# Analyzing the Impact of Climate Change with major emphasis on pollution: A
Comparative Study of ML and Statistical Models in Time Series Data

1st Anurag Mishra, 2nd Ronen Gold, 3rd Sanjeev Vijayakumar  Golisano College
of Computing and Information Sciences, Rochester Institute of Technology
Rochester, NY, USA
{am2552, rgg2706<EMAIL_ADDRESS>
###### Abstract

Industrial operations have grown exponentially over the last century, driving
advancements in energy utilization through vehicles and machinery.This growth
has significant environmental implications, necessitating the use of
sophisticated technology to monitor and analyze climate data.The surge in
industrial activities presents a complex challenge in forecasting its diverse
environmental impacts, which vary greatly across different regions.Aim to
understand these dynamics more deeply to predict and mitigate the
environmental impacts of industrial activities.

###### Index Terms:

Pollution Impact Analysis, Climate Change Forecasting, Machine Learning in
Climate Modeling, Statistical Models in Environmental Studies, Time Series
Analysis, Long Short-Term Memory (LSTM) Networks, Spiking Neural Networks
(SNN), Autoregressive Integrated Moving Average (ARIMA),

##  I Introduction

In an era marked by significant industrial expansion, the consequent rise in
environmental pollutants has precipitated a critical need for advanced
methodologies to analyze and forecast the environmental impacts of these
activities. This research paper presents a comparative analysis of machine
learning and statistical models to study the effects of pollution on climate
change, utilizing time series data. The focus is on understanding how
different modeling approaches—specifically Long Short-Term Memory networks
(LSTMs), Spiking Neural Networks (SNNs), and Autoregressive Integrated Moving
Average (ARIMA) models—can be employed to predict future climate conditions in
response to varying pollution levels. Our study leverages two key datasets:
the Earth Surface Temperature Data, which provides detailed global temperature
records, and the Global CO2 Dataset, which offers geolocated information on
CO2 emissions. By integrating these datasets, we aim to offer insights into
the direct relationship between CO2 emissions and temperature changes, thereby
supporting the development of targeted environmental policies to mitigate the
adverse effects of industrial pollution.

###  I-A Problem Statement

Climate change is not a problem that humanity is not aware about. But it is
important to stablish how significant it is to know the severity of this
problem so that most of the policies that people want to create our aim
towards solving this crisis at hand . Over the past century, there has been a
notable increase in the growth of industrial operations. With the use of
sophisticated technology, we can now more efficiently harness energy for the
operation of industrial machinery and automobiles in our daily life. But there
are environmental consequences to this increase in industrial activity that
need to be carefully considered. Our team wants to use the most recent
machine-learning techniques to evaluate available climate data and develop a
predictive model that can identify the direction of climate change in relation
to pollution data particular to a certain region.

Our project will find trends in the data to forecast future changes in climate
and give our team the tools to analyse possible environmental effects of
industrial operations in various locations.Hence resulting in a comparative
study which will compare different aspects of machine learning and how machine
learning can emphasise the severity of the issue of climate crisis, this
comparative study will also give us a deep insight into how different models
use different techniques to predict and forecast the quantities and how they
deal with time series data. Time series has been challenging in the days of AI
revolution because the current state of the art transformer models struggle
with it and hence we as a community haven’t found a really good model that
handles time series data and gives us good predictions over a period of time
this project aims to use this opportunity. With du dive into the ability of
multiple models like GRUs and LSTMs and even biologically inspired spike
neural networks as well as statistical machine learning models like the
ARIMA(auto regressive integrated moving average) and the SARIMA(seasonal
autoregressive integrated moving average) models and compare them and how they
tackle and what are the ability they possess in handling time series data some
models are highly computational while others are light on the computation but
might result in a competitive result this curiosity to compare these models
and also at the same time stablish the core of the climate crisis with the
help of data set in regards to pollution as well we tend to move towards a
project that is not just a comparative study but concrete proof of how real
the problem of climate crisis is.

###  I-B Hypotheses

H1: Approaching the problem of global warming by forecasting global average
temperature forecasts until the year 2100 using Statistical Methods,
Biologically-inspired models, and Transformers to enhance or debate climate
predictions and provide hotspot regions of impact.

