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Abstract
Solutions are obtained for the problem of multiple scattering by a plane parallel atmosphere with anisotropic phase functions typical of cloud and haze particles. The resulting albedos, angular distributions of intensities, and planetary magnitudes are compared to solutions obtained with approximate analytic phase functions and, in the case of the cloud phase function, to the solution obtained with the forward diffraction peak omitted from the phase function.
It is shown that the cloud phase function with the truncated peak yields results practically identical to those obtained with the complete cloud phase function, not only for albedos and magnitudes, but also for the angular distribution; the approximation introduces errors of several per cent in the angular distribution for direct backscattering (the region of the glory), for emergent angles near grazing regardless of the incident angle, and, of course, a larger error occurs for total scattering angles near 0°. However, the errors are unimportant for many applications, and hence a large reduction in computer time is possible. This is particularly useful, for example, in making practical the computations needed for interpreting the phase curve, limb darkening and spectral reflectivity of Venus.
It is shown that the Henyey-Greenstein phase function, based on the asymmetry factor 〈cosθ〉, yields spherical and plane albedos and planetary magnitudes (for optically thick atmospheres) close to those obtained with the cloud and haze phase functions. The Kagiwada-Kalaba phase function, based on the ratio of forward to backward scattering, gives significantly less satisfactory results for the same quantities. Neither of the two analytic phase functions can accurately duplicate the true angular distribution of scattering by thin clouds; however, the results are better with thick layers, especially for hazes. The results indicate that the Henyey-Greenstein phase function may be useful for problems such as line formation in planetary atmospheres.
Abstract
Solutions are obtained for the problem of multiple scattering by a plane parallel atmosphere with anisotropic phase functions typical of cloud and haze particles. The resulting albedos, angular distributions of intensities, and planetary magnitudes are compared to solutions obtained with approximate analytic phase functions and, in the case of the cloud phase function, to the solution obtained with the forward diffraction peak omitted from the phase function.
It is shown that the cloud phase function with the truncated peak yields results practically identical to those obtained with the complete cloud phase function, not only for albedos and magnitudes, but also for the angular distribution; the approximation introduces errors of several per cent in the angular distribution for direct backscattering (the region of the glory), for emergent angles near grazing regardless of the incident angle, and, of course, a larger error occurs for total scattering angles near 0°. However, the errors are unimportant for many applications, and hence a large reduction in computer time is possible. This is particularly useful, for example, in making practical the computations needed for interpreting the phase curve, limb darkening and spectral reflectivity of Venus.
It is shown that the Henyey-Greenstein phase function, based on the asymmetry factor 〈cosθ〉, yields spherical and plane albedos and planetary magnitudes (for optically thick atmospheres) close to those obtained with the cloud and haze phase functions. The Kagiwada-Kalaba phase function, based on the ratio of forward to backward scattering, gives significantly less satisfactory results for the same quantities. Neither of the two analytic phase functions can accurately duplicate the true angular distribution of scattering by thin clouds; however, the results are better with thick layers, especially for hazes. The results indicate that the Henyey-Greenstein phase function may be useful for problems such as line formation in planetary atmospheres.
Abstract
The linear polarization of sunlight reflected by Venus is analyzed by comparing observations with extensive multiple scattering computations. The analysis establishes that Venus is veiled by a cloud or haze layer of spherical particles. The refractive index of the particles is 1.44±0.015 at λ=0.55 μm with a normal dispersion, the refractive index decreasing from 1.46±0.015 at λ=0.365 μm to 1.43±0.015 at λ=0.99 μm. The cloud particles have a narrow size distribution with a mean radius of ∼1 μm; specifically, the effective radius of the size distribution is 1.05±0.10 μm and the effective variance is 0.07±0.02. The particles exist at a high level in the atmosphere, with the optical thickness unity occurring where the pressure is about 50 mb.
The particle properties deduced from the polarization eliminate all but one of the cloud compositions which have been proposed for Venue. A concentrated solution of sulfuric acid (H2SO4-H2O) provides good agreement with the polarization data.
