Parameterization of surface fluxes
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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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Parameterization of surface fluxes

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Parameterization of surface fluxes

Parameterization of surface fluxes

Bart van den Hurk

(KNMI/IMAU)

HTESSEL parameterization


General form of land surface schemes

General form of land surface schemes

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


Soil hydrology

Soil hydrology

  • 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


Soil heat flux

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

HTESSEL parameterization


Main sections

Main sections

  • Surface tiling

  • Surface energy balance & vegetation

  • Soil heat transfer

  • Soil hydrology

  • Snow hydrology & albedo

  • Surface characteristics (“climate fields”)

HTESSEL parameterization


Tile structure of htessel

Tile structure of HTESSEL

  • 6 fractions (“tiles”)

  • Aerodynamic coupling

  • Vegetatie

    • Verdampingsweerstand

    • Wortelzone

    • Neerslaginterceptie

  • Kale grond

  • Sneeuw

HTESSEL parameterization


Tile structure of htessel1

Tile structure of HTESSEL

  • 6 fractions (“tiles”)

  • Aerodynamic coupling

    • Wind speed

    • Roughness

    • Atmospheric stability

  • Vegetatie

    • Verdampingsweerstand

    • Wortelzone

    • Neerslaginterceptie

  • Kale grond

  • Sneeuw

HTESSEL parameterization


Tile structure of htessel2

Tile structure of HTESSEL

  • 6 fractions (“tiles”)

  • Aerodynamic coupling

    • Wind speed

    • Roughness

    • Atmospheric stability

  • Vegetation

    • Canopy resistance

    • Root zone

    • Interception

  • Kale grond

  • Sneeuw

HTESSEL parameterization


Tile structure of htessel3

Tile structure of HTESSEL

  • 6 fractions (“tiles”)

  • Aerodynamic coupling

    • Wind speed

    • Roughness

    • Atmospheric stability

  • Vegetation

    • Canopy resistance

    • Root zone

    • Interception

  • Bare ground

  • Sneeuw

HTESSEL parameterization


Tile structure of htessel4

Tile structure of HTESSEL

  • 6 fractions (“tiles”)

  • Aerodynamic coupling

    • Wind speed

    • Roughness

    • Atmospheric stability

  • Vegetation

    • Canopy resistance

    • Root zone

    • Interception

  • Bare ground

  • Snow

HTESSEL parameterization


Tile fractions calculated every time step

Tile fractions (calculated every time step)

  • 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

Parameterization of surface energy balance and evaporation

HTESSEL parameterization


Aerodynamic exchange

Aerodynamic exchange

  • 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


Treatment of tiled evaporation

Treatment of tiled evaporation

  • 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


More on the canopy resistance

More on the canopy resistance

  • Active regulation of evaporation via stomatal aperture

  • Empirical (Jarvis-Stewart) approach:

    rc = (rc,min/LAI) f(K) f(D) f(W)

HTESSEL parameterization


Jarvis stewart functions

Jarvis-Stewart functions

  • Shortwave radiation:

  • Atmospheric humidity deficit (D):

    f3 = exp(-cD)(c  0 for forest only)

HTESSEL parameterization


Jarvis stewart functions1

Jarvis-Stewart functions

  • Soil moisture ( = weighted mean liquid water over root profile):

  • Standard approach: linear profile

1

HTESSEL parameterization


Specification of vegetation types

Specification of vegetation types

HTESSEL parameterization


Soil heat flux1

Soil heat flux

HTESSEL parameterization


Numerical solution

Numerical solution

  • 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


Numerical solution1

Numerical 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)

HTESSEL parameterization


Soil heat transfer

Soil heat transfer

HTESSEL parameterization


Heat transport in soil

Heat transport in soil

  • 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 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

HTESSEL parameterization


Freezing of soil water

Freezing of soil water

  • 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

Parameterization of soil hydrology

HTESSEL parameterization


Soil water flow

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)

HTESSEL parameterization


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

HTESSEL parameterization


Darcy and richards equation

Darcy and Richards equation

qz = flux

HTESSEL parameterization


Darcy and richards equation1

Darcy and Richards equation

 = vol. soil moisture content (m3/m3)

K = hydraulic conductivity (m/s)

D = hydraulic diffusivity (m2/s)

HTESSEL parameterization


Implementation in discrete form

Implementation in discrete form

  • In (discrete) flux form:

  • With F specified as:

root extraction

diffusion term gravity term

HTESSEL parameterization


Parameterization of k and d

Parameterization 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 ( @  = -3m or -0.33 bar)

HTESSEL parameterization


Boundary conditions

Boundary 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

Pl

Eint

T

Wl

Esoil

M

Rs

S

Rd

HTESSEL parameterization


Parameterization of interception

Parameterization of interception

  • 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

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

Infiltration curve

(dep on W and

orograpy)

Surface runoff

HTESSEL parameterization


Parameterization of snow

Parameterization of snow

HTESSEL parameterization


Snow parameterization

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

HTESSEL parameterization


Parameterization of snow water

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)

HTESSEL parameterization


Snow energy budget

Snow energy budget

  • 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

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.

HTESSEL parameterization


Surface characteristics surface climate fields

Surface characteristics(surface ‘climate fields’)

HTESSEL parameterization


Surface climate fields

Surface climate fields

  • 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


Vegetation distribution

Vegetation distribution

HTESSEL parameterization


Climatological albedo static vegetation

Climatological albedo (static vegetation)

Jan

Jul

HTESSEL parameterization


Prognostic quantities

Prognostic quantities

  • 4 soil temperatures

  • 4 soil moisture contents

  • interception reservoir depth

  • snow depth

  • snow albedo

  • snow density

  • snow temperature

  • (skin temperature) (adjusts rapidly)

HTESSEL parameterization


More information

More information

  • Bart van den Hurk

    • [email protected]

HTESSEL parameterization


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