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Flexible district heating grids form an important part of future, low-carbon energy systems. We examine probabilistic state estimation in such grids, i.e., we aim to estimate the posterior probability distribution over all grid state variables such as pressures, temperatures, and mass flows conditional on measurements of a subset of these states. Since the posterior state distribution does not belong to a standard class of probability distributions, we use Markov Chain Monte Carlo (MCMC) sampling in the space of network heat exchanges and evaluate the samples in the grid state space to estimate the posterior. Converting the heat exchange samples into grid states by solving the non-linear grid equations makes this approach computationally burdensome. However, we propose to speed it up by employing a deep neural network that is trained to approximate the solution of the exact but slow non-linear solver. This novel approach is shown to deliver highly accurate posterior distributions both for classic tree-shaped as well as meshed heating grids, at significantly reduced computational costs that are acceptable for online control. Our state estimation approach thus enables tightening the safety margins for temperature and pressure control and thereby a more efficient grid operation. • Novel approach combining classic statistical analysis and AI. • The estimated state distributions are not standard distributions. • MCMC and Bayesian calculus can be used to approximate state distributions. • MCMC requires mapping demands to grid states in every step. • Deep Neural Networks can speed this up by orders of magnitude. [ABSTRACT FROM AUTHOR]

Abstract: For a long time, classical ensemble forecasts have concentrated on simulating the uncertainties of the observations by variations of the initial and boundary conditions. To supplement this with inherent contributions from the forecast model itself, stochastic physics has been proposed as an appropriate approach to improve the forecast quality and to increase the ensemble spread of underdispersive ensembles. Concentrating on cloud processes and their temporal development we here introduce a set of stochastic parameters into existing deterministic physical parameterization schemes as for the trigger function, closure assumption and turbulent mixing in the convection scheme, for the initial ice concentration and turbulent collection kernel in the grid scale precipitation/microphysics scheme and for the subgrid scale cloud cover in the radiation scheme. Considering the stochastic parameters to be subject to unresolved turbulent fluctuations, we derive the corresponding stochastic processes from a Langevin equation based on an approach of direct numeric simulation. This allows for the inclusion of a turbulent autocorrelation time calculated from the eddy dissipation rate and the turbulent kinetic energy of the hosting model. Ensemble simulations of two meteorologicaly different real cases are compared to deterministic control simulations and observations of 1h precipitation sums. The turbulent autocorrelation time shows pronounced spatial variability correlated with frontal dynamics and convective activity. Maps of spatial precipitation patterns and continuous ranked probability score (CRPS) improvements show a better forecast quality of the ensemble mean including stochastic physics. Depending on the meteorological situation, the ensemble spread and the CRPS improvement both exhibit a spin up time and reach a saturation. For air-mass convection/postfrontal showers the spread and the CRPS improvement are higher than for frontal precipitation. The stochastic parameterization of subgrid scale cloud cover is found to degrade the forecast quality of the ensemble. This is explained by a too homogeneous spatial distribution of the added variability. Consequently, this part of the stochastic parameterization has been excluded from the ensemble simulations and is left in its operational deterministic version. [Copyright &y& Elsevier]

• Compares results of spectral microphysical with parametrized fog model. • Shows influence of clouds on evolution of radiation fog. • Uses two-dimensional size distribution for aerosol particles and cloud droplets. • Shows influence of radiation term in droplet growth equation. The spectral microphysics cloud scheme MiFog and the two-moment cloud scheme PaFog are implemented in a single-column model of the atmospheric boundary layer for the numerical simulation of a radiation fog event. Results of numerical sensitivity studies are presented where the influence of cloudiness on the evolution of the fog has been investigated. It is shown that the appearance of cloudiness in the morning hours triggers an efficient dissolution of the fog. During situations with weak turbulence, quasi-periodic oscillations of the liquid water content occur in the MiFog simulations. It turns out that these fluctuations are caused by the direct interaction of diffusional droplet growth and gravitational settling of the droplets. Comparison of the MiFog and the PaFog model runs reveals that most of the time PaFog is capable of simulating the bulk fog properties sufficiently well. [ABSTRACT FROM AUTHOR]

