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- Author or Editor: R. A. Pielke x
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Abstract
Natural land surfaces are usually heterogeneous over the resolvable scales considered in atmospheric numerical models. Therefore, model surface parameterizations that assume surface homogeneity may fail to represent the surface forcing accurately.
In this paper, a parameterization of the subgrid-scale forcing of heterogeneous land surfaces for atmospheric numerical models is suggested. In each surface grid element of the numerical model similar homogeneous land patches located at different places within the element are regrouped into subgrid classes. Then, for each one of the subgrid classes, a sophisticated micrometeorological model of the soil-plant-atmosphere system is applied to assess the surface temperature, humidity, and fluxes to the atmosphere. The global fluxes of energy between the grid and the atmosphere are obtained by averaging according to the distribution of the subgrid classes. In addition to the surface forcing, detailed micrometeorological conditions of the patches are assessed for the domain simulated by the atmospheric model.
This parameterization was incorporated into a mesoscale numerical model to test the impact of subgrid-scale land surface heterogeneities on the development of local circulations. Where strong contrasts in total sensible heat flux are generated by land surface heterogeneities, circulations as strong as sea breezes may develop.
Abstract
Natural land surfaces are usually heterogeneous over the resolvable scales considered in atmospheric numerical models. Therefore, model surface parameterizations that assume surface homogeneity may fail to represent the surface forcing accurately.
In this paper, a parameterization of the subgrid-scale forcing of heterogeneous land surfaces for atmospheric numerical models is suggested. In each surface grid element of the numerical model similar homogeneous land patches located at different places within the element are regrouped into subgrid classes. Then, for each one of the subgrid classes, a sophisticated micrometeorological model of the soil-plant-atmosphere system is applied to assess the surface temperature, humidity, and fluxes to the atmosphere. The global fluxes of energy between the grid and the atmosphere are obtained by averaging according to the distribution of the subgrid classes. In addition to the surface forcing, detailed micrometeorological conditions of the patches are assessed for the domain simulated by the atmospheric model.
This parameterization was incorporated into a mesoscale numerical model to test the impact of subgrid-scale land surface heterogeneities on the development of local circulations. Where strong contrasts in total sensible heat flux are generated by land surface heterogeneities, circulations as strong as sea breezes may develop.
Abstract
Values of p for the exponent-type wind profile formulation, used in vertical extrapolations of wind speed, were derived for the marine atmospheric surface layer. Nomograms were constructed providing p values as dependent on a single elevation measurement of the air temperature, wind speed, and the surface water temperature. The range of p values in the unstable surface layer is between 0.02 to 0.2, while for stable situations the range is 0.1 to possibly ∼1.0. The values of p converge to about 0.2 for high wind speeds.
Abstract
Values of p for the exponent-type wind profile formulation, used in vertical extrapolations of wind speed, were derived for the marine atmospheric surface layer. Nomograms were constructed providing p values as dependent on a single elevation measurement of the air temperature, wind speed, and the surface water temperature. The range of p values in the unstable surface layer is between 0.02 to 0.2, while for stable situations the range is 0.1 to possibly ∼1.0. The values of p converge to about 0.2 for high wind speeds.
Abstract
The fractal dimension, Lyapunov-exponent spectrum, Kolmogorov entropy, and predictability are analyzed for chaotic attractors in the atmosphere by analyzing the time series of daily surface temperature and pressure over several regions of the United States and the North Atlantic Ocean with different climatic signal-to-noise ratios. Though the total number of data points (from about 13 800 to about 36 500) is larger than those used in previous studies, it is still too small to obtain a reliable estimate of the Grassberger–Procaccia correlation dimension because of the limitations discussed by Ruelle. However, it can be shown that this dimension is greater than 8. Also, it is pointed out that most, if not all, of the previous estimates of low fractal dimensions in the atmosphere are spurious. These results lead us to claim that there probably exist no low-dimensional strange attractors in the atmosphere. Because the fractal dimension has not yet been saturated, the Kolmogorov entropy and the error-doubling time obtained by the method of Grassberger and Procaccia are sensitive to the selection of the time delay and are thus unreliable. Geographic variability of the fractal dimension is suggested, but further verification is needed.
A practical and more reliable method for estimating the Kolmogorov entropy and error-doubling time involves the computation of the Lyapunov-exponent spectrum using the algorithm of Zeng et al. Using this method, it is found that the error-doubling time is about 2–3 days in Fort Collins, Colorado, about 4–5 days in Los Angeles, California, and about 5–8 days in the North Atlantic Ocean. The predictability time is longer over regions with a higher climatic signal-to-noise ratio (e.g., Los Angeles), and the predictability time of summer and/or winter data is longer than for the entire year. The difference between these estimates of error-doubling time and estimates based on general circulation models (GCMs) is discussed. It is also mentioned that the computation of the Lyapunov exponents is slightly sensitive to the selection of the time delay, possibly because the fractal dimension is very high in the atmosphere. Such sensitivity has not been mentioned in previous similar studies.
Abstract
The fractal dimension, Lyapunov-exponent spectrum, Kolmogorov entropy, and predictability are analyzed for chaotic attractors in the atmosphere by analyzing the time series of daily surface temperature and pressure over several regions of the United States and the North Atlantic Ocean with different climatic signal-to-noise ratios. Though the total number of data points (from about 13 800 to about 36 500) is larger than those used in previous studies, it is still too small to obtain a reliable estimate of the Grassberger–Procaccia correlation dimension because of the limitations discussed by Ruelle. However, it can be shown that this dimension is greater than 8. Also, it is pointed out that most, if not all, of the previous estimates of low fractal dimensions in the atmosphere are spurious. These results lead us to claim that there probably exist no low-dimensional strange attractors in the atmosphere. Because the fractal dimension has not yet been saturated, the Kolmogorov entropy and the error-doubling time obtained by the method of Grassberger and Procaccia are sensitive to the selection of the time delay and are thus unreliable. Geographic variability of the fractal dimension is suggested, but further verification is needed.
A practical and more reliable method for estimating the Kolmogorov entropy and error-doubling time involves the computation of the Lyapunov-exponent spectrum using the algorithm of Zeng et al. Using this method, it is found that the error-doubling time is about 2–3 days in Fort Collins, Colorado, about 4–5 days in Los Angeles, California, and about 5–8 days in the North Atlantic Ocean. The predictability time is longer over regions with a higher climatic signal-to-noise ratio (e.g., Los Angeles), and the predictability time of summer and/or winter data is longer than for the entire year. The difference between these estimates of error-doubling time and estimates based on general circulation models (GCMs) is discussed. It is also mentioned that the computation of the Lyapunov exponents is slightly sensitive to the selection of the time delay, possibly because the fractal dimension is very high in the atmosphere. Such sensitivity has not been mentioned in previous similar studies.
Abstract
An analytical evaluation of the vertical heat fluxes associated with the mesoscale flow generated by thermal inhomogeneities in the PBL in the absence of a synoptic wind is presented. Results show that the mesoscale fluxes are of the same order as the diabatic heat fluxes.
In the sea-breeze case results show that in the lower layer of the atmosphere the heat flux is positive over the land and negative over the sea with an overall positive horizontal average. In the free atmosphere above the PBL the mesoscale vertical heat flux is negative over the land and over the sea; that is, the lower atmosphere becomes warmer while the free atmosphere above becomes cooler. As a result the mesoscale flow contributes to the weakening of the atmospheric stability within a region that extends a Rossby radius distance from the coastline, and up to an altitude larger than twice the depth of the convective PBL. The average momentum flux equals zero because the momentum removed over the sea is fed back into the atmosphere over the land.
