## 2 Methodology  
### Data and Study Area  
HF Doppler systems are important tools used to understand the ionosphere-thermosphere system at low latitudes. The HF Doppler system used in our research consists of a transmitter located at Abuja (ABU; geographic coordinates: 7.39\({}^{\circ}\) E, 8.99\({}^{\circ}\) N; dip latitude: \(-1.37^{\circ}\)) and a receiver stationed in Lagos (LAG; geographic coordinates: 3.27\({}^{\circ}\) E, 6.48\({}^{\circ}\) N; dip latitude: \(-1.72^{\circ}\)). Figure 1 presents a schematic diagram of the experimental setup, while the precise locations of the transmitter and receiver within Nigeria are shown in Figure 2. The system operates at a frequency of 6.957 MHz. The transceiver in Abuja consists of an ICOM 718, a stable reference oscillator (OCXO 32 MHz), a terminated folded dipole antenna (Diamond WD30), a Raspberry Pi 3B (Rpi), and a PC monitor, while the receiver in Lagos consists of a digital receiver (WiNRADiO WR-G313i), a stable external reference oscillator, an active loop antenna, and a personal computer. More details about the instrument setup can be found in [29]. Doppler sounding is one of the best-known means of observing the bottomside ionosphere. It is based on the transmission of a stable sine wave at a frequency of several MHz that reflects from the ionosphere, roughly at the height where its frequency \(f\) matches the local plasma frequency, \(f_{p}\). The reflection is exactly at \(f=f_{p}\) for a vertically propagating ordinary wave. The Doppler shift, \(f_{D}\), in a received signal may be expressed as the time derivative of the phase path of the radio signal [30]:  
\[f_{D}=-2\frac{f}{c}\frac{d}{dt}\int_{0}^{ZR}(n.dr)=-2\frac{f}{c}\int_{0}^{ZR} \frac{\delta n}{dN}\cdot\frac{\delta N}{dt}\cdot dr \tag{2}\]  
where \(c\) is the speed of light, \(n\) is the real part of the refractive index for electromagnetic waves, N is the electron (plasma) density, and \(ZR\) is the height of reflection. The observational data had a significant number of missing values, which may affect the integrity of the results. Hence, gridded GNSS TEC data from NASA ([[https://cddis.nasa.gov/Data_and_Derived_Products/GNSS/atmospheric_products.html](https://cddis.nasa.gov/Data_and_Derived_Products/GNSS/atmospheric_products.html)]([https://cddis.nasa.gov/Data_and_Derived_Products/GNSS/atmospheric_products.html](https://cddis.nasa.gov/Data_and_Derived_Products/GNSS/atmospheric_products.html)), referred to as NASA data) for the two locations during the period under review were also considered. Data validation was carried out to determine the reliability of the gridded data using linear regression and correlation analysis. The seasonal analysis employed in this study was adapted from [31]. The seasons were as follows: December sol  
Figure 1: Schematic diagram of the experimental setup. Figure 2: Map of Nigeria showing the locations of the HF Doppler transmitter “Tx” and receiver “Rx”. The dotted blue line across the figure is the approximate location of the dip equator ([[http://wdc.kugi.kyoto-u.ac.jp/igrf/gggm/index.html](http://wdc.kugi.kyoto-u.ac.jp/igrf/gggm/index.html)]([http://wdc.kugi.kyoto-u.ac.jp/igrf/gggm/index.html](http://wdc.kugi.kyoto-u.ac.jp/igrf/gggm/index.html)), website accessed on 23 November 2023). December, January, and February); March equinox (March and April); June solstice, or J season (May, June, July, and August); and September equinox (September and October). Linear regression analysis is used to determine the response of a dependent variable (\(y\)) to another variable called the independent variable (\(x\)). It is assumed that a linear relationship between \(x\) and \(y\) exists in the form  
\[y=mx+c \tag{3}\]  
where \(m\) and \(c\) are the slope and intercept, respectively. For a model that mirrors the observational data, there is a one-to-one correspondence with a slope value of 1 and an intercept of 0 on the y-axis. A correlation analysis gives the level of the linear relationship between two variables. In this study, the Pearson correlation was considered.