## 2 Materials and Methods
### Assumptions
In accordance with the forecasted changes in net rainfall (\(\pm\) %), the future mean values of hazard-relevant streamflow, \(Q_{average}\) (annual), \(Q_{min,average}\) (dry period), and \(Q_{max,average}\) (wet period) are determined as follows:  
\[Q^{x}\]  
_average,future_ = ( \[(\pm\) %)/100+1)-Q^{x}\]  
_average,historic_ (3)  
The obtained values were used to calculate the \(k^{x}\)_future_ coefficient using the correlation function \(k^{x}\)_future_ = _f_(Q^x_average,future_/\(Q_{average,future}\)). \(Q^{x}\)_average,future_ was multiplied by \(k^{x}\)_future_ to determine \(D^{x}\)_future_, ea. range of \(Q^{x}\)_future_ and the difference between the highest and lowestvalues that define the level of variability and risk for engineered water systems (water abstraction facility):  
\[k^{x}_{future}\cdot Q^{x}_{average\_future}=D^{x}_{future} \tag{4}\]  
The historical and calculated variables were compared and analyzed to gain insight into the level of possible changes in flows and risk. The required FOS sizes were considered for \(Q_{max}\) (flood hazard), \(Q_{min}\) (drought hazard), and \(Q_{average}\) (demand risk). The selected FOS\({}^{\mathsf{X}}\) was multiplied by \(D^{x}_{future}\) to determine the project operational range (\(D^{x}_{design}\)); that is, the designed performance of the system \(D^{x}_{design}=FOS^{x}\cdot D^{x}_{future}\), and \(Q^{x}_{average\_future}\) to determine the hazard-relevant streamflow for future climate conditions to be used to design the abstraction facility; \(Q^{x}_{design}=FOS^{x}\cdot Q^{x}_{average\_future}\). The FOS\({}^{\mathsf{x}}\) or suitable marginal safety of infrastructure in future water resource systems is determined by expert judgment, considering the obtained values for \(Q^{x}_{average\_future}\), \(D^{x}_{future}\), and \(k^{x}_{future}\); characteristics of the applied climate change scenario (pessimistic, optimistic, etc. ); design period (usually 50 years); and vulnerability of the water abstraction facility. The expert considered several levels of FOS\({}^{\mathsf{x}}\), as well as resilience concepts, and consulted with stakeholders to reach a consensus on the necessary characteristics and capacity, as well as the cost of the water abstraction facility. This is a general concept of \"resilience by design.\" The proposed approach is straightforward, flexible, and understandable to engineers and stakeholders. This is similar to the Factor Analysis method, in which a set of interdependent relationships is examined to design water infrastructure facilities for unknown or untrusted future climate conditions. The factors used were concepts that described observed phenomena. Water security issues arise when the conditions of \"deep\" uncertainty are identified, but poorly described. This is a much broader and more complex natural and socioeconomic problem that includes issues and concepts of risk and uncertainty related to capacity expansion, vulnerability to hazards, development needs, and sustainability [1]. The tools presented in this study aim to facilitate the technical/engineering assessment of water supply sustainability within natural and socioeconomic system relationships and water security issues. In a broader analysis of the problem, it is necessary to consider sensitive system variables along with stakeholders to strengthen water security during existing and uncertain future periods [20]. According to [PERSON] and [PERSON] (2020), knowledge about sensitive system variables is crucial to understanding the effects of different visions and, hence, action within the human-water system to cover the whole range of social responses. The human-water interaction in modern society is complex. Therefore, the application of methods and tools to strengthen resilience should be adapted to the level, time, and features of the specific problem being addressed. Flexibility and wider coverage that respects local and global issues related to human-water interactions and sustainability are needed, and this is not the topic of this work.