Hydrograph Modeling

1. Hydrograph Modeling Goal: Simulate the shape of a hydrograph given a known or designed water input (rain or snowmelt)

2. Hydrograph Modeling: The input signal Hyetograph can be A future �design� event What happens in response to a rainstorm of a hypothetical magnitude and duration See http://hdsc.nws.noaa.gov/hdsc/pfds/ A past storm Simulate what happened in the past Can serve as a calibration data set

3. Hydrograph Modeling: The Model What do we do with the input signal? We mathematically manipulate the signal in a way that represents how the watershed actually manipulates the water Q = f(P, landscape properties)

4. Hydrograph Modeling What is a model? What is the purpose of a model? Types of Models Physical http://uwrl.usu.edu/facilities/hydraulics/projects/projects.html Analog Ohm�s law analogous to Darcy�s law Mathematical Equations to represent hydrologic process

5. Types of Mathematical Models Process representation Physically Based Derived from equations representing actual physics of process i.e. energy balance snowmelt models Conceptual Short cuts full physics to capture essential processes Linear reservoir model Empirical/Regression i.e temperature index snowmelt model Stochastic Evaluates historical time series, based on probability Spatial representation Lumped Distributed

6. Hydrograph Modeling Physically Based, distributed

7. Hydrologic ModelingSystems Approach

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9. Transfer Functions 2 Basic steps to rainfall-runoff transfer functions 1. Estimate �losses�. W minus losses = effective precipitation (Weff) (eqns 9-43, 9-44) Determines the volume of streamflow response 2. Distribute Weff in time Gives shape to the hydrograph

10. Transfer Functions General Concept

11. Loss Methods Methods to estimate effective precipitation You have already done it one way�how? However, �

12. Loss Methods Physically-based infiltration equations Chapter 6 Green-ampt, Richards equation, Darcy� Kinematic approximations of infiltration and storage

13. Examples of Transfer Function Models Rational Method (p443) qpk=urCrieffAd No loss method Duration of rainfall is the time of concentration Flood peak only Used for urban watersheds (see table 9-10) SCS Curve Number Estimates losses by surface properties Routes to stream with empirical equations

14. SCS Loss Method SCS curve # (page 445-447) Calculates the VOLUME of effective precipitation based on watershed properties (soils) Assumes that this volume is �lost�

15. SCS Concepts Precipitation (W) is partitioned into 3 fates Vi = initial abstraction = storage that must be satisfied before event flow can begin Vr = retention = W that falls after initial abstraction is satisfied but that does not contribute to event flow Qef = Weff = event flow Method is based on an assumption that there is a relationship between the runoff ratio and the amount of storage that is filled: Vr/ Vmax. = Weff/(W-Vi) where Vmax is the maximum storage capacity of the watershed If Vr = W-Vi-Weff,

16. SCS Concept Assuming Vi = 0.2Vmax (??) Vmax is determined by a Curve Number

17. Curve Number

18. Curve Number Related to Land Use

19. Transfer Function 1. Estimate effective precipitation SCS method gives us Weff 2. Estimate temporal distribution

20. Transfer Function 2. Estimate temporal distribution of effective precipitation Various methods �route� water to stream channel Many are based on a �time of concentration� and many other �rules� SCS method Assumes that the runoff hydrograph is a triangle

21. Transfer Functions Time of concentration equations attempt to relate residence time of water to watershed properties The time it takes water to travel from the hydraulically most distant part of the watershed to the outlet Empically derived, based on watershed properties

22. Transfer Functions 2. Temporal distribution of effective precipitation Unit Hydrograph An X (1,2,3,�) hour unit hydrograph is the characteristic response (hydrograph) of a watershed to a unit volume of effective water input applied at a constant rate for x hours. 1 inch of effective rain in 6 hours produces a 6 hour unit hydrograph

23. Unit Hydrograph The event hydrograph that would result from 1 unit (cm, in,�) of effective precipitation (Weff=1) A watershed has a �characteristic� response This characteristic response is the model

24. Unit Hydrograph How do we Develop the �characteristic response� for the duration of interest � the transfer function ? Empirical � page 451 Synthetic � page 453 How do we Apply the UH?: For a storm of an appropriate duration, simply multiply the y-axis of the unit hydrograph by the depth of the actual storm (this is based convolution integral theory)

25. Unit Hydrograph Apply: For a storm of an appropriate duration, simply multiply the y-axis of the unit hydrograph by the depth of the actual storm. See spreadsheet example Assumes one burst of precipitation during the duration of the storm

26. What if storm comes in multiple bursts? Application of the Convolution Integral Convolves an input time series with a transfer function to produce an output time series

27. Convolution integral in discrete form

28. Unit Hydrograph Many ways to manipulate UH for storms of different durations and intensities S curve, instantaneous� That�s for an engineering hydrology class YOU need to know assumptions of the application

29. Unit Hydrograph How do we derive the characteristic response (unit hydrograph)? Empirical

31. Unit Hydrograph Assumptions Linear response Constant time base

32. Unit Hydrograph Construction of characteristic response by synthetic methods Scores of approaches similar to the SCS hydrograph method where points on the unit hydrograph are estimated from empirical relations to watershed properties. Snyder SCS Clark

33. Snyder Synthetic Unit Hydrograph Since peak flow and time of peak flow are two of the most important parameters characterizing a unit hydrograph, the Snyder method employs factors defining these parameters, 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.

34. SCS Synthetic Unit Hydrograph

35. Synthetic Unit Hydrograph ALL are based on the assumption that runoff is generated by overland flow What does this mean with respect to our discussion about old water � new water? How can Unit Hydrographs, or any model, possibly work if the underlying concepts are incorrect?

36. Other Applications What to do with storms of different durations?

37. Other Applications Deriving the 1-hr UH with the S curve approach