ERS 482/682 (Fall 2002) Lecture 4 - 1

Precipitation

ERS 482/682Small Watershed Hydrology

ERS 482/682 (Fall 2002) Lecture 4 - 2

Watershed definitions• watershed

– ridge or stretch of high land dividing the areas drained by different rivers or river systems (e.g., Continental Divide)

– the area drained by a river or river system

• waterbody– geographically defined portion of navigable waters,

waters of the contiguous zone, and ocean waters under the lakes, wetlands, coastal waters, and ocean waters (NRC 2001)

• watershed management (per Lee MacDonald, CSU)– the art and science of managing the land and water

resources of a drainage basin for the production and protection of water supplies, water resources, and water-dependent resources

ERS 482/682 (Fall 2002) Lecture 4 - 3

Precipitation

• Water that falls to the earth (and reaches it)– Rain– Snow– Ice pellets (sleet)– Hail– Drizzle

ERS 482/682 (Fall 2002) Lecture 4 - 4

Process of precipitation

• Global circulation• Formation of precipitation

– uplift– temperature

ERS 482/682 (Fall 2002) Lecture 4 - 5

Global circulation

• Distribution of solar radiation intensity

Figure 3-4: Dingman (2002)

ERS 482/682 (Fall 2002) Lecture 4 - 6

Global circulation

• Earth’s rotation

Figure 4.1: Manning (1987)

ERS 482/682 (Fall 2002) Lecture 4 - 7

Formation of precipitation

• Water vapor importation• Cooling of air to

dewpoint temperature• Condensation• Growth of droplets or

crystals

See Appendix D for more detail

ERS 482/682 (Fall 2002) Lecture 4 - 8

Air cooling

• Cyclonic uplift

Figures 4.2 and 4.3: Manning (1987)

ERS 482/682 (Fall 2002) Lecture 4 - 9

Air cooling

• Thunderstorm uplift

Figure 4.4: Manning (1987) Figure 4-7: Dingman (2002)

ERS 482/682 (Fall 2002) Lecture 4 - 10

Air cooling

• Orographic uplift

Figure 4.5: Manning (1987)

ERS 482/682 (Fall 2002) Lecture 4 - 11

Condensation

Figure 2.1: Hornberger et al. (1998)

ERS 482/682 (Fall 2002) Lecture 4 - 12

CondensationAssumption:Pressure isconstant

Figure 2.1: Hornberger et al. (1998)

ERS 482/682 (Fall 2002) Lecture 4 - 13

Formation of droplets

Figure D-7: Dingman (2002)

Condensation requires condensation nuclei

ERS 482/682 (Fall 2002) Lecture 4 - 14

Measuring precipitation

• Units– Depth (L)– Intensity (L T-1)

Figure 2-2; Dunneand Leopold

(1978)

ERS 482/682 (Fall 2002) Lecture 4 - 15

Precipitation characteristics

• Typical precipitation intensities <1”/hr• General rule: longer storm duration

lower average intensity

ERS 482/682 (Fall 2002) Lecture 4 - 16

Figure 4-51 (a): Dingman (2002)

ERS 482/682 (Fall 2002) Lecture 4 - 17

Figure 4-51(c): Dingman (2002)

ERS 482/682 (Fall 2002) Lecture 4 - 18

Precipitation characteristics

• Typical precipitation intensities <1”/hr• General rule: longer storm duration

lower average intensity• Larger area lower average intensity

ERS 482/682 (Fall 2002) Lecture 4 - 19

Rainfall amounts between 5:30 and 11:00 MDT on 7/28/97for Fort Collins, CO (http://www.cira.colostate.edu/ramm/jw/flood/flood0.htm)

~1 mi

ERS 482/682 (Fall 2002) Lecture 4 - 20

Precipitation characteristics

• Typical precipitation intensities <1”/hr• General rule: longer storm duration

lower average intensity• Larger area lower average intensity

– Cannot extrapolate directly from point to area; must correct for area!

• Extremely variable in time and space!!!Extremely variable in time and space!!!- more precipitation less relative variability

%100.. xs

VC

ERS 482/682 (Fall 2002) Lecture 4 - 21

Precipitation-gage networks

• World Meteorological Association recommendations: Table 4-6 (Dingman text)

• Need ~ 1 gage every km2 (250 acres) to get error under ~10%

ERS 482/682 (Fall 2002) Lecture 4 - 22

Figure 4-31Dingman text

ERS 482/682 (Fall 2002) Lecture 4 - 23

Precision

• Precision improves with:– Increasing density of gage network– Extending period of measurement– Increase in time and cost!

