The Research of Key Roles of Logistic Regression Model and
Random Forest Model in Numerical Weather Prediction
Yishun Zhang
Jingqiu international school, Qingdao, Shandong Province, 266000, China
Keywords: Random Forest, Logistic Regression, Prediction Model, Weather Forecast.
Abstract: Weather forecasting has evolved from ancient observations of clouds and wind patterns to a sophisticated
science driven by advanced technology. Today, it plays a crucial role in disaster mitigation, agriculture,
transportation, and daily life. Modern forecasting relies on satellite imagery, radar systems, supercomputers,
and complex algorithms to predict weather phenomena with increasing accuracy. This paper focuses on the
application of Numerical Weather Prediction (NWP) models and machine learning techniques like logistic
regression in analyzing weather patterns across diverse U.S. regions, particularly in complex terrains. NWP
models process vast atmospheric data to simulate weather systems, while logistic regression helps classify
and predict extreme weather events. Their combined use enhances forecast precision in challenging areas such
as mountainous zones and coastlines, where traditional methods often struggle. These technological
advancements not only improve early warning systems but also contribute to more resilient infrastructure
planning and better emergency preparedness, ultimately saving lives and reducing economic losses.
1 INTRODUCTION
Weather forecasting has become an indispensable
part of the modern life. It plays a vital role in many
aspects. For example, in agriculture, farmers rely on
weather forecasting to arrange planting, irrigation,
harvesting and avoid adverse weather. Prevent frost
and hail in advance to reduce crop losses. In the
transportation industry, aviation and navigation need
to avoid flight delays or navigation accidents caused
by bad weather, and early warning of fog, snow and
ice in highway safety to reduce traffic accidents. The
capacity to use numerical models to simulate intricate
physical systems has been one of the most significant
scientific breakthroughs of the last century. The
Numerical Weather Prediction (NWP) is one of
several models that this paper can use to forecast
variable weather. It has several benefits, including the
ability to forecast weather days ahead of time with a
high degree of confidence and a better understanding
of the factors causing climate change and its likely
timing and severity (Agepati et al., 2023).
However, a century ago, weather prediction was
still a very uncertain thing, without specific
theoretical research, people usually had to complete
the weather prediction with more "soil methods" and
life "experience" to make a judgment on what to do
next, but it was often inaccurate, resulting in
economic losses and countless inefficient events.
Forecasting was more of an art than a science back
then, and forecasters relied on intuition, local
climatology knowledge, and rudimentary
extrapolation methods (Gregory and Russ, 2018).
Advection, or the transfer of fluid characteristics by
the fluid's own motion, is the primary physical
mechanism that forecasters concentrate on. The main
characteristic of advection, however, is that it is
nonlinear. While human forecasters may infer trends
by assuming constant winds, they are unable to
intuitively comprehend the nuances of intricate
advection processes (Peter, 2008).
Lorentz's groundbreaking work on "deterministic
aperiodic flows" in 1963 put chaos theory at the
center of meteorology and significantly altered the
trajectory of weather and climate forecasting for the
next decades. Indeed, one might argue that the theory
of the atmosphere (and subsequently the ocean) as a
chaotic system has shaped the understanding of
weather forecasting and, therefore, climate
predictability. This ushered in a "new era" of weather
forecasting (Mat, 2007).
Based on previous studies and the development of
computer science, people invented NWP to study
644
Zhang, Y.
The Research of Key Roles of Logistic Regression Model and Random Forest Model in Numerical Weather Prediction.
DOI: 10.5220/0013848500004708
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy (IAMPA 2025), pages 644-648
ISBN: 978-989-758-774-0
Proceedings Copyright © 2025 by SCITEPRESS – Science and Technology Publications, Lda.
specific weather. NWP uses numerical simulation to
quantitatively forecast how temperature, wind,
humidity, and pressure will affect the condition of the
atmosphere. The present state of the atmosphere is
determined by internal input of various observations
on the grid points of the model in normal space. The
dominant relation of atmospheric movement in the
model is to project the future state, which is
synthesized from the initial state. When forecasters
prepare climate forecasts, the numerical output from
the model serves as a guide to interpreting local
climate factors. Ocean wave heights will be
diagnosed using the output value. Objective
explanations of climatic variables, such as maximum
and minimum temperatures and precipitation
probability, are also provided by statistical models
(Jana et al., 2017).
Logistic regression is often considered a crucial
technique for weather forecasting in NWP. A
statistical model that represents the logarithmic
likelihood of an occurrence as a linear combination of
one or more independent variables is known as
logistic regression. Among statistical forecasting
algorithms, logistic regression is the most widely
used and has a long history in NWP, and is perhaps
the easiest and most directly explained by its
regression coefficient (Han et al., 2016). Operational
regression approaches, like statistical hurricane
intensity prediction systems, may demonstrate the
distinct influence of each component of the present
weather on the final forecast by using regression
coefficients. logistic regression is also surprisingly
effective in predicting binary weather events. By
using the characteristics of temperature, humidity,
pressure and other historical data, the logistic
regression model is trained to predict whether rain
will fall in the next 24 hours. The result is a
probability value, and the binary classification result
can be generated by dividing threshold values (Julia
and Tim, 2011).
It is often tempting to use an algorithm that does
not make these assumptions when physical
correlations are unknown or difficult to quantify. The
Random Forest (RF) approach is one example of this.
A random forest is a classifier that has many decision
trees, and the mode of the categories that each tree
produces determines the category of the output (Ben,
2008). The categorization of storm types, turbulence,
cloud cover and visibility, convective initiation, and
hail size are only a few of the many uses of RF in
NWP. This algorithm is more widely used than
logistic regression (Wilks and Wilby, 1999).
This article will take the analysis of climate
change in many places in the United States as an
example, describe the specific methods and analyses
of logistic regression and random forest model in
NWP weather prediction, as well as the shortcomings
of these models and the prospect of future climate
prediction (Shri, 2014).
2 METHODS
2.1 Data Source
The European Centre for Medium-Range Weather
Forecasts (ECMWF) and the National Oceanic and
Atmospheric Administration (NOAA) provided the
data used in this investigation. Temperature, humidity,
pressure, wind speed, precipitation, and other
meteorological variables are included in the dataset,
which spans the years 2010–2023. The dataset
comprises over 50,000 observations from multiple
weather stations across the United States, ensuring a
comprehensive representation of diverse climatic
conditions.
2.2 Variables and Data Preprocessing
The dataset comprises 6 variables, as detailed in
Table 1. These six variables are key elements in the
study of weather, and they are temperature, humidity,
wind speed, pressure, precipitation and visibility are
given in the table 1.
Table 1: Variable description.
Variables
Explanation
temperature
Daily average
temperature in
degrees Celsius
humidity
Relative humidity in
percentage
Wind speed
Average wind speed
in meters per second
pressure
Atmospheric
pressure in
hectopascals (HPa)
precipitation
Daily precipitation in
millimeters (mm)
Visibility
Visibility in
kilometers
Categorical variables like "weather condition" and
"location" were converted into numerical values for
data preparation. Missing values, which accounted
The Research of Key Roles of Logistic Regression Model and Random Forest Model in Numerical Weather Prediction
645
for less than 5% of the dataset, were imputed using
the mean for continuous variables and the mode for
categorical variables.
2.3 Machine Learning Models
Two models were employed for weather prediction:
Logistic Regression (LR): A statistical model used to
predict the probability of a binary outcome (e.g.,
precipitation). The model was trained using the "glm"
function in R, and multicollinearity was assessed
using Variance Inflation Factor (VIF).
Random Forest (RF): An ensemble learning
method that constructs multiple decision trees. The
optimal parameters for the RF model were
determined through cross-validation, with "ntree" set
to 200 and "mtry" set to 3.
The dataset was split into training (80%) and
testing (20%) sets. Model performance was evaluated
using accuracy, derived from the confusion matrix.
Logistic regression maps the output of linear
regression to the interval [0, 1] through the Sigmoid
function (logic function), representing the probability:


