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Parameterization of surface fluxes

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Parameterization of surface fluxes

Bart van den Hurk

(KNMI/IMAU)

HTESSEL parameterization

Q*

H

E

PSN

ESN

Accumulation

G

M

- Energy balance equation
K(1 – a) + L – L + E + H = G

- Water balance equation
W/t = P – E – Rs – D

S/t = Psn – Esn – M

P

E

Rs

Infiltration

D

HTESSEL parameterization

- 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

Pl

Eint

T

Wl

Esoil

M

Rs

S

Rd

HTESSEL parameterization

- 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

HTESSEL parameterization

- Surface tiling
- Surface energy balance & vegetation
- Soil heat transfer
- Soil hydrology
- Snow hydrology & albedo
- Surface characteristics (“climate fields”)

HTESSEL parameterization

- 6 fractions (“tiles”)
- Aerodynamic coupling
- Vegetatie
- Verdampingsweerstand
- Wortelzone
- Neerslaginterceptie

- Kale grond
- Sneeuw

HTESSEL parameterization

- 6 fractions (“tiles”)
- Aerodynamic coupling
- Wind speed
- Roughness
- Atmospheric stability

- Vegetatie
- Verdampingsweerstand
- Wortelzone
- Neerslaginterceptie

- Kale grond
- Sneeuw

HTESSEL parameterization

- 6 fractions (“tiles”)
- Aerodynamic coupling
- Wind speed
- Roughness
- Atmospheric stability

- Vegetation
- Canopy resistance
- Root zone
- Interception

- Kale grond
- Sneeuw

HTESSEL parameterization

- 6 fractions (“tiles”)
- Aerodynamic coupling
- Wind speed
- Roughness
- Atmospheric stability

- Vegetation
- Canopy resistance
- Root zone
- Interception

- Bare ground
- Sneeuw

HTESSEL parameterization

- 6 fractions (“tiles”)
- Aerodynamic coupling
- Wind speed
- Roughness
- Atmospheric stability

- Vegetation
- Canopy resistance
- Root zone
- Interception

- Bare ground
- Snow

HTESSEL parameterization

- 3 ‘static’ tiles
- high vegetation
- low vegetation
- bare ground

- 3 ‘dynamic’ tiles
- interception reservoir
- snow low/bare
- snow forest

HTESSEL parameterization

Parameterization of surface energy balance and evaporation

HTESSEL parameterization

- Turbulent fluxes are parameterized as (for each tile):
- Solution of CH requires iteration:
- CH = f(L)
- L = f(H)
- H = f(CH)

L = Monin-Obukhov length

HTESSEL parameterization

- Potential evaporation (P):
a = s = CHU = 1/raH

- Transpiration (T)
a = s = 1/(raH + rc)

- Combined snow tile (S)

T

P

T

S

T

P

HTESSEL parameterization

- Active regulation of evaporation via stomatal aperture
- Empirical (Jarvis-Stewart) approach:
rc = (rc,min/LAI) f(K) f(D) f(W)

HTESSEL parameterization

- Shortwave radiation:
- Atmospheric humidity deficit (D):
f3 = exp(-cD)(c 0 for forest only)

HTESSEL parameterization

- Soil moisture ( = weighted mean liquid water over root profile):
- Standard approach: linear profile

1

HTESSEL parameterization

HTESSEL parameterization

HTESSEL parameterization

- Solution of energy balance equation
- With (all fluxes positive downward)
- Express all components in terms of Tsk (with Tp = Tskt -1)

netradiation

sensible heat flux

latent heat flux

soil heat flux

HTESSEL parameterization

- 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)

HTESSEL parameterization

Soil heat transfer

HTESSEL parameterization

- Multi-layer scheme
- Solution of diffusion equation
- with
- C [J/m3K] = volumetric heat capacity
- T [W/mK] = thermal diffusivity

- with boundary conditions

tiled soil heat flux direct absorption snow base heat flux

HTESSEL parameterization

- 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

HTESSEL parameterization

- In case of melt/freezing, and extra heat capacity term is added:
- The ice fraction is a diagnostic variable:

fixed value, to decouple water

and temperature eqs

HTESSEL parameterization

Parameterization of soil hydrology

HTESSEL parameterization

- 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

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

HTESSEL parameterization

strong adhesy/

capillary forces

dewatering from

large to small pores

retention curve

HTESSEL parameterization

qz = flux

HTESSEL parameterization

= vol. soil moisture content (m3/m3)

K = hydraulic conductivity (m/s)

D = hydraulic diffusivity (m2/s)

HTESSEL parameterization

- In (discrete) flux form:
- With F specified as:

root extraction

diffusion term gravity term

HTESSEL parameterization

- 2 ‘schools’
- Clapp & Hornberger ea
- single parameter (b)

- Van Genuchten ea
- more parameters describing curvature better

- Clapp & Hornberger ea
- Defined ‘critical’ soil moisture content
- wilting point ( @ = -150m or -15 bar)
- field capacity ( @ = -3m or -0.33 bar)

HTESSEL parameterization

- 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

Pl

Eint

T

Wl

Esoil

M

Rs

S

Rd

HTESSEL parameterization

- Simple budget equation
- with
- El = evaporation
- D = dew collection
- I = interception from precipitation

- Points for attention:
- maximum storage reservoir ~ 0.2 mm per m2 leaf/ground area
- rapid process (water conservation in discrete time step needs care)
- interception efficiency depends on type of precipitation (large scale precip: very efficient. convective precip: more falls off)

HTESSEL parameterization

- Simple approach
- Infiltration excess runoff
Rs = max(0, T – Imax), Imax = K()

- Difficult to generate surface runoff with large grid boxes

- Infiltration excess runoff
- Explicit treatment of surface runoff
- ‘Arno’ scheme

Infiltration curve

(dep on W and

orograpy)

Surface runoff

HTESSEL parameterization

Parameterization of snow

HTESSEL 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

- open vegetation/bare ground

HTESSEL parameterization

- 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)

- with

HTESSEL parameterization

- with
- (C)sn = heat capacity of snow
- (C)i = heat capacity of ice
- GsnB = basal heat flux (T/rs)
- Qsn = phase change due to melting (dependent on Tsn)

HTESSEL parameterization

- 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.

HTESSEL parameterization

Surface characteristics(surface ‘climate fields’)

HTESSEL parameterization

- Vegetation types
- Vegetation cover
- Surface geopotential
- Land/sea mask
- oro (for runoff and for z0m(orographic part)
- vegetation roughness z0m
- thermal roughness z0h
- monthy background (snowfree) albedo
- Soil type (for hydraulic properties)

HTESSEL parameterization

HTESSEL parameterization

Jan

Jul

HTESSEL parameterization

- 4 soil temperatures
- 4 soil moisture contents
- interception reservoir depth
- snow depth
- snow albedo
- snow density
- snow temperature
- (skin temperature) (adjusts rapidly)

HTESSEL parameterization

- Bart van den Hurk
- hurkvd@knmi.nl

HTESSEL parameterization