The Central African Republic is a landlocked country located between approximately 2˚N-11˚N and 14˚E-27˚E in the heart of Central Africa (Figure 1). The topographic height over Central African Republic is also shown in Figure 1. The CAR region is predominantly characterized by plains, with two elevated terrain areas located on its eastern and western flanks. The climate is characterized by two dominant seasons: a dry season (November-March) and a rainy season (April-October). The seasonal cycle is governed primarily by the north-south migration of the Intertropical Convergence Zone (ICTZ). During the dry season, reduced cloud cover and rainfall promote stronger surface heating, particularly in the northern regions. During the rainy season, enhanced cloudiness and deep convection lad to more homogeneous temperature distributions.

Figure 1. Spatial distribution of topographic height over Central African Republic, showing the study area.

2.2.1. Satellite Derived Temperature Data (AMSU-A)

The satellite-derived atmospheric temperature data used in the present study is obtained from the Advanced Microwave Sounding Unit-A (AMSU-A) instruments flown on the series of polar-orbiting satellites from the National Oceanic and Atmospheric Administration (NOAA). AMSU-A is a passive microwave radiometer that is designed to measure the thermal emission from atmospheric oxygen absorption bands at 50 - 60 GHz frequency ranges, thus providing vertically weighted atmospheric temperature profiles in the troposphere and lower stratosphere ([37]). It consists of 15 channels of microwaves with frequency ranges between 23.8 and 89 GHz.

AMSU-A instruments have flown on several polar-orbiting satellites from the NOAA series, including NOAA-15, NOAA-16, NOAA-17, NOAA-18, NOAA-19, as well as the European Space Agency’s MetOp-A, MetOp-B, and MetOp-C satellites since 1998, thus providing a long-term global atmospheric temperature data set ([9]). It has a swath width of 1650 km with a nadir spatial resolution of 40 - 50 km. Satellite data from AMSU-A are also useful in climate studies in the Central African Republic (CAR), where there are extremely limited data from ground-based meteorological stations. For data-scarce regions, satellite data are useful in providing spatially continuous data on the variability and trends in atmospheric temperature. However, it should be noted that there are various sources of uncertainty in using data from AMSU-A. For example, there are concerns related to surface emissivity, effects of clouds and precipitation, and those related to the retrieval of atmospheric temperature using microwave radiances ([21]). To mitigate potential contamination from complex surface conditions, this investigation restricts attention to AMSU-A channels 5, 7, and 9, with weighting function maxima near 500 hPa, 250 hPa, and 100 hPa, respectively. Consequently, the observed brightness temperatures are indicative of atmospheric temperatures at these respective levels.

It should also be noted that AMSU-A makes use of a cross-scan approach in collecting data, where a change in scan angle varies the field of view of the instrument. While it has a spatial resolution of 50 km at nadir points, it reduces to almost 200 km at the extremes of the scan swath. There are also differences in various instruments flown on successive satellites, where calibration biases and orbital drift are also concerns ([21]). For climate studies to be consistent, several studies have established homogenized temperature data sets from the AMSU-A satellite-based brightness temperatures. This has been done through the inter-satellite calibration techniques to produce long-term stable atmospheric temperatures for climate trend analysis ([21]; [30]).

The present study utilizes the AMSU-A gridded climate dataset developed by ([29]). The AMSU-A gridded atmospheric temperature dataset is created using a step-by-step process that includes calibrating the measurements, checking for quality issues, correcting for diurnal variation, adjusting for differences between satellites, removing cloud effects, and building layers of temperature data using specific channel weights. Brightness temperature data from different NOAA satellites are matched during times when they overlap to make sure the data stays consistent over time ([29]). Then, monthly average temperatures are put on a regular grid and averaged across regions to create time series. This helps reduce sudden changes and lowers errors caused by satellite movement or switching between satellites. Testing has shown that the AMSU-A dataset gives a good picture of how the atmosphere’s temperature changes over time and shows long-term trends ([29]). Comparing it with radiosonde data and modern climate models shows that they agree well in the middle and upper parts of the atmosphere.

As CAR is situated predominantly over land, this study focuses on AMSU-A channel 5 and channels with higher-peaking weighting functions to minimize the influence of uncertainties in surface emissivity. Table 1 provides the pressure levels corresponding to the peaks of the weighting functions for each channel. The analysis period spans January 2000 to December 2020. While the AMSU-A channels actually measure vertically weighted brightness temperatures, the reanalysis data provide air temperatures at specific pressure levels. As a result, the two are physically different quantities, and any numerical comparison between the two is therefore necessarily approximate. To help mitigate this problem, the reanalysis temperature profiles were convolved with the appropriate AMSU-A weighting functions to produce synthetic brightness temperatures, prior to the calculation of trends, with the differences between the original and synthetic data being recognised as a systematic uncertainty, as discussed in Section 7.

2.2.2. Reanalysis Datasets

Global reanalysis products represent another category of regularly gridded long-term datasets suitable for climate research. Employing sophisticated numerical models, these products utilize model simulations as background fields and incorporate as many reliable observations as possible through data assimilation techniques to generate analysis fields that are statistically optimal estimates of the true state. While continuously refining their numerical weather prediction models, numerous countries have developed their own global reanalysis datasets. To ensure the generality of our findings, three reanalysis products developed by different institutions are selected herein: ERA5, JRA-55, AND MERAA-2.

ERA5 (ECMWF 5th Generation Atmospheric Reanalysis) is the fifth generation atmospheric reanalