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.

Combined Global Surface Summary of Day and European Climate Assessment and Dataset daily meteorological data sets (around 9000 stations) were used to build spatio‐temporal geostatistical models and predict daily air temperature at ground resolution of 1 km for the global land mass. Predictions in space and time were made for the mean, maximum, and minimum temperatures using spatio‐temporal regression‐kriging with a time series of Moderate Resolution Imaging Spectroradiometer (MODIS) 8 day images, topographic layers (digital elevation model and topographic wetness index), and a geometric temperature trend as covariates. The accuracy of predicting daily temperatures was assessed using leave‐one‐out cross validation. To account for geographical point clustering of station data and get a more representative cross‐validation accuracy, predicted values were aggregated to blocks of land of size 500×500 km. Results show that the average accuracy for predicting mean, maximum, and minimum daily temperatures is root‐mean‐square error (RMSE) =±2°C for areas densely covered with stations and between ±2°C and ±4°C for areas with lower station density. The lowest prediction accuracy was observed at high altitudes (>1000 m) and in Antarctica with an RMSE around 6°C. The model and predictions were built for the year 2011 only, but the same methodology could be extended for the whole range of the MODIS land surface temperature images (2001 to today), i.e., to produce global archives of daily temperatures (a next‐generation http://WorldClim.org repository) and to feed various global environmental models.