Edelweiss Applied Science and Technology 
ISSN: 2576-8484 
Vol. 8, No. 6, 520-537 
2024 
Publisher: Learning Gate 
DOI: 10.55214/25768484.v8i6.2117 

© 2024 by the authors; licensee Learning Gate 

© 2024 by the author; licensee Learning Gate 
* Correspondence:  lawalyb@tut.ac.za 

 
 
 
 
 

Performance of advanced-deep learning algorithm for modeling and 
prediction of rain height over some selected locations in the tropics and 
sub-tropics zone for radio propagation applications 

 
Yusuf Babatunde Lawal1*, Pius Adewale Owolawi2, Chunling Tu3, Etienne Van Wyk4, Joseph Sunday 
Ojo5 
1,2,3Department of Computer Systems Engineering, Tshwane University of Technology, South Africa; lawalyb@tut.ac.za (Y. B. 
L.), owolawipa@tut.ac.za (P. A. O.), duc@tut.ac.za (C. T.) 
4Faculty of Information and Communications Technology, Tshwane University of Technology, South Africa; 
vanwykea@tut.ac.za (E.V. W.) 
5Department of Physics, Federal University of Technology, Akure, Nigeria; ojojs_74@futa.edu.ng (J. S. O.) 

 

 

Abstract: As demand for high-frequency broadband communication services keeps rising, rain-induced 
attenuation remains the predominant threat to radiowave propagation. Accurate prediction of 
attenuation requires continuous measurement and monitoring of rain-induced meteorological 
parameters, specifically rain rate and rain height, due to their spatio-temporal variations. Rain height is 
an upper dataset mostly computed from Zero- degree Isotherm Heights (ZDIH) measured by radar. 
This research proposes a novel approach for predicting rain height from earth surface data such as 
surface temperature, pressure, total cloud cover, dew point temperature, surface solar radiation, water 
vapor amount in the air, and humidity. This research investigates the relationship between 
meteorological surface data and rain height. Subsequently, six machine learning models were employed 
for predicting rain height using the ten years surface data as input variables. The models were applied to 
six sub-tropical (Polokwane, Pretoria. and Cape Town) and tropical (Sokoto, Akure, and Port Harcourt 
(PH)) stations in South Africa and Nigeria, respectively. Analysis of the results shows that the Gradient 
Boosting Algorithm (GBA) performed best with determination coefficients greater than 0.80 and RMSE 
less than 350 in all three stations in South Africa.  However, all the models failed to produce good result 
for the Nigeria stations. The Random Forest model has the fairest performance metrics with r2 of 0.40, 
0.46 and 0.46 in Sokoto, Akure and PH. respectively. GBA is recommended for predicting rain height in 
South Africa. The research outcome would assist radio engineers in improving the prediction of rain-
induced attenuation and determining appropriate fade mitigation techniques. 

Keywords: Advanced deep learning, Gradient boosting model, Rain height, Rain-induced attenuation, Spatio-temporal 
variation, ZDIH. 

 
1. Introduction  

Rain height, the distance from the Earth’s surface up to the top of the precipitation column, is one of 
the most important parameters in meteorology and telecommunications. It is thus necessary to know 
the height of the rain for predicting the rain-induced attenuation on satellite communication systems 
operating above 10 GHz. Especially in the tropical and sub-tropical regions where severe and frequent 
rainfalls happen. Rain attenuation to estimate the necessary fade margin and recommend appropriate 
fade mitigation techniques to alleviate the rain effect on communication networks. The traditional 
methods of measuring rain height from freezing level heights are mainly through satellite radar or 
ground-based radar such as MRR. Several studies have revealed that the satellite method is not ideal for 



521 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

the measurement of localized high-resolution lower atmospheric data due to the variability of 
atmospheric parameters, satellite distance to target variables, comparatively low spatio-temporal 
resolution, etc [1-3]. The ground-based radar method is popularly preferred because for localized 
measurement [4]. However, there are few  ground-based radar observatory stations across the world 
due to procurement, installation costs, and complex maintenance [5]. Most weather observatory 
stations are equipped with multiple sensors that can measure atmospheric variables such as temperature, 
pressure, humidity, solar radiation, wind speed, precipitation, etc at the earth surface and near-earth 
surface.  

The motivation for this study is the scarcity of accurate localized real-time rain height data for 
estimation of rain-induced attenuation and fade margin especially in the subtropical region. The 
research seek to investigate whether it is possible to process lower atmospheric data with the help of 
machine learning algorithms to estimate the rain height more accurately. These models will deploy 
input parameters such as surface temperature, surface pressure, total cloud cover, dew point 
temperature, surface solar radiation, the amount of water vapor in the air, and humidity to enhance the 
estimation. The aim of the research is to apply machine learn models to predict rain heights from the 
earth surface atmospheric variables for tropical and sub-tropical regions.  Variables of interest that 
influence ZDIH and rain height shall be identified while ML models such as Surface Vector Regressor, 
Random Forest, Gradient Boosting, XGboost, and Neural Network shall be deployed to predict rain 
heights 

