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Presentation at Agua2009, November 2009 in Cali, Colombia. Dimitri Solomatine

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- 1. AGUA 2009 Hydroinformatics and some of its roles in the view of climate variability Dr. Dimitri P. Solomatine Professor of Hydroinformatics 1 Quick start: role of uncertainty in flood management 80 So, issue a flood alarm or not?.. 70 Alarm level O est i m e U ne at pper bound Forecasted river discharge Low bound er 60 Deterministic forecast 50 Prediction interval Di schar ge 40 (uncertainty) 30 20 10 0 1 11 21 31 41 51 Ti me 2 D.P. Solomatine. Hydroinformatics.
- 2. Climate is changing… http://www.globalwarmingart.com/wiki/File:Holocene_Temperature_Variations_Rev_png 3 D.P. Solomatine. Hydroinformatics. Global warming 4 D.P. Solomatine. Hydroinformatics.
- 3. Variability in annual temperatures locally Source: www.john-daly.com, based on data from NASA Goddard Institute (GISS), USA, and Climatic Research Unit (CRU) of the University of East Anglia, Norwich, UK 5 D.P. Solomatine. Hydroinformatics. Climate is changing… There are many factors leading to changes in the rate of climate change Whatever the main reason is, the climate variations prompt for developing the water management strategies that take climate uncertainties into account the need for More observation systems Better predictive modelling tools Analytical methods to handle uncertainty Changes in design and adaptive management practices Changes in educational programmes at all levels These issues are the current focus of Hydroinformatics 6 D.P. Solomatine. Hydroinformatics.
- 4. Encapsulation of knowledge related to water Tacit (implicit) knowledge embedded within a person Words, texts, images printed stored in electronic media Mathematical models formulas, algorithms algorithms encapsulated in computer programs (software) Integrated systems encapsulating all of above - Hydroinformatics systems 7 D.P. Solomatine. Hydroinformatics. Hydroinformatics modelling, information and communication technology, computer sciences applied to problems of aquatic environment 1991 with the purpose of proper management 2008 8 D.P. Solomatine. Hydroinformatics.
- 5. Flow of information in a Hydroinformatics system Data Models Knowledge Decisions Earth observation, Numerical Weather Data modelling, Access to Decision monitoring Prediction Models integration with modelling support hydrologic and results hydraulic models Map of flood probability 9 D.P. Solomatine. Hydroinformatics. Where is data coming from? 10 D.P. Solomatine. Hydroinformatics.
- 6. ∂Q ∂ ⎛ Q 2 ⎞ ∂h + ⎜ ⎜ A ⎟ + gA ∂x − gAS o + gAS f = 0 ⎟ ∂t ∂x ⎝ ⎠ Modelling is the heart of Hydroinformatics 11 D.P. Solomatine. Hydroinformatics. Modelling Model is … a simplified description of reality an encapsulation of knowledge about a particular physical or social process in electronic form Goals of modelling are: understand the studied system or domain (the past) predict the future use the results of modelling for making decisions (change the future) 12 D.P. Solomatine. Hydroinformatics.
- 7. Modelling is at heart of Hydroinformatics Hydroinformatics deals with the technologies ensuring the whole information cycle, and integrates data, models, people 13 D.P. Solomatine. Hydroinformatics. Main modelling paradigms Physically-based model (process, simulation, numerical) is based on the understanding of the underlying processes Data-driven model is based on the recorded values of variables characterising the system. They need less knowledge about the physical behaviour Agent-based model consists of dynamically interacting relatively simple rule-based computational codes (agents) 14 D.P. Solomatine. Hydroinformatics.
- 8. Applications of models River/urban flood forecasting and management Reservoir operations Sediment transport and morphology Ecology and water quality Storm surges and coastal flooding Dredging and reclamation Urban sewers and drainage Water distribution networks etc. 15 D.P. Solomatine. Hydroinformatics. Example: a physically-based model of open channel flow: Saint Venant equations The 1D continuity and momentum equations for open channel flow are also referred as Saint Venant equation Form a pair of non-linear hyperbolic partial differential equations in Q (flow) and h (depth) ∂A ∂Q + = qL Continuity equation ∂t ∂x ∂Q ∂ ⎛ Q 2 ⎞ ∂h + ⎜ ⎜ A ⎟ + gA ∂x − gAS o + gAS f = 0 ⎟ Momentum equation ∂t ∂x ⎝ ⎠ x=distance, t=time, A=cross-section, S0=bottom slope, Sf=energy grade line slope, B=width Analytically can not be solved Numerically can be solved using finite differences (explicit, implicit schemes), finite elements 16 D.P. Solomatine. Hydroinformatics.
