herbivory cycling
(^)
%Mid-latitude, Atlantic production cycle driven by irradiance (W/m∧2)
%variation (modeled after Brock, 1981), nutrient and herbivory cycling.
clear all %Location and run length:
Lat=47.; nyears=1; %Storage vectors:
Daystr=NaNones(365nyears,1); Pstr=Daystr; Nutstr=Daystr; %Storage vectors:
Hstr=Daystr; MLZ=zeros(1,365); DayNstr=NaNones(2,365nyears);
%Solar constant (W/m∧2), atmospheric attenuation, PAR fraction):
SolarK=1373; AtmAtt=0.5; ParFrac=0.48;
%Light (water extinction, phyto extinction), from Fasham et al. (1990):
ex=.1; ey=0.12; %Nutrient Parameters, starting nutrients and mixing depths:
Ks=1.5; DeepNut=10.0; Nut=5.4541; Mprev=62;
%Phyto growth (alpha [h∧-1/W m∧-2], Vmax[d∧-1], m=mortality [d∧ -1]), and starting
value:
alpha=0.04; Vmax=0.7; P=1.1228; m=0.07;
%Hebivore parameters – grazing rate (c&d), threshold P, growth efficiency,
%starting value, death rate:
c=0.35; d=1.0; Po=0.1; f=0.35; H=0.4048; carn=0.07;
%Generate yearly sequence of mixed layer depths (MLZ):
%for Yr=1:nyears %(remove % for random effects on MLZ)
for i=1:365
%X=1.-2.rand; %(remove % for random effects on MLZ)
X=1. ; %(add % for random effects on MLZ)
if i<58; MLZ(i)=X+62+i18/58;
elseif i >= 58 && i <81; MLZ(i)= X+80;
elseif i >80 && i <101; MLZ(i)=X+80-45(i-80)/20;
elseif i >100 && i <250; MLZ(i)=X+35;
elseif i>=250; MLZ(i)=X+35+27(i-250)/115.;
end
end
for Yr=1:nyears %Year-to-year loop (add
% for random effects on MLZ)
for i=1:365 %Main daily loop
Day=(Yr-1)365+i; Daystr(Day)=Day;
NL=VmaxNut/(Ks+Nut); diff=0.025MLZ(i);
ext=ex+eyP;
% Surface PAR at latitude for times of day from dawn to noon and
% production rate integration down to MLD:
%I. Declination=angle of sun above the equator:
D1=23.45sind(360.(284.+i)/365.);
%II. Angle(deg.) between south (i.e., noon) and setting sun:
W1=acosd(-1.(tand(Lat)tand(D1)));
%III. One-half daylength, hours dawn to noon:
L1=W1/15.; % Earth rotates 15=degrees/hour
%IV. Distance of Earth from sun relative to average, a minor effect:
Rx=1./sqrt(1.+0.033cosd(360.i/365.)); %bookkeeping:
VTofD=L1/40.; TofD=12.01-L1-VTofD; SGr=0.;
for j=1:40 %summing production dawn to noon in 40 steps
TofD=TofD+VTofD; %for the following see Brock (1981):
W2=(TofD-12.)15.;
CosZen=sind(D1)sind(Lat)+cosd(D1)cosd(Lat)cosd(W2);
Isurf=SolarKCosZen/(RxRx);
Io=IsurfAtmAttParFrac;
%Sum photosynthesis down to MLZ, meter by meter
for k=1:MLZ(i) %progressive light extinction to MLZ(i):
Iz=Ioexp(-1extk);
% Denman-Pena function for phyto growth, scaled (0-1):
Gr=1-exp(-alphaIz/Vmax);
SGr=SGr+Gr;
end
end
AveGr=2VmaxSGr/(MLZ(i)40.); %(2 to get dawn to dusk)
%convert rate to daily growth multiplier:
if NL < AveGr