Precipitation
Objectives:
1) to understand how rainfall data is collected and how it is useful to the
hydrologist
2) to be able to determine the average rate of runoff flow for basins with either
uniform or non-uniform distribution of rain gages
Background:
Precipitation, in inches or millimeters of water, is measured either by non-recording or
recording precipitation gauges. Both types of gauges consist of a bucket or container with
vertical sides which is capable of collecting water. The depth of water accumulation is
dependent upon the cross-sectional area of the container and so different sizes of
containers placed at the same location would yield different water depths. To prevent this
discrepancy, most rain gages are made a standard size so that their readings can be easily
compared relative to the readings obtained by other rain gauges.
The standard non-recording rain gauge consists of a cylindrical bucket with a funnel and a
measuring tube in its interior. A standard size 8 inch funnel tapers down to an inner
cylindrical tube which has a cross-sectional area of 10% of the 8 inch opening. This
decrease in area allows for a more precise measurement of water depth, measurement to a
hundredth of an inch! The gauge can measure up to 2 inches of rainfall in the small
inner-diameter tube and anything in excess of 2 inches overflows into the outer 8 inch
cylinder and which can then be measured incrementally by emptying and refilling the
inner tube. Non-recording rain gauges are the most common type used because they
require less operation and maintenance and volunteer observers are commonly used to
read and relay their information to the appropriate agencies periodically. The
disadvantage to non-recording rain gauges is that they record only an accumulated rainfall
depth of the time between readings. It is, therefore, difficult to get an estimate of the
intensity of rainfall.
Recording rain gauges are used when it is necessary to know the various intensities
throughout a storm. A typical recording gauge is a weighing gauge. An 8 inch diameter
bucket sits on a scale and collects precipitation. As the precipitation increases in the
bucket, the weight increases. At given time intervals, a mechanical device drives a pen to
mark the inches of water collected, as calibrated by the weight of water in the bucket at
the time. Because of the mechanical nature of these gages, they are much more expensive
than the non-recording gauges, but they have the advantage of allowing the recording of
rainfall intensities.
The National Weather Service, part of National Oceanic and Atmospheric Administration
(NOAA), is the primary agency responsible for collecting rainfall data throughout the
United States. They maintain an extensive network of both recording and non-recording
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precipitation gauges measuring rainfall in all cities and most towns in the U.S. Official
weather observers or volunteers read and record the rainfall in non-recording gauges
while data is often sent by satellite from the automatic recorders.
Rainfall data, along with stream gaging (stage) data, help hydrologists and weather
forecasters monitor the progress of storms and provide a basis for determining
relationships between the amount, duration, and intensity of rainfall and the amount and
rate of runoff expected as a result. Hydrologists can theoretically predict floods using
expected rainfall data. By warning townspeople ahead of time of impending danger,
levees could be built or communities could be evacuated in time so that damage and loss
of life can be lessened.
3 Methods of Determining the Average Depth of Rainfall in a
Watershed
When estimating the average depth of rainfall over an entire watershed, it is important to
consider the number and spatial distribution of the rainfall data that you have available to
you. The more raingages in the watershed, the better the estimated rainfall depth.
However, if all the raingages are all located in just one corner of the watershed, and no
raingages are located in other large portions of the watershed, then simply taking a simple
arithmetic average is not going to accurately estimate the average rainfall over the
watershed area as a whole. This is because the large areas of the watershed that had no
raingages could have had significantly higher or lower rainfall than the area of known
rainfall depth, since some areas invariably receive heavy rainfall while others receive only
minor amounts, and still other areas may not get any. These variations could significantly
change the average depth over the entire watershed area if the depths of rainfall were
known in those ungaged areas.
Method One: Arithmetic Mean (Uniform distribution of raingages)
If raingages are uniformly distributed throughout the watershed, then a simple
arithmetic average can be taken and used as a fairly good estimate of the average depth
of rainfall over the area. For an arithmetic average, all values of rainfall depth collected
at each raingage are added together and divided by the number of raingages involved.
Method Two: Isohyetal Method (Non-uniform distribution of raingages)
If the raingages are non-uniformly distributed throughout the basin, then there are two
different methods that can be used to determine the average depth of rainfall. One
method, called the Isohyetal Method, involves rainfall contouring. In its simplest form,
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this method involves drawing isohyets, or lines of equal rainfall, on a map of the
watershed (similar to elevation contour lines on a topographic map). The contouring
method results in an isohyetal map, that differs with each storm. The hydrologist then
looks at the lines of equal rainfall for the given storm and takes into account the relative
areas bounded by each isohyet to come up with the average rainfall depth over the basin.
Procedure for Isohyetal Method:
1. Draw isohyets (lines of equal rainfall) on the map.
2. Fill out the data table. First, find the average precipitation between isohyets. This
will be the arithmetic average of the two isohyets. For example, between the 5 and 10
inch isohyets the average would be (5+10)/2 or 7.5 inches.
3. Find the area between the two isohyets by counting the number of boxes and use the
scale to determine the areas.
4. Multiply the area between isohyets by the average precipiation (average isohyet).
Sum these values.
5. Divide the above sum by the total area of the basin.
Average Rainfall Depth = sum of all the (avg isohyet x area between isohyets)
area of the entire watershed
Method Three: Theissen Method (Non-uniform distribution of raingages)
Another perhaps more common method of estimating the average depth of rainfall is the
Theissen Method. This method assigns, somewhat arbitrarily, distinct geographical
regions of the watershed to each of the raingages in it. No matter what the characteristics
of a given storm, the region belonging to a raingaging station is fixed for any storm in the
basin. This is a disadvantage of the method. The following is the procedure for
determining the average depth of precipitation using the Theissen Method.
Procedure for Theissen Method:
1. Use pencil and draw light, straight, dashed lines connecting each point to each next
point for the points that are closest to the watershed boundary. You will form a closed
polygon shape.
2. Lightly draw dashed straight lines from each of the points on your polygon to any
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points inside the polygon that are nearest to each outside point. You will be making a
series of triangles. Also draw dashed straight lines from point to point for points
entirely inside of that original polygon, as long as those lines do not cross any other
line you have drawn. **Note: Not every point on the polygon will connect with every
point inside the polygon.
3. For each dashed straight line drawn between two points, locate its midpoint and draw a
short mark perpendicular to that dashed line at that point (the midpoint).
4. Now, you will begin to form a polygon around each raingage. Keep in mind that the
goal of the following step is to have a polygon fashioned out of the perpendicular
lines which completely surrounds or isolates each raingage from one another.
Look at one of the points (raingages) toward the center of the polygon (not the ones on
the outer polygon). Notice how perpendicular marks seem to surround the raingage. If
the perpendicular lines were longer, they would intersect and form a polygon around
the raingage. Extend the perpendicular lines to start forming this polygon. Extend
perpendicular lines that are farther from the raingage, toward the raingage until they
intersect with another extended perpendicular line, and then extend those
perpendicular lines no farther. If you did extend them farther, erase the extensions that
go beyond the intersection of the perpendiculars. **NOTE: Extended perpendicular
lines may not meet until they are extended to outside the particular triangle or even
outside of the watershed. This is ok.
5. Extend the perpendicular lines that are closest to the watershed boundary out so they
reach a little past the boundary but not necessarily connecting to any other
perpendicular line.
Interior points should now be surrounded by extended
perpendicular lines. The outer points may not be surrounded by all perpendiculars.
It’s polygon may consist of an extended perpendicular line or two but also of a piece of
the watershed boundary.
6. Darken those lines (the extended perpendiculars that form the polygons and extend to
the watershed boundary.
7. You may now erase the dashed straight lines you drew originally.
8. To find the area covered by each raingage station, count the number of boxes in that
gage’s polygon and use the scale to determine its area. Use the data table to record the
number of boxes and the scale factor and then determine the actual area of each
polygon.
9. Fill out the last column of the data table by multiplying the amount of rainfall in each
raingage by the area of its polygon surrounding it. Add the areas of each polygon
together to get the total watershed area and write that area at the bottom of the data
table. Also add all the weighted precipitation x areas together for the top part of the
following equation. To get the average precipitation over the entire watershed, you
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will use the values from the data table to get a weighted average as follows: (Show
your work by filling in the appropriate numbers from your data table into this equation
as you calculate this average.)
Average Rainfall Depth = sum of all the (precip. x polygon area for that gage)
area of the entire watershed
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