Presentation on theme: "Hyetographs and Hydrographs"— Presentation transcript:
1 Hyetographs and Hydrographs CE 3372 – Lecture 11With slides adapted from:
2 Outline Understand where rainfall data comes from Know how to develop rainfall data through hyetographsBe able to generate a synthetic hydrographDifference in UH and regular HydrographHyetograph is either incremental or cumulative (Precipitation (in) vs. time)
3 Time of Concentration Sheet Flow – Overland Flow Shallow Concentrated FlowChannel Flow
7 PrecipitationAll forms of water that reach the earth from the atmosphere is called precipitationRainfall, snowfall, frost, hail, dewRainfall is the main form of precipitation and is used synonymously with precipitationIn H&H rainfall and precip is used interchangably.The problem with rainfall is that it can fall at any time or place – temporal and spatial variationTemporal variation may be defined as hourly, daily, monthly, seasonal variationWe have to measure rainfall in order to create some form of accurate data that we can use to calculate volume of rainfall so we know how much to store for.However almost ALL of the rainfall data that you use is NOT from a gauge, gauges are spread out.
8 Rain Gauges 1. Non recording gauge Precipitation gauge 1-pole 2-collector3-support- galvanized metal sheet4-funnel5-steel ring1. Non recording gauge
9 Rain Gauges 2. Recording gauge It allows continuous measurement of the rainfall.The graphic rain gauge1-receiver2-floater3-siphon4-recording needle 5-drum with diagram6-clock mechanism2. Recording gauge
10 3. Tele-rain gauge with tilting baskets Rain GaugesThe tele-rain gauge is used to transmit measurements of precipitation through electric or radio signals.1 - collecting funnel2 - tilting baskets3 - electric signal4 - evacuationThe sensor device consists of a system with two tilting baskets, which fill alternatively with water from the collecting funnel, establishing the electric contact.The number of tilting is proportional to the quantity of precipitation hp3. Tele-rain gauge with tilting baskets
11 Rain GaugesThe meteorological radar is a powerful instrument for measuring with a good degree of accuracy:area extentLocationmovement of rainstormamount of rainfallThe radar emits a regular succession of pulse of electromagnetic radiation in a narrow beam so that when the raindrops intercept a radar beam, its intensity can easily be known.4. Radars
12 Rain Gauges World Meteorological Organization (WMO) recommendation: In flat regions of temperate, Mediterranean and tropical zonesIdeal 1 station for 600 – 900 km2Acceptable 1 station for 900 – 3000 km2In mountainous regions of temperate , Mediterranean and tropical zonesIdeal 1 station for 100 – 250 km2Acceptable 1 station for 250 – 1000 km2In arid and polar zone1 station for 1500 – 10,000 km2
13 Rain GaugesBefore using rainfall data, it is necessary to check the data for continuing and consistencymissing datarecord errorsRain gauges rainfall represent only point sampling of the areal distribution of a stormTo convert the point rainfall values at various stations to an average value over the area:arithmetic meanThiessen polygonsisohyets method
15 Thiessen PolygonsAttributes to each station an “influence zone” which are represented by convex polygons.Polygons are obtained by connecting perpendicular line across the middle of the link lines which link each station to the closest neighboring stations
18 Isohyetal Method Pn – the values of the isohytes ai – are the inter isohytes area respectivelyA – the total catchment area– the mean precipitation over the catchmentAn isohyet is a line joining points of equal rainfall magnitude. Similar to contour linesThe isohyet method is superior to the other two methods (especially when the stations are large in number)
19 10.08Da56C129.212a4a37.0B47.2AEa210.0So these are 3 methods of how to get precipitation. Now what happens if the place we’re designing for doesn’t have the rainfall data for the specific design storm and duration that we need?You can generate rainfall data based on SCS design storm and empirical hyetographs9.14.0a1a1F864