- 9. Why 2D/3D modelling? Often 1D model is not enough Horizontal velocity fields Vertical velocity fields 17 D.P. Solomatine. Hydroinformatics. Some examples of using modelling in water-related issues 18 D.P. Solomatine. Hydroinformatics.
- 10. Warragamba Dam, Australia Warragamba Dam - 65 km west of Sydney in the Burragorang Valley provides the major water supply for Sydney Warragamba River flows through a 300-600 m wide gorge, about 100 m deep before opening out into a large valley. This allows a relatively short and high dam to impound a vast quantity of water. A dam break of the Warragamba Dam would be a major disaster. SOBEK (Delft Hydraulics) software was used for simulation 19 D.P. Solomatine. Hydroinformatics. Warragamba Dam, Australia Simulation of the dam break with SOBEK by Deltares The animation shows the simulation results. They may be used for disaster management, evacuation planning, flood damage assessment, urban planning 20 D.P. Solomatine. Hydroinformatics.
- 11. Models are indispensable in dealing with floods 21 D.P. Solomatine. Hydroinformatics. Example: Hydroinformatics systems for flood warning – MIKE FloodWatch MIKE Flood Watch (Danish Hydraulic Institute), a decision support system for real-time flood forecasting: advanced time series data base MIKE 11, for hydrodynamic modeling MIKE 11 FF, real-time forecasting system, ArcView, Geographical Information System (GIS) 22 D.P. Solomatine. Hydroinformatics.
- 12. Hydroinformatics systems for flood warning: MIKE FloodWatch 23 D.P. Solomatine. Hydroinformatics. Ecosystem Integrated Model: a Case Study for Sonso Lake, Colombia Problem: 70% of the surface area of this shallow lake is covered by an invasive macrophite Water Hyacinth Causes: Nutrients pollution from agricultural use of land Lack of sustainable management of the lake Methodology: Ecological modelling of Water Hyacinth Its integration with hydrodynamic model Analysis of Alternatives to Manage the Water Hyacinth Infestation 24 D.P. Solomatine. Hydroinformatics.
- 13. Ecosystem Integrated Model: a Case Study for Sonso Lake, Colombia Ref: MSc study by Carlos Velez (Colombia), UNESCO-IHE & Delft Hydraulics Solar WATER SURFACE Radiation 2 3 5 6 16 Sobek Rural Sobek Rural 1 Water Volume 15 1D2D DELWAQ 5 13 Norg Porg 7 9 10 Water Velocity 14 Hydro Water 4 NH4 Hyacinth dynamic Water Depth 11 Quality PO4 12 Flow 6 NO3 8 9 Ecosystem SEDIMENT Organic Matter Settled PROCESSES Water Hyacinth 1. Input / Output 5. Input / Output 9. Resuspension 13. Photosynthesis Model (coded 2. Rainfall 6. Input / Output 10. Hydrolysis 14. Respiration using SOBEK 3. Evapotranspiration 7. Sedimentation 11. Oxidation 15. Mortality RURAL Open 4. Advection/Dispersion 8. Resuspension 12. Uptake/Growth 16. Losses 25 Process Library) D.P. Solomatine. Hydroinformatics. Hydrodynamic Model 1D River and Nutrients Model (Phosphate PO4) 2D Lake (Water Level) Processes included: Growth and Mortality Respiration/Photosynthesis Transportation by flow and wind Uptake/release of Nutrients from the water Mechanical, Biological and Chemical Control Options Water Hyacinth Integrated Model (Plant Density) 26 D.P. Solomatine. Hydroinformatics.
- 14. Beyond “classical” modelling: current developments in Hydroinformatics Machine learning in data-driven modelling Multi-objective optimisation Information theory Predicting models’ uncertainty Integration 27 Data-Driven Modelling Uses (numerical) data (time series) describing some physical process Establishes functions that link variables outputs = F (inputs) Valuable when physical processes are unknown Also useful as emulators of complex physically-based models (surrogate models) Actual (observed) Modelled output Y Input data X (real) system Learning is aimed at minimizing this Machine difference learning (data-driven) model Predicted output Y’ 28 D.P. Solomatine. Hydroinformatics.
