Neural network modelling of non-linear hydrological relationships R. J. Abrahart, L. M. See To cite this version: R. J. Abrahart, L. M. See. Neural network modelling of non-linear hydrological relationships. Hydrol- ogy and Earth System Sciences Discussions, European Geosciences Union, 2007, 11 (5), pp.1563-1579. hal-00305094 HAL Id: hal-00305094 https://hal.archives-ouvertes.fr/hal-00305094 Submitted on 20 Sep 2007 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Hydrol. Earth Syst. Sci., 11, 1563–1579, 2007 www.hydrol-earth-syst-sci.net/11/1563/2007/ Hydrology and © Author(s) 2007. This work is licensed Earth System under a Creative Commons License. Sciences Neural network modelling of non-linear hydrological relationships R. J. Abrahart1 and L. M. See2 1School of Geography, University of Nottingham, Nottingham NG7 2RD, UK 2School of Geography, University of Leeds, Leeds, LS2 9JT, UK Received: 8 January 2007 – Published in Hydrol. Earth Syst. Sci. Discuss.: 22 February 2007 Revised: 26 July 2007 – Accepted: 10 September 2007 – Published: 20 September 2007 Abstract. Two recent studies have suggested that neural net- 1 Introduction work modelling offers no worthwhile improvements in com- parison to the application of weighted linear transfer func- The last decade has witnessed a virtual explosion of neu- tions for capturing the non-linear nature of hydrological re- ral network (NN) modelling activities throughout the hy- lationships. The potential of an artificial neural network to drological sciences. It is readily apparent from the increas- perform simple non-linear hydrological transformations un- ing number of published case studies that the development der controlled conditions is examined in this paper. Eight of data-driven solutions based on the use of neural tools or neural network models were developed: four full or partial smart technologies is being trialled and tested in most sec- emulations of a recognised non-linear hydrological rainfall- tors of hydrological modelling and hydraulic engineering. runoff model; four solutions developed on an identical set Numerous extended descriptions exist and for detailed sum- of inputs and a calculated runoff coefficient output. The use maries the interested reader is referred to the following pa- of different input combinations enabled the competencies of pers: ASCE (2000a, b); Maier and Dandy (2000); Dawson solutions developed on a reduced number of parameters to & Wilby (2001) and edited volumes: Govindaraju and Rao be assessed. The selected hydrological model had a limited (2000); Abrahart et al. (2004). Neural technologies con- number of inputs and contained no temporal component. The tinue to make enormous strides in their struggle to become modelling process was based on a set of random inputs that established as recognized tools that offer efficient and ef- had a uniform distribution and spanned a modest range of fective solutions for modelling and analysing the behaviour possibilities. The initial cloning operations permitted a direct of complex dynamical systems. Time series forecasting has comparison to be performed with the equation-based rela- been a particular focus of interest and superior performing tionship. It also provided more general information about the models have been reported in a diverse set of fields that in- power of a neural network to replicate mathematical equa- clude rainfall-runoff modelling (ASCE, 2000a, b; Dawson tions and model modest non-linear relationships. The sec- and Wilby, 2001; Birikundavy et al., 2002; Campolo et al., ond group of experiments explored a different relationship 2003; Huang et al., 2004; Riad et al., 2004; Hettiarachchi that is of hydrological interest; the target surface contained a et al., 2005; Senthil Kumar et al., 2005) and sediment pre- stronger set of non-linear properties and was more challeng- diction (Abrahart and White, 2001; Nagy et al., 2002; Yitian ing. Linear modelling comparisons were performed against and Gu, 2003; Kisi, 2004; Bhattacharya et al., 2005; Kisi, traditional least squares multiple linear regression solutions 2005). Moreover, for flood forecasting purposes, neural so- developed on identical datasets. The reported results demon- lutions offer practical advantages related to operational costs strate that neural networks are capable of modelling non- and socio-economic resources that would be of interest in linear hydrological processes and are therefore appropriate developing countries, e.g. rapid development; rapid execu- tools for hydrological modelling. tion; parsimonious requirements; open source code (Sham- seldin, 2007). Two recent catchment studies have neverthe- less questioned the use of such tools for non-linear hydro- logical modelling purposes. Gaume and Gosset (2003) and Han et al. (2007) concluded: (1) that for short term fore- Correspondence to: R. J. Abrahart casting purposes neural solutions offered no real advantages ([email protected]) over traditional linear transfer functions; (2) that the demands Published by Copernicus Publications on behalf of the European Geosciences Union. 1564 R. J. Abrahart and L. M. See: Neural network modelling of non-linear hydrological relationships and complexities involved in the development of neural so- transformations is a fundamental aspect of most hydrologi- lutions made them difficult to use and therefore “uncompeti- cal modelling applications and real-time forecasting opera- tive” (Han et al., 2007, p.227); (3) that there is still much to tions. The need to question technological and methodolog- be done to improve our understanding about the uncertain na- ical approaches that fail to encapsulate such properties is ture and hydrological characteristics of neural solutions “be- paramount. Neural solutions purport to model simple lin- fore [such mechanisms] could be used as a practical tool in ear, complex non-linear, or multifaceted hybrid relationships real-time operations” (Han et al., 2007, p.228); and (4) that so the potential reasons for such apparent shortcomings must the potential merit of putting further resources into the de- be clarified. It is not sufficient for such matters to be left velopment of black box computational intelligence method- unanswered. The current paper will address a straightfor- ologies such as feedforward neural networks remains ques- ward matter: NN capabilities to discover and reproduce non- tionable since “the quest for a universal model requiring no linear hydrological relationships. The need for more exper- hydrological expertise might well be hopeless” (Gaumeand iments of a similar nature that attempt to settle fundamen- Gosset, 2003, p.705). tal issues within the hydrological sciences is also champi- The main objective of this paper is to evaluate the ability oned. It is suggested that a complacent misbelief has devel- of a NN model to capture non-linear effects within the non- oped; enthusiasts and proponents of neural solutions might linearity range employed in traditional rainfall-runoff models well consider a set of recorded findings that document the of the type that are widely used in operational flood forecast- power of such technologies to model non-linear relationships ing systems, e.g. black box and conceptual rainfall-runoff as tantamount to a “confirmation of established science” or models. There are various sources of non-linearities in the about “preaching to the converted”. The main issues can per- rainfall-runoff transformation process, e.g. antecedent con- haps be related to a common trigger; most inventions and ditions are a substantial cause of such effects. The present discoveries experience initial rapid development that is often paper will examine hydrological non-linearities attributed to accompanied by exaggerated claims about what can or can- spatial variation of maximum soil moisture storage capaci- not be achieved. However, following an initial series of re- ties as implemented in the Xinanjiang Rainfall-Runoff Model ported successes, a detailed set of methodological underpin- (Zhao et al., 1980). No specific river records were involved; nings is required to support the development of subsequent so no general principles, derived from a single, perhaps atyp- applications. NN hydrological modelling has now reached ical case, would be produced, i.e. arising out of the partic- this stage; there are large gaps in our knowledge and substan- ularities of an observed dataset or related to an individual tial issues still need to be resolved. Han et al. (2007, p.223) catchment. The modelling procedures that are presented in commented that the large number of unsolved questions con- this paper can also be used to capture other sources of non- tinues to hinder the application of such tools amongst prac- linearity in that particular model as well as hydrological non- tising hydrologists. Neural solutions also encounter “insti- linearities that are simulated in a complex physical-based tutional barriers”: Zhang et al. (2004, p.iv) noted that “. it model. This paper considers the potential