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Understanding E and Λe

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Understanding E and Λe Understanding E and λE Michael L. Roderick Research School of Biology and Research School of Earth Sciences Australian National University, Canberra, Australia Session: Meet the expert in hydrology - The mystery of evaporation European Geosciences Union Annual Meeting, 16 April 2015 E is a mass flux that is all about: PHASE CHANGE Geosciences: E is the net mass flux (net) E = vaporization – condensation + sublimation – deposition 3 Geosciences: E is the net mass flux λE (or LE) is latent heat flux Latent: Called that because it is “hidden” heat. “Hidden”: cannot be sensed with a thermometer. Need to measure the composition. 4 λE (sometimes called LE): λE (or LE) is the Latent Heat Flux Define the Gibbs function, G G = H – T S dG = V dP – S dT {G = f(T, P)} G is VERY USEFUL for experimental work. Can control T and P in the laboratory. KEY APPLICATION In a phase change, dG(phase 1) = dG(phase 2) P, T are uniform throughout both phases, so we have, V1 dP – S1 dT = V2 dP – S2 dT ⇒ dP / dT = (S2 – S1) / (V2 – V1) Clausius–Clapeyron relation During a phase change from liquid (l) to gas (g) g (gas) one can use the Gibbs function to show that: l (liquid) dP/dT = (sg – sl) / (vg – vl) = (hg – hl) / {T (vg – vl)} {Since dh = TdS at constant P} Since vg >> vl, and setting L = hg – hl {vg, vl are volume per mol} dP/dT ≈ L / (T vg) 2 ≈ L P / (R T ) {Ideal Gas: vg = RT / P} For water vapour: 2 dPsat/dT ≈ Psat {L / (Rv T )} NOTE: s entropy, h enthalpy, L latent heat of vapourisation Latent Heat of Vaporisation - Liquid Water 2.55 2.5 2.45 Thermodynamic Data 2.4 2.35 L (MJ/kg) L from experiment 2.3 2.25 2.2 0 20 40 60 80 100 120 T (degC) ~ 2.5 MJ of heat needed to evaporate 1 kg of water. There is a slight dependence of L on T. e.g. 2.5 MJ/kg at 0 degC, 2.25 MJ/kg at 100 degC. Often use 2.45 MJ/kg as a default. L = hg – hl L = Enthalpy Gas Phase – Enthalpy Liquid Phase (UNITS: J mol-1 or J Kg-1) Note: This is for liquid to gas. For solid to gas follow the same procedure. L [J/g] (from -40 to 50 degC) 3500 3000 2500 2000 L (J/g) 1500 1000 500 0 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 T (degC) Commonly known as Wilhelm Schmidt, 1915 Slatyer & McIlroy 1961 Thermodynamics Equilibrium Evaporation (Independent Result – not attributed to Schmidt because they did not know) air Psat (T ) T water ∆ RH=100% Add energy Q LE = Q ∆ + γ air + Psat (T dT ) dP T+dT ∆ = sat dT T water L is latent heat of vaporization Example: E = 6 mm day-1 (mass flux) What is λE? (latent heat flux) λE Remember: 1 J m-2 s-1 = 1 W m-2 Rough but easy to remember approximation: 1 W m-2 of λE ~ 1 mm month-1 of E 6 mm day-1 ~ 180 mm month-1 of E ~ 180 W m-2 of λE. Does E “have” to increase in a warmer world Short answer: No -1 If T increases then es increases. {~+7% K , called CC scaling} T, es are state variables. es is saturated vapour pressure at T E is a flux. E does not “have” to increase. It might, or it might not. It all depends on a lot of things like radiation, humidity, wind, etc.. → See next TALK by Christel Why is: Public Perception and Science out of step? PUBLIC PERCEPTION SCIENCE T ↑ is the “cause” of E ↑ E ↑ is the “cause” of Ts ↓ (Energy Balance) No wonder there is a lot of confusion. Evaporation Removes Heat and leaves the evaporating surface cooler Uniform E, ~uniform Ts Higher E, lower Ts Aminzadeh & Or (2014) J Hydrology Soil Drying E declines as soil moisture declines Key Concepts: Stage 1 Evaporation Stage 2 Evaporation E as a mass flux λE as a heat flux Ts increases as E declines Aminzadeh & Or (2014) J Hydrology → See TALK after next by Henk Lab Field Understanding principles Applying principles Precise and Controllable Not so precise Subject to vagaries of weather Spatial scale not large enough Land-Atmosphere feedbacks develop for all feedbacks to develop e.g. stomato close in mid-afternoon, VPD increases, (stomato may close even further), Sensible Heat Flux increases, Atmospheric convection enhanced, Thunderstorms develop, ………. Some Typical Field Measures Eddy Flux Stream Gauge – ACTUAL ET – long term E = P – Q - ACTUAL ET - {ignore storage} Calculate using Large Apertute SAT OBS and Scintillometer Met Data – ACTUAL ET - ACTUAL ET Evaporation Pan Your new method goes here ! – E is never supply-limited Laser scintillometer receiver transmitter For details, ask HENK Pan Evaporation: Why so much interest Peterson et al 1995 Nature 377:687-688 Presented averages for: - 190 pans in Former Soviet Union (FSU) - 746 pans in US - Pan evap. declining Same results found for: India, China, Thailand, Tibetan Plateau, Australia, New Zealand, South Africa, ……… DECLINGING NEARLY EVERYWHERE. AND STILL DECLINING. Typical rates ~ 3 mm/annum/annum Roderick et al 2009 Geography Compass, McVicar et al 2012 J Hydrology Is 3 mm a-2 a big deal ? Remember our trick to ~ relate energy and mass 1 W m-2 of latent heat ~ 1 mm month-1 of evaporation 3 mm a-2 ~ 3/12 mm month-1 a-1 -2 -1 -2 -1 ~ 3/12 W m a = 0.25 W m a -2 Over 30 years, dEpan is ~ - 7.5 W m – cf. TOA forcing for 2 X CO2, + 3.7 W m-2 Conclude: Magnitude is a BIG deal. (Sign ± an even bigger deal) Energy, water, carbon, and …… E is the key integrator Rs - α Rs + RL,i – RL,o = Rn = λE + H + G {Energy} PHYSICS dS/dt = P – E – Q {Water} E = Et + Es {= Transpiration + all other E} {Partitioning E} Et = f(A, …) {Water Use Efficiency = A/Et} dC/dt = A – Rh – Ra {Carbon: Assimilation and Respiration} BIOLOGY Nitrogen, Phosphorous, etc., ……. {Biogeochemistry} THANK YOU QUESTIONS .
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