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Abstract
A simple analytical expression for indexing the orographic precipitation rate over high mountains is presented. The formula is based upon the assumption that the moisture convergence in the mountainous boundary layer approximately equals the precipitation. Realistic precipitation distributions are obtained when numerical advection is permitted for the Himalayas, Equadorian Andes and the Sierra Nevada Mountains in California. In the latter case the simulated distributions compete well with a fully two-dimensional precipitation model for some unusual stormy events. Following the model results over high mountains, it is suggested that for the distribution of precipitation, particularly over the high mountains, the detailed microphysical processes may play a lesser essential role than that for small to medium size mountains.
The elevation of maximum orographic precipitation zm , is investigated and an analytical expression for zm is derived for a bell-shaped mountain. This expression predicts zm values that are in general agreement with observations. The elevation of maximum precipitation zm is found to always be shifted to lower levels than the point of the steepest slope. It is also shown that an upper limit for zm exists. This upper limit is independent of the mountain height and is determined mainly by the moisture scale height and the tropospheric wide height.
In addition to the two maxima of precipitation over the Himalayas that have been observed in the foothills and at about 2–2.4 km, a third unknown maxima is predicted by the theory. This unobserved maxima is predicted over the Great Himalayan Range at the height of 4 km. Such a maxima, if it exists, could not be detected due to the lack of enough observations at high elevations.
Abstract
A simple analytical expression for indexing the orographic precipitation rate over high mountains is presented. The formula is based upon the assumption that the moisture convergence in the mountainous boundary layer approximately equals the precipitation. Realistic precipitation distributions are obtained when numerical advection is permitted for the Himalayas, Equadorian Andes and the Sierra Nevada Mountains in California. In the latter case the simulated distributions compete well with a fully two-dimensional precipitation model for some unusual stormy events. Following the model results over high mountains, it is suggested that for the distribution of precipitation, particularly over the high mountains, the detailed microphysical processes may play a lesser essential role than that for small to medium size mountains.
The elevation of maximum orographic precipitation zm , is investigated and an analytical expression for zm is derived for a bell-shaped mountain. This expression predicts zm values that are in general agreement with observations. The elevation of maximum precipitation zm is found to always be shifted to lower levels than the point of the steepest slope. It is also shown that an upper limit for zm exists. This upper limit is independent of the mountain height and is determined mainly by the moisture scale height and the tropospheric wide height.
In addition to the two maxima of precipitation over the Himalayas that have been observed in the foothills and at about 2–2.4 km, a third unknown maxima is predicted by the theory. This unobserved maxima is predicted over the Great Himalayan Range at the height of 4 km. Such a maxima, if it exists, could not be detected due to the lack of enough observations at high elevations.
Abstract
The diurnal and interdiural wind variabilities are defined in terms of the “relative gustiness” −σν/V̄. The proportion α between the diurnal and the interdiurnal variabilities thus defined is suggested as a useful index in mesoscale studies. The α index is calculated in more than 30 stations in the Israel area during summer and winter, and is shown as a simple tool for the identification of climatic-geographic regions in which:
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The variability due to the changes of the large-scale pressure gradients may or may not be ignored in mesoscale models. An α index larger than 1 indicates the dominance of the diurnal processes over the interdiumal processes in producing wind variability, in which case large-scale effects are relatively small.
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Hodograph representation for the average diurnal wind variation is or is not a faithful picture of the actual wind observations on a particular day. An α index larger than 1 suggests a more faithful representation of the wind hodograph.
As expected, the α index is larger than 1 during summer in nearly all stations in Israel while during winter it is less than 1.
The values of α during summer are very high. They are generally between 1.5 and 2.5 but in the Jordan Valley, Arava and the Negev desert α indices reach 3 or even 4–5, indicating both vigorous mesoscale forcing due to channeling and/or differential heating and the reduced cited of the migrating cyclones. In the winter only few southern stations get α-values slightly larger than 1, indicating the general dominance of the large-scale (synoptic) variability relative to the locally induced mesoscale variability.
Abstract
The diurnal and interdiural wind variabilities are defined in terms of the “relative gustiness” −σν/V̄. The proportion α between the diurnal and the interdiurnal variabilities thus defined is suggested as a useful index in mesoscale studies. The α index is calculated in more than 30 stations in the Israel area during summer and winter, and is shown as a simple tool for the identification of climatic-geographic regions in which:
-
The variability due to the changes of the large-scale pressure gradients may or may not be ignored in mesoscale models. An α index larger than 1 indicates the dominance of the diurnal processes over the interdiumal processes in producing wind variability, in which case large-scale effects are relatively small.