H2: Aiming to quantify the impact of pollutants using the dataset [10] in the
escalating trend of global warming, thereby streamlining the strategic focus
for impactful measures to mitigate global warming effects.

H3: Through an exploration of diverse approaches to the same problem, a
comparison and contrast of the algorithms presented is aimed to be conducted.

##  II Literature Survey

One of the major contribution of the Paper [1] is the robust review on their
performances whilst elaborating on many intricate aspects of Spike Neural
Networks. Moreover, since SNNs are based on biological neurons, the paper also
provides a comprehensive overview of the exchange of signals between two
biological neurons, in addition to summarizing their detailed orientation with
respect to potential differences. Specifically, they focus on Spiking Neural
Network Models, Spike Neural Network Learning Mechanisms, and Spike Encodings.
The equations governing the implemented model, the Leaky Integrate and Fire
(LIF) are depicted in equations 1 and 2. A more specific approach of Spike
Neural Networks in its time-series forecasting task has been depicted in Paper
[2]. This study focuses on using one-step ahead forecasting problems by
combining a PulseWidth Modulation based encoding-decoding algorithm integrated
with a Surrogate Gradient Method.They are known to induce long latency in
addition to an ultra-low power consumption advantage because of using a SNN,
thereby ensuring consistent spikes necessary for efficient forecasts.

$C_{m}\frac{dV_{m}(t)}{dt}=I_{ion}(t)+I_{syn}(t)$ (1)

$I_{ion}(t)=G_{K}n^{4}(V_{m}-E_{K})+G_{Na}m^{3}h(V_{m}-E_{Na})+G_{L}(V_{m}-E_{L})$
(2)

Divulging from the central idea of spike neural networks, Paper [4] proposes a
framework consists of a hybrid module with each module consisting of a
position-aware dilated CNN and a hop/non-hop auto-regression component
combined with residual learning. Equation 3 is used as an embedding layer
where $W_{p}$ is a learnable parameter matrix. Further, equation 4 represents
the combination of inputs using residual learning. The paper [12] lies in the
foundation of how we are implementing our statistical modelling and the
importance of basic moving average component and auto correction function,
used in the deployment of autoregressive integrated moving average algorithms.
Further, with the help of seasonal autoregressive integrated moving average
this paper was able to forecast and predict that there is a significant
seasonal pattern of rainfall.

$p_{i}=\psi(e_{i})=e_{i}^{T}Wp$ (3)

$x_{i+1}=\text{ReLU}(x_{i}+\phi(x_{i}))$ (4)

The paper [14] proposes a novel approach in the realm of prediction
performance in multivariate time series task with the fundamental focus on
temporal change in the information. Though this paper might be focused more on
LSTM for long short term memory network but it helps in analyzing how we need
to handle the tiny or small amount of discrete changes in our data. It also
brings forth an objective function modification where mean absolute error and
mean squared error losses are integrated within the object function to
evaluate the amplitude of errors. Further, the paper [15] specializes in
environmental forecasting. The study covers a broad spectrum and multiple 16
environment variables across the frequencies and hence evaluate the
performance of different models on the environmental data set it uses one of
our own data set and hence is what makes this paper really important for our
literature survey.

A novel proposal by the paper [18] introduces the ClimateLearn a Benchmarking
Machine Learning for Weather and Climate Modeling. The library aims to bridge
the gap and producibility and standardization of deep learning models for
providing quantitative and qualitative analysis of climate and weather
modeling task. This library helps us not only have an evaluation criteria
already fixed inside the library but also makes us work really really easy
since it helps us implement visualization and quantification of data models
that we will be building without writing the basic evaluation criteria
functions by ourselves. Finally, the paper concludes by addressing the need
for standardized and reproducible framework for applying machine learning and
deep learning climate science models for climate modelling and hence it
produces us with an open source library that runs on pytorch and has ample
amount of evaluation criteria is within itself as well as training setups and
data set handling features for climate modelling which will be really helpful
for our project.