(1)
where is the probability of the event given
features X.
3 RESULTS AND DISCUSSION
3.1 Model Performance Comparison
The accuracy, precision, recall, and F1-score of the
logistic regression (LR) and random forest (RF)
models were used to assess their performance. Table
2 displays the findings.
Table 2: Model Performance Comparison.
Metric
Logistic
Regression
Random Forest
Accuracy
0.872
0.901
Precision
0.855
0.887
Recall
0.830
0.892
F1-score
0.842
0.889
The RF model outperformed the LR model across all
metrics, achieving an accuracy of 90.1% compared to
87.2% for LR. This suggests that the ensemble
approach of RF, which aggregates multiple decision
trees, captures nonlinear relationships and
interactions between variables more effectively than
the linear LR model.
For each model, predictions were categorized as:
True Positives (TP): Correctly predicted precipitation
events. False Positives (FP): Non-precipitation events
incorrectly predicted as precipitation. False Negatives
(FN): Precipitation events missed by the model. True
Negatives (TN): Correctly predicted non-
precipitation events.
Accuracy: Measures overall correctness:



(2)
Precision: Quantifies reliability of positive
predictions:



(3)
Recall (Sensitivity): Captures the model’s ability to
detect actual events.



(4)
F1-score: Harmonizes precision and recall.
  


