Spatio-temporal variations and uncertainty in land surface modelling for high latitudes: univariate response analysis

A range of applications analysing the impact of environmental changes due to climate change, e.g. geographical spread of climate-sensitive infections (CSIs) and agriculture crop modelling, make use of land surface modelling (LSM) to predict future land surface conditions. There are multiple LSMs to choose from that account for land processes in different ways and this may introduce predictive uncertainty when LSM outputs are used as inputs to inform a given application. For useful predictions for a specific application, one must therefore understand the inherent uncertainties in the LSMs and the variations between them, as well as uncertainties arising from variation in the climate data driving the LSMs. This requires methods to analyse multivariate spatio-temporal variations and differences. A methodology is proposed based on multiway data analysis, which extends singular value decomposition (SVD) to multidimensional tables and provides spatio-temporal descriptions of agreements and disagreements between LSMs for both historical simulations and future predictions. The application underlying this paper is prediction of how climate change will affect the spread of CSIs in the Fennoscandian and north-west Russian regions, and the approach is explored by comparing net primary production (NPP) estimates over the period 1998-2013 from versions of leading LSMs (JULES, CLM5 and two versions of ORCHIDEE) that are adapted to high-latitude processes, as well as variations in JULES up to 2100 when driven by 34 global circulation models (GCMs). A single optimal spatio-temporal pattern, with slightly different weights for the four LSMs (up to 14% maximum difference), provides a good approximation to all their estimates of NPP, capturing between 87% and 93% of the variability in the individual models, as well as around 90% of the variability in the combined LSM dataset. The next best adjustment to this pattern, capturing an extra 4% of the overall variability, is essentially a spatial correction applied to ORCHIDEEHLveg that significantly improves the fit to this LSM, with only small improvements for the other LSMs. Subsequent correction terms gradually improve the overall and individual LSM fits but capture at most 1.7% of the overall variability. Analysis of differences between LSMs provides information on the times and places where the LSMs differ and by how much, but in this case no single spatio-temporal pattern strongly dominates the variability. Hence interpretation of the analysis requires the summation of several such patterns. Nonetheless, the three best principal tensors capture around 76% of the variability in the LSM differences and to a first approximation successively indicate the times and places where ORCHIDEE-HLveg, CLM5 and ORCHIDEE-MICT differ from the other LSMs. Differences between the climate forcing GCMs had a marginal effect up to 6% on NPP predictions out to 2100 without specific spatio-temporal GCM interaction.