Paper [23] evaluates the accuracy of CNNs and ANNs for weather prediction and
compares which model is better for accurate predictions. CNNs are classifiers
based on their ability to handle non-stationary and unstable datasets by
adjusting model parameters. ANNs are highlighted for their error minimization
capabilities and ease of instantiation in weather prediction techniques. The
comparative analysis from CNNs to ANNs highlights which is better regarding
climate change data classification. In one instance, CNN’s ability to classify
weather-dependent recognition on images showed a high accuracy of 82.2
percent, which exceeded traditional ML methods. Deviating off-course, and
delving in to theoritical physics model, the paper [24] incorporates physics
laws directly into machine learning for weather and climate modeling. The
algorithms cover GANs, LSTMs, and CNNS with custom-design loss functions,
physics regularizations, and parameter-specific model architectures that
represent physics constraints.

When coming to environmental models in particular, the paper [28] complies
multiple deep-learning techniques to identify leaf stressing in different
plants with CNN architectures. The research evaluates the techniques based on
stress type, dataset size, training, test sets, and the model used. The
purpose is to highlight the usefulness of machine learning in agriculture and
provide a benchmark for readers to understand how this technology could be
applied to improve our environment further. Papers like these enables this
study to be led in this direction to allow for an efficient climate predictor
model to suggest preventive measures in advance.

##  III Method

###  III-A Datasets

Dataset 1: Climate Change: Earth Surface Temperature Data

  * •

The dataset encompasses a total of 1.6 billion samples. Considering its
archaic nature, it will really benefit in capturing long-term and short-term
trends. Further, it also addresses the historical complexities such as the
uncertainty in values captured. Moreover, basing on the various features
available, the dataset has been classified in to the following:

    * –

GlobalTemperatures.csv \- Global Land and Ocean-and-Land Temperatures

    * –

GlobalLandTemperaturesByCountry.csv \- Global Average Land Temperature by
Country

    * –

GlobalLandTemperaturesByState.csv \- Global Average Land Temperature by State

    * –

GlobalLandTemperaturesByMajorCity.csv \- Global Land Temperatures By Major
City

    * –

GlobalLandTemperaturesByCity.csv \- Global Land Temperatures By City

  * •

The important features include from the primary file
(GlobalTemperature.csv) include:

    * –

Date(YYYY-MM-DD): We aim in pre-processing with Datetime Feature engineering,
that involves, fabricating datasets with different frequency intervals to
expand the learning range of the model. In addition to this, the dataset we
plan on adding a time lag variable, that refurnishes the dataset with each
sample

Dataset 2: Global Air Pollution Dataset

  * •

This dataset presents geolocated information on air pollution, a critical
environmental issue affecting public health.

  * •

It includes data on major pollutants: Nitrogen Dioxide (NO2), Ozone (O3), and
so on.

  * •

The dataset features AQI values and categories, providing an overall
assessment of air quality in various countries and cities…

  * •

The prime features include: Country: Name of the country, City, AQI Value, AQI
Category, CO AQI Value, CO AQI Category, Ozone AQI Value, Ozone AQI Category,
NO2 AQI Value, NO2 AQI Category, PM2.5 AQI Value, PM2.5 AQI Category

Our ultimate goal is to present a study by training models on these two
datasets and analyze the pollution trend over the years contributing to the
upcoming rise in Average Global Temperatures, caused by global warming. Based
on this, upon compiling data from the 1700s until the present, we aim to come
up with a factor of contribution (FOC) of pollution to global warming.

###  III-B Preprocessing

Sanjeev Vijayakumar

The dataset spans time series values from the 1800s to 2014, with each sample
representing a day in history and containing average values for that area. It
encompasses global temperatures across countries, cities, and major cities.
For training, I utilized the dataset clustered over major cities, providing
ample data. Using pandas, I split it into 100 datasets based on cities,
enabling sequential model training for generalization and smooth forecasting.

To process the data for spike neural networks, I employed temporal encoding
that are summarized as follows:

###  III-C Spike Neural Networks

  1. 1.

