Abstract. Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with probability aggregation methods in a geostatistical framework for the stochastic estimation of unsampled points. Histogram via entropy reduction (HER) predicts conditional distributions based on empirical probabilities, relaxing parameterizations and, therefore, avoiding the risk of adding information not present in data. By construction, it provides a proper framework for uncertainty estimation since it accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. We investigate the framework using synthetically generated data sets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties. HER shows a comparable performance to popular benchmark models, with the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory.

Abstract. In this study, we propose a data-driven approach for automatically identifying rainfall-runoff events in discharge time series. The core of the concept is to construct and apply discrete multivariate probability distributions to obtain probabilistic predictions of each time step that is part of an event. The approach permits any data to serve as predictors, and it is non-parametric in the sense that it can handle any kind of relation between the predictor(s) and the target. Each choice of a particular predictor data set is equivalent to formulating a model hypothesis. Among competing models, the best is found by comparing their predictive power in a training data set with user-classified events. For evaluation, we use measures from information theory such as Shannon entropy and conditional entropy to select the best predictors and models and, additionally, measure the risk of overfitting via cross entropy and Kullback–Leibler divergence. As all these measures are expressed in “bit”, we can combine them to identify models with the best tradeoff between predictive power and robustness given the available data. We applied the method to data from the Dornbirner Ach catchment in Austria, distinguishing three different model types: models relying on discharge data, models using both discharge and precipitation data, and recursive models, i.e., models using their own predictions of a previous time step as an additional predictor. In the case study, the additional use of precipitation reduced predictive uncertainty only by a small amount, likely because the information provided by precipitation is already contained in the discharge data. More generally, we found that the robustness of a model quickly dropped with the increase in the number of predictors used (an effect well known as the curse of dimensionality) such that, in the end, the best model was a recursive one applying four predictors (three standard and one recursive): discharge from two distinct time steps, the relative magnitude of discharge compared with all discharge values in a surrounding 65 h time window and event predictions from the previous time step. Applying the model reduced the uncertainty in event classification by 77.8 %, decreasing conditional entropy from 0.516 to 0.114 bits. To assess the quality of the proposed method, its results were binarized and validated through a holdout method and then compared to a physically based approach. The comparison showed similar behavior of both models (both with accuracy near 90 %), and the cross-validation reinforced the quality of the proposed model. Given enough data to build data-driven models, their potential lies in the way they learn and exploit relations between data unconstrained by functional or parametric assumptions and choices. And, beyond that, the use of these models to reproduce a hydrologist's way of identifying rainfall-runoff events is just one of many potential applications.

Abstract. In this study, we propose a data-driven approach to automatically identify rainfall-runoff events in discharge time series. The core of the concept is to construct and apply discrete multivariate probability distributions to obtain probabilistic predictions of each time step being part of an event. The approach permits any data to serve as predictors, and it is non-parametric in the sense that it can handle any kind of relation between the predictor(s) and the target. Each choice of a particular predictor data set is equivalent to formulating a model hypothesis. Among competing models, the best is found by comparing their predictive power in a training data set with user-classified events. For evaluation, we use measures from Information Theory such as Shannon Entropy and Conditional Entropy to select the best predictors and models and, additionally, measure the risk of overfitting via Cross Entropy and Kullback–Leibler Divergence. As all these measures are expressed in bit, we can combine them to identify models with the best tradeoff between predictive power and robustness given the available data. We applied the method to data from the Dornbirnerach catchment in Austria distinguishing three different model types: Models relying on discharge data, models using both discharge and precipitation data, and recursive models, i.e., models using their own predictions of a previous time step as an additional predictor. In the case study, the additional use of precipitation reduced predictive uncertainty only by a small amount, likely because the information provided by precipitation is already contained in the discharge data. More generally, we found that the robustness of a model quickly dropped with the increase in the number of predictors used (an effect well known as the Curse of Dimensionality), such that in the end, the best model was a recursive one applying four predictors (three standard and one recursive): discharge from two distinct time steps, the relative magnitude of discharge in a 65-hour time window and event predictions from the previous time step. Applying the model reduced the uncertainty about event classification by 77.8 %, decreasing Conditional Entropy from 0.516 to 0.114 bits. Given enough data to build data-driven models, their potential lies in the way they learn and exploit relations between data unconstrained by functional or parametric assumptions and choices. And, beyond that, the use of these models to reproduce a hydrologist's way to identify rainfall-runoff events is just one of many potential applications.

The study describes applications of Geographic Information Systems (GIS) associated with Standard Penetration Test (SPT) reports as a support tool for planning and decision-making in public and private spheres. The chapter begins with a bibliography compilation showing recent applications carried out around the world. Following this, the description of the geological-geotechnical method using SPT information applied in two case studies is presented in particular. For that, an extensive detailing of SPT reports treatment is done to enable the composition of a geological-geotechnical database. Two cases are shown to exemplify the method application and its results, including the characterization of the topographic relief through Digital Elevation Model (DEM), slope and hydrographic map and the development of soil, groundwater and foundation maps using a geological-geotechnical database composed basically by SPT data. The cases approach a larger scale using 507 SPT boreholes to analyze a university campus with 1 km 2 and on a smaller scale using 537 SPT boreholes to analyze a city with 207.2 km 2 of urban area. Different possibilities of applications for information management are discussed over the chapter.

We thank the second referee for their contributions. As our reply contains a figure and a section directly addressed to the editor, we attached it in the form of a supplement.