Modelling Socio-hydrological Systems : A Review of Concepts , Approaches and Applications

Interactions between humans and the environment are occurring on a scale that has never previously been seen; one environmental facet that has seen particular co-evolution with society is water. The ::: the : scale of human interaction with the water cycle, along with the coupling present between social and hydrological systems, means that decisions that impact water also impact people. Models are often used to assist in decision-making regarding hydrological systems, and so in 5 order for effective decisions to be made regarding water resource management, these interactions and feedbacks should be accounted for in models used to analyse systems in which water and humans interact. This paper reviews literature surrounding aspects of socio-hydrological modelling. It begins with background information regarding the current state of socio-hydrology as a discipline, before covering reasons for modelling and potential applications. Some important concepts 10 that underlie socio-hydrological modelling efforts are then discussed, including ways of viewing socio-hydrological systems, space & time in modelling, complexity, data and model conceptualisation. Several modelling approaches are described, the stages in their development detailed and their applicability to socio-hydrological cases discussed. Gaps in research are then highlighted to guide directions for future research. The review of literature suggests that the nature of socio-hydrological 15 study, being interdisciplinary, focusing on complex interactions between human and natural systems, and dealing with long horizons, is such that modelling will always present a challenge; it is, however, the task of the modeller to use the wide range tools afforded to them to overcome these challenges as much as possible. The focus in socio-hydrology is on understanding the human-water system in a holistic sense, which differs from the problem solving focus of other water management fields, and 20 as such models in socio-hydrology should be developed with a view to gaining new insight into these dynamics. There is an essential choice that socio-hydrological modellers face in deciding between

III) Missing differences between socio-ecology and socio-hydrology 1) Pleased to see discussion on the differences between socio-ecology and socio-hydrology, however suggests missing differences (e.g. flowing water, hydrological cycle).
2) The omissions that you highlight in the differences between socio-ecology and sociohydrology are important, and so the fact that socio-hydrology deals with flowing water and the hydrological cycle will be included in the revised version of this manuscript. 3) These differences are included in the appropriate section of the manuscript now IV) Summary section regarding similarities and differences between socio-hydrology and other subjects 1) Following from including the missing differences between socio-ecology and socio-hydrology, and as part of the restructuring that is detailed later, there is a suggestion of a summary section focusing on the similarities and differences between socio-hydrology and socioecology (and possibly eco-hydrology/IWRM) 2) As part of the restructuring which is detailed later, the suggested summary section discussing the similarities and differences between socio-ecology and socio-hydrology will be included. 3) As part of the restructuring, which is mentioned in a different point, a section which concisely details the similarities and differences between socio-hydrology and other subjects has been added. V) A more comprehensive discussion of data in socio-hydrology 1) Suggested that there should be a more comprehensive discussion of the role of data in sociohydrology, the new/unconventional types of data that might be gathered and the ensuing empirical data-theory-model development process. 2) We agree wholeheartedly that the issue of data in socio-hydrology merits more discussion, and so will also further discuss it, particularly referencing new/unconventional types of data, and data-theory-model development processes and feedbacks. 3) Data has received more discussion in the revised version of the manuscript. The sub-goal of socio-hydrology regarding data is a part of this, and is complemented by an added paragraph in the data section, and a revised conclusion VI) Need to be more critical of traditional modelling techniques when applying to new subject 1) Much of the literature review focuses on traditional modelling approaches. Traditional modelling approaches should be looked at critically, rather than accepted without examination. 2) This is a very good point, thank you for making it. When revising the manuscript, I will cast a critical eye over the application of traditional techniques to this new subject area and change the material accordingly. Modelling techniques used in socio-hydrology will likely have their roots in traditional techniques, and so it seems appropriate to consider these traditional techniques as a starting point, however it is true that the characteristics of socio-hydrological systems will likely mean that these approaches will require alteration/adaptation, and could indeed render some inapplicable. 3) This comment has been addressed in two senses.
i) A statement has been made in the 'Approaches' subsection, in which the reason for reviewing traditional modelling techniques has been highlighted and the potential for new/hybrid modelling techniques mentioned. ii) In covering each of the modelling techniques, a more critical approach has been taken when thinking about their application to socio-hydrology. This is done by considering the distinctive aspects of socio-hydrology (e.g. long-term focus, wild uncertainties & unknowns, unconventional/new data types and the role of changing values and norms) VII) The role of changing norms and values in socio-hydrology should be more prominent 1) Lack of attention paid to the role of changing norms and values, and how understanding these dynamics requires collaboration with social scientists and sociologists 2) I am glad that the review comes across as recognising the applicability of socio-hydrology in long-term analysis. The role of changing social norms and values is extremely important in this respect, and so their importance will be highlighted in the revised version of this manuscript. I agree that collaboration with social scientists and sociologists will be critical in gaining understanding the dynamics of changing values and norms, and so will highlight this in the revised version of the manuscript.
3) The role of changing norms and values has more prominence in the revised version of this manuscript. This is reflected by inclusion in critical discussion surrounding the application of traditional modelling techniques to socio-hydrology, where the ability of different techniques to cope with changing norms is discussed, and in increased coverage of the role of changing norms in earlier sections (Background to socio-hydrology, forecasting & prediction, coevolutionary systems). The importance of working with sociologists and social scientists has also been included. VIII) An expanded section on uncertainty 1) Extension of the section about uncertainty, in particular to include the role of surprise.
2) Thank you for this point, it is well taken. The issue of uncertainty is certainly of vital importance in socio-hydrology, particularly uncertainty in forms not seen as much in traditional hydrology. I was previously unsure of how much detail to go into regarding uncertainty in this review, since it could certainly be the subject of a review paper on its own! I would, however, agree that more should be included and will include more detail, particularly regarding the issues of surprise, and aleatory and epistemic uncertainties in this section. The suggested references of Di Baldassarre et al. (2015) and Merz et al. (2015) will be used in this.
3) The section on uncertainty has been expanded to incorporate the roles of aleatory uncertainty, surprise, and epistemic uncertainties. This section still does not cover these subjects in a huge amount of depth (since to do so would require almost a paper in itself), and so there is a statement in this section which states how big a topic uncertainty is, and gives justification for not including it in the full depth that it could be covered in, directing people towards Di Balsassarre (2015) and . IX) Need to be critical on the application of game theory to socio-hydrology 1) Comment on the difficulties that would be faced in applying game theory in socio-hydrology, particularly uncertainty. 2) It is a good point that, while game theory might be applied in socio-hydrology, there are difficulties that must be overcome when doing so, which I have not mentioned. I will amend this by mentioning the uncertainties present, which differ from those traditionally incorporated into game theory models.
3) The section on game theory has been appended with a statement stating that special attention would need to be paid to uncertainties if game theory were applied to sociohydrology. X) Odd Sounding Sentence 1) A minor point regarding an odd sounding sentence, p.8775 line 17-21 in HESSD manuscript.
2) In this sentence, I was trying to point out the fact that there are two sides to the complex systems 'coin'. On the one hand, complex systems can be very difficult to manage, due to difficulties in ascertaining the end results of interventions in systems of complex interaction, while on the other hand, the many parts in complex systems means that there can be multiple system components that can be targeted in efforts to manage these systems, which helps when trying to manage them. I will, however, make this sentence clearer and will point out that these aspects reveal a tension in management. 3) This sentence has been clarified by explicitly stating that the difficulties in managing complex systems are clear before continuing to describe the other 'side' to the complex systems 'coin'.
An extra sentence has also been added in the next paragraph to highlight the tension that the referee points out regarding feedbacks resulting in very different solutions being suggested. XI) Paying more attention to the precursors of socio-hydrology, 1) Comment regarding the need to incorporate discussion of precursors to socio-hydrology in the water sciences, particularly integrated assessment modelling and global water resource models. 2) Thank you for this comment, it is well received. I agree that giving background to the subject through detailing the work of subjects which came before it is an important step, and agree that, while I have given attention to subjects that studied human-nature and nature-water interactions, I have perhaps neglected to give enough attention to subjects other than sociohydrology which integrate human and water systems in some sense. As you suggest, integrated assessment models and global water resource models are good examples of this, and so I will use these in this discussion. While doing this, I will also point out the differences between socio-hydrology and these subjects, in particular the focus on bi-directional interactions and the role of long-term dynamics in socio-hydrology, such as changing social norms, which other subjects have not yet incorporated. 3) A paragraph has been included which discusses integrated assessment modelling and global water resource models, as well as hydro-economic modelling. XII) Restructuring 1) The suggestion that there should be more separation from other recent studies (Troy et al., 2015;Sivapalan and Blöschl, 2015) and and a more targeted, goal-oriented approach to the review via restructuring existing material around new headings and subheadings. 2) Thank you for this comment, it is well received and is very useful. You are indeed correct in thinking that the reason that some aspects of this review are similar to those of Troy et al. (2015) and Sivapalan and Blöschl (2015) is due to the fact that they were published in the latter stages of this paper being written. I have, therefore, now given attention to these papers in order to ascertain the aspects that they have covered, and so the ways in which this review may separate itself from them for the benefit of readers. Troy et al. (2015) covers the current state of socio-hydrology and gives an outline of the different research methodologies that can be used in socio-hydrology (of which modelling is one). An area that this paper covers particularly well is the role of researchers in socio-hydrology, particularly the impartiality required to do research in this area being in tension with the research process where researchers' ideas can influence the work that they do and the models they create. The way forward for socio-hydrology as a subject is then covered. Sivapalan and Blöschl (2015) gives in-depth analysis of: co-evolutionary processes in a mathematical sense; the nature of human versus environmental systems and the implications of this for modelling; the overall modelling process that should be followed in socio-hydrology across modelling techniques and the different model archetypes that might be produced (i.e. stylised versus comprehensive models). I agree that the material present in this review could be restructured and re-targeted towards an area that would provide separation. I feel that the areas in which this review can distinguish itself are: the background that it gives regarding other similar subjects, such as socio-ecology, and so looking at the ways in which socio-hydrology can learn from modelling in other synthesis subjects, while acknowledging the aspects which make socio-hydrology unique and so tailoring study to be appropriate; and in critically analysing the applicability of specific modelling approaches that may be used in socio-hydrology, and so detailing how different types of model (i.e. system dynamics versus agent-based) would be developed (as opposed to the general socio-hydrological model development process). To this end, the paper will be restructured and headings will be changes as is suggested, with the goal of providing guidance on choosing an appropriate modelling technique for different purposes in socio-hydrology. 3) This point has been addressed in a number of different ways i) Particular attention has been brought to the studies that are mentioned. They are mentioned in the introduction, where the areas that they cover are stated, and the points of separation between those papers and this are laid out. ii) The paper has been restructured in a minor/moderate fashion, as suggested, in order to provide a more goal oriented approach. The paper has been structured around answering the questions of why, what and how (in regard to undertaking socio-hydrological modelling). Sections of text have been moved to fit in with this structure. The majority of the text has stayed the same (as suggested), though some text has been added/removed in order to give sense to the new structure. XIII) Figure Displaying the Structure of the paper 1) Issues with the ease of reading of the paper, due to its length and variety of topics.
2) This is a fair comment -the paper is indeed very long and covers many subjects. This, it was felt, was necessary in order to give a proper idea of how socio-hydrology and sociohydrological modelling have developed, and where the subject may lead. 3) On restructuring the paper, it was felt that the new structure provided a more accessible picture of how the paper fitted together. A description of the structure of the paper is provided in the introduction, and so it was felt that a figure giving the same information would not benefit the paper greatly. If the editor feels that a figure would, in fact, be of benefit, I am, however, happy to produce this. XIV) Typos highlighted by referees 1) A few typographic mistakes were spotted by referees 2) These errors have been corrected 3) Changes made are: i) 'is was' changed to 'it was' ii) 'has lead' changed to 'has led' iii) In the section 'understanding system resilience and vulnerability', there was an error whereby references already within brackets were not appearing as they should. The error was due to the use of the \citep command within parentheses, and so the parentheses have been replaced with commas. XV) Other typos 1) While proofreading, some typos were spotted by the author.
2) Typographic mistakes that were spotted during corrections and proofreading have been corrected. 3) Changes made are: i) 'Route causes' changed to 'root causes' in policy & decision-making section. ii) 'It is a commonly stated that' changed to 'It is commonly stated that' XVI) Other changes 1) While there were no referee comments regarding this, literature within socio-hydrology has advanced slightly while this paper has been undergoing production and review. As such, it was felt appropriate to include some other papers in this review.
2) New literature of importance to this review has been included.
3) The references incorporated are (only the in-text citation is included here -for the full references please see the manuscript): i) Grames, 2015 ii) Hu, 2015 iii) Sivapalan, 2015a XVII) Inclusion of sub-goal of Understanding Socio-hydrology 1) The referee comment regarding the sub-goal of insights into data prompted a further point 2) In socio-hydrology, development of system understanding is driven by development of understanding (and understanding what we do/don't understand) in socio-hydrology 3) A section on understanding socio-hydrology has been added XVIII) Acknowledgements 1) I felt it appropriate that the referees be acknowledged for their contribution to this article.
3) As the only named referee, Giuliano Di Baldassarre has been acknowledged by name; anonymous referees have been thanked also.
processes occurring on different spatio-temporal scales. Such dynamics include 'pendulum swings' that have been observed in areas such as the Murray-Darling Basin, where extensive agricultural development was followed by a realisation of the impacts this was having and subsequent implementation of environmental protections policies van Emmerik et al., 2014), the co-evolution of landscapes with irrigation practices and community dynamics (Parveen et al., 2015), as well as instances of catastrophe in which hydrological extremes not been catastrophic in themselves, rather social processes that result in vulnerability have made extreme events catas-100 trophic (Lane, 2014). There are also cases where social systems have not interacted with water in the way that was anticipated: examples include the virtual water efficiency and peak-water paradoxes discussed by Sivapalan et al. (2014), and yet others where the perception, rather than the actuality, that people have of a natural system determines the way it is shaped (Molle, 2007). Studying these systems requires not only an interdisciplinary approach, but also an appreciation of two poten-105 tially opposing ontological & epistemological views: the Newtonian view, whereby reductionism of seemingly complex systems leads to elicitation of fundamental processes, and the Darwinian view, in which patterns are sought, but complexity of system processes is maintained (Harte, 2002). Taking a dualistic worldview encompassing both of these perspectives, as well as the manner in which man and water are related (Falkenmark, 1979), allows for an appreciation of impacts that actions 110 will have due to physical laws, as well as other impacts that will be brought about due to adaptations from either natural or human systems.
In understanding socio-hydrology as a subject, it may be useful to also briefly understand the history of terminology within hydrological thinking, and how this has led to the current understanding.
Study of the hydrologic cycle began to 'serve particular political ends' (Linton and Budds, 2013), 115 whereby maximum utility was sought through modification of the cycle, and was viewed initially as fairly separate from human interactions: after several decades this led to a focus on water resources development in the 1970s, language clearly indicative of a utility-based approach. However, a change in rhetoric occurred in the 1980s, when water resources management (WRM) became the focus, and from this followed integrated water resource management (IWRM) and adaptive water 120 management (AWM) , the shift from 'development' to 'management' showing a change in the framing of water, while the concepts of integrated analysis and adaptivity show a more holistic mindset being taken. The introduction of the hydrosocial cycle (Swyngedouw, 2009) shows another clear development in thought, which aimed to 'avoid the pitfalls of reductionist ... water resource management analysis' (Mollinga, 2014) for the purpose of better water management. 'A 125 science, but one that is shaped by economic and policy frameworks' (Lane, 2014), socio-hydrology also represents another advancement in hydrological study, which requires further rethinking of how hydrological science is undertaken.

