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On August 8, 2010, a derecho swept over Northern Europe, causing widespread wind damage and more than 2 million Euros in economic loss in Estonia during its most destructive stage. This paper presents a modelling study of the derecho-producing storm utilising the Hirlam Aladin Research for Mesoscale Operational Numerical Weather Prediction in Europe (HARMONIE) model. The model setup is chosen to mimic near-future, nearly kilometre-scale, operational environments in European national weather services. The model simulations are compared to remote sensing and in situ observations. The HARMONIE model is capable of reproducing the wind gust severity and precipitation intensity. Moreover, 2.5-km grid spacing is shown to be sufficient for producing a reliable signal of the severe convective storm. Storm dynamics are well simulated, including the rear inflow jet. Although the model performance is promising, a strong dependence on the initial data, a weak trailing stratiform precipitation region and an incorrect timing of the storm are identified.

The high-resolution reanalysis data-base BaltAn65+ covers the period of 1965–2005. Here, this dataset is used to derive essential climate parameters for the Baltic Sea region and Estonia. In particular, monthly mean temperature and total precipitation are calculated and a trend analysis is performed to analyze the temporal evolution of these climatological parameters during the reanalysis period. Monthly, seasonal, and annual maps of the climate characteristics, including trend maps, are created for the Baltic Sea region. Time series of monthly and annually averaged temperature and precipitation sum are presented over the Baltic Sea and Estonian domains together with fitted linear trends and trend significance analysis. Then, comparison with an observational database is performed to assess the quality of the reanalysis database. Additionally, the time series are compared with official climate normals for the period of 1971–2000, as calculated by the Estonian Environment Agency (EtEA). Findings of other publications in the scientific literature dealing with the climate of similar time period for Estonia and the Baltic Sea region are discussed. The quality of the BaltAn65+ reanalysis is found to be generally good for temperature but weak for precipitation.

Orographic drag formation is investigated using a numerical wave model (NWM), based on the pressure-coordinate dynamics of non-hydrostatic HIRLAM. The surface drag, wave stress (vertical flux of horizontal momentum), and wave drag are split to the longitudinal and transverse components and presented as Fourier sums of their spectral amplitudes weighted with the power spectrum of relative orographic height. The NWM is accomplished, enabling a spectral investigation of the buoyancy wave stress, and drag generation by orography and is then applied to a cold front, characterised by low static stability of the upper troposphere, large vertical and directional wind variations, and intensive trapped wave generation downstream of obstacles. Resonances are discovered in the stress and drag spectra in the form of high narrow peaks. The stress conservation problem is revisited. Longitudinal stress conserves in unidirectional flow, 2D orography conditions, but becomes convergent for rotating wind or 3D orography. Even in the convergent case the vertical momentum flux from the troposphere to stratosphere remains substantial. The transverse stress never conserves. Disappearing at the surface and on the top, it realises the main momentum exchange between lower an upper parts of the troposphere. Existence of stationary stratospheric quasi-turbulence (SQT) is established above wind minimum in the stratosphere.

Regional reanalysis database BaltAn65+ comprising meteorological data for Baltic Sea region for the time period 1965–2005 is described. For data assimilation and hindcasts, the numerical weather prediction model HIRLAM 7.1.4 is applied, with 11 km horizontal and 60-layer vertical resolution. Reanalysis includes three-dimensional weather analysis data. Standard surface observations and meteorological soundings together with ship and buoy measurements from WMO observational network are used in analysis. Boundary fields are obtained from ECMWF ERA-40 global re-analysis. The BaltAn65+ can be considered as a regional refinement of ERA-40 for Baltic Sea region, providing the historical weather and climate data with enhanced spatial resolution, which is main motivation for creation of this novel reanalysis database.

The equation of radiative transfer in a semi-infinite homogeneous atmosphere with different internal sources is solved by the method of kernel approximation—the kernel in the equation for the Sobolev resolvent function is approximated by a Gauss–Legendre sum. Then the obtained approximate equation can be solved exactly and the solution is a weighted sum of exponentials. All the necessary coefficients of the solutions may be easily found. Since the resolvent function is closely connected with the Green function of the integral radiative transfer equation, the radiation field for different internal sources can be found by simple integration. For the considered cases the formulas for the radiation field are obtained and the respective accuracy estimated. The package of codes in Fortran-77 is given at http://www.aai.ee/ ∼ viik/homogen.for .

To solve a horizontally spectral, vertically discrete buoyancy wave equation in conditions of arbitrary wind and temperature distribution with height, a novel method is applied, which consists of a presentation of the solution in the form of a cumulative product of complex decrease factors. For decrease factors, a nonlinear, inhomogeneous, two-member recurrence formula follows that is initiated, assuming the radiative condition at the top. Singularities of the wave equation, corresponding to a critical layer in the vicinity of evanescent wind, are eliminated by turbulent friction. The estimation of minimal vertical resolution is derived, enabling solution stability and accuracy. The areas of application of the developed numerical scheme are the high-precision modeling of orographic waves for arbitrary orography in general atmospheric stratification conditions and testing of adiabatic kernels of numerical weather prediction models.

