Regularity of pressure in the neighbourhood of regular points of weak solutions of the Navier-Stokes equations

summary:In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved

An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions

summary:The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends only on certain norms of the given data. In the proof we use a fixed point theorem method in Sobolev spaces with non-integer order derivatives. The proof is performed for Lipschitz domains and a wide class of data

Remark on regularity of weak solutions to the Navier-Stokes equations

summary:Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space $L^2(0,T,W^{1,3}(\varOmega)^3)$ are regular

Využití Standardizovaného srážkového evapotranspiračního indexu pro hodnocení vegetačního období v České republice =The application of the Standardized Precipitation Evapotranspiration Index for the assessment the driest and wetness characteristics during the growing season in the Czech Republic

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Influence of Bias Correction Methods on Simulated Köppen−Geiger Climate Zones in Europe

Our goal was to investigate the influence of bias correction methods on climate simulations over the European domain. We calculated the Köppen−Geiger climate classification using five individual regional climate models (RCM) of the ENSEMBLES project in the European domain during the period 1961−1990. The simulated precipitation and temperature data were corrected using the European daily high-resolution gridded dataset (E-OBS) observed data by five methods: (i) the empirical quantile mapping of precipitation and temperature, (ii) the quantile mapping of precipitation and temperature based on gamma and Generalized Pareto Distribution of precipitation, (iii) local intensity scaling, (iv) the power transformation of precipitation and (v) the variance scaling of temperature bias corrections. The individual bias correction methods had a significant effect on the climate classification, but the degree of this effect varied among the RCMs. Our results on the performance of bias correction differ from previous results described in the literature where these corrections were implemented over river catchments. We conclude that the effect of bias correction may depend on the region of model domain. These results suggest that distribution free bias correction approaches are the most suitable for large domain sizes such as the pan-European domain

Climatic Changes and Their Relation to Weather Types in a Transboundary Mountainous Region in Central Europe

A first-time common cross-border assessment of observed climatic changes in the Saxon–Bohemian region was the aim of the German–Czech climate cooperation INTERKLIM. This paper focuses on the observed changes of temperature and precipitation averages and extremes within the period 1961–2010, investigating how variations of a range of climate indices were regionally shaped by changes in frequency and character of weather types. This investigation serves to enhance our understanding of the regional climate characteristics to develop transboundary adaptation strategies and focuses on the classification of the “Grosswetterlagen” using the parameters of air temperature and precipitation. Climate data were quality controlled and homogenized by a wide range of methods using the ProClimDB software with a subsequent comprehensive regional visualization based on Geographical Information Systems. Trends for the temperature averages showed increasing trend values mainly from January to August, especially for high temperature extremes. Precipitation trends displayed regionally varying signals, but a strong spatially uniform decrease from April to June (early growing season) and a distinctive increase from July to September (late growing season). Climatic changes were supported by frequency changes of weather types, e.g., the drying from April to June was related to a decrease/increase in patterns causing rather wet/dry conditions, while from July to September opposite trends were observed. Our results represent regional climatic changes in a complex topography and their dependency on variations in atmospheric circulation peculiarities

Czech Drought Monitor System for monitoring and forecasting of agricultural drought and drought impacts

The awareness of drought and its impacts on Central Europe increased after the significant drought episodes in 2000, 2003, 2012 and 2015, which were all estimated to have caused over 500 million Euro in damage in the Czech Republic alone. These events indicated the need for timely and highresolution monitoring tools that would enable analysing, monitoring and forecasting of drought events. Monitoring soil water availability in near real time and at high-resolution (up to 0.5 × 0.5 km for some products) helps farmers and water managers to mitigate impacts of these extreme events. The Czech Drought Monitor was developed between 2012 and 2014 and has since been operational as an online platform. It uses an operational modelling system that consists of four pillars: (a) weekly soil moisture estimates based on spaceborne Advanced Scatterometer sensor measurements; (b) the daily SoilClim soil moisture model, which runs based on high-density network data from the Czech Hydrometeorological Institute with a 55-year reference period; (c) weekly reports on vegetation condition, which is deduced from satellite-based vegetation indices and early warnings of imminent drought impacts; and (d) weekly reports of soil moisture, especially after drought impacts, which are provided by dozens of experts. Since 2016 the drought forecast (+9 days) has been released daily based on an ensemble of five numerical weather prediction models combined with a weekly drought outlook (+2 months). The analysis of four recent episodes (2000, 2003, 2012 and 2015) clearly showed that both large-scale and regionally restrained drought episodes posed serious risks in terms of their impacts and damage. Comparisons with historical droughts showed that these events, especially the 2000, 2003 and 2015 events, were among the top five drought episodes in the June–August period observed in the Czech Republic since 1961 in terms of spatial extent, magnitude and duration