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The importance of socio-hydrology has been recognised since its introduction: The International Association of Hydrological Sciences (IAHS) has designated the title of their 'Scientific Decade' (2013-2022) as 'Panta Rhei (Everything flows)' , in which the aim 'is to reach an improved interpretation of the processes governing the water cycle by focusing on their changing dynamics in connection with rapidly changing human systems' .

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In the IAHS's assessment of hydrology at present , it is recognised that current hydrological models are largely conditioned for analysis of pristine catchments and that societal 5 interaction is generally included in separately developed models, so that interactions between the two are not well handled: socio-hydrological study is posited as a step towards deeper integration that has long been called for (Falkenmark, 1979). The recent series of 'Debates' papers in Water Resources

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Research (Di Baldassarre et al., 2015b;Sivapalan, 2015;Gober and Wheater, 2015;Loucks, 2015; ?) ::::::::::::::::::::::::: (Di Baldassarre et al., 2015b; a real, continued commitment to the development of socio-hyrology as a subject; the unified conclusion of these papers is that the inclusion the interaction between society and water is necessary in modelling, though the authors varied in their views on how this should be conducted, the sphere within which socio-hydrology should operate, and the value that socio-hydrological models may 175 have. The continued commitment necessary to the subject is highlighted via the statement that 'if we who have some expertise in hydrologic modelling do not some other discipline will [include nonhydrologic components in hydrologic models]' (Loucks, 2015).

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Socio-hydrology can learn many lessons from other, similarly interdisciplinary subjects. Ecohydrology is one such subject, whereby the interaction between ecology and hydrology is explicitly included. Rodriguez-Iturbe (2000) gives a number of the questions that ecohydrology attempts to answer, which may be very similar to the questions that socio-hydrology attempts to answer: -'Is there emergence of global properties out of these [eco-hydrological] dynamics?'

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-'Does it tend to any equilibrium values?' -'Is there a spontaneous emergence ... associated with the temporal dynamics?' -'Can we reproduce some of the observed ... patterns?' -'Is there a hidden order in the space-time evolution which models could help to uncover?' -'Does the system evolve naturally, for example, without being explicitly directed to do so?' 220 Ecohydrology would ::::: could also necessarily be a constituent part of socio-hydrological models, since anthropogenic influences such as land cover ::::: change : have ecological impacts, which will themselves create feedbacks with social and hydrological systems. Another subject that ::::::: Another ::::: aspect :: to ::: the ::::::: question :: of ::::: 'why socio-hydrologymay learn a great deal from is socio-ecology, a subject studying the interrelations between ecological and social systems.

Socio-ecology
The study of socio-ecological systems (SESs) and coupled human and natural systems (CHANS), involves many aspects similar to that of socio-hydrology: feedbacks (Runyan et al., 2012) , non-linear dynamics (Garmestani, 2013) , co-evolution (Hadfield and Seaton, 1999) , adaptation  , resilience (Folke et al., 2010) , vulnerability (Simelton et al., 2009) , issues of complexity (Liu et al., 2007a) , 230 governance (Janssen and Ostrom, 2006) , policy (Ostrom, 2009) and modelling (Kelly (Letcher) et al., 2013; are all involved in thinking around, and analysis of, SESs. As such, there is much thatsocio-hydrology can learn from this fairly established (Crook, 1970) discipline, and so in this paper a proportion of the literature presented comes from the field of socio-ecology due to its relevance. Learning from the approaches taken in socio-ecological studies would be prudent for future socio-hydrologists, and 235 so much can be learnt from the manner in which characteristics such as feedback loops, thresholds, time-lags, emergence and heterogeneity, many of which are included in a great number of socio-ecological studies (Liu et al., 2007a) are dealt with. Many key concepts are also applicable to both subject areas, including the organisational, temporal and spatial (potentially boundary-crossing) coupling of systems bringing about behaviour 'not belonging to either human or natural systems separately, 240 but emerging from the interactions between them' (Liu et al., 2007b) , and the required nesting of systems on various spatio-temporal scales within one another.Socio-hydrology may :: ?' :: is :::: that, in some ways, be thought of as a sub-discipline of socio-ecology (?) , and indeed some studies that have been carried out under the banner of socio-ecology could well be termed socio-hydrologic studies (e.g. (Roberts et al., 2002;Schlüter and Pahl-Wostl, 2007;Marshall and Stafford Smith, 2013;Molle, 2007) ), 245 and Welsh et al. (2013) terms rivers 'complicated socio-ecological systems that provide resources for a range of water needs' . There are however, important differences between socio-ecology and socio-hydrology which should be kept in mind when transferring thinking between the two disciplines, for example infrastructure developments such as dams introduce system intervention on a scale rarely seen outside thissphere (Elshafei et al., 2014) , and the speed at which some hydrologic 250 processes occur at means that processes on vastly different temporal scales must be accounted for  . There are also unique challenges in hydrologic data collection, for example impracticably long timescales are often being required to capture hydrologic extremes and regime changes (Elshafei et al., 2014) . In a study comparable to this, though related to socio-ecological systems, Schlüter (2012) gives research issues in socio-ecological modelling; these issues are also 255 likely to be pertinent in socio-hydrological modelling: Along with studying similarly defined systems and the usage of similar techniques, socio-ecology has suffered problems that could also potentially afflict socio-hydrology. For example, different contributors have often approached problems posed in socio-ecological systems with a bias towards their own field of study, and prior to great efforts to ensure good disciplinary integration social 260 scientists may have 'neglected environmental context' (Liu et al., 2007b) and ecologists 'focused on pristine environments in which humans are external' (Liu et al., 2007b) . Even after a coherent SES framework was introduced (Liu et al., 2007b) , some perceived it to be 'lacking on the ecological side' (Epstein and Vogt, 2013) , and as such missing certain 'ecological rules'. Since socio-hydrology has largely emerged via scholars with water resources backgrounds , inclusion of knowledge from 265 the social sciences, and collaboration with those : a ::::: world :::::: where ::: the :::::::: decisions ::: that :::::::: mankind :::::: makes :::: have :::: such :::::::: influence, ::::: those :::: who :::: make ::::: those :::::::: decisions :::::: should :: be :::::::::::: well-informed :: as :: to ::: the ::::::: impacts :::: their ::::::: decisions :::: may ::::: have. ::: As ::::: such, ::::: those ::::::: working :: in ::::: water :::::::: resources :::::: should ::: be ::::::::: well-versed : in this field, should therefore be high on the agenda of those working in socio-hydrology to avoid similar issues.

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whereas decision-makers prefer solutions to be simple (Ostrom, 2007) , and while the inclusion of complexities and interrelations in models is necessary, including a great deal of complexity can result in opacity for those not involved in model development, leading to a variety of issues.

The Demand for Socio-hydrological System Models
There :::::::: Regarding :::: why ::::::::: modelling :::::: would :: be ::::::::: conducted :: in :::::::::::::: socio-hydrology, :::: there : could be significant demand for socio-hydrological system models in several circumstances, however there are three The purpose of this section is to give an idea of why socio-hydrological modelling may be con-295 ducted, as the techniques used should be steered by what is required of their outputs. This section is linked to, though separated from, current and future applications, since the applications will likely require study in all three of the mentioned spheres in the solution of complex problems(examples of applications will later be given in a further section). In this section, the significance of modelling in each of these areas will be introduced, the limitations that current techniques have investigated, 300 and so the developments that socio-hydrological modelling could bring determined. The three typologies of socio-hydrological study that Sivapalan et al. (2012) presents (historical, comparative and process) could all be used in the different spheres. There are of course, significant difficulties in 9 socio-hydrological modelling, which should not be forgotten, in particular due to the fact that 'characteristics of human variables make them particularly difficult to handle in models' (Carey et al.,305 2014), as well as issues brought about by emergence, as models developed on current understanding may not be able to predict behaviours that have not previously been observed, or they may indeed predict emergent properties that do not materialise in real-world systems.

