Optimized Stochastic Representation of Soil States Model Uncertainty of WRF (v4.2) in the Ensemble Data Assimilation System

Abstract. The ensemble data assimilation (EDA) system represents the model uncertainties by ensemble spread that is a standard deviation of ensemble background error covariance (BEC). However, this ensemble spread is usually underestimated due to insufficient ensemble size, sampling errors, and imperfect models: it often causes a filter divergence problem as the analysis ignores the observation due to insufficient model uncertainty. This phenomenon is also found in the coupled land-atmospheric modeling system, especially near the surface where the heat flux exchanges are crucial as the lower boundary conditions. We have developed the stochastic perturbations to soil states scheme (SPSS) within the coupled Weather Research and Forecasting-Noah Land Surface Model (WRF-Noah LSM) to represent the near surface uncertainty. It perturbs soil temperature and soil moisture, respectively, by adding the random forcing to inflate the ensemble spread. The random forcing used in perturbation is controlled by the tuning parameters such as amplitude, decorrelation length and time scale, which vary depending on the target variables. To obtain the optimal random forcing tuning parameters to the soil states, we have implemented a global optimization algorithm – the micro-genetic algorithm, which operates the principles of natural selection or survival of the fittest to evolve the best potential solution having small populations. Optimizations are performed on daytime and nighttime to account for diurnal variations of soil states and evaluated by a fitness function that describes the interaction between the land and atmospheric systems in terms of accuracy. As a result, the soil temperature and soil moisture perturbations with SPSS can indirectly inflate the ensemble BECs of temperature and water vapor mixing ratio in the planetary boundary layer (PBL) of the EDA system. The SPSS with diurnal variations depicts reasonable ensemble spread for soil states, but the ensemble spread for atmospheric states from the propagation of the soil states perturbations is less effective. Furthermore, the inflated soil temperature helps to produce an adequate analysis increment reducing the background error of temperature in PBL. Soil moisture, however, requires more prescriptions to generate an adequate analysis increment reducing the background error of water vapor mixing ratio in PBL.