Incorporating uncertainty in gully erosion calculations using the random forests modelling approach Petra M. Kuhnert 1 * ,y , Anne-Kinsey Henderson 2 , Rebecca Bartley 3 and Alexander Herr 4 1 CSIRO Mathematical and Information Sciences, PO Box 120, Cleveland, QLD 4163, Australia 2 CSIRO Land and Water, Davies Lab, PMB PO, Aitkenvale, QLD 4814, Australia 3 CSIRO Land and Water, Meiers Rd, Indooroopilly, QLD 4068, Australia 4 CSIRO Sustainable Ecosystems, Bellenden St, GPO Box 284, Crace, ACT 2601, Australia SUMMARY Gully erosion represents one of the greatest threats to agricultural watersheds around the world and this is exacerbated with continual changes to land practices and changing climatic condition at a temporal scale. Catchment based models which include gully erosion have received increased attention in recent years due to the impact of gully erosion on downstream water quality. These types of models take gully erosion calculated via a deterministic model at a particular spatial location, along with other measures of erosion to provide an end-of- catchment load. Although seen as a major contributor to erosion in this type of modelling framework, the error surrounding the gully erosion calculation is ignored in the sediment model. We propose a methodology that investigates the error in the gully erosion model. The methodology uses Random Forests to predict gully density and its associated prediction error across a catchment using environmental variables, which are then incorporated into the gully erosion model. We demonstrate the approach using the Burdekin catchment in Queensland, Australia, where only a very small proportion of gullies (0.88%) have been mapped. Our results cast doubt in the predictive ability of models of sediment transportation that use gully erosion where the error is estimated high. Copyright # 2009 John Wiley & Sons, Ltd. key words: bootstrap; dependence; gully density; gully erosion; prediction uncertainty; random forests 1. INTRODUCTION Gully erosion is one of three primary contributors to sediment loss in rivers and catchments all over the world. It is a process that results in the removal of soil along drainage lines by runoff water, which produces deep cuts in the land known formally as gullies. This can have devastating effects on catchments, particularly those of an agricultural nature (Valentin et al., 2005b). Gully erosion is a global problem (Valentin et al., 2005a) and this has come about from a combination of changes in land use and climatic condition. Up until recently, it was thought that erosion ENVIRONMETRICS Environmetrics 2010; 21: 493–509 Published online 18 August 2009 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/env.999 *Correspondence to: P. M. Kuhnert, CSIRO Mathematical and Information Sciences, PO Box 120, Cleveland QLD 4163, Australia. y E-mail: Petra.Kuhnert@csiro.au Copyright # 2009 John Wiley & Sons, Ltd. Received 22 August 2008 Accepted 17 March 2009