Many-objective risk assessment framework for guiding operational decisions on multiple reservoirs
Authors: Dau Quan , Dorchies David , Bader Jean-Claude 
Published: March 2021

&lt;p&gt;Effective optimisation methods have emerged over the last few decades to deal with the management of multiple reservoirs serving multiple and often conflicting objectives. Despite the abundant literature on the subject, the practical use of these techniques in the field remains very limited because they are perceived as &amp;#8220;black boxes&amp;#8221; whose behaviour is difficult to understand for users and decision-makers (Pianosi et al. 2020).&lt;/p&gt;&lt;p&gt;Optimisation using one or more aggregated objectives can create stakeholder reluctance when they do not recognize their values and objectives in the optimization formulation, while also raising ethical concerns related to the inclusion of undesirable and/or hidden trade-offs. In contrast, an approach considering many non-aggregated objectives has the potential to bring out alternative courses of action that better reflect the diverging perspectives of stakeholders, and align better with ethical concerns (Kasprzyk et al. 2016).&lt;/p&gt;&lt;p&gt;To deal with this problem, we here follow the Wierzbicki's (1979) &quot;reference objective&quot; concept considering each single objective as a utopia point optimised separately by deterministic dynamic programming. The optimisation, taking into account given hydroclimatic conditions and a chosen set of constraints, provides yearly probabilistic upper or lower rule curves reflecting the risk of failing to achieve each of the objectives in the future (Bader 1992). In order to use these data, we have developed a graphical user interface based on an R Shiny application showing the risk probability of future failure of each objective depending on the calendar day and the current or forecasted storage state of each reservoir.&lt;/p&gt;&lt;p&gt;This framework is applied on the Seine catchment area in Paris, France, which includes a system of 4 large reservoirs to protect against floods and water shortages for multiple flow thresholds and multiple locations downstream from the reservoirs. Historical datasets as well as climate change projections are used to take into account the non-stationarity nature of hydroclimatic conditions. Among other applications, this example shows the utility of such a tool in order to justify the stakeholders decisions to discard minor objectives when they undermine the chances of success of major objectives in critical situations.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;References&lt;/p&gt;&lt;p&gt;----------&lt;/p&gt;&lt;p&gt;Bader, J.-C., 1992. Consignes de gestion du barrage &amp;#224; vocation multiple de Manantali: d&amp;#233;termination des cotes limites &amp;#224; respecter dans la retenue [Multiple use management of Manantali Dam: determination of limiting storage levels]. Hydrologie Continentale 7, 3&amp;#8211;12.&lt;/p&gt;&lt;p&gt;Kasprzyk, J.R., Reed, P.M., Hadka, D.M., 2016. Battling Arrow&amp;#8217;s Paradox to Discover Robust Water Management Alternatives. Journal of Water Resources Planning and Management 142, 04015053. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000572&lt;/p&gt;&lt;p&gt;Pianosi, F., Dobson, B., Wagener, T., 2020. Use of Reservoir Operation Optimization Methods in Practice: Insights from a Survey of Water Resource Managers. Journal of Water Resources Planning and Management 146, 02520005. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001301&lt;/p&gt;&lt;p&gt;Wierzbicki, A.P., 1979. The Use of Reference Objectives in Multiobjective Optimization - Theoretical Implications and Practical Experience (No. WP-79-66). International Institute for Applied Systems Analysis, Laxenburg, Austria.&lt;/p&gt;