Assessing the predictive capability of randomized tree-based ensembles in streamflow modelling

Abstract. Combining randomization methods with ensemble prediction is emerging as an effective option to balance accuracy and computational efficiency in data-driven modelling. In this paper, we investigate the prediction capability of extremely randomized trees (Extra-Trees), in terms of accuracy, explanation ability and computational efficiency, in a streamflow modelling exercise. Extra-Trees are a totally randomized tree-based ensemble method that (i) alleviates the poor generalisation property and tendency to overfitting of traditional standalone decision trees (e.g. CART); (ii) is computationally efficient; and, (iii) allows to infer the relative importance of the input variables, which might help in the ex-post physical interpretation of the model. The Extra-Trees potential is analysed on two real-world case studies – Marina catchment (Singapore) and Canning River (Western Australia) – representing two different morphoclimatic contexts. The evaluation is performed against other tree-based methods (CART and M5) and parametric data-driven approaches (ANNs and multiple linear regression). Results show that Extra-Trees perform comparatively well to the best of the benchmarks (i.e. M5) in both the watersheds, while outperforming the other approaches in terms of computational requirement when adopted on large datasets. In addition, the ranking of the input variable provided can be given a physically meaningful interpretation

Automatic design of basin-specific drought indexes for highly regulated water systems

[EN] Socio-economic costs of drought are progressively increasing worldwide due to undergoing alterations of hydro-meteorological regimes induced by climate change. Although drought management is largely studied in the literature, traditional drought indexes often fail at detecting critical events in highly regulated systems, where natural water availability is conditioned by the operation of water infrastructures such as dams, diversions, and pumping wells. Here, ad hoc index formulations are usually adopted based on empirical combinations of several, supposed-to-be significant, hydro-meteorological variables. These customized formulations, however, while effective in the design basin, can hardly be generalized and transferred to different contexts. In this study, we contribute FRIDA (FRamework for Index-based Drought Analysis), a novel framework for the automatic design of basin-customized drought indexes. In contrast to ad hoc empirical approaches, FRIDA is fully automated, generalizable, and portable across different basins. FRIDA builds an index representing a surrogate of the drought conditions of the basin, computed by combining all the relevant available information about the water circulating in the system identified by means of a feature extraction algorithm. We used the Wrapper for Quasi-Equally Informative Subset Selection (W-QEISS), which features a multi-objective evolutionary algorithm to find Pareto-efficient subsets of variables by maximizing the wrapper accuracy, minimizing the number of selected variables, and optimizing relevance and redundancy of the subset. The preferred variable subset is selected among the efficient solutions and used to formulate the final index according to alternative model structures. We apply FRIDA to the case study of the Jucar river basin (Spain), a drought-prone and highly regulated Mediterranean water resource system, where an advanced drought management plan relying on the formulation of an ad hoc "state index" is used for triggering drought management measures. The state index was constructed empirically with a trial-and-error process begun in the 1980s and finalized in 2007, guided by the experts from the Confederacion