INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 32: 941–952 (2012) Published online 19 April 2011 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/joc.2317 Optimizing the location of weather monitoring stations using estimation uncertainty Ana M. T. Amorim, a Alexandre B. Gon¸ calves, b,c * Lu´ ıs Miguel Nunes d and Ant´ onio Jorge Sousa b,e a Instituto Superior T´ ecnico, Technical University of Lisbon, Lisbon, Portugal b Department of Civil Engineering, Architecture and Georesources, Instituto Superior T´ ecnico, Tech. Univ. of Lisbon, Lisbon, Portugal c ICIST – Institute for Structural Engineering, Territory and Construction, IST, Lisbon, Portugal d Faculty of Sciences and Technology, University of Algarve, Algarve, Portugal e CERENA – Centre for Natural Resources and the Environment, IST, Lisbon, Portugal ABSTRACT: In this article, we address the problem of planning a network of weather monitoring stations observing average air temperature (AAT). Assuming the network planning scenario as a location problem, an optimization model and an operative methodology are proposed. The model uses the geostatistical uncertainty of estimation and the indicator formalism to consider in the location process a variable demand surface, depending on the spatial arrangement of the stations. This surface is also used to express a spatial representativeness value for each element in the network. It is then possible to locate such a network using optimization techniques, such as the used methods of simulated annealing (SA) and construction heuristics. This new approach was applied in the optimization of the Portuguese network of weather stations monitoring the AAT variable. In this case study, scenarios of reduction in the number of stations were generated and analysed: the uncertainty of estimation was computed, interpreted and applied to model the varying demand surface that is used in the optimization process. Along with the determination of spatial representativeness value of individual stations, SA was used to detect redundancies on the existing network and establish the base for its expansion. Using a greedy algorithm, a new network for monitoring average temperature in the selected study area is proposed and its effectiveness is compared with the current distribution of stations. For this proposed network distribution maps of the uncertainty of estimation and the temperature distribution were created. Copyright  2011 Royal Meteorological Society KEY WORDS geostatistical modelling; optimization of weather monitoring networks; simulated annealing; greedy algorithm; air temperature Received 21 April 2010; Revised 23 December 2010; Accepted 10 February 2011 1. Introduction 1.1. Weather monitoring planning as a location problem Planning a network of monitoring stations is a topic that has attracted the attention of planners and researchers, as the advantages of proper planning and management of these facilities translate into both economic and sci- entific benefits. Two concurrent but incompatible main goals are identifiable in any planning action of such net- works: the economic aspect favours a network with few stations, whereas an efficient network able to provide a good/accurate estimate of an observed variable is likely to require more stations. A balance between these two requirements must therefore be found. Even when this number is established, another important question is to locate an ideal set of stations that guarantee the best pos- sible estimation results. These two questions, concerning the number and location of monitoring stations, have no immediate answer and can be difficult to resolve, given * Correspondence to: Alexandre B. Gon¸ calves, ICIST, Instituto Supe- rior T´ ecnico, Lisbon, Portugal. E-mail: alexg@civil.ist.utl.pt the large number of possibilities inherent to the combi- natorial problems of this type, named normative location problems. These problems, for which locational analysis deals with the formulation and solution methodologies, occur in many and varied contexts, addressing a number of questions such as the quantity, shape, size and internal relations with the facilities being located (Daskin, 1995; Church, 2002; Church and Murray, 2009). All normative location problems share some similarities, and diverse taxonomies have been suggested. These classifications explore the fundamental components that may be identi- fied (Brandeau and Chiu, 1989; Laurini and Thompson, 1992; Hamacher and Nickel, 1998), and some of them extend the scope to include more than point location problems. In general, location problems are formulated in an economic context where demand and offer relate each other in a specific space and the location decision concerns the placement of offer while optimizing the cost and service function, called the objective function (a function describing the optimization objective in the problem). The most common objective functions are used Copyright  2011 Royal Meteorological Society