Numerous researches have been conducted to provide various methods of rain height estimation 
since it cannot be measured directly. Conventional techniques involve the use of precipitation data 
obtained from radar measurements for direct estimates of rain profiles. The two common types of radar 
observation are satellite-borne and ground-based radars. For instance, the satellite-borne Tropical 
Rainfall Measuring Mission (TRMM) precipitation radar, which provides freezing level height useful in 
international rainfall height imagery [6-7]. The Dual Precipitation Radar (DPR) of the Global 
Precipitation Measurement (GPM) mission, which is the successor of the TRMM, is capable of 
providing detailed vertical profiles of precipitation, which aid in the measurement of the bright band, the 
zero-degree isotherm height, and the rain height [8]. The ground-based radar uses Doppler radar to 
remotely measure the vertical profile of the troposphere up to about 10 km above ground level. These 
radars detect the speed and intensity of the precipitation particles needed to estimate the position of the 
melting layer, which is often referred to as the bright band, and freezing level heights from radar 
reflection. The bright band is a region with increased radar reflectivity as a result of melting snowfall, 
and it is normally situated close to the zero isotherm height. Rain height estimation could be enhanced 
using considerable information such as zero isotherm height, bright band, shape, and orientation of 
hydrometeors from dual-polarisation radars [9]. However, these techniques are based on remote 
sensing of upper-air atmospheric variables through radar echo. The radiosonde method provides a more 
accurate approach for measuring upper data due to its in situ nature. Although this method provides 
localised data, which is preferred to satellite-borne radar, there is insufficient global data due to the 
limited number of radio-sounding stations across the world. Algorithms and models, such as artificial 
neural networks and regression trees, have also been developed to estimate rain height from radar data. 
For instance, Meneghini et al applied the Surface Reference Technique (SRT) to the radar signal's 
interaction with the Earth's surface to calibrate the radar and improve rain height estimates in [10]. 
Upper air atmospheric parameters and 0°C isotherm levels were integrated into a single unique model 
through the use of machine learning by Mandeep (2008) [11] to enhance rain height estimation in 
Malaysia. Lawal et al recommended a latitude-dependent equation for the computation of rain heights in 
Nigeria in [12]. The equation has a determination coefficient of 0.8, which implies that more research 
could be carried out to improve the estimation accuracy. Nalinggam et al created rain attenuation 
models in [13] for Southeast Asia and stressed how machine learning could be useful in studying rain in 
tropical regions. 



522 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

However, none of these investigations utilized machine learning to estimate rain heights from the 
earth's surface or near-surface atmospheric data at the regional level, particularly in the areas where 
climate change is evident. Akure is one of the study stations located in Nigeria, and it experiences a 
tropical climate. Similarly, Pretoria is located in South Africa, a subtropical region where rainfall also 
has devastating effects on radio signals operating above 10 GHz. Therefore, these locations are 
obviously convenient to study, model, and develop machine learning techniques for rain height 
estimation from atmospheric variables at the earth surface. This study intends to address this challenge 
by using data of the local atmosphere and ML models to enhance the accuracy of rain height estimations 
for tropical and subtropical zones.  
 
1.1. Climatology of Research Locations and Data Acquisition 

The research locations are Polokwane, Pretoria, and Cape Town in South Africa, and Sokoto, Akure, 
and Port Harcourt in Nigeria. According to the climatological classifications of African countries, the 
former country lies in the sub-tropical region, while the latter is categorised under the tropical region. 
The coordinates and elevations of the study locations are presented in Table 1. The locations were 
selected based on latitudinal distribution across the country since some previous works reported 
latitudinal dependence of rain heights [14-17] and [12]. South Africa is a sub-tropical region located in 
the southernmost part of the African continent. It experiences four seasons of weather annually, namely: 
summer (December–February), autumn (March–May), winter (June–August), and spring (September–
November). It is a subtropical highland climate, characterized by warm, rainy summers and mild, dry 
winters. 

Table 1. 
The six study locations and their geographical coordinates. 

Zone Station Lat (o) Long (o) Elevation (m) 
South Africa -Sub-tropical Zone Polokwane -23.905 29.467 1315 

Pretoria -25.733 28.183 1332 
Cape Town -33.917 18.425 25 

Nigeria -Tropical Zone Sokoto 13.023 5.245 296 
Akure 7.255 5.206 353 
Port Harcourt 4.078 7.005 16 

 
Nigeria has diverse geoclimatic characteristics, ranging from the Sahel region at the north to the 

Savannah at the Center to the coastal region at the southernmost part of the country. The average 
annual temperature is approximately between 26 and 28 oC, while the average annual rainfall is about 
2000 m, especially in the coastal region. Nigeria experiences rainy and dry seasons only. The rainy 
season runs approximately between May and September, while the dry season reigns between 
November and March. High humidity is dominant and longer rainy seasons are dominant in the south, 
while intense heat and longer dry seasons reign in the north [18-20]. 
 

2. Overview of the ML Models 
2.1. Random Forest Model 

The Random Forest Model is a machine learning algorithm that deploys a combination of several 
decision trees to produce a unique result. It is an ensemble of learning that is suitable for classification 
and regression analysis. Its working principle involves building several decision trees during the 
training phase and then providing its final decision in the form of the class modes for classification 
analysis or the mean of the individual trees’ predictions for regression analysis.  

The model integrates multiple decision trees to improve predictive performance and control 
overfitting through the processes of bootstrap sampling, tree construction, and aggregation. The 
bootstrap stage randomly generates a bootstrap sample size and replaces it with a training set k from 
the original data. At the tree construction stage, the bootstrap sample grows a decision tree Tb using a 



523 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

subset of features, m <<p, where p is the total number of features. Equations (1) and (2) are used at the 
prediction stage for classification and regression analysis, respectively. 

𝑌
^

= 𝑚𝑜𝑑𝑒{𝑇𝑖
𝑏(𝑋)}𝑏=1

𝐵             (1) 

𝑌𝑖

^
=

1

𝐵
∑ 𝑇𝑖

𝑏(𝑋)𝐵
𝑏=1             (2) 

where 𝑌𝑖

^
 is the final prediction for input sample X. 𝐵 is the total trees in the forest. 𝑇𝑖

𝑏 is the prediction 
from the bth tree for the ith sample X. The model leverages the multiple decision trees in the forest to 
improve prediction accuracy. 

