Four-dimensional Variational Data Assimilation Scheme Research Articles

A Multi-Time-Scale Four-Dimensional Variational Data Assimilation Scheme and Its Application to Simulated Radial Velocity and Reflectivity Data

AbstractIn this study, a multi-time-scale four-dimensional variational data assimilation (MTS-4DVar) scheme is developed and applied to the assimilation of radar observations. The MTS-4DVar employs multitime windows with various time lengths in the framework of incremental 4DVar in the Weather Research and Forecasting Data Assimilation (WRFDA). The objective of MTS-4DVar is to enable the 4DVar data assimilation system to extract multiscale information from radar observations, and the algorithm of MTS-4DVar is first discussed in detail. Using a heavy rainfall case, it is shown that the nonlinearity growth of reflectivity is faster than that of radial velocity, suggesting that the time window for assimilating reflectivity in the incremental 4DVar should be shorter than that of radial velocity. A series of single observation tests and observing system simulation experiments (OSSEs) are then presented to examine the physical characteristics and performance of MTS-4DVar. These experiments demonstrate that the MTS-4DVar is capable of combining the larger-scale information from a longer time window and the local-scale features from a shorter time window. With the OSSEs it is shown that the value of the cost function is reduced properly in the minimization of the MTS-4DVar with a combination of longer and shorter time windows. By assimilating the radar radial velocity alone, we found that the MTS-4DVar reduces the analysis and forecast errors and improves the precipitation forecasts in comparison with the normal incremental 4DVar. Additional assimilation of reflectivity further improved the precipitation forecasts, and the results show that the radar reflectivity can also be well assimilated by using MTS-4DVar.

Upper Ocean Four-Dimensional Variational Data Assimilation in the Arabian Sea and Bay of Bengal

ABSTRACTA regional ocean circulation model with four-dimensional variational data assimilation scheme is configured to study the ocean state of the Indian Ocean region (65°E–95°E; 5°N–20°N) covering the Arabian Sea (AS) and Bay of Bengal (BoB). The state estimation setup uses 10 km horizontal resolution and 5 m vertical resolution in the upper ocean. The in-situ temperature and salinity, satellite-derived observations of sea surface height, and blended (in-situ and satellite-derived) observations of sea surface temperature alongwith their associated uncertainties are used for data assimilation with the regionally configured ocean model. The ocean state estimation is carried out for 61 days (1 June to 31 July 2013). The assimilated fields are closer to observations compared to other global state estimates. The mixed layer depth (MLD) of the region shows deepening during the period of assimilation with AS showing higher MLD compared to the BoB. An empirical forecast equation is derived for the prediction of MLD using the air–sea forcing variables as predictors. The surface and sub-surface (50 m) heat and salt budget tendencies of the region are also investigated. It is found that at the sub-surface, only the advection and diffusion temperature and salt tendencies are important.

An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part II: Observing System Simulation Experiments with Advanced Research WRF (ARW)

Abstract An ensemble-based four-dimensional variational data assimilation (En4DVAR) algorithm and its performance in a low-dimension space with a one-dimensional shallow-water model have been presented in Part I. This algorithm adopts the standard incremental approach and preconditioning in the variational algorithm but avoids the need for a tangent linear model and its adjoint so that it can be easily incorporated into variational assimilation systems. The current study explores techniques for En4DVAR application in real-dimension data assimilation. The EOF decomposed correlation function operator and analysis time tuning are formulated to reduce the impact of sampling errors in En4DVAR upon its analysis. With the Advanced Research Weather Research and Forecasting (ARW-WRF) model, Observing System Simulation Experiments (OSSEs) are designed and their performance in real-dimension data assimilation is examined. It is found that the designed En4DVAR localization techniques can effectively alleviate the impacts of sampling errors upon analysis. Most forecast errors and biases in ARW are reduced by En4DVAR compared to those in a control experiment. En3DVAR cycling experiments are used to compare the ensemble-based sequential algorithm with the ensemble-based retrospective algorithm. These experiments indicate that the ensemble-based retrospective assimilation, En4DVAR, produces an overall better analysis than the ensemble-based sequential algorithm, En3DVAR, cycling approach.

An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test

Abstract Applying a flow-dependent background error covariance (𝗕 matrix) in variational data assimilation has been a topic of interest among researchers in recent years. In this paper, an ensemble-based four-dimensional variational (En4DVAR) algorithm, designed by the authors, is presented that uses a flow-dependent background error covariance matrix constructed by ensemble forecasts and performs 4DVAR optimization to produce a balanced analysis. A great advantage of this En4DVAR design over standard 4DVAR methods is that the tangent linear and adjoint models can be avoided in its formulation and implementation. In addition, it can be easily incorporated into variational data assimilation systems that are already in use at operational centers and among the research community. A one-dimensional shallow water model was used for preliminary tests of the En4DVAR scheme. Compared with standard 4DVAR, the En4DVAR converges well and can produce results that are as good as those with 4DVAR but with far less computation cost in its minimization. In addition, a comparison of the results from En4DVAR with those from other data assimilation schemes [e.g., 3DVAR and ensemble Kalman filter (EnKF)] is made. The results show that the En4DVAR yields an analysis that is comparable to the widely used variational or ensemble data assimilation schemes and can be a promising approach for real-time applications. In addition, experiments were carried out to test the sensitivities of EnKF and En4DVAR, whose background error covariance is estimated from the same ensemble forecasts. The experiments indicated that En4DVAR obtained reasonably sound analysis even with larger observation error, higher observation frequency, and more unbalanced background field.

Performance of the ECMWF Operational Analyses over the Tropical Indian Ocean

The quality of the ECMWF operational analyses is evaluated against independent upper-air sounding data collected during the Joint Air–Sea Monsoon Interaction Experiment (JASMINE; April–May 1999) and the Indian Ocean Experiment (INDOEX; February–March 1999). Statistics of the difference between observations and analyses are compiled for temperature, humidity, and wind speed. The results show that the analyzed temperature has a cold bias between 1000 and 750 hPa. However, in the upper troposphere, a warm bias occurs between 350 and 150 hPa, while a cold bias is seen above 150 hPa. Compared to the observations, the analyzed humidity is lower between 1000 and 950 hPa and higher between 950 and 750 hPa. The analyzed wind speeds are close to observations over much of the troposphere, except near the tropopause, where they are overestimated by 1–2 m s−1 in the analyses. The low-level (1000– 750 hPa) biases in moisture and temperature in the ECMWF analyses over the Indian Ocean are similar to those reported for the tropical Pacific Ocean in past studies. The occurrence of a cold and dry bias in the lowest 50 hPa indicates reduced convective available potential energy, which will render difficult the initiation and development of convection in numerical models initialized with these analyses. The moisture biases arise most likely because of the poor fit to humidity observations by the four-dimensional variational data assimilation scheme. This suggests that a better fit to humidity observations will yield an improved water vapor climatology over the Arabian Sea and Indian Ocean.