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Abstract
The elements of an eigenfunction expansion for time-dependent currents as a function of depth are worked out for viscosity that is given as a parabolic function of depth that goes to zero at both the bottom and top of the water. This yields currents with logarithmic behavior characteristic of turbulent boundary layers at both the bottom and top. Also, solutions are obtained for the two viscosity functions that are half a parabola, going to zero at either the bottom or top but not both. In all cases the solutions are Legendre functions. In some cases the eigenfunctions are Legendre polynomials.
Abstract
The elements of an eigenfunction expansion for time-dependent currents as a function of depth are worked out for viscosity that is given as a parabolic function of depth that goes to zero at both the bottom and top of the water. This yields currents with logarithmic behavior characteristic of turbulent boundary layers at both the bottom and top. Also, solutions are obtained for the two viscosity functions that are half a parabola, going to zero at either the bottom or top but not both. In all cases the solutions are Legendre functions. In some cases the eigenfunctions are Legendre polynomials.
Abstract
Solutions of a linear hydrodynamic equation of motion with linear boundary conditions are obtained to describe the horizontal current, as a function of depth and time, determined by a given history of the wind force and pressure gradient up to that time, at a fixed point in the horizontal plane, in well-mixed water of finite depth. The bottom friction is assumed to be proportional to the bottom current, with zero bottom current and zero bottom friction considered as limiting cases. The general solution is established as an eigenfunction expansion when the eddy viscosity is given as a positive function of depth. Explicit formulas are worked out for viscosity functions that are constant, exponential, or varying as a power of the height from somewhere below the bottom or above the top of the water. For the latter the limit as the viscosity goes to zero at the bottom or top is considered. Numerical results are presented for viscosities that are constant, exponential, linear, or varying as the 3/4 power.
Abstract
Solutions of a linear hydrodynamic equation of motion with linear boundary conditions are obtained to describe the horizontal current, as a function of depth and time, determined by a given history of the wind force and pressure gradient up to that time, at a fixed point in the horizontal plane, in well-mixed water of finite depth. The bottom friction is assumed to be proportional to the bottom current, with zero bottom current and zero bottom friction considered as limiting cases. The general solution is established as an eigenfunction expansion when the eddy viscosity is given as a positive function of depth. Explicit formulas are worked out for viscosity functions that are constant, exponential, or varying as a power of the height from somewhere below the bottom or above the top of the water. For the latter the limit as the viscosity goes to zero at the bottom or top is considered. Numerical results are presented for viscosities that are constant, exponential, linear, or varying as the 3/4 power.
Abstract
A previously developed eigenfunction expansion, that describes horizontal current as a function of depth and time, is extended to include any eddy viscosity given as a product of a function of depth and a function of time.
Abstract
A previously developed eigenfunction expansion, that describes horizontal current as a function of depth and time, is extended to include any eddy viscosity given as a product of a function of depth and a function of time.
Abstract
This study used a two-dimensional coupled land–atmosphere (cloud resolving) model to investigate the influence of land cover on the water budgets of convective lines in West Africa. Study simulations used the same initial sounding and one of three different land covers: a sparsely vegetated semidesert, a grassy savanna, and a dense evergreen broadleaf forest. All simulations began at midnight and ran for 24 h to capture a full diurnal cycle. During the morning, the forest had the highest latent heat flux, the shallowest, moistest, slowest growing boundary layer, and more convective available potential energy than the savanna and semidesert. Although the savanna and forest environments produced virtually the same total rainfall mass (semidesert 18%), the spatial and temporal patterns of the rainfall were significantly different and can be attributed to the boundary layer evolution. The forest produced numerous convective cells with very high rain rates mainly during the early afternoon. During the morning, the savanna built up less but still significant amounts of convective available potential energy and enough convective inhibition so that the strongest convection in the savanna did not occur until late afternoon. This timing resulted in the largest, most intense convective line of the three land covers.
Abstract
This study used a two-dimensional coupled land–atmosphere (cloud resolving) model to investigate the influence of land cover on the water budgets of convective lines in West Africa. Study simulations used the same initial sounding and one of three different land covers: a sparsely vegetated semidesert, a grassy savanna, and a dense evergreen broadleaf forest. All simulations began at midnight and ran for 24 h to capture a full diurnal cycle. During the morning, the forest had the highest latent heat flux, the shallowest, moistest, slowest growing boundary layer, and more convective available potential energy than the savanna and semidesert. Although the savanna and forest environments produced virtually the same total rainfall mass (semidesert 18%), the spatial and temporal patterns of the rainfall were significantly different and can be attributed to the boundary layer evolution. The forest produced numerous convective cells with very high rain rates mainly during the early afternoon. During the morning, the savanna built up less but still significant amounts of convective available potential energy and enough convective inhibition so that the strongest convection in the savanna did not occur until late afternoon. This timing resulted in the largest, most intense convective line of the three land covers.
The three-dimensional global wind field is the most important remaining measurement needed to accurately assess the dynamics of the atmosphere. Wind information in the tropics, high latitudes, and stratosphere is particularly deficient. Furthermore, only a small fraction of the atmosphere is sampled in terms of wind profiles. This limits our ability to optimally specify initial conditions for numerical weather prediction (NWP) models and our understanding of several key climate change issues.
Because of its extensive wind measurement heritage (since 1968) and especially the rapid recent technology advances, Doppler lidar has reached a level of maturity required for a space-based mission. The European Space Agency (ESA)'s Atmospheric Dynamics Mission Aeolus (ADM-Aeolus) Doppler wind lidar (DWL), now scheduled for launch in 2015, will be a major milestone.
