the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Feb 2026
Incorporating spatial heterogeneity into evapotranspiration estimates for bioretention basins
Abstract. Green stormwater infrastructure (GSI) systems like bioretention basins are frequently used in urban settings to reduce the amount of stormwater runoff entering combined sewer systems, thus protecting downstream waterbodies. Retaining stormwater in GSI allows it to infiltrate into the soil or return to the atmosphere via evapotranspiration (ET). While infiltration rates can be quantified with reasonable accuracy, methods of quantifying ET typically rely on models designed for homogeneous landcover like agricultural fields; the high spatial variation in factors including vegetation, light, and soil moisture renders estimates of ET from bioretention basins highly uncertain. To assess the influence of such variation on basin-scale ET and evaluate means of correcting for it, we quantified ET for a bioretention basin in Philadelphia, USA using three approaches: (1) an empirically-based model that incorporated direct measurements of ET and accounted for heterogeneity in plant size, light conditions, and microtopography, (2) an empirical estimate of ET based on changes in soil moisture that did not account for spatial heterogeneity, and (3) a series of conventional ET models that did not account for spatial heterogeneity. We further evaluated three methods of adjusting modeled ET estimates to better align with ours. Our empirically-based model found basin-scale daily ET to range from 0–6 mm d-1, with temporal variation dependent on weather conditions and time of year. A sensitivity analysis demonstrated that the spatial composition of plant height and shade strongly influenced basin-scale estimates. The soil moisture-based method found daily values to range from 0–4 mm d-1, which largely agreed with the empirically-based modeling estimates for the location where sensors were placed, but underpredicted estimates of basin-scale ET. Most conventional models overpredicted ET compared to our empirically-based values on average, though three were less sensitive to variation in atmospheric conditions (Granger-Grey, Hargreaves-Samani, and Matt-Shuttleworth) and thus overpredicted ET at the low to middle part of the range but underpredicted ET at the upper end of the range. This limited the ability of additive or multiplicative adjustments to improve agreement, though adjustments were highly effective for the three conventional models more sensitive to atmospheric conditions (Penman-Monteith ASCE, Penman-Monteith FAO, and Priestly-Taylor). The strongest agreement we could achieve came from an additive adjustment to Penman-Monteith-derived values (subtracting 2.31 mm d-1 from the ASCE formulation or 1.82 mm
d-1 from the FAO formulation). Multiplicative adjustments (i.e., landscape coefficients) and corrections accounting for shade were also effective. Our results highlight the importance of implicitly or explicitly accounting for spatial heterogeneity when quantifying ET, especially with respect to vegetation height and shade. For basins similar to our focal basin, this can be accomplished through the provided adjustments to conventional models. Additional calibration is required otherwise, but the growing availability of required data makes this increasingly viable.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-22', emmanuel berthier, 17 Apr 2026
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AC1: 'Reply on RC1', Josh Caplan, 21 Apr 2026
Thank you for the time and effort you dedicated to this review. We appreciate the positive feedback as well as constructive comments. Once we have the full set of reviews, and assuming a revision is requested, we will attempt to address all of the comments in our next version of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-22-AC1 -
AC3: 'Reply on RC1', Josh Caplan, 30 Jul 2026
First, I must acknowledge that I did not fully understand the HESS review process and therefore did not initially respond to this reviewer’s comments in a useful way. Thankfully, a coauthor clarified the process for me so I will now provide a response more useful for determining how to proceed.
The supportive comments from this reviewer are gratifying, especially given the extensive and careful work we have put into this work. The requests for additional details (notably for the empirical/statistical model, which were also made by reviewer 2) can be readily accommodated.
Addressing the variation in wind speed and VPD on ET in the discussion is a very good idea. It will necessarily be speculative, but the reviewer has provided some interesting possibilities already. Regarding the weather station data though, one station was in the basin while the other was well above it, so a comparison of the wind speed and VPD datasets would not be as informative as one would like. Still, we can address likely possibilities for how these factors influence ET (in the context of both conventional models and our chamber-based estimates) and point out the value of better characterizing them in future work, as suggested. We agree that the lack of variation in wind speed in our empirical/chamber-based estimates could help to explain the offset with some of the conventional models (notably PM), and will include this idea in a revision, if invited.
The reviewer’s observations on water stress (namely the apparent lack of it) are insightful and dovetail with a comment from the other reviewer. We would like to quantitatively evaluate the effect on conventional ET model estimates using water stress corrections, as suggested by the second reviewer. Although we expect the effect to be small (as suggested by this reviewer), quantifying it will not be difficult and will be a useful addition to the manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-22-AC3
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AC1: 'Reply on RC1', Josh Caplan, 21 Apr 2026
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RC2: 'Comment on egusphere-2026-22', Anonymous Referee #2, 15 May 2026
I welcome the authors efforts to address this complex challenge. The work provides valuable real insights into the heterogeneity encountered when attempting to characterise bioretention basins. The chamber data and spatial characterisation of the basin are valuable and useful contributions to science in their own right.
I feel the paper should be published subject to the following comments being addressed:
The naming of the three approaches, e.g. in the abstract, does not seem to be as precise and unambiguous as it could be. (1) and (2) both refer to ‘empirically-based estimates’ (vague), and could perhaps be better distinguished by specific reference to (1) chamber measurements undertaken at multiple locations and (2) a single vertical profile of measured soil moisture content.
The development of the statistical model (1) – Section 2.5 – is difficult to follow and not particularly transparent. The parameterized model, i.e. the final selected regression coefficients and parameters, should be clearly presented in the main body of the paper (e.g. within the Results, Section 3.1).
Define R2marg and R2cond.
For completeness, (for readers unfamiliar with the use of chamber experiments) please state how ET in mmol m-2 s-1 is converted into ET in mm day-1. This could be included in the Supplementary Material.
I can see the value of comparing ET estimates based on soil moisture measurements against the chamber experiments, but I don’t understand the logic of deliberately trying to capture the heterogeneity with the chamber experiments compared with sampling at only one location with the soil moisture sensor. This is not really comparing the two measurement techniques, rather it’s comparing two spatial sampling approaches while also varying the measurement technique! Why did you not use multiple soil moisture sensors to better understand the localised variations in ET? This also leads to some speculation around line 346-7. The authors have noted that multiple sensors would be better (Line 350-351), but this doesn’t remove the question around experimental design. Consider simply introducing the soil moisture measurement approach as an order-of-magnitude sense check to the chamber-based model.
I am confused about whether/why moisture stress factors were, or were not, included in the application of the conventional models, Section 2.8. For FAO PM, normal practice would be to apply a water stress factor to the reference ETo in order to estimate actual ET. However, the commentary in Section 3.5 suggests that you did not include water stress. It looks as though (Supplement 3) you (potentially) included soil moisture content in the development of your empirical model, but then excluded it from your comparisons against the conventional ET models – I’m not sure that this is a fair comparison.
I understand that you have used KL as a calibration coefficient to scale the estimates from the conventional ET models to better match your chamber measurements. I believe that the values ranged between 0.5-1.0 (Line 393). Please refer to Table 3 at this point in the text, as the actual values are easy to miss within the table.
The additive correction does not seem to be well justified or transferable, and could potentially lead to negative ET estimates. Is there a precedent in the literature for doing this? This is likely to be quite case-specific and not generally transferable. The reader can already see the offsets in Figure 7. It would be more useful to explore whether the inclusion of moisture stress factor addressed some or all of the overprediction observed with the conventional models.
Lines 464-466. Again a request to actually share the fitted statistical model so that the reader can see for themselves how ET varies explicitly with plant height.
Minor corrections:
- Line 25 – ‘align with ours’ should be ‘align with the ET estimate based on the chamber measurements’.
- Line 67 – ‘such multiplying’ should be ‘such as multiplying’.
- Line 106-108 – where exactly is the ‘rocky gabion’? What do you mean by ‘above’, ‘below’ and ‘lower’ in this context? Are these relative elevations, or upstream/downstream or north/south? Please also check lines 170-171 re the use of the terms lower and upper.
- Line 247 – should ‘raw time of solar radiation’ be ‘raw time series of solar radiation’. I don’t think you adjusted the time.
- Do ‘tall’ and ‘short’ (Table 1) equate to ‘large’ and ‘small’ (Figure 2)? Please use consistent terminology.
Citation: https://doi.org/10.5194/egusphere-2026-22-RC2 -
AC2: 'Reply on RC2', Josh Caplan, 29 Jul 2026
We appreciate the reviewer acknowledging the strengths of our work, as well as making several recommendations that will improve it. The requests for clarification and further explanation (especially about the statistical model) are all straightforward; some of the comments will require more effort to address but can be done successfully in a revision.
For one, we agree that using a single profile of soil moisture sensors to estimate ET is insufficient to capture spatial variation; in addition to taking the reviewer’s suggestion on presenting this method as an order of magnitude check, we would also like to point out that it is a somewhat common practice to calculate ET this way by stormwater engineers.
Along similar lines, we have seen many stormwater engineers most often using ET model output without correction (which is why we present the conventional model results that way), though we agree that soil moisture corrections should be applied. If invited to review, we could present a second set of convention model ET estimates that include these corrections. That said, we suspect that soil moisture was high enough that the difference will be relatively small. We may therefore make this a supplemental figure.
Regarding additive correction, we certainly agree that multiplicative corrections are more common. However, there are examples of additive correction in the literature, sometimes being called bias correction (e.g., https://doi.org/10.1016/j.agwat.2018.08.003). We do not think that the reviewer is asking us to remove it, but the comment indicates that some additional contextual statements may be helpful.
Citation: https://doi.org/10.5194/egusphere-2026-22-AC2
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General comments:
Very interesting article on how estimate at high spatial resolution the evapotranspiration fluxes (ET) in the very heterogeneous urban canopy. The subject is important for the estimation of the runoff reduction in green space but also of the water need of urban green space.
The article is outstanding due to the diversity of estimation, with measurements (chamber as the reference but also soil water content) and modeling (empirical-statistical as the reference but also a wide range of conventionnal formula).
The work is very clearly presented, with a very complete and rigourus methodology combining different aspects (shading, vegetation characterisitcs, statistical test, ...). The database with the characterisation of the site (soil, vegetation, topography, urban scene) and with the temporal series of different hydrological and meteorological variables is really interesting and outstanding.
The form is perfect, with clear text and illustration ; I do not have a look to the data (https://www.hydroshare.org/resource/ba487d9c6e4b473f88d8298499ee1c6d/), due to a lack of time.
Specific comments:
See the pdf file for specific and detailed comments.
I suggest "Minor revision" (rather than "accepted subject to technical corrections") because I suggest to add some details on the development & performance of the empirical model (adding a chapter in the Supplementary Information at least). The evaluation is presented positivly in two lines in the article (L284-285), even though the model is subsequently used as a reference throughout the rest of the article. It would be useful, at the very least, to show and discuss the observed/simulated scattergram at the basin scale, and, if possible, at the various measurement points as well.
Three other points could be add in the discussions part:
- the spatial role of other micrometeorological conditions than the radiation, for example the wind or the VPD ? Do you have some site informations of these variability (contrast in the two weather station for example) ? For another work, it could be possible / interesting to introduce such spatial variables in the empirical model ?
- At different lines in the article, the validity of conventional models (=formulas) is debated in terms of whether or not they take water stress into account (for example, lines 427–429). Upon examining the soil water content at -5cm (Fig. 3d), I find that the values are not particularly low (and one would expect higher values at greater depths) and that it is not certain that ET could be limited by soil water availability. This hypothesis is consistent with the shape of the scatter plots between ET values simulated by the empirical model and the different formulas: for example, this relationship is highly linear for the PM formulas across all ranges of ET values (Fig7), including high values whereas for these high values one might expect more severe water stress to occur. In summary, I get the impression that ET water limited situations are rare in the database, and therefore that the reasons for the offset between the empirical model and the PM models must be sought elsewhere ;
- The linearity of the relationships between the empirical and PM models, which consistently involve a simple offset, is truly impressive. A theoretical comparison of the two models could be useful for analyzing the following observation:
+ the empirical model uses the following explanatory variables: topography (via a 1/0 index), vegetation height (spatial variability only?), VPD (temporal variability only?), solar radiation (spatial and temporal variability), and soil moisture status (temporal variability at a single point); it is statistically calibrated on 7 x 11 daily ETs;
+ PM formulas primarily use the temporal variability of solar radiation, VPD, wind, and temperature, with a constant vegetation height.
So, for example, the effect of wind is taken into account in PM (via its aerodynamic term), which is not the case in the empirical model. Could this be a source of overestimation of PM ET ?