Abstract
The challenging task of generating a synthetic time series at finer temporal scales than the observed data, embeds the reconstruction of a number of essential statistical quantities at the desirable (i.e., lower) scale of interest. This paper introduces a parsimonious and general framework for the downscaling of statistical quantities based solely on available information at coarser time scales. The methodology is based on three key elements: (a) the analysis of statistics’ behaviour across multiple temporal scales; (b) the use of parametric functions to model this behaviour; and (c) the exploitation of extrapolation capabilities of the functions to downscale the associated statistical quantities at finer scales. Herein, we demonstrate the methodology using residential water demand records and focus on the downscaling of the following key quantities: variance, L-variation, L-skewness and probability of zero value (no demand; intermittency), which are typically used to parameterise a stochastic simulation model. Specifically, we downscale the above statistics down to a 1 min scale, assuming two scenarios of initial data resolution, i.e., 5 and 10 min. The evaluation of the methodology on several cases indicates that the four statistics can be well reconstructed. Going one step further, we place the downscaling methodology in a more integrated modelling framework for a cost-effective enhancement of fine-resolution records with synthetic ones, embracing the current limited availability of fine-resolution water demand measurements.
Highlights
Risk-aware analysis and modelling of water systems typically involve stochastic simulation schemes to generate statistically consistent synthetic scenarios for the variables and processes of interest
Another characteristic example of limited availability of records is met at the domain of residential water demand, which is a key element of urban water systems and, at the same time, one of the most influential sources of uncertainty, due to its high spatio-temporal variability across all scales
The framework can be applied for any statistical quantity, here we focus on the necessary elements to set up typical stochastic simulation models, e.g., pulse-based and models that describe directly the discrete-time process, such as the Nataf-based models
Summary
Risk-aware analysis and modelling of water systems typically involve stochastic simulation schemes to generate statistically consistent synthetic scenarios for the variables and processes of interest. Water 2021, 13, 3429 methodology, and we discuss how we can take advantage of such a development to enhance the availability of fine-resolution records which remain limited both in terms of length and spatial coverage In this context, we place the proposed downscaling methodology in a more integrated modelling framework for the enhancement of water demand records at fine time scales (e.g., 1 min), going beyond the description of key statistical quantities of this non-physical process at multiple levels of aggregation (e.g., [34,35]). The paper is structured as follows: Section 2 formalizes the Statistics’ Downscaling problem, introduces the key concepts and the downscaling methodological framework, and presents candidate parametric functions/models suitable to describe, in a multi-scale context, key statistical quantities typically involved in stochastic simulation schemes (in particular: the variance, probability of zero value, L-variation and L-skewness). The description and mathematical expressions of the two models are given in the two sections
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
