Using Wavelet to Analyze Periodicities in Hydrologic Variables

The trend and shift in the seasonal temperature, precipitation and streamflow time series across the Midwest have been analyzed, for the period 1960-2013, using the statistical analyses (Mann-Kendall test with and without considering short term persistence (MK2 and MK1, respectively) and Pettitt test). The paper also utilizes a relatively new approach, wavelet analysis, for testing the existence of trend and shift in the time series. The method has the ability to decompose a time series in to lower (trend) and higher frequency components (noise). Discrete wavelet transform (DWT) has been employed in the present study with an aim to find which periodicities are mainly responsible for trend in the original data. The combination of MK1, MK2, and DWT along with Pettitt test hasn't been extensively used up to this time, especially in detecting trend and shift in the Midwest. The analysis of climate division temperature and precipitation data and USGS naturalized streamflow data revealed the presence of periodicity in the time series data. All the incorporated time series data were seasonal to analyze the trends and shifts for four seasons-winter, spring, summer and fall independently. D3 component of DWT were observed to be influential in detecting real trend in temperature, precipitation and streamflow data, however unlike temperature, precipitation and streamflow showed decreasing trend as well. Shift was relatively observed more than trend in the region with dominance of D3 component in the data. The result indicate the significant warming trend which agrees with the "increasing temperature" observations in the past two decades, however a clear explanation for precipitation and streamflow is not obvious.