please do it with matlab, and write a disscusion please.

Use of Splines to estimate heat transfer (Numerical Differentiation) Lakes in the temperate zone become thermally stratified during the summer. Such stratification effectively divides the lake vertically into two layers; the epilimnion and the hypolimnion, separated by a plane called the thermocline. The location of the Thermodine has great significance for exvironmental engineers. In particular, thermocline greatly diminishes mising between the two layers, as a result, the decomposition of organic matter can lead to severe depletice of oxygen in the isolated bottom waters. The location of the therasocline can be deflined as the inflectioa point of the temperaturedepth curve; that is, the point at which (d2T/dx2)=0, it is also the point at which the absolute value of the first derivative or gradient is a manimum. Use cubic splines to determine the thermocline depth for a Lake for which the Temperature vs Depth data is given as follows The purpose of this task is to analyze the data with the use ef MATL.AB spline built-in function. a) First, plot the data points with MATLAB, (notice that x-axis values are Temperatures, while y-axis values are depth) >pplot(z,7,r,) (doa't forket your axas labels and other details in your plot) b) on top of this plot, also plot the results of MATLAB spline interpolant using built-in function "spline" (use help to learn more on spline command) olot (ax,73) betect a different eates if yoe dika c) Now use FDD, BDD, or CDD (whichever is appropriate) to find the 1st and 2nd derivative of Temperature (T) with respect to depth (a) with O(h2). Plot these results separately, and locate the thermocline from d2T/dz2 plot. (Formulations for FDD, BDD, and CDD are given in Figures 21.3, 21.4, and 21.5, respectively). Remember Thermocline is at a depth where (d2T/Ax2)=0. derivative of Temperature ( T ) with respect to depth (z) with O(h2). Plot these results separately, and locate the thermocline from d2T/dz2 plot. (Formulations for FDD, BDD, and C.DD are given in Figures 21.3,21.4, and 21.5 , respectively). Remember Thermocline is at a depth where (d2r/dz2)=0. nouer 71.3 Houns it A version incorporates mote tems of the Tovior series exponsion and is, consequently. more occurale. 4 | FIGURE 21.5 Centered finitedfference formulas two versions are preserted for each dervat ve. The loter version incorporates more lems of the Toylor series exparsion and is, consequently, more accurate. d) If the heat flux from the surface to the bottom layer can be computed with Fourier's LAW J=kdzdT Compute the flux at this thermocline interface (k=0.01cal/(s.cm.C)) NOTE: Please check "help spline" and "help diff" to get more information on using built in functions