 
2.2. Gradient Boosting Model 

Gradient Boosting is a meta-algorithm ensemble learning method where weak models like decision 
trees are built stage wise consecutively in a sequential fashion to reduce the magnitude of a given loss 
function to the barest minimum. This method is used to break down a strong predictor into multiple 
weak predictors in order to deal with a complex data set [21]. The aim of Gradient Boosting is to 
produce a model F(x) that predicts the target variable y. It builds the model incrementally by adding 
weak learners hm (x), usually decision trees, in such a way that each new model fixes the flaws in the 
previous ones. The algorithm starts with an initial model which is usually the mean value of the target 
variable for regression problems as defined in equation (3) [22-23]. 

𝐹0(𝑥) = 𝑎𝑟𝑔 𝑚𝑖𝑛 ∑ 𝐿(𝑦𝑖 , 𝑐)𝑛
𝑖=1                 (3) 

where  𝐿 is the loss function, 𝑦𝑖   and 𝑐 are the true values and constant respectively. 
The succeeding model is an additive model built in a stage-wise manner using equation (4). The loss 

function at each stage m is minimized by adding a base learner hm (x) defined by equation (5). This is 
accomplished by fitting hm (x) to the loss function’s negative gradient. 

𝐹𝑚(𝑥) = 𝐹𝑚−1(𝑥) + 𝑣ℎ𝑚(𝑥)               (4) 
where hm (x) is the new base learner added at stage m and v is the learning rate which controls the 
impart of each base learner. 

ℎ𝑚(𝑥) = 𝑎𝑟𝑔 𝑚𝑖𝑛ℎ ∑ [−
𝜕𝐿(𝑦𝑖,𝐹𝑚−1(𝑥𝑖))

𝜕𝐹𝑚−1(𝑥𝑖)
]𝑛

𝑖=1

2

         (5) 

Equation (4) is updated continuously by adding new base learners scaled by the learning rate. 
 
2.3.  XGBoost Model 

The XGBoost is an optimized version of the gradient boosting model with focus on flexibility, 
higher efficiency, and portability. The Machine learning algorithm is initiated by the objective function 
which combines the loss function and a regularization term that helps to control the model complexity 
as stated in equation (6) Chen & Guestrin, 2016 [23]). 

ℓ(𝜃) = ∑ 𝐿(𝑦𝑖 , �̂�𝑖) +𝑛
𝑖=1 ∑ 𝛺(𝑓𝑘)𝐾

𝑘=1     (6) 

where 𝐿 is the loss function such as mean squared error for regression), 𝛺(𝑓𝑘) is the regularization 

term, 𝜃 represents the parameters of the model, �̂� is the predicted value, and fk are the individual trees in 
the ensemble. The objective function is optimized by applying the second-order Taylor expansion to 
approximate the loss function, hence the objective function is expressed by equation (7) as; 

ℓ(𝑡) = ∑ [𝑔𝑖𝑓𝑖(𝑥𝑖) +
1

2
𝑛
𝑖=1 ℎ𝑖𝑓𝑖(𝑥𝑖)2] + 𝛺(𝑓𝑡)    (7) 

where 𝑔𝑖 = 𝜕�̂�(𝑡−1)𝐿
(𝑦𝑖,𝑦�̂�(𝑡−1))

  𝑎𝑛𝑑   ℎ𝑖 = 𝜕2
�̂�(𝑡−1)𝐿

(𝑦𝑖,𝑦�̂�(𝑡−1))
 are the first and second derivatives of the 

loss function with respect to the prediction. 
 
2.4.  Support Vector Regressor Model 

SVR is a type of support vector machine algorithm that attempts to find a function whose difference 
in value between that function and the observed value is not greater than a specified margin.  The model 



524 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

ensures that the function is as flat as possible. It is commonly used for regression analysis. Equation (8) 
is used to obtain the most deviated function f(x) within a specified margin, which is known as the 
objective function. 

𝑓(𝑥) = ⟨𝑤, 𝑥⟩ + 𝑏                             (8) 

where ⟨𝑤, 𝑥⟩ denotes the dot product of the weight vector 𝑤 and input vector 𝑥, 𝑏 is the bias term. 

The SVR loss function is epsilon-insensitive i.e. the errors within the margin of the ∈ is ignored, thus 

the loss function is given by [24]. The optimal values of 𝑤𝑎𝑛𝑑𝑥 can be obtained using complex 
optimization procedure described in the work of [25] and [26] 

𝐿 = {|𝑦−𝑓(𝑥)|−∈              𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
0                                     𝑖𝑓  |𝑦−𝑓(𝑥)≤∈

              (9) 

The regression function for the non-linear regression after optimization is given by equation (10). 

 𝑓(𝑥) = ∑ (𝛾𝑖 −𝑛
𝑖=1 𝛾𝑖

∗)𝐾⟨𝑥𝑖, 𝑥⟩ + 𝑏             (10) 

where 𝛾𝑖  and 𝛾𝑖
∗are the Lagrange multipliers, K is the kernel function 

 
2.5. Neural Network Model 

It is an advanced machine learning model whose computing structure and function are similar to 
those of biological neural networks in animals. It consists of interconnected nodes (neurons) of layers 
that can learn to recognize patterns in data trends. It is made up of a minimum of one hidden layer and 
an output layer. Each layer contains several neuronees, and the neuronees of each layer are 
interconnected to every other neurons in other layers. The activation function in equation (11) is 
performed by each neurone in the network layer as the inputs weighted sum. For instance, the aj for a 
neuron j in the network layer l is given by; 

𝑎𝑗
(𝑙)

= 𝜙 (∑ 𝑤𝑖.𝑗
(𝑙)

𝑎𝑖
(𝑙)

+ 𝑏𝑗
(𝑙)

𝑖 )            (11) 

Where 𝜙 is the activation function, 𝑤𝑖.𝑗
(𝑙)

 is the weight connecting neuron i in layer 𝑙 − 1to neuron j  

in layer 𝑙, 𝑙, 𝑎𝑖
(𝑙−1)

 is the output of neuron 𝑖 in the previous layer, and 𝑏𝑗
(𝑙)

  is the bias term. The loss 

function L which determines the performance of the neuron network is obtained by comparing the 

network output �̂� with the true target𝑦. Equation (12) is the loss function used for the regression 
analysis [27] and [28]. 