20 HyetographsThis is hella important!!! You need to understand how to use rainfall data!
21 Hyetographs Graphical representation of depth or intensity vs time So for this rainfall it started off drizzling, had a giant thunderstorm, drizzled, a storm, and ligh rain throughoutWE have an agreement from here on out, whenever we refer to precipitation/depth/intensity, it’s over the entire area. Runoff volume = total runoff * drainage area (this seems to be what we need right? Wrong I’ll explain why later)1” of excess rain over 1 acre represents 3,630 cubic feet = 27,154 gallonsThe AREA under the hyetograph Represents TOTAL amount of precipitation dropped by the storm over its duration by : sum total inches or sum (intensity*time intervals)Incremental
22 Hyetographs Incremental Cumulative You get the cumulative depth just by continually adding. And vice versaSo technically what do the slopes represent?? If I drew a cumulative that didn’t have a slopeThe AREA under the hyetograph Represents TOTAL amount of precipitation dropped by the storm over its duration by : sum total inches or sum (intensity*time intervals)IncrementalCumulative
23 Hyetographs Excess rainfall = observed rainfall – abstractions Abstractions/losses – difference between total rainfall hyetograph and excess rainfall hyetographAbstraction rainfall lostevaporationinfiltrationdepression storageExcess------rainfall which runs off (this is what we’re concerned with)phi-index: Constant rate of abstraction yielding excess rainfall hyetograph with depth equal to depth of direct runoffUsed to compute excess rainfall hyetograph when observed rainfall and streamflow data are availableWhat if you don’t have rainfall data for the specific storm youre designing for?To design urban storm water infrastructures, hydrologists apply the SCS Type I and II 24-hr rainfall distribution curves to create various rainfall hyetographs by which storm runoff can be predicted accordingly.
25 SCS Hyetograph MethodSCS type curves are in the form of percentage mass (cumulative) curves based on 24-hr rainfall of the desired frequency.If a single precipitation depth of desired frequency is known, the SCS type curve is rescaled (multiply by the known number) to get the time distributionAka dimensionless mass curve methodNote that diff curves per region ONLY USA. But MOST commonAnd they’re dimensionless fractions that someone who studied tons of observed rainfall across USA created these and said this is how rain usually falls, a little, a lot then thins out againThe SCS method (1973) presents the 24-hr Type I, IA, II, and IIA rainfall time distributions for runoff predictions.
26 SCS type curves for Texas (II&III) SCS 24-Hour Rainfall DistributionsT (hrs)Fraction of 24-hr rainfallType IIType III0.00.00011.50.2830.2981.00.0110.01011.80.3570.3392.00.0220.02012.00.6630.5003.00.0340.03112.50.7350.7024.00.0480.04313.00.7720.7515.00.0630.05713.50.7990.7856.00.0800.07214.00.8200.8117.00.0980.08915.00.8548.00.1200.11516.00.8800.8868.50.1330.13017.00.9030.9109.00.1470.14818.00.9220.9289.50.1630.16719.00.9380.9439.80.1720.17820.00.9520.95710.00.1810.18921.00.9640.96910.50.2040.21622.00.9760.98111.00.2350.25023.00.9880.99124.01.000So at time _ , it rains this fraction of rain.
27 SCS Method StepsDetermine Pd for 24-hr storm (from DDF/IDF curves or equations)Pick a SCS type curve based on location – obtain the cumulative fractionCalculate the cumulative rainfall = cumulative fraction * 24hrCalculate the incremental precipitation from the curve to develop the design hyetograph = current – preceding cumulative rainfall
28 Example – SCS Hyetograph Find - rainfall hyetograph for a 25-year, 24-hour duration SCS Type-III storm in Harris County using a one-hour time incrementwhere a = 81, b = 7.7, c = (from Tx-DOT hydraulic manual)Step 1
29 Example – SCS Hyetograph Easy way to find intensities: EBDLKUP.xlsxA 24-hour, 25-year design storm for Harris County, TexasIntensity = inches
30 Example – SCS Hyetograph Step 2/3Cumulative fraction - interpolate SCS tableCumulative rainfall = cumulative fraction * total depth at 24-hour rainfall (10.01 in)Incremental rainfall = difference between current and preceding cumulative rainfallStep 4
31 Triangular Hyetograph Method TimeRainfall intensity, ihtatbTdTd: hyetograph base length = precipitation durationta: time before the peakr: storm advancement coefficient = ta/Tdtb: recession time = Td – ta = (1-r)TdGiven Td and frequency/T, find the design hyetographCompute P/i (from DDF/IDF curves or equations)Use equations to get ta, tb, Td and h (r is available for various locations)
32 Example - Triangular Hyetograph Find - rainfall hyetograph for a 25-year, 6-hour duration in Harris County. Use storm advancement coefficient of 0.5.3 hr3 hrRainfall intensity, in/hr2.246 hrTime
33 Alternating Block/IDF Method Given Td and T/frequency, develop a hyetograph in dt incrementsUsing T, find i for dt, 2dt, 3dt,…ndt Use the IDF curves for the specified locationUsing i compute P for dt, 2dt, 3dt,…ndt. This gives cumulative P.Compute incremental precipitation from cumulative P.Pick the highest incremental precipitation (maximum block) and place it in the middle of the hyetograph. Pick the second highest block and place it to the right of the maximum block, pick the third highest block and place it to the left of the maximum block, etc.