Abstract
The linear polarization of sunlight reflected by Venus is analyzed by comparing observations with extensive multiple scattering computations. The analysis establishes that Venus is veiled by a cloud or haze layer of spherical particles. The refractive index of the particles is 1.44±0.015 at λ=0.55 μm with a normal dispersion, the refractive index decreasing from 1.46±0.015 at λ=0.365 μm to 1.43±0.015 at λ=0.99 μm. The cloud particles have a narrow size distribution with a mean radius of ∼1 μm; specifically, the effective radius of the size distribution is 1.05±0.10 μm and the effective variance is 0.07±0.02. The particles exist at a high level in the atmosphere, with the optical thickness unity occurring where the pressure is about 50 mb.
The particle properties deduced from the polarization eliminate all but one of the cloud compositions which have been proposed for Venue. A concentrated solution of sulfuric acid (H2SO4-H2O) provides good agreement with the polarization data.
Abstract
High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.
Abstract
High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.
Abstract
The effect of bottom roughness on setup dynamics was investigated using high-resolution observations across a laboratory fringing reef profile with roughness elements scaled to mimic the frictional wave dissipation of a coral reef. Results with roughness were compared with smooth bottom runs across 16 offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at 17 locations along the flume and consisted of cross-shore pressure and radiation stress gradients whose sum was balanced by quadratic mean bottom stresses. The introduction of roughness had two primary effects. First, for runs with roughness, frictional wave dissipation occurred on the reef slope offshore of the breakpoint, reducing wave heights prior to wave breaking. Second, offshore-directed mean bottom stresses were generated by the interaction of the combined wave–current velocity field with the roughness elements. These two mechanisms acted counter to one another. Frictional wave dissipation resulted in radiation stress gradients that were predicted to generate 18% (on average) less setup on the reef flat for rough runs than for smooth runs when neglecting mean bottom stresses. However, mean bottom stresses increased the predicted setup by 16% on average for runs with roughness. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modeling studies of reefs and also to discuss the broader implications for how large roughness influences setup dynamics in the nearshore zone.
Abstract
The effect of bottom roughness on setup dynamics was investigated using high-resolution observations across a laboratory fringing reef profile with roughness elements scaled to mimic the frictional wave dissipation of a coral reef. Results with roughness were compared with smooth bottom runs across 16 offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at 17 locations along the flume and consisted of cross-shore pressure and radiation stress gradients whose sum was balanced by quadratic mean bottom stresses. The introduction of roughness had two primary effects. First, for runs with roughness, frictional wave dissipation occurred on the reef slope offshore of the breakpoint, reducing wave heights prior to wave breaking. Second, offshore-directed mean bottom stresses were generated by the interaction of the combined wave–current velocity field with the roughness elements. These two mechanisms acted counter to one another. Frictional wave dissipation resulted in radiation stress gradients that were predicted to generate 18% (on average) less setup on the reef flat for rough runs than for smooth runs when neglecting mean bottom stresses. However, mean bottom stresses increased the predicted setup by 16% on average for runs with roughness. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modeling studies of reefs and also to discuss the broader implications for how large roughness influences setup dynamics in the nearshore zone.
Abstract
Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free-long-wave generation, through breakpoint forcing and bound-wave release mechanisms, we highlight the importance of an additional free-long-wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free-long-wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.
Abstract
Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free-long-wave generation, through breakpoint forcing and bound-wave release mechanisms, we highlight the importance of an additional free-long-wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free-long-wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.
Abstract
Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.
Abstract
Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.
Abstract
A model description and numerical results are presented for a global atmospheric circulation model developed at the Goddard Institute for Space Studies (GISS). The model version described is a 9-level primitive-equation model in sigma coordinates. It includes a realistic distribution of continents, oceans and topography. Detailed calculations of energy transfer by solar and terrestrial radiation make use of cloud and water vapor fields calculated by the model. The model hydrologic cycle includes two precipitation mechanisms: large-scale supersaturation and a parameterization of subgrid-scale cumulus convection.
Results are presented both from a comparison of the 13th to the 43rd days (January) of one integration with climatological statistics, and from five short-range forecasting experiments. In the extended integration, the near-equilibrium January-mean model atmosphere exhibits an energy cycle in good agreement with observational estimates, together with generally realistic zonal mean fields of winds, temperature, humidity, transports, diabatic heating, evaporation, precipitation, and cloud cover. In the five forecasting experiments, after 48 hr, the average rms error in temperature is 3.9K, and the average rms error in 500-mb height is 62 m. The model is successful in simulating the 2-day evolution of the major features of the observed sea level pressure and 500-mb height fields in a region surrounding North America.