Normalizing data within the range [0, 1] is crucial to avoid gradient
explosion in Spike Neural Networks, which output discrete spikes.

  2. 2.

A threshold of 0.5 enables the neuron voltage to generate spikes.

  3. 3.

Initializing the TIME_STEPS variable, temporal encoding maps each sample into
an array spanning TIME_STEPS, with spikes occurring at different intervals.

  4. 4.

Encoding each sample into a time series input includes the TIME_WINDOW
variable to capture statistical data dependencies.

###  III-D ARIMA

ARIMA (AutoRegressive Integrated Moving Average) is a forecasting technique
that models time series data based on differences between observations
(integrated), trends (autoregressive), and noise (moving average). ARIMA
Parameters (p, d, q):

  1. 1.

p: Autoregressive terms (lags of the series)

  2. 2.

d: Differencing order (number of times the data have had past values
subtracted)

  3. 3.

q: Moving average terms (lags of the forecast errors)

We need a way to integrate and test whether the data given to us is stationary
or not to check that the data given to us is stationary or not we did the
Utilized Augmented Dickey-Fuller (ADF) test to check for stationarity, this
gave us the result that the data was stationary. Hence our model could be
applied to it as both.ARIMA and SARIMA require the data to be stationary for
it to be applied and get the predictions out of it otherwise the statistical
model will fail and will not give correct predictions. To incorporate CO2
emissions required method so that correlation could be established with
temperatures and to do that. We need to go deeper and search for a tool inside
the SARIMA model to incorporate the correlation and hence we found exogenous
variable that we can use to incorporate the emissions by country whose city we
are predicting the temperature for hence we Integrated annual CO2 emissions as
an exogenous variable in the SARIMAX model.

Ronen Gold

The first method used to forecast temperatures is a Long Short-Term Memory
(LSTM) neural network that aims to map the temporal relationships between air
pollution and temperature. The data was preprocessed using different
techniques for input to the LSTM model. The temperature data was labeled with
the date (YYYY-MM-DD), city, country, and respective temperature collected
dating back to the 1800s, while the pollution data has geolocated information
on the CO2 emissions of the respective city and country.

###  III-E Methodology

Sanjeev Vijayakumar

With a review of Spike Neural Networks and Biologically-inspired algorithms,
it became clear that Spike Neural Networks are pivotal. These networks rely on
precise data pre-processing, generating spike trains that match forecast
times. For instance, our dataset spans multiple days, distributed across
discrete time steps. Each sample undergoes binary encoding, producing spikes
at specific time intervals, facilitating a shift to time-based encoding, also
known as Temporal Encoding.

Initially, we favored Spike Neural Networks in BindsNET for their efficiency
and robustness. However, the Spiking Jelly Framework in Torch offered
versatility with feedforward layers. Thus, our architecture, based on the
Spiking Jelly framework, includes a Flattening Layer, Feedforward input and
hidden neural networks, and a Leaky Integrate and Fire (LIF) Node, depicted in
Figure.

Figure 1: Spiking Neural Network Architecture. Model architecture depicted for
Spike Neural Network Architecture utilized to forecast global land
temperatures.

Anurag Mishra
The AR part of the ARIMA model captures the feedback relationship between past
observations and future values:

$AR(p)=\phi_{1}Y_{t-1}+\phi_{2}Y_{t-2}+\dots+\phi_{p}Y_{t-p}$ (5)

where $\phi_{1},\phi_{2},\dots,\phi_{p}$ are the parameters of the AR part of
the model, and $Y_{t-k}$ represents the value of the series at time $t-k$.

Integrated Term

This refers to the number of differences required to make the series
stationary:

$\nabla Y_{t}=Y_{t}-Y_{t-1}$ (6)

For higher-order differencing:

$\nabla^{2}Y_{t}=Y_{t}-2Y_{t-1}+Y_{t-2}$ (7)

Moving Average (MA) Term

This part models the dependency between an observation and a residual error
from a moving average model applied to lagged observations:

$MA(q)=\theta_{1}\epsilon_{t-1}+\theta_{2}\epsilon_{t-2}+\dots+\theta_{q}\epsilon_{t-q}$
(8)

where $\theta_{1},\theta_{2},\dots,\theta_{q}$ are the parameters of the MA
part of the model, and $\epsilon_{t-k}$ is the white noise error term at time
$t-k$.

