There has been a series of papers (e.g., Palmer and Characklis, 2009; Zeff et al., 2014; Herman et al., 2014) suggesting the use of an approximate risk-of-failure (ROF) metric, as opposed to the more conventional days of supply remaining, for utilities’ managers to decide when to enact not only water use restrictions, but also water transfers between utilities. This approach was expanded to decisions about the best time and in which new infrastructure project a utility should invest (Zeff at al., 2016), as opposed to setting fixed times in the future for either construction or options evaluation. What all these papers have in common is that drought mitigation and infrastructure expansion decisions are triggered when the values of the short and long-term ROFs, respectively, for a given utility exceeds those of pre-set triggers.
For example, the figure below shows that as streamflows (black line, subplot “a”) get lower while demands are maintained (subplot “b”), the combined storage levels of the fictitious utility starts to drop around the month of April (subplot “c”), increasing the utility’s short-term ROF (subplot “d”) until it finally triggers transfers and restrictions (subplot “e”). Despite the triggered restriction and transfers, the utility’s combined storage levels crossed the dashed line in subplot “c”, which denotes the fail criteria (i.e. combined storage levels dropping below 20% of the total capacity).
It is beyond the scope of this post to go into the details presented in all of these papers, but even after reading them the readers may be wondering how exactly ROFs are calculated. In this post, I’ll try to show in a graphical and concise manner how short-term ROFs are calculated.
In order to calculate a utility’s ROF for week m, we would run 50 independent simulations (henceforth called ROF simulations) all departing from the system conditions (reservoir storage levels, demand probability density function, etc.) observed in week m, and each using one of 50 years of streamflows time series recorded immediately prior to week m. The utility’s ROF is then calculated as the number of ROF simulations in which the combined storage level of that utility dropped below 20% of the total capacity in at least one week, divided by the number of ROF simulations ran (50). An animation of the process can be seen below.
For example, for a water utility who started using ROF triggers on 01/01/2017, this week’s short-term ROF (02/13/2017, or week m=7) would be calculated using the recorded streamflows from weeks 6 through -47 (assuming here a year of 52 weeks, for simplicity) for ROF simulation 1, the streamflows from weeks -48 to -99 for ROF simulation 2, and so on until we reach 50 simulations. However, if the utility is running an optimization or scenario evaluation and wants to calculate the ROF in week 16 (04/10/2017) of a system simulation, ROF simulation 1 would use 10 weeks of synthetically generated streamflows (16 to 7) and 42 weeks of historical records (weeks 6 to -45), simulation 2 would use records for weeks -46 to -97, and so on, as in a 50 years moving window.
In another blog post, I will show how to calculate the long-term ROF and the reasoning behind it.
Herman, J. D., H. B. Zeff, P. M. Reed, and G. W. Characklis (2014), Beyond optimality: Multistakeholder robustness tradeoffs for regional water portfolio planning under deep uncertainty, Water Resour. Res., 50, 7692–7713, doi:10.1002/2014WR015338.
Palmer, R., and G. W. Characklis (2009), Reducing the costs of meeting regional water demand through risk-based transfer agreements, J. Environ. Manage., 90(5), 1703–1714.
Zeff, H. B., J. R. Kasprzyk, J. D. Herman, P. M. Reed, and G. W. Characklis (2014), Navigating financial and supply reliability tradeoffs in regional drought management portfolios, Water Resour. Res., 50, 4906–4923, doi:10.1002/2013WR015126.
Zeff, H. B., J. D. Herman, P. M. Reed, and G. W. Characklis (2016), Cooperative drought adaptation: Integrating infrastructure development, conservation, and water transfers into adaptive policy pathways, Water Resour. Res., 52, 7327–7346, doi:10.1002/2016WR018771.