Sodankylä Summer School Modelling of transient vegetation and soil related processes Patrick Samuelsson Swedish Meteorological and Hydrological Institute

Sodankylä Summer School

Modelling of transient vegetationand soil related processes

Patrick SamuelssonSwedish Meteorological and Hydrological Institute

[email protected]


• The Rossby Centre Regional Climate Model Land Surface Scheme (LSS) (Samuelsson and Gollvik)

• The ECMWF TESSEL LSS (Viterbo et al.)


Outline

Introduction Net radiation Physiography Surface fluxes Surface resistances The forest tile Interception of rain Soil heat storage Soil properties Soil water Interception of snow


The role of the land surface inNWP/climate models

• Act as a lower boundary for the atmosphere.

• Provide diagnostic values of 2m temperature and humidity and 10m wind speed.

•Partitioning between sensible heat and latent heat determines soil wetness,

acting as one of the forcings of low frequency variability (e.g. extended drought

periods).

•At higher latitudes, soil water only becomes available for evaporation after the

ground melts. The soil thermal balance and the timing of snow melt (snow

insulates the ground) also controls the seasonal cycle of evaporation.

•The outgoing surface fluxes depend on the albedo, which in turn depends on

snow cover, vegetation type and season.

Viterbo, 2004


Runoff

Precipitation Evapotranspiration

Storage of water

Runoff - Evap. - Prec. storage in change

The role of the land surface inNWP/climate modelsThe water balance components

ERA40:2.2 mm d-1

ERA40:-1.4 mm d-1

ERA40:-0.9 mm d-1

ERA40 from P. Viterbo


Definitions of evaporation

Field capacity

Unstressed evaporationorPotential evapotranspiration(dry vegetation)

Potential evaporation(wet vegetation)


The hydrological rosette(Dooge, 1992)

A-B: After a long episode of rainfall soil moisture is available in abundance. The atmosphere controls the rate of evaporation.

B-C: Soil water has decreased to a level where it starts to limit the rate of evaporation.

C-D: Precipitation refills the soil water by infiltration.

D-A: Maximum soil water level is reached. All precipitation from this point goes to runoff.


EvapotranspirationLatent heat (LE)

Storage of heat

ch. phase storage in change LEHRn

Sensible heat (H)

Incoming shortwave (S↓)

Incoming longwave (L↓)

Phasechanges

The role of the land surface inNWP/climate models modelThe energy balance components

ERA40 NetSW:134 Wm-2

ERA40 NetLW:-65 Wm-2

ERA40:-40 Wm-2

ERA40:-27 Wm-2

ERA40 from P. Viterbo


Surface net radiation

Arya, 1988

s

sn

T

TLSR

)()1( 4

Albedo

Emissivity

Surface temperature


Surface net radiation

in the forest

RnforcRnforc

Rnfors

Rnforsn

The sky view factor divides the radiationbetween the canopy and the forest floor:


Surface evaporative fraction1 (EF), impacting on low level cloudiness, impacting on surface radiation, impacting on …

Bowen ratio2 (Bo), impacting on cloud base, impacting on intensity of convection, impacting on soil water, impacting on …

Feedback mechanisms involving

land surface processes

(1) EF = (Latent heat)/(Net radiation) (2) Bo = (Sensible heat)/(Latent heat)

P. Viterbo (2004)


History of land-surface modelling(Viterbo, 2002)

• Richardsson (1922): In his book on numerical weather prediction he identified all the principles used by most current LSS.

• Manabe (1969): The “bucket model” for evaporation and runoff.

• Deardorff (1978) introduced the importance of vegetation in controlling the evaporation. Many of today’s LSS are build on these principles.

• Jarvis (1976) described how different stress functions affect the stomatal conductance.


The mixture contra the tile approach(Koster and Suarez, 1992)

Averaged surface properties

The Mixture approach The Tile approach

SnowLowvegetation

Coniferous forest

Deciduous forest

All individual sub-surfaces have their own set of parameters as well as separate energy balances.

One value each for parameters like LAI, albedo, emissivity, aerodynamic resistance,… per grid square. One single energy balance.

Most schemessomewhere in

between


Physiographic information of tilesECOCLIMAP (Masson et al. 2001)

In RCA we have two main land tiles: forest and open land.

For snow conditions we also have forest snow and open-land snow.

Leaf Area Index (LAI) is (projected area of leaf surface)/(surface area)


Diagnostic LAIHagemann et al. (1999)

LAI as a function of deep soil temperature Tsoil

= 4th layer in RCA at 65 cm (unaffected by diurnal variations)

where

where Tmax and Tmin are 293.0 and 273.0 K, respectively.