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'Perhaps a way to combat environmental problems is to understand the interrelations between ourselves and nature' (Norgaard, 1995). Understanding the mechanisms behind system behaviour can lead to a more complete picture of how a system will respond to perturbations, and so guide action to derive the best outcomes. For example, understanding the mechanisms that bring about droughts, which can have exceptionally severe impacts, can allow for better preparation as well as 315 mitigative actions (?) :::::::::::::::::::::: (Wanders and Wada, 2015) . Creating models to investigate system behaviour can lead to understanding in many areas, for example ? :::::::::::::::: Levin et al. (2012) gives the examples of socio-ecological models leading to understanding of how individual actions create system-level behaviours, as well as how system-level influences can change individual behaviours.
IWRM has been the method used to investigate human-water interactions in recent years, but the 320 isolation in which social and hydrological systems are generally treated in this framework leads to limitations in assimilating 'the more informative co-evolving dynamics and interactions over long periods' (Elshafei et al., 2014) that are present. This isolation has also led to the understanding of mechanisms behind human-water feedback loops currently being poor, and so integration has become a priority .

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If models of the coupled human-water system could be developed, this could give great insight into the interactions that occur, the most important processes, parameters and patterns, and therefore how systems might be controlled . Historical, comparative and process-based studies would all be useful in this regard, as understanding how systems have evolved (or indeed co-evolved (Norgaard, 1981)) through time, comparing how different locations have responded to 330 change and investigating the linkages between different parameters are all valuable in the creation of overall system understanding. Improved system understanding would also lead to an improvement in the ability for interpretation of long-term impacts of events that have occurred . It is important to note that, while this study focuses on modelling, system understanding cannot be brought about solely through modelling, and other, more qualitative studies are of value, 335 particularly in the case of historical investigations (e.g. (Paalvast and van der Velde, 2014)).

Forecasting & Prediction
Once a system is understood, it may be possible to use models to predict what will happen in the future. Predictive and forecasting models estimate future values of parameters based on the current 360 state of a system and its known (or rather supposed) behaviours. Such models generally require the use of past data in calibration and validation. Being able to forecast future outcomes in sociohydrological systems would be of great value, as it would aid in developing foresight as to the long-term implications of current decisions, as well as allowing a view to what adaptive actions may be necessary in the future. ? :::::::::::::::::::::: Wanders and Wada (2015) state that 'Better scenarios of future human 365 water demand could lead to more skilful projection for the 21st century', which could be facilitated by 'comprehensive future socio-economic and land use projections that are consistent with each other', as well as the inclusion of human water use and reservoirs, which now have 'substantial impacts on global hydrology and water resources', as well as 'modelling of interacting processes such as human-nature interactions and feedback'; socio-hydrological modelling may be able to contribute 370 in all of these areas.
An example area of study in prediction/forecasting is resilience: prediction of regime transitions is very important in this sphere (Dakos et al., 2015), and while IWRM does explore the relationship between people and water, it does so in a largely scenario-based fashion, which leaves its predictive capacity for co-evolution behind that of socio-hydrology (Sivapalan et al., 2012), and so in study of 375 such areas a co-evolutionary approach may be more appropriate.

Policy & Decision-making
Decision-making and policy formation are ultimately where model outputs can be put into practice to make a real difference. Models may be used to differentiate between policy alternatives, or optimise management strategies, as well as to frame policy issues, and can be very useful in all of these cases. However, there are real problems in modelling and implementing policy in areas such as in 395 the management of water resources (Liebman, 1976): it is a commonly stated that planning involves 'wicked' problems, plagued by issues of problem formulation, innumerable potential solutions, issue uniqueness and the difficulties involved in testing of solutions (it being very difficult to accurately test policies without implementing them, and then where solutions are implemented, extricating the impact that a particular policy has had is difficult, given the number of variables typically involved 400 in policy problems) (Rittel and Webber, 1973). Models necessarily incorporate the perceptions of developers, which can certainly vary, and so models developed to investigate the same issue can also be very different, and suggest varying solutions (Liebman, 1976). Appropriate timescales should be used in modelling efforts, as unless policy horizons are very short, neglecting slow dynamics in socio-ecological systems has been said to produce indequate results (Crépin, 2007). There are 405 also the issues of policies having time lags before impacts (this is compounded by discounting the value of future benefits), uncertainty in their long-term impacts at time of uptake, route ::: root causes of problems being obscured by complex dynamics and the fact that large-scale, top down policy solutions tend not to produce the best results due to the tendency of water systems to be 'resistant to fundamental change' (Gober and Wheater, 2014). Complex ::::: While ::: the ::::::::: difficulties :: in ::::::::: managing 410 ::::::: complex systems (such as human-water systems) ::: are ::::: clear, :::: they can, however, be good to manage, as multiple drivers and feedbacks mean that there are multiple targets for policy efforts that may make at least a small difference (Underdal, 2010).

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Good evidence is required for the formation of good policy (Ratna Reddy and Syme, 2014), and so providing this evidence to influence, and improve policy and best management practices should be an aim of socio-hydrology (Pataki et al., 2011), in particular socio-hydrological modelling. Changes in land-use are brought about by socio-economic drivers, including policy, but these changes in landuse can have knock-on effects that can impact upon hydrology (Ratna Reddy and Syme, 2014), and 430 so land-productivity, water availability and livelihoods to such an extent that policy may be altered in the future. Socio-hydrology should at least attempt to take account of these future policy decisions, and the interface between science and policy to improve long-term predictive capacity (Gober and Wheater, 2014). There is a call for a shift in the way that water resources are managed, towards an ecosystem-based approach, which will require a 'better understanding of the dynamics and links 435 between water resource management actions, ecological side-effects, and associated long-term ramifications for sustainability' (Mirchi et al., 2014). SES analysis has already been used in furthering perceptions on the best governance structures, and has found that polycentric governance can lead to increased robustness (Marshall and Stafford Smith, 2013), and it may well be that socio-hydrology leads to a similar view of SHSs.

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In order for outputs from policy-making models to be relevant they must be useable by stakeholders and decision-makers, not only experts (Kain et al., 2007). Participatory modelling encourages this through the involvement of stakeholders in model formulation, and often improves 'buy-in' of stakeholders, and helps in their making sensible decisions (Kain et al., 2007), as well as an increase in uptake in policy (Sandker et al., 2010). This technique could be well used in socio-hydrological mod-445 elling. Gober and Wheater (2015) take the scope of socio-hydrology further, suggesting a need to 13 include a 'knowledge exchange' (Gober and Wheater, 2015) component in socio-hydrological study, whereby the communication of results to policy makers and their subsequent decision-making mechanisms are included to fully encompass socio-hydrological interactions. However, Loucks (2015) points out that the prediction of future policy decisions will be one of the most challenging aspects 450 of socio-hydrology.

Current & Future Applications
This section follows from the areas of demand for socio-hydrological to give a few examples (not an exhaustive list) of potential, non-location-specific examples of how socio-hydrological modelling 455 could be used. These applications will incorporate system understanding, forecasting & prediction and policy formation, and where these spheres of study are involved they will be highlighted. SES models have been applied to fisheries, rangelands, wildlife management, bioeconomics, ecological economics, resilience and complex systems (Schlüter, 2012), and have resulted in great steps forward. Application of socio-hydrological modelling in the following areas could too result in progress 460 in understanding, forecasting, decision-making and the much-needed modernisation of governance structures (Falkenmark, 2011) in different scenarios. This section should provide insight as to the situations where socio-hydrological modelling may be used in the future, and so guide the discussion of suitable modelling structures.

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Resilience can be defined as the ability for a system to persist in a given state subject to perturbations (Folke et al., 2010;Berkes, 2007), and so this 'determines the persistence of relationships within a system' and can be used to measure the 'ability of these systems to absorb changes of state variables, driving variables, and parameters' (Holling, 1973). Reduced resilience can lead to regime shift, 'a relatively sharp change in dynamic state of a system' (Reyer et al., 2015), which can certainly have 470 negative social consequences. SES literature has studied resilience in a great number of ways, and has found it is often the case that natural events do not cause catastrophe on their own, rather catasrophe is caused by the interactions between extreme natural events and a vulnerable social system (Lane, 2014). Design principles to develop resilience have been developed in many spheres (for instance, design principles for management institutions seeking resilience (Anderies et al., 2004)), though in 475 a general sense Berkes (2007) terms four clusters of factors which can build resilience: -'Learning to live with change and uncertainty -Nuturing various types of ecological, social and political diversity -Increasing the range of knowledge for learning and problem solving -Creating opportunities for self-organisation' Exposure to natural events can lead to emergent resilience consequences in some cases, as in the case where a policy regime may be altered to increase resilience due to the occurrence of a catastrophe( : , for example London after 1953 (Lumbroso and Vinet, 2011), or Vietnamese agriculture (Adger, 1999)), where the same event could perhaps have caused a loss in resilience were a different social structure in place (Garmestani, 2013).

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In all systems, the ability to adapt to circumstances is critical in creating resilience (though resilience can also breed adaptivity (Folke, 2006); in the sphere of water resources, the adaptive capacity that a society has towards hydrological extremes determines its vulnerability to extremes to a great extent, and so management of water resources in the context of vulnerability reduction should involve an assessment of hydrological risk coupled with societal vulnerability (Pandey et al., 2011). An example 490 scenario where socio-hydrological modelling may be used is in determining resilience/vulnerability to drought : , ::: the ::::::::: importance :: of :::::: which : is :::::::::: highlighted :: by ::::::::::::::::::::::::: AghaKouchak et al. (2015) in :::: their ::::::::: discussion :: of ::::::::: recognising ::: the :::::::::::: anthropogenic ::::: facets :: of ::::::: drought; sometimes minor droughts can lead to major crop losses, whereas major droughts can sometimes results in minimal consequences, which would indicate differing socio-economic vulnerabilities between cases which 'may either counteract or amplify 495 the climate signal' (Simelton et al., 2009). Studies such as that carried out by Fraser et al. (2013), which uses a hydrological model to predict drought severity and frequency coupled with a socioeconomic model to determine vulnerable areas, and Fabre et al. (2015), which looks at the stresses in different basins over time caused by hydrologic and anthropogenic issues, have already integrated socio-economic and hydrologic data to perform vulnerability assessments. Socio-hydrological mod-500 elling could make an impact in investigating how the hydrologic and socio-economic systems interact (the mentioned studies involve integration of disciplines, though not feedbacks between systems) to cause long-term impacts, and so determine vulnerabilities over the longer term. The most appropriate form of governance in socio-hydrological systems could also be investigated further, as differing governance strategies lead to differing resilience characteristics 505 2007): Fernald et al. (2015) has investigated community-based irrigation systems (Acequias) and found that they produce great system resilience to drought, due to the 'complex self-maintaining interactions between culture and nature' and 'hydrologic and human system connections'. There is also a question of scale in resilience questions surrounding water resources, which socio-hydrology could be used to investigate: individual resilience may be developed through individuals' use of 510 measures of self-interest (for example digging wells in the case of drought vulnerability), though this may cumulatively result in a long-term decrease in vulnerability (Srinivasan, 2013).
An area that socio-hydrological modelling would be able to contribute in is determining dynamics that are likely to occur in systems: this is highly relevant to resilience study, as system dynamics and characteristics that socio-hydrological models may highlight, such as regime shift, tipping points, bistable states and feedback loops, all feature in resilience science. The long-term view that sociohydrology should take will be useful in this, as it is often long-term changes in slow drivers that drive systems towards tipping points (Biggs et al., 2009). Modelling of systems also helps to determine indicators of vulnerability that can be monitored in real situations. Areas where desertification has/may take place would be ideal case-studies, since desertification may be viewed as 'a transition between 520 stable states in a bistable ecosystem' (D'Odorico et al., 2013), where feedbacks between natural and social systems bring about abrupt changes. Socio-hydrology may be able to forecast indicators of posible regime shifts, utilising SES techniques such as identification of critical slowing down (CSD) (Dakos et al., 2015), a slowing of returning to 'normal' after a perturbation which can point to a loss of system resilience, as well as changes in variance, skewness and autocorrelation, which may all 525 be signs of altered system resilience (Biggs et al., 2009), to determine the most effective methods of combating this problem.
In studying many aspects of resilience, historical socio-hydrology may be used to examine past instances where vulnerability/resilience has occurred unexpectedly and comparative studies could be conducted to determine how different catchments in similar situations have become either vulnerable 530 or resilient; combinations of these studies could lead to understanding of why different social structure, governance regimes, or policy frameworks result in certain levels of resilience. Modelling of system dynamics for the purposes of system understanding, prediction and policy development are all clearly of relevance when applied to this topic, since in these the coupling is key in determination of the capacity for coping with change (Schlüter and Pahl-Wostl, 2007).

