INTRODUCTION TO HYDROLOGY (GEOG 3511):
Instructor: Mark Williams
Intensity - Duration Analysis of Rainfall and
Spatial Distribution of Rainfall
||Tuesday, Oct 9
||Friday, Oct 12
||Thursday, Oct 11
|Monday, Oct 15
- 40 possible points.
- SHOW ALL YOUR WORK.
- WRITE NEATLY and LEGIBLY.
- WRITE THE QUESTION AT THE START OF EACH ANSWER.
- Use a summer rainstorm record at Williams Lake (3600 m elevation
in the San Juan Mountains) to evaluate intensity - duration
relationships and to estimate empirical storm probabilities.
- Use point measurements of annual precipitation to determine the
spatial distribution of rainfall in Boulder Creek.
"At-a-point" records of precipitation are often evaluated for
(rate of rainfall) and duration.
Both of these will influence streamflow responses dynamically:
high intensities and long durations are both
associated with higher flows.
Scaling point measurements to the basin scale is problematic.
The data table of storm depths (mm) and durations (hr) for
June, July and August 1972
includes 72 separate storms
which is a small sample for what you are to attempt.
Click here for the data:
Williams Lake rainfall data .
Annual precipitation amount (depth in inches) from 5 precipitation
gauges at various elevations in Boulder Canyon.
Click here for the data:
Annual precipitation depth (in) from Boulder
Creek basin .
- Plot histograms of storm duration and depth. Use a bin size of
0.25 hr for storm duration and 0.25 mm for storm depth. Is the duration
of these storms normally distributed? Is the depth of these storms
normally distributed? If the distributions are not normally
distributed, how could you alter the data to obtain a normal
distribution? What does this information tell you about mountain
EXCEL HINT: The 'Histogram' data analysis tool will compute a
table of frequency of occurance. In order to use the tool you first
need to create a data series of the bin boundaries
[0,0.25,0.5,0.75,...] To create a histogram plot of the data, create a
vertical column chart. Get rid of the gaps between the columns by using
the Format Data Series... menu command.
- Convert the record to precipitation intensities (mm/hr). Plot
intensity (y) vs duration (x). Describe how storm intensity varies with
Plot storm depth (y) vs duration (x). Describe how storm depth varies
- Calculate the mean, standard deviation and coefficient of
variability for storm depth. What was the maximum storm depth? What is
the probability that storm depth will be equal to or less than 10-mm,
using the z-statistic approach? What is the probability that storm
depth will exceed 10 mm?
- On log-normal probability coordinates, draw cumulative
probability plots for (a) storm depth and (b) storm intensity. Now use
these plots to estimate the probability of (c) a storm exceeding 10 mm rainfall and (d) a storm with an average intensity greater
than 10 mm/hr.
EXCEL HINT: Make a copy of the log-normal-probability chart
that has been set up. To add a data series to the chart, 1-create a new
data sheet, 2-create the following columns:
a) storm depth sorted in ascending order,
b) the rank (cumulative order number) of the data [1,2,3,4...],
c)the z-score based on the rank, the mean, and the standard deviation,
d) the probability associated with each z value (using
the Excel function
Add a data series with the z-score as the x-data and the storm
depth as the y-axis.
- Lets evaluate the spatial distribution of rainfall in the
Boulder Creek basin. For the data given, what is the mean, standard
deviation, and CV of annual precipitation amount?
- Plot measured precipitation values (y-axis) against elevation
(x-axis). What is the orographic equation (ppt = a + bz)?
- You might expect precipitation amount to increase with elevation
in a mountain area. Does precipitation increase with elevation in
Boulder Creek basin? If so, at what rate? How well does precipitation amount track changes in elevation. How can you quantify this relationship?
- Download this table and answer
the following questions? What is the precipitation amount for each
elevation increment? (Hint: Use the orographic equation to estimate the
precipitation amount at each elevation increment z(h).) What is the
area-weighted precipitation amount for each elevation increment? (Hint:
Calculate the area-weighted precipitation amount for each elevation
increment by multiplying the area fraction by precipitation amount for
that elevation increment.) What is the precipitation amount for the
Boulder Creek basin using the hypsometric method?
- Assume that the area of the Boulder Creek basin is 100 km2. What
is the annual precipitation volume in cubic meters using these three
a) lowest elevation site;
b) mean annual precipitation;
c) hypsometric method;
Why do the three methods differ? Which is the best estimate?