River Quality Modeling: Frequency Domain Approach

Complete and equally spaced river quality variables specific conductance (SPC, $\mu S{\mathrm{cm}}^{-1}$), total dissolved solids (TDS, $\mathrm{mg}{L}^{-1}$), and the logarithm of the daily discharge mean (DDM, $m^3{s}^{-1}$) are used in frequency domain modeling. Significant autocorrelation values at lags 1 and 12 indicate that the observations are not random and have a yearly periodicity. Cross‐correlations also indicate the yearly periodicity as well as a negative relationship between TDS and DDM, and SPC and TDS. The cross‐correlation is positive between SPC and TDS. The spectral and cross‐spectral analyses show a significant periodicity at a frequency of ${\nu }_k=0.078$ cycles per month, or a period of one year. Because these variables are linearly correlated, an impulse response function can be used to determine the lagging, leading, and/or immediate response of the input(s) on the output. It is found that the best predictor of SPC is DDM. The small contribution from TDS is ignored. Significant coherence and F statistic at a frequency of 0.093 confirms the strong linear relationship between these two variables.