34 Example - Alternating Block Method Find: Design precipitation hyetograph for a 2-hour storm (in 10 minute increments) in Denver with a 10-year return period 10-minute
35 Empirical HyetographDimensionless Hyetograph is parameterized to generate an input hyetograph thats 24 hours long and produces the 25- year depth.For this example, will use the median (50th percentile) curve0 – 9.5 inches0 – 24 hours
36 Example – Empirical Hyetograph Find - rainfall hyetograph for a 25-year, 24-hour in Harris County using a one-hour time incrementStep 1
37 Use tabular values for the 50th percentile (similar to the fraction type curves) This column scales TIME This column scales DEPTH (as a percentage!)
40 Hydrograph Graph – Flow at the Outlet vs. Time Assumptions How discharge changes over time ( min, hours, years,decade etc.)EXPLAIN that it’s the volume of flow to the outlet.So you couldn’t use volumes from hyetographs to design because, the actual volumes of rain changes as it flows through the land, out the outlet.Area under the hydrograph represents a volume of water (total volume of rainfall that fell on the basin and appeared as runoff)Saw video that rain accumulates and then tapers. Peak of the hydrograph is the max flowsONLY EXCESS, not infiltration and evap.Can be used to derive runoff from any excess rainfall on the watershed.AssumptionsExcess rainfall has constant intensity during durationExcess rainfall is uniformly distributed on watershed
41 Hydrographs Shape of Hydrograph represents basin characteristics Area Stream patternSlopesLand roughnessInfiltration rates
43 Hydrograph Lag Time (L) Time to Peak (Tp) Rainfall Duration Time interval from the center of mass of the rainfall-excess to the peak of the hydrographTime to Peak (Tp)Time interval from the start of the rainfall- excess to the peak of the hydrographRainfall DurationTime interval from the start to the end of rainfall-excessTime of Concentration (tc)Time interval from the end of the rainfall- excess to the point of inflection on the hydrograph recession curveTime required for runoff to travel from the hydraulically most distant point on the watershed to the point of interest
44 Watersheds response to a given amount of excess precipitation is just a multiplier of the unit hydrographUse unit hydrograph as a basis to determine the storm hydrograph from any given rainfall distributionThe hydrograph of direct runoff that results from 1-inch (or 1 unit) of excess precipitation spread uniformly in space and time over a watershed for a given duration.
45 Unit Hydrograph Assumptions If the area under the hydrograph represents 1 unit of rainfall-excess over the entire drainage basin then the hydrograph is called a UNIT hydrographAssume that identical rainfalls with the same antecedent conditions produce identical hydrographsThe time bases of all hydrograph from rainfalls of the same duration with the same antecedent conditions are equalSimilar to using empirical/type curves with hyetographs
46 UH – Superposition Example Superposition: If the storm duration is the same, the hydrograph of a 2inch storm is twice the amount of a 1inch storm.
47 UH – ExampleAfter a 2-hour storm, a station downstream from a 45 square mile drainage basin measures 9400 cfs as a peak discharge and 3300 acre-feet as total runoff.a) Find the 2-hour unit hydrograph peak discharge.b) What would be the peak runoff and design flood volume if a 2-hour storm dropped 2.5 inches of net precipitation?
