## 1 Introduction  
The gas exchange between the atmosphere and terrestrial ecosystem represents a large proportion of CO\({}_{2}\) and CH\({}_{4}\) atmospheric budgets [1]. Soil CO\({}_{2}\) budget and efflux due to land-use change averaged globally from 2009-2018 were estimated at 5496-8793.6 PgCO\({}_{2}\) and 5.49 PgCO\({}_{2}\)yr\({}^{-1}\) respectively [2], as for the comparison, the emission due to fossil fuel combustion and the cement industry is around 33.4 PgCO\({}_{2}\)yr\({}^{-1}\)[3]. Adequate and trustworthy monitoring strategies of natural gas exchange will help understand the local variability of gas concentration in the soil, e.g., in anticipation of the CO\({}_{2}\) injection [4, 5] and promote public acceptability [6], or for ecological studies on terrestrial greenhouse gases emissions [3, 7, 8, 9]. Generally, GHG (Greenhouse gasses) emissions from the soilsare being measured in both laboratories and directly in the field [3]. The most widely used approaches in this context are chambers methods (soil-air interface) [1; 10; 11; 12], micro-meteorological eddy covariance method (vegetation-atmosphere interface) [9; 13; 14; 15], and the gradient method (subsoil gas transport) [1; 16; 17; 18; 19]. The monitoring of sub-soil CO\({}_{2}\) significantly helps define the overall balance between soil production and GHG consumption [20]. This soil CO\({}_{2}\) monitoring is also useful for comparing the carbon exchange quantification at the ecosystem level resulting from the flux tower [9; 21; 22]. It is widely believed that the soil CO\({}_{2}\) concentration generally increases as the depth, from the near-atmospheric layer up to a few meters below the topsoil. The CO\({}_{2}\) concentration below 20 cm for most soil types is between 0.2 and 4% [23]. Meanwhile, the CO\({}_{2}\) concentration above 10% is generally found in the active geothermal area with a significant pressure gradient transport instead of the solely diffusive process [24; 25]. Although molecular diffusion plays a significant part in soil CO\({}_{2}\) emission, the physical components such as soil ventilation in highly porous surface layers, known as advective CO\({}_{2}\) transport involving wind speed, friction velocity (u*), or air pressure, are also important [26]. Friction velocity is a crucial parameter in the study of boundary layers. It can be described as u*2 = \(\tau/\rho\), where \(\rho\) is the fluid density and \(\tau\) is the shear stress. Friction velocity in a turbulent flow in the atmosphere is approximately constant up to the lowest several meters [27; 28]. Nonetheless, multiple velocimeters that are positioned precisely are required in order to estimate the friction velocity. As alternatives, inertial dissipation, turbulent kinetic energy method, and eddy correlation method might be employed to produce reliable estimation [29]. The porous soil structure is continuously changing due to numerous factors, including water gains and losses, soil redistribution, changes in matrix structure because of the earthworms, and deformation due to compaction [30]. Some studies reported that the CO\({}_{2}\) dissolution and ventilation process plays a significant role in storing and releasing a large amount of CO\({}_{2}\) in subsurface cracks, pores, and cavities [31; 32; 33]. Nonetheless, most of the studies carried on forest soil mainly focused at a depth of 0 to 1 m, where the soil CO\({}_{2}\) production occurs from an autotrophic component and heterotrophic components. The deep soil zone, marginally influenced by the atmospheric conditions, is a perfect location to create a CO\({}_{2}\) baseline for a wide range of geological storage applications, including but not limited to the CCS (carbon capture and storage) [6; 34; 35] and hydrogen storage monitoring programs [36]. However, there was substantial evidence from previous works that soil gas transport in the unsaturated zone was predominantly affected by the water table variations.