-
Hodograph representation for the average diurnal wind variation is or is not a faithful picture of the actual wind observations on a particular day. An α index larger than 1 suggests a more faithful representation of the wind hodograph.
As expected, the α index is larger than 1 during summer in nearly all stations in Israel while during winter it is less than 1.
The values of α during summer are very high. They are generally between 1.5 and 2.5 but in the Jordan Valley, Arava and the Negev desert α indices reach 3 or even 4–5, indicating both vigorous mesoscale forcing due to channeling and/or differential heating and the reduced cited of the migrating cyclones. In the winter only few southern stations get α-values slightly larger than 1, indicating the general dominance of the large-scale (synoptic) variability relative to the locally induced mesoscale variability.
Abstract
In a first theoretical study, the reasons for anti-clockwise rotation (clockwise rotation in the Southern Hemisphere) of the wind hodograph in the boundary layer are investigated. As observations of wind hodographs show two different kinds of anti-clockwise rotation (ACR), one frequently observed, which is highly irregular with partly ACR and the other with clear ACR, two methods have been applied. At first a two-dimensional nonlinear model which includes sea-land breezes as well as a mountain reveal partly ACR at the lee of the mountain. By analyzing the different terms in the equation for the wind vector rotation, it is shown that the pressure-gradient term is usually the leading one, and the advection term is very small. But the latter becomes important in cases of ACR. Second, a linear model is solved analytically showing that inclusion of a rotating thermal force in the ACR sense generates clear ACR. It is shown that a critical value for the phase shift between the thermal forces in the horizontal directions exists. At that value, transition to ACR occurs. The critical curves are drawn as function of latitude, friction and relative amplitudes of the thermal forces. Common features of hodographs obtained by observations such as eccentricity, shape, tilt and sense of rotation might be explained in view of the theory.
Abstract
In a first theoretical study, the reasons for anti-clockwise rotation (clockwise rotation in the Southern Hemisphere) of the wind hodograph in the boundary layer are investigated. As observations of wind hodographs show two different kinds of anti-clockwise rotation (ACR), one frequently observed, which is highly irregular with partly ACR and the other with clear ACR, two methods have been applied. At first a two-dimensional nonlinear model which includes sea-land breezes as well as a mountain reveal partly ACR at the lee of the mountain. By analyzing the different terms in the equation for the wind vector rotation, it is shown that the pressure-gradient term is usually the leading one, and the advection term is very small. But the latter becomes important in cases of ACR. Second, a linear model is solved analytically showing that inclusion of a rotating thermal force in the ACR sense generates clear ACR. It is shown that a critical value for the phase shift between the thermal forces in the horizontal directions exists. At that value, transition to ACR occurs. The critical curves are drawn as function of latitude, friction and relative amplitudes of the thermal forces. Common features of hodographs obtained by observations such as eccentricity, shape, tilt and sense of rotation might be explained in view of the theory.
Abstract
In contrast to earlier studies, where only binary tropical storms were explored, the rotation at midlatitude and the subtropics is studied here. The point vortex theory applied to two neighboring cyclonic vortices isolated from external forcing predicts the following features: rotation in a cyclonic sense at a rate directly proportional to the sum of the cyclones' intensities and inversely to the square of their separation, with the weaker cyclone rotating faster than the more intense one. This interaction, noticed in the Tropics, was entitled the Fujiwhara effect or binary interaction. Objective analysis of 17 313 cyclone pairs using ECMWF initialized datasets was done to examine the existence and behavior of binary interaction between extratropical cyclones. The impact of anticyclones is studied through the moments of distribution for the relative vorticity. The anticyclonic shear of the background flow and the prevalence of anticyclones in the subtropics are suggested to explain the absence of binary rotation there. Midlatitude cyclone pairs with separations of up to 2000 km are indeed found to rotate cyclonically about each other at a rate proportional to their combined intensities, in agreement with theory. The binary rotation rate decreases with the square of the separation distance, as in the point vortex theory, up to 1400 km. But a pronounced unexpected peak was found near 1800 km. No significant correlation was found between the individual rotation speeds ratios and that of the intensities of the interacting cyclones. Only partial agreement between the observed rotation of midlatitude surface binary cyclones and the barotropic predictions indicates the need to adopt a more elaborate model. Indeed, the 500-hPa binary interaction study reveals a much better agreement with theory. In a companion study, the authors propose a two-level conceptual model that employs the PV ideas for exploring the binary surface cyclone behavior.