Sinusoidally periodic thermal inhomogeneities induce periodic atmospheric cells of the same horizontal scale. The intensity of mesoscale cells increases for increasing values of the wavenumber, reaches its maximum value when the wavelength of the forcing is of the order of the local Rossby radius, and then decreases as the wavelength of the forcing decreases, because of the destructive interference between mesoscale cells. The intensity of the vertical velocity and vertical fluxes is, however, only a weak function of the wavenumber, at large wavenumber. Therefore, the intensity of the mesoscale heat flux does not decrease substantially at high wavenumbers; however, the transport of cool air over small heated patches of land may cut off the temperature gradient in the atmosphere between the land and water early in the day, thereby reducing the duration of the mesoscale activity. Also horizontal diffusion of heat in the convective boundary layer can significantly weaken horizontal temperature gradients for large wavenumbers. Periodic square-wave thermal inhomogeneities are more effective than sinusoidal waves in generating mesoscale cells; that is, the intensity of the flow is generally stronger. When dealing with low resolution models, which do not resolve explicitly the mesoscale activity, the mesoscale heat fluxes have to be introduced in a parametric form, using this or a similar theory.
Abstract
An analytical evaluation of the vertical heat fluxes associated with the mesoscale flow generated by thermal inhomogeneities in the PBL in the absence of a synoptic wind is presented. Results show that the mesoscale fluxes are of the same order as the diabatic heat fluxes.
In the sea-breeze case results show that in the lower layer of the atmosphere the heat flux is positive over the land and negative over the sea with an overall positive horizontal average. In the free atmosphere above the PBL the mesoscale vertical heat flux is negative over the land and over the sea; that is, the lower atmosphere becomes warmer while the free atmosphere above becomes cooler. As a result the mesoscale flow contributes to the weakening of the atmospheric stability within a region that extends a Rossby radius distance from the coastline, and up to an altitude larger than twice the depth of the convective PBL. The average momentum flux equals zero because the momentum removed over the sea is fed back into the atmosphere over the land.
Sinusoidally periodic thermal inhomogeneities induce periodic atmospheric cells of the same horizontal scale. The intensity of mesoscale cells increases for increasing values of the wavenumber, reaches its maximum value when the wavelength of the forcing is of the order of the local Rossby radius, and then decreases as the wavelength of the forcing decreases, because of the destructive interference between mesoscale cells. The intensity of the vertical velocity and vertical fluxes is, however, only a weak function of the wavenumber, at large wavenumber. Therefore, the intensity of the mesoscale heat flux does not decrease substantially at high wavenumbers; however, the transport of cool air over small heated patches of land may cut off the temperature gradient in the atmosphere between the land and water early in the day, thereby reducing the duration of the mesoscale activity. Also horizontal diffusion of heat in the convective boundary layer can significantly weaken horizontal temperature gradients for large wavenumbers. Periodic square-wave thermal inhomogeneities are more effective than sinusoidal waves in generating mesoscale cells; that is, the intensity of the flow is generally stronger. When dealing with low resolution models, which do not resolve explicitly the mesoscale activity, the mesoscale heat fluxes have to be introduced in a parametric form, using this or a similar theory.
A brief overview of chaos theory is presented, including bifurcations, routes to turbulence, and methods for characterizing chaos. The paper divides chaos applications in atmospheric sciences into three categories: new ideas and insights inspired by chaos, analysis of observational data, and analysis of output from numerical models. Based on the review of chaos theory and the classification of chaos applications, suggestions for future work are given.
A brief overview of chaos theory is presented, including bifurcations, routes to turbulence, and methods for characterizing chaos. The paper divides chaos applications in atmospheric sciences into three categories: new ideas and insights inspired by chaos, analysis of observational data, and analysis of output from numerical models. Based on the review of chaos theory and the classification of chaos applications, suggestions for future work are given.