𝐿(𝑦, �̂�) =
1

2
∑ (𝑦𝑖 − �̂�𝑖)2𝑛

𝑖=1                   (12) 

The loss function gradients with respect to the weights are computed using equation (13) and the 
result is used to update the weights to minimize the loss. 

𝛿𝐿

𝛿𝜔
𝑖,𝑗
(𝑙) = 𝛿𝑗

(𝑙)
𝑎𝑖

(𝑙−1)
             (13) 

where 𝛿𝑗
(𝑙)

 is the error term for neuron 𝑗in layer 𝑙 

 
2.6.  K-Nearest Neighbors (KNN) model 

K-Nearest Neighbors (KNN) algorithm is a non-parametric, supervised machine learning model 
that stores all available data and makes predictions based on the most similar instances in the training 
data. It is commonly used for regression and classification [29] and [30]). The distance metrics such as 

Euclidean distance in equation (14) is used to find the 𝑘 nearest neighbor. 

𝑑(𝑥𝑖 , 𝑥𝑗) = √∑ (𝑥𝑖𝑚, 𝑥𝑗𝑚)2𝑝
𝑚=1               (14) 

where 𝑥𝑖𝑎𝑛𝑑𝑥𝑗are two points in p-dimensional feature space. The algorithm computes the distance 

between a test point, say 𝑥 and all the points in the training set and picks the 𝑘 point with the smallest 

distances for regression analysis. The target value 𝑦𝑖 is predicted by averaging the target values of the 

𝑖 − 𝑡ℎ 𝑘 nearest neighbor, thus the predicted value �̂�𝑖 is given by equation (15) [30].  



525 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

�̂� =
1

𝑘
∑ 𝑦𝑖

𝑘
𝑖=1                (15) 

 

3. Methodology 
Ten years of earth surface atmospheric daily data for the two stations were downloaded from the 

Era-5 Climate Data Store of the European Centre for Medium-Range Weather Forecast (ECMWF). 
The atmospheric variables deployed from the dataset are: earth surface temperature in Kelvin, earth’s 
surface pressure in Pascal, earth's surface due point temperature in kelvin, wind speed magnitude in 
meters per second, total cloud cover in 0-1, total precipitation in meters, earth's surface solar radiation 
in joules per square meter, total precipitation in meters, and relative humidity in percentage. The 
corresponding daily mean rain heights for the study periods and stations were also computed from zero-
degree isotherm heights using the ITU-R P.839-3 procedure in [31] with the aid of the Python 
programming language. The atmospheric variables were correlated with rain height to study the 
relationship between each of the atmospheric surface variables and rain height. The scatter plots were 
also generated for visualization. It was preprocessed by handling missing values and outliers. Rain 
heights were modelled using six deep-learning models by applying the surface data as the independent 
input variables. The advanced machine learning models applied are Random Forest, Gradient Boosting, 
XGBoost, Support Vector Regressor, Neural Network, and K-Nearest Neighbors. The parameters 
applied to each model are presented in Table 2. The data was split into train and test sections. The 
models were trained using different subsets of features variables. The performance of each model was 
evaluated and compared using performance metrics such as R², RMSE, MAE, and cross-validation.  
 
Table 2. 
The machine learning models and the applied parameter values. 

 Models Parameters Applied values 
1 Random Forest n_estimators, max_depth, min_sample_list, 

min_sample_leaf 
200, 20, 2, 1 

2 Gradient 
Boosting 

n_estimators, learning_rate, max_depth, 
subsample 

200, 0.1, 5, 0.9 

3 XGBoost n_estimators, learning_rate, max_depth, 
subsample, 

200, 0.1, 5, 0.9 

4 Neural Network hidden_layer_sizes, activation, solver, alpha (100, 50), relu, adam, 0.0001 
5 SVR C, gamma, kernel 1, scale, rbf 
6 KNN n_neigbors, weights, metric 5, distance, euclidean 

 
The performance of the best model among the rest was improved by gridsearch hyper parameter 

tuning and feature engineering through date inclusion. The influence and contribution of each input 
variables was identified and analyze feature importance analysis for the most preferred model 
 

4. Results 
4.1. Seasonal Trend of Rain Heights 

The time series plots of the rain height data used for the research are presented in Figures 1–6. It 
was observed that the South African stations exhibited a sinusoidal trend pattern over the years, while 
the Nigerian stations produced apparently irregular patterns. This could be attributed to the frequent 
rainfall associated with the tropical regions, as reported by [20]. Although heavy precipitations are 
usually experienced during the rainy season, occasional rainfalls occur in almost all the dry season 
months, especially in the coastal stations. The dominant influence of temperature on rain height, which 
was discussed in subsequent sections, is also responsible for the clear crest and trough pattern in South 

Africa. Extreme minimum and maximum temperatures are usually experienced during the winter 
and summer, respectively. For instance, Pretoria has a minimum and maximum annual temperature of 5 



526 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

oC and 30 oC, respectively, which implies a difference of 25 oC. Polokwane and Cape Town exhibit 
similar differences [32-34]. On the contrary, the stations in Nigeria possess lower differences. Akure 
has a maximum and minimum annual temperature of about 22 oC and 33 oC, respectively. The difference 
between the two extremes annually in Port Harcourt is about 8 oC. Sokoto has similar differences [36] 
and [37]. 
 

