Reply to comment by Binayak P. Mohanty and Zhenlei Yang on “A simulation analysis of the advective effect on evaporation using a two-phase heat and mass flow model”


  • Yijian Zeng,

    Corresponding author
    1. Faculty of Geo-Information Science and Earth Observation, University of Twente, Enschede, Netherlands
    • Corresponding author: Y. Zeng, Faculty of Geo-Information Science and Earth Observation, University of Twente, Hengelosestraat 99, NL-7514 AE Enschede, Netherlands. (

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  • Zhongbo Su

    1. Faculty of Geo-Information Science and Earth Observation, University of Twente, Enschede, Netherlands
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1. Introduction

[1] We thank Mohanty and Yang [2013] (hereafter referred to as MY) for their comment on our paper “A simulation analysis of the advective effect on evaporation using a two-phase heat and mass flow model” [Zeng et al., 2011b]. We appreciate the effort by MY to look critically at our paper. We hope that the responses to their comments will help to clarify the issues they raised and to communicate better our approach and contributions to the reader. By reviewing MY's comments, it is clear to us that we need to provide further clarification on the details of the key aspects of our paper. As shall be seen in following sections, we disagree with all of their objections. Before we issue the point-to-point rebuttal to the two key points MY raised, we want to clarify the approaches we presented in our paper. In such way, we hope to assist the reader to have a systematic view on the key aspects and make definite conclusions on its merits and validity.

[2] The main objective of our paper was to identify the controlling mechanism for the advective effect on soil evaporation. When excluding soil airflow, the advective flux can lead to the underestimation of surface evaporative flux [Zeng et al., 2011a, 2011b]. To identify such mechanism, a systematic approach, including both experimental and numerical ones, should be applied. We implemented an in situ experiment and developed a two-phase heat and mass flow model to serve this purpose. With the calibrated two-phase model, the detailed driving force (e.g., matric potential gradient, soil air pressure gradients, and soil temperature gradients) and conductivity fields can be used to investigate and identify what exactly drives the underestimation error. The comparison in the modeled surface fluxes (e.g., evaporative fluxes) with and without soil airflow can identify the underestimation error. The modeled surface flux is a total flux, which is the summation of thermal and isothermal fluxes, and advective fluxes (e.g., when soil airflow being considered). Therefore, it requires a systematic view to decompose the total flux into different components, based on different driving forces. This is what we discussed at the beginning of section 3.3 in our original paper [Zeng et al., 2011b], from where we have analyzed the direct and indirect controlling mechanisms.

[3] Based on the diurnal variation pattern of matric potential gradients above the depth of 50 cm, upward during the day and downward during the night, the original paper targets the isothermal flux as the direct driving factor for the underestimation error (e.g., the upward isothermal flux is higher when considering airflow than that without airflow). The inverse variation pattern of soil temperature and soil air pressure gradients, compared to the matric potential one, precludes their direct influence on the underestimation error. However, soil temperature gradient may have an indirect effect on the error (e.g., the downward thermal flux is lower when considering airflow than that without airflow). To verify the above hypothesis, the original paper compares the gradient and conductivity fields by using a normalized scale index (NSI). It is found that the indirect effect of thermal fluxes on the error is invalid because the downward thermal flux with airflow mechanism is larger than that without airflow. This is in contrast to the hypothesis. On the other hand, the original paper verifies the isothermal flux as the direct driving factor accounting for the underestimation error. The upward isothermal flux with airflow mechanism is indeed larger than that without airflow.

[4] From Figure 4 of Zeng et al. [2011b], it is obvious that the advective effect is the most significant on day 2, which is chosen for analyzing the controlling mechanism behind the effect. The most significant effect, on day 2, implies the dominance of isothermal fluxes, which can be inferred by comparing the magnitude of different component fluxes [Zeng et al., 2009b]. From day 2 onward, the thermal fluxes start to dominate. As the soil temperature gradient is downward during daytime, it can be inferred that the dominance of thermal fluxes will minify the advective effect. This is because both fluxes (downward thermal and upward isothermal fluxes) will cancel each other out. This can also be inferred from the diurnal patterns of matric potential and soil temperature gradient in Figure 5 of Zeng et al. [2011b].

[5] The further analysis identifies the isothermal hydraulic conductivity as the key factor accounting for the advective effect since it is increased largely when considering airflow. One of the possible mechanisms for such increase is that the vapor brought by the downward advective flux from the atmosphere moistens the top surface layer. This moistening increases the hydraulic conductivity in the top soil layer. Although thermal flux is downward as well, it is not possible for it to bring vapor from the atmosphere into the top layer. This is because the surface temperature is higher than the air temperature during most of daytime, which precludes its influence on increasing hydraulic conductivity. However, we do realize that there are often many different approaches, which may be applied to explore solutions for every problem. To this point, we are still far from completely understanding the advective effect. Nevertheless, that was beyond the scope and not the intention of our paper. Now we will present point-to-point rebuttals to MY's comments.

2. MY's Arguments on Advective Effect on Increasing Isothermal Hydraulic Conductivity Is Probably Overestimated

2.1. Conductivity NSI Was Calculated by Ignoring Its “Sign Effect”

[6] We agree with MY's assertion that during the nighttime, and before the early morning, the isothermal liquid flux is downward as can be seen in Figure 7E of Zeng et al. [2011b]. However, we disagree with MY's argument, “In other words, this larger isothermal hydraulic conductivity was contributing to infiltration or redistribution process but not to evaporation process during the nighttime.”

[7] The downward isothermal liquid flux has no absolute meaning in contributing to infiltration. It is only one of the component fluxes contributing to the total flux. Only the direction of the total flux can tell whether the soil water moving downward or upward. For the case on day 2, the isothermal liquid flux is downward during the nighttime and before the early morning. On the other hand, the thermal liquid flux is upward during the same period. The summation of these two fluxes produces an upward total surface flux. This invalidates the basis of MY's assertion, “it overestimates the airflow advective effect because the large KLh (with airflow) during the night used for soil water infiltration or redistribution after rainfall is also incorrectly used for soil evaporation during the daytime.” Therefore, we disagree with MY's comment that the NSI for isothermal hydraulic conductivity should be averaged separately during the different time within 1 day (e.g., day/night) corresponding to the direction of hydraulic gradient. There are two extra points for our disagreement: first, such kind of separation has been done for gradient NSI in our paper, and second, only the gradient can determine the direction of fluxes, while the conductivity contributes to the magnitude of fluxes.

2.2. Underestimation Error Is Most Significant on Day 2 When the Downward Advective Flux Is Smallest

[8] We agree with MY's interpretation that the downward advective flux on day 2 should be much smaller than that during days 3–6. However, MY simply associates the downward advective flux with the advective effect and assumes that larger advective fluxes will lead to larger advective effect. Subsequently, MY comes to the unsupported conclusion that the underestimation error of evaporation when neglecting airflow should be larger during days 3–6 and smaller on day 2 in both high- and low-permeability soils. Since advective flux is only one of the component fluxes contributing to the total flux, it is not systematic to investigate/understand the influence of advective flux on surface evaporative fluxes, by employing the advective flux alone. During days 3–6, the soil temperature gradient is larger than on day 2 [see Zeng et al., 2011b, Figures 5E and 5F]. It implies that the downward thermal flux driven by soil temperature gradient (during daytime) will be larger than that on day 2 as well. Thus, even if the larger advective flux may increase, the upward isothermal liquid fluxes will be canceled out by the downward thermal fluxes. It means that a larger advective flux does not have to lead to more significant underestimation error as we discussed in section 1 in this response.

2.3. Analysis on the More Obvious Advective Effect in the Low-Permeability Than High-Permeability Soil Is Elusive

[9] It seems that most of their statements on this argument actually support or repeat what has been discussed in our original paper. MY's assertion, “in fact, although air pressure head gradient is small (except equal to 0) in high permeability soils, the actual advective flux is not necessarily small considering the large air velocity in high permeability soils … the advective fluxes in high permeability soils should be a little higher than that in low permeability soils,” actually supports the statement in our paper. In paragraph [26] of Zeng et al. [2011b], we can find “The high permeability leads to high soil air velocity … however, the high air velocity means the soil air pressure can equilibrate quickly with the atmospheric pressure, which will result in a small air pressure gradient in the soil. This is the reason that the advective effect is relatively weaker in the high-permeability soil while strong in the low-permeability soil.”

[10] MY's another assertion supports our conclusion as well, which is read as “It turns out that the true reason for why underestimation error is larger (advective effect is stronger) in low permeability soils is the larger difference (between with and without airflow) in the upward isothermal liquid flux during the day but not the higher soil air pressure gradient.” This is what we discussed in section 1 in this response, and in the paragraph [50] of our paper, from where we can find “The difference of the hydraulic conductivity induced by neglecting airflow is the key to explaining the error … this discussion also explains why the advective effect is more evident in the low-permeability soil.” [Zeng et al., 2011b, paragraph [50]].

2.4. The Rainfall Itself That Makes the Advective Airflow Effect Becomes Important on Day 2

[11] We agree with MY that without this rainfall event, we could expect that during the entire 6 days, the evaporation rate between with-airflow and without-airflow should be the same just as the first day shows. However, we disagree with MY's statement on “Therefore, we believe it is the rainfall itself that make the advective airflow effect become important on day 2,” and their reasoning associated with it. The advective effect on evaporation is not controlled by a single factor but a systematic output of the complex two-phase heat and mass flow system. It means that the total flux, as an integrator, should be hold in mind when dealing with component fluxes. From MY's reasoning, it is obvious that the influence of thermal flux on the advective effect was ignored, and only the isothermal and advective fluxes were considered. For example, it is not correct to assess the significance of advective effect solely on whether the order of magnitude of soil matric potential is comparable to that of soil air pressure or not.

[12] In addition, MY has a doubt on why the evaporation rate is the largest (or spikes) on the midnight of the first day, which can be resolved easily if we checked the boundary condition section in our paper [Zeng et al., 2011b, equation (17)]. Equation (17) indicates that the evaporation is calculated by the vapor deficit between the soil and the atmosphere while constrained by the soil surface resistance and the aerodynamic resistance [Camillo and Gurney, 1986; Campbell, 1985]. In our case, at the very beginning of the rainfall event, the soil moisture in the top layer was increased effectively in a short time, which leads to a sharp drop of the soil surface resistance γs (e.g., result not shown here due to the page limit). It is this sharp drop of γs accounting for the “spike” evaporation on the midnight of the first day. After a while, as expected, when the rainfall intensity increased the evaporation ceased quickly while the infiltration and redistribution took over [Zeng et al., 2009a]. This “spike” evaporation was well captured by the in situ measurement, using eddy covariance approach [Zeng et al., 2011a].

3. MY's Arguments on Underestimation of Evaporation May Also Be a Result of Neglecting Isothermal Liquid Film Flow

[13] We thank MY's effort in reviewing the importance of including isothermal film flow in calculating evaporation. We agree with MY that the isothermal film flow is critical in capturing soil water flow at low water content range (e.g., matric potential lower than −105 cm), which has been intensively studied in the recent decade as cited by MY. It is clear that the matric potential is attributed to not only the capillary force but also the adsorptive surface force [Lebeau and Konrad, 2010]. The soil water retention curve has two different behaviors: power law (e.g., sigmoidal) behavior and logarithmic behavior. The power law behavior is at high and medium water content where the capillary retention mechanism is dominant. The logarithmic behavior is at low water contents where adsorption is dominant [Rossi and Nimmo, 1994]. With the above-mentioned concept, the full range water retention curve has been developed. Based on such development, the hydraulic conductivity function is conceptualized as the summation of the pore bundle model (e.g., Mualem's [1976] model) and an empirical (e.g., power function) [Peters and Durner, 2008] or analytical [Tokunaga, 2009; Lebeau and Konrad, 2010] model. The pore bundle model is for capillary flow, accounting for the full range soil water content. The empirical or analytical model is for modeling film flow due to adsorptive surface forces. The approach for summation is either in a weighted form or in a straightforward addition.

