PRECIPITATION

ANNOUNCEMENTS  Seminar #1 - Philippe Quevauviller  European Commission – Director General for Research  Seminar report due Wed  See class webpage for guidelines  Summary of report  Comparison of U.S. vs. EU methods for natural resource protection  If not covered in talk  ask questions

MOISTURE IN THE ATMOSPHERE

 Evaporation  Water changes from liquid to vapor

 Precipitation  Water changes from vapor to liquid  Evaporation and precipitation controlled by:  Air temperature  Moisture content of the atmosphere  The relative humidity is a measure of the amount of water in the air

MOISTURE IN THE ATMOSPHERE  Precipitation is formed from water vapor  As air cools its capacity to hold water decreases  Saturated (100% relative humidity)  Saturation at 70 oF vs. 32 oF  Air can hold 4 times more water at 70 oF  Cooling effect can cause moist unsaturated air to become saturated (dew point)  Cooling beyond 100 % saturation causes water vapor to condense and change to liquid or solid (snow/hail) water.  Water droplets on cold glass  Dew on grass  Hail

The relationship between water content of air at saturation and air temperature

PRECIPITATION Occurs when three conditions are met: 1. Atmosphere is saturated  Atmosphere becomes saturated when the air mass is cooled usually by lifting.  Air mass lifting caused by: 1. Frontal systems (warm moist air meets colder heavier air). 2. Orographic effects (induced by mountains) 3. Convection (air expands when heated by solar energy and becomes lighter than the air around it.

PRECIPITATION

2. Small particles are present  Dust, ocean salt, smoke 3. Drops reach a size that causes them to fall toward Earth.  May collect additional condensed vapor  May evaporate

 The movement and collision of air masses lead to atmospheric instability  The result is often precipitation

FRONTAL SYSTEMS

 Cold fronts  High intensity / short duration / narrow zone  Typical in the spring and fall  Warm fronts  Gentle rainfall / long term / widespread  Typical in the winter  Orographic precipitation  Increasing rainfall with increasing elevation  Convective precipitation  High intensity / short duration / limited area  Earth surface and air close to surface heated  lifted  Typical summer thunderstorm

Typical in the winter Typical in the spring and fall Typical in coastal mountain regions Typical in the summer

Cold front producing a high intensity rainfall event. Cold air coming from the left colliding with warm air on the right.

PRECIPITATION Measurement, Estimation and Probability

PRECIPITATION DATA

 Necessary for most land use plans  Municipal / industrial / agricultural / forestry / flood prevention / recreation  Data collection by State and Federal agencies  Much of the data is now on-line via the internet  Precipitation records report amounts  Yearly / monthly / daily / hourly

RAINFALL  Large variation depending on  Location and time of year  Some deserts get 0 in./yr of rain  Atacama Desert in Chile (2010 mine accident)

 Cherrapunji, India has gotten 1000 in./yr (83 ft)  Combined orographic effects and monsoons  Units of measurement  depth (in. / mm / etc.)  Can get volume easily by multiplying by area  Accuracy of measurement  0.01 in.  Misleading since no two rain gages will ever record the same amount of rain even if they are side by side!

RAINFALL  Data widely available.  Typically two types of rain gauges  Non-recording  Low cost / maintenance free  Accuracy = 0.1 in.  Labor intensive  Recording  Datalogger  Pen and paper  NEXRAD  Radar based

RECORDING RAIN GAGES Weighing bucket type Good for large rainfall events Can’t accurately measure (weigh) small rainfall events

Tipping bucket type Good for small rainfall events Can’t keep up during heavy rainfall events. Each tip = 0.01”

SNOW-PACK MEASUREMENT

 80 to 90% of annual precipitation is snow in some areas  High elevation snow country is often forested  75% of the water supply in western U.S. is from forests  Water equivalent (depth after melting)  For fresh snow 10 inches deep:  5% to 20% is water  0.5” to 2.0” water  For snow in late summer  up to 60%

RAINFALL MEASUREMENT  Standard rain gages are point samples only  Generally a high degree of variation in any rainfall  Rain gages are usually cylindrical with circular top  Therefore least subjected to edge effect errors  Mounted vertically  Height of 2 m (about 6 ft)  2:1 obstruction rule  If top of object is 30 ft above gage  Place gage 60 ft away  Eliminates obstructions that may affect rainfall capture

MEASUREMENT OF PRECIPITATION 

What we want:  Total rainfall amount 

Rainfall intensity  in./hr or mm/hr  Rainfall distribution  Over time  Over space What we have:  Point measurements at a few locations  Must extrapolate over the entire watershed 



volume = depth x area

RAINFALL ON A WATERSHED SCALE 

3 common methods for estimating average rainfall. 1. Arithmetic Mean 2. Thiesson polygon method 3. Isohyetal method

- All use the same algorithm to calculate average rainfall 1. 2. 3.