The anelastic sigma-coordinate version of the pseudo-anelastic Miller-Pearce model is developed. The pseudo-anelastic model is characterized by the presence of external-mode acoustic perturbations which propagate in the horizontal, compromising the model performance by the need to use smaller time steps than would otherwise be required. The approach developed in this study allows for the filtering of acoustic waves and adjustment of surface pressure perturbations. The approach is tested in a new numerical implementation of an adiabatic sigma-coordinate non-hydrostatic model and results are found to be comparable to the unadjusted version, and to theory when applicable. The new code is found to allow for significantly larger time steps whilst still retaining numerical stability, showing the possibility of further model improvements.

Snow samples from 18 sites in Estonia were collected in February and March 1996 after 72–110 days of permanent snow cover. Three snow layers corresponding to different snow accumulation periods were separated in each sampling site. Snow water samples were analysed for sulphate (SO4 2-), nitrate (NO3 -), and chloride (Cl-) ions and elemental composition. Deposition fluxes of 27 chemical species were used for factor, cluster and correlation analysis. The effects of cement dust, oil shale fly ash, sulphur dioxide and chlorine from emissions of thermal power plants were distinguished. A large number of trace metals are strongly correlated with each other (R > 0.8) and with macro-components (except NO3 -), which refers to a common origin, identified as the mineral part of oil shale. Deposition fluxes of Ca, Mg, SO4 2- and a number of mineral components exceed near the power plants 1–2 decimal orders the background value. The deposition fluxes in forested sites are up to 2 times higher than in open land sites. This difference may be caused by more efficient turbulent transfer over rougher surface. It is suggested, that NO3 - and Zn originate mainly and Pb, Cd and Cu partially from non-local or diffuse sources (traffic, domestic heating, far transport). The results of this research could be used to evaluate the air pollution deposition models and for ecological impact estimations.

Estimation of accuracy of different high-resolution, sound-filtered, pressure-coordinate models is carried out by modeling their response to orographic forcing. Evaluated models are the elastic nonhydrostatic model (EFM), the anelastic nonhydrostatic model (AEM), and the hydrostatic primitive equation model (HSM). These models are compared to the exact, nonfiltered, nonhydrostatic, pressure-coordinate dynamics (ExM). All model equations are linearized, a wave equation for vertical displacements of air particles is derived, and exact analytical stationary solutions for each model are compared for uniform flow over given smooth orography (bell-shaped mountain). These linear solutions reveal that compressible (ExM, EFM) and incompressible (AEM, HSM) models are different at long horizontal scales l ∼ 1000 km. Differences are especially large in the vertical velocity field (up to 100%) at the medium and upper levels of the atmosphere, where incompressible models give systematic reductions of wave ampl...

The least action principle is described for general (non-hydrostatic, compressible, acoustically non-filtered) pressure-coordinate equations of atmospheric dynamics (Room 1989), which represents a generalization of the Least Action Principle, first developed for the pressure-coordinate representation of atmospheric dynamics by Salmon and Smith (1994).

A nonhydrostatic, acoustically filtered model of atmospheric dynamics in pressure coordinates is derived using a special filtering technique. The initial complete nonhydrostatic equations in pressure space are linearized. The linearized system is divided into two subsystems—an independent equation for potential vorticity, which determines the quasi-solenoidal horizontal flow and is a local invariant in the absence of heat sources, and a fourth-order wave system describing acoustical and buoyancy waves. A Lagrangian function, corresponding to the wave equations, is derived. The acoustic filtering is carried out in the Lagrangian. The approximated Lagrangian generates filtered wave equations and the linear filtered equations of motion. As a final step, the linear model is extended to a nonlinear nonhydrostatic acoustically filtered model by inclusion of advection terms in the vorticity equation and by nonlinear generalization of the Hamiltonian principle for the wave system. Thus, variational princ...

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller–Pearce–White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the numerical modelling results with known stationary linear test solutions. Numerical stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The numerical scheme with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.

Pressure (isobaric or p-) coordinates in non-hydrostatic (NH) dynamics with pressure in the role of the vertic al coordinate were first introduced by (1974), and generalized to sigma-coordinate framework by (1984). First numerical applicat ions of the NH model in pressure related coordinates where developed by (1991) for twodimensional case, and by (1992) for three-dimensional motion.

The Gaussian type air pollution dispersion and deposition model AEROPOL is developed at the Tartu Observatory, Estonia (Kaasik and Room, 1997). The multiple reflections with partial adsorption from the underlying surface and capping inversion, as well as the initial rise of a buoyant plume with the inversion penetration, are included. The wet deposition is included considering different features of rain and snow. The concentrations of pollutants, dry and wet deposition fluxes could be computed. The computing code is written in Turbo Pascal and designed for operational use in Windows’95.

A nonhydrostatic pressure-coordinate model of atmospheric dynamics is developed. The model filters acoustic mode. Internal acoustic waves are filtered using the assumption of non-divergence of motion in pressure-space. External (Lamb mode) waves are filtered using the surface pressure adjustment. The model is implemented in the framework of the numerical weather prediction model HIRLAM (High Resolution Limited Area Model) as an extension to the hydrostatic kernel. The integration scheme is either the explicit or semi-implicit Eulerian leapfrog time stepping. Due to the acoustic filtration, the explicit scheme supports quite large time-steps. To check the validity of the model, several flow experiments with artificial orography are performed. The hydrostatic and nonhydrostatic flow regimes are investigated. The results of different models are compared mutually and with the analytic solutions. The real situation simulations are also presented to show the model’s forecasting capabilities. DOI: 10.1034/j.1600-0870.2003.00018.x