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Abstract. Vegetation indices based on satellite images, such as the normalized difference vegetation index (NDVI), have been used in countries like the USA, Canada and Spain for damaged pasture and forage insurance over the last few years. This type of agricultural insurance is called satellite-index-based insurance (SIBI). In SIBI, the occurrence of damage is defined as normal distributions. In this work a pasture area at the north of the Community of Madrid (Spain) has been delimited by means of Moderate Resolution Imaging Spectroradiometer (MODIS) images. A statistical analysis of NDVI histograms was applied to seek for alternative distributions using the maximum likelihood method and χ2 test. The results show that the normal distribution is not the optimal representation and the generalized extreme value (GEV)
distribution presents a better fit through the year based on a quality
estimator. A comparison between normal and GEV is shown with respect to the
probability under a NDVI threshold value throughout the year. This suggests that
an a priori distribution should not be selected and a percentile methodology
should be used to define a NDVI damage threshold rather than the average and
standard deviation, typically of normal distributions. Highlights.
The GEV distribution provides better fit to the NDVI historical observations than the normal one.
Differences between normal and GEV distributions are higher during spring and autumn, which are transition periods in the precipitation regimen. NDVI damage threshold shows evident differences using normal and GEV distributions both covering the same probability (24.20 %). NDVI damage threshold values based on percentile calculation are proposed as an improvement in the index-based insurance in damaged pasture.

Index-based insurance (IBI) is a risk transfer tool that is widely used in low-incomes countries, especially catered to smallholder farmers. A good correlation between the selected index (in this case Normalized Difference Vegetation Index -NDVI-) and the crop losses of the insured area is a key requirement for well-performing system. Usually, IBI application area is defined by political boundaries, despite that variation in soil, topography, and climate is more important. In this work, agro-ecological variability effects will be studied in the IBI context. The case study was the rice crop failure in Babahoyo canton (Ecuador), using NDVI as the crop damage indicator. In a previous study, zones of similar soil, topographic and climatic characteristics (AHZs) were defined using principal component analysis in Babahoyo canton. Two largest AHZs were found in this canton. They were f7 and f15, which account for 91% of the total rice crop area in Babahoyo. We sampled reflectance values of red, blue, near infra-red (NIR) and medium infra-red (MIR) bands over bare soil (1st of January) by observation points, within f7 and f15. The reflectance band values were used to study whether the difference between the two AHZs could be appreciated through remote sensing. Then, we did the same but for NDVI average of the rice crop cycle, i.e., 15th of January to 15th of May (NDVI_ave). It was done for confirming that the AHZs (f7 and f15) have an influence over rice crop development. The used product was MODIS imagery (2001?2017). We stratified the sampling through the AHZs, applying 30% density for ensuring the accuracy of the selected pixels. Statistically significant differences between the f7 and f15 zones were found in all the analysed reflectance bands and in NDVI_ave. This found supported the differences that the agro-ecological map pointed out in its database. At the same time, the NDVI_ave distribution for each AHZ presented a statistically significant difference of the accumulated probability below the threshold (0.4), ...

Climate change is on the policy agenda at the global level, with the aim of understanding and reducing its causes and to mitigate its consequences. In most of the countries and international organisms UNO, OECD, EC, etc … the efforts and debates have been directed to know the possible causes, to predict the future evolution of some variable conditioners, and trying to make studies to fight against the effects or to delay the negative evolution of such. Nevertheless, the elaboration of a global model was not boarded that can help to choose the best alternative between the feasible ones, to elaborate the strategies and to evaluate the costs. As in all natural, technological and social changes, the best-prepared countries will have the best bear and the more rapid recover. In all the geographic areas the alternative will not be the same one, but the model should help us to make the appropriated decision. It is essential to know those areas that are more sensitive to the negative effects of climate change, the parameters to take into account for its evaluation, and comprehensive plans to deal with it. The objective of this paper is to elaborate a mathematical model support of decisions, that will allow to develop and to evaluate alternatives of adaptation to the climatic change of different communities in Europe and Latin-America, mainly, in vulnerable areas to the climatic change, considering in them all the intervening factors. The models will take into consideration criteria of physical type (meteorological, edaphic, water resources), of use of the ground (agriculturist, forest, mining, industrial, urban, tourist, cattle dealer), economic (income, costs, benefits, infrastructures), social (population), politician (implementation, legislation), educative (Educational programs, diffusion), sanitary and environmental, at the present moment and the future.

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

At present, the water resources are a strategic element each time more necessary and limited becoming a source of conflicts. For that, it is fundamental to create an independent and competent entity with good reputation and social acceptation. This entity must be able to obtain, store and process all data dispersed in different entities creating a network for these purposes. Finally, it must be able to organize different branches between the government and the final users. Using one of the wellknown Multicriteria Decision Methods(MCDM) with several realistic alternatives and several criteria identified in expert seminars in Salta and Madrid, we have obtained hopeful results and more recently new modifications introduced have generated better results.

Abstract. Risk assessment constitutes the first part within the risk management framework and involves evaluating the importance of a risk, either quantitatively or qualitatively. Risk assessment consists of three steps, namely risk identification, risk estimation and risk evaluation. Nevertheless, the risk management framework also includes a fourth step, i.e., the need for feedback on all the risk assessment undertakings. However, there is a lack of such feedback, which constitutes a serious deficiency in the reduction of environmental hazards at the present time. Risk identification of local or regional hazards involves hazard quantification, event monitoring including early warning systems and statistical inference. Risk identification also involves the development of a database where historical hazard information and hazard effects are included. Similarly, risk estimation involves magnitude–frequency relationships and hazard economic costs. Furthermore, risk evaluation consists of the social consequences of the derived risk and involves cost-benefit analysis and community policy. The objective of this review paper is twofold. On the one hand, it is to address meteorological hazards and extremes within the risk management framework. Analysis results and case studies over Mediterranean ecosystems with emphasis on the wider area of Greece, in the eastern Mediterranean, are presented for each of the three steps of risk assessment for several environmental hazards. The results indicate that the risk management framework constitutes an integrated approach for environmental planning and decision-making. On the other hand, it sheds light on advances and current trends in the considered meteorological and environmental hazards and extreme events, such as tornadoes, waterspouts, hailstorms, heat waves, droughts, floods, heavy convective precipitation, landslides and wildfires, using recorded datasets, model simulations and innovative methodologies.