Combining the Components

The full ARIMA model combines these components into a single equation:

$Y_{t}^{\prime}=c+\phi_{1}Y_{t-1}^{\prime}+\dots+\phi_{p}Y_{t-p}^{\prime}+\theta_{1}\epsilon_{t-1}+\dots+\theta_{q}\epsilon_{t-q}+\epsilon_{t}$
(9)

where $Y_{t}^{\prime}$ is the differenced series, $c$ is a constant, and
$\epsilon_{t}$ is the error term at time $t$. Hence in Conclusion The ARIMA
model’s ability to model and forecast time series data by accounting for
various underlying patterns makes it a powerful tool in quantitative analysis.
Proper selection of its parameters, $p$, $d$, and $q$, is crucial for
achieving reliable and accurate forecasts. Hence, what we did was, we took in
the data from the past and associated each variable that was required for this
algorithm to work and then tried on multiple different statistical models that
are the versions of Arima and then we finalized that for our first prediction,
ARIMA(5,1,3) give the best results for predicting the temperature to the most
accuracy and precision.

Ronen Gold

We isolated the relevant parts of the data to train an individual model per
city. This process allowed each model to be trained on its respective
temperature data to provide accurate results in the specified city. The
process identified errors for the Global Temperature dataset and interpolated
any missing values. We resampled the data to a monthly average to reduce
noise. Normalization was applied using the MinMaxScaler to scale the feature
values between 0 and 1. The normalization aids in the convergence of the
network but also standardizes the distribution of the input features. To
improve the predictive capability of the LSTM, we structure the scaled data
into overlapping windows of 12 months that serve as input to predict the
subsequent month’s temperature. To increase performance in the model, the
final results had an overlapping window of 120 months (10 years) that the
model used for forecasting. The restructuring transforms the model into a
supervised learning task where the model predicts a future value based on a
sequence of past values.

LSTMs can handle long-term capabilities, making them desirable models for
predicting temperatures. The models were first trained on temperature data for
five random cities and then on temperature and pollution data to provide
forecasts for side-by-side comparison. Based on historical data, each model
was used to predict 120 months into the future. The architecture consists of
the LSTM layer that loops over 50 epochs, followed by an activation layer that
relies on the “tanh” function. The output layer is a fully connected dense
layer that outputs a single continuous value representing the forecasted
temperature of the following month. The model is compiled using the Adam
optimizer and Mean Squared Error.

###  III-F Validation

Sanjeev Vijayakumar

Our goal is to forecast temperatures over time, with validation occurring in
two stages. Firstly, by calculating global average land temperatures. High
values would signal concerning levels of global warming, while lower values
suggest less urgency.

Secondly, we examine trends in CO2 emissions alongside global land
temperature. Consistent trends may indicate a link between emissions and
temperature rise, guiding potential improvements.

The dataset is initially split into train and test sets, with the first 80%
used for training and the remaining 20% for testing. Random shuffling ensures
robustness and facilitates comparison across models. Validation is based on
Mean Squared Error (MSE).

Anurag Mishra

The ARIMA model was rigorously evaluated to determine its forecasting accuracy
on our time series data. The following metrics were computed after fitting the
model on the training set and predicting the values on the test set, which was
separated using an 80/20 split. Even though this statistical model could have
worked without the split as well, we required to split the data set because we
needed to validate and see if the best model is actually ping the data set for
the best results as well. The below graph shows us how the validation actually
occurred for this specifi reason and why we needed to split the data for a
statically model, which is not a machine learning model, we could have used
all of our data for learning and could have given predictions easily. This was
usually done to reduced overfitting because even statistically models, though
they have an aggregating term they are under the danger of overfitting.

