Global patterns of directed soil moisture influence on air temperature

Guo, Xiaohang; Han, Jichong; Shao, Huaiyong; Zhu, Xinyan; Sun, Xiaofei; Ling, Long; Chen, Zimeng; Liu, Gang

doi:10.5194/egusphere-2026-2866

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https://doi.org/10.5194/egusphere-2026-2866

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15 Jun 2026

| 15 Jun 2026

Global patterns of directed soil moisture influence on air temperature

Xiaohang Guo, Jichong Han, Huaiyong Shao, Xinyan Zhu, Xiaofei Sun, Long Ling, Zimeng Chen, and Gang Liu

Abstract. Soil moisture regulation of near-surface air temperature is essential for improving global climate prediction skill. Yet conventional statistical methods are often insufficient to establish causality, and the dominant pathways of this coupling remain poorly understood at the global scale. Here we combine multiple datasets with the information flow method to quantify the effects of soil moisture on temperature. We find that significant soil moisture–temperature causality exists over about 37 % of the global land area. This causality is dominated by the evaporative and sensible heat pathways, affecting 33.5 % and 18.5 % of land area, respectively, while both pathways co-occur over an additional 7.6 % of land area. In addition, these strong causal relationships are mainly driven by soil moisture variability, while most CMIP6 models tend to overestimate the likelihood of such coupling. Our study identifies the main characteristics of land–atmosphere interactions from a causal perspective and provides an important scientific basis for improving land-surface processes in future climate models.

Received: 18 May 2026 – Discussion started: 15 Jun 2026

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Xiaohang Guo, Jichong Han, Huaiyong Shao, Xinyan Zhu, Xiaofei Sun, Long Ling, Zimeng Chen, and Gang Liu

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-2866', Anonymous Referee #1, 21 Jul 2026
General Comments:
The manuscript addresses an interesting topic by applying the Liang–Kleeman information flow framework to investigate soil moisture–temperature coupling at the global scale. The analysis is comprehensive, examining the problem from different angles, including coupling pathways, seasonality, reanalysis vs GCMs, among others. However, several aspects of the manuscript organization and interpretation should be improved before publication.
The manuscript would benefit from a clearer discussion of its scientific contribution relative to the existing literature. Several findings, such as, the stronger coupling in regions with high soil moisture variability, or the persistence of coupling in deeper soil layers, are generally expected and consistent with well-established knowledge. The authors should better position their results with respect to previous studies (e.g., compare the identified hotspots with previous work) and explicitly state the added value of applying the Liang–Kleeman framework over existing approaches.

The organization of Sections 3–5 is somewhat inadequate. Subsections 4.1 and 4.2 primarily present results and would fit better within Section 3 (Results) rather than in Section 4 (Discussion). The actual discussion starts in Sections 4.3 and 4.4, which could either remain as the Discussion section or be merged with Section 5 into a combined Discussion and Conclusions. Moreover, the current Conclusion section is rather limited and does not address the gaps identified in the introduction (e.g. L38-41).

Specific Comments:
Section 2.1: Please report the spatial resolution of ERA5.

Please include Table S1 (list of GCMs) in the main manuscript. It would also be useful to report the native resolution of each GCM and the soil depth represented by “mrsos”.

L72: Please clarify what is meant by “model structural diversity”.

The manuscript should explain how the different soil depths among ERA5, GLEAM, and the CMIP models are handled to perform a fair comparison.

L93–101: The description of the Liang–Kleeman information flow framework should be revised for clarity. There are several grammatical and notation inconsistencies (e.g., incorrect capitalization after equations and identation). In addition, using (T) for both temperature and the information flow (Eq. 1) is potentially confusing and should be clarified or replaced with less ambiguous notation. Lastly, it would be helpful to briefly explain the physical interpretation of each term of Eq. 1 and the possible range of the index.

L165 and L259: Although significant coupling persists in the second soil layer, Fig. S1 shows a marked reduction in both spatial extent and strength with increasing depth. The discussion should better reflect this overall weakening rather than support that “deeper soil moisture layers continue to exert significant control on temperature…”.

L182: The discussion highlights Australia as presenting a strong SSM->SH relationship, whereas Fig. 2b shows relatively weak coupling there. Other regions seem to exhibit much stronger signals.

Fig. 2: Please clarify whether the analysis corresponds to the top soil layer.

