## 2 Materials and Methods
### The Net Biome Exchange, the Carbon and Water Balance  
The hourly Fq and Fc fluxes were cumulated over the course of the day during the extended growth season to establish the water and carbon balance in this cropping system. The net flux of CO\({}_{2}\), which represents the net ecosystem exchange (NEE), also referred to as ecosystem productivity (NEP), is given by:  
\[NEE=GPP+R_{eco}, \tag{3}\]  
where all terms are in g C m\({}^{-2}\); \(GPP\) denotes the gross primary production (carbon assimilated via photosynthesis) and \(R_{eco}\) represents the total ecosystem respiration. Both parameters were estimated by the EC measurements and FVS partitioning. In accordance with atmospheric conventions, fluxes moving downward from the atmosphere to the ecosystem (\(GPP\)) are negative, while fluxes moving upward are positive (\(R_{eco}\)). To determine if the watermelon crop under the present conditions can be classified as a carbon sink (C-sink, indicating carbon uptake from the atmosphere, negative) or a carbon source (C-source, indicating carbon loss from the ecosystem to the atmosphere, positive), the net biome exchange (\(NBE\), [38; 39]) is calculated by:  
\[NBE=NEE+FC_{harvest}, \tag{4}\]  
where \(FC_{harvest}\) denotes the organic carbon exported through watermelon fruit harvesting. The carbon budget of the watermelon field can be assessed by considering all C inputs and outputs. Rigorously, the CH\({}_{4}\) flux should also be included in the C balance [40]. However, for this study, this term was not considered, and a simplified version was used for the variation in soil organic carbon stock (\(\Delta\)SOC) over time (\(\Delta\)t):  
\[\Delta SOC/\Delta t=NEE+FC_{in}+FC_{out}, \tag{5}\]  
where \(FC_{in}\) and \(FC_{out}\) are the organic carbon imported (positive) and exported (negative), respectively. Negative values of \(NEE\) by Equation (3) indicate C import to the field; hence, for this balance, the sign must be inverted. The total organic carbon input is given by:  
\[FC_{in}=FC_{green.mannure}+FC_{org.fert}+FC_{mulching.film}, \tag{6}\]  
where \(FC_{green.mannure}\) is the organic carbon imported via green manure from broccoli, watermelon plants and fruits, \(FC_{org.fert}\) is the organic carbon imported by fertilization and \(FC_{mulching.film}\) is the organic carbon imported via the incorporation of the biodegradable munching film into the soil. The total organic carbon out is given by:  
\[FC_{out}=FC_{harvest}+FC_{leach} \tag{7}\]  
where \(FC_{leach}\) represents the organic carbon lost by leaching. \(\Delta\)SOC was measured in a 0-0.30 m soil layer, where all green manure operations were conducted and more than 80% of the total root length was found [41]. To determine the C content (%) in the fresh biomass and the biodegradable munching film, a CHN Elemental Analyzer (Flash EA 1112, Thermo Scientific, Waltham, MA, USA) was employed. Broccoli biomass, watermelon plants and harvested fruit biomass were collected in triplicate samples of 1 m\({}^{2}\), randomly collected in the area around the EC tower. The \(\Delta\)SOC of Equation (5) was computed by sampling soil before seeding after the green manure of the broccoli crop and at the end of the monitoring period (24 May 2023 and 30 November, respectively). On air-dried and sieved soil samples (0.5 mm particle size), SOC was measured by dry combustion [42] with a Vario Select analyzer (Elementar, Hanau, Germany). C lost via leaching was estimated according to [43], by measuring the soil water-extractable organic carbon (WEOC) content at the beginning and end of the trial. WEOC was measured according to a protocol reported by [44]. Finally, the uncertainties on the presented terms of the C balance were evaluated using the error propagation law [45], where the final uncertainty is the sum of the absolute errors calculated through the relative error on the sampled values. In arid and semi-arid areas with minimal slopes, surface runoff can be neglected, and capillary rise is nearly non-existent in shallow soils [4].