Basic Hydrology & Hydraulics: DES 601 Module 8 Rainfall Distributions

Rainfall distributions Rainfall distributions represent temporal patterns of a storm. A rainfall distribution is also called a hyetograph. Rainfall distributions are used when we need to estimate an entire hydrograph. Module 8

Rainfall distributions Each “block” represents the amount of rainfall for the time interval The diagram is called “incremental” rainfall The running sum of the blocks is the cumulative distribution Module 8

Rainfall distributions Distributions are created from historical storms and analyzed to generate statistical models of rainfall – these models are called design storms. Design storm distributions are typically dimensionless hyetographs NRCS Type Storms Empirical Texas Hyetographs Module 8

SCS Rainfall Type Curves SCS(1973) analyzed DDF curves to develop dimensionless rainfall temporal patterns called type curves for four different regions in the US. SCS type curves are in the form of percentage mass (cumulative) curves based on 24-hr rainfall of the desired frequency. Intended for use with the SCS Curve Number runoff generation model! Module 8

SCS Rainfall Type Curves Location selects the Type Curve Module 8

SCS Rainfall Type Curves The 24-hour precipitation depth of desired frequency is specified (DDF Atlas), the SCS type curve is rescaled (multiplied by the known number) to get the time distribution. Module 8

Rainfall distributions Module 8

SCS Rainfall Type Curves Using the Type Curves Use DDF Atlas, TP-40, etc. to set total depth, P for the 24 hour storm. Pick appropriate SCS type curve (location). Multiply (rescale) the type curve with P to get the design mass curve. Get the incremental precipitation from the rescaled mass curve to develop the design hyetograph. Module 8

Example: Generate SCS Design Storm Generate a design hyetograph for a 25-year, 24-hour duration SCS Type-III storm in Harris County using a one-hour time increments Look up 24-hour,25-year depth for Harris County in the DDF Atlas. Cumulative fraction - interpolate SCS table Cumulative rainfall = product of cumulative fraction * total 24-hour rainfall (10.01 in) Incremental rainfall = difference between current and preceding cumulative rainfall Module 8

Example: Generate SCS Design Storm Look up 24-hour,25-year depth for Harris County in the DDF Atlas. P ~ 10 inches Module 8

Example: Generate SCS Design Storm SCS Tabulation DDF Atlas Module 8

Exercise: Generate SCS Design Storm Generate a 24-hour,2-year SCS Design storm for Bexar County. Use DDF Curve already created for Bexar County. Select the appropriate Type Curve (Type II or III). Multiply the depth for 24-hour by the cumulative values in the SCS Tabulation. Difference the values to obtain incremental hourly depths. Module 8

Texas Empirical Hyetographs Alternative to SCS Type Curves is the Texas Empirical Hyetographs Based on Texas data. Reflects “front loading” observed in many real storms. Rescales time and depth. Module 8

Texas Empirical Hyetographs Rescale Depth Average Intensity Rescale Time Module 8

Texas Empirical Hyetographs Use the 50th percentile curve (median storm). Multiply the time axis by the storm duration. Multiply the depth axis by the storm depth. Result is a design storm for given duration and AEP. Module 8

Example: Texas Empirical Hyetographs Construct a design storm for the 3-hour, 2-year rainfall in Harris County using the Texas Empirical Hyetograph Obtain the depth from the DDF Atlas Rescale the depth and time using the Texas Empirical Hyetograph Module 8

Example: Texas Empirical Hyetographs 2.6 inches 1.3 inches 0 hours 3 hours 1 hours 2 hours Module 8

Example: Texas Empirical Hyetographs Probably easier to use the tabulation SIR-2004-5075 Module 8

Rainfall Distributions These distributions are used in the unit hydrograph methodology to specify a sequence of inputs, each of which generates a response These responses are then superimposed in time to generate a runoff hydrograph The “time-step” (block width) needs to be consistent with the UH duration to produce results without “aliasing” Module 8

Loss models A loss model represents all of the processes that abstract or remove water from the gross rainfall volume. What remains after losses is what runs off- “EXCESS rainfall”. Losses are a function of TIME Loss models are often confused with infiltration models. They are not the same thing. Infiltration is a component of losses, but alone does not account for all observed losses. Module 8

Infiltration models commonly incorporated into loss models Horton’s equation- empirical exponential decay-type model. Usually parameterized by infiltrometer data Green-Ampt- theoretically based decay model. Usually parameterized from physical characteristics of soil, as represented in tables. Module 8

Loss Models Basin loss models in the HDM include: Initial and Constant rate loss NRCS Curve Number Green-Ampt Table 4-29 in HDM provides use guidance Loss Module 8

Basin response models Basin response models include unit hydrograph models documented in the HDM including: Snyder NRCS DUH Combined with routing the collective “model” is called a rainfall-runoff model Module 8

Timing Strictly speaking, each unit hydrograph has a particular duration associated with it. That duration must coincide with the time step size used in discrete aggregation. Each watershed has a characteristic response time Module 8

Timing The time step size for aggregation must the same as the duration, and the time-to-peak for the watershed must be an integer multiple of that value. The time-to-peak of the watershed is related to physical characteristics of the watershed- contributing area, slope, etc. Module 8

Estimating Timing The HDM presents several methods to estimate the characteristic time among these are: Kerby-Kirpich Snyder’s Unit Hydrograph Time of Concentration Module 8

Time of concentration Time of concentration, tc = ∑L/V, where L is flow segment length and V is flow segment velocity. tc = toverland + tchannel flow Estimate tchannel flow with Manning’s eqn. Assume discharge Compute velocity Measure distance Compute travel time Estimate toverland from TxDOT HDM Module 8

TxDOT HDM overland flow velocity Module 8

Time of concentration Kerby Equation for Overland Flow Can be used in smaller watersheds where overland flow is a substantial component of overall travel time. Overland flow length can be up to 1200’ Tc = K(LxN)0.467S-0.235 where: K = 0.828 (English units conversion coefficient) L = overland flow distance, in ft. N = Retardance Coefficient S = slope of overland flow path, ft/ft Module 8

Kerby Retardance Coefficient Time of concentration Kerby Retardance Coefficient Generalized Terrain Condition Dimensionless Retardance Coefficient (N) Pavement .02 Smooth, bare, packed soil .10 Poor grass, cultivated row crops, or moderately rough packed surfaces .20 Pasture, average grass .40 Deciduous forest .60 Dense grass, coniferous forest, or deciduous forest with deep litter .80 Module 8

Time of concentration Kirpich Equation for Channelized Flow Tc = KL0.770S-0.385 where: K = 0.0078 (English units conversion coefficient) L = overland flow distance, in ft. S = channel slope, ft/ft Module 8

Time of concentration Alternate “ballpark” method – applicable for preliminary design or as a reasonableness check of other methods: Tc = A0.5 where Tc = Time of Concentration, in hours A = Contributing watershed area in square miles. Module 8

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Summary The time step size for aggregation must the same as the duration, and the time-to-peak for the watershed must be an integer multiple of that value. The time-to-peak of the watershed is related to physical characteristics of the watershed- contributing area, slope, etc. Module 8