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JANUARY 1986 HAROLD RITCHIE 135 Eliminating the Interpolation Associated with the Semi-Lagrangian Scheme HAROLD RITCHIEDivision de Recherche en Pr~vision Num~rique, Service de l'Environne~nent Atmosphdrique, Dorval, Qudbec, Canada H9P 1J3(Manuscript received 4 December 1985, in final form 14 August 1985) ABSTRACT There are
JANUARY 1986 HAROLD RITCHIE 135 Eliminating the Interpolation Associated with the Semi-Lagrangian Scheme HAROLD RITCHIEDivision de Recherche en Pr~vision Num~rique, Service de l'Environne~nent Atmosphdrique, Dorval, Qudbec, Canada H9P 1J3(Manuscript received 4 December 1985, in final form 14 August 1985) ABSTRACT There are
the Williamson et al. (1992) flow over a midlatitude mountain using a hexagonal grid of 40 962 cells and midpoint interpolation of PV from vertices to edges. This interpolation means that grid-scale PV oscillations can be present on the vertices, but not on the edges and so they are not present in the discretized solution of the momentum equation. Fig . 1. Relative vorticity after 50 days for the Williamson et al. (1992) flow over a mountain using various interpolation schemes for PV
the Williamson et al. (1992) flow over a midlatitude mountain using a hexagonal grid of 40 962 cells and midpoint interpolation of PV from vertices to edges. This interpolation means that grid-scale PV oscillations can be present on the vertices, but not on the edges and so they are not present in the discretized solution of the momentum equation. Fig . 1. Relative vorticity after 50 days for the Williamson et al. (1992) flow over a mountain using various interpolation schemes for PV
1981 A. C. L O R E N C 701A Global Three-Dimensional Multivariate Statistical Interpolation Scheme A. C. LORENC1European Centre for Medium Range Weather Forecasts, Reading, Berkshire, England(Manuscript received 3 September 1980, in final form 5 December 1980)ABSTRACT A three-dimensional statistical interpolation method, multivariate in geopotential height, thickness -and wind
1981 A. C. L O R E N C 701A Global Three-Dimensional Multivariate Statistical Interpolation Scheme A. C. LORENC1European Centre for Medium Range Weather Forecasts, Reading, Berkshire, England(Manuscript received 3 September 1980, in final form 5 December 1980)ABSTRACT A three-dimensional statistical interpolation method, multivariate in geopotential height, thickness -and wind
190g JOURNAL OF APPLIED METEOROLOGY VOLUME32A Semi-Lagrangian Transport Scheme with Spectral Interpolation H. N. LEEEnvironmental Measurements Laboratory, U.S. Department of Energy, New York, New York(Manuscript received 20 October 1992, in final form 10 May 1993)ABSTRACT Advective transport using the flexible and stable semi-Lagrangian scheme coupled with the highly accuratespectral
190g JOURNAL OF APPLIED METEOROLOGY VOLUME32A Semi-Lagrangian Transport Scheme with Spectral Interpolation H. N. LEEEnvironmental Measurements Laboratory, U.S. Department of Energy, New York, New York(Manuscript received 20 October 1992, in final form 10 May 1993)ABSTRACT Advective transport using the flexible and stable semi-Lagrangian scheme coupled with the highly accuratespectral
, often the extent of nested domains may be such that their boundaries coincide with regions where the gradients in variables of interest are relatively large. A desired characteristic of interpolation schemes employed in the specification of boundary conditions for nested models is their ability to allow all resolvable waves to propagate across the coarse–fine grid interface with minimal distortion so thatcompatibility between the solutions computed on the different grids can be maintained. In this
, often the extent of nested domains may be such that their boundaries coincide with regions where the gradients in variables of interest are relatively large. A desired characteristic of interpolation schemes employed in the specification of boundary conditions for nested models is their ability to allow all resolvable waves to propagate across the coarse–fine grid interface with minimal distortion so thatcompatibility between the solutions computed on the different grids can be maintained. In this
at standard depths calculated from the JODC observation datasets. Pre-2000, the standard depth data provided by JODC were constructed basically from the reported values from each organization where the data originated, with methods of interpolation differing among the organizations. It is desirable to use a unified and reliable interpolation scheme to prepare the standard depth data. The NODC applied an elaborate interpolation scheme for the compilation of the World Ocean Database 1998 (WOD98) (e
