Application Semi-Lagrangian Advection for Estimation Energy Transition in the Atmosphere Shpyg Vitalii and Pishniak Denys Ukrainian Hydrometeorological Institute
03028, Ukraine, Kyiv, Prospekt Nauky, 37 fax: (044) 525 53 63, е-mail:
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1. Introduction. Growth of economic infrastructure complexity and manufacture globalization reduces to risks increase, which are connected with unfavorable consequences of atmospheric hazards. Considerable part of such hazards due to large scale atmospheric processes. Such phenomena existence straight in the atmosphere keeps up by accumulation and transformation different kind of energy. In one cases energy transformations lead to arising of synoptical scale objects, in other they favour localization on mesoscale level. In this research atmospheric processes are considered with the position of energy analysis, seeking key factors which are charged with cyclones and atmospheric fronts intensification.
2. Methodology. For the estimation of energy transformations Semi-Lagrangian scheme of partial derivative calculation was used. The WRF ARW v. 2.2.1 forecast results were given as input data. Semi-Lagrangian scheme may be used for the assessment of advection value in grid point, when the way, which passed by air particle during interval of time discretization, is greater considerably (several times) than horizontal steps of domain. The principle of such scheme working in some variants of realization is shown on Fig. 1. The coordinates of advection point (xA, yA) from which air mass comes in set grid point with coordinates x,y are calculated, when wind direction and velocity are well known. Most reliable definition of advection point Q t 1 Qxt , y QxA reaches by stream line approximation. Additional sub, yA Q t discretization by time was used for the approximation of stream Fig. 1 Principle scheme of computation line. It was realized in numerical algorithm in such way that maximal length of rectilinear part of trajectory was not greater than value of grid step. Re-computation of ui vi is executed for each calculation of additional sub-discretization by 4-D linear interpolation between nearest 8 grid points and between base time moments. It is easy to calculate partial derivative by time through subtraction from the first second value, when we have current values in concerned grid points and advective value is determined by way that described above. Two initial times for 08.04.2012 (00 and 12 UTC) were used in further Fig. 2 Model domain and investigated computations. The model domain is shown on Fig. 2 area (red frame)
4. Modeling results. Obtained fields of precipitation have good consistency with clouds from satellite images. But contribution of convective precipitation was not very large accordingly to model outputs. Kinetic (KE), internal (IE) and latent energy (LE) conversions are obtained based on WRF model simulations and further post-processing meteorological fields. 4.1. KE conversions. Total increasing of kinetic energy is prevailing in low level of troposphere in stage of cyclonic deepening. Intensive band of decreasing kinetic energy arose at low level after 8 hours (see Fig. 9). This means starts of conversion of kinetic energy to potential on the front line. Such effect is typical for stage of maximal development and cyclone decay. Intensity of frontal kinetic energy transformation is equal to energy conversions induced by orographic factor over mountains. Proposed calculation method has dependence from input data discretization in time. Fig. 9 KE spatial distribution at different time In this investigation data with one hour time discretization have been used. But, if we take more rarefied data, for example with three hours discretization, obtained results will be more smoothly and shifted a little. A quantitative correlation between Fig. 10 Correlation between points of these two fields is present horizontal fields of KE (see Fig. 10). 4.2. LE conversions. Latent energy has two main sources. First from them is evaporation from surface penetrating to 2 km high in day time. Second is precipitation evaporation that take place up to 4 km in cold air before warm front of cyclone. Sometimes clouds evaporation can be significant, particularly in mountain regions. Outflow of latent energy occurred in the areas of intensity cloud and precipitation formation, preliminary on fronts of cyclone, and near mountains chain. It was obtained that conversions of frontal latent energy tracing more then 5 km high (see Fig. 11). 4.3. IE conversions. Changes of potential temperature can be used for estimation of diabatic sources of heating in the atmosphere. They include water phase transition, thermal conductivity and radiation exchange. Vapor condensation is the main source of heating in free atmosphere, that may leads to local volume warming more then 2°С per hour. Significant cooling of atmosphere takes place especially near warm front line, where clouds and precipitation partial evaporate, it leads to increase frontal instability. In daytime lower layers obtain warm from surface (up to 2 km in this case), but in night time this layers loose heat, same as rest part of the atmosphere through long wave radiation (Fig. 12).
3. Weather conditions.
Fig. 3 Surface chart
Fig. 4 Weather phenomena
Fig. 5 Satellite image ir 10.8
Fig. 6 Satellite image ir 10.8
During the 8-9-th of April 2012 difficult weather conditions were observed over Ukraine and Romania and they were connected with cyclone formation process. Heavy snowfalls were fixed over Carpathian Region and West of Ukraine but rainfalls and thunderstorms were observed in central and north regions of Ukraine. Accordingly COSMO results in deep convection cores surface CAPE may reach Fig. 7 Surface CAPE (1800 UTC) 2000 J/kg. For more detail see Fig. 3-7. 4.4. Vertical structure of energy changes near front line. Vertical cross-sections of different energy changes are shown on Fig. 13. They were built along A-B-C line on the field of heat energy change. A-B line are oriented along convection bend, crossing front in place of most intensive precipitation (B point) and then B-C part goes near warm front in cyclone. Sharpness of IE the front maintains by latent heat energy conversions in layer from 0.5 to 2.5 km. Such energy transformations were obtained not only through atmosphere heating on warm side but also by cooling of air on cold side of the front. Maximal energy transformations on vertical cross -section coincide with intensive precipitation in B. In current model resolution IE local parcel heating on this perturbation reaches 4 °С, when cooling go up to 1.5 °С per hour. Vertical cross-section of KE derivative shows presence of the tie in B between perturbation and high troposphere jet-stream. LE
5. Conclusions.
KE
Fig. 11 LE spatial distribution at different time Cloud water
Rain water
Fig. 12 IE spatial distribution at different time
Fig. 13 Vertical cross-sections (1500 UTC)
•An universal method for partial time derivatives estimation based on SemiLagrangian advection is proposed. •Derivatives of the fields may be obtained from different models datasets in wide range of its time discretization. In this study the partial derivatives by time were used for estimations of energy transfer in the atmosphere. •Fields of some energies changes were shown for case of intensive cyclone over East Europe. Energy transitions on cyclonic area and atmospheric fronts show presence of dependence from cyclone evolution stage. Such energy changes estimation can be used to provide comparison between different model simulations, for physical consistency control within model atmosphere and physical analyses of meteorological processes. •Most active energy transformation processes were observed within the range of precipitating clouds.
