the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Jun 2026
Structural limits and ill-posedness of soil water storage balance method for diagnosing root water uptake
Abstract. Depth-resolved root water uptake (RWU) can be inferred through soil water storage balance (SWSB) from soil water content observations, yet their fundamental identifiability and robustness remain unclear. Using controlled numerical experiments with prescribed contrasting RWU profiles, we systematically evaluate the performance of SWSB-based RWU inversion under varying spatiotemporal aggregation and upper boundary conditions. Our results show that while accurate estimates can be obtained under idealized, error-free datasets, even modest uncertainties in soil hydraulic parameters (±10 %) and soil water content measurements (±1 %) lead to error amplification in RWU estimates by around 60-fold. Furthermore, the sensitivity analysis shows that SWSB-based RWU inversion is highly sensitive to soil water content, as it directly influences storage change (ΔV) and regulates the relationships between soil water content (θ) and pressure head (h), as well as saturated (ks) and unsaturated (k) hydraulic conductivities. These findings highlight SWSB-based RWU inversion is fundamentally ill-posed and becomes non-identifiable under realistic uncertainties. Overall, this study delineates the conditions under which SWSB-based RWU inversion can be reliably applied and emphasizes the need for additional independent constraints.
- Preprint
(4231 KB) - Metadata XML
- BibTeX
- EndNote
Status: final response (author comments only)
-
RC1: 'Comment on egusphere-2026-2437', Anonymous Referee #1, 12 Aug 2026
- AC1: 'Reply on RC1', Han Fu, 26 Sep 2026
-
RC2: 'Comment on egusphere-2026-2437', Anonymous Referee #2, 19 Sep 2026
Summary:
Fu et al. aimed to identify the conditions under which water balance-based methods of estimating root water uptake become mechanistically and numerically imprecise. The team used a series of controlled numerical modeling experiments whereby a physically based model, MOIST, generated various soil eco-hydrological profile conditions (wet vs dry; deep vs shallow roots) which were used to compare performance of water-balance derived trapezoidal flux estimation from direct MOIST outputs. The results indicate that periods with repeated, ample precipitation supply may obscure the root water uptake signal in the water balance approach and that error propagation is far greater, particularly with increasing soil layer differentiation. The authors maintain that these tests provide a reliable delineation of what conditions make the soil water storage balance approach (SWSB) ill-posed.
General Comment
I think that both the aim and the results of this study are relevant, interesting, and its execution relatively straightforward. The manuscript is also very well-articulated, generally. It also does not appear, by my read, to have any fundamental flaws in design or execution, but it could benefit from some basic clarifications in description and delivery—along with some minor technical points shown below. Overall it was an enjoyable read, and will no doubt be a useful study to those who used relatively practical but simplified SWSB-type approaches in the field.
Main points:
MOIST description: The paper could use a little more emphasis and effort in describing the key properties of RWU and drainage quantification methodology that make it robust to the experimental constraints composed here. See specific comments.
More depiction of the soil profile dynamics for the model cases (I am pasting a “specific comment” here which captures the point): “Lines 436-437; "dry periods" (here and throughout): I would strongly advise giving more detail exactly how dry this scenario was (water content range; potential etc.--ideally in a figure) to increase transferability and make sure that "dry" is not equated with "minimal precipitation."
Specific Comments
-Line 55; "inversion": "inverse modeling" is probably a more universal term here.
- Line 55; "differencing operations": not clear what is meant
- Lines 55-57: It's not clear exactly, as written, why these approaches amplify uncertainty--particularly in comparison to other listed methods
- Equation 8: Please list pressure and conductivity variables, explicitly
- Lines 126-127; small technical point:
1) you can certainly estimate fluxes using various lysimeters, etc. if carefully oriented
2) the authors just described a way to infer these under discrete, deterministic calculations (maybe just be extra be specific in the meaning of "numerical" in this case)-- solving diff eq. etc.
- Line 159: "... benchmark fluxes obtained directly from MOIST"
The authors are really comparing the applicability of the water balance trapezoidal method vs MOIST derived drainage and RWU fluxes. The water balance method is nicely articulated in prose, but the MOIST model is essentially buried in citations until now. The authors should put a much greater emphasis on explicit methodology used to produce these fluxes in MOIST and any apparent biases or advantages.
- Line 167: "MOIST-derived RWU profiles" or similar, not “true”
- Line 204: Which observational data? Seems like the authors are providing observation error distributions, not observational forcing data per se.
