Boundary layer processes

Sonia I. Seneviratne and Christoph Schär 1

Land-Atmosphere-Climate Interactions Winter term 2006/07

Land-surface processes in the global energy and water cycles.

Part (b)

Sonia Seneviratne

Institute for Atmospheric and Climate Science ETH Zürich

sonia.seneviratne@env.ethz.ch

Land-Atmosphere-Climate Interactions

Chapter 2b

Land-surface processes in the global energy and water cycles (b)

Sonia I. Seneviratne and Christoph Schär, Institute for Atmospheric und Climate Science, ETH Zürich Winter term 2006/2007

Outline

• Land energy and water balances, radiation balance (quick recapitulation)

• Atmospheric moisture

• Turbulent transport, boundary layer processes

• Latent heat flux / Evapotranspiration

Land energy and water balances

!

"H_s

"t = R* –SH–LH–G

change in energy storage

net radiation

sensible heat flux

latent heat flux

ground

heat flux change in water storage

precipi- tation

evapotrans- piration

surface runoff

groundwater runoff

5

dH_s/dt

H₂O, CO₂

SW_net LW_net LH=!E SH

G

Land energy balance

Land energy balance

Today’s topic

Outline

• Land energy and water balances, radiation balance (quick recapitulation)

• Atmospheric moisture

• Turbulent transport, boundary layer processes

• Latent heat flux / Evapotranspiration

Equation of states for dry air and water vapor

Ideal gas law for dry air:

universal gas constant: R^*=8.3143 J Mol^-1 K^-1 gas constant for dry air: R=R^*/M_a =287.04 J kg^-1 K^-1 average molecular weight of dry air: M_a=28.96 g Mol^-1

Ideal gas law for water vapor:

vapor pressure: e

gas constant for vapor: R_v =R^*/M_W = 461.9 J kg^-1 K^-1 molecular weight of vapor: M_W=18 g Mol^-1

!

p_a = "_a RT

!

e= "_vR_vT = "_v

(

)

!

" = R /R_v = M_W / M_a =0.622

8

Air Water vapor

p

= !

^RT

!

(

" )

Remove wall:

Isotherm compression:

p = p _a + e

Moist air

! = !

+ !

Mass conservation:

Dalton’s law of partial pressures

9

Using Dalton‘s law of partial pressures, the following equation of state for moist air can be derived:

where:

total density

virtual temperature [K]

specific humidity [g/ kg]

(for many applications the contribution of water vapor is negligible and the equation of state can be used with T instead of T_v )

p = !R T_v

!=!_a +!_v

T_v =T 1+q_v 1

! ^"1

#

$ % &

' ( )

* + ,

- . =T

[

]

q_v = !_v

!

!

Equation of state for moist air

10

Specific humidity [kg H₂O-vapor / kg air]:

Absolute humidity [kg H₂O-vapor / m³ air ]:

Vapor pressure [Pa]: obtained through division of with the equation of state for moist air

q_v = !_v

!

!_v =q_v!

e= !_v(R ")^T

e = q_v

1+q_v 0.608 1

! ^{p" qv} 1

! ^p

Definitions: Moist air

11

Specific humidity [kg H₂O-vapor / kg air]:

Absolute humidity [kg H₂O-vapor / m³ air ]:

Vapor pressure [Pa]: obtained through division of with the equation of state for moist air

q_v = !_v

!

!_v =q_v!

e= !_v(^R ")^T

e = q_v

1+q_v 0.608 1

! ^{p" qv} 1

! ^p

Definitions: Moist air

!

q_v "# ^e p

12

Relative humidity:

(often expressed in %)

Saturation vapor pressure [Pa]:

(only a function of temperature)

Dew point temperature [K]: Temperature to which an air parcel must be cooled, at constant pressure, for saturation to occur

Clausius-Clapeyron equation (approximation):

e = 2.71828

e_so = 6.108 hPa a = 17.27 T_o = 273.16 K b = 35.86 K

U = e e_sat(T)

Definitions: Moist air

e_sat(T)

e_sat(T) = e_so e^a

T–T_o T–b

13

Over liquid water

Saturation vapor pressure [hPa]

Temperature [^oC]

Saturation vapor pressure curve

Over ice

For each ºC of warming, the air can contain ~6% more

water vapor Undersaturation

Water evaporates

Oversaturation

Water vapor condensates

supercooled water

Outline

• Land energy and water balances, radiation balance (quick recapitulation)

• Atmospheric moisture

• Turbulent transport, boundary layer processes

• Latent heat flux / Evapotranspiration

15

dH_s/dt

H₂O, CO₂

SW_net LW_net LH=!E SH

G

Land energy balance

Land energy balance

Turbulent fluxes

16

Laminar advection: Transport occurs through the mean flow

Transport processes

humid dry Turbulent advection: Major departures from

the mean flow: This can allow transport that is not necessarily parallel to the mean flow (e.g evapotranspiration)

[Conceptually some similarities with diffusion;

but much more efficient!]

