Basic Hydrology: Rainfall-runoff based methods – II

Rainfall distributions Rainfall distributions represent temporal patterns of a storm. Rainfall distributions are presented as a cumulative curve (accumulated depth versus time), or as an incremental curve (depth for a time interval versus time) A rainfall distribution is also called a hyetograph

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

Rainfall distributions Distributions can be created from historical storms for analysis Design storm distributions are typically dimensionless hyetographs NRCS Type Storms Empirical Texas Hyetographs

Rainfall distributions SCS(1973) analyzed DDF 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.

Rainfall distributions If a single 24-hour precipitation depth of desired frequency is known, the SCS type curve is rescaled (multiplied by the known number) to get the time distribution.

Rainfall distributions For durations less than 24 hr, the steepest part of the type curve for required duration is used (i.e. 6-hour as shown) 1.0 Fractional Depth 0.0 6 hours

Rainfall distributions

Rainfall distributions Given duration (Td) and AEP, construct a design hyetograph Use DDF Atlas, TP-40, to set total depth for the duration Pick appropriate SCS type curve (location) If Td = 24 hour, multiply (rescale) the type curve with P to get the design mass curve If Td is less than 24 hr, pick the steepest part of the type curve for rescaling Get the incremental precipitation from the rescaled mass curve to develop the design hyetograph

Rainfall distributions Example Rainfall hyetograph for a 25-year, 24-hour duration SCS Type-III storm in Harris County using a one-hour time increment a = 81, b = 7.7, c = 0.724 (from EBDLKUP) 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

Rainfall distributions If a hyetograph for less than 24 needs to be prepared, pick time intervals that include the steepest part of the type curve (to capture peak rainfall). For 3-hr pick 11 to 13, 6-hr pick 9 to 14 and so on.

Rainfall distributions Dimensionless Hyetograph is parameterized to generate an input hyetograph Process is similar Estimate depth Rescale plot in magnitude and time Rescale Depth Average Intensity Rescale Time

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”

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.

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.

Loss Models Basin loss models in the HDM include: Initial and Constant rate loss NRCS Curve Number Green-Ampt (in HDM it is called a loss model) Table 4-29 in HDM provides use guidance Loss

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

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

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.

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

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 with figs. from TxDOT HDM (see pages that follow)

TxDOT HDM overland flow velocity

Time of concentration Kerby-Kirpich Method Combines Kerby overland method with Kirpich channel flow method Will be incorporated into TxDOT HDM with next update

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

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

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

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.

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.