As noted above, a key limitation in previous studies is that comparisons of AET performance have been made between entire models, rather than isolating the contribution of individual AET equations. Thus, it is impossible to tell whether differences in performance are due to the AET equation used within the model or the surrounding model structure. To address this, we systematically substitute a range of AET equations into a fixed model structure, testing each in turn. To ensure the findings are not model-specific, this process is repeated across three commonly used conceptual hydrological models, treating each model as a consistent “container” for testing the equations.

The AET equations are based on the study of Knoben et al. (2019), who conducted a systematic review of 47 existing conceptual rainfall runoff models, compiling them into the Modular Assessment of Rainfall-Runoff Models Toolbox (MARRMoT) framework. This framework's structure isolates the unique equations used for a particular process such as AET – i.e. although there are 47 models, there are not 47 different AET equations because multiple models may use the same AET equation. This unique MARRMoT list forms the basis of the AET equations tested here. In addition, MARRMoT is used for the simulation experiment itself. It provides an effective framework for addressing these challenges because it is set up to ensure consistent model implementation, allowing for intercomparison and modification of model structures and internal components. By leveraging MARRMoT, the performance of various AET equations can be systematically investigated within consistent conceptual model structures, addressing the gaps identified above. By advancing the representation of AET, this study contributes to more robust and reliable hydrological modelling practices particularly under changing environmental conditions, where traditional model assumptions are increasingly challenged.

Specifically, (as indicated in Fig. 1), this study systematically evaluates 15 evapotranspiration (AET) equations by substituting them into the models, applied across seven catchments. Each model is individually calibrated (15×3×7=315 calibrations) using a multi-objective function that equally weights the match to both streamflow and flux tower-derived AET data. All simulations were performed at a daily time step, and a catchment water balance was applied to the flux tower derived AET, discussed in detail in Sect. 2.4.

We utilise flux tower data as our benchmark for evaluating actual evapotranspiration (AET) in hydrological models because it provides direct, high-temporal resolution observations of surface energy and water fluxes (Beringer et al., 2022). Compared to remotely sensed AET estimates, which offer broader spatial coverage, flux tower data avoids uncertainties related to satellite retrieval algorithms and coarse spatial and temporal resolution, including uncertainty around overpass timing, which may not align well with daily model time steps. Additionally, Gardiya Weligamage et al. (2025b) assessed the quality of remotely sensed AET across Australia and identified several limitations of remotely sensed AET, including seasonal inconsistencies and variability issues. The flux tower data used here is sourced from the TERN-OzFlux (Terrestrial Ecosystem Research Network) dataset, which is the Australia and New Zealand portion of the Fluxnet network of stations that measure carbon, water, and energy fluxes (Beringer et al., 2022).

Nonetheless, flux tower measurements are point-based, while hydrological models simulate catchment-averaged fluxes, leading to a scale mismatch that requires careful consideration. A recent study by Gardiya Weligamage et al. (2025b) paired 15 OzFlux sites with nearby catchments from the CAMELS-AUS dataset (Fowler et al., 2025) and evaluated simulations from several models. To further address this issue, we applied strict selection criteria, focusing only on flux tower–catchment pairs where we had reasonable confidence in representativeness. In addition to geographic proximity, we required close alignment in precipitation and temperature regimes, and placed particular emphasis on land cover similarity, given the importance of vegetation dynamics in controlling AET. Sites were excluded where vegetation type, structure, or density diverged markedly between the tower footprint and the broader catchment. This process aimed to reduce discrepancies between observed and modelled AET that could otherwise result from mismatched biophysical controls.

While we acknowledge the scale limitations of point-based flux data, supplementary analysis from Gardiya Weligamage et al. (2025b) suggests that even distant flux tower observations (up to hundreds of kilometres away) often provide more realistic AET estimates than co-located remotely sensed data. This highlights the value of flux tower measurements for hydrological model evaluation, particularly when accompanied by rigorous site selection.

The selected flux tower sites represent a range of climatic zones and vegetation types characteristic of the diverse Australian hydrological conditions, as outlined in Table 1, and shown in Fig. 2. Their selection ensures that the findings are applicable to broader Australian conditions.

