WOLFRAM SYSTEM MODELER

Scenario_1

Original WORLD3 model

Diagram

Wolfram Language

In[1]:=
SystemModel["SystemDynamics.WorldDynamics.World3.Scenario_1"]
Out[1]:=

Information

This is the original WORLD3 model without any interventions. In the book Limits to Growth: The 30-Year Update it is referred to as Scenario #1.


References:

  1. Meadows, D.H., D.L. Meadows, J. Randers, and W.W. Behrens III (1972), Limits to Growth: A Report for the Club of Rome's Project on the Predicament of Mankind, Universe Books, New York, 205p.
  2. Meadows, D.L., W.W. Behrens III, D.M., Meadows, R.F. Naill, J. Randers, and E.K.O. Zahn (1974), Dynamics of Growth in a Finite World, Wright-Allen Press, 637p.
  3. Meadows, D.H., D.L. Meadows, and J. Randers (1992), Beyond the Limits, Chelsea Green, 300p.
  4. Meadows, D.H., J. Randers, and D.L. Meadows (2004), Limits to Growth: The 30-Year Update, Chelsea Green, 368p.


Simulate the model from 1900 until 2100, and display the same variables as in the book Limits to Growth: The 30-Year Update at page 169:


The results obtained are not exactly the same as those shown in the book Limits to Growth: The 30-Year Update due to the integration algorithm in use. Most Modelica simulation environments uses by default a variable-step / variable-order DASSL algorithm, whereas STELLA, just like the older Dynamo software, uses by default a fixed-step Euler algorithm with a step size of 1 time unit.

A second even more important difference is that my Modelica code treats all variables as real-valued floating-point numbers, whereas the STELLA model treated some variables (e.g., population) as integers, whereas it treated other variables as fixed-point variables with only two significant digits after the comma. This led to a quite noticeable quantization error.

As I didn't see any good reason for unnecessarily mutilating the capabilities of the Modelica simulation environment, I decided not to replicate these features of the STELLA code here.


Parameters (77)

agr_mtl_toxic_index

Value: 1

Type: Real (1/dollar)

Description: Agricultural materials toxicity index

assim_half_life_1970

Value: 1.5

Type: Real (yr)

Description: Pollution assimilation half life in 1970

avg_life_land_norm

Value: 1000

Type: Real (yr)

Description: Normal life span of land

des_compl_fam_size_norm

Value: 3.8

Type: Real

Description: Desired normal complete family size

des_food_ratio_dfr

Value: 2

Type: Real

Description: Desired food ratio

des_ppoll_index_DPOLX

Value: 1.2

Type: Real

Description: Desired persistent pollution index

des_res_use_rt_DNRUR

Value: 4800000000.0

Type: Real (ton/yr)

Description: Desired resource utilization rate

food_short_perc_del

Value: 2

Type: Real (yr)

Description: Food shortage perception delay

fr_agr_inp_pers_mtl

Value: 0.001

Type: Real

Description: Effective fraction of agricultural pollution input

frac_res_pers_mtl

Value: 0.02

Type: Real

Description: Effective fraction of resource utilization on pollution generation

hlth_serv_impact_del

Value: 20

Type: Real (yr)

Description: Health service impact delay

income_expect_avg_time

Value: 3

Type: Real (yr)

Description: Income expected average time

ind_mtl_emiss_fact

Value: 0.1

Type: Real (1/ton)

Description: Industrial materials emission factor

ind_mtl_toxic_index

Value: 10.0

Type: Real

Description: Industrial materials toxicity index

ind_out_pc_des

Value: 400

Type: Real (dollar/yr)

Description: Desired annual industrial per capita output

ind_out_in_1970

Value: 790000000000.0

Type: Real (dollar/yr)

Description: Industrial output in 1970

inherent_land_fert

Value: 600

Type: Real (kg/(hectare.yr))

Description: Inherent land fertility

labor_force_partic

Value: 0.75

Type: Real

Description: Percentage of participating labor force

labor_util_fr_del_time

Value: 2

Type: Real (yr)

Description: Labor utilization fraction delay time

land_fr_harvested

Value: 0.7

Type: Real

Description: Land fraction harvested

life_expect_norm

Value: 28

Type: Real (yr)

