Analysis of the terrestrial carbon cycle through data assimilation and remote sensing Mathew Williams, University of Edinburgh Collaborators L Spadavecchia, M Van Wijk. B Law, J Irvine, P Schwarz, M Kurpius, T Quaife, P Lewis M Disney G Shaver, L Street

Source: CD Keeling, NOAA/ESRL Sampling at 3397 meters, well mixed free troposphere

Harvard Forest Data since 1989

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 AtAt F t+1 F´ t+1 OPERATOR A t+1 D t+1 Assimilation Initial stateForecast Observations Predictions Analysis P Ensemble Kalman Filter Drivers

C cycling in Ponderosa Pine, OR Flux tower (2000-2) Sap flow Soil/stem/leaf respiration LAI, stem, root biomass Litter fall measurements

Time (days since 1 Jan 2000) Williams et al GCB (2005) Chambers Sap-flow A/Ci EC Chambers

Time (days since 1 Jan 2000)

GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Temperature controlled 5 model pools 10 model fluxes 11 parameters 10 data time series R total & Net Ecosystem Exchange of CO 2 C = carbon pools A = allocation L = litter fall R = 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)

Data brings confidence  = observation — = mean analysis | = SD of the analysis (Williams et al 2005)

Assimilating EO reflectance data DALEC AtAt F t+1 Reflectance t +1 Radiative transfer A t+1 MODIS 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) (Williams et al. in press) macroscalemicroscale A multi-scale experimental design

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

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

Frequency histograms for LAI estimates in the microscale site at a range of resolutions. (Williams et al. in press)

Semi-variogram for LAI in the microscale study

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

TechniqueGround LAI Landsat NDVI RMSEMAE Inverse distance weighting (IDW) yesno Linear correlation model (LCM) yes Ordinary Kriging (OK)yesno External drift Kriging (EDK) yes Extrapolation models

Kriging Error (Williams et al. in press) IDW Landsat 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 X CO2 )  Links to atmospheric CO 2 using CTMs.  Designing experimental network  Boundaries in natural systems

Thank you Funding support: NERC NASA DOE

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

Regional Flux Estimation Experiment, stage 1 Flux data MODIS LAI MDF Full analysis Model parameters Forecasts DALEC model Training Runs - FluxNet data - synthetic data Deciduous forest sites Coniferous forest sites Assimilation Output

 observations (with noise)  truth  predictions  uncertainty Synthetic evergreen forest 2 years obs., 1 year prediction Figure by Andrew Fox

REFLEX, stage 2 Flux data MODIS LAI MDF Model parameters DALEC model Testing predictions With 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?