Preprints
https://doi.org/10.5194/hess-2023-161
https://doi.org/10.5194/hess-2023-161
01 Aug 2023
 | 01 Aug 2023
Status: this discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.

Technical note: Quantification of flow field variability using intrinsic random function theory

Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsian Lee

Abstract. Much of the stochastic analysis of flow field variability in heterogeneous aquifers in the literature assumes that the parameters in the associated stochastic flow equation are weakly (second order) stationary. On this basis, the spectral representation approach can then be used to quantify the variability of the flow fields given known covariance functions of the input parameters. However, the condition of second-order stationarity is rarely encountered in nature and is difficult to verify using the limited experimental data available. The purpose (or novelty) of this work, therefore, is to develop a new framework for modeling the variability of the flow fields that generalizes the stochastic theory that applies to stationary second-order random input parameters to intrinsic (nonstationary) random input parameters. In this work, the log hydraulic conductivity and log aquifer thickness are assumed to be intrinsic random functions for flow through heterogeneous confined aquifers of variable thickness. On this basis, semivariograms of depth-averaged hydraulic head and integrated specific discharge fields are developed to characterize the variability of flow fields. The application of the proposed stochastic theory to the case where the variability of a random input parameter can be characterized by a linear semivariogram model is provided.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsian Lee

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2023-161', Anonymous Referee #1, 16 Nov 2023
    • AC1: 'Reply on RC1', Chuen-Fa Ni, 07 Dec 2023
  • RC2: 'Comment on hess-2023-161', Anonymous Referee #2, 03 Dec 2023
    • AC2: 'Reply on RC2', Chuen-Fa Ni, 07 Dec 2023

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2023-161', Anonymous Referee #1, 16 Nov 2023
    • AC1: 'Reply on RC1', Chuen-Fa Ni, 07 Dec 2023
  • RC2: 'Comment on hess-2023-161', Anonymous Referee #2, 03 Dec 2023
    • AC2: 'Reply on RC2', Chuen-Fa Ni, 07 Dec 2023
Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsian Lee
Ching-Min Chang, Chuen-Fa Ni, Chi-Ping Lin, and I-Hsian Lee

Viewed

Total article views: 391 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
283 72 36 391 29 22
  • HTML: 283
  • PDF: 72
  • XML: 36
  • Total: 391
  • BibTeX: 29
  • EndNote: 22
Views and downloads (calculated since 01 Aug 2023)
Cumulative views and downloads (calculated since 01 Aug 2023)

Viewed (geographical distribution)

Total article views: 377 (including HTML, PDF, and XML) Thereof 377 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
1
 
 
 
 
Latest update: 13 Jul 2024
Download
Short summary
The stochastic theories developed here, namely the semivariograms of depth-averaged hydraulic head and integrated specific discharge used to characterize flow field variability, can address the effects of nonstationarity due to variations in parameters and output. The proposed stochastic theories generalize existing stochastic theory, which applies to second order stationary random input parameters, to nonstationary random input parameters.