[14] We appreciate MY's suggestion on including film flow to make a comprehensive investigation of evaporation, which was beyond the scope of our original paper. However, we disagree with MY's hypothesis that the underestimation of evaporation, even using Zeng et al.'s [2011a] model considering airflow effect, could be explained by ignoring isothermal film flow. Although MY cited the published studies to indicate the underestimation of evaporation by neglecting film flow and implied our results may be improved by applying the same approach, it is not necessarily the case after checking those cited literature:

[15] Peters and Durner [2008, 2010] stated that part of the hydraulic conductivity that is primarily affected by film flow lies in the moderately dry region, i.e., at the pressure heads between about −102.5 and −104 cm. The variation of the pressure head on day 2 in our original paper (i.e., −720 to −1.05 × 103 cm) is actually in this range. This might make their conclusion applicable to our case (e.g., evaporation rate could be underestimated by more than an order of magnitude by neglecting film flow). However, from Figure 1 in their commentary [Peters and Durner, 2010], we can see that the coupled moisture and heat transport models with and without film flow do not differ from each other significantly as the commentary stated, “The combined fluxes are now in the same order of magnitude for both models.” Although Peters and Durner [2010] argued that as the capillary model does not represent the measured data in the range from about −1.3 × 103 to −3 × 103 cm, vapor flow is probably highly overestimated, there is no further explanation or discussion made on this argument. This relaxes the applicability of their conclusion to our case. Furthermore, from Figure 3 of Peters and Durner [2010], it is seen that vapor flux dominates the water transport only in the upper 1 m for the model with film flow but in the upper 3 m for the model without film flow. Considering their intentionally designed unrealistic scenario (5 m long soil column with homogeneous hydraulic properties, 3000 days of identical atmospheric evaporative demand, 0.2 cm d−1), it seems more reasonable for the vapor flux to be dominating in the upper 3 m than only in the upper 1 m.

Figure 1.

(left) The input data for calculating film flow hydraulic conductivity: soil temperature and soil matric potential and (right) the comparison between the capillary flow and film flow hydraulic conductivities.

[16] Based on Fick's law, Goss and Madliger [2007] calculated the upward diffusive vapor flux in different soil layers. This upward diffusive vapor flux in the top layer (0 to −1.5 cm) is referred as the evaporative flux into the atmosphere. With the calculated results, they found that except for the top layer, there was almost no net upward diffusive vapor transport below the layer. Therefore, they inferred that water transport up to the top layer must have occurred in “film flow.” As they did not consider liquid flow in their analysis, this notion of “film flow” in their context should be arguably deemed as the liquid flow which includes the flows induced by both capillary forces and adsorptive surface forces. However, we do realize that the conductivity estimated by their data is about 5 orders of magnitude higher than that estimated from pedotransfer functions combined with the van Genuchten approach (e.g., pore bundle model for capillary flow). This may indicate the existence of film flow in their case. However, the medium they employed is clay loam (or sandy loam) and can be defined as fine texture soil (e.g., not fine sand), of which the soil water retention curve and hydraulic conductivity function should behave differently from the desert sand studied in our original paper. Therefore, it is not appropriate to infer or extrapolate directly from Goss and Madliger's [2007] results to our case. The same logic can also be applicable to Massman's [2012] studies on soil heating and moisture transport during forest fires and slash pile burns, which can be defined as extreme heating events. Although the inclusion of film flow mechanism is applauded by Massman [2012] in improving modeling of soil heating and moisture transport during fires, he pointed out the necessity in improving understanding of the thermodynamics of bound water and better parameterizations of the water retention curve.

[17] Smits et al. [2012] stated that the isothermal film flow is expected to be more significant in finer textured soils with smaller mean grain diameter (dg, or effective grain diameter). As the contribution of the hydraulic conductivity due to film flow is a function of dg, when dg decreases (e.g., from a coarse-grained sand to a fine sand), the contribution due to film flow increases. On this basis, MY argued that the fine sand in our paper was expected to have significant film flow effect. However, there are two points ignored by MY: first, Smits et al. [2012] precluded the vapor enhancement factor which was previously included in their model. This enlarges indirectly the effect of isothermal film flow on evaporation because the inclusion of vapor enhancement factor will suppress evaporation during daytime due to downward temperature gradient (the effect of this factor during nighttime reverses but is infinitesimal) [Zeng et al., 2011b], and second, even with the preclusion of the vapor enhancement factor (e.g., increase indirectly the effect of film flow), Smits et al. [2012] indicated that not including film flow had a very small effect on the cumulative evaporation and saturation profile. The latter point actually matches Peters and Durner's [2010] results in Figure 1 in their commentary.

