Parameterization of land surface
Bart van den Hurk
(KNMI/IMAU)
Land surface in climate models
Last week: Orders of magnitude
• Estimate the energy balance of a given surface type
– What surface?
– What annual cycle?
– 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 setup of General Circulation
Models (3)
• Many processes are sub-grid, and need to be
parameterized
– Fine scale processes (fluxes) expressed in terms of
resolved variables (mean state) using (semi-)
empirical, observation based equations
• Example: turbulent sensible heat flux
H   c pUC H  s   a 
H = Sensible heat flux [W/m2]
 = air density [kg/m3]
cp = specific heat [J/kg K]
U = wind speed [m/s]
CH = exchange coefficient [-]
s - a = temperature gradient [K]
a
a
H
s
s
Land surface in climate models
General form of land surface schemes
• Energy balance equation
Q*
H LE
K(1 – a) + L – L + E + H = G
G
• Water balance equation
W/t = P – E – Rs – D
P
E
Rs
Infiltration
D
Land surface in climate models
General form of land surface schemes
• Energy balance equation
Q*
H LE
K(1 – a) + L – L + E + H = G
G
• Water balance equation
W/t = P – E – Rs – D
P
E
Rs
• Coupled via the evaporation
Infiltration
D
Land surface in climate models
Land surface heterogeneity
• Land surface is heterogeneous blend of vegetation at many
scales
– forest/cropland/urban area
– within forest: different trees/moss/understories
• Most LSMs use set of parallel “plant functional types” (PFTs)
with specific properties
– gridbox mean or tiled
– Some ecological models treat species competition and
dynamics within PFTs
• Properties of PFTs
– LAI
– rooting depth
– roughness
– albedo
– emission/absorption of organic compounds
Land surface in climate models
Development history of land schemes
• Late 1960’s: bucket scheme (Manabe, 1969) with
depth of the reservoir = 15cm
P
E
Direct runoff
E = (W/Wmax) Epot
R=0
R = P – LE
(W<Wmax)
(WWmax)
Land surface in climate models
Penman Monteith equation
• Given:
LE  L 
H   cp
 
q s( Ts )  qa
ra  rc
Ts  Ta
ra
 qs
T
Q *  G  H  LE  A
D  q s( Ta )  qa
• The Penman-Monteith
equation can be derived:
LE 
 A  D  c p / ra
cp 
rc 
1  

L 
ra 
Land surface in climate models
Development history of land schemes
• Mid 1970’s: explicit treatment of vegetation
(Penman-Monteith ‘big leaf’)
P
E
Direct runoff
LE 
 Q *  G    c p / ra D
    rc / ra 
• To be combined with submodel for soil
infiltration/runoff
Land surface in climate models
First Soil-Vegetation-Atmosphere Scheme
(SVAT)
• Deardorff (1978) combined
– Penman-Monteith
– Partial vegetation coverage, but
still one energy balance equation
(lumped surface types)
• ‘effective’ surface resistance
(interpolating between canopy
value for full vegetation, and
large value for bare ground)
Land surface in climate models
Explicit multi-component SVATs
• Separate treatment of vegetation and
understory/bare ground (Shuttleworth et al,
1988)
– canopy resistance
– evap. resistance for bare ground
• Complex rewriting of PM, involving
– separate net radiation for two
components
– solution of T,q “within canopy” (at
network node)
– separate aerodynamic coupling of two
components
• Evaporation at bare ground affects canopy
transpiration and vice versa
Land surface in climate models
Tiled scheme
• For instance ECMWF (2000)
• Multiple fractions (“tiles”)
– vegetation (transpiration)
– bare ground (evaporation)
– interception/skin reservoir
(pot. evaporation)
– snow (sublimation)
• Multi-layer soil
– diffusion
– gravity flow
• Explicit root profile
Land surface in climate models
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)
• 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)
• 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)
• 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)
• 6 fractions (“tiles”)
• Aerodynamic coupling
– Wind speed
– Roughness
– Atmospheric stability
• Vegetation
– Canopy resistance
– Root zone
– Interception
• Bare ground
• Snow
Land surface in climate models
Components discussed
• Definition of vegetation
• Canopy resistance
• Aeordynamic exchange and numerical
solution
• Soil water and runoff
• Snow
Land surface in climate models
Maps of PFTs
• Based on remote sensing/local inventories
Area
(VIS) (NIR) NDVIJJA NDVIDJF
Pine forest
Deciduous forest
Grassland
Crops
Bare soil
low
low
middle
middle
high
high
high
high
high
low
high
high
middle
high
low
high
low
middle
low
low
• Available at high resolution (1km)
• Various versions produced for different PFTclassifications
– Global Land Cover Climatology (GLCC)
– ECOCLIMAP
Land surface in climate models
Vegetation distribution
Land surface in climate models
Global distribution of forest/low vegetation
in HTESSEL
Land surface in climate models
Specification of vegetation types
Land surface in climate models
The coupled CO2 – H2O pathway in vegetation
models
E  a
q in  q air
ra  rc
• qin = qsat(Ts)
• Traditional (“empirical”) approach:
rc = rc,min  f(LAI)  f(light)  f(temp)  f(RH)  f(soil m)
Land surface in climate models
More 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
• Shortwave radiation:
f1(Rs)
Jarvis-Stewart functions
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
200
400
600
Shortwave radiation (W/m2)
• Atmospheric humidity deficit (D):
f3 = exp(-cD)
(c depends on veg.type)
Land surface in climate models
Jarvis-Stewart functions
• Soil moisture (W = weighted mean over root
profile):
• Standard approach: linear profile
f2 = 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
Carbon 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)
Land surface in climate models
Modelling 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
Aerodynamic exchange
• Turbulent fluxes are parameterized as (for each tile):
H   a c p C H U T a  gz l  T sk