 
Figure 1. 
Seasonal trend of rain heights in Polokwane. 

 

 
Figure 2. 
Seasonal trend of rain heights in Pretoria. 

 
 



527 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

 
Figure 3. 
Seasonal trend of rain heights in Cape Town. 

 

 
Figure 4. 
Seasonal trend of rain heights in Sokoto. 

 



528 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

 
Figure 5. 
Seasonal trend of rain heights in Akure. 

 

 
Figure 6. 
Seasonal trend of rain heights in port Harcourt (PH). 

 
4.2. Comparison of the Models 

The six models described above were applied to all the stations and the results obtained are 
presented in Table 3-8 and Figures 7-12. Comparison of the performance metrics revealed that gradient 
boosting model performed better across all the stations. The performance of the gradient boosting 
Regressor was further improved by hyper-parameter tuning and feature engineering. The grid search 
hyper-parameter method was applied with n_estimators, learning_rate and max_depth, of 100, 0.2, 8 
respectively. 

Tables 3-8 present the values of the performance metrics for all the studied stations while Figures 
7-12 give the graphical representation. The stations in South Africa are well favoured by the models 
with gradient boosting model having the best performance. The regular trend pattern observed for all 
South Africa stations in the section 4.1 is responsible for the optimal fitting of the models. Cape Town 
has the highest determination co-efficient of 0.84 and minimum RMSE and MAE of 336.51 m and 262 
m respectively.  



529 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

The co-efficient of determination r2 and other performance metrics for the stations in the Nigeria 
indicated that none of these models is good for rain height prediction in the tropical region.  
 

Table 3.  
Comparison of models performance metric for Polokwane. 

Models R2 MSE RMSE MAE 
Random forest 0.764 55460 235.50 170 
Gradient boosting 0.800 56659 238.03 173 
XGBoost 0.767 54593 233.65 167 
Support vector regressor 0.578 99125 314.84 224 
Neural network 0.707 68900 262.49 192 
K-Nearest neighbors 0.620 89015 298,36 216 

 
Table 4.  
Comparison of models performance metric for Pretoria. 

Models R2 MSE RMSE MAE 

Random forest 0.777 56365 237.41 167 
Gradient boosting 0.816 45390 213.05 150 
XGBoost 0.783 54808 234.11 164 
Support vector regressor 0.591 103317 321.43 227 
Neural network 0.728 68782 262.27 190 
K-Nearest neighbors 0.654 87551 295.89 215 

 
Table 5.  
Comparison of models performance metric for Cape Town. 

Models R2 MSE RMSE MAE 
Random Forest 0.786 125239 353.89 274 
Gradient boosting 0.841 113236 336.51 262 
XGBoost 0.790 122919 350.60 272 
Support vector regressor 0.613 226837 476.27 354 
Neural network 0.778 129957 360.50 278 
K-nearest neighbors 0.703 174238 417.42 329 

 
Table 6.  
Comparison of models performance metric for Sokoto. 

 R2 MSE RMSE MAE 
Random forest 0.379 12441 111.54 85 
Gradient boosting 0.323 13570 116.49 87 
XGBoost 0.332 13396 115.74 87 
Support vector regressor 0.185 16339 127.83 98 
Neural network 0.094 18178 134.83 104 
K-Nearest neighbors 0.162 16796 129.60 98 

 
Table 7.  
Comparison of models performance metric for Akure. 

Models R2 MSE RMSE MAE 
Random forest 0.456 7652 87.48 68 
Gradient boosting 0.447 7772 88.16 68 
XGBoost 0.437 7919 88.99 68 
Support vector regressor 0.358 9028 95.02 78 
Neural network 0.117 12424 111.47 82 
K-Nearest neighbors 0.357 9051 95.14 74 

 



530 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

Table 8.  
Comparison of models performance metric for port Harcourt (PH). 

Models R2 MSE RMSE MAE 
Random forest 0.458 7496 86.58 65 
Gradient boosting 0.455 7503 86.62 65 
XGBoost 0.456 7496 86.58 65 
Support vector regressor 0.412 8099 90.00 68 
Neural network 0.219 10763 103.75 80 
K-Nearest neighbors 0.281 9901 99.51 76 

 

 
Figure 7. 
Performance metrics of the models for Polokwane. 

 

 
Figure 8. 
Performance metrics of the models for Pretoria. 

 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

50

100

150

200

250

300

350

Random
Forest

Gradient
Boosting

XGBoost Support
Vector

Regressor

Neural
Network

K-Nearest
Neighbors

R
-S

q
u

ar
ed

M
A

E 
an

d
 R

M
SE

 (
m

)

RMSE MAE R2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

50

100

150

200

250

300

350

Random
Forest

Gradient
Boosting

XGBoost Support
Vector

Regressor

Neural
Network

K-Nearest
Neighbors

R
-S

q
u

ar
ed

M
A

E 
an

d
 R

M
SE

 (
m

)

RMSE MAE R2



531 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

 
Figure 9. 
Performance metrics of the models for cape Town. 

 

 
Figure 10. 
Performance metrics of the models for Sokoto. 

 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

100

200

300

400

500

600

Random
Forest

Gradient
Boosting

XGBoost Support
Vector

Regressor

Neural
Network

K-Nearest
Neighbors

R
-S

q
u

ar
ed

M
A

E 
an

d
 R

M
SE

 (
m

)

RMSE MAE R2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0

20

40

60

80

100

120

140

160

Random
Forest

Gradient
Boosting

XGBoost Support
Vector

Regressor

Neural
Network

K-Nearest
Neighbors

R
-S

q
u

ar
ed

M
A

E 
an

d
 R

M
SE

 (
m

)

RMSE MAE R2



532 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

 
Figure 11. 
Performance metrics of the models for Akure. 