OzFlux eddy covariance evapotranspiration data were accessed from OzFlux towers through the Terrestrial Ecosystem Research Network (TERN) data portal (https://portal.tern.org.au/, 2024 Version 2, last access: 7 March 2025) using level 6, quality controlled and gap filled daily time scales. The dates of the flux tower data availability differ between sites. The full data periods used in calibration are shown in Table S1 of the Supplement, where any missing values were excluded from the analysis.

Remaining hydrometeorological data were sourced from the CAMELS-AUS dataset which covers the period from 1 January 1950 to 26 May 2022. Potential evapotranspiration data (specifically Morton's Wet Environment Evaporation) are provided in CAMELS and sourced from the Scientific Information for Land Owners, or SILO, database, published by the state of Queensland (https://www.longpaddock.qld.gov.au/silo/, last access: 15 January 2025). Precipitation data were provided in CAMELS and sourced from the Australian Gridded Climate Data (AGCD) dataset of the Bureau of Meteorology (https://portal.ga.gov.au/, last access: 15 January 2025). Streamflow data were also obtained from this dataset, and any missing values were excluded from the analysis.

Building on the careful selection of representative tower-catchment pairs (Sect. 2.1), we further adjusted the flux tower AET data to improve comparability with catchment-scale values. Since actual evapotranspiration at the catchment scale is not directly measurable, we applied a long-term water balance approach to provide an independent estimate of long-term catchment-average AET and adjust the flux tower data accordingly. This adjustment involved calculating a linear scaling factor that was applied to the full flux tower AET time series, correcting the long-term average without altering the intra-annual shape of the AET curve. This approach assumes that while the temporal dynamics of AET at the flux tower (e.g. seasonal dynamics) are broadly representative of catchment-scale behaviour, the magnitude may differ due to spatial heterogeneity in vegetation, soil properties, or microclimate.

To derive the scaling factor via catchment water balance, we assumed negligible long-term change in storage (ΔS≈0). This is a common assumption in hydrology, justified here by the fact that the water balance components: precipitation (P), streamflow (Q), and AET, are aggregated over a multi-year period. As such, any difference in storage between the start and end of the period is small relative to the cumulative fluxes and has minimal influence on the resulting estimate. The catchment water balance therefore simplifies to: 1ΔS=P-Q-AET→AETcatchment=P-Q, where P is long-term average precipitation and Q is long-term average streamflow, both measured over the same period as the flux tower record. The corresponding long-term average AET from the flux tower, AET_tower, was calculated from the eddy covariance measurements. A scaling factor f was then derived as: 2f=AETcatchmentAETtower, This factor was applied to the full flux tower time series: 3AETadjustedt=f×AETtower(t), This adjustment ensures that the flux tower data matches the long-term magnitude of AET estimated at the catchment scale, while preserving its temporal variability. Combined with careful catchment selection, this was deemed the most practical method available to reduce scale mismatch and increase confidence in data used for the model evaluation.

This experimental setup, introduced in Sect. 2.1, was applied across three model structures – GR4J, Simhyd, and VIC – which were selected from the 47 options in MARRMoT to represent a range of complexity and conceptual assumptions. GR4J is the most parsimonious model, with four parameters and two representative storages (Perrin et al., 2003). Simhyd represents an intermediate level of complexity, with seven parameters and three storages (Chiew et al., 2002). VIC is the most complex model chosen, comprising ten parameters and three storages (Liang et al., 1994). In Simhyd and VIC, AET is drawn from multiple storages, and the evaluation of AET simulations was always conducted on the sum of AET across these storages. However, this still leaves the question of which storage is subject to the experimental changes in equations. For the purposes of this study, the AET equation was substituted into only the primary soil moisture storage, which is assumed to contribute most to total evapotranspiration in these model structures. The remaining storages retained their original AET formulations.

The decision to apply the equation changes only to the primary soil moisture storage was made a priori, recognising that the contribution of each storage may vary depending on parameter values. As stated, calibration and evaluation performance scores are based on the total modelled AET, regardless of the internal distribution across storages.

