Why it's wrong to try relating cumulative consumption to cumulative degree days

You sometimes see words to this effect in an energy consultant's survey report:
"... Cumulative gas consumption is plotted against cumulative degree days in figure xx. This diagram exhibits various changes in gradient which could not be explained."
Here's the explanation.

In the ideal case a perfectly-behaved heating system would consume energy E in relation to degree days D according to a straight-line relationship:

E = k0 + k1.D

Where k0 is the fixed monthly consumption and k1 is the consumption per degree day. At the end of the nth month the cumulative degree days will be Dn and the cumulative consumption, En, will be given by

En = n.k0 + k1.Dn

The consultant is interested in the ratio En/Dn, which he thinks should remain constant. But:

En/Dn = (n.k0 + k1.Dn)/Dn

which can be rearranged as

En/Dn = k0 ( n/Dn ) + k1

The right-hand side of this equation is constant only if k0 is zero (a building with no fixed component of demand) or if n/Dn is constant, which it never is, because a different number of degree days are added to Dn each time n increases by 1. In winter, when values of D are high, the term n/Dn falls; in summer, when values of D are low, it goes back up.

To be sure, the seasonal variation becomes relatively insignificant as n and Dn tend towards infinity, but that isn't quite the point. If even an 'ideal' heating system is guaranteed to exhibit variation of slope, the method of cumulative consumption versus cumulative degree days is a waste of time. There is, however, a method which works.

A better idea

Degree Days Direct opening page