Georgia Papacharalampous

Georgia Papacharalampous, Hristos Tyralis, Anastasios Doulamis et al.

Merging satellite products and ground-based measurements is often required for obtaining precipitation datasets that simultaneously cover large regions with high density and are more accurate than pure satellite precipitation products. Machine and statistical learning regression algorithms are regularly utilized in this endeavour. At the same time, tree-based ensemble algorithms are adopted in various fields for solving regression problems with high accuracy and low computational cost. Still, information on which tree-based ensemble algorithm to select for correcting satellite precipitation products for the contiguous United States (US) at the daily time scale is missing from the literature. In this study, we worked towards filling this methodological gap by conducting an extensive comparison between three algorithms of the category of interest, specifically between random forests, gradient boosting machines (gbm) and extreme gradient boosting (XGBoost). We used daily data from the PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) and the IMERG (Integrated Multi-satellitE Retrievals for GPM) gridded datasets. We also used earth-observed precipitation data from the Global Historical Climatology Network daily (GHCNd) database. The experiments referred to the entire contiguous US and additionally included the application of the linear regression algorithm for benchmarking purposes. The results suggest that XGBoost is the best-performing tree-based ensemble algorithm among those compared...

Georgia Papacharalampous, Hristos Tyralis, Anastasios Doulamis et al.

Gridded satellite precipitation datasets are useful in hydrological applications as they cover large regions with high density. However, they are not accurate in the sense that they do not agree with ground-based measurements. An established means for improving their accuracy is to correct them by adopting machine learning algorithms. This correction takes the form of a regression problem, in which the ground-based measurements have the role of the dependent variable and the satellite data are the predictor variables, together with topography factors (e.g., elevation). Most studies of this kind involve a limited number of machine learning algorithms, and are conducted for a small region and for a limited time period. Thus, the results obtained through them are of local importance and do not provide more general guidance and best practices. To provide results that are generalizable and to contribute to the delivery of best practices, we here compare eight state-of-the-art machine learning algorithms in correcting satellite precipitation data for the entire contiguous United States and for a 15-year period. We use monthly data from the PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) gridded dataset, together with monthly earth-observed precipitation data from the Global Historical Climatology Network monthly database, version 2 (GHCNm). The results suggest that extreme gradient boosting (XGBoost) and random forests are the most accurate in terms of the squared error scoring function. The remaining algorithms can be ordered as follows from the best to the worst: Bayesian regularized feed-forward neural networks, multivariate adaptive polynomial splines (poly-MARS), gradient boosting machines (gbm), multivariate adaptive regression splines (MARS), feed-forward neural networks, linear regression.

Hristos Tyralis, Georgia Papacharalampous

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users' needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

Hristos Tyralis, Georgia Papacharalampous, Nikolaos Doulamis et al.

Knowing the actual precipitation in space and time is critical in hydrological modelling applications, yet the spatial coverage with rain gauge stations is limited due to economic constraints. Gridded satellite precipitation datasets offer an alternative option for estimating the actual precipitation by covering uniformly large areas, albeit related estimates are not accurate. To improve precipitation estimates, machine learning is applied to merge rain gauge-based measurements and gridded satellite precipitation products. In this context, observed precipitation plays the role of the dependent variable, while satellite data play the role of predictor variables. Random forests is the dominant machine learning algorithm in relevant applications. In those spatial predictions settings, point predictions (mostly the mean or the median of the conditional distribution) of the dependent variable are issued. The aim of the manuscript is to solve the problem of probabilistic prediction of precipitation with an emphasis on extreme quantiles in spatial interpolation settings. Here we propose, issuing probabilistic spatial predictions of precipitation using Light Gradient Boosting Machine (LightGBM). LightGBM is a boosting algorithm, highlighted by prize-winning entries in prediction and forecasting competitions. To assess LightGBM, we contribute a large-scale application that includes merging daily precipitation measurements in contiguous US with PERSIANN and GPM-IMERG satellite precipitation data. We focus on extreme quantiles of the probability distribution of the dependent variable, where LightGBM outperforms quantile regression forests (QRF, a variant of random forests) in terms of quantile score at extreme quantiles. Our study offers understanding of probabilistic predictions in spatial settings using machine learning.