Regionální klimatický model ALARO-Climate, validace experimentu s rozlišením 25 km =ALARO-Climate regional climate model: validation of experiment at 25 km horizontal resolution

Regionální klimatický model ALARO-Climate byl vyvinut z konfigurace numerického předpovědního modelu ALADIN cy36, která byla nedávnou předpovědní provozní verzí v ČHMÚ. Oproti konfiguraci ALADIN2 Climate/CZ disponuje současná verze modelu ALARO-Climate mimo jiné prognostickým schématem mikrofyziky oblačnosti a srážek a hluboké konvekce se srážkami. Zmíněná schémata jsou koncipována tak, aby bylo možné model spustit i pro velmi jemný krok horizontální sítě, kdy je hluboká konvekce částečně rozlišena, při zachování relativně nízkých dodatečných nákladů na výpočty. V tomto článku předkládáme validaci verze s rozlišením 25 km řízené reanalýzou ERA-40 pro období 1961-1990, která slouží jako výchozí pro připravovaný experiment v rozlišení 6 km. Model je schopen reálně simulovat sezonní pole přízemního tlaku vzduchu nad Evropou a roční chod teplot i srážek v České republice. Nadhodnocuje však úhrny srážek ve všech měsících, což je důsledkem mimo jiné většího počtu dní se slabým deštěm (do 1 mm/den). Maximální denní teploty vzduchu jsou v modelu nižší než v pozorovaných datech, k podhodnocení dochází též u průměrných teplot a denní amplitudy teploty vzduchu. Současné podhodnocení teplot a nadhodnocení srážek může částečně souviset s nadhodnocením nízké oblačnosti v modelu, které se objevuje na jaře, v létě a na podzim. Nejsou tím ale vysvětleny tytéž problémy v zimě, kdy je celkově oblačnost modelována ve shodě s řídící reanalýzou.The ALARO-Climate regional climate model is based on the ALADIN cy36 numerical weather prediction model recently used for operational weather forecasting at the Czech Hydrometeorological Institute. The current model version includes improved prognostic schemes of cloud and precipitation microphysics and moist deep convection. The schemes are designed to run the model at resolutions up to a very fine mesh-size where moist deep convection is partly resolved, but with a minimal overhead in the computational costs. In this paper, we present a validation of the ALARO-Climate experiment at 25 km horizontal resolution driven by ERA40 reanalysis for the period 1961-1990. The analysed simulation serves as a basis for the forthcoming experiment with 6 km resolution. The model is capable of reliably simulating seasonal sea level pressure fields in Europe and the annual cycle of air temperature and precipitation in the Czech Republic. However, precipitation amounts are overestimated in all months which are due to, among other reasons, a higher number of light precipitation days (up to 1 mm.day-1). Maximum and mean daily temperatures, and also daily temperature ranges, are generally lower in the model than observed. The simultaneous underestimation of temperatures and overestimation of precipitation may partly be associated with the overestimated low cloud cover, appearing in spring, summer, and autumn. However, this cannot explain the same deficiencies in winter when the simulated cloud cover is in an agreement with the driving reanalysis.334

Drought Prediction System for Central Europe and Its Validation

In recent years, two drought monitoring systems have been developed in the Czech Republic based on the SoilClim and AVISO soil moisture models. The former is run by Mendel University and Global Change Research Institute (CAS), while the latter, by the Czech Hydrometeorological Institute. SoilClim is based more on real soil properties and aimed primarily at agriculture, while AVISO complements the system with more theoretical presumptions about soil, showing, rather, climatological potential. Both soil moisture models were complemented by forecasts on a daily basis, taking meteorological inputs from NWP (Numerical Weather Prediction) models and thus giving short- to mid-range outlooks up to 9 days ahead. Validation of the soil moisture and drought intensity prediction was performed and is presented in this article showing its prediction reliability and potential. In the analysis, we focus mainly on the past year, 2017. The tool has strong predictive power for soil moisture and drought intensity so it is suitable for farmers who need to make decisions about irrigation and production activities. The presented system is fully functional and can be applied in the coming years