R = precipitation W = weighting factor i = number of gauges

Wi Ri  R Wi

CALCULATING AVERAGE PRECIPITATION OVER AN AREA  Arithmetic mean method  Assumes uniform rainfall distribution  Very seldom occurs  Easiest to use but least accurate  Thiessen polygon method  Assumes linear variation  Use when gages are not uniformly distributed  Can use gages outside of watershed  Isohyetal method  Theoretically the most accurate  Most time consuming method  Can use gages outside of the watershed

Measured Rainfall at Six Rainfall Gages Watershed boundary P6 = 1.81”

P4 = 2.26”

P2 = 2.15” P1 = 1.62”

P5 = 2.18”

P3 = 1.80”

ARITHMETIC MEAN METHOD 

Pavg = [ Wi x Pi ] /  Wi  All gages given equal weight  Weight = 1  Pavg = (1.82 + 2.15 + 2.26 + 2.18 + 1.62 + 1.8) / 6  Pavg = 1.97 in.

THIESSEN POLYGON METHOD 

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First: Draw straight dashed lines between each rainfall gage Second: Draw solid perpendicular bisectors to these lines so that watershed area associated with each gage is enclosed by bisector lines  These enclosed areas are known as Thiessen Polygons  The area within each polygon is closer to the rain gage enclosed than any other rain gage.  The rainfall measured in the polygon is assumed to be representative of the rainfall in the entire polygon

THIESSEN POLYGON METHOD 

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Third: Determine the area of each polygon  The rain gage weight is the area of the polygon it is located in Fourth: Calculate the average rainfall using:  Pavg = [ (Wi x Pi )] /  Wi

Step #1: Dashed Lines Between Each Rain Gage Watershed boundary P6 = 1.81” P2 = 2.15” P4 = 2.26” P1 = 1.62”

P5 = 2.18”

P3 = 1.80”

Step #2: Draw the Perpendicular Bisector Lines Watershed boundary

Step #3: Determine the Area of Each Polygon Watershed boundary

A6= 65 ac

A4= 269 ac A2= 150 ac

A1= 56 ac A5= 216 ac A3= 136 ac

STEP #4: CALCULATE THE AVERAGE RAINFALL 

Pavg = [ (Wi x Pi )] /  Wi  Pavg = [(65x1.81)+(150x2.15)+(269x2.26)+ (216x2.18)+(56x1.62)+(136x1.8)] / [65+150+269+ 216+56+136]  Pavg = 2.08 in.

Mean Annual Rainfall in inches with the longitude parallels 98o and 100o also shown

Average Rainfall in the U.S.

Average Global Rainfall

NEXRAD

POINT PRECIPITATION PATTERNS  Often

want to predict rain in the future rather than use historical rainfall  Rainfall Depth-Duration and Frequency  Rainfall Intensity-Duration and Frequency  TP 40 and similar documents provide this information.  NRCS program / report

PRECIPITATION DATA  When

planning/designing we need to know three things.  What is the depth or intensity of the rainfall we are designing for?  What is the length of time (duration) of that rainfall?  How often will rainfall of that depth and duration return (what is its frequency?)

RETURN PERIOD AND PROBABILITY  T-year

event – an event of such magnitude that over a long period of time, the average time between events having a magnitude greater than the Tyear event is T years.  The expected number of occurrences of a T-year event in an N-year period is N/T.  On average we expect a T-year event to occur once in T-years.

RAINFALL AND FREQUENCY 

The 25-yr, 24-hr rainfall for Houston is 10 in. (25 cm)  The depth is 10 inches, the duration is 24 hours and the frequency is 25 years.  The frequency is also known as the return period.  This means that on average a 10 in. rainfall event will occur four times in 100 yrs .  It does not mean that a 10 in. rainfall event will happen exactly every 25 years and it does not mean that there will be exactly 4, 10 in. rainfall events in 100 yrs.

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The probability of a T-yr event in any given year is a 1/T  A 25 year event has a 4% chance of occurring in a single year (1/25 * 100).  Likewise a 10 yr event = 10% chance [(1/10)*100]  Likewise a 50 yr event = 2% chance [(1/50)*100]

DEPTH - DURATION - FREQUENCY CURVES INTENSITY – DURATION – FREQUENCY CURVES

 DDF or IDF curves have been developed for many cities and locations around the U.S.  When using an IDF curve rainfall depth (in) is found by multiplying the intensity (in/hr) by the duration (hr).

