Appendix A
Great Bay Model
Equations
(Note: parameter values provided in Table 1)
Eelgrass
Submodel (Shoots and Roots and Rhizomes)
RootsRhy(t) = RootsRhy(t - dt) + (NPhBio_GPP - PI_transfer -
NPhBio_Resp - NPhBio_mort - NPhBio_consumed) * dt
INIT RootsRhy =
¥cell_size*ic_mac_NPhBio
INFLOWS:
NPhBio_GPP =
PHMAC_to_Roots*PhBio_GPP
OUTFLOWS:
PI_transfer =
RootsRhy*¥Translocation*¥PI_trans_rate
NPhBio_Resp =
¥NPhBio_resp_rate*Mac_Temp_Resp_Lim*RootsRhy
NPhBio_mort = RootsRhy*NPhBio_mort_rate
NPhBio_consumed =
Cons_ingest_NPhBio
Shoots(t) = Shoots(t - dt) + (PhBio_GPP + PI_transfer -
NPhBio_GPP - PhBio_Resp - PhBio_consumed - PhBio_litterfall - PhBio_Mortality)
* dt
INIT Shoots =
¥cell_size*(¥ic_mac_PhBio/¥sept_to_jan_conv)
INFLOWS:
PhBio_GPP =
¥Mac_PP_rate*Mac_Prod_lim*Shoots^¥Alpha_PhBio
PI_transfer =
RootsRhy*¥Translocation*¥PI_trans_rate
OUTFLOWS:
NPhBio_GPP =
PHMAC_to_Roots*PhBio_GPP
PhBio_Resp =
¥PHBio_resprate*Mac_Temp_Resp_Lim* Shoots
PhBio_consumed =
Cons_ingest_PhBio
PhBio_litterfall =
¥litterfall_season*Shoots*¥max_litterfall_rate
PhBio_Mortality =
¥PhBio_Mort_Rate*Shoots
actual_leaf_growth =
(PhBio_GPP+PI_transfer-NPhBio_GPP)*1000/¥cell_size
ic_mac_NPhBio =
¥Perc_NPhBio*(¥ic_mac_PhBio/¥sept_to_jan_conv)
Leaf_Limit_Coeff = if
RootsRhy=0 then 0 else MAX(0,(1-Shoots/(RootsRhy*¥L_to_R_limit)))
Mac_NPP =
NPhBio_NPP+PhBio_Net_Prod
Mac_Nut_lim = min(
¥DIN_sed_conc/ (¥DIN_sed_conc+¥Mac_Sat_N), ¥PO4_sed_conc/
(¥PO4_sed_conc+¥Mac_Sat_P) )
Mac_Prod_lim =
Mac_Light_lim*Mac_Nut_lim*Mac_Temp_lim
Mac_Temp_lim = min(1,
0.22*exp((0.07-0.00001*exp(0.28*¥H20_Temp))*¥H20_Temp)
Mac_Temp_Resp_Lim =
0.0107*exp(0.16*¥H20_Temp)
NPhBio_mort_rate =
(0.00125)*(Q10_2)/4
NPhBio_NPP =
NPhBio_GPP-NPhBio_Resp
PhBio_Lttr_ratio = IF
Shoots=0 THEN 0 ELSE (PhBio_litterfall/Shoots)
PhBio_Net_Prod =
PhBio_GPP-NPhBio_GPP-PhBio_Resp
PHMAC_to_Roots =
(1-Leaf_Limit_Coeff)*¥leaf_grow_season
Q10_2 = EXP (0.069*¥H20_Temp)
Root_depth =
(1-¥L_to_R_limit)*RootsRhy/¥cell_size*¥Nph_dpth_to_dens
R_to_L = if Shoots=0 then 0
else RootsRhy/Shoots
Shoot_Mort_Ratio = if
Shoots=0 then 0 else (PhBio_litterfall+PhBio_Mortality)/Shoots
Detritus
Submodel (Eelgrass Wrack and Seeds)
Seeds(t) = Seeds(t - dt) + (Seed_drop_out - seed_loss) * dt
INIT Seeds = 0
INFLOWS:
Seed_drop_out =
wrack*¥Seed_prod*¥Seed_wgt
OUTFLOWS:
seed_loss = Seeds*¥seed_loss_rt
Wrack(t) = wrack(t - dt) + (Wrack_produced + Wrack_X_in -
Wrack_consumed - Wrack_OM_decomp - Wrack_X_out - Seed_drop_out - wrack_sinking)
* dt