[18] Nevertheless, we calculate the order of magnitude of isothermal film flow on day 2 to demonstrate if it is important or not in our study. The hydraulic conductivity due to film flow can be expressed with Zhang's [2011] approach, which adapted Tokunaga's [2009] formula to natural porous media by introducing a soil-dependent correction factor accounting for the lumped impacts of particle shape and surface roughness:

display math
display math(1)
display math
display math
display math
display math

where f is a dimensionless correction factor, b is a dimensionless constant, h is matric potential head (m), inline image is the saturated hydraulic conductivity corresponding to h = 0 due to film flow, inline image is the porosity (∼0.41), dg is the effective grain diameter (m, ≈ d10), ρ is the density of water (∼1 × 103 kg m−3), g is the gravitational acceleration (=9.81 m2 s−1), σ is the surface tension (10−3 N m−1, B = 235.8 × 10−3 N m−1, c = −0.625; ξ = 1.256, Tc = 647.15 K) [Vargaftik et al., 1983], μw is the dynamic viscosity of water (kg m−1 s−1, μw0 = 2.4152 × 10−5 Pa s, μ1 = 4.7428 kJ mol−1, R = 8.314472 J mol−1 K−1) [Fogel'son and Likhachev, 2000], T is the temperature in Celsius, ε is the dimensionless relative permittivity of water (=78.54), ε0 is the permittivity of free space (=8.85 × 10−12°C2 J−1 m−1), kb is the Boltzmann constant (=1.381 × 10−23 J K−1), i is the magnitude of ionic charge (dimensionless, ∼1), and a is the electron charge (=1.602 × 10−19i).

[19] Equation (1) needs matric potential and temperature on day 2 as the input (e.g., the data for low-permeability soil are used, Figure 1, left). Except for the values indicated above, the rest of input data include the porosity and the effective grain diameter, which have been introduced by Zeng et al. [2009a] with a value of 0.382 and 0.082 mm, respectively. With all the input data, Figure 1 (right) demonstrates the large differences in orders of magnitude between the capillary flow hydraulic conductivity and the film flow hydraulic conductivity. The capillary flow KLh in our paper is 7 orders of magnitude larger than the film flow conductivity Kfilm, which indicates that the inclusion of film flow in our case seems not necessary. With the above approach for calculating Kfilm, we use data from Goss and Madliger [2007] and Smits et al. [2012] to check the consistency of the approach.

[20] The input data from Goss and Madliger [2007] are average temperature of 30°C and average matric potential of −1.5 × 10−5 and −4 × 10−5 cm. As the soil is classified as a Haplic Acrisol (Food and Agriculture Organization taxonomy) with 49% sand, 4% silt, and 47% clay, the effective diameter of this medium can be approximated as that of clay loam [Zhang, 2011] (as 0.035 mm) so does the porosity (as 0.5). The Kfilm values at the two matric potential levels were calculated as 7.3698 × 10−17 and 2.1050 × 10−17 cm s−1, respectively. Compared to Goss and Madliger's [2007] values of conductivity (3.8 × 10−11 and 2.2 × 10−12 cm s−1), it seems that the film flow conductivity was overestimated in their case. As the data were analyzed only by using Fick's law, a more comprehensively coupled moisture and heat transport model, considering film flow, should be applied to investigate further before reaching a conclusive statement. In Smits et al.'s [2010, 2012] case, the matric potential is not expected too low (e.g., −3 × 103 cm) in the top soil layer after 14 days evaporation, and the average temperature reaches about 20°C. The effective grain diameter is set as 0.52 mm, and the porosity is 0.334. The film flow conductivity is calculated as 3.92 × 10−12 cm s−1, which has the same order of magnitude as Smits et al.'s [2012] calculation of film flow conductivity in the top soil layer in their Figure 9.

4. Concluding Remarks

[21] It is important to note that the advective effect on evaporation should be perceived with a systematic point of view. Either isothermal flux, or thermal flux, or advective flux alone is not enough to investigate the advective effect. We agree with MY that the isothermal film flow is important to be included in understanding comprehensively the underestimation of evaporation on day 2. However, the calculation of the film flow hydraulic conductivity suggests that it is 7 orders of magnitude smaller than the capillary flow hydraulic conductivity in our paper. Furthermore, few studies suggest that the inclusion or preclusion of film flow in the coupled moisture and heat transport models does not differ with each other significantly in calculating evaporation [Peters and Durner, 2010; Smits et al., 2012]. It is necessary to investigate and explore further the thermodynamics of bound water and better parameterizations of the water retention curve as Massman [2012] suggested.