analysis of the terrestrial carbon cycle through data assimilation and remote sensing

Analysis of the terrestrial carbon cycle through data assimilation

and remote sensing

Mathew Williams, University of EdinburghCollaborators

L Spadavecchia, M Van Wijk. B Law, J Irvine, P Schwarz, M Kurpius,

T Quaife, P Lewis M DisneyG Shaver, L Street

Source: CD Keeling, NOAA/ESRL

Sampling at 3397 meters, well mixed free troposphere

Harvard ForestData since 1989

Harvard Forest [CO2]

340

350

360

370

380

390

400

410

420

0 30 60 90 120 150 180 210 240 270 300 330 360

Time (day of year 1998)

[CO

2 ]Harvard Forest

Mauna Loa

Source: Wofsy et al, Harvard Forest LTER

Hourly data ~5 m above canopy

Talk outline

What are the uncertainties in temporal and spatial extrapolation of C cycle estimates?

1. Using multiple time series data to constrain C cycle analyses

2. Use multiscale spatial studies to determine up-scaling uncertainties

PART 1: Time

Improving estimates of C dynamics

MODELS OBSERVATIONS

FUSION

ANALYSIS

MODELS+ Capable of interpolation

& forecasts- Subjective & inaccurate?

OBSERVATIONS+Clear confidence limits

- Incomplete, patchy- Net fluxes

ANALYSIS+ Complete

+ Clear confidence limits+ Capable of forecasts

Time update“predict”

Measurement update

“correct”

A prediction-correction system

Initial conditions

The Kalman Filter

MODEL At Ft+1 F´t+1OPERATOR

At+1

Dt+1

Assimilation

Initial state Forecast ObservationsPredictions

Analysis

P

Ensemble Kalman Filter

Drivers

C cycling in Ponderosa Pine, OR

Flux tower (2000-2)Sap flowSoil/stem/leaf respirationLAI, stem, root biomassLitter fall measurements

Time (days since 1 Jan 2000)Williams et al GCB (2005)

ChambersSap-flowA/Ci

EC

Chambers

Time (days since 1 Jan 2000)

GPP Croot

Cwood

Cfoliage

Clitter

CSOM/CWD

Ra

Af

Ar

Aw

Lf

Lr

Lw

Rh

D

Temperature controlled

5 model pools10 model fluxes11 parameters10 data time series

Rtotal & Net Ecosystem Exchange of CO2

C = carbon poolsA = allocationL = litter fallR = respiration (auto- & heterotrophic)

Time (days since 1 Jan 2000)

= observation— = mean analysis| = SD of the analysis

(Williams et al 2005)

Time (days since 1 Jan 2000)

= observation— = mean analysis| = SD of the analysis

(Williams et al 2005)

0 365 730 1095-4

-3

-2

-1

0

1

2

0 365 730 1095-4

-2

0

2

Time (days, 1= 1 Jan 2000)

b) GPP data + model: -413±107 gC m-2

0 365 730 1095-4

-3

-2

-1

0

1

2

c) GPP & respiration data + model: -472 ±56 gC m-2NE

E (

g C

m-2 d

-1)

0 365 730 1095-4

-2

0

2

a) Model only: -251 ±197 g c m-2

d) All data: -419 ±29 g C m-2

Data brings confidence

= observation— = mean analysis| = SD of the analysis

(Williams et al 2005)

Assimilating EO reflectance data

DALECAt Ft+1

Reflectance

t+1

Radiativetransfer

At+1

MO

DIS

t+1

DA

GPP results

No assimilation

Assimilating MODIS

(bands 1 and 2)

Quaife et al, RSE (in press)

Summary: time

Multiple time series data generate powerful constraints on analyses

For improved predictions, better constraints on long time constant processes are required

Error characterisation is vital EO data can be assimilated with appropriate

observation operators

PART 2: Space

(Street et al 2007, Shaver et al 2007)

(Van Wijk & Williams 2005)

0.2 m 0.5 m

1.0 m

1.5 m

2.0 m

3.0 m

0.1 m0.75 m1.5 m2.35 m3.0 m4.5 m

Height of sensor and field of view

Distance (m) Distance (m)

(Williams et al. in press)

macroscale microscale

A multi-scale experimental design

0.4 0.5 0.6 0.7 0.80.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

y = 0.24 + 0.72 x

R2 = 0.90

y = 0.26 + 0.70 x

R2 = 0.86

0.4 0.5 0.6 0.7 0.80.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

9.0 m resolution

6.0 m resolution4.5 m resolution

3.0 m resolution1.5 m resolution

0.4 0.5 0.6 0.7 0.80.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

y = 0.25 + 0.70 x

R2 = 0.86

ND

VI (

diffu

ser)

0.4 0.5 0.6 0.7 0.80.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

y = 0.23 + 0.75 x

R2 = 0.81

0.4 0.5 0.6 0.7 0.80.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90NDVI (averaged)

y = 0.26 + 0.70 x

R2 = 0.91

NDVI (averaged)