Georgia Papacharalampous, Hristos Tyralis, Nikolaos Doulamis et al.

Regression algorithms are regularly used for improving the accuracy of satellite precipitation products. In this context, satellite precipitation and topography data are the predictor variables, and gauged-measured precipitation data are the dependent variables. Alongside this, it is increasingly recognised in many fields that combinations of algorithms through ensemble learning can lead to substantial predictive performance improvements. Still, a sufficient number of ensemble learners for improving the accuracy of satellite precipitation products and their large-scale comparison are currently missing from the literature. In this study, we work towards filling in this specific gap by proposing 11 new ensemble learners in the field and by extensively comparing them. We apply the ensemble learners to monthly data from the PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) and IMERG (Integrated Multi-satellitE Retrievals for GPM) gridded datasets that span over a 15-year period and over the entire the contiguous United States (CONUS). We also use gauge-measured precipitation data from the Global Historical Climatology Network monthly database, version 2 (GHCNm). The ensemble learners combine the predictions of six machine learning regression algorithms (base learners), namely the multivariate adaptive regression splines (MARS), multivariate adaptive polynomial splines (poly-MARS), random forests (RF), gradient boosting machines (GBM), extreme gradient boosting (XGBoost) and Bayesian regularized neural networks (BRNN), and each of them is based on a different combiner. The combiners include the equal-weight combiner, the median combiner, two best learners and seven variants of a sophisticated stacking method. The latter stacks a regression algorithm on top of the base learners to combine their independent predictions...

Georgia Papacharalampous, Hristos Tyralis, Nikolaos Doulamis et al.

Merging satellite and gauge data with machine learning produces high-resolution precipitation datasets, but uncertainty estimates are often missing. We addressed the gap of how to optimally provide such estimates by benchmarking six algorithms, mostly novel even for the more general task of quantifying predictive uncertainty in spatial prediction settings. On 15 years of monthly data from over the contiguous United States (CONUS), we compared quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machine (LightGBM), and quantile regression neural networks (QRNN). Their ability to issue predictive precipitation quantiles at nine quantile levels (0.025, 0.050, 0.100, 0.250, 0.500, 0.750, 0.900, 0.950, 0.975), approximating the full probability distribution, was evaluated using quantile scoring functions and the quantile scoring rule. Predictors at a site were nearby values from two satellite precipitation retrievals, namely PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) and IMERG (Integrated Multi-satellitE Retrievals), and the site's elevation. The dependent variable was the monthly mean gauge precipitation. With respect to QR, LightGBM showed improved performance in terms of the quantile scoring rule by 11.10%, also surpassing QRF (7.96%), GRF (7.44%), GBM (4.64%) and QRNN (1.73%). Notably, LightGBM outperformed all random forest variants, the current standard in spatial prediction with machine learning. To conclude, we propose a suite of machine learning algorithms for estimating uncertainty in spatial data prediction, supported with a formal evaluation framework based on scoring functions and scoring rules.

Georgia Papacharalampous, Hristos Tyralis

Probabilistic forecasting is receiving growing attention nowadays in a variety of applied fields, including hydrology. Several machine learning concepts and methods are notably relevant towards addressing the major challenges of formalizing and optimizing probabilistic forecasting implementations, as well as the equally important challenge of identifying the most useful ones among these implementations. Nonetheless, practically-oriented reviews focusing on such concepts and methods, and on how these can be effectively exploited in the above-outlined essential endeavour, are currently missing from the probabilistic hydrological forecasting literature. This absence holds despite the pronounced intensification in the research efforts for benefitting from machine learning in this same literature. It also holds despite the substantial relevant progress that has recently emerged, especially in the field of probabilistic hydrological post-processing, which traditionally provides the hydrologists with probabilistic hydrological forecasting implementations. Herein, we aim to fill this specific gap. In our review, we emphasize key ideas and information that can lead to effective popularizations, as such an emphasis can support successful future implementations and further scientific developments. In the same forward-looking direction, we identify open research questions and propose ideas to be explored in the future.

