FACTS: Fuzzy Assessment and Control for Temperature Stabilization

Regulating Global Carbon Emissions with a Fuzzy Approach to Climate Projections

Bernardo A. Bastien Olvera

and Carlos Gay y Garcia

1,2

Programa de Investigaci

on en Cambio Clim

atico, Universidad Nacional Aut

onoma de M

exico,

Ciudad de M

exico, Mexico

Centro de Ciencias de la Atm

osfera, Universidad Nacional Aut

onoma de M

exico, Ciudad de M

exico, Mexico

Keywords:

Climate Change, Temperature Stabilization, Carbon Emissions, Fuzzy Logic, Fuzzy Inference System, Neural

Network.

Abstract:

This work presents a new approach for assessing the climate system and for stabilizing the temperature and

other climate parameters. FACTS, as we call it, is a fuzzy inference system that overview certain climate state,

and is able to generate the CO2 emissions reduction needed to implement in order to stabilize the temperature.

FACTS was constructed using a neural network optimization process along with data generated by a classical

emissions pathﬁnder. Then, it was embedded in MAGICC6, a simple climate model that was forced by the

four Representative Concentration Pathways until and ultimately stabilized by the proposed methodology.

1 INTRODUCTION

In the process of understanding and modelling the cli-

mate system is involved a trade-off between resolu-

tion, computational efﬁciency and focus on individ-

ual parameters. Every level of complexity for climate

models has its own beneﬁts and the choice of using

one or another depends on the purpose of the study.

Simple climate models such as MAGICC (Mein-

shausen et al., 2011) could emulate complex three-

dimensional coupled atmosphere-ocean general cir-

culation models (AOGCMs), and focus on just some

speciﬁc parameters and on their effects on climate.

This simple models alongside with clear climate

goals, are very useful for policy-makers to easily

asses the impacts of possible green-house gases emis-

sions. The current climate target is to stabilize the

surface temperature well bellow 2

◦

C above preindus-

trial levels (UNFCC, 2015).

A methodology to reach a long-term temperature

target is to discover, build up, or imagine the path-

ways that could lead to the stabilization (Garg et al.,

2014; Belenky, 2015; Rogelj et al., 2013) and try

to adjust the real emissions rate to one of the possi-

ble stabilization routes (UNEP, 2015) . Meinshausen

et al. (2005) created SiMCaP, an algorithm that is

able to ﬁnd multi-gas emissions pathways that stabi-

lize the temperature (using the MAGICC 4.1 model)

through a trial and error selection process of existing

economically-feasible scenarios in the literature and

an extrapolation to other gases using an equal quan-

tile way.

We used the ANFIS structure (Shing and Jang,

1993) to create and optimize our model. Particu-

larly in this study, we used the CO

stabilization

routes given by SiMCaP to relate each year emissions

growth or decrease, to the climate variables of the pre-

vious year through a sugeno-type fuzzy inference sys-

tem. The fuzzy inference system learnt rules based in

a neural network optimization process, in order to cre-

ate a mean global temperature control that is function

of just climate variables.

The ’Fuzzy Assessment and Control for Tempera-

ture Stabilization’ (FACTS) that we propose has great

advantages in terms of its capability for creating path-

ways independently of preconceived scenarios in lit-

erature. Its fuzzy nature is able to absorb the uncer-

tainty associated to the input climate variables, and

the simplicity of its mathematical structure allows to

insert FACTS into different simple climate models in

order to reach the temperature stabilization in real-

time mode while running the model.

Moreover, FACTS perform a fuzzy assessment of

the climate state at every time-step, through the eval-

uation of the membership degree of certain climate

parameters to fuzzy sets deﬁned linguistically. This is

Olvera, B. and García, C.

FACTS: Fuzzy Assessment and Control for Temperature Stabilization - Regulating Global Carbon Emissions with a Fuzzy Approach to Climate Projections.