Sn

ow

in f

ore

st

Fo

rest

can

op

y(s

tom

ata

and

inte

rc. w

ater

)B

are

soil

Sn

ow

on

op

enla

nd

Fo

rest

flo

or

The surface energy balance componentsof heat fluxes in the tile approach

Lo

w v

eget

atio

n

(sto

mat

a an

din

terc

. wat

er)

ELatent heat

HSensible heat


Parameterisation of energy fluxes

Sensible heat flux (W m-2)

Latent heat flux (W m-2)

the aerodynamic resistance ra is defined as

qam

rscrsoil

Ts

Tam

ra ra

u

Where ρ is air density cp is air heat capacity λ is latent heat of vaporisation qs is specific humidity at saturation


Land surface – atmospherefeedback mechanisms

Experiences from one of the PILPS projects


Land surface – atmospherefeedback mechanisms

Runoff (-) and evaporation (---) forcoupled runs LSS-RCA atmosphere

Runoff (-) and evaporation (---) forLSS forced by observations

Z0h « z0m

Z0h = z0m

Z0h « z0m

Z0h = z0m


Sn

ow

in f

ore

st

Fo

rest

can

op

y(s

tom

ata

and

inte

rc. w

ater

)B

are

soil

Sn

ow

on

op

enla

nd

Fo

rest

flo

or


Lo

w v

eget

atio

n

(sto

mat

a an

din

terc

. wat

er)

ELatent heat

HSensible heat


The Jarvis approach for the

canopy surface resistance, rsc

1

)(54321min

i

asata

a

saascsc

f

eTeD

T

TffDfTfPARfrr

3/1 f

2/1 f

1/1 f

Dickinson et al 1991

Temperature Vapour pressure def.

PAR - Photosyntheticactive radiation

near surface air temperature

near surface vapourpressure def.

f5(Ts) is added in RCA to restrictevapotranspiration when soil is frozen


4/1 f

Shuttleworth 1993

~0.15

Field capacity, θdWilting point, θw

~0.30

Soil water availability

θ: volumetric soil moisture (m3 m-3)

The Jarvis approach for the

canopy surface resistance, rsc

Combined with soil depth this gives the water holding capacity.


Sn

ow

in f

ore

st

Fo

rest

can

op

y(s

tom

ata

and

inte

rc. w

ater

)B

are

soil

Sn

ow

on

op

enla

nd

Fo

rest

flo

or


Lo

w v

eget

atio

n

(sto

mat

a an

din

terc

. wat

er)

ELatent heat

HSensible heat


The soil surface resistance rsoil for

bare ground evaporationSoil (bare ground) evaporation is due to:

Molecular diffusion from the water in the pores of the soil matrix up to the interface soil atmosphere (z0q)

Laminar and turbulent diffusion in the air between z0q and screen level height

All methods are sensitive to the water in the first few cm of the soil (where the water vapour gradient is large). In very dry conditions, water vapour inside the soil becomes dominant

fc

fcw

w

wfc

wsoilsoil

soila

amsswa

ffrr

rr

qTqE

1

1

1

1111min,

1

0

)(

where

van den Hurk et al. (2000)Viterbo (2004)

added a restriction due to frozen soil


Sn

ow

in f

ore

st

Fo

rest

can

op

y(s

tom

ata

and

inte

rc. w

ater

)B

are

soil

Sn

ow

on

op

enla

nd

Fo

rest

flo

or


Lo

w v

eget

atio

n

(sto

mat

a an

din

terc

. wat

er)

ELatent heat

HSensible heat


qfora

Characterized by low tree heat capacity & small rb

Tam qam

rafor

wcfor rs, rb

rd

rsoilsc

Tforsnrd

Tforc

Tfora

are canopy air temperature and humidity

The forest tile sensible heat flux

qforaTfora

where Tfora is solved from the relationship


qfora

Tam qam

rafor

wcfor rs, rb

rd

rsoilsc

Tforsnrd

Tforc

Tfora

The forest tile aerodynamic

resistances rb and rd

The aerodynamic resistance

))(,,( 111 foraforcforb TTuLAIfr

Choudhury and Monteith (1988)

Sellers et al. (1986)

The aerodynamic resistance

))(,,( 11 foraforsforford TTuzfr

Choudhury and Monteith (1988)

Sellers et al. (1986, 1996)

rb10% of rd


qfora


Tam qam

rafor

wcfor rs, rb

rd

rsoilsc

Tforsnrd

Tforc

Tfora


The forest tile latent heat flux

qforaTfora

where qfora is solved for in a similar manner asfor Tfora using a balance between latent heat fluxes


