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Ensemble-Based Exigent Analysis. Part II: Using Ensemble Regression to Estimate Conditions Antecedent to Worst-Case Forecast Damage Scenarios

Daniel GombosAtmospheric and Environmental Research, Lexington, Massachusetts

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Ross N. HoffmanAtmospheric and Environmental Research, Lexington, Massachusetts

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Abstract

In Part I of this series on ensemble-based exigent analysis, a Lagrange multiplier minimization technique is used to estimate the exigent damage state (ExDS), the “worst case” with respect to a user-specified damage function and confidence level. Part II estimates the conditions antecedent to the ExDS using ensemble regression (ER), a linear inverse technique that employs an ensemble-estimated mapping matrix to propagate a predictor perturbation state into a predictand perturbation state. By propagating the exigent damage perturbations (ExDPs) from the heating degree days (HDD) and citrus tree case studies of Part I into their respective antecedent forecast state vectors, ER estimates the most probable antecedent perturbations expected to evolve into these ExDPs. Consistent with the physical expectations of a trough that precedes and coincides with the anomalously cold temperatures during the HDD case study, the ER-estimated antecedent 300-hPa geopotential height trough is approximately 59 and 17 m deeper than the ensemble mean at around the time of the ExDP as well as 24 h earlier, respectively. Statistics of the explained variance and from leave-one-out cross-validation runs indicate that the expected errors of these ER-estimated perturbations are smaller for the HDD case study than for the citrus tree case study.

Corresponding author address: Dr. Ross N. Hoffman, Atmospheric and Environmental Research, 131 Hartwell Ave., Lexington, MA 02421. E-mail: ross.n.hoffman@aer.com

Abstract

In Part I of this series on ensemble-based exigent analysis, a Lagrange multiplier minimization technique is used to estimate the exigent damage state (ExDS), the “worst case” with respect to a user-specified damage function and confidence level. Part II estimates the conditions antecedent to the ExDS using ensemble regression (ER), a linear inverse technique that employs an ensemble-estimated mapping matrix to propagate a predictor perturbation state into a predictand perturbation state. By propagating the exigent damage perturbations (ExDPs) from the heating degree days (HDD) and citrus tree case studies of Part I into their respective antecedent forecast state vectors, ER estimates the most probable antecedent perturbations expected to evolve into these ExDPs. Consistent with the physical expectations of a trough that precedes and coincides with the anomalously cold temperatures during the HDD case study, the ER-estimated antecedent 300-hPa geopotential height trough is approximately 59 and 17 m deeper than the ensemble mean at around the time of the ExDP as well as 24 h earlier, respectively. Statistics of the explained variance and from leave-one-out cross-validation runs indicate that the expected errors of these ER-estimated perturbations are smaller for the HDD case study than for the citrus tree case study.

Corresponding author address: Dr. Ross N. Hoffman, Atmospheric and Environmental Research, 131 Hartwell Ave., Lexington, MA 02421. E-mail: ross.n.hoffman@aer.com
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