Understanding Risk in Socio-hydrological Systems
Risk is a hugely important area of hydrological study in the wider context: assessing the likelihood and possible consequences of floods and droughts constitutes an area of great importance, and models to determine flood/drought risk help to determine policy regarding large infrastructure decisions, 540 as well as inform insurance markets on the pricing of risk. However, the relationship between humans and hydrological risk is by no means a simple one, due to the differing perceptions of risk as well as the social and cultural links that humans have with water (Linton and Budds, 2013), and so providing adequate evidence for those who require it is a great challenge.
The way in which risk is perceived determines the actions that people take towards it, and this can 545 create potentially unexpected effects. One such impact is known as the 'levee effect' (White, 1945), whereby areas protected by levees are perceived as being immune from flooding (though in extreme events floods exceed levees, and the impacts can be catastrophic when they do), and so are often heavily developed, leading people to demand further flood protection and creating a positive feedback cycle. Flood insurance is also not required in the USA if property is 'protected' by levees de-550 signed to protect against 100-year events (Ludy and Kondolf, 2012), leading to exposure of residents to extreme events. Socio-hydrologic thinking is slowly being applied to flood risk management, as is seen in work such as that of Falter et al. (2015), which recognises that 'A flood loss event is the outcome of complex interactions along the flood risk chain, from the flood-triggering rainfall event through the processes in the catchment and river system, the behaviour of flood defences, the spa-555 tial patterns of inundation processes, the superposition of inundation areas with exposure and flood damaging mechanisms', and that determining flood risk involves 'not only the flood hazard, e.g. discharge and inundation extent, but also the vulnerability and adaptive capacity of the flood-prone regions.' Socio-hydrology could, however, further investigate the link between human perceptions of risk, the actions they take, the hydrological implications that this has, and therefore the impact 560 this has on future risk to determine emergent risk in socio-hydrological systems.
The impact that humans have on drought is another area that socio-hydrology could be used; work on the impact that human water use has upon drought has been done (e.g. (?) :::::::::::::::::::::: (Wanders and Wada, 2015) ), where is : it : was found that human impacts 'increased drought deficit volumes up to 100% compared to pristine conditions', and suggested that 'human influences should be included in projections of 565 future drought characteristics, considering their large impact on the changing drought conditions'.
Socio-hydrology could perhaps take this further and investigate the interaction between humans and drought, determining different responses to past drought and assessing how these responses may influence the probability of future issues and changes in resilience of social systems.

Transboundary Water Management
Across the World, 276 river basins straddle international boundaries (Dinar, 2014); the issue of transboundary water management is a clear case where social and hydrological systems interact to create a diverse range of impacts that have great social consequences, but which are very hard to predict. These issues draw together wholly socially constructed boundaries with wholly natural hy-575 drologic systems when analysed. The social implications of transboundary water management have been studied and shown to lead to varying international power structures (Zeitoun and Allan, 2008) (e.g. 'hydro-hegemony' (Zeitoun and Warner, 2006)), as well as incidences of both cooperation and conflict (in various guises) (Zeitoun and Mirumachi, 2008) dependent on circumstance. The virtual water trade (Hoekstra and Hung, 2002) also highlights an important issue of transboundary water 580 management: the import and export of goods almost always involves some 'virtual water' transfer since those goods will have required water in their production. This alters the spatial scale appropriate to transboundary water management (Zeitoun, 2013) and investigating policy issues related to this would very interesting from a socio-hydrologic perspective (Sivapalan et al., 2012).
Socio-hydrologic modelling could be used to predict the implications that transboundary policies 585 may have on hydrologic systems, and so social impacts for all those involved. However, the prediction of future transboundary is highlty uncertain and subject to a great many factors removed entirely from the hydrologic systems that they may impact, and so presents a significant challenge.

Land-use Management
The final example situation where socio-hydrological modelling may be applicable is in land-use 590 management. Changes in land-use can clearly have wide-ranging impacts on land productivity, livelihoods, health, hydrology, ecosystems services, which all interact to create changes in perception, which can feed back to result in actions being taken that impact on land management. Fish et al.
(2010) posits the idea of further integrating agricultural and water management: 'Given the simultaneously human and non-human complexion of land-water systems it is perhaps not surprising that 595 collaboration across the social and natural sciences is regarded as a necessary, and underpinning, facet of integrated land-water policy'. Modelling in socio-hydrology may contribute in this sphere through the development of models which explore the feedbacks mentioned above, and which can determine the long-term impacts of interaction between human and natural systems in this context.

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-Non-linear dynamics: socio-hydrology will involve investigating non-linear dynamics, possibly including regime shift, tipping points and time lags, all of which have been investigated in socio-ecology.
-Feedbacks: the two-way interactions between humans and water will bring about feedbacks between the two, which have important consequences. Discerning impacts and 680 causations in systems with feedbacks, and learning to manage such systems have been covered in socio-ecology and eco-hydrology.
-Uncertainties: while some aspects of the uncertainty present in socio-hydrology are not found in other subjects (see Unique Aspects of Socio-hydrology), some aspects are common with socio-ecology and eco-hydrology. In particular, propogative uncertainties present due to feed- -Inter-scale analysis: both socio-ecology and eco-hydrology involve processes which occur on different spatio-temporal scales, so methods for this integration can be found in these subjects.
-Incorporation of trans-/inter-disciplinary processes: socio-ecological models have needed to incorporate social and ecological processes, and so while the particular methods used to incorporate social and hydrological processes may be different, lessons may certainly be learnt in integrating social and biophysical processes.
-Disciplinary bias: researchers in socio-ecology generally came from either ecology or the social sciences, and so studies could occasionally be biased towards either of these. Critiquing 695 and correcting these biases is something that socio-hydrologists can certainly learn from.

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-Nature of water: water is a unique subject to model in many ways. It obeys physical rules, but has cultural and religious significance beyond most other parts of the physical world. It flows, is recycled via the water cycle, and is required for a multitude of human and natural functions. Hydrological events of interest are also often extremes.
-Nature of social system: aspects of social systems, such as decision-making mechanisms 705 and organisational structures, require models to deal with more than biophysical processes.
-Particular human-water interactions: there will be particular processes which occur on the interface between humans and people which and neither wholly social nor wholly physical processes. These will require special attention when being modelled, and will 710 necessitate the use of new forms of data.
-The role of changing norms: one of the focuses of socio-hydrological study is the impact of changing social values. Norms change on long timescales and are highly unpredictable, and so will present great difficulties in modelling.
-Scale: socio-hydrological systems will involve inter-scale modelling, but the breadth of spatial 715 and temporal scales necessary for modelling will present unique problems.

Human-Water System Representations
People interact with water in complex ways which extend between the physical, social, cultural and spiritual (Boelens, 2013). How the human-water system is perceived is a vital component of sociohydrological modelling, since this perception will feed into the system conceptualisation (Sivapalan et al., 2003), which will then feed into the model, and as such its outputs. In the past, linear, one-way 730 relationships have often been used, which observations have suggested 'give a misleading representation of how social-ecological systems work' (?) ::::::::::::::::  . This unidirectional approach may have been more appropriate in the past when anthropogenic influences were smaller, but since the interactions between hydrology and society have changed recently (as has been described previously), 'new connections and, in particular, more significant feedbacks which need to be understood, 735 assessed, modelled and predicted by adopting an interdisciplinary approach' , and so the view of systems in models should appreciate this. Views and knowledge of the humanwater system have changed over time, and these changes themselves have had a great impact on the systems due to the changes in areas of study and policy that perception and knowledge can bring about (Hadfield and Seaton, 1999).

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The concept of the hydrosocial cycle has been a step forward in the way that the relationship between humans and water is thought about, as it incorporates both 'material and sociocultural relations to water' (Wilson, 2014). This links well with the view of Archer (1995), who pictured society as a 'heterogeneous set of evolving structures that are continuously reworked by human action, leading to cyclic change of these structure and their emergent properties' (Mollinga, 2014).

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Socio-hydrology uses this hydrosocial representation, and also incorporates human influences on hydrology, whereby 'aquatic features are shaped by intertwining human and non-human interaction' to form a bi-directional view of the human-water system (Di Baldassarre et al., 2013a). Technology could also be included in these representations, as was the case in a study by Mollinga (2014), where irrigation was considered in both social and technical terms. Socio-hydrological human-water system representations should be considered in a case-specific manner, due to the fact that the relationship is very different in different climates. To give an extreme example, the way in which humans and water interact is atypical in a location such as Abu Dhabi, where water is scarce, desalination and water recycling provide much of the freshwater, and as such energy plays a key role (McDonnell, 2013). In this case, energy should certainly be included 755 in socio-hydrological problem formulations since it plays such a key role in the relationship (Mc-22 Donnell, 2013). Figure 2 shows an example of a conceptualised socio-hydrological system (Elshafei et al., 2014), which gives insight into the view that the author has of the system. It shows the linkage perceived between the social and hydrological systems, and the 'order' in which the author feels interactions 760 occur. In this system conceptualisation it is perceived that there are two feedback loops which interact to form system behaviour. One is a reinforcing loop, whereby increases in land productivity lead to economic gain, increased population, a higher demand for water and as such changes in management decisions, likely to be intensification of land-use (and vice versa); the other loop is termed the 'sensitivity loop' (Elshafei et al., 2014), whereby land intensification may impact upon ecosystem 765 services, which, when the climate and socio-economic and political systems are taken into account may increase sensitivity to environmentally detrimental effects, and cause behavioural change. This second loop acts against the former and forms dynamic system behaviour. Others may have different views on the system, for example there may be more (or less) complexity involved in the system, as well as different interconnections between variables, and this would lead to a different conceptual 770 diagram.
When forming a system representation, the topics of complex and co-evolutionary systems should be kept in mind so that these concepts may be applied where appropriate. These concepts are introduced in the following sections.

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Complex systems have been studied in many spheres, from economics (Foster, 2005), physics, biology, engineering, mathematics, computer science, and indeed in inter/trans-disciplinary studies involving these areas of study (Chu et al., 2003), or other systems involving interconnected entities within heterogeneous systems . By way of a definition of complex systems, Ladyman et al. (2013) give their view on the necessary and sufficient conditions for a system to be considered 780 complex: -An 'ensemble of many elements': there must be different elements within the system in order for interactions to occur, and patterns to emerge -'Interactions': elements within a system must be able to exchange or communicate -'Disorder': the distinguishing feature between simple and complex systems is the apparent 785 disorder created by interactions between elements -'Robust order': elements must interact in the same way in order for patterns to develop -'Memory': robust order leads to memory within a system Complex systems representations rely on mechanistic relationships between variables, meaning that the dynamic relationship between different system components do not change over time (Norgaard,790 23 1981), as opposed to evolutionary relationships, whereby responses between components change over time due to natural selection (Norgaard, 1981). Magliocca (2009) investigates the interactions between humans and their landscapes, and determines that emergent behaviours in these systems are due to the 'induced coupling' between them, and so should be modelled and managed using complex-systems-appropriate techniques. Resilience has also been studied with regard to complex 795 systems, and the interactions in complex systems have been said to lead to resilience (Garmestani, 2013). Complex systems are an excellent framework within which to study socio-hydrological systems, since they allow for the discernment of the origin of complex behaviours, such as cross-scale interactions, non-linearity and emergence (Falkenmark and Folke, 2002), due to their structure being decomposable and formed of subsystems that may themselves be analysed.