INIT wrack = ¥ic_wrack *¥cell_size
INFLOWS:
Wrack_produced =
PhBio_litterfall
Wrack_X_in = wrack_X_E@W:0+wrack_X_N@S:0+wrack_X_S@N:0+wrack_X_W@E:0
OUTFLOWS:
Wrack_consumed =
Cons_ingest_Wr
Wrack_OM_decomp = IF ¥on_map
= 2 THEN wrack*decomp_temp_Air ELSE wrack*decomp_temp_H2O
Wrack_X_out = IF ¥on_map = 2
THEN 0 ELSE (wrack_X_E+wrack_X_N+wrack_X_S+wrack_X_W)
Seed_drop_out =
wrack*¥Seed_prod*¥Seed_wgt
wrack_sinking =
¥Sink_rt*wrack
decomp_temp_Air = IF
¥Air_temp<=0 THEN 0 ELSE (¥Air_temp)^4/(¥half_sat_Air^4+¥Air_temp^4)
decomp_temp_H2O = IF
¥Air_temp<=0 THEN 0 ELSE (¥Air_temp)^4/(¥half_sat_H2O^4+¥Air_temp^4)
E_wrack_vector = IF
E_vector<0 THEN 0 ELSE E_vector+¥Wind_Wrack_factor*EW_wind_vector
N_wrack_vector = IF
N_vector<0 THEN 0 ELSE N_vector+(¥Wind_Wrack_factor*NS_wind_vector)
S_wrack_vector = IF
S_vector<0 THEN 0 ELSE S_vector+(¥Wind_Wrack_factor*NS_wind_vector)
Vector_Abs_Sum =
ABS(E_wrack_vector)+ABS(N_wrack_vector)+
ABS(S_wrack_vector)+ABS(W_wrack_vector)
wrack_X_E = if
Vector_Abs_Sum=0 then 0 else
(wrack*(E_wrack_vector/Vector_Abs_Sum))/sqrt(¥cell_size)
wrack_X_N = if
Vector_Abs_Sum=0 then 0 else (wrack*(N_wrack_vector/Vector_Abs_Sum))/sqrt(¥cell_size)
wrack_X_S = if
Vector_Abs_Sum=0 then 0 else
(wrack*(S_wrack_vector/Vector_Abs_Sum))/sqrt(¥cell_size)
wrack_X_W = if
Vector_Abs_Sum=0 then 0 else
(wrack*(W_wrack_vector/Vector_Abs_Sum))/sqrt(¥cell_size)
W_wrack_vector = IF
W_vector<0 THEN 0 ELSE W_vector+(¥Wind_Wrack_factor*EW_wind_vector)
Epiphytes
Submodel
Epiphytes(t) = Epiphytes(t - dt) + (Epi_Gross_PP + Epi_seeding -
Epi_resp - Epi_consumed - Epi_mort) * dt
INIT Epiphytes =
¥cell_size*ic_epiphytes
INFLOWS:
Epi_Gross_PP =
Epi_prod_lim*Epiphytes
Epi_seeding = If (Random(0,1)
< 0.1 AND Shoots>1) then ¥Epi_Seeding_rt ELSE 0
OUTFLOWS:
Epi_resp =
Epi_Resp_Temp_lim*Epiphytes^¥Alpha_Epi
Epi_consumed =
Cons_ingest_Epi
Epi_mort = if Shoots=0 then
Epiphytes else Epiphytes*(Shoot_Mort_Ratio)
Epi_NPP = Epi_Gross_PP-Epi_resp
Epi_Nut_lim =
min(DIN_conc/(DIN_conc+¥Epi_Sat_N), PO4_conc/(PO4_conc+¥Epi_Sat_P))
Epi_prod_lim =
Epi_Temp_lim*Epi_Light_lim*Epi_Nut_lim*¥Epi_pp_rt
Epi_Resp_Temp_lim =
¥Epi_resp_rt*(0.16*exp(0.054*¥H20_Temp))
Epi_Temp_lim = min(1,
0.22*exp((0.07-0.00001*exp(0.28*¥H20_Temp))*¥H20_Temp))
ic_epiphytes =
0.1*(¥ic_mac_PhBio/¥sept_to_jan_conv)
Phytoplankton
Submodel
Phytoplankton(t) = Phytoplankton(t - dt) + (Pht_Gross_PP - Pht_resp -
Pht_consumed - Pht_mortality) * dt
INIT Phytoplankton =
water_depth*¥cell_size*¥ic_Pht
INFLOWS:
Pht_Gross_PP = if SF_water=0
then 0 else Pht_Prod_lim*¥Pht_Gross_PP_rt*Phytoplankton
OUTFLOWS:
Pht_resp =
¥Pht_resp_rt*Pht_Temp_lim*Phytoplankton
Pht_consumed =
Cons_ingest_Pht
Pht_mortality =
Phytoplankton*¥Pht_mortality_rt
Pht_conc =
Phytoplankton/SF_water
Pht_NPP =
Pht_Gross_PP-Pht_resp
Pht_nut_limit = min(
DIN_conc/(DIN_conc+¥Pht_Sat_N), PO4_conc/(PO4_conc+¥Pht_Sat_P))
Pht_Prod_lim =
Pht_Temp_lim*Pht_Light_lim*Pht_nut_limit
Pht_Temp_lim = min(1,
0.22*exp(0.065*¥H20_Temp))
Light
Submodel
Cloud_cover = IF Rand <
few_clouds THEN 3*(Rand/few_clouds) ELSE IF Rand > some_clouds THEN
6.6+3*((Rand-some_clouds)/(100-some_clouds)) ELSE
3.3+3*((Rand-few_clouds)/(some_clouds-few_clouds))
Epi_Light_lim =
PAR_Epi/(PAR_Epi+¥Ik_Epi)
k_H2O =
¥k_water+(¥k_Pht*Pht_conc)
Mac_Light_lim =
PAR_Shoots/(PAR_Shoots+¥Ik_Shoot)
PAR_Epi =
PAR_Surface*exp(-k_H2O*max(0,(water_depth-¥leaf_length)))
PAR_Pht =
PAR_Surface*EXP(-k_H2O*max(water_depth*0.5,0))
PAR_Shoots = if Shoots=0 then
0 else if Epiphytes>Shoots then 0 else
PAR_Epi*(1-(0.75*SQRT(Epiphytes/Shoots)))
PAR_Surface =
Solar_radiation*(1-(0.071*Cloud_cover))
Percent_Light =
PAR_Shoots/PAR_Surface
Photo_period =
7.639437*h_angle
Pht_Light_lim = PAR_Pht/(PAR_Pht+¥Ik_Pht)
Rand = RANDOM(0,100)
Reflection =
0.5*((((SIN(Zenith-Angle_of_refraction))^2)
/((SIN(Zenith+Angle_of_refraction))^2))
+(((TAN(Zenith-Angle_of_refraction))^2)/((TAN(Zenith+Angle_of_refraction))^2)))
SDCLN =
0.00678+0.39762*COS(0.0172142*(Days-172))
+0.00613*SIN(0.0172142*(Days-172))-0.00661*COS(0.034428*(Days-172))-0.00159*SIN(0.034428*(Days-172))
Solar_radiation =
0.7*(916.73*(h_angle*SIN(¥Latitude*0.0174533)*SDCLN+SIN(h_angle)
*COS(¥Latitude*0.0174533)*COS(Decline)))
sunlight = Solar_radiation
Angle_of_refraction =
GRAPH(SIN(Zenith)/1.3398)
(-1.00, -1.57), (-0.75,
-1.12), (-0.5, -0.644), (-0.25, -0.305), (0.00, 0.00), (0.25, 0.305), (0.5,
0.644), (0.75, 1.12), (1.00, 1.57)
Decline = GRAPH(SDCLN)
(-1.00, -1.57), (-0.75,
-1.12), (-0.5, -0.644), (-0.25, -0.305), (0.00, 0.00), (0.25, 0.305), (0.5,
0.644), (0.75, 1.12), (1.00, 1.57)
few_clouds = GRAPH(Days)
(0.00, 20.0), (36.5, 20.0),
(73.0, 10.0), (110, 10.0), (146, 30.0), (182, 30.0), (219, 20.0), (256, 10.0),
(292, 10.0), (328, 10.0), (365, 20.0), (402, 20.0), (438, 10.0), (474, 10.0),
(511, 30.0), (548, 30.0), (584, 20.0), (620, 10.0), (657, 10.0), (694, 10.0),
(730, 20.0)
h_angle =
GRAPH(-TAN(¥Latitude*0.0174533)*TAN(Decline))
(-1.00, 3.14), (-0.75, 2.42),
(-0.5, 2.09), (-0.25, 1.82), (0.00, 1.57), (0.25, 1.32), (0.5, 1.05), (0.75,
