# 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.

# Energy per capita

It doesn´t come as a surprise that bigger countries consume larger amounts of energy than smaller ones. In general, at least. And yet, there are exceptions to this rule. US consumption of primary energy was 2204.1 Mtoe in 2009 according to BP´s Statistical Review of World Energy 2011. In the same year Canada used some 312.5 Mtoe.  The two neighbours are roughly equivalent in terms of economic performance (with GDP per capita in the US being larger than the respective quantitiy for Canada). Thus the main reason for explaining the difference is by reference to the population numbers. Here the US with 307 millions outweighs Canada with 33 millions. However, there are also other factors coming into play, as we shall see later.

A nice example that population is not the only parameter steering energy needs is given by comparing Germany and Mexico. Although Mexico has considerably more inhabitants (107 millions vs. 82) its consumption figures are significantly lower than the German ones (167 Mtoe vs. 307 Mtoe).

A sensible quantity for measuring the energy hunger of a particular economy is the primary energy consumption per capita. In that way, size effects stemming from largely different populations are normalised. The philosophy behind this is similar to the one of energy intensity which measures consumption per unit of GDP.

In the following we consider a number of developed economies and look at their energy hunger per head. We will find out that there are considerable differences between those countries although, at first sight, they may appear to be very similar in nature. The raw data for the following investigations have been taken from BP´s Statistical Review of World Energy, from the UN Statistics Division and from the CIA World Factbook.

Fig. 1 Primary energy consumption per capita in ktoe, 1991-2010

Although each of these countries is part of the wealthier economies of our planet, their energy consumption per head reveals some striking differences. We may observe that during the past 20 years the figures have not changed dramatically. Norway´s figures, though, show some variation, however, without any clear trend to higher or lower values.

One of the intentions of our choice was to highlight consumption characteristics between northern and southern countries. And indeed, the southern branch consisting of Italy, Portugal and Spain is well separated from their northern counterparts Canada, Norway, Finland and Sweden. In fact, there is even a significant gap between Sweden and Finland on the one hand and Canada and Norway on the other.

Having the north-south distinction as a particular feature we may come forward with some explanations on the seemingly unbridgable gap between the northern and southern economies. Obviously, one of the strongest arguments is based on climatic variations. Average temperatures are lower in nordic countries than in the southern ones which explains part of the difference. In order to have a reliable measure on how energy consumption is triggered by climatic circumstances we apply the concept of heating-degree days (HDD) which is used by Eurostat. Apparently, there are two parameters governing the HDD: the temperature and the number of days when heating is necessary. Without going into details we may state that the  nordic countries (except Canada) had more than 5000 HDD in 2009, whereas the Mediterranean countries managed with well under 2000 HDD.

Although the HDD concept is able to explain much of the difference, it is still not reflecting reality in total. The other factor coming into play here is the economic performance of each country expressed in GDP per head. Here, too, we see a gap between the two blocs. In order to visualise differences we take the average of both, the GDP and the energy consumption per capita, and scrutinize the deviations of both of the blocs from the mean value. The result is given in Fig. 2.

Fig. 2 Deviation of GDP and energy consumption per head from average in %. Data from 2009.

Fig. 2 gives us an indication that the energy intensity (which is pegged to the GDP) is closely linked to the consumption per capita, thus reflecting the economic performance of a country and its inhabitants. Those countries with a higher GDP per head tend to have also a higher primary energy consumption per inhabitant than the countries with a below average GDP per capita.

Although the term “energy per capita” has some intrinsic limitations, it represents nevertheless a sensible quantity if we are to understand consumption patterns and their causes. It is particularly sensitive to take into account factors like the degree of economic development and the temperature zone of a given country. Otherwise our conclusions might be distorted, especially when comparing countries with different economic background and/or geographic distribution. It goes without saying that Canada will consume more energy per inhabitant than, say, Portugal, simply because of its relative positioning on the globe. However, geography does not account for everything. We have to make allowances for differences in industrial and economic power as well. And again Canada, having a considerably higher GDP per head, is better off  than Portugal. Putting everything together will allow us to draw the right conclusions from the rough picture the concept of “energy per capita” provides us with.