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. 2007 ) are taken a step further into a multidimensional spatiotemporal domain. To achieve this, we apply algebraic similarity mapping, a method for quantitative comparison of any number of input datasets, maps, or models, which was first developed for resource exploration ( Herzfeld and Merriam 1990 ) and is adapted here for climate data analysis and the WALE experiment. Similarity mapping, or algebraic map comparison, utilizes a multidimensional algebraic algorithm to compare any number of input
. 2007 ) are taken a step further into a multidimensional spatiotemporal domain. To achieve this, we apply algebraic similarity mapping, a method for quantitative comparison of any number of input datasets, maps, or models, which was first developed for resource exploration ( Herzfeld and Merriam 1990 ) and is adapted here for climate data analysis and the WALE experiment. Similarity mapping, or algebraic map comparison, utilizes a multidimensional algebraic algorithm to compare any number of input
) datasets for nine years (1992–2000) simultaneously. The map comparison method is based on an algebraic approach that proceeds by 1) standardizing input values in each map or spatial model, 2) forming a functional of pairwise differences of standardized values, and 3) applying a seminorm to the functional in step 2, for each point in the 25-km 2 EASE Grid of the WALE region. The result is a spatial grid model of similarity values, which may be mapped to show areas of similarity versus areas of
) datasets for nine years (1992–2000) simultaneously. The map comparison method is based on an algebraic approach that proceeds by 1) standardizing input values in each map or spatial model, 2) forming a functional of pairwise differences of standardized values, and 3) applying a seminorm to the functional in step 2, for each point in the 25-km 2 EASE Grid of the WALE region. The result is a spatial grid model of similarity values, which may be mapped to show areas of similarity versus areas of
advantage of weighting the stations or gridpoints equallythereby not biasing the position of synoptic centers.If a research area had a very strong variance ratio,this might prove an advantage. A disadvantage of acorrelation matrix input is that it yields normalizeddeparture fields with isolines being non-dimensional.This is a disadvantage since the comparison of theactual fields to the map types is purely a function ofshape and not intensity. A cross products matrix can als0 be input andwould yield
advantage of weighting the stations or gridpoints equallythereby not biasing the position of synoptic centers.If a research area had a very strong variance ratio,this might prove an advantage. A disadvantage of acorrelation matrix input is that it yields normalizeddeparture fields with isolines being non-dimensional.This is a disadvantage since the comparison of theactual fields to the map types is purely a function ofshape and not intensity. A cross products matrix can als0 be input andwould yield
Okhotsk and the 400-ft. negativeerrors over the North Sea.The forecast program was then changed so that theinitial values of vorticity on the rows and columns ad-jacent to the boundaries were retained with no change[V. V7=0 FIRST ROW IN FROMBOUNDARY 'FIGURE 8.-Mean algebraic errors of 48-hour barotropic forecastsmade from six initial maps. Errors in feet.during the forecast (zero Jacobians at these points).The average algebraic error for the same six cases is shownin figure 8b. Although the error was
Okhotsk and the 400-ft. negativeerrors over the North Sea.The forecast program was then changed so that theinitial values of vorticity on the rows and columns ad-jacent to the boundaries were retained with no change[V. V7=0 FIRST ROW IN FROMBOUNDARY 'FIGURE 8.-Mean algebraic errors of 48-hour barotropic forecastsmade from six initial maps. Errors in feet.during the forecast (zero Jacobians at these points).The average algebraic error for the same six cases is shownin figure 8b. Although the error was
assumption isalready implicit in the algebraic solution for the nondivergent case, which also satisfies (25)-(27) only withneglect of advective affects. While this seems a ratherstrong constraint, the solutions obtained from actualdata appear to justify it.a. Rectangular coordinates, elliptic data Exact solutions are available in the rectangulargeometry and this fact minimizes the effects of truncation error in comparison of results. It is a straightforward matter to verify that, for a pressure
