Evidently, if the percentage reduction is small, the trend surface 
is weak; indeed, if the deviations are truly random components in such 
instances, the question could be raised whether there is in fact any trend 
present at all. We shall see that this latter assumption is not correct 
in the Rudee Inlet study. Computer programs for more formal analysis of 
fitted surfaces, including setting confidence intervals around them 
(Krumbein, 1963), became available while this final draft was written, 
and reliance here is placed upon substantive evaluation of the trend maps 
computed in this study. 
ANALYSIS OF MEAN PARTICLE SIZE DATA 
Figure 8 shows the pattern of mean particle size observed in the 
study area. "Observed maps" show the contour pattern of the original "raw 
data," and in many instances these maps are very informative, especially 
when the contours show relatively strong patterns. When the pattern is 
weak, or complicated by numerous irregularities in the contour lines, sub- 
stantive evaluation is more difficult, and there may be some doubt whether 
a definite trend is present. 
iad 
In the present map we notice a "ridge" of relatively large values 
that coincides with the zone of outflowing current shown on Figure 3. At 
a point just seaward of the breaker line (dotted) is a pronounced hump of 
high values. The linear trend surface fitted to these data is shown on 
Figure 9. The linear surface dips to the northeast at 0.02 mm. per 87 
feet (26 m.), indicating a decrease in mean size in the direction of 
current flow. This reflects the negative current velocity gradient from 
Rudee Inlet seaward, because of the known variation (cf. Bruun and Lackey, 
1962) in the diameter of sediment particles with the critical tractive 
force, which is in turn velocity dependent. The linear surface for mean 
size is in fact quite weak, inasmuch as only 11.3 percent of the total sum 
of squares can be attributed to it. 
Figure 10 shows the deviations from the linear mean size surface. 
These deviations show a pattern trending roughly parallel to outflow from 
the inlet, and an area of high values similar to the one noted on the 
observed map. This suggests the presence of trend components higher than 
linear in the deviations. Hence, it was deemed worth while to examine the 
quadratic surface. 
The quadratic surface for mean grain size is shown in Figure 11. The 
contours parallel to the shore are to be ignored for the moment; the 
quadratic surface itself is a simple ellipsoid with maximum values near 
the inlet mouth, and a systematic decrease in mean grain size symmetri- 
cally away from the higher portion. The quadratic surface accounts for 
47.7 percent of the total sum of squares; and because the linear surface 
accounted for only 11.3 percent, the contribution of the “pure quadratic" 
is 36.4 percent. The deviations on the quadratic surface are shown in 