The spatial patterns in Figs. 1 and 2 are difficult to reconcile. Figure 1 indicates that significant SSM→T coupling is confined to relatively limited regions, whereas the individual pathways in Fig. 2 appear significant over much larger areas. In particular, the terrestrial legs (SSM→ET and SSM→SH) are broadly consistent with Fig. 1, whereas the atmospheric legs (ET→T and SH→T) extend across most continents. Since Fig. 2 is intended to explain the mechanisms behind Fig. 1, I would expect greater spatial consistency. Would masking the atmospheric maps to regions with significant terrestrial coupling, or using a different color scale or class intervals, improve the interpretation?

Fig. 3: Panel (c) This is an interesting figure, but the probability values are difficult to distinguish. The meaning of the circle sizes should be explained in the caption, and a discrete color scale (e.g., 5% intervals) would facilitate interpretation. Similar suggestions apply to Figs. S6–S7 and Fig. 7. Panel (d): Why are the soil moisture variability percentile bins defined using unequal intervals?

L216: The relationship between soil moisture variability and coupling strength is largely expected, since temporal variability is a prerequisite for soil moisture to influence temperature. This result therefore seems to reinforce the existing understanding rather than represent a novel finding and should be discussed in the context of previous literature. In addition, the manuscript repeatedly refers to land-atmosphere “feedbacks”, although only the directed influence of soil moisture on temperature is evaluated; but the reciprocal atmospheric influence required to characterize a feedback is not analyzed.

Fig. 4: It would be helpful to include the global ERA5-Land map as a visual reference.

L268–277: I disagree with the interpretation because the discussion overlooks the opposite seasons of the two hemispheres. The results indicate stronger coupling during the warm season of each hemisphere, rather than during the boreal warm season alone. A version of Fig. 5 separated by hemisphere could help illustrate this point.

Section 5 concludes that deeper soil moisture exerts more persistent influence on temperature. Given that deeper layers generally exhibit longer memory, this conclusion appears expected. The discussion should better distinguish between expected behavior and genuinely new insights.

Technical Comments:
L164: I believe the correct reference is Fig. 1b rather than Fig. 1a.

Fig. 1: Please add latitude–longitude gridlines in the map to facilitate the link with panel (a).

Supplementary figures are not presented in the order in which they are first cited in the manuscript. For example, Fig. S10 is discussed before Figs. S2 and S3.
Citation: https://doi.org/10.5194/egusphere-2026-2866-RC1
- AC1: 'Reply on RC1', jichong han, 05 Oct 2026
  
  We sincerely thank the reviewer for their careful evaluation of our manuscript and constructive suggestions, which have helped us improve the paper.
  Our detailed point-by-point responses are provided in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2026-2866-AC1
RC2:
'Comment on egusphere-2026-2866', Anonymous Referee #2, 08 Sep 2026