DOI: 10.5220/0006011603570362

In Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2016), pages 357-362

ISBN: 978-989-758-199-1

357

Figure 1: Structure of FACTS incrusted on a simple climate model.

presented as a new methodology for describing more

realistically the climate system in simple and clear

words in order to create a common language between

decision-makers and the modelling community.

2 FACTS STRUCTURE

A concise overview of the ’Fuzzy Assessment and

Control for Temperature Stabilization’ is presented in

Figure 1.

(1) First, FACTS receive climate parameters of

year i: the CO

emissions; the atmospheric CO

con-

centration; the average global temperature; and the

temperature change (T

− T

i−1

(2) Each variable’s domain is divided in three

fuzzy sets that represent the linguistic categories low,

medium and high, or null, low and medium, depend-

ing on the variable, so that every value in the domain

has its membership degree to the fuzzy sets, ranging

from zero (no membership) to one (full membership)

(Zadeh, 1965). In this stage the climate assessment

takes place in order to provide a fuzzy description of

the climate state.

In step (3) takes place a combination of fuzzy

sets from the different climate variables, which

creates all possible -81- climate states, such

as: 1. low emissions/concentration/temperature

& null temperature increment, 2. medium

emissions/concentration/temperature & low

temperature increment, 3. high emis-

sions/concentration/temperature & medium tem-

perature increment, 4. high emissions/concentration,

medium temperature & null temperature increment,

and so on. The eighty one climate states are repre-

sented by a combination of four climate fuzzy sets

linked by an ’&’ operator, which assigns a weight to

the combination: the minimum membership degree

of the four climate parameters (given in step (1))

evaluated in the four fuzzy sets that build up the

climate state.

(4) Each climate state lead to an IF-THEN rule

(Zadeh, 1975; Takagi and Sugeno, 1985), which re-

lates the membership degree of the parameters to the

climate state k, to the function f

that describes, for

that particular climate state, the change in emissions

that would need to be made in the year i + 1 in order

to stabilize the mean temperature.

Finally, a weighted sum of the eighty one infer-

ence rules is made in step (5) using the weight as de-

scribed in step (3), so we obtain the ultimate value

of the change in future CO

emissions and add it to

the emission scenario baseline (6), which serves as an

input for the climate model (7).

3 OPTIMIZATION PROCESS

A neural network was formed by operational nodes

and links that receive an input matrix and create

multiple signal ﬂows through the system which ul-

timately give as a result a single output that is com-

pared with an output target, then, its made a parame-

ter adjustment in the operational nodes using an error-

MSCCES 2016 - Special Session on Applications of Modeling and Simulation to Climatic Change and Environmental Sciences

358

Figure 2: Temperature stabilization from SiMCaP data

(Meinshausen et al., 2005).

decreasing function (Jang et al., 1997). In the opti-

mization process of FACTS, a fuzzy inference system

is encrusted in a neural network, and the parameter

tuning is made in the eighty one functions of the step

(4) in Figure 1, that way we created a neuro-adaptive

fuzzy inference system (Shing and Jang, 1993).

The input matrices used for optimizing FACTS

were 5 time-series (P475, S400 2015-2020, S400

2020-2025, S450 2015-2020, S450 2020-2025) of cli-

mate parameters (CO

emissions, atmospheric CO

concentration, average global temperature and tem-

perature change) from 2005 to 2200, that reach tem-

perature stabilization between 1.5

◦

C and 2

◦

C, within

years 2100 and 2200, as shown in Figure 2. The cli-

mate parameters are the result of running MAGICC4

(Wigley, 2003) with 5 multi-gas pathways found by

SiMCaP (Meinshausen et al., 2005), the CO

com-

Figure 3: Original SiMCaP reduction pathways (Mein-

shausen et al., 2005) and FACTS generated pathways.

ponents of this pathways were the output target of

FACTS, since the objective is to ﬁnd fuzzy inference

rules that stabilize temperature through CO

emis-

sions control.

