the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note: Quantification of flow field variability using intrinsic random function theory
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.
- Preprint
(995 KB) - Metadata XML
- BibTeX
- EndNote
Status: closed
-
RC1: 'Comment on hess-2023-161', Anonymous Referee #1, 16 Nov 2023
This technical note provides a stochastic analysis of spatial variability in steady groundwater flow through a heterogeneous confined aquifer of variable thickness. The random log hydraulic conductivity and log thickness are assumed to be nonstationary intrinsic random functions. The article is well written, with clear objectives and development. Essentially, the authors calculate the semivariogram of the hydraulic head and the depth-hydraulic head for a linear and exponential random function model along the mean flow direction. After examining the manuscript I find that the article is small in scope given the large body of literatura in this area (even for a technical note). The authors state that there is no works on intrinsic random functions but I think this is not totally correct. For instance, Mizell et al (1992), WRR, provide a similar analysis. The authors should clearly evaluate the literatura on this topic to be able to clearly state the scientific contribution and the objective of the technical note. The work seems also limited in scope as the authors do not seem to investigate the anisotropy of the head variogram which seems to be restricted to the mean flow direction only. Also, no efforts to provide approximate solutions are given and in the end the head variogram seems to be calculated numerically. In summary, the manuscript seems correct and somehow interesting but requires more efforts in terms of literatura review and analysis of the results.
Citation: https://doi.org/10.5194/hess-2023-161-RC1 - AC1: 'Reply on RC1', Chuen-Fa Ni, 07 Dec 2023
-
RC2: 'Comment on hess-2023-161', Anonymous Referee #2, 03 Dec 2023
This technical note provides a solution for flow field variability in the stochastic sense when the hydraulic parameters are not second order stationary, but rather can be seen as intrinsic random functions. The work develops all the equations for depth-averaged heads and flow mean and variogram. Non-stationarity is here given by variability in thickness, which is only one of the many possibilities to have such non-stationarity. As a Technical Note, everything is correct: equations, text, figures are balanced, and they provide exactly what they say.
I am not sure about the significance of this work, compared for example to another one by the same group of authors published just one year ago: Stochastic Environmental Research and Risk Assessment (2022) 36:2503–2518 https://doi.org/10.1007/s00477-021-02125-7, where the authors write specifically that they do the following: “A spectrally based perturbation approach is used to arrive at the general results for the statistics of the flow fields in the Fourier domain, such as the variance of the depth-averaged head, and the mean and variance of integrated discharge”. So, the work is indeed different, but I am not sure about the significance of this additional step in the integration.
Citation: https://doi.org/10.5194/hess-2023-161-RC2 - AC2: 'Reply on RC2', Chuen-Fa Ni, 07 Dec 2023
Status: closed
-
RC1: 'Comment on hess-2023-161', Anonymous Referee #1, 16 Nov 2023
This technical note provides a stochastic analysis of spatial variability in steady groundwater flow through a heterogeneous confined aquifer of variable thickness. The random log hydraulic conductivity and log thickness are assumed to be nonstationary intrinsic random functions. The article is well written, with clear objectives and development. Essentially, the authors calculate the semivariogram of the hydraulic head and the depth-hydraulic head for a linear and exponential random function model along the mean flow direction. After examining the manuscript I find that the article is small in scope given the large body of literatura in this area (even for a technical note). The authors state that there is no works on intrinsic random functions but I think this is not totally correct. For instance, Mizell et al (1992), WRR, provide a similar analysis. The authors should clearly evaluate the literatura on this topic to be able to clearly state the scientific contribution and the objective of the technical note. The work seems also limited in scope as the authors do not seem to investigate the anisotropy of the head variogram which seems to be restricted to the mean flow direction only. Also, no efforts to provide approximate solutions are given and in the end the head variogram seems to be calculated numerically. In summary, the manuscript seems correct and somehow interesting but requires more efforts in terms of literatura review and analysis of the results.
Citation: https://doi.org/10.5194/hess-2023-161-RC1 - AC1: 'Reply on RC1', Chuen-Fa Ni, 07 Dec 2023
-
RC2: 'Comment on hess-2023-161', Anonymous Referee #2, 03 Dec 2023
This technical note provides a solution for flow field variability in the stochastic sense when the hydraulic parameters are not second order stationary, but rather can be seen as intrinsic random functions. The work develops all the equations for depth-averaged heads and flow mean and variogram. Non-stationarity is here given by variability in thickness, which is only one of the many possibilities to have such non-stationarity. As a Technical Note, everything is correct: equations, text, figures are balanced, and they provide exactly what they say.
I am not sure about the significance of this work, compared for example to another one by the same group of authors published just one year ago: Stochastic Environmental Research and Risk Assessment (2022) 36:2503–2518 https://doi.org/10.1007/s00477-021-02125-7, where the authors write specifically that they do the following: “A spectrally based perturbation approach is used to arrive at the general results for the statistics of the flow fields in the Fourier domain, such as the variance of the depth-averaged head, and the mean and variance of integrated discharge”. So, the work is indeed different, but I am not sure about the significance of this additional step in the integration.
Citation: https://doi.org/10.5194/hess-2023-161-RC2 - AC2: 'Reply on RC2', Chuen-Fa Ni, 07 Dec 2023
Viewed
HTML | XML | Total | BibTeX | EndNote | |
---|---|---|---|---|---|
310 | 83 | 39 | 432 | 31 | 24 |
- HTML: 310
- PDF: 83
- XML: 39
- Total: 432
- BibTeX: 31
- EndNote: 24
Viewed (geographical distribution)
Country | # | Views | % |
---|
Total: | 0 |
HTML: | 0 |
PDF: | 0 |
XML: | 0 |
- 1