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Application of Optimum Interpolation to the Analysis of Precipitation in Complex Terrain

Meenu BhargavaDepartment of Computer Science, University of Victoria, Victoria, British Columbia, Canada

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Maurice DanardDepartment of Computer Science, University of Victoria, Victoria, British Columbia, Canada

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Abstract

Optimum interpolation is a procedure that allows the combination of observations with preliminary trial fields of the same quantities in order to produce an updated field in which the error variance is minimized. In this paper, an operational method is described to analyze observed precipitation amounts based on optimum interpolation. Since the area dealt with is topographically complex, this factor has been included in the operational method. The trial fields are provided by a three-dimensional numerical weather prediction model. This paper presents an estimation of the covariances of observational and trial field errors. Two mathematical assumptions are made: 1) trial field errors and observational errors are not correlated with each other; 2) observational errors and the deviations of the trial field values from the observations are uncorrelated. The first assumption is customarily made in any application of optimum interpolation. The second assumption is specific to this paper. These two statements together imply that observational errors are uncorrelated. A technique is derived to determine which observations influence a given grid point and their respective weights. The selection of influencing observations is done by calculating the spatial dependence of r, the trial field error covariance. A cutoff point is determined on the smoothed curve where the r value is a small fraction of the r value at the origin. The procedure is applied to the heavy rainstorm of 11–13 July 1983 in the upper Columbia River watershed in southeastern British Columbia. Certain practical problems do arise in the implementation. The noncoincidence of model day and climate day tends to introduce systematic errors within the observations. This result conflicts with the assumption that observational errors am uncorrelated. Additionally, the observing system is not designed to make allowance for topographical detail. Errors are thus introduced in the observations from a variety of sources.

Abstract

Optimum interpolation is a procedure that allows the combination of observations with preliminary trial fields of the same quantities in order to produce an updated field in which the error variance is minimized. In this paper, an operational method is described to analyze observed precipitation amounts based on optimum interpolation. Since the area dealt with is topographically complex, this factor has been included in the operational method. The trial fields are provided by a three-dimensional numerical weather prediction model. This paper presents an estimation of the covariances of observational and trial field errors. Two mathematical assumptions are made: 1) trial field errors and observational errors are not correlated with each other; 2) observational errors and the deviations of the trial field values from the observations are uncorrelated. The first assumption is customarily made in any application of optimum interpolation. The second assumption is specific to this paper. These two statements together imply that observational errors are uncorrelated. A technique is derived to determine which observations influence a given grid point and their respective weights. The selection of influencing observations is done by calculating the spatial dependence of r, the trial field error covariance. A cutoff point is determined on the smoothed curve where the r value is a small fraction of the r value at the origin. The procedure is applied to the heavy rainstorm of 11–13 July 1983 in the upper Columbia River watershed in southeastern British Columbia. Certain practical problems do arise in the implementation. The noncoincidence of model day and climate day tends to introduce systematic errors within the observations. This result conflicts with the assumption that observational errors am uncorrelated. Additionally, the observing system is not designed to make allowance for topographical detail. Errors are thus introduced in the observations from a variety of sources.

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