1. Lecture 14 - 1 ERS 482/682 (Fall 2002) Rainfall-runoff modeling ERS 482/682 Small Watershed Hydrology

2. Lecture 14 - 2 ERS 482/682 (Fall 2002) What are models? A model is a conceptualization of a system response external stimuli –In hydrology, this usually involves the response of a system to an external stimuli runoff(discharge) rainfall

3. Lecture 14 - 3 ERS 482/682 (Fall 2002) What are models? A model is a conceptualization of a system response external stimuli –In hydrology, this usually involves the response of a system to an external stimuli Models are tools that are part of an overall management process

4. Lecture 14 - 4 ERS 482/682 (Fall 2002) Management objectives, options, constraints Model development and application Make management decisions Data collection

5. Lecture 14 - 5 ERS 482/682 (Fall 2002) Why model? Systems are complex http://water.usgs.gov/outreach/OutReach.html

6. Lecture 14 - 6 ERS 482/682 (Fall 2002) Why model? Systems are complex If used properly, can enhance knowledge of a system Models should be built on scientific knowledge Models should be used as ‘tools’

7. Lecture 14 - 7 ERS 482/682 (Fall 2002) Rules of modeling RULE 1: We cannot model reality –We have to make assumptions DOCUMENT!!!! RULE 2: Real world has less precision than modeling

8. Lecture 14 - 8 ERS 482/682 (Fall 2002) Precision vs. accuracy Precision –Number of decimal places –Spread of repeated computations Accuracy –Error between computed or measured value and true value error of estimate = field error+ model error

9. Lecture 14 - 9 ERS 482/682 (Fall 2002) The problem with precise models… we get more precision from model than is real

10. Lecture 14 - 10 ERS 482/682 (Fall 2002) Fundamental model concepts DRIVER Q RESPONSE SYSTEM REPRESENTATION area topography soils vegetation land use etc.

11. Lecture 14 - 11 ERS 482/682 (Fall 2002) Basic model Mathematical equations and parameters DRIVER RESPONSE SYSTEMREPRESENTATION

12. Lecture 14 - 12 ERS 482/682 (Fall 2002) Figure 9-37 (Dingman 2002) The whole world The model world

13. Lecture 14 - 13 ERS 482/682 (Fall 2002) Runoff processes to model ASSUMPTION! Small watershed Table 9-8 (Dingman 2002)

14. Lecture 14 - 14 ERS 482/682 (Fall 2002) Effective water input, W eff Effective (excess) rainfall –Does not include evapotranspiration or ground water storage that appears later ASSUMPTION! whereET = event water evapotranspired during event  S c = canopy storage during event  D = depression storage during event  = soil-water storage during event usually small antecedent soil-water content,  0ASSUMPTION!

15. Lecture 14 - 15 ERS 482/682 (Fall 2002) Estimating W eff constant fraction constant rate initial abstraction infiltration rate Figure 9-40 (Dingman 2002)

16. Lecture 14 - 16 ERS 482/682 (Fall 2002) Estimating W eff SCS curve-number method whereV max = watershed storage capacity [L] W= total rainfall [L] initial abstraction Figure 9-42 (Dingman 2002)

17. Lecture 14 - 17 ERS 482/682 (Fall 2002) Estimating W eff SCS curve-number method whereV max = watershed storage capacity [inches] W= total rainfall [inches] Based on land use in Table 9-12, soil group in Table 9-11, and soil maps from NRCS

18. Lecture 14 - 18 ERS 482/682 (Fall 2002) Example 9-6 Land cover Soil group Area (mi 2 ) Fraction of total area ForestB0.720.58 ForestC0.150.12 MeadowA0.260.21 MeadowB0.110.09 58 72 30 58 Table 9-12 Given:W = 4.2 in T W = 3.4 hr A = 1.24 mi 2 L = 0.84 mi S = 0.08 From NRCS soils maps and GIS Condition II CN

19. Lecture 14 - 19 ERS 482/682 (Fall 2002) Example 9-6 Land cover Soil group Area (mi 2 ) Fraction of total area ForestB0.720.58 ForestC0.150.12 MeadowA0.260.21 MeadowB0.110.09 58 72 30 58 Table 9-13 Given:W = 4.2 in T W = 3.4 hr A = 1.24 mi 2 L = 0.84 mi S = 0.08 Condition I CN X 38 X 53 X 15 X 38

20. Lecture 14 - 20 ERS 482/682 (Fall 2002) SCS method for peak discharge ft 3 s -1 inches mi 2 hr

21. Lecture 14 - 21 ERS 482/682 (Fall 2002) SCS method for peak discharge From Table 9-9

22. Lecture 14 - 22 ERS 482/682 (Fall 2002) SCS method for peak discharge Example 9-7 Given:W = 4.2 in T W = 3.4 hr A = 1.24 mi 2 L = 0.84 mi S = 0.08 W eff = 0.57 in for Condition II T c = 0.44 hr from Table 9-9

