ATM 301 Lecture #9 (sections 3.3, 3.5, 6.1)

ET Overview & Turbulent Fluxes

• Evaporation process

• Turbulent Fluxes at the surface

• Surface Heat fluxes

• Controls of ET

• Measurements of ET

Evapotranspiration in the Global Hydrologic Cycle:

About 65% of land-precipitation is returned to the atmosphere by evapotranspiration

Why study evapotranspiration(ET)?

• (P-ET) = runoff + storage changes = water available for human use

• Humans can have big impacts on ET (irrigation, land surface and vegetation changes)

• Changes of ET with climate can lead to further climate changes

• Need to understand ET to effectively:• Design irrigation strategies and crop planting• Manage reservoirs and water resources• Predict streamflow and flooding

ET includes:• Evaporation from water surface• Evaporation from wet bare soil surface• Evaporation from water on vegetation (leaves, canopy)• Evaporation from plant tissues (transpiration)

Wang and Dickinson (2012)

ET is often simply called evaporation (E)

Thus E usually includesplant transpiration.

ET is a more accurate term

ET is a surface water flux

Water Vapor Variables- Water vapor mixing ratio r = water vapor mass/ dry air mass- Saturated vapor pressure (es) is the equilibrium vapor pressure over a

water surface. es = 6.112 mb at oC. es increases exponentially with air temperature T (oC): es = 6.112 exp [ 17.67T/(T + 243.5)] (Bolton 1980).

- Vapor pressure (e) is the partial pressure exerted by water vapor in the air. It is a function of es and RH: e = es RH/100. e=P*r/(0.622+r)

- Relative humidity RH(%)=100*e/es=100*r/rs : a measure of water vapor saturation level in the air

- Specific humidity q = water vapor mass (g) / total air mass (kg) in a given volume of air. q = r/(1+r), r=q/(1-q) = 0.622e/(P-e)

- Absolute humidity AH = water mass per unit air (g/m3): 0-30g/m3

- Precipitable water (PW) is the column-integrated total water vapor content, often expressed in mm depth over a unit surface

- Dew point depression (DPD) is the temperature difference between the air temperature and the dew point temperature

The Clausius-Clapeyron Relation

• The Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, is a way of characterizing a discontinuous phase transition between two phases of matter of a single constituent. On a pressure–temperature (P–T) diagram, the line separating the two phases is known as the coexistence curve. The Clausius–Clapeyron relation gives the slope of the tangents to this curve. The exact equation for es(T) is determined in labs and may vary slightly.

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The C-C Eq. for water vapor:

Saturation Vapor Pressure Equations: There are many similar equations for estimating es over water and over ice:

• Suggest to use WMO (2008) recommended Equations (t in oC and e in hPa):

• ew = 6.112 e(17.62 t/(243.12 + t)) saturation vapor pressure over liquid water

• ei = 6.112 e(22.46 t/(272.62 + t)) saturation vapor pressure over solid ice

See http://faculty.eas.ualberta.ca/jdwilson/EAS372_13/Vomel_CIRES_satvpformulae.html

Differences for ew Eqs. Differences for ei Eqs.ew increases with T

Saturation Vapor Pressure Difference over Water and Ice:

• esw is slightly higher than esi at the same T

• This can lead to growth of ice particles at the expense of liquid droplets inside cold clouds when esi < e < esw (the Bergeron-Wegner-Findeisen process)

esw - esi4% of esw

Evaporation Process: some water molecules on a water surface may have enough kinetic energy to break the hydrogen bonds and enter the thin layer of air just above the water surface. The vapor molecules are then mixed upward away from the water surface, creating a water flux called Evaporation. This evaporation process is the same over water and ice surface, soil pores, plant tissues, and cloud droplets.

E is determined by vapor pressure gradient at the interface:

• If es*(Ts) > ea, evaporation is occurring (it may form a fog or mist if RH=100%);

• If es*(Ts) < ea, water vapor is condensing on the surface; and

• If es*(Ts) = ea, neither evaporation nor condensation is occurring.

• Note: ea is determined by how quickly the water molecules are removed from the layer adjacent to the interface by turbulent mixing.

Need energy to break up the hydrogen bonds

Latent Heat of Vaporization (v): -- The energy needed for H2O molecules (of one unit of mass) to break up the hydrogen bonds during evaporation at the water surface • Evaporation transfers heat from the surface into the air, thus cooling the surface

• Condensation in the air releases the same amount of heat, warming the air

• Condensation at the surface transfer heat from the air to the surface, thus cooling the air and warming the surface

• These processes are called latent-heat exchange.

