Search Results
), this leads to a system of d = 5 × N × M × L nonlinear algebraic equations. These are solved with Δ S as a control parameter using a pseudoarclength continuation method; details on this methodology are provided in Dijkstra (2005) . For each of the steady states, we now consider the evolution of infinitesimally small disturbances within the model. Linearizing (1) and (2) in the amplitude of the perturbations and separating the equations for these disturbances in time, an elliptic
), this leads to a system of d = 5 × N × M × L nonlinear algebraic equations. These are solved with Δ S as a control parameter using a pseudoarclength continuation method; details on this methodology are provided in Dijkstra (2005) . For each of the steady states, we now consider the evolution of infinitesimally small disturbances within the model. Linearizing (1) and (2) in the amplitude of the perturbations and separating the equations for these disturbances in time, an elliptic
RockyMountains west of the frontal system was removed andreplaced by a smaller isosteric zone. Fro. 11. Twelve-hourly precipitation summary centered about00 GMT 12 December 1965. Values in parentheses are reportsreceived for the 6 h period after map time. Other reports are for6 h period prior to map t!me.FIG. 12. D-values of non-dimensionalized specific volume for sigma level 5, 00 GMT, 12 December 1965. Pattern comparisons between observed and variationally adjusted fields are summarized in Table
RockyMountains west of the frontal system was removed andreplaced by a smaller isosteric zone. Fro. 11. Twelve-hourly precipitation summary centered about00 GMT 12 December 1965. Values in parentheses are reportsreceived for the 6 h period after map time. Other reports are for6 h period prior to map t!me.FIG. 12. D-values of non-dimensionalized specific volume for sigma level 5, 00 GMT, 12 December 1965. Pattern comparisons between observed and variationally adjusted fields are summarized in Table
radiosonde data and National Meteorological Center (NMC) analyses. Vertical motions were computed for all days inMarch-April and September-October 1990. The radiosonde data are available at 0000 and 1200 UTCdaily. The sounding times with largest computed upward and largest downward motion at 500 hPa (about5.6 km above sea level) in the spring and fall wereselected for presentation here. The operational surfacesynoptic weather maps for these four cases, given inFig. 1, will be discussed in detail as
radiosonde data and National Meteorological Center (NMC) analyses. Vertical motions were computed for all days inMarch-April and September-October 1990. The radiosonde data are available at 0000 and 1200 UTCdaily. The sounding times with largest computed upward and largest downward motion at 500 hPa (about5.6 km above sea level) in the spring and fall wereselected for presentation here. The operational surfacesynoptic weather maps for these four cases, given inFig. 1, will be discussed in detail as
comparisons of significant wave height measured with the buoy (gray) and radar (black): (top) standard averaging and (bottom) the Fedje 2 case. These data are from March 2000. Fig . 6. As in Fig. 5 , but for mean direction. Fig . 7. Scatterplots of significant wave height: (left) standard averaging and (right) the Fedje 2 case. Fig . 8. As in Fig. 7 , but for mean direction. Fig . 9. Maps of significant wave height and direction measured with the Miami WERA system at 0805 UTC 25 Sep 2004: (top) standard
comparisons of significant wave height measured with the buoy (gray) and radar (black): (top) standard averaging and (bottom) the Fedje 2 case. These data are from March 2000. Fig . 6. As in Fig. 5 , but for mean direction. Fig . 7. Scatterplots of significant wave height: (left) standard averaging and (right) the Fedje 2 case. Fig . 8. As in Fig. 7 , but for mean direction. Fig . 9. Maps of significant wave height and direction measured with the Miami WERA system at 0805 UTC 25 Sep 2004: (top) standard
the followingdefinitions for the scaled wind images ( U, V) in termsof rotated (~/, -) and local Cartesian wind components(u, v): = [-sinX -cosX]u L cosX -sinXJ\v) a~, /' (6) For a polar stereographic projection, the map scalefactor rn is defined as follows: ( 1 + sinqoo) m= ( 1 + sinqo)where qOo is the latitude at which the plane of
the followingdefinitions for the scaled wind images ( U, V) in termsof rotated (~/, -) and local Cartesian wind components(u, v): = [-sinX -cosX]u L cosX -sinXJ\v) a~, /' (6) For a polar stereographic projection, the map scalefactor rn is defined as follows: ( 1 + sinqoo) m= ( 1 + sinqo)where qOo is the latitude at which the plane of