23. Lecture 14 - 23 ERS 482/682 (Fall 2002) Rational method AssumesAssumes a proportionality between peak discharge and rainfall intensity whereu R = unit-conversion factor (see footnote 7 on p. 443) C R = runoff coefficient i eff = rainfall intensity [L T -1 ] A D = drainage area [L 2 ] proportionality coefficient Q=CIA

24. Lecture 14 - 24 ERS 482/682 (Fall 2002) Rational method assumptionsAdditional assumptions: –Rainstorm of uniform intensity over entire watershed –Negligible surface storage –T c has passed –Return period for storm is same for discharge Apply to small (<200 ac) suburban and urban watersheds Q=CIA

25. Lecture 14 - 25 ERS 482/682 (Fall 2002) Rational method The proportionality coefficient, C R accounts for –Antecedent conditions –Soil type –Land use –Slope –Surface and channel roughness Q=CIA

26. Lecture 14 - 26 ERS 482/682 (Fall 2002) Rational method Approach –Estimate T c Q=CIA Figure 15.1 (Viessman and Lewis 1996) –Estimate C R Table 9-9 –Estimate i eff for return period T Usually use intensity-duration-frequency (IDF) curves Table 9-10 or Table 10-9 (Dunne and Leopold 1978)

27. Lecture 14 - 27 ERS 482/682 (Fall 2002) Rational method Approach –Estimate T c Q=CIA –Estimate C R Table 9-9 –Estimate i eff for return period T Usually use intensity-duration-frequency (IDF) curves Table 9-10 or Table 10-9 (Dunne and Leopold 1978) –Apply equation to get q p Return period (yrs)Multiplier for C R 2-10 25 50 100 1.0 1.1 1.2 1.25 Viessman and Lewis (1996)

28. Lecture 14 - 28 ERS 482/682 (Fall 2002) Rational method vs. SCS CN method Rational method –Small (<200 acres) urbanized watershed –Small return period (2-10 yrs) –Have localized IDF curves SCS Curve Number method –Rural watersheds –Average soil moisture condition (Condition II)

29. Lecture 14 - 29 ERS 482/682 (Fall 2002) Adaptations Rational method –Modifications for greater return periods –Runoff coefficients for rural areas (Table 10-9: Dunne and Leopold 1978) –Modified rational method for T c  T W SCS TR-55 method –Applies to urban areas –Has a popular computer program

30. Lecture 14 - 30 ERS 482/682 (Fall 2002) Adaptations SCS TR-55 method (cont.) –Approach Find the type of storm that applies from Figure 16.19 (Viessman and Lewis 1996) Use CN to determine I a from Table 15.5 (Viessman and Lewis 1996) Calculate I a /P Find q u = unit peak discharge from figure for storm type in cfs mi -2 in -1 (Viessman and Lewis 1996) Find runoff Q in inches from Figure 10-8 (Dunne and Leopold 1978) for P Find peak discharge for watershed as Q p = q u QA

31. Lecture 14 - 31 ERS 482/682 (Fall 2002) Definition: hydrograph due to unit volume of storm runoff generated by a storm of uniform effective intensity occurring within a specified period of time Unit hydrograph Assumption Assumption: W eff = Q ef Multiply unit hydrograph by W eff to get storm hydrograph Q ef 1 unit uniform intensity over T W

32. Lecture 14 - 32 ERS 482/682 (Fall 2002) Unit hydrograph development Choose several hydrographs from storms of same duration (~X hours) (usually most common/critical duration) For each storm, determine W eff and plot the event flow hydrograph for each storm For each storm, multiply the ordinates on the hydrograph by W eff -1 to get a unit hydrograph Plot all of the unit hydrographs on the same graph with the same start time Average the peak values for all of the unit hydrographs, and the average time to peak for all of the hydrographs Sketch composite unit graph to an avg shape of all the graphs Measure the area under the curve and adjust curve until area is ~1 unit (in or cm) of runoff Figure 9-45 End result: X-hr unit hydrograph

33. Lecture 14 - 33 ERS 482/682 (Fall 2002) Unit hydrograph application Multiply unit hydrograph by storm size Add successive X-hour unit hydrographs to get hydrographs of successive storms (Figures 9-46 and 9-47)

34. Lecture 14 - 34 ERS 482/682 (Fall 2002) Unit hydrograph Predicts flood peaks within ±25% Need only a short period of record Can apply to ungauged basins by regionalizing the hydrograph –Synthetic unit hydrographs

35. Lecture 14 - 35 ERS 482/682 (Fall 2002) Synthetic unit hydrograph Unit hydrograph for ungauged watershed derived from gauged watershed –Example (Dingman 2002): –Example (Dunne and Leopold 1978): whereC t = coefficient (1.8-2.2) L = length of mainstream from outlet to divide (miles) L c = distance from outlet to point on stream nearest centroid (miles) C p = coefficient (370-440) T b = duration of the hydrograph (hrs)

36. Lecture 14 - 36 ERS 482/682 (Fall 2002)  -index Figure 8-7 (Linsley et al. 1982) Figure 10-7 (Dunne & Leopold 1978)