Multivariate ensemble sensitivity analysis applied for an extreme rainfall over Indian subcontinent

Ensemble sensitivity analysis (ESA) uses sample statistics of ensemble forecasts to estimate relationships between forecast metrics and initial conditions. The ensemble sensitivity analysis is often considered as a simple univariate regression as it includes an approximation of analysis covariance matrix with corresponding diagonal elements. In this work, univariate ensemble sensitivity is extended to multivariate ensemble sensitivity that incorporates the contribution from the full covariance matrix in the sensitivity calculations. The performance of multivariate ensemble sensitivity over univariate is examined for meso- and convective scale ensemble forecasts of a heavy rainfall event that happened over the Chennai city in India in December 2015. The ensemble forecasts and analyses are generated using the Advanced Research - Weather Research and Forecasting (WRF) model Data Assimilation Research Testbed (DART) based Ensemble Kalman Filter (EnKF). Multivariate ensemble sensitivity shows organized sensitivity patterns, while the sensitivity values are found to be broadly distributed in univariate ensemble sensitivity. Both the methods are validated using a perturbed initial condition approach, and the results indicate that the multivariate ensemble sensitivity method is effective in predicting the forecast response closest to the actual model response compared to the univariate ensemble sensitivity. The impact of model error on sensitivity calculations is examined by generating a new set of ensembles that uses the Stochastic Kinetic Energy Backscatter Scheme (SKEBS). In the presence of added model error, the forecast response estimated by multivariate using SKEBS ensembles compares better with the actual response. It is found that the performance of the multivariate approach depends on the optimal choice of localization radius, and if insufficient localization is applied, the spurious long-distance correlation contaminates the performance of the multivariate ensemble sensitivity method. The impact of various forecast lead times on the univariate and multivariate ensemble sensitivity analysis indicates that responses using multivariate ensemble sensitivity are more accurate than univariate, especially at longer lead times when nonlinearity becomes significant. The performance of univariate and multivariate methods in convection-permitting scale is examined by using the high-resolution ensemble forecasts, and it is found that the multivariate sensitivity with localization substantially improves the estimates in finer scales.