0.723), (1.00, 0.00)
some_clouds = GRAPH(Days)
(0.00, 60.0), (36.5, 70.0),
(73.0, 50.0), (110, 50.0), (146, 60.0), (182, 50.0), (219, 40.0), (256, 40.0),
(292, 50.0), (328, 50.0), (365, 60.0), (402, 70.0), (438, 50.0), (474, 50.0),
(511, 60.0), (548, 50.0), (584, 40.0), (620, 40.0), (657, 50.0), (694, 50.0),
(730, 60.0)
Zenith =
GRAPH((SIN(¥Latitude*0.0174533)*SIN(Decline)+COS(¥Latitude*0.0174533)*COS(Decline)*SIN(h_angle)))
(-1.00, 3.14), (-0.75, 2.42),
(-0.5, 2.09), (-0.25, 1.82), (0.00, 1.57), (0.25, 1.32), (0.5, 1.05), (0.75,
0.723), (1.00, 0.00)
Nutrients
Submodel
DIN_conc =
DIN_Maps*¥DIN_scen*River_N
PO4_conc =
PO4_Maps*River_P*¥PO4_scen
¥DIN_scen = 1
¥PO4_scen = 1
Consumers Submodel
Consumers(t) = Consumers(t - dt) + (Cons_ingest + Cons_in_X -
cons_egest - cons_mortality - Cons_respiration - Cons_out_X) * dt
INIT Consumers = ic_consumer
*¥cell_size
INFLOWS:
Cons_ingest =
(Cons_ingest_Epi+Cons_ingest_NPhBio+Cons_ingest_PhBio+Cons_ingest_Pht+Cons_ingest_Wr)
Cons_in_X =
ConstoE@W+ConstoN@S+ConstoS@N+ConstoW@E
OUTFLOWS:
cons_egest = Cons_ingest*¥C_egest_eff
cons_mortality =
Consumers*¥C_mort_rt
Cons_respiration =
Consumers*Cons_activity*(¥C_resp_rt)
Cons_out_X =
ConstoE+ConstoN+ConstoS+ConstoW
Consdens = Consumers/¥cell_size
ConstoE = if
(Density_X_E+Food_X_E) > 1 then Consumers else
(Density_X_E+Food_X_E)*Consumers
ConstoN = if
(Density_X_N+Food_X_N) > 1 then Consumers else
(Density_X_N+Food_X_N)*Consumers
ConstoS = if
(Density_X_S+Food_X_S) > 1 then Consumers else
(Density_X_S+Food_X_S)*Consumers
ConstoW = if
(Density_X_W+Food_X_W) > 1 then Consumers else
(Density_X_W+Food_X_W)*Consumers
Cons_ingest_Epi = Min
(Epiphytes,(¥EP_pref/pref_tot)*Con_pot_ingest)
Cons_ingest_NPhBio = Min
(RootsRhy,(¥RR_pref/pref_tot)*Con_pot_ingest)
Cons_ingest_PhBio = Min
(Shoots,(¥SH_pref/pref_tot)*Con_pot_ingest)
Cons_ingest_Pht = Min
(Phytoplankton,(¥PH_pref/pref_tot)*Con_pot_ingest)
Cons_ingest_Wr = Min
(wrack,(¥Wr_pref/pref_tot)*Con_pot_ingest)
Con_pot_ingest = Min
(OMtotBio,(¥Ingestion_rt*Cons_activity)*Consumers)
Density_X_E = IF Consdens
< Consdens@E THEN 0 ELSE ((¥Travel_time)*(Consdens-Consdens@E))/Consdens
Density_X_N = IF Consdens
< Consdens@N THEN 0 ELSE ((¥Travel_time)*(Consdens-Consdens@N))/Consdens
Density_X_S = IF Consdens
< Consdens@S THEN 0 ELSE ((¥Travel_time)*(Consdens-Consdens@S))/Consdens
Density_X_W = IF Consdens
< Consdens@ THEN 0 ELSE ((¥Travel_time)*(Consdens-Consdens@W))/Consdens
Food_X_E = IF OMtotBio >
OMtotBio@E THEN 0 ELSE ((¥Travel_time)*(OMtotBio@E-OMtotBio))/OMtotBio
