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is integrated for 40 years at a spectral resolution of T42, i.e., a triangular truncation where the highest retained wavenumber and total wavenumber both equal 42, and 40 evenly spaced pressure levels. The time–space analysis is performed on the last 38 years of the integration, after a 2-yr spinup time. d. Shallow-water model simulations To understand the governing mechanism behind the effects of upscale energy cascade on the parity distribution, we use the framework of the forced
is integrated for 40 years at a spectral resolution of T42, i.e., a triangular truncation where the highest retained wavenumber and total wavenumber both equal 42, and 40 evenly spaced pressure levels. The time–space analysis is performed on the last 38 years of the integration, after a 2-yr spinup time. d. Shallow-water model simulations To understand the governing mechanism behind the effects of upscale energy cascade on the parity distribution, we use the framework of the forced
Improved Precipitation Typing Using POSS Spectral Modal Analysisthe model components required for the forward simulation of the POSS Doppler spectrum. Section 4 explains the Doppler spectral modal frequency of occurrence matrix and plots. Section 5 explores the effect of various factors on the modal centroid distributions. Section 6 presents the multiple discriminant analysis (MDA) of the centroid distributions for the identification of type. Section 7 gives several case studies comparing POSS precipitation classification to collocated images of
the model components required for the forward simulation of the POSS Doppler spectrum. Section 4 explains the Doppler spectral modal frequency of occurrence matrix and plots. Section 5 explores the effect of various factors on the modal centroid distributions. Section 6 presents the multiple discriminant analysis (MDA) of the centroid distributions for the identification of type. Section 7 gives several case studies comparing POSS precipitation classification to collocated images of
consistent with the enforced inflows and outflows at the boundaries ( Leung et al. 2003 ). When integrating over a large domain, the model biases could accumulate continuously in the inner domain and lead to the deviation of RCMs’ large-scale circulation from observations. To ensure the dynamic consistency between the simulated large-scale variables and the driving fields, the interior nudging technique, including grid nudging ( Bowden et al. 2012 ) and spectral nudging ( von Storch et al. 2000 ; Tang
consistent with the enforced inflows and outflows at the boundaries ( Leung et al. 2003 ). When integrating over a large domain, the model biases could accumulate continuously in the inner domain and lead to the deviation of RCMs’ large-scale circulation from observations. To ensure the dynamic consistency between the simulated large-scale variables and the driving fields, the interior nudging technique, including grid nudging ( Bowden et al. 2012 ) and spectral nudging ( von Storch et al. 2000 ; Tang
to a null spectral model based on an AR(1) process (e.g., Mann and Lees 1996 ; von Storch 1999 ). A number of more-detailed processes have also been proposed for representing null spectral models, including integrated and moving averages ( Box et al. 2015 ; Klaus et al. 2015 ), use of a portion of the sample autocorrelation function ( Priestley 1981 ; Garrido and GarcĂa 1992 ; Goff 2020 ), and power-law distributions ( Vaughan 2005 ). Which of these processes, if any, is an adequate
to a null spectral model based on an AR(1) process (e.g., Mann and Lees 1996 ; von Storch 1999 ). A number of more-detailed processes have also been proposed for representing null spectral models, including integrated and moving averages ( Box et al. 2015 ; Klaus et al. 2015 ), use of a portion of the sample autocorrelation function ( Priestley 1981 ; Garrido and GarcĂa 1992 ; Goff 2020 ), and power-law distributions ( Vaughan 2005 ). Which of these processes, if any, is an adequate
: information on global-scale TMT changes is available from three satellite research groups ( Mears and Wentz 2016 ; Zou et al. 2018 ; Spencer et al. 2017 ), and “synthetic” TMT has been calculated from over three dozen climate models ( Santer et al. 2018 ). Operating in the frequency domain has a number of advantages ( Vyushin and Kushner 2009 ). Spectral analysis facilitates model-versus-data comparisons of the overall spectral “shape,” the interdecadal variance relevant to detection of an anthropogenic
: information on global-scale TMT changes is available from three satellite research groups ( Mears and Wentz 2016 ; Zou et al. 2018 ; Spencer et al. 2017 ), and “synthetic” TMT has been calculated from over three dozen climate models ( Santer et al. 2018 ). Operating in the frequency domain has a number of advantages ( Vyushin and Kushner 2009 ). Spectral analysis facilitates model-versus-data comparisons of the overall spectral “shape,” the interdecadal variance relevant to detection of an anthropogenic