 

 
Figure12. 
Performance metrics of the models for PH. 

 
4.3. Correlation between Atmospheric Variables and Rain Height 

The relationship between the input variables and rain height was investigated through correlation. 
Table 9 presents the correlation coefficient between each of the atmospheric earth surface variables and 
rain height for a typical station (Cape Town), since similar results were obtained for all stations. Figures 
13a–h indicate the scatter plots of the variables. Surface temperature and due point temperature have 
very strong positive correlations of 0.79 and 0.59 on rain height, as presented in Table 9. This is due to 
the effect of solar radiation on the melting layer. An increase in temperature reduces the bright band 
and raises the height of the water region in the atmosphere. The path travelled by water droplets before 
the earth surface becomes higher, i.e., the rain eight, However, this does not imply that the total volume 
of water reaching the earth's surface is increased proportionately, thus a weak correlation of about 0.41. 
Surface pressure and Earth’s surface solar radiation also have similar effects, as they both enhance the 
melting of the ice, thus increasing the rain height. This observation was corroborated by [38] and [39], 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

20

40

60

80

100

120

Random
Forest

Gradient
Boosting

XGBoost Support
Vector

Regressor

Neural
Network

K-Nearest
Neighbors

R
-S

q
u

ar
ed

M
A

E 
an

d
 R

M
SE

 (
m

)

RMSE MAE R2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

20

40

60

80

100

120

Random
Forest

Gradient
Boosting

XGBoost Support
Vector

Regressor

Neural
Network

K-Nearest
Neighbors

R
-S

q
u

ar
ed

M
A

E 
an

d
 R

M
SE

 (
m

)

RMSE MAE R2



533 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

who reported strong positive correlations between the pair of meteorological observables. Oher 
variables which exhibit positive but very poor correlation are total cloud cover, total precipitation. 
 

Table 9. 
Correlation co-efficient between earth surface variables and rain height on a typical day for cape town station. 

Earth surface variables (Unit) Symbol Correlation co-efficient (r2) 
Surface temperature (K) t2m 0.76 
Due point temperature (K) d2m 0.59 
Surface pressure (Pa) sp -0.47 
Surface solar radiation (J/m2) ssrd 0.62 
Total cloud cover (0-1) tcc 0.36 
Total precipitation (m) tp 0.41 
Wind speed (m/s) wind_speed -0.04 
Relative humidity (%) relative_humidity -0.51 

 

   

  



534 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

   

   
Figure13a-h.  
The scatter plots of the atmospheric variables on rain height for cape town station. 

 
4.4. Feature Importance of the Input Variables 

The contributions of each input variable used for the modeling were analyzed and weighted through 
feature importance calibrations. The results obtained are presented in Figures 14 (e.g). Among all the 
surface atmospheric variables, the earth surface temperature makes over 60% contribution to the 
regression fit across all the stations, as depicted in Figures 14 (e-g). This implies that temperature has 
the most significant influence on rain height variability. This is a manifestation of the strong positive 
correlation reported in Section 4.3. All other variables contribute less than 20% to the rain height 
model. For instance, in Polokwane, the total precipitation, surface pressure, earth surface due point 
temperature, wind speed, relative humidity, and total clover contribute about 15.4%, 15.1%, 13.8%, 8.5%, 
6.1%, 2.8%, and 2.2%, respectively. 
 



535 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

   
 

   
 

   
Figure.14a-f  
The feature importance of each input variable in the model for; (a) Polokwane, (b) Pretoria, (c) Cape Town, (d) Sokoto, (e) 
Akure, and (f) Port Harcourt (in progress) 

 



536 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

5. Conclusion 
The study examines the annual trend of rain height over the studied years. Findings show that 

South African stations possess a well-defined sinusoidal wave-like pattern, with peak and trough values 
occurring in the summer (December–January) and winter (May–August), respectively. In Nigeria, rain 
height is generally low during the rainy season and high in the dry season. Generally, temperature has 
the greatest influence on rain height due to the high rate of ice melting in the bright band during solar 
active periods. The prediction accuracy of the machine learning models increases as we move away from 
the equator. All the South African stations are situated farther away from the equator compared to the 
Nigerian stations; hence, better performance metrics were observed. The gradient boosting model out 
performed other five models considered in all the stations. Cape Town, which is the farthest station 
from the equator, possesses the best performance metrics with r2, MSE, RMSE, and MAE of 0.84, 
113,236 m2, 336.5 m, and 262 m, respectively. Overall, the research provides an alternative means of 
computing rain height for better prediction of rain-induced attenuation, which is a major threat to 
earth-space on radio links. 
 
Funding: 
This research is supported by Tshwane University of Technology South Africa. 
 
Copyright:  
© 2024 by the authors. This article is an open access article distributed under the terms and conditions 
of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). 

 
References  
[1] Y. Wen, L. Liao, D. Wolff, R. Meneghini, and T. Schuur. “Joint Collaboration on Comparing NOAA’s Ground-Based 

Weather Radar and NASA–JAXA’s Spaceborne Radar,” Bulletin of the American Meteorological Society, vol. 104, no. 8. 
2023. E1435–E1451. https://doi.org/10.1175/BAMS-D-22-0127.1  

[2] L. Liao, D. Wolff, R. Meneghini, and T. Schuur, T. “Systematic Differences in Reflectivity between NOAA WSR-88D 
and NASA–JAXA DPR,” Journal of Applied Meteorology and Climatology.  

