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arxiv: 2607.06182 · v1 · pith:KSLIU2PG · submitted 2026-07-07 · physics.flu-dyn

A systematic evaluation of the Richards equation for predicting soil moisture in Irish grasslands

S Kumar , S Mathias , E Ruelle , H Khan , O Fenton , K Shishkin , L O'Naraigh , GP Benham This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-08 14:01 UTCglm-5.2pith:KSLIU2PGrecord.jsonopen to challenge →

classification physics.flu-dyn
keywords Richards equationsoil moistureFeddes functionwaterlogged soilsgrasslandplant water uptakeanaerobic conditionsvan Genuchten
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The pith

Soil moisture model fixed for waterlogged grasslands

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The Richards equation is the standard physics-based model for water flow through unsaturated soil, but it systematically over-predicts soil moisture when soils stay near saturation for long periods. This paper pinpoints the cause: the Feddes plant water uptake function, a widely used sub-model that sets plant water extraction to zero once soil becomes waterlogged (anaerobic). While that assumption captures the suppression of transpiration, it ignores continued evaporation from near-saturated soil surfaces. The result is that the model traps water in the soil profile and fails to reproduce the modest but real seasonal drying that field observations show. The authors propose a minimal fix: set the Feddes anaerobic uptake parameter to a small non-zero value (0.01 instead of 0), allowing a trickle of residual water loss even under waterlogged conditions. They test this against three datasets from Irish grasslands spanning different soil types and observation periods, and show that the modified model reproduces observed seasonal moisture cycles across all three cases where the standard model fails. The paper also compares the Richards equation model against an established water-balance tool (MoSt), finding that the physics-based approach better captures integrated root-zone water stress, while the simpler model handles near-surface variability better. A secondary finding is that in seasonally drying (rather than waterlogged) soils, the dominant source of error shifts from the Feddes assumption to uncertainty in soil hydraulic parameters estimated from texture data.

Core claim

The central mechanism is the Feddes plant stress function's anaerobic uptake parameter, conventionally set to zero. Setting it to a small non-zero value (f_2a = 0.01) allows residual evaporation losses to persist when soil is near saturation, which corrects the systematic over-prediction of soil moisture in persistently wet grasslands. The paper demonstrates this across three case studies with distinct soil types and hydrological regimes, and further shows that the dominant source of model error depends on the prevailing conditions: the Feddes assumption controls performance in waterlogged soils, while hydraulic parameter uncertainty dominates in seasonally drying soils.

What carries the argument

The Richards equation (a partial differential equation for unsaturated flow), the van Genuchten-Mualem constitutive relationships for soil hydraulic properties, the Feddes plant water uptake function with its anaerobic threshold parameter f_2a, Monte Carlo simulation over pedotransfer-function-derived parameters, and comparison against both tensiometer and TDR field observations as well as the MoSt water-balance model.

If this is right

  • Any Richards-equation-based soil moisture model deployed in humid, poorly drained, or waterlogged environments may inherit the same systematic over-prediction bias if it uses the standard Feddes formulation with zero anaerobic uptake.
  • Grass-growth forecasting tools that depend on soil moisture inputs could produce more reliable predictions in wet climates by adopting the modified f_2a value, particularly for estimating water stress during prolonged wet periods.
  • The finding that error sources shift with hydrological regime suggests that model calibration strategies should be regime-aware: fixing the Feddes parameter in wet soils and improving hydraulic property estimation in drying soils.
  • The approach could be extended to other environments with persistent near-saturation, such as wetlands, rice paddies, or poorly drained agricultural soils in maritime climates beyond Ireland.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The optimal f_2a value of 0.01 is identified by visual comparison against a single dataset and lacks a physical derivation. If this value varies with soil type, climate, or vegetation density, the fix may need to be re-calibrated for each new environment, limiting its generality.
  • The modified Feddes function conflates evaporation from the soil surface with root water uptake, treating both through a single sink term. A more physically complete approach would partition potential evapotranspiration into separate evaporation and transpiration components, which could make the f_2a modification unnecessary.
  • The sensitivity analysis spans only one case study (Johnstown Castle, Diamond and Sills dataset). Testing f_2a values against a broader range of waterlogged sites would establish whether 0.01 is a robust default or site-specific coincidence.
  • The comparison with MoSt relies on a water stress normalization that removes systematic bias; this means the two models could agree on plant stress while disagreeing on absolute soil moisture, which has implications for any downstream application that uses raw moisture rather than stress.

