An intermediate‐complexity model for four‐dimensional variational data assimilation including moist processes

Abstract

This article presents a new Moist Atmosphere Dynamics Data Assimilation Model (MADDAM), an intermediate-complexity system for four-dimensional variational (4D-Var) data assimilation. The prognostic model equations simulate nonlinear moisture advection, precipitation, and the impact of condensational heating on circulation. The 4D-Var assimilation applies the incremental approach and uses transformed relative humidity as a control variable. In contrast to the model dynamical variables, which are analyzed in multivariate fashion using equatorial wave theory, moisture data are assimilated univariately. MADDAM is applied to study the extraction of wind information from time series of moisture observations in the Tropics, where the lack of wind information is most critical. Results show that wind tracing in the unsaturated atmosphere depends largely on the ability of the assimilation model to resolve spatial gradients in the moisture field, which is determined by the spatial density and accuracy of observations. In the saturated atmosphere, a combined assimilation of moisture and temperature data is shown to improve wind analyses significantly, as the intensity of the condensation process is susceptible to the slightest changes in saturation humidity and thus temperature. Moreover, a perfect-model 4D-Var with moisture observations can extract wind information even in precipitating regions and strongly nonlinear flow, provided sufficient observations of humidity gradients are available. MADDAM is envisaged to serve as a testbed for new developments in 4D-Var assimilation, with a focus on interactions between moist processes and dynamics across many scales. KEYWORDShumidity control variable, moist 4D-Var, moisture observations, tropical data assimilation, wind tracing INTRODUCTIONSimplified numerical prediction models are valuable testbeds for data assimilation research. An idealized framework, with respect to numerical weather prediction (NWP) models, aids understanding and simplifies research. Simplified models allow us to (a) develop and implement new algorithms faster than in the NWP case, and (b) perform numerical experiments in a controlled environment in which various issues, difficult to grasp in a real NWP, can be understood more easily. At the same time, simplified models should still be complex enough to capture the main dynamical and physical aspects of the phenomena of interest, in order to explain the observed features of the circulation and to be of any value for NWP. An important model of this type is based on the rotating nonlinear shallow-water equations (for example, Vallis, 2006), which include both balanced (vorticity-dominated) dynamics and gravity-wave dynamics as well as their interactions. Shallow-water models (SWMs) were applied in a number of data assimilation studies to develop new concepts and to study the value of mass-field and wind-field observations (for example, Žagar et al., 2004a, and references therein). This question is especially important in the Tropics, where wind-field informati...

The intricacies of identifying equatorial waves

“…Improvements in NWP in the Tropics can come from both advancements in model initialization and model development. More accurate initial states (analyses) are produced using new observations and improved data assimilation schemes (e.g., Žagar, 2004; Zaplotnik et al ., 2018). Current methodologies do not account sufficiently for EWs, which, together with sparse wind observations and deficient moist dynamics, lead to uncertainties in tropical analysis datasets (Podglajen et al ., 2014; Žagar et al ., 2016).…”

Inferring atmospheric dynamics from aerosol observations in 4D‐Var

“…These challenges motivated the present in‐depth investigation of the couplings between aerosols, moisture, and dynamical variables. For this purpose, we extended an intermediate‐complexity model MADDAM (Zaplotnik et al ., , ZZG18) using the aerosol prognostic equation, which represents the most dominant aerosol processes on the time‐scale of the typical assimilation window: advection and wet deposition.…”

“…Zaplotnik et al . (), hereafter ZZG18, demonstrated that winds can also be retrieved from time series of moisture observations in perfect‐model 4D‐Var in the presence of a moisture sink in the form of a simple, flow‐convergence initiated precipitation process. In the case of linear flow, the observation spatial sampling was found to be more important than the observation update frequency, whereas for nonlinear flow the update frequency becomes crucial.…”

Techniques and challenges in the assimilation of atmospheric water observations for numerical weather prediction towards convective scales

“…This is the "Hólm transform", which is used in the ECMWF 4D-Var system. It is also used, with adaptations, in HIRLAM (Gustafsson et al, 2011), in Met Office Var systems (Ingleby et al, 2013b), and in an intermediate research model (Zaplotnik et al, 2018). Since there is little literature on the Hólm transform itself, we provide some detail here.…”