• The latent heat flux (LH) per unit area is related to evaporation rate (E, which is also per unit area):

LH E = v w E

where v (in J /kg) decreases slightly with temperature (t, in oC) of the evaporating surface (Rogers and Yau 1989):

v (J kg-1) = 1000(− 0.0000614342 t3 + 0.00158927 t2 − 2.36418 t + 2500.79)

and v =2.467 106 J kg-1 for t=14.35oC (or 287.5K)

w 1000 kg/m3

= v w= 2.467 x 109 J/m3

E (in mm/day) must be converted into m/s for this equation, which gives LH in unit of J/s /m2 = W/m2 (watts per square meter).

1mm/day = 10-3m/(24x3600s) = 10-3 m/(86400 s) = 1.1574x10-8 m/s Example: Calculate LH for E = 10 mm/day at t=14.35oC.

Note: Eq. (3.18) on p. 116 should be v (MJ/kg)= 2.501 – 0.00236 Ts(oC)

Evaporation over Ice or Snow – Sublimation:

• Evaporation over ice or snow needs extra energy to disrupt the molecular structure of ice (i.e., by melting)

• After that, the same amount of latent energy as over water surface is needed to break up the

hydrogen bonds

• Thus, the latent heat flux (LH) during sublimation is:

LH E = (v + f ) w E

where f =0.334x106 J /kg, only about 13% of v (2.467x106 J /kg)

f is the latent heat of fusion, i.e., the heat required to melt unit mass of ice.

f + v is the latent heat of sublimation.

Example: calculate the LH for E = 10mm/day over ice surface

Turbulent Eddy Mixing:• Without eddy mixing, surface air will quickly become saturated and evaporation will stop!• Vertical turbulent mixing or exchange is critical for continued evaporation.

What is Turbulence?• Turbulence or turbulent flow is a flow regime with chaotic changes in flow velocity, pressure, and

other properties of a fluid (such as air or water). It has low momentum diffusion but high momentum convection. The friction from eddies dominates. Reynolds Number Re=inertial force/viscous force=wUL/ > 5000

• In contrast, laminar flow is a flow regime where molecular viscosity is important. Re < 5000.

• Turbulence causes eddies, which are the swirling structures of a fluid in a turbulent flow.

• Turbulent fluxes: the fluxes of momentum, mass and heat carried by the eddies in a turbulent flow. They are the most important way of mixing in the planetary boundary layer (the lower 1km of the atmosphere) above the surface, especially in the vertical direction. This turbulent mixing is also called turbulent diffusion.

https://www.youtube.com/watch?v=e1TbkLIDWys

https://www.youtube.com/watch?v=ZPoxsiDbxx0

Turbulent boundary layers due to friction & heating

Friction (3min):

Heating (30sec.):

Near-surface wind velocity profiles:

• The Prandtl-von Kármán universal velocity (u) distribution:

where zd = 0.7 zveg is the zero-plane displacement height, and zo = 0.1 zveg is the surface roughness height, zveg = average vegetation height, and u* is the friction velocity:

u’ and w’ are horizontal and vertical velocity fluctuations.

zm = measurement height for u(zm), zm = 2m or 10m, and is a constant (=0.4).

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Mixed layer(~1km deep)

Interfacial sublayer

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Near-surface turbulent flux: Evaporation (or Evapotranspiration)

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• Evaporation rate E is proportional to the product of near-surface wind speed and surface-air vapor pressure difference (following Fick’s law of diffusion: F=-K dC/dx):

E = KE u(zm) [es – e(zm)] -- called bulk formula in climate modeling

KE = water-vapor transfer coefficient (p.126, using Fick’s law and the universal u distribution):

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Near-surface turbulent flux: Latent Heat

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• Latent heat flux is also proportional to the product of near-surface wind speed and surface-air vapor pressure difference:

LH E = w v E = w v KE u(zm) [es – e(zm)]

v (x106J/kg) = 2.50 – 2.36 x 10-3 T (oC)

Near-surface turbulent flux: Sensible Heat

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• Sensible heat is the heat exchanged by differences in temperature. • Sensible heat flux (SH) is proportional to the product of near-surface wind speed and surface-air

temperature difference (following Fick’s law of diffusion):

SH = KH u(zm) [Ts – T(zm)]

KH = sensible-heat transfer coefficient (pp. 127-128):

cp=specific heat of air at constant pressure =1.005x10-3MJ kg-1 K-1

Ts = surface temperature T(zm)= air temperature at height zm

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The Bowen Ratio (B):

