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Parameterization of surface fluxes - PowerPoint PPT Presentation

Parameterization of surface fluxes. Bart van den Hurk (KNMI/IMAU). General form of land surface schemes. Q*. H.  E. P SN. E SN. Accumulation. G. M. Energy balance equation K  (1 – a ) + L  – L  +  E + H = G Water balance equation  W / t = P – E – R s – D

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Presentation Transcript

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

• 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)

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/ = 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 =

• velocity head (0.5 v2/g) +

• pressure head ( = z = p/g)

HTESSEL parameterization

capillary forces

dewatering from

large to small pores

retention curve

HTESSEL parameterization

Darcy and Richards equation content

qz = flux

HTESSEL parameterization

Darcy and Richards equation content

 = 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

Parameterization of K and D content

• 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 ( @  = -3m or -0.33 bar)

HTESSEL parameterization

Boundary conditions content

• 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

Parameterization of runoff content

• 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 and

orograpy)

Surface runoff

HTESSEL parameterization

Parameterization of snow content

HTESSEL parameterization

Snow parameterization content

• 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

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)

HTESSEL parameterization

Snow energy budget content

• 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

Snow melt content

• 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.

HTESSEL parameterization

Surface characteristics content(surface ‘climate fields’)

HTESSEL parameterization

Surface climate fields content

• Vegetation types

• Vegetation cover

• Surface geopotential

• 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

Vegetation distribution content

HTESSEL parameterization

Jan

Jul

HTESSEL parameterization

Prognostic quantities content

• 4 soil temperatures

• 4 soil moisture contents

• interception reservoir depth

• snow depth

• snow albedo

• snow density

• snow temperature