation method that exploits the strengths of both the ensemble Kalman filter (EnKF) and the 4DVar assimilation method. Its feasibility and validity have been demonstrated using ideal models through observing system simulation experiments (OSSEs). In this study, we further utilise this approach to build a PODEn4DVar-based radar data assimilation scheme (PRAS). In a PRAS, radar observations including radial velocity and reflectivity, after some necessary data preprocessing, are assimilated directly to improve model initialisation. A group of single-observation-based OSSEs are first designed to generally evaluate the validity of PRAS. Subsequently, a group of comparison experiments are also carried out between PRAS and an LETKF-based radar assimilation scheme (LRAS), which shows that PRAS is able to produce results better than (at least as good as) LRAS. Thirdly, to evaluate the potential impact for PRAS in the operational context, a group of cycling assimilation experiments of radar data are performed, which demonstrates that PRAS can gradually improve the accuracy of analysis field by cycling assimilation. Finally, a heavy convective-rainfall case study was selected to investigate the performance of PRAS in assimilating real radar observations and the impacts of assimilating radar observations on numerical forecasts, with the Weather Research and Forecasting (WRF) model as our forecasting model. The results show that significant improvements in predicting heavy rainfall can be achieved due to the improved initial conditions for the convective system's dynamics and microphysics after assimilating the radar observations with PRAS. In summary, the results show that the PODEn4DVar is a promising method for atmospheric data assimilation.

Comparison of the ensemble Kalman filter and 4D-Var assimilation methods using a stratospheric tracer transport model

Abstract. An ensemble Kalman filter (EnKF) assimilation method is applied to the tracer transport using the same stratospheric transport model as in the four-dimensional variational (4D-Var) assimilation system BASCOE (Belgian Assimilation System for Chemical ObsErvations). This EnKF version of BASCOE was built primarily to avoid the large costs associated with the maintenance of an adjoint model. The EnKF developed in BASCOE accounts for two adjustable parameters: a parameter α controlling the model error term and a parameter r controlling the observational error. The EnKF system is shown to be markedly sensitive to these two parameters, which are adjusted based on the monitoring of a χ2 test measuring the misfit between the control variable and the observations. The performance of the EnKF and 4D-Var versions was estimated through the assimilation of Aura-MLS (microwave limb sounder) ozone observations during an 8-month period which includes the formation of the 2008 Antarctic ozone hole. To ensure a proper comparison, despite the fundamental differences between the two assimilation methods, both systems use identical and carefully calibrated input error statistics. We provide the detailed procedure for these calibrations, and compare the two sets of analyses with a focus on the lower and middle stratosphere where the ozone lifetime is much larger than the observational update frequency. Based on the observation-minus-forecast statistics, we show that the analyses provided by the two systems are markedly similar, with biases less than 5% and standard deviation errors less than 10% in most of the stratosphere. Since the biases are markedly similar, they most probably have the same causes: these can be deficiencies in the model and in the observation data set, but not in the assimilation algorithm nor in the error calibration. The remarkably similar performance also shows that in the context of stratospheric transport, the choice of the assimilation method can be based on application-dependent factors, such as CPU cost or the ability to generate an ensemble of forecasts.

Assimilation of Earth rotation parameters into a global ocean model: excitation of polar motion

Abstract. The oceanic contribution to Earth rotation anomalies can be manifold. Possible causes are a change of total ocean mass, changes in current speed or location and changes in mass distribution. To derive the governing physical mechanisms of oceanic Earth rotation excitation we assimilate Earth rotation observations with a global circulation ocean model. Before assimilation, observations of length of day and polar motion were transformed into estimates of ocean angular momentum. By using the adjoint 4D-VAR assimilation method we were able to reproduce these estimated time series. Although length of day was assimilated simultaneously the analysis in this paper focuses on the oceanic polar motion generation. Our results show that changes in mass distribution and currents contribute to oceanic polar motion generation. Both contributions are highly correlated and show similar amplitudes. The changes in the model done by the assimilation procedure could be related to changes in the atmospheric forcing. Since for geometrical reasons the change of total ocean mass does not project on polar motion, we conclude that the polar motion is mainly generated by a geostrophic response to atmospheric momentum forcing. In geostrophic currents mass displacement and current speed entail each other. This way the large similarity of mass and current generated ocean angular momentum can be explained.

Simulation of a Midlatitude Convective Storm Initialized with Bistatic Doppler Radar Data

An analysis is developed to initialize a cloud-resolving model from an explicit structure of a precipitating convective system derived from multiple-Doppler radar observations. The different fields of the model prognostic variables that compose the initial state of the simulation are estimated or retrieved using a 4DVAR assimilation method in which the model is used as a weak constraint using two time level observations. This allows for the retrieval of physical fields consistent with the observations and the equations of the model. This method is applied on a midlatitude summer storm sampled by the McGill bistatic Doppler radar network that occurred on 2 August 1997. During the 30-min-forward simulation, the model succeeds in representing the observed features of the three main cells that compose the storm in terms of precipitation distribution and evolution of the convective activity. After this period, the model produces less stratiform precipitations. Comparisons with a Lagrangian persistency prediction are performed and show a notable improvement in the short-term forecast.

The Impact of Observational and Model Errors on Four-Dimensional Variational Data Assimilation

The impact of observational and model errors on four-dimensional variational (4DVAR) data assimilation is analyzed for a general dynamical system. Numerical experiments with both the barotropic vorticity equation and the shallow water system are conducted. It is shown from the analysis and the numerical experiments that when there are random errors in observations or in model parameterizations, the 4DVAR assimilation method can suppress these errors; however, when the errors are systematic or biased, the 4DVAR assimilation method tends to either converge to the erroneous observations or introduce the model error into the data analysis, or both. For a multiple-timescale fluid dynamical system, such as the shallow water equations with fluid depth corresponding to the external mode, the skewness in the system can amplify the errors, especially in the fast variable (e.g., the geopotential or height field). Forecasts using the assimilated initial condition with an imperfect model indicate that the forecasts may or may not be improved, depending upon the nature of the model and observational errors, and the length of the assimilation and forecast periods.