Long-term Change and Variability of Warmth Index and Coldness Index

Abstract

Time series of two kinds of climatic indices, the warmth index (WI) and the coldness index (CI), which were proposed to correlate the geographical distribution of plants with thermal resources, were analyzed mainly statistically in order to make clear the long-term change and the variability of climatic resources for natural vegetation. Meteorological data of about 230 stations including around 80 stations in Japan were used in calculations. The results obtained can be summarized as follows.
1. The warmth index representing the total amount of heat available for the growth of plants showed a clear systematic fluctuation during the past 80 years, although there is some difference in the amplitude and the phase among stations. At almost all stations in Japan, the increase of WI values was observed between 1950's and 1960's. Since then it seems to be continuously decreasing to date. The fluctuation of CI was found to be nearly inverse to that of WI in the phase, indicating that there is a negative correlation between |CI| and WI values. Fig. 3 illustrates an influence of the urbanization on the climatic conditions in large cities such as Tokyo, Osaka and Fukuoka. The values of WI at Tokyo with a population of about 9 million and an energy consumption density of 420×10⁹ kcal/km² increased by a rate of 2.7°Cmonth/10 year during the period from 1900 to 1975. The value of CI decreased inversely by a rate of 0.05°Cmonth/10 year during this period. Although similar changes of WI and CI were also observed at Osaka and Fukuoka, the rates of change of WI and CI values were about two-thirds of that at Tokyo.
2. The latitudinal average of WI near the equator was retained at the level of around 240°C month. Poleward of the latitude 25°N it showed a drastic decrease with latitude and became zero at about 70°N. The latitudinal distribution of WI shown in Fig. 4 agreed well with that of the sum of effective temperature (Uchijima, 1976a). On the other hand, the value of |CI| was zero in latitudinal bands lower than 25°N and increased rapidly poleward of this latitude. The latitudinal distributions of both indices were well approximated by Eq. (3).
3. The frequency distribution curves of WI and CI varied appreciably with the place. The standard deviations characterizing the frequency distribution curves of WI and CI increased proportionally with the square root of the mean value of those quantities, as indicated in Fig. 6. The dependence of standard deviation and coefficient of variance on the mean value was found to be in good agreement with the relationships derived from the gamma distribution function (Eq. 6). The scale and shape parameters obtained for the distribution function of CI varied also clearly with the mean value (see Fig. 7). This result indicates that the gamma distribution function is applicable to analyzing the chance occurrence of WI and CI for vegetation growth.
4. The correlogram and the power spectrum of the fluctuations of WI and CI were calculated by the conventional method. As shown in Fig. 8, the correlogram for the time fluctuations of 10 yearly running means of both the indices has a relatively long tail compared with those of the original fluctuations. The correlogram of the fluctuations of 10 yearly running means of CI at Okayama, Kochi, Miyazaki and Kagoshima showed a wavy tail with a clear peak in the lag-time of 20 to 30 years. Such a wavy variation of the correlogram was not obtained for Hokkaido district.
The power spectrum of the original fluctuations of both indices was mainly in the frequency range from 0.1 to 0.5 cycles/year at almost all stations except Hamamatsu where there was a clear peak in the frequency band between 0.04 and 0.07cycles/year.