## 2 Materials and Methods
### Soil Respiration Measurement  
The nonsteady-state, nonthrough-flow close chamber method (in classification [31]) was used to measure the rate of CO\({}_{2}\) efflux from soil. During the nonsnow period, 5 steel chambers with a diameter of 10 cm and a height of 12 cm were used for SR measurements (Figure 1b). The top of the chamber was equipped with a rubber septum for collecting gas samples. These chambers were inserted into the soil at a depth of 4 cm after cutting of green plant parts until 1 cm height. Gas samples were collected using 23 mL plastic syringes at 0, 10, and 20 min after the installation of the chambers.  
During the snow period, 5 chambers were PVC plastic pipes with a diameter of 20 cm and a height of 60 cm, which were stationary inserted into the soil at a depth of 10 cm after removing a living plant's canopy (Figure 1c). These were installed shortly before the first frost and removed after the melting of the snow cover. The chambers were supplied with additional sections when the snow depth exceeded the chambers height. Gas samples were collected using syringes at 0, 20, and 40 min after closing the chambers with cups. Gas samples had been immediately moved to a laboratory and analyzed with an infrared CO\({}_{2}\) analyzer (Li-Cor LI-820, Lincoln, NE, USA)  
Partitioning of Total CO\({}_{2}\) Efflux from Soil for Contribution of Heterotrophs and Root-Derived CO\({}_{2}\)  
HR was estimated by the root exclusion method. PVC plastic pipes of 20 cm diameter were cut into the soil at the depth of 45 cm. The upper part of the pipes protruded from the soil by 10-15 cm and was chamber walls that closed with cups with rubber septa. During the cutting process, soil layers of 2-cm thickness were removed step by step from the inner space of the pipes (Figure 1d). The soil had been freed from roots and was then sieved through a 5-mm screen. Prepared soil was removed into the pipes while maintaining the order of layers and density (compacting soil by a wooden pole) after the installation of the pipes at the indicated depth. It was possible to install the pipes without severely disturbing its structure due to the sandy structure of the soil. Leaf litter horizon was preserved in the forest site. Due to the absence of litter horizon in the grassland site, the surface of the bare soil in the chambers was covered by the nonwoven material that fits into the diameter of the pipe. This prevents the disturbance of soil surface during rain and reduces overheating and over-drying of the topsoil. HR measurements were performed similarly to soil respiration.  
We prepared and installed 5 chambers for HR measurements at the end of May 2022. The measurements of CO\({}_{2}\) emissions began 1 month after the installation of HR chambers. A posteriori comparison of CO\({}_{2}\) efflux from HR chambers installed in different years allowed us to establish that a period of 2-3 months is sufficient for the stabilization of CO\({}_{2}\) efflux from the soil, but a major decrease in extra flux is observed during the first month (Figure 11). There was no visible systematic decrease in HR observed over the two years based on a comparison of two series of chambers that were installed in consecutive years. The soil in the chambers was somewhat wetter than that around it due to the absence of plant transpiration (Figure 12).  
The above-described method allows us to measure HR associated with the decomposition of SOM as well as litter in the forest. It is worth considering that when soil wassieved, the part detritus fraction (up to 5 mm) and the remains of thin roots remained in the soil. Note that the pool of soil detritus in the topsoil of HR chambers in the forest was replenished by leaf and stem litter, whereas the replenishment of aboveground plant residues in the grassland was absent. The RR included the CO\({}_{2}\) from roots and rhizosphere microbiomes.