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Daniel Gombos
and
James A. Hansen

Abstract

Hakim and Torn (HT) presented a statistical piecewise potential vorticity (PV) regression technique that uses flow-dependent analysis covariances from an ensemble square root filter to statistically infer the relationship between the PV and state fields. This paper illustrates that the PV perturbation effectively regressed by HT’s regression is the projection of the PV perturbation onto the ensemble PV anomalies that define the regression operator. It is shown that the piecewise PV inversion of this effective PV perturbation via the technique presented in Davis and Emanuel yields nearly identical heights to those from an HT regression performed in the subspace of the leading PV singular vectors.

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Daniel Gombos
and
Ross N. Hoffman

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.

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Daniel Gombos
and
Ross N. Hoffman

Abstract

Exigent analysis supplements an ensemble forecast of weather-related damage with a map of the worst-case scenario (WCS), a multivariate confidence bound of the damage. For multivariate Gaussian ensembles, ensemble-based exigent analysis uses a Lagrange multiplier technique to identify the unique maximizing damage map at a given uncertainty level based on the ensemble-estimated covariance of the damage. Exigent analysis is applied to two case studies. First, using ensemble forecasts of 2-m temperature and estimates of the number of inhabitants at each location, exigent analysis is applied to forecast the worst-case heating demand for a large portion of the United States on 8–9 January 2010. The WCS at the 90th percentile results in only 1.26% more heating demand than the ensemble mean. Second, using ensemble forecasts of 2-m temperature and estimates of the number of citrus trees at each location, exigent analysis is applied to forecast the worst-case freeze damage to Florida citrus trees on 11 January 2010. For this case study, the WCS at the 90th percentile damages about 14.2 million trees, about 4.3 times more than the ensemble mean.

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Daniel Gombos
,
Ross N. Hoffman
, and
James A. Hansen

Abstract

Ensemble regression (ER) is a simple linear inverse technique that uses correlations from ensemble model output to make inferences about dynamics, models, and forecasts. ER defines a multivariate regression operator in the principal component subspaces of ensemble forecasts and analyses of atmospheric fields. ER uses the ensemble members of a predictor and a predictand field as training samples to compute the ensemble anomaly (with respect to the ensemble mean of the predictand field) with which a dynamically relevant ensemble anomaly (with respect to the ensemble mean of the predictor field) is linearly related. Specifically, an ER operator defined by the Japan Meteorological Agency’s ensemble forecast 500-hPa geopotential height and 1000-hPa potential vorticity is used to show that Supertyphoon Sepat’s (2007) track strongly covaried with the position and strength of the antecedent steering subtropical high to its northeast and the trough to its northwest. The case study illustrates how ER can identify, in real time, the dynamical processes that are particularly relevant for operational forecasters to make specific forecasting decisions and can help researchers to infer physical relationships from multivariate statistical sensitivities.

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Daniel Gombos
,
James A. Hansen
,
Jun Du
, and
Jeff McQueen

Abstract

A minimum spanning tree (MST) rank histogram (RH) is a multidimensional ensemble reliability verification tool. The construction of debiased, decorrelated, and covariance-homogenized MST RHs is described. Experiments using Euclidean L2, variance, and Mahalanobis norms imply that, unless the number of ensemble members is less than or equal to the number of dimensions being verified, the Mahalanobis norm transforms the problem into a space where ensemble imperfections are most readily identified. Short-Range Ensemble Forecast Mahalanobis-normed MST RHs for a cluster of northeastern U.S. cities show that forecasts of the temperature–humidity index are the most reliable of those considered, followed by mean sea level pressure, 2-m temperature, and 10-m wind speed forecasts. MST RHs of a Southwest city cluster illustrate that 2-m temperature forecasts are the most reliable weather component in this region, followed by mean sea level pressure, 10-m wind speed, and the temperature–humidity index. Forecast reliabilities of the Southwest city cluster are generally less reliable than those of the Northeast cluster.

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Robert Atlas
,
Ross N. Hoffman
,
Joseph Ardizzone
,
S. Mark Leidner
,
Juan Carlos Jusem
,
Deborah K. Smith
, and
Daniel Gombos

Abstract

The ocean surface wind mediates exchanges between the ocean and the atmosphere. These air–sea exchange processes are critical for understanding and predicting atmosphere, ocean, and wave phenomena on many time and space scales. A cross-calibrated multiplatform (CCMP) long-term data record of satellite ocean surface winds is available from 1987 to 2008 with planned extensions through 2012. A variational analysis method (VAM) is used to combine surface wind data derived from conventional and in situ sources and multiple satellites into a consistent nearglobal analysis at 25-km resolution, every 6 h. The input data are cross-calibrated wind speeds derived from the Special Sensor Microwave Imager (SSM/I; F08F15), the Tropical Rainfall Measuring Mission Microwave Imager (TMI), and the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E), and wind vectors from SeaWinds on the NASA Quick Scatterometer (QuikSCAT) and on the second Japanese Advanced Earth Observing Satellite (ADEOS- 2; i.e., the Midori-2 satellite). These are combined with ECMWF reanalyses and operational analyses by the VAM. VAM analyses and derived data are currently available for interested investigators through the Jet Propulsion Laboratory (JPL) Physical Oceanography Distributed Active Archive Center (PO.DAAC). This paper describes the methodology used to assimilate the input data along with the validation and evaluation of the derived CCMP products.

A supplement to this article is available online:

DOI: 10.1175/2010BAMS2946.2

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