Physical Hydrology & Hydroclimatology ( Multiscale Hydrology)

1. Physical Hydrology & Hydroclimatology(Multiscale Hydrology) A science dealing with the properties, distribution and circulation of water. R. Balaji balajir@colorado.edu CVEN5333 http://civil.colorado.edu/~balajir/CVEN5333

2. Lectures 3-4-5 • Reservoir sizing • Sequent Peak method • Estimating mass balance quantities (especially ET) • Under uncertainty • Quantifying temporal variability • Basic statistics • Coefficient of variability • Persistence • Autocorrelation • Flow Duration Curve (FDC)

3. Storage-Yield Analysis • Used to size a reservoir given a streamflow time series.

4. Colorado River Basin Overview 7 States, 2 Nations Upper Basin: CO, UT, WY, NM Lower Basin: AZ, CA, NV Fastest Growing Part of the U.S. Over 1,450 miles in length Basin makes up about 8% of total U.S. lands Highly variable Natural Flow which averages 15 MAF 60 MAF of total storage 4x Annual Flow 50 MAF in Powell + Mead Irrigates 3.5 million acres Serves 30 million people Very Complicated Legal Environment ‘Law of the River’ Denver, Albuquerque, Phoenix, Tucson, Las Vegas, Los Angeles, San Diego all use CRB water DOI Reclamation Operates Mead/Powell 1 acre-foot = 325,000 gals, 1 maf = 325 * 109 gals 1 maf = 1.23 km3 = 1.23*109 m3

5. UC CRSS stream gauges LC CRSS stream gauges Colorado River Demand - Supply

6. Below normal flows into Lake Powell 2000-2004 62%, 59%, 25%, 51%, 51%, respectively 2002 at 25% lowest inflow recorded since completion of Glen Canyon Dam Some relief in 2005 105% of normal inflows Not in 2006 ! 73% of normal inflows 2007 at 68% of Normal inflows 2008 at 111% of Normal inflows 2009 at 88% and 2010 at 72.5% Decadal Variability! MotivationRecent conditions in the Paleo Context 5 year running average Woodhouse et al., WRR, 2007

7. % Total Runoff Runoff Basin Area • Most runoff comes from small part of the basin > 9000 feet • Very Little of the Runoff Comes from Below 9000’ (16% Runoff, 87% of Area) • 84% of Total Runoff Comes from 13% of the Basin Area – all above 9000’

8. Rt = y Storage-Yield Analysis • Sequent Peak Procedure Kt = Kt-1 + Rt – Qt If Kt < 0, Kt=0 S = Max(Kt)

9. Loucks, Chapter 11 Pages 342-346

13. Reservoir Storage-Yield Analysis R/Q

14. Reservoir Reliability Analysis

15. Optimal Yield Y = Yield (MaF) Spillt= Overflow (MaF) Qt = Paleo-reconstructed inflow (MaF/yr) K = Reservoir capacity (MaF) St-1= Previous year storage (MaF) St= Current storage (MaF) Minimum Storage is specified System storage = 60MaF • Average storage is computed for the optimal yield Yopt, as the average of:

16. Why not build more storage? • Plot of Optimal yield vs. storage potential • larger tub does NOT lead to greater yield • optimal yield plateaus at ~15MaF at around 70 MaF Temporal Variability! The cause

17. Estimation of Areal ET P ET Gin Q S Gout

18. Estimation of areal ET • Assume Gin and Goutsmall and at equilibrium Change in storage is zero • ET = P - Q • Assume storage is negligible • mET = mp – mQ • Errors: model and measurement • Accuracy of precipitation and streamflow • Absolute and relative uncertainty • Independent errors s2x+y = s2x + s2y

19. Estimation of areal ET • Assume Gin and Gout small • Assume storage is negligible • mET = mp – mQ • Errors: model and measurement • Accuracy of precipitation and streamflow • Relative uncertainty (uP) is measurement uncertainty or accuracy • Absolute uncertainty (mpuP) • Assuming Normal Distribution of measurement errors • Pr{mp- mpuP<= true precipitation <= mp+mpuP} = 0.95 • mpuP= 2*sP Where sPis the estimated standard deviation for precipitation • Similarly for Q and ET

20. Example of ET estimate (2-1) • NH Oyster river • Average precip1066mm/year, uncertain 10% (at 95% level) • Average drainage outflow 551 mm/year, 5% uncertain • mET= 1066 – 551 mm/year = 515 mm/yr • Uncertainty = SQRT {(1066*.1)**2 + (551*.05)**2} = 55.1 mm/yr • Relative uncertainty = 2 (55.1/515) = 0.214 • Pr {405 < mET < 625} = .95

21. Exercise 2-1

22. Exercise 2-1 • M(ET) = m(p) – m(q) • s^2(ET) = s^2(p) + s^2(q) • Convert from m^3/s to mm/yr • Q/A=386 m^3/s /20370km^2 = 598 mm/yr • S(p)=0.1*p = 110 mm/yr • S(q) = 0.05*598 mm/yr • S(ET) = sqrt( s(q)^2 +s(p)^2) = 114 mm/yr • Relative error =114 mm/yr/598 mm/y=23% • Similarly: Yukon River 115/398 = 29% • Euphrates: 32/190 = 17% • Mekong: 221/832 = 27%

23. Scale issues in the interpretation of measurements and modeling data The scale triplet a) Extent b) Spacing c) Support From: Blöschl, G., (1996), Scale and Scaling in Hydrology, Habilitationsschrift, Weiner Mitteilungen Wasser Abwasser Gewasser, Wien, 346 p.

24. From: Blöschl, G., (1996), Scale and Scaling in Hydrology, Habilitationsschrift, Weiner Mitteilungen Wasser Abwasser Gewasser, Wien, 346 p.

25. Temporal Variability of Hydrologic Data Colorado River Lees Ferry

26. From NRC Colorado River Basin Management, 2007

27. From NRC Colorado River Basin Management, 2007

28. From NRC Colorado River Basin Management, 2007

29. Logan River Annual Aggregate Time Series 2500 mean cfs 7 day min cfs max cfs 2000 1500 cfs 1000 500 0 1920 1930 1940 1950 1960 1970 1980 1990 2000

30. Random variables Probability density function Cumulative distribution function

31. Space/time variability • Continuous series – samples • Expectation, Mean, standard deviation, median, extremes (max/min), percentile, coefficient of variation (CV) • Flow duration curves (FDC) flow rate (q) vs. cumulative distribution (Q) • Exceedence probability E PQ(qp) = 1 – FQ(qp) = Pr {Q>qp}

32. From Dingman, 2002

33. From Dingman, 2002

34. FDC can be constructed on 7-day Min Flow Average daily flow Average annual flow etc • Relatively flat slopes at Upper end of FDC • Snowmelt driven floods • Large basin with storms of several days • Steep slopes at Upper end of FDC • Flashy streams • Intense storms of short duration • Flat slopes at low end • significant groundwater storage • frequent precipitation inputs

37. Mean of Monthly Streamflow. Alafia River

39. From Dingman, 2002

40. From Dingman, 2002

41. Alafia river: Autocorrelation Autocorrelation of standardized flow

42. Alafia River:Monthly streamflow distribution

43. Time Series Box Plot Median Box (Red Lines) enclose 50% of the values

44. Box Plot Outliers: beyond 1.5*IQR Whiskers: 1.5*IQR or largest value Box: 25th %tile to 75th %tile Line: Median (50th %tile) - not the mean Note: The range shown by the box is called the “Inter-Quartile Range” or IQR. This is a robust measure of spread. It is insensitive to outliers since it is based purely on the rank of the values.