Effects of systematic measurement errors on detection of climate change

Global warming is expected to increase approximately exponentially over a period of decades. The observational systems, for example satellite instruments, typically must be replaced periodically. These instruments each have offset errors which change from one instrument to the next. This paper examines the effect of these offset errors on the detectibility of climate change. Year-to-year variations of temperature (or other observed parameter) are included. Random measurement errors are indistinguishable from interannual variations and thus simply increase the effective variability of the interannual variations of the temperature. Also, the effects of cyclical variations of multi-year periods are studied. A two-fold approach is used, whereby the process is simulated and also is treated by analysis.

A temperature change a at the beginning of the measurement period, the exponential rate of increase b and a year-to-year variability of temperature are assumed and the detectibility of the change is computed as time passes and the change increases. Because the change is exponential with time, a and b must be computed as solutions of non-linear equations. The non-linearity of the relations causes a bias in the least-squares estimate of a and b. This bias is a function of a, b and the year-to-year variations. A cyclical climate variation with a period the order of the observation period can mask or exaggerate the climate change, depending on the phase of the cycle over the observation period, though a short term cycle has little influence on the detection of climate change.