## 3 Methodology
### [PERSON]'s Approach to Yield Estimation
#### 3.1.3 Soil Quality Index  
SQ is one of the most prevalent notions to have arisen in recent years, and it is used to analyse soil in many systems. In practice, soil quality is evaluated based on soil effects on crop yield, erosion, surface and ground, food, and air quality [26]. Maintaining good agricultural yields requires the evaluation of management-induced changes in SQ. Based on relative soil properties and crop output, a wide variety of cultivated soils must be properly identified using the SQI. Numerous attempts have been made to estimate SQI for vast soils around the world, but there is no defined standard approach. Therefore, there is an urgent need to produce a user-friendly and trustworthy SQI by comparing the various methodologies now available. It can be utilised as a standard in the yield estimation calculations of the SQI result regardless of the product type. The SQI varies among soil types in the study and spans from 0 to 1. (1 is the maximum SQI). Using the Mamatkulov approach, these signs were later evaluated on a scale ranging from 0 to 100. The relationship between crop yield and SQ is undeniable, yet SQ in different tiers may not be the same, influencing crop yield. However, a stronger correlation coefficient was discovered in the 0-20 cm soil layer than in the deeper soil profile, most likely due to the greater plant root density in the topsoil [27]. Traditionally, the MEDALUS approach is calculated using different SQ indices by rooting the multiplied indices by n-degree which n is the number of indices [28]. However, these calculations usually include indices obtained from laboratory results. In the MEDALUS approach [28], in which we choose to calculate the SQI variable utilised in the formula using only RS data, we evaluate the SQ based on the physical, chemical, and biological soil qualities, RS data, and GIS methodology. In our approach, different SQ parameters were re-evaluated by being calculated via RS data. Using DEM and Sentinel-2 data, physiographic units were identified in order to meet the research objective:  
* field report data to verify the physiographic outputs. * construction of the spatial model for the SQI evaluation
* estimating the Yield gradient index including validation percentage using the field capacity and observed values of the survey area. SQ calculation we developed based on the MEDALUS method is based on the following formula [19]. \[\text{SQI }=\sqrt[\text{(STI*SGI*SDI*NDMI*TICI*SI)} \tag{7}\]  
Here, the SQI slope gradient index, SDI soil depth index, and NDMI is showing drainage status. Soil Texture Index  
Many physical and chemical properties and behaviours of soil, such as water storage, cation exchange capacity, soil fertility, internal drainage, and absorption capabilities, are believed to be influenced by soil texture [29; 30]. It is much simpler to collect RS data for detailed descriptions of expansive regions. Therefore, RS data can serve as valuable supplementary variables for estimating surface soil texture. Using laboratory soil reflection data and satellite RS data [31], numerous researchers have focused on the GIS estimation of STI [32]. \[\text{STI}=\frac{\text{SWIR1}-\text{SWIR2}}{\text{SWIR1}+\text{SWIR2}} \tag{8}\]Soil Depth Index  
Topsoil is the soil's uppermost layer. It consists of mineral particles and biological stuff and often spans between 13 and 25 centimetres deep. Together, they provide a substrate capable of retaining water and air, so fostering biological activity. As plants derive the majority of their important nutrients from the topsoil, it typically contains a high root density. It also harbours extensive bacterial, fungal, and insect activity, where SQ degrades and becomes less accessible to plants. A healthy topsoil layer is home to a diverse community of microorganisms. As a strong correlation was discovered in the 0-20 cm soil layer with the SQ than in the deeper soil profile, soil depth is essential for agriculture, more precisely, yield estimation methods [33].