Types of River Models

1. Types of River Models Hydrologic Hydraulic Load Biological (Channel & Floodplain) Conservation of Momentum and Mass for solvent and solutes predicts: Conc.& transport Over time Various predicts: habitat quality or Population size Or composition Conservation of Mass Conservation of Momentum (energy) predicts: Depth, Velocity distributions over time Conservation of Mass {continuity} predicts: Water discharge rate over time Theory base WSP HEC-2 HEC-RAS HEC-4 SWMM HEC-6 SWMM AGNIPSSWAT HEC-RAS BASINS Rational method HEC-1 HEC-HMS TR-20 TR-55 HSI IFIM RIVPAKS {SEM} {MLR}

2. Storm ( DRO) hydrographs

3. Time base Storm ( DRO) hydrographs Time of rise Time to peak [from midpoint of precip event ]

4. Base flow separation HEWLETT's METHOD (1967) of flow separation Hewlett's method provides a standardized graphical approach to flow separation based upon the flowing algorithm: A. let diff=(Q(day)-Q(day-1)) B. if diff>0 then let baseflow(day)=baseflow(day-1) + K C. if diff<=0 then let baseflow(day)=baseflow(day-1) D. if baseflow(day)>Q(day) then let baseflow(day)=Q(day) K= c * catchment area (sq miles); c=.001-.00001 Wild River, Me [ from 411 worksheet Flowsep.mcd]

5. the Rational Method Storm ( DRO) hydrographs

6. the Rational Method Qp = C I A (Mulvaney 1851, Kuichling 1889) Qpis peak discharge at time of concentration (tc) I is rainful intensity at chosen frequency for duration equal to tc [in/hr] A is catchment area in acres [ <1 sq mile] tctime of concentration: time for rainfall at most distant region of catchment to travel to the outlet Cis the runoff coefficient ~ (Runoff volume) / (Rainfall volume)

7. Rainfall IDF curves: Assumes tc=duration; what determines tc?

9. Unit Hydrographs Obs. Hydrograph DRO Hydrograph

10. DRO Hydrograph Adjust Q to give 1 unit DRO by dividing Q values by 1/DRO total as depth Unit Hydrograph

11. Because of their assumed linearity... Unit hydrographs (UH) of short duration can be used to generate longer duration UH S-curve Method

12. S-curve Method

14. n i Qn = SPiU n-i+1 Hydrograph Convolution UH’s can also be used to estimate DRO hydrographs from complex precip events...

15. Hydrograph Convolution n i Qn = SPiU n-i+1

18. Synthetic unit hydrographs Issues: slope routing storage Methods: Snyder SCS Epsey Empirical relationships for key parameters

19. Synthetic unit hydrographs Methods: Snyder SCS Epsey Empirical relationships for key parameters Qp = Peak Q; tp = time to peak Q; Tr = rise time D = precip duration; Tr + B = time base

20. Snyder’s Synthetic Unit Hydrograph method Qpeak(cfs) = 640 Cp AREA(mi2) tp Tbase(days) = 3 + tp/8 tp(hrs)=Ct(L Lc )0.3 Cp= storage coeff. from .4 to .8 Ct= coeff. ususally 1.8-2.2 [0.4-8.0] Lc=length along channel to watershed centroid L= length of main stem to divide (ft)

21. SCS Method [ TR-20; TR-55] Lfcoef = 484 or fitted [10- 500]

22. 1000 abstraction 10 curve number

25. Hydraulic Geometry Relations for a cross-section {Station Geometry} Q = D V W implies all are functions of Q Typically, at any cross section, relation modeled as a power function: V = a Qb where a and b are constant coefficients W = c Qd where c and d are constant coefficients D = e Qf where e and f are constant coefficients Since D V W = Q a Qb *c Qd *e Qf = a*c*e *Q b+d+f = Q and therefore the coeffs are constrained such that, a*c*e = 1 AND b+d+f =1