- 15. Example of a data-driven model Linear regression model Y = a0 + a1 X observed data characterises the Y input-output relationship actual output (e.g., flow) X Y value model parameters are found by optimization model predicts new the model then predicts output output value for the new input without actual knowledge of what drives Y new input X value (e.g. rainfall) Which model is “better”: green, red or blue? 29 D.P. Solomatine. Hydroinformatics. Data-driven rainfall-runoff models: Case study Sieve (Italy) mountaneous catchment in Southern Europe area of 822 sq. km 30 D.P. Solomatine. Hydroinformatics.
- 16. SIEVE: visualization of data FLOW1: effective rainfall and discharge data Discharge [m3/s] Eff.rainfall [mm] 800 0 2 700 4 600 Effective rainfall [mm] 6 500 8 400 10 Discharge [m3/s] 12 300 14 200 16 100 18 0 20 0 500 1000 1500 2000 2500 Time [hrs] variables for building a decision tree model were selected on the basis of cross-correlation analysis and average mutual information: inputs: rainfalls REt, REt-1, REt-2, REt-3, flows Qt, Qt-1 outputs: flows Qt+1 or Qt+3 Solomatine. Hydroinformatics. D.P. 31 Using data-driven methods in rainfall-runoff modelling Qtup Available data: rainfalls Rt runoffs (flows) Qt Inputs: lagged rainfalls Rt Rt-1 … Rt-L Rt Qt Output to predict: Qt+T Model: Qt+T = F (Rt Rt-1 … Rt-L … Qt Qt-1 Qt-A … Qtup Qt-1up …) (past rainfall) (autocorrelation) (routing) Questions: how to find the appropriate lags? how to build non-linear regression function F ? Linear regression, neural network, support vector machine etc. 32 D.P. Solomatine. Hydroinformatics.
- 17. Artificial neural network: a universal function approximator (=non-linear regression model) weights weights x1 a ij b jk y1 ⎛ N hid ⎞ x2 u 1x y2 yk = F ⎜ bok + ⎜ ⎝ ∑ b jk u j ⎟ ⎟ ⎠ i =1 x3 y3 k=1,..., N out xn us ym Inputs Hidden layer Outputs F(v) ⎛ N inp ⎞ 1 uj = F ⎜ aoj + ⎜ ∑ aij xi ⎟ ⎟ ⎝ i =1 ⎠ 0 v j=1,..., N hid Non-linear sigmoid function: F(v) = 1/ (1 + e-v) There are (Ninp+1)Nhid + (Nhid+1)Nout parameters (weights) to be identified by optimisation process (training) 33 D.P. Solomatine. Hydroinformatics. Neural network tool interface 34 D.P. Solomatine. Hydroinformatics.
- 18. SIEVE: Predicting Q(t+3) three hours ahead (ANN learned the relationship btw rainfall and flow) Prediction of Qt+3 : Verification performance ANN verification 350 RMSE=11.353 NRMSE=0.234 300 Observed Modelled (ANN) COE=0.9452 250 Modelled (MT) Q [ m 3 /s ] 200 MT verification RMSE=12.548 150 NRMSE=0.258 100 COE=0.9331 50 0 0 20 40 60 80 100 120 140 160 180 t [hrs] 35 D.P. Solomatine. Hydroinformatics. Use of machine learning (data-driven) models in water resources Hydrological modelling Water demand forecasting Prediction of ocean surges Models of wind-wave interaction Sedimentation modelling Meta-models (emulating, fast models) of water systems – to replace complex physically-based models 36 D.P. Solomatine. Hydroinformatics.
- 19. MULTI-OBJECTIVE OPTIMIZATION Finding variables’ values that bring the value of the “objective function” to a minimum In water resources many problems require solving an optimization problem 37 D.P. Solomatine. Hydroinformatics. Many optimization problems in water resources are multi-objective there are several objectives that are to be optimized often they are in conflict, i.e. minimizing one does not mean minimizing another one a solution (the set of decision variables) is always a compromise Examples: multi-purpose reservoir operation electricity generation vs. irrigation vs. navigability models calibration (error minimization) models good "on average" vs. good for particular hydrologic conditions (floods) pipe networks optimization (design and rehabilitation) costs vs. reduction of flood damage 38 D.P. Solomatine. Hydroinformatics.
- 20. Model-based optimization of urban drainage network MOUSE modelling system (DHI Water and Environment) 1D model of free-surface flow is used 39 D.P. Solomatine. Hydroinformatics. Urban drainage system rehabilitation: use of multi-objective optimization rehabilitation: changing pipes, creating additional storages optimization by multi-objective genetic algorithm: find a compromise btw. min. cost and min. damage due to flooding Compromise Flood Damage optimal solutions Wastewater System Pipe Network Model (MOUSE) Data Processor Data Processor Optimization Procedure Costs (GLOBE, NSGA-II) 40 D.P. Solomatine. Hydroinformatics.
- 21. INFORMATION THEORY Shannon entropy provides a mathematical framework to evaluate the amount of information contained in a data series H = −∑ p log2 p Average mutual information (AMI) is measure of information available from one set of data having knowledge of another set of data AMI can be used to investigate dependencies and lag effects in time series data ⎡ PXY ( xi , y j ) ⎤ AMI= ∑ PXY ( xi , y j ) log 2 ⎢ ⎥ i, j ⎢ PX ( xi ) P ( y j ) ⎥ ⎣ Y ⎦ 41 D.P. Solomatine. Hydroinformatics. Information theory and optimization for sensors locations for contaminant detection in water distribution systems Three criteria considered: Concentration Volume of contaminated water delivered Time of detection PhD research of Mr. Leonardo Alfonso, UNESCO-IHE. L. Alfonso , A. Jonoski , D.P. Solomatine. Multi-objective optimisation of operational responses for contaminant flushing in water distribution networks. ASCE J. Water Res. Plan.Manag., 2009. 42 D.P. Solomatine. Hydroinformatics.
- 22. Multi-objective optimization of sensors locations to detect contamination Location of 5 sensors Scenario: 2 sources of pollution Time of Detection 40 50 Contaminated Volume Contaminant concentration 501 Tank A 80 140 60 30 90 150 170 502 100 Tank B 70 160 130 500 20 110 120 Source Locations found using different method 43 D.P. Solomatine. Hydroinformatics. Average mutual information in optimizing the structure of a Neural Network model Rainfall-runoff forecasting model: Rt Qt Qt+T = F (Rt Rt-1 … Rt-L … Qt Qt-1 Qt-A) (past rainfall) (autocorrelation) Finding optimal lags between Qt+T and rainfall Rt 1.0 0.30 0.8 0.25 0.20 Corr. Coef. 0.6 AMI 0.15 0.4 0.10 0.2 0.05 0.0 0.00 0 5 10 15 20 Time lags (hours) Cross-correlation Autocorrelation AMI 44 D.P. Solomatine. Hydroinformatics.
- 23. UNCERTAINTY Uncertainties associated with climate change are very high Different IPCC scenarios lead to very different results of water models Any study exploring the impacts of CC needs powerful tools for analysing and predicting uncertainty 45 D.P. Solomatine. Hydroinformatics. Uncertainty in flood management: evacuate? 80 70 O est i m e ne at Upper bound Low bound er 60 50 Di schar ge 40 30 20 10 0 1 11 21 31 41 51 Ti me 46 D.P. Solomatine. Hydroinformatics.
- 24. Point forecasts vs. Uncertainty bounds 4000 3500 3000 Discharge(m3/s) 2500 2000 1500 1000 500 0 900 920 940 960 980 1000 1020 Time(days) 47 D.P. Solomatine. Hydroinformatics. Sources of uncertainty in modelling y = M(x, s, θ) + εs + εθ + εx + εy Inputs Model parameters Calibration data p X(t) Q(t) Model 48 D.P. Solomatine. Hydroinformatics.
- 25. Monte Carlo simulation of parametric uncertainty y = M(x, s, θ) + εs + εθ + εx + εy 49 D.P. Solomatine. Hydroinformatics. 80 Uncertainty analysis: issues 70 O est i m e ne at Upper bound Low bound er 60 50 Di schar ge 40 30 20 10 0 1 11 21 31 41 51 Ti me Most methods are aimed at analysing average model uncertainty, but not predicting it for the new inputs Most uncertainty analysis studies focus on the parametric uncertainty only. More has to be done to analyse and predict: Input data uncertainty Residual uncertainty (uncertainty associated with the deficiencies of the “optimal” model) Model uncertainty is estimated. What next?: Should we combine in an ensemble several “good” models, instead of using one calibrated model? How can we predict model uncertainty for the future situations? How to communicate uncertainty to decision makers? 50 D.P. Solomatine. Hydroinformatics.