This paper reviews the expected impact of DWL measurements on NWP and climate research, measurement concepts, and the recent advances in technology that will set the stage for space-based deployment. Forecast impact experiments with actual airborne DWL measurements collected over the North Atlantic in 2003 and assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) operational model are a clear indication of the value of lidar-measured wind profiles. Airborne DWL measurements collected over the western Pacific in 2008 and assimilated into both the ECMWF and U.S. Navy operational models support the earlier findings.
These forecast impact experiments confirm observing system simulation experiments (OSSEs) conducted over the past 25–30 years. The addition of simulated DWL wind observations in recent OSSEs performed at the Joint Center for Satellite Data Assimilation (JCSDA) leads to a statistically significant increase in forecast skill.
The three-dimensional global wind field is the most important remaining measurement needed to accurately assess the dynamics of the atmosphere. Wind information in the tropics, high latitudes, and stratosphere is particularly deficient. Furthermore, only a small fraction of the atmosphere is sampled in terms of wind profiles. This limits our ability to optimally specify initial conditions for numerical weather prediction (NWP) models and our understanding of several key climate change issues.
Because of its extensive wind measurement heritage (since 1968) and especially the rapid recent technology advances, Doppler lidar has reached a level of maturity required for a space-based mission. The European Space Agency (ESA)'s Atmospheric Dynamics Mission Aeolus (ADM-Aeolus) Doppler wind lidar (DWL), now scheduled for launch in 2015, will be a major milestone.
This paper reviews the expected impact of DWL measurements on NWP and climate research, measurement concepts, and the recent advances in technology that will set the stage for space-based deployment. Forecast impact experiments with actual airborne DWL measurements collected over the North Atlantic in 2003 and assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) operational model are a clear indication of the value of lidar-measured wind profiles. Airborne DWL measurements collected over the western Pacific in 2008 and assimilated into both the ECMWF and U.S. Navy operational models support the earlier findings.
These forecast impact experiments confirm observing system simulation experiments (OSSEs) conducted over the past 25–30 years. The addition of simulated DWL wind observations in recent OSSEs performed at the Joint Center for Satellite Data Assimilation (JCSDA) leads to a statistically significant increase in forecast skill.
The deployment of a space-based Doppler lidar would provide information that is fundamental to advancing the understanding and prediction of weather and climate.
This paper reviews the concepts of wind measurement by Doppler lidar, highlights the results of some observing system simulation experiments with lidar winds, and discusses the important advances in earth system science anticipated with lidar winds.
Observing system simulation experiments, conducted using two different general circulation models, have shown 1) that there is a significant improvement in the forecast accuracy over the Southern Hemisphere and tropical oceans resulting from the assimilation of simulated satellite wind data, and 2) that wind data are significantly more effective than temperature or moisture data in controlling analysis error. Because accurate wind observations are currently almost entirely unavailable for the vast majority of tropical cyclones worldwide, lidar winds have the potential to substantially improve tropical cyclone forecasts. Similarly, to improve water vapor flux divergence calculations, a direct measure of the ageostrophic wind is needed since the present level of uncertainty cannot be reduced with better temperature and moisture soundings alone.
The deployment of a space-based Doppler lidar would provide information that is fundamental to advancing the understanding and prediction of weather and climate.
This paper reviews the concepts of wind measurement by Doppler lidar, highlights the results of some observing system simulation experiments with lidar winds, and discusses the important advances in earth system science anticipated with lidar winds.
Observing system simulation experiments, conducted using two different general circulation models, have shown 1) that there is a significant improvement in the forecast accuracy over the Southern Hemisphere and tropical oceans resulting from the assimilation of simulated satellite wind data, and 2) that wind data are significantly more effective than temperature or moisture data in controlling analysis error. Because accurate wind observations are currently almost entirely unavailable for the vast majority of tropical cyclones worldwide, lidar winds have the potential to substantially improve tropical cyclone forecasts. Similarly, to improve water vapor flux divergence calculations, a direct measure of the ageostrophic wind is needed since the present level of uncertainty cannot be reduced with better temperature and moisture soundings alone.
Abstract
A data assimilation system (DAS) is described for global atmospheric reanalysis from 0- to 100-km altitude. We apply it to the 2014 austral winter of the Deep Propagating Gravity Wave Experiment (DEEPWAVE), an international field campaign focused on gravity wave dynamics from 0 to 100 km, where an absence of reanalysis above 60 km inhibits research. Four experiments were performed from April to September 2014 and assessed for reanalysis skill above 50 km. A four-dimensional variational (4DVAR) run specified initial background error covariances statically. A hybrid-4DVAR (HYBRID) run formed background error covariances from an 80-member forecast ensemble blended with a static estimate. Each configuration was run at low and high horizontal resolution. In addition to operational observations below 50 km, each experiment assimilated 
Abstract
A data assimilation system (DAS) is described for global atmospheric reanalysis from 0- to 100-km altitude. We apply it to the 2014 austral winter of the Deep Propagating Gravity Wave Experiment (DEEPWAVE), an international field campaign focused on gravity wave dynamics from 0 to 100 km, where an absence of reanalysis above 60 km inhibits research. Four experiments were performed from April to September 2014 and assessed for reanalysis skill above 50 km. A four-dimensional variational (4DVAR) run specified initial background error covariances statically. A hybrid-4DVAR (HYBRID) run formed background error covariances from an 80-member forecast ensemble blended with a static estimate. Each configuration was run at low and high horizontal resolution. In addition to operational observations below 50 km, each experiment assimilated
