Dynamics and Modeling of Thermally and Orographically Forced Flows and Convection

Abstract

Many big cities around the world are located near the mountains. In city-mountain regions, thermally and topographically forced local winds are produced and they affect the transport of pollutants emitted into the urban atmosphere. A better understanding of the dynamics of thermally and topographically forced local winds is necessary to improve the prediction of local winds and to cope with environmental problems. In this study, the interactions of urban breezes with mountain slope winds in the presence of basic-state wind are theoretically examined within the context of the response of a stably stratified atmosphere to prescribed thermal and mechanical forcing. The interactions between urban breezes and mountain slope winds are viewed through the linear superposition of individual analytical solutions for urban thermal forcing, mountain thermal forcing, and mountain mechanical forcing. A setting in which a city is located downwind of a mountain is considered. In the nighttime, in the mountain-side urban area, surface/near-surface horizontal flows induced by mountain cooling and mountain mechanical forcing cooperatively interact with urban breezes, resulting in strengthened winds. In the daytime, in the urban area, surface/near-surface horizontal flows induced by mountain heating are opposed to urban breezes, giving rise to weakened winds. It is shown that the degree to which urban breezes and mountain slope winds interact is sensitive to the mountain height and the basic-state wind speed. Particularly, a change in the basic-state wind speed affects not only the strength of thermally and mechanically induced flows (internal gravity waves) but also their vertical wavelengths and decay rates. The examination of a case in a setting in which a city is located upwind of a mountain reveals that the direction of basic-state wind significantly affects the interactions between urban breezes and mountain slope winds. The urban breeze circulation (UBC) is a thermally forced mesoscale circulation characterized by low-level inward flows toward the urban center, updrafts near the urban center, upper-level outward flows, and weak downdrafts outside the urban area. Previous numerical modeling studies indicate that in the early morning the direction of the UBC can be reversed. Here, the dynamics of a reversed UBC is studied in the context of the response of the atmosphere to a specified thermal forcing, which represents the diurnally varying urban heating. For this, linearized, two-dimensional, hydrostatic, and Boussinesq airflow system in a rotating frame with a specified thermal forcing is solved using the Fourier transform method. The occurrence of a reversed UBC in the early morning is confirmed. The Coriolis parameter affects the strength and vertical structure of the UBC, whose role is similar to that of the coefficient of Rayleigh friction and Newtonian cooling. The occurrence condition, strength, and vertical structure of a reversed UBC are examined. The Coriolis force as well as urban heating alters the occurrence time of the reversed UBC. For a strongly viscous system, a reversed UBC occurs only in high latitudes with low occurrence possibility. A simple oscillation-type model for the horizontal velocity is constructed to get some dynamical insights into a reversed UBC. The analysis results also show that the Coriolis force alters the occurrence time of the reversed UBC. Dynamical aspects of flows forced by either convective heating or a mountain have been extensively studied, but those forced by both convective heating and a mountain have been less studied. Here, we theoretically examine the orographic-convective flows, gravity-wave reflection, and gravity-wave momentum fluxes in stably stratified two-layer hydrostatic and nonhydrostatic atmospheres. The upper layer (stratosphere) has a larger static stability than the lower layer (troposphere), and the basic-state wind has a constant shear in the troposphere and is uniform in the stratosphere. The equations governing small-amplitude perturbations in a two-dimensional, steady-state, and nonrotating system in the presence of orographic forcing and convective forcing are analytically solved. Then, the analytic solutions are analyzed to understand how orographically and convectively forced flows vary with changes in the basic-state wind speed, stratospheric static stability, and the location of the convection relative to the mountain. In a two-layer hydrostatic atmosphere, over the upslope of the mountain, the convectively forced deep upward motion is positively combined with the orographic uplift, thus giving rise to enhanced upward motions there. The ratio of the convectively forced vertical velocity to the orographically forced vertical velocity at the cloud base height over an upslope location of the mountain is analyzed to further understand the linear interaction between orographically and convectively forced flows. The gravity-wave reflection at the tropopause plays an important role in orographic-convective flows. The gravity-wave reflection at the tropopause acts to amplify the symmetric (anti-symmetric) structure of orographically (convectively) forced waves. The vertical fluxes of the horizontal momentum are analytically obtained. The total momentum flux contains the component resulting from the nonlinear interaction between orographically and convectively forced waves. It is found that the nonlinear interaction component can be as important as each of the orographic and convective components in the total momentum flux depending on the location of the convection relative to the mountain. A nondimensional governing equation system including the Rayleigh friction and the Newtonian cooling is considered to theoretically investigate the nonhydrostatic effects on convectively forced flows in a single layer nonhydrostatic atmosphere. The nondimensionalized airflow system contains the nonhydrostaticity factor β (= U/Na, where U is the basic-state wind speed, a is the half-width of the convective forcing, and N is the basic-state buoyancy frequency). In an inviscid-limit system, the solutions for vertical velocity are classified into the propagating mode (k ≤ β–1, where k is the nondimensional horizontal wavenumber) and the evanescent mode (k > β–1). As β increases, an alternating wavy pattern of updrafts and downdrafts appears downstream of the convective forcing with a horizontal wavelength of 2πβ corresponding to the critical horizontal wavenumber kc = β–1. The momentum flux analysis shows that the alternating updrafts and downdrafts are almost horizontally propagating gravity waves of the propagating mode whose k is slightly smaller than kc and that these gravity waves strengthen the momentum flux above the convective forcing. In a viscid system, the solution for vertical velocity has propagating and decaying components simultaneously such that they cannot be explicitly separated. Here, the propagating mode and two evanescent modes are defined by comparing the magnitudes of the vertical wavenumber and decay rate. For large viscous coefficient, the k-range of the propagating mode becomes narrow and the alternating updrafts and downdrafts dissipate. As β increases, the propagating mode, which strengthens the momentum flux above the convective forcing, effectively dissipates even with small viscous coefficient. In a two-layer nonhydrostatic atmosphere, the wave components form modified Bessel functions of the purely imaginary order. The wave components in the stratosphere are sinusoidal or exponential depending on the horizontal wave number, tropospheric basic-state wind shear, and stratospheric static stability. Resonant waves corresponding to the horizontal wavelength of the zeros of the denominator of the solution are nonhydrostatically generated downstream of the convective forcing. Without stratospheric stability jump, the horizontal wavelengths of resonant waves are the zeros of Kiμ(ξ0). Relatively short waves are trapped at a certain height because the wave behavior changes from sinusoidal to exponential. Most of the resonant waves are in the range of the sinusoidal asymptotic of the modified Bessel function. Using that fact, the wavelengths of resonant waves in the case of Ri = 9, 36, and 144 are approximated. Stratospheric stability jump conditionally reflects totally or partially and transmits the resonant waves. Relatively short waves are totally trapped in the troposphere by the gravity-wave reflection and the window is broader in the case with stronger wind shear. The transmitted resonant waves vertically propagate in the stratosphere and transport wave energy. Aerosol effects on orographic precipitation from shallow and deep convective clouds over mountains with different windward-widths are numerically studied using the Weather Research and Forecasting model which includes a bin microphysics scheme. Forced uplift by a mountain in a potentially unstable atmosphere results in cellular-type convective orographic clouds. In the cases with shallow and warm clouds, more cloud droplets are produced under higher aerosol number concentration. As a result, the growth of cloud droplets into raindrops is inhibited, the total and maximum precipitation amounts decrease, and the maximum precipitation occurs downstream. In addition, stronger convection is generated because of stronger condensational heat release, and more liquid drops of small sizes are distributed in a deeper layer. In the case of narrower windward-width, compared to the case with symmetric mountain, the steeper upslope generates stronger convection with a shorter advection time scale, hence stronger precipitation is concentrated over a narrower area. Accordingly, the aerosol effects, which result in a decrease in the total precipitation amount and a downstream shift of the location of the maximum precipitation, are clearer here than in the cases with the symmetric mountain. In the case with a wider windward-width, the gentler upslope generates a weaker convection, while a large portion of liquid drops precipitate over the wide upslope with a long-enough advection time scale. The orographic precipitation amount and the location of its maximum are more sensitive to the aerosol number concentration when the mountain upslope is steeper. In the cases with deep and mixed-phase clouds, orographic precipitation occurs mainly from lower-level clouds and its dependency on the aerosol number concentration and upslope steepness is similar to that in the case with shallow and warm convective clouds in the early stage. As time goes on, lower-level convective clouds vigorously develop and an upper-level mixed-phase cloud extends upstream depending on the case, and strong interactions between lower- and upper-level clouds result in strong precipitation via melting or direct sedimentation of ice-phased particles if both conditions are satisfied. The mixed-phase processes (freezing, WBF process, and riming) during the interaction is stronger in the case of higher aerosol number concentration, resulting in enhanced surface precipitation on the symmetric mountain. In the cases with asymmetric mountains, the trends are not monotonic. In the case with steep upslope, the liquid drop growth is slower compared to the clean case and the condensational latent heating is weaker compared to the polluted case, and these characteristics inhibit the interaction between lower- and higher-level clouds and the mixed-phase processes result in the minimal surface precipitation amount in the control case. In the case with a gentle upslope, on the other hand, stronger condensational heating than the clean case and faster growth of liquid drops than the polluted case enhance the interaction between lower- and higher-level clouds and the mixed-phase processes result in the maximal surface precipitation amount in the control case. A real orographic precipitation event over the Taebaek Mountains from 26 to 27 June 2015 with three different aerosol number concentrations is numerically simulated to examine aerosol effects on real orographic precipitation. Near Sokcho, orographic clouds are warm-phased. In this region, an increase in aerosol number concentration results in the increased cloud droplet mixing ratio and the decreased raindrop mixing ratio. However, the change of the surface precipitation amount is not monotonic. Both the increased raindrop mixing ratio in the clean case and the decreased cloud droplet mixing ratio in the polluted case result in enhanced surface precipitation. Near Mt. Kumgang, ice particles in the upper-level cloud play an important role in controlling the surface precipitation amount. In this region, the increase in aerosol number concentration results in the increased surface precipitation amount through the increase the ice-phased particle mixing ratio.