Abstract: A method is presented to reduce the time-splitting errors of one-dimensional flux form advection schemes. In multidimensional applications deformational correction terms are included in each one-dimensional advection step whereby all correction terms add up to zero. With the correction terms a consistent form of a given one-dimensional advection scheme is achieved when time-splitting is performed. Positive definiteness and shape preservation of the scheme are obtained by nonlinear limitation of the advective fluxes and the deformational correction terms. Large Courant numbers are treated by applying local timestep reduction. The resulting scheme is strictly one-dimensional, mass conservative and positive definite. Shape preservation of the method is nearly achieved. Two- and three-dimensional test runs are presented demonstrating that the method yields satisfactory results. The horizontal flow in a terrain with a steep mountain ridge is investigated by utilizing a terrain following vertical coordinate. It is shown that even in steep orographical terrain the method works quite well, however, small errors occur in the shape preservation of the scheme. These errors increase with increasing spatial variation of the vertical grid mesh. [ABSTRACT FROM AUTHOR]

Abstract: Convection can cause severe precipitation events and is thus of major interest for quantitative precipitation forecasts. Due to its small horizontal scale convection usually has to be parameterized in numerical weather prediction (NWP) models as a subgrid scale phenomenon. Classical mass flux convection schemes assume grid box sizes much larger than the scale of the convective circulation. Thus, the convective mass transport is closed in the local grid column and no net mass transport occurs on the grid scale. In contemporary NWP models with grid sizes of a few kilometers, where convection is already partially resolved, the classical approach leads to a conceptual problem. This can be overcome by a hybrid mass flux convection scheme (HYMACS), in which only the small scale convective updrafts and downdrafts are parameterized, whereas the treatment of the larger scale environmental subsidence is left to the grid scale equations. Different to the classical schemes, HYMACS produces a net convective mass flux exerting pressure gradient forces to the grid scale model. We discuss real cases of different meteorological situations simulated with the operational weather forecast model COSMO of the German Meteorological Service as the hosting model of HYMACS. Precipitation and cloud top pressures simulated with HYMACS are compared with results from classical convection schemes and observational data from the DWD station network and the SEVIRI (MSG) satellite instrument. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present a rigorous derivation of a model equation system for the mass and energy open precipitating atmosphere. The derivation is based on the treatment of the atmosphere in terms of three open thermodynamic subsystems consisting of cloudy air, rain water and snow, respectively. Each of the three subsystems moves with a different velocity as caused by the different fall velocities of rain and snow in comparison to the cloudy air. A basic assumption of the model consists in the neglect of the inertia terms in the momentum equation of the falling hydrometeors. It will be shown that this simplification yields additional source terms in the budget equations of the total momentum and the total kinetic energy of the system. However, the prognostic equations for the atmospheric wind field and the corresponding kinetic energy equation remain free of these source terms. The model equations strictly conserve the total mass and energy of the system. It is concluded that the combination of the barycentric velocity of the cloudy air and the total density of the system is the best choice to describe the time evolution of the atmospheric wind field. [Copyright &y& Elsevier]

The new one-dimensional forecast model PAFOG for radiation fogs and low-level stratiform clouds will be presented. The aim of the model is to improve the local visibility forecast on airports and other traffic locations where fog and low-level stratus frequently occur. PAFOG has been developed on the basis of the microphysical fog model MIFOG of Bott et al. [J. Atmos. Sci. 47 (1990) 2153]. To obtain a numerically efficient model, the detailed spectral cloud microphysics of MIFOG has been replaced by the parameterization scheme of Chaumerliac et al. [J. Geophys. Res. 92 (1987) 3114]. Furthermore, according to Siebert et al. [Beitr. Phys. Atmos. 65 (1992a) 93], a model for low vegetation is included in PAFOG so that now fog evolution as influenced by different types of vegetation can also be accounted for.The performance of PAFOG has been tested by comparing the model results with routine observations of the German Weather Service. Nine different weather periods comprising a total of 45 days have been investigated. In 41 cases, PAFOG yields agreement with the observations in terms of occurrence or nonoccurrence of fog or stratiform clouds. During radiation fogs, the calculated and observed visibilities are quite similar. However, in the model simulations the formation of dense fogs tends to be somewhat delayed. From the case studies with stratiform clouds, it is seen that cloud evolution in time and space strongly depends on the value of the large-scale subsidence. Since this quantity is not available from measurements, it must be provided by means of a numerical weather forecast model. [Copyright &y& Elsevier]