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Grant Branstator

Abstract

The variability in skill of NMC 72-h 500 mb forecasts during recent winter is examined. Root-mean-square error, anomaly correlation, and the Fisher z-transformation of the anomaly correlation are used as measures of skill. This latter score is appropriate for measuring variability because it produces nearly Gaussian distributions of scores. The annual mean skill of the forecasts improves throughout the period examined, but there is no trend in the variability of the z-transformed anomaly correlations. Thus model improvements do not seem to have improved forecast reliability. The temporal power spectrum of skill is red and the 1-day lag correlation of anomaly correlation scores is 0.60 during our sample period. Heights at 500 mb have a similar spectrum during the sampling period, so it may be that certain elements of the atmospheric flow can be used to predict the likely skill of a forecast. A few potential predictors are tested and some of these, e.g., the persistence of the flow and the spatial standard deviation of the predicted anomalies, are shown to predict 10 to 20% of the variance in skill.

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Grant Branstator
,
Andrew Mai
, and
David Baumhefner

Abstract

To determine if some flow components are systematically forecast more accurately than others, 990 wintertime medium-range forecasts made at the European Centre for Medium-Range Weather Forecasts (ECMWF) are examined. It is found that forecasts skill of 500-mb extratropical large-scale heights tends to be a function of empirical orthogonal function (EOF) index, with those components that project onto the leading EOFs being markedly better forecast than the components that project onto the hailing EOFS. This is true for instantaneous forecasts of as long as 10 days’ duration. Furthermore, by answering the question, Of all possible structures which structure on average is most accurately forecast? the potential for constructing a basis that is even more adept than EOFs at distinguishing well-forecast from poorly forecast flow elements is shown. Similarly, it is found that 10-day average ECMWF forecasts, as well as 29-day average forecasts produced by a general circulation model at the National Center for Atmospheric Research, can be effectively decomposed into components that on average are either easy or difficult to predict. Using the ability to make such a decomposition, spatial filters are designed that remove those components that are usually poorly forecast. These filters can markedly improve the skill scores of medium-and extended-range forecasts, though the more effective filters substantially reduce the explained variance of the forecasts. The filters are especially effective in the extended range. For example, one filter, by removing 43% of the variance, can improve the average anomaly correlation of verified 29-day average forecasts to 0.66 from an unfiltered skill of 0.46. Such filters are proposed as a means of enhancing the utility of extended-range forecasts.

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Thomas W. Schlatter
and
Grant W. Branstator

Abstract

Using an 8-day series (18–26 August 1975) of multivariate statistical analyses of European radiosonde data together with a measure of analysis error, we have estimated error statistics from 959 Nimbus 6 temperature profiles for 10 isobaric layers in the troposphere and lower stratosphere. The mean error or bias is largest near the tropopause (+0.9°C) but changes sign several times in the vertical so that the integrated mean error for the atmospheric column 1000–70 mb is small (−0.1°C). The root-mean-square error peaks at the tropopause (2.9°C) with a minimum in the midtroposphere (1.0°C). In all layers, the horizontal correlation of retrieval error shows little systematic dependence on direction but strong dependence on distance. The correlation is greater than 0.50 at distances less than 400 km and less than 0.10 at 800 km and beyond, and it can be approximated by a Gaussian curve. The vertical correlations are greatest between adjacent layers (∼0.50); negative correlations exist between layers on opposite sides of the tropopause. This information is useful in any statistical objective analysis which accounts for observational error.

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Thomas W. Schlatter
,
Grant W. Branstator
, and
Linda G. Thiel

Abstract

A multivariate statistical analysis procedure has been developed for estimating geopotential height h and wind (u, v) on a global latitude-longitude grid. Estimates are obtained by modifying the “first guess” from a prediction model by a linear combination of forecast errors deduced from observed data. Because the scheme is multivariate, the regression coefficients (weights) are matrices, which depend upon covariance among forecast errors in h, u and v. These covariances are modeled mathematically with geostrophic constraints. In the tropics, however, only the wind field is analyzed, covariances are modeled under the constraint of nondivergence, and heights are obtained from a balance equation. At high latitudes, analyses are performed in polar stereographic coordinates.

The objective analysis scheme fits observed data as well as the “Cressman scheme” that was used operationally at the National Meteorological Center until recently and also as well as a skilled analyst. In data-rich areas, the analyses are insensitive to the type of fist guess. Realistic ageostrophic and divergent components are present in the analyzed winds, and the kinetic energy spectrum at 40°N is reasonable at zonal wavenumbers less than 20. When both wind and height observations are plentiful, two univariate schemes (one for height, one for wind) fit the data as well as the multivariate scheme, but forecasts based upon the latter are consistently better. Experiments suggest that for a fixed amount of initial data, small gains in forecast accuracy can be made by improving the analysis procedure.

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Thomas W. Schlatter
,
Grant W. Branstator
, and
Linda G. Thiel

Abstract

No abstract available.

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Wayman E. Baker
,
Stephen C. Bloom
,
John S. Woollen
,
Mark S. Nestler
,
Eugenia Brin
,
Thomas W. Schlatter
, and
Grant W. Branstator

Abstract

A three-dimensional (3D), multivariate, statistical objective analysis scheme (referred to as optimum interpolation or OI) has been developed for use in numerical weather prediction studies with the FGGE data. Some novel aspects of the present scheme include 1) a multivariate surface analysis over the oceans, which employs an Ekman balance instead of the usual geostrophic relationship, to model the pressure-wind error cross correlations, and 2) the capability to use an error correlation function which is geographically dependent.

A series of 4-day data assimilation experiments are conducted to examine the importance of some of the key features of the OI in terms of their effects on forecast skill, as well as to compare the forecast skill using the OI with that utilizing a successive correction method (SCM) of analysis developed earlier. For the three cases examined, the forecast skill is found to be rather insensitive to varying the error correlation function geographically. However, significant differences are noted between forecasts from a two-dimensional (2D) version of the OI and those from the 3D OI, with the 3D OI forecasts exhibiting better forecast skill. The 3D OI forecasts are also more accurate than those from the SCM initial conditions.

The 3D OI with the multivariate oceanic surface analysis was found to produce forecasts which were slightly more accurate, on the average, than a univariate version.

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