Co-designing Indus Water-Energy-Land Futures

The Indus River Basin covers an area of around 1 million square kilometers and connects four countries: Afghanistan, China, India, and Pakistan. More than 300 million people depend to some extent on the basin’s water, yet a growing population, increasing food and energy demands, climate change, and shifting monsoon patterns are exerting increasing pressure. Under these pressures, a “business as usual” (BAU) approach is no longer sustainable, and decision makers and wider stakeholders are calling for more integrated and inclusive development pathways that are in line with achieving the UN Sustainable Development Goals. Here, we propose an integrated nexus modeling framework co-designed with regional stakeholders from the four riparian countries of the Indus River Basin and discuss challenges and opportunities for developing transformation pathways for the basin’s future

An approach for valid covariance estimation via the Fourier series

The use of kriging for construction of prediction or risk maps requires estimating the dependence structure of the random process, which can be addressed through the approximation of the covariance function. The nonparametric estimators used for the latter aim are not necessarily valid to solve the kriging system, since the positive-definiteness condition of the covariance estimator typically fails. The usage of a parametric covariance instead may be attractive at first because of its simplicity, although it may be affected by misspecification. An alternative is suggested in this paper to obtain a valid covariance from a nonparametric estimator through the Fourier series tool, which involves two issues: estimation of the Fourier coefficients and selection of the truncation point to determine the number of terms in the Fourier expansion. Numerical studies for simulated data have been conducted to illustrate the performance of this approach. In addition, an application to a real environmental data set is included, related to the presence of nitrate in groundwater in Beja district (Portugal), so that pollution maps of the region are generated by solving the kriging equations with the use of the Fourier series estimates of the covariance.Universidade do Minho. Centro de Investigação de Matemática (CMAT)Fundação para a Ciência e a Tecnologia (FCT