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predictability (e.g., Gamage and Blumen 1993 ; Mak 1995 ). In this paper, we present a spectral variant of EOF analysis, which we term spectral empirical orthogonal function (SEOF) analysis, in conformity with standard nomenclature in weather and climate studies. This approach differs from standard EOF methods employed in the previously cited. It can be shown that SEOF modes are identical to optimal response modes of a stochastically forced nonnormal linear dynamical system if the forcing consists of white
predictability (e.g., Gamage and Blumen 1993 ; Mak 1995 ). In this paper, we present a spectral variant of EOF analysis, which we term spectral empirical orthogonal function (SEOF) analysis, in conformity with standard nomenclature in weather and climate studies. This approach differs from standard EOF methods employed in the previously cited. It can be shown that SEOF modes are identical to optimal response modes of a stochastically forced nonnormal linear dynamical system if the forcing consists of white
Staggered-PRT Sequences for Doppler Weather Radars. Part I: Spectral Analysis Using the Autocorrelation Spectral Densityuniform-PRT sequence. Further, we derive autocorrelation estimators that are compatible with staggered-PRT processing and explore the utility of the ASD for spectral analysis of staggered-PRT sequences. This work is used by Warde and Torres (2016, manuscript submitted to J. Atmos. Oceanic Technol. , hereafter Part II) as a basis for integrating the CLEAN-AP filter into the WSR-88D staggered-PRT algorithm. 2. The ASD of staggered-PRT sequences The ASD was introduced by Warde and Torres (2014) as a
uniform-PRT sequence. Further, we derive autocorrelation estimators that are compatible with staggered-PRT processing and explore the utility of the ASD for spectral analysis of staggered-PRT sequences. This work is used by Warde and Torres (2016, manuscript submitted to J. Atmos. Oceanic Technol. , hereafter Part II) as a basis for integrating the CLEAN-AP filter into the WSR-88D staggered-PRT algorithm. 2. The ASD of staggered-PRT sequences The ASD was introduced by Warde and Torres (2014) as a
been discussed in detail in Penland and Ghil (1993) and Penland and Matrosova (1994) . A detailed analysis of cross spectral analysis may be found in chapter 9 of Priestley (1983) . The contribution to the spectra of linear combinations is actually the real part of the complex cross-spectra. It is convenient conceptually to consider the cross-spectrum between all the normal modes and all the stochastic forcings separately. In addition, to facilitate decomposition of the desired linear
been discussed in detail in Penland and Ghil (1993) and Penland and Matrosova (1994) . A detailed analysis of cross spectral analysis may be found in chapter 9 of Priestley (1983) . The contribution to the spectra of linear combinations is actually the real part of the complex cross-spectra. It is convenient conceptually to consider the cross-spectrum between all the normal modes and all the stochastic forcings separately. In addition, to facilitate decomposition of the desired linear
Improved Precipitation Typing Using POSS Spectral Modal Analysisphysical size of the particle. For radars like POSS scattering by solid particles meeting the Rayleigh criteria will depend only on the square of their mass. Also, in general, optical sensors require more field maintenance to keep optics clean and aligned. This paper presents an analysis technique to better distinguish precipitation types, particularly for solid precipitation, by using the POSS Doppler spectral modal data. Historically, for the automated weather station application, the modal velocity
physical size of the particle. For radars like POSS scattering by solid particles meeting the Rayleigh criteria will depend only on the square of their mass. Also, in general, optical sensors require more field maintenance to keep optics clean and aligned. This paper presents an analysis technique to better distinguish precipitation types, particularly for solid precipitation, by using the POSS Doppler spectral modal data. Historically, for the automated weather station application, the modal velocity
; Gleckler et al. 2008 ). In the context of modeling very large basins, domination of the discharge variability by a small range of frequencies (e.g., cycles at the annual scale) means that analysis with traditional metrics is not a problem and cross-spectral methods are not needed. However, in general, with the exception of MBE, these metrics often fail to provide sufficiently unambiguous insights into the ways in which particular model outputs differ from observations or from other models ( Lane 2007
; Gleckler et al. 2008 ). In the context of modeling very large basins, domination of the discharge variability by a small range of frequencies (e.g., cycles at the annual scale) means that analysis with traditional metrics is not a problem and cross-spectral methods are not needed. However, in general, with the exception of MBE, these metrics often fail to provide sufficiently unambiguous insights into the ways in which particular model outputs differ from observations or from other models ( Lane 2007