The application of three-dimensional time-dependent models to weather modification experiments along with the ways in which mesoscale simulations may be used as an aid in clarifying and formulating the physical basis of a weather modification hypothesis is discussed. It is furthermore pointed out that such models can be an aid in the design of field experiments, in the evaluation of field experiments, and in decision making during the daily operations of the experiment. Not only does the challenge of weather modification require considerable advancement in our understanding of the complex physics and dynamics of mesoscale processes, but it is also essential that we develop parameterizations of these processes in order for a mesoscale model to be of value in the post hoc analyses of weather modification experiments and as a decision aid.
The application of three-dimensional time-dependent models to weather modification experiments along with the ways in which mesoscale simulations may be used as an aid in clarifying and formulating the physical basis of a weather modification hypothesis is discussed. It is furthermore pointed out that such models can be an aid in the design of field experiments, in the evaluation of field experiments, and in decision making during the daily operations of the experiment. Not only does the challenge of weather modification require considerable advancement in our understanding of the complex physics and dynamics of mesoscale processes, but it is also essential that we develop parameterizations of these processes in order for a mesoscale model to be of value in the post hoc analyses of weather modification experiments and as a decision aid.
Abstract
The meteorological data collected during the 1973 NOAA-EML Florida Area Cumulus Experiment was used to describe the mesoscale weather patterns on 4 August 1973. It was found that the high rainfall on this date was due to the superposition of a synoptic-scale disturbance and the normal shallow sea breeze convergence field. The synoptic disturbance was not resolved from the conventional synoptic analyses. On this date, the thunderstorm activity was highly correlated with the diurnal heating and apparently developed in favored regions related to both the sea breeze convergence zone along the west coast and to the larger scale disturbance. The surface wind and temperature patterns Were found to be strongly controlled by the diurnal heating cycle, and by the occurrence or non-occurrence of showers. It is concluded that the reduction in lower level wind speed after a rain occurrence was a result of surface cooling causing a decoupling of the surface from the larger scale pressure gradient.
The analysis of cloud base vertical velocity and its variance illustrates a strong coupling between the mesoscale and the thermal scale in spite of the fact that spectral analysis indicated a marked scale separation between the thermal convective scale and its larger scale. The strong excursion of the slope of the vertical velocity energy spectrum from a −5/3 slope over the scale range of 0.2–0.8 km indicates that eddies on this scale range are a strong source of kinetic energy generation.
Abstract
The meteorological data collected during the 1973 NOAA-EML Florida Area Cumulus Experiment was used to describe the mesoscale weather patterns on 4 August 1973. It was found that the high rainfall on this date was due to the superposition of a synoptic-scale disturbance and the normal shallow sea breeze convergence field. The synoptic disturbance was not resolved from the conventional synoptic analyses. On this date, the thunderstorm activity was highly correlated with the diurnal heating and apparently developed in favored regions related to both the sea breeze convergence zone along the west coast and to the larger scale disturbance. The surface wind and temperature patterns Were found to be strongly controlled by the diurnal heating cycle, and by the occurrence or non-occurrence of showers. It is concluded that the reduction in lower level wind speed after a rain occurrence was a result of surface cooling causing a decoupling of the surface from the larger scale pressure gradient.
The analysis of cloud base vertical velocity and its variance illustrates a strong coupling between the mesoscale and the thermal scale in spite of the fact that spectral analysis indicated a marked scale separation between the thermal convective scale and its larger scale. The strong excursion of the slope of the vertical velocity energy spectrum from a −5/3 slope over the scale range of 0.2–0.8 km indicates that eddies on this scale range are a strong source of kinetic energy generation.
Abstract
For a propagating mesoscale system whose intensity and structure is not changing with time, relatively coarse horizontal profiler resolution is sufficient to resolve the feature since the circulation would pass by the profiler sites quickly enough to construct a three-dimensional analysis. This is generally not true for a thermally forced mesoscale system. For mesoscale systems generated by surface inhomogeneities in surface heating (e.g., land-sea contrasts, nonuniform soil wetness, etc.), such propagation is often slow. Therefore, ideally, if thermally surface-forced systems are to be directly resolved by a profiler network, a necessary condition is that their spacing be close enough to adequately resolve the motion field of the mesoscale system. As concluded from the analyses in this paper, higher spatial resolution is required to directly monitor the horizontal wind field than the temperature field, since the horizontal wind is proportional to the horizontal gradient of temperature. Similarly, even higher resolution of vertical velocity is required since ascent and descent are proportional to the horizontal gradient of the horizontal velocity.