dynamic forecasting models ( Straus and Shukla 1981 ; Lau and Chang 1992 ; Doblas-Reyes et al. 1998 ). Figure 2 shows that the variability in the 30- and 60-day bands for 1976 displays greater spectral energy during winter months. This result raises the question of whether this type of linear or nonlinear effect tends to be observed in a particular season. Figure 3 shows the distribution of the occurrence of significant spectral densities in the bandwidth between 30 and 60 days as a function of
dynamic forecasting models ( Straus and Shukla 1981 ; Lau and Chang 1992 ; Doblas-Reyes et al. 1998 ). Figure 2 shows that the variability in the 30- and 60-day bands for 1976 displays greater spectral energy during winter months. This result raises the question of whether this type of linear or nonlinear effect tends to be observed in a particular season. Figure 3 shows the distribution of the occurrence of significant spectral densities in the bandwidth between 30 and 60 days as a function of
– 54 , https://doi.org/10.1134/S0001433813010040 . Glegg , S. , and W. Devenport , 2017 : Aeroacoustics of Low Mach Number Flows: Fundamentals, Analysis, and Measurement . Elsevier, 554 pp. Goedecke , G. H. , D. K. Wilson , and V. E. Ostashev , 2006 : Quasi-wavelet models of turbulent temperature fluctuations . Bound.-Layer Meteor. , 120 , 1 – 23 , https://doi.org/10.1007/s10546-005-9037-1 . Grossmann , S. , and V. S. L’vov , 1993 : Crossover of spectral scaling in
– 54 , https://doi.org/10.1134/S0001433813010040 . Glegg , S. , and W. Devenport , 2017 : Aeroacoustics of Low Mach Number Flows: Fundamentals, Analysis, and Measurement . Elsevier, 554 pp. Goedecke , G. H. , D. K. Wilson , and V. E. Ostashev , 2006 : Quasi-wavelet models of turbulent temperature fluctuations . Bound.-Layer Meteor. , 120 , 1 – 23 , https://doi.org/10.1007/s10546-005-9037-1 . Grossmann , S. , and V. S. L’vov , 1993 : Crossover of spectral scaling in
Estimating Four-Dimensional Internal Wave Spectrum in the Northern South China Seaz , ω ) can be obtained finally. However, it is notable that for the component with a horizontal wavelength smaller than the minimum array spacing, the MLM may give a white azimuthal spectrum because of the aliasing caused by sparse array spacing. In such a case, only the integral of spectral energy along θ , not the distribution of spectral energy along θ , makes sense. 3. Validation and analysis of results a. Validation of 4D internal wave spectrum Based on the Fourier analysis, the
z , ω ) can be obtained finally. However, it is notable that for the component with a horizontal wavelength smaller than the minimum array spacing, the MLM may give a white azimuthal spectrum because of the aliasing caused by sparse array spacing. In such a case, only the integral of spectral energy along θ , not the distribution of spectral energy along θ , makes sense. 3. Validation and analysis of results a. Validation of 4D internal wave spectrum Based on the Fourier analysis, the
theoretical paper by Malkus and Veronis (1958) established the two-dimensional spectral framework that he followed. Saltzman (1962) meticulously developed the structure of a family of LOM ( n ) for n ≤ 52. This family of models has been the basis for numerous subsequent studies. The well-known LOM (3), known as the Lorenz 1963 model ( Lorenz 1963 ), is a member of this family of models as are the ones in Curry (1978) . By way of illustration, Saltzman (1962) concluded his paper with a preliminary
theoretical paper by Malkus and Veronis (1958) established the two-dimensional spectral framework that he followed. Saltzman (1962) meticulously developed the structure of a family of LOM ( n ) for n ≤ 52. This family of models has been the basis for numerous subsequent studies. The well-known LOM (3), known as the Lorenz 1963 model ( Lorenz 1963 ), is a member of this family of models as are the ones in Curry (1978) . By way of illustration, Saltzman (1962) concluded his paper with a preliminary
1. Introduction When computing spectra from observed or model data, the main focus is often on the slope of the spectrum as a function of wavenumber on a log–log plot. Nevertheless, if such spectra are to be quantitatively compared with those obtained in other studies (as in, e.g., Skamarock 2004 ; Hamilton et al. 2008 ), it is important to be able to correctly compute the magnitude of the energy spectral density. The goal of this article is to facilitate such comparisons. The discrete
1. Introduction When computing spectra from observed or model data, the main focus is often on the slope of the spectrum as a function of wavenumber on a log–log plot. Nevertheless, if such spectra are to be quantitatively compared with those obtained in other studies (as in, e.g., Skamarock 2004 ; Hamilton et al. 2008 ), it is important to be able to correctly compute the magnitude of the energy spectral density. The goal of this article is to facilitate such comparisons. The discrete
