Time series forecasting techniques can be categorized as either single-variable or multiple-variable. In exploring Univariate Time-series Forecasting, a solitary variable is employed to analyze the isolated time series. Multivariate Time-series Forecasting involves multiple variables, where one variable is time and the others are multiple parameters. The univariate forecasting method was implemented to predict upcoming Tmax, Tmin, and max wind speed, assuming that future time series values are exclusively influenced by past values, indicating that this approach may offer distinct benefits compared to multivariate time series forecasting (Brownlee. 2019).
Choosing input variables with utmost attention can substantially enhance the effectiveness of a model. Feature selection is crucial in determining a model's most valuable input variables, significantly improves its performance and efficiency. The choice of optimal input variables for the output variable is possible through different methods, including the Gamma test, PCA, and Average Mutual Information (AMI) (Batina et al. 2011; Ghorbani et al. 2022). Average Mutual Information, as a measuring method, quantifies the information acquired about a random variable through another random variable. Appraising the connection between input and output variables assists in identifying the most informative input variables for selection purposes (Wallot and Mønster, 2018). When examining a time series from a previous period, AMI assists in quantifying the amount of information gathered about its value at a particular lag, considering time series analysis. Figure 6 provides insights into the relationship between the lowest AMI value and a delay, allowing for determining optimal delay values for minimum and maximum temperature and wind speed at the six cities.
Mathematica software was used in this research to determine the optimal parameters with the AMI selection method and train DL and CNN models to predict the maximum and minimum temperature and maximum wind speed monthly. Statistical and visual analysis were utilized to predict the maximum and minimum temperature, and maximum wind speed values to evaluate the performance of two distinct models, DL and CNN. Table 3 displays the calculated values for performance measures like R, RMSE, and NS during test periods.
Table 3
Analyzing statistics on performance levels of DL and CNN models in test periods for six important cities
|
Tmax
|
Tmin
|
Winmax
|
City
|
Model
|
RMSE
(Co)
|
R
|
NS
|
Model
|
RMSE
(Co)
|
R
|
NS
|
Model
|
RMSE
(km/h)
|
R
|
NS
|
Abuja
|
CNN-M1
|
0.209
|
0.998
|
0.97
|
CNN-M1
|
0.203
|
0.997
|
0.93
|
CNN-M1
|
0.652
|
0.998
|
0.97
|
CNN-M2
|
0.103
|
0.999
|
0.98
|
CNN-M2
|
0.104
|
0.998
|
0.95
|
CNN-M2
|
0.463
|
0.999
|
0.98
|
CNN-M3
|
0.230
|
0.998
|
0.97
|
CNN-M3
|
0.111
|
0.998
|
0.95
|
CNN-M3
|
0.783
|
0.998
|
0.97
|
DL-M1
|
1.399
|
0.955
|
0.87
|
CNN-M4
|
0.244
|
0.997
|
0.93
|
CNN-M4
|
0.536
|
0.998
|
0.97
|
DL-M2
|
1.014
|
0.956
|
0.81
|
CNN-M5
|
0.104
|
0.999
|
0.97
|
DL-M1
|
2.477
|
0.979
|
0.90
|
DL-M3
|
1.319
|
0.950
|
0.85
|
DL-M1
|
1.677
|
0.923
|
0.8
|
DL-M2
|
2.402
|
0.977
|
0.91
|
|
|
|
|
DL-M2
|
1.429
|
0.976
|
0.88
|
DL-M3
|
2.379
|
0.979
|
0.92
|
|
|
|
|
DL-M3
|
1.872
|
0.853
|
0.86
|
DL-M4
|
1.305
|
0.989
|
0.93
|
|
|
|
|
DL-M4
|
1.399
|
0.979
|
0.90
|
|
|
|
|
|
|
|
|
DL-M5
|
1.008
|
0.993
|
0.91
|
|
|
|
|
Lagos
|
CNN-M1
|
0.111
|
0.998
|
0.98
|
CNN-M1
|
0.126
|
0.998
|
0.97
|
CNN-M1
|
1.034
|
0.998
|
0.98
|
CNN-M2
|
0.131
|
0.998
|
0.98
|
CNN-M2
|
0.092
|
0.999
|
0.99
|
CNN-M2
|
0.885
|
0.998
|
0.99
|
CNN-M3
|
0.093
|
0.999
|
0.99
|
DL-M1
|
1.187
|
0.843
|
0.64
|
CNN-M3
|
0.941
|
0.998
|
0.98
|
DL-M1
|
1.302
|
0.805
|
0.68
|
DL-M2
|
1.011
|
0.950
|
0.67
|
CNN-M4
|
1.191
|
0.997
|
0.95
|
DL-M2
|
1.237
|
0.927
|
0.69
|
|
|
|
|
CNN-M5
|
1.175
|
0.997
|
0.96
|
DL-M3
|
1.127
|
0.970
|
0.71
|
|
|
|
|
DL-M1
|
1.926
|
0.979
|
0.93
|
|
|
|
|
|
|
|
|
DL-M2
|
1.029
|
0.989
|
0.96
|
|
|
|
|
|
|
|
|
DL-M3
|
1.148
|
0.989
|
0.94
|
|
|
|
|
|
|
|
|
DL-M4
|
1.703
|
0.988
|
0.92
|
|
|
|
|
|
|
|
|
DL-M5
|
1.052
|
0.989
|
0.96
|
Sokoto
|
CNN-M1
|
0.113
|
0.999
|
0.99
|
CNN-M1
|
0.163
|
0.997
|
0.99
|
CNN-M1
|
1.177
|
0.997
|
0.96
|
CNN-M2
|
0.106
|
0.999
|
0.99
|
CNN-M2
|
0.156
|
0.998
|
0.97
|
CNN-M2
|
0.648
|
0.998
|
0.99
|
CNN-M3
|
0.149
|
0.998
|
0.97
|
CNN-M3
|
0.206
|
0.995
|
0.96
|
CNN-M3
|
0.772
|
0.998
|
0.99
|
CNN-M4
|
0.100
|
0.999
|
0.99
|
CNN-M4
|
0.168
|
0.997
|
0.99
|
DL-M1
|
1.745
|
0.978
|
0.90
|
DL-M1
|
1.618
|
0.919
|
0.70
|
DL-M1
|
1.528
|
0.974
|
0.76
|
DL-M2
|
2.332
|
0.974
|
0.89
|
DL-M2
|
1.587
|
0.961
|
0.74
|
DL-M2
|
1.781
|
0.895
|
|
DL-M3
|
2.757
|
0.944
|
0.86
|
DL-M3
|
1.668
|
0.929
|
0.71
|
DL-M3
|
1.745
|
0.893
|
|
|
|
|
|
DL-M4
|
1.980
|
0.881
|
0.68
|
DL-M4
|
2.222
|
0.868
|
|
|
|
|
|
Table 3
|
Tmax
|
Tmin
|
Winmax
|
Cities
|
Model
|
RMSE
(Co)
|
R
|
NS
|
Model
|
RMSE
(Co)
|
R
|
NS
|
Model
|
RMSE
(km/h)
|
R
|
NS
|
Maiduguri
|
CNN-M1
|
0.139
|
0.999
|
0.99
|
CNN-M1
|
0.177
|
0.997
|
0.98
|
CNN-M1
|
0.420
|
0.998
|
0.98
|
CNN-M2
|
0.121
|
0.999
|
0.99
|
CNN-M2
|
0.097
|
0.999
|
0.99
|
CNN-M2
|
0.366
|
0.998
|
0.99
|
CNN-M3
|
0.232
|
0.998
|
0.97
|
CNN-M3
|
0.180
|
0.997
|
0.98
|
CNN-M3
|
0.468
|
0.998
|
0.98
|
DL-M1
|
1.698
|
0.895
|
0.72
|
CNN-M4
|
0.153
|
0.998
|
0.97
|
DL-M1
|
1.872
|
0.985
|
0.95
|
DL-M2
|
1.465
|
0.944
|
0.75
|
DL-M1
|
2.248
|
0.959
|
0.88
|
DL-M2
|
1.640
|
0.988
|
0.96
|
DL-M3
|
1.414
|
0.966
|
0.79
|
DL-M2
|
1.620
|
0.971
|
0.90
|
DL-M3
|
2.042
|
0.979
|
0.95
|
|
|
|
|
DL-M3
|
1.779
|
0.958
|
0.89
|
|
|
|
|
|
|
|
|
DL-M4
|
1.373
|
0.982
|
0.91
|
|
|
|
|
Calabar
|
CNN-M1
|
0.194
|
0.997
|
0.97
|
CNN-M1
|
0.149
|
0.998
|
0.99
|
CNN-M1
|
0.660
|
0.997
|
0.96
|
CNN-M2
|
0.141
|
0.998
|
0.99
|
CNN-M2
|
0.120
|
0.998
|
0.99
|
CNN-M2
|
0.599
|
0.998
|
0.99
|
CNN-M3
|
0.204
|
0.996
|
0.97
|
CNN-M3
|
0.151
|
0.998
|
0.99
|
CNN-M3
|
0.648
|
0.997
|
0.97
|
CNN-M4
|
0.163
|
0.998
|
0.98
|
DL-M1
|
1.562
|
0.929
|
0.64
|
CNN-M4
|
0.726
|
0.997
|
0.7
|
DL-M1
|
1.232
|
0.841
|
0.67
|
DL-M2
|
1.362
|
0.930
|
0.64
|
DL-M1
|
1.972
|
0.978
|
0.94
|
DL-M2
|
1.151
|
0.914
|
0.72
|
DL-M3
|
1.262
|
0.972
|
0.65
|
DL-M2
|
1.965
|
0.979
|
0.94
|
DL-M3
|
1.165
|
0.953
|
0.72
|
|
|
|
|
DL-M3
|
2.381
|
0.979
|
0.93
|
DL-M4
|
1.428
|
0.803
|
0.67
|
|
|
|
|
DL-M4
|
1.194
|
0.989
|
0.95
|
Port Harcourt
|
CNN-M1
|
0.174
|
0.997
|
0.98
|
CNN-M1
|
0.150
|
0.998
|
0.97
|
CNN-M1
|
1.036
|
0.997
|
0.96
|
CNN-M2
|
0.160
|
0.998
|
0.99
|
CNN-M2
|
0.111
|
0.999
|
0.99
|
CNN-M2
|
0.609
|
0.998
|
0.99
|
CNN-M3
|
0.215
|
0.996
|
0.97
|
CNN-M3
|
0.153
|
0.997
|
0.97
|
CNN-M3
|
0.648
|
0.997
|
0.98
|
CNN-M4
|
0.162
|
0.998
|
0.99
|
DL-M1
|
1.587
|
0.923
|
0.62
|
CNN-M4
|
0.863
|
0.997
|
0.98
|
DL-M1
|
1.194
|
0.897
|
0.70
|
DL-M2
|
1.516
|
0.842
|
0.62
|
DL-M1
|
2.249
|
0.979
|
0.87
|
DL-M2
|
1.171
|
0.902
|
0.71
|
DL-M3
|
1.287
|
0.941
|
0.64
|
DL-M2
|
1.348
|
0.989
|
0.94
|
DL-M3
|
1.853
|
0.762
|
0.68
|
|
|
|
|
DL-M3
|
1.945
|
0.980
|
0.93
|
DL-M4
|
1.875
|
0.867
|
0.69
|
|
|
|
|
DL-M4
|
1.440
|
0.983
|
0.93
|
According to Table 3, obtained from evaluating the performance indices of the two models used, it is possible to understand the acceptable performance of both DL and CNN models derived from artificial intelligence and machine learning. According to the table, the deep learning model has favorable results for the minimum and maximum temperature parameters. However, it performed better predicting the maximum wind speed than other parameters. In general, deep learning with error (1.008 < RMSE < 2.75), correlation coefficient (0.764 < R < 0.993) and Nash Sutcliffe coefficient (0.97 < NS < 0.99). On the other hand, the convolutional neural network model had a high performance compared to deep learning in predicting all three parameters, so it has an error (0.097 < RMSE < 0.941), correlation coefficient (0.996 < R < 0.999) and Nash Sutcliffe coefficient (0.97 < NS < 0.99). According to the results obtained from the AMI method, this study used four delays. By analyzing the used scenarios, it can be found that the delay until two months ago (M2) has good results compared to the rest of the scenarios and can be used to predict the parameters. The results of this research can be verified with previous research.
A study conducted by Jeong et al. (2021) examines the use of a deep neural network and convolution neural network for predicting temperatures based on time-series weather data obtained from an automatic weather station and image data from RDAPS. Elmaz et al. (2021) present a unique Convolutional Neural Networks-Long Short-Term Memory (CNN-LSTM) architecture that leverages convolutional layers for feature extraction and LSTM for capturing sequential dependencies in temperature data analysis. For hourly temperature prediction, Hou et al. (2022) incorporated two advanced deep-learning techniques, a convolutional neural network (CNN) and long short-term memory (LSTM), into their CNN-LSTM network model. Utilizing 60,133 hourly climatological measurements consisting of air temperature, dew point, air pressure, wind direction, wind speed, and cloud cover obtained between January 2000 and October 2020 at the Yinchuan climatological station in China led to the formation of the training and validation sets and result show CNN-LSTM model accurately forecasts hourly temperatures. Trebing and Mehrkanoon (2022) made a unique model utilizing convolutional neural networks (CNNs) to predict wind speeds. Considering Fig. 7, which shows the time series graphs for the best scenarios of the CNN and DL models in the test phase, it can be seen that the CNN model has a better forecast than the DL model in all six cities and in all three maximum, medium and minimum modes have acceptable efficiency.
Figure 8 shows the box diagram of three parameters of minimum and maximum temperature and maximum wind speed for six critical cities in Nigeria. By observing Fig. 8, it can be found that the DL model has satisfactory results in predicting and estimating the maximum wind speed compared to other parameters (minimum and maximum temperature). Its box shape is very similar to the actual values. On the other hand, compared with the CNN model, this model (DL) has significant errors in some cities, and its box plot differs significantly from the observed values. In general, it can be said that the CNN model is more accurate than the DL model in all selected parameters and cities.