A Multivariate Additive Inflation Approach to Improve Storm‐Scale Ensemble‐Based Data Assimilation and Forecasts: Methodology and Experiment With a Tornadic Supercell

Abstract

Recently, multiple ensemble-based data assimilation (DA) methods, such as the ensemble Kalman filter (e.g.,

Improving CONUS Convective‐Scale Forecasting With Simultaneous Multiscale Data Assimilation

“…In this study, the mathematical formulation of simultaneous multiscale DA using SDL and VDL in the GSI‐based EnVar system is identical to Wang and Wang (2023b), with notations also mirroring Wang (2010), Wang et al. (2013, 2021), Wang and Lei (2014) and Huang et al.…”

“…Following the study of Huang et al. (2021) and Wang and Wang (2023b), SDL and VDL are implemented by further extending the control variable a , which concatenates the vectors a k , k = 1, …, K . The k th control variable vector a k is further extended for each decomposed scale and each partitioned variable group, and denotes as, $$${\mathbf{a}}_{k}=\left[\begin{array}{@{}c@{}}{\mathbf{a}}_{k,1}\\ {\mathbf{a}}_{k,2}\\ \begin{array}{c}{\vdots}\\ {\mathbf{a}}_{k,J}\end{array}\end{array}\right],\text{and}\,{\mathbf{a}}_{k,j}=\left[\begin{array}{@{}c@{}}{\mathbf{a}}_{k,j,1}\\ {\mathbf{a}}_{k,j,2}\\ \begin{array}{c}{\vdots}\\ {\mathbf{a}}_{k,j,V}\end{array}\end{array}\right].$$$ In Equation , the vector a k , j is the further extended control variable vector and concatenates V vectors of a k , j , v at the j th scale for the k th ensemble member, where a k , j , v denotes the control variable vector for all variables in the same v th variable group at the j th scale for the k th member.…”

“…Accurate predictions of convective storms using convection‐allowing models (CAMs) require an accurate initialization of not only the storm scales but also its synoptic‐scale and mesoscale environments (Fabry & Meunier, 2020; Flournoy & Rasmussen, 2021; Lombardo & Colle, 2013; Majumdar et al., 2021; Schumacher et al., 2021; Sodhi & Fabry, 2022; Wang & Wang, 2023b; Wang et al., 2021; Workoff et al., 2012). To address this challenge, a commonly used approach is to assimilate observations by sampling larger scales first.…”

Simultaneous Multiscale Data Assimilation Using Scale‐ and Variable‐Dependent Localization in EnVar for Convection Allowing Analyses and Forecasts: Methodology and Experiments for a Tornadic Supercell

“…The RTPS inflation is intended to alleviate excessively reduced spread by the assimilation of observations due to sampling errors. This study further adopts the constant inflation and additive inflation methods (Dowell & Wicker, 2009; Dowell et al., 2011; Y. Wang & Wang, 2017, 2020, 2023; Whitaker et al., 2008; Yussouf et al., 2013) wherever the observed reflectivity exceeds 25 dBZ to account for the ensemble misrepresentation of model error. Each ensemble analysis member is first inflated using constant inflation with a coefficient of 1.04.…”

“…Among the available DA methods, the ensemble‐based DA approaches are popular for the use of flow‐dependent background error covariances (BECs). These ensemble‐based approaches for radar DA include the ensemble Kalman filter (EnKF, e.g., Dowell & Wicker, 2009; Dowell et al., 2004; Johnson et al., 2015; Jung et al., 2008; T. Lei et al., 2009; Tong & Xue, 2005; Yussouf et al., 2013; Zeng et al., 2020) and the ensemble‐variational (EnVar, e.g., Duda et al., 2019; Gasperoni et al., 2022; Y. Wang & Wang, 2017, 2020, 2021, 2023) methods. These radar DA methods by design only correct the storm scale, although the radar observation innovation contains information beyond the storm scales.…”