Hyetographs and Hydrographs CE 3372 – Lecture 11 With slides adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

Outline Understand where rainfall data comes from Know how to develop rainfall data through hyetographs Be able to generate a synthetic hydrograph Difference in UH and regular Hydrograph Hyetograph is either incremental or cumulative (Precipitation (in) vs. time)

Time of Concentration Sheet Flow – Overland Flow Shallow Concentrated Flow Channel Flow

Sheet Flow Precipitation Sheet Flow Sheet flow Infiltration

Sheet Flow Sheet Flow Sheet flow Infiltration L ???

Shallow Concentrated Flow

Precipitation All forms of water that reach the earth from the atmosphere is called precipitation Rainfall, snowfall, frost, hail, dew Rainfall is the main form of precipitation and is used synonymously with precipitation In 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 variation Temporal variation may be defined as hourly, daily, monthly, seasonal variation We 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.

Rain Gauges 1. Non recording gauge Precipitation gauge 1-pole 2-collector 3-support- galvanized metal sheet 4-funnel 5-steel ring 1. Non recording gauge

Rain Gauges 2. Recording gauge It allows continuous measurement of the rainfall. The graphic rain gauge 1-receiver 2-floater 3-siphon 4-recording needle 5-drum with diagram 6-clock mechanism 2. Recording gauge

3. Tele-rain gauge with tilting baskets Rain Gauges The tele-rain gauge is used to transmit measurements of precipitation through electric or radio signals. 1 - collecting funnel 2 - tilting baskets 3 - electric signal 4 - evacuation The 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 hp 3. Tele-rain gauge with tilting baskets

Rain Gauges The meteorological radar is a powerful instrument for measuring with a good degree of accuracy: area extent Location movement of rainstorm amount of rainfall The 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

Rain Gauges World Meteorological Organization (WMO) recommendation: In flat regions of temperate, Mediterranean and tropical zones Ideal  1 station for 600 – 900 km2 Acceptable 1 station for 900 – 3000 km2 In mountainous regions of temperate , Mediterranean and tropical zones Ideal  1 station for 100 – 250 km2 Acceptable  1 station for 250 – 1000 km2 In arid and polar zone 1 station for 1500 – 10,000 km2

Rain Gauges Before using rainfall data, it is necessary to check the data for continuing and consistency missing data record errors Rain gauges rainfall represent only point sampling of the areal distribution of a storm To convert the point rainfall values at various stations to an average value over the area: arithmetic mean Thiessen polygons isohyets method

Arithmetic Mean

Thiessen Polygons Attributes 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

P7 P6 A7 A6 P2 A2 A1 A8 A5 P1 P8 P5 A4 A3 P3 P4

Isohyetal Method Pn – the values of the isohytes ai – are the inter isohytes area respectively A – the total catchment area – the mean precipitation over the catchment An isohyet is a line joining points of equal rainfall magnitude. Similar to contour lines The isohyet method is superior to the other two methods (especially when the stations are large in number)

10.0 8 D a5 6 C 12 9.2 12 a4 a3 7.0 B 4 7.2 A E a2 10.0 So 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 hyetographs 9.1 4.0 a1 a1 F 8 6 4

Hyetographs This is hella important!!! You need to understand how to use rainfall data!

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 throughout WE 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 gallons The 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

Hyetographs Incremental Cumulative You get the cumulative depth just by continually adding. And vice versa So technically what do the slopes represent?? If I drew a cumulative that didn’t have a slope The 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 Cumulative

Hyetographs Excess rainfall = observed rainfall – abstractions Abstractions/losses – difference between total rainfall hyetograph and excess rainfall hyetograph Abstraction--------rainfall lost evaporation infiltration depression storage Excess------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 runoff Used to compute excess rainfall hyetograph when observed rainfall and streamflow data are available What 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.

Hyetograph Methods SCS Method Triangular IDF relationships Empirical Hyetographs (Texas specific)

SCS Hyetograph Method SCS 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 distribution Aka dimensionless mass curve method Note that diff curves per region ONLY USA. But MOST common And 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 again The SCS method (1973) presents the 24-hr Type I, IA, II, and IIA rainfall time distributions for runoff predictions.

SCS type curves for Texas (II&III) SCS 24-Hour Rainfall Distributions T (hrs) Fraction of 24-hr rainfall Type II Type III 0.0 0.000 11.5 0.283 0.298 1.0 0.011 0.010 11.8 0.357 0.339 2.0 0.022 0.020 12.0 0.663 0.500 3.0 0.034 0.031 12.5 0.735 0.702 4.0 0.048 0.043 13.0 0.772 0.751 5.0 0.063 0.057 13.5 0.799 0.785 6.0 0.080 0.072 14.0 0.820 0.811 7.0 0.098 0.089 15.0 0.854 8.0 0.120 0.115 16.0 0.880 0.886 8.5 0.133 0.130 17.0 0.903 0.910 9.0 0.147 0.148 18.0 0.922 0.928 9.5 0.163 0.167 19.0 0.938 0.943 9.8 0.172 0.178 20.0 0.952 0.957 10.0 0.181 0.189 21.0 0.964 0.969 10.5 0.204 0.216 22.0 0.976 0.981 11.0 0.235 0.250 23.0 0.988 0.991 24.0 1.000 So at time _ , it rains this fraction of rain.

