*Email: carl.haines@pgr.reading.ac.uk*

Haines, C., M. J. Owens, L. Barnard, M. Lockwood, and A. Ruffenach, 2019: The Variation of Geomagnetic Storm Duration with Intensity. *Solar Physics*, **294**, https://doi.org/10.1007/s11207-019-1546-z

Variability in the near-Earth solar wind conditions can adversely affect a number of ground- and space-based technologies. Some of these space weather impacts on ground infrastructure are expected to increase primarily with geomagnetic storm intensity, but also storm duration, through time-integrated effects. Forecasting storm duration is also necessary for scheduling the resumption of safe operating of affected infrastructure. It is therefore important to understand the degree to which storm intensity and duration are related.

In this study, we use the recently re-calibrated aa index, aa_{H} to analyse the relationship between geomagnetic storm intensity and storm duration over the past 150 years, further adding to our understanding of the climatology of geomagnetic activity. In particular, we construct and test a simple probabilistic forecast of storm duration based on storm intensity.

Using a peak-above-threshold approach to defining storms, we observe that more intense storms do indeed last longer but with a non-linear relationship (Figure 1).

Next, we analysed the distribution of storm durations in eight different classes of storms dependent on the peak intensity of the storm. We found them to be approximately lognormal with parameters depending on the storm intensity. A lognormal distribution is defined by the mean of the logarithm of the values, μ, and the standard deviation of the logarithm of the values, σ. These parameters were found from the observed durations in each intensity class through Maximum Likelihood Estimation (MLE) and used to create a lognormal distribution, plotted in Figure 2 in dark purple. The light purple distribution shows a histogram of the observed data as an estimate of the probability density function (PDF). By eye, the lognormal distribution provides a reasonable first-order match at all intensity thresholds.

On this basis we created a method to probabilistically predict storm duration given peak intensity. For each of the peak intensity classes, we have calculated the values of μ and σ for the lognormal fits to the duration distributions shown as the black points in Figure 3. It is clear from the points in the left panel of Figure 3 that μ increases as intensity increases, agreeing with the previous results in Figure 1 (i.e., duration increases as intensity increases).

The parameter μ can be approximated as a function of storm intensity by:

μ(intensity) = A ln (B intensity−C)

where A, B and C are free parameters. A least squares fit was implemented, and the coefficients A, B and C were found to be 0.455, 4.632, 283.143 respectively and this curve is plotted, along with uncertainty bars, in Figure 3 (left). Although the fit is based on weighted bin-centres of storm intensity, the equation can be used to interpolate for a given value of intensity. σ can be approximated by a linear fit to give σ as a function of the peak intensity. Figure 3 (right) shows the best fit line which has a shallow gradient of −5.08×10−4 and y-intercept at 0.659.

These equations can be used to find lognormal parameters as a function of storm peak intensity. From these, a distribution of duration can be created and hence a probabilistic estimate of the duration of this storm is available. This can be used to predict the probability a storm will last at least e.g. 24 hours. Figure 4 shows the output of the model for a range of storm peak intensity compared against a test set of the aa_{H} index. The model has good agreement with the observations and provides a robust method for estimating geomagnetic storm duration.

The results demonstrate significant advancements in not only understanding the properties and structure of storms, but also how we can predict and forecast these dynamic and hazardous events.

For more information, please see the open-access paper.