Thursday, 3 October 2013

Heat-waves, time-series and Voronoi tiling

I'm currently working on using HadISD to study some heat-waves (mainly ones which have been studied in detail before).  A number of options present themselves when studying heat-waves, and Sarah Perkins (UNSW) has done some assessments on the best types of indices to use for heat-wave studies (2012, J. Climate, 26, 4500–451).  For the moment, however, I've stuck with something I've used before when assessing the performance of HadISD, and also something new to show spatial extents.

Time Series

To study the effect at an individual station what we can do with the HadISD data is to show the time-series from a particular year against the range expected from a climatology period.  As HadISD covers the span 1973-2012 (for v1.0.1.2012p), we have used the 30 year period of 1975-2004. 
Fig. 1. The daily temperatures from 2010 (green) shown on the 5th - 95th percentile range derived from the 30 year climatology over 1975-2004 (yellow band) for Moscow Botanical Gardens.

Fig. 1 shows the daily temperature for 2010 for the station in the Moscow Botanical Gardens (276120-99999, 55.833N, 37.617E).  To create the daily temperature we have required that there are at least 4 observations in a day (24hrs) and that these are spread over at least 12 hours.  For a climatology to be calculated, we require that valid days be present over at least 20 years in the 30 year period.  We also show the 5th - 95th percentile range in the yellow band, and have highlighted the days where the daily average temperatures are above the 95th percentile in red, and below the 5th percentile in blue.

The extreme warm period in late July and early August is clearly visible, and gives some impression as to the intensity and duration of the heat wave at this one station.  The magnitude of this event becomes clearer if we show the same plot for Paris-Montsouris (071560-99999, 48.817N, 2.333E) in 2003, Fig. 2.
Fig. 2. The daily temperatures from 2003 (green) shown on the 5th - 95th percentile range derived from the 30 year climatology over 1975-2004 (yellow band) for Paris-Montsouris

Spatial Extent & Voronoi Tiling

However, what about showing the spatial extent of a heat-wave.  With station data, we can show the value for each station as a coloured dot.  This isn't the clearest way of presenting the data, as is hopefully obvious in Fig. 3. 

Fig. 3 The 2010 Moscow heat-wave in HadISD for July.  Each station has been coloured by the number of degree days over climatology (see text for details)
What is plotted in Fig. 3 is basically the integral of the area highlighted in red in Fig. 1 & 2.  It is the sum over one month within a given year (July 2010 in this case) of the number of degrees the daily average is above the 95th percentile of the climatology (1975-2004 as above).   We are not counting the periods where the daily average is below the 5th percentile in the sum.  This measure gives an indication of the combined duration and intensity of an event.  A long event of only a few degrees above the 95th percentile would give the same signal of a short event which is many degrees above.  A few "bulls-eye" stations do stand out, which have high values but are not close to the centre of the heat-wave.

To try and improve the presentation of this heat map I played around with something called Voronoi tessellation (also known as Theissen Polygons).  This technique divides up an area on which a number of fixed points such that each edge of a polygon bisects the distance between two centres.  This is hopefully clear in the example below, which just colours each polygon by random, but also shows the lines which are bisected in red.
Fig. 4 Voronoi tiling.  The red lines show the connections between all the points, forming a set of Delaunay Triangles.  The Voronoi polygons are formed by joining all the bisectors of the edges of the triangles.
Combining the Voronoi method with the HadISD station distribution and the heat-wave index outlined above, results in the following map, also for July 2010.
Fig. 5 The heat map for Moscow in July 2010 using the Voronoi tiling method.  The location of each station is shown by a grey dot, usually close to the middle of the polygon, but not always so.
Using this method, the intensity of the heat-wave is much clearer than Fig. 3.  The few stations which for some reason have high values but are not in the heat-wave region (e.g. south Ukraine and central Turkey) stand out just as much as in Fig. 3.  By the nature of the tiling method, it is assumed that a station is representative of the area surrounding it.  Many stations are on the coast (UK, Norway etc.) and these are not clearly visible in Fig. 3, however the areas they represent are very clear in this representation.

An alternative way of presenting this kind of data would have been to grid up the individual stations into grid boxes.  Although this would have shown a very similar pattern, it would not be immediately clear from the resulting map, how many stations were contributing to a grid box.  Some gridding methods do not require any stations within the grid box, but use a weighted average of those stations within a search radius. The gridding process also would act as a smoothing function on the data, reducing the intensity of the maxima and minima.

Personally I think this is a good way of presenting the station data of HadISD in a space filling way without resorting to gridding.