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Richard C. J. Somerville

)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

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Leela M. Frankcombe
and
Henk A. Dijkstra

), 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

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G. D. Nastrom
,
W. L. Clark
,
K. S. Gage
,
T. E. VanZandt
,
J. M. Warnock
,
R. Creasey
, and
P. M. Pauley

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

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C. Prabhakara
,
I. Wang
,
A. T. C. Chang
, and
P. Gloersen

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

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W. J. Koshak

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

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John G. W. Kelley
,
Jay S. Hobgood
,
Keith W. Bedford
, and
David J. Schwab

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

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Charles K. Stidd

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

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Ibrahima Diouf
,
Roberto Suárez-Moreno
,
Belen Rodríguez-Fonseca
,
Cyril Caminade
,
Malick Wade
,
Wassila M. Thiaw
,
Abdoulaye Deme
,
Andrew P. Morse
,
Jaques-André Ndione
,
Amadou T. Gaye
,
Anta Diaw
, and
Marie Khemesse Ngom Ndiaye

decomposition (SVD) to the cross-covariance matrix C between Y and Z to maximize it. The SVD is an algebraic technique to diagonalize nonsquare matrices, like the covariance matrix of two fields with different sizes ( von Storch and Frankignoul 1998 ). The S4CAST performs cross-validated hindcasts following the leave-one-out method ( Dayan et al. 2014 ). This method is intended as a model validation technique. In the first step, data for the predictor and the predictand fields are removed for a

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John G. Williams
and
Werner H. Terjung

data matrix has asymmetric 134 x 134 covariance matrix, with thevariance of the data at each grid point on the maindiagonal, and the covariances between the grid-pointdata elsewhere. The covariance between the data attwo grid points is a measure of the tendency of thevalues at the grid points to vary from their means282JOURNAL OF APPLIED METEOROLOGYFIo, 1. Areas covered by the pressure data at 500 mb (left) and at sea level (right). Grid locations are shown on the 500 mb map.VOLUME 20in the

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Peter D. Killworth
and
Jeffrey R. Blundell

our numerics completely accurate, the bottom condition would be satisfied everywhere (i.e., ω would be the solution to each local problem). Errors tend to compound along rays, and, when they reach a cutoff value, we choose to terminate the ray. 5 The computations were repeated with the mean flow set to zero for more immediate comparison with KB99 , as well as a check on the algebra. Subject to the proviso that N 2 now varies across the basin, and the use of a more recent global dataset, the

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