Apply a hydrological model to estimate local temperature trends

Abstract

Continuous times series {f(x)} such as a depth of water is written f(x) = T(x)+P(x)+S(x)+C(x) in hydrological science where T(x),P(x),S(x) and C(x) are called the trend, periodic, stochastic and catastrophic components respectively. We simplify this model and apply it to the local temperature data such as given E. Halley (1693), the UK (1853-2010), Germany (1880-2010), Japan (1876-2010). We also apply the model to CO2 data. The model coefficients are evaluated by a symbolic computation by using a standard personal computer. The accuracy of obtained nonlinear curve is evaluated by the arithmetic mean of relative errors between the data and estimations. E. Halley estimated the temperature of Gresham College from 11/1692 to 11/1693. The simplified model shows that the temperature at the time rather cold compared with the recent of London. The UK and Germany data sets show that the maximum and minimum temperatures increased slowly from the 1890s to 1940s, increased rapidly from the 1940s to 1980s and have been decreasing since the 1980s with the exception of a few local stations. The trend of Japan is similar to these results.