Calculating temperature dependence over long time periods: derivation of methods

Rates of ecological processes are usually influenced by temperature. For simplicity and efficiency of ecosystem models it is often necessary to summarize information about temperature dependence from short, e.g., hourly, time intervals over longer, e.g. monthly, time periods, i.e. to calculate long term expected values of dependence functions. This aim can seldom be achieved by applying the temperature function to the mean temperature, because temperature dependencies are in many cases nonlinear. Therefore, we derived seven new, general methods for a temporal aggregation of temperature dependence. The methods determine the expected value interpreting either hourly temperature, daily temperature mean, or daily temperature mean and amplitude as random variables. The dependence function is approximated by a piecewise linear function. Some methods use a triangle as approximation for the daily temperature course, some a parabola as approximation for the density function of the normal distribution. The resulting methods cover a range of temperature data resolutions: monthly mean and standard deviation of hourly temperatures; daily temperature extrema; daily temperature means; and amplitudes, or daily temperature means alone. The methods can be applied to all types of dependence functions, in particular to nonlinear ones.