This study applies the Liang-Kleeman information flow to understanding the causal SM→T relationship. I think the main research idea is very good, and the use of the LKIF is relevant for exploring this, however, I find quite a lot scientific shortcomings in the design, the method application and the write up. The motivation of using the climate models, I think, is quite a disadvantage, as this has been explored quite well for this coupling. I believe the LKIF, as an independent method, can be used for much more than this presentation here. Nonetheless, within the current set up, there is still some merit from this study, and I have provided detailed comments to help the authors think carefully about the study. Please find my comments below.
1. Lines 25: It might be helpful to define what the authors mean by land–atmosphere coupling here. The definition by Seneviratne et al. (2010), Appendix A is helpful.
2. Line 26-27: It's a bit ambiguous how surface partitioning would become increasingly complex. A reference and a more targeted detail would be more helpful to make the case.
3. Lines 27-29: This sentence is key for making the argument for the paper, however, I think the case has not been well made. A rewrite is important here. Firstly, I suggest starting with land–atmosphere coupling/interaction, from which which the SM–T coupling would emerge, linked to the water, energy and carbon cycles, and then eventually, to extremes in the past and their implications for the future. Having done that, this sentence can be refined to make the argument.
4. Lines 31-35: As a causality expert, I agree with this sentence and encourage seeing it more in literature. However, I think it is also an understatement to lump all existing studies, nitpicking some, into a correlation/statistics bubble. Very early studies like the GLACE experiments relied more on sensitivity climate model simulations with soil moisture, use of some key methods like the Empirical Feedback Analysis, etc. The approach of Schwingshackl et al, cited here for instance, is a very physical method. Also, the method presented by Dirmeyer 2011 (GRL) is also a rather helpful one, as well as the study by Hsu & Dirmeyer 2021 (WRR). For a helpful list, see this link: https://www.pauldirmeyer.com/coupling-metrics. It's important to properly acknowledge the body of works existing.
5. Line 36-38: This is quite an anti-climax. Firstly, please check your references very carefully. Secondly, I think just mentioning 'information flow technique' here does not really help the argument the authors are trying to make. The methods in the references do not do information flow explicitly. Please revise the literature review used here.
6. Lines 38-39: Again, I think a better argument can be made here. Causality, as used in this paper, is firstly not defined. Secondly, please consider works like Dirmeyer et al (2006) and others that have explored the mechanisms within this pathway.
7. Lines 40-41: Dear authors, please consider your literature review and the exact studies needed to make the arguments here. I would disagree that after works like Hsu&Dirmeyer (2023), etc..., we can say this is poorly separated. This is quite a harsh discrediting of their study, which I disagree.
8. Line 42: Climate models are one way. Not the primary tool. See the LoCo paper by Santanello et al 2010 (BAMS). Also, while it's not wrong to use feedbacks here, I am not sure if the use here is a matter of language consistency. When does the paper choose to use interaction/coupling/feedback? Please consider adding a reference.
9. Line 45: Please specify which feedback is meant by 'this feedback'
10. Lines 46-50: This sentence might need a rewrite. Maybe, start from Koster et al (2004,2006) and build on that. The current two sentences a bit conflicting.
11. Lines 50-52: I don't think this true. The GLACE experiment already did a lot for us in this regard. Since then, other studies have done more of that too.
12. Lines 55-56: "we investigate the physical processes mediating these land–atmosphere interactions"...this is quite a statement. Perhaps, restrict it to connecting SM to T (Again, see Santanello et al 2010). A better framing of the sentence would be helpful.
13. Any reason why evaporatranspiration, rather than latent heat is used? Since Sensible heat is also used here.
14. Line 57: I suggest removing "the strength of". Note that the Liang-Kleeman information flow measures the rate of entropy fundamentally from which causality is inferred. The strength, in that regard, is therefore mainly relative to the framework, although we might be able to draw some helpful general conclusions from it. But it's still within a framework. Thus different causal frameworks would also give varying degrees of causal strenghth. It would be difficult to compare the absolute IF of SM→LH and IF of SM→SH since these are two different reference systems. Liang (2015) suggested normalizing the IF for such comparisons.
15. Line 58: Any specific reason why only 10models were selected?
16. Line 63: I would like to note here that ERA5-Land is an uncoupled framework, which is quite different from the coupled systems the CMIP6 are based on. Therefore this would already introduce some uncertainties since they may be fundamentally answering different questions.
17. Line 68: ERA5-Land comes with the evaporation components. By ET, do the authors refer to the transpiration part or the total evaporation?
18. Lines 71-72: I think some more details would better justify the choice of 10 models. Which specific paramters were chosen such that only 10 models could provide that?
19. Line 74: Is this referring to a downscaling of the climate models from their native resolutions? Was this done before of after the information flow computation? Before would be quite an uncertain step.
20. Line 80: note that GLEAM is also uncoupled. Again, which evaporation of GLEAM was used? If actual evaporation was used, authors should note that this would include interception, which would mean that not all the interaction can be directly related to soil moisture.
21. Line 91: What does the net contribution of the variation mean?
22. Line 94: 'the rate of information flowing from Y2 to Y1...'
23. Line 96: sample covariances
24. Line 102: indicates soil moisture is non-causal to air temperature
25. Lines 105-107: If the main focus is on the strength, perhaps, the normalized IF should have been used to make intercomparison more justifiable.
26. Lines 126-129: There is a crucial point here that might need addressing. As the authors have noted already, soil moisture partitions net radiation, loosely speaking, into sensible heat and latent heat (this latter is related to evaporation). This ideally means that in the absence of water, all the energy is basically SH to warm up the atmosphere. On the other hand, where there is water, energy is mainly converted to LH which cools down the temperature. This is the main formulation of the bowen ratio or evaporative fraction, such that these two are back-to-back. To put such a decomposition forward would imply that there is some independence. Since LH and SH are not fully independent, wouldn't looking at one imply the other? Is there a reason we should expect these two to be significant at different regions of the world? More importantly, IF(SSM->T) would not be the same as SSM->ET & ET->T. This is because the formulation of LKIF used here assumes that SSM->T is a direct process. Please see Section 2 of https://doi.org/10.1175/JCLI-D-16-0727.1 for some theoretical background, especially equation 4.
27. Line 140: May I ask the authors to provide a proper justification for this annual causal strength?
28. Line 141: Not so clear to me how this was done. If I have understood the work flow, this means that we could have October SSM of say 2000 (t) to lead the T of April 2001 (t+1), right? how do we explain these time jumps?
29. Lines 148-156: I think this would also suffer from the time concatenation problem I have highlighted above.
30. Line 163-164: Perhaps, a more honest interpretation would be that the Great plains and 'Indian subcontinent' are not well captured compared with existing studies. But I am convinced that this is because the whole year is taken together instead of just the boreal or austral summers.
31. Figure 1: Is this based on normalized IF or absolute IF? If it's the latter, the values are surprising (although not impossible). But please verify.
32. Figure 2: How do the authors explain any physical differences between a & b? Same potentially applies to c & d. Also, any thoughts on why we have ET->T in the desert regions like the Sahara? Figure 2e also shows both paths over the Kalahari desert in Africa, and quite a significant SSM->SH->T in the Congo basin. Any thoughts why this is the case? More importantly, how do we. explain the dominance of the widespread of blue in the northern hemisphere? What does that mean for the other pathway? Finally, it's not clear to me how the full pathway is computationally achieved in FIgure 2e.
33. Lines 206-209: This not true. A quick look at any relevant study on the topic, including several referenced here would show that most make such plots based on soil moisture climatology. We know that the transition regions (based on climatology) have the strongest Land–atmosphere signal (See Koster et al 2004, Miralles et al 2012, etc) because this is also where we have the strongest variability. And if fact, this is what the results in Fig 2b show. The intermediate regions are exactly the transition regions where we expect to find a strong coupling. More importantly, we have to look at this over seasons. A quick replotting of Figure 3a–b based on JJA would show this very clearly. Or else, a very straightforward question would be how the authors would explain the strong signal over India in Fig 3a, and yet the missing SSM->T IF signal.
34. Lines 211-213: I would disagree with the way this statement has been derived to the conclusion it lays out. I don't see why we wouldn't come to this conclusion given that the IF was calculated based on detrended covariances. I don't think this is a scientific conclusion.
35. Lines 211: How was the probability calculated?
36. Line 255: Any reason why ERA5-Land temperature was used instead the atmospheric reanalysis product?
37. Line 364-366: I think this is a misunderstanding of the LKIF. Liang 2014 mainly uses the MLE to approximate the LKIF which ends up as an equation of sample covariances. Nonetheless, the actual IF equation itself is a physical quantify, just limited to this statistical approximation. These two ideas should not be decoupled.
38. Conclusions: while I agree that it's helpful to show this from a causal perspective, it's still not clear what the novelty of this study is. How does it compare Koster et al 2006, Notaro 2008, Dirmeyer 2011, Miralles et al 2012, Gavaert et al 2018, Schwingshackl 2017, 2018, etc...and Hagan et al 2026 where they even showed detailed thermodynamic and dynamic mechanisms for the coupling? I encourage the authors to think more carefully about this to better highlight the novelty.
39. Lines 520-522: Wrong reference?

Citation: https://doi.org/10.5194/egusphere-2026-2866-RC2
- AC2: 'Reply on RC2', jichong han, 05 Oct 2026
  
  We sincerely thank the reviewer for their careful evaluation of our manuscript and constructive suggestions, which have helped us improve the paper.
  Our detailed point-by-point responses are provided in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2026-2866-AC2

Xiaohang Guo, Jichong Han, Huaiyong Shao, Xinyan Zhu, Xiaofei Sun, Long Ling, Zimeng Chen, and Gang Liu

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Xiaohang Guo, Jichong Han, Huaiyong Shao, Xinyan Zhu, Xiaofei Sun, Long Ling, Zimeng Chen, and Gang Liu

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Short summary

We quantify how soil moisture influences near-surface air temperature using a causal information-flow method. Significant soil moisture–temperature causality appears across about 37 % of global land, mainly through evapotranspiration and sensible heat pathways. The coupling is driven more by soil moisture variability than by mean soil moisture, while CMIP6 models tend to overestimate its likelihood and spatial extent.


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