Capitulo IV Análisis e interpretación de resultados
4.2. Insumos
4.2.1. Planificación del PEI: Componente teleológico y conceptual
Our statistical downscaling consists in using statistical relationships between the CLIMBER global model’s output (Y, the predictand) and the regional-scale climate variable for the corresponding time period (variables X1,...,Xp, the predictors). These statistical relationships need to be calibrated upon an observed or modelled climate. For the fitting of the GAM all the data must be represented at the same spatial resolution. We use a resolution of 1.5°x0.75° over the Fennoscandian area (59° N… 70° N and 3° E … 35° E) as illustrated in Figure 17. The CLIMBER-2, the RCA3 and the CRU data were interpolated bi-linearly onto this resolution, in which the SICOPOLIS data were already given. The statistical relationships are calibrated by stepwise screening of the data, using the data for one month at a time.
For present-day climate predictors we use CRU observed monthly mean temperature and precipitation data (see Chapter 3.2.2) and for present day topography we utilize NOAA terrain data (see Chapter 3.2.3). For climate and topography predictors of 44 kyr BP and 21 kyr BP we utilize temperature, precipitation and elevation data of the RCA3 model simulations described in Kjellström et al. (2009). We calculated the direction and the angle of the steepest slope from the elevation data sets for each time period.
Figure 17. The downscaling area and resolution for the GAM. The land grid cell nearest to Olkiluoto is marked green.
The statistical model GAM is a non-linear multi-regression method. We model the statistical expectation (E) of the predictand (Y) using a sum of univariate smooth functions of the p predictors (X1,...,Xp), such that
H } )
¦
( ) X | ( 1 p 1 j p j j X f X Y Ewhere the potentially non-linear smooth functions fj have a non-parametric form. It is assumed in this model, that the residuals
İ
follow a normal distribution. Our aim is to downscale the mean temperature and the total precipitation for each month. Therefore, the predictand Y will be either the monthly mean surface air temperature or the log- transformed monthly mean total precipitation of CLIMBER (shown for temperature in Figure 18). The total precipitation is better modelled by log-normal than by normaldistribution (Cheng & Qi 2002). In the fitting of the GAM, we have on the predictor side (the right-hand side of the equation) information for each grid point on the elevation, the shortest distance to the nearest glacier, the latitude and the longitude of each grid point, and the direction and angle of the steepest slope as shown for temperature in Figure 18.
The GAM is fitted to the three different climate periods at the same time. We assume that if the fitted GAM is valid in all these three different climate situations (interglacial climate (present-day), glacial climate (21 kyr BP) and permafrost climate (44 kyr BP), then this GAM can be used for downscaling the CLIMBER simulations throughout the full glacial cycle, i.e., the simulations of the last glacial cycle and the future 280 ppm simulation. The climate of the future 400 ppm simulation is crucially different from the 280 ppm simulation, the former being mostly as warm as today or even warmer. Therefore, for the temperature of the 400 ppm scenario, we use a GAM which was fitted by finding the statistical relations of the CLIMBER present-day and CRU observational data only. In Appendix 2 we show that the fitted GAMs are able to explain more than 94 % (45 %) of the surface air temperature (precipitation) spatial variance (see Appendix 2 Table A2.1 (Table A2.2)), and to reproduce approximately the observed and RCA3-simulated monthly mean temperatures and total precipitation (see Appendix 2, Figures A2.1 – A2.6).
In Figure 19 we depict the utilisation of the GAM for temperature of the Last Glacial Cycle simulation of CLIMBER. As input we have the bi-linearly interpolated CLIMBER temperature data and elevation and ice sheet data of the SICOPOLIS model. The statistical relationships achieved from fitting of the GAM are now used to produce downscaled temperature and log-precipitation of the last glacial cycle CLIMBER data. As output we get downscaled temperature data for the last glacial cycle. We compared the direct coarse output of the CLIMBER model (Last Glacial Cycle run) and the downscaled GAM output to Holocene proxy data. The comparison shows that the downscaling with the GAM improves the course output of CLIMBER model simulations of annual mean temperature (see Appendix 2 Figures A2.8 – A2.9.) In the next chapters, we use these fitted GAMs to downscale the whole CLIMBER-2 simulation of the last glacial cycle (Chapter 4) and four simulations 100–120 kyr into the future (Chapter 5).
Figure 18. Flow diagram of the fitting of a GAM for downscaling monthly mean surface temperature by finding statistical relationships between the global model output (predictors) and the regional-scale climate variables (predictands). Abbreviations are explained in Table 6.
Figure 19. Flow diagram of the utilization of the GAM for downscaling large scale global model output into regional scale.
Table 6. Abbreviations of data fluxes shown in Figure 18 and Figure 19. Abbreviations
T Surface Air temperature
el elevation of the surface (land, ice sheet or sea)
st direction of the steepest slope
ic distance to the ice sheet margin (or nearest ice cap)
CRU data of the Climate Research Unit
NG data of the National Geophysical Data Center
RC model output or setup of the RCA3 model
CLI model output of the CLIMBER model
SIC model output of the SICOPOLIS model
GAM statistical model
lat latitude lon longitude