Description: Normal life expectancy

lifet_perc_del

Value: 20

Type: Real (yr)

Description: Perceived life-time delay

max_tot_fert_norm

Value: 12

Type: Real

Description: Normal maximal total fertility

p_avg_life_agr_inp_1

Value: 2

Type: Real (yr)

Description: Default average life of agricultural input

p_avg_life_agr_inp_2

Value: 2

Type: Real (yr)

Description: Controlled average life of agricultural input

p_avg_life_ind_cap_1

Value: 14

Type: Real (yr)

Description: Default average life of industrial capital

p_avg_life_ind_cap_2

Value: 14

Type: Real (yr)

Description: Controlled average life of industrial capital

p_avg_life_serv_cap_1

Value: 20

Type: Real (yr)

Description: Default average life of service sector capital

p_avg_life_serv_cap_2

Value: 20

Type: Real (yr)

Description: Controlled average life of service sector capital

p_fioa_cons_const_1

Value: 0.43

Type: Real

Description: Default fraction of industrial output allocated to consumption

p_fioa_cons_const_2

Value: 0.43

Type: Real

Description: Controlled fraction of industrial output allocated to consumption

p_ind_cap_out_ratio_1

Value: 3

Type: Real (yr)

Description: Default industrial capital output ratio

p_land_yield_fact_1

Value: 1

Type: Real

Description: Default land yield factor

p_nr_res_use_fact_1

Value: 1

Type: Real

Description: Default non-recoverable resource utilization factor

p_ppoll_gen_fact_1

Value: 1

Type: Real

Description: Default persistent pollution generation factor

p_serv_cap_out_ratio_1

Value: 1.0

Type: Real (yr)

Description: Default fraction of service sector output ratio

p_serv_cap_out_ratio_2

Value: 1.0

Type: Real (yr)

Description: Controlled fraction of service sector output ratio

pot_arable_land_tot

Value: 3200000000.0

Type: Real (hectare)

Description: Total potential arable land

ppoll_in_1970

Value: 136000000.0

Type: Real

Description: Persistent pollution in 1970

ppoll_trans_del

Value: 20

Type: Real (yr)

Description: Persistent pollution transmission delay

processing_loss

Value: 0.1

Type: Real

Description: Processing loss

reproductive_lifetime

Value: 30.0

Type: Real (yr)

Description: Reproductive life time

social_adj_del

Value: 20

Type: Real (yr)

Description: Social adjustment delay

social_discount

Value: 0.07000000000000001

Type: Real (1/yr)

Description: Social discount

subsist_food_pc

Value: 230

Type: Real (kg/yr)

Description: Available per capita food

tech_dev_del_TDD

Value: 20

Type: Real (yr)

Description: Technology development time

urb_ind_land_dev_time

Value: 10

Type: Real (yr)

Description: Urban and industrial land development time

t_air_poll_time

Value: 4000

Type: Real (yr)

Description: Air pollution change time

t_fcaor_time

Value: 4000

Type: Real (yr)

Description: Year of capital allocation to resource use efficiency

t_fert_cont_eff_time

Value: 4000

Type: Real (yr)

Description: Year of continued fertility change

t_ind_equil_time

Value: 4000

Type: Real (yr)

Description: Year of industrial equilibrium

t_land_life_time

Value: 4000

Type: Real (yr)

Description: Land life time

t_policy_year

Value: 4000

Type: Real (yr)

Description: Year of policy change

t_pop_equil_time

Value: 4000

Type: Real (yr)

Description: Population equilibrium time

t_zero_pop_grow_time

Value: 4000

Type: Real (yr)

Description: Time to zero population growth

p_fr_cap_al_obt_res_2

Value: {1, 0.2, 0.1, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05}

Type: Real[:]

Description: Non-renewable resource fraction remaining

p_ppoll_tech_chg_mlt

Value: {0, 0, 0, 0}

Type: Real[:]

Description: Persistent pollution technology change multiplier

p_res_tech_chg_mlt

Value: {0, 0, 0, 0}

Type: Real[:]

Description: Resource technology change multiplier

p_yield_tech_chg_mlt

Value: {0, 0, 0, 0}

Type: Real[:]

Description: Yield technology change multiplier

agr_inp_init

Value: 5000000000.0

Type: Real (dollar/yr)