Each year i in the time-series contains the four in-

put climate parameters and the output target, which

is sufﬁcient to evaluate the error-decreasing function

and make a small adjustment to the FACTS parame-

ters. Since the time-series have 195 years, there were

made 975 parameters’ adjustments each epoch, and

we ran the optimization process from 1 to 30 epochs

in order to ﬁnd the point where the least error between

the FACTS output and the output target was reached,

which was localized in the epoch number 3. So we

used the FACTS that was optimized 3 epochs, i.e. al-

most 3 000 small parameters’ adjustments.

4 VALIDATION

The remaining time-series of Figure 2 that were not

used in the optimization process: P500, S450 and

S500 served for validating FACTS efﬁciency. As we

can see in Figure 3, the result of using FACTS to cal-

culate what should be the future emissions to ﬁt the

temperature stabilization pathways is very close to the

real calculation by SiMCaP.

We can observe (Figure 3) that the FACTS gen-

erated emissions are closer to the SiMCaP original

pathways in the case of P500 and S400, nevertheless,

in the case of S450, FACTS created a more intense

reduction pathway than the original. This is by virtue

of the fuzzy nature of the system, which absorbed in

the optimization process a greater amount of output

targets that tend to 1.5

◦

Fuzzy logic is not a precise method for measure

variables or relating values, but is powerful by means

of absorbing uncertainty and solving problems efﬁ-

ciently. In that context, it is recognizable the fuzzy

behaviour in S450 FACTS pathway.

5 RESULTS

We implement FACTS control on emissions in differ-

ent climate scenarios in order to stabilize the global

average temperature. We used the four Representative

Concentration Pathways (RCPs) (Moss et al., 2007) to

run MAGICC6 and create different climate scenarios

until 2025, when FACTS control begins and propose a

5-year-constant change in CO

emissions until 2100.

Despite FACTS was tuned with climate parame-

ters coming from MAGICC4.1 (Wigley, 2003), in this

experiment we used MAGICC6 (Meinshausen et al.,

FACTS: Fuzzy Assessment and Control for Temperature Stabilization - Regulating Global Carbon Emissions with a Fuzzy Approach to

Climate Projections

359

Figure 4: Fuzzy climate states at year 2025. This diagram

represents four climate scenarios obtained by MAGICC6

and evaluated by FACTS fuzzy sets, each column repre-

sent an RCP scenario that contains the membership degree

of the climate parameter (CO

emissions, CO

atmospheric

concentration, Temperature and Temperature change) to cli-

mate fuzzy descriptors such as low, medium or high.

2011) in order to have better climate projections ac-

cording to the adjustments in the carbon cycle and

other important improvements in the new release.

FACTS was activated at year 2025 in order to sim-

ulate a real-life situation with 2 important character-

istics. First, according to the Paris Agreement (UN-

FCC, 2015), the countries will release new CO

emis-

sion goals every ﬁve years starting in 2025. Second,

the years gap that exist from now to 2025, is crucial

in the formation of the climate states that will serve

as the ﬁrst input for FACTS in 2025, that is the reason

why we let the climate states to build up before 2025

under the 4 RCPs, as we can see in Figure 4.

The FACTS output is the next-year change in

emissions, but in this experiment we conﬁgured

FACTS in order to give the average change in the next

5 years. This was made assuming that national gov-

ernments are able to pursue more easily a constant

emissions’ reduction rather than a 5-year not-constant

emissions pathway.

The Figure 5 shows the temperature projections

under the four RCPs, with (solid lines) and with-

out (dashed lines) control in emissions. As we can

see, FACTS controls the temperature under 2

◦

C when

the climate state in 2025 was driven by RCP3 and

RCP4.5; when the climate state was driven by RCP6,

FACTS control the temperature around 2.1

◦

C; ﬁnally,

if we follow the business as usual pathway until 2025

(RCP 8.5), FACTS is not capable to stabilize the tem-

perature at the levels agreed by the international com-

munity.

