land surface in climate models parameterization of surface fluxes bart van den hurk (knmi/imau)

Land surface in climate models

Parameterization of surface fluxes

Parameterization of surface fluxes

Bart van den Hurk(KNMI/IMAU)

Land surface in climate models

Orders of magnitudeOrders of magnitude

• Estimate the energy balance of a given surface type– What surface?– What time averaging? Peak during day?

Seasonal/annual mean?– How much net radiation?– What is the Bowen ratio (H/LE)?– How much soil heat storage?– Is this the complete energy balance?

• The same for the water balance– How much precipitation?– How much evaporation?– How much runoff?– How deep is the annual cycle of soil storage?– And the snow reservoir?

Land surface in climate models

General form of land surface schemes

General form of land surface schemes

• Energy balance equation

K(1 – a) + L – L + E + H = G

• Water balance equation

W/t = P – E – Rs – D

Q*H E

G

P E

Infiltration

Rs

D

Land surface in climate models

Structure of a land-surface scheme (LSS or SVAT)

Structure of a land-surface scheme (LSS or SVAT)

• 6 fractions (“tiles”)• Aerodynamic coupling• Vegetatie

– Verdampingsweerstand– Wortelzone– Neerslaginterceptie

• Kale grond• Sneeuw

Land surface in climate models

Structure of a land-surface scheme (LSS or SVAT)

Structure of a land-surface scheme (LSS or SVAT)

• 6 fractions (“tiles”)• Aerodynamic coupling

– Wind speed– Roughness– Atmospheric stability

• Vegetatie– Verdampingsweerstand– Wortelzone– Neerslaginterceptie

• Kale grond• Sneeuw

Land surface in climate models

Structure of a land-surface scheme (LSS or SVAT)

Structure of a land-surface scheme (LSS or SVAT)

• 6 fractions (“tiles”)• Aerodynamic coupling

– Wind speed– Roughness– Atmospheric stability

• Vegetation– Canopy resistance– Root zone– Interception

• Kale grond• Sneeuw

Land surface in climate models

Structure of a land-surface scheme (LSS or SVAT)

Structure of a land-surface scheme (LSS or SVAT)

• 6 fractions (“tiles”)• Aerodynamic coupling

– Wind speed– Roughness– Atmospheric stability

• Vegetation– Canopy resistance– Root zone– Interception

• Bare ground• Sneeuw

Land surface in climate models

Structure of a land-surface scheme (LSS or SVAT)

Structure of a land-surface scheme (LSS or SVAT)

• 6 fractions (“tiles”)• Aerodynamic coupling

– Wind speed– Roughness– Atmospheric stability

• Vegetation– Canopy resistance– Root zone– Interception

• Bare ground• Snow

Land surface in climate models

Specification of vegetation typesSpecification of vegetation types

Land surface in climate models

Vegetation distributionVegetation distribution

Land surface in climate models

Aerodynamic exchangeAerodynamic exchange

• Turbulent fluxes are parameterized as (for each tile):

• Solution of CH requires iteration:– CH = f(L)– L = f(H)– H = f(CH)

2UC

TqqE

TgzTUCcH

Ma

sksatsaaa

sklaHpa

aHH rUC /1

L = Monin-Obukhov length

s

a Ta+gz

s

a

H

Land surface in climate models

More on the canopy resistanceMore on the canopy resistance

• Active regulation of evaporation via stomatal aperture

• Two different approaches– Empirical (Jarvis-Stewart)

rc = (rc,min/LAI) f(K) f(D) f(W) f(T)

– (Semi)physiological, by modelling photosynthesis

An = f(W) CO2 / rc

An = f(K, CO2)

CO2 = f(D)

Land surface in climate models

Jarvis-Stewart functionsJarvis-Stewart functions

• Shortwave radiation:

• Atmospheric humidity deficit (D):f3 = exp(-cD) (c depends on veg.type)

0.00.1

0.20.30.40.5

0.60.70.8

0.91.0

0 200 400 600

Shortwave radiation (W/m2)

f1(R

s)

Land surface in climate models

Jarvis-Stewart functionsJarvis-Stewart functions

• Soil moisture (W = weighted mean over root profile):

• Standard approach: linear profilef2 = 0 (W < Wpwp)

= (W-Wpwp)/(Wcap-Wpwp) (Wpwp<W<Wcap)

= 1 (W > Wcap)

• Alternative functions (e.g. RACMO2)

Lenderink et al, 2003

Land surface in climate models

Effective rooting depthEffective rooting depth

• Amount of soil water that can actively be reached by vegetation

• Depends on– root depth (bucket depth)– stress function– typical time series of precip & evaporation

• See EXCEL sheet for demo

Land surface in climate models

Numerical solutionNumerical solution

• Solution of energy balance equation

• With (all fluxes positive downward)

• Express all components in terms of Tsk (with Tp = Tskt

-1)

GEHQ *

)(

)1(* 4

soilsksk

sksatsaaa

sklaHpa

skTs

TTG

TqqE

TgzTUCcH

TRRaQ

net radiation

sensible heat flux

latent heat flux

soil heat flux

)()()(

)(4 344

pskT

satpsatsksat

pskppsk

TTT

qTqTq

TTTTT

p

Land surface in climate models

Numerical solutionNumerical solution

• Substitute linear expressions of Tsk into energy balance equation

• Sort all terms with Tsk on lhs of equation

• Find Tsk = f(Tp , Tsoil , CH , forcing, coefficients)

Land surface in climate models

Carbon exchangeCarbon exchange

• Carbon & water exchange is coupled

• Carbon pathway:– assimilation via photosynthesis– storage in biomass

• above ground leaves• below ground roots• structural biomass (stems)

– decay (leave fall, harvest, food)– respiration for maintenance, energy etc

• autotrophic (by plants)• heterotrophic (decay by other organisms)

CO2

H2O

Land surface in climate models

The gross vegetation carbon budget

The gross vegetation carbon budget

GPP = Gross Primary Production

NPP = Net Primary Production

AR = Autotrophic Respiration

HR = Heterotrophic Respiration

C = Combustion

GPP120 AR

60HR55NPP

60

C4

Land surface in climate models

The coupled CO2 – H2O pathway in vegetation models

The coupled CO2 – H2O pathway in vegetation models

• qin = qsat(Ts)

• Traditional (“empirical”) approach:rc = rc,min f(LAI) f(light) f(temp) f(RH) f(soil

m)

ca

airina rr

qqE

Land surface in climate models

Modelling rc via photosynthesisModelling rc via photosynthesis

• An = f(soil m) CO2 / rc

• Thus: rc back-calculated from

– Empirical soil moisture dependence

– CO2-gradient CO2

• f(qsat – q)

– Net photosynthetic rate An

• An,max

• Photosynthetic active Radiation (PAR)• temperature

• [CO2]

Land surface in climate models

Parameterization of soil and snow hydrology

Parameterization of soil and snow hydrology

Bart van den Hurk(KNMI/IMAU)

Land surface in climate models

Soil heat fluxSoil heat flux

• Multi-layer scheme• Solution of diffusion equation

• with C [J/m3K] = volumetric heat capacity T [W/mK] = thermal diffusivity

• with boundary conditions– G [W/m2] at top– zero flux at bottom

Land surface in climate models

Heat capacity and thermal diffusivity

Heat capacity and thermal diffusivity

• Heat capacity

sCs 2 MJ/m3K, wCw 4.2 MJ/m3K

• Thermal diffusivity depends on soil moisture– dry: ~0.2 W/mK; wet: ~1.5 W/mK

wwsssataaawwwssssoil CCCxCxCxC )1(

Land surface in climate models

Soil water flowSoil water flow

• Water flows when work is acting on it– gravity: W = mgz– acceleration: W = 0.5 mv2

– pressure gradient: W = m dp/ = mp/• Fluid potential (mechanical energy / unit mass)

= gz + 0.5 v2 + p/p = gz g(z+z) = gh

• h = /g = hydraulic head = energy / unit weight = – elevation head (z) +– velocity head (0.5 v2/g) + – pressure head ( = z = p/g)

Land surface in climate models

Relation between pressure head and volumetric soil moisture content

Relation between pressure head and volumetric soil moisture content

strong adhesy/capillary forces dewatering from

large to small pores

retention curve

Land surface in climate models

Parameterization of K and DParameterization of K and D

• 2 ‘schools’– Clapp & Hornberger ea

• single parameter (b)

– Van Genuchten ea• more parameters describing curvature better

• Defined ‘critical’ soil moisture content– wilting point ( @ = -150m or -15 bar)– field capacity ( @ = -1m or -0.1 bar)

• Effect on water balance: see spreadsheet

32

)(

b

satsatKK

bsat

Land surface in climate models

pF curves and plant stresspF curves and plant stress

• Canopy resistance depends on relative soil moisture content, scaled between wilting point and field capacity

pF curve

0.01

0.1

1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Volumetric soil moisture (m3/ m3)

Pre

ssu

re h

ead

(h

Pa)

txsture 1texture 2texture 3texture 4texture 5texture 6

Land surface in climate models

Boundary conditionsBoundary conditions

• Top:F [kg/m2s] = T – Esoil – Rs + M

• Bottom (free drainage)F = Rd = wK

• with– T = throughfall (Pl – Eint – Wl/t)– Esoil = bare ground evaporation– Eint = evaporation from interception reservoir– Rs = surface runoff– Rd = deep runoff (drainage)– M = snow melt– Pl = liquid precipitation– Wl = interception reservoir depth– S = root extraction

Sz

FFS

z

F

t wbottop

ww

Pl

TEint

Wl

MEsoilRs

Rd

S

Land surface in climate models

Parameterization of runoffParameterization of runoff

• Simple approach– Infiltration excess runoff

Rs = max(0, T – Imax), Imax = K()

– Difficult to generate surface runoff with large grid boxes

• Explicit treatment of surface runoff– ‘Arno’ scheme

Infiltration curve(dep on W andorograpy)

Surface runoff

Land surface in climate models

Snow parameterizationSnow parameterization

• Effects of snow– energy reflector– water reservoir acting as buffer– thermal insolator

• Parameterization of albedo– open vegetation/bare ground

• fresh snow: albedo reset to amax (0.85)

• non-melting conditions: linear decrease (0.008 day-1)

• melting conditions: exponential decay

– (amin = 0.5, f = 0.24)

– For tall vegetation: snow is under canopy• gridbox mean albedo = fixed at 0.2

Land surface in climate models

Parameterization of snow waterParameterization of snow water

• Simple approach– single reservoir– with

• F = snow fall• E, M = evap, melt• csn = grid box fraction with snow

• Snow depth

– with sn evolving snow density (between 100 and 350

kg/m3)• More complex approaches exist (multi-layer,

melting/freezing within layers, percolation of water, …)

Land surface in climate models

Snow energy budgetSnow energy budget

• with

– (C)sn = heat capacity of snow

– (C)i = heat capacity of ice

– GsnB = basal heat flux (T/r)

– Qsn = phase change due to melting (dependent on Tsn)

Land surface in climate models

Snow meltSnow melt

• Is energy used to warm the snow or to melt it? In some stage (Tsn 0C) it’s both!

• Split time step into warming part and melting part

– first bring Tsn to 0C, and compute how much energy is needed

– if more energy available: melting occurs– if more energy is available than there is

snow to melt: rest of energy goes into soil.

Land surface in climate models

ExerciseExercise

• Given:

• Derive the Penman-Monteith equation:

aas

s

a

asp

ca

ass

qTqD

ALEHGQTq

rTT

cH

rrqTq

LLE

)(

*

)(

a

cp

ap

rr

L

c

rcDALE

1

/

Land surface in climate models

More informationMore information

• Bart van den Hurk– hurkvd@knmi.nl