Methodology - Response of Flood Events to Land Use and Climate Change - page 54

Table 3.1 Different interpolation characteristics (Modified information based on [ 1 , 14 , 19 , 20 ,

78 , 139 ]
Method Speed Comments

Spline Fast Available in ArcGIS; estimates values using a

mathematical function that minimizes overall
surface curvature.

IDW Fast Available in ArcGIS; tends to generate bull's eye

patterns; simple and effective with dense data; no
extrapolation.

Topo to Raster Slow/Medium Available in ArcGIS; interpolates a hydrologically

''correct'' grid from a set of point, based on
procedures developed by Hutchinson [ 19 , 20 , 78 ].

Kriging Slow Available in ArcGIS; very flexible range of methods

based on modeling variogram; can provide
extrapolation and prediction error estimates; speed
not substantially affected by increasing the number
of data points.

Spline

The Spline method applies mathematical functions minimized on the overall
surface curvature to estimate the unknown values. The Spline results represent a
smooth surface passed exactly through the input points while minimizing the total
curvature of the surface [ 12 , 13 ; 14 ]. The algorithm used for the Spline method
applies the following equations:

Sx ; ðÞ¼ Tx ; ðÞþ X

N

k j R ð r j Þ ð 3 : 1 Þ

j ¼ 1

where:
j is 1, 2,…, N; N is the number of points; k j are coefficients found by the
solution of a system of linear equations; r j is the distance from the point (x, y)to
the jth point.
For the regularized option the formula is as follows:

Tx ; ðÞ¼ a i þ a i x þ a 3 y ð 3 : 2 Þ

where:
a i are coefficients found by the solution of a system of linear equations. And,