)and (31) we obtain a coupled system of (2M+I)N prognostic ordinary differential equations of the form d --(Xi) = fi. dtHere the Xi are the (2M-I-1)N Fourier amplitudes, andthe f~ are algebraic functions of the wave numbers,the four dimensionless parameters (A,a,R,b), and theX~ themselves. Once values of the parameters and initialconditions for the X~ are specified, this system may besolved numerically as a marching problem. All of thenumerical solutions described
)and (31) we obtain a coupled system of (2M+I)N prognostic ordinary differential equations of the form d --(Xi) = fi. dtHere the Xi are the (2M-I-1)N Fourier amplitudes, andthe f~ are algebraic functions of the wave numbers,the four dimensionless parameters (A,a,R,b), and theX~ themselves. Once values of the parameters and initialconditions for the X~ are specified, this system may besolved numerically as a marching problem. All of thenumerical solutions described
well as p g ( x ) and p c ( x ), are probability density functions (pdfs); the terms “distribution” and “density” are used interchangeably. Hence, the population mean and variance of the mixture distribution are Here, the population mean and variance of the ground and cloud flashes are, respectively, Obtaining the results in (2) are straightforward, and the second result in (2) requires a little algebra. 3. Bayesian inference of model parameters a. The MAP solution As discussed above, the
well as p g ( x ) and p c ( x ), are probability density functions (pdfs); the terms “distribution” and “density” are used interchangeably. Hence, the population mean and variance of the mixture distribution are Here, the population mean and variance of the ground and cloud flashes are, respectively, Obtaining the results in (2) are straightforward, and the second result in (2) requires a little algebra. 3. Bayesian inference of model parameters a. The MAP solution As discussed above, the
temperaturegradient during the period November 1978 to March1979 along the circumpolar front in the SouthernHemisphere shown by SMMR (see Figs. 3 and 4) isin good agreement with climatological maps. TheSMMR map of 25 October-25 November 1978 whencompared with the NMFS map of SST for November1978 shows a good agreement over the open ocean.In Fig. 5a two comparisons of SST derived fromSMMR versus NMFS are shown along the 140-W and165 -W longitudes from 50-N to 30-S. The comparisonshows that the SMMR estimation is
temperaturegradient during the period November 1978 to March1979 along the circumpolar front in the SouthernHemisphere shown by SMMR (see Figs. 3 and 4) isin good agreement with climatological maps. TheSMMR map of 25 October-25 November 1978 whencompared with the NMFS map of SST for November1978 shows a good agreement over the open ocean.In Fig. 5a two comparisons of SST derived fromSMMR versus NMFS are shown along the 140-W and165 -W longitudes from 50-N to 30-S. The comparisonshows that the SMMR estimation is
to the 0.5-m depth of the observations ( Gilhousen 1987 ). The LST forecasts at buoy 45005 were also evaluated in terms of relative performance by comparing the predictions against an hourly LST climatology. Comparisons between lake forecasts, hindcasts, climatology, and observations were done using graphical techniques and statistical measures. These statistical measures included two absolute quantities, mean algebraic and absolute differences, one relative quantity, the index of agreement (IOA
to the 0.5-m depth of the observations ( Gilhousen 1987 ). The LST forecasts at buoy 45005 were also evaluated in terms of relative performance by comparing the predictions against an hourly LST climatology. Comparisons between lake forecasts, hindcasts, climatology, and observations were done using graphical techniques and statistical measures. These statistical measures included two absolute quantities, mean algebraic and absolute differences, one relative quantity, the index of agreement (IOA
to account for 93% of the "variance" in the original 12 X60 matrix ofraw data and they are also found to have features in common with three natural cycles of annual precipitationin Nevada. The effect of station elevation on each eigenvector is determined by linear correlation. Thestation multipliers, corrected to a mean elevation, are plotted and analyzed on three maps. These three mapsplus the corresponding eigenvectors and elevation regressions supply all the information needed to estimatethe
to account for 93% of the "variance" in the original 12 X60 matrix ofraw data and they are also found to have features in common with three natural cycles of annual precipitationin Nevada. The effect of station elevation on each eigenvector is determined by linear correlation. Thestation multipliers, corrected to a mean elevation, are plotted and analyzed on three maps. These three mapsplus the corresponding eigenvectors and elevation regressions supply all the information needed to estimatethe