The use of mesoscale numerical models as analysis tools, however, offers the opportunity to obtain fine-scale horizontal resolution with only relatively coarse atmospheric data. Such fine scale resolution is obtained because the surface thermal forcing can be resolved with high spatial accuracy and, through nonlinear advection and the pressure gradient force in the numerical model, fine-scale atmospheric structure can be produced.
Finally, stringent data initialization requirements would result if one attempted to insert mesoscale resolution profiler-derived temperature or wind data into a model. Even if 10-km horizontal resolution were obtained with a profiler network and if relative errors in the temperature measurements were only 0.24°C through a depth of 2 km or so, a fictitious 1 m s−1 h−1 acceleration would result. For the same resolution, for winds from one profiler of 0, 5, and 10 m s−1, an error from the adjacent profiler of 2.4, 0.5, and 0.3 m s−1, respectively, would result in the same erroneous acceleration.
Abstract
For a propagating mesoscale system whose intensity and structure is not changing with time, relatively coarse horizontal profiler resolution is sufficient to resolve the feature since the circulation would pass by the profiler sites quickly enough to construct a three-dimensional analysis. This is generally not true for a thermally forced mesoscale system. For mesoscale systems generated by surface inhomogeneities in surface heating (e.g., land-sea contrasts, nonuniform soil wetness, etc.), such propagation is often slow. Therefore, ideally, if thermally surface-forced systems are to be directly resolved by a profiler network, a necessary condition is that their spacing be close enough to adequately resolve the motion field of the mesoscale system. As concluded from the analyses in this paper, higher spatial resolution is required to directly monitor the horizontal wind field than the temperature field, since the horizontal wind is proportional to the horizontal gradient of temperature. Similarly, even higher resolution of vertical velocity is required since ascent and descent are proportional to the horizontal gradient of the horizontal velocity.
The use of mesoscale numerical models as analysis tools, however, offers the opportunity to obtain fine-scale horizontal resolution with only relatively coarse atmospheric data. Such fine scale resolution is obtained because the surface thermal forcing can be resolved with high spatial accuracy and, through nonlinear advection and the pressure gradient force in the numerical model, fine-scale atmospheric structure can be produced.
Finally, stringent data initialization requirements would result if one attempted to insert mesoscale resolution profiler-derived temperature or wind data into a model. Even if 10-km horizontal resolution were obtained with a profiler network and if relative errors in the temperature measurements were only 0.24°C through a depth of 2 km or so, a fictitious 1 m s−1 h−1 acceleration would result. For the same resolution, for winds from one profiler of 0, 5, and 10 m s−1, an error from the adjacent profiler of 2.4, 0.5, and 0.3 m s−1, respectively, would result in the same erroneous acceleration.
Abstract
A three-dimensional numerical mesoscale model has been applied over the irregular terrain of northern Israel in order to simulate the local surface climate pattern associated with typical July stagnate synoptic meteorological conditions. Comparison of model-evaluated surface flow and temperature fields against observed data illustrate the role in which mesoscale models can be used in order to provide additional insight into the analyses of persistent regional climatological patterns.
Abstract
A three-dimensional numerical mesoscale model has been applied over the irregular terrain of northern Israel in order to simulate the local surface climate pattern associated with typical July stagnate synoptic meteorological conditions. Comparison of model-evaluated surface flow and temperature fields against observed data illustrate the role in which mesoscale models can be used in order to provide additional insight into the analyses of persistent regional climatological patterns.
