## 2 Materials and Methods
### Models Used to Access Ecosystem Services  
Modeling of the ES helps the researcher to quantify, spatially locate, and potentially evaluate the economic trends. [PERSON] et al. [19] point out that this information plays a vital role in the decision making of urban planners, urban designers, and policymakers attempting to understand the effect of urban expansion on ES. In the present scenario, there is a proliferation of models and tools that helps us to map and access ES and vice versa [42; 50; 51]. Over time, numerous studies tried to simultaneously understand land use changes and their impact on ES, which helped designers and policymakers take appropriate steps to overcome the issue. To monitor LULC changes and ES changes, satellite images have been globally used as the most accurate tool [52; 53]. Models are used to investigate the interactions (such as a trade-off, synergies, bundles/clusters, and flows) of ES, and deliberately put forward benefits that are enjoyed by humans for their well-being [54; 55; 56]. There is much importance given to enhancing ecosystem service management by objectively quantifying interactions among various ES [57]. Integrated Valuation of Environmental Services and Trade-offs (InVEST) is a globally accepted tool that was developed inside the Natural Capital Project [50; 54; 55; 56; 57; 58; 59]. The InVEST model can illustrate a spatially visualized map of the ESs. Comparing the InVEST model with other models, InVEST does not require any expertise; this model provides a nearly accurate assessment with limited demand of data input criteria, and is relevant in understanding the areas dealing with ecological processes [50; 51; 60]. InVEST model is a  
Figure 4: Number of publications on ecosystem services classification. Where PES denotes provisioning ecosystem services, RES is regulating ecosystem services, CES is cultural ecosystem services, and SES is supporting ecosystem services. useful tool for assessing small-scale and local studies which give relevant and credible results for LULC and ES [58]. The InVEST toolbox is used to determine nearly 14 ES for supply changes using user-defined base setups like land use land cover and climatic changes [61,62]. The Soil and Water Assessment Tool (SWAT) is considered universally to simulate hydrological processes [63]. Further, the model has the flexibility in a spatial discretization that evaluates the space, locally, regionally, and globally. Like this, a decent number of models are used to assess ES changes; some of them are ARIES, LUCI, CA- Markov, SLEUTH, CLUES, etc. The study of ecosystem services is performed quantitatively using mapping and modeling techniques. Researchers also have used a combination of models to assess ES, such as a combination of model mapping ES (such as InVEST, SWAT, ARIES) and model mapping urban expansion. With the help of the statistical model, the mapping was carried out. Urban expansion models such as LUSD-urban (Land Use Scenario Dynamics-urban) [64] help in a multi-scale simulation of urban expansion, LUSD-urban along with Cellular Automata (CA) and system dynamics models signifies micro-scale evolutionary factors and macro-scale resource constraints. This model has undergone certain iterations in recent years, with improved accuracy and an average kappa index [65]. The other models are SLEUTH (slope, land use, exclusion, urban extent, transportation, and hill shade) [66], CLUE-S (the Conversion of Land Use and its Effects at Small regional extent) [67]. Statistical models such as correlation analysis [13,68], regression analysis [28], and root mean square deviation were used [69]. This combination of models is efficient at forming the correlation among a few variables but is not considered to be functionally viable. The most celebrated models are InVEST, ARIES, and SWAT. ]. Figure 5 gives a brief idea of various models used by researchers. The most commonly used base data are LULC, soil data, terrain data, and hydrological data.