26. Hydraulic Geometry Relations between Stations {Basin Geometry} Given that the water balance implies Qmean = x AREAy where x and y are coefficients, continuity implies: Vmean = a AREAb where a and b are constant coefficients Wmean = c AREAd where c and d are constant coefficients Dmean = e AREAf where e and f are constant coefficients similarly.. a AREAb *c AREAd *e AREAf = a*c*e *AREA b+d+f = Q and therefore the coeffs are constrained such that, a*c*e = x AND b+d+f =y Catchment AREA

27. Predictive Modeling of Flow Duration Curves Exceedence Flows (5% --> 95%) can be estimated by multiple regression using geology, land use and other landscape factors as predictive variables. General form of the Synthetic Flow Duration Model is Qex = a*Catchment_Areab1 + landscape_factor1b2*landscape_factor2b3 … landscape_factorN bN-1 Landscape factor variables are derived from GIS analysis of statewide digital map covers and include: mean annual precipitation, average catchment slope, % of various landcover types, % of certain surficial geology types.

28. Relative fits (R2 values) for Synthetic Flow Duration Models of streamflow in Michigan’s lower peninsula Percent Ground Water Runoff streams Exceedence R2 R2 5 0.96 0.99 10 0.97 0.98 25 0.97 0.96 50 0.97 0.93 75 0.94 0.91 90 0.93 0.91 95 0.92 0.90

29. # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # A g r i c u l t u r e # # B a r r e n # # # # # # # # # # # # # # F o r e s t # # # # # # # # # # # # # # # # F o r e s t e d w e t l a n d # # # # # # # # # # # # # # N o n f o r e s t e d w e t l a n d # # # # R a n g e # # # # # # # N # # # # U r b a n # # # W a t e r # # # # # # # # # # # # W E # # # # # # # # # # # # # # # # # # # # # # # # # # # # S # # # # # # # Landcover for Michigan Presettlement ca.1830 MIRIS 1978

30. 2.4 0.0 2.7 0.0 13.6 11.7 Agriculture 27.3 Forest 0.0005 Forested Wetland 3.5 10.0 Non-Forested Wetland Barren 0.03 Range 5.0 Urban 19.0 61.4 Water 9.9 33.4 Presettlement (1830) MIRIS (1978) Percentage Landcover Type

31. # S S # S # S # S # # S S # S # S # # S S # S # # S S # # S S # # S # S S # # S S # # S # S # S # S S # # S S # # S # S S # # S S # # S # S S # S # # S # S S # S # # S # S S # # S S # # S # S S # S # # S S # S # # S S # S # S # S # S # S # # S S # # S # S # S # S # S # S # S # S S # S # S # S # S # S # # S S # S # # S # S S # Low Flow Yield is a measure of baseflow conditions standardized by catchment area. Nearly 6 of 10 rivers in this study (59.8%) have lower baseflow yields now. However, many rivers have increased baseflow yields. Red have become lower Blue have become higher

32. # S S # S # S # S # # S S # # S S # # S # S S # S # S # # S # S S # S # S # # S S # # S # S S # S # S # # S # S # S S # # S # S S # # S S # S # # S # S # S # S # S # S # S # S # S # S # S # S # S S # S # S # S # # S S # S # # S # S S # S # S # # S # S S # # S # S S # S # # S # S # S # S # S S # # S # S # S # S S # S # S # S # The Runoff Coefficient is a measure of magnitude of the difference between the high flows and the low flows The majority of catchments had increased runoff coefficients (57.6%). Both increases and decreases were observed. Red have become higher Blue have become lower or not changed

33. Types of River Models Hydrologic Hydraulic Load Biological (Channel & Floodplain) Conservation of Momentum and Mass for solvent and solutes predicts: Conc.& transport Over time Various predicts: habitat quality or Population size Or composition Conservation of Mass Conservation of Momentum (energy) predicts: Depth, Velocity distributions over time Conservation of Mass {continuity} predicts: Water discharge rate over time Theory base WSP HEC-2 HEC-RAS HEC-4 SWMM HEC-6 SWMM AGNIPSSWAT HEC-RAS BASINS Rational method HEC-1 HEC-HMS TR-20 TR-55 HSI IFIM RIVPAKS {SEM} {MLR}