Spatial Data - MATLAB Recipes for Earth Sciences - page 269

points are ot en beyond the range of the measured z -values.
plot(XI,ZI,'k'), hold on
plot(data(:,1),data(:,3),'o')
text(data(:,1)+1,data(:,3),labels)
title('Biharmonic Spline Interpolation'), hold off
h is can sometimes be appropriate and does not smooth the data in the
way that bilinear gridding does. However, introducing very close control
points with dif erent z -values can cause serious artifacts. As an example we
introduce one reference point with a z -value of +5 close to a reference point
with a negative z -value of around -26.
data(79,:) = [450 105 5];
labels = num2str(data(:,3),2);
ZI = griddata(data(:,1),data(:,2),data(:,3),XI,YI,'v4');
v = -40 : 10 : 20;
contourf(XI,YI,ZI,v), colorbar, hold on
plot(data(:,1),data(:,2),'ko')
text(data(:,1)+1,data(:,2),labels), hold off
h e extreme gradient at the location (450,105) results in a paired low and
high (Fig. 7.8). In such cases, it is recommended that one of the two control
points be deleted and the z -value of the remaining control point be replaced
by the arithmetic mean of both z -values.
Extrapolation beyond the area supported by control points is a common
feature of spline interpolation (see also Section 5.5). Extreme local trends
combined with large areas with no data ot en result in unrealistic estimates.
To illustrate these edge ef ects we eliminate all control points in the upper-
let corner.
[i,j] = find(data(:,1)<435 & data(:,2)>105);
data(i,:) = [];
labels = num2str(data(:,3),2);
plot(data(:,1),data(:,2),'ko'), hold on
text(data(:,1)+1,data(:,2),labels), hold off
We again use the biharmonic spline interpolation technique.
[XI,YI] = meshgrid(420:0.25:470,70:0.25:120);
ZI = griddata(data(:,1),data(:,2),data(:,3),XI,YI,'v4');
v = -40 : 10 : 40;
contourf(XI,YI,ZI,v)
caxis([-40 40])
colorbar
hold on