Kwok P Chun, Thanti Octavianti, Nilay Dogulu et al.

Managing complex disaster risks requires interdisciplinary efforts. Breaking down silos between law, social sciences, and natural sciences is critical for all processes of disaster risk reduction. This enables adaptive systems for the rapid evolution of AI technology, which has significantly impacted the intersection of law and natural environments. Exploring how AI influences legal frameworks and environmental management, while also examining how legal and environmental considerations can confine AI within the socioeconomic domain, is essential. From a co-production review perspective, drawing on insights from lawyers, social scientists, and environmental scientists, principles for responsible data mining are proposed based on safety, transparency, fairness, accountability, and contestability. This discussion offers a blueprint for interdisciplinary collaboration to create adaptive law systems based on AI integration of knowledge from environmental and social sciences. Discrepancies in the use of language between environmental scientists and decision-makers in terms of usefulness and accuracy hamper how AI can be used based on the principles of legal considerations for a safe, trustworthy, and contestable disaster management framework. When social networks are useful for mitigating disaster risks based on AI, the legal implications related to privacy and liability of the outcomes of disaster management must be considered. Fair and accountable principles emphasise environmental considerations and foster socioeconomic discussions related to public engagement. AI also has an important role to play in education, bringing together the next generations of law, social sciences, and natural sciences to work on interdisciplinary solutions in harmony.

Hristos Tyralis, Georgia Papacharalampous, Nilay Dogulu et al.

Typical machine learning regression applications aim to report the mean or the median of the predictive probability distribution, via training with a squared or an absolute error scoring function. The importance of issuing predictions of more functionals of the predictive probability distribution (quantiles and expectiles) has been recognized as a means to quantify the uncertainty of the prediction. In deep learning (DL) applications, that is possible through quantile and expectile regression neural networks (QRNN and ERNN respectively). Here we introduce deep Huber quantile regression networks (DHQRN) that nest QRNN and ERNN as edge cases. DHQRN can predict Huber quantiles, which are more general functionals in the sense that they nest quantiles and expectiles as limiting cases. The main idea is to train a DL algorithm with the Huber quantile scoring function, which is consistent for the Huber quantile functional. As a proof of concept, DHQRN are applied to predict house prices in Melbourne, Australia and Boston, United States (US). In this context, predictive performances of three DL architectures are discussed along with evidential interpretation of results from two economic case studies. Additional simulation experiments and applications to real-world case studies using open datasets demonstrate a satisfactory absolute performance of DHQRN.

Hristos Tyralis, Georgia Papacharalampous

The Nash-Sutcliffe efficiency ($\text{NSE}$) is a widely used, positively oriented relative measure for evaluating forecasts across multiple time series. However, it lacks a decision-theoretic foundation for this purpose. To address this, we examine its negatively oriented counterpart, which we refer to as Nash-Sutcliffe loss, defined as $L_{\text{NS}} = 1 - \text{NSE}$. We prove that $L_{\text{NS}}$ is strictly consistent for an elicitable and identifiable multi-dimensional functional, which we name the Nash-Sutcliffe functional. This functional is a data-weighted component-wise mean. The common practice of maximizing the average NSE across multiple series is the sample analog of minimizing the expected $L_{\text{NS}}$. Consequently, this operation implicitly assumes that all series originate from a single non-stationary, stochastic process. We introduce Nash-Sutcliffe linear regression, a multi-dimensional model estimated by minimizing the average $L_{\text{NS}}$, which reduces to a data-weighted least squares formulation. By reorienting the sample average loss function, we extend the previously proposed evaluation and estimation framework to forecasting multiple stationary dependent time series with differing stochastic properties. This constitutes a more natural empirical implementation of the $\text{NSE}$ than the earlier formulation. Our results establish a decision-theoretic foundation for $\text{NSE}$-based model estimation and forecast evaluation in large datasets, while further clarifying the benefits of global over local machine learning models.