How close can we get to the true value?

ERS 482/682 (Fall 2002) Lecture 4 - 24

• Probable maximum precipitation (PMP)– “theoretically the greatest depth of

precipitation for a given duration that is physically possible over a given size of storm area at a particular geographical location at a certain time of year”

– Available in HMRs (Fig. 16.2 V&L (1996))

Extremes

– Hershfield (1961)nKSPPMP 24

24-hr PMP24-hr PMP

Mean of 24-hr annual maximumsMean of 24-hr annual maximumsover period of recordover period of record

1515 Std dev of the 24-hr maximumsStd dev of the 24-hr maximums

ERS 482/682 (Fall 2002) Lecture 4 - 25

Extremes

• Probable maximum precipitation (PMP)– General guidelines:

• Critical storm size basin size• Critical duration time of concentration

– Significance:• Used to determine the probable maximum flood (PMF)• PMF is used to

– Design dam spillways– Locate essential public utilities

ERS 482/682 (Fall 2002) Lecture 4 - 26

Extremes

• Depth-Duration-Frequency analysis (DDF)– Determine point rainfall depth for storm of

particular• Return period (e.g., 25-year, 100-year, etc.)• Duration (e.g., 1-hr, 2-hr, 6-hr, 24-hr, etc.)

ERS 482/682 (Fall 2002) Lecture 4 - 27

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 28

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 29

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 30

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 31

Discrete vs. continuous data

• Discrete data can only take on discrete values within a range

• Continuous data can take on any value within a range

ERS 482/682 (Fall 2002) Lecture 4 - 32

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 33

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 34

Normal distribution

• 2-parameter distribution:– Mean () – Standard deviation ()

xestimated byestimated by s

2

2

1

2

1

x

exf

data are symmetric

ERS 482/682 (Fall 2002) Lecture 4 - 35

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 36

Plot cumulative probability

• Calculate cumulative probability for the sorted (i.e., ranked) data points with plotting position formula:– nm

1nm

- Weibull:

m = rankn = number of observations

ERS 482/682 (Fall 2002) Lecture 4 - 37

Example 4- 6 (Dingman)

0

0.5

1

1.5

2

2.5

0.01 0.1 1

Probability that annual 1-hr precip will be greater than or equal to

the indicated value

1-hr

ann

ual m

axim

um

prec

ipit

atio

n (i

n)

log scale

ERS 482/682 (Fall 2002) Lecture 4 - 38

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 39

Lognormal distribution

• Plotting the log of the data resembles a normal distribution

n

xn

ii

1

ln• Mean (LX) is estimated by

• Standard deviation (LX) is estimated bytaking the std. dev. of the ln xi data:

1

lnln1

2

1

2

nn

xxnn

i

n

iii

ERS 482/682 (Fall 2002) Lecture 4 - 40

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

log, ln, 3,

ERS 482/682 (Fall 2002) Lecture 4 - 41

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 42

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 43

Extremes

• Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum)

Rank the data

Plot frequency distribution (histogram)

Plot probability distribution (divide by N observations)

Evaluate normalityCalculate cumulative probability

Plot on normal probability paper

Estimate recurrence intervals or depths

Transform data

yes no

ERS 482/682 (Fall 2002) Lecture 4 - 44

Calculate mean (AVERAGE), standard deviation (STDEV) and use NORMINV function in Excel

non-exceedence probability = 1 – EPnon-exceedence probability = 1 – EP

Note: If you have transformed your data, you should use the mean and std dev of the transformed data and

UNTRANSFORM the result!!!

ERS 482/682 (Fall 2002) Lecture 4 - 45

Extremes

• Depth-Duration-Frequency analysis (DDF)– Determine point rainfall depth for storm of

particular• Return period (e.g., 25-year, 100-year, etc.)• Duration (e.g., 1-hr, 2-hr, 6-hr, 24-hr, etc.)– Adjust point estimate to areal estimate• Equation 4-29 or Figure 4-52 or Figures 16.10 and

16.13 of Viessman and Lewis (1996)