mapspamc models
The mapspamc package depends on General Algebraic
Modeling System (GAMS) (GAMS Development
Corporation 2019) to solve the cross-entropy and fitness score
models. GAMS is commercial software, designed for modelling and solving
large complex optimization problems. To be able to solve the models in
mapspamc a GAMS licence is required that includes full
access (without size limitations) to CPLEX and IPOPT solvers (but see
below for potential alternative solvers). The function
run_mapspamc activates GAMS to run the model as defined by
the user in the model setup step. The GAMS model log will be sent to the
screen after the model run has finished. The log is a text file, which
names starts with model_log_ and is saved in the
processed_data/intermediate_output folder after the model
has finished. The GAMS code (gms files) is stored in the
gams folder in the mapspamc R library folder.
Interested users might want to take a look and, if necessary, modify the
code and run it directly in GAMS, separately from the
mapspamc package.
The GAMS code involves the use of a slack variable to deal with data
inconsistencies, which result in infeasible models. A slack variable
transforms an inequality constraint in an equality constraint by adding
‘slack’ (Boyd and Vandenberghe 2004). This
makes it possible to solve the model even though it is technically
infeasible. Different weights (i.e. penalties) are used to capture the
interaction and trade-offs between the different slack variables (e.g. a
lower slack for irrigated area may result in a higher slack for
available cropland). Relatively high weights are used to minimize the
slack for cropland availability and irrigated area, whereas low weights
are used for the subnational statistics, which values are considered
less reliable (see GAMS gms files for which weights are used). After the
model is run, the slack variables are saved in the model output gdx
file, which is stored in the
processed_data/intermediate_output folder.
Excessive slack points at inconsistencies between the (sub)national statistics and the available crop and irrigated area to which the statistics are allocated. To deal with these inconsistencies, the first step is to closely inspect the data, and in particular the subnational crop statistics, for data entry errors (e.g. missing values) and, if needed, correct them. If there are still problems, we recommend by adjusting the subnational statistics as they are sometimes inconsistent with the FAOSTAT national statistics.
Depending on the licence, GAMS is installed with several solvers. For
each type of problem a default solver is pre-selected. Unless changed by
the user, the run_mapspamc function will use the GAMS
default solvers for linear-problems (i.e. the max_score
model) and non-linear problems (i.e. the min_entropy model)
to solve the models. To find out which solvers are available and which
are the default, open the GAMS IDE: file -> options -> solvers.
The user has the option to select one of the other linear- and
non-linear solvers supported by GAMS: ANTIGONE, BARON, CPC, CPLEX,
CONOPT4, CONOPT, GUROBI, IPOPT, IPOPTH, KNITRO, LGO, LINDO, LOCALSOLVER,
MINOS, MOSEK, MSNLP, OSICPLEX, OSIGUROBI, OSIMOSEK, OSIXPRESS, PATHNLP,
SCIP, SNOPT, SOPLEX, XA, XPRESS.
For the max_score model, which is a linear problem, it
is recommended to use CPLEX. For
non-linear problems, such as the min_entropy model, is not
possible to predict at forehand, which solver performs best. It is
recommended to start with using the IPOPT, which
has shown good performance in solving cross-entropy models. An
alternative option is CONOPT4,
which, however, is often much slower, and in some cases is not able to
solve the model.
mapspamc and SPAM
There are several differences between mapspamc and SPAM
(Yu et al. 2020) related to the allocation
algorithm, calculation of priors and the input data (Table
@ref(tab:tab-spam-dif)). A main innovation is that apart from the SPAM
cross-entropy model, mapspamc also provides the option to
use an alternative ‘fitness score’ model. This model was developed to
create crop distribution maps at a higher resolution of 30 arc seconds
(Dijk et al. 2022). As a consequence of
using priors based on socio-economic and biophysical suitability
measures, the cross-entropy approach allocates relatively small shares
of a large number of crops and farmings systems to grid cells. This is
plausible for a 5 arc minute resolution when grid cells are relatively
large (~ 10x10 km) and a large diversity of crops and farmings systems
is to be expected. This is, however, less likely for high resolutions of
30 arc seconds, where grid cells are much smaller (~ 1x1 km) and it is
more likely to observe clusters of grid cells that are populated by a
small number of crops and production systems. To simulate this process,
a ‘fitness’ score between 0 and 100, which measures both the
socio-economic and biophysical suitability, is calculated for each grid
cell. Crops and production systems will be allocated in such a way that
the crop area weighted fitness score is maximized, subject to
subnational crop area information and availability of cropland and
irrigated area.
Another difference related to the allocation algorithm is the use of
slacks in the constraints to better deal with data inconsistencies (see
above). We also dropped the suitability constraint in
mapspamc. In SPAM, the suitable crop area, calculated as
the biophyiscal suitability times the cropland area in a grid cell, was
used as a hard constraint. In practice, this constraint was often
dropped because it severely limits the space to allocate crops,
resulting in infeasible models. As an alternative, the cross-entropy and
fitness score models in mapspam use the suitability
information to inform the priors and fitness scores, in particular for
the subsistence and low-input production systems. We also slightly
modified the calculation of the high-input and irrigated crops, which
are now based on the geometric average of accessibility and potential
revenue indicators that are normalized by means of the min-max
method.