The forest tile

results


The forest tile

results

qfora

Tam qam

raforwcfor rs, rb

rdrsoil

sc

Tforsnrd

Tforc

Tfora


Sn

ow

in f

ore

st

Fo

rest

can

op

y(s

tom

ata

and

inte

rc. w

ater

)B

are

soil

Sn

ow

on

op

enla

nd

Fo

rest

flo

or

Now all the surface fluxes areknown…

Lo

w v

eget

atio

n

(sto

mat

a an

din

terc

. wat

er)

ELatent heat

HSensible heat

… so we can solve for the storages ofheat (temperatures) and water…


Snow water eq.

Liquid waterInterceptedwater

Interceptedwater

Snow water eq.

Liquid water

Surface (0-7 cm) anddeep (7-227 cm) soil water

T_snT_low_veg_and_soil

T_canopy

T_snfor

Five layers in the soildown to three meters(from 1 to 190 cm thick)

T_for_floor

The storage of heat and waterin the tile approach


Interception of rain

Interception layer represents the water collected by interception of precipitation and dew deposition on the canopy leaves (and stems)

Interception (I) is the amount of precipitation (P) collected by the interception layer and available for “direct” (potential) evaporation. I/P ranges over 0.15-0.30 in the tropics and 0.25-0.50 in mid-latitudes.

Two issues

Size of the reservoir

Cl, fraction of a gridbox covered by the interception layer

T=P-I; Throughfall (T) is precipitation minus interception

Viterbo (2004)



Canopy water budget

canopy theof bottom at the oughfall thr

waterdintercepte ofn evaporatio

ionprecipitat modified

onintercepti of efficiency

waterdIntercepte

*

*

T

Ec

P

e

w

EcITEcPet

w

ll

i

l

llllil

T

*Pei llEc

Viterbo (2004)


Interception layer for rainfall and dew deposition

form) droplet from (2/3

leaf single a on stored water

soil) top to (input lThroughfal

ionprecipitatby coveredbox -grid of fraction

ionprecipitat modified

3/2

max

max

*

*

/

/

,max

lmxll

lmx

nllmx

i

lll

wwc

W

WLAIvegw

IPT

k

kPP

t

wwPeI

EcIt

w

Viterbo (2004)


Canopy water budget



results


Back to hvfor

Total evapotranspiration from canopy

Viterbo (2004)

Where the Halstead coefficient is (Noilhan and Planton,1989)

25.0

/ 3/2

k

wwc lmxll

transpiration + interception

Allows transpiration also at maximum

interception reservoir, δ=1!


Forest temperatures

qfora


Tam qam

rafor

wcfor rs, rb

rd

rsoilsc

Tforsnrd

Tforc

Tfora


qforaTfora

where

Cforc defined according to Verseghy et al., (1993)


The soil

zT1

zT2

zT3

zT4

zT5

zθ1

zθ2

TssnTsc TsnsTscsn

TsncTsn

No-flux boundary condition at 3 m depth

Time scale:(very dependent onsoil moisture)

1 month -

1 week – 1 month

1 day - 1 week

– 1 hour

1 hour – 1 day1.0 cm

6.2 cm

21.0 cm

72.0 cm

189.0 cm


The soil energy equation

2

2s

g

T

T

g

Ts

g

z

Tk

t

T

k

Cz

T

zz

G

t

TC

soil, shomogeneou anFor

ydiffusivit Thermal C

tyconductivi Thermal

capacityheat volumetric Soil

In the absence of phase changes, heat conduction in the soil obeys a Fourier law

Boundary conditions:•Top Net surface heat flux•BottomNo heat flux OR prescribed climate

Viterbo (2004)


Soil water freezing/thawingViterbo et al. (1999)

water frozen Soil

T

I

Iwfs t

Lz

T

zt

T)C(

Soil heat transfer equation

)T(f)T(II

z

T

zt

T

T

fL)C( Twfs

Apparent heat capacity

Viterbo (2004)


Numerical solution of the soil

energy equations

0

5.0

2/41

2/1

1

111

2/1,1

2/1

12/1

12/11

G

EHRG

DD

TTG

D

GGTT

t

C

n

jj

nj

nj

jTnj

j

nj

njn

jnj

j

changes phase

conditionsBoundary

1,...,4j

DjTj

j+1

Gj+1/2

Gj-1/2

Viterbo (2004)