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-Identify evolutionary (sub)systems and entities -Provide a characterisation of variation in each system -Identify mechanisms that generate, winnow and provide continuity for variation in each system -Describe one or more potential sequences of reciprocal change that result in an evolutionary change in one or more systems -Identify possible reciprocal interactions between systems -Identify effects of reciprocal interactions Whether or not the biophysical, hydrological system is viewed as evolutionary in nature determines whether socio-hydrological dynamics may be termed co-evolutionary, since Winder et al. (2005) state that 'Linking an evolutionary system to a non-evolutionary system does not produce co-evolutionary dynamics. It produces simple evolutionary dynamics coupled to a mechanistic environment', which would imply that socio-hydrological systems are not co-evolutionary in nature, perhaps rather being complex systems, or systems of 'cultural ecodynamics' (Winder et al., 2005). Norgaard (1984Norgaard ( , 1981 allows for a looser definition of a co-evolutionary relationship, whereby 830 two systems interact and impact one another such that they impact one another's developmental trajectory. Norgaard (1981Norgaard ( , 1984 gives the example of paddy rice agriculture as an example of a co-evolutionary system: in this example, changes in agricultural practice (investment in irrigation systems for example) led to higher land productivity and to societal development; the usage of paddy-based techniques then required the development of social constructs (water-management in-835 stitutions and property rights) to sustain such farming methods, which served to socially perpetuate paddy farming and to alter ecosystems further in ways that made the gap between land productivity between farming techniques greater, and so led to yet greater societal and ecosystem change.
Western monoculture may also be viewed in the same light, with social systems such as insurance markets, government bodies and agro-technological and agrochemical industries developed to be 840 perfectly suited to current agriculture (Norgaard, 1984), but these constructs having been borne out of requirements by monocultures previously, and also serving to perpetuate monoculture and make its usage more attractive. The crucial difference between the two views is that Winder et al. (2005) do not consider biophysical systems, such as hydrological or agricultural systems, evolutionary in their nature (Kallis, 2007), since the biophysical mechanisms behind interactions in these systems 845 are governed by Newtonian, rather than Darwinian, mechanisms.
Even if the strict definition of a co-evolutionary system does not apply to socio-hydrology, the coevolutionary framework may be used as an epistemological tool (Jeffrey and McIntosh, 2006), a way to develop understanding, and so the subtle difference between complex and co-evolutionary systems should be kept in mind when developing socio-hydrological models, if for no other reason than it 850 may remind developers that non-stationary responses may exist (whether this implies co-evolution or not), largely in terms of social response to hydrological change. The usage of a co-evolutionary framework also allows the usage of the teleological principle (i.e. an end outcome has a finite cause), which allows, for example, for policy implications to be drawn (Winder et al., 2005).
There are already examples where a co-evolutionary perspective has been taken on an issue that 855 may be termed socio-hydrological/-ecological; these examples and how useful the co-evolutionary analogy is are examined here. Kallis (2010) uses a co-evolutionary perspective to look at how water resources have been developed in the past: Athens in Greece is used as an example, where expansions in water supply led to increases in demands, which required further expansion. However, this cycle is not seen as predetermined and unstoppable, rather it is dependent on environmental conditions, governance regimes, technology and geo-politics, all of which are impacted by, and evolve with, the changes in water supply and demand, as well as each other. The relationship between the biophysical environment and technology is particularly interesting: the environment is non-stationary as water supply expands, as innovation and policy, driven by necessity to overcome environmental constraints, result in environmental changes, both expected and unforeseen, which then result in so-865 cioeconomic changes and new environmental challenges to be solved. The evolutionary perspective used in looking at innovation overcoming temporary environmental constraints, but also creating new issues in the future is very useful in understanding how human-water systems develop. A study by Lorenzoni et al. (2000); Lorenzoni (2000) takes a co-evolutionary approach to climate change impact assessment and determines that using indicators of sustainability in a bi-directional manner 870 (both as inputs to and outputs from climate scenarios) is possible, and that a co-evolutionary view of the human-climate system, involving adaptation as well as mitigation measures, results in a 'more sophisticated and dynamic account of the potential feedbacks' . The dynamics that are implied using co-evolutionary frameworks are also interesting, as shown in studies by Liu et al. (2014), whereby the co-evolution of humans and water in a river basin system brings about 875 long stable periods of system equilibrium, punctuated by shifts due to internal or external factors, which indicates a 'resonance rather than a cause-effect relationship' (Falkenmark, 2003) between the systems.
The usage of a co-evolutionary framework could be beneficial in governance and modelling of sociohydrological systems, and the previously mentioned IAHS paper  states that 880 the co-evolution of humans and water 'needs to be recognized and modelled with a suitable approach, in order to predict their reaction to change'. The :::::::::: co-evolution :: of ::::::: societal :::::: norms :::: with :::::::::::: environmental :::: state :::: may :: be :::::::::: particularly :::::::: interesting :: in :::: this :::::: respect. :::: The 'lock-in' that is created by technological and policy changes in co-evolutionary systems, which can limit reversibility of decisions in terms of how resources are allocated (Van den Bergh and Gowdy, 2000), also means that improving the predictive 885 approach taken should be a matter of priority, decisions taken now may result in co-evolutionary pathways being taken that cannot be altered later . The implication of a potential lack of knowledge of long-term path dependencies for current policy decisions should be that, rather than seeking optimal policies in the short term, current decisions should be made that allow development in the long term and maintain the potential for system evolution in many directions 890 (Rammel and van den Bergh, 2003).

Complex Adaptive Systems
In understanding the concept of sustainability, Jeffrey and McIntosh (2006) explains that the dynamic behaviour seen in natural systems, 'is distinct from (simple or complex) dynamic or (merely) evolutionary change', and is instead a complex mixture of mechanistic and evolutionary behaviours.
applicable in socio-ecological systems, and so perhaps a better term to be used would be 'complex adaptive systems' (?) ::::::::::::::::  . Complex adaptive systems are a subset of complex systems in which systems or system components that exhibit adaptivity (not necessarily all elements or subsystems); Lansing (2003) gives a good introduction. The important distinction between complex 900 systems and complex adaptive systems is that, in complex systems, if a system reaches a previously seen state, this indicates a cycle, and so the system will return to this state at another point. Due to the adaptivity and time-variant responses, this is not the case in complex adaptive systems.
The complex adaptive systems paradigm has already been used in a socio-hydrological context, being used to investigate Balinese water temples that are used in irrigation (Lansing et al., 2009;905 Lansing and Kremer, 1993;Falvo, 2000). Policy implications of complex adaptive systems have also been investigated by ? ::::::::::::::: Levin et al. (2012) and Rammel et al. (2007), and are summarised as: -Nonlinearilty -should be included in models such that surprises aren't so surprising. Time variant responses also mean that adaptive, changing management practices should be used, as opposed to stationary practices 910 -Scale issues -processes occur on different spatial scales and timescales, and so analysis of policy impacts should be conducted on appropriate, and possible on multiple, scales -Heterogeneity -heterogeneity in complex systems results in the application of homogeneous policies often being sub-optimal -Risk & uncertainty -Knightian (irreducible) uncertainty exists in complex adaptive systems

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-Emergence -surprising results should not be seen as surprising, due to the complex, changing resposnes within systems -Nested hierarchies -impacts of decisions can be seen on multiple system levels due to the hierarchies within complex adaptive systems As can be seen, these policy issues are very similar to those mentioned in previous sections relating 920 to management of socio-hydrological and socio-ecological systems, which is not surprising.
Ultimately, in the modelling of socio-hydrological systems, it is not necessary to state whether the system is being treated as a complex system, a co-evolutionary system or a complex adaptive system, rather it is the implications that the lens through which the system is seen has, via the representation of the system in model equations, that are most important. There are clearly dynamics that both do 925 and do not vary in time in socio-hydrological systems, and so these should all be treated appropriately. Perhaps the most important outcome of the human-water system representation should be a mindset to be applied in socio-hydrological modelling, whereby mechanistic system components are used in harmony with evolutionary and adaptive components to best represent the system.

Space and Time in Socio-hydrological Modelling
In several previous sections, the issues of scale that socio-ecological and socio-hydrological systems can face were presented and their significance stressed. As such, a section looking at space and time in socio-hydrology is warranted. Hydrology involves 'feedbacks that operate at multiple spatiotemporal scales' (Ehret et al., 2014), and when coupled with human activities, which are also complex on spatial and temporal scales (Ren et al., 2002), this picture becomes yet more complicated, though implementation is of great importance, as both of these factors can have great impacts on the end results (Manson, 2008).
In terms of space, the interactions that occur between natural and constructed scales are superim-945 posed with interactions occuring between local, regional and global spatial scales. Basins and watersheds are seen as "natural" (Blomquist and Schlager, 2005) scales for analysis, since these are the spatial units in which water flows (though there are of course watersheds of different scales and watersheds within basins, and so watershed-scale analysis does not answer the question of spatial scale on its own), however these often do not match with the scales on which human activities occur, and 950 indeed human intervention has, in some cases, rendered the meaning of a 'basin' less relevant due to water transfers (Bourblanc and Blanchon, 2013). The importance of regional and global scales has been recognised, with Falkenmark (2011) stating that 'the meso-scale focus on river basins will no longer suffice'. Another issue of spatial scale is that of the extents on which issues are created and experienced (Zeitoun, 2013): some issues, for instance point-source pollution, are created locally 955 and experienced more widely, whereas issues of climate are created globally, but problems are experienced more locally in the form of droughts and floods. This dissonance between cause and effect can only be combated with policy on the correct scale. Creating models involves scale decisions, often involving trade-offs between practicalities of computing power and coarseness of representation (Evans and Kelley, 2004), which can impact the quality of model output. The previous points all 960 indicate there being no single spatial scale appropriate for socio-hydrological analysis; instead, each problem should be considered individually, with the relevant processes and their scales identified and modelling scales determined accordingly. This could result in potentially heterogeneous spatial scales within a model.
The interactions between slow and fast processes create the temporal dynamics seen in socio-965 ecological systems (Crépin, 2007); slow, often unnoticed, processes can be driven which lead to 28 regime shift on a much shorter timescale , and in modelling efforts these slow processes must be incorporated with faster processes. Different locations will evolve in a sociohydrological sense at different paces, due to hydrogeological (Perdigão and Blöschl, 2014) and social factors, and so socio-hydrological models should be devloped with this in mind. Also, dif-970 ferent policy options are appropriate on different timescales, with efforts such as rationing and source-switching appropriate in the short-term, as opposed to infrastructure decisions and water rights changes being more appropriate in the long term . All of these factors mean that a variety of timescales, and interactions between these, should be included in models, and analyses on different timescales should not be seen as incompatible (Ertsen et al., 2014).

Data
One of the cornerstones of study in hydrological sciences is data. However, there are significant problems in obtaining the data required in a socio-hydrological sense. Some of the issues present in this area are: -Timescales: an issue in accruing data for long-term hydrological studies is that 'detailed hy-980 drologic data has a finite history' (Troy et al., 2015b). Good data from historical case studies is difficult to obtain, and so shorter-term studies sometimes have to suffice. The focus on long-term analysis that socio-hydrology takes exacerbates this problem, particularly since historical case studies are of great use during the system-understanding phase that the subject is currently in.

