CE 394K.2 Hydrology, Lecture 3 Water and Energy Flow

1. CE 394K.2 Hydrology, Lecture 3Water 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) Outputs, Q(t) Inputs, I(t) A hydrologic system transforms inputs to outputs Hydrologic Processes I(t), Q(t) Hydrologic conditions I(t) (Precip) Physical environment Q(t) (Streamflow)

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

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) Outputs, Q(t) Inputs, I(t) Hydrologic Processes I(t), Q(t) How do we characterize uncertain inputs, outputs and system transformations? Hydrologic conditions Physical environment Ref: Figure 1.4.1 Applied Hydrology

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) Precipitation 100 Atmospheric moisture flow 39 Precipitation 385 Evaporation 424 Evaporation 61 Surface Outflow 38 Land (148.7 km2) (29% of earth area) Ocean (361.3 km2) (71% of earth area) Subsurface Outflow 1 Units are in volume per year relative to precipitation on land (119,000 km3/yr) which is 100 units

10. Global water balance (mm/yr) Precipitation 800 Atmospheric moisture flow 316 Precipitation 1270 Evaporation 1400 Evaporation 484 Outflow 316 Land (148.7 km2) (29% of earth area) Ocean (361.3 km2) (71% of earth area) 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 Hydrologic systems are nearly always open systems, which means that it is difficult to do material balances on them I(t) (Precip) What time period do we choose to do material balances for? dS/dt = I(t) – Q(t) Q(t) (Streamflow) Closed system if

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

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. Sea surface Ellipsoid Earth surface Geoid Surface and Groundwater Flow Levelsare related to Mean Sea Level 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 hf energy grade line y1 water surface y2 bed z1 z2 L Datum How do we relate friction slope, to the velocity of flow?

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

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

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

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 (Eu) • Internal energy • Sensibleheat – 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/s2 • 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. Water Volume [L3] (acre-ft, m3) Water flow [L3/T] (cfs or m3/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/L2T] in Watts/m2 Energy fluxes and flows Energy flow of 1 Joule/sec Area = 1 m2

27. MegaJoules • When working with evaporation, its more convenient to use MegaJoules, MJ (J x 106) • So units are • Energy amount (MJ) • Energy flow (MJ/day, MJ/month) • Energy flux (MJ/m2-day, MJ/m2-month)

28. Internal Energy of Water Water vapor Water Ice Heat Capacity (J/kg-K) Latent Heat (MJ/kg) Ice 2220 0.33 Water 4190 2.5 2.5/0.33 = 7.6 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)

29. Water Volume, V [L3] (acre-ft, m3) Water flow, Q [L3/T] (cfs or m3/s) Water flux, q [L/T] (in/day, mm/day) Water mass [m = rV] (Kg) Water mass flow rate [m/T = rQ] (kg/s or kg/day) Water mass flux [M/L2T = rq] in kg/m2-day Water Mass Fluxes and Flows Water flux Area = 1 m2

30. Water flux Evaporation rate, E (mm/day) Energy flux Latent heat flux (W/m2), Hl Latent heat flux r = 1000 kg/m3 lv = 2.5 MJ/kg 28.94 W/m2 = 1 mm/day Area = 1 m2

31. Radiation • Two basic laws • Stefan-Boltzman Law • R = emitted radiation (W/m2) • e = emissivity (0-1) • s = 5.67x10-8W/m2-K4 • T = absolute temperature (K) • Wiens Law • l = wavelength of emitted radiation (m) All bodies emit radiation Hot bodies (sun) emit short wave radiation Cool bodies (earth) emit long wave radiation

32. Net Radiation, Rn Ri Incoming Radiation • Ro =aRi Reflected radiation • = albedo (0 – 1) Re Rn Net Radiation Average value of Rn over the earth and over the year is 105 W/m2

33. Net Radiation, Rn H – Sensible Heat LE – Evaporation G – Ground Heat Flux Rn Net Radiation Average value of Rn over the earth and over the year is 105 W/m2

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

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

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

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

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

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

40. Energy balance at earth’s surfaceDownward 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) Why is the net radiation large over the oceans and small over the Sahara? http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm