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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– [email protected]