# Model Documentation

### | Version 4.0

created with goxygen 0.21.1

# 62_material

# Material (62_material)

## Description

The material module describes the demand for material usage based on historical data. Material uage is derived from FAO's "other utils" category, and includes for example the use of agricultural products for cosmetics, chemical usage or textiles. In contrast to FAO's other util category, the use for bioenergy (oils and ethanol) has been excluded and is accounted for in the demand for bioenergy. Material demand in this context can be considered as a subset of "other utils" category of FAO.

## Interfaces

Interfaces to other modules

### Input

module inputs (A: exo_flexreg_apr16)
| Description | Unit | A
--- | --- | --- | ---
vm_dem_food (i, kall) | Food demand | \(10^6 tDM/yr\) | x

### Output

module outputs
| Description | Unit
--- | --- | ---
vm_dem_material (i, kall) | Demand for material usage | \(10^6 tDM/yr\)

## Realizations

### (A) exo_flexreg_apr16

In the exo_flexreg_apr16 realisation, demand for material usage is estimated to grow proportional to food demand calculated by `vm_dem_food` interface in food module(15_food). Observed material demand is fed as an input to the material module based on historical data. The assumption that material demand grows proportional to food demand is a simplification that can be justified by the minor importance of non-bioenergy material usage of agricultural products.

Estimation of material demand depends on the value set by switch `s62_historical`. When it is set to 1, the material demand is estimated purely based on the historical material demand as reported by FAO. When `s62_historical` is switched to 0, the Material demand is calculated as the scaled version of material demand in last historical timestep depending on a scaling factor. This scaling factor is calculated as the ratio beween the food demand from last timestep and the food demand from the last historical time step.

\[\begin{multline*} vm\_dem\_material(i2,kall) = \sum_{ct}f62\_dem\_material(ct,i2,kall) \cdot s62\_historical + \left(p62\_dem\_material\_lh(i2,kall) \cdot \frac{ \sum_{kfo} vm\_dem\_food.l(i2,kfo) }{p62\_dem\_food\_lh(i2)}\right) \cdot \left(1-s62\_historical\right) \end{multline*}\]

Results are stored in the interface `vm_dem_material` and this interface is then used in demand(16_demand) module as a part of global supply-demand balance for crop, livestock, secondary products and residues.

For the time period beloning to the historical time period (y1965 to y2010 in this version of the model), the scalar `s62_historical` is set to 1 and for the non-historical time periods, `s62_historical` is set to 0. How this switch affects the material demand calculations is explained in the equation(s) accompanying this module.

    if (sum(sameas(t_past,t),1) = 1,
      s62_historical=1;
    else
     s62_historical=0;
    );

The parameters `p62_dem_material_lh` and `p62_dem_food_lh` are overwritten based on each time step optimization, in order to be used in next step. This is only carried out when the model is still running in the time period before (and including) y2010 with this model version.

    if (sum(sameas(t_past,t),1) = 1,
     p62_dem_material_lh(i,kall) = f62_dem_material(t,i,kall);
     p62_dem_food_lh(i)=  sum(kfo, vm_dem_food.l(i,kfo));
    );

> Limitations There are no known limitations.

## Definitions

### Objects

module-internal objects (A: exo_flexreg_apr16)
| Description | Unit | A
--- | --- | --- | ---
f62_dem_material (t_all, i, kall) | Historical material demand | \(10^6 tDM\) | x
p62_dem_food_lh (i) | Food demand in last historical timestep | \(10^6 tDM/yr\) | x
p62_dem_material_lh (i, kall) | Material demand in last historical timestep | \(10^6 tDM/yr\) | x
q62_dem_material (i, kall) | Estimating material demand | \(10^6 tDM/yr\) | x
s62_historical | Switch for turning off historical material demand | \(1\) | x

### Sets

sets in use
| description
--- | ---
i | World regions
kall | All products in the sectoral version
t_all | 5-year time periods

## Authors

Benjamin Bodirsky

## See Also

15_food, 16_demand

## References