Diffusion: Transport due to Brownian motion (random motion " net transport from

locations with high concentrations to locations with low concentration)

Boundary layer

(Stull 1988)

Boundary layer processes

+

Mittlere Strömung Resultierende Turbulenz

– + –

u (z), w (z), T (z), q (z) u ,! w ,! T ,! q !

Mean flow Resulting turbulence

Boundary layer processes

+

Mittlere Strömung Resultierende Turbulenz

– + –

u (z), w (z), T (z), q (z) u ,! w ,! T ,! q !

Mean flow Resulting turbulence

Mean quantities

Anomalies

Boundary layer processes

+

Mittlere Strömung Resultierende Turbulenz

– + –

u (z), w (z), T (z), q (z) u ,! w ,! T ,! q !

Mean flow Resulting turbulence Decompose variables T, u, w, q :

! = Air density (u,v,w) = Wind

q = Specific humidity

= Average over time

´ = Anomalies from mean

! = ! (z) + !' (x,y,z,t)

Boundary layer processes

+

Mittlere Strömung Resultierende Turbulenz

– + –

u (z), w (z), T (z), q (z) u ,! w ,! T ,! q !

Mean flow Resulting turbulence Decompose variables T, u, w, q :

! = Air density (u,v,w) = Wind

q = Specific humidity

= Average over time

´ = Anomalies from mean

! = ! (z) + !' (x,y,z,t)

e.g.: On homogeneous terrain and in quasi-stationary conditions:

evapotranspiration is almost

identical to the mean moisture flux in the boundary layer:

[kg mET = ! q " w " ^–2 s^-1]

22

Fluxes:

Boundary layer theory:

Provides relationships between mean state and turbulent fluxes:

where:

u_a horizontal wind at height z_a (e.g. z_a=10m)

q_s, T_s specific humidity and temperature at the surface q_a, T_a specific humidity and temperatur at height z_a

C_W, C_H aerodynamic transfer coefficients for humidity and heat

(dependent on stability, structure of the boundary layer, surface properties, etc...)

LH = L ET = L ! q " w " SH = c_p ! T " w "

q ! w ! " C_W u_a

(

)

[W m^–2 ]

Boundary layer theory

c_p: specific heat of air

Latent heat flux Sensible heat flux

(1a,1b)

(2a,2b)

23

Use of (2a,2b) in (1a,1b) yields:

Note:

• the fluxes are proportional to the wind speed

• the evapotranspiration is proportional to the humidity difference q_s - q_a between the surface and the atmosphere. From

(#=0.622, see pp.19-20) follows a linear dependency on the relative humidity U, and an exponential dependency on the temperature T.

• The validity of relationships (3a, 3b) is limited by uncertainties in the terms C_W and C_H .

For neutral conditions and z_a = 10m: C_W ! C_H ! 2·10^–3

LH = L ! C_W u_a

(

)

q = ! e

p = ! U e_sat(T) p

Boundary layer theory

(3a,3b)

Bowen Ratio

Bowen ratio: Ratio between sensible und latent heat fluxes:

=> B << 1 moist surface, LH dominates over SH

=> B >> 1 dry surface, SH dominates over LH From boundary layer theory (3a,3b):

and with C_W ! C_H :

the Bowen ratio is less dependent on details of the structure of the boundary layer than the fluxes SH and LH

B = SH LH

LH = L ! C_W u_a

(

)

B = c_p L

(T_s !T_a) (q_s !q_a)

25

Seasonal Cycle of Soil Moisture

Month

Soil moisture [mm]

Bowen Ratio

B << 1 B >> 1

26

Eddy-Covariance Measurement:

Measurement of w‘, T‘, and q‘ with Sonic-Anemometer (ultrasounds):

measurement of anomalies with very high temporal resolution (up to ~100 Hz)

Measurements of T‘ (SH) more accurate than those of q‘ (LH)

SH = c_p ! T " w "

LH = L ! q " w "

Measurement of turbulent fluxes

27

FLUXNET project

http://www-eosdis.ornl.gov/FLUXNET/

(see also excursion)

Outline

• Land energy and water balances, radiation balance (quick recapitulation)

• Atmospheric moisture

• Turbulent transport, boundary layer processes

• Latent heat flux / Evapotranspiration

• involved processes

• measurements, estimation

Components of evapotranspiration

Total Evapotranspiration ET : Total Evaporation at the surface:

with:

E_b: Evaporation from top soil (bare soil evaporation)

E_i: Evaporation from interception storage (Earth‘s surface and vegetation)

E_s: Snow sublimation

TR: Transpiration from vegetation ET =E_b + E_i +E_s +TR

Components of evapotranspiration

Total Evapotranspiration ET : Total Evaporation at the surface:

with:

E_b: Evaporation from top soil (bare soil evaporation)

E_i: Evaporation from interception storage (Earth‘s surface and vegetation)

E_s: Snow sublimation

TR: Transpiration from vegetation ET =E_b + E_i +E_s +TR

Provide various time scales for land-atmosphere coupling!

