## 1 Introduction
### The Gradient-Flux Method: Set-Ups, Approaches, Uncertainties  
While the physical background of the gradient method is accurate and valid, the actual application requires common simplifications from practical gas sampling and gas analysis, necessary assumptions (homogeneous production of gases, soil structure and moisture) to dealing with limited data (measurements). A careful consideration of the simplifications made and the assumptions met can help to assess the sources of uncertainty of the estimated flux value. Different methodologies have been developed over the decades to sample soil gas. From simple manual sampling using syringes with needles that are inserted into ground to sophisticated sampling devices that allow online monitoring of soil gas concentrations [44]. The first can be used quick and easily. But they do not allow for repeated sampling at the same location, since they disturb the soil structure. Monitoring purposes usually require a permanent installation of a soil gas sampler. Different designs have been developed and optimized to measure repeatedly at certain locations in the soil. The set-ups include simple, thin open-end metal or plastic tubes that are inserted to a specific depth. They require active sampling of air by sucking the air through the access tubes. Yet, it can be difficult to assign a precise depth to the sample if it is drawn under moist conditions and low air-filled pore volume around the sampling location. For accurate assignment of sampling location passive sampling systems are recommended [16; 69; 70]. Passive sampling means that the air is not aspirated into a vial or inlet, but it allows the air within the sampler to equilibrate with the surrounding soil air [70]. This can be achieved by using a silicon tube [71], highly gas permeable tubes [70], or multi-level samplers [69; 72]. Measurements of soil gas profiles have followed different paths during recent years. Sampling of soil air and subsequent analysis of the gas vials in the laboratory using gas chromatography (GC) represents the traditional way for precise gas analysis. The development of small solid-state CO\({}_{2}\) sensors has greatly simplified and facilitated CO\({}_{2}\) concentration measurements, so that these sensors can be easily installed into the soil to monitor soil CO\({}_{2}\) concentrations online [9; 64; 65; 73; 74]. These sensors are inexpensive and easy to handle and allow a very simple set-up (no extra sampler required), yet their application is limited to CO\({}_{2}\). The development of highly sensitive laser spectrometers and other technologies for field measurements has facilitated online measurements of additional gases such as N\({}_{2}\)O and CH\({}_{4}\), including their isotopic composition [75; 11; 70]. Such devices and set-ups usually allow a high precision of the measurements, but their demand for resources is quite high (power, costs, sensitive to harsh environments), and they usually measure only one or two gas species. Traditional GC is still an important technology because it allows analysing very small gas volumes at a high precision for up to several gases at a time. The combination of GC analysis and passive samplers facilitates suitable designs for monitoring purposes, because electrical power is not needed at the monitoring sites for the samplers, and samples from several sites can be analysed by one GC system. Different approaches for the calculation of the soil gas fluxes have been proposed, from direct simple calculations to analytical and numerical solutions [44]. It is important to consider the implicit assumptions of each calculation approach, since flux estimation can be sensitive to the different calculation procedures [76]. The estimation of soil gas diffusivity has a direct effect on the flux estimation and is, thus, another relevant source of uncertainty. Different models have been developed that allow deriving soil gas diffusivity from soil physical parameters and soil moisture measurements. However, knowing a priori the best suited model for a soil is impossible.