Load-bearing premise

The value f_2a = 0.01 is adopted as a baseline after a sensitivity sweep on a single case study, with the optimal value identified by visual comparison against one dataset. There is no independent physical derivation of the 0.01 value, and the authors acknowledge it is a pragmatic approximation rather than a physically rigorous representation. If the optimal f_2a varies systematically with soil type, climate, or vegetation, the generality of the fix is limited.

What would settle it

If applying f_2a = 0.01 to waterlogged soils in other climates or soil types does not improve model-observation agreement, or if a different f_2a value is optimal in those settings, then the proposed fix is site-specific rather than a general correction to the Feddes formulation.

Figures

Figures reproduced from arXiv: 2607.06182 by E Ruelle, GP Benham, H Khan, K Shishkin, L O'Naraigh, O Fenton, S Kumar, S Mathias.

Figure 1
Figure 1. Figure 1: Schematic diagram of the Richards Equation (RE) model used to simulate soil water [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Map of Ireland showing the location of the study sites in County Wexford, Ireland [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Plot of a) daily rainfall 𝑞𝑟 (mm/day), b) potential evapotranspiration (𝐸𝑇0) (mm/day), c) depth-averaged soil moisture (𝜃¯), and d) depth-averaged water tension (𝜓¯) time series for the Diamond and Sills (2001) dataset at Clonroche. The line represents the mean (𝜇) and the shaded zone represents values within one standard deviation (𝜎) of the mean. 16 [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plot of a) daily rainfall 𝑞𝑟 (mm/day), b) potential evapotranspiration (𝐸𝑇0) (mm/day), c) depth-averaged soil moisture (𝜃¯), and d) depth-averaged water tension (𝜓¯) time series for the Diamond and Sills (2001) dataset at Johnstown Castle. Diamond and Sills Dataset: The meteorological data (daily rainfall 𝑞𝑟 and 𝐸𝑇0), along with depth-averaged soil moisture (𝜃¯) and water tension (𝜓¯) for Clonroche and Joh… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of predicted water tension (hPa) values at different depths against [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of predicted water tension (hPa) values at different depths against [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Plot of a) daily rainfall 𝑞𝑟 (mm/day), b) potential evapotranspiration (𝐸𝑇0) (mm/day), c) depth-averaged soil moisture (𝜃¯), and d) depth-averaged water tension (𝜓¯) time series for the ISMON dataset at Johnstown Castle. We present a more detailed study in [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of predicted soil moisture, 𝜃 values at different depths against observed soil moisture, 𝜃 at Johnstown Castle for the ISMON dataset. 3.3 Cross-comparison: RE model, observations, and MoSt model We present here a cross-comparison between the RE model, the observations, and the MoSt model. Because the MoSt model only gives values for the water storage values at 10 cm (Θ10) and 100 cm (Θ100), our … view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of predicted water storage values until 10 cm depth and 100 cm depth [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Water stress (RE model and MoSt model) at different depths for Johnstown Castle [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of RE predicted water tension values for all depths with varying [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of RE predicted water tension values for all depths with varying [PITH_FULL_IMAGE:figures/full_fig_p030_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of RE predicted water tension values for all depths with varying [PITH_FULL_IMAGE:figures/full_fig_p031_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of RE predicted soil moisture values for all depths with reduced [PITH_FULL_IMAGE:figures/full_fig_p032_14.png] view at source ↗
read the original abstract