Food_X_N = IF OMtotBio >
OMtotBio@N THEN 0 ELSE ((¥Travel_time)*(OMtotBio@N-OMtotBio))/OMtotBio
Food_X_S = IF OMtotBio >
OMtotBio@S THEN 0 ELSE ((¥Travel_time)*(OMtotBio@S-OMtotBio))/OMtotBio
Food_X_W = IF OMtotBio >
OMtotBio@W THEN 0 ELSE ((¥Travel_time)*(OMtotBio@W-OMtotBio))/OMtotBio
ic_consumer =
(¥ic_mac_PhBio/¥sept_to_jan_conv)*.01
OMtotBio =
Phytoplankton+Shoots+RootsRhy+Epiphytes+ wrack
pref_tot =
¥EP_pref+¥PH_pref+¥RR_pref+¥SH_pref+¥Wr_pref
veg_structure =
(¥veg_dens_coeff/¥cell_size)*(Shoots+RootsRhy+ Epiphytes)
Cons_activity = GRAPH
(¥H20_Temp)
(0.00, 0.115), (2.33, 0.13),
(4.67, 0.135), (7.00, 0.165), (9.33, 0.285), (11.7, 0.77), (14.0, 1.00), (16.3,
1.00), (18.7, 1.00), (21.0, 0.765), (23.3, 0.46), (25.7, 0.295), (28.0, 0.25)
Global Submodel
Days(t) = Days(t - dt) +
(Count_hours) * dt
INIT Days = 0
INFLOWS:
Count_hours = IF Hours = 0
THEN 1*DT ELSE 0
Angle =
(ABS(Current_direction-¥Wind_direction)/8)*(2*PI)
Current_direction = IF
NS_vector=0 AND EW_vector=0 THEN 0 ELSE (IF (450-(ARCTAN(NS_vector/EW_vector)*(360/(2*PI))))
>360 THEN (450-(ARCTAN(NS_vector/EW_vector)*(360/(2*PI))))-360 ELSE
(450-(ARCTAN(NS_vector/EW_vector)*(360/(2*PI)))))
Current_velocity =
sqrt(EW_vector^2+NS_vector^2)
DW_Wave_L =
(9.8*(Wave_period^2))/(2*PI)
EW_vector = E_vector+W_vector
EW_wind_vector =
(¥Wind_speed*¥convert_wspd)*SIN(((180+¥Wind_direction)*2*PI)/360)
E_vector = if
E_Current_Vector<0 then 0 else
(E_Current_Vector*¥convert_currents)+(0.035*EW_wind_vector)
Fetch = IF ¥Wind_direction
< 45 THEN ¥F_North ELSE IF ¥Wind_direction <135 THEN ¥F_East ELSE IF
¥Wind_direction < 225 THEN ¥F_South ELSE If ¥Wind_direction < 315 THEN
¥F_West ELSE ¥F_North
H2O_Temp =
14-14*cos(2*p*(Days-31)/365)
Hours = MOD(TIME,24)
Loc_SA =
-TAN(¥Latitude*PI/180)*TAN(max_Sun_angle)
L_of_Day =
24*((PI/2)-ARCTAN(Loc_SA/SQRT(1-Loc_SA^2)))/ p
max_Sun_angle = 0.4093*SIN((Days-82)/58.1)
NS_vector = N_vector+S_vector
NS_wind_vector =
(¥Wind_speed*¥convert_wspd)*Cos(((¥Wind_direction+180)*2*PI)/360)
N_vector = if
N_Current_Vector<0 then 0 else
(N_Current_Vector*¥convert_currents)+(0.035*NS_wind_vector)
SF_water =
¥cell_size*water_depth
S_vector = if
S_Current_Vector<0 then 0 else (S_Current_Vector*¥convert_currents)+(0.035*NS_wind_vector)
W_vector = if
W_Current_Vector<0 then 0 else
(W_Current_Vector*¥convert_currents)+(0.035*EW_wind_vector)
¥cell_size = 10,000
¥Air_temp = GRAPH(Days)
¥H20_Temp = GRAPH(Days)
¥Wind_direction = GRAPH(Days)
¥Wind_speed = GRAPH(Days)
