## Materials and Methods
### Measurement of the Surface Roughness Value for Sandstone Slabs
Then, a total of 262,144 points (512 \(\times\) 512) around each selected location (the certain surface domain of 50 \(\times\) 50 \(\upmu\)m) of the slab were scanned by an SPM (Scanning Probe Microscope; Icon-PT-PLUS, Bruker, Bremen, Germany). The SPM included a cantilever tip connected to a probe with the laser beam, which was used to measure the height difference at each point and at the standard level (mean height), in nanometers, finally acquiring a 3-dimensional surface image profile for the certain surface domain of a slab (Figure 3). The information acquired from SPM analysis is useful not only for the surface image but also for more quantitative parameters to evaluate the roughness degree of the surface [50; 51]. Several surface roughness parameters have been developed, and in this study, a surface roughness value (\(SR_{\text{RMS}}\)) was used to reduce all of the information in the 3-dimensional surface image to a single number representing the degree of the surface roughness [52; 53]. For this study, the \(SR_{\text{RMS}}\) for the specific surface domain on each slab was calculated from the RMS (root mean square), for which the data can be acquired by measuring the height difference between the standard level (\(Z_{0}\) is the mean height from all points in a surface domain) and the height of each point in a domain [52]. Figure 3: Schematic of the SPM (Scanning Probe Microscope) analysis to calculate \(SR_{\text{RMS}}\) (surface roughness value). The following equation was used to calculate the \(SR_{\text{RMS}}\) (unit: \(\upmu\)m) for a specific surface domain:  
\[SR_{\text{RMS}}=\sqrt{\frac{1}{n}\ \sum_{i=1}^{n}\ \Delta z_{i}^{2}} \tag{1}\]  
where \(n\) is the total point number (262,144) in the surface domain, and \(\Delta z_{i}\) is the vertical height difference from the mean height (\(Z_{\text{o}}\)) to the \(i\)th point in the domain [54]. The degree to which the initial surface roughness differed from the reacted surface roughness at a certain reaction time was determined by comparing their \(SR_{\text{RMS}}\) values. The interrelationship between the degree of the surface roughness and the extent of the geochemical reaction was investigated and the potential application of \(SR_{\text{RMS}}\) to quantify the weathering process originating from the scCO\({}_{2}\)-sandstone-groundwater reaction was also evaluated by the experiment. The \(SR_{\text{RMS}}\) values acquired from all minerals' \(SR_{\text{RMS}}\) values were plotted at different reaction times, and the trend of \(SR_{\text{RMS}}\) change was compared with the trend of the physical property change of sandstones and the cation concentration change in groundwater, which verified that the surface roughness change reflects the extent of the geochemical weathering process and the rock property change. To verify that the scCO\({}_{2}\)-sandstone-groundwater reaction occurs actively, SEM/EDS analyses for the slab surface were performed and the mineralogical transfer and compositional change on the slab surface were investigated. Three milliliters of groundwater were sampled from the cell at different reaction times (maximum of 150 days) for the chemical analysis, and the same amount of groundwater was added into the cell. The pH and the concentrations of six main cations (Al\({}^{3+}\), Ca\({}^{2+}\), Fe\({}^{2+}\), K\({}^{+}\), Na\({}^{+}\), and Si\({}^{4+}\)) in the groundwater sample were analyzed via ICP/AES (Inductively Coupled Plasma/Atomic Emission Spectrometer; Optima 7300V, Perkin Elmer, Waltham, MA, USA) and using a pH meter, and they were plotted at different reaction times (0-150 reaction days). The relationship among pH change, cation concentration change, physical property change, and \(SR_{\text{RMS}}\) change was investigated to verify the feasibility of \(SR_{\text{RMS}}\) usage as a parameter to quantify the extent of the geochemical reaction.