[3]  Z. Yu, X. Zheng, and T. Sun. “Three-Dimensional Slope Imaging Method for Ground-Based Real-Aperture Radar. 
Sensors, vol. 21, no. 10. 2021 https://doi.org/10.3390/s21103511  

[4] Y. Hong, K. Hsu, and S. Sorooshian. “Remote Sensing Precipitation: Sensors, Retrievals, Validations , and 
Applications,” SpringerLink. 2022. https://doi.org/10.1007/978-3-319-07184-0  

[5] Y. Zhao, X. Liu, M. Xian, and T. Gao. “Statistical Study of Rainfall Inversion Using the Earth-space Link at the Ku 
Band: Optimization and Validation for 1 Year of Data,” IEEE Journal of Selected Topics in Applied Earth Observations 
and Remote Sensing, vol. 14, pp. 9486-9494, 2021 

[6] D. A. Short, and K. Nakamura.2000). “TRMM Radar Observations of Shallow Precipitation over the Tropical 
Oceans,” Journal of Climate, vol. 13, no. 23, pp. 4107-4124, 2000. http://dx.doi.org/10.1175/1520-
0442(2000)013<4107:TROOSP>2.0.CO;2  

[7] T. Iguchi, N. Kawamoto, and R. Oki. “Detection of Intense Ice Precipitation with GPM/DPR,” America Meteorological 
Society. Vol. 35, no. 3, pp. 491-502, 2018. DOI: https://doi.org/10.1175/JTECH-D-17-0120.1 

[8] M. Kojima, T. Miura, K. Furukawa, Y. Hyakusoku. T. Ishikiri, H. Kai, T. Iguchi, and H. Hanado. “Dual-frequency 
precipitation radar (DPR) development on the global precipitation measurement (GPM) core observatory,” Proc. 
SPIE 8528, Earth Observing Missions and Sensors: Development, Implementation, and Characterization II, 85281A, 2012 
https://doi.org/10.1117/12.976823  

[9] D. S. Zrnic, and A. V. Ryzhkov. “Polarimetry for weather surveillance radars,”  Bulletin of the American Meteorological 
Society, vol. 80, no. 3, pp. 389-406, 1999 https://doi.org/10.1175/1520-0477(1999)080<0389>2.0.CO;2  

[10] R. Meneghini, H. Kim, L. Liao, J. A. Jones, J. M. Kwiatkowski. “An initial assessment of the surface reference 
technique applied to data from the Dual-Frequency Precipitation Radar (DPR) on the GPM satellite,” Journal of 
Atmospheric and Oceanic Technology, vol. 32, no. 11, pp. 2281-2296, 2015 https://doi.org/10.1175/JTECH-D-15-0044.1  

[11] J. S. Mandeep, “Atmospheric effects on Ku-band satellite communication links during the Malaysian rainy season,” 
International Journal of Satellite Communications and Networking, vol. 26, no. 5, pp.447-462, 2008. 
https://doi.org/10.1002/sat.893  

[12] Y. B. Lawal, J. S. Ojo, S. E. Falodun, and E. O. Olurotimi. ”Geoclimatic characterization and latitudinal dependence of 
rain heights over Nigeria,” Journal of Physics: Conference Series. 2034 012010, 2021. IOP Publishing 
https://doi.org/10.1088/1742-6596/2034/1/012010  

https://creativecommons.org/licenses/by/4.0/
https://doi.org/10.1175/BAMS-D-22-0127.1
https://doi.org/10.3390/s21103511
https://doi.org/10.1007/978-3-319-07184-0
http://dx.doi.org/10.1175/1520-0442(2000)013%3c4107:TROOSP%3e2.0.CO;2
http://dx.doi.org/10.1175/1520-0442(2000)013%3c4107:TROOSP%3e2.0.CO;2
https://doi.org/10.1175/JTECH-D-17-0120.1
https://doi.org/10.1117/12.976823
https://doi.org/10.1175/1520-0477(1999)080%3c0389%3e2.0.CO;2
https://doi.org/10.1175/JTECH-D-15-0044.1
https://doi.org/10.1002/sat.893
https://doi.org/10.1088/1742-6596/2034/1/012010


537 

 

 

Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 520-537, 2024 
DOI: 10.55214/25768484.v8i6.2117 
© 2024 by the authors; licensee Learning Gate 

 

[13] K. Nalinggam, H. Ahmad, and S. Abdullah, “The role of satellite-derived data in rainfall estimation over the tropics: 
case study over Malaysia,” Hydrological Processes, vol. 27, no. 24, pp. 3453-3465, 2013. 
https://doi.org/10.1002/hyp.9433  

[14] J. Goldhirsh, and I. Katz, “Useful experimental results for earth-satellite rain attenuation modelling,” IEEE Trans 
Antennas & Propagation, AP-27 pp. 413–415, 1979 

[15] G. O. Ajayi, and F. Barbaliscia. “Prediction of Attenuation Due to Rain: Characteristics of the 0 oC Isotherm in 
Temperate and Tropical Climates,” Int. J. of Sat. Comm, vol. 8, pp. 187–196, 1990. 

