Anti-persistence in levels of Lake Naivasha: Assessing effect of human intervention through time-series analysis

Lake Naivasha in Kenya is an important natural fresh water reserve, supporting surrounding wildlife as well as agriculture and industry. Uncontrolled use of the lake water for the past few decades is causing concern for environmentalists. In the present paper, fluctuations in the lake level for the last half century are analysed using standard tools for time-series analysis. The intervals 1951-1980 (period I) and 1981-2000 (period II) are treated separately, to look for any difference in their statistical patterns. From period II onwards, increased human consumption is believed to affect the level significantly. We analyse the data using three different approaches: (i) rescaled range analysis (R/S), (ii) roughness scaling analysis and (iii) a Lomb periodogram. R/S analysis shows no difference between the behavior in periods I and II, but the other methods reveal different fluctuation patterns for the two periods. The water level shows stronger fluctuations in period I compared to II. R/S analysis, however, shows an interesting anti-persistence with a Hurst exponent 0.44, which is not usually observed in natural time series.