Cross-spectral analysis of rainfall and runoff for Raritan and Mullica river basins in New Jersey

Cross-correlation and cross-spectral analysis were employed in the analysis of rainfall and runoff in two river basins: the Raritan and Mullica River basins in New Jersey. Cross-covariance and coherence were studied in the correlograms for the following correlation cases: (a) rainfall-runoff for each one basin separately; (b) rainfall-rainfall analysis for two main meteorological stations in each one of the basins; (c) runoff-runoff for two main gaging stations in each one of the basins. From the estimates of the coherence at various frequencies the cross-spectral analysis shows a highly nonlinear relationship between rainfall and runoff in Raritan and Mullica River basins. A poor coherence observed at the annual cycles for each basin makes it difficult to predict the annual oscillations of runoff from those of rain-fall by a linear regression model. The high coherence between rainfall (or runoff) at the first station and rainfall (or runoff) at the second station within the same basin at almost all frequencies establishes an accurate prediction on a linear basis.