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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
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
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
defined as nodes that are wet at any point during the simulation. The nonoptimal QoI map stations , shown in Fig. 12 , identify as a larger event in the parameter space as shown in Fig. 13 . Figure 9 shows that the QoI map formed from the nonoptimal set of stations is highly skewed in comparison to the QoI maps formed from the optimal and near-optimal sets of stations. The estimated volume of the region of interest for the nonoptimal QoI map 1.917 × 10 −2 is about 250% greater than that of
defined as nodes that are wet at any point during the simulation. The nonoptimal QoI map stations , shown in Fig. 12 , identify as a larger event in the parameter space as shown in Fig. 13 . Figure 9 shows that the QoI map formed from the nonoptimal set of stations is highly skewed in comparison to the QoI maps formed from the optimal and near-optimal sets of stations. The estimated volume of the region of interest for the nonoptimal QoI map 1.917 × 10 −2 is about 250% greater than that of
, ETKF, and SV techniques, and their similarities and differences are described in section 2 . Guidance maps for two hurricane forecasts are presented in section 3 . A quantitative comparison of guidance from the respective techniques on large and local scales is performed in section 4 . Concluding remarks follow in section 5 . 2. Adaptive observing techniques The five types of adaptive observing guidance for TCs are summarized in Table 1 . The ensemble DLM wind variance only considers the
, ETKF, and SV techniques, and their similarities and differences are described in section 2 . Guidance maps for two hurricane forecasts are presented in section 3 . A quantitative comparison of guidance from the respective techniques on large and local scales is performed in section 4 . Concluding remarks follow in section 5 . 2. Adaptive observing techniques The five types of adaptive observing guidance for TCs are summarized in Table 1 . The ensemble DLM wind variance only considers the
March 1968Frederick G. Shuman and John D. Stackpole157NOTE ON THE FORMULATION OF FINITE DIFFERENCE EQUATIONS INCORPORATING A MAP SCALE FACTOR FREDERICK G. SHUMAN and JOHN D. STACKPOLE National Meteorological Center, Weather Bureau, ESSA, Washington, D.C.ABSTRACTNumerical experimentation with various finite difference formulations of a particular set of differential equationsincorporating a map scale factor indicates that the stability of the calculations is as dependent upon the
March 1968Frederick G. Shuman and John D. Stackpole157NOTE ON THE FORMULATION OF FINITE DIFFERENCE EQUATIONS INCORPORATING A MAP SCALE FACTOR FREDERICK G. SHUMAN and JOHN D. STACKPOLE National Meteorological Center, Weather Bureau, ESSA, Washington, D.C.ABSTRACTNumerical experimentation with various finite difference formulations of a particular set of differential equationsincorporating a map scale factor indicates that the stability of the calculations is as dependent upon the
deviation.I V-V, 1 is indicated in the upper diagram of figure 3.Tlle mode is 2 4 m. sec.-l, the n1edia.n is 10 m. sec-l andtile mean is 12 m. sec.". I n 15 percent of the cases thetleviation is greater than 20m.sec.-l. For comparison,Jfachta found an average ~7alue of 13 m. sec.-l f o r the vectorgeostrophic deviation at 300 mb. during the winternlonths. His chta were obhined by comparing the windand pressure gradient (geostrophic wind) on analyzedsynoptic maps.The absolute magnitudes of the cross
deviation.I V-V, 1 is indicated in the upper diagram of figure 3.Tlle mode is 2 4 m. sec.-l, the n1edia.n is 10 m. sec-l andtile mean is 12 m. sec.". I n 15 percent of the cases thetleviation is greater than 20m.sec.-l. For comparison,Jfachta found an average ~7alue of 13 m. sec.-l f o r the vectorgeostrophic deviation at 300 mb. during the winternlonths. His chta were obhined by comparing the windand pressure gradient (geostrophic wind) on analyzedsynoptic maps.The absolute magnitudes of the cross
for sake of comparison. Overall, GC performs the worst with numerical blow up at . The scalar map ME2 produces improved filter estimates over GC except on but it converges for the case of . The vector map ME2 beats these two cases on all counts. Also, the filtering skills of the vector maps ME1 and ME2 are visually indistinguishable. For some of the fields, most notably for , , , and , their skills are close to that of the perfect-model vector map experiment PM . Interestingly, in
for sake of comparison. Overall, GC performs the worst with numerical blow up at . The scalar map ME2 produces improved filter estimates over GC except on but it converges for the case of . The vector map ME2 beats these two cases on all counts. Also, the filtering skills of the vector maps ME1 and ME2 are visually indistinguishable. For some of the fields, most notably for , , , and , their skills are close to that of the perfect-model vector map experiment PM . Interestingly, in