Abstract
A model description and numerical results are presented for a global atmospheric circulation model developed at the Goddard Institute for Space Studies (GISS). The model version described is a 9-level primitive-equation model in sigma coordinates. It includes a realistic distribution of continents, oceans and topography. Detailed calculations of energy transfer by solar and terrestrial radiation make use of cloud and water vapor fields calculated by the model. The model hydrologic cycle includes two precipitation mechanisms: large-scale supersaturation and a parameterization of subgrid-scale cumulus convection.
Results are presented both from a comparison of the 13th to the 43rd days (January) of one integration with climatological statistics, and from five short-range forecasting experiments. In the extended integration, the near-equilibrium January-mean model atmosphere exhibits an energy cycle in good agreement with observational estimates, together with generally realistic zonal mean fields of winds, temperature, humidity, transports, diabatic heating, evaporation, precipitation, and cloud cover. In the five forecasting experiments, after 48 hr, the average rms error in temperature is 3.9K, and the average rms error in 500-mb height is 62 m. The model is successful in simulating the 2-day evolution of the major features of the observed sea level pressure and 500-mb height fields in a region surrounding North America.
Abstract
There is an urgent need to develop and optimize tools for designing large wind farm arrays for deployment offshore. This research is focused on improving the understanding of, and modeling of, wind turbine wakes in order to make more accurate power output predictions for large offshore wind farms. Detailed data ensembles of power losses due to wakes at the large wind farms at Nysted and Horns Rev are presented and analyzed. Differences in turbine spacing (10.5 versus 7 rotor diameters) are not differentiable in wake-related power losses from the two wind farms. This is partly due to the high variability in the data despite careful data screening. A number of ensemble averages are simulated with a range of wind farm and computational fluid dynamics models and compared to observed wake losses. All models were able to capture wake width to some degree, and some models also captured the decrease of power output moving through the wind farm. Root-mean-square errors indicate a generally better model performance for higher wind speeds (10 rather than 6 m s−1) and for direct down the row flow than for oblique angles. Despite this progress, wake modeling of large wind farms is still subject to an unacceptably high degree of uncertainty.
Abstract
There is an urgent need to develop and optimize tools for designing large wind farm arrays for deployment offshore. This research is focused on improving the understanding of, and modeling of, wind turbine wakes in order to make more accurate power output predictions for large offshore wind farms. Detailed data ensembles of power losses due to wakes at the large wind farms at Nysted and Horns Rev are presented and analyzed. Differences in turbine spacing (10.5 versus 7 rotor diameters) are not differentiable in wake-related power losses from the two wind farms. This is partly due to the high variability in the data despite careful data screening. A number of ensemble averages are simulated with a range of wind farm and computational fluid dynamics models and compared to observed wake losses. All models were able to capture wake width to some degree, and some models also captured the decrease of power output moving through the wind farm. Root-mean-square errors indicate a generally better model performance for higher wind speeds (10 rather than 6 m s−1) and for direct down the row flow than for oblique angles. Despite this progress, wake modeling of large wind farms is still subject to an unacceptably high degree of uncertainty.
Computational fluid dynamics (CFD) model simulations of urban boundary layers have improved in speed and accuracy so that they are useful in assisting in planning emergency response activities related to releases of chemical or biological agents into the atmosphere in large cities such as New York, New York. In this paper, five CFD models [CFD-Urban, Finite Element Flow (FEFLO), Finite Element Model in 3D and Massively-Parallel version (FEM3MP), FLACS, and FLUENT–Environmental Protection Agency (FLUENT-EPA)] have been applied to the same 3D building data and geographic domain in Manhattan, using approximately the same wind input conditions. Wind flow observations are available from the Madison Square Garden 2005 (MSG05) field experiment. Plots of the CFD models' simulations and the observations of near-surface wind fields lead to the qualitative conclusion that the models generally agree with each other and with field observations over most parts of the computational domain, within typical atmospheric uncertainties of a factor of 2. The results are useful to emergency responders, suggesting, for example, that transport of a release at street level in a large city could extend for a few blocks in the upwind and crosswind directions. There are still key differences among the models for certain parts of the domain. Further examination of the differences among the models and the observations are necessary in order to understand the causal relationships.
