The PyRICE Model

Authored by Max Reddel

This is a simulation model implementation of the RICE2010 model by Nordhaus. It is modified in a way, such that alternative ethical problem formulations and the level of aggregation can be selected. The aggregation levels refer whether to disaggregate utility and disutility.

Ethical Premises

• utilitarian
• sufficientarian
• egalitarian
• prioritarian

Aggregation Levels

• aggregated
• disaggregated

Table of Contents

1. Context
2. Uncertainty Modules
3. Repository Structure
4. The PyRICE Model
   1. Model Flow
   2. XLRM
   3. 12 Regions
5. Using the Simulation Model
   1. Initialization
   2. Run
   3. Results

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1. Context

This project has been developed within a master's thesis at the TU Delft during the academic year 2021/22 (Q3 and Q4). It is a continuation of the same author's work during his internship at the Hippo DAI Lab at the TU Delft during the academic year 2021/22 between (Q1 and Q2). This model is based on the work of Ivar Tjallingii who developed a working version of PyRICE. The initial contribution (during the internship) of Max Reddel lies in refactoring the PyRICE model, such that modularity, object-orientation, and thus reusability are enabled. Ivar's original model can be found in this repository. Further changes with respect to the exact design of the social welfare functions and the disaggregation of utility and disutility have followed during this project.

The topic of equity in climate change policy is itself motivated by many international developments and especially the so-called double inequality The term \textit{double inequality} which has been coined to describe the inverse relationship of the distributions of risks and responsibilities. Figure 1 shows a visual representation. The left image shows Cumulative CO₂ emissions by Country. The right image shows the vulnerability that measures a country's exposure, sensitivity and ability to adapt to the negative impact of climate change. (The images have been created by Palok Biswas and can be found here and here, respectively.)

Fig.1 - Double Inequality

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2. Uncertainty Modules

The PyRICE has been connected to the SSP scenarios by aggregating country statistics into 12 RICE regions. Extra climate uncertainties have been added to analyze the expsosure of alternative abatement pathways to deep uncertainty in climate change. To use the uncertainty modules, additional packages need to be installed to connect to the ema_workbench.

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3. Repository Structure

./PyRICE_2022/
├── dmdu
│   ├── exploration   
│   │   ├── data                                # resulting data from experiments          
│   │   ├── epsilon_determination.ipynb         
│   │   ├── exploration_damage_gini.ipynb
│   │   ├── exploration_damage_threshold.ipynb
│   │   ├── open_exploration.ipynb
│   │   ├── perform_experiments.py
│   │   └── sensitivity_analysis.ipynb
│   ├── general         
│   │   ├── convergence.py                        
│   │   ├── directed_search.py
│   │   ├── timer.py
│   │   ├── visualization.py                    # functions for data visualization
│   │   └── xlm_constants_epsilons.py           # functions to return X, L, M, epsilon values and constants
│   ├── outputimages                            # images resulting from data visualization
│   │   ├── boxplots
│   │   ├── exploration
│   │   ├── iEMSs
│   │   ├── optimalpolicies
│   │   ├── pathways
│   │   ├── relativemedians
│   │   ├── scenariodiscovery
│   │   ├── seeds
│   │   └── tradeoffs
│   ├── policydiscovery
│   │   ├── analysis
│   │   │   ├── seedanalysis                    # scripts and notebooks for seed analysis
│   │   │   ├── boxplots.ipynb
│   │   │   ├── convergence.ipynb
│   │   │   ├── high_level_pathways.ipynb
│   │   │   ├── iEMSs.ipynb
│   │   │   ├── more_pathways.ipynb
│   │   │   ├── pareto_front.ipynb
│   │   │   ├── pathways.ipynb
│   │   │   ├── pf_median_grids.ipynb
│   │   │   ├── policy_selection.ipynb
│   │   │   ├── regional_pathways.ipynb
│   │   │   ├── robustness.py
│   │   │   ├── robustness_analysis.ipynb
│   │   │   ├── selected_policies.ipynb
│   │   │   └── trade_offs.ipynb
│   │   ├── data                                # data from optimizations and consequent experiments
│   │   ├── paretosorting                       # non-dominated sorting post optimization
│   │   │   ├── data
│   │   │   │   ├── final
│   │   │   │   ├── input
│   │   │   │   └── output
│   │   │   ├── prepare_input.py
│   │   │   ├── prepare_output.ipynb
│   │   │   └── README.md
│   │   ├── directed_policy_search.py
│   │   ├── experimentation.py
│   │   └── seed_experimentation.py
│   └── scenariodiscovery         
│       ├── clustering
│       │   ├── data
│       │   ├── clustering.ipynb
│       │   ├── silhouette_widths.py
│       │   └── worst_scenarios.ipynb
│       ├── search
│       │   ├── data
│       │   ├── convergence.ipynb
│       │   ├── directed_scenario_search.py
│       │   └── worst_scenarios.ipynb
│       └── selection
│           ├── data
│           ├── reference_scenarios.ipynb
│           └── scenario_selection.py
├── examples
│   ├── simulation.ipynb                        # example notebook to run the PyRICE model    
│   └── simulation.py                           # example script to run PyRICE model
├── images                                      # images for md files
├── model                                       # entire model implementation
│   ├── inputdata                   
│   ├── outputdata           
│   ├── submodels                   
│   │   ├── carbon_cycle_model.py     
│   │   ├── climate_model.py          
│   │   ├── economy_model.py         
│   │   └── utility_model.py               
│   ├── data_sets.py                 
│   ├── enumerations                            # Custom enums   
│   ├── model_limits.py                         
│   └── pyrice.py                               # Main model       
├── README.md 
└── requirements.txt         

The model directory contains all model relevant components, including the main model pyrice, its submodels, data sets, etc. You can run the model by using the notebook simulation.ipynb which provides a walkthrough the most important parameters, how to run the model, and how to view the results.