[16] E. Matricciani, “Rain attenuation predicted with a two layer rain model,” Electron Lett (UK), vol. 29, pp. 72–73, 1993. 
[17] A. I. O. Yussuff, and N. H. H. Khamis, “Comparative analysis of bright band data from TRMM and ground radar data 

in Malaysia,” International Journal of Networks and Communications, vol. 3, Issue 4, pp.  99-109, 2013. 
[18] O. J. Olaniran, and G. N. Sumner, “A Study Of Climatic Variability In Nigeria Based On The Onset, Retreat, And 

Length Of The Rainy Season,” International Journal Of Climatology, vol. 9, pp. 253-269, 1988 
[19] N. P. Iloeje. “A New Geography of Nigeria,” New Revised Edition, Longman Nig. Ltd., Lagos, p. 200, 2001. 
[20] A. Taiwo, E. U. Utah, and T. E. Sombo. “Monthly Variation and Annual Trends of Rainfall across Major Climatic 

Zones in Nigeria,” IOSR Journal of Applied Physics, e-ISSN: 2278-4861, vol. 10, no. 4, pp. 15-28, 2018. 
[21] J. H. Friedman. “Greedy function approximation: A gradient boosting machine,” The Annals of Statistics, vol. 29, no. 5, 

pp. 1189-1232, 2001. https://doi.org/10.1214/aos/1013203451  
[22] J. H. Friedman. “Stochastic gradient boosting,” Computational Statistics & Data Analysis, vol. 38, no. 4, pp. 367-378, 

2002. https://doi.org/10.1016/S0167-9473(01)00065-2  
[23] T. Chen, and C. Guestrin, “XGBoost: A scalable tree boosting system,” Proceedings of the 22nd ACM SIGKDD 

International Conference on Knowledge Discovery and Data Mining, pp. 785-794, 2016 
[24] A. J. Smola, and B. Schölkopf. “A tutorial on support vector regression,” Statistics and Computing, vol.14, pp. 199-222, 

2004. https://doi.org/10.1023/B.0000035301.49549.88  
[25] V. Vapnik. “The Nature of Statistical Learning Theory,” Springer-Verlag New York, Inc. 1st ed., 1995. 

https://doi.org/10.1007/978-1-4757-2440-0  
[26] H. Drucker, C. J. C. Burges, L. Kaufman, A. J. Smola, and V. Vapnik. “Support Vector Regression Machines,” Advances 

in Neural Information Processing Systems, vol. 9, pp. 155-161, 1997. https://doi.org/10.5555/2998981.2999003  
[27] D. E. Rumelhart, G. E. Hinton, and R. J. Williams. “Learning representations by back-propagating errors,” Nature, 

vol. 323, no. 6088, pp. 533-536, 1986. https://doi.org/10.1038/323533a0  
[28] I. Goodfellow, Y. Bengio, and A. Courville. “Deep Learning” MIT Press, Available online: 

http://www.deeplearningbook.org/   
[29] N. S. Altman. “An Introduction to Kernel and Nearest Neighbor Nonparametric Regression,” The American 

Statistician, vol. 46, pp. 175-185, 1992. 
[30] T. Hastie, R. Tibshirani, and J. Friedman. “The Elements of Statistical Learning: Data Mining,” Inference, and 

Prediction, 2nd ed. Stanford, CA: Stanford University, 2009. 
https://web.stanford.edu/~hastie/Papers/ESLII.pdf https://doi.org/10.1007/978-0-387-84858-7 

[31] ITU-R P.839-3. “Rain height model for prediction methods,” P Series Radiowave Propagation. International 
Telecommunication Union, Radiocommunication Section (ITU-R), Geneva, Switzerland, P.839-3, 2001. 

[32] P. D. Tyson, and R. A. Preston-Whyte. “The Weather and Climate of Southern Africa” Oxford University Press. 2000. 
[33] A. C. Kruger, and S. Shongwe. “Temperature trends in South Africa 1960–2003,” International Journal of Climatology, 

vol. 24, no. 15, pp. 1929-1945, 2004. https://doi.org/10.1002/joc.1096  
[34] M. New, B. Hewitson, D. B. Stephenson, A. Tsiga, A. Kruger, A. Manhique, and R. Lajoie, “Evidence of trends in 

daily climate extremes over southern and west Africa,” Journal of Geophysical Research: Atmospheres, vol.111, no. D14, 
2006. https://doi.org/10.1029/2005JD006289  

[35] R. K. Udo. “Geographical Regions of Nigeria,” Heinemann Educational Books, London. 1970. 
[36] A. A. Adebayo. “The Environment and Climate Change,” The Costs of Inaction. Environment Institute report, 2011 
[37] E. A. Adefisan, and A. A. Abatan. “Rainfall distribution and change detection across climatic zones in Nigeria,” 

Journal of Geography and Regional Planning, vol. 8, no. 4, pp. 123-135. https://doi.org/10.5897/JGRP2014.0432  
[38] K. Paulson, and A. Al-Mreri. “Trends in the Incidence of Rain Height and the Effect on Global Satellite 

Telecommunication,” IET Microwaves Antennas & Propagation, vol. 5, no. 14, pp. 1710-1713, 2011. 
https://doi.org/10.1049/iet-map.2010.0507 

[39] Y. B. Lawal, S. E. Falodun and J. S. Ojo. “Temporal Evolution of Atmospheric Parameter-Profiling on Rain Height 
Over Two Geoclimatic regions in Nigeria,” Journal of Atmospheric and Solar Terrestrial Physics (JASTP). Vol. 211, 
105482. 1364-6826/©2020 Elsevier Ltd, 2020. https://doi.org/10.1016/j.jastp.2020.105482  

 
 

https://doi.org/10.1002/hyp.9433
https://doi.org/10.1214/aos/1013203451
https://doi.org/10.1016/S0167-9473(01)00065-2
https://doi.org/10.1023/B.0000035301.49549.88
https://doi.org/10.1007/978-1-4757-2440-0
https://doi.org/10.5555/2998981.2999003
https://doi.org/10.1038/323533a0
http://www.deeplearningbook.org/
https://web.stanford.edu/~hastie/Papers/ESLII.pdf
https://doi.org/10.1007/978-0-387-84858-7
https://doi.org/10.1002/joc.1096
https://doi.org/10.1029/2005JD006289
https://doi.org/10.5897/JGRP2014.0432
https://doi.org/10.1049/iet-map.2010.0507
https://doi.org/10.1016/j.jastp.2020.105482