Actual ET, potential ET, potential evaporation

Actual evapotranspiration ET: limited by

• Energy supply (radiation balance at the surface)

• Water availability (soil moisture, interception storage)

• Vegetation processes

• Near-surface conditions (temperature, humidity, wind, boundary layer characteristics)

Potential evapotranspiration ET_pot : ET from vegetated surfaces without limitations of water supply

Potential evaporation E_pot : E from free water surface

Bouchet’s hypothesis

Bouchet, 1963: Complementary relationship between actual evapotranspiration and potential evapotranspiration

!

ET

+ ET

= k ET

ET_a: actual ET ET_p: potential ET

ET_w: wet environment ET

(see publications by e.g. Brutsaert and Parlange, Nature, 1998; Ramirez et al. GRL 2005)

Vegetation controls

Dependence of transpiration (and photosynthesis) of vegetation on several factors:

• soil moisture

• phenology

• rooting depth

• leaf area index

• CO₂

• ...

35

Dry lake bed Field of mature corn Well-irrigated alfafa field

Diurnal cycle of energy budget terms

LE = LH = latent heat flux

(Hartmann, 1994)

Leaf area index

Ratio of leaf surface (one side) to soil surface

Examples (maximum of vegetation):

Tundra ~1

Grasland 1-4

Deciduous forest (temperate regions) 3-7 Coniferous forest (temperate regions) 10-40

Leaf area index from grassland

Relationship between height of

grass and leaf area index Time series of leaf area index (Rietholzbach 1994)

Photosynthesis

(Sellers et al. 1997)

Stomate density: 10‘000 - 100‘000 / cm²

Outline

• Land energy and water balances, radiation balance (quick recapitulation)

• Atmospheric moisture

• Turbulent transport, boundary layer processes

• Latent heat flux / Evapotranspiration

• involved processes

• measurements, estimation

Measurement of potential evaporation

Evaporation pan:

approximate measurement of E_pot

Error sources:

• small specific heat of pan => stronger warming and higher evaporation in comparison with natural water surface (e.g. lake)

• small horizontal scale $ oasis effect (overestimation of evaporation)

=> use of correction factor (typically ~0.7) as approximate correction for the errors

“Class A Pan”

41

see Rietholzbach site:

http://www.iac.ethz.ch/research/rietholzbach

Measurement of actual evapotranspiration from

changes in weight and water balance (need to measure P and lysimeter runoff)

Measurement of actual ET: Lysimeter

42

43

Diurnal cycle lysimeter

Weight change [mm/h]

Day total: –10.3 mm

Precipitation [mm/5 min]

Sum: 0 mm

Runoff

River [l/s]

Lysimeter [1.5/1000 mm/h]

Day total: 5.4 mm

Radiation [W/m2]

Global radiation Reflected radiation ––> ET: 4.9 mm

Rietholzbachgebiet 24.05.1999

45

Precipitation [mm/d]

Temperature [^oC]

Evapotranspiration [mm/d]

Seasonal cycle lysimeter

Indirect ET estimation from surface energy balance

The terms on the right-hand side are estimated in the following way:

• for time periods > 1 day, G + "H_s/"t ! 0 .

• R^*= SW_net + LW_net is measured

• SH is measured or estimated ET = 1

L

(

)

!

"H_s

"t = R* –SH–LH–G

Indirect ET estimation from surface energy balance

The terms on the right-hand side are estimated in the following way:

• for time periods > 1 day, G + "H_s/"t ! 0 .

• R^*= SW_net + LW_net is measured

• SH is measured or estimated ET = 1

L

(

)

!

"H_s

"t = R* –SH–LH–G

Computation of ET following Budyko

Bowen-Ratio B

can be computed if temperature and humidity are measured on two separate levels.

ET can be obtained from the combination with the surface energy balance

(use LH = L ^. ET and SH = B ^. L ^. ET and solve for ET) B = SH

LH = c_p L

(T_s !T_a) (q_s !q_a)

!H_s !t = R* " SH " LH " G

ET = 1 L

1

1+B R* ! G ! "H_s

"t

#

$ % &

' (

~ R*

49

• Used to derive maps of ET based on measurements of T and q on several levels

• Good approach for saturated areas (in particular oceans) using q_s = q_sat(T_s) (potential evaporation)

• For unsaturated areas, the determination of q_s is difficult

Use of Budyko method

Example: Map of evaporation

Atmospheric water balance estimate of evaporation

Atmospheric water balance:

(Yeh et al. 1998)

Q

P E

W

Atmospheric water balance estimate of evaporation

Atmospheric water balance:

(Yeh et al. 1998)

Q

P E

W

Remote sensing of vegetation cover

Albedo / Absorption in visible and near-infrared depend highly on vegetation

Example:

Normalized Difference Vegetation Index NDVI:

a_V, a_N : reflectances in visible and near infrared measured from the satellite

corrections required for cloud cover, snow, zenith angle, measurement errors, data gaps

NDVI = a_N ! a_V a_N + a_V

Satellite products NDVI

Reto Stöckli, NASA / ETH Zürich