• The Bowen ratio is the ratio of the sensible to latent heat fluxes: B SH/LH

where

is called the psychrometric constant

• Evaporation fraction (EF) is the ratio of the latent heat flux to the total turbulent heat flux:

• Example: for LH=20 W/m2 and SH=10 W/m2, calculate B and EF

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The Bowen Ratio: Typical values

SH dominates over arid areas and deserts (B>1)LH dominates over oceans, tropical and temperate forests (B<1)

ET is often estimated under various conditions:

• Type of surface: open water, bare soil, leaf or leaf canopy, a reference crop, or a land region

• Availability of water: water-limited or –unlimited (i.e., energy-limited).

• Stored-energy use: surface energy storage change (U/ t) may be significant or negligible; and

• Water-advected energy use: the Aw term may be significant or negligible.

Classification of ET Processes:

Controls of ET • Vegetation plays a key role by drawing water

from deep soils.

• Energy availability: E is large in daytime and warm seasons

• Soil water availability: Dry soils reduce E

• Wind speed: Strong winds increase mixing, lead to higher E

• Air Temperature: higher T is associated with higher Rn and larger stomal openings in leaves, leading to higher E.

• Relative humidity: E decreases as RH increases.

ET vs. Temperature Correlation (Jung et al. 2010)High Correlation implies energy limitation on ET

ET vs. Precip. Correlation (Dong and Dai 2015)High correlation implies water-limited ET

Direct Measurement of ET • Lysimeter Method:

Use a tank of 1-5m2 to estimate ET. Weighing and Nonweighing

Gross and Ehlers (2009)

Evapotranspiration: direct measurement is HARD (and expensive)

http://www.iac.ethz.ch/en/research/riet/instruments.html

• Can directly measure ET with a lysimeter by weight & water balance of a column of “natural” soil

• Very expensive ($10k-100k’s) and cumbersome, so uncommon

• …and large uncertainties due to spatial variations!

We need other methods to:1. Estimate ET indirectly2. Understand and predict ET

• Eddy Covariance (EC) Method: It measures SH and LH fluxes from their covariance with vertical velocity using rapid response sensors at frequencies ≥10Hz. First used by Australian scientists in the 1950s, now used at 500+ FLUXNET sites. Error range: 5-20%.

Other Methods for Measuring ET

Satellite Retrieval of ET • Satellites can not directly measure ET• Various methods have been developed to use satellite measured

surface temperatures and other properties to derive ET using either the Monin-Obukhov similarity theory (MOST) or Penman-Monteith (P-M) method.

• Wang and Dickinson (2012) describe these methods.

Other Methods for Measuring E • Scintillometer Method: A scintillometer consists of a transmitter (picture) and a receiver, which measures the fluctuations in the radiation emitted by the

transmitter caused by scattering associated with variations in the refractive index due turbulent eddies along the path. Effects of T and q are mostly at the optical and radio wave frequencies, respectively; thus both SH and LH aggregated along the path can be derived with the help of MOST. A relatively new method.

• E from Surface Water Balance: E = P – R – dW/dt on a basin or continental scale. Large errors in P, R and dW/dt

• E from Atmospheric Water Balance Method: E = P + h Vq + W/tNeed atmospheric data, large errors for small regions.

Evapotranspiration: surface budget approach

• Since direct observation of ET is hard, we often try to estimate (or predict) it indirectly using budgets of energy and water at the surface

• We can convert between energy and water changes due to ET through the Latent Heat of Vaporization (λv)

• If we can estimate all other terms in a budget equation, we can infer ET.

• This is also useful for understanding the physical controls on ET and for making predictions

where

U/ t = energy storage change within the surface layer S = net shortwave (i.e. solar) radiation into the layer (positive down) L = net longwave (i.e. infrared) radiation into the layer (positive down)

E = latent heat flux (positive upward) SH = sensible heat flux (positive upward) G = downward heat flux through conduction (often small) Aw = net energy input associated with inflows and outflows of water (often small)

Thus, evaporation is constrained by and can be derived using the surface energy balance.

Surface Energy Balance: A constraint on E

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Estimating E• Energy Balance Bowen Ratio (BR) Method: It uses

measurements of vertical gradients of T and q to partition the available energy into sensible (H) and latent (E) heat fluxes. Suitable for short vegetation.

The Bowen Ratio (B) is estimated as

The T and q gradients may be small, which could lead to large errors in B.

E is then estimated from the surface energy balance equation:

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Need to know surface energy fluxes – next lecture