## EXERCISE 5 Intensity - Duration Analysis of Rainfall and Spatial Distribution of Rainfall

 Section Lab Assigned Due 012,013 Tuesday Tuesday, Oct 9 Friday, Oct  12 011 Thursday Thursday, Oct 11 Monday, Oct 15

• 40 possible points.
• WRITE NEATLY and LEGIBLY.
• WRITE THE QUESTION AT THE START OF EACH ANSWER.
OBJECTIVES.
1. 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.
2. Use point measurements of annual precipitation to determine the spatial distribution of rainfall in Boulder Creek.

### BACKGROUND

"At-a-point" records of precipitation are often evaluated for intensity (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.

### DATA

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 .

### PROBLEMS:

1. 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 storms?
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.

2. Convert the record to precipitation intensities (mm/hr). Plot intensity (y) vs duration (x). Describe how storm intensity varies with duration.
Plot storm depth (y) vs duration (x). Describe how storm depth varies with duration.
3. 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?
4. 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 NORMSDIST)
Add a data series with the z-score as the x-data and the storm depth as the y-axis.

5. 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?
6. Plot measured precipitation values (y-axis) against elevation (x-axis). What is the orographic equation (ppt = a + bz)?
7. 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?
8. 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?
9. Assume that the area of the Boulder Creek basin is 100 km2. What is the annual precipitation volume in cubic meters using these three approaches:
a) lowest elevation site;
b) mean annual precipitation;
c) hypsometric method;
Why do the three methods differ? Which is the best estimate?