The Costate Variable in a Stochastic Renewable Resource Model

In this paper we discuss the costate variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the costate variable in deterministic control models has been discussed extensively in the literature. See, for example, Lyon (1999), Clark (1990, pp. 102-107), and Arrow and Kurz (1970, pp. 35-37); however, there is little discussion of this variable for stochastic models, even though the costate variable has similar roles in the two models. In both models the costate variable is a shadow value of the associated state variable, and as such has the role of rationing the use of the state variable. In addition, as has been shown in Lyon (1999), in natural resource problems the costate variable can be partitioned into a scarcity effect and a cost effect. We show that this same partitioning can be done in the stochastic renewable resource problem. We discuss and contrast the similarities and differences in these concepts for deterministic and stochastic models. In addition, we present a numerical example to help solidity the results

Addressing diarrhea prevalence in the West African Middle Belt: social and geographic dimensions in a case study for Benin

<p>Abstract</p> <p>Background</p> <p>In West Africa, the Northern Sahelian zone and the coastal areas are densely populated but the Middle Belt in between is in general sparsely settled. Predictions of climate change foresee more frequent drought in the north and more frequent flooding in the coastal areas, while conditions in the Middle Belt will remain moderate. Consequently, the Middle Belt might become a major area for immigration but there may be constraining factors as well, particularly with respect to water availability. As a case study, the paper looks into the capacity of the Middle Belt zone of Benin, known as the Oueme River Basin (ORB), to reduce diarrhea prevalence. In Benin it links to the Millennium Development Goals on child mortality and environmental sustainability that are currently farthest from realization. However, diarrhea prevalence is only in part due to lack of availability of drinking water from a safe source. Social factors such as hygienic practices and poor sanitation are also at play. Furthermore, we consider these factors to possess the properties of a local public good that suffers from under provision and requires collective action, as individual actions to prevent illness are bound to fail as long as others free ride.</p> <p>Methods</p> <p>Combining data from the Demographic Health Survey with various spatial data sets for Benin, we apply mixed effect logit regression to arrive at a spatially explicit assessment of geographical and social determinants of diarrhea prevalence. Starting from an analysis of these factors separately at national level, we identify relevant proxies at household level, estimate a function with geo-referenced independent variables and apply it to evaluate the costs and impacts of improving access to good water in the basin.</p> <p>Results</p> <p>First, the study confirms the well established stylized fact on the causes of diarrhea that a household with access to clean water and with good hygienic practices will, irrespective of other conditions, not suffer diarrhea very often. Second, our endogeneity tests show that joint estimation performs better than an instrumental variable regression. Third, our model is stable with respect to its functional form, as competing specifications could not achieve better performance in overall likelihood or significance of parameters. Fourth, it finds that the richer and better educated segments of the population suffer much less from the disease and apparently can secure safe water for their households, irrespective of where they live. Fifth, regarding geographical causes, it indicates that diarrhea prevalence varies with groundwater availability and quality across Benin. Finally, our assessment of costs and benefits reveals that improving physical access to safe water is not expensive but can only marginally improve the overall health situation of the basin, unless the necessary complementary measures are taken in the social sphere.</p> <p>Conclusion</p> <p>The ORB provides adequate water resources to accommodate future settlers but it lacks appropriate infrastructure to deliver safe water to households. Moreover, hygienic practices are often deficient. Therefore, a multifaceted approach is needed that acknowledges the public good aspects of health situation and consequently combines collective action with investments into water sources with improved management of public wells and further educational efforts to change hygienic practices.</p

On Capturing Human Agency and Methodological Interdisciplinarity in socio-hydrology Research

Socio-hydrology has expanded and been effective in exposing the hydrological community to ideas and approaches from other scientific disciplines, and social sciences in particular. Yet it still has much to explore regarding how to capture human agency and how to combine different methods and disciplinary views from both the hydrological and the social sciences to develop knowledge. A useful starting ground is noting that the complexity of human–water relations is due to interactions not only across spatial and temporal scales but also across different organizational levels of social systems. This calls for consideration of another analytical scale, the human organizational scale, and interdisciplinarity in study methods. Based on the papers published in this journal’s Special Issue Advancing Socio-hydrology over 2019–2022, this paper illuminates how the understanding of coupled human–water systems can be strengthened by capturing the multi-level nature of human decision making and by applying an interdisciplinary multi-method approach