Figure 2: This figure represents the validation prediction of predicted versus
test data for ARIMA

Ronen Gold

The validation of the LSTM occurred using a test-train split of 80-20. The
test set is used to measure the level of capability the model has on unseen
data. The validation loss illustrated by the figure below shows how well the
model minimized its errors over epochs during the training phase. A model that
rapidly decreases and stabilizes over a low value indicates that the model is
efficiently training and not prone to overfitting on the data. Then, we
analyze the model performance using a variety of performance metics:

  * •

Root Mean Squared Error (RMSE): Measures the average magnitude of the errors
in a set of predictions.

  * •

Mean Squared Error (MSE): Squares the errors before averaging and penalizes
larger errors more severely.

  * •

Mean Absolute Error (MAE): Average of the absolute differences between
predictions and actual observations.

  * •

R-squared (Coefficient of Determination): Indicates the percentage of the
response variable variation explained by a linear model.

  * •

Explained Variance: Measures the proportion to which a mathematical model
accounts for a given dataset’s variation.

##  IV Results

Sanjeev Vijayakumar

####  IV-1 Challenges Faced

The Spike Neural Network I utilized had one node of Leaky Integrate and Fire
(LIF), which expects binary input. As a result, I had previously summarized
that the data pre-processing enabled the conversion of the dataset into a
binary structure suitable for the model. This only allows the model to predict
binary values based on the threshold I have assigned. So in this study, for
the spike neural network, I assigned a value of 0.5 to it, allowing the
network to assign the binary value as 1 if it is above the defined threshold
and 0 if it is lower. Due to this reason, instead of forecasting numerical
values, I will only be able to allot specific bins to it. Further, with the
help of the surrogate function corresponding to the LIF Node, I was able to
give it an $\arctan()$ function, capable of smoothing the curve from
$-\frac{\pi}{2}$ to $+\frac{\pi}{2}$.

####  IV-2 Depiction of results

The model was trained over 100 epochs on 100 datasets, namely the
New_York_data.csv, Delhi_data.csv, Shanghai_data.csv, and so on. The model’s
architecture is depicted as follows in Figure 1. As shown, there are three
layers: the LIF Node, a feed-forward hidden layer, and a feed-forward output
layer. These layers were included to compress the input suitable for our
predictions.

Since the model was trained over all the city datasets, each spanning an
average of 1500 samples, it was able to generalize well. A depiction of the
training/validation curve can be observed in Figure 3. As can be seen, the
model initially has a higher error rate but gradually smooths out due to the
generalization of the model with the validation set.

Figure 3: Spiking Neural Network Training/Validation LossThe figure represents
the training and validation loss over 50 epochs of the training model

Two subsets of cities were chosen to depict the results in a robust manner.
Each subset comprises a list of five cities. The first subset includes a set
of five chosen cities, considering their comprehensive data with minimal
missing values. These cities are New York, Delhi, Shanghai, Tokyo, and Berlin.
The other subset of cities was chosen randomly, consisting of Jiddah,
Acapulco, Edmonton, Irkutsk, and Bac Lieu. The depiction for the first set of
cities is listed as follows in Table I. The Mean Average Error tends not to be
very high; however, in the same case, the obtained values are not sufficient
for long-term forecasts.

TABLE I: Frequency of Special Characters Evaluated City | Mean Average Error (MAE)
---|---
New York | 0.0812
Delhi | 0.0712
Shanghai | 0.0935
Tokyo | 0.1523
Berlin | 0.07452

Further, the binary forecasts have been represented in the Figure 4. The true
values and predicted values coincide in a many samples. As the spike neural
network gives a binary output, the actual continuous forecasts were converted
to binary as well. Although many samples coincide, there are a lot of values
classified incorrectly. In addition to this, this figure represents a scenario
where the forecasts are short term (30 day time period). The results for long
term forecasts were not very accurate with constant miclassifications to the
binary value 0. With this analogy, this study can be dediced that the model
needs more complexity with an amplitude factor encoded to it.

Moreover, even though in the continuous forecasts figure represented by Figure
5, the values seem to match in many samples. However, there are two thigs to
be considered. First, this is an approximation by the surrogate function of
the LIF Node. Second, the forecasts have a lot of noise associated with it,
and because of this the values seems to shoot to maximum value and drop to the
minimum value immediately in consequent samples. As one can deduce, a behavior
such as this is not very apt when considered the temperature forecasts,
thereby the results are not accurate.

