A .mat file is provided. The file contains water profiles measurements the follo

Question

A .mat file is provided. The file contains water profiles measurements the following variables: depth, temperature,

density, PAR, oxygen, fluorescence from station M3 in Long Island Sound in July 1998. (a) Plot each of the six

variables versus depth using a subplot function, i.e., all the six graphs should appear on one page. Make

sure depth increases downward, label each graph and label the axes. Do not bother about the units.

(b) Interpret your results by describing what you see. For example, how does oxygen change with water

depth, etc.

This is the file our professor gave us:

http://www.fileconvoy.com/dfl.php?id=g35b1a6de10fc97d1999291959f2a5b284602a3fd3

Explanation / Answer

SOLUTION L = 200; % length [L] s1 = 0.5; % infiltration velocity [L/T] s2 = 0; % bottom suction head [L] T = 4; % maximum time [T] qr = 0.218; % residual water content f = 0.52; % porosity a = 0.0115; % van Genuchten parameter [1/L] n = 2.03; % van Genuchten parameter ks = 31.6; % saturated conductivity [L/T] x = linspace(0,L,100); t = linspace(0,T,25); options=odeset('RelTol',1e-4,'AbsTol',1e-4,'NormControl','off','InitialStep',1e-7) u = pdepe(0,@unsatpde,@unsatic,@unsatbc,x,t,options,s1,s2,qr,f,a,n,ks); figure; title('Richards Equation Numerical Solution, computed with 100 mesh points'); subplot (1,3,1); plot (x,u(1:length(t),:)); xlabel('Depth [L]'); ylabel('Pressure Head [L]'); subplot (1,3,2); plot (x,u(1:length(t),:)-(x'*ones(1,length(t)))'); xlabel('Depth [L]'); ylabel('Hydraulic Head [L]'); for j=1:length(t) for i=1:length(x) [q(j,i),k(j,i),c(j,i)]=sedprop(u(j,i),qr,f,a,n,ks); end end subplot (1,3,3); plot (x,q(1:length(t),:)*100) xlabel('Depth [L]'); ylabel('Water Content [%]'); % ------------------------------------------------------------------------- function [c,f,s] = unsatpde(x,t,u,DuDx,s1,s2,qr,f,a,n,ks) [q,k,c] = sedprop(u,qr,f,a,n,ks); f = k.*DuDx-k; s = 0; % ------------------------------------------------------------------------- function u0 = unsatic(x,s1,s2,qr,f,a,n,ks) u0 = -200+x; if x < 10 u0 = -0.5; end % ------------------------------------------------------------------------- function [pl,ql,pr,qr] = unsatbc(xl,ul,xr,ur,t,s1,s2,qr,f,a,n,ks) pl = s1; ql = 1; pr = ur(1)-s2; qr = 0; %------------------- soil hydraulic properties ---------------------------- function [q,k,c] = sedprop(u,qr,f,a,n,ks) m = 1-1/n; if u >= 0 c=1e-20; k=ks; q=f; else q=qr+(f-qr)*(1+(-a*u)^n)^-m; c=((f-qr)*n*m*a*(-a*u)^(n-1))/((1+(-a*u)^n)^(m+1))+1.e-20; k=ks*((q-qr)/(f-qr))^0.5*(1-(1-((q-qr)/(f-qr))^(1/m))^m)^2; end

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