Simulating Marginal and Dependence Behaviour of Water Demand Processes at Any Fine Time Scale

Abstract

Uncertainty-aware design and management of urban water systems lies on the generation of synthetic series that should precisely reproduce the distributional and dependence properties of residential water demand process (i.e., significant deviation from Gaussianity, intermittent behaviour, high spatial and temporal variability and a variety of dependence structures) at various temporal and spatial scales of operational interest. This is of high importance since these properties govern the dynamics of the overall system, while prominent simulation methods, such as pulse-based schemes, address partially this issue by preserving part of the marginal behaviour of the process (e.g., low-order statistics) or neglecting the significant aspect of temporal dependence. In this work, we present a single stochastic modelling strategy, applicable at any fine time scale to explicitly preserve both the distributional and dependence properties of the process. The strategy builds upon the Nataf’s joint distribution model and particularly on the quantile mapping of an auxiliary Gaussian process, generated by a suitable linear stochastic model, to establish processes with the target marginal distribution and correlation structure. The three real-world case studies examined, reveal the efficiency (suitability) of the simulation strategy in terms of reproducing the variety of marginal and dependence properties encountered in water demand records from 1-min up to 1-h.

A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes

“…Therefore, based on the scientific boost, the climacogram (and not the other two metrics) was found to be adequate for the identification and model building of a stochastic process. Since then, interest in the scale domain and the climacogram estimator has increased, and the climacogram has been implemented in education material [49], and has been used to identify the LTP behaviour in various scientific studies, such as 2D precipitation fields [50], multidimensional spatiotemporal domain [51], paleoclimatic temperature [52] and precipitation [53,54], Bayesian statistical models of rainfall and temperature [55], higher-order moments of skewness and kurtosis vs. scale in grid turbulence [26], annual precipitation [56], water demand [57], daily river flows [58], precipitation and temperature for a bivariate drought analysis [59], wind and solar energy [60], water-energy nexus [61], solar radiation [62], wave height and period [63], daily streamflow [64], and monthly temperature and precipitation ( [65,66]), annual streamflow ( [30,66]), ecosystem variability [67], 2D rock formations [68], urban streamflows [69], global temperature and wind of resolution spanning 10 orders of magnitude from ms to several decades [70], disaggregation schemes from daily to hourly rainfall and runoff [71], hourly wind and daily precipitation [26], fine scale precipitation [3,22,[72][73][74][75][76][77][78], fine scale wind …”

Bottom-Up Generation of Peak Demand Scenarios in Water Distribution Networks

“…Other kinds of approaches can be used when larger time steps are considered. If the focus is to reproduce nodal demand time series with values aggregated at temporal step ranging from minutes to hours, methodologies such as those proposed in the works [7][8][9][10] can be used. The output of these methodologies can be used as an input to the extended period simulation, which represents the behavior of the WDN as a succession of steady states [5].…”

“…Furthermore, Creaco et al [10] also presented a procedure to reconcile the generated demand time series with demand pulses generated at fine time step, thus enabling reconstruction of demand at any time step. The methodology of Kossieris et al [9] is based on the mixed-type distribution for the representation of demand time series, while yielding similar performance to the methodology of Creaco et al [10].…”

Some comments and suggestions

“…As in the case of random variables and multivariate distributions, also in this case copulas offer the necessary flexibility for modelling/simulation of non-Gaussian processes. For instance see the works of Lee and Salas (2011), Chen et al (2015) and Hao and Singh (2013), as well as recent approaches in hydrological domain, based on the Gaussian copula (a construct related with the Nataf's joint distribution; see Lebrun and Dutfoy (2009), and references below for a discussion in a hydrological context) that allow the parsimonious simulation of multivariate stationary and cyclostationary processes with any marginal distribution and correlation structure (Kossieris et al, 2019;Tsoukalas et al, 2020Tsoukalas et al, , 2018aTsoukalas et al, , 2018b -also in a multi-scale/disaggregation context (Tsoukalas et al, 2019).…”