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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

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



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 content

qz = flux

HTESSEL parameterization


Darcy and richards equation1
Darcy and Richards equation content

 = 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 content

  • 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 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
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


Parameterization of interception
Parameterization of interception content

  • 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 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

Parameterization of snow content

HTESSEL parameterization


Snow 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


Parameterization of snow water
Parameterization of snow water content

  • 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 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
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 surface climate fields

Surface characteristics content(surface ‘climate fields’)

HTESSEL parameterization


Surface climate fields
Surface climate fields content

  • 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 content

HTESSEL parameterization


Climatological albedo static vegetation
Climatological albedo (static vegetation) content

Jan

Jul

HTESSEL parameterization


Prognostic quantities
Prognostic quantities content

  • 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 content

HTESSEL parameterization


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