A Constraint Method for Supersaturation in a Variational Data Assimilation System

Ken Sawada,Yuki Honda

doi:10.1175/mwr-d-20-0357.1

Abstract

Abstract The reproducibility of precipitation in the early stages of forecasts, often called a spindown or spinup problem, has been a significant issue in numerical weather prediction. This problem is caused by moisture imbalance in the analysis data, and in the case of the Japan Meteorological Agency’s (JMA’s) mesoscale data assimilation system, JNoVA, we found that the imbalance stems from the existence of unrealistic supersaturated states in the minimal solution of the cost function in JNoVA. Based on the theory of constrained optimization problems, we implemented an exterior penalty function method for the mixing ratio within JNoVA to suppress unrealistic supersaturated states. The advantage of this method is the simplicity of its theory and implementation. The results of twin data assimilation cycle experiments conducted for the heavy rain event of July 2018 over Japan show that—with the new method—unrealistic supersaturated states are reduced successfully, negative temperature bias to the observations is alleviated, and a sharper distribution of the mixing ratio is obtained. These changes help to initiate the development of convection at the proper location and improve the fractions skill score (FSS) of precipitation in the early stages of the forecast. From these results, we conclude that the initial shock caused by moisture imbalance is mitigated by implementing the penalty function method, and the new moisture balance has a positive impact on the reproducibility of precipitation in the early stages of forecasts.

Highlights

The reproducibility of precipitation in the early stages of forecasts, especially for the spindown problem, has been an issue in numerical weather prediction since the resolution of forecast models reached the convective scale, i.e., 1–10 km
We have introduced an exterior penalty function method into the minimization process employed in variational assimilation in order to suppress nonphysical supersaturated or negative moisture states and to reduce the moisture imbalance in the analysis data that may cause a degradation of the precipitation reproducibility
The exterior penalty function method is a numerical algorithm used for solving constrained optimization problems, and the simplicity of implementing it within the assimilation procedure is a significant advantage

Summary

Introduction

The reproducibility of precipitation in the early stages of forecasts, especially for the spindown problem (spurious excessive precipitation), has been an issue in numerical weather prediction since the resolution of forecast models reached the convective scale, i.e., 1–10 km. The major method for handling the moisture imbalance problem is to construct proper control variables (parameters) This involves selecting valid moisture variables that are convenient for considering the balance with other variables at the convective scale (depending on the numerical models or the atmospheric states) and/or applying nonlinear transformations to obtain a Gaussian-like error distribution (Hólm et al 2002; Gustafsson et al 2018; Ingleby et al 2013). In this paper we aim to obtain a minimal solution that has a more realistic moisture balance and that suits our forecast model by suppressing the unrealistic moisture states better in the minimizing process of the variational method For this purpose, we propose implementing an exterior penalty function method in the constrained optimization problem.

Penalty function method

Findings

Summary