## Global Future Model

### Theoretical model

A model is a hypothetical and simplified description of the real world. It defines a set of 21 variables representing the events, states and the most important equations which we assume exist among the entities.

The Global Future Model describes how we assume the variables are linked to each along a time axis. Two types of variable are distinguished: 1. stock variables referring to variable values at a point on the time axis (e.g. population at end of a year), and 2. flow variable (e.g. number of births and deaths during a year) referring to variable values between 2 points of time on the axis.

Each variable value must therefore be identified by both name and time reference. We refer to a time period as a year. The model is called dynamic because some variable values can be related to other variable values with different time references (e.g. population value at the end of this year is determined by the population value at the end of the previous year plus the births minus the deaths within the population this year).

The Global Future Model relates the variable to each other by definition and structural equations. A definition equation expresses how variable values are associated by arithmetic operators (as the population at the end of this year in the last example of the previous paragraph). A structural equation is more complex specified by a function (e.g. linear, product, exponential function) with one or more parameters characterizing the equation (e.g. the birth and the death rates in a population change equation). The parameter values must either be estimated (e.g. the birth rate) or autonomously set (e.g. a policy parameter referring to investment allocation). Both stock variables start values and parameter values can be changed in the run menu.

### Definition equations

The first equation we introduce in the model to be used for reflecting possible possible global future scenarios is the definition of the stock variable global population represented by the variable id Pop(t) where the index t points to the end of the year to which the variable relates. We define the value of this variable as already indicated above. Since we are considering global entities, we don't have to worry about migration.

Pop(t) = Pop(t-1) + Births(t) - Deaths(t)

The variables in this equation are expressed in million persons (Mp).

The next variable is the production capital. Cap(t) changes from the end of one year to the end of next by the investment symbolized by Inv(t) minus by the depreciation Depr(t) of capital :

Cap(t) = Cap(t-1) + Inv(t) - Depr(t)

The model distinguishes between two sets of energy resources, the non-renewable, NRes(t), and the renewable, RRes(t), resources. The NRes(t) summarizes the known non-renewable energy resources left at the end of year t:

NRes(t) = NRes(t-1)-NUsed(t)

where NUsed(t) is the amount of non-renewable resources used during the year t. New non-renewable energy resources identified are ignored in the model.

The variable RRes(t) indicates the amount of existing renewable energy resources at the end of year t:

RRes(t) = RRes(t-1) + RDev(t)

The increase of new renewable resources RDev(t) is the amount of new renewable resource capacity developed during the year t. In the model, all renewable resources applied during the year are assumed to be ready for reuse at the end of each year. Depreciated renewable resources are ignored in the model.

The last resource included in the model is arable land. Land(t) expresses the value of arable land at the end of year t valued in 2014 USD. The annual change to this resource is the investment in cultivating new land, Cult(t) minus the value of decayed land, Decay(t), during the year t:

Land(t) = Land(t-1) + Cult(t) - Decay(t)

The climate is a major factor for the global population. The cumulating man-made greenhouse gas concentration in the atmosphere is assumed to be a dominant factor of changing climate. The stock variable, Gas(t), is an indicator representing the result of cumulated emission of CO2 at t and measured in ppm (particles per million). The value difference between the beginning and end of a year is the flow variables annual emission Em (t) also expressed in ppm:

Gas(t) = Gas(t-1) + Em(t)

The greenhouse gases are assumed to be irreversible in the short run.

The next definition equation expresses a balance restriction, i.e. that the different uses of annual products, including consumption Consume(t). must add up to the production:

GWP(t) - Inv(t) - RDev(t) - Cult(t) - Consume(t) = 0

The energy used from the two sources introduced above is assumed to equal the energy required by the production. The model assumes that all available renewable energy resources at the start of a year are utilized. Non-renewable resources are used to fill the energy gap if Energy(t)-RRes(t-1)>0:

Energy(t)- NUsed(t) - RRes(t-1) = 0

All variable values, except for the population, greenhouse gas and gas emission, are expressed in 2014 Million USD value.