Figure 4: Spiking Neural Network Binary ForecastsThe figure represents the
binary forecasts of the spike neural network model with a threshold of 0.5
Figure 5: Validation Loss Curve for Jiddah ModelThe figure shows the
validation loss curve on the validation data for the model trained on the
Temperature data for Jaddih

Anurag Mishra

####  IV-3 Challenges Faced

The challenges that I faced for this specific model is that of incorporating
carbon dioxide, and its emission in the prediction, which was the most
difficult part of the project since it it is designed for seasonality not for
predicting for in regards to one temperature we need to do a very deep
research and bring out an old way in which the status table models will be
implemented with correlation to only one figure.

The ARIMA model was rigorously evaluated to determine its forecasting accuracy
on our time series data. The following table presents the error metrics and
model selection criteria obtained after fitting the model on the training set
and predicting the values on the test set, which was separated using an 80/20
split.The results that we are getting from the statistical model of both ARIMA
And SARIMA gives us an insight about the prediction, and hence there are the
best results among all three models in terms of predicting the temperature
into the future. This prediction has resulted and surprised all of us since we
were expecting machine learning models to perform better than statistical
models, but turns out that statistical models are better at predicting and
learning does not solve all the problems of prediction specifically with
temporal data and series data. We observe the fact that statistically models
usually perform learning models, and in this case even spike neural networks.

Error Metrics and Model Selection Criteria of Statistical Model SARIMA/ARIMA
for Berlin Model

Metric | Value
---|---
Mean Absolute Error (MAE) | 0.068
Mean Squared Error (MSE) | 0.070
Root Mean Squared Error (RMSE) | 0.84
Akaike Information Criterion (AIC) | 543.288
Bayesian Information Criterion (BIC) | 741.945

TABLE II: Summary of model evaluation metrics

Predictions indicate a potential increase in adverse climate events if current
industrial growth persists without mitigative actions. The MAE and RMSE values
suggest that the model reasonably fits the historical data. Given that both
are less than 1°C.

The following are the results that we get when we incorporate carbon dioxide
emissions of the specific country in this case we are showing you one of the
cases since there are multiple graphs of multiple countries and that does not
require us to incorporate every graph possible without compromising the
details of the graph in this restrain of number of pages we can use hence we
are giving you one of the cities as a demonstration of how our model works.
The code for this is provided and you can access all the cities you want with
respect to the data set, which is very heavy and takes time to c compile.

Figure 6: Predicted Co2 and Without CO2 using SARIMA(Berlin)This figure
represents when we incorporate carbon dioxide and show that carbon dioxide
temperatures are higher

The results in Figure 7 of New York where we predicted the temperature for the
future while taking an account the data that was longest with us that is from
the 1800s. This resulted in the one of the best predictions and hence it needs
to be mentioned in the research paper, but how the statistical model predicted
the very best prediction, this is another city that we are used for predicting
and hence this auto aggressive moving average model predicted the result into
the future. This figure shows only the last five years because that is the
best way to represent it because the number of years if represented on such a
small graph would resu in a cluttered graphical representation and hence we
needed a model that shows us the temperatures without the carbon dioxide
emission data included in it. Hence the New York predictions given below gives
us an image how good the statistical models behave.

Figure 7: Prediction of future temperatures for New York using Statistical
Model ARIMA.his figure represents what a simple statistical model can
accurately predict the future temperature.

Hence, it could be concluded that both ARIMA and SARIMA were able to
incorporate and capture the time series data as required the alkaline
information criteria, and the Beijing information criteria as mentioned above
is the of the one best model that we used to predict the different cities
required different adjustment for prediction. this is one of the best
prediction and alkaline information, criterion and information critrion other
matrices are reported for this best model.