48 UH – Example a) Find the 2-hour unit hydrograph peak discharge. Find volume of runoff which represents 1 inch of excess runoff over the 45 square mile drainage area45 square miles * 1 inch = 2400 acre-ftActual measured 3,300 acre-ft > 2400 acre-ft for inch of runoff
49 UH – Example a) Find the 2-hour unit hydrograph peak discharge. The ratio of 3300/2400=1.375; the storm had inches of excess runoffIf the peak discharge is 9400 cfs for a runoff of inches then the ratio of the peak discharge of the unit hydrograph must be:2400/3300 (or 1/1.375) = 0.727Peak discharge=0.727*9400 = 6,800 cfs
50 UH – Exampleb) What would be the peak runoff and design flood volume if a 2-hour storm dropped 2.5 inches of net precipitation?Once you know the peak flow and runoff volume that represents 1 inch of excess rainfall, then you just use ratios:2.5*6,800 cfs= 17,000 cfs2.5*2400 acre-ft = 6,000 acre-ft
51 Methods of Developing Hydrographs From Streamflow Data (not typical)SyntheticallySnyderSCSClarks“Fitted” Distributions
52 Snyder MethodSnyder method employs factors defining peak flow and time to peak flow, which are then used in the synthesis of the unit graph (Snyder, 1938).The parameters are Cp, the peak flow factor, and Ct, the lag factor.The basic assumption in this method is that basins which have similar physiographic characteristics are located in the same area will have similar values of Ct and Cp.Therefore, for ungaged basins, it is preferred that the basin be near or similar to gaged basins for which these coefficients can be determined.Doesn’t need rainfall-runoff data
53 Snyder Equations https://www.youtube.com/watch?v=CEUSiVH2Ieg A synthetic unit hydrograph is derived from theory and experience, and its purpose is to simulate basin diffusion by estimating the basin lag based on a certain formula or procedure.The first synthetic unit hydrograph was developed by Snyder in In order to provide sufficient flexibility for simulating a wide range of diffusion amounts, Snyder devised two parameters: (1) a time parameter Ct, and (2) a peak parameter Cp. A larger Ct meant a greater basin lag and, consequently, greater diffusion. A larger Cp meant a greater peak flow and, consequently, less diffusion.
54 Snyder ShapeThe final shape of the Snyder unit hydrograph is controlled by the equations for width at 50% and 75% of the peak of the UHG:
55 NRCS (SCS) Method A is the drainage area in square miles Q is the runoff volume in inchesTp is the time to peak in hours, andqp is the peak flow rate in cfs.484 Comes from the initial assumption that 3/8 of the volume under the UHG is under the rising limb and the remaining 5/8 is under the recession limb.To use the SCS DUH, we need to determine only two things:1. Time to peak, Tp (hr), and2. Peak discharge, qp (cfs).
56 NRCS (SCS) MethodTo use the SCS DUH, we need to determine only two things:1. Time to peak, Tp (hr), and2. Peak discharge, qp (cfs).Tp=(D/2)+TlTl is the lag time (hr)D = duration of the rainfall (hr)The DUH has point of inflection located at approximately 1.7Tp. So, using our relation of Tl=0.6*Tc, we can compute D as:D = 0.2*Tp or D = 0.133*Tc.Small variation in D is ok, but it should not exceed 0.25Tp or 0.17Tc.
57 The peak discharge can be determined as follows: qp=(484*A)/Tp, which is same as the equation shown previously, but with Q = 1.0 inch for the unit hydrograph.If you need to determine the discharge for any other runoff volume, you can multiply the qp with appropriate runoff depth, Q (in).Once we determine Tp and qp, we can calculate D-hr unit hydrograph for our drainage area of interest using following co-ordinates:
60 SCS dimensionless hydrograph Synthetic UH in which the discharge is expressed by the ratio of q to qp and time by the ratio of t to TpIf peak discharge and lag time are known, UH can be estimated.Tc: time of concentrationC = 2.08 (483.4 in English system)A: drainage area in km2 (mi2)
61 Ex. 7.7.3 Construct a 10-min SCS UH. A = 3.0 km2 and Tc = 1.25 h q7.49 m3/s.cmMultiply y-axis of SCS hydrograph by qp and x-axis by Tp to get the required UH, or construct a triangular UHt2.22 h
62 Clark UH Method Based on the use of time-area method. Concept of instantaneous unit hydrograph (IUH)
63 Time-AreaSynthetic time-area curve - The U.S. Army Corps of Engineers (HEC 1990)
64 Hypothetical ExampleA 190 mi2 watershed is divided into 8 isochrones of travel time.The linear reservoir routing coefficient, R, estimated as 5.5 hours.A time interval of 2.0 hours will be used for the computations.
65 Basin BreakdownThe linear reservoir routing coefficient can be estimated as approximately 0.75 times the time of concentration.
68 Instantaneous UHGDt = the time step used n the calculation of the translation unit hydrographThe final unit hydrograph may be found by averaging 2 instantaneous unit hydrographs that are a Dt time step apart.