Soil moisture as the dominant driver of CO₂ efflux in Mediterranean urban green spaces: evidence for a Gaussian temperature response and mechanistic modelling of moisture and temperature interactions

Alía, Teresa; González-Ubierna, Sergio; Sánchez-Jiménez, Abel; Abad-Calderón, Rubén; Casermeiro, Miguel Ángel

doi:10.5194/egusphere-2026-3814

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https://doi.org/10.5194/egusphere-2026-3814

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22 Jul 2026

| 22 Jul 2026

Status: this preprint is open for discussion and under review for SOIL (SOIL).

Soil moisture as the dominant driver of CO₂ efflux in Mediterranean urban green spaces: evidence for a Gaussian temperature response and mechanistic modelling of moisture and temperature interactions

Teresa Alía, Sergio González-Ubierna, Abel Sánchez-Jiménez, Rubén Abad-Calderón, and Miguel Ángel Casermeiro

Abstract. Soil respiration, the release of carbon dioxide (CO₂) from the soil to the atmosphere, is a major component of the global carbon cycle, yet its dynamics in urban Mediterranean environments remain poorly understood. This study investigated the effects of soil temperature, soil moisture, and plant community identity on soil CO₂ efflux in urban green spaces of Madrid (Spain), a city with a Mediterranean climate characterized by pronounced summer drought. Four dominant ruderal plant communities (Diplotaxis virgata, Hordeum leporinum, Malva spp, and Dactylis glomerata) were monitored across three urban parks, with CO₂ efflux, temperature, and moisture measured biweekly over one year using an infrared gas analyzer. Contrary to the Q₁₀ exponential assumption, soil respiration showed a Gaussian relationship with temperature, with a positive correlation below a breakpoint of 18.4 °C and a negative effect above this threshold, consistent across plant communities. Soil respiration exhibited a positive exponential relationship with soil moisture and a logarithmic relationship with a rewetting index for values below 20. A mechanistic model described soil respiration as the joint outcome of temperature-driven moisture loss and moisture-stimulated CO₂ emissions. Plant community identity had a limited effect, with the exception of Malva spp., which consistently produced higher emissions. These findings challenge the universal applicability of temperature-based respiration models and highlight soil moisture as the dominant driver of CO₂ efflux in water-limited urban ecosystems. As climate change is expected to intensify both the urban heat island effect and summer drought in Mediterranean cities, soil moisture emerges as a critical variable for projecting urban soil CO₂ fluxes and for designing evidence-based management strategies for Mediterranean urban green spaces, including improved soil infiltration capacity, moisture-sensitive irrigation planning, and the incorporation of moisture-temperature coupling into urban carbon monitoring protocols.

Received: 27 Jun 2026 – Discussion started: 22 Jul 2026

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Teresa Alía, Sergio González-Ubierna, Abel Sánchez-Jiménez, Rubén Abad-Calderón, and Miguel Ángel Casermeiro

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RC1: 'Comment on egusphere-2026-3814', Susana Ferreira, 30 Jul 2026 reply

I found this manuscript to be well designed, clearly written, and scientifically relevant. The authors address an important question regarding the controls of soil respiration in Mediterranean urban green spaces and propose an interesting mechanistic framework linking soil temperature, soil moisture, and CO₂ efflux. The dataset is comprehensive, covering one full annual cycle, and the statistical analyses are generally appropriate and well described. Overall, I believe this work represents a valuable contribution to urban soil ecology and carbon cycling.

I have only a few comments that, in my opinion, would further strengthen the manuscript.

Major comments

Model validation
- The proposed mechanistic model is one of the main strengths of the manuscript. However, its performance would be easier to evaluate if it were quantitatively compared with more conventional approaches (e.g. the classical Q₁₀ model or other empirical temperature-response models).
- Including model performance metrics (for example, RMSE, AIC, BIC, or cross-validation statistics, if available) would provide stronger evidence that the proposed model offers a genuine improvement rather than simply a more complex fit.
Breakpoint robustness
- The identified breakpoint at 18.4 °C is central to the manuscript and underpins much of the subsequent interpretation.
- It would be helpful to provide additional information on the uncertainty associated with this estimate (e.g. confidence intervals or standard error) and briefly discuss its robustness.
Repeated measurements
- The statistical approach is generally appropriate, but I would appreciate a short clarification regarding the temporal structure of the data.
- Measurements were collected repeatedly over the same plots during one year. Please clarify whether temporal autocorrelation was assessed or considered during model development, or explain why it was not necessary.

Minor comments

Although the conclusions are generally well balanced, I suggest slightly moderating a few statements referring to Mediterranean urban ecosystems in general, as the study was conducted in three urban green spaces within a single metropolitan area. The current discussion already acknowledges this limitation, but a slightly more cautious wording in the Conclusions would improve consistency.
The manuscript is very well written. I only noticed a few minor typographical and grammatical issues that can easily be corrected during the final revision.
Figures are generally of high quality and effectively support the results. The only suggestion would be to ensure that all axis labels and symbols remain easily readable after journal formatting.

Citation: https://doi.org/10.5194/egusphere-2026-3814-RC1

AC1: 'Reply on RC1', Sergio González Ubierna, 15 Aug 2026 reply

We would like to thank Dr Ferreira for her very positive evaluation of the manuscript and her constructive suggestions, which have strengthened the statistical robustness and interpretability of the proposed model. We have addressed the minor comments and are now working on the major ones.

Minor comments:

We have revised four sentences in Section 6 that referred broadly to 'Mediterranean urban ecosystems/cities', so that they now refer specifically to the three urban green spaces studied. This is consistent with the caveat already present in Section 5 (Limitations).
We corrected a typo in the word 'Antrosols/Anthrosols' (also noted by the other referee), an incorrect plant-community code in Section 4 ('AG-D', corrected to 'AH-D'), and a missing space after a citation in Section 4.
We reviewed all figures and confirmed that fonts and statistical symbols are legible at the current resolution. We also enlarged Figure 2 as requested by the other referee and will verify legibility again at the galley-proof stage..

Major comments

We agree that addressing all three major comments would strengthen the manuscript, and we are currently carrying out the relevant analyses. Due to the technical nature of these analyses, and the summer holiday period, we kindly ask Dr Ferreira to understand that the full results will be presented in our final response at the end of the discussion period, together with the revisions made to the manuscript. Our planned approach to each point is as follows:

Model validation: we will fit a standard Q₁₀ exponential model to the same dataset and report the root mean square error (RMSE), Akaike information criterion (AIC) and/or Bayesian information criterion (BIC) for both the Q₁₀ model and our proposed mechanistic model in an expanded Table 6, as well as providing a corresponding summary in Section 3.4 and the Discussion.
Breakpoint robustness: We will report the standard error and 95% confidence interval of the 18.4 °C breakpoint. These results will be presented in Sections 2.3 and 3.2.1/3.3, together with a brief discussion of the robustness of the breakpoint.
Temporal autocorrelation: We will assess the residual temporal autocorrelation of the fitted mixed models using ACF/Durbin–Watson tests. The outcome will be reported in Section 2.3. If autocorrelation is detected, the models will be refitted using a first-order autoregressive correlation structure, and the results will be compared to confirm robustness.

We would like to thank Dr Ferreira again for these constructive suggestions and will continue to engage with any further comments during the open discussion period.

Citation: https://doi.org/10.5194/egusphere-2026-3814-AC1

AC4: 'Reply on AC1', Sergio González Ubierna, 27 Aug 2026 reply

We thank Dr. Ferreira for her patience while we completed the additional analyses requested for the three major comments. We present the completed results below.

Model validation

We fitted both a standard Q₁₀ exponential model and the Gaussian model of Lellei-Kovács et al. (2011) — already cited in the manuscript — to the same dataset, and compared them against our proposed mechanistic model:

Q₁₀	4451.04	4465.18	3.602	< 2.2×10⁻¹⁶
Gaussian (Lellei-Kovács et al., 2011)	4365.95	4384.80	3.417	0.017
Proposed mechanistic model	4362.26	4385.83	3.405	— (reference model)

Our proposed model achieved the lowest AIC and RMSE of the three, and a BIC essentially equivalent to the Gaussian model (difference < 1.5 points), despite BIC's stronger penalty for additional parameters. Likelihood-ratio tests confirmed that our model significantly reduces deviance relative to both alternatives (Q₁₀: p < 2.2×10⁻¹⁶; Gaussian: p = 0.017), providing direct statistical evidence that the improvement in fit reflects genuine explanatory gain rather than simply added flexibility.

We also note that our model is not substantially more complex than the alternatives: it has 4 free parameters (same order of complexity as a standard Gaussian model) and these parameters are already used in Section 2.4 (Eqs. 6–7) to analytically derive the biologically interpretable quantities Tᴄₘₐₓ and Cᴄₘₐₓ reported in Table 6, which the purely empirical Q₁₀ and Gaussian formulations do not provide.

Finally, addressing the referee's specific mention of cross-validation statistics, we performed a leave-one-plot-out cross-validation of the proposed mechanistic model:

Original fit	3.217	2.359	0.007	0.224
Leave-one-plot-out CV	3.287	2.417	0.011	0.189

The cross-validated metrics are very close to the original in-sample fit, indicating that the model is not overfitted and generalises well to plots not used in parameter estimation. This model comparison and cross-validation will be added as a new Table 7 and Table 8 at the end of Section 3.4, with a corresponding summary sentence added to the Discussion.

Breakpoint robustness

We report the standard error and 95% confidence interval of the breakpoint, obtained via confint.segmented() (R package segmented, Muggeo, 2008): the estimated breakpoint of 18.4 °C has a 95% CI of (17.17, 19.79) °C. This relatively narrow interval (±1.3 °C around the central value) supports the robustness of this threshold as a meaningful biological value rather than a statistical artefact. This will be added to Sections 2.3 and 3.2.1, with a brief discussion of its robustness added to the Discussion.

Repeated measurements / temporal autocorrelation

We agree that the random intercept per plot already described in Section 2.3 addresses spatial pseudoreplication (multiple plant communities nested within the same plot) but does not by itself account for temporal autocorrelation of the fortnightly repeated measurements within each plot over the annual cycle. We explored this for the mechanistic model described in Section 2.4.

The purpose of this analysis was not to estimate population-level or plot-level effects, nor to quantify between-plot variance, but to test whether the theoretically derived functional form could reproduce the observed relationship between soil respiration and soil temperature. We nonetheless fitted a nonlinear mixed-effects version of the model, including plot as a random effect and alternative temporal correlation structures. Models incorporating a first-order autoregressive structure (corAR1) converged and yielded parameter estimates broadly consistent with the original fit (Supplementary Table S2, Supplementary Fig. S1), with optimum temperatures (Tᴄₘₐₓ) shifting modestly (+0.5 to +1.5 °C) while preserving the same ranking between plant communities. More complex correlation structures (e.g., corARMA) also converged but were less stable, with parameter estimates more sensitive to model specification.

Residual temporal autocorrelation could not be fully eliminated under any structure tested; we consider this likely to reflect shared seasonal environmental drivers acting on soil respiration across all plots simultaneously, rather than a violation of the independence assumption for which the model was not designed. Because the mixed-effects formulation introduces variance components that are not part of the theoretical relationship being tested, and given the sensitivity of these components to model specification, we regard the mixed-effects results primarily as a sensitivity analysis rather than as an alternative primary estimate; the original model (Table 6, Fig. 12) is retained as our main result.

For reference, the corAR1 parameter estimates are shown below (Supplementary Table S2):

AH-D	0.0751	0.0014	0.6856	17.77	4.95
AG-H	0.1516	0.0028	0.3323	19.50	6.71
PH-M	0.0758	0.0014	1.3376	17.93	7.97
PG-D	0.0746	0.0012	0.9744	16.83	4.94

Compare with the original fit in Table 6 (Section 3.4). The ranking of optimum temperatures between communities (PG-D < AH-D ≈ PH-M < AG-H) is preserved relative to the original model, so the interpretive statements in the Discussion regarding PH-M and AG-H remain valid under this sensitivity analysis.

The corresponding fitted curves (Supplementary Fig. S1, attached) are shown below, for direct comparison with Fig. 12.

Citation: https://doi.org/10.5194/egusphere-2026-3814-AC4

RC2:
'Comment on egusphere-2026-3814', Anonymous Referee #2, 13 Aug 2026 reply
The authors demonstrate the importance of soil moisture in regulating soil respiration under a Mediterranean climate, where water limitation can constrain the temperature response of soil respiration. This study also highlights the importance of water management in urban green areas, given the potential effects of urban warming on soil respiration. However, the manuscript contains numerous formatting, typographical, and presentation errors throughout the text. The authors are strongly encouraged to revise the manuscript carefully to ensure that the main arguments are presented clearly, consistently, and accurately.
Comments:
p3: Typo? Antrosols → Anthrosols

Could you provide more details about the study sites? I am curious about the study areas (size) and how the four plant communities were distributed within each study site. How many replicate sampling points do you have?

Table captions should be placed above the table.

Gas sampling time is important because temperature varies throughout the day. Could you clarify how the measurements were randomized? Were there differences in measurement timing among plant communities or study sites? Could you also provide the range of measurement times?

4.1 Could the higher CO2 emissions in PH-M be related to higher temperatures at the time of measurement?
4.2 Given the large diurnal temperature variation in this region, it is unclear what the 18.4 °C breakpoint represents. Do the confounding effects of soil temperature and moisture occur mainly at the diurnal scale or at the seasonal scale?
How did you measure the evapotraspiration level (mm day-1; A different unit is used in Figure2)?

Figure 2: Please increase the font size in the figure.

Figure 8: The graph on left and right looks the same.

Reply
Citation: https://doi.org/10.5194/egusphere-2026-3814-RC2
- AC2: 'Reply on RC2', Sergio González Ubierna, 15 Aug 2026 reply
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3814/egusphere-2026-3814-AC2-supplement.zip
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2026-3814-AC2
- AC3: 'Reply on RC2', Sergio González Ubierna, 15 Aug 2026 reply
  
  We would like to thank the referee for their positive assessment of the relevance of the study and for their detailed comments aimed at improving the clarity, consistency and accuracy of the manuscript. All comments have been addressed, as summarised below.
  1. Typo: “Antrosols” → “Anthrosols” --> Corrected throughout the manuscript.
  2. Details on study sites
  
  The study was conducted in three urban green spaces in Madrid: Ciudad Universitaria, La Elipa and Pinar de Conde Orgaz, which spanned approximately 1.9, 0.8 and 0.5 km along their longest axis, respectively. Within each site, three replicate sampling points were established for each of the four plant communities (three replicates × four communities = 12 points per site; total n = 36 sampling points). The following information will be added to Sections 2.1–2.2: site extent, spatial distribution of communities, and replicate information. The caption of Table 1 will be amended to n = 3 and the relevant sentence in Section 3.1 will be revised. The coordinates of all sampling points are provided in a new Supplementary Table S1. We have also attached a map showing the sampling points.
  3. Table captions above the table --> Agreed; all table captions will be moved above their corresponding tables.
  4. Gas sampling time and randomization
  
  The order in which the three parks were visited was systematically rotated so that each sampling campaign began at a different park, and within each park the order of visiting the 12 sampling points was randomized using a 12-sided die. Measurements were carried out between 08:00 and 18:00–19:00 h local time. We will add this description to Section 2.2.
  5. Could higher CO₂ emissions in PH-M reflect measurement-time temperature differences?
  
  This is unlikely, as soil and atmospheric temperatures did not differ significantly among plant communities (see Table 2), and as mentioned above, the sampling order was rotated and randomised across a wide daily timeframe. We will add a clarifying sentence to the Discussion section.
  6. What does the 18.4 °C breakpoint represent given diurnal temperature variation?
  
  The breakpoint is derived from a piecewise regression on the full annual dataset and therefore predominantly reflects seasonal rather than diurnal variation in soil temperature. We will add a paragraph to the Discussion clarifying this point.
  7. Evapotranspiration unit and measurement method --> The correct unit is mmol mol⁻¹, measured directly by the LI-8100 chamber as the water vapor mole fraction at the soil surface; Figure 2 was already correct. We will correct the unit in Section 2.3 and in the Table 2 legend, and add a sentence describing the measurement method.
  8. Figure 2: font size --> Figure 2 will be regenerated with larger axis titles, tick labels and legend text.
  9. Figure 8: left and right panels look the same --> Sorry, this was a mistake. The left panel should show the correlations (SST <18.4°C) instead of the partial ones. We will correct it.
  We would like to thank the referee again for these valuable comments. We believe that they will substantially improve the clarity and rigour of the manuscript.
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2026-3814-AC3

Teresa Alía, Sergio González-Ubierna, Abel Sánchez-Jiménez, Rubén Abad-Calderón, and Miguel Ángel Casermeiro

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Short summary

Urban parks store and release carbon, but what controls this process in Mediterranean cities remains poorly understood. We monitored carbon dioxide emissions from soils in three Madrid parks over one year and found that soil moisture, not temperature, is the main driver. Surprisingly, emissions declined at high temperatures, not because heat suppresses soil life, but because hot summers dry out the soil. Keeping urban soils moist is key to managing their carbon balance under climate change.


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