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the radiative transfer equation employed by all spectral wave models to predict wave spectrum F: where the two other sources of wind input S in and resonant nonlinear four-wave interactions S nl are also explicitly mentioned. All the source terms, as well as the spectrum itself, are functions of wavenumber k, frequency ω , time t , and spatial coordinate x. Since the major, if not dominant part of S ds is attributed to energy losses due to wave breaking, and the breaking has been
the radiative transfer equation employed by all spectral wave models to predict wave spectrum F: where the two other sources of wind input S in and resonant nonlinear four-wave interactions S nl are also explicitly mentioned. All the source terms, as well as the spectrum itself, are functions of wavenumber k, frequency ω , time t , and spatial coordinate x. Since the major, if not dominant part of S ds is attributed to energy losses due to wave breaking, and the breaking has been
not made during theperiod. A radiative transfer calculation was made todetermine the variability of the atmospheric attenuation correction for the 10-11 um channel (T2). Thecorrection was 8.1K for the driest of the Bermudasoundings and 9.0K for the wettest for satellite measurements made within 1- latitude of Bermuda. Since themagnitude of the correction and the probable spreadof the precipitable water in cloud-free conditions areAemL1972 WILLIAM E. SHENK AND VINCENT V. SALOMONSON
not made during theperiod. A radiative transfer calculation was made todetermine the variability of the atmospheric attenuation correction for the 10-11 um channel (T2). Thecorrection was 8.1K for the driest of the Bermudasoundings and 9.0K for the wettest for satellite measurements made within 1- latitude of Bermuda. Since themagnitude of the correction and the probable spreadof the precipitable water in cloud-free conditions areAemL1972 WILLIAM E. SHENK AND VINCENT V. SALOMONSON
ArRIL1972 GILBERT N. PLASS AND GEORGE W. KATTAWAR 139Monte Carlo Calculations of Radiative Transfer in the Earth's Atmosphere-Ocean System: I. Flux in the Atmosphere and Ocean GILBERT iN. PLASS AND GEORGE W. KATTAWARDept. of Physics, Texas A&M University, College Station 77843(Manuscript received 22 December 1971, in revised form 8 February 1972)ABSTRACT The upward and downward
ArRIL1972 GILBERT N. PLASS AND GEORGE W. KATTAWAR 139Monte Carlo Calculations of Radiative Transfer in the Earth's Atmosphere-Ocean System: I. Flux in the Atmosphere and Ocean GILBERT iN. PLASS AND GEORGE W. KATTAWARDept. of Physics, Texas A&M University, College Station 77843(Manuscript received 22 December 1971, in revised form 8 February 1972)ABSTRACT The upward and downward
linear analysis shows that radiating instabilities occur over the longwave end for each mode (sinuous or varicose). It is qualitatively consistent with Kamenkovich and Pedlosky (1996) and Hristova et al. (2008) . Although radiating modes are able to transfer energy away from the unstable region to affect the interior, they have smaller growth rates than the most unstable mode in this inviscid linear theory. Friction can suppress the unstable inviscid radiating modes, leaving the significance of
linear analysis shows that radiating instabilities occur over the longwave end for each mode (sinuous or varicose). It is qualitatively consistent with Kamenkovich and Pedlosky (1996) and Hristova et al. (2008) . Although radiating modes are able to transfer energy away from the unstable region to affect the interior, they have smaller growth rates than the most unstable mode in this inviscid linear theory. Friction can suppress the unstable inviscid radiating modes, leaving the significance of
-ocean applications and the near shore, and either as stand-alone wave prediction models, or as part of coupled ocean–atmosphere models for global circulation and climate studies (e.g., The WAMDI Group 1988 ; Tolman 1991 ; Komen et al. 1994 ; Booij et al. 1999 ; Wise Group 2007 ). These so-called third-generation wave models are invariably based on some form of the radiative transfer equation (or action balance) which describes the evolution of the variance (or action) density spectrum E ( k , x , t
-ocean applications and the near shore, and either as stand-alone wave prediction models, or as part of coupled ocean–atmosphere models for global circulation and climate studies (e.g., The WAMDI Group 1988 ; Tolman 1991 ; Komen et al. 1994 ; Booij et al. 1999 ; Wise Group 2007 ). These so-called third-generation wave models are invariably based on some form of the radiative transfer equation (or action balance) which describes the evolution of the variance (or action) density spectrum E ( k , x , t
