Ensemble Statistics for Diagnosing Dynamics: Tropical Cyclone Track Forecast Sensitivities Revealed by Ensemble Regression

Author: Daniel Gombos and Ross N. Hoffman
January 25, 2012
92nd American Meteorological Society Annual Meeting

Daniel Gombos, R. N. Hoffman and J. Hansen. Ensemble Statistics for Diagnosing Dynamics: Tropical Cyclone Track Forecast Sensitivities Revealed by Ensemble Regression. 92nd American Meteorological Society Annual Meeting January 25, 2012, New Orleans, LA.

We use ensemble regression (ER; Gombos and Hansen 2008; Gombos 2009) to study the sensitivity of ensemble Japanese Meteorological Association (JMA; Nakagawa 2009) tropical cyclone track forecasts to geopotential heights. This demonstrates that the utility of ensembles transcends simply measuring forecast spread by applying an ER technique to extract currently underutilized information supplied by ensembles.

ER is a simple linear inverse technique that uses correlations from ensemble model output to make inferences about dynamics, models, and forecasts. ER determines multivariate linear relationships between forecast and/or analysis fields through the use of an ensemble-derived covariance-based mapping matrix that propagates a perturbation in one (predictor) atmospheric field into a perturbation in another (predictand) atmospheric field. ER uses the ensemble members of these fields as training samples to compute the predictand ensemble anomaly (i.e., the anomaly wrt the ensemble mean) with which a user-chosen predictor ensemble anomaly is linearly related. ER can be considered a multivariate extension to the point-correlations used in ensemble synoptic analysis (ESA; Hakim and Torn 2008) and other probabilistic analysis (Zhang 2005; Hawblitzel et al. 2007; Sippel and Zhang 2008) sensitivity techniques. The use of a multidimensional operator enables inferences of how entire fields jointly relate, rather than just of how scalars individually relate.

In the current study, ER is used to study the sensitivity of Supertyphoon Sepat's (2007) track to the position and strength of the antecedent mid-tropospheric geopotential height (Z) field. Specifically, a backward-in-time ER operator is defined using as predictor the 72-hr (approximate time of landfall) forecast 1000 hPa potential vorticity (PV) and as predictand the 6-hr ensemble forecast 500 hPa Z, both initialized at 1200 UTC 14 August 2007. 72-hr forecast PV perturbations (which represent the along-track (AT) and cross-track (CT) 1000 hPa position variability at landfall, respectively) are applied to this ER operator to determine the most probable states of the antecedent pre-landfall 500 hPa Z ensemble anomalies given that the eventual cyclone at landfall is located anomalously AT and CT, respectively, of the ensemble mean location.

The resulting ER predictand perturbations imply that Sepat's 72-hr AT and CT position strongly covaried with the position and strength of the 6-hr trough to its northwest and to the position and strength of the 6-hr 500 hPa subtropical high to its northeast.

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 for researchers to infer dynamical relationships from multivariate statistical sensitivities. Using ensemble data available in real-time, the analysis illustrated that statistical patterns computed from ER are consistent with physical expectations and, without the need for an a priori understanding of the system dynamics, ER can identify the atmospheric features most strongly coupled with Sepat's track at different lead times. This sensitivity guidance might be useful to forecasters attempting to objectively estimate a deterministic forecast from ensemble model output.