Search Results
You are looking at 1 - 3 of 3 items for
- Author or Editor: D. E. Barrick x
- Refine by Access: Content accessible to me x
Abstract
A general hydrodynamic solution is derived for arbitrary gravity-wave fields on the ocean surface by extending Stokes' (1847) original perturbational analysis. The solution to the nonlinear equations of motion is made possible by assuming that the surface height is periodic in both space and time and thus can be described by a Fourier series. The assumption of periodicity does not limit the generality of the result because the series can be made to approach an integral representation by taking arbitrarily large fundamental periods with respect to periods of the dominant ocean waves actually present on the surface. The observation areas and times over which this analysis applies are assumed small, however, compared to the periods required for energy exchange processes; hence an “energy balance” (or steady-state) condition is assumed to exist within the observed space-time intervals. This in turn implies the condition of statistical stationarity of the Fourier height coefficients when one generalizes to a random surface. Part I confines itself to the formulation of a perturbation solution (valid to all orders) for the higher order terms resulting from a two-dimensional arbitrary periodic description of the surface height. The method is demonstrated by deriving (to second order) the height correction to the sea and (to third order) the first nonzero correction to the lowest order gravity-wave dispersion relation.
Abstract
A general hydrodynamic solution is derived for arbitrary gravity-wave fields on the ocean surface by extending Stokes' (1847) original perturbational analysis. The solution to the nonlinear equations of motion is made possible by assuming that the surface height is periodic in both space and time and thus can be described by a Fourier series. The assumption of periodicity does not limit the generality of the result because the series can be made to approach an integral representation by taking arbitrarily large fundamental periods with respect to periods of the dominant ocean waves actually present on the surface. The observation areas and times over which this analysis applies are assumed small, however, compared to the periods required for energy exchange processes; hence an “energy balance” (or steady-state) condition is assumed to exist within the observed space-time intervals. This in turn implies the condition of statistical stationarity of the Fourier height coefficients when one generalizes to a random surface. Part I confines itself to the formulation of a perturbation solution (valid to all orders) for the higher order terms resulting from a two-dimensional arbitrary periodic description of the surface height. The method is demonstrated by deriving (to second order) the height correction to the sea and (to third order) the first nonzero correction to the lowest order gravity-wave dispersion relation.
Abstract
In a previous paper (Weber and Barrick, 1977), a generalization of Stokes’ perturbational technique permitted us to obtain solutions to higher orders for gravity-wave parameters for an arbitrary, two-dimensional periodic surface. In particular, the second-order wave-height correction and the third-order dispersion relation correction were derived there. In this paper, we interpret and apply those solutions in a variety of ways. First of all, we interpret the dispersion relation (and its higher order corrections) physically, as they relate to the phase velocity of individual ocean wave trains. Second, the validity of the two results derived previously is established by comparisons in the appropriate limiting cases with classical results available from the literature. It is shown how the solutions—derived for periodic surface profiles—can be generalized to include random wave fields whose average properties are to be specified. Then a number of examples of averaged higher order wave parameters, are given, and in certain cases a Phillips’ one-dimensional wave-height spectral model is employed to yield a quantitative feel for the magnitudes of these higher order effects. Both the derivations and the examples have direct application to the sea echo observed with high-frequency radars, and relationships with the radar observables are established and discussed.
Abstract
In a previous paper (Weber and Barrick, 1977), a generalization of Stokes’ perturbational technique permitted us to obtain solutions to higher orders for gravity-wave parameters for an arbitrary, two-dimensional periodic surface. In particular, the second-order wave-height correction and the third-order dispersion relation correction were derived there. In this paper, we interpret and apply those solutions in a variety of ways. First of all, we interpret the dispersion relation (and its higher order corrections) physically, as they relate to the phase velocity of individual ocean wave trains. Second, the validity of the two results derived previously is established by comparisons in the appropriate limiting cases with classical results available from the literature. It is shown how the solutions—derived for periodic surface profiles—can be generalized to include random wave fields whose average properties are to be specified. Then a number of examples of averaged higher order wave parameters, are given, and in certain cases a Phillips’ one-dimensional wave-height spectral model is employed to yield a quantitative feel for the magnitudes of these higher order effects. Both the derivations and the examples have direct application to the sea echo observed with high-frequency radars, and relationships with the radar observables are established and discussed.
