Impact of gravels and organic matter on the thermal properties of grassland soils in southern France

Introduction Conclusions References Tables Figures


Impact of gravels and organic matter on the thermal properties of grassland soils in southern France
Response to Reviewer #1 and changes in the revised version of the paper (X. Xiao, xinhua.xiao@aamu.edu; xiaoxinhua2009@gmail.com) The authors thank Dr. Xinhua Xiao (NC State University Soil Physics) for her review of the manuscript and for the fruitful comments.
1.1 [Accuracy of predicative λ λ λ λ models highly depends on accurate estimation of λ λ λ λsat and q, which has been oversimplified as sand fraction. It is interesting and important to predict q and λ λ λ λsat in λ λ λ λ models using data of soil texture and gravel and SOM and to further examine their impacts on λ λ λ λ models. The methodology in this work to address the research question is appropriate. Discussion of model applicability is covered. The new pedotransfer functions for λ λ λ λsat and q derived from their original data will add good contribution to the literature. I however have major concerns about the presentation/organization of this paper that I feel in some sections focus is lacking and/or reorganization needed. Better justification of adopting some key empirical models and more relevant discussion are also desired.]

RESPONSE 1.1
Many thanks for these positive comments. We will do our best to account for your remarks in a revised version of the manuscript.

Additional comments
In response to the reviewers' comments, we have revised our approach. The λ λ λ λ retrievals influenced by heterogeneities in soil properties are now sorted out. As a result, we now obtain realistic λ λ λ λ sat values for 14 soils. We improved the assessment of uncertainties on the pedotranfer function for quartz volumetric fraction: Yes, two key equations are used for λ dry and for K e (Eqs. (7) and (9), respectively).
For λ dry we used the Lu et al. (2007) parameterization. Figure R1.1 shows that this parameterization produces larger λ dry values than the λ dry estimates derived from Côté and Konrad (2005) for mineral soils. We checked that using Côté and Konrad (2005)   In the first version of this work, we used the Kersten number calculation used by Yang et al. (2005). Figure        Yes. It is interesting to test the statistical relationships we get between f q retrievals and soil characteristics using the independent data from Lu et al. (2007) and Tarnawski et al. (2009).
We checked that the pedotransfer function(s) we get from our observations produce λ sat values close to those observed for the fine-textured Lu soils.

CHANGES 1.4 (Sect. 4.3)
The characteristics of ten Chinese soils used by Lu et al. (2007) to investigate soil thermal conductivity are given in Table S1 (Supplement). We used three soils from the Lu et al. We derived gravimetric and volumetric fraction of quartz (Q and f q , respectively) from the λ sat observations of Lu et al. (2007). Figure 10 shows that f q correlates to m sand better than Q.
Similar results are found for other predictors. This is consistent with the results we obtained for 14 French soils: pedotransfer functions for quartz present systematically better scores using f q instead of Q, as shown by Fig. 5.       Tarnawski et al. (2009) for 10 Chinese soils, using the gravimetric fraction of sand m sand as a predictor of f q . Dark dots correspond to the estimations obtained using the m sand pedotransfer function for southern France and the three soils for which m sand /m SOM < 40 are indicated by green diamonds. Red triangles correspond to the estimations obtained using the m sand pedotransfer function for the seven soils for which m sand /m SOM > 40.  Yes. In the revised version of this work, we will use a slightly more sophisticated q retrieval technique able to cope with soil heterogeneities (see the response to Reviewer 2). The details will be described in a supplement, making the main text more concise. We agree. The Abstract will be rewritten.