Description: Initial agricultural input

arable_land_init

Value: 900000000.0

Type: Real (hectare)

Description: Initial arable land

industrial_capital_init

Value: 210000000000.0

Type: Real (dollar)

Description: Initial industrial investment

labor_util_fr_del_init

Value: 1

Type: Real

Description: Initial delayed labor utilization fraction

land_fertility_init

Value: 600

Type: Real (kg/(hectare.yr))

Description: Initial industrial investment

nr_resources_init

Value: 1000000000000.0

Type: Real (ton)

Description: Initial available non-recoverable resources

perc_food_ratio_init

Value: 1

Type: Real

Description: Initial perceived food ratio

pers_pollution_init

Value: 25000000.0

Type: Real

Description: Initial persistent pollution

pop1_init

Value: 650000000.0

Type: Real

Description: Initial population 14 years and younger

pop2_init

Value: 700000000.0

Type: Real

Description: Initial population 15 to 44 years old

pop3_init

Value: 190000000.0

Type: Real

Description: Initial population 45 to 64 years old

pop4_init

Value: 60000000.0

Type: Real

Description: Initial population 65 years and older

pot_arable_land_init

Value: 2300000000.0

Type: Real (hectare)

Description: Initial potential arable land

ppoll_tech_init

Value: 1

Type: Real

Description: Initial persistent pollution technology change factor

res_tech_init

Value: 1

Type: Real

Description: Initial non-recoverable resource technology factor

service_capital_init

Value: 144000000000.0

Type: Real (dollar)

Description: Initial service sector investment

urban_ind_land_init

Value: 8200000.0

Type: Real (hectare)

Description: Initial urban and industrial land

yield_tech_init

Value: 1

Type: Real

Description: Initial yield technology factor

Outputs (16)

population

Type: Real

Description: Total human world population

food

Type: Real (dollar/yr)

Description: Total annually produced food

industrial_output

Type: Real (dollar/yr)

Description: Total annual world industrial output

ppoll_index

Type: Real

Description: Persistent pollution index

nr_resources

Type: Real

Description: Remaining non-recoverable natural resources

fioa_ind

Type: Real

Description: Fraction of industrial output allocated to industrial/military complex

s_fioa_agr

Type: Real

Description: Fraction of industrial output allocated to food production

s_fioa_cons

Type: Real

Description: Fraction of industrial output allocated to consumption

s_fioa_serv

Type: Real

Description: Fraction of industrial output allocated to service sector

s_fr_cap_al_obt_res

Type: Real

Description: Fraction of capital allocated to resource use efficiency

life_expectancy

Type: Real (yr)

Description: Life expectancy

food_pc

Type: Real (dollar/yr)

Description: Total annual food per person

serv_out_pc

Type: Real (dollar/yr)

Description: Total annual services per person

ind_out_pc

Type: Real (dollar/yr)

Description: Total annual consumer goods per person

human_ecological_footprint

Type: Real (Gha)

Description: Human ecological footprint

human_welfare_index

Type: Real

Description: Human welfare index

Components (13)

Population_Dynamics1

Type: Population_Dynamics

Description: Population dynamics

Pollution_Dynamics1

Type: Pollution_Dynamics

Description: Persistent pollution generation

Arable_Land_Dynamics1

Type: Arable_Land_Dynamics

Description: Arable land dynamics

Food_Production1

Type: Food_Production

Description: Food production

Human_Ecological_Footprint1

Type: Human_Ecological_Footprint

Description: Human ecological footprint

Human_Fertility1

Type: Human_Fertility

Description: Human fertility

Human_Welfare_Index1

Type: Human_Welfare_Index

Description: Human welfare index

Industrial_Investment1

Type: Industrial_Investment

Description: Industrial investment

Labor_Utilization1

Type: Labor_Utilization

Description: Labor utilization

Land_Fertility1

Type: Land_Fertility

Description: Land fertility

Life_Expectancy1

Type: Life_Expectancy

Description: Life expectancy

NR_Resource_Utilization1

Type: NR_Resource_Utilization

Description: Non-recoverable natural resource utilization

Service_Sector_Investment1

Type: Service_Sector_Investment

Description: Service sector investment