RAINFALL / FLOOD RETURN FREQUENCY AND DURATION  Return frequency used in engineering designs:  Depends on economic value  Rural roads (not much traffic)  5 to 10 year return  Interstate highways  50 to 100 year return period  Design duration depends on size of watershed  Small to medium watersheds (1 to 100 mi2)  Duration of 5 minutes to 24 hours  Large watersheds (over 100 mi2) up to 1 mo. duration  River basin studies up to 1 yr may be needed

10 YR 24 HOUR DDF

Depth (D) – Read from chart Duration (D) = 24 hr Frequency (F) = 10 yr

Intensity – Duration – Frequency (IDF) Curves

PUBLICATIONS OF DDF  TP-40

 Contains

DDF data for the U.S. for durations of 30 min. to 24 hr and frequencies from 1 to 100 years.

 HYDRO-35

 Gives

DDF for Eastern US for durations of 5 to 60 minutes and frequencies to 100 years.

 NOAA

Atlases  For use in western U.S.

RAINFALL TIME DISTRIBUTION 



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Ultimately we are building up to developing runoff hydrographs (runoff depth vs. time). In order to do so we need not only depth, duration and frequency of a storm but also distribution of rainfall within its duration. Plot of time distribution of rainfall intensity is known as the rainfall hyetograph.

PRECIPITATION TERMS 

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

Hyetograph  A plot of rainfall intensity vs. time Isohyete  Contours of constant rainfall  Similar to contours of constant elevation Isohyetal Map  Map with contours of constant rainfall

PROBABILITY 

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Return period for rainfall events and floods  Important for planners and designers May have only 10 or 15 years of data  Need to extrapolate to predict 25 or 50 or 100 year events Many statistical methods can be used  The Hazen method is commonly used by the Natural Resource Conservation Service (NRCS)

THE HAZEN METHOD

1. Start with a “long-term” data set  Long-term is at least 10 good data points 2. Apply statistical algorithms to get distribution 3. Plot the distribution points on logprobability paper 4. Draw a “best-fit” line that minimizes the distance each point is off of the line 5. Read off the values associated with the best fit line

Year

Rain (in.)

1934

14.6

1935

21.7

1936

12.1

1937

22.4

1938

23.4

1939

13.1

1940

19.2

1941

32.8

1942

11.2

1943

18.2

1944

19.2

1945

11.6

1946

11.6

1947

12.7

1948

7.2

1949

8

1950

10.6

1951

8.2

1952

26.2

1953

9.5

Given: Annual Precipitation Los Angles, CA 1934 to 1953 (Example 2.5 text)

Year

Rain (in.)

Rank (n)

1941

32.8

1

1952

26.2

2

1938

23.4

3

1937

22.4

4

1935

21.7

5

1944

19.2

6

1940

19.2

7

1943

18.2

8

1934

14.6

9

1939

13.1

10

1947

12.7

11

1936

12.1

12

1945

11.6

13

1946

11.6

14

1942

11.2

15

1950

10.6

16

1953

9.5

17

1951

8.2

18

1949

8

19

1948

7.2

20

The Hazen Method Step 1: Re-order rainfall records high to low

Step 2: Assign rank (n)

Hazen Method / Step 3: Calculate the plotting position Fa = 100(2n-1)/2y Where n = rank, y = 20 = number of points in data set

Year 1941 1952 1938 1937 1935 1944 1940 1943 1934 1939 1947 1936 1945 1946 1942 1950 1953 1951 1949 1948

Rain (in.) Rank (n) Plotting Position (Fa) 32.8 1 2.5 26.2 2 7.5 23.4 3 12.5 22.4 4 17.5 21.7 5 22.5 19.2 6 27.5 19.2 7 32.5 18.2 8 37.5 14.6 9 42.5 13.1 10 47.5 12.7 11 52.5 12.1 12 57.5 11.6 13 62.5 11.6 14 67.5 11.2 15 72.5 10.6 16 77.5 9.5 17 82.5 8.2 18 87.5 8 19 92.5 7.2 20 97.5

THE HAZEN METHOD  Step 4:  Use the log-probability graph paper to plot:  Rainfall on the y-axis (log scale!  so be careful)  Probability of Occurrence (Fa) on the xaxis  Use the top x-axis to be consistent with the text  Step 5:  After all points are plotted:  Draw a “best-fit” line on the graph  Try to minimize the distance the points are off of the line

THE HAZEN METHOD  

Use the best fit line to find the amount of rainfall associated with a given return period For example:  What is the rainfall for a 2-yr storm event?  1’st calculate the probability of occurrence for a 2-yr event  Probability of Occurrence = 1/2-yr = 0.5 = 50%  Go to 50 on the top axis  Come down vertically to the “best-fit” line  Go horizontally to the y-axis and read the rainfall value  I get 14.2 in.  the book gets 15 in.  Difference is the “best-fit’ line

Fa = 50%

Best fit line

Annual Precipitation = 14.2 in.