Abstract
In contrast to earlier studies, where only binary tropical storms were explored, the rotation at midlatitude and the subtropics is studied here. The point vortex theory applied to two neighboring cyclonic vortices isolated from external forcing predicts the following features: rotation in a cyclonic sense at a rate directly proportional to the sum of the cyclones' intensities and inversely to the square of their separation, with the weaker cyclone rotating faster than the more intense one. This interaction, noticed in the Tropics, was entitled the Fujiwhara effect or binary interaction. Objective analysis of 17 313 cyclone pairs using ECMWF initialized datasets was done to examine the existence and behavior of binary interaction between extratropical cyclones. The impact of anticyclones is studied through the moments of distribution for the relative vorticity. The anticyclonic shear of the background flow and the prevalence of anticyclones in the subtropics are suggested to explain the absence of binary rotation there. Midlatitude cyclone pairs with separations of up to 2000 km are indeed found to rotate cyclonically about each other at a rate proportional to their combined intensities, in agreement with theory. The binary rotation rate decreases with the square of the separation distance, as in the point vortex theory, up to 1400 km. But a pronounced unexpected peak was found near 1800 km. No significant correlation was found between the individual rotation speeds ratios and that of the intensities of the interacting cyclones. Only partial agreement between the observed rotation of midlatitude surface binary cyclones and the barotropic predictions indicates the need to adopt a more elaborate model. Indeed, the 500-hPa binary interaction study reveals a much better agreement with theory. In a companion study, the authors propose a two-level conceptual model that employs the PV ideas for exploring the binary surface cyclone behavior.
Abstract
A simple method is developed for computing the interactions among various factors influencing the atmospheric circulations. It is shown how numerical simulations can be utilized to obtain the pure contribution of any factor to any predicted field, as well as the contributions due to the mutual interactions among two or more factors. The mathematical basis for n factors is developed, and it is shown that 2 n simulations are required for the separation of the contributions and their possible interactions. The method is demonstrated with two central factors, the topography and surface fluxes, and their effect on the rainfall distribution for a cyclone evolution in the Mediterranean.
Abstract
A simple method is developed for computing the interactions among various factors influencing the atmospheric circulations. It is shown how numerical simulations can be utilized to obtain the pure contribution of any factor to any predicted field, as well as the contributions due to the mutual interactions among two or more factors. The mathematical basis for n factors is developed, and it is shown that 2 n simulations are required for the separation of the contributions and their possible interactions. The method is demonstrated with two central factors, the topography and surface fluxes, and their effect on the rainfall distribution for a cyclone evolution in the Mediterranean.
Abstract
A one-level sigma-coordinate model originally developed by Danard and modified by Mass and Dempsey and Alpert et al., is applied to the study of surface flow over an averaged summer diurnal cycle in Israel. The detailed flow features are compared to three-dimensional modeling studies and to dense surface wind observations.
The winds al a height of 10 m from the one-level model were found comparable to those obtained by three-dimensional simulations, and in some cases the one-level model predicted observed surface flow features that were not simulated by the three-dimensional simulations, probably because of the finer horizontal grid resolution in the one-level model. The two models had similar deficiencies in diagnosing observed flow features in many cases. A severe drawback of the one-level model is the inability to advance the sea-breeze front (SBF) over a ridge crest correctly. Based upon an earlier vertical cross-sectional study by Alpert et al., an explanation for this discrepancy is suggested.
In a detailed, high-resolution analysis of the summer mesoscale flow, the surface horizontal winds from the one-level high-resolution model and the three-dimensional model are compared to the relatively dense network of wind observations in Israel every three hours, for an averaged diurnal cycle. Several features of the surface flow are revealed and illustrated, including
(i) Flow convergence in the evening near the coast;
(ii) A convergence line south of Lake Kinneret (Sea of Galilee) that forms in the morning, moves southward along the Jordan Rift Valley, and finally merges with the SBF in the afternoon;
(iii) Relatively strong nocturnal flow at the southern Mediterranean coast of Israel, possibly due to the concave shoreline there.
