1. CE 394K.2 Hydrology, Lecture 3 Water and Energy Flow Literary quote for today: “If I should die, think only this of me; That there's some corner of a foreign field That is for ever England. ” Rupert Brooke, English poet, “The Soldier” (he died in WWI and is buried on the island of Skyros in Greece)

2. Watershed system

3. Hydrologic System Take a watershed and extrude it vertically into the atmosphere and subsurface, Applied Hydrology, p.7- 8 A hydrologic system is “a structure or volume in space surrounded by a boundary, that accepts water and other inputs, operates on them internally, and produces them as outputs”

4. System Transformation Transformation Equation Q(t) =  I(t) Inputs, I(t) Outputs, Q(t) A hydrologic system transforms inputs to outputs Hydrologic Processes Physical environment Hydrologic conditions I(t), Q(t) I(t) (Precip) Q(t) (Streamflow)

5. NWIS ArcGIS Excel NCAR Unidata NASA Storet NCDC Ameriflux Matlab AccessJava Fortran Visual Basic C/C++ Some operational services CUAHSI Web Services Data Sources Applications Extract Transform Load http://www.cuahsi.org/his/

6. Concept of Transformation In hydrology, we associate transformation with the connection between inflow and outflow of water, mass, energy In web services, we associate transformation with flow of data (extract, transform, load) Can we link these two ideas?

7. Stochastic transformation System transformation f(randomness, space, time) Inputs, I(t) Outputs, Q(t) Ref: Figure 1.4.1 Applied Hydrology How do we characterize uncertain inputs, outputs and system transformations? Hydrologic Processes Physical environment Hydrologic conditions I(t), Q(t)

8. Questions for discussion on Tuesday (from Chapters 1 and 2 of Text) How is precipitation partitioned into evaporation, groundwater recharge and runoff and how does this partitioning vary with location on the earth? Can a closed water balance be developed using discrete time rainfall and streamflow data for a watershed? How do the equations for velocity of water flow in streams and aquifers differ, and why is this so? How is net radiation to the earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?

9. Global water balance (volumetric) Land (148.7 km 2 ) (29% of earth area) Ocean (361.3 km 2 ) (71% of earth area) Precipitation 100 Evaporation 61 Surface Outflow 38 Subsurface Outflow 1 Precipitation 385 Evaporation 424 Atmospheric moisture flow 39 Units are in volume per year relative to precipitation on land (119,000 km 3 /yr) which is 100 units

10. Global water balance (mm/yr) Land (148.7 km 2 ) (29% of earth area) Ocean (361.3 km 2 ) (71% of earth area) Precipitation 800 Evaporation 484 Outflow 316 Precipitation 1270 Evaporation 1400 Atmospheric moisture flow 316 What conclusions can we draw from these data? Applied Hydrology, Table 1.1.2, p.5

11. Digital Atlas of the World Water Balance (Precipitation) http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm

12. Questions for discussion on Tuesday (from Chapters 1 and 2 of Text) How is precipitation partitioned into evaporation, groundwater recharge and runoff and how does this partitioning vary with location on the earth? Can a closed water balance be developed using discrete time rainfall and streamflow data for a watershed? How do the equations for velocity of water flow in streams and aquifers differ, and why is this so? How is net radiation to the earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?

13. Continuity equation for a watershed I(t) (Precip) Q(t) (Streamflow) dS/dt = I(t) – Q(t) Closed system if Hydrologic systems are nearly always open systems, which means that it is difficult to do material balances on them What time period do we choose to do material balances for?

14. Continuous and Discrete time data Continuous time representation Sampled or Instantaneous data (streamflow) truthful for rate, volume is interpolated Pulse or Interval data (precipitation) truthful for depth, rate is interpolated Figure 2.3.1, p. 28 Applied Hydrology Can we close a discrete-time water balance?

15. Questions for discussion on Tuesday (from Chapters 1 and 2 of Text) How is precipitation partitioned into evaporation, groundwater recharge and runoff and how does this partitioning vary with location on the earth? Can a closed water balance be developed using discrete time rainfall and streamflow data for a watershed? How do the equations for velocity of water flow in streams and aquifers differ, and why is this so? How is net radiation to the earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?

16. Surface and Groundwater Flow Levels are related to Mean Sea Level Earth surface Ellipsoid Sea surface Geoid Mean Sea Level is a surface of constant gravitational potential called the Geoid

17. http://www.csr.utexas.edu/ocean/mss.html

18. Vertical Earth Datums A vertical datum defines elevation, z NGVD29 (National Geodetic Vertical Datum of 1929) NAVD88 (North American Vertical Datum of 1988) takes into account a map of gravity anomalies between the ellipsoid and the geoid

19. Energy equation of fluid mechanics Datum z1z1 y1y1 bed water surface energy grade line hfhf z2z2 y2y2 L How do we relate friction slope,to the velocity of flow?