coupling coefficient is of order ω 2 / gk , which is typically O (10 −3 ). It is therefore the large gap between the internal wave frequency ω and the surface wave frequency that generates small coefficients and thus weak coupling. Note that the small ratio enters the coupling coefficient in a quadratic way and the transfer integral (see below) as fourth power. The pumping induced by W ( k , ω ) at the mixed layer base establishes the generation of internal waves that radiate downward from
coupling coefficient is of order ω 2 / gk , which is typically O (10 −3 ). It is therefore the large gap between the internal wave frequency ω and the surface wave frequency that generates small coefficients and thus weak coupling. Note that the small ratio enters the coupling coefficient in a quadratic way and the transfer integral (see below) as fourth power. The pumping induced by W ( k , ω ) at the mixed layer base establishes the generation of internal waves that radiate downward from
; Komen et al. 1994 ; Booij et al. 1999 ; Cavaleri et al. 2007 ) to the point that they are now routinely used for global and regional applications, either as stand-alone or coupled to atmosphere, climate, or coastal transport and circulation models. Invariably, such operational wave models are based on some form of the radiative transfer equation (RTE), which transports the variance density spectrum E ( k , x , t ) through geographical space ( x = [ x 1 , x 2 ] T ), wavenumber space ( k = [ k
; Komen et al. 1994 ; Booij et al. 1999 ; Cavaleri et al. 2007 ) to the point that they are now routinely used for global and regional applications, either as stand-alone or coupled to atmosphere, climate, or coastal transport and circulation models. Invariably, such operational wave models are based on some form of the radiative transfer equation (RTE), which transports the variance density spectrum E ( k , x , t ) through geographical space ( x = [ x 1 , x 2 ] T ), wavenumber space ( k = [ k
the global ocean, with 2.5 TW contributed by the semidiurnal lunar tides. Egbert and Ray (2000 , 2001) have examined least squares fits of models for the global barotropic tide to TOPEX/Poseidon altimetry data, and they interpret model residuals in terms of “tidal dissipation.” In Egbert and Ray's studies, dissipation refers to any mechanisms that transfer energy away from the barotropic tide: they are not able to distinguish whether barotropic energy is lost to baroclinic waves (the internal
the global ocean, with 2.5 TW contributed by the semidiurnal lunar tides. Egbert and Ray (2000 , 2001) have examined least squares fits of models for the global barotropic tide to TOPEX/Poseidon altimetry data, and they interpret model residuals in terms of “tidal dissipation.” In Egbert and Ray's studies, dissipation refers to any mechanisms that transfer energy away from the barotropic tide: they are not able to distinguish whether barotropic energy is lost to baroclinic waves (the internal
radiate from the mixed layer as horizontally and vertically propagatingnear-inertial internal gravity waves. To study the timescale of the decay of mixed layer energy and the magnitudeof the energy transfer to the ocean below, the authors developed a numerical, linear model on a ~ plane, usingbaroclinic modes to describe the velocity field. The model is unforced--wave propagation is initiated by specifying the mixed layer currents that would be generated by a moving atmospheric front. The numerical
radiate from the mixed layer as horizontally and vertically propagatingnear-inertial internal gravity waves. To study the timescale of the decay of mixed layer energy and the magnitudeof the energy transfer to the ocean below, the authors developed a numerical, linear model on a ~ plane, usingbaroclinic modes to describe the velocity field. The model is unforced--wave propagation is initiated by specifying the mixed layer currents that would be generated by a moving atmospheric front. The numerical
al. 2012 ), to point out some principal properties of the wave–mean flow interaction in terms of energy transfers. Section 3 revisits the continuous description of a wave field using the radiative transfer equation including wave–mean flow interaction, which is used in section 4 to derive integrated energy compartments for the interaction with a unidirectional flow. Section 5 details simple closures for wave–wave interactions and dissipation for these compartments, which are used in
al. 2012 ), to point out some principal properties of the wave–mean flow interaction in terms of energy transfers. Section 3 revisits the continuous description of a wave field using the radiative transfer equation including wave–mean flow interaction, which is used in section 4 to derive integrated energy compartments for the interaction with a unidirectional flow. Section 5 details simple closures for wave–wave interactions and dissipation for these compartments, which are used in
