Abstract
The rainfall‐runoff relation was expressed by the convolution integral. The kernel function was evaluated by the Fourier and Laplace gamma transforms and by the direct method. Three analytical examples (known kernels) were analyzed and used to compare the effectiveness of these methods. The Fourier transform method was used for field data. The results indicated that for a third of the storms oscillatory kernels were obtained. Oscillations were not necessarily due to nonlinearities but could arise from random noise in the data. Low‐pass digital filtering of input (excess rainfall) and output (direct runoff) eliminated the kernel oscillations in most cases. The cutoff frequency was approximately the sampling frequency. Accurate output reproduction was obtained by convolution of the original kernel, the smoothed kernel, or the kernel resulting from the filtered data.
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