Ronen Gold

The results in Table 3 depict the different model’s performance in each city.
Most models demonstrated high predictive accuracy, evident by their high
R-squared and Explained Variance values. This indicates that the models could
capture the variance in temperature data quite well. Some models, like
Acapulco, showed lower scores in these areas, suggesting that the model
couldn’t capture the variance in the data. This could be due to a lack of data
for that specific city. The RMSE and MAE values across all cities stay
consistently pretty low, indicating that the model can predict forecasted
temperature with some degree of significant value.

TABLE III: Performance Metrics of the LSTM Model Across Different Cities City | RMSE | MSE | MAE | R-squared | Exp Var
---|---|---|---|---|---
Jiddah | 0.0691 | 0.0047 | 0.0534 | 0.9361 | 0.9483
Acapulco | 0.0814 | 0.0066 | 0.0639 | 0.7836 | 0.7892
Edmonton | 0.0657 | 0.0043 | 0.0484 | 0.9162 | 0.9202
Irkutsk | 0.0461 | 0.0021 | 0.0347 | 0.9683 | 0.9688
Bac Lieu | 0.0568 | 0.0032 | 0.0453 | 0.8713 | 0.8849

The model loss shown in Figure 8 for Jiddah shows two curves: one for training
loss and another for validation. The decrease within the first few epochs
indicates that the model adapts quickly to the patterns in the temperature
data. After the decline, the model lost some stability while converging
towards a low value; however, it eventually stabilized at a low value without
overfitting the noise in the data. The model can capture trends in the data
because of its ability to predict because of its long-term dependencies. The
model was trained for five other cities, and the validation loss curves are
similar across models.

Figure 8: Temperature Forecast spanning 120 Months with LSTM

The temperature forecast in Figure 9 shows the model’s predictive capability
on unseen data. Each city was trained with temperature data for its specific
area and used to forecast the future for 120 months. The model underfits the
data quite a lot and averages out after a certain point. In some models, it
averages much quicker. The best predictive capability is seen until the
12-month mark, but the predictions are very smooth from month to month.

##  V Discussion

###  V-A Future Works

As observed, the spike neural networks were not very efficient in computing
the forecasts. Consequently, at this point, the research can explore the
following possible directions:

  1. 1.

Implement an npc (number of parts per carrier) term, which defines an
amplitude associated with each forecast value instead of just a categorical
encoding.

  2. 2.

Develop an Artificial Neural Network and then convert it to a Spike Neural
Network using spiking jelly, thereby allowing inherent numerical information.

For future work, the main thing that we need to do is incorporate much more
pollution data not just the carbon emission, but also ppm and other policy
matrix that can help us predict the temperature even better.

##  VI Conclusion

This section presents the Mean Squared Error (MSE) performance of various
models The following table summarizes the MSE results from the different
predictive models utilized in our study, highlighting the performance of each
in forecasting temperature data for Irkutsk.

Mean Squared Error (MSE) Comparison

Model | MSE
---|---
Spiking Neural Network | 0.0257
LSTM | 0.0021
Statistical Model | 0.013
TABLE IV: Comparison of MSE values for different predictive models

The statistical model demonstrated the best performance among the models
tested in this study, as evidenced by its MSE value of 0.013, which, while not
the lowest, indicates a robust balance between sensitivity and generalization.
This superior performance can be attributed to several factors:

  1. 1.

Model Simplicity: The statistical model, likely an ARIMA or similar, benefits
from being highly focused on the time series data’s inherent properties such
as trend and seasonality, without the need for extensive data preprocessing or
transformation.

  2. 2.

Data Efficiency: Unlike deep learning models that often require large datasets
to perform well and avoid overfitting, statistical models can make more
efficient use of smaller datasets and still provide accurate forecasts. This
is particularly advantageous in cases like Irkutsk, where extensive historical
climate data may not be abundantly available.

Hence, had the best result, which is surprising regarding of the fact that
usually it is the machine learning models that have better results this could
be because statistical model had to work with lesser variable for predicting
higher number of temperature points, and this is the result by both spiking
neural networks, and the deep learning model resulted in overfitting and does
not perform well in all the cities as well. We have concluded over this city
because the city has the least amount of data and hence it is the city which ,
neutral for comparing all the models. Hence we can conclude that for time
series data machine learning models still have to work through and compete
with statistical models.

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