A framework for ‘Inclusive Multiple Modelling’ with critical views on modelling practices – Applications to modelling water levels of Caspian Sea and Lakes Urmia and Van

Abstract A framework is formulated in this paper for data-driven modelling practices to characterise Inclusive Multiple Modelling (IMM) practices with multiple goals of enhancing the extracted information from given datasets and learning from multiple models. This can be a shift from traditional practices with the single goal of selecting a ‘superior’ model from multiple models without a statistical justification, which may be referred to as Exclusionary Multiple Modelling (EMM) practices. The dimensions of the framework for IMM practices are: Model R euse (M R ), H ierarchy and/or Recursion ( H R), a provision of ‘ E lastic’ model-Learning Environment ( E LE) and Goal- O rientation (G O ) – leading to the acronym of RHEO. Proof-of-concept is presented for IMM-RHEO using three testcases: the Caspian Sea (19-years of data), Lake Urmia (50-years of data) and Lake Van (73-years of data), approx. 500 km apart. IMM practices are implemented by investigating four strategies for each testcase. The learning from the results includes: (i) the IMM strategies are capable of enhancing the accuracy of predicted water levels; (ii) the accuracy of predicting the sea-state of the Caspian Sea serves confidence building on accuracy; and (iii) the time-length of the record of Lake Van is long enough for the confidence building on the study of possible trends. IMM serves a bottom-up learning opportunity for Lake Urmia that its distressed state is due to being deprived of compensation flows without contributions from climate change. Arguably, a good management policy is the key for its restoration. IMM is at its infancy but arguably, its potential application areas are wide.

[1]  Michel Lang,et al.  Review of trend analysis and climate change projections of extreme precipitation and floods in Europe , 2014 .

[2]  A. Castelletti,et al.  Climate-informed environmental inflows to revive a drying lake facing meteorological and anthropogenic droughts , 2018, Environmental Research Letters.

[3]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[4]  K. Madani,et al.  Aral Sea syndrome desiccates Lake Urmia: Call for action , 2015 .

[5]  Frank T.-C. Tsai,et al.  Bayesian model averaging assessment on groundwater management under model structure uncertainty , 2010 .

[6]  Mansour Talebizadeh,et al.  Uncertainty analysis for the forecast of lake level fluctuations using ensembles of ANN and ANFIS models , 2011, Expert Syst. Appl..

[7]  Vladimir Vapnik,et al.  An overview of statistical learning theory , 1999, IEEE Trans. Neural Networks.

[8]  F. J. Anscombe,et al.  The Examination and Analysis of Residuals , 1963 .

[9]  M. Ghorbani,et al.  Inter-comparison of time series models of lake levels predicted by several modeling strategies , 2014 .

[10]  S. P. Neuman,et al.  On model selection criteria in multimodel analysis , 2007 .

[11]  Michael Sturm,et al.  ‘PALEOVAN’, International Continental Scientific Drilling Program (ICDP): site survey results and perspectives , 2009 .

[12]  Harun Aydin,et al.  Estimation of evaporation for Lake Van , 2016, Environmental Earth Sciences.

[13]  A A Nadiri,et al.  Supervised Intelligent Committee Machine Method for Hydraulic Conductivity Estimation , 2014, Water Resources Management.

[14]  Upmanu Lall,et al.  Improved Combination of Multiple Atmospheric GCM Ensembles for Seasonal Prediction , 2004 .

[15]  S. Hagemann,et al.  Prediction of the Caspian Sea level using ECMWF seasonal forecasts and reanalysis , 2014, Theoretical and Applied Climatology.

[16]  Gábor Lugosi,et al.  Introduction to Statistical Learning Theory , 2004, Advanced Lectures on Machine Learning.

[17]  Mohammad Ali Ghorbani,et al.  Dynamics of hourly sea level at Hillarys Boat Harbour, Western Australia: a chaos theory perspective , 2011 .

[18]  G. Hardin,et al.  The Tragedy of the Commons , 1968, Green Planet Blues.

[19]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[20]  Robert Babuska,et al.  A Survey of Actor-Critic Reinforcement Learning: Standard and Natural Policy Gradients , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[21]  A. Kislov.  The interpretation of secular Caspian Sea level records during the Holocene , 2016 .

[22]  Mohammad Ali Ghorbani,et al.  Investigating chaos in river stage and discharge time series , 2012 .

[23]  M. Vaziri.  Predicting Caspian Sea Surface Water Level by ANN and ARIMA Models , 1997 .

[24]  A. Altunkaynak,et al.  Fuzzy logic model of lake water level fluctuations in Lake Van, Turkey , 2007 .

[25]  Hafzullah Aksoy,et al.  Prediction of Water Level using Monthly Lagged Data in Lake Urmia, Iran , 2016, Water Resources Management.

[26]  Rahman Khatibi,et al.  Mapping specific vulnerability of multiple confined and unconfined aquifers by using artificial intelligence to learn from multiple DRASTIC frameworks. , 2018, Journal of environmental management.

[27]  Henk M. Haitjema,et al.  Analytic Element Modeling of Groundwater Flow , 1995 .

[28]  Zaher Mundher Yaseen,et al.  Learning from Multiple Models Using Artificial Intelligence to Improve Model Prediction Accuracies: Application to River Flows , 2018, Water Resources Management.

[29]  R. Clemen.  Combining forecasts: A review and annotated bibliography , 1989 .

[30]  Rahman Khatibi,et al.  Formulating a strategy to combine artificial intelligence models using Bayesian model averaging to study a distressed aquifer with sparse data availability , 2019, Journal of Hydrology.

[31]  Mohammadreza Rezaee,et al.  A committee machine with intelligent systems for estimation of total organic carbon content from petrophysical data: An example from Kangan and Dalan reservoirs in South Pars Gas Field, Iran , 2009, Comput. Geosci..

[32]  W. T. Singleton,et al.  Man-machine systems , 1974 .

[33]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[34]  Mohammad Ali Ghorbani,et al.  Stream flow predictions using nature-inspired Firefly Algorithms and a Multiple Model strategy - Directions of innovation towards next generation practices , 2017, Adv. Eng. Informatics.

[35]  S. Kempe,et al.  A geological study of lake van, Eastern Turkey , 1984 .

[36]  Otto D Strack,et al.  Principles of the analytic element method , 1999 .

[37]  C. West Churchman,et al.  The Systems Approach , 1979 .

[38]  Yousef Hassanzadeh,et al.  Determining the Main Factors in Declining the Urmia Lake Level by Using System Dynamics Modeling , 2011, Water Resources Management.

[39]  Mohammad Ali Ghorbani,et al.  Comparison of three artificial intelligence techniques for discharge routing , 2011 .

[40]  Hafzullah Aksoy,et al.  Stochastic modeling of Lake Van water level time series with jumps and multiple trends , 2013 .

[41]  Roger Koenker,et al.  A note on studentizing a test for heteroscedasticity , 1981 .

[42]  David Draper,et al.  Assessment and Propagation of Model Uncertainty , 2011 .

[43]  A. Unal,et al.  Analysis of decadal land cover changes and salinization in Urmia Lake Basin using remote sensing techniques , 2017 .

[44]  Xin-She Yang,et al.  Firefly algorithm, stochastic test functions and design optimisation , 2010, Int. J. Bio Inspired Comput..

[45]  A. Altunkaynak.  Forecasting Surface Water Level Fluctuations of Lake Van by Artificial Neural Networks , 2007 .