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4. The PyRICE Model

4.1 Model Flow

The model uses four sub-models: economy_model, carbon_cycle_model, climate_model, and utility_model. Each is responsible for its own domain. The flow within one time step is depicted below.

Fig.2 - PyRICE Model Flow

This simple representation of the model flow is useful but it obfiscuates the feedback loops within the model. For this purpose, we also want to show the following figure.

Fig.3 - IAM

4.2 XLRM

Within the XLRM framework, the PyRICE model can be represented as seen in the figure 4.

Fig.4 - XLRM for PyRICE

4.2.1 X: Uncertainties

Fig.5 - X: Uncertainties

4.2.2 L: Levers

Fig.6 - L: Levers

4.2.3 M: Metrics

The metrics depend on the exact problem formulation. There are 8 problem formulations, which is a combination of an ethical premise and an aggregation level. Figure 7 provides an overview.

Fig.7 - Problem Formulations

Each cell in this table represents one problem formulation. A (+) after an objective indicates that the desired optimization direction is maximization. The lack of such a symbol indicates minimization as the desired optimization direction.

The individual metrics are listed and explained in Figure 8 below.

Fig.8 - M: Metrics

4.3 Regions

The used regions within this PyRICE model are depicted in the following table:

RICE Region	Description
US	The United States of America
OECD-Europe	European countries that are members of the OECD
Japan	Japan
Russia	Russia
Non-Russia Eurasia	Countries that are in Eurasia \ {Russia}
China	China
India	India
Middle East	Middle-Eastern countries
Africa	Countries of the African continent
Latin America	Countries of Latin America
OHI	Other high income countries
Other non-OECD-Asia	Countries in Asia that are not members of the OECD

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5 How to Use the PyRICE Model

5.1 Intialize the PyRICE Model

The most important parameters are listed below. Use simply model = PyRICE() with the following parameters.

Model Parameters

Bolded elements are model default values.

Variable	Values	Description
model_specification	ModelSpec.STANDARD ModelSpec.Validation_1 ModelSpec.Validation_2	Standard for simulation and optimizaiton Replicating RICE2010 Deterministic RICE2010
damage_function	DamageFunction.NORDHAUS DamageFunction.NEWBOLD DamageFunction.WEITZMAN	Nordhaus + SLR Newbold & Daigneault Weitzman
welfare_function	WelfareFunction.UTILITARIAN WelfareFunction.EGALITARIAN WelfareFunction.SUFFICIENTARIAN WelfareFunction.PRIORITARIAN	Total aggregated utility Equal distribution of risks & benefits People above some threshold Wellbeing of worst-off region

5.2 Run the PyRICE Model

Next, we can run the model with specific lever values. The most important parameters are listed below. The default values of the lever parameters represent the original Nordhaus policy.

If the model has been initialized with e.g., model = PyRICE(), we can simply use the call function model() with the parameters below.

Levers

Variable	Values	Default	Description
sr	[0.1, 0.5]	0.248	Savings rate
miu	[2005, 2305]	2135	Emission control rate target (year of zero-emission)
irstp_consumption	[0.001, 0.015]	0.015	Initial rate of social time preference of consumption
irstp_damage	[0.001, 0.015]	0.015	Initial rate of social time preference of damage

Miscellaneous Parameters

Variable	Values	Default	Description
precision	{10, 20, 30}	10	Precision of timeseries data of final outcomes in years

Precision indicates how precise you want your timeseries data to be in the final outcomes. E.g., 10 means, you get a value every 10 years.

5.3 View Results

Running the model will return a dictionary containing all outcome variables. This dictionary is handy for conducting further optimization. It is, however, not handy, to inspect the results.

An alternative data structure for this is in form of a Results object which is also saved within the model and contains the same information as the dictionary.

With results = model.get_better_formatted_results(), you will get this object.

All relevant outcome data is saved into a results object and can be accessed via its attributes. Results is an object that contains several pandas dataframes and 3 highly aggregated float variables.

Results

Attribute	Data Type	Description
aggregated_utility	float	Total aggregated utility
aggregated_utility_gini	float	Total aggregated utility GINI
aggregated_impact_gini	float	Total aggregated impact GINI
df_population	dataframe	Population over regions over years
df_cpc	dataframe	Consumption per capita over regions over years
df_cpc_pre_damage	dataframe	Pre-damage consumption per capita over regions over years
df_cpc_post_damage	dataframe	Post-damage consumption per capita over regions over years
df_main	dataframe	Over years with following columns: - damages - utility lowest income per capita - highest climate impact per capita - distance to threshold - population under threshold - intratemporal utility GINI - intratemporal impact GINI - atmospheric temperature

You can also view the attributes in a convenient way with the method model.view_better_formatted_results().