- 26. UNEEC: Novel uncertainty prediction method D.P. Solomatine, D.L. Shrestha. A novel method to estimate model uncertainty using machine learning techniques. Water Resources Res., 45, W00B11, doi:10.1029/ 2008WR006839, 2009. A calibrated model M of a water system is considered M is run for the past hydrometeorological events It is assumed that the errors of model M characterize the “residual” uncertainty in different situations (events) This data is used to train the machine learning model U that predicts the error (uncertainty) of model M, which is specific for a particular hydrometeorological event UNEEC-M: parametric and input uncertainty is added as well 51 D.P. Solomatine. Hydroinformatics. UNEEC: fuzzy clustering and ANN in encapsulating the model uncertainty Error limits past records Error distribution in cluster Error (or prediction (examples in the intervals) ∑ μi N ∑ μi i =1 space of inputs) N (1 − α / 2) ∑ μi i =1 Flow Qt-1 N α / 2 ∑ μi i =1 Train regression (ANN) Prediction interval models: PIL = fL (X) PIU = fU (X) Rainfall Rt-2 New record. The trained f L and f U models will estimate the prediction interval 52 D.P. Solomatine. Hydroinformatics.
- 27. Estimated prediction bounds: verification (Bagmati river basin, Nepal) Rainfall-Discharge plot 6000 0 50 5000 100 Precip itation [mm] Runoff [Cumec] 4000 150 3000 200 250 2000 300 1000 350 0 400 Jan-88 M ay-88 Sep-88 Feb-89 Jun-89 Oct-89 M ar-90 Jul-90 Nov-90 Apr-91 Aug-91 Jan-92 M ay-92 Sep-92 Feb-93 Jun-93 Oct-93 M ar-94 Jul-94 Dec-94 Apr-95 Aug-95 Time [days] Runoff [Cumec] Precipitation [mm] 4000 90% prediction limits Observed flow (m /s) Observed flow 3000 3 SF – Snow RF – Rain EA – Evapotranspiration SP – Snow cover SF RF IN – Infiltration 2000 EA R – Recharge SM – Soil moisture CFLUX – Capillary transport SP UZ – Storage in upper reservoir IN PERC – Percolation 1000 SM LZ – Storage in lower reservoir R CFLUX Qo – Fast runoff component Q0 Q1 – Slow runoff component UZ Q – Total runoff 0 PERC Q1 Q=Q0+Q1 750 775 800 825 850 LZ Transform Time(day) 53 function D.P. Solomatine. Hydroinformatics. Hydroinformatics is about INTEGRATION of data, models and people 54 D.P. Solomatine. Hydroinformatics.
- 28. Integration of atmospheric, hydro- and environmental models, data systems HBV 55 D.P. Solomatine. Hydroinformatics. Integration of models, communications and people Internet – models on demand, distributed DSS Mobile telephony – a channel for hazards warnings and advice systems Ref: MSc by L. Alfonso (Colombia), UNESCO-IHE 56 D.P. Solomatine. Hydroinformatics.
- 29. Integration of Hydroinformatics systems and decision making Multi-criteria, multi-stakeholder 80 scenario analysis 70 O est i m e ne at Upper bound Communication of model Low bound er 60 uncertainty to managers 50 Di schar ge 40 30 20 10 0 1 11 21 31 41 51 Ti me Map of flood probability 57 D.P. Solomatine. Hydroinformatics. Education: Hydroinformatics at UNESCO-IHE, Delft, The Netherlands 58 D.P. Solomatine. Hydroinformatics.
- 30. Postgraduate Education, Training and Capacity Building in Water, Environment and Infrastructure 59 D.P. Solomatine. Hydroinformatics. UNESCO-IHE: 14,000 Alumni UNESCO-IHE Alumni Community 0 - 50 51-150 151-300 301-500 501-850 851-1200 60 D.P. Solomatine. Hydroinformatics.