Temperatures in RCA


Soil properties

The soil is a 3-phase system, consisting of Solid minerals and organic matter Water trapped in the pores Moist air trapped in the pores

The Texture triangle –the size distribution of soil particles

Hillel 1982


Soil properties

Fractions of clay and sand from ECOCLIMAP (Masson et al. 2001)


Soil properties

~0.15

Field capacity, θdWilting point, θw

~0.30

Soil water availability

θ: volumetric soil moisture (m3 m-3)

Soil porosity

~0.45


Soil properties

Rosenberg et al 1983

The thermal conductivity

where θ is volumetric soil moisture (m3 m-3)θsat is total porosity (m3 m-3)a is an empirical parameterψsat is matric potential at saturation (m)b is Clapp and Hornberger parameter


Soil water flux

Soil water flux is usually expressed by Richards equation

where θ is volumetric soil moisture (m3 m-3)λ hydraulic diffusivity (m2 s-1)γ hydraulic conductivity (m s-1)S source/sink term (precipitation, through fall, snowmelt, evapotranspiration by root extraction)


Soil water flux

> 3 orders of

magnitude > 6 orders of

magnitude

Mahrt and Pan 1984

Hydraulic diffusivity and conductivity


Soil water flux

In RCA the 2nd term on the rhs is replaced by the β formulation

where θ is volumetric soil moisture (m3 m-3)θwi is wilting pointθfc is field capacity

Sdr(θ,z0) is precipitation, through fall, snowmeltSdr(θ,z1) is root extraction and drainage Sdr(θ,z2) is root extraction and runoff


Snow interception


Why Include Interception of Snow?

Intercepted snow feels much less aerodynamic resistance

than forest floor snow.

25-45% of an annual snowfall can evaporate from

intercepted snow (Pomeroy et al. 1998).

Affects evaporation/runoff partition.


SOURCES:

Snow interception, SI (m/s)

Intercepted water friezes, wcfor (m)

Sublimation of water vapor, E/w (m/s)

qca

Tam qam

rafor

wcfor rs, rb

rd

rsoils

c

Tsncrd

Tc

Tca

SNcfor

SINKS:

Evaporation of snow, E/ρw rb10% of rd

Snow unloading, UL (m/s)

Interception of Snow

tULtEwtSISNSN wcforcforcfor /1

Change of intercepted snow:


Snow Interception Model

The snow interception (SI) and snow unloading (UL) part of the model is based on Hedstrom and Pomeroy (1998):

))exp(1)(( max, SNcforcfor kPSNSNtSI

where SNcfor,max = f(LAI, 1/sn(Tc)) ~ 20 mm k = (snow-leaf contact area) / SNcfor,max PSN = snowfall

)exp(( tUSNtUL cfor

where U = a constant unloading rate coefficient (SNcfor is put to zero for Tc>0ºC)


b

cacsatas r

qTqE

)(

Snow Interception Model

The snow sublimation (E/ρw) part of the model is parameterized as

where a = air density q = specific humidity rb = aerodynamic resistance βs = evaporative efficiency (modified from Nakai et al. 1999)

βs

SNcfor / SNcfor,max

qca

Tam qam

rafor

wcfor rs, rb

rd

rsoils

c

Tsncrd

Tc

Tca

SNcfor


RCA simulation

Simulated seasonal intercepted snow evaporation (mm)

Simulated intercepted(snow evaporation)/snow (%)

Boundaries: ERA-15, Res.: ~20 km, dt=15 min.Accumulated results Sep 1996 - May 1997


RCA simulation and observations

RCA Sodankylä

northern Finland

Other studies

(observations)

Snow interception

% of seas. snowfall

max duration:

duration > 1 day:

70%

40 days

20 events

Obs. durations from days

up to weeks (Bründl et al.

1997)

Max daily interc. snow

evap.:

75 W m-2

2.5 mm day-1

1.3 – 3.9 mm day-1

(Lundberg & Halldin, 2001)

Mean interc. snow evap.:

Seasonal:

13 W m-2

0.44 mm day-1

25% 10 – 50% (L&H, 2001)


Conclusions about snow interception

The presented parameterization of snow interception gives reasonable

results compared to many studies but does not perform well according to

eddy-correlation measurements in Sodankylä.

As stated by Lundberg and Halldin (2001) the evaporation is very

sensitive to the aerodynamic resistance.

To improve these preliminary model results we need better physiographic

description (LAI, forest structure) and we also need more observations to

be able to validate the results.

Documents

Sodankylä Summer School Modelling of transient vegetation and soil related processes Patrick Samuelsson Swedish Meteorological and Hydrological Institute