Vol 59, No 2 (2023)

Cities have a significant impact on the environment, forming such microclimatic features as an urban heat island, an increase in the intensity of convective weather events, etc. Numerical models of the atmosphere with an integrated block that describes the interaction between the urbanized surface and the atmosphere – urban parameterization – reproduce well the meteorological features of the urban environment. The review studies on urban parameterizations are mostly outdated, and the recent ones do not fully cover aspects of the methods used in the models to describe physical processes. The paper is devoted to updating information on urban parameterizations, comparing the approaches used in them to describe physical processes and forming proposals for their improvement. Based on the most common urban parameterizations of various levels of complexity, the main groups of physical processes describing “urban surface – atmosphere” interaction are identified. They are the surface energy balance, radiation heat transfer, surface moisture balance, turbulent heat and moisture exchange in the urban canopy, anthropogenic influence on heat and moisture fluxes, radiation and turbulent interaction with urban vegetation. The main approaches to parameterization of physical processes defined within each block are described. Modern trends in the development of urban parameterizations are highlighted: 1) over the past 10 years, parameterizations have become more complicated due to the addition of the building energy model, a three-dimensional structure of urban vegetation, and vertical resolution when calculating turbulent fluxes; 2) at the same time, little attention is paid to revising the original empirical formulas, often obtained on the basis of single field or laboratory e-xperiments. Ways to improve urban parameterizations are proposed by clarifying the basic dependencies used mainly in the calculation of turbulent fluxes, particularly, using the results of highly detailed Large-eddy simulation modeling, which, with growing computational power, is increasingly used to simulate explicit heat transfer between the atmosphere and individual elements of the urban environment.

Within the framework of a discrete quasi-geostrophic model with two vertical levels, the problem of linear stability of the flow of a stratified rotating fluid with constant vertical and horizontal velocity shifts is solved. It is shown that taking into account the horizontal shear leads to a qualitative change in the dynamics of unstable wave disturbances. The main feature is related to the effect of temporary exponential growth of unstable perturbations, i.e. growth over a finite time period. This effect manifests itself in the alternation of stages of smooth oscillating behavior (in time) with stages of exponential (explosive) growth of finite duration. A kinematic interpretation of the effect of temporal exponential growth is given, which is associated with the passage of a time-dependent perturbation wave vector through the region of exponential instability that exists in the absence of a horizontal shear. It is shown that mathematically this effect is described by solutions of a second-order differential equation containing turning points. Asymptotic solutions of the equation are given for weak horizontal shifts.

Atmospheric nitric acid (HNO₃) has a significant impact on the formation of the ozone layer; therefore, its content is regularly monitored using various local and remote-sensing methods. We used ground-based measurements of solar IR spectra with a Bruker 125HR Fourier spectrometer to derive information on the HNO₃ content at the St.Petersburg observational NDACC site in Peterhof. The HNO₃ time series obtained showed a pronounced seasonal cycle with a maximum in winter and early spring and a minimum in summer and early autumn. The averaged seasonal variations in nitric acid varied from –30 to +60% for the 0–15 km layer, from –25 to +25% for the 15–50 km layer, and from –25 to +30% for total columns. For 2009–2022 measurement period, no statistically significant trend was found in the time series considered. Comparison of HNO₃ stratospheric columns with independent satellite measurements by the MLS and ACE-FTS instruments showed their qualitative and quantitative agreement; the correlation coefficient between ground-based and satellite measurements totals 0.88–0.93. Time series on the vertical structure of the atmospheric nitric acid measured at the St.Petersburg site can be used both to analyze the state of the ozonosphere and to validate satellite measurements and refine the parameters of atmospheric models.

The development of a variational method for solving the problem of quasi-geostrophic dynamics in a two-layer periodic channel is considered. The development of the method is as follows. First, the formulation of the variational problem is generalized: the turbulent exchange coefficient of a quasi-geostrophic potential vorticity (QGPV) is included in the control vector. Secondly, the solution area more accurately describes the size of the Antarctic Circumpolar Current (ACC). Using the selection of linear meridional transport and the expansion of the solution in a Fourier series, the problem is reduced to a nonlinear system of ordinary differential equations (ODEs) in time. The doubly connected domain leads to the fact that the solution of the ODE must satisfy an additional stationary relation that determines the transport of the ACC. The variational algorithm is reduced to solving a system of forward and adjoint equations minimizing the mean squared error of the stationary relation. The QGPV turbulent exchange coefficient is determined in the process of solving the optimal problem. The numerical runs are carried out for a periodic channel simulating the water area of the ACC in the Southern Ocean. The characteristics of stationary current regimes are studied for different values of the model parameters. Typical is a sinusoidal circulation in both layers with a linear transfer with the wind, depending on the bottom topography. In some cases, under the sinusoidal, in the lower layer, a cellular circulation is formed, and sometimes an undercurrent occurs. In this case, the solution of the optimal problem is characterized by a low value of the turbulent viscosity coefficient and a low transport in the lower layer.

In 1982 Lovejoy has published an illustration to Mandelbrot proposal how to characterize the area-perimeter ratio of complicated planar forms and it was found that exponent \(\beta \) for the satellite- and radar-determined cloud and rain areas of such a fractal is 1.35 close to 4/3. Later on it was notified that the same exponent was found also for noctilucent clouds. Such a value might be related to classic turbulence theory of 1941. This text demonstrates this relation using two basic papers by Kolmogorov and Obukhov. The role of prefractal multipliers is revealed, they form a couple of the peculiar invariants for cloud fields and a non-dimensional self-similarity numbers for these fields of sizes \(1 - {{10}^{6}}\,\,{\text{k}}{{{\text{m}}}^{2}}.\) The peculiarity is in their dimensional dependence and in the presence of few invariants, not usual invariants in cloud forms. Further research on random walk of a fluid particle in the 6D phase-space may lead to new discoveries.