SCS Method Steps Determine Pd for 24-hr storm (from DDF/IDF curves or equations) Pick a SCS type curve based on location – obtain the cumulative fraction Calculate the cumulative rainfall = cumulative fraction * depth @ 24hr Calculate the incremental precipitation from the curve to develop the design hyetograph = current – preceding cumulative rainfall

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 increment where a = 81, b = 7.7, c = 0.724 (from Tx-DOT hydraulic manual) Step 1

Example – SCS Hyetograph Easy way to find intensities: EBDLKUP.xlsx A 24-hour, 25-year design storm for Harris County, Texas Intensity = 10.01 inches

Example – SCS Hyetograph Step 2/3 Cumulative fraction - interpolate SCS table Cumulative rainfall = cumulative fraction * total depth at 24-hour rainfall (10.01 in) Incremental rainfall = difference between current and preceding cumulative rainfall Step 4

Triangular Hyetograph Method Time Rainfall intensity, i h ta tb Td Td: hyetograph base length = precipitation duration ta: time before the peak r: storm advancement coefficient = ta/Td tb: recession time = Td – ta = (1-r)Td Given Td and frequency/T, find the design hyetograph Compute P/i (from DDF/IDF curves or equations) Use equations to get ta, tb, Td and h (r is available for various locations)

Example - Triangular Hyetograph Find - rainfall hyetograph for a 25-year, 6-hour duration in Harris County. Use storm advancement coefficient of 0.5. 3 hr 3 hr Rainfall intensity, in/hr 2.24 6 hr Time

Alternating Block/IDF Method Given Td and T/frequency, develop a hyetograph in dt increments Using T, find i for dt, 2dt, 3dt,…ndt Use the IDF curves for the specified location Using 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.

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

Empirical Hyetograph Dimensionless 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) curve 0 – 9.5 inches 0 – 24 hours

Example – Empirical Hyetograph Find - rainfall hyetograph for a 25-year, 24-hour in Harris County using a one-hour time increment Step 1

Use tabular values for the 50th percentile (similar to the fraction type curves) This column scales TIME This column scales DEPTH (as a percentage!)

Example – Emp. Hyet.

Hydrographs Using DDF Atlas, ~9-10= 9.5 inches

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 flows ONLY EXCESS, not infiltration and evap. Can be used to derive runoff from any excess rainfall on the watershed. Assumptions Excess rainfall has constant intensity during duration Excess rainfall is uniformly distributed on watershed

Hydrographs Shape of Hydrograph represents basin characteristics Area Stream pattern Slopes Land roughness Infiltration rates

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 hydrograph Time to Peak (Tp) Time interval from the start of the rainfall- excess to the peak of the hydrograph Rainfall Duration Time interval from the start to the end of rainfall-excess Time of Concentration (tc) Time interval from the end of the rainfall- excess to the point of inflection on the hydrograph recession curve Time required for runoff to travel from the hydraulically most distant point on the watershed to the point of interest

Watersheds response to a given amount of excess precipitation is just a multiplier of the unit hydrograph Use unit hydrograph as a basis to determine the storm hydrograph from any given rainfall distribution The 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.

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 hydrograph Assume that identical rainfalls with the same antecedent conditions produce identical hydrographs The time bases of all hydrograph from rainfalls of the same duration with the same antecedent conditions are equal Similar to using empirical/type curves with hyetographs

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.

UH – Example After 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?

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 area 45 square miles * 1 inch = 2400 acre-ft Actual measured 3,300 acre-ft > 2400 acre-ft for 1 inch of runoff

UH – Example a) Find the 2-hour unit hydrograph peak discharge. The ratio of 3300/2400=1.375; the storm had 1.375 inches of excess runoff If the peak discharge is 9400 cfs for a runoff of 1.375 inches then the ratio of the peak discharge of the unit hydrograph must be: 2400/3300 (or 1/1.375) = 0.727 Peak discharge=0.727*9400 = 6,800 cfs

UH – Example b) 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 cfs 2.5*2400 acre-ft = 6,000 acre-ft

Methods of Developing Hydrographs From Streamflow Data (not typical) Synthetically Snyder SCS Clarks “Fitted” Distributions

Snyder Method Snyder 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

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 1938.1 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. https://www.youtube.com/watch?v=CEUSiVH2Ieg

Snyder Shape The final shape of the Snyder unit hydrograph is controlled by the equations for width at 50% and 75% of the peak of the UHG:

NRCS (SCS) Method A is the drainage area in square miles Q is the runoff volume in inches Tp is the time to peak in hours, and qp 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), and 2. Peak discharge, qp (cfs).

NRCS (SCS) Method To use the SCS DUH, we need to determine only two things: 1. Time to peak, Tp (hr), and 2. Peak discharge, qp (cfs). Tp=(D/2)+Tl Tl 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.

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:

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 Tp If peak discharge and lag time are known, UH can be estimated. Tc: time of concentration C = 2.08 (483.4 in English system) A: drainage area in km2 (mi2)

Ex. 7.7.3 Construct a 10-min SCS UH. A = 3.0 km2 and Tc = 1.25 h q 7.49 m3/s.cm Multiply y-axis of SCS hydrograph by qp and x-axis by Tp to get the required UH, or construct a triangular UH t 2.22 h

Clark UH Method Based on the use of time-area method. Concept of instantaneous unit hydrograph (IUH)

Time-Area Synthetic time-area curve - The U.S. Army Corps of Engineers (HEC 1990)

Hypothetical Example A 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.

Basin Breakdown The linear reservoir routing coefficient can be estimated as approximately 0.75 times the time of concentration.

Incremental Area

Cumulative Time-Area Curve

Instantaneous UHG Dt = the time step used n the calculation of the translation unit hydrograph The final unit hydrograph may be found by averaging 2 instantaneous unit hydrographs that are a Dt time step apart.

Computations

Incremental Areas

Incremental Flows

Instantaneous UHG

Lag & Average