-polarization spectral analysis is demonstrated for ice precipitation studies ( Moisseev et al. 2004 ). It was shown that a combination of Doppler measurements taken at a 45° elevation angle and dual-polarization observations can be used to distinguish between different types of ice hydrometeors within a radar volume. In this paper we further develop this idea. The purpose of the study is to show that dual-polarization spectral measurements taken at a high elevation angle can be used for the retrieval of ice
-polarization spectral analysis is demonstrated for ice precipitation studies ( Moisseev et al. 2004 ). It was shown that a combination of Doppler measurements taken at a 45° elevation angle and dual-polarization observations can be used to distinguish between different types of ice hydrometeors within a radar volume. In this paper we further develop this idea. The purpose of the study is to show that dual-polarization spectral measurements taken at a high elevation angle can be used for the retrieval of ice
of the spatial and temporal variability of cloud properties. In this study, we focus on the intercomparison of the spatiotemporal variability in different archived datasets. Spectral analysis techniques have proven to be effective in identifying and isolating dominant variability both spatially and temporally through the decomposition of the data covariance matrix. These methods can also be used in the comparison of multiple datasets of the same physical parameter; by comparing the spatial and
of the spatial and temporal variability of cloud properties. In this study, we focus on the intercomparison of the spatiotemporal variability in different archived datasets. Spectral analysis techniques have proven to be effective in identifying and isolating dominant variability both spatially and temporally through the decomposition of the data covariance matrix. These methods can also be used in the comparison of multiple datasets of the same physical parameter; by comparing the spatial and
future modeling and theoretical analysis. Furthermore, the spectra show that divergence and T b behave reasonably similarly. Both T b and divergence are related to convection, so it is therefore to be expected that these two variables should have similar spectral properties, but nonetheless reassuring to see in the reanalysis data. Convection is driven by the vertically integrated low-level divergence; however, because of the complex vertical structure of the boundary and cloud layers, divergence
future modeling and theoretical analysis. Furthermore, the spectra show that divergence and T b behave reasonably similarly. Both T b and divergence are related to convection, so it is therefore to be expected that these two variables should have similar spectral properties, but nonetheless reassuring to see in the reanalysis data. Convection is driven by the vertically integrated low-level divergence; however, because of the complex vertical structure of the boundary and cloud layers, divergence
. Boyd , J. P. , 2005 : Limited-area Fourier spectral models and data analysis schemes: Windows, Fourier extension, Davies relaxation, and all that . Mon. Wea. Rev. , 133 , 2030 – 2042 . Davies , H. C. , 1976 : A lateral boundary formulation for multilevel prediction models . Quart. J. Roy. Meteor. Soc. , 102 , 405 – 418 . de ElÃa , R. , R. Laprise , and B. Denis , 2002 : Forecasting skill limits of nested, limited-area models: A perfect-model approach . Mon. Wea. Rev. , 130
. Boyd , J. P. , 2005 : Limited-area Fourier spectral models and data analysis schemes: Windows, Fourier extension, Davies relaxation, and all that . Mon. Wea. Rev. , 133 , 2030 – 2042 . Davies , H. C. , 1976 : A lateral boundary formulation for multilevel prediction models . Quart. J. Roy. Meteor. Soc. , 102 , 405 – 418 . de ElÃa , R. , R. Laprise , and B. Denis , 2002 : Forecasting skill limits of nested, limited-area models: A perfect-model approach . Mon. Wea. Rev. , 130
use of the classical PCA in association with Fourier spectral analysis and frequency filtering (e.g., Kidson 1999 ; Power et al. 1999 ; Kessler 2001 ; Wheeler and Hendon 2004 ; Roundy and Schreck 2009 ; Chen and Wallace 2016 ; Chen et al. 2017 ; Wills et al. 2018 ). For the spectral PCA, the linear relations between the variables leading to the spectral PCs are defined directly in the Fourier frequency domain. While sPCA (also known as frequency domain EOF) was introduced and theorized in
use of the classical PCA in association with Fourier spectral analysis and frequency filtering (e.g., Kidson 1999 ; Power et al. 1999 ; Kessler 2001 ; Wheeler and Hendon 2004 ; Roundy and Schreck 2009 ; Chen and Wallace 2016 ; Chen et al. 2017 ; Wills et al. 2018 ). For the spectral PCA, the linear relations between the variables leading to the spectral PCs are defined directly in the Fourier frequency domain. While sPCA (also known as frequency domain EOF) was introduced and theorized in