CHANGES 1.7
New abstract: "The information on quartz fraction in soils is usually unavailable but has a major effect on the accuracy of soil thermal conductivity models and on their application in land surface models. This paper investigates the influence of quartz fraction, soil organic matter (SOM) and gravels on soil thermal conductivity. Field observations of soil temperature and water content from 21 weather stations in southern France, along with the information on soil texture and bulk density, are used to estimate soil thermal diffusivity and heat capacity, and then thermal conductivity. The quartz fraction is inversely estimated using an empirical thermal conductivity model. Several pedotransfer functions for estimating quartz content from soil texture information are analysed. It is found that the soil volumetric fraction of quartz (f q ) is systematically better correlated to soil characteristics than the gravimetric fraction of quartz. More than 60 % of the variance of f q can be explained using indicators based on the sand fraction. It is shown that SOM and (or) gravels may have a marked impact on thermal conductivity values depending on which predictor of f q is used. For the grassland soils examined in this study, the ratio of sand to SOM fractions is the best predictor of f q . An error propagation analysis and a comparison with independent data from Lu et al. (2007) show that the gravimetric fraction of sand is the most robust predictor of f q when a larger variety of soil types is considered." We mean that today, q estimates are not given in global digital soil maps. Therefore, land surface modellers need to use a pedotransfer function for q.
1.9 [Page 745 Line 9. How/why is 0.4 chosen/set as cutoff of saturation degree?] RESPONSE 1.9 In dry conditions, conduction is not the only mechanism for heat exchange in soils, as the convective water vapour flux may become significant (Schelde et al., 1998, Parlange et al. 1998). Also, the K e functions found in the literature display more variability in dry conditions (see Fig. R1.2). Therefore, this threshold value of S d = 0.4 results from a compromise between the need of limiting the influence of convection, of the shape of the K e function on the retrieved values of λ sat , and of using as many observations as possible in the retrieval process.
For example, if we had taken a threshold of 0.6, we would not have been able to retrieve λ sat for SBR, SVN, LZC, PRD, LGC, BRN, and CBR. Agreed.

CHANGES 1.13
New Table 2 is as follows:  Yes. This typo will be corrected. Many thanks for these encouraging comments. We will do our best to account for your remarks in a revised version of the manuscript.

Additional comments
In response to the reviewers' comments, we have revised our approach. The λ λ λ λ retrievals influenced by heterogeneities in soil properties are now sorted out. As a result, we now obtain realistic λ λ λ λ sat values for 14 soils. We improved the assessment of uncertainties on the pedotranfer function for quartz volumetric content: • a variety of pedotransfer functions is now proposed, not only one • a confidence interval for the coefficients of pedotransfer functions is given

RESPONSE 2.2
Yes, we agree. This is a very good point.
We acknowledge that the impact of vertical heterogeneities in λ values has to be properly accounted for in the λ retrieval technique we used. In order to address this issue, we revised our data analysis procedure in order to limit this effect as much as possible. In particular, we used only the soil temperature data presenting a relatively low vertical gradient close to the soil surface, where most differences with deeper layers are found. This refined data sorting increased the λ sat retrieved value for all the stations. A very interesting side effect of the improved procedure was that LHS, SVN, and PRD now present non-zero values of q. On the other hand, the NBN observations are now filtered out as NBN presents very large differences in soil density from one soil depth to another. The new procedure is described below.
The 1D Fourier equation in heterogeneous soil conditions can be written as: and discretized as: In this study, we assume that the retrieved λ values, at a depth of −0.10m, are representative of a bulk soil layer including the three soil temperature probes used to retrieve the thermal diffusivity, and do not differ much from the interfacial λ values along the bottom and top edges of the considered soil layer (λ i+1/2 and λ i-1/2 , respectively): In reality, differences may occur: Considering the temperature gradient ratio R TG at a given time n: and combining Eqs. (R4), (R5) and (R6), the retrieved λ can be written as: Since soil temperature gradients were more pronounced close to the soil surface and since soil density presented smaller values close to the soil surface, the ∆λ, R TG , and R TG ∆λ values were ≥ 0. Since in the soils considered in this study, differences in soil density were much less pronounced at depth than between the −0.05m and −0.10m soil layers, we considered that λ i+1/2 was closer to the final value to be retrieved, λ*, than the initial λ retrieval: Eq. (R8) shows that the target λ* value is larger than the initial λ retrieval. The relative error on λ* can be written as R TG ∆λ/λ* (dimensionless). We used R TG ∆λ/λ* as an indicator of the quality of the λ retrieval, with large values of R TG ∆λ/λ* corresponding to erroneous estimates.
In the revised data analysis procedure, a subset of 20 λ retrievals per station was used, at most, corresponding to the lowest R TG ∆λ/λ* values, with the condition R TG ∆λ/λ* < 10%.
Since the NBN station presented R TG ∆λ/λ* values systematically higher than 10%, the NBN data were excluded from the analysis.
The impact of the refined data selection is illustrated in   In practise, the ∆λ term was estimated using top-soil and deep dry density observations (at −0.05m and −0.10m, respectively) and the sensitivity of λ to changes in dry density, ∆λ/∆ρ d .
The latter was derived numerically using the Eqs. (10)-(13) model, in soil wetness conditions ranging from S d = 0.4 to S d = 1. Since the derivation of ∆λ/∆ρ d depends on the obtained q pedotransfer function (Eq. (12)), ∆λ/∆ρ d values were recalculated with the new pedotransfer function, and a few iterations permitted refining these estimates.
The ∆ρ d term ranged from 10 kg m −3 for CBR to 284 kg m −3 for NBN. R TG ranged between 0.5 and 2.4, with a median value of 1.3.