Computational fluid dynamics (CFD) model simulations of urban boundary layers have improved in speed and accuracy so that they are useful in assisting in planning emergency response activities related to releases of chemical or biological agents into the atmosphere in large cities such as New York, New York. In this paper, five CFD models [CFD-Urban, Finite Element Flow (FEFLO), Finite Element Model in 3D and Massively-Parallel version (FEM3MP), FLACS, and FLUENT–Environmental Protection Agency (FLUENT-EPA)] have been applied to the same 3D building data and geographic domain in Manhattan, using approximately the same wind input conditions. Wind flow observations are available from the Madison Square Garden 2005 (MSG05) field experiment. Plots of the CFD models' simulations and the observations of near-surface wind fields lead to the qualitative conclusion that the models generally agree with each other and with field observations over most parts of the computational domain, within typical atmospheric uncertainties of a factor of 2. The results are useful to emergency responders, suggesting, for example, that transport of a release at street level in a large city could extend for a few blocks in the upwind and crosswind directions. There are still key differences among the models for certain parts of the domain. Further examination of the differences among the models and the observations are necessary in order to understand the causal relationships.
The NASA Glory mission is intended to facilitate and improve upon long-term monitoring of two key forcings influencing global climate. One of the mission's principal objectives is to determine the global distribution of detailed aerosol and cloud properties with unprecedented accuracy, thereby facilitating the quantification of the aerosol direct and indirect radiative forcings. The other is to continue the 28-yr record of satellite-based measurements of total solar irradiance from which the effect of solar variability on the Earth's climate is quantified. These objectives will be met by flying two state-of-the-art science instruments on an Earth-orbiting platform. Based on a proven technique demonstrated with an aircraft-based prototype, the Aerosol Polarimetry Sensor (APS) will collect accurate multiangle photopolarimetric measurements of the Earth along the satellite ground track within a wide spectral range extending from the visible to the shortwave infrared. The Total Irradiance Monitor (TIM) is an improved version of an instrument currently flying on the Solar Radiation and Climate Experiment (SORCE) and will provide accurate and precise measurements of spectrally integrated sunlight illuminating the Earth. Because Glory is expected to fly as part of the A-Train constellation of Earth-orbiting spacecraft, the APS data will also be used to improve retrievals of aerosol climate forcing parameters and global aerosol assessments with other A-Train instruments. In this paper, we detail the scientific rationale and objectives of the Glory mission, explain how these scientific objectives dictate the specific measurement strategy, describe how the measurement strategy will be implemented by the APS and TIM, and briefly outline the overall structure of the mission. It is expected that the Glory results will be used extensively by members of the climate, solar, atmospheric, oceanic, and environmental research communities as well as in education and outreach activities.
The NASA Glory mission is intended to facilitate and improve upon long-term monitoring of two key forcings influencing global climate. One of the mission's principal objectives is to determine the global distribution of detailed aerosol and cloud properties with unprecedented accuracy, thereby facilitating the quantification of the aerosol direct and indirect radiative forcings. The other is to continue the 28-yr record of satellite-based measurements of total solar irradiance from which the effect of solar variability on the Earth's climate is quantified. These objectives will be met by flying two state-of-the-art science instruments on an Earth-orbiting platform. Based on a proven technique demonstrated with an aircraft-based prototype, the Aerosol Polarimetry Sensor (APS) will collect accurate multiangle photopolarimetric measurements of the Earth along the satellite ground track within a wide spectral range extending from the visible to the shortwave infrared. The Total Irradiance Monitor (TIM) is an improved version of an instrument currently flying on the Solar Radiation and Climate Experiment (SORCE) and will provide accurate and precise measurements of spectrally integrated sunlight illuminating the Earth. Because Glory is expected to fly as part of the A-Train constellation of Earth-orbiting spacecraft, the APS data will also be used to improve retrievals of aerosol climate forcing parameters and global aerosol assessments with other A-Train instruments. In this paper, we detail the scientific rationale and objectives of the Glory mission, explain how these scientific objectives dictate the specific measurement strategy, describe how the measurement strategy will be implemented by the APS and TIM, and briefly outline the overall structure of the mission. It is expected that the Glory results will be used extensively by members of the climate, solar, atmospheric, oceanic, and environmental research communities as well as in education and outreach activities.