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-Availability: where data is widely available, it may be possible for minimal analysis to be carried out, and for data-centric studies to be carried out (Showqi et al., 2013), but when the boundaries of the system of interest are expanded to include the social side of the system, data requirements naturally increase, and modellers are exposed to data scarcity in multiple disciplines (Cotter et al., 2014). Hydrological modelling often suffers from data unavail-990 ability , but significant work has recently been carried out in recent years on prediction in ungauged basins (Hrachowitz et al., 2013;Wagener and Montanari, 2011) to reduce this, and so perhaps the potential multi-disciplinary data scarcity issues in socio-hydrology could borrow and adapt some techniques. Papers discussing solutions for a lack of data in a socio-hydrologic context are also already appearing (Zlinszky and Timár, lumped conceptual models tend to have 'more modest... data requirements' (Sivapalan et al., 2003), whereas distributed, physically-based models tend to have 'large data and computer requirements' (Sivapalan et al., 2003). A smaller amount of data may be necessary in some socio-hydrological studies, since the collection of a significant quantity of extra data (when compared to hydrological studies) also incurs an extra cost, both in terms of cost and time (Pataki et al., 2011).
-Inter-disciplinary Integration: the integration of different data types from different fields is complex (Cotter et al., 2014); socio-hydrology will have to cope with this, since some aspects of socio-hydrological study are necessarily quantitative and some qualitative. Since the sub-1005 ject of socio-hydrology has come largely from those with a hydrology background, integrating qualitative data sources with more quantitative sources that hydrologists are commonly more comfortable with could pose some issues (Troy et al., 2015b). However, the necessary interdisciplinary nature of socio-hydrology also means that communication between model developers from different subject areas should be enhanced (Cotter et al., 2014), so that everyone 1010 may gain.
-New data: in order to capture some of the complex socio-hydrological interactions, sociohydrology should seek to go beyond merely summing together hydrological and social data, and instead investigate the use of new, different data types. Saying that this should be done is easy, but carrying it out in practice may be much more difficult, since the nature of this data and

Complexity
The expansion of system boundaries to include both social and hydrological systems introduces more complexity than when each system is considered separately. The increased complexity of the system leads to a greater degree of emergence present in the system, though this doesn't necessarily mean more complex behaviours (Kumar, 2011). The level of complexity required in a model of a more complex system will probably itself be more complex (though not necessarily, as ? ::::::::::::::: Levin et al. (2012) said, 'the art of modelling is to incorporate the essential details, and no more') than that of a simpler system, since model quality should be judged by the ability to match the emergent properties of the behaviour a system (Kumar, 2011). Manson (2001) introduces the different 1030 types of complexity: -Algorithmic complexity: this may be split into two varieties of complexity. One is the computational effort required to solve a problem, and the other is complexity of the simplest algorithm capable of reproducing system behaviour.
-While the first side of algorithmic complexity is important in socio-hydrological modelling, since mathematical problems should be kept as simple as is practicable, the second facet of algorithmic complexity is most applicable to socio-hydrologic modelling, as modellers should be seeking to develop the simplest possible models that can replicate the behaviour of socio-hydrological systems.
-Deterministic complexity: the notion that every outcome has a root cause that may be determined, however detached they may seemingly be, is at the heart of deterministic complexity.
Feedbacks, sensitivities to changes in parameters and tipping points are all part of deterministic complexity.
-The study of complex systems using mechanistic equations implies that there are deterministic relationships within a system; since socio-hydrological modelling will use 1045 such techniques, deterministic complexity is of interest. Using deterministic principles, modellers may seek to determine the overall impacts that alterations to a system may have.
-Aggregate complexity: this is concerned with the interactions within a system causing overall system changes. The relationships within a system lead to the emergent behaviours that 1050 are of such interest, and determining the strengths of various correlations and how different interactions lead to system level behaviours gives an idea of the aggregate complexity of a system.
-Aggregate complexity is of great interest to modellers of socio-hydrological systems.
Determining how macro-scale impacts are created via interactions between system vari-1055 ables is a central challenge in the subject, and so determining the aggregate complexity of socio-hydrological systems may be an interesting area of study.
The increased complexity of the system, and the previously mentioned issues of possible data scarcity from multiple disciplines, could lead to issues. Including more complexity in models does not necessarily make them more accurate, particularly in the case of uncertain or poor resolution 1060 input data (Orth et al., 2015); this should be kept in mind when developing socio-hydrological models, and in some cases simple models may outperform more complex models. Keeping in mind the various forms of complexity when developing models, socio-hydrologists should have an idea of how models should be developed and what they may be capable of telling us.

1065
As well as being structured in different ways, there are different ways in which models can be used to obtain results via different resolutions. Methods include analytical resolution, Monte Carlo simulations, scenario-based techniques and optimisation (Kelly (Letcher) et al., 2013). Analytical resolutions, while they give a very good analysis of systems in which they are applied, will generally be inapplicable in socio-hydrological applications, due to the lack of certain mathematical formula-1070 tions and deterministic relationships between variables which are required for analytical solutions.
Monte-carlo analyses involve running a model multiple times using various input parameters and initial conditions. This is a good method for investigating the impacts that uncertainties can have (an important aspect in socio-hydrology), though the large number of model runs required can lead to large computational requirements. Optimisation techniques are useful when decisions are to be 1075 made; using computer programs to determine the 'best' decision can aid in policy-making, however, optimisation techniques should be used with care: the impacts that uncertainties can have, as well as issues of subjectivity and model imperfections can (and have) lead to sub-optimal decisions being made. Techniques such as multi-objective optimisation (Hurford et al., 2014) seek to make more clear the trade-offs involved in determining 'optimal' strategies.

Uncertainty in Hydrological Models
Hydrological models on their own are subject to great uncertainties, which arise for an array of rea-1095 sons and from different places, including external sources (for instance uncertainties in precipitation or human agency, internal sources (model structure and parameterisation), as well as data issues and problem uniqueness (Welsh et al., 2013). In the current changing world, many of the assumptions on which hydrological models have been built, for instance non-stationarity (Milly et al., 2008), have been challenged, and new uncertainties are arising (Peel and Blöschl, 2011). However, the extensive investigations into dealing with uncertainty (particularly the recent focus on prediction in ungauged basins (Wagener and Montanari, 2011)) can only be of benefit to studies which widen system boundaries. The trade-offs between model complexity and 'empirical risk' (Arkesteijn and Pande, 2013) 32 in modelling, ways to deal with large numbers of parameters and limited data (Welsh et al., 2013), as well as statistical techniques to cope with uncertainties (Wang and Huang, 2014) have all been well investigated, and knowledge from these areas can certainly be applied to future studies.

Uncertainty in Coupled Socio-hydrological Models
Interactive and compound uncertainties are an issue in many subjects, and indeed already in water science (particularly the policy domain). Techniques already exist in water resource management for taking action under such uncertainties, for instance the method used by Wang and Huang 1110 (2014), whereby upper and lower bounds are found for an objective function that is to be minimised/maximised to help identify the 'best' decision, and to identify those that may suffer due to various uncertainties. This approach extends that taken in sensitivity analyses, and is a step forward, since sensitivity analyses usually examine 'the effects of changes in a single parameter... assuming no changes in all other parameters' (Wang and Huang, 2014), which can fail to detect the impact of 1115 combined uncertainies in systems with a great deal of interconnections and feedbacks. The amplifications that feedback loops can induce in dynamic systems mean that the impact of uncertainties, particularly initial condition uncertainties, can be great (Kumar, 2011).
There are numerous ways to classify models, and so before each individual modelling technique is detailed, the more general classifications will be detailed. The distinction between these different types of model is fairly clear: physics-based models use mathematical representations of physical processes to determine system response, data-based models seek to reproduce system behaviour utilising available data (Pechlivanidis and Jackson, 2011) (there 1180 also exist hybrid models using a combination of these two approaches), and conceptual models are based on a modeller's conceptual view of a system. The common criticisms of the two approaches are that physics-based model results are not always supported by the available data (Wheater, 2002) and are limited due to the homogenous nature of equations in a heterogeneous world (Beven, 1989), while metric models can represent processes that have no physical relevance (Malanson, 1999).

Bottom-up vs Top-down
There is a similar distinction between bottom-up and top-down models as between metric and physically-based. Bottom-up modelling techniques involve the representation of processes (not necessarily physical) to develop system behaviour, whereas top-down approaches look at system outcomes and try to look for correlations to determine system behaviours. Top-down approaches have 1190 been criticised for their inability to determine base-level processes within a system, and so their inability to model the impact of implementing policies and technologies (Srinivasan et al., 2012).
Bottom-up methods, while the message they present doesn't need to be 'disentangled' , require a great deal of knowledge regarding specific processes and sites, which in social circumstances in particular can be very challenging (Sivapalan, 2015) and specific in both a spatial 1195 and temporal sense. More detail on bottom-up and top-down modelling approaches will be given in the sections on agent based modelling and system dynamics modelling, since these are the archetypal bottom-up and top-down approaches respectively.

Distributed vs Lumped
The final distinction that is drawn here is that of distributed and lumped models. Distributed models 1200 include provisions for spatial, as well as temporal, heterogeneity, while lumped models concentrate study at discrete spatial points, where dynamics vary only in time. The advantages of distributed models are clear, particularly in a hydrological context where spatial heterogeneity is of such importance, however the drawbacks of high-resolution data requirements, with high potential for uncertainty, and larger computational requirements (Sivapalan et al., 2003) mean that lumped models can 1205 be an attractive choice.
In the discussions that follow, the factors that would affect the choice of modelling approach will also be used. These are: -Model purpose -Data availability (quantity, quality and whether it is quantitative or qualitative) Now that these pre-discussions have been included, a section on the importance of model conceptualisation is included, before each modelling approach is focused on.

The Importance of Model Conceptualisation
The previously mentioned statement of modelling being 'thinking made public' (Liebman, 1976) highlights the significance of the process behind model development for the distribution of knowl-1240 edge. The conceptual basis on which a model is built defines the vision that a developer has of a system ('framing the problem' (Srinivasan, 2015)), and is therefore both a vital step in model development and a way that understanding can be shared. Conceptualisations often involve 'pictures', whether these be mental or physical pictures, and these pictures can be an excellent point of access for those who wish to understand a system, but who do not wish to delve into the potentially more 1245 quantitative or involved aspects. In some cases, a conceptual modelling study can also be an important first step towards the creation of a later quantified model (e.g. (Liu et al., 2014(Liu et al., , 2015a).
There are certain facets of socio-hydrology that should be captured in all SHS models, and so frameworks for socio-hydrological models should underly conceptualisations. Two frameworks for socio- Both of these frameworks give a view of the key parts of socio-hydrological systems: the second gives a good base for modelling the entirety of the system, and has a very abstracted point of view of the societal dynamics, whereas the former takes a more detailed look at the societal constructs that lead to a particular response. Depending on the level of detail that is sought, either or both of these frameworks could be used as a basis for a socio-hydrological conceptualisation.

Agent-Based Modelling (ABM)
Having its origins in object-oriented programming, game theory and cognitive psychology , ABM is a bottom-up approach to the modelling of a system, in which the focus is on the behaviour and decision-making of individual 'agents' within a system (Bousquet and Le Page, 2004).
These agents may be individuals, groups of individuals, or institutions, but are defined by the at-1275 tributes of being autonomous and self-contained, the presence of a state and the existence of interactions with other agents and/or the environment in which an agent exists (Macal and North, 2010).
Decision rules are determined for agents (these may be homogeneous or heterogeneous), which determine the interactions and feedbacks that occur between agents (often agents on different organisational levels (Valbuena et al., 2009)), as well as between agents and the environment. ABMs are 1280 almost necessarily coupled in a socio-ecological sense (though they are often not necessarily termed as such), given that they use the decision-making processes of those within a society to determine the actions that they will take, and as such their impacts upon the environment and associated feedbacks, though they might not fully look at impacts that society has upon the environment, and rather look at human reactions to environmental changes.

