Assimilation of Precipitation and Nonlocal Observations in the LETKF, and Comparison of Coupled Data Assimilation Strategies with a Coupled Quasi-geostrophic Atmosphere-Ocean Model
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Among the data assimilation methods, the Ensemble Kalman Filter (EnKF) has gained popularity due to its ease of implementation and incorporation of the “errors of the day” [Kalnay, 2003]. While the EnKF can successfully assimilate a wide range of observations, it encounters difficulty handling two types of observations: a) observations with non-Gaussian errors such as hydrometeors and precipitation, and b) nonlocal (i.e., path-integrated) observations such as radiance, both of which are vital for weather monitoring and forecasting, since non-Gaussian observations are often associated with severe weather, and nonlocal observations contribute the most to the improved weather forecast skill in the modern assimilation systems. The satellite mission, the Global Precipitation Measurement (GPM), provides several products belonging to these two types of observations since its launch in 2014. Different strategies are developed in this dissertation to assimilate these two types of observations in the EnKF system.
To assimilate GPM surface precipitation with non-Gaussian errors, we extended the Gaussian transformation approach developed by Lien et al. [2013, 2016a, b] to a regional model. We transformed the observed and modeled precipitation into Gaussian variables, whose errors also become more Gaussian. We then allowed the transformed precipitation to adjust the dynamic variables and hydrometeors directly through the ensemble error covariance in the EnKF so that the model could “remember” the correct dynamics. Four typhoon cases in 2015 were studied to investigate the impact of GPM precipitation assimilation on typhoon forecast. Results show that model analysis by additional precipitation assimilation agrees more favorably with various independent observations, which leads to an improved typhoon forecast up to 72 hours.
Localizing nonlocal observations in the EnKF is another challenging problem. Observation localization is needed in the EnKF to reduce sampling errors caused by the small ensemble size. Unlike conventional observations with single observed locations, those nonlocal observations such as radiance are path-integrated measurements and do not have single observed locations. One common empirical single-layer vertical localization (SLVL) approach localizes nonlocal observations at their weighting function (WF) peaks with symmetric Gaussian-shape localization functions. While the SLVL approach is appropriate for observations with symmetric Gaussian-shaped WFs, it might have difficulty handling observations properly with broad asymmetric WFs or multiple WF peaks, which are typical for clear-sky radiance from sounding or trace-gas sensitive channels of hyperspectral infrared sensors. A multi-layer vertical localization (MLVL) method is developed as an extension of the SLVL, which explicitly considers the WF shape in the formulation and generates the localization value based on the cumulative influences from all components that constitute the nonlocal observations. Observing system simulation experiments assimilating 1-D and 3-D nonlocal observations show that the MLVL has comparable or better performance than the SLVL when assimilating narrow-WF observations, and superior performance than the SLVL when assimilating observations with broad WFs or multiple WF peaks.
In the last part, we switch our focus to coupled data assimilation in preparation for assimilating GPM precipitation into different earth components through strongly-coupled data assimilation. Few studies have systematically compared ensemble and variational methods with different coupled data assimilation (CDA) strategies (i.e., uncoupled DA (UCDA), weakly-coupled DA (WCDA), and strongly-coupled DA (SCDA)) for coupled models, though such comparison are essential to understand different methods and have been extensively conducted for uncoupled models. We developed a coupled data assimilation testbed for a coupled quasi-geostrophic atmosphere-ocean model that allows systematic comparison between ensemble and variational methods under different CDA strategies. Results show that WCDA and SCDA improve the coupled analysis compared with UCDA for both 3D-Var and ETKF. It is found that the ocean analysis by SC ETKF is consistently better than the one by WC ETKF, a phenomenon not observed for the 3D-Var method. Different SCDA methods are then compared together under different observation networks. When both atmosphere and ocean observations are assimilated, the SC incremental 4D-Var and ETKF share a similar analysis RMSE smaller than SC 3D-Var, for both atmosphere and ocean. An ECMWF CERA-like assimilation system, which adopts the outer-loop-coupling approach instead of utilizing the coupled-state background error covariance, achieves a similar RMSE as the SC 4D-Var and ETKF. When only atmospheric observations are assimilated, all variational-based DA methods using static background error covariance fail to stabilize the RMSE for the ocean within the experiment periods (about 27.4 years), while the flow-dependent ETKF does stabilize the analysis after about 10 years. Among all the variational systems, CERA shows larger ocean analysis RMSE than SC 3D-Var and 4D-Var, which indicates the outer-loop-coupling alone is not enough to replace the role of a coupled-state background error covariance.