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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
the interpolation, detecting erroneous maps using a machine learning approach, and establishing the most appropriate parameterization scheme for the interpolation model. While the default parameters in the autoKrige function may produce gridded estimates that validate well, this does necessarily mean that a realistic rainfall surface will be produced. The incorporation of a low-level machine learning algorithm trained to evaluate and classify an unrealistic map output is therefore a critical step
the interpolation, detecting erroneous maps using a machine learning approach, and establishing the most appropriate parameterization scheme for the interpolation model. While the default parameters in the autoKrige function may produce gridded estimates that validate well, this does necessarily mean that a realistic rainfall surface will be produced. The incorporation of a low-level machine learning algorithm trained to evaluate and classify an unrealistic map output is therefore a critical step
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
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
Interpolation of Operational Radar Data to a Regular Cartesian Grid Exemplified by Munich’s Airport Radar Configurationalready pointed out by Bousquet et al. (2016) , there exist only a small amount of publications that deal with the finding of an optimal interpolation scheme depending on the radar geometry and scanning strategy (e.g., Zhang et al. 2005 ; Lakshmanan et al. 2006 ). These publications consider the interpolation of reflectivity data rather than wind. In this paper, a method is presented to deal with the challenge of interpolating wind data from operationally used radars. This is unique, as differences
already pointed out by Bousquet et al. (2016) , there exist only a small amount of publications that deal with the finding of an optimal interpolation scheme depending on the radar geometry and scanning strategy (e.g., Zhang et al. 2005 ; Lakshmanan et al. 2006 ). These publications consider the interpolation of reflectivity data rather than wind. In this paper, a method is presented to deal with the challenge of interpolating wind data from operationally used radars. This is unique, as differences
, 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
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
function on that node. Naturally, we cannot assume the interpolation weights to be the same for all types of field α = 0, 1, 2, and 3. We should expect the coefficients to depend on the choice of basis functions . By analogy, with bilinear and conservative interpolation, we write where T is the target: a point , line, surface, or volume. Expressions (2) – (4) are very general; they apply to all field staggerings in 3D, irrespective of the order of the interpolation scheme. Let us look at
function on that node. Naturally, we cannot assume the interpolation weights to be the same for all types of field α = 0, 1, 2, and 3. We should expect the coefficients to depend on the choice of basis functions . By analogy, with bilinear and conservative interpolation, we write where T is the target: a point , line, surface, or volume. Expressions (2) – (4) are very general; they apply to all field staggerings in 3D, irrespective of the order of the interpolation scheme. Let us look at
IMERG V06: Changes to the Morphing Algorithmscheme, a vector was computed so long as there was at least one grid box above the threshold.) Of the six variables, only TQV and Q500 consistently provide vectors at all locations; Q850 is globally complete except in areas of high surface altitude. Vector fields with missing values are filled in using the same temporal and spatial interpolation schemes developed for the IR-based vectors. Here, we only show results for MERRA-2 variables, since results for GEOS FP are similar. A brief discussion on
scheme, a vector was computed so long as there was at least one grid box above the threshold.) Of the six variables, only TQV and Q500 consistently provide vectors at all locations; Q850 is globally complete except in areas of high surface altitude. Vector fields with missing values are filled in using the same temporal and spatial interpolation schemes developed for the IR-based vectors. Here, we only show results for MERRA-2 variables, since results for GEOS FP are similar. A brief discussion on
