Feature

The 100-Year Drought?

Statistics suggest that a 1-in-100 year drought may be more common than we think.

By Earl Bardsley

Electricorp has blamed the hydro-storage problems on the occurrence of a 100-year drought, a 1-in-100 year event. Given this dominant contribution by nature,  the question arises as to the chance of a repeat occurrence in the future. Related to this is the issue of whether the low hydro inflows really do represent a 100-year event.

The basic statistical model is very simple, involving just the toss of a weighted coin for each year. The probability of "no 100-year drought" is 0.99, and the probability of a "100-year drought" is 0.01. Statistics shows that this gives a probability of about 1 in 20 that a drought of similar magnitude will occur within the next 5 years. This is a rather high risk, given the potential for economic disruption.

The reason for this high risk lies in the time intervals which separate 100-year events. Despite the fact that the average time, or return period, between the events is 100 years, the coin shows that it would not be unusual to have 100-year events separated by just 5 years. Nor would it be unusual to have consecutive 100-year events separated by as much as 300 years.

The diagram below shows a typical pattern of frequency of N-year events along a time line. Fifty-year events within 50-year periods have the same pattern and frequency as 100-year events within 100-year periods.

A similar mix of small and large between-event intervals in typical data records illustrates the problem of assigning a return period to the 1992 drought: the large time intervals ensure that there will be very few such events recorded in the past, but the return period must be estimated from this data record.

Such sparseness of data is a statistical disaster in terms of accuracy of estimating return periods. The question arises as to how to interpret a long period of record (such as from the start of the recorded data to 1992) which shows no events of the 1992 magnitude.

Does this represent a "typical" between-event interval of about the same size as the return period, or were we just lucky enough to have spent our lives in one of those between-event intervals very much larger than the true return period? If the latter, the risk of a near-future repeat of this year's event might be considerably more than the 1 in 20 chance given earlier.

A few numbers serve to illustrate the uncertainty of estimating drought return periods. If just one "event" (a severe drought) is recorded somewhere within the past N years, then a 95% confidence lower bound on the return period of that event is given by 0.21N. That is, there is still a 5% chance that the true return period might be less than 0.21N. Thus, even if only a single "event" is recorded over the last 100 years, it is not beyond the realms of possibility for the true return period to be as short as 21 years. A return period of this length gives about a 1 in 5 chance of the event happening again in the next 5 years.

The 0.21N expression is conservative, so things may not be quite as bad. However, the important message is that there is considerable uncertainty about the drought's return period. Its true return period could be just about anything. And there would still be a fair degree of risk and uncertainty even if we could be sure that the return period of the drought was exactly 100 years.

Finally, it is open to question whether the constant-coin model should be applied to droughts at all. For example, England is currently experiencing a most un-coinlike third successive year of drought. Unlike floods, individual droughts represent at least a temporary shift in local climatic factors, giving rise to the possibility that the climatic coin might be changing itself in favour of low hydro storages. The introduction of a more risky hydro operating policy by Electricorp would have the same effect.

With uncertainties compounding uncertainties, it would probably be wise to run the hydro system in a conservative fashion over the next few years -- even if this means higher power prices -- and seek alternative modes for both electricity generation and hydro storage.

Dr Earl Bardsley is senior lecturer in hydrology at Waikato University.