Abstract
Water vapor mass mixing ratio profiles from NASA's Lidar Atmospheric Sensing Experiment (LASE) system acquired during the Atmospheric Radiation Measurement (ARM)–First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE) Water Vapor Experiment (AFWEX) are used as a reference to characterize upper-troposphere water vapor (UTWV) measured by ground-based Raman lidars, radiosondes, and in situ aircraft sensors over the Department of Energy (DOE) ARM Southern Great Plains (SGP) site in northern Oklahoma. LASE was deployed from the NASA DC-8 aircraft and measured water vapor over the ARM SGP Central Facility (CF) site during seven flights between 27 November and 10 December 2000. Initially, the DOE ARM SGP Cloud and Radiation Testbed (CART) Raman lidar (CARL) UTWV profiles were about 5%–7% wetter than LASE in the upper troposphere, and the Vaisala RS80-H radiosonde profiles were about 10% drier than LASE between 8 and 12 km. Scaling the Vaisala water vapor profiles to match the precipitable water vapor (PWV) measured by the ARM SGP microwave radiometer (MWR) did not change these results significantly. By accounting for an overlap correction of the CARL water vapor profiles and by employing schemes designed to correct the Vaisala RS80-H calibration method and account for the time response of the Vaisala RS80-H water vapor sensor, the average differences between the CARL and Vaisala radiosonde upper-troposphere water vapor profiles are reduced to about 5%, which is within the ARM goal of mean differences of less than 10%. The LASE and DC-8 in situ diode laser hygrometer (DLH) UTWV measurements generally agreed to within about 3%–4%. The DC-8 in situ frost point cryogenic hygrometer and Snow White chilled-mirror measurements were drier than the LASE, Raman lidars, and corrected Vaisala RS80H measurements by about 10%–25% and 10%–15%, respectively. Sippican (formerly VIZ Manufacturing) carbon hygristor radiosondes exhibited large variabilities and poor agreement with the other measurements. PWV derived from the LASE profiles agreed to within about 3% on average with PWV derived from the ARM SGP microwave radiometer. The agreement between the LASE and MWR PWV and the LASE and CARL UTWV measurements supports the hypotheses that MWR measurements of the 22-GHz water vapor line can accurately constrain the total water vapor amount and that the CART Raman lidar, when calibrated using the MWR PWV, can provide an accurate, stable reference for characterizing upper-troposphere water vapor.
Abstract
Water vapor mass mixing ratio profiles from NASA's Lidar Atmospheric Sensing Experiment (LASE) system acquired during the Atmospheric Radiation Measurement (ARM)–First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE) Water Vapor Experiment (AFWEX) are used as a reference to characterize upper-troposphere water vapor (UTWV) measured by ground-based Raman lidars, radiosondes, and in situ aircraft sensors over the Department of Energy (DOE) ARM Southern Great Plains (SGP) site in northern Oklahoma. LASE was deployed from the NASA DC-8 aircraft and measured water vapor over the ARM SGP Central Facility (CF) site during seven flights between 27 November and 10 December 2000. Initially, the DOE ARM SGP Cloud and Radiation Testbed (CART) Raman lidar (CARL) UTWV profiles were about 5%–7% wetter than LASE in the upper troposphere, and the Vaisala RS80-H radiosonde profiles were about 10% drier than LASE between 8 and 12 km. Scaling the Vaisala water vapor profiles to match the precipitable water vapor (PWV) measured by the ARM SGP microwave radiometer (MWR) did not change these results significantly. By accounting for an overlap correction of the CARL water vapor profiles and by employing schemes designed to correct the Vaisala RS80-H calibration method and account for the time response of the Vaisala RS80-H water vapor sensor, the average differences between the CARL and Vaisala radiosonde upper-troposphere water vapor profiles are reduced to about 5%, which is within the ARM goal of mean differences of less than 10%. The LASE and DC-8 in situ diode laser hygrometer (DLH) UTWV measurements generally agreed to within about 3%–4%. The DC-8 in situ frost point cryogenic hygrometer and Snow White chilled-mirror measurements were drier than the LASE, Raman lidars, and corrected Vaisala RS80H measurements by about 10%–25% and 10%–15%, respectively. Sippican (formerly VIZ Manufacturing) carbon hygristor radiosondes exhibited large variabilities and poor agreement with the other measurements. PWV derived from the LASE profiles agreed to within about 3% on average with PWV derived from the ARM SGP microwave radiometer. The agreement between the LASE and MWR PWV and the LASE and CARL UTWV measurements supports the hypotheses that MWR measurements of the 22-GHz water vapor line can accurately constrain the total water vapor amount and that the CART Raman lidar, when calibrated using the MWR PWV, can provide an accurate, stable reference for characterizing upper-troposphere water vapor.