Additionally, extending alternative AET formulations to all storages would require introducing additional parameters for each storage, substantially increasing model dimensionality and calibration complexity. This would make it more difficult to reliably attribute differences in model performance to the AET formulation itself. Furthermore, maintaining a consistent implementation across different model structures is important for intercomparison. Applying different modifications across models would reduce comparability of results. Finally, some storages (e.g. interception) represent fundamentally different physical processes, and modifying their AET formulation would be inconsistent with their conceptual role. The chosen approach therefore represents a pragmatic compromise that allows differences in AET formulation to be isolated while maintaining model interpretability.

Across the 47 models in MARRMoT there are 23 unique AET equations, but the experiment did not test all 23 because some are incompatible with the three chosen models, and because we found some redundancy between the equations. For instance, some equations used different names for equivalent parameters, such as maximum storage represented as “Smax” in one equation, and “S3 parameter” in another. When simplified, these equations were found to have the same functionality. Additionally, two equations were excluded because they were designed to operate on soil moisture storages defined in a “deficit” manner, which was not compatible with the three selected models. Following the process of simplifying equations to ensure compatibility with the chosen models and removing redundant parameters, 15 of the 23 equations remained. These equations retained their original naming according to the MARRMoT framework.

Table 2 provides an overview of the selected 15 equations, including their corresponding number within MARRMoT, the number of additional parameters required, descriptions as provided in MARRMoT, and simplified formulas. Additionally, the list of models that utilise each equation can be found in Table S2 of the Supplement. The resulting 15 AET equations represent diverse approaches to modelling the conversion of potential evapotranspiration (PET) into actual evapotranspiration (AET) as a function of soil moisture. This diversity of equations allows for a robust experiment that represents the diversity of current practice in conceptual modelling. These approaches fall into five major relationship types, which are summarised below:

Linear relationships with soil moisture (AET equations evap_1, 7 and 11) assume a direct proportionality between soil moisture and evapotranspiration.

The calibration approach was based on single objective optimisation to a composite objective function that equally weighted the performance of the model against streamflow data from CAMELS-AUS and AET data from the flux towers. For streamflow (Q), a Kling–Gupta Efficiency (KGE) (Gupta et al., 2009) derived objective function was used that incorporates separate penalties for bias in high- and low-flow regimes, as described in Trotter et al. (2023, p. 1) (Eq. 4). Specifically, the component of Eq. (4) assessing low-flow performance is the KGE calculated on flow raised to the power of 0.2, the component focussed on high flows is the standard KGE, and the component focussed on bias is the final term in the equation. Please see Trotter et al. (2023) for more information. For AET, the KGE was applied to square-root-transformed data, following Gardiya Weligamage et al. (2025a) (Eq. 5, where d is daily and m is monthly). This calibration approach ensured that both monthly and seasonal dynamics of AET were incorporated, alongside a commonly used method for streamflow. Both objective functions are similarly bounded KGE-based metrics and therefore exhibit comparable numerical ranges during calibration. As a result, equal weighting of the two objective functions leads to approximately equal contribution to the combined objective function value (OFV), which was computed as the mean of the streamflow and AET objective values (Eq. 6). 4OFVStreamflow=12KGEQ+KGEQ0.2-5⋅ln⁡1+mean(Qsimulated-Qobserved)mean(Qobserved)2.5,5OFVAET=12KGEAET_d0.5+KGEAET_m0.5,6OFV=0.5⋅OFVStreamflow+OFVAET, Model calibration was performed using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm, a high performing algorithm commonly used in hydrology (Arsenault et al., 2014), as implemented in the default calibration framework of MARRMoT v2.1 (Trotter et al., 2022). This study focuses on identifying a single optimal parameter set for each configuration, rather than exploring the full parameter uncertainty space.

In order to systematically test the available AET equations, the 15 AET equations were individually substituted into each model. This was repeated for all seven catchments, resulting in 315 calibrations. AET equations were ranked to determine which performed best according to the objective function values described above.