a  Ta+gz
a
 E   a   a q a   s q sat T sk 
    aC M U
2
H
s
s
C H U  1 / raH
• Solution of CH requires iteration:
– CH = f(L)
– L = f(H)
L = Monin-Obukhov length
– H = f(CH)
Land surface in climate models
Numerical solution
• Solution of energy balance equation
Q *  H  E  G
• With (all fluxes positive downward)
Q *  (1  a ) R s   R T   T sk
4
H   a c p C H U T a  gz l  T sk
net radiation

sensible heat flux
 E   a   a q a   s q sat T sk 
latent heat flux
G   sk (T sk  T soil )
soil heat flux
• Express all components in terms of Tsk (with Tp = Tskt -1)
T sk  T p  4 T p (T sk  T p )
4
4
3
q sat (T sk )  q sat (T p ) 
 q sat
T
(T sk  T p )
Tp
Land surface in climate models
Effective 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
Soil 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
 C soil  x s  s C s  x w  w C w  x a  a C a  (1   sat )  s C s   w C w
– 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
Land surface in climate models
Soil water flow
• Water flows when work is acting on it
– gravity: W = mgz
– acceleration: W = 0.5 mv2
– pressure gradient: W = m  dp/ = mp/
• Fluid potential (mechanical energy / unit mass)
 = gz + 0.5 v2 + p/
p = gz
  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
strong adhesy/
capillary forces
water held by
capillary forces
retention curve
Land surface in climate models
Parameterization of K and D
• 2 ‘schools’
– Clapp & Hornberger ea
b
• single parameter (b)    sat
 
K ( )  K sat 
  sat




2b3
– 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
Land surface in climate models
pF curves and plant stress
• Canopy resistance depends on relative soil moisture
content, scaled between wilting point and field
capacity
pF curve
1000
clay
100
Pressure head (hPa)
txsture 1
texture 2
texture 3
texture 4
texture 5
texture 6
10
1
organic
sand
0.1
0.01
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Volumetric soil moisture (m3/m3)
Land surface in climate models
Boundary conditions
w
•
•
•

t

F
z
 wS 
Ftop  Fbot
z
 wS
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
Rs
– Rd = deep runoff (drainage)
– M = snow melt
– Pl = liquid precipitation
– Wl = interception reservoir depth
– S = root extraction
Pl
T
Wl
Eint
Esoil M
S
surface in climate models
RLand
d
Parameterization 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
Surface runoff
Infiltration curve
(dep on W and
orograpy)
Land surface in climate models
Snow 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 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 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 melt
• Is energy used to warm the snow or to melt it? In
some stage (Tsn  0C) it’s both!
• Split time step into warming part and melting part
– first bring Tsn to 0C, 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
Next week
• How would a parameterization scheme for
irrigation look like?
– External (static) variables
– Resolved variables (boundary conditions)
– Prognostic quantities
– Main processes
Land surface in climate models
More information
• Bart van den Hurk
– hurkvd@knmi.nl
Land surface in climate models