- 31. Hydroinformatics Masters programme Fundamentals, hydraulic, hydrologic and environmental processes Information systems, GIS, communications, Internet • ArcGIS • Matlab • JAVA • Access Tools • Delphi • UltraDev Physically-based Physically- • SOBEK • MIKE 11 simulation modelling • RIBASIM • Delft 3D • HEC-RAS HEC- • MIKE 21 with applications to: and tools • SWAT • MIKE SHE - River basin management • EPANET • RIBASIM • MOUSE • WEST++ - Flood management Data-driven modelling Data- • Aquarius • MODFLOW - Urban systems and computational • NeuroSolutions - Coastal systems • NeuralMachine intelligence tools • AFUZ - Groundwater and • WEKA catchment hydrology Systems analysis, • LINGO - Environmental systems decision support, • GLOBE • BSCW (options) optimization • AquaVoice Integration of technologies, project management Elective advanced topics 61 D.P. Solomatine. Hydroinformatics. Hydroinformatics Study Modules Introduction to Water science and Engineering Applied Hydraulics and hydrology Geo-information systems Computational Hydraulics and Information Management Modelling theory and applications Computational Intelligence and Control Systems River Basin Modelling Fieldtrip to Florida, USA Selective modelling subjects (2 modules each): Flood risk management Urban water systems modelling Environmental systems modelling Hydroinformatics for Decision Support Groupwork Research proposal drafting and Special Topics MSc research 62 D.P. Solomatine. Hydroinformatics.
- 32. Examples of MSc topics Hydroinformatics for real time water quality management and operation of distribution networks, case study Villavicencio, Colombia Water distribution modelling with intermittent supply: sensitivity analysis and performance evaluation for Bani-Suhila City, Palestine Urban Flood Warning System with wireless technology, case study of Dhaka City, Bangladesh Flood modelling and forecasting for Awash river basin in Ethiopia Harmful Algal Bloom prediction, study of Western Xiamen Bay, China Application of Neural Networks to rainfall-runoff modelling in the upper reach of the Huai river basin, China Heihe River Basin Water Resources Decision Support System Decision Support System for Irrigation Management in Vietnam 1D-2D Coupling Urban Flooding Model using radar data in Bangkok Using chaos theory to predict ocean surge 63 D.P. Solomatine. Hydroinformatics. A new programme is planned: International Masters in Hydroinformatics UNESCO-IHE – UniValle-Cinara Hidroinformática modelación y sistemas de información para la gestión del agua Programa Internacional de Maestría en Ciencia jointly delivered by UNESCO-IHE Institute for Water Education, Delft, The Netherlands and Universidad del Valle (UNIVALLE, Cinara), Cali, Colombia and leading to the degree of Master of Science in Water Science and Engineering, specialisation in Hydroinformatics, accredited by the Dutch Ministry of Education Planned to start in September 2010 Fliers are available Hydroinformatics. D.P. Solomatine. 64
- 33. Programme structure Taught part Block 1: Location: UNIVALLE, Cali ECTS Fundamental subjects for 15 hydroinformatics Period: September-January Block 2: Location UNESCO-IHE Hydroinformatics theory and Period: Mid-January – end-August: 9 applications modules of the existing UNESCO-IHE ECTS WSE-HI programme (modules 4-12) 45 Thesis part Block 3: Location: Any of the core partners (in MSc thesis proposal the beginning UNESCO-IHE) preparation + special topics Period: Begin-September – Mid- October ECTS 10 Block 4: Location: Any of the core or the MSc Thesis research associated partners (at least the last month at UNESCO-IHE) ECTS Period: Mid-October – mid-April. 36 Public MSc defence and graduation – end of April 65 D.P. Solomatine. Hydroinformatics. What Hydroinformatics alumni say... the course has opened the new horizons in my professional life 66 D.P. Solomatine. Hydroinformatics.
- 34. Conclusion Hydroinformatics is a unifying approach to water modelling and management Specialists in hydroinformatics play an integrating role linking various specialists and decision makers Access to information by widening groups of stakeholders leads to democratisation of water services One of the roles of Hydroinformatics is developing analytical methods to deal with climatic variability in modelling and management practice Focus should be on education and training 67 D.P. Solomatine. Hydroinformatics. …more data is needed… 68 D.P. Solomatine. Hydroinformatics.

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