Ensemble Sensitivity Analysis (ESA), as defined by Torn and Hakim (2008) and Ancell and Hakim (2007), is essentially a lagged linear regression between a dependent variable (in this instance, the leading EOF of MSLP within a pre-defined domain) and an independent variable (e.g., 500-hPa height or MSLP at an earlier time). ESA has been used in both research and operations, with one example from SUNY Stony Brook providing a real-time ESA page as part of CSTAR.

The plots below show GFS and ECMWF ensemble ESA for multiple variables at multiple valid lead times, as well as the leading EOF1 MSLP pattern. The EOF2 MSLP pattern and sensitivity are available for EPS only. Scroll down for a quick explanation of how to use this product, and to the bottom for acknowledgements!

NOTICE: This page is not operational, and is currently still in development. Runs may occasionally partly or completely fail to plot, and additional changes are possible.

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Thanks to SUNY Stony Brook for providing the inspiration for this page from their highly useful Ensemble Sensitivity Analysis page, and to Simon Lee for helping with the code!

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ESA starts off with identifying a dependent variable, which in this page is the variability of mean sea level pressure (MSLP) within the purple highlighted domain. This is identified using the leading Empirical Orthogonal Function pattern (EOF1), meaning the dominant mode of variability.

Let's start with an example from the late January 2022 blizzard. The background shading is the EPS ensemble mean MSLP, and the contours are the EOF1 pattern. This is valid at hour 66 lead time. Notice how there's negative EOF1 values both on top of the ensemble mean low position, but the most negative EOF1 values are west of the ensemble mean low. This suggests we have variability in both the cyclone position (i.e., east-west variability), and amplitude (i.e., stronger/weaker cyclone).



Compare the image above to the individual EPS ensemble members, courtesy of WeatherBell. When comparing the individual ensemble member low positions to the ensemble mean, it's apparent that there's a cluster of members west of the ensemble mean, and that the farther west members are also stronger than the eastern members. This is a good way of quickly confirming what the EOF1 pattern above highlighted.



Next, we look at the ensemble sensitivity analysis below, correlating the 500-hPa heights at forecast hour 66 to the EOF1 MSLP variability pattern at hour 66 (shown as the 1st figure above, and also in the bottom right of the figure below). The ensemble mean 500-hPa height is contoured. Blue colors correlate with negative (dotted) EOF1 patterns, and red colors correlate with positive (solid line) EOF1 patterns.

This tells us that for a farther west and stronger cyclone at forecast hour 66, we'd want to see (a) lower 500-hPa heights at the base of the trough and upstream of it, and (b) higher 500-hPa heights downstream of the trough. Altogether, this corresponds to a more meridional 500-hPa waveguide than the ensemble mean. The opposite is true for a weaker and farther east cyclone.



Using the slider tool above, we can then see how this correlation changes at earlier forecast times. Now we're correlating 500-hPa heights at forecast hour 54 to the EOF1 MSLP variability pattern at hour 66.

This tells us that for a farther west and stronger cyclone at forecast hour 66, we'd most notably want to see (a) lower 500-hPa heights in the eastern side of the base of the trough, and (b) more ridging downstream of the trough. Specifically, (a) implies here that the 500-hPa low would close off earlier than the ensemble mean shows, which would result in an earlier occlusion of the surface cyclone and accordingly a farther west track, than if the 500-hPa low were to close off later and the surface cyclone would continue to progress downstream (i.e., northeast) before becoming occluded.