Hidrografica del Jucar (CHJ). Our results show that the automated variable selection outcomes align with CHJ's 25-year-long empirical refinement. In addition, the resultant FRIDA index outperforms the official State Index in terms of accuracy in reproducing the target variable and cardinality of the selected inputs set.The work has been partially funded by the European Commission under the IMPREX project belonging to Horizon 2020 framework programme (grant no. 641811). The authors would like to thank the planning office of the Confederacion Hidrografica del Jucar (CHJ) for providing the data used in this study.Zaniolo, M.; Giuliani, M.; Castelletti, A.; Pulido-Velazquez, M. (2018). Automatic design of basin-specific drought indexes for highly regulated water systems. HYDROLOGY AND EARTH SYSTEM SCIENCES. 22(4):2409-2424. https://doi.org/10.5194/hess-22-2409-2018S24092424224AghaKouchak, A.: Recognize anthropogenic drought, Nature, 524, p. 409, 2015a. aAghaKouchak, A.: A multivariate approach for persistence-based drought prediction: Application to the 2010–2011 East Africa drought, J. Hydrol., 526, 127–135, 2015b. aAlcamo, J., Flörke, M., and Märker, M.: Future long-term changes in global water resources driven by socio-economic and climatic changes, Hydrolog. Sci. J., 52, 247–275, 2007. aAndreu, J., Capilla, J., and Sanchís, E.: AQUATOOL, a generalized decision-support system for water-resources planning and operational management, J. Hydrol., 177, 269–291, 1996. aAndreu, J., Ferrer-Polo, J., Pérez, M., and Solera, A.: Decision support system for drought planning and management in the Jucar river basin, Spain, in: 18th World IMACS/MODSIM Congress, Cairns, Australia, vol. 1317, 2009. a, bBowden, G. J., Dandy, G. C., and Maier, H. R.: Input determination for neural network models in water resources applications. Part 1 – Background and methodology, J. Hydrol., 301, 75–92, https://doi.org/10.1016/j.jhydrol.2004.06.021, 2005. aByun, H.-R. and Wilhite, D. A.: Objective quantification of drought severity and duration, J. Climate, 12, 2747–2756, 1999. aCarmona, M., Máñez Costa, M., Andreu, J., Pulido-Velazquez, M., Haro-Monteagudo, D., Lopez-Nicolas, A., and Cremades, R.: Assessing the effectiveness of Multi-Sector Partnerships to manage droughts: The case of the Jucar river basin, Earth's Future, 5, 750–770, https://doi.org/10.1002/2017EF000545, 2017. a, b, c, dChangnon, S. A.: Detecting drought conditions in Illinois, Circular (Illinois State Water Survey), 1–36, Illinois, USA, 1987. aCHD: Plan Especial de Actuación en situaciones de alerta y eventual sequía, Plan Especial de Actuación en situaciones de alerta y eventual sequía en la cuenca del Duero, TYPSA, Valladolid, 2007. aCHE: Plan especial de actuación en situaciones de alerta y eventual sequia en la cuenca hidrográfica del Ebro, MARM, Zaragoza, 2007. aCHG: Plan especial de actuación en situaciones de alerta y eventual sequía de la cuenca hidrográfica del Guadalquivir, CHG, Seville, Spain, 2007. aCHJ: Plan especial de alerta y eventual sequía en la confederación hidrográfica del Júcar, Confederación Hidrográfica del Júcar, Jucar River Basin Management Authority, Ministry of Agriculture, Food and Environment, Spanish Government, Valencia, Spain, 2007a (in Spanish). a, b, c, dCHJ: Anejo2 – Plan especial de alerta y eventual sequía en la confederación hidrográfica del Júcar, Confederación Hidrográfica del Júcar, Jucar River Basin Management Authority, Ministry of Agriculture, Food and Environment, Spanish Government, Valencia, Spain, 2007b (in Spanish). aCunningham, P.: Dimension reduction, in: Machine learning techniques for multimedia, 91–112, Springer, Cognitive Technologies, Springer, Berlin, Heidelberg, 2008. aDracup, J. A., Lee, K. S., and Paulson, E. G.: On the definition of droughts, Water Resour. Res., 16, 