1. Final Format
Open Book. Answer all questions. Please answer on separate sheets of paper. You may refer to the textbook, notes, solutions to homeworks and any other written or printed reference material that you have brought with you.
Calculator and computer use. You may use a programmable calculator, portable computer or equivalent calculating device (e.g. calculator functionality on a phone). You should limit the use of the calculating device to the performance of calculations or reference to material provided for this class. You may use spreadsheets or programs that you have written to evaluate quantities commonly used in this class (e.g. saturation vapor pressure).
You may not send messages or use the internet to communicate in any way with anyone other than the instructor or moderator regarding solutions to these questions.

2. Water Balance Atmospheric Water Soil Water Surface Water Groundwater
Change of Storage
= Inflow - Outflow

3. Watershed water balanceP ET
Gin Q S
Gout

4. The climate system and global hydrology
Perform simple analysis of the global energy balance and sensitivity of surface temperature to factors involved, such as albedo and the greenhouse effect

5. The Greenhouse Effect - Two layer atmosphere energy balance
Refer to Box 3-2 for definitions of quantities and numerical estimates of parameters

6. From Dingman, 1994

7. E/P=(R/P) Budyko, 1974 E/P R/P Evaporative Fraction 1
  2
Dryness (Available Energy/Precip)

8. Water Balance (Budyko curve)
Evapotranspiration fraction
Dryness (available energy /precip) 1
humid
arid
energy limited
water limited
R/P
E/P
E = R : energy limited upper bound
large
small
Soil Storage/ Retention or Residence time
medium
E = P : water limited upper bound
Increasing variability in soil capacity or areas of imperviousness
Increasing variability in P – both seasonally and with storm events
Increasing Retention or Soil capacity

9. Precipitation
Area Averaging

10. Infiltration follows preferential pathways
(a) Photograph of cross section through soil following dye tracing experiment. (b) Moisture content inferred from dye tracing experiment. (Courtesy of Markus Weiler)

11. Infiltration capacity Saturation OF Saturation
Surface Water Input
Evapotranspiration
Hortonian OF
Infiltration capacity
Saturation OF
Saturation
Variable
source area
Infiltration
Return flow
Soil regolith
Regolith subsurface flow
(interflow)
Percolation
Deeper groundwater aquifer
Aquifer subsurface flow
(baseflow)
Figure 13. Hydrological Pathways involved in different runoff generation processes. Infiltration excess pathways are shown in red. Saturation excess and subsurface stormflow pathways are shown in blue. Groundwater and baseflow pathways in black and Evapotranspiration is green.

12. The particular runoff process that dominates is place and time dependent

13. Figure 21. Cross section through an unsaturated porous medium (from Chow et al. 1988)

14. From Brutsaert, 2005

15. Residual moisture content r =5%
Characteristic curve relating moisture content to pressure head (from Freeze and Cherry, 1979).

16. Infiltration and unsaturated flow
Be able to calculate infiltration, infiltration capacity and runoff rates using the methods described in the Rainfall Runoff workbook chapter 5 and Dingman chapter 6.
Surface Runoff occurs when surface water input exceeds infiltration capacity. (a) Infiltration rate = rainfall rate which is less than infiltration capacity. (b) Runoff rate = Rainfall intensity – Infiltration capacity. (from Dunne and Leopold, 1978)

17. Green-Ampt model idealization of wetting front penetration into a soil profile
Moisture content, 
0.5
0.4
0.3
0.2
0.1
Depth, z, (cm) 10 20 30 40 t1 t2 t3 t4 L 
Initial moisture content o
Saturation moisture content s equivalent to porosity, n
Figure 37. Green-Ampt model idealization of wetting front penetration into a soil profile.

18. Infiltrability – Depth Approximation

19. Infiltration Capacity Runoff Runoff
Surface Water Input
Infiltration Capacity
Runoff
Runoff
Figure 41. Pulse runoff hyetograph obtained from surface water input hyetograph and variable infiltration capacity.
Time

20. Calculate infiltration capacity fc from Ft, column 1 of table.
Initialize: at t = 0, Ft = 0
Calculate infiltration capacity fc from Ft, column 1 of table.
fc £ wt
fc> wt
Is fc £ wt C B
Ponding occurs throughout interval: Ft+Dt calculated using infiltration under ponded conditions equations with ts=t and Fs= Ft.
Column 3.
No ponding at the beginning of the interval. Calculate tentative values
and column 1. D
Ponding starts during the interval. Solve for Fp from wt, column 2.
Dt' = (Fp-Ft)/wt
Ft+Dt calculated using infiltration under ponded conditions equations with ts=t+Dt' and Fs= Fp. Column 3. E
No ponding throughout interval
Figure 42. Flow chart for determining infiltration and runoff generated under variable surface water input intensity.
Infiltration is ft = Ft+Dt-Ft
Runoff generated is rt= wtDt - ft F G
Increment time t=t+Dt

21. Flow Related Terrain Information
Deriving hydrologically useful information from Digital Elevation Models
Raw DEM
Pit Removal (Filling)
Flow Field
Flow Related Terrain Information
This slide shows the general model for deriving flow field related derivative surfaces from digital elevation data. The input is a raw digital elevation model, generally elevation values on a grid. This is basic information used to derive further hydrology related spatial fields that enrich the information content of this basic data. The first step is to remove sinks, either by filling, or carving. Then a flow field is defined. This enables the calculation of flow related terrain information. My focus has been on flow related information working within this framework. I try to leave other GIS functionality, like radiation exposure, line of sight analyses and visualization to others. I have distributed my software in ways that it easily plugs in to mainstream systems, such as ArcGIS to enhance ease of use.

22. Grid Network

23. Watershed Draining to Outlet

24. Specific Catchment Area (a)
Slope (S)
Wetness Index
Specific Catchment Area (a)
Wetness Index ln(a/S)

25. TOPMODEL Key Ideas
Surface saturation and soil moisture deficits based on topography
Slope
Specific Catchment Area
Topographic Convergence
Partial contributing area concept
Saturation from below (Dunne) runoff generation mechanism
Map of saturated areas showing expansion during a single rainstorm. The solid black shows the saturated area at the beginning of the rain; the lightly shaded area is saturated by the end of the storm and is the area over which the water table had risen to the ground surface. [from Dunne and Leopold, 1978]

26. Topmodel – Wetness Index Histogram
Topographic variability for runoff generation summarized by distribution of wetness index expressed as a histogram
Specific catchment area a [m2/m  m]
(per unit coutour length)
Increasing D
saturated
Recharge
Drainage S zw q
D= ezw
ln 𝑎/𝑆

27. Rainfall – Runoff Analysis
From Mays, 2011, Ground and Surface Water Hydrology

28. Linear Response at Discrete Time Steps
Excess Precipitation

29. A Du hour unit hydrograph is the characteristic response of a given watershed to a unit volume (e.g. 1 in or cm) of effective water input (usually rain) applied at a constant rate for Du hours
Runoff (mm/hr)
Runoff and Flow
Flow (m3/s)
Time

30. Calculating a Hydrograph from a Unit Hydrograph and visa versa
𝑄 1 = 𝑃 1 𝑈 1
𝑄 2 = 𝑃 2 𝑈 1 + 𝑃 1 𝑈 2
𝑄 3 = 𝑃 3 𝑈 1 + 𝑃 2 𝑈 2 + 𝑃 1 𝑈 3
...
𝑄 𝑀 = 𝑃 𝑀 𝑈 1 + 𝑃 𝑀−1 𝑈 2 +…+ 𝑃 1 𝑈 𝑀
𝑄 𝑀+1 =0+ 𝑃 𝑀 𝑈 2 + 𝑃 𝑀−1 𝑈 3 +…+ 𝑃 1 𝑈 𝑀+1
𝑄 𝑁 =0+0+… 𝑃 𝑀 𝑈 𝑁−𝑀+1
𝑄 𝑛 = 𝑚=1 𝑀 𝑃 𝑚 𝑈 𝑛−𝑚+1 for n=1 ... N
𝑀=3 𝑝𝑟𝑒𝑐𝑖𝑝 𝑖𝑛𝑝𝑢𝑡𝑠
𝐿=5 𝑢𝑛𝑖𝑡 ℎ𝑦𝑑𝑟𝑜𝑔𝑟𝑎𝑝ℎ
𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠
𝑁=7 𝑑𝑖𝑟𝑒𝑐𝑡 𝑟𝑢𝑛𝑜𝑓𝑓
ℎ𝑦𝑑𝑟𝑜𝑔𝑟𝑎𝑝ℎ
𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠
𝑁=𝐿+𝑀−1
From Mays, 2011, Ground and Surface Water Hydrology

31. Solar Radiation
Be able to calculate incoming solar radiation as a driver of evaporation and snowmelt based on of geographic location (latitude and longitude), date, time of day and atmospheric conditions

32. Global Energy Balance
How much evaporation is represented by the latent heat flux of 82 W/m2?
From Lindzen (1990), Bulleting AMS 71(3):

33.  Eqn. E-3
Day Angle 
Eqn E-1 ro
Eo=(ro/r)2 Eqn. E-2 r
From Dingman, 1994

34. Equivalent plane at latitude eq
Sloping surface
angle 
eq
Latitude 
Slope Sunrise Tsr Eqn E-24a
Equivalent sloping plane radiation
Daily total KET Eqn E-25
Slope Sunset Tss Eqn E-24b

35. Direct approach to radiation calculation
Slope illumination angle z
Surface
Normal
North
Solar azimuth angle A
Slope azimuth angle 
Slope angle 

36. Clear sky attenuation of solar radiation passing through atmosphere
0.5 sK'ET
K'ET
K'dir =  K'ET
0.5 sK'ET
0.5 a sK'g
and s - appendix E
optical air mass
precipitable water
dust
backscattering
Optical air mass – Dingman Fig E-4

37. ET involves Energy exchanges and energy balance
Turbulent diffusion into the atmosphere
Adjustment and balance Rn G + -

38. Turbulent convection transports heat, vapor and momentum
𝑣 𝑎 Ta ea
𝑧 𝑚 Ts es

39. Summary of ET Equations
Bowen Ratio
Mass Transfer
Combination
Priestly Taylor
What happens in these equations if the wind speed doubles?

40. Method Information Requirements
Mass Transfer
Bowen Ratio / Energy Balance RN
Combination