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Joint Multifractal Analysis of Crop Yield and Terrain Slope

Dep. of Nat. Resources and Environ. Sci., Univ. of Illinois, 1102 S. Goodwin Ave., Urbana, IL 61801-4798 USA

View larger version (51K): [in a new window]   Fig. 1 Locations of the elevation measurements taken with a SOKKIA SET 5 total station (SOKKIA, Overland Park, KS) and the elevation map used for deriving the terrain slope. The elevation map was obtained by inverse-distance weighting of the measured data with power of 2 and the no. of the closest neighbors equal to 6. The map cell size is equal to 8 m

View larger version (53K): [in a new window]   Fig. 2 Scatter plots of the three simulated data sets with correlation coef. between the two variables equal to (a) 0.91, (b) 0.00, and (c) -0.12. Joint multifractal spectra for the two variables and single multifractal spectra for the second variable at the lowest and highest q values of the first variable demonstrate the effect of data correlation on the shape of the joint and single multifractal spectra

View larger version (34K): [in a new window]   Fig. 3 (a) Multifractal spectrum, (b) joint multifractal spectrum, and yield multifractal spectra at (c) low and (d) high slope values for the 1994 corn yield. The notations yield and slope correspond to 1(q1, q2) and 2(q1, q2) defined by Eq. [17] and [18], respectively. Intersections of the horizontal and vertical lines mark the points with the max. f(1, 2) values [f(1, 2) = 2] that are reached at q1 = q2 = 0

View larger version (34K): [in a new window]   Fig. 4 (a) Multifractal spectrum, (b) joint multifractal spectrum, and yield multifractal spectra at (c) low and (d) high slope values for the 1995 corn yield. The notations yield and slope correspond to 1(q1, q2) and 2(q1, q2) defined by Eq. [17] and [18], respectively. Intersections of the horizontal and vertical lines mark the points with max. f(1, 2) values [f(1, 2) = 2] that are reached at q1 = q2 = 0

View larger version (34K): [in a new window]   Fig. 5 (a) Multifractal spectrum, (b) joint multifractal spectrum, and yield multifractal spectra at (c) low and (d) high slope values for the 1996 corn yield. The notations yield and slope correspond to 1(q1, q2) and 2(q1, q2) defined by Eq. [17] and [18], respectively. Intersections of the horizontal and vertical lines mark the points with max. f(1, 2) values [f(1, 2) = 2] that are reached at q1 = q2 = 0

View larger version (34K): [in a new window]   Fig. 6 (a) Multifractal spectrum, (b) joint multifractal spectrum, and yield multifractal spectra at (c) low and (d) high slope values for the 1997 corn yield. The notations yield and slope correspond to 1(q1, q2) and 2(q1, q2) defined by Eq. [17] and [18], respectively. Intersections of the horizontal and vertical lines mark the points with max. f(1, 2) values [f(1, 2) = 2] that are reached at q1 = q2 = 0

View larger version (35K): [in a new window]   Fig. 7 (a) Multifractal spectrum, (b) joint multifractal spectrum, and yield multifractal spectra at (c) low and (d) high slope values for the 1998 corn yield. The notations yield and slope correspond to 1(q1, q2) and 2(q1, q2) defined by Eq. [17] and [18], respectively. Intersections of the horizontal and vertical lines mark the points with max. f(1, 2) values [f(1, 2) = 2] that are reached at q1 = q2 = 0

View larger version (50K): [in a new window]   Fig. 8 Monthly precipitation data for Mar. through Sept. 1994–1998 and the historical avg. from 1961–1990 for the studied field