This thesis applies rearrangement and optimal mass transfer theory to weather forecast error decomposition. Errors in weather forecasting are often due to displacement of key features; conventional error scores do not necessarily favour good forecasts, nor are they descriptive of how the forecast failed. We study forecast error decomposition, where error is split into an error due to displacement and an error due to differences in qualitative features. In its simple formulation, we seek re-arrangements of the forecast which are a best fit to the actual data, and then find the “least kinetic energy” of a notional velocity transporting the forecast to a best fit. In mathematical terms, we are characterising those elements of a set of rearrangements which are closest (in the sense of L2) to a prescribed square integrable function, and seeking the least 2-Wasserstein distance squared between the forecast and the closest displaced forecasts. We demonstrate that there are closest rearrangements, and characterise this set; the best fitting rearrangements are determined up to rearrangement on the level sets of positive size of the prescribed function. Displacement error is calculated by finding the minimum value of an optimal mass transfer problem; we review previous work, demonstrating the connection with transport of the forecast to the best fit. A problem with the simple formulation of forecast error decomposition is that because the qualitative features error is taken first, an error in qualitative features may be penalise as a large displacement error. We conclude this thesis by considering a formulation which minimises both errors simultaneously.
|Date of Award||28 May 2012|
|Supervisor||Robert Douglas (Supervisor) & David Jones (Supervisor)|
Weather Forecast Error Decomposition using Rearrangements of Functions
Lanagan, G. D. E. (Author). 28 May 2012
Student thesis: Doctoral Thesis › Doctor of Philosophy