## 3 Results and Discussions
### General Observations and Analysis of the Results  
The outcome of the program (C programming language; Visual Studio 2019) is defined under two terms; recurrences and averaged percentage of error, as seen in Figure 5. The recurrences refer to the number of combinations of two equations encountered that scored the lowest percentage of error, which is the second term, to that of the original. It is worth noting that Figure 5 demonstrates the best scores achieved in both cases for a single equation (i.e., E2, E3, E4, and E5) and the average of two summed equations (e.g., E3E5, E3E4, etc.). In addition, E1 is observed to have failed to achieve any significant results on its own as opposed to others.  
Sorting the results as described earlier revealed that averaging two summed equations may potentially lead to better estimations compared to single equations. The highest recorded recurrences (more than one-third of the results) were achieved by averaging E3E4 and E3E5, having relatively low average estimation errors of 10.93% and 18.72%, respectively.  
Not far from expectations, the subsequent significant recurrences were scored by three single equations (i.e., E3, E4, and E5). The three single equations managed to score an accumulation of 48 recurrences with average estimation errors as low as 7.96% to 9.16% and as high as 30.71%.  
Interestingly, from Figure 5, equations E3, E4, and E5, individually and in combination with each other, seem to be responsible for the most significant recurrences (75.5% of the results). In contrast, equations in combination with E1 and E2 were either marginally considerable or deemed negligible due to their meagre number of recurrences. This observation is particularly notable in three sources, as demonstrated in Figure 6, which is considered as a promising indicator. The reason being, the other three sources [3; 14; 15] were used to derive some of the empirical equations in Table 1, whereas sources  
Figure 5: Illustrated outcome of equation recurrences scores based on the lowest expected percentage of error in estimating visibility at a given value of TSP concentration.  
in Figure 6 are independent of any derivation process; hence, it is safe to assume the unbiased significance of these equations.  
According to some studies, the relationship between visibility and dust concentration is influenced by a few factors such as dust particle size [24], extensivity of the data set used for derivations, measurement accuracy, and the distance of the measurement device from the source of the eroding soils [11].  
While the geographical location of the experiment may account for some factors influencing empirical relationship development (e.g., distance from eroding soil), others are subject to the methods and equipment used. Previous studies exploring the relationship of visibility to TSP concentrations (e.g., [PERSON]'s equation, E1; [PERSON] and [PERSON]'s equation, E2) were based on field experiments. However, the relatively recent studies have become more innovative given the vast technological advancements for data collection, validation, and monitoring techniques (e.g., MODIS [25]).  
For instance, [PERSON] et al.'s [15] (Equation E5) methodology employed data from a high-volume sampler and dust monitoring devices for improved concentration estimates and to derive instantaneous values of total suspended dust concentration from time-averaged values. Similarly, [PERSON] et al.'s study [14], based on an extensive set of measurements, produced two expressions to accommodate two different dust-concentration-to-visibility relationship scenarios: one for distant dusts cases (threshold visibility \(\geq\)3.5 km) and the other for local dust (threshold visibility \(<\)3.5 km). This, in turn, may suggest that the combination of the prevailing equations (E3, E4, and E5) may have inherited such characteristics, thus resulting in estimations that are comparatively more accurate.