Preparing for Weather Extremes
In previous posts, we discussed approaches to estimate the impact of a shifting climate. While these models were useful in estimating the typical and anomalous, they are insufficient to capture weather extremes at the long tail of distributions of meteorological variables. In mainstream media and risk industry jargon, one may have come across examples of quantifications of such extremes - a 1-in-100 year flood or 1-in-500 year heatwave. In this post, we discuss approaches we have taken to make such quantifications available to any location with the most updated data from the latest weather observations and climate projection datasets.
Background
To understand climate shift, for example to quantify the nature of change in maximum temperatures across decades, Tmax is modeled as a normally distributed quantity within a climatological period. Subsequently, parameters of this distribution across different periods are compared to understand the nature of change, for example, if the variance and/or mean have changed. Further, it is relatively straightforward to estimate the change in the number of ‘really hot days’ (95th percentile Tmax) and ‘typical’ days (mean/median of Tmax) across periods . However, in order to understand the impact of extreme events (e.g. the worst heat-waves across a 3 day period, the most intense rain in a 24hr period), it was necessary to apply Extreme Value Theory to the relevant meteorological variables.
Modelling Extremes
The typical and anomolous can be estimated by modeling the distribution of the variable (e.g. Tmax as being normally distributed or Precipitation as being exponentially distributed)
However, the most extreme values that occur on the tail of these distributions occur rarely and need to be modeled separately. There are several approaches that can be taken and our current implementation is a simple one called Block Maxima Method.
We select the most extreme ‘rare’/’extreme events’ within non-overlapping blocks of time (e.g. select the maximum 1 day rainfall in a year, the maximum Tmax in a year). We then fit a probability distribution to this dataset. Typically the GEV (Generalized Extreme Value Distribution) models the extremes and we use an off-the-shelf technique called MLE (Maximum Likelihood Estimation) to determine the parameters of the distribution.
So far, we have evaluated the fit for temperature and precipitation and noticed that a few rounds of experimentation are needed to deal with slightly different shapes of distributions (skews) across different locations.
The ‘extreme events’ we choose are not limited to single day events. We use windowed aggregation to compute extreme multi-day streaks that help us estimate the occurrence of ‘worst heatwave’ or ‘worst wet-spell’.
Quantified Extremes
Extremes events are quantified by computing their probability of occurence. The inverse of that probability is called return period. A return period of 10 years (or 1-in-10 yr event) has a p=0.1 any given year. It follows that the probability of a 1-in-10 year event occurring at least once in a 30 year period is 95%. (1-(1-p)^n, n=30, p=0.1)
For example, in the graph below, the light blue line (representing 2001-2049) shows that the probability of exceeding 40 C is 0.1 (10 year return period). The dark blue line (representing 1951-2000) shows the corresponding return value is closer to 100 years, showing that the extreme event of exceeding 40C has changed from being a relatively rare event to a more frequent one.
In this example of precipitation extremes of New York, it is possible to determine return period changes for various amounts of rain across different time windows. As always, the completeness of data (coverage) is always present in the results.
What’s Next
As we mentioned earlier in the blog, we are evaluating the models for better fit (especially Tmax, Tmin). Additionally, we have plans to derive extreme rainfall intensity from (sub)hourly datasets and augment the existing windowed aggregation of precipitation. We also plan to add Wet Bulb/Heat Index derived from hourly datasets to address ‘Humid-Heat’ extremes.
Medium term, we will improve on the techniques to model extremes (Peaks-over-Threshold) and expand our datasets to include more granular observations from international weather stations. If you are a climate scientist, statistician or data scientist who finds this interesting and would like to contribute, please get in touch.
Update (Sep 2023)
We have derived extreme rainfall intensity from (sub)hourly datasets to add to the existing windowed aggregation of daily precipitation. We have also added Wet Bulb Temperature derived from hourly datasets to address ‘Humid-Heat’ extremes.