In addition to traditional objective function values, we conducted a more comprehensive assessment of model performance by analysing results based on evapotranspiration signatures, as defined by Gardiya Weligamage et al. (2025a). These signatures, similar to commonly used streamflow signatures (e.g. McMillan, 2021), provide insights into whether the models can reproduce specific aspects of AET. The eight calculated AET signatures are: long-term median and inter-annual variability for annual dynamics; peak timing and lag-12 correlation for seasonal dynamics; water stress, variability, and synchronicity for monthly dynamics; and rainfall event responsiveness for daily dynamics.

Finally, we conducted split-sample testing to evaluate how well the updated models responded to previously unseen data. In this study, split-sample testing refers specifically to temporal split-sample validation, and does not assess spatial transferability or proxy-basin performance. Evaluating with data outside the calibration period ensured that the identified improvements in model performance were not an artifact of overfitting but instead reflected a more generalisable enhancement in AET representation. For brevity, this test was conducted only on the highest performing AET equation in calibration, as a final robustness check, rather than as a systematic assessment of overfitting across all equations which would add substantial complexity.

The available AET data were divided in half, with calibration performed on the first half and evaluation on the second and repeated in reverse for a second calibration. The length of the calibration and evaluation periods varied between catchments, reflecting differences in the availability of flux tower observations (see Table S6). The relatively short duration of flux tower records at some sites may limit the ability of the split-sample test to fully capture long-term model behaviour. This procedure was applied to all catchments and all three models, comparing the original model formulation with the version incorporating the best-performing evapotranspiration equation.

Figure 3 provides an example of AET model outputs by showing a time series of simulated AET at one of the seven sites, Wombat Forest, using the Simhyd model. In this figure, Simhyd was recalibrated with each of the 15 AET equations independently, such that differences in simulated AET arise solely from the choice of equation, with all other model components held constant. The observed flux tower AET (catchment adjusted) is shown as a thick blue line, while the model outputs from the various AET equations are displayed in different colours. PET (grey) and rainfall (inverted, light blue) are also shown to illustrate the key drivers of AET and help contextualise model behaviour.

This figure highlights the variation in simulated AET that arises solely from substituting the AET equation, demonstrating the sensitivity of model outputs to this component. Similar outcomes were observed across other catchments and model structures (21 figures total), with the remaining plots included in the Supplement (S3) for reference.

As noted, each AET equation is optimised individually across streamflow and actual evapotranspiration (AET) objective function values (OFV), resulting in 315 calibrations (3 models × 7 catchments × 15 equations). Table 3 displays the summary of these results by ranking the combined OFVs to two decimal places for each model and catchment, with a rank of 1 indicating the best-performing equation. Equal ranks were assigned when the rounded values (to two decimal places) were equal. Full tables with raw OFV scores and rankings are included in the Supplement (S4). The summary shown here aggregates rankings across all catchments for each model and provides an overall ranking across all models.

AET equation evap_19 emerges as the overall top performer, achieving the highest average rank. AET equations 3, 8, and 21 also rank highly, though their performance varies more noticeably across model structures (e.g., Simhyd vs. GR4J).

To further explore the calibration results, Fig. 4 separates the combined objective function values into their two components: streamflow and AET performance. Each subplot represents a catchment, showing variations across all models and AET equations (15 points per model, 45 total). The most effective AET equations appear toward the top-right quadrant, indicating strong performance on both streamflow and AET objectives. The native (original) AET equation used in each model is marked with a black star, and AET equation evap_19 is highlighted in red for reference. These plots visually represent that while some models exhibit catchment-specific variations (e.g., GR4J's poor performance for Whroo), evap_19 consistently ranks among the best.

Despite some promising results, certain hydrological behaviours remain poorly represented. For instance, even the four best-performing AET equations (3, 8, 19, and 21) fail to perform adequately at specific sites. This is evident when comparing results at Tumbarumba and Litchfield (Fig. 5a and b, respectively). All models provide reasonable estimates of AET at Tumbarumba, and both Simhyd and VIC perform reasonably well at Litchfield. However, GR4J significantly overpredicts AET at Litchfield.