The Richards equation (RE) is widely used to model water flow in unsaturated soils, but its performance in persistently wet grassland systems remains uncertain. This is particularly relevant in Irish grasslands, where soils often remain close to saturation for extended periods and seasonal waterlogging is common. Here, we evaluate the RE against three soil moisture datasets from County Wexford, Ireland, spanning different locations, soil types, and observation periods. We show that the standard RE formulation systematically over-predicts soil moisture under prolonged near-saturated conditions. We find that this arises from the commonly used Feddes plant water uptake function, which suppresses water losses under anaerobic conditions, despite continued evaporation from near-saturated soils. To address this limitation, we introduce a simple modification that retains a small non-zero water loss rate in the anaerobic regime. The modified model produces substantially improved agreement with observations across all three datasets. These results provide a systematic evaluation of RE-based soil moisture modelling in Irish grasslands. More broadly, they identify an important limitation of conventional RE implementations in waterlogged environments and demonstrate a practical approach for improving soil moisture predictions in persistently wet soils.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 8 minor

Summary. This manuscript evaluates the 1D Richards equation (RE) for predicting soil moisture in Irish grasslands using three case studies from County Wexford, Ireland, spanning different soil types and observation periods. The authors compare RE predictions against observations from the Diamond and Sills (2001) tensiometer dataset (Clonroche and Johnstown Castle sites) and the ISMON TDR dataset (Johnstown Castle). The central finding is that the standard Feddes plant water uptake function, which sets f_2a = 0 under anaerobic conditions, causes systematic over-prediction of soil moisture in persistently wet soils. The authors propose setting f_2a = 0.01 to retain a small non-zero water loss rate, which they show improves agreement with observations. Monte Carlo simulations are used to quantify uncertainty in van Genuchten hydraulic parameters, and a cross-comparison with the operational MoSt grass growth model is provided via a water stress metric.

Significance. The paper addresses a practically important problem: the performance of physically-based soil moisture models in persistently wet grasslands, a setting that has received relatively little attention. The identification of the Feddes f_2a = 0 assumption as a source of systematic bias in waterlogged conditions is a useful and transferable finding. The inclusion of three datasets, Monte Carlo uncertainty quantification, and comparison with an operational model (MoSt) adds value. The model code is made publicly available via a GitHub repository, supporting reproducibility. The proposed modification is simple and practical, which is appropriate for the stated goal of informing operational grassland forecasting tools. However, the significance is tempered by the lack of quantitative goodness-of-fit metrics for the primary soil moisture and pressure head comparisons, which makes it difficult to assess the magnitude of improvement objectively.

major comments (3)
  1. The abstract, Section 3.1, and Section 4 repeatedly claim that setting f_2a = 0.01 'substantially improves agreement with observations across all three datasets.' However, no quantitative goodness-of-fit metrics (RMSE, Nash-Sutcliffe, R², bias) are reported for any of the primary soil moisture (θ) or pressure head (ψ) comparisons in Figures 3–8. The only quantitative metrics appear in Section 3.3 for the derived water stress comparison (Fig. 10), which is a normalised quantity, not the primary variable. Without metrics, the reader cannot verify the magnitude of improvement, compare it against the Monte Carlo uncertainty bands, or assess whether the improvement is indeed 'substantial.' The addition of at least one standard metric (e.g., RMSE or bias) for the θ and ψ comparisons in Figures 3–8, reported for both f_2a = 0 and f_2a = 0.01, is needed to support the central claim.
  2. The value f_2a = 0.01 is selected via a sensitivity sweep (Appendix A, Figs. 11–13) on a single case study (Johnstown Castle, Diamond and Sills dataset) by visual inspection. No formal optimisation or objective function is used. The authors acknowledge this is 'a pragmatic approximation rather than a physically rigorous representation' (Section 4), but the manuscript does not discuss whether the optimal value might vary systematically with soil type, climate, or vegetation. Since the claim of generality across 'all three datasets' rests on this single-case calibration, the authors should either (a) provide a more formal justification for why f_2a = 0.01 is expected to be robust across sites, or (b) temper the generality claim and frame the value as site-specific pending further validation.
  3. For the ISMON case study (Section 3.1), the authors adjust θ_r to 0.01 (reduced well below the ROSETTA 3 range) and θ_s (reduced for gravel layers) to improve the fit. These post-hoc parameter adjustments are acknowledged but not rigorously justified — the authors note that 'there are good reasons to expect discrepancies' but do not provide independent measurements or literature values to support the specific adjustments. This weakens the claim of 'improved agreement' for the ISMON dataset, since the improvement may come from the parameter tuning rather than from the f_2a modification. The authors should clarify the relative contribution of the f_2a change versus the θ_r/θ_s adjustments to the ISMON fit, or restrict the 'substantial improvement' claim to the two Diamond and Sills datasets where only f_2a was changed.
minor comments (8)
  1. Highlights: 'persisently' should be 'persistently.'
  2. Section 2.1.1, Eq. (9): the parameter 'a' is described as dimensionless, but the text states values of 'a = 1 m' and 'L_r = 2 m,' which implies a has units of length. Please clarify the dimensions of a (and whether the stated value is '1' or '1 m').
  3. Section 2.1.1: the values h_a = −0.05 m, h_d = −4 m, and h_w = −150 m are stated as being taken from the literature, but it would help to note that these are standard Feddes values for grassland specifically, not just in passing.
  4. Table 7: the adjusted θ_s values (0.280 and 0.350) for the gravel drainage layers are shown in brackets, but the table caption should explicitly state which depth ranges the adjusted values apply to.
  5. Section 3.1, ISMON subsection: the text mentions reducing θ_r to 0.01 'for each soil layer,' but it is unclear whether this applies to all layers or only those above the gravel drains. Please clarify.
  6. Figures 3–8: the time axis labels use a date-month-year format that is difficult to read at the scale shown. Consider enlarging or simplifying the axis labels to facilitate visual comparison.
  7. Section 3.3: the RMSE values for the water stress comparison (0.264, 0.371, 0.075, 0.134) are reported without specifying the time period or number of data points over which they were computed.
  8. The reference to 'Richardson–Richard equation' in the Zha et al. (2019) citation should be 'Richards equation.'