297–302, https://doi.org/10.1029/WR016i002p00297, 1980. aEstrela, T. and Vargas, E.: Drought management plans in the European Union. The case of Spain, Water Resour. Manag., 26, 1537–1553, 2012. a, bEU: Water Scarcity and Droughts, Second Interim Report, Tech. rep., 2007. aFalkenmark, M., Lundqvist, J., and Widstrand, C.: Macro-scale water scarcity requires micro-scale approaches, in: Natural resources forum, vol. 13, 258–267, Wiley Online Library, Blackwell Publishing Ltd, 1989. aGalelli, S. and Castelletti, A.: Tree-based iterative input variable selection for hydrological modeling, Water Resour. Res., 49, 4295–4310, 2013. aGalelli, S., Humphrey, G. B., Maier, H. R., Castelletti, A., Dandy, G. C., and Gibbs, M. S.: An evaluation framework for input variable selection algorithms for environmental data-driven models, Environ. Modell. Softw., 62, 33–51, https://doi.org/10.1016/j.envsoft.2014.08.015, 2014. aGarrote, L., Martin-Carrasco, F., Flores-Montoya, F., and Iglesias, A.: Linking drought indicators to policy actions in the Tagus basin drought management plan, Water Resour. Manag., 21, 873–882, 2007. a, bGiorgi, F. and Lionello, P.: Climate change projections for the Mediterranean region, Global Planet. Change, 63, 90–104, 2008. aGómez, C. M. G. and Blanco, C. D. P.: Do drought management plans reduce drought risk? A risk assessment model for a Mediterranean river basin, Ecol. Econ., 76, 42–48, 2012. aGustard, A. and Demuth, S.: Operational Hydrology Report No. 50 German National Committee for the International Hydrological Programme (IHP) of UNESCO and the Hydrology and Water Resources Programme (HWRP) of WMO, Koblenz, 2009. aGuyon, I.: An Introduction to Variable and Feature Selection, J. Mach. Learn. Res., 3, 1157–1182, 2003. aHadka, D. and Reed, P.: Borg: An auto-adaptive many-objective evolutionary computing framework, Evol. Comput., 21, 231–259, 2013. aHao, Z. and AghaKouchak, A.: Multivariate standardized drought index: a parametric multi-index model, Adv. Water Resour., 57, 12–18, 2013. aHaro, D., Solera, A., Paredes, J., and Andreu, J.: Methodology for drought risk assessment in within-year regulated reservoir systems. application to the orbigo river system (Spain), Water Resour. Manag., 28, 3801–3814, 2014a. a, bHaro, D., Solera, A., Pedro-Monzonís, M., and Andreu, J.: Optimal Management of the Jucar River and Turia River Basins under Uncertain Drought Conditions, Procedia Engineer., 89, 1260–1267, 2014b. a, bHaro-Monteagudo, D., Solera, A., and Andreu, J.: Drought early warning based on optimal risk forecasts in regulated river systems: Application to the Jucar River Basin (Spain), J. Hydrol., 544, 36–45, 2017. a, b, cHeim Jr., R. R.: A review of twentieth-century drought indices used in the United States, B. Am. Meteorol. Soc., 83, 1149–1165, 2002. a, b, cHuang, G.-B., Zhu, Q.-Y., and Siew, C.-K.: Extreme learning machine: theory and applications, Neurocomputing, 70, 489–501, 2006. a, bHuang, G.-B., Zhou, H., Ding, X., and Zhang, R.: Extreme learning machine for regression and multiclass classification, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 42, 513–529, 2012. aKarakaya, G., Galelli, S., Ahipasaoglu, S. D., and Taormina, R.: Identifying (Quasi) Equally Informative Subsets in Feature Selection Problems for Classification: A Max-Relevance Min-Redundancy Approach, IEEE Transactions on Cybernetics, PP, 1, https://doi.org/10.1109/TCYB.2015.2444435, 2015. a, b, c, d, eKeyantash, J. and Dracup, J. A.: The quantification of drought: an evaluation of drought indices, B. Am. Meteorol. Soc., 83, 1167–1180, 2002. aKeyantash, J. A. and Dracup, J. A.: An aggregate drought index: Assessing drought severity based on fluctuations in the hydrologic cycle and surface water storage, Water Resour. Res., 40, 1–13, 2004. aKummu, M., Ward, P. J., de Moel, H., and Varis, O.: Is physical water scarcity a new phenomenon? Global assessment of water shortage over the last two millennia, Environ. Res. Lett., 5, 034006, 2010. aLaaha, G., Gauster, T., Tallaksen, L. M., Vidal, J.