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 ~ 3/12 W m-2 a-1 = 0.25 W m-2 a-1
-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