Lecture 3: Energy Balance

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Presentation transcript:

Lecture 3: Energy Balance Reading: Applied Hydrology Sections 2.4-2.6 Subjects for today: Heat energy Energy fluxes and flows Energy balance of the earth

Heat energy Energy Internal energy Potential (mgz), Kinetic (1/2 mv2), Internal (Eu) 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

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

Energy fluxes and flows 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 flow of 1 Joule/sec Area = 1 m2

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)

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)

Water Mass Fluxes and Flows 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 flux Area = 1 m2

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

Radiation Two basic laws Stefan-Boltzman Law All bodies emit radiation 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

Average value of Rn over the earth and 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

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

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

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

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

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

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

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

Latent heat flux, Jan 2003, 1500z