CTCD: Strand 2

Strand 2: Reducing C flux uncertainty through data assimilation

2.1 Data Assimilation Techniques

Background
There are two broad approaches to directly quantifying landscape C dynamics – by measuring changes in C stocks over time, or by measuring fluxes of C directly. Generating regional assessments of source and sink strengths from such data is complicated by their patchiness in space and time, and problems with data quality.

An alternative approach to generating C budgets has been to use process-based models, constructed to simulate the key processes. Models can be extended across large spatial domains and into the future. But there is always a danger that the model’s representation of the system is not accurate. Model parameters are generally poorly known and have to be derived from data, somehow.

To overcome these limitations, we are applying an approach, data assimilation, with a long history from fields such as numerical weather forecasting. The premise of data assimilation is that neither models nor observations can perfectly describe a system, but an analysis that combines model and data will provide a better estimate of system dynamics than model or observations alone. Thus, data assimilation (DA) is a process for the optimal combination of information about a system.

Progress to date
We have demonstrated how the application of data assimilation techniques results in improved estimates of ecosystem C stocks and fluxes, with reduced uncertainty compared to the original observations, or the model alone. By combining measurements and modelling through data assimilation, we generate more precise estimates of C dynamics, and simultaneously highlight areas where model improvement is required (Williams et al. 2005). Our approach has been to use the Ensemble Kalman filter.

Williams, M., P.A. Schwarz, B.E. Law, J. Irvine & M. Kurpius (2005). An improved analysis of forest carbon dynamics using data assimilation. Global Change Biology 11, 89-105.

Current work
Our current goals are to integrate earth observation data into the assimilation scheme outlined above, and to tackle the procedures for applying DA in a spatial mode.
With this in mind, we are addressing three particular questions:

Do measurements at multiple resolutions of the same physical variable provide a gain in information? For instance, can we usefully combine monthly radiance at decametric resolution and daily radiances at kilometric resolution?
How can information provided by point measurements (from flux tower or soil sampling) be propagated into the surroundings where such detailed data are not available?
How effectively can measurements integrated on a large region (e.g., stream flow gauges on a catchment, or tall tower flux data) provide spatial information within the region?

We are exploring linking geospatial statistics with data assimilation approaches. Our study regions range from the Oregon Cascades (working with Dr. Bev Law), the Canadian boreal forests (the BOREAS programme), to Europe and the globe.

Figure 1. We undertook an analysis for a young ponderosa pine stand in central Oregon. The panels show daily analyses over three years (red lines) of net ecosystem carbon exchange (NEE) generated using (a) model only, no observations; b) model plus gross primary production (GPP, derived from sap flow data) estimates only; and c) model plus GPP and total respiration data (Rtot, generated from soil, stem and leaf chamber data). NEE observations from an eddy flux station are shown as open circles. Grey lines indicate the standard deviation around the mean of the ensembles used in the data assimilation. The figure shows how the assimilation of data into the model improves analyses of NEE, and that the data assimilation approach generates a realistic assessment of analytical error. In panel A, the model is relatively poor, but the broad confidence intervals still encompass the majority of the NEE data. As GPP and Rtot data are assimilated (panels B and C), the analysis improves and confidence intervals shrink correspondingly.

2.2 Assimilating Radiance Data Into Biospheric Models
Earth Observation (EO) makes measurements of the radiance scattered by an area on the Earth's land surface into the view of a satellite sensor. One approach to using EO data with ecosystem models is to obtain estimates of canopy parameters (e.g. leaf area index, LAI, or fAPAR, Figure 2) from the EO data and use these either to test or to calibrate the ecosystem models. The advantage of this approach is that we can use existing satellite products, such as from MODIS..

Figure 2. MODIS LAI image for day 201 of the year 2000, illustrating LAI values during the summer. The problems with this technique are clear: the saturation of the product means that LAI>3 are impossible to differentiate. Also, factors such as cloud contamination seem to cause poor estimates; over the UK midlands the suggestion of low LAI values, caused by cloudiness obscuring the landsurface, is unrealistic for this time of year.

The problem with this technique is that the LAI estimate derived in such a way is generally of unknown accuracy and may be based on a different set of assumptions to those used in the ecosystem model. An alternative approach, in which it is more straightforward to keep track of error terms, is to use the state variables of the ecosystem model to drive a 'remote sensing' model to predict top of canopy reflectance (or radiance) and then to assimilate first order EO measurements of radiance/ reflectance. The model linking the ecosystem model output and the EO products is called the observation operator. Ideally, such a model would be coupled to an atmospheric scattering/ attenuation code (6s, MODTRAN) and top-of-atmosphere observations assimilated, but a lack of sensitivity of the ecosystem models to many of the atmospheric parameters may make it more practical to consider assimilating surface radiance estimated from these data (provided uncertainty due to atmospheric ‘correction’ can be determined). In the medium term, we will move towards using such first order products. The problem then is one of developing a reflectance observation operator and its linearised form.

The state vector describing the land surface in most global vegetation/C models is simple - foliar C mass and a plant functional type classifier are the typical descriptors of the canopy. The parameters controlling scattering from vegetation are far more numerous, including foliage area density and orientation, and factors governing leaf-level scattering, such as chlorophyll concentration (Figure 3).

Figure 3. Angular reflectance (rcanopy, BRDF) modelled using the Kuusk model (plane parallel radiative transfer model) showing visible red (left panel) and near infra-red (NIR, right panel). In each case we show results with two extremes of relative leaf size (small / large) and two extremes of clumping (homogeneous and heterogeneous). LAI is 2 in all cases and the sun is at nadir. Differences in clumping and leaf shape have significant impacts on reflectance.

We are working to determine the minimum parameter set required to drive the observation operator (H). It is likely that, at a minimum, H will require state variables not directly contained in the C models (e.g. chlorophyll concentration) but these might be initially assigned from a knowledge of land cover and ultimately linked through process-based or empirical relationships with C model variables.