EVALUACIÓN DEL MODELO DE PÉRDIDA ESPERADA (TEORÍA DE

The significant linear relationship between subsurface CO2 concentration gradient and surface CO2

flux rate (R2 _{= 0.91, p <0.001; Figure 4.9) is strong evidence that molecular diffusion processes, as}

described by Fick’s Law, dominate CO2 fluxes. The slope of the line approximates the effective

diffusivity, De. However, advection caused by wind-induced pressure fluctuations (termed "wind pumping" or "pressure pumping"; Fukuda, 1955; Massman et al., 1997), which can be further modified by interactions with surface topography (Colbeck, 1989; Clarke and Waddington, 1991), must be considered. Wind pumping acts to enhance the rate of diffusive gas transport along a given concentration gradient, thereby producing flux rates greater than those expected from molecular diffusion alone (Bowling and Massman, 2011). This enhancement may be represented

mathematically as an additive component to the effective diffusivity in a Fick’s Law representation of gas transport:

𝑄𝑄 = (𝐷𝐷𝑠𝑠+ 𝐾𝐾)𝑑𝑑𝐶𝐶_{𝑑𝑑𝑑𝑑 ,} (4.27) where Q is the gas flux, De is the effective molecular diffusivity, K is a wind-dependent enhanced diffusivity parameter (Bowling and Massman, 2011), and dC/dz is the gas concentration gradient.

Figure 4.9 Relationship between subsurface CO2 concentration gradient and surface CO2 flux on

combined data from Days 1 and 2, Site B, Taylor Valley. The solid black line represents a linear relationship: y = 0.032x + 8E-07; the slope of the line represents the effective diffusivity of CO2 in the soil. Anomalous data from 06:30 h on Day 2 were excluded.

Therefore, the slope of the line in Figure 4.9 may be an overestimate of the true effective molecular diffusivity if it incorporates a wind pumping enhancement. Takle et al. (2004) found that under conditions conducive to wind pumping, surface soil CO2 flux rates were up to ten times greater than

those expected from molecular diffusion alone. Similarly, in a study of CO2 transport in a mountain

forest snowpack, Bowling and Massman (2011) found that wind pumping enhanced transport of CO2

by up to 40% in the short term (hours). In this study, wind speed was measured 1.2 m above the soil surface at Site A, located 2.8 km east of Site B. The strong diel pattern in wind strength is consistent with an anabatic easterly wind blowing up-valley during the warmest parts of the day. It is almost certain that the same wind blew at Site B; at the very least, the exposed nature of the site means that wind speeds at Site B were unlikely to have been lower than those measured at Site A.

If wind pumping significantly enhanced the surface CO2 flux rate for a given concentration gradient,

then positive fluxes during the warmest parts of the day, when the wind was strongest (~ 4 m s−1_),

would be greater than negative fluxes, which occurred during colder parts of the day when wind speeds were lower. This would manifest in a plot of concentration gradient versus surface CO2 flux

rate (Figure 4.9) as distinct linear relationships within the positive (steeper gradient) and negative (shallower gradient) flux domains. If such data were fitted with a single line, that line would have a significant, greater-than-zero, intercept. The intercept in Figure 4.9 is not significantly different from zero (p = 0.067). Further evidence of the relative unimportance of a wind pumping effect at this site is seen in a plot of wind speed versus surface CO2 flux rate (Figure 4.10), which, despite the

significant relationship (p = 0.027), accounts for only 40% of the variation in flux rate.

Figure 4.10 Relationship between wind speed and surface CO2 flux rates at Site B, Taylor Valley. The

The apparent insignificance of wind pumping in this study is in contrast to Risk et al.’s (2013) study of CO2 fluxes in the Dry Valleys, which found that measured CO2 fluxes were best related to average

wind speeds in the 16 days prior to flux measurements. However, given that CO2 fluxes in Risk et al.’s

(2013) year-long study were only sampled every 4 days during winter, and that Antarctic dry valley soils are characteristically dry and porous (McCraw, 1967; Campbell et al., 1997), it seems unlikely that any wind pumping due to strong winds over the previous 16 days would influence surface CO2

fluxes. Any enhancement of surface CO2 fluxes by wind pumping would likely be related to wind

speed and associated changes in pressure at the time of sampling (e.g. Takle et al., 2004). However, differences in the frequency of sampling and the period over which data were obtained between this study and Risk et al.’s (2013) study means that there is not a good basis for comparing the datasets. The time-series of flux measurements presented in this study is too short to investigate long lag-time effects.

Therefore, assuming the slope of the line in Figure 4.9 is a reliable estimate of the effective (molecular) diffusivity De, and that the low soil moisture contents had a negligible influence on CO2

diffusivity in the liquid phase (Fang and Moncrieff, 1999), particularly in this very dry soil, the relationship

𝐷𝐷𝑠𝑠= 𝐷𝐷 ∙ 𝜀𝜀 ∙ 𝜏𝜏 , (Massman, 2006) (4.28) where D is the free air diffusivity, and ε is the air-filled soil porosity, can be used to estimate the tortuosity factor, τ. Using a free air diffusivity for CO2 (at 1°C and atmospheric pressure) of 0.140 cm2

s−1 _{(Marrero and Mason, 1972), a soil porosity of 0.4 (from empirical data), a soil moisture content of} 0.01, and a De of 0.032 ± 0.003 cm2 _s−1 _{yields a tortuosity value of 1.8 ± 0.2. This value is in good}

agreement with the range of tortuosity values (1.5 – 2.0) calculated by McKay et al. (1998) in their gas diffusion experiments on Dry Valley soils, and lends further support to the inference that wind pumping was not a significant modulator of CO2 fluxes in this study. A wind pumping effect

contributing to an overestimate of De would result in an unexpectedly large tortuosity factor.

In addition, the effective diffusivity determined from Figure 4.9 is in reasonable agreement with that

estimated from the Millington−Quirk equation which is regarded as the best-performing soil type- independent model of gas diffusivity (Moldrup et al., 2004). A more advanced soil type-dependent prediction of gas diffusivity was not determined, owing to the unavailability of soil water

characteristic data. Furthermore, the extremely low soil moisture content at this site meant that McCarthy and Johnson’s (1995) modified version of the Millington−Quirk equation, which includes