- Lines 226-228: citation, please
- Line 237: grammatical correction "...the trapezoidal rule assumptions of..."
- Figure 2: "1D vs 7D" is not easily inferred as one day vs 7 day timesteps from the figure alone. Please specify in caption; the right half of figure with faceted plots will need larger labels (very hard to see); "panels a and b... c and d ..." are not specified in figure;
-Lines 274-280; greater success in deeper layers etc.: How is this reconciled with the 7 d integration in deeper root systems showing worse performance based on EDM (Figure 2)?
- Lines 338-342: interesting (and relevant)!
- Lines 436-437; "dry periods" (here and throughout): I would strongly advise giving more detail exactly how dry this scenario was (water content range; potential etc.--ideally in a figure) to increase transferability and make sure that "dry" is not equated with "minimal precipitation."
Citation: https://doi.org/10.5194/egusphere-2026-2437-RC2 - AC2: 'Reply on RC2', Han Fu, 26 Sep 2026
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 112 | 74 | 30 | 216 | 20 | 16 |
- HTML: 112
- PDF: 74
- XML: 30
- Total: 216
- BibTeX: 20
- EndNote: 16
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
The manuscript provides a systematic and rigorous evaluation of the soil water storage balance method for determining root water uptake (RWU) profiles. Using controlled numerical experiments and global sensitivity analysis, the authors demonstrate that while the method is conceptually appealing due to its simplicity, it is fundamentally ill-posed and lacks robustness. The manuscript is a valuable contribution to the field, offering an important critique of a common hydrological tool. I recommend acceptance after moderate revisions.
General comments
The manuscript is well structured and while the introduction, discussion and conclusion reads very well and clear, the presentation of materials and methods and results need improvement.
My biggest concern is that the forward simulation is not well motivated: It is not clear why the authors choose a forward time step of 1 day or 7 days. The types of soil-water-content sensors are not discussed in the manuscript, but the temporal resolution of most sensor types is between seconds and minutes, so there is no such restriction.
It would strengthen the manuscript to describe experimental set ups relevant for SWSB based RWU.
Section 2.1 should be carefully revised, and presentation of results should be improved (see detailed comments).
Detailed comments
Section 2.1: Please state the units of the relevant quantities explicitly.
L77: Please explain why this assumption is necessary. What would be the consequences if this assumption were not made?
Equation (2): Why is (Q) introduced here? It does not appear to be used subsequently.
Equations (3)–(4): There appears to be an error in these equations, possibly an extra Laplace symbol on the right-hand side. Please check the equations carefully.
L90: The term “drainage flux” may not be appropriate here, since depending on the bottom boundary condition, water could also move upward through the bottom boundary. “Bottom boundary flux” or simply (Q) may be more appropriate. In addition, using (D) for this flux is potentially confusing because (D) is commonly used to denote a diffusion or dispersion coefficient.
Equation (7): Both the cumulative flux and the flux itself are denoted by (D), which is confusing, particularly because they have different units. Please use different symbols for these quantities.
Equations (8)–(9): The variable (k) is not introduced. Please define it. Furthermore, when calculating an effective hydraulic conductivity for flow perpendicular to a sequence of layers, the harmonic mean should be used rather than the arithmetic mean.
Equations (14)–(15): Please explain how (R) can be calculated from measurements. In particular, if (D := D(\theta)), how is (\Delta V) obtained from the measured data?
L124: (D) is referred to here as “interlayer flux,” whereas it was previously described as a drainage flux. Please use consistent terminology throughout.
Figure 1: The red arrow indicating the right-to-left direction appears to be missing. Please check the figure.
Equation (17): Please state the units.
L179: Please rephrase this sentence. No analysis appears to be presented in Section 2.2.2, so the current wording is misleading.
Figure 2: Panels (c) and (d) appear to be superfluous, as their information could be conveyed adequately in the text. The remaining panels are currently too small to interpret easily. I recommend enlarging them and, if necessary, presenting the results over more than one figure.
L236: Is this a typo? Should the labels be 2j, 2p, 2v, and 2bb? More generally, I recommend organizing the subpanels in a more meaningful and intuitive order, potentially across more than one figure. The individual figures and subpanels should also be described in greater detail in the text so that the reader can understand the key findings without having to infer the intended comparison from the figure alone.