ANNOUNCEMENTS. Seminar #1 - Philippe Quevauviller

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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
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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 o F vs. 32 o F Air can hold 4 times more water at 70 o F 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 volume = depth x area 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 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. R = precipitation R W R i W i i 2. W = weighting factor 3. i = number of gauges 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 P 6 = 1.81 Watershed boundary P 4 = 2.26 P 2 = 2.15 P 1 = 1.62 P 5 = 2.18 P 3 = 1.80 ARITHMETIC MEAN METHOD P avg = [ W i x P i ] / W i All gages given equal weight Weight = 1 P avg = ( ) / 6 P avg = 1.97 in. THIESSEN POLYGON METHOD 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 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: P avg = [ (W i x P i )] / W i Step #1: Dashed Lines Between Each Rain Gage P 6 = 1.81 Watershed boundary P 2 = 2.15 P 4 = 2.26 P 1 = 1.62 P 5 = 2.18 P 3 = 1.80 Step #2: Draw the Perpendicular Bisector Lines Watershed boundary Step #3: Determine the Area of Each Polygon Watershed boundary A 6 = 65 ac A 4 = 269 ac A 2 = 150 ac A 1 = 56 ac A 5 = 216 ac A 3 = 136 ac STEP #4: CALCULATE THE AVERAGE RAINFALL P avg = [ (W i x P i )] / W i P avg = [(65x1.81)+(150x2.15)+(269x2.26)+ (216x2.18)+(56x1.62)+(136x1.8)] / [ ] P avg = 2.08 in. Mean Annual Rainfall in inches with the longitude parallels 98 o and 100 o 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 T- year 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. 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 mi 2 ) Duration of 5 minutes to 24 hours Large watersheds (over 100 mi 2 ) 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 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 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 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.) Given: Annual Precipitation Los Angles, CA 1934 to 1953 (Example 2.5 text) Year Rain (in.) Rank (n) 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 Rain (in.) Rank (n) Plotting Position (Fa) 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 x- axis 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.
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