Finally, we updated several input data sources with more recent and
higher resolution products, in particular (a) accessibility, which is
now based on travel time (Weiss et al.
2018), (b) population, taken from Tatem
(2017), (c) urban extent taken from Schiavina et al. (2022), (d) irrigated area,
which is a synergy product, based on GIA (Siebert
et al. 2013) and GMIA (Meier, Zabel, and
Mauser 2018), and (e) cropland, taken from several recent
cropland products that can be combined to generate a synergy cropland
map in the pre-processing step. We also reduced the number of standard
crops from 42 in SPAM to 40 in mapspamc by merging the two
millet (pearl and small millet) and coffee (arabica and robusta) species
because statistical information is difficult to find at such detailed
crop level (see below).
As a consequence of these modifications, the maps created with
mapspamc will deviate from comparable information presented
by SPAM. Nonetheless, output is expected to be comparable if similar
model settings are used.
| item | SPAM | mapspamc |
|---|---|---|
| Allocation algorithm | ||
| Objective function | Minimization of cross-entropy | Minimization of cross-entropy and maximization of fitness score |
| Resolution | 5 arc minutes | 5 arc minutes & 30 arc seconds |
| Slack variable | Used for model checking only | Added to the objective function to improve flexibility |
| Suitability constraint | Allocation cannot be larger than biophysically suitable cropland area | No longer implemented |
| Calculation of priors | ||
| Subsistence priors | based on share of rural population | based on share of rural population but set to zero when bio-physical suitability is zero |
| Low-input priors | based on potential revenue times accessibility | based on min-max normalized suitability |
| High-input priors | based on potential revenue times accessibility | based on weighted average of min-max normalized potential revenue and accessibility |
| Irrigated-area priors | based on potential revenue times accessibility | based on weighted average of min-max normalized potential revenue and accessibility |
| Data | ||
| Number of crops | 42 | 40 |
| Accessibility | Based on population density | Based on time to travel |
| Population | SEDAC v4 | WorldPop |
| Urban extent | GRUMP | GHL-SMOD |
| Irrigation | GMIA | GIA & GMIA |
| Cropland | SASAM | Recent cropland products |
mapspamc crops
mapspamc identifies 40 different crop (and crop groups)
that together cover the full agricultural sector and are each identified
by a four letter code (Table 1). The main reason for this classification
is the limited availability of crop-specific biophysical suitability
maps, which form a key input of the crop allocation process (see pre-processing spatial
data for more information). It would be relatively easy to add new
crops by splitting them off from broader crop groups (e.g. separate
tomatoes from vegetables) if appropriate agricultural statistics and
suitability maps are available. We plan to add an example on how to do
this in future updates. The actual number of crops in the model is
determined by the number of crops for which statistical information is
provided.
| number | name | group |
|---|---|---|
| 1 | Wheat | Cereals |
| 2 | Rice | Cereals |
| 3 | Maize | Cereals |
| 4 | Barley | Cereals |
| 5 | Millet | Cereals |
| 6 | Sorghum | Cereals |
| 7 | Other Cereals | Cereals |
| 8 | Potato | Roots & Tubers |
| 9 | Sweet Potato | Roots & Tubers |
| 10 | Yams | Roots & Tubers |
| 11 | Cassava | Roots & Tubers |
| 12 | Other Roots | Roots & Tubers |
| 13 | Bean | Pulses |
| 14 | Chickpea | Pulses |
| 15 | Cowpea | Pulses |
| 16 | Pigeon Pea | Pulses |
| 17 | Lentil | Pulses |
| 18 | Other Pulses | Pulses |
| 19 | Soybean | Oilcrops |
| 20 | Groundnut | Oilcrops |
| 21 | Coconut | Oilcrops |
| 22 | Oilpalm | Oilcrops |
| 23 | Sunflower | Oilcrops |
| 24 | Rapeseed | Oilcrops |
| 25 | Sesame Seed | Oilcrops |
| 26 | Other Oil Crops | Oilcrops |
| 27 | Sugarcane | Sugar Crops |
| 28 | Sugarbeet | Sugar Crops |
| 29 | Cotton | Fibres |
| 30 | Other Fibre Crops | Fibres |
| 31 | Coffee | Stimulates |
| 32 | Cocoa | Stimulates |
| 33 | Tea | Stimulates |
| 34 | Tobacco | Stimulates |
| 35 | Banana | Fruits |
| 36 | Plantain | Fruits |
| 37 | Tropical Fruit | Fruits |
| 38 | Temperate Fruit | Fruits |
| 39 | Vegetables | Vegetables |
| 40 | Rest Of Crops | Other |