Linear averaged Skye NDVIs (collected at 0.2 x 02 m resolution with diffuser off) versus measured NDVIs at coarser spatial scales with diffuser on

Microscale study:Scale invariance

0.5 0.6 0.7 0.8 0.90.0

0.4

0.8

1.2

1.6 y = 0.00067 exp(9.237x)

R2 = 0.80RMSE = 0.178

0.5 0.6 0.7 0.8 0.90.0

0.4

0.8

1.2

1.6 y = 0.00059 exp(9.502x)

R2 = 0.90RMSE = 0.119

9.0 m resolution

6.0 m resolution4.5 m resolution

3.0 m resolution1.5 m resolution

0.5 0.6 0.7 0.8 0.90.0

0.4

0.8

1.2

1.6

y = 0.00072 exp(9.294x)

R2 = 0.87RMSE = 0.120

Leaf

are

a in

dex

(LA

I)

0.5 0.6 0.7 0.8 0.90.0

0.4

0.8

1.2

1.6

y = 0.00156exp(8.212x)

R2 = 0.84RMSE = 0.131

0.5 0.6 0.7 0.8 0.90.0

0.4

0.8

1.2

1.6

y = 0.00044 exp(9.911x)

R2 = 0.94RMSE = 0.083

NDVI (averaged)

NDVI (averaged)

Relationships between estimated LAI (using both Skye NDVI and LI-COR LAI-2000 observations at 0.2 m resolution, linearly averaged for upscaling) versus Skye NDVI at different spatial scales.

Microscale study:Scale invariance

0 1 2 3 40

500

1000

15000.2 m

0 1 2 3 40

50

100

150

2001.5 m

0 1 2 3 40

20

40

60

Fre

quen

cy

3.0 m

0 1 2 3 40

5

10

15

20

254.5 m

0 1 2 3 40

5

10

15

LAI

6.0 m

0 1 2 3 40

1

2

3

LAI

9.0 m

Frequency histograms for LAI estimates in the microscale site at a range of resolutions.

(Williams et al. in press)

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7 8

Separation (m)

Sem

ivar

ianc

eSemi-variogram for LAI in the microscale study

0.60 0.64 0.68 0.72 0.76 0.80 0.840

10

20

30

40

50

Fre

qu

en

cy

NDVI (ground)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.605

1015202530

LAI

0.20 0.25 0.30 0.35 0.40 0.45 0.500

10

20

30

40

50

NDVI (Landsat)

Measured in a ground survey, 2004

Satellite overpass, ETM+, August 2001

Inferred from ground NDVI

Macroscale study: Frequency histograms

A significant but poor correlation with LandSat data

Macroscale study: Semivariograms

Measured in a ground survey, 2004

Satellite overpass, ETM+, August 2001

Inferred from ground NDVI

Technique Ground LAI

Landsat NDVI

RMSE MAE

Inverse distance weighting (IDW)

yes no 0.27 0.21

Linear correlation model (LCM)

yes yes 0.28 0.21

Ordinary Kriging (OK) yes no 0.28 0.21

External drift Kriging (EDK)

yes yes 0.29 0.22

Extrapolation models

Kriging Error

(Williams et al. in press)

IDWLandsat

Kriging

Summary: space

Scale invariance in LAI-NDVI relationships at scales > vegetation patches

However spatial variability is high so Kriging has limited usefulness

Over scales >50 m interpolation error was of similar magnitude to the uncertainty in the Landsat NDVI calibration to LAI

Characterisation of spatial LAI errors provides key data for spatial data assimilation

Key challenges and opportunities

Coping with variable data richness Identifying and removing model bias Estimating representation and data errors Making use of remote sensing (optical

and XCO2) Links to atmospheric CO2 using CTMs. Designing experimental network Boundaries in natural systems

Thank you

Funding support:NERCNASADOE

REFLEX: GOALS

To identify and compare the strengths and weaknesses of various MDF techniques

To quantify errors and biases introduced when extrapolating fluxes made at flux tower sites using EO data

Closing date for contributions: 31 October

www.carbonfusion.org

Regional Flux Estimation Experiment, stage 1

Flux dataMODIS LAI

MDF

Full analysisModel parameters

Forecasts

DALECmodel

Training Runs- FluxNet data- synthetic data

Deciduous forest sites

Coniferous forest sites

Assimilation

Output

www.carbonfusion.org

observations (with noise) truth predictions uncertainty

Synthetic evergreen forest2 years obs., 1 year prediction

Figure by Andrew Fox

REFLEX, stage 2

Flux dataMODIS LAI

MDF

Model parameters

DALECmodel

Testing predictionsWith only limited EO data

MDF

MODIS LAI

Analysis

Flux data

testing

Assimilation

FluxNet – Integrating worldwide CO2 flux measurements

How to upscale from site locations to regions and the globe?

Mauna Loa CO2 record

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1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Time

[CO

2]

Harvard Forest [CO2]

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0 30 60 90 120 150 180 210 240 270 300 330 360

Time (day of year 1998)

[CO

2 ]