Figure 6 shows the emissions pathways that lead

Figure 5: Temperature stabilization using FACTS.

to the temperatures observed in Figure 5. RCP3 and

RCP6 are scenarios that start with not very high emis-

sions, so the post-2025 stabilization route is some-

what smooth. On the other hand, RCP4.5 starts with

higher emissions, which eventually lead the stabiliza-

tion route to reach the maximum decreasing capacity,

in 2050. Finally, RCP8.5 states a climate state in 2025

that immediately pushes FACTS to decrease the max-

imum possible emissions.

The ﬁnal state of the climate is evaluated ﬁnally

by FACTS at year 2100, as shown in Figure 7. It

is clear the change in speciﬁc parameters that match

with an stabilized climate, such as the low emissions,

high concentration, high temperature and null or low

temperature change.

6 DISCUSSION

FACTS is not just a simple control on emissions, Fig-

ure 4 shows that every time FACTS is used, there is

an evaluation of the climate state that could be de-

scribed in a linguistic way, for example, we can say

that RCP3 generates an scenario in 2025 where CO

emissions are fairly high (”fairly” is a fuzzy concept

that could be result of the combination of the mem-

bership degree 0.23 to medium and 0.78 to high), the

atmospheric CO

concentration is signiﬁcantly high,

the temperature is moderately medium and the tem-

perature change is kind of low.

The climate states trigger different amounts of re-

duction in order to reach an stable climate state as

shown in Figure 7. Nevertheless, much more work

need to be done, almost counter-intuitive, we can ob-

serve that the projected temperature under RCP 8.5 in

2100 does not belong to any fuzzy set, while it should

completely belong to the high temperature fuzzy set.

This is because fuzzy sets were made to ﬁt the data

used as training in the optimization process. So fuzzy

MSCCES 2016 - Special Session on Applications of Modeling and Simulation to Climatic Change and Environmental Sciences

360

Figure 6: FACTS control in Emissions.

Figure 7: Fuzzy climate states after the control was imple-

mented. Year 2100. This diagram represents four climate

scenarios obtained by MAGICC6 and evaluated by FACTS

fuzzy sets, each column represent an RCP scenario that

contains the membership degree of the climate parameter

(CO

emissions, CO

atmospheric concentration, Temper-

ature and Temperature change) to climate fuzzy descriptors

such as low, medium or high.

sets must be tuned manually in order to broaden their

domain, for example, any temperature from 2.5C to

inﬁnity should belong to the high temperatures’ fuzzy

set.

The optimization data was taken from SiMCaP

simulations, that were created based on literature

scenarios, nevertheless, FACTS structure allows to

merge the strategies used these different world-wide

proposed scenarios. That is the reason why FACTS is

able to create stabilization pathways that match with

feasible reduction rates, and not always will be pos-

sible to stabilize temperature as observed in RCP85

FACTS (Figure 5).

Finally it is important to specify that FACTS never

really uses the great number of inference rules (81) at

the same time. Whenever it is used with certain cli-

mate parameters, there is an automatic elimination of

inference rules, that provide a lot simpler fuzzy con-

trol. In Figure 4 if we eliminate the rules that are

linked to the fuzzy sets which membership degree is

zero (or very close to zero) for the climate parameters

of RCP3 at year 2025, the number of inference rules

reduces to 12. Since fuzzy inference systems are eval-

uated parallel and the functions of each rule are linear

equations, is very efﬁcient to embed FACTS in a cli-

mate model such as MAGGIC and run the stabiliza-

tion process and the model projections within a few

seconds (∼ 5s) in an ordinary personal computer.

7 CONCLUSIONS

Even for scientists is hard to understand the con-

sequences of increasing the temperature certain de-

grees in certain period of time. In negotiations, there

is a continuous translation between climate numeri-

cal parameters and human communication structure.

FACTS presents an straightforward bridge between

both languages, that allows stake-holders to negotiate

in the same language that is used in a climate stabi-

lizer and descriptor. In the context of the actual cli-

mate change challenge that is facing humanity, this

singular type of climate approaches are very impor-

tant.

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