-P., Stahl, K., Prudhomme, C., Heudorfer, B., Vlnas, R., Ionita, M., Van Lanen, H. A. J., Adler, M.-J., Caillouet, L., Delus, C., Fendekova, M., Gailliez, S., Hannaford, J., Kingston, D., Van Loon, A. F., Mediero, L., Osuch, M., Romanowicz, R., Sauquet, E., Stagge, J. H., and Wong, W. K.: The European 2015 drought from a hydrological perspective, Hydrol. Earth Syst. Sci., 21, 3001–3024, https://doi.org/10.5194/hess-21-3001-2017, 2017. aLorenzo-Lacruz, J., Vicente-Serrano, S. M., López-Moreno, J. I., Beguería, S., García-Ruiz, J. M., and Cuadrat, J. M.: The impact of droughts and water management on various hydrological systems in the headwaters of the Tagus River (central Spain), J. Hydrol., 386, 13–26, https://doi.org/10.1016/j.jhydrol.2010.01.001, 2010. aMacian-Sorribes, H. and Pulido-Velazquez, M.: Integrating Historical Operating Decisions and Expert Criteria into a DSS for the Management of a Multireservoir System, J. Water Res. Pl., 143, 04016069, https://doi.org/10.1061/(ASCE)WR.1943-5452.0000712, 2017. aMacKay, D. J.: Information theory, inference and learning algorithms, Cambridge university press, 2003. aMarcos-Garcia, P., Lopez-Nicolas, A., and Pulido-Velazquez, M.: Combined use of relative drought indices to analyze climate change impact on meteorological and hydrological droughts in a Mediterranean basin, J. Hydrol., 554, 292–305, 2017. aMcKee, T. B., Doesken, N. J., Kleist, J., et al.: The relationship of drought frequency and duration to time scales, in: Proceedings of the 8th Conference on Applied Climatology, vol. 17, 179–183, American Meteorological Society Boston, MA, 1993. a, bMinisterio del Medio Ambiente: Plan Hidrológico Nacional, ≪BOE≫ núm. 161, de 6 de julio de 2001, 24228–24250, Madrid, Espana, 2000. aMishra, A. K. and Singh, V. P.: A review of drought concepts, J. Hydrol., 391, 202–216, https://doi.org/10.1016/j.jhydrol.2010.07.012, 2010. a, b, c, dNarasimhan, B. and Srinivasan, R.: Development and evaluation of Soil Moisture Deficit Index (SMDI) and Evapotranspiration Deficit Index (ETDI) for agricultural drought monitoring, Agr. Forest Meteorol., 133, 69–88, https://doi.org/10.1016/j.agrformet.2005.07.012, 2005. aOki, T. and Kanae, S.: Global hydrological cycles and world water resources, Science, 313, 1068–1072, 2006. aPalmer, W. C.: Meteorological drought, vol. 30, US Department of Commerce, Weather Bureau Washington, DC, 1965. aPedro-Monzonís, M., Ferrer, J., Solera, A., Estrela, T., and Paredes-Arquiola, J.: Water Accounts and Water Stress Indexes in the European Context of Water Planning: the Jucar River Basin, Procedia Engineer., 89, 1470–1477, 2014. aPedro-Monzonìs, M., Solera, A., Ferrer, J., Estrela, T., and Paredes-Arquiola, J.: A review of water scarcity and drought indexes in water resources planning and management, J. Hydrol., 527, 482–493, https://doi.org/10.1016/j.jhydrol.2015.05.003, 2015. a, b, c, dRaskin, P., Gleick, P., Kirshen, P., Pontius, G., and Strzepek, K.: Water futures: Assessment of long-range patterns and problems, Comprehensive assessment of the freshwater resources of the world, SEI, 1997. aReed, P. M., Hadka, D., Herman, J. D., Kasprzyk, J. R., and Kollat, J. B.: Evolutionary multiobjective optimization in water resources: The past, present, and future, Adv. Water Resour., 51, 438–456, 2013. aRijsberman, F. R.: Water scarcity: fact or fiction?, Agr. Water Manage., 80, 5–22, 2006. a, bScott, D. W.: Multivariate density estimation and visualization, in: Handbook of Computational Statistics, edited by: Gentle, J., Härdle, W., and Mori Y., Springer Handbooks of Computational Statistics, Springer, Berlin, Heidelberg, 