20. Open channel flow Manning’s equation Channel Roughness Channel Geometry Hydrologic Processes (Open channel flow) Physical environment (Channel n, R) Hydrologic conditions (V, S f )

21. Subsurface flow Darcy’s equation Hydraulic conductivity Hydrologic Processes (Porous medium flow) Physical environment (Medium K) Hydrologic conditions (q, S f ) A q q

22. Comparison of flow equations Open Channel Flow Porous medium flow Why is there a different power of S f ?

23. Questions for discussion on Tuesday (from Chapters 1 and 2 of Text) How is precipitation partitioned into evaporation, groundwater recharge and runoff and how does this partitioning vary with location on the earth? Can a closed water balance be developed using discrete time rainfall and streamflow data for a watershed? How do the equations for velocity of water flow in streams and aquifers differ, and why is this so? How is net radiation to the earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?

24. Heat energy Energy –Potential, Kinetic, Internal (E u ) Internal energy –Sensible heat – heat content that can be measured and is proportional to temperature –Latent heat – “hidden” heat content that is related to phase changes

25. Energy Units In SI units, the basic unit of energy is Joule (J), where 1 J = 1 kg x 1 m/s 2 Energy can also be measured in calories where 1 calorie = heat required to raise 1 gm of water by 1°C and 1 kilocalorie (C) = 1000 calories (1 calorie = 4.19 Joules) We will use the SI system of units

26. Energy fluxes and flows Water Volume [L 3 ] (acre-ft, m 3 ) Water flow [L 3 /T] (cfs or m 3 /s) Water flux [L/T] (in/day, mm/day) Energy amount [E] (Joules) Energy “flow” in Watts [E/T] (1W = 1 J/s) Energy flux [E/L 2 T] in Watts/m 2 Energy flow of 1 Joule/sec Area = 1 m 2

27. MegaJoules When working with evaporation, its more convenient to use MegaJoules, MJ (J x 10 6 ) So units are –Energy amount (MJ) –Energy flow (MJ/day, MJ/month) –Energy flux (MJ/m 2 -day, MJ/m 2 -month)

28. Internal Energy of Water Heat Capacity (J/kg-K)Latent Heat (MJ/kg) Ice22200.33 Water41902.5 Ice Water Water vapor Water may evaporate at any temperature in range 0 – 100°C Latent heat of vaporization consumes 7.6 times the latent heat of fusion (melting) 2.5/0.33 = 7.6

29. Water Mass Fluxes and Flows Water Volume, V [L 3 ] (acre-ft, m 3 ) Water flow, Q [L 3 /T] (cfs or m 3 /s) Water flux, q [L/T] (in/day, mm/day) Water mass [m =  V] (Kg) Water mass flow rate [m/T =  Q] (kg/s or kg/day) Water mass flux [M/L 2 T =  q] in kg/m 2 - day Water flux Area = 1 m 2

30. Latent heat flux Water flux –Evaporation rate, E (mm/day) Energy flux –Latent heat flux (W/m 2 ), H l Area = 1 m 2  = 1000 kg/m 3 l v = 2.5 MJ/kg 28.94 W/m 2 = 1 mm/day

31. Radiation Two basic laws –Stefan-Boltzman Law R = emitted radiation (W/m2)  = emissivity (0-1)  = 5.67x10 -8 W/m2-K 4 T = absolute temperature (K) –Wiens Law  = wavelength of emitted radiation (m) Hot bodies (sun) emit short wave radiation Cool bodies (earth) emit long wave radiation All bodies emit radiation

32. Net Radiation, R n R i Incoming Radiation R o =  R i Reflected radiation  albedo (0 – 1) R n Net Radiation ReRe Average value of R n over the earth and over the year is 105 W/m 2

33. Net Radiation, R n R n Net Radiation Average value of R n over the earth and over the year is 105 W/m 2 G – Ground Heat Flux LE – EvaporationH – Sensible Heat

34. http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/energy/radiation_balance.html Energy Balance of Earth 6 4 100 70 51 21 26 38 6 20 15 Sensible heat flux 7 Latent heat flux 23 19

35. Energy balance at earth’s surface Downward short-wave radiation, Jan 2003 600Z

36. Energy balance at earth’s surface Downward short-wave radiation, Jan 2003 900Z

37. Energy balance at earth’s surface Downward short-wave radiation, Jan 2003 1200Z

38. Energy balance at earth’s surface Downward short-wave radiation, Jan 2003 1500Z

39. Energy balance at earth’s surface Downward short-wave radiation, Jan 2003 1800Z

40. Energy balance at earth’s surface Downward short-wave radiation, Jan 2003 2100Z

41. Latent heat flux, Jan 2003, 1500z

42. Digital Atlas of the World Water Balance (Temperature) http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm

43. Digital Atlas of the World Water Balance (Net Radiation) http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm Why is the net radiation large over the oceans and small over the Sahara?