Deriving Bayesian Posterior Distributions for Weather Research and Forecasting (WRF) Model Parameters: Enhancing Severe Typhoon Prediction Near Japan

Typhoons are one of the most severe meteorological phenomena that cause various disasters due to intense rainfall, strong winds, and storm surges. Improving the accuracy of typhoon forecasts using meteorological models is crucial for mitigating these disasters. The accuracy of the widely used WRF (Weather Research and Forecasting) model has been enhanced through various studies, including methods to improve the parameters of its physical schemes. The WRF model contains numerous adjustable parameters, and it is well-known that changes in these parameters can significantly alter the outcomes. While a bottom-up approach can be employed to adjust the parameters of each scheme based on fundamental principles, the complex interactions between multiple parameters often necessitate further adjustments to other parameters, which means that adjusting one parameter may not always improve typhoon prediction accuracy. Consequently, various methods have been developed to calibrate multiple parameters simultaneously. In this study, 23 parameters were selected from WRF’s surface layer scheme, cumulus scheme, microphysics scheme, shortwave radiation, longwave radiation, land surface, and boundary layer schemes to evaluate their impact on typhoon reproducibility and to explore more appropriate parameter values. Specifically, we used the error between observations and WRF model predictions as a skill score or likelihood to derive the posterior distribution of parameter values using Bayesian estimation. The posterior distributions obtained from this process provide helpful information for data assimilation with time-varying model parameters, serving as constraints on the parameters. This study focuses on very strong typhoons that rapidly develop over the southern seas near Japan. Due to the limited availability of observational data over the ocean, we used longwave radiation data from the Himawari geostationary satellite. Previous research has primarily focused on calibrating WRF parameters using ground-based observational data, such as wind speed, temperature, and precipitation, while few studies have utilized satellite data. Therefore, this study attempts to improve typhoon prediction accuracy using satellite data. To obtain robust results applicable to various typhoons, we analyzed multiple strong typhoons: Jebi (2018), Hagibis (2019), Haishen (2020), and Nanmadol (2022). Initially, we performed a sensitivity analysis of the 23 parameters to the satellite brightness temperature of Himawari and found that two microphysics scheme parameters and one boundary layer scheme parameter exhibited significant sensitivity. We then focused on improving the values of these three parameters and estimated their posterior distributions. We assumed a uniform prior distribution around the standard WRF parameter value for the Bayesian estimation of model parameters. Using 300 parameter combinations from the prior distribution, we conducted WRF simulations for each of the typhoon cases and compared the spatial distributions of longwave brightness temperatures with the observations from Himawari. We evaluated their error using SSIM (Structural Similarity Index), which can ignore slight positional deviations in typhoons when comparing spatial distributions, and used it as the likelihood function for calculating posterior distributions via the MCMC (Markov Chain Monte Carlo) method. Since the MCMC method requires numerous SSIM calculations between WRF and observational data, running WRF simulations for each iteration is practically impossible. To avoid this, we constructed a surrogate model using Gaussian process regression from the 300-member simulation results for use in the MCMC calculations. When estimating parameters using Himawari data, we found that one of the microphysics scheme parameters (the scaling factor applied to ice fall velocity) exhibited the highest sensitivity to the brightness temperature distribution in the WRF output. Increasing this factor significantly from the default value of 14,900 to around 39,000-43,000 improved accuracy, although the optimal value varied by typhoon case. When WRF simulations were rerun using the posterior distributions of the three sensitive parameters that were analyzed, SSIM improved, indicating enhanced reproducibility of the spatial distribution of brightness temperature. Parameter calibration using Himawari brightness temperature did not result in significant improvements in typhoon intensity, track, or precipitation distribution. The schemes used in this experiment resulted in smaller cloud and precipitation areas compared to observations, suggesting potential improvement by replacing the physical schemes. The advantage of this method lies in its consistent approach to parameter improvement, applicable to any scheme. In the future, we plan to apply this method to various schemes and work on improving typhoon accuracy using satellite data.