at standard depths calculated from the JODC observation datasets. Pre-2000, the standard depth data provided by JODC were constructed basically from the reported values from each organization where the data originated, with methods of interpolation differing among the organizations. It is desirable to use a unified and reliable interpolation scheme to prepare the standard depth data. The NODC applied an elaborate interpolation scheme for the compilation of the World Ocean Database 1998 (WOD98) (e
interest and each neighboring station. Other methods such as local interpolation only use climatic data from weather stations. Among these, IDW is usually used for missing data estimation ( Di Piazza et al. 2011 ). It computes a weighted average, using the inverse distance between target and surrounding station. Several variants of IDW have been developed, with principal focus on weighting schemes ( Teegavarapu and Chandramouli 2005 ; You et al. 2008 ). Kriging and its variants ( Goovaerts 1997
interest and each neighboring station. Other methods such as local interpolation only use climatic data from weather stations. Among these, IDW is usually used for missing data estimation ( Di Piazza et al. 2011 ). It computes a weighted average, using the inverse distance between target and surrounding station. Several variants of IDW have been developed, with principal focus on weighting schemes ( Teegavarapu and Chandramouli 2005 ; You et al. 2008 ). Kriging and its variants ( Goovaerts 1997
A Methodology for Fitting the Time Series of Snow Depth on the Arctic Sea Icei th IP is the same as the p ( i )th point in the time series; that is, p (1) = 1, p ( K ) = N , and P ( i ) = ( i − 1)Δ t + 1, i = 2, 3, …, K − 1, where Δ t = ( N − 1)/( K − 1) is the interval between two adjacent IPs. As in Jin et al. (2018) , the cubic spline interpolation is applied to the IP scheme. The parameters A [ p ( i )] and B [ p ( i )] at IPs are selected as independent parameters and those at the other points are obtained by cubic spline interpolation; that is, (4
i th IP is the same as the p ( i )th point in the time series; that is, p (1) = 1, p ( K ) = N , and P ( i ) = ( i − 1)Δ t + 1, i = 2, 3, …, K − 1, where Δ t = ( N − 1)/( K − 1) is the interval between two adjacent IPs. As in Jin et al. (2018) , the cubic spline interpolation is applied to the IP scheme. The parameters A [ p ( i )] and B [ p ( i )] at IPs are selected as independent parameters and those at the other points are obtained by cubic spline interpolation; that is, (4
in a similar way to the optimal interpolation (OI) scheme ( Daley 1985 ; Lorenc 1981 ; Daley 1991 ). Unlike the HS00 scheme where K parallel data assimilation cycles for the K members were required, in the EB04 scheme, a single update of the mean was performed, while the ETKF transformed the background perturbations into analysis perturbations in a computationally efficient manner. EB04 found that the performance of the hybrid scheme using the ETKF ensemble was comparable to that
in a similar way to the optimal interpolation (OI) scheme ( Daley 1985 ; Lorenc 1981 ; Daley 1991 ). Unlike the HS00 scheme where K parallel data assimilation cycles for the K members were required, in the EB04 scheme, a single update of the mean was performed, while the ETKF transformed the background perturbations into analysis perturbations in a computationally efficient manner. EB04 found that the performance of the hybrid scheme using the ETKF ensemble was comparable to that
Inversion of Tidal Open Boundary Conditions of the M2 Constituent in the Bohai and Yellow Seas, and the vertical eddy viscosity profiles with the IP scheme. The influence of initial guesses, model errors, and data number on inversion was also discussed. As an extension, Zhang and Lu (2010) explored the inversion of OBCs in detail with the same model. Cao et al. (2012) inverted two-dimensional tidal OBCs in the Bohai and Yellow Seas (BYS), showing that using two IPs yielded the best simulated results. Guo et al. (2012) suggested that the scheme with three IPs and an interpolation radius
, and the vertical eddy viscosity profiles with the IP scheme. The influence of initial guesses, model errors, and data number on inversion was also discussed. As an extension, Zhang and Lu (2010) explored the inversion of OBCs in detail with the same model. Cao et al. (2012) inverted two-dimensional tidal OBCs in the Bohai and Yellow Seas (BYS), showing that using two IPs yielded the best simulated results. Guo et al. (2012) suggested that the scheme with three IPs and an interpolation radius
