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Mathematical modeling typically aims to delineate different elements of the actual world, their interaction or connection, and dynamics using mathematical concepts. These models often assume various forms, for instance, game-theoretic models and differential equations (Zulkardi et al., 2; Abassian 54). In science, this conceptualization is believed to have three primary phases: prediction, modeling, and observation (Sokolowski 96; Porgo et al. 127). It is characterized by principles and methodologies that can be applied successfully. These precepts are comprehensive, and meta-principles are expressed as questions regarding mathematical modeling’s purposes and intentions.
On the other hand, spatial modeling relates to a specific disaggregation approach, which involves dividing a region into several indistinguishable or identical units. It is a set or a methodology of analytical processes utilized to derive data regarding spatial interconnections between geographic episodes or occurrences (Pourghasemi and Gokceoglu 12). This analytical procedure is typically performed in synchrony with a geographical information system (GIS). There are two major types of spatial models: vector and raster. Its primary objective is to facilitate the evaluation and simulation of spatial phenomena occurring in the actual world and allow for planning and problem-solving approaches.
Advantages of Spatial Modeling
Spatial models are typically categorized into two major categories: raster and vector. The latter facilitates the delineation of spatial feature locations based on coordinate pair methodology. This approach has several advantages; first, it allows for the representation of data in its original form and resolution without generalization. Second, the resulting graphic output is typically aesthetically appealing (Bearman 396). Third, this technique does not necessitate any data conversions since substantial data amounts are in vector forms. Fourth, it enhances the maintenance of accurate geographic data locations, and effective topology encoding, thereby enhancing operations efficiency.
The raster model involves merging spatial object representation and its pertinent non-spatial features into consolidated information or data files. This methodology has also been associated with several benefits; first, each cell’s geographic location is inferred by its cell-matrix position instead of its original or actual point. Second, it allows for the easy programming and prompt analysis of data due to its information storage technique. Third, the raster map’s inherent nature is preferably suited for quantitative evaluation and mathematical modeling. Fourth, discrete information such as forestry stands is assimilated or acclimatized appropriately, synonymous with continuous data, and it fosters the integration of the two forms of data. Lastly, grid-cell frameworks are well-matched with raster-based output technologies.
Disadvantages of Spatial Modeling
Some of the drawbacks of vector models include; first, each vertex’s location is stored separately. Second, this approach demands the conversion of vector information into a topological structure. This, according to José and Jorge, requires the extensive cleansing of data and is processing-intensive (101). Furthermore, the editing or updating of vector information necessitates topology re-building due to topology’s static nature. Third, Pourghasemi and Gokceoglu underscore the complexity of analysis and manipulative function algorithms and can be rigorous or processing-intensive (26). Fourth, the approach also limits the effective representation of continuous data. According to Pourghasemi and Gokceoglu, considerable data interpolation or generalization is required for the above-mentioned information layer (26). Lastly, it is impossible to perform spatial filtering and analyses within polygons.
Various shortcomings have been linked with rater spatial models; first, this approach constrains the adequate representation of linear aspects depending on the resolution of the cell. Second, researchers are likely to encounter significant difficulties in processing related attribute data, particularly if there is an extensive amount of information. Third, information has to be subjected to vector-to-raster remodeling because significant data amounts are in vector form; this, in turn, increases data integrity issues and processing requirements. Lastly, many output maps generated from grid-cell systems or programs do not adhere to high-quality cartographic demands.
Challenges of Being Only a Front-End User of Models
A website’s or software program’s frontend is similar to the user interface. It is an abstraction that simplifies the underlying component by offering a user-friendly interface. A frontend user, commonly referred to as a website user, refers to an account developed for an individual that allows him to log into the intranet’s front end. These users typically encounter significant challenges, and some of these drawbacks include, first, significant difficulties in keeping a proper balance between short- and long-term design conclusions or questions. Second, frontend model users experience considerable issues in balancing iteration periods between significant framework upgrades and automated testing. These professionals also face considerable hurdles in communicating various search engine optimization (SEO) concepts, ensuring that each UI element functions as intended, and ensuring that other employees understand the model, view, and controller (MVC).
An Example of Spatial Modeling in Meteorology
Spatial modeling may be utilized to plot the spatial distribution of specific atmospheric events. A study conducted by Walawender et al., which aimed to delineate climate mapping approaches used for spatially intermittent atmospheric occurrence, revealed spatial modeling’s efficiency in enhancing researchers’ understanding of meteorological (650). According to Walawender et al., spatial modeling fosters one’s understanding of the spatial intensity and variability of extreme weather conditions (648). It makes it possible for scientists to ascertain an area’s sensitivity or susceptibility to extreme or utmost atmospheric perils at dissimilar risk levels. Therefore, spatial modeling represents an appropriate approach for mapping spatially sporadic atmospheric conditions.
Spatial modeling is an indispensable procedure integrated with spatial analysis. On the other hand, mathematical configuration refers to an abstract model that utilizes mathematical language to delineate a system’s behavior. Spatial modeling has significant advantages and disadvantages associated with its application. Some of the challenges encountered by front end-users include difficulties maintaining an effective balance between short- and long-term design conclusions and balancing iteration periods. Spatial modeling can be instrumental in mapping the spatial distribution of specific atmospheric events.
Abassian, Aline. “Five Different Perspectives on Mathematical Modeling in Mathematics Education.” Journal of Investigations in Mathematics Learning, vol. 12, no. 1, 2020, pp. 53–65. Taylor and Francis Online. Web.
Journal of Geography in Higher Education, vol. 40, no. 3, 2016, pp. 394 -408. Taylor and Francis Online. Web.
José, António T., and Rocha Jorge. Spatial Analysis, Modelling and Planning. IntechOpen, 2018.
Porgo, Teegwendé V., et al. (2019). “The Use of Mathematical Modeling Studies for Evidence Synthesis and Guideline Development: A Glossary.” Research Synthesis Methods, vol. 10, no. 1, 2019, pp. 125–133. NCBI. Web.
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Pourghasemi, Hamid R., and Candan, Gokceoglu. Spatial Modeling in GIS and R for Earth and Environmental Sciences. Elsevier, 2019.
Sokolowski, Andrzej. “The Effects of Mathematical Modelling on Students’ Achievement-Meta-Analysis of Research.” IAFOR Journal of Education, vol. 3, no. 1, 2015, pp. 93–114. ResearchGate. Web.
Walawender, Ewelina et al. “Geospatial Predictive Modelling for Climate Mapping of Selected Severe Weather Phenomena Over Poland: A Methodological Approach.” Pure Applied Geophysics, vol. 174, 2017, pp. 643–659. SpringerLink. Web.
Zulkardi Zulkardi, et al. “Mathematical Modeling in Realistic Mathematics Education.” Journal of Physics Conference Series, vol. 943, no. 1, 2017, pp. 1-10. ResearchGate. Web.