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MADHAV L. KHANDEKAR

Abstract

A statistical theory developed previously is applied to predictions made with three simple atmospheric models under similar boundary and initial conditions. The theory gives minimum variances in height fields of various isobaric levels. The governing equations of each model are utilized to transform these initial variances to final variances of forecast fields. These variances are a measure of the theoretical minimum errors expected at any future states due to presence of initial uncertainties. Using the normal frequency function, these theoretical variances are further transformed to probabilities of obtaining forecast heights within specified magnitudes of true heights. These theoretical probabilities are compared with observed probabilities of errors in forecast fields obtained by various models for three synoptic situations.

The theoretical probabilities are found to be larger everywhere than the observed ones, in support of the statistical theory that provides limiting probabilities not to be exceeded. A comparison of theoretical minimum variances indicates that the growth of these variances is more pronounced in more complex models that incorporate additional terms in the governing equations. The effect of hypothetically increasing the number of reporting stations indicates that a substantial reduction in initial and final variances is realized when the number of reporting stations is increased by two to three times the present number.

The results of this study offer a possibility of choosing an optimum model to obtain the most reliable short-range weather prediction for a given synoptic situation.

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Amir Shabbar
,
Barrie Bonsal
, and
Madhav Khandekar

Abstract

Precipitation responses over Canada associated with the two extreme phases of the Southern Oscillation (SO), namely El Niño and La Niña, are identified. Using the best available precipitation data from 1911 to 1994, both the spatial and temporal behavior of the responses are analyzed from the El Niño/La Niña onset to several seasons afterward. Composite and correlation analyses indicate that precipitation over a large region of southern Canada extending from British Columbia, through the prairies, and into the Great Lakes region is significantly influenced by the SO phenomenon. The results show a distinct pattern of negative (positive) precipitation anomalies in this region during the first winter following the onset of El Niño (La Niña) events. During this same period, significant positive precipitation anomalies occur over the northern prairies and southeastern Northwest Territories in association with El Niño events. Statistical significance of the responses is tested by the Student’s t-test and the Wilcoxon rank-sum test, while field significance is established through the Monte Carlo procedure. All of the significant precipitation anomalies can be explained by the associated upper-atmospheric flow patterns, which during the first winter following the onset of El Niño (La Niña) events resemble the positive (negative) phase of the Pacific–North American (PNA) pattern. Significant correlations between Southern Oscillation index (SOI) values and the observed precipitation anomalies over southern Canada suggest the possibility of developing a long-range forecasting technique for Canadian precipitation based on the occurrence and evolution of the various phases of the SO.

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