Machine learning algorithms have become very popular for spatial mapping of the environment due to their ability to fit nonlinear and complex relationships. However, this ability comes with the disadvantage that they can only be applied to new data if these are similar to the training data. Since spatial mapping requires predictions to new geographic space which in many cases goes along with new predictor properties, a method to assess the area to which a prediction model can be reliably applied is required. Here, we suggest a methodology that delineates the ‘area of applicability’ (AOA) that we define as the area where we enabled the model to learn about relationships based on the training data, and where the estimated cross‐validation performance holds. We first propose a ‘dissimilarity index’ (DI) that is based on the minimum distance to the training data in the multidimensional predictor space, with predictors being weighted by their respective importance in the model. The AOA is then derived by applying a threshold which is the (outlier‐removed) maximum DI of the training data derived via cross‐validation. We further use the relationship between the DI and the cross‐validation performance to map the estimated performance of predictions. We illustrate the approach in a simulated case study chosen to mimic ecological realities and test the credibility by using a large set of simulated data. The simulation studies showed that the prediction error within the AOA is comparable to the cross‐validation error of the trained model, while the cross‐validation error does not apply outside the AOA. This applies to models being trained with randomly distributed training data, as well as when training data are clustered in space and where spatial cross‐validation is applied. Using the relationship between DI and cross‐validation performance showed potential to limit predictions to the area where a user‐defined performance applies. We suggest to add the AOA computation to the modeller's standard toolkit and to present predictions for the AOA only. We further suggest to report a map of DI‐dependent performance estimates alongside prediction maps and complementary to (cross‐)validation performance measures and the common uncertainty estimates.

The recent wave of published global maps of ecological variables has caused as much excitement as it has received criticism. Here we look into the data and methods mostly used for creating these maps, and discuss whether the quality of predicted values can be assessed, globally and locally.

Several spatial and non‐spatial Cross‐Validation (CV) methods have been used to perform map validation when additional sampling for validation purposes is not possible, yet it is unclear in which situations one CV method might be preferred over the other. Three factors have been identified as determinants of the performance of CV methods for map validation: the prediction area (geographical interpolation vs. extrapolation), the sampling pattern and the landscape spatial autocorrelation. In this study, we propose a new CV strategy that takes the geographical prediction space into account, and test how the new method compares with other established CV methods under different configurations of these three factors. We propose a variation of Leave‐One‐Out (LOO) CV for map validation, called Nearest Neighbour Distance Matching (NNDM) LOO CV, in which the nearest neighbour distance distribution function between the test and training data during the CV process is matched to the nearest neighbour distance distribution function between the target prediction and training points. Using random forest as a machine learning algorithm, we then examine the suitability of NNDM LOO CV as well as the established LOO (non‐spatial) and buffered‐LOO (bLOO, spatial) CV methods in two simulations with varying prediction areas, landscape autocorrelation and sampling distributions. LOO CV provided good map accuracy estimates in landscapes with short autocorrelation ranges, or when estimating geographical interpolation map accuracy with randomly distributed samples. bLOO CV yielded realistic error estimates when estimating map accuracy in new prediction areas, but generally overestimated geographical interpolation errors. NNDM LOO CV returned reliable estimates in all scenarios we considered. While LOO and bLOO CV provided reliable map accuracy estimates only in certain situations, our newly proposed NNDM LOO CV method returned robust estimates and generalised to LOO and bLOO CV whenever these methods were the most appropriate approach. Our work recognises the necessity of considering the geographical prediction space when designing CV‐based methods for map validation.

Spatial predictions of near-surface air temperature ( $T_{air}$ ) in Antarctica are required as baseline information for a variety of research disciplines. Since the network of weather stations in Antarctica is sparse, remote sensing methods have large potential due to their capabilities and accessibility. Based on the MODIS land surface temperature (LST) data, $T_{air}$ at the exact time of satellite overpass was modelled at a spatial resolution of 1 km using data from 32 weather stations. The performance of a simple linear regression model to predict $T_{air}$ from LST was compared to the performance of three machine learning algorithms: Random Forest (RF), generalized boosted regression models (GBM) and Cubist. In addition to LST, auxiliary predictor variables were tested in these models. Their relevance was evaluated by a Cubist-based forward feature selection in conjunction with leave-one-station-out cross-validation to reduce the impact of spatial overfitting. GBM performed best to predict $T_{air}$ using LST and the month of the year as predictor variables. Using the trained model, $T_{air}$ could be estimated with a leave-one-station-out cross-validated $R^2$ of 0.71 and a RMSE of 10.51 ${}^{\circ }$ C. However, the machine learning approaches only slightly outperformed the simple linear estimation of $T_{air}$ from LST ( $R^2$ of 0.64, RMSE of 11.02 ${}^{\circ }$ C). Using the trained model allowed creating time series of $T_{air}$ over Antarctica for 2013. Extending the training data by including more years will allow developing time series of $T_{air}$ from 2000 on.