Emerging Themes and Future Directions of Multi-Sector Nexus Research and Implementation

Water, energy, and food are all essential components of human societies. Collectively, their respective resource systems are interconnected in what is called the “nexus”. There is growing consensus that a holistic understanding of the interdependencies and trade-offs between these sectors and other related systems is critical to solving many of the global challenges they present. While nexus research has grown exponentially since 2011, there is no unified, overarching approach, and the implementation of concepts remains hampered by the lack of clear case studies. Here, we present the results of a collaborative thought exercise involving 75 scientists and summarize them into 10 key recommendations covering: the most critical nexus issues of today, emerging themes, and where future efforts should be directed. We conclude that a nexus community of practice to promote open communication among researchers, to maintain and share standardized datasets, and to develop applied case studies will facilitate transparent comparisons of models and encourage the adoption of nexus approaches in practice

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focussed on process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come

Emerging Themes and Future Directions of Multi-Sector Nexus Research and Implementation

Water, energy, and food are all essential components of human societies. Collectively, their respective resource systems are interconnected in what is called the “nexus”. There is growing consensus that a holistic understanding of the interdependencies and trade-offs between these sectors and other related systems is critical to solving many of the global challenges they present. While nexus research has grown exponentially since 2011, there is no unified, overarching approach, and the implementation of concepts remains hampered by the lack of clear case studies. Here, we present the results of a collaborative thought exercise involving 75 scientists and summarize them into 10 key recommendations covering: the most critical nexus issues of today, emerging themes, and where future efforts should be directed. We conclude that a nexus community of practice to promote open communication among researchers, to maintain and share standardized datasets, and to develop applied case studies will facilitate transparent comparisons of models and encourage the adoption of nexus approaches in practice

Hydro-social metabolism: data underlying observed scaling relationship between birth rate and regional water use

Data underlying Figures 1 to 6 in "Hydro-social Metabolism: Scaling of birth rate with regional water use.

Probabilistic Wrapper Approach to Predictor Subset Selection in Local Learning Algorithm

Local learning algorithms are plagued with the curse of dimensionality. Locality is introduced based on the definition of “similarity”, which is distance based. With respect to model output, the presence of marginally relevant or irrelevant input dimensions significantly influences the performance of various local learning algorithms. Furthermore, a high dimensionality of inputs also influence an algorithm’s generalization ability. A theoretically sound wrapper approach to dimensionality reduction (feature subset selection) is therefore introduced and applied to a water resource management problem involving the prediction of daily canal diversions. The general argument in favor of wrapper methods is that using the basic induction algorithm (learning algorithm) in feature subset selection incorporates the induction bias. However, the major disadvantage of wrapper methods is that it is time consuming as the evaluation of various possible subsets of features in wrapper methods is generally done by cross validation. Incorporating locally weighted cross validation error (to retain the local nature of feature subset selection) as an evaluation measure, a fast method for cross-validation is introduced (“Local Schemata”). This evaluation measure is “estimated” in the sense that it measures the “utility” (or usefulness) over finite sample data. Since the environment is always uncertain, there is always a discrepancy between the “estimated” utility and the actual (“true”) utility. Moreover since the estimation of utilities is based on finite number of samples, one would expect any algorithm to return only approximately correct feature subset. Thus “Local Schemata” is modified further such that a feature subset is selected that is epsilon close to the true optimal (underlying but unknown) with some probability of error. This epsilon-optimal feature subset could be visualized as one of the epsilon-equivalent best feature subsets and the probability of error provides an upper bound on the error that we make in concluding that

Fixed endpoint optimal control

This note offers a new proof of the necessary conditions for fixed endpoint optimal control. Our approach simplifies the conventional derivation of the necessary conditions by using a transversality condition to ensure feasibility of modifications to the optimal path. We further prove that this transversality condition holds automatically at the optimum and can therefore be ignored in the statement of the necessary conditions. Copyright Springer-Verlag Berlin/Heidelberg 2005Fixed endpoint, Optimal control, Necessary conditions.,