Generic Framework for Downscaling Statistical Quantities at Fine Time-Scales and Its Perspectives towards Cost-Effective Enrichment of Water Demand Records

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.

Revisiting Flood Hazard Assessment Practices under a Hybrid Stochastic Simulation Framework

“…This implies that the cumulativ of each hyetograph, consisting of 96 partial depths, should equal the 24 h rainfa dictated by the corresponding combination of 𝑇 and 𝐶𝐿 . This challenging employed through (a) a novel downscaling approach for reconstructing the key s properties (i.e., mean, variance, probability dry, and autocorrelation) at the tim interest [26], (b) a multiscale distribution fitting approach, using the Burr distribution [27], and (c) a novel, recently introduced disaggregation approach disaggregate the 24 h maximum rainfall values to the temporal level of 15 m underline that the first two steps are required due to the lack of raw data at the resolution. If such data were available, only step (c) would be necessary, as statistical quantities at that timescale would be inferred from the historical samp We remark that, for each return period 𝑇 (10 in total) and confidence level in total), we generate 20 equally probable hyetograph realizations, aiming to acc the uncertainty in the time profile of rainfall at the temporal resolution of 15 min.…”

“…This implies that the cumulative rainfall of each hyetograph, consisting of 96 partial depths, should equal the 24 h rainfall value, dictated by the corresponding combination of T and CL. This challenging task is employed through (a) a novel downscaling approach for reconstructing the key statistical properties (i.e., mean, variance, probability dry, and autocorrelation) at the timescale of interest [26], (b) a multiscale distribution fitting approach, using the Burr type XII distribution [27], and (c) a novel, recently introduced disaggregation approach [26] to disaggregate the 24 h maximum rainfall values to the temporal level of 15 min. We underline that the first two steps are required due to the lack of raw data at the required resolution.…”