APPENDIX D: SOURCES OF UNCERTAINTY AND ERROR ANALYSIS
Sources of uncertainty in the Landsat estimate
If it is assumed that all scenes have this same er-
of surface area and storage capacity are explained
ror, then each capacity increment also has the
below.
same percentage error, because it is the product of
surface area and depth (unaffected by this error);
the total capacity, because it is the sum of the in-
Mudflats (#1)
The Landsat scenes classified using TM Bands
crements, again has the same percentage error.
4 and 5, as described in the Water Classification
If it is assumed that the ground control points
section, had three classes: water, shoreline, and
(GCPs) used in rectifying the data are in error by
land. The concern here is the shoreline class. One
one pixel, it translates into a plus or minus 0.35%
would expect the shoreline class to be composed
uncertainty in pixel area and thereby a (worst
of just edge pixels, which include part water and
case) plus or minus 0.35% uncertainty in capacity.
part land, and thus trace a one-pixel-wide rim
If it is assumed that the uncertainty in the DLG
encircling the reservoir. This does happen in
data is the same as that for the 1:100,000-scale pa-
many parts of the reservoir, but there are parts,
per maps from which they are derived, as listed
especially at the upper end of the reservoir, where
in the National Map Accuracy Standards (USGS
the shoreline class is extensive (for instance, p. 24,
1998b), then 90% of well-defined points on the
the classification of the 27 June 1993 scene). The
map should be within one-fiftieth of an inch of
hypothesis is that these extensive shoreline areas
their true position at the scale of the map (50.8 m
are mud flats or very shallow water. It is not clear
on the ground). If it is assumed that the map
whether these areas should be counted as water
points used for GCPs in rectifying the model map
or land. To estimate the effect of this uncertainty
to the DLG data are off (either too far out or too
on the storage capacity estimate, these extensive
far in) by this amount, the pixel area uncertainty,
areas were isolated, and the water surface area
and thereby the worst case capacity uncertainty,
was recomputed twice: once including them as
translates to 0.62%. The uncertainty due to digiti-
100% water, and again excluding them entirely
zation, 0.003 in. (7.62 m on the ground), was not
from the surface area estimate. As can be seen in
considered.
Table 13, the "mudflats" uncertainty is the largest
Because the DLG uncertainty was the bigger, it
one, affecting the capacity estimate by +40,000 or
was used in estimating the effect on storage ca-
30,000 acre-ft at spillway elevation.
pacity. At spillway elevation, this worst case un-
certainty is plus or minus about 15,000 acre-ft.
Rectification (#2)
The 1993 surface area acreage values, and
Wind setup (#3)
hence the storage capacity values, are dependent
In the above estimates, it was assumed that
on the Landsat pixels being a known size, which
there was no wind setup and the water surface of
is determined by the accuracy of the rectification
the reservoir was level, and that the elevation
procedure. This is dependent on how well each
readings taken at the dam hold for the whole
image is warped to match the model image (7
reservoir. It is known that wind can affect this; if
March 1993), how well the model image is
there is a west wind, for instance, then the
warped to match the 1:100,000 scale DLG data,
elevation of the water surface at the east end of
and the uncertainty in the 1:100,000-scale DLG
the reservoir will be higher than that at the west
data.
end, making a tilted rather than level water
A given percent error in the pixel size for a
surface. The surface area for this tilted surface is
Landsat scene translates into the same percentage
assumed to be halfway between the area of level
error in the capacity estimate. The water surface
surface for the lower elevation and that for the
area estimate has the same percent error, because
higher elevation.
the surface area is just the sum of the pixel areas.
45
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