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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
DECEMBER 1990 NOTES AND CORRESPONDENCE 2781The Equivalency of the Tangent and Secant Lambert Conformal Map Projections HARRY R. GLAHNTechniques Development Laboratory, O~ce of Systems Develop~nent, National Weather Service, NOAA, Silver Spring, Maryland26 March 1990 and 7 July 1990 ABSTRACT There is a popular misconception that the secant form of the Lambert conformal map
DECEMBER 1990 NOTES AND CORRESPONDENCE 2781The Equivalency of the Tangent and Secant Lambert Conformal Map Projections HARRY R. GLAHNTechniques Development Laboratory, O~ce of Systems Develop~nent, National Weather Service, NOAA, Silver Spring, Maryland26 March 1990 and 7 July 1990 ABSTRACT There is a popular misconception that the secant form of the Lambert conformal map
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
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