These, as well as many other observed flow features, are simulated by both the one-level model and the three-dimensional model, though the one-level model required only modest computer resources. Hence, this study illustrates that the trade-off between horizontal resolution and explicit vertical resolution may be most beneficial, at least when topographic and surface forcing dominate.
Abstract
A one-level sigma-coordinate model originally developed by Danard and modified by Mass and Dempsey and Alpert et al., is applied to the study of surface flow over an averaged summer diurnal cycle in Israel. The detailed flow features are compared to three-dimensional modeling studies and to dense surface wind observations.
The winds al a height of 10 m from the one-level model were found comparable to those obtained by three-dimensional simulations, and in some cases the one-level model predicted observed surface flow features that were not simulated by the three-dimensional simulations, probably because of the finer horizontal grid resolution in the one-level model. The two models had similar deficiencies in diagnosing observed flow features in many cases. A severe drawback of the one-level model is the inability to advance the sea-breeze front (SBF) over a ridge crest correctly. Based upon an earlier vertical cross-sectional study by Alpert et al., an explanation for this discrepancy is suggested.
In a detailed, high-resolution analysis of the summer mesoscale flow, the surface horizontal winds from the one-level high-resolution model and the three-dimensional model are compared to the relatively dense network of wind observations in Israel every three hours, for an averaged diurnal cycle. Several features of the surface flow are revealed and illustrated, including
(i) Flow convergence in the evening near the coast;
(ii) A convergence line south of Lake Kinneret (Sea of Galilee) that forms in the morning, moves southward along the Jordan Rift Valley, and finally merges with the SBF in the afternoon;
(iii) Relatively strong nocturnal flow at the southern Mediterranean coast of Israel, possibly due to the concave shoreline there.
These, as well as many other observed flow features, are simulated by both the one-level model and the three-dimensional model, though the one-level model required only modest computer resources. Hence, this study illustrates that the trade-off between horizontal resolution and explicit vertical resolution may be most beneficial, at least when topographic and surface forcing dominate.
Abstract
A deep polar air-mass penetration to the eastern Mediterranean in November 1982 is described. The unusual weather and, in particular, the rain pattern is discussed. This event contributes to heavy rain in the inland stations, of particular importance in the semiarid zone.
The stability characteristics of the polar air mall on its way to the eastern Mediterranean are investigated and compared to a similar case in the western Mediterranean. It is suggested that the land-sea distribution along the path of the penetrating polar air mass is responsible for the significant differences that were found.
Abstract
A deep polar air-mass penetration to the eastern Mediterranean in November 1982 is described. The unusual weather and, in particular, the rain pattern is discussed. This event contributes to heavy rain in the inland stations, of particular importance in the semiarid zone.
The stability characteristics of the polar air mall on its way to the eastern Mediterranean are investigated and compared to a similar case in the western Mediterranean. It is suggested that the land-sea distribution along the path of the penetrating polar air mass is responsible for the significant differences that were found.
Abstract
A two-dimensional mesometerological model was originally constructed by Alpert et a.. to simulate the summer air circulation in the area between the eastern Mediterranean waters and the Golan Heights involving en route Lake Kinneret (the Sea of Galilee). In this study the same model is applied to the case of the nocturnal circulation across southern Lake Michigan. The case simulated is for a wintry day in November 1978, the data for which were documented in a recent article by Passarelli and Braham.
The results of the simulation are very encouraging. Particular mention should be made of the fact that the predicted location of the maximum upward velocities close to the Wisconsin shore of Lake Michigan and the associated lake-breeze front at the convergence zone of the lake breezes of the opposite shores are well predicted by the model. The observed land-breeze front was accompanied by the development of snow bands. The main purpose of this study is to demonstrate that a computationally inexpensive two-dimensional model can adequately simulate coastal flows like that of Lake Michigan in the present study, making it a potentially useful forecasting and diagnostic tool. It was our intention as well to test the same model (physics and numerics) with a different lake-circulation problem. Despite the great differences in the physical characteristics of topography, size and meteorological conditions of the two lakes to which the model was applied (in the lake Kinneret case, it is the lake which is cooler than the surrounding hot summer air of the Jordan Valley while in the Lake Michigan case it is the relatively warm lake which contrasts the polar air mass). However, in both cases the forcing is similar (10–15°C); it was found to do reasonably well. On the more theoretical side, this numerical study presents the first example of a strongly developed land-breeze front.
