WOLFRAM SYSTEM MODELER
Scenario_1Original WORLD3 model |
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Diagram
Wolfram Language
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SystemModel["SystemDynamics.WorldDynamics.World3.Scenario_1"]
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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:
- 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.
- 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.
- Meadows, D.H., D.L. Meadows, and J. Randers (1992), Beyond the Limits, Chelsea Green, 300p.
- 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)
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Population_Dynamics1 |
Type: Population_Dynamics Description: Population dynamics |
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Pollution_Dynamics1 |
Type: Pollution_Dynamics Description: Persistent pollution generation |
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Arable_Land_Dynamics1 |
Type: Arable_Land_Dynamics Description: Arable land dynamics |
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Food_Production1 |
Type: Food_Production Description: Food production |
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Human_Ecological_Footprint1 |
Type: Human_Ecological_Footprint Description: Human ecological footprint |
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Human_Fertility1 |
Type: Human_Fertility Description: Human fertility |
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Human_Welfare_Index1 |
Type: Human_Welfare_Index Description: Human welfare index |
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Industrial_Investment1 |
Type: Industrial_Investment Description: Industrial investment |
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Labor_Utilization1 |
Type: Labor_Utilization Description: Labor utilization |
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Land_Fertility1 |
Type: Land_Fertility Description: Land fertility |
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Life_Expectancy1 |
Type: Life_Expectancy Description: Life expectancy |
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NR_Resource_Utilization1 |
Type: NR_Resource_Utilization Description: Non-recoverable natural resource utilization |
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Service_Sector_Investment1 |
Type: Service_Sector_Investment Description: Service sector investment |