geog 441 watershed systems precipitation monday 1/26/2009

GEOG 441Watershed Systems

PrecipitationMonday 1/26/2009

Precipitation

• Characteristics– Spatial– Temporal

• Frequency Analysis

Precipitation

• Units- Volume (L3) or Depth/Time (L/T)• Input in the mass balance• Continuous random variable

Spatial Characteristics

• Point measurements


• Radar


• Hyetographs

Temporal Characteristics

• Intensity– Rate of precip over some period of time

• Duration• Frequency

Review

• Histograms• Normal distributions• Extreme value distributions• Cumulative Distributions

• An example with UNC graduate salaries

Review

Normal distributions

meanStd dev

Annual Rainfall

• Assumes data follows normal distribution• Typically works for annual precipitation

data

Annual Precip Trends

0

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1400

1600

1930 1940 1950 1960 1970 1980 1990 2000

S eattle

S an Diego

Denver

Was hington

Annual Rainfall Histograms and Cumulative Distributions

S eattle His tog ram

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B in

Frequency

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F requency

C umulative %



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B in

Frequency

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F requency

C umulative %Washington Histogram

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Bin

Frequency

0.00%

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Frequency

Cumulative %



02468

1012141618

100300500700900110013001500More

B in

Frequency

0.00%

20.00%

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F requency

C umulative %

Washington Histogram

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Bin

Frequency

0.00%

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Frequency

Cumulative %

S an Dieg o His tog ram

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100 300500 700900110013001500More

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Frequency

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F requenc y

C umulative %

• Different distributions required for shorter time periods

Exceedance Probabilities

• [dimensionless], the relative frequency associated with a random variable attaining a value greater than some specified value.

• For example- calculate probability that annual precipitation in any given year will exceed 1.0 m

Exceedance Probabilities

Exceedance Probability1. Normalize data to a z value

2. Find cumulative probability for a given value (Table A3.2)

Annual Maxima• Takes the highest value for the entire year

Partial Duration

• All values above a certain base• Closely related to annual values for long

return periods• Could be more (frequent) or less

(infrequent) values than annual maxima for a given threshold

Partial Duration Series –RDU Airport

ARI*(years)

1 0.39 1.34 1.56 2.37 2.83 7.92 12.16

2 0.46 1.61 1.86 2.84 3.42 9.32 14.16

5 0.53 1.95 2.29 3.52 4.27 10.83 15.98

10 0.59 2.24 2.65 4.11 4.93 12 17.38

25 0.65 2.58 3.08 4.89 5.83 13.54 19.17

50 0.69 2.83 3.43 5.56 6.54 14.72 20.53

100 0.73 3.08 3.76 6.22 7.26 15.89 21.83

200 0.76 3.31 4.09 6.93 8 17.06 23.09

500 0.79 3.6 4.51 7.88 8.99 18.62 24.7

1000 0.82 3.82 4.84 8.69 9.77 19.8 25.9

60 day

Precipitation Frequency Estimates (inches)

30 day 24 hr 5 min 60 min 120 min 12 hr

Precipitation FrequencyExamples from AZ and NC http://hdsc.nws.noaa.gov/hdsc/pfds/index.html

http://hdsc.nws.noaa.gov/hdsc/pfds/index.html

Return Period

• What is the probability of a storm of X magnitude this year?

• Inverse of exceedance probability

Treturn= (n+1)/mn= # of years of observationm= rank

Return Period- Washington, DCColumn1 Rank Percent Return Per

1433 1 100.00% 511341 2 97.90% 25.51322 3 95.90% 171320 4 93.80% 12.751318 5 91.80% 10.21283 6 89.70% 8.51278 7 87.70% 7.2857141202 8 85.70% 6.3751189 9 83.60% 5.6666671178 10 81.60% 5.1

R eturn P eriod

1

10

100

0 200 400 600 800 1000 1200 1400 1600

S eries 1

Data from Table 2.1 plotted

geog 441 watershed systems precipitation monday 1/26/2009

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