Abstract
A two-dimensional mesometerological model was originally constructed by Alpert et a.. to simulate the summer air circulation in the area between the eastern Mediterranean waters and the Golan Heights involving en route Lake Kinneret (the Sea of Galilee). In this study the same model is applied to the case of the nocturnal circulation across southern Lake Michigan. The case simulated is for a wintry day in November 1978, the data for which were documented in a recent article by Passarelli and Braham.
The results of the simulation are very encouraging. Particular mention should be made of the fact that the predicted location of the maximum upward velocities close to the Wisconsin shore of Lake Michigan and the associated lake-breeze front at the convergence zone of the lake breezes of the opposite shores are well predicted by the model. The observed land-breeze front was accompanied by the development of snow bands. The main purpose of this study is to demonstrate that a computationally inexpensive two-dimensional model can adequately simulate coastal flows like that of Lake Michigan in the present study, making it a potentially useful forecasting and diagnostic tool. It was our intention as well to test the same model (physics and numerics) with a different lake-circulation problem. Despite the great differences in the physical characteristics of topography, size and meteorological conditions of the two lakes to which the model was applied (in the lake Kinneret case, it is the lake which is cooler than the surrounding hot summer air of the Jordan Valley while in the Lake Michigan case it is the relatively warm lake which contrasts the polar air mass). However, in both cases the forcing is similar (10–15°C); it was found to do reasonably well. On the more theoretical side, this numerical study presents the first example of a strongly developed land-breeze front.
Abstract
Trends in the orographic rainfall ratio R 0 over Israel are reevaluated. It is shown that the rainfall has not changed significantly over most of the mountainous stations, with some significant increases over the central mountains. The overall evaluation of R 0 for all potential station pairs, calculating the ratio of each mountain station separately over each coastal or seashore station, indicates that about 50% of all pairs show a positive trend in R 0. The high spatial variability, especially over the mountains, allows for finding orographic rainfall ratio trends that are significant in both the positive and negative directions. The correct definition of R 0 in the Israeli case requires the use of a seashore cluster of stations. If some of the seashore stations are replaced by inland stations, and in particular stations that are right over the region of maximum positive rainfall urban enhancement due to the thermal heat island or other urban effects, a seemingly decreasing “orographic ratio” is unavoidable. In such a case, urban dynamical positive effects on coastal rainfall can be erroneously interpreted as pollution suppression of orographic rainfall. When seashore stations are selected as required by a proper definition of the orographic ratio, increasing R 0 is obtained over central Israel and an insignificant trend over the north is found. Furthermore, evaluation of the ratio of rainfall for the upwind in comparison with the downwind side of the Galilee Mountains exhibits an increasing trend, opposite to the recent findings of Givati and Rosenfeld. The rainfall analysis shows no evidence of any suppression of rainfall over the mountains due to pollution, and at least in Israel other factors besides aerosols are predominant in defining the trends in the orographic rainfall ratio.
Abstract
Trends in the orographic rainfall ratio R 0 over Israel are reevaluated. It is shown that the rainfall has not changed significantly over most of the mountainous stations, with some significant increases over the central mountains. The overall evaluation of R 0 for all potential station pairs, calculating the ratio of each mountain station separately over each coastal or seashore station, indicates that about 50% of all pairs show a positive trend in R 0. The high spatial variability, especially over the mountains, allows for finding orographic rainfall ratio trends that are significant in both the positive and negative directions. The correct definition of R 0 in the Israeli case requires the use of a seashore cluster of stations. If some of the seashore stations are replaced by inland stations, and in particular stations that are right over the region of maximum positive rainfall urban enhancement due to the thermal heat island or other urban effects, a seemingly decreasing “orographic ratio” is unavoidable. In such a case, urban dynamical positive effects on coastal rainfall can be erroneously interpreted as pollution suppression of orographic rainfall. When seashore stations are selected as required by a proper definition of the orographic ratio, increasing R 0 is obtained over central Israel and an insignificant trend over the north is found. Furthermore, evaluation of the ratio of rainfall for the upwind in comparison with the downwind side of the Galilee Mountains exhibits an increasing trend, opposite to the recent findings of Givati and Rosenfeld. The rainfall analysis shows no evidence of any suppression of rainfall over the mountains due to pollution, and at least in Israel other factors besides aerosols are predominant in defining the trends in the orographic rainfall ratio.
