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Scale-Dependent Relationship between Wheat Yield and Topographic Indices

A Wavelet Approach

Dep. of Soil Science, Univ. of Saskatchewan, Saskatoon, Canada, S7N 5A8

View larger version (30K): [in a new window]   Fig. 1. The Harr wavelet and the Mexican hat wavelets for different scales and translation. (a) The Harr wavelet for scale = 1 (solid line) and 0.5 (dashed line); (b) the Mexican hat wavelets for scale = 1 (solid line) and 0.5 (dashed line); (c) the Harr wavelets for location = 0 (solid line) and 2 (dashed line); and (d) the Mexican hat wavelets for location = 0 (solid line) and 4 (dashed line).

View larger version (31K): [in a new window]   Fig. 2. Measured elevation, curvature, upslope length, the wetness index of Beven and Kirkby (1979), and grain yield as a function of distance along the transect.

View larger version (58K): [in a new window]   Fig. 3. Local (a) wavelet spectrum and (b) global wavelet power spectrum of grain yield. Gray scale is expressed as the natural logarithm of the local wavelet spectrum. The dashed line in (b) is the power spectra of a red noise at a confidence level of 99%.

View larger version (54K): [in a new window]   Fig. 4. Local (a) wavelet spectrum and (b) global wavelet power spectrum of upslope length. Gray scale is expressed as the natural logarithm of the local wavelet spectrum. The dashed line in (b) is the power spectra of a red noise at a confidence level of 99%.

View larger version (60K): [in a new window]   Fig. 5. Local (a) wavelet spectrum and (b) global wavelet power spectrum of the wetness index of Beven and Kirkby (1979). Gray scale is expressed as the natural logarithm of the local wavelet spectrum. The dashed line in (b) is the power spectra of a red noise at a confidence level of 99%.

View larger version (56K): [in a new window]   Fig. 6. Local (a) wavelet cross-spectrum and (b) global wavelet cross-spectrum of grain yield and upslope length. Gray scale is expressed as the natural logarithm of the local wavelet spectrum. The dashed line in (b) is the power spectra of a red noise at a confidence level of 99%.

View larger version (59K): [in a new window]   Fig. 7. Local (a) wavelet cross-spectrum and (b) global wavelet cross-spectrum of grain yield and the wetness index of Beven and Kirkby (1979). Gray scale is expressed as the natural logarithm of the local wavelet spectrum. The dashed line in (b) is the power spectra of a red noise at a confidence level of 99%.