Weather Forecast Error Decomposition using Rearrangements of Functions

摘要: v Abstract. This thesis applies rearrangement and optimal mass transfer theory to weather forecast error decomposition. Errors in forecasting are often due displacement of key features; conventional scores do not necessarily favour good forecasts, nor they descriptive how the failed. We study decomposition, where is split into an differences qualitative features. In its simple formulation, we seek rearrangements which a best fit actual data, then find “least kinetic energy” notional velocity transporting fit. mathematical terms, characterising those elements set closest (in sense L2) prescribed square integrable function, seeking least 2Wasserstein distance squared between displaced forecasts. demonstrate that there rearrangements, characterise this set; fitting determined up on level sets positive size function. Displacement calculated by finding minimum value problem; review previous work, demonstrating connection with transport A problem formulation decomposition because features taken first, may be penalise as large error. conclude considering minimises both errors simultaneously.