1Division of Atmospheric Sciences, Department of Physical Sciences, University of Helsinki, POBox 64, FIN-00014, Helsinki, Finland (email: Andrei.Sogachev@helsinki.fi).

2Institute of Bioclimatology, University Göttingen, Büsgenweg 2, D-37077, Göttingen, Germany (email: opanfyo@gwdg.de)

Sogachev Andrey1 and Panferov Oleg2

Gennady Menzhulin, St. PetersburgJon Lloyd, Jena

Gode Gravenhorst, GöttingenTimo Vesala, Helsinki

Contributors / Discussants:

The world-wide network of carbon flux measuring sitesThe world-wide network of carbon flux measuring sites

(total of 216 towers as of July 2003)

(Schmid, 2002, AFM)

CO2

What part of the ecosystem does the flux sensor ‘see’ ?

Interpretation of measurement dataInterpretation of measurement data

dxdyzyxfyxFzF mm ),,()0,,(),0,0(0

(Schmid, 2002, AFM)

Source weight function or flux footprintSource weight function or flux footprint Definition

In a simple form «footprint» or «source weight function» f (x,y,zm) is the transfer function between the measured value at a certain point F(0,0,zm) and the set of forcings on the surface-atmosphere interface F(x,y,0) (Schuepp et al., 1990, Schmid, 2002).

Eulerian analytic models (Schuepp et al.,1990; Horst and Weil, 1992) (zm, z0, d, u*, L)

Lagrangian stochastic models (zm, z0, d, u*, L, TL, σu, σv, σw )Forward (pre-defined sources) (Leclerc et al., 1990; Wilson and Flesch, 1993)).Backward (pre-defined sensor location) (Flesch et al.,1995; Kljun et al., 1999).

Model approaches for flux footprint estimationModel approaches for flux footprint estimation

(Schmid, 2002)

High tower Low tower

Approaches based on Navier-Stokes equationsApproaches based on Navier-Stokes equations

Large-eddy simulation (Hadfield, 1994; Leclerc et al., 1997)

Ensemble-averaged model (K-theory) (Sogachev et al., 2002)

Most ecosystems are not spatially homogeneous. Linking the patch patterns to the carbon cycle is a serious challenge.

Methods of estimation of source weight function Methods of estimation of source weight function in ensemble-averaged modelin ensemble-averaged model

i = 1, 2, 3, k-2, k-1, k, I

WindF (CO2)

Z2m

Z1m

F (CO2)Z2m

Z1m

i = 1, 2, 3, k-2, k-1, k, I

WindI

i = 1, 2, 3, k-2, k-1, k, I

WindF (CO2) Z2m

Z1m

II

i = 1, 2, 3, k-2, k-1, k, I

WindF (CO2)

Z2m

Z1m

III

i indicates a model grid cell within a domain of I grid cells. k is the investigated grid cell (measurement point) . Z1 and Z2 are the heights for which the footprint is estimated. The dashed areas depict high intensity areas of vertical scalar flux.

(Sogachev and Lloyd, 2004)

q(t),T(t), C(t), V(t), U(t)

Clouds (t)

T(soil), q(soil), FCO2(soil), V = 0, U = 0

Q0(t),

l o w e r b o u n d a r y c o n d i t i o n s

3 km

1 - 10 km

Upper boundary conditions

Scheme of the SCADIS (Scheme of the SCADIS (scascalar lar disdistribution) modeltribution) model

FCO2 E R H

G

yf

xf

,

10 - 100 m

f = U, V, T, q , C, for x = ±X,y = ±Y

10 - 100 km

f(x,y,z,t)

-X-Y

+X+Y

c o

n d

i t i

o n

s o

n

lateral borders

SCADIS is high resolution 3-D numerical model capable of computing the physical processes within both plant canopy and atmospheric boundary layer simultaneously.

advection

y

f

x

f

,

(Sogachev et al., 2002)

Terrain-following coordinate system

Basic equations: momentum, heat,moisture,scalars (CO2, SO2, O3), turbulent kinetic energy (E)One-and-a-half-order turbulence closurebased on equations of E and ε or ω: E-l, E-ε, E-ω.)

Structure of vegetationpresented by type of vegetation (vertical profile of LAD, leaf or needle size,optical properties, aerodynamic drag coefficients …)

Vertical resolution75 - 110 model levels from 0 to 3025 m, 42 of it between 0 and 35 m.

Basic characteristics of the SCADIS modelBasic characteristics of the SCADIS model

(Sogachev et al., 2002; Sogachev et al., 2004, TAC)

LAD ( m-1 )

0.0 0.1 0.2 0.3 0.4 0.5

Hei

ght

( m

)

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

K ( m2 s-1 ), Ux ( m s-1 )

0 1 2 3 4 5 6 7

K

Ux

LAD

Zm = 30 m

Upwind distance ( m )

1000 900 800 700 600 500 400 300 200 100 0 -100

Foo

tprin

t (

m -1

)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Cum

ulat

ive

flux

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Zm = 50 m

Upwind distance ( m )

2000 1800 1600 1400 1200 1000 800 600 400 200 0

Fo

otp

rin

t (m

-1 )

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

Cu

mu

lativ

e f

lux

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Footprint and contribution function predictedFootprint and contribution function predicted by different methodsby different methods

Spatially homogeneous source located at a fixed height

Effect of the vertical distribution of sources within a plant canopy

Effect of φ=|Sc/S0|

S0 is the soil respiration intensity;

Sc is the photosyntheticactivity of the canopy.