To explore this discrepancy, GR4J was recalibrated for Litchfield using only AET, giving the model the best possible chance to match observed AET without the constraint of streamflow calibration. However, even under these conditions, GR4J still failed to replicate AET accurately at this site, indicating a possible structural limitation in the model. Results of this analysis are shown in the Supplement (S5), which includes the performance of all plausible equations under AET-only calibration. No improvement in AET performance was observed compared to the results shown in Fig. 5b.

Beyond matching overall OFV scores, AET equations were also assessed using evapotranspiration signatures (Gardiya Weligamage et al., 2025a). Similar to hydrological signatures, these metrics break down AET behaviour into distinct components, focusing on characteristics such as the mean, variability and periodicity of AET. Across all eight signature plots, we observe broadly consistent patterns in terms of model performance, so only one representative scatterplot is shown here. An exception was the interannual variability signature (Fig. S24), which exhibited very similar patterns across all models and AET formulations. This may suggest that this signature is primarily driven by the precipitation forcing rather than differences in model structure or AET formulation. An alternative view, given this signature is not very well simulated, is that all models tested are subject to similar limitations in simulating this aspect of AET dynamics, regardless of choice of equation. Either way, it provides limited discriminatory power for evaluating AET equation performance in this framework.

Below we focus on a timing-based signature, namely monthly AET asynchronicity with PET (Fig. 6), while the remaining signatures are shown in the Supplement (S6). This signature captures the degree to which AET follows the seasonal cycle of PET, independent of magnitude, with greater asynchronicity suggesting a decoupling between the two. Including this signature helps evaluate whether equations reproduce not just how much evapotranspiration occurs, but when it occurs – a key aspect of improving process representation in conceptual models. For example, high asynchronicity might suggest that a model fails to capture stomatal regulation or delayed transpiration responses to atmospheric demand, processes that are critical under drought or seasonal stress.

The results indicate that while some equations clearly perform poorly, there are a few that consistently align well with the observed signatures, including across multiple metrics. These better-performing equations also generally agree with those identified through OFV-based testing. Notably, AET equation evap_19 is among the top performers across all signature comparisons.

As an evaluation of robustness, a split-sample test was conducted, comparing the original model formulations with those incorporating the best-performing evapotranspiration equation, AET equation evap_19 (Fig. 7). Each model was calibrated on one half of the data and evaluated on the other, with results reported separately for AET and streamflow (Q).

For the calibration period, (and as shown previously), models using evap_19 achieved higher AET objective function values (OFVs) across all catchments compared to the base equations (Fig. 7a). Streamflow performance also generally improved under evap_19 during this period (Fig. 7b). As for the evaluation period for AET, equation evap_19 consistently improved performance, maintaining higher OFVs across most catchments, similar to the trend observed in calibration (Fig. 7c).

For streamflow, the evaluation period results were more variable. While some catchments showed improvements with evap_19, others performed similarly or worse than the original formulation (Fig. 7d). Notably, catchments that performed poorly under the original AET equation also tended to have low performance under evap_19.

It is important to acknowledge that the available flux tower data covers a relatively short timeframe, which may limit the reliability of this test in fully capturing long-term model behaviour (see Supplement S1). This constraint could, in part, explain discrepancies in streamflow performance during evaluation. Despite this, the results provide evidence that integrating evap_19 enhances AET representation and, in many cases, improves model performance beyond AET.

Overall, with an appropriate choice of equation, the models capture AET dynamics relatively well compared to the default options. However, a key feature that emerged upon closer examination of the time series (Fig. 5) was that modelled actual evapotranspiration (AET) appeared to peak earlier than observed flux tower data. This pattern is also apparent in most other catchments (see Supplement S3). To investigate this further, we expanded the analysis of the “monthly peak” signature. Specifically, we examined a 7-month window centred on the observed peak month (i.e., three months before, the peak month itself, and three months after). Based on the time series patterns, it appeared that the models were overestimating AET before and during the peak while underestimating it afterward.

To test this, we quantified the proportion of AET occurring in the three months leading up to and including the peak, expressed as a percentage of the total AET over the 7-month period. This metric was then used to assess how well the models reproduced the observed AET distribution. The calculation was focused on the best-performing evaporation equation (evap_19), for the three hydrological models across the seven catchments under the multi-objective calibration to both streamflow and AET (Fig. 8a).