1285
Agent-based models themselves come in many forms, for example: -Microeconomic: agent rules are prescribed to optimise a given variable, for instance profit, and make rational (or bounded rational) choices with regards to this (e.g. (Becu et al., 2003;Filatova et al., 2009;Nautiyal and Kaechele, 2009)).
-Scenario-based: various environmental scenarios are investigated to see the impact upon be-1295 haviours, or different scenarios of societal behaviours are investigated to see impacts upon the environment (e.g. (Murray-Rust et al., 2013)).
The development of an ABM involves a fairly set method, the general steps of which are: 1. Problem definition 2. Determination of relevant system agents 1300 3. Description of the environment in which agents exist 4. Elicitation of agent decision-making process and behaviours (Elsawah et al., 2015) 5. Determination of the interactions between agents 6. Determination of the interactions between agents and the environment 7. Development of computational algorithms to represent agents, environment, decision-making 1305 processes, behaviours and interactions

Model validation and calibration
The results from ABMs will generally be spatially explicit representations of system evolution over time, and so lend themselves well to integration with GIS software .
ABMs may be used in socio-hydrological modelling in two contexts: firstly, the discovery of emer- ena that may be difficult to represent mathematically (Lempert, 2002). ABMs are also very applicable in the area of policy-making, as the outcomes of different policy options may be compared when the impact of agent behaviours are accounted for; for instance, O'Connell and O'Donnell (2014) suggest that ABMs may be more useful in determining appropriate flood investments than current cost-benefit analysis (CBA) methods. In the area of resilience, the importance of human be-1320 haviours in creating adaptive capacity of socio-ecological systems (Elsawah et al., 2015) has meant that ABMs have been used to look at the varying levels of differing levels of resilience in different governance regimes (Schlüter and Pahl-Wostl, 2007). The usage of ABM can be particularly strong in participatory modelling (Purnomo et al., 2005), where agents may be interviewed to determine their strategies, and then included in subsequent modelling stages. While ABM is seen by many as a 1325 technique with a wide range of uses, others are less sure of it's powers (Couclelis, 2001), particularly in predictive power at small scales , along with the difficulties that can be present in validation and verification of decision-making mechanisms . One study that has been carried out in the specific area of socio-hydrology which incorporates agent-based aspects is that of Srinivasan (2013). In this historical study, social and hydrological change in Chennai, India (Srinivasan, 1330 2013) was investigated to determine the vulnerability of those within the city to water supply issues.

1355
System dynamics (and the linked technique of system analysis (Dooge, 1973)) takes a very much top-down view of a system; rather than focusing on the individual processes that lead to overall system behaviours, system dynamics looks at the way a system converts inputs to outputs and uses this as a way to determine overall system behaviour. In system dynamics, describing the way a system 'works' is the goal rather than determining the 'nature of the system' (Dooge, 1973) by examining 1360 the system components and the physical laws that connect them. System dynamics can, therefore, avoid the potentially 'misleading ' ::::::::: misleading : analysis of the interactions and scaling up of smallscale processes (potentially misleading due to the complexity present in small-scale interactions not scaling up) (Sivapalan et al., 2003). Macro-scale outcomes such as non-linearities, emergence, crossscale interactions and surprise can all be investigated well using system dynamics (Liao, 2013), and 1365 it's high-level system outlook allows for holism in system comprehension (Mirchi et al., 2012).
An important facet of the system dynamics approach is the development procedure: a clear and helpful framework that is integral in the development of a successful model, and also provides an important part of the learning experience. As with other modelling techniques, this begins with a system conceptualisation, which, in this case, involves the development of a causal loop diagram This allows for a model developer to visualise the potential feedbacks and interconnections that may lead to system-level behaviours (Mirchi et al., 2012) from a qualitative perspective, without needing to delve into the quantitative identification of the significance of the different interconnections. Depending on how a modeller wishes to represent a 1375 system, different levels of complexity may be included in a CLD (this complexity may then later be revisited during the more quantitative model development phases), and CLDs (and indeed SD models) of different complexity may be useful in different circumstances. The differences in complexity between Figures 4 and 5 show very different levels of complexity that modellers may choose to use (particularly since Figure 4 is only a CLD for one of four linked subsystems). Once a CLD 1380 has been devised, the next stage in model development is to turn the CLD into a Stocks and Flows Diagram (SFD). This process is detailed in Table 2, and essentially involves a qualitative process of determining the accumulation and transfer of 'stocks' (the variables, or proxy variables used to measure the various resources and drivers) in and around a system. Figure 6 shows the SFD developed from a CLD. SFD formulation lends itself better to subsequent development into a full quantitative The application of a top-down modelling strategy, such as system dynamics, carries with it certain advantages. The impact that individual system processes and interactions thereof may be identified, as the root causes of feedbacks, time-lags and other non-linear effects can be traced. This trait makes system dynamics modelling particularly good in system understanding applications. The usefulness of SD in learning circumstances is increased by the different levels on which system understanding 1400 can be generated: the different stages of model development, varying from entirely qualitative and visual to entirely quantitative, allow for those with different levels of understanding and inclination to garner insight at their own level, and during different stages of model development. As such, system dynamics is an excellent tool for use in participatory modelling circumstances. SD techniques also give a fairly good level of control over model complexity to the developer, since the level at which subsystems and interactions is defined by the model developer. There are clear outcomes that emerge in many socio-ecological and socio-hydrological systems, but the inherent complexity and levels of interaction of small-scale processes 'prohibits accurate mechanistic modelling' (Scheffer et al., 2012), and so viewing (and modelling) the system from a level at which complexity is appreciated but not overwhelming allows for modelling and analyses. Another advantage that follows from this point is that system dynamics may be used in situations where the physical basis for a relationship is either unknown or difficult to represent, since correlative relationships may be used as a basis for modelling (Öztürk et al., 2013). The nature of SD models also makes it easy to integrate the important (Gordon et al., 2008) aspect of spatio-temporal scale integration, and the data-based typology of system dynamics means that the 'opportunity' (Rosenberg and Madani, 2014) presented 1415 by big data can be harnessed in water resource management.
There are, of course, reasons why system dynamics would not be chosen as a modelling technique.
The first of these is the fundamental issue that all models that view systems from a top-down perspective, inferring system characteristics from behaviours, can only produce deterministic results (Liu et al., 2006). Great care must also be taken with the level of complexity included in a sys-1420 tem dynamics model, since very simplistic relationships between variables will fail to capture the complexity that is present , while the inclusion of too much complexity is easy, and can result in relationships that do not occur in the real world (Kelly (Letcher) et al., 2013).
Of all of the modelling techniques detailed in this review, system dynamics has perhaps seen the most explicit usage in socio-hydrology thus far. This is perhaps due to the usefulness of SD in developing system understanding (the stage that socio-hydrology would currently be characterised as being at), and the ease with which disciplines may be integrated. Models thus far have generally been fairly simple, involving five or so system components, using proxy measures for high sent the risk taking attitude of a society, its collective memory and trust in risk-reduction strategies are investigated, alongside a development ::::::::::: developments in which a stochastic hydrologic input was used (Viglione et al., 2014) :::: were ::::: used ::::::::::::::::::: (Viglione et al., 2014) , ::: and :: a ::::: study :: in :::::: which :::::: control :::::: theory ::: was :::: used :: to ::::::::: investigate ::::::::: optimality :: in ::: this ::::::: context, :::: and :: in ::::: which ::: the :::::::: stochastic :::::::: elements :: of ::: the :::::: model :::: were ::::::: replaced ::::: with ::::::: periodic ::::::::::: deterministic :::::::: functions :::::::::::::::::: (Grames et al., 2015) . The model was further developed, this time simplified in structure, by Di Baldassarre et al. (2015b); here, the core dynamics were focused on, and the number of parameters and variables reduced. This step of simplification is surely good in system dynamics models, isolating the core features and relationships which produce system-level outcomes, while reducing the risks of overparameterisation and excessive model complexity. The structure of the modelling framework allowed for the development of a fairly simple 1450 model that could show complex interactions between society and hydrology, producing emergent outcomes, and lead to development in thought around the subject. Another example of a system dynamics approach being taken in socio-hydrological study is the work of Kandasamy et al. (2014), where the co-evolution of human and water systems in the Murrumbidgee Basin (part of the Murray Darling Basin) was investigated in a qualitative sense to form a system conceptualisation; this was 1455 then followed by work by van Emmerik et al. (2014) in which this conceptualised system view was turned into a quantitative model, formed of coupled differential equations, capable of modelling past system behaviour. In this case, a slightly different set of variables are investigated (reservoir storage, irrigated area, human population, ecosystem health and environmental awareness), which provide indicators of the economic and political systems in a more indirect (e.g. the irrigated area giving 1460 an idea of economic agricultural production), but directly measurable way. Again, this fairly simple mathematical model was able to replicate the complex, emergent behaviours seen in the system, particularly the 'pendulum swing' between behaviours of environmental exploitation and restoration. Studies investigating the Tarim Basin, Western China, have followed a similar development process, with a conceptual model developed (Liu et al., 2014) first to examine the system from a 1465 qualitative, historical perspective, before a quantitative approach (Liu et al., 2015a), including proxy variables for hydrological, ecological, economic and social sub-systems, is taken to develop further understanding of how and why specific co-evolutionary dynamics have occurred; the focus in this study was on system learning, and so a simple model was developed to facilitate easy understanding. The final socio-hydrological study that explicitly takes a system dynamics approach looks at 1470 the dynamics of lake systems (Liu et al., 2015b); this study involves a slightly more complex SD model, but is an excellent example of the development path through conceptualisation, CLD formation, conversion to an SFD and subsequent quantitative analysis. The five feedback loops that exist within the model, and their significance in terms of system behaviour, are well explained. Again, similar (though a slightly higher number of) variables are used in the model, including population, 1475 economics, water demand, discharge, pollutant load and water quality. As is clear from the choice of variables, the hydrological system is viewed in more detail in this study, and the aspect of community sensitivity and behavioural responses are not included explicitly.
As is clear from the studies highlighted, system dynamics has been well applied to socio-hydrological studies. The ease with which SD facilitates system learning, the ability for relatively simple models to (re)produce emergent phenomena seen in socio-hydrological systems, and the clear model development process have led to this being a common choice of modelling framework in early socio-hydrological system study. The highlighted studies make clear the aspects of integrated sociohydrological systems that should be included in all such studies (i.e. some inclusion of hydrological systems, impacts on livelihoods and societal responses), but also the importance of tailoring models 1485 to show in more detail those aspects that are pertinent to a particular case study.

Pattern-oriented Modelling (POM)
The previously described techniques of agent-based modelling and system dynamics are archetypal examples of bottom-up and top-down modelling frameworks respectively. The advantages and disadvantages of these approaches have been detailed earlier, but are summed up in Table 3. Over-1490 coming these deficiencies is key in furthering the pursuit of accurate, useful modelling. One way of attempting to overcome the difficulties posed by top-down and bottom-up strategies is to attempt to 'meet in the middle' (something that has been called for a long while (Veldkamp and Verburg, 2004)), and this is where POM sits. Pattern-oriented models are essentially process-based (and so bottom-up) models where system results are matched to observed patterns of behaviour in the model 1495 calibration/validation stage (Grimm et al., 1996). The use of patterns in calibration, as opposed to exact magnitudes of output parameters, makes validation simpler (Railsback, 2001), since maximum use may be found for data that is available, and the often impracticable collection of data regarding all output parameters becomes less necessary. Also, imperfect knowledge of base-level processes may be overcome through emergent pattern identification (Magliocca and Ellis, 2013). The use of 1500 POM would allow for a simpler process-based model, with few parameters, overcoming the problems associated with the complexity in bottom-up models, whereby overparameterisation may lead to the tendency for models to be able to fit data despite potentially incorrect processes and structure, as well as reducing model uncertainty, while also being defined by processes, rather than data, and so overcoming the criticisms commonly levelled at top-down approaches. There are, of course, 1505 drawbacks to the use of POM: a model being able to fit patterns does not necessarily mean that the mechanisms included in the model are correct, and the data required for model validation may be quite different to that which is commonly required at present, and so using POM may require a different approach to data collection (Wiegand et al., 2003). Also, pattern-oriented models may still be significantly more complex than system dynamics models, due to the modelling of base-level pro-1510 cesses. ::: The :::: very :::: fact ::: that :::: they ::: are ::::::::::::: pattern-oriented :::: also ::::: leaves ::::::::: difficulties :: in ::::::: dealing :::: with ::::::: surprise, :: a :::: very :::::::: important ::::: aspect :: of :::::::::::::: socio-hydrology. : The model development process in POM is thus (Wiegand et al., 2003): Pattern-oriented models would be well applied in socio-hydrological situations. The various emergent characteristics and patterns that are created in coupled socio-ecological and socio-hydrological systems lend themselves perfectly to the integrated use of processes and patterns, particularly since there are sub-systems and processes which are well understood and the dynamics of which can be well modelled, but also those system components which are less well understood. In less well under-1525 stood system sections, underlying processes may be uncovered by using the patterns which define the system (Grimm et al., 2005). POM has already found applications in socio-ecological investigations into land-use change (Evans and Kelley, 2008;Iwamura et al., 2014), though it has potential uses in many other areas.

