FLOOD03186

• County: Statewide
• Community: All
• Stream Name: All
• Basin: Statewide
• Title: Benefit-Cost Analysis of Hazard Mitigation Projects
• Date: 1/1/1996
• Prepared For: FEMA
• Prepared By: FEMA
• Floodplain - Doc Type: Educational/Technical/Reference Information

VERSION 1.0 1/12/95

B-C PROGRAM: Flood Hazard Risk

Flood Elevation
vs. Flood Depth

Review of
Scientific
Notation

This analysis gives the Annual Exceedance Probability for all floods,
in one-foot increments of depth. From the Annual Exceedance
Probabilities, calculated as described above, the Expected Annual
Number of Floods in a given one-foot increment are calculated from
the difference in exceedance probabilities of two flood depths. For
example, the expected annual number for a 2-foot flood (i.e., all floods
between 1.5 and 2.5 feet) at a given site (with a given Zero Flood
Depth Elevation) is calculated as the exceedance probability for a 1.5-
foot flood minus the exceedance probability for a 2.5-foot flood.

For a given flood (e.g., a 100-yearflood), the elevation of the flood
water surface varies with location along the stream as shown by the
Flood Profile (see pages 7-2 to 7-4). Furthermore, at a given location
along the stream the flood depth corresponding to a 1 OO-year flood
varies depending on the Zero Fiood Depth Elevation of the building
under evaluation. In the Benefit-Cost Program, the Expected Annual
Number of Fioods are shown for each flood depth from -2 to 18 feet
for the building under evaluation. For a different building with a
different Zero Flood Depth Elevation, the Expected Annual Number
of Floods for each flood depth will be different. Thus, for example, the
depth of a 1 OO-year flood will differ for buildings at different Zero Flood
Depth Elevations.

The annual probabilities of floods are expressed in scientific notation
because the probabilities may vary from nearly 1 to much less than 1 in
a million (0.000001). Scientific notation is a widely-used convenient
method of expressing numbers which vary over a very wide range.

In scientific notation, as in the Calculated Annual Probability of
Floods table, numbers are expressed in two parts: a prefix and a
power of 10. For example, 6E+02, where 6 is the prefix and +02 is the
power of 10, means 6 times 102, or 6 times 100, or 600.

Another way of thinking about scientific notation is that the power of 10
part of the number tells which direction and how much to move the
decimal place. Thus, 6E+02 is 6 with the decimal placed moved to
places to the positive (right) direction or 600. Thus, 6E+03 is 6000.
Scientific notation with negative powers of ten means to move the
decimal place to the negative (left) direction. Thus, 6E-02 is 0.06; 6E-
03 is 0.006 and so on. E+OO, means don't move the decimal place.
Thus, 6E+00 is simply 6.

Scientific notation may seem cumbersome with routine numbers, but it
is very convenient when numbers are very large or very small or to
compare the relative sizes of very large or small numbers. Thus, 6E-
11 is a more convenient way of expressing 0.00000000006.

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