assumption isalready implicit in the algebraic solution for the nondivergent case, which also satisfies (25)-(27) only withneglect of advective affects. While this seems a ratherstrong constraint, the solutions obtained from actualdata appear to justify it.a. Rectangular coordinates, elliptic data Exact solutions are available in the rectangulargeometry and this fact minimizes the effects of truncation error in comparison of results. It is a straightforward matter to verify that, for a pressure
krn Constant Altitude Plan Position Indicator (CAPPI) maps would outline these cores. [The technique of these CAPPI maps has been de scribed more recently by Marshall and Ballantyne (1975)]. Good correlation was found in time and azimuth between the recorded sferics and the cores as displayed on the 7 km CAPPI maps, which we shall refer to as "Larsen regions." (Further comparison was 0021-8952/78/02o6-o212505.0o ~) 1978 American Meteorological Societymade on strip charts with azimuth and time as
krn Constant Altitude Plan Position Indicator (CAPPI) maps would outline these cores. [The technique of these CAPPI maps has been de scribed more recently by Marshall and Ballantyne (1975)]. Good correlation was found in time and azimuth between the recorded sferics and the cores as displayed on the 7 km CAPPI maps, which we shall refer to as "Larsen regions." (Further comparison was 0021-8952/78/02o6-o212505.0o ~) 1978 American Meteorological Societymade on strip charts with azimuth and time as
conditions. In Brink's model the response istherefore dependent on location; in MF's model it isnot. Also, Brink's boundary conditions limit the zonalfetch, whereas MF's model has unlimited fetch. Brinksucceeds in reproducing characteristic features of hisobserved coherence maps. In this paper we show thatMF's model also reproduces the characteristic featuresof observed coherence maps. One reason why we recalculate coherence maps using MF's model is that itis algebraically simpler because it assumes
conditions. In Brink's model the response istherefore dependent on location; in MF's model it isnot. Also, Brink's boundary conditions limit the zonalfetch, whereas MF's model has unlimited fetch. Brinksucceeds in reproducing characteristic features of hisobserved coherence maps. In this paper we show thatMF's model also reproduces the characteristic featuresof observed coherence maps. One reason why we recalculate coherence maps using MF's model is that itis algebraically simpler because it assumes
chosen fromindicated maps. Comparison values for hemisphere are fromTables 1, 20, 25. Units are m2. None (climatology)Point E' E" Predictor mapsPresent map Present mappast map past map past progE~ E' E~ Ett1 21595 24164 4212 4315 2752 28082 22758 19566 4131 3983 2606 26023 2895 2159 816 543 779 5474
chosen fromindicated maps. Comparison values for hemisphere are fromTables 1, 20, 25. Units are m2. None (climatology)Point E' E" Predictor mapsPresent map Present mappast map past map past progE~ E' E~ Ett1 21595 24164 4212 4315 2752 28082 22758 19566 4131 3983 2606 26023 2895 2159 816 543 779 5474
, B. J. Etherton , and Z. Toth , 2002b : Adaptive sampling with the ensemble transform Kalman filter. Part II: Field program implementation. Mon. Wea. Rev. , 130 , 1356 – 1369 . Majumdar , S. J. , S. D. Aberson , C. H. Bishop , R. Buizza , M. S. Peng , and C. A. Reynolds , 2006 : A comparison of adaptive observing guidance for Atlantic tropical cyclones. Mon. Wea. Rev. , 134 , 2354 – 2372 . Noble , B. , and J. W. Daniel , 1988 : Applied Linear Algebra . 3d
, B. J. Etherton , and Z. Toth , 2002b : Adaptive sampling with the ensemble transform Kalman filter. Part II: Field program implementation. Mon. Wea. Rev. , 130 , 1356 – 1369 . Majumdar , S. J. , S. D. Aberson , C. H. Bishop , R. Buizza , M. S. Peng , and C. A. Reynolds , 2006 : A comparison of adaptive observing guidance for Atlantic tropical cyclones. Mon. Wea. Rev. , 134 , 2354 – 2372 . Noble , B. , and J. W. Daniel , 1988 : Applied Linear Algebra . 3d
. radar at the location of a gage even if the Z-Rrelation, the map projection, and the raingage locationson the map are perfect. However, the resulting error inestimating point rainfall should not be systematic.5. Results The raingage (G) and radar observations (R~) permitted 50 comparisons, none of which involved seededclouds. These comparisons are tabulated in. Table 1 andsummarized in Table 2. Using the raingage results asthe standard, the mean absolute difference is about 30%while the mean
. radar at the location of a gage even if the Z-Rrelation, the map projection, and the raingage locationson the map are perfect. However, the resulting error inestimating point rainfall should not be systematic.5. Results The raingage (G) and radar observations (R~) permitted 50 comparisons, none of which involved seededclouds. These comparisons are tabulated in. Table 1 andsummarized in Table 2. Using the raingage results asthe standard, the mean absolute difference is about 30%while the mean
