National water, food, and trade modeling framework: The case of Egypt.

This paper introduces a modeling framework for the analysis of real and virtual water flows at national scale. The framework has two components: (1) a national water model that simulates agricultural, industrial and municipal water uses, and available water and land resources; and (2) an international virtual water trade model that captures national virtual water exports and imports related to trade in crops and animal products. This National Water, Food & Trade (NWFT) modeling framework is applied to Egypt, a water-poor country and the world's largest importer of wheat. Egypt's food and water gaps and the country's food (virtual water) imports are estimated over a baseline period (1986-2013) and projected up to 2050 based on four scenarios. Egypt's food and water gaps are growing rapidly as a result of steep population growth and limited water resources. The NWFT modeling framework shows the nexus of the population dynamics, water uses for different sectors, and their compounding effects on Egypt's food gap and water self-sufficiency. The sensitivity analysis reveals that for solving Egypt's water and food problem non-water-based solutions like educational, health, and awareness programs aimed at lowering population growth will be an essential addition to the traditional water resources development solution. Both the national and the global models project similar trends of Egypt's food gap. The NWFT modeling framework can be easily adapted to other nations and regions.

Test to determine the Markov order of a time series.

The Markov order of a time series is an important measure of the "memory" of a process, and its knowledge is fundamental for the correct simulation of the characteristics of the process. For this reason, several techniques have been proposed in the past for its estimation. However, most of this methods are rather complex, and often can be applied only in the case of Markov chains. Here we propose a simple and robust test to evaluate the Markov order of a time series. Only the first-order moment of the conditional probability density function characterizing the process is used to evaluate the memory of the process itself. This measure is called the "expected value Markov (EVM) order." We show that there is good agreement between the EVM order and the known Markov order of some synthetic time series.

Mean first passage times of processes driven by white shot noise.

We consider mean first passage times in systems driven by white shot noise with exponentially distributed jump heights. Simple interpretable results are obtained and the linkage between those results and the steady-state probability density function of the process is presented. The virtual waiting-time or Takács process (constant losses) and the shot noise process with linear losses are analyzed in depth, along with a more complex process with useful implications for the modeling of the soil moisture dynamics in hydrology.