Multi-scale stochastic analysis and modelling of residential water demand processes

P. Kossieris, Multi-scale stochastic analysis and modelling of residential water demand processes, PhD thesis, 350 pages, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, February 2020.



Residential water demand is a key element of urban water systems and, at the same time, one of the most influential sources of uncertainty due its high spatio-temporal variability and random nature. Embracing and incorporating uncertainty in the modelling of urban water systems is of high-importance for their uncertainty-aware planning, management and performance evaluation. This is feasible by treating water demand as a stochastic process that is analysed on the basis of probabilistic and stochastic concepts. Such considerations allow, among others, the development of stochastic modelling and simulation methodologies that generate synthetic time series that can be employed as non-deterministic inputs to assess system responses under different load scenarios.

At the same time, technological innovations in Information and Communication Technologies provide new opportunities for the design, operation and management of urban water systems. A case in point is smart metering systems which provide the means to advance risk-based modelling of the urban water systems by delivering new streams of data that in turn pave the ground for a thorough analysis, modelling and simulation of water demand processes. With these new richer datasets at hand, much effort has been invested in the development of stochastic methodologies to generate synthetic water demand series at very fine temporal (i.e., down to 1 s) and spatial (i.e., at household or even water appliance level) scales. These synthetic series can be then aggregated temporally and/or spatially, following a bottom-up procedure, to construct the coarser-resolution synthetic demand series which are to be used as inputs in system models. This approach receives more and more attention due to the more realistic representation of the varying and uncertain character of the process at fine scales. It also poses a series of intriguing challenges which have been only partially addressed to date, thus opening up a promising domain for further research.

The peculiarities of water demand processes at fine scales, such as their non-Gaussian behaviour, the intermittent nature, the variety of temporal and spatial dependence structures and the various types of seasonality make its modelling and simulation a rather hard task. The problem is getting even more demanding considering that these peculiarities depend on the temporal and spatial scale of study, while applications require statistically and stochastically consistent synthetic series across a wide range of scales.

Further to the modelling challenges, another issue is the deployment of such methodologies, and hence the implementation of uncertainty-aware study of the systems, on a broader scale that is currently hampered by the limited availability of fine-resolution demand observations. In this respect, the existing demand datasets have a key role to play as a valuable source of information through which we can extract concrete and possible transferable insights on the peculiarities of the processes. Despite its practical significance, the systematic and extensive analysis of such datasets, has currently received little attention. Although very high-resolution demand data is generally unavailable, longer series at coarser resolution (e.g., 5-min or 15-min) do exist and are becoming increasingly more available, while the metering devices with such sampling capabilities have potential for a wider deployment in the near future. Having said this, a major question that naturally arises is whether and how we can take advantage of these coarser measurements to enrich the information at finer scales (both in terms of data and characteristics of the process) addressing the issue of data unavailability in a cost-effective way.

Following from the above, the main objectives of this thesis are: a) The systematic analysis and modelling of the marginal and stochastic behaviour of water demand process on a multi-scale basis; b) The study of existing approaches as well as the development of novel methodologies for stochastic modelling and simulation of water demand process in single and multi-scale context; c) The development of methodologies to enhance the availability of information on water demand process (in terms of data and statistics) at fine time scales.

Specifically, in this thesis, we analyse, model, and simulate residential water demand as a discrete-time stochastic process and we treat the observed data as realisations of it. As a first step, the marginal and stochastic properties of the process are investigated, across a wide range of fine time scales, i.e., from 1 s up to 1 h. Various statistical and probabilistic concepts and tools (novel and classical) are introduced for the first time in the field of water demand. The analyses reveal the most suitable probability distribution models to describe the non-zero demand values, the scaling behaviour of the intermittent nature of the process (i.e., probability of no demand over temporal scales) and the scaling behaviour of its temporal auto-dependence structure (i.e., second-order properties across scales). In order to obtain concrete insights on these characteristics, we take advantage of two large datasets of demand measurements.

We examine the well-established pulse-based schemes, by comparing two non-cluster Poisson models along with two Bartlett-Lewis models, highlighting the flexibility of the clustering mechanism in terms of better reproducing the above described peculiarities of the discrete-time process, across different temporal scales. Additionally, we introduce in water demand modelling a novel modelling strategy that combines the widely-used class of linear stochastic models with the Nataf’s joint distribution model; thereby allowing the preservation of the entire marginal distribution and correlation structure of the processes. The problem of multi-scale modelling is examined and addressed via a scale- and model-free disaggregation framework where the generated synthetic series are fully consistent with (i.e., sum up exactly to) the coarser-level given data. The applicability and flexibility of this framework is demonstrated by employing both pulse- and Nataf-based schemes.

With these modular components at hand we then develop an integrated framework to enhance the availability of information at fine time scales. In this context, we also develop lower-scale extrapolation methodologies to provide estimations of the essential statistics (i.e., probability of no demand and second-order properties) for model’s setup at a finer scale, based on available coarser level information and scaling behaviour. The framework is demonstrated under different scenarios in terms of data availability, revealing the tradeoff between estimation accuracy and metering resolution.

Our works that reference this work:

1. I. Tsoukalas, P. Kossieris, and C. Makropoulos, Simulation of non-Gaussian correlated random variables, stochastic processes and random fields: Introducing the anySim R-Package for environmental applications and beyond, Water, 12 (6), 1645, doi:10.3390/w12061645, 2020.
2. P. Kossieris, I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Generic framework for downscaling statistical quantities at fine time-scales and its perspectives towards cost-effective enrichment of water demand records, Water, 13 (23), 3429, doi:10.3390/w13233429, 2021.
3. G. Moraitis, I. Tsoukalas, P. Kossieris, D. Nikolopoulos, G. Karavokiros, D. Kalogeras, and C. Makropoulos, Assessing cyber-physical threats under water demand uncertainty, Environmental Sciences Proceedings, 21 (1), 18, doi:10.3390/environsciproc2022021018, October 2022.

Tagged under: Stochastic disaggregation, Stochastics, Urban water