## Appendix 2: Information on recent methods to calculate carbon stocks in Scottish soils

### Mapping soil carbon stocks based on 1:250,000 soil map polygons

**(Baggaley et al., 2016, Lilly & Baggaley, 2013)**

Soil profiles are classified as soil series based on their morphological characteristics. When soils were mapped at the 1:250 000 scale, polygons were drawn around landscape units with a distinctive set of soil types (Soil series). For each soil series the horizon characteristics such as sand, silt and clay content, carbon concentration, horizon depth and stone content will vary. These characteristics will also vary depending on whether the soil is under cultivation or not.

Representative soil profiles were derived for each soil series within the 1:250 000 National Soil Map of Scotland for both semi natural and cultivated land uses. The average and range of carbon concentration, based on data from 6000 soil horizons held in the Scottish Soils database, was then calculated for each soil horizon (layer) for each soil type. Using bulk density data from a smaller number of horizons where data were available, a regression equation was derived relating it to soil texture and carbon concentration along with the uncertainty in the relationship. Soil carbon stocks for each soil type were calculated by multiplying the soil bulk density, carbon concentration and horizon depth together, correcting for stone content and summing to 1 m depth. The total stock for Scotland was determined by multiplying the stocks for each soil type by the area of Scotland where the soil occurs, and then summing these contributions from each soil type. The uncertainty in these estimates was calculated using a statistical method that accounted for the variability in the soil carbon concentrations (based on the number of points available for each horizon and the standard deviation of measured concentrations) combined with the uncertainty in predicting the bulk densities using a regression equation. This analysis showed the importance of the accurate prediction of bulk densities when calculating soil carbon stocks and is something that is currently being further investigated.

### Mapping soil carbon stocks based on geostatistical modelling

**(Poggio & Gimona, 2014)**

The modelling was done in two steps, both of which have uncertainty associated with them. Bulk density was measured for 900 horizons from the National Soil Inventory of Scotland (2007-2009) dataset. These data were used to develop a model to predict the volume of soil (bulk density corrected by the volume of stones) based on the more widely available measurements of pH and organic matter. The predicted volume of soil was multiplied by the measured carbon concentrations at 19,500 soil horizons to calculate carbon stocks (75% of the total available). A model was then developed between soil carbon stock in each of the soil horizons from the Scottish Soils Database and the terrain and satellite-derived variables. The model was used to interpolate the calculated carbon stocks in 3 dimensions: 5 cm layers in each cell on a 1 km grid to those locations where there were no measurements. The model that was used involved an approach defined as Generalized Additive Models exploiting the neighbouring soil properties values in both lateral and vertical space. A further correction was applied using a method (error kriging) that tries to minimise discrepancies between the estimates and the observations

The uncertainty was calculated with a large number of iterations of the model with slightly different spatial configurations of the data. This produced a range of values for each 5 cm layer within each 1 km square that were summarised and provided a measure of uncertainty. The model outputs were validated by comparison of the predicted values with the values available from the 25% (6500) soil horizons not used to build the model. This important step provides a more robust assessment of the results and uncertainty obtained.

### Mapping soil carbon stocks based on neural network modelling

**(Aitkenhead & Coull, 2016)**

This method used two steps. The first was to generate a neural network model that predicted soil carbon density (soil carbon percentage multiplied by bulk density) from Loss on Ignition (LOI) data and depth. This was developed using the National Soil Inventory of Scotland (2007-2009) dataset where all three parameters had been measured. A second neural network was then developed based on a larger number of points to predict LOI and profile depth from variables that influence soil formation and distribution in the landscape, in this case topography, land cover, data from the soil map, rainfall and temperature. This spatial model was then applied to predict LOI at every 1 cm depth interval to the maximum modelled depth in 100 m grid cells across Scotland where it had not been measured.

The range of values for each grid cell and at each depth within those cells was calculated as a result of validating the model against measured stocks that were not used in the model development. This range is a function of the inherent variability of soil carbon in the landscape, imperfections in the model (no statistical approach can fully capture the relationships expressed by reality) and the fact that not all explanatory variables can be included in any modelling approach. In some cases large uncertainty limits are due to the application of two different neural networks to the data due to the smaller number of points where bulk density had been measured.

### References:

Aitkenhead, MJ; Coull, MC. 2016. Mapping soil carbon stocks across Scotland using a neural network model. Geoderma, 262, 187-198. DOI: 10.1016/j.geoderma.2015.08.034.

Baggaley, N.; Poggio, L.; Gimona, A.; Lilly, A. 2016. Comparison of traditional and geostatistical methods to estimate and map the carbon content of Scottish soils. Book chapter In: Digital Soil Mapping Across Paradigms, Scales and Boundaries. Editors: Zhang, G.-L., Brus, D., Liu, F., Song, X.-D., Lagacherie, P. ISBN 978-981-10-0415-5

Lilly, A.; Baggaley, N.J. 2013. The potential for Scottish cultivated top soils to lose or gain soil organic carbon. Soil Use and Management, 29, 39-47.

Poggio, L; Gimona, A. 2014. National scale 3D modelling of soil organic carbon stocks with uncertainty propagation - An example from Scotland. Geoderma, 232, 284-299. DOI: 10.1016/j.geoderma.2014.05.004