[ ] Wu et al. (2000): ( ) b = + 1 1 b 2 Requires - - PowerPoint PPT Presentation

α and β coefficients for evaporation from the soil surface

fc fc

θ θ π θ θ β <                      − =

1 2

, 1 cos 1 4 1      − = exp T R g

w

ψ α

( )

[ ]

2

1

1 1

b sat

b θ θ β − + =

Philip (1957): Requires extrapolation to surface soil moisture, to calculate ψ0. Wu et al. (2000): Requires appropriate values for b1 and b2, soil moisture and porosity in top layer Lee and Pielke (1992): Requires soil moisture in top layer, and the field capacity of the soil.

fc

θ θ ≥

1

Canopy Conductance in CLASS 2.x

• employs the multiplicative Jarvis-Stewart approach to

represent the response to environmental stresses

• gc scales linearly with leaf area index (Λ)

( ) [ ]

max max ,

Λ Λ = Λ

c c

g g

( ) (

) (

) ( )

a r s c c

T f f e f K f g g

4 3 2 1 ,

ˆ ψ ∆ =

↓

where: is a composite value of over the 4 vegetation groups K↓ is incoming solar radiation ∆e is vapour pressure deficit ψs,r is soil water suction in the rooting zone Ta is air temperature

c

g ˆ

( )

Λ

c

g

Ta (°C)

• 10

10 20 30 40 50

f(Ta)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

K↓ (W·m-2)

250 500 750 1000

f(K↓)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

∆e (kPa)

1 2 3 4

f(∆e)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Canopy Conductance in CLASS 2.x

• gc,max is hard coded as 20 mm·s-1 for all vegetation types
• functions f1 - f4 are the same for all vegetation types

( ) (

) (

) ( )

a r s c c

T f f e f K f g g

4 3 2 1 ,

ˆ ψ ∆ =

↓

ψ (MPa)

• 2.
• 1.5
• 1.0
• 0.5

0.0

f(ψ)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Q↓ (W·m-2)

250 500 750 1000

f(Q↓)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Canopy Conductance in CLASS 3.0

Following papers by Schulze, Kelliher, Leuning and Raupach (1995):

• The maximum unstressed stomatal conductance is gs,max
• We model a hyperbolic response to solar radiation

where: Q↓ is incoming photosynthetically active radiation, Ql1/2 is the value of Q↓ where gs = gs,max/2

2 / 1 max , l s s

Q Q Q g g + =

↓ ↓

• Assuming photosynthetically active radiation at height h (Qh)

declines exponentially through the canopy with cumulative leaf area index (ξ) where cQ is an extinction coefficient

• Differentiating with respect to ξ and assuming that gc is the

parallel sum of gs through the canopy, we can combine the previous two equations to yield which is canopy conductance in the absence of stress caused by humidity, water availability and air temperature

( )

ξ

Q h

c Q Q − =

↓ exp

Canopy Conductance in CLASS 3.0

( )

        + Λ − + =

↓ ↓ 2 1 2 1 / / max ,

exp ln Q c Q Q Q c g g

Q Q s c

Canopy Conductance in CLASS 3.0

• We can represent stress caused by humidity, water availability

and temperature using multiplicative functions, as

• To represent various vegetation types, f(∆e) and f(ψs,r) have

adjustable coefficients that, along with Q1/2, can be read from the initialization file, while default values are provided for major vegetation categories.

( )

( )

( )

( )

a r s Q Q s c

T f f e f Q c Q Q Q c g g ⋅ ⋅ ∆ ⋅         + Λ − + =

↓ ↓ , / / max ,

exp ln ψ

2 1 2 1

• To prevent step changes in CLASS’s output:
• f(Ta) has been changed,

using more gradual bounds.

