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...

In the article a virus transmission model is constructed on a simplified social network. The social network consists of more than 2 million nodes, each representing an inhabitant of Slovenia. The nodes are organised and interconnected according to the real household and elderly-care center distribution, while their connections outside these clusters are semirandomly distributed and undirected. The virus spread model is coupled to the disease progression model. The ensemble approach with the perturbed transmission and disease parameters is used to quantify the ensemble spread, a proxy for the forecast uncertainty. The presented ongoing forecasts of COVID-19 epidemic in Slovenia are compared with the collected Slovenian data. Results show that at the end of the first epidemic wave, the infection was twice more likely to transmit within households/elderly care centers than outside them. We use an ensemble of simulations (N = 1000) and data assimilation approach to estimate the COVID-19 forecast uncertainty and to inversely obtain posterior distributions of model parameters. We found that in the uncontrolled epidemic, the intrinsic uncertainty mostly originates from the uncertainty of the virus biology, i.e. its reproduction number. In the controlled epidemic with low ratio of infected population, the randomness of the social network becomes the major source of forecast uncertainty, particularly for the short-range forecasts. Virus transmission models with accurate social network models are thus essential for improving epidemics forecasting.

This article explores the potential of aerosol observations to provide wind information in four-dimensional variational data assimilation (4D-Var). It is shown that the relative horizontal gradients, crucial for wind extraction from tracers, are on average greater for the aerosol mixing ratio than for the specific humidity, observations of which are known to provide significant information on the wind field. The potential of aerosols to infer atmospheric dynamics is investigated in the Tropics, where the wind information is most critical. An intermediate-complexity incremental 4D-Var system, the Moist Atmosphere Dynamics Data Assimilation Model (MADDAM), has been developed, with a forecast model that simulates most dominant processes involving moisture, aerosols, and dynamics: nonlinear advection, condensation, and wet deposition. The results of 4D-Var experiments reveal a detrimental impact of saturation-related nonlinearities and aerosol wet deposition on the extraction of wind from aerosol data. Fraternal-twin experiments show about 30%smaller impact of aerosol data on the wind analysis compared with humidity data, mainly due to the greater aerosol observation error and suboptimal background-error covariance model. However, the assimilation of aerosol data together with temperature and humidity observations shows significant added value for wind analyses. K E Y W O R D Saerosols, background-error model, data assimilation, humidity, tracing, wind extraction, 4D-Var

We assess the scale-dependent growth of forecast errors based on a 50-member global forecast ensemble from the European Centre for Medium Range Weather Forecasts. Simulated forecast errors are decomposed into scales and a new parametric model for the representation of the error growth is applied independently to every zonal wavenumber. In contrast to the standard fitting method, the new fitting function involves no time derivatives and provides the asymptotic values of the forecast errors as a function of the fitting parameters. The range of useful prediction skill, estimated as a scale where forecast errors exceed 60% of their asymptotic values is around 7 days on large scales and 2-3 days at 1000 km scale. The new model is easily transformed to the widely used model of Dalcher and Kalnay (1987) to discuss the scale-dependent growth as a sum of two terms, the so-called α and β terms. Their comparison shows that at planetary scales their contributions to the growth in the first two days are similar whereas at small scales the β term describes most of a rapid exponential growth of errors towards saturation.

<p>This study explores the possible drivers of the recent Hadley circulation strengthening in modern reanalyses. Predominantly, two recent generations of reanalyses provided by the European Centre for Medium-range Weather Forecasts (ECMWF) are used: the fifth-generation atmospheric reanalysis (ERA5) and the interim reanalysis (ERA-Interim). Some results are also evaluated against other long-term reanalyses: ERA-20C, CERA-20C, NOAA-20CR and NCAR/NCEP. To assess the origins of the Hadley cell (HC) strength variability we employ the Kuo-Eliassen equation. ERA5 shows that both HCs were strengthening prior to 2000s, but they have been weakening or remained steady afterwards. Most of the long-term variability in the strength of the HCs is explained by the meridional gradient of diabatic latent heating, which is related to precipitation gradients. However, the strengthening of both HCs in ERA5 is larger than the strengthening expected from the observed zonal-mean precipitation gradient (via Global Precipitation Climatology Project, GPCP). This suggests that the HC strength trends in the recent decades in ERA5 can be explained partly as an artifact of the misrepresentation of latent heating and partly through physical long-term variability. To show that the latter is true, we analyze ERA5 preliminary data for the 1950-1978 period, other long-term (e.g. 20<em><sup>th</sup></em> century) reanalyses, and sea surface temperature observational data. This reveals that the changes in the HC strength can be a consequence of the Atlantic multidecadal oscillation (AMO) and related diabatic and frictional processes, which in turn drive the global HC variability. This work has implications for further understanding of the long-term variability of the Hadley circulation.</p>