Article:
Lischke, H., T. J. Loeffler & A. Fischlin, 1997. Calculating temperature
dependence over long time periods: A comparison and study of methods.
Agricultural and Forest Meteorology,
86(3-4):169-181. doi: 10.1016/S0168-1923(97)00015-4
Abstract:
Nonlinear temperature dependence plays a major role in a large variety of ecological models. For the sake of simplicity and efficiency, the temperature dependence functions in many models are calculated for monthly or yearly time intervals, using temperature means or interpolations between means as input. As a consequence, information about the variability of the temperature input data is lost, which leads to a bias in the temperature dependence function and to errors in the model results. We tested the performance of a range of methods against this common approach for calculating temperature dependence on a larger time scale, i.e. for a temporal aggregation. The methods estimate the expected value of the dependence function in different ways, using the mean or standard deviation of temperature variables in different temporal resolutions as input. In our tests we used temperature dependence functions from four different ecological fields; hourly temperature data sets from various climatically differing sites were used as input. The precision of the tested methods increased with the resolution of the input data, although computing time increased. The mean errors ranged from less than 1% to about 8% for the aggregation to 1 month and from about 1% to over 30% for the aggregation to 10 years. The most precise and efficient method is the explicit calculation of the expected value for the dependence function, which is based on the mean and standard deviation of hourly temperatures. The least precise but most efficient method is the common application of the dependence function to mean values. The quality of these methods is mainly determined by the quality of the approximation of the temperature variability. Condensing highly resolved input data into means is only appropriate if either the dependence functions are linear in the observed temperature range, or low precision but very high computing efficiency is required. Given a certain requirement on precision or computing efficiency, we are now able to indicate for a number of input data resolutions the appropriate method to calculate temperature dependence over long time periods.