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Feature calibration and alignment to represent model forecast errors: Empirical regularization

A method for characterizing errors for weather forecasts and analyses, called feature calibration and alignment (FCA), decomposes model forecast error into phase error, amplitude error and residual error. Phase and amplitude errors are represented by large‐scale displacements and biases of a field. In this study FCA is used to represent errors in realistic univariate two‐dimensional analysis and forecast fields. In previous work FCA was tuned subjectively. Here, a methodology to determine an empirical constraint that regularizes the FCA solutions is developed. This version of FCA still has some tunable parameters, but the new method greatly reduces the subjective nature of FCA. The data used are European Centre for Medium‐Range Weather Forecasts analyses and one‐ to ten‐day forecasts of 500 hPa geopotential height. A stepwise procedure is used to derive the statistics of the error components for ideally chosen spectral truncations. The stepwise FCA statistics are then used to define a constraint that controls the size of the spectral coefficients of the FCA representation of the phase and amplitude errors. A large fraction (∼90%) of the 500 hPa geopotential‐height forecast‐error variance is explained by FCA, demonstrating that a large part of the forecast error can be described as large‐scale phase and bias errors. The fraction of variance explained increases with forecast length, and is slightly larger in winter than in summer. The constrained FCA solutions are more efficient and exhibit less of a tendency for multiple solutions when compared to the unconstrained FCA solutions. Copyright © 2003 Royal Meteorological Society