549–569, Springer, 2012. aShafer, B. and Dezman, L.: Development of a Surface Water Supply Index (SWSI) to assess the severity of drought conditions in snowpack runoff areas, in: Proceedings of the western snow conference, vol. 50, pp. 164–175, Colorado State University Fort Collins, CO, 1982. aSharma, A.: Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 1 – A strategy for system predictor identification, J. Hydrol., 239, 232–239, 2000. aSharma, A. and Mehrotra, R.: An information theoretic alternative to model a natural system using observational information alone, Water Resour. Res., 50, 650–660, 2014. a, bSpinoni, J., Naumann, G., Vogt, J., and Barbosa, P.: Meteorological Droughts in Europe, Publications Office of the European Union, ISBN-13: 978-92-79-55097-3, 2016. a, b, c, d, eStahl, K., Kohn, I., Blauhut, V., Urquijo, J., De Stefano, L., Acácio, V., Dias, S., Stagge, J. H., Tallaksen, L. M., Kampragou, E., Van Loon, A. F., Barker, L. J., Melsen, L. A., Bifulco, C., Musolino, D., de Carli, A., Massarutto, A., Assimacopoulos, D., and Van Lanen, H. A. J.: Impacts of European drought events: insights from an international database of text-based reports, Nat. Hazards Earth Syst. Sci., 16, 801–819, https://doi.org/10.5194/nhess-16-801-2016, 2016. aStaudinger, M., Stahl, K., and Seibert, J.: A drought index accounting for snow, J. Hydrol., 6, 2108–2123, https://doi.org/10.1002/2012WR013085, 2014. aSullivan, C. A., Meigh, J. R., and Giacomello, A. M.: The water poverty index: development and application at the community scale, in: Natural Resources Forum, vol. 27, 189–199, Wiley Online Library, 2003. aTallaksen, L. M. and Van Lanen, H. A.: Hydrological drought: processes and estimation methods for streamflow and groundwater, vol. 48, Elsevier, Amsterdam, NL, 2004. aTaormina, R., Galelli, S., Karakaya, G., and Ahipasaoglu, S.: An information theoretic approach to select alternate subsets of predictors for data-driven hydrological models, J. Hydrol., 542, 18–34, 2016. a, b, cVan Loon, A. F. and Van Lanen, H. A. J.: A process-based typology of hydrological drought, Hydrol. Earth Syst. Sci., 16, 1915–1946, https://doi.org/10.5194/hess-16-1915-2012, 2012. a, bVan Loon, A. F. and Van Lanen, H. A. J.: Making the distinction between water scarcity and drought using an observation-modeling framework, Water Resour. Res., 49, 1483–1502, https://doi.org/10.1002/wrcr.20147, 2013. aVicente-Serrano, S. M. and López-Moreno, J. I.: Hydrological response to different time scales of climatological drought: an evaluation of the Standardized Precipitation Index in a mountainous Mediterranean basin, Hydrol. Earth Syst. Sci., 9, 523–533, https://doi.org/10.5194/hess-9-523-2005, 2005.  aVicente-Serrano, S. M., Beguería, S., and López-Moreno, J. I.: A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index, J. Climate, 23, 1696–1718, 2010. a, bWanders, N., Van Lanen, H. A., and van Loon, A. F.: Indicators for drought characterization on a global scale, Tech. rep., Wageningen Universiteit, 2010. aWitten, I. H. and Frank, E.: Data Mining: Practical machine learning tools and techniques, Morgan Kaufmann, Cambridge, USA, 2005. aYang, H., Reichert, P., Abbaspour, K. C., and Zehnder, A. J.: A water resources threshold and its implications for food security, Environ. Sci. Technol., 37, 3048–3054, 2003. aYang, Y. and Pedersen, J. O.: A comparative study on feature selection in text categorization, International Conference of Machine Learning ICML, 97, 412–420, 1997. aZaniolo, M., Giuliani, M., Castelletti, A., and Pulido-Velàzquez, M.: Raw and processed hydro-meteorological variables of Jucar river basin for feature selection, https://doi.org/10.5281/zenodo.1185084, 2018. a, bZargar, A., Sadiq, R., Naser, B., and Khan, F. I.: A review of drought indices, Environ. Rev., 19, 333–349, 2011. 

