FLOOD06680

• County: Statewide
• Basin: Statewide
• Title: Flood Damage in the United States, 1926-2000
• Date: 6/1/2000
• Prepared By: NOAA
• Floodplain - Doc Type: Flood Documentation Report

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Figures 5-1 (a,b) show scatterplots of (a) the IDE vs. actual costs and (b) the PDA vs.
actual costs. Logarithmic scales are used on the axes to highlight proportional differences
between estimates and actual costs. The solid diagonal line represents perfect agreement. Data
points outside of the two dashed lines are cases in which the estimate differs from the actual
costs by more than a factor of two. Clearly the IDE is less accurate than the PDA: the points are
much more scattered. (Correlations between the logs of estimates and actual costs are r = 0.46
for the IDE and 0.88 for the PDA.)

Since the Initial Damage Estimates are based on rather superficial damage descriptions, it
is not surprising that large errors are the norm: Over half of the IDEs (18 out of 33) are off by at
least a factor of two, and 13 of them ate off by more than a factor of four. As a percentage of
the actual costs, the IDE errors can be enormous, ranging from a 99.5% underestimate in Santa
Barbara County to a 2170% overestimate in Tehama County. The Preliminary Damage
Assessments are somewhat better, yet over one-third (15 out of 42) are off by at least a factor of
two and 3 of them are off by more than a factor of four. The PDA errors range from a 77%
underestimate in Humboldt County to a 393% overestimate in Yolo County.

The population of some California counties exceeds that of many small states. So
estimation errors in the larger counties are indicative of the error levels to be expected in many
states. For example, Los Angeles County, with a 1990 population of 8.9 million, is larger than
42 of the states. Table 5-1 shows that, in this disaster, the IDE underestimated actual costs by
82%.

To check for systematic bias in these early damage estimates, we used a statistical paired-
comparison test. A systematic tendency to underestimate might be expected if some types of
damage cannot be observed without careful inspection. On the other hand, we wondered if there
might be a tendency for local officials to overestimate damage in order to increase the chance of
being considered for federal aid. The IDE and PDA estimates were compared with actual costs,
as follows:

Let ei = estimated damage, ai = actual cost. We wish to test the null hypothesis that the
geometric mean of e;/ai = 1. This is equivalent to the hypothesis that mean[log(ei) -Iog(ai)] = o.
We tested the hypothesis twice, first letting ei represent the IDE values in Table 5-1 (N = 33),
then letting ei represent the PDA values (N = 42). A t-test is appropriate, even in these small
samples, because the sample values log(ei) -Iog(ai) are approximately normally distributed. For
the IDE, t = -1.27, and for the PDA, t = -1.10, neither of which is statistically significant at a
95% confidence level. Though there may be a tendency to underestimate the amount of damage,
the bias is not statistically significant.

In summary, this example indicates that positive and negative estimation errors tend to
average out when estimates are highly aggregated in a large flood event (over $300 million
damage in 1998 dollars, in this case). The initial rough estimates (IDE) tended to underestimate
actual damage and the more careful PDA estimates were reasonably accurate. It shows,
however, that in smaller flood events ($30 million damage or less in 1998 dollars), which
involve substantially less aggregation, the errors can be extremely large. Half of the PDA
estimates

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