(5)
3.2 Feature Importance in Random
Forest
The importance of each feature in the RF model was
assessed using the mean decrease in Gini impurity.
The results are shown in Table 3. Importance Score is
to evaluate the specific importance of elements in
weather prediction. Through numerical methods, this
paper can intuitively see which factors are important
and which are not so important. For example,
temperature occupies the highest proportion in the
icon, so temperature is the factor this paper gives
priority to in weather prediction.
Table 3: Feature Importance in the RF Model.
Importance Score
0.245
0.198
0.176
0.152
0.112
0.087
Temperature emerged as the most influential feature,
followed by humidity and pressure. This aligns with
meteorological principles, as these variables are
critical in atmospheric processes and weather
formation.
IAMPA 2025 - The International Conference on Innovations in Applied Mathematics, Physics, and Astronomy
646
3.3 Logistic Regression Coefficients
Table 4 displays the logistic regression model's
coefficients, which provide vital information about
how each predictor variable relates to the desired
result. When all other variables are held constant,
these coefficients, which are given in log-odds units,
measure how the log-odds of the target variable (such
as the incidence of precipitation) change with a one-
unit rise in the related predictor variable. Whereas a
negative coefficient implies an inverse association, a
positive coefficient shows that an increase in the
predictor variable raises the chance of the event
happening. For continuous variables, the coefficient
reflects the change in log-odds per unit increment; for
categorical variables, it represents the difference in
log-odds compared to the reference category. The
magnitude of each coefficient corresponds to the
strength of association, with larger absolute values
indicating more substantial influences on the outcome.
Importantly, these log-odds coefficients can be
transformed into odds ratios through exponentiation,
which offers a more intuitive interpretation of the
effect sizes. The statistical significance of these
coefficients, typically assessed through Wald tests or
likelihood ratio tests, determines whether the
observed relationships are likely to exist in the
population rather than occurring by random chance.
This parametric output of logistic regression proves
particularly valuable for understanding the
directional effects and relative importance of
different meteorological factors in precipitation
forecasting.
Table 4: Logistic Regression Coefficients.
Feature
Coefficient
p-value
Temperature
-2.345
<0.001
Humidity
0.876
0.002
Wind speed
1.203
<0.001
Pressure
-0.654
0.012
Precipitation
0.432
0.045
Visibility
1.987
<0.001
All coefficients were statistically significant (p <
0.05), indicating that each feature contributes
meaningfully to the prediction. Humidity and
precipitation showed the strongest positive
associations with the target variable, while pressure
had a negative effect.
4 CONCLUSION
Numerical weather prediction (NWP) has evolved
significantly with the integration of machine learning
techniques, particularly logistic regression (LR) and
random forest (RF) models. This study compared the
performance of these two approaches in predicting
binary weather events (e.g., precipitation) using
historical meteorological data from NOAA and
ECMWF. The results demonstrate that both models
offer valuable insights, but RF exhibits superior
predictive accuracy and robustness in handling
complex atmospheric interactions.
The logistic regression model achieved an
accuracy of 87.2%, with humidity (OR = 3.329, p <
0.001) and precipitation (OR = 7.296, p < 0.001)
emerging as statistically significant predictors. While
LR provides interpretable coefficients-valuable for
understanding linear relationships-its performance is
constrained by inherent assumptions of linearity and
additivity. In contrast, the random forest model
outperformed LR with an accuracy of 90.1%, higher
precision (0.887), and better recall (0.892). RF's
ensemble approach effectively captured nonlinear
patterns and variable interactions, with temperature
(Gini importance = 0.245), humidity (0.198), and
pressure (0.176) identified as the most influential
features. This aligns with meteorological theory,
where these variables drive convective processes and
weather system dynamics.
The practical implications of these findings are
substantial. For operational meteorology, RF's higher
accuracy supports its use in short-term forecasting,
particularly for extreme weather warnings. Its ability
to rank feature importance also aids in optimizing
data collection-for instance, prioritizing temperature
and humidity measurements over less critical
variables like solar radiation. However, LR retains
utility for scenarios requiring model interpretability,
such as communicating forecast uncertainty to
stakeholders.
In conclusion, this study underscores machine
learning's transformative potential in NWP. RF's
superior performance highlights its suitability for
operational forecasting, while LR offers a simpler,
interpretable alternative. By integrating these tools
with traditional physical models, meteorologists can
achieve more accurate, actionable forecasts-
ultimately benefiting agriculture, transportation, and
disaster preparedness. Future research should focus
on hybrid modeling approaches and real-time system
integration to further advance weather prediction
capabilities.
The Research of Key Roles of Logistic Regression Model and Random Forest Model in Numerical Weather Prediction
647
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