### Structural equations

The births and deaths mechanisms in the global population are described by births, Births(t),and deaths, Deaths(t) , respectively. These two flow variable are assumed to be determined by functions, f1() and f2(), of the stock variable Pop(t-1) at the end of the previous year :

Births(t) = f1(Pop(t-1))

and

Deaths(t) =f2(Pop(t-1))

The Gross World Product, GWP(t), is an important flow variable representing the value of all products and services available for the world population during the year. It corresponds in principle to the sum of the GDP of all countries/societies in the world. The value of GWP(t) is assumed to be a function fb() of the 2 stock variables Pop(t-1) and Cap(t-1) :

GWP(t) =fb( Pop(t-1), (Cap(t-1))

The energy resources required for GWP(t) are expressed by the function fe() of GWP(t):

Energy(t)=fe(GWP(t))

Investment, Inv(t), in the world production capital, Cap(t), is an assumed political determined percent p1 of the GWP(t) ( This entity excludes investment, RDev(t), in renewable energy resources, RRes(t), and investment, Cult(t)), in arable land, Land(t), which are treated separately):

Inv(t) = p1*GWP(t)

The value of annual capital depreciation, Depr(t), is assumed to be a function d() of Cap(t-1):

Depr(t) = d(Cap(t-1))

Cultivating new and maintaining old land areas for harvesting food requires also its share in percent, p2 of GWP(t):

Cult(t) =p2*GWP(t)

A part of the land area Land(t-1) also decays during the year symbolized by the function d3():

Decay(t) = d3(Land(t-1) )

The percent of GWP(t) spent on developing new renewable energy resources is represented by the policy parameter p3:

RDev(t)=p3*GWP(t)

The use of non-renewable resources, NUsed(t), during the year is determined by energy requirements Energy(t) and the available renewable resources RRes(t-1) at the start of the year. If required Energy(t)<= RRest(-1), the value of NUsed(t) becomes 0. By means of the parameter p4 the development of new reneable energy resources can in this situation be reset to a percentage, p4, of previous year's RDev(t-1):

RDev(t)=p4*RDev(t-1)

to avoid unwanted cycling.

The use of non-renewable energy resources, NUsed(t), generates the annual greenhouse gas emission, Em(t) symbolized by the function a3():

Em(t) = a3(NUsed(t))

The changes in climate are indicated by changing global temperature, Temp(t), which is determined by the cumulative green house gas variable, Gas(t-1), represented in the model by the function a4():

Temp(t)=a4(Gas(t-1))

The temperature is expressed relative to the mean world surface temperature for the period 1961-1990.

Food(t) is determined by the available cultivated Land(t-1) . The function a5() represents the agriculture production :

Food(t) =a5(Land(t-l))

The well-being of the global human population is indicated by the variable Welfare(t) determined by a function w() of the variables Food(t) and Consume(t), both adjusted for the size of the population, Pop(t-1), and the global climate indicated by the temperature variable Temp(t).

Welfare(t) = w(Food(t)/Pop(t-1), Consume(t))/Pop(t-1), Temp(t))

Note that the the last function is an arbitrary preference function which is, in the real world, implicitly determined by political decisions.

## Statistics

To obtain a computable model, initial values for the stock values and estimates for the functions are needed. A number of international organizations compile relevant statistics. Unfortunately, neither are statistics for all variables available nor are those available accurate because of the complexity of the implied measurement. For this model, data from a number of international organizations are used:

CIA (US Central Intelligence Agency), FAO (UN Food and Agriculture Organization), IPCC (UN Intergovernmental Panel on Climate Change), UNSTAT (UN Statistical Division), and the World Bank.

Stock variables at the end of year 0, i.e. 2014, are frequently extrapolations from statistics for earlier years. Data for some variables, e.g. Capital(t) , are not available on a world basis and are rough estimates. Data for remaining non-renewable energy resouces, NRes(t), are being revised frequently because of new resources found. These and similar data uncertainties are not as critical as they may appear if flow variable values for their annual changes are available.

Default values used are adjusted such that the model computations will provide results approximately corresponding to forecasts or recommendations from different UN organizations.

To learn more about how the model can be used, you are invited to inspect the Experiments.

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