TY - JOUR
T1 - Sizing a rainwater harvesting cistern by minimizing costs
AU - Pelak, Norman
AU - Porporato, Amilcare
N1 - Funding Information:
We acknowledge the financial support from National Science Foundation ( DGE-1068871 , NSF-EAR-0838301 , NSF-EAR-1331846 , and NSF-EAR-1316258 ) and Duke Wireless Intelligent Sensor Networks (WISeNet) Integrative Graduate Education and Research Training (IGERT) program, and by the US Department of Defense through the NDSEG Fellowship program.
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - Rainwater harvesting (RWH) has the potential to reduce water-related costs by providing an alternate source of water, in addition to relieving pressure on public water sources and reducing stormwater runoff. Existing methods for determining the optimal size of the cistern component of a RWH system have various drawbacks, such as specificity to a particular region, dependence on numerical optimization, and/or failure to consider the costs of the system. In this paper a formulation is developed for the optimal cistern volume which incorporates the fixed and distributed costs of a RWH system while also taking into account the random nature of the depth and timing of rainfall, with a focus on RWH to supply domestic, nonpotable uses. With rainfall inputs modeled as a marked Poisson process, and by comparing the costs associated with building a cistern with the costs of externally supplied water, an expression for the optimal cistern volume is found which minimizes the water-related costs. The volume is a function of the roof area, water use rate, climate parameters, and costs of the cistern and of the external water source. This analytically tractable expression makes clear the dependence of the optimal volume on the input parameters. An analysis of the rainfall partitioning also characterizes the efficiency of a particular RWH system configuration and its potential for runoff reduction. The results are compared to the RWH system at the Duke Smart Home in Durham, NC, USA to show how the method could be used in practice.
AB - Rainwater harvesting (RWH) has the potential to reduce water-related costs by providing an alternate source of water, in addition to relieving pressure on public water sources and reducing stormwater runoff. Existing methods for determining the optimal size of the cistern component of a RWH system have various drawbacks, such as specificity to a particular region, dependence on numerical optimization, and/or failure to consider the costs of the system. In this paper a formulation is developed for the optimal cistern volume which incorporates the fixed and distributed costs of a RWH system while also taking into account the random nature of the depth and timing of rainfall, with a focus on RWH to supply domestic, nonpotable uses. With rainfall inputs modeled as a marked Poisson process, and by comparing the costs associated with building a cistern with the costs of externally supplied water, an expression for the optimal cistern volume is found which minimizes the water-related costs. The volume is a function of the roof area, water use rate, climate parameters, and costs of the cistern and of the external water source. This analytically tractable expression makes clear the dependence of the optimal volume on the input parameters. An analysis of the rainfall partitioning also characterizes the efficiency of a particular RWH system configuration and its potential for runoff reduction. The results are compared to the RWH system at the Duke Smart Home in Durham, NC, USA to show how the method could be used in practice.
KW - Cost minimization
KW - Optimal size
KW - Rainwater harvesting
KW - Sustainable water use
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U2 - 10.1016/j.jhydrol.2016.08.036
DO - 10.1016/j.jhydrol.2016.08.036
M3 - Article
AN - SCOPUS:84992157096
SN - 0022-1694
VL - 541
SP - 1340
EP - 1347
JO - Journal of Hydrology
JF - Journal of Hydrology
ER -