Equations for Randers's Revised DDT Model

The Stella equations for the model in Figure 12.14 are listed below:

DDT_in_fish(t) = DDT_in_fish(t - dt) + (Uptake_rate_in_fish - Dead_fish_remaining_in_ocean - Toxic_excretion_rate - Fish_consumed - Harmless_excretion_rate) * dt
INIT DDT_in_fish = 0

INFLOWS:
Uptake_rate_in_fish = Concentration_in_plankton*Mass_of_fish*Body_weights_eaten_per_year

OUTFLOWS:
Dead_fish_remaining_in_ocean = Deaths_of_fish*(1-Consumed_fraction)
Toxic_excretion_rate = DDT_excretion_rate_from_fish*(1-Degraded_fraction)
Fish_consumed = Deaths_of_fish*Consumed_fraction
Harmless_excretion_rate = DDT_excretion_rate_from_fish*Degraded_fraction

DDT_in_ocean(t) = DDT_in_ocean(t - dt) + (Precipitation_on_ocean + Dead_fish_remaining_in_ocean + Toxic_excretion_rate - Degradation_rate_in_ocean - Uptake_rate_in_fish) * dt
INIT DDT_in_ocean = 0

INFLOWS:
Precipitation_on_ocean = (Evaporation_rate_from_soil+Application_rate)*(1-Soil_fraction)
Dead_fish_remaining_in_ocean = Deaths_of_fish*(1-Consumed_fraction)
Toxic_excretion_rate = DDT_excretion_rate_from_fish*(1-Degraded_fraction)

OUTFLOWS:
Degradation_rate_in_ocean = DDT_in_ocean/(1.5*Degradation_halflife_in_ocean)
Uptake_rate_in_fish = Concentration_in_plankton*Mass_of_fish*Body_weights_eaten_per_year

DDT_in_soil(t) = DDT_in_soil(t - dt) + (Application_rate + Precipitation_on_soil - Degradation_rate_in_soil - Evaporation_rate_from_soil) * dt
INIT DDT_in_soil = 0

INFLOWS:
Application_rate = Application_rate_input*10000*(1-Airborne_fraction)
Precipitation_on_soil = (Application_rate+Evaporation_rate_from_soil)*Soil_fraction

OUTFLOWS:
Degradation_rate_in_soil = DDT_in_soil/(1.5*Degradation_halflife_in_soil)
Evaporation_rate_from_soil = (DDT_in_soil/(1.5*Evaporation_halflife_in_soil))

Airborne_fraction = 0.5
Body_weights_eaten_per_year = 10
Concentration_in_fish = DDT_in_fish/Mass_of_fish
Concentration_in_ocean = DDT_in_ocean/Mass_of_mixed_layer
Concentration_in_plankton = Ocean-plankton_concentration_factor*Concentration_in_ocean
Consumed_fraction = 0.5
DDT_excretion_rate_from_fish = DDT_in_fish/(1.5*Excretion_halflife_from_fish)
Deaths_of_fish = DDT_in_fish/(1.5*Halflife_of_fish)
Degradation_halflife_in_ocean = 15
Degradation_halflife_in_soil = 10
Degraded_fraction = 0.1
Evaporation_halflife_in_soil = 2
Excretion_halflife_from_fish = 0.3
fish_con_in_pphm = Concentration_in_fish*100e6
Halflife_of_fish = 3
Mass_of_fish = 6*10^8
Mass_of_mixed_layer = 3*10^16
ocean_con_in_pphm = Concentration_in_ocean*100e6
Ocean-plankton_concentration_factor = 2000
plankton_con_in_pphm = Concentration_in_plankton*100e6
Soil_fraction = 0.3
Application_rate_input = GRAPH(TIME)
(1943, 0.00), (1948, 4.00), (1953, 9.00), (1958, 13.0), (1963, 16.0), (1968, 17.5), (1973, 17.5), (1978, 11.0), (1983, 7.00), (1988, 4.00), (1993, 1.00), (1998, 0.00)