Propagating Uncertainty Through Carbon Models

Geostatistical methods allow us to develop continuous fields of parameters and meteorological drivers for ecosystem models. One of the principal benefits of spatiotemporal geostatistics is the ability to retrieve uncertainties for regionalised drivers via simulation techniques. Simulation techniques produce a sets of equally possible regionalisations which preserve the characteristics of the data set, including the distribution and covariance of the observations. If a sufficiently large ensemble of drivers is produced, these can be propagated through the model to generate uncertainties on outputs.

In this example, we examine the sources and magnitude of uncertainty in the interannual carbon budget of a small area of central Oregon. We undertake our carbon modelling using the Data Assimilation Linked Ecosystem Carbon model (DALEC_CW); a simple forest carbon/water dynamics model. The model consists of a 'big leaf' surface exchange scheme, which regulates the flow of carbon and water between the atmosphere and the land surface. The fate of the carbon within the land surface is controlled by a carbon module, which apportions fixed carbon amongst plant carbon pools (roots, woody growth and leaves). The carbon within the plant pools is then deposited over time into litter pools, where it is decomposed and returned to the atmosphere.

DALEC C and Water dynamics model. Pools are shown as grey boxes, whilst fluxes are represented as arrows. The left hand plot illustrates the C module: GPP (gross primary production) is allocated to foliage (f), roots (r) or woody (w) material. Allocation fluxes are marked A, whilst losses are marked L. C loss is through respiration fluxes (R), split between autotrophic (a) and heterotrophic (h) sources. The right panel details the flow of water through the model: Precipitation (P) is allocated between 10 soil water layers (W1…10). Vertical drainage flows (F1…9) occur when soil layers are saturated. Water may be lost through gravitational drainage (Fg) to groundwater or evapotranspiration (ET).

Assessing Parameter Uncertainty

The rate of carbon exchange is dependent on the driving meteorology, and a set of rate parameters which must be known or estimated before modelling can proceed. These rate parameters are physiologically meaningful, and may be measured to some extent. However, some rate parameters have long time constants and may be difficult to measure in practice, and as such there are inherent uncertainties in the parameter measurements and estimates. We calibrated the model parameters using a data assimilation technique (the ensemble Kalman filter), which corrects the parameters sequentially by confronting model estimates (which are dependent on the current parameter set) with observations. The model parameters are adjusted in a way which balances the uncertainty of the observations with the uncertainty of the model, such that the most likely parameter set is returned. The resultant parameter distributions are outlined below.

We calibrated the model against observations made at the Metolius 'young' flux tower, at which measurements of forest carbon and water exchange are made via the eddy covariance technique. The calibrated model performed well, and reasonably reproduced the observed data for the study site

Assessing Meteorological Driver Uncertainty

We produced a 1000 member ensemble of weather scenarios for the study area surrounding the Metolius 'young' flux tower via geostatistical simulation. Meteorological observations are also made at the Young tower, but these were excluded from the simulation exercise. The ensembles were conditioned on meteorological observations from stations surrounding the site (see the other examples for maps of the meteorological network). The range of the ensemble reflects the uncertainty surrounding the estimation of meteorological drivers for the site, whilst the mean of the ensemble is equivalent to the Kriging estimate of the meteorology.

Assessing Modelled Carbon Uncertainty

Having established the uncertainties surrounding the parameters and drivers of the model, we were able to run a number of experiments to assess the uncertainty of the final carbon budget for the study site. In the first experiment we generated an ensemble of parameterisations, whilst using the site observations of meteorology to drive the model. In the second experiment, we parameterised the model with the ensemble mean of the parameter set and drove the model with 1000 equiprobable meteorological scenarios. In the final experiment we sampled the full range of uncertainty from both the parameter and meteorological ensembles.

The results of the experiments showed that parameter uncertainty dominated the uncertainty in the final carbon budget; in this case up to 50% of the predicted carbon uptake. The uncertainty in meteorology was much less significant, accounting for <5% of the total carbon budget. The combined uncertainty accounted for ~54% of the total carbon budget. We repeated the analysis, conditioning the meteorological simulations on data further from the study site (results not shown), and found a maximum uncertainty of ~20% in the total carbon budget when utilising stations >100km away from the site. We conclude that improvements in model parameterisation are more critical than improvements in driver quality for the estimation of regional carbon budgets.