Ta (°C)

• 10

10 20 30 40 50

f(Ta)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

CLASS 2 CLASS 3

ψ (MPa)

• 2.0
• 1.5
• 1.0
• 0.5

0.0

f(ψ)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

CLASS 2 CLASS 3

• The step change at a wilting

point has been removed from f(ψs,r)

Canopy Conductance in CLASS 3.0

Previous wilting point

A i r t e m p e r a t u r e ( ° C )

• 6
• 4
• 2

2 4 6 8 1 0

f

s n o w

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

S t e p c h a n g e G r a d u a l l i n e a r P o l y n o m i a l

Partitioning Rainfall and Snowfall In CLASS 3.0

• CLASS 2 employed a step change function:

Air temperature ≤ 0 °C → Snow Air temperature > 0 °C → Rain

• CLASS 3 provides a choice of three functions:

1. The step change function from CLASS 2 2. A gradual linear change between 0 and 2 °C 3. A polynomial based on Auer (1974) and recommended by Fassnacht.

Fresh Snow Density In CLASS 3

• CLASS 2 assumed a constant snow density of

100 kg·m-3.

• CLASS 3 employs a variable density based on

air temperature.

A i r t e m p e r a t u r e ( ° C )

• 1 0
• 8
• 6
• 4
• 2

2 4 6 8

ρ

f r e s h s n o w

( k g · m

• 3

)

5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0 2 2 5

C L A S S 3 C L A S S 2

S n o w d e p t h ( m )

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0

m a x i m u m ρ

s n o w

( k g · m

• 3

)

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

T s n o w < 0 ° C T s n o w = 0 ° C

Maximum Snow Density In CLASS 3

• In CLASS 2, the maximum density that a snow-

pack could achieve in the absence of melting, was set to 300 kg·m-3.

• In CLASS 3, the maximum density that a snow-

pack can achieve in the absence of melting varies with snow depth, and is larger for a snowpack at a temperature of 0 °C than for a colder snowpack.

Snow Interception In CLASS 3

• If we define snow interception (I) as snow that falls the canopy, I

is found as: the rate of snowfall x (1 – the sky view factor),

• In CLASS 2, all intercepted snow stayed on the canopy until

until the interception capacity (I*) was reached. I* for water and snow was 0.2·LAI (in kg·m-2). However, snow acts as a bridge between branches and between conifer needles. Hedstrom and Pomeroy (1998) have shown that the average I* is about 0.5·LAI.

• In CLASS 3, I* = 6·LAI·(0.27+46/ρfresh snow)

• In CLASS 3, not all of the intercepted snow stays on the canopy.
• Snow added to the canopy interception store (Sload) is found as:

where 0.697 is a dimensionless snow unloading coefficient, ∆T is the model time step in seconds, and I0 is the initial amount of snow stored on the canopy.

• Not all of the intercepted snow (I.e. snow that lands
• n the canopy) stays on the canopy. This snow that

falls or drips from the canopy is found as: I – Sload.

Snow Interception In CLASS 3

( )

        − −       ∆ ⋅ =

−

*

1 3600 697 .

* load I I

e I I T S

Schematic representation of aerodynamic resistances to the transfer

• f momentum and to the transfer of scalar properties, showing the

excess resistance rb due to molecular effects and the relation between the surface temperature θ0 and the temperature θ(z0).

(From J.R. Garratt, “The Atmospheric Boundary Layer”)

QH,T (Ta,c – Ta) = QH,c (Tc – Ta,c) + QH,g (Tg – Ta,c) QH,c QH,T QH,g Schematic representation of the main elements of a non-isothermal or two- component canopy model. Linked to the atmosphere (via resistances rs, rb and ra), to the soil or undergrowth (via resistance rd) and the deep soil (via evapotranspiration), the canopy and upper soil layer are at temperatures Tf and Tg. Pg is the precipitation reaching the soil surface.

(From J.R. Garratt, “The Atmospheric Boundary Layer”)

Patch 1 Patch 2 Patch 3

• ni is the number of grid

elements (grid cells)

• nm is the number of

mosaic elements (patches in each grid-cell)

( ) ( ) ∑

=

m

m i X i X , Prognostic variable matrix arrays gathered from mosaic grid onto vector array X′((i-1)·nm+1) X′((i-1)·nm+2) X′((i-1)·nm+3) Prognostic variable arrays scattered back onto original matrix grid Grid-cell averages calculated For the ith grid-cell:

CLASS

X(i,1) X(i,2) X(i,3) X(i,1) X(i,2) X(i,3)