Gas diffusivity in chinampas soils in Mexico City Difusión de gases en suelos de chinampas en la Ciudad de México Difusão de gases em solos chinampas da Cidade do México

In this laboratory experiment we measured soil gas diffusion coefficients (D) on undisturbed cores of anthropogenic chinampas soils and tested the validity of some classical gas diffusivity models for predicting the ratio of D to the gas diffusion coefficient in free air (D0) as a function of the soil airfilled porosity (ε). The A1 horizon (0-7 cm) of chinampas soils had the highest gas diffusivity and a linear relationship between D/D0 and ε, and thus, the Penman model gave an adequate prediction for this sub-horizon. The Millington-Quirk model was similar to the D/D0 at all values of ε for the A2 sub-horizon (7-18 cm) and at ε < 0.5 cm3 cm-3 for the A3 (18-30 cm) and A4 (30-50 cm) subhorizons. Gas diffusivities in chinampas soils were lower than in mineral soils, as predicted by D/D0 (ε) models, likely due to the high content of soil organic carbon. The predictive models could be used for the evaluation of greenhouse gases emission from chinampas soil.


Introduction
Diffusive transport is the major mechanism responsible for the movement of gases in soils and for gaseous exchange between soils and atmosphere (Kruse et al. 1996).Prediction of flow and transport processes in soil is crucial in many areas of soil and environmental sciences.The gas diffusion coefficient (D) is a widely used parameter for the evaluation of greenhouse gas emission from soil to atmosphere (Hashimoto and Komatsu 2006;Pingintha et al. 2010).Numerous models have been developed for the relative diffusion coefficient, defined as the ratio of the diffusion coefficient in the soil to that in free air (D 0 ), as a function of soil type and the air-filled porosity (ε).One of the classical D(ε) models is the linear model by Penman (1940); other simple, nonlinear D(ε) models take into account both ε and total porosity (Ф) (Buckingham 1904;Marshall 1959;Millington and Quirk 1961;Lai et al. 1976;Moldrup et al. 2000) (Table 1).The predictive models introduce a minor soil type effect through Ф that is dependent on, for example, soil texture and management (Moldrup et al. 2004).The existing data show that the soil gas diffusivity depends on soil type, and existing studies cover many of the natural groups of mineral soils (Moldrup et al. 2004;Kristensen et al. 2010) and organic soils (Iiyama and Hasehawa 2005).However, for some endemic soil groups, such as anthropogenic agricultural soils, the data regarding soil gas diffusivity are still insufficient.One such understudied soil type is the anthropogenic chinampas soil in Mexico City.Pre-Hispanic cultures in Mexico developed a specific technology for cultivating wetlands around the lakes in the Valley of Mexico by constructing elevated fields ("chinampas") for agricultural production (Ezcurra 1990;Ramos-Bello et al. 2011).Presently, the gas diffusion coefficient for chinampas soils has not been documented, which makes it difficult to predict the amount and the rate of gas transport and emission from this soil type.

Table 1. Relative gas diffusion coefficient models
Gas diffusion coefficients can be measured without removing soil from its natural location in field (Rolston et al. 1991) or in laboratory conditions which allow a varying soil water and evaluating D after establishing a steady state gas concentration (Hashimoto and Komatsu 2006).In this laboratory experiment, we determined the relative gas diffusion coefficient (D/ D 0 ) in undisturbed samples of anthropogenic chinampas soils.The results were compared to existing D(ε) models.
The chambers with the soil cores were brought into the laboratory with high soil moisture and stored at room temperature for 2-6 weeks to redistribute the soil water content.Some chambers were covered with a polyethylene sheet in order to keep the high soil water content in the soil cores.The gaseous diffusion coefficients of undisturbed soil cores were measured using the method described by Richter (1987) using CH 4 as the diffusing gas.This laboratory method is based on establishing a high initial gas concen-tration within a single diffusion chamber for a soil core.A digital pressure meter was used to monitor the pressure inside the gas chambers and care was taken to minimize any extra pressure buildup inside the chambers.The decrease of the gas concentration was followed over time by the regular withdrawal of gas samples from the chamber's headspace through a hole sealed with silicon septa (Corning System, USA) with a gastight 100 µL syringe (Hamilton Company).The decrease in the amount of gas in the chamber was expressed as the product of the decrease in the concentration with time and the volume of soil core and chamber.The gas samples were analyzed using a gas chromatograph (HP Agilent, 6890 GC System, GMI, USA), with the temperature of the column of 35 °С and temperature of the detector of 300 °С, using N 2 as carrier gas.
[ In the course of a preliminary three day experiment we detected no methane consumption in chinampas soils (unpublished results), and so the methane consumption in the soil cores was considered negligible during the measurement periods (minutes to a few hours depending on water content of the soil cores).The weighing of the diffusion chambers with the soil cores before and after measurements showed that there was negligible change in the soil water content during the measurements period for each core.At the end of each experiment, the soil cores were placed in an oven to determine their volumetric water content and air-filled porosity.To determine the soil moisture content the soil samples of known volume were weighed before and after drying at 105 °С for 24 h.The air-filled porosity of soil cores was calculated using the values for the total porosity (Table 2) and the soil moisture content.
Where appropriate, the D/D 0 data under different ε values were fitted with a non-linear function by means of a Statgraphics program (StatPoint Technologies, Inc.).

Results and discussion
The relative diffusion coefficient (D/D 0 ) increased with increasing air porosity for all soil sub-horizons (Figure 1).The A1 sub-horizon (0-7 cm) demonstrated a linear relationship between D/D 0 and air-filled porosity (ε), whereas for the A2-A4 sub-horizons the relationship was non-linear.The relative gas diffusivities for A2-A4 sub-horizons did not vary significantly within the air porosity range from 0 to 0.25 m 3 m -3 , but with the increase of air-filled pore space the D/ D 0 increased significantly and the highest measured relative gas diffusion coefficient values were determined at the highest ε.Moldrup et al. (2001) showed that pore size has little effect on gaseous diffusion, which is instead controlled by pore tortuosity and connectivity.At low air-filled porosity transport occurs only in pores with low tortuosity (Kristensen et al. 2010), whereas at high ε values some small and tortuous pores are drained and contribute non-linearly to gas diffusivity (Moldrup et al. 2001).When the soil is wet, the water causes a change in the pore shape and configuration of air-filled pores, which leads to increased tortuosity and lower pore connectivity for gas transport (Moldrup et al. 2000).
The A1 sub-horizon exhibited higher relative gas diffusivities compared with the A2-A4 subhorizons at the same air porosities.This could be explained by the differences in soil properties between these horizons since soil type, texture, structure and management have been shown to control gas transport in natural undisturbed soils (Moldrup et al. 2004).The A1 sub-horizon had the highest organic carbon content and total soil porosity and the lowest bulk density across all investigated horizons (Table 2).Hamamoto et al. (2009) showed that higher gas diffusion coefficients were observed in soils with larger particle sizes and pore diameters due to rapid gas diffusion through the less tortuous largepore networks.The higher D/D 0 values of the A1 sub-horizon may therefore be associated with lower pore tortuosity values.Furthermore, as was shown by Lange et al. (2009), the higher D/ D 0 values of the A1 sub-horizon could be associated with macropores such as cracks.These authors noted that while D/D 0 variability within a soil profile could not be explained solely by the variability in bulk density and total soil porosity, the soil macroporosity and layering greatly influenced variability of gas movement.
Figure 1 shows that while there were no major discrepancies between the relative gas diffusion coefficients of the A2-A4 sub-horizons, the D/D 0 values of the A4 sub-horizon when compared with A2 and A3 sub-horizons tended to be higher at ε from 0.2 to 0.3 cm 3 cm -3 and lower at ε > 0.6 cm 3 cm -3 .
All measured relative gas diffusion coefficients were optimized and presented as a function of air-filled porosity.Comparisons of the gas diffusivity models with measured data are shown in Figure 2. The Penman model gave a similar and adequate prediction for the soil of the A1 sub- horizon, while the Marshall model was similar to the measured data at ε lower than 0.5 cm 3 cm -3 and the Lai model provided an approximate upper limit for most measuring points (Figure 2a).The other models underestimated the diffusivities of the A1 sub-horizon.For the A2 sub-horizon the Millington-Quirk model provided the best overall fit over the entire range of ε while the other models largely overestimated measured D/D 0 (Figure 2b).For the A3 and A4 horizons the Millington-Quirk model gave fairly accurate estimates of gas diffusivities at low ε (ε < 0.5 cm 3 cm -3 ), but at higher ε this model overestimated the measured D/D 0 values (Figure 2c, d).The gas diffusion coefficient is better described by D/ D 0 = 0.939ε 2.897 and D/D 0 = 0.574ε 2.269 for the A3 and A4 horizons respectively.
For A2-A4 sub-horizons the classical predicted models generally predicted a higher gas diffusivity than the measured data (Figure 2b-d), probably because the predicted models were based on D/D 0 measurements in mineral soils, while chinampas soils, as was shown by Ramos-Bello et al. (2011) andIkkonen et al. (2012), have a high organic carbon content resembling that of organic soils.Gas diffusion has been shown to be lower in organic soils than mineral soils (Ikkonen and Tolstoguzov 1996;Iiyama and Hasegawa 2005;Lange et al. 2009).Organic compounds exhibit a high affinity for water and the chances of forming inter-particle water films are higher in soils with a higher organic matter content (Pokhrel et al. 2011).Soil gas diffusivity in organic soils has been suggested to decrease with the increase of soil organic carbon content (Iiyama and Hasegawa 2005).

Conclusions
In the chinampas soils the Penman and Millington-Quirk models offered the best prediction of gas diffusivity in the A1 and A2 sub-horizons, respectively.For the A3 and A4 sub-horizons, the Millington-Quirk model gave a similar prediction at ε < 0.5 cm 3 cm -3 .At ε > 0.5 cm 3 cm -3 the D/D 0 values were best described by D/D 0 = 0.939ε 2.897 for the A3 sub-horizon, and D/D 0 = 0.574ε 2.269 for the A4 sub-horizons.The chosen predictive models could be used for evaluation of emission of greenhouse gases from chinampas soils to atmosphere.

Acknowledgements
The authors acknowledge the financial support of the SEMARNAT-CONACyT, Project No. 23489, and PAPIIT, Project No. IN224410.The authors express their gratitude to Mr. J. M. Hernández-Solís (Centro de Ciencias de la Atmósfera, UNAM, México) for the contribution to the laboratory analyses.

Table 2 .
(Ikkonen et al. 2012)INAMPAS SOILS IN MEXICO CITY ]The organic carbon content, bulk density and total porosity in chinampas soils of the Xochimilco study area(Ikkonen et al. 2012)