Hristos Tyralis, Georgia Papacharalampous

Loss functions constructed by applying transformations to the realization and prediction variables of (strictly) consistent loss functions have been extensively studied empirically, yet their theoretical foundations remain unexplored. To address this gap, we establish formal characterizations of (strict) consistency for such transformed loss functions and their corresponding elicitable functionals. Our analysis focuses on two interrelated cases: (a) transformations applied solely to the realization variable and (b) bijective transformations applied jointly to both the realization and prediction variables. These cases extend the well-established framework of transformations applied exclusively to the prediction variable, as formalized by Osband's revelation principle. We further develop analogous characterizations for (strict) identification functions. The resulting theoretical framework is broadly applicable to statistical and machine learning methodologies. When applied to Bregman and expectile loss functions, our framework enables two key advancements: (a) the interpretation of empirical findings from models trained with transformed loss functions and (b) the systematic construction of novel identifiable and elicitable functionals, including the g-transformed expectation and g-transformed expectile. By unifying theoretical insights with practical applications, this work advances principled methodologies for designing loss functions in complex predictive tasks. Applications of the framework to simulated and real-world data illustrate its practical utility in diverse settings.

Georgia Papacharalampous, Hristos Tyralis, Nikolaos Doulamis et al.

To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct advantages over quantile regression, including the ability to model intermittency as well as a stronger ability to extrapolate beyond the training data, which is critical for predicting extreme precipitation. Therefore, here, we introduce the concept of distributional regression in precipitation dataset creation, specifically for the spatial prediction task of correcting satellite precipitation products. Building upon this concept, we formulated new ensemble learning methods that can be valuable not only for spatial prediction but also for other prediction problems. These methods exploit conditional zero-adjusted probability distributions estimated with generalized additive models for location, scale and shape (GAMLSS), spline-based GAMLSS and distributional regression forests as well as their ensembles (stacking based on quantile regression and equal-weight averaging). To identify the most effective methods for our specific problem, we compared them to benchmarks using a large, multi-source precipitation dataset. Stacking was shown to be superior to individual methods at most quantile levels when evaluated with the quantile loss function. Moreover, while the relative ranking of the methods varied across different quantile levels, stacking methods, and to a lesser extent mean combiners, exhibited lower variance in their performance across different quantiles compared to individual methods that occasionally ranked extremely low. Overall, a task-specific combination of multiple distributional regression algorithms could yield significant benefits in terms of stability.

Georgia Papacharalampous, Hristos Tyralis, Nikolaos Doulamis et al.

Predictions in the form of probability distributions are crucial for effective decision-making. Quantile regression enables such predictions within spatial prediction settings that aim to create improved precipitation datasets by merging remote sensing and gauge data. However, ensemble learning of quantile regression algorithms remains unexplored in this context and, at the same time, it has not been substantially developed so far in the broader machine learning research landscape. Here, we introduce nine quantile-based ensemble learners and address the aforementioned gap in precipitation dataset creation by presenting the first application of these learners to large precipitation datasets. We employed a novel feature engineering strategy, which reduces the number of predictors by using distance-weighted satellite precipitation at relevant locations, combined with location elevation. Our ensemble learners include six that are based on stacking ideas and three simple methods (mean, median, best combiner). Each of them combines the following six individual algorithms: quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machines (LightGBM), and quantile regression neural networks (QRNN). These algorithms serve as both base learners and combiners within different ensemble learning methods. We evaluated performance against a reference method (i.e., QR) using quantile scoring functions and a large dataset. The latter comprises 15 years of monthly gauge-measured and satellite precipitation in the contiguous United States (CONUS). Ensemble learning with QR and QRNN yielded the best results across the various investigated quantile levels, which range from 0.025 to 0.975, outperforming the reference method by 3.91% to 8.95%...