To determine whether this timing mismatch was due to model structure, we repeated the analysis calibrating solely to AET to assess whether the models had the capacity to match the observed timing more accurately (Fig. 8b). This approach was chosen to isolate the influence of streamflow constraints on seasonal AET behaviour.

Finally, we calibrated to streamflow alone to evaluate how much the AET timing deteriorated when AET was not explicitly considered in the calibration process (Fig. 8c). The results of this analysis are presented in Fig. 8, which confirms the initial impression about early timing of simulated AET. Further, it shows that although the AET distribution improves when calibrating to AET alone, seasonal AET timing remains a clear limitation of the models, even when utilising equation evap_19. To assess whether this behaviour is sensitive to the choice of PET forcing, an additional analysis using an alternative PET formulation is presented in the Supplement (S8), where the overall results were consistent with the original PET input results seen in Fig. 8.

This study systematically tested 15 AET equations within three widely used conceptual rainfall-runoff models across seven catchments with nearby flux tower AET data. This responds to the call for evaluation of evapotranspiration in hydrological models in previous work (e.g. Kelleher and Shaw, 2018; Dembélé et al., 2020), by isolating equation performance from model structure. Our results show that, while absolute performance varied across catchments and models, a small subset of AET equations, particularly equation evap_19, consistently ranked among the top performers relative to the others. Equations (3), (8), and (21) also performed well in some cases but exhibited more variability across models and sites.

While this study primarily focuses on AET equation performance rather than inter-model comparisons, some patterns emerged. For example, GR4J struggled to replicate AET at certain sites (e.g., Litchfield), even when recalibrated using AET-only optimisation. This suggests possible structural limitations in GR4J's partitioning of available water between AET and runoff, highlighting the importance of model-specific considerations when selecting or modifying AET equations.

The main remaining issue across models was that AET often peaked earlier than observed in the flux tower data. While Equation evap_19 consistently outperformed the others, it only partially addressed this problem – reducing but not eliminating the seasonal timing mismatch. Below, we first examine why equation evap_19 provides superior simulations, before unpacking the broader implications, both for equation evap_19 and the remaining challenges highlighted by this study.

To understand why evap_19 provides improved simulations, we first need to examine how it differs from other formulations. The structure of the equation is: 7AET=minS,PET,p1⋅PET⋅SSmaxp2, Two key features stand out: (i) its ability to restrict AET to below PET, even under high soil moisture conditions, via the p1 parameter; and (ii) its concave, non-linear relationship between AET and relative soil moisture, shaped by the p2 parameter. Both parameters are restricted between 0 and 1.

The p1 parameter introduces a physically meaningful limitation, reflecting that vegetation or atmospheric conditions often prevent actual evapotranspiration from reaching its potential rate (Fig. 9a).

The p2 parameter governs how AET responds to soil moisture: when p2=1, the relationship is linear; when p2<1, the relationship becomes concave, meaning AET increases rapidly at low soil moisture levels but tapers off as soil moisture becomes abundant (Fig. 9b). This behaviour appears to better reflect vegetation function in these catchments, where plants actively transpire when water is limited but taper water use under wet conditions, aligning with the need for more physically grounded representations of vegetation-mediated water use (Deb and Kiem, 2020).

The calibrated values of these parameters across the seven catchments and three models (see Supplement S9) show that p1 values were generally well below 1.0, indicating that this PET-limiting feature was frequently required to match observed AET patterns. For instance, in VIC, p1 ranged from 0.28 (Gingin) to 1.00 (Robson Creek), with similarly constrained values in GR4J and Simhyd. This suggests that the models often needed to invoke sub-PET limitations, which may reflect transport limitations on evapotranspiration, although further evidence is needed to confirm this. The p2 values also varied between catchments, often falling below 0.5 (e.g., Wombat Forest, Tumbarumba), indicating the need for a concave soil moisture response. That is, AET increases quickly under dry to moderate conditions but becomes less sensitive as soil moisture approaches saturation. While some evapotranspiration equations assume AET will continue increasing proportionally with soil moisture, this behaviour appears inconsistent with the flux tower data and the known role of vegetation in regulating water loss.

Together, these features help explain why equation evap_19 outperformed alternatives: it avoids the assumption that AET always equals PET under moist conditions, reduces over-extraction of water, and better captures the dynamic relationship between soil moisture and evapotranspiration observed in flux tower data.

Conversely, the poorer-performing AET equations exhibited several recurring issues. Many lacked explicit constraints or responded too linearly to changes in soil moisture, resulting in rapid water depletion and elevated AET values that rarely match flux tower behaviour. Several formulations allowed AET to equal PET frequently – an outcome that overlooks the regulatory role of vegetation and other limiting processes.

However, despite evap_19's relative improvements, it does not fully resolve all issues. As shown in Fig. 8, it still overestimates AET in early-season periods. This suggests our conceptual models are lacking the knowledge that water availability does not lead to immediate transpiration. AET equation evap_19 mitigates this issue more effectively than the other tested equations, but the challenge remains.

Accurate AET representation is essential for reliable hydrological modelling, particularly when applied to future climate scenarios (Zhao et al., 2013). Incorrect AET modelling could propagate errors, leading to misleading projections of water availability, catchment response, and long-term water balance estimates. Ensuring that AET equations appropriately constrain AET to realistic values is therefore required to improve model robustness and predictive capacity.

The findings of this study highlight how assumptions embedded within many conceptual models, especially linear or overly simplified relationships between PET and soil moisture, can lead to systematic biases in AET simulations. These relationships are often taken for granted rather than being critically evaluated, despite their substantial influence on model behaviour. By drawing attention to this issue, we hope to encourage deeper scrutiny of the ways AET is represented within hydrological models, particularly in light of observed vegetation responses (Duethmann et al., 2020).

The strong performance of AET equation evap_19 could potentially be attributed to its origin of purpose, in the conceptual hydrological model LASCAM, which, during its creation, included thought on the inclusion of vegetation impacts (Sivapalan et al., 1996). This included the interaction of the deep-rooted eucalyptus trees found within Australia, leading to the use of constraints on soil moisture availability and AET behaviour, which (as demonstrated here) are more realistic when evaluated against flux tower data. These insights suggest that existing models could benefit from replacing simplistic AET equations with more process-informed alternatives or by developing new formulations inspired by evap_19.

The additional parameters introduced in equation evap_19 (p1 and p2) exhibit substantial variability across catchments (Table S7), suggesting that location-specific calibration is necessary. These parameters represent unresolved controls on evapotranspiration, rather than strictly physical quantities. Their variability likely reflects differences in local evaporative regimes, vegetation characteristics, and climate conditions across catchments.

Therefore, an important direction for future research is to assess whether these parameters can be regionalised using mappable catchment attributes, such as aridity indices, vegetation functional types, or remotely sensed indicators of canopy dynamics. Additionally, incorporating spatially varying PET scaling approaches, such as crop coefficients or vegetation-adjusted PET, may help reduce the need for empirical suppression of AET under high moisture availability. These approaches would require more explicit representation of vegetation processes, which is beyond the scope of the current conceptual modelling framework but represents a promising avenue for future work.

While AET equation evap_19 consistently improved model performance, its limitations offer insight into deeper ecohydrological processes that remain unaccounted for, such as the seasonal partitioning of AET. Although evap_19 better matches overall AET signatures, it does not fully capture the observed differences in AET between the beginning and end of the season. Specifically, the catchments appear to be photosynthesising at a lower-than-expected rate (using less water and thus exhibiting lower AET) early in the season. This discrepancy likely arises because conceptual models, which lack explicit vegetation components, assume that water availability directly translates into immediate AET increases. In contrast, observed data suggest that the catchment does not use all available water at the start of the season, possibly due to physiological constraints on vegetation growth. If plants transpired at the rate the model predicts, they could experience excessive growth that would not be sustainable through the dry season. Similar findings have been reported in previous studies, such as Stephens et al. (2025), which found that catchments in intermediately wet regions (i.e. not arid or very wet) often exhibited lower-than-expected AET in wet periods. Lower-than-expected wet season transpiration was also demonstrated by Eamus et al. (2000) in savannah trees, suggesting that the vegetation's capacity to transport moisture may limit AET during the wet season.

The problems we found with seasonal timing of AET indicate that, even with improved AET parameterisation, conceptual models may still lack a critical physical mechanism governing seasonal water use. Future work should explore ways to incorporate such ecohydrological feedbacks into hydrological models, ensuring that the representation of AET accounts for vegetation constraints and long-term water availability strategies. Additionally, further studies should investigate whether this catchment behaviour is unique to Australian ecosystems or occurs more broadly. Australia's high interannual climate variability may encourage conservative water use strategies in vegetation that differ from those in more temperate or consistently wet climates (Norton et al., 2022). Exploring such geographic differences could help tailor model structures to better reflect regional vegetation–climate interactions.

An important source of uncertainty not explicitly explored in this study is the estimation of potential evapotranspiration (PET). Numerous studies have demonstrated that different PET formulations can produce different estimates of atmospheric evaporative demand, with implications for simulated evapotranspiration, soil moisture, and runoff (e.g. Oudin et al., 2005; Pimentel et al., 2023). In the present analysis, PET formulation was held constant across all experiments to isolate the effects of AET formulation specifically. To understand the implications of PET formula choice for a key finding of this paper, we reproduced Fig. 8 with Mortons Point Potential PET (Fig. S30). As part of this additional analysis, all three models were re-calibrated across the seven catchments using the alternative PET forcing. While some catchment-specific differences in the magnitude of timing mismatch were observed, the overall patterns and conclusions remained unchanged. The timing bias in simulated AET persisted across PET formulations, indicating that the early seasonal peak identified in the original analysis is not a consequence of the choice of PET input.

Moving forward, systematic evaluations of internal flux equations in hydrological models should become standard practice, particularly when combined with multi-objective calibration approaches that leverage real-world data such as flux tower observations. Although we recognise limitations associated with flux tower coverage, using such data helps highlight where improvements to model structure, rather than parameterisation alone, may be needed. Additionally, further integration of empirically driven, process-based enhancements in hydrological models could help refine AET representation. These improvements would aid hydrologists in selecting AET equations that best match their specific modelling objectives, ultimately enhancing the reliability of hydrological simulations across diverse environmental conditions.

Our study's inclusion of many models, catchments, and AET equations provides a comprehensive assessment, but future work should explore individual model performance in greater detail. A logical next step would be to test AET equation evap_19 within all 47 available hydrological models, using the same methodology applied here, to assess whether similar performance trends hold across a greater range of models. Additionally, this study did not evaluate AET equations in deficit-style hydrological models. Future research should extend this analysis to these alternative modelling frameworks to determine whether similar AET performance patterns emerge, particularly given evidence of more realistic AET dynamics in deficit models in water limited conditions (Fowler et al., 2021). Additionally, future research should consider testing these findings under spatial transferability and proxy-basins, explicitly targeting regionalisation or prediction in ungauged basins, an important avenue that lies beyond the intended scope of the present study.

It is also important to note that all results presented here are based on a single optimal parameter set for each model and catchment. Due to equifinality, there may exist a range of alternative parameter sets that produce similarly good performance but exhibit different trade-offs between streamflow and AET simulation, as well as different transferability properties (Khatami et al., 2019). For example, the strong performance of equation evap_19 for AET, coupled with occasional reductions in streamflow performance, may in part reflect calibration trade-offs within a single optimal solution. A more comprehensive assessment of model behaviour could therefore be achieved by analysing ensembles of near-optimal parameter sets, which would allow uncertainty in parameter estimation and trade-offs between objectives to be more fully characterised. While this was beyond the scope of the present study, it represents an important direction for future work and should be considered when interpreting the robustness of the results.

Lastly, we note the limitation discussed above, namely that the best-performing AET formulation – which we recommend other researchers test and, if appropriate, adopt – does not entirely solve the issues regarding seasonal timing of AET in the catchments tested here. Continued exploration of equation-level performance in controlled testing frameworks, like the one used here, will help tfo identify process representations that bridge conceptual and process-based modelling – a critical direction for future model development (Knoben et al., 2019; McMillan, 2021).