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive review. The referee raises three major comments, all of which we find legitimate. We agree that quantitative goodness-of-fit metrics should be added, that the generality claim for f_2a = 0.01 needs more careful framing, and that the relative contributions of the f_2a modification versus the theta_r/theta_s adjustments in the ISMON case study need to be disentangled. We address each point below.

read point-by-point responses

  1. Referee: No quantitative goodness-of-fit metrics (RMSE, NSE, R², bias) are reported for the primary theta and psi comparisons in Figures 3-8. The central claim of 'substantial improvement' rests on visual inspection alone. At least one standard metric for theta and psi, reported for both f_2a = 0 and f_2a = 0.01, is needed.

    Authors: The referee is correct. We will add RMSE and bias metrics for the depth-averaged theta and psi comparisons (and for theta at individual depths where available) for both f_2a = 0 and f_2a = 0.01, for all three case studies. These will be reported in a summary table and referenced in the relevant figure captions. This will allow readers to assess the magnitude of improvement objectively and compare it against the Monte Carlo uncertainty bands. We agree that without these metrics the claim of 'substantial improvement' is not adequately supported, and we will temper the language in the abstract and Section 4 to match what the metrics show. revision: yes

  2. Referee: The value f_2a = 0.01 is selected via a sensitivity sweep on a single case study (Johnstown Castle, Diamond and Sills dataset) by visual inspection, with no formal optimisation. The manuscript does not discuss whether the optimal value might vary with soil type, climate, or vegetation. The authors should either provide a more formal justification for robustness across sites, or temper the generality claim and frame the value as site-specific pending further validation.

    Authors: We agree that the current framing overstates the generality of f_2a = 0.01. The sensitivity sweep was conducted on the Johnstown Castle Diamond and Sills case study, and the same value was then applied to the Clonroche case study (also Diamond and Sills) and the ISMON case study. We will revise the manuscript to explicitly acknowledge that f_2a = 0.01 was calibrated on a single case study and has not been independently optimised for the other sites. We will also add a brief discussion of the physical reasoning for why a small non-zero value might be expected to be broadly applicable — namely, that it represents residual evaporation from near-saturated soil, a process that is not strongly soil-type-dependent — while making clear that this is a hypothesis, not a demonstrated result. We will temper the claim of generality across 'all three datasets' and frame f_2a = 0.01 as a pragmatic default pending validation at additional sites with different soil types, climates, and vegetation covers. revision: yes

  3. Referee: For the ISMON case study, the authors adjust theta_r to 0.01 and theta_s (reduced for gravel layers) to improve the fit, but these post-hoc adjustments are not rigorously justified. The improvement may come from parameter tuning rather than the f_2a modification. The authors should clarify the relative contribution of the f_2a change versus the theta_r/theta_s adjustments, or restrict the 'substantial improvement' claim to the two Diamond and Sills datasets where only f_2a was changed.