Georgia Papacharalampous, Hristos Tyralis, Yannis Markonis et al.

A comprehensive understanding of the behaviours of the various geophysical processes and an effective evaluation of time series (else referred to as "stochastic") simulation models require, among others, detailed investigations across temporal scales. In this work, we propose a novel and detailed methodological framework for advancing and enriching such investigations in a hydroclimatic context. This specific framework is primarily based on a new feature compilation for multi-scale hydroclimatic analyses, and can facilitate largely interpretable feature investigations and comparisons in terms of temporal dependence, temporal variation, "forecastability", lumpiness, stability, nonlinearity (and linearity), trends, spikiness, curvature and seasonality. Multifaceted characterizations are herein obtained by computing the values of the proposed feature compilation across nine temporal resolutions (i.e., the 1-day, 2-day, 3-day, 7-day, 0.5-month, 1-month, 2-month, 3-month and 6-month ones) and three hydroclimatic time series types (i.e., temperature, precipitation and streamflow) for 34-year-long time series records originating from 511 geographical locations across the contiguous United States. Based on the acquired information and knowledge, similarities and differences between the examined time series types with respect to the evolution patterns characterizing their feature values with increasing (or decreasing) temporal resolution are identified. Moreover, the computed features are used as inputs to unsupervised random forests for detecting any meaningful clusters between the examined hydroclimatic time series. This clustering plays an illustrative role within this research, as it facilitates the identification of spatial patterns (with them consisting an important scientific target in hydroclimatic research) and their cross-scale comparison...

Georgia Papacharalampous, Hristos Tyralis, Ilias G. Pechlivanidis et al.

Statistical analyses and descriptive characterizations are sometimes assumed to be offering information on time series forecastability. Despite the scientific interest suggested by such assumptions, the relationships between descriptive time series features (e.g., temporal dependence, entropy, seasonality, trend and linearity features) and actual time series forecastability (quantified by issuing and assessing forecasts for the past) are scarcely studied and quantified in the literature. In this work, we aim to fill in this gap by investigating such relationships, and the way that they can be exploited for understanding hydroclimatic forecastability and its patterns. To this end, we follow a systematic framework bringing together a variety of -- mostly new for hydrology -- concepts and methods, including 57 descriptive features and nine seasonal time series forecasting methods (i.e., one simple, five exponential smoothing, two state space and one automated autoregressive fractionally integrated moving average methods). We apply this framework to three global datasets originating from the larger Global Historical Climatology Network (GHCN) and Global Streamflow Indices and Metadata (GSIM) archives. As these datasets comprise over 13 000 monthly temperature, precipitation and river flow time series from several continents and hydroclimatic regimes, they allow us to provide trustable characterizations and interpretations of 12-month ahead hydroclimatic forecastability at the global scale...

Georgia Papacharalampous, Andreas Langousis

Machine and statistical learning algorithms can be reliably automated and applied at scale. Therefore, they can constitute a considerable asset for designing practical forecasting systems, such as those related to urban water demand. Quantile regression algorithms are statistical and machine learning algorithms that can provide probabilistic forecasts in a straightforward way, and have not been applied so far for urban water demand forecasting. In this work, we aim to fill this gap by automating and extensively comparing several quantile-regression-based practical systems for probabilistic one-day ahead urban water demand forecasting. For designing the practical systems, we use five individual algorithms (i.e., the quantile regression, linear boosting, generalized random forest, gradient boosting machine and quantile regression neural network algorithms), their mean combiner and their median combiner. The comparison is conducted by exploiting a large urban water flow dataset, as well as several types of hydrometeorological time series (which are considered as exogenous predictor variables in the forecasting setting). The results mostly favour the practical systems designed using the linear boosting algorithm, probably due to the presence of trends in the urban water flow time series. The forecasts of the mean and median combiners are also found to be skilful in general terms.