1530
Often, relationships between variables are stochastic, rather than deterministic, i.e. a given input does not always give the same output and instead there is a distribution of possible outputs. In such situations, Bayesian networks are well applied. The advantages of using Bayesian Networks come directly from the modelling approach: uncertainties are directly and explicitly accounted for since all inputs and outputs are stochastic (Kelly (Letcher) et al., 2013), and the use of Bayes' theorem 1535 means that probability distributions of output variables may be 'updated' as new knowledge and data becomes available (Barton et al., 2012). Using Bayes' theorem also allows the use of prior knowledge, since distributions of output parameters are required to be specified prior to model start-up (to then be changed and updated), and these prior distributions may be informed by literature (Barton et al., 2012). The fact that there are relationships (albeit stochastic rather than deterministic) be-1540 tween variables also means that direct causal links between variables may be established (Jellinek et al., 2014). The drawbacks in using BNs are the difficulties present in modelling dynamic systems, since BNs tend to be set up as 'acyclic' (Barton et al., 2012) (though object-oriented (Barton et al., 2012) and Dynamic Bayesian Networks (Nicholson and Flores, 2011), which can model dynamic feedbacks, are being developed and becoming more prevalent), and in the potential statistical 1545 complexities present. A Bayesian Network may be seen as a stochastic version of a system dynamics model, and so many of the criticisms of SD models may also be applicable to BNs; in particular, the fact that BNs are largely based around data-defined relationships (as opposed to physically determined or process-based relationships) between variables means that BNs can only yield determinstic (albiet stochastically deterministic) results that arise from data. 1. The model is conceptualised, with variables represented as 'nodes' in the network and causal linkages between variables determined 2. 'Parent' and 'child' nodes are related with a conditional probability distribution determining how a 'child' node changes in relation to parent nodes (Jellinek et al., 2014) 1555 3. Data is collected and fed into the model 4. This new data causes output probability distributions to be updated 5. As new data and knowledge is accumulated, the network can be continually updated, and so the previous two points may be carried out cyclically Many uncertain relationships exist within hydrology and sociology, and indeed in the linkages be-1560 tween the two. Perhaps , ::: so :::::: perhaps : the use of stochastic relationships and the BN framework would be an appropriate technique in socio-hydrological studies. ::::::: However ::::: adept :::: BNs ::: are :: at :::::: dealing ::::: with :::::: aleatory :::::::::::: uncertainties, :::: they :::: still :::::: cannot :::::: include :::::::::: information ::::: about ::::: what ::: we ::: do ::: not ::::: know ::: we ::::: don't ::::: know, ::: and ::: so ::: the ::::: issues ::: of :::::: dealing :::: with ::::::::: epistemic ::::::::: uncertainty :::: and ::::::: surprise ::: are :::: still :::::::: prevalent.

Coupled Component Modelling (CCM)
Coupled component models take specialised, disciplinary models for each part of a system and integrate them to form a model for the whole system. Kelly (Letcher) et al. (2013) describe how this may be 'loose', involving the external coupling of models, or much more 'tight', involving the integrated 1575 use of inputs and outputs. CCM therefore offers a flexibility of levels of integration (this is of course dependent on the degree to which models are compatible), and can be a very efficient method of model development, since it takes knowledge from models that already exist, and will already have some degree of validity in the system that they are modelling. The flexibility also extends into the fact that different modelling techniques may be integrated, and so those techniques that suit specific 1580 disciplines may be utilised. CCM can also be an excellent catalyst for interdisciplinary communication; models that experts from different disciplines have developed may be integrated, necessitating communication between modellers and leading to development in understanding of modelling in different disciplines.
However, there are of course drawbacks to using CCM; the models used may not be built for integration (Kelly (Letcher) et al., 2013), which may lead to difficulties and necessitate significant recoding.

Scenario-Based Modelling
While perhaps not a 'modelling technique' per se, and rather a method of resolution that can be applied, the usage of scenarios in analysis has important implications for modelling that warrant discussion. Scenario-based approaches fall into two main categories, those which investigate different policy implementation scenarios, and those which use scenarios of different initial conditions (within this, initial conditions could be for instance different socio-economic behavioural patterns, or future system states). This means that the impact that policies may have can be analysed from two angles; that of assuming knowledge of system behaviour and comparing decisions that may be made, as well as admitting lack of system knowledge and analysing how different system behaviour may impact the results that decisions have (indeed these may also be mixed). There are several issues that socio-hydrological modelling studies may encounter that will lead to scenario-based techniques being applicable. Firstly, long-term modelling of systems that will involve a large amount of uncertainty, particularly in terms of socio-economic development, is difficult due to the snowballing of uncertainties; as such, using likely scenarios of future development may be a more prudent starting point for modelling studies that go a long way into the future. :: In :: a :::::: similar :::: way, :::::::: scenarios :::: that :::: look 1625 : at ::: the :::::::::: occurrence :: of :::::::: different :::::::: surprising :::::: events ::::: would ::: be ::::: useful :: in ::::::::::::::: socio-hydrology. Even if uncertainties are deemed acceptable, the computational effort required to conduct integrated modelling studies far into the future may make such studies infeasible, and so the use of scenarios as future initial conditions may be necessary. Thirdly, particularly ::::::::: Particularly : in a policy context, policies are generally discrete options, and so the first use of scenario-based approaches mentioned (compar-1630 ing options) certainly makes sense. Studies conducted on the subject of climate change tend to use a scenario-based approach for socio-economic development, and CHANS studies also sometimes use scenario-based approaches (e.g. (Monticino et al., 2007)). The usage of scenarios has been said to have improved recently (Haasnoot and Middelkoop, 2012), with more scenarios generally being used, and appropriate interpretation of the relative probabilities of different scenarios occurring 1635 being investigated. While the use of a scenario-based approach for analysing policy alternatives involves very few compromises, the use of scenarios as initial conditions for modelling future system states can involve compromise in that the 'dynamic interactions' between social and hydrological systems will be lost (Carey et al., 2014) in the intervening period between model development and the time at which the model is analysing. Heuristic modelling involves collecting knowledge of a system and using logic or rules to infer outcomes (Kelly (Letcher) et al., 2013). The process of model development here is quite clear, with an establishment of the system boundaries and processes, and simply gathering knowledge of system behaviour to determine outcomes. As with scenario-based modelling and coupled component modelling, the use of heurism in models allows the use of different modelling techniques within the tag of 'heurism', for example Acevedo et al. (2008); Huigen (2006) have used ABMs encoded with a great deal of heuristic knowledge. The advantage of heuristic modelling is in the heurism: experience and knowledge of systems is a valuable source of information, and if system processes are understood well enough that logic may be used to determine outcomes, then this is an excellent method.
1650 However, where system knowledge is incomplete, or imperfect in any way ::: (as :: in :::::::::::::: socio-hydrology : at :::::::: present), then the usefulness of experience-based techniques falls down. Heuristic modelling is also not generally all that useful in system learning applications, though in cases where disciplinary models are integrated, new heurism may be generated in the interplay between subjects. Gober and Wheater (2015) have identified that some current socio-hydrological models (that of Di practical, applicable value, in that some conceptualised models of socio-hydrological systems tend to assume relationships between variables, rather than define them via data. This gives a different value to the term heuristic, and implies the development of models of different structure via heuristic means. The challenge in taking this approach 'is to avoid biasing the model to predict the social 1660 behaviour that we think should happen' (Loucks, 2015).

Conclusions
This paper has reviewed the literature surrounding the modelling of socio-hydrological systems, including concepts that underpin all such models (for example conceptualisation, data and complexity) and modelling techniques that have and/or could been applied in socio-hydrological study. It shows 1665 that there is a breadth of issues to consider when undertaking model-based study in socio-hydrology, and also a wide range of techniques and approaches that may be used. Essentially, however, in socio-hydrological modelling, there is a decision to be made between top-down and bottom-up modelling, which represents a choice between representing individual system processes (including the behaviours and decisions of people in this case) and viewing the system as a whole; both of these 1670 approaches have advantages and disadvantages, and the task to the modeller is to maximise the advantages and minimise the disadvantages. There are significant challenges in representing, modelling and analysing coupled human-water systems, though the importance of the interactions that now occur between humans and water means that these challenges should be the focus of significant research efforts. With regards to future research that could be conducted following the work that has 1675 been reviewed here, without resorting to the platitudes of improving predictions, reducing & managing uncertainties, increasing interdisciplinary integration and improving data, there are several examples of areas in which research would be of benefit. Some of these topics are common to other subjects, however there are specific aspects that are of particular importance in socio-hydrology: -Conceptual models of stylised socio-hydrological systems, for example systems of inter-basin 1680 water transfer, drought or agricultural water use: the strength that socio-hydrology should bring is a greater understanding of how human-water interaction affects overall system behaviour. A great deal of understanding can be generated through conceptual studies of generalised systems, and so modelling of archetypal systems would be of benefit. The challenge here is to move beyond models developed to mimic behaviour that we expect, towards those 1685 capable of giving insight.
-Determining the appropriate complexity for models of highly interconnected socio-hydrological systems: the broadening of system boundaries brings issues regarding model complexity and trade-offs between deterministic uncertainty and uncertainty propagation. Quantifying these trade-offs in socio-hydrological circumstances, and so determining the appropriate level of 1690 abstraction for modelling would allow for more effective modelling efforts.

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-Gathering data in socio-hydrological studies: as an interdisciplinary subject, data in sociohydrological study will come from a variety of sources. While methods for collection of hydrological data are well established, the social data that will be required, and indeed the new, unconventional data that may be required to describe socio-hydrological processes may pose 1695 issues in availability and collection. The challenge here is to maximise the utility of what is available and to develop models in an iterative fashion, allowing early-stage, conceptual models to guide data collection, and adapting models to suit what data is available.
-Determining methods for calibration and validation in socio-hydrology: calibration and validation are issues in almost all modelling areas. However, as a new subject, there is no cali-1700 bration/validation protocol for socio-hydrological modelling, and with the aforementioned issues with social science data, conducting formal calibration & validation may be difficult. As such, the development of guidelines regarding what constitutes 'validation' in socio-hydrology would be worthy of investigation.
-Discussion of emergence in socio-hydrological systems, particularly emergence of more ab-1705 stract properties, such as risk, vulnerability and resilience: the stochastic nature of hydrological drivers and the unpredictability of human responses renders any definite statement regarding system behaviour largely anecdotal (though often anecdotes of merit), and so acknowledging this stochasticity in analysis and discussion, using properties of more abstract meaning to describe the system may be useful in socio-hydrology.

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-More in-depth socio-hydrological modelling studies across social, economic and hydrological gradients: while conceptual modelling can build understanding to a point, case-based models can often give a greater insight into specific system behaviours. Applying socio-hydrological models to a range of cases will help build understanding in this way, particularly if these cases are similar, but differentiated in some way (e.g. responses to drought across a range of levels of 1715 economic development). The challenge (and opportunity) that this presents is understanding the dynamics which are general across cases, those which vary across gradients and those which are place-specific.
-Determining how best to present and use findings from socio-hydrological studies in policy applications: the way that socio-hydrological understanding will likely be applied in the real 1720 world is via policy decisions. As such, understanding the best way to communicate findings in socio-hydrology is vital. The challenge here is to communicate the differences between the outcomes predicted by traditional analyses and socio-hydrological studies regarding the way that policy decisions may impact the system in the long term, while acknowledging the limitations in both approaches.
The unifying feature of these future research topics is the development of understanding regarding socio-hydrological systems. The most important way in which socio-hydrology differs from other water management subjects is in understanding the system as a whole, as opposed to focusing on problem solving. As such, the research priorities at this stage are focused on different ways of improving and communicating understanding.