Lecture 2: Precipitation

Transcription

1 2-1 GEOG415 Lecture 2: Precipitation Why do we study precipitation? Precipitation measurement -- depends on the study purpose. Non-recording (cumulative) Recording (tipping bucket) Important parameters Amount (mm) Intensity (mm/hr) Duration (minutes, hours) 50 cumulative pcp (mm) time (min)

2 2-2 Precipitation measurement: Point vs Area Drainage basin: Why do we want a basin-average precipitation? Orographic effect Convective 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

3 2-3 Precipitation data: quality control (1) Missing data at A B Stations B, C, and D have complete records. How do you estimate P A? Pitfalls of this method? D A C (2) Consistency of records Relocation 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

4 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?

5 2-5 Theoretical vs observed frequency distribution 15 Saskatoon, SK Frequency 10 5 Mean = 360 mm S.D. = 68 mm Annual precipitation (mm) Normal probability paper Cumulative probability (%) Saskatoon, SK Annual precipitation (mm)

6 2-6 Cumulative percentage frequency (F) F = Year Pcp (mm) m: rank n: number of samples Rank F Statistically stationary processes have all statistical parameters (mean, standard deviation, etc.) independent of time. Climate change? Large-scale landuse change? Annual precipitation (mm) Saskatoon, SK

7 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.

8 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 = What is the size of the 20-year storm? What does this mean? How can this information be used? Dunne and Leopold, 1978, Fig 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?

9 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 all storms 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). 2. Determine the rainfall intensity corresponding to several values of return period (2-yr, 5-yr,...) 3. Repeat Steps 1 and 2 for other durations (5-min, 10-min,, 24-hr) Hydrological Atlas of Canada, Fig. 3

10 Plot the intensity and duration of each data point on a log-log graph paper and tie the points with smooth curves. What is the return period of the 3-hr storm having an intensity of 20 mm/hr? Hydrological Atlas of Canada, Fig. 4 The IDF curves of many meteorological stations have been prepared by Environment Canada. ( What are they used for? For a rough estimate of IDF relationship, The Hydrological Atlas of Canada (Environment Canada, 1978) is useful.

11 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

12 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. (

13 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 This type of correlation is usually site-specific. Do not expect Fig to be applicable in Alberta.

14 2-14 Temporal distribution: mass curves Typical mass curves for various storm durations for the San Francisco Bay region. Cumulative precip. (%) hr 6-hr Cumulative time (%) Prepared from Dunne and Leopold, 1978, Table 2-3 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-km 2 basin to obtain the 10-yr, 1-hr storm over the whole 100 km 2. Why?

15 2-15 Dunne and Leopold, 1978, Fig 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-km 2 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?