Towards global empirical upscaling of FLUXNET eddy covariance observations: validation of a model tree ensemble approach using a biosphere model

Global, spatially and temporally explicit estimates of carbon and water fluxes derived from empirical up-scaling eddy covariance measurements would constitute a new and possibly powerful data stream to study the variability of the global terrestrial carbon and water cycle. This paper introduces and validates a machine learning approach dedicated to the upscaling of observations from the current global network of eddy covariance towers (FLUXNET). We present a new model TRee Induction ALgorithm (TRIAL) that performs hierarchical stratification of the data set into units where particular multiple regressions for a target variable hold. We propose an ensemble approach (Evolving tRees with RandOm gRowth, ERROR) where the base learning algorithm is perturbed in order to gain a diverse sequence of different model trees which evolves over time. We evaluate the efficiency of the model tree ensemble (MTE) approach using an artificial data set derived from the Lund-Potsdam-Jena managed Land (LPJmL) biosphere model. We aim at reproducing global monthly gross primary production as simulated by LPJmL from 1998-2005 using only locations and months where high quality FLUXNET data exist for the training of the model trees. The model trees are trained with the LPJmL land cover and meteorological input data, climate data, and the fraction of absorbed photosynthetic active radiation simulated by LPJmL. Given that we know the 'true result' in the form of global LPJmL simulations we can effectively study the performance of the MTE upscaling and associated problems of extrapolation capacity. We show that MTE is able to explain 92% of the variability of the global LPJmL GPP simulations. The mean spatial pattern and the seasonal variability of GPP that constitute the largest sources of variance are very well reproduced (96% and 94% of variance explained respectively) while the monthly interannual anomalies which occupy much less variance are less well matched (41% of variance explained). We demonstrate the substantially improved accuracy of MTE over individual model trees in particular for the monthly anomalies and for situations of extrapolation. We estimate that roughly one fifth of the domain is subject to extrapolation while MTE is still able to reproduce 73% of the LPJmL GPP variability here. This paper presents for the first time a benchmark for a global FLUXNET upscaling approach that will be employed in future studies. Although the real world FLUXNET upscaling is more complicated than for a noise free and reduced complexity biosphere model as presented here, our results show that an empirical upscaling from the current FLUXNET network with MTE is feasible and able to extract global patterns of carbon flux variability.