Incorporating flexibility in the long-term design of water distribution systems using operational variables

This work investigates the effect of operational variables on water distribution system design optimisation. The “Anytown” problem is approached with three formulations of the operational decision variables to examine how different models of such components affect the design solutions and the optimisation process. The formulations that jointly optimise operations and design decision variables can double the energy surplus for the same cost compared to a design-only formulation

Contrasting farmers' perception of climate change and climatic data: How (in)consistency supports risk reduction and resilience?

Farmers’ adaptation to climate change is a two-step process that involves perceiving stressors and identifying impacts to respond to variability and changes through specific actions and strategies. Hence, successful adaptation depends on how well changing climate is perceived, either from a ‘bottom-up’ pathway –where farmers observe and identify changes through past experience–, or by using a ‘top-down’ pathway –where changes are identified through climate records. A gap between both pathways tends to be related to farmers’ misperception. For example, as life experiences influence perception, farmers who have been directly affected by extreme climatic events tend to report that the probability of such event happening again is relatively high. Furthermore, as perception is in part a subjective phenomenon, therefore, different farmers in the same locality might construct different perceptions of climate change impacts even though they experience the same weather patterns. Consequently, increased attention has been put on combining the ‘civic science’ of farmers’ perceptions with the ‘formal science’ from meteorological reports to identify the (in)consistency between perceived and observed data and how this affect farmers’ resilience when facing climate change impacts. This contribution provides a review comparing farmers’ perception and climate observations to address a twofold research question: 1) Which extreme events and compound risks are perceived by farmers in contrast with observed data? And 2) How do past experiences and social-learning influence farmers’ resilience and their adaptive capacity? We analyze a portfolio of 147 articles collected from Scopus library catalogue since 2000. The bibliometrics analysis was coupled with the systematic review to 103 articles selected from the original portfolio. Comparison between perceived and observed changes were focus on what was changing (onset, duration or cessation regarding temperature and rainfall patterns) and how it was changing (amount, frequency, intensity or inter-annual variability). Results will be useful for managers, developers, and policymakers of climate adaptation strategies to be more in tune with farmers’ understandings of when and how weather is changing. Furthermore, the review could generate recommendations for the design, formulation, and implementation of adaptation policies that are better tailored to farmers’ perception at local conditions, being more efficient and conducive to risk analysis when facing climate change

Soft Body Impact Against Aeronautical Structures

Statistics show that impacts of soft body against aeronautical structure are not so rare events. The damage caused by the impact of hailstones or of birds can sometimes be so heavy to compromise the service life of the vehicle. Companies, research centers and universities are interested in the evaluation of the effects of this kind of events and lots of researching works have been recently developed in this field. In this paper, an overview of the last studies performed at the Laboratory for the Safety in Transports (LaST – Crash Lab.) of Politecnico of Milan are presented throughout experimental tests and numerical finite element models. The validity of the correlation results method to prevent possible heavy consequence caused by these events is shown