Hristos Tyralis, Georgia Papacharalampous

Machine learning algorithms have been extensively exploited in energy research, due to their flexibility, automation and ability to handle big data. Among the most prominent machine learning algorithms are the boosting ones, which are known to be "garnering wisdom from a council of fools", thereby transforming weak learners to strong learners. Boosting algorithms are characterized by both high flexibility and high interpretability. The latter property is the result of recent developments by the statistical community. In this work, we provide understanding on the properties of boosting algorithms to facilitate a better exploitation of their strengths in energy research. In this respect, (a) we summarize recent advances on boosting algorithms, (b) we review relevant applications in energy research with those focusing on renewable energy (in particular those focusing on wind energy and solar energy) consisting a significant portion of the total ones, and (c) we describe how boosting algorithms are implemented and how their use is related to their properties. We show that boosting has been underexploited so far, while great advances in the energy field are possible both in terms of explanation and interpretation, and in terms of predictive performance.

Georgia Papacharalampous, Hristos Tyralis

Delivering useful hydrological forecasts is critical for urban and agricultural water management, hydropower generation, flood protection and management, drought mitigation and alleviation, and river basin planning and management, among others. In this work, we present and appraise a new simple and flexible methodology for hydrological time series forecasting. This methodology relies on (a) at least two individual forecasting methods and (b) the median combiner of forecasts. The appraisal is made by using a big dataset consisted of 90-year-long mean annual river flow time series from approximately 600 stations. Covering large parts of North America and Europe, these stations represent various climate and catchment characteristics, and thus can collectively support benchmarking. Five individual forecasting methods and 26 variants of the introduced methodology are applied to each time series. The application is made in one-step ahead forecasting mode. The individual methods are the last-observation benchmark, simple exponential smoothing, complex exponential smoothing, automatic autoregressive fractionally integrated moving average (ARFIMA) and Facebook's Prophet, while the 26 variants are defined by all the possible combinations (per two, three, four or five) of the five afore-mentioned methods. The new methodology is identified as well-performing in the long run, especially when more than two individual forecasting methods are combined within its framework. Moreover, the possibility of case-informed integrations of diverse hydrological forecasting methods within systematic frameworks is algorithmically investigated and discussed. The related investigations encompass linear regression analyses, which aim at finding interpretable relationships between the values of a representative forecasting performance metric and the values of selected river flow statistics...

Hristos Tyralis, Georgia Papacharalampous, Andreas Langousis

Daily streamflow forecasting through data-driven approaches is traditionally performed using a single machine learning algorithm. Existing applications are mostly restricted to examination of few case studies, not allowing accurate assessment of the predictive performance of the algorithms involved. Here we propose super learning (a type of ensemble learning) by combining 10 machine learning algorithms. We apply the proposed algorithm in one-step ahead forecasting mode. For the application, we exploit a big dataset consisting of 10-year long time series of daily streamflow, precipitation and temperature from 511 basins. The super learner improves over the performance of the linear regression algorithm by 20.06%, outperforming the "hard to beat in practice" equal weight combiner. The latter improves over the performance of the linear regression algorithm by 19.21%. The best performing individual machine learning algorithm is neural networks, which improves over the performance of the linear regression algorithm by 16.73%, followed by extremely randomized trees (16.40%), XGBoost (15.92%), loess (15.36%), random forests (12.75%), polyMARS (12.36%), MARS (4.74%), lasso (0.11%) and support vector regression (-0.45%). Based on the obtained large-scale results, we propose super learning for daily streamflow forecasting.