Biological Oceanography

                    G=NL;

            else

                    G=AveGr;

            end 

%mixing due to  mixing  layer   deepening,  zeta:

            if  MLZ(i)  >   Mprev;  zeta=MLZ(i)-Mprev;

            else    zeta=0.;    end

%update state   variables   (P, Nut,    H)

            graz=c*(P-Po)/(d+P-Po);

            if  P   <   Po; graz=0.;    end

            xmix=(diff+zeta)/MLZ(i);    

            P=P+G*P-m*P-graz*H-xmix*P;  

            Nut=Nut-G*P +   0.5*m*P +   xmix*(DeepNut-Nut)  +   0.5*graz*H;

            DelH=f*graz*H-carn*H-(MLZ(i)-Mprev)*H/MLZ(i);

            H=H+DelH;   %change to  new mixed   layer   depth:

            Mprev=MLZ(i);   %store  variables   for plotting:

            Pstr(Day)=P;    %   For P   as  Chl,    multiply    P   by  *8*12/50;

%   8=C/N,  12=mg   C/mmoleC,   50=C/Chl

            Nutstr(Day)=Nut;    DayNstr(1,Day)=Day; DayNstr(2,Day)=Nut; 

            Hstr(Day)=H;    

    end

end 

%plot   results vs. days    from    start   on  1   January:

plotyy(Nutstr(1:end),′k′,Pstr(1:end),′g′);  %Chlorophyll,   green   line

%Nutrient,  mmoles/m∧3  fixed   nitrogen,   blue    line

ylabel(′Nutrient    Units′);

hold    on  %Herbivores as  nitrogen,   red line

plot(Daystr(1:end),Hstr(1:end),′r′);

(^)
The model was run until the cycle was stable (takes ∼3 years; we used 6), and then
restarted with the sixth year values for January 1 (as in Box 4.4). The result (Fig. 4.6a)
shows a cycle (that recurs consistently) with a spring bloom in April, summer low in
P, small fall bloom, and winter low. The nutrient cycles inversely and zooplankton
bring down the phytoplankton bloom and peak toward the end of May. The timing of
the spring bloom is about right for the Atlantic at the modeled latitude, 47°N.
Nutrients (fixed nitrogen here) are drawn down to realistically low values for the
North Atlantic. Phytoplankton growth is light limited until the peak of the spring
bloom and again shortly after the fall bloom; it is nutrient limited from mid-April to
September (Fig. 4.6b).
Fig. 4.6 (a) The annual cycle of the modified Evans–Parslow model. Right scale in
nutrient-content units (μM) for phytoplankton (dashed lines) and grazers (thin lines);
left scale for nutrient (μM, thick lines). (b) Comparison of the effects of light and
nutrient limitation of phytoplankton growth rate in the mixed layer. The smaller of the
light-limitation (solid line: rate = Vmax Az{1 − exp[αIz/Vmax]}, where Az means
average over depth) or the nutrient limitation (dashed line: rate = Vmax N/[Ks + N])
operates each model day. (c) Effect on Evans–Parslow model output of increasing
grazing rate; the spring bloom is suppressed and replaced by low-level summer
oscillations.