# How Do Heating Degree Days Vary With Temperature?

Once again heating degree days (HDD). In two of our previous postings we investigated the correlation between HDDs and energy consumption. The first posting aimed at highlighting the influence of the number of HDDS on gross energy consumption, while the second focused on more specific data, namely the amount of energy devoted to heating purposes. The results were not very encouraging, since no strong correlation between the two parameters could be found. In fact, we might have expected otherwise.

In this posting we aim at a more fundamental approach. Is is clear from the definition of HDD that changes in temperature are reflected in the number of days where the heating needs to be switched on. This argument is straightforward on a daily basis. But does it also hold if we take monthly averages instead? Intuitively, the answer would be yes. But what we want to know is to what extent a montly average temperature may be considered a reliable measure for determining the value of HDDs.

In order to find the solution to this riddle we analysed the data from Sweden during the period 2003 – 2011. The baseline heating temperature for our investigation was taken to be 20°C, but HDDs for other baseline temperatures may easily be calculated. Our analysis lead to the conclusion that there is a very strong and reliable (negative) correlation between the average outside temperature and the number of HDDs over the years. As the annual data show consistently the same pattern we are not surprised to find that the same relationship holds for the multi-annual averages taken over a 30-year period as is shown in Fi.g 1.

Fig. 1 Average temperature and HDD in Sweden over a 30-year period

After these enouraging findings we might wonder if we could go one step further and look at the correlation between the annual data. Thus, we take the annual average temperature and relate it to the number of HDDs per year. As the resolution gets coarser we might expect a weakening of the relationship. However, the results are once again quite stimulating since at annual level the relationship between the two sets of parameters does not seem to loosen.  This is demonstrated in Fig. 2.

Fig. 2 Annual average temperature and HDD, 2003-2011

There is a nice negative correlation between the mean outside temperature and the number of HDDs, similar to the one we have seen for the monthly data.

A numerical analysis of our findings leads to the conclusion that, on a monthly basis, one degree of temperature difference (T,in – T,out) in centigrade corresponds to 30.5 HDD. Thus, if the monthly average temperature drops by 1 °C the number of HDD increases by 30.5. As a consequence, the number of HDDs may be directly calculated from the mean temperatures. Needless to say, that this is in perfect agreement with our own expectations.

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