2-1 GEOG415 Lecture 2: Precipitation - University of...
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2-1 GEOG415 Lecture 2: Precipitation Why do we study precipitation? Precipitation measurement -- depends on the study purpose. Non-recording (cumulative) Recording (tipping bucket) 0 10 20 30 40 50 0 60 120 180 time (min) cumulative pcp (mm) Important parameters Amount (mm) Intensity (mm/hr) Duration (minutes, hours)
Transcript of 2-1 GEOG415 Lecture 2: Precipitation - University of...
2-1
GEOG415 Lecture 2: Precipitation
Why do we study precipitation?
Precipitation measurement -- depends on the study purpose.Non-recording (cumulative)Recording (tipping bucket)
0
10
20
30
40
50
0 60 120 180time (min)
cum
ulat
ive
pcp
(mm
)
Important parametersAmount (mm)Intensity (mm/hr)Duration (minutes, hours)
2-2
Precipitation measurement: Point vs Area
Drainage basin:
Why do we want a basin-average precipitation?
Orographic effectConvective storm
(a)
Dunne and Leopold, 1978, Fig. 2-4
Methods for computing the areal average precipitation.Advantage? Disadvantage?
(a) Arithmetic average
(b) Thiessen-weighted average
(c) Isohyetal method
2-3
Precipitation data: quality control
(1) Missing data at A
A
B
CD
Stations B, C, and D have complete records.
How do you estimate PA?
Pitfalls of this method?
(2) Consistency of recordsRelocation or upgrading of a station (e.g. U of C station)→ systematic inconsistency of records?
Double-mass curve analysis
Dunne and Leopold, 1978, Fig. 2-6
2-4
Statistical analysis: introductory comments
Properties of the “ideal” data set.
Random
Independent
Homogeneous
Normally distributed
“Equal variability” -- stationary
Dunne and Leopold, 1978, Fig. 2-8
Normal distribution is commonly assumed in hydrological data analysis. How do we know for sure the data are distributed normally?
2-5
Theoretical vs observed frequency distribution
0
5
10
15
150 200 250 300 350 400 450 500 550
Annual precipitation (mm)
Freq
uenc
y
Saskatoon, SK 1908-1999
Mean = 360 mm
S.D. = 68 mm
Normal probability paper
200 300 400 500 600Annual precipitation (mm)
50
16
2.3
0.13
84
97.7
99.87
Cum
ulat
ive
prob
abili
ty (%
)
Saskatoon, SK 1908-1999
2-6
Cumulative percentage frequency (F)
m: rank n: number of samplesF =
Year Pcp (mm)1990 2661991 4771992 3251993 3691994 3681995 3761996 4461997 3131998 2801999 401
Rank F1 266 9.0923456789
10 477
200
300
400
500
600
1900 1920 1940 1960 1980 2000
Ann
ual p
reci
pita
tion
(mm
)
Saskatoon, SK 1908-1999
Statistically stationary processes have all statistical parameters (mean, standard deviation, etc.) independent of time.
→ Climate change? Large-scale landuse change?
2-7
Characteristics of individual storms
Why are we interested?
Intensity-duration frequency (IDF) analysis
For point rainfall, the data from recording rain gage can be used for IDF analysis. Note that the extrapolation of the point rainfall data to basin-average rainfall is not trivial. Why?
Analysis of annual maximum series
Pick out the maximum intensity storm of each year and form a series. For example, steps for obtaining the annual maximum series of 24-hr storm is as follows.
1. Estimate maximum 24-hour rainfall for all storms in a given year.
2. Compare the maximum amount of all storms and select the storm with the highest maximum 24-hr amount → annual maximum 24-hr storm.
3. Make a table of annual maximum series.
4. Rank them from highest (m = 1) to lowest (m = n).
5. Calculate p = m/(1+n)
6. Plot p on the extreme-value probability (Gumbel) paper.
2-8
7. Fit a straight line by visual examination (“eye-ball”).
8. The straight line gives exceedence probability (p) for a given size of 24-hr rainfall.
9. Recurrence interval or return period (T) is given by
T =
Dunne and Leopold, 1978, Fig. 2-14
What is the size of the 20-year storm?
What does this mean?
How can this information be used?
Suppose we just had a 24-hr storm of 86 mm this year. What is the probability that a 24-hr storm exceeding 86 mm will occur next year?
2-9
Partial duration series
Annual maximum series ignores the 2nd, 3rd, … largest storms in a given year, which may be larger than the largest storm in another year. Partial duration series consists of allstorms greater than some arbitrary set size.
Differences between annual maximum and partial duration
Construction of IDF curves
1. Establish the relationship between the intensity and the return period for 60-min storms (see the graph).
Hydrological Atlas of Canada, Fig. 3
3. Repeat Steps 1 and 2 for other durations (5-min, 10-min, …, 24-hr)
2. Determine the rainfall intensity corresponding to several values of return period (2-yr, 5-yr, ...)
2-10
4. Plot the intensity and duration of each data point on a log-log graph paper and tie the points with smooth curves.
Hydrological Atlas of Canada, Fig. 4
What is the return period of the 3-hr storm having an intensity of 20 mm/hr?
The IDF curves of many meteorological stations have been prepared by Environment Canada.(http://www.msc-smc.ec.gc.ca/climate/products_services/engineering_products/energy4_e.cfm)
What are they used for?
For a rough estimate of IDF relationship, The Hydrological Atlas of Canada (Environment Canada, 1978) is useful.
2-11
10-min rainfall, 10-yr return period
Hydrological Atlas of Canada, Plate 4C
24-hr rainfall, 10-yr return period
Hydrological Atlas of Canada, Plate 6C
2-12
The Hydrological Atlas also contains many other useful data, for example the mean annual precipitation.
Hydrological Atlas of Canada, Plate 3
Mean annual precipitation of many Canadian cities, as well as other climate data can be found in Environment Canada’s web site. (http://www.msc-smc.ec.gc.ca/climate/climate_normals/index_e.cfm)
2-13
Correlation analysis
Determining the IDF curves is time consuming and also requires detailed rainfall data from recording gages.
How do we estimate the intensity of 24-hr rainfall, 50-yr return period for a station without a recording gage?
British Isles
Dunne and Leopold, 1978, Fig. 2-18
This type of correlation is usually site-specific. Do not expect Fig. 2-18 to be applicable in Alberta.
2-14
Temporal distribution: mass curves
0
20
40
60
80
100
0 20 40 60 80 100Cumulative time (%)
Cum
ulat
ive
prec
ip. (
%)
1-hr
6-hr
Prepared from Dunne and Leopold, 1978, Table 2-3
Typical mass curves for various storm durations for the San Francisco Bay region.
What do these curves imply?
Spatial distribution: point vs areal average
It is not permissible to average the 10-yr, 1-hr storm at five stations in a 100-km2 basin to obtain the 10-yr, 1-hr storm over the whole 100 km2. Why?
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Dunne and Leopold, 1978, Fig. 2-23
Why does shorter-duration storms have more significant reduction than longer-duration storms?
Implications for environmental planning?
Summary
Suppose you are given a project to characterize the precipitation over a 200-km2 watershed in a remote area in Africa. There is no meteorological station, and your budget is fairly limited (just enough money to buy one recording gauge). What will you do?
