In a scientific effort to better understand and control pollutant transport in water

bodies, diffusion coefficients are calculated from the variances observed in the distribution of

conservative tracers. These coefficients are crucial for understanding of how substances spread

in water bodies and can aid in the development of better environmental protection strategies. In

this specific study, an $8$ kg amount of Methylene Blue was introduced into the stagnant water

body. This act was part of a controlled experiment to track and analyse how such substances

diffuse in surface waters. The diffusion of the dye was closely monitored by measuring the

concentration distribution of the tracer at three$-$hour intervals throughout a $15-$hour period. This

period coincides with daylight hours to ensure visibility of the tracer. The distribution data

collected includes the horizontal variances of the tracer cloud, which vary over time and provide

key insights into the diffusion process. Based on the provided data, estimate the horizontal

diffusion coefficients at x and y directions for t$=1\mathrm{.}5$ h$,3\mathrm{.}5$ h$,8$ h$,10$ h and $13$ h$.($Hint: You can

assume each interval is linear.$)$