    Authors: This is a fair and important point. We acknowledge that the ISMON case study involves two simultaneous modifications — the f_2a change and the theta_r/theta_s adjustments — and the current manuscript does not disentangle their relative contributions. We will address this in two ways. First, we will add a brief analysis (either in the main text or an appendix) showing the ISMON results with f_2a = 0.01 but the original ROSETTA 3 theta_r and theta_s values, so that the reader can see the effect of the f_2a modification alone. Second, we will restrict the claim of 'substantial improvement due to the f_2a modification' to the two Diamond and Sills datasets, where only f_2a was changed. For the ISMON dataset, we will reframe the discussion to clearly state that the improvement comes from a combination of the f_2a modification and the hydraulic parameter adjustments, and that the dominant source of error in that case study is associated with hydraulic parameter uncertainty rather than the anaerobic uptake assumption. This is in fact already partially stated in the manuscript (Section 3.1 and Section 4), but we will make the separation explicit. revision: yes

Circularity Check

2 steps flagged

f_2a=0.01 selected by visual fit on one case study, then 'improvement' reported on same dataset without quantitative metrics; ISMON case study involves post-hoc parameter adjustment to data

specific steps
  1. fitted input called prediction [Appendix A; Section 3.1; Abstract]
    "To investigate the sensitivity of the model to this assumption, a parameter study was performed using the Johnstown Castle case study from the Diamond and Sills dataset. Values of f_2a between 0 and 0.5 were considered... As f_2a is increased above zero, the model allows limited water extraction under near-saturated conditions, leading to improved agreement with the observations up to about f_2a = 0.01. For larger values of f_2a, the model tends to over-dry the soil, and the agreement with observations deteriorates... Based on this analysis, a value of f_2a = 0.01 was adopted in the main simul"

    The parameter f_2a=0.01 is selected by a sensitivity sweep on the Johnstown Castle (Diamond and Sills) dataset to maximize visual agreement with that same dataset. The abstract then claims 'substantially improved agreement with observations across all three datasets,' but one of those three is the very dataset used to fit f_2a. The 'improvement' on the fitting dataset is statistically forced by construction. The claim of improvement on the other two datasets (Clonroche, ISMON) is not circular per se, but the claim of improvement 'across all three' conflates a fitted result with a predicted one. The absence of any quantitative goodness-of-fit metric (RMSE, NSE, R^2) for the primary soil moisture comparisons makes it impossible to distinguish genuine predictive skill from the visual fit.

  2. fitted input called prediction [Section 3.1 (ISMON dataset); Appendix B]
    "It is clear from these results that the model experiences θ≈0.2 as an effective lower bound. To mitigate the effect of this effective lower bound, we have tried systematically reducing the parameter value θ_r down to 0.01 for each soil layer. By re-running the simulation, there is much better qualitative and quantitative agreement between the model and the observations... Similar adjustment was made to θ_s to account for presence of drainage layers... Consequently, the values of θ_s for the affected layers were reduced accordingly."