(Sogachev and Lloyd, 2004)

Generalized effect of different disturbances Generalized effect of different disturbances on the airflow, scalar flux fields and the footprinton the airflow, scalar flux fields and the footprint

(Sogachev et al., 2004, TAC)

b

Upwind distance ( m )

800 700 600 500 400 300 200 100 0

Cu

mu

lative

flu

x

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Fo

otp

rin

t (

m-1 )

0.000

0.001

0.002

0.003

0.004

0.00503:00 LT

15:00 LTZm = 34 m

( contour intervals = 0.002 )

34 m, 32,8% 34 m, 88,1%

( contour intervals = 0.01 )

( contour intervals = 0.001 )

50 m, 18,9%

( contour intervals = 0.01 )

50 m, 70,1%

( contour intervals = 0.0005 )

75 m, 6,4%

( contour intervals = 0.005 )

75 m, 42,8%

34 m, 96,6%

( contour intervals = 0.01 )50 m, 84,9%( contour intervals = 0.01 )

75 m, 63,2%

( contour intervals = 0.005 )

03.00 LT 15.00 LT

15.00 LT

( contour intervals = 0.002 )

34 m, 32,8%

( contour intervals = 0.002 )

34 m, 32,8%

( contour intervals = 0.002 )

34 m, 32,8% 34 m, 88,1%

( contour intervals = 0.01 )

34 m, 88,1%

( contour intervals = 0.01 )

34 m, 88,1%

( contour intervals = 0.01 )

( contour intervals = 0.001 )

50 m, 18,9%

( contour intervals = 0.001 )

50 m, 18,9%

( contour intervals = 0.001 )

50 m, 18,9%

( contour intervals = 0.01 )

50 m, 70,1%

( contour intervals = 0.01 )

50 m, 70,1%

( contour intervals = 0.01 )

50 m, 70,1%

( contour intervals = 0.0005 )

75 m, 6,4%

( contour intervals = 0.0005 )

75 m, 6,4%

( contour intervals = 0.0005 )

75 m, 6,4%

( contour intervals = 0.005 )

75 m, 42,8%

( contour intervals = 0.005 )

75 m, 42,8%

( contour intervals = 0.005 )

75 m, 42,8%

34 m, 96,6%

( contour intervals = 0.01 )

34 m, 96,6%

( contour intervals = 0.01 )

34 m, 96,6%

( contour intervals = 0.01 )50 m, 84,9%( contour intervals = 0.01 )50 m, 84,9%( contour intervals = 0.01 )50 m, 84,9%( contour intervals = 0.01 )

75 m, 63,2%

( contour intervals = 0.005 )

75 m, 63,2%

( contour intervals = 0.005 )

75 m, 63,2%

( contour intervals = 0.005 )

03.00 LT 15.00 LT

15.00 LT

1. Effect of natural complex terrain on footprint1. Effect of natural complex terrain on footprint Tver region, Russia

a

(Sogachev and Lloyd., 2004)

b

N

1 km

2. Effect of natural complex terrain on footprint2. Effect of natural complex terrain on footprint Hyytiälä, Finland

(Sogachev et al., 2004, AFM)

Net flux

Upwind distance from measuring tower ( m )

1000 750 500 250 0

Co

ntr

ibu

tion

fu

nct

ion

*1

03 (

m-1 )

2

4

6

8

0

UniformSouth - north wind directionNorth - south wind direction

CF (S0, Sc / 3)

CF (S0, Sc)

3. Effect of natural complex terrain on footprint3. Effect of natural complex terrain on footprint Solling, Germany

100 m

N

(Sogachev et al., 2004, TAC)

Fetch ( m )

0 400 800 1200 1600

Flu

x / F

lux

( u

nifo

rm fo

rest

)

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Cd = 0.2Cd = 0.3Cd = 0.4Cd = 0.5

H = 20 m, LAI = 1.8 m2 m-2

Fetch( m )

0 400 800 1200 1600

Flu

x / F

lux

( un

iform

fore

st )

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

LAD ( m2 m-3 )

0.0 0.1 0.2 0.3 0.4 0.5

z / H

0.0

0.2

0.4

0.6

0.8

1.0

1.2Zm = 27 m

Fetch x / H

-40 -20 0 20 40

Fo

otp

rin

t *

10

3 (

m-1 )

0

1

2

3

4

5

6

7

Effect of forest edge on footprintEffect of forest edge on footprint Modelling aspects

(Klaassen et al., 2002)

To improve our understanding of the carbon cycle…To improve our understanding of the carbon cycle…Valkea-Kotinen Lake, Finland

Tower

Eddy covariance measuring system provide a piece of the C balance puzzle

The footprint of a turbulent flux measurement defines its spatial context. That is required for correct interpretation of experimental data.

Footprint models should produce realistic results in real-world situations

There are several methods to describe airflow (transported signal) in such situations by economical computing way with accuracy sufficient enough for practical tasks (K-l, K-ε, K-ω).

It has been demonstrated that they are suitable for footprint estimation.

SummarySummary

Problems of airflow parameterization to be solved:

-wake turbulence description within vegetation canopy remain uncertain. (1-D verification is insufficient. It can lead to wrong conclusions). -soil (surface) flux description under condition of weak turbulence-flow separation within vegetation canopy: both for a dence forest on a flat surface and for topography variations