Toward Generalizing the Impact of Surface Heating, Stratification, and Terrain Geometry on the Daytime Heat Export from an Idealized Valley

Abstract

The convective export of heat from different types of idealized valleys for fair-weather daytime conditions is studied with the Weather Research and Forecasting (WRF) Model. The goal is to test the hypothesis that the total export of heat over the course of the day depends on a so-called breakup parameter B. The breakup parameter is the ratio between the energy required to neutralize the initially stably stratified valley atmosphere and the total energy provided by the surface sensible heat flux. To achieve this goal, simulations with different surface heating, initial stability, and terrain geometry are performed. The fraction of the sensible heat provided at the surface that is exported at crest height over the course of the day depends exponentially on B. The effects of variations of the valley width, crest height, forcing amplitude, and initial stratification on the total export of heat can be described by this function. The complete neutralization of the stratification in the valley is never reached if B exceeds a critical value of about 0.65 for an initially constant stratification. For a valley geometry with linear slopes and sharp crests, up to 60% of the provided heat is exported for the strongest forcing and the weakest stability (i.e., B ≈ 0.1), whereas less than 5% is exported for B > 0.65. The minimum heat export for larger B is higher for rounded crests (10%) and for a deep residual layer that extends to above crest height (17%).

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

“…Hence, the tracer mass turnover can be effectively parameterized by B [102]. Similar results have been found for the export of heat [221]. Because B is affected by valley width, crest height, forcing amplitude, and stratification, it quantifies the joint impact of all these factors on the total heat export from the valley atmosphere.…”

“…The atmospheric and diabatic factors controlling the transport and exchange of heat and mass are the ambient (large-scale) wind speed and direction, the static stability of the valley atmosphere, the radiative forcing, and the associated surface sensible heat flux, as well as latent heat release in clouds [102,103,221]. The most important geometric factors are the valley width and depth, the inclination of the valley floor, and the along-valley variability of the valley cross-section [121,126,162].…”

“…No viable methodology to solve this problem exists so far, because the breakup parameter method has only been used to parameterize the total, i.e., time-integrated, exchange [102,221]. To illustrate the possible approaches to the problem, it is useful to recall some basic aspects of ABL parameterization.…”

Current Challenges in Understanding and Predicting Transport and Exchange in the Atmosphere over Mountainous Terrain

“…Left column: momentum flux profile from airborne observations over the Rocky Mountains during the occurrence of a stationary wave (top) and streamfunction isopleths to show the topography (bottom) after Lilly and Kennedy [33] (© Copyright (1973) American Meteorological Society (AMS) Middle column: heat exchange (ratio of exported sensible heat through the top of the valley and provided heat by solar radiation ) over an idealized two-ridge valley as a function of the breakup parameter (i.e., a measure of the valley heat deficit). The symbols represent individual simulations and the lines are fits for different initial stability profiles; from Leukauf et al [34] (© Copyright (2017) American Meteorological Society (AMS)). Right column: daily cycle of moisture flux out of the Riviera Valley (Switzerland).…”

“…Middle column: heat exchange (ratio of exported sensible heat through the top of the valley Q exp and provided heat by solar radiation Q prov ) over an idealized two-ridge valley as a function of the breakup parameter (i.e., a measure of the valley heat deficit). The symbols represent individual simulations and the lines are fits for different initial stability profiles; from Leukauf et al [34] (© Copyright (2017) American Meteorological Society (AMS)). Right column: daily cycle of moisture flux out of the Riviera Valley (Switzerland).…”