    For the ISMON case study, the authors adjust θ_r (reduced to 0.01) and θ_s (reduced for gravel layers) post-hoc by observing that the model could not reproduce the dry summer periods. The adjusted parameters lie outside the ROSETTA 3 uncertainty range. The reported 'improved agreement' for this case study is thus partly a consequence of fitting parameters to the target data. While the authors are transparent about this ('we have tried systematically reducing...'), the abstract's claim of 'substantially improved agreement with observations across all three datasets' does not distinguish between improvement from the f_2a modification (the paper's central proposal) and improvement from post-hoc parameter fitting to the same observations.

full rationale

The paper's central claim—that setting f_2a=0.01 improves soil moisture predictions—is not fully circular: the parameter is tuned on one case study (Johnstown Castle D&S) and then applied to two others (Clonroche D&S and ISMON) that were not used for the sweep. However, the claim of improvement 'across all three datasets' conflates the fitting dataset with the prediction datasets. The ISMON case study further involves post-hoc adjustment of θ_r and θ_s to improve model-data agreement, meaning the reported improvement for that case is partly a fit. The absence of quantitative metrics for the primary variables makes the magnitude of genuine out-of-sample improvement unverifiable. Score 4 reflects that the central claim has independent content (two non-fitted datasets) but is partially contaminated by fitting and by the conflation of fitted and predicted results.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The paper introduces no new physical entities, particles, forces, or dimensions. The f_2a parameter is an existing parameter of the Feddes model; the contribution is setting it to a non-zero value. The 'residual water loss under anaerobic conditions' is a process representation, not a new entity. All axioms are standard domain assumptions except the evaporation-under-anaerobiosis hypothesis, which is the paper's central physical argument and is acknowledged as approximate.

free parameters (6)
  • f_2a = 0.01
    The Feddes anaerobic uptake parameter, set to 0.01 based on a sensitivity sweep on the Johnstown Castle (Diamond and Sills) dataset (Appendix A). Identified as improving fit up to ~0.01 and deteriorating beyond. No physical derivation provided.
  • θ_r (ISMON) = 0.01
    Residual soil moisture for the ISMON dataset, manually reduced from ROSETTA 3 estimates (mean ~0.128) to 0.01 to improve summer dryout agreement (Section 3.1, Appendix B). Acknowledged as outside ROSETTA 3 uncertainty range.
  • θ_s (ISMON, gravel layers) = 0.280 (0.3-0.5m), 0.350 (0.6-2.0m)
    Saturated soil moisture adjusted downward from ROSETTA 3 estimates (~0.471) for soil layers affected by gravel drainage (Table 7, Section 3.1). Values chosen based on observed maximum θ not exceeding 0.30 and 0.35 at 30 cm and 50 cm depths.
  • ET0 calibration factor = 0.375
    Linear calibration coefficient relating Hargreaves to Penman-Monteith ET0 estimates (Eq. 16), used for 1998-2000 Diamond and Sills datasets. R² = 0.85, RMSE = 0.410.
  • h_a, h_d, h_w = -0.05 m, -4 m, -150 m
    Feddes pressure head thresholds for anaerobiosis, water-limited ET, and wilting point. Taken from literature (Mathias et al., 2014; Feddes et al., 1976). Not fitted in this study but are free parameters of the Feddes model.
  • a, L_r = 1, 2 m
    Root density shape parameter and root depth. Assumed values from Mathias et al. (2014). Not fitted to the Irish sites.
axioms (5)
  • standard math Darcy's law governs unsaturated flow in soil
    The Richards equation (Eq. 1) is derived from Darcy's law and mass conservation. Standard assumption in soil physics (Richards, 1931).
  • domain assumption van Genuchten-Mualem constitutive relationships adequately represent soil hydraulic behavior
    Eqs. 2a-2b are used to relate θ, h, and K. Standard in hydrological modeling but known to have limitations in structured soils (Section 4).
  • domain assumption ROSETTA 3 pedotransfer function provides reasonable estimates of VG parameters from soil texture
    Used throughout to estimate VG parameters from sand/silt/clay data (Section 2.1.1). The paper acknowledges limitations, especially for the ISMON site where adjustments were needed.
  • domain assumption 1D vertical flow is sufficient for these field sites
    Lateral flow is neglected (Section 4). Justified by computational cost and data requirements but may be important in artificially drained soils.
  • ad hoc to paper Evaporation from near-saturated soils continues even when transpiration is suppressed by anaerobic conditions
    This is the physical motivation for the f_2a modification (Section 1, Section 2.1.1). It is plausible but not independently verified in the paper; the modification is described as 'pragmatic' rather than 'physically rigorous' (Section 4).

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Reference graph

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