CHANGES 2.2
The data selection method described above was included in a Supplement, together with

RESPONSE 2.3
Yes, soil-specific values for the volumetric heat capacity of soil minerals (C hmin ) may be more appropriate than using a constant standard value. However, we were not able to find such values in the literature and we did not measure this quantity.
We investigated the sensitivity of our results to these uncertainties, considering the following minimum and maximum C hmin values:   2.5 [Third, no independent data or measurements were used to evaluate the estimates of soil thermal conductivity and quartz fraction. In Table 2,

RESPONSE 2.5
It must be noted that in many studies (e.g. Lu et al., 2007) λ sat estimates are derived from reassembled sieved soil samples excluding the gravels, while our data concern undisturbed soils.
In our revised analysis, we found λ sat values ranging between 1.26 Wm −1 K −1 and 2.80 The empirical Eq. (13) for θ sat is used for the end-to-end simulation for the sensitivity study of Table 3, as such an equation has to be used in land surface models. Eq. (14) is equivalent to Eq. (1). The impact of using Eq. (13) in the sensitivity study (current Sect. 4.1) will be shown and discussed. Note that we found and corrected a bug in the program we developed to perform this sensitivity analysis. In the revised manuscript, the sensitivity study will be performed with and without using this equation, and for several plausible pedotransfer functions.

CHANGES 2.6
Sect. 3.2: "Modelled values of λ λ λ λ sat (λ λ λ λ satMOD ) can be derived from f qMOD using Eq. (10) together with θ θ θ θ sat observations. The λ λ λ λ satMOD r 2 , RMSD, and mean bias scores are given in Table 5. Again, the best scores are obtained using the m sand /m SOM predictor of f q , with r 2 , RMSD, and mean bias values of 0.86, 0.14 Wm -1 K -1 , and +0.01 Wm -1 K -1 , respectively  Model configuration Predictor of f q  Yes, in the revised version of the manuscript, the effects of gravels and organic matter on soil thermal conductivity values will be included in the result section. More information of vegetation characteristics will be given.

CHANGES 2.7
Title: "gravels and organic matter" was replaced by "quartz". Yes, this sentence will be rephrased. Note however that such measurements are currently not made in operational meteorological networks. Using standard soil moisture and soil temperature observations is a way to investigate soil thermal properties over a large variety of soils, as the access to such data is facilitated by online databases (e.g. https://ismn.geo.tuwien.ac.at/). Yes. This typo will be corrected.

RESPONSE 2.12
Yes, we will publish a Supplement to the final version of the paper explaining the various calculation steps.

RESPONSE 2.13
In the revised version of the manuscript, we will improve the description and the assessment of the uncertainties affecting the obtained pedotransfer function(s).

CHANGES 2.13
We improved the assessment of uncertainties on the pedotranfer function for quartz volumetric content: • a variety of pedotransfer functions is now proposed, not only one

RESPONSE 2.14
The difficulties we had can be explained by heterogeneities in soil properties, soil density in particular. An enhanced procedure was implemented in order to mitigate this effect (see RESPONSE 2.2). LHS, SVN, and PRD now present non-zero values of q and the NBN observations are filtered out. We had no difficulty in measuring soil temperature and soil moisture, including at the BRN soil presenting the largest fraction of gravel (see Fig. R2.8).
Note that the sensors we use are designed to work in such difficult conditions. The ThetaProbe and PT100 sensors have very strong rods, 0.06 m and 0.10 m long, respectively. In order to clarify the definition of symbols, the volumetric fraction of quartz is now written as "f q " (instead of "q"): with Q representing the fraction of quartz within soil solids. Yes. This typo will be corrected. given soil moisture conditions, λ depends to a large extent on the fraction of soil minerals 83 presenting high thermal conductivities such as quartz, hematite, dolomite or pyrite (Côté and 84 Conrad, 2005). At mid-latitudes, quartz is the main driver of λ. The information on quartz 85 fraction in a soil fraction of quartz is usually unavailable generally unknown as it can only be 86 measured using X-ray diffraction or X-ray fluorescence techniques, which are difficult to 87 implement (Schönenberger et al., 2012). This has a major effect on the accuracy of thermal 88 conductivity models and their applications (Bristow, 1998). The porosity values at a depth of 0.10 m are listed in Table 1 together with gravimetric and 161 volumetric fractions of soil particle-size ranges (sand, clay, silt, gravel) and SOM. The porosity, 162 or soil volumetric moisture at saturation (θ sat ), is derived from the bulk dry density ρ d , together However, large differences in soil bulk density, from the top soil layer to deeper soil layers were 185 observed for some soils (see Supplement 1). In order to limit this effect as much as possible, we 186 only used the soil temperature data presenting a relatively low vertical gradient close to the soil 187 surface, where most differences with deeper layers are found. This data sorting procedure is 188 where θ and f min represent the volumetric soil moisture and the volumetric fraction of soil 212 minerals, respectively. and vValues of 4.2×10 6 Jm -3 K -1 , 2.0×10 6 Jm -3 K -1 , and 2.5×10 6 Jm -3 K -1 , are 213 used for C hwater , C hmin , C hSOM , respectively. 214 The λ values at 0.10 m are then derived from the D h and C h estimates (Eq. (2)). The f q q retrievals can be used to assess the possibility to estimate f q q using other soil 309 characteristics, which can be easily measured. Another issue is whether volumetric or gravimetric 310 fraction of quartz should be used. Figure 4 presents the fraction of variance (r 2 ) of Q and f q 311 explained by various indicators. A key result is that f q is systematically better correlated to soil 312 characteristics than Q. More than 60 % of the variance of f q can be explained using indicators 313 based on the sand fraction (either f sand or m sand ). The use of other soil mineral fractions does not 314 give good correlations, even when they are associated to the sand fraction as shown by Fig. 4. For  315 example, the f gravel and f gravel +f sand indicators present low r 2 values of 0.04 and 0.24, respectively. 316 The f q values cannot be derived directly from the indicators as illustrated by The values of q MOD vs. q are shown in Fig. 5.  330 The a 0 and a 1 coefficients are given in Table 3 for four pedotransfer functions based on the best  331 predictors of f q . The pedotranfer functions are illustrated in Fig. 6. The scores are displayed in 332 Table 4. The bootstrapping indicates that the SBR sandy soil has the largest individual impact on 333 the obtained regression coefficients. This is why the scores without SBR are also presented in 334 Table 4. function is that the confidence interval for the a 0 and a 1 coefficients derived from bootstrapping is 347 narrower than for the other pedotransfer functions (Table 3), indicating a more robust relationship 348 of f q with m sand /m SOM than with other predictors. 349 Modelled values of λ sat (λ satMOD ) can be derived from f qMOD q MOD using Eq. (10) together with θ sat 350 observations. and tThe λ satMOD following r 2 , RMSD, and mean bias scores are obtained for 351 λ satMOD , with respect to the λ sat retrievals: 0.87, 0.15 Wm −1 K −1 , and −0.01 Wm −1 K −1 , respectively 352 (Table 3)given in Table 5. Again, the best scores are obtained using the m sand /m SOM predictor of 353 f q , with r 2 , RMSD, and mean bias values of 0.86, 0.14 Wm -1 K -1 , and +0.01 Wm -1 K -1 , respectively 354 ( Fig. 7). 355 Finally, we investigated the possibility of estimating θ sat from the soil characteristics listed in 356 Table 1 and of deriving a statistical model for θ sat (θ satMOD ). We found the following statistical Neglecting gravels (f gravel = 0 m 3 m −3 ) also has a limited impact but triggers the underestimation 381 (overestimation) of λ sat for the m sand /m SOM (m sand *) pedotransfer function, by −0.12 Wm −1 K −1 382 (+0.11 Wm −1 K −1 ). 383 On the other hand, iIt appears that combining these assumptions has a marked impact on all the 384 pedotransfer functions. Nneglecting gravels (f gravel = 0 m 3 m -3 ) and imposing f SOM = 0.013 m 3 m −3 385 has a major impact on λ sat : the modelled λ sat is overestimated by all the pedotransfer functions 386 (with a mean bias of ranging from +0.165 Wm −1 K −1 to +0.24 Wm −1 K −1 ) and r 2 = 0.65is markedly 387 smaller, especially for the m sand and m sand * pedotransfer functions. while the full model is 388 virtually unbiased and presents a r 2 value of 0.87. These results are illustrated in Fig. 8 in the case 389 of the m sand * pedotransfer function. Figure 8 also shows that using the θ sat observations instead of 390 θ satMOD (Eq. (13)) has little impact on λ satMOD (Sect. 3.2) but tends to enhance the impact of 391 neglecting gravels. A similar result is found with the m sand pedotransfer function (not shown). 392 Neglecting SOM also triggers an overestimation of λ sat (+0.12 Wm −1 K −1 ) but has no impact on r 2 .

393
On the other hand, although neglecting SOM while accounting for gravels has no impact on r 2 , 394 neglecting SOM tends to amplify the detrimental impact of neglecting gravels: r 2 = 0.51 and the 395 mean bias is equal to +0.41 Wm −1 K −1 . Assuming q = f sand tends to trigger an underestimation of 396 λ sat (−0.22 Wm −1 K −1 ), and to compensate for the bias caused by neglecting SOM. Combining Eq.

397
(12) and Eq. (1), it appears that Eq. (12) boils down to q = 1.075 × f sand for θ sat values close to 398 0.35 m 3 m -3 . For higher θ sat values, q tends to be higher than 1.075 × f sand . Since θ sat is higher than 399 0.35 m 3 m -3 at all the sites (Table1), the q = f sand assumption tends to underestimate q and, 400 subsequently, λ sat . 401 Table 3 shows that in the configuration representative of most soil thermal conductivity models 402 currently used in LSMs (i.e. neglecting gravels and SOM while assuming q = f sand ), only 61 % of 403 the λ sat variance is explained by the model (r 2 = 0.61), and λ sat is markedly overestimated (the 404 mean bias is equal to +0.24 Wm −1 K −1 ). The impact of this model configuration is illustrated in 405  Table 4. Using f sand as a predictor of q gives a r 2 value of 0.66, against 0.78 for Eq. 408 (12). Gravels and silt have the largest impact on r 2 (r 2 = 0.12 and r 2 = 0.38, respectively). 409 On the other hand, it must be noted that Eq. (12) predicts very low values of q for f clay + f silt + 419 f gravel + f SOM close to 0.65 m 3 m -3 . All the retrieved null values of q are obtained below this 420 threshold (Fig. 4), from 0.43 to 0.54 m 3 m -3 . Therefore, a possible marked underestimation of 421 either f clay , f silt , f gravel , or f SOM may explain these discrepancies, or the overestimation of f sand or θ sat .

422
In this study, the de Vries (1963) mixing model is applied to estimate soil volumetric heat 423 capacity, and a fixed value of 2.0×10 6 Jm -3 K -1 is used for soil minerals (Eq. (6)). Soil-specific 424 values for C hmin may be more appropriate than using a constant standard value. For example, 425 Tarara and Ham (1997) used a value of 1.92×10 6 Jm -3 K -1 . However, we did not measure this 426 quantity and we were not able to find such values in the literature. 427 We investigated the sensitivity of our results to these uncertainties, considering the following 428 minimum and maximum C hmin values: C hmin = 1.92×10 6 J m −3 K −1 and C hmin = 2.08×10 6 J m −3 429 K −1 . The impact of changes in C hmin on the retrieved values of λ sat and f q is presented in Fig. 9. On 430 average, a change of + (−) 0.08×10 6 J m −3 K −1 in C hmin triggers a change in λ sat and f q of + 1.7 % 431 (− 1.8 %) and + 4.8 % (− 7.0 %), respectively. 432 The impact of changes in C hmin on the regression coefficients of the pedotransfer functions is 433 presented in Table 3 (last column). The impact is very small, except for the a 1 coefficient of the 434 m sand * pedotransfer function. However, even in this case, the impact of C hmin on the a 1 coefficient 435 is much lower than the confidence interval given by the bootstrapping, indicating that the 436 relatively small number of soils considered in this study (as in other studies, e.g. Lu et al. (2007)) 437 is a larger source of uncertainty. 438 Moreover, uUncertainties in these f clay , f silt , f gravel , or f SOM fractions may be caused by (1) 12)). This equation should be evaluated for other regions. In particular, hematite has to be 476 considered together with quartz for tropical soils. According to Eq. (12), q is close to 0.7 for 477 sandy soils and in such conditions, one should ensure that q ≤ f sand . 478 While the pedotransfer function we get for θ sat (Eq. (13)) is valid for the specific sites considered 479 in this study and is used to conduct the sensitivity study of Sect. 4.1, Eq. (13) cannot be used to 480 predict porosity in other regions. 481 In order to assess the applicability of the pedotransfer function for quartz obtained in this study, 482 we used the independent data from Lu et al. (2007) and Tarnawski et al. (2009), for ten Chinese 483 soils (see Supplement 3 and Table S3.1). These soils consist of reassembled sieved soil samples 484 and contain no gravel, while our data concern undisturbed soils. Moreover, most of these soils 485 contain very little organic matter and the m sand /m SOM ratio can be much larger that the m sand /m SOM 486 values measured at our grassland sites. For the 14 French soils used to determine pedotransfer 487 functions for quartz, the m sand /m SOM ratio ranges from 3.7 to 37.2 (Table 2) Table S3.1). 490 We used λ sat experimental values derived from Table 3  These results are illustrated by Fig. 11 for the m sand predictor of f q . Figure 11 also shows the f q 502 and λ sat estimates obtained using specific coefficients in Eq. (12), based on the seven Lu et al.

503
(2007) soils presenting m sand /m SOM values larger than 40. These coefficients are given together 504 with the scores in Table 6. Table 6 also present these values for other predictors of f q . It appears 505 that m sand gives the best scores. The contrasting coefficient values between Table 6 and Table 3  506 (Chinese and French soils, respectively) illustrate the variability of the coefficients of 507 pedotransfer functions from one soil category to another, and the m sand /m SOM ratio seems to be a 508 good indicator of the validity of a given pedotransfer function. 509 On the other hand, the m sand /m SOM ratio is not a good predictor of f q for the Lu et al. (2007) soils 510 presenting m sand /m SOM values larger than 40, and r 2 presents a small value of 0.40 (Table 6). This 511 can be explained by the very large range of m sand /m SOM values for these soils (see Table S3.1). 512 Using ln(m sand /m SOM ) instead of m sand /m SOM is a way to obtain a predictor linearly correlated to f q . 513 This is shown by Fig. 12 Tables 3, 4, and 6, it can be concluded that m sand is the best 518 predictor of f q across mineral soil types. The m sand /m SOM predictor is relevant for the mineral soils 519 containing the largest amount of organic matter. 520 The results presented in this study suggest that the m sand /m SOM ratio can be used to differentiate 521 temperate grassland soils containing a rather large amount of organic matter (3.7 < m sand /m SOM < 522 40) from soils containing less organic matter (m sand /m SOM > 40). The m sand predictor can be used 523 in both cases, with the following a 0 and a 1 coefficient values in Eq. (12): 0.15 and 0.572 for 524 m sand /m SOM ranging between 3.7 and 40 (Table 3), and 0.04 and 0.386 for m sand /m SOM > 40 (Table  525 6), respectively. 526 Although the m sand /m SOM predictor gives the best r 2 scores for the 14 grassland soils considered in 527 this study, it seems more difficult to apply this predictor to other soils, as shown by the high 528 MAE score (MAE = 0.135 m 3 m -3 ) for the corresponding Lu et al. (2007) soils in Table 4. 529 Moreover, the scores are very sensitive to errors in the estimation of m SOM as shown by Table 5. 530 Although the m sand * predictor gives slightly better scores than m sand (Table 4), the a 1 coefficient in 531 more sensitive to errors in C hmin (Table 3) Using standard soil moisture and soil temperature observations is a way to investigate soil 537 thermal properties over a large variety of soils, as the access to such data is facilitated by online 538 databases (Dorigo et al., 2013). 539 A key limitation of the data used in this study, however, is that soil temperature observations (T i ) 540 are recorded with a resolution of ∆T i = 0.1 °C only (see Sect. 2.1). This low resolution affects the 541 accuracy of the soil thermal diffusivity estimates. In order to limit the impact of this effect, a data 542 filtering technique is used (see Supplement 4) and D h is retrieved with a precision of 18 %. 543 Since T i is recorded with a resolution of 544 France. For the grassland soils examined in this study, the ratio of sand to SOM fractions is the 583 best predictor of f q . A sensitivity study shows that gravels have a major impact on λ sat and that 584 omitting gravels and the SOM information has a major impact on λ sat tends to enhance this 585 impact. Eventually, an error propagation analysis and a comparison with independent λ sat data 586 from Lu et al. (2007) show that the gravimetric fraction of sand within soil solids, including 587 gravels and SOM, is a good predictor of the volumetric fraction of quartz when a larger variety of 588 soil types is considered. This technique is easy to implement and is based on fully automatic in 589 situ observations associated to a characterisation of soil properties in the lab. Therefore, this 590 study could be extended to other regions and biomes. However, using temperature records with a 591 resolution of 0.1 °C limits the applicability of the method. It is recommended to acquire 592 temperature measurements with a better resolution. More precision in the λ estimates would then 593 permit investigating other processes of heat transfer in the soil such as those related to water 594 transport (Rutten, 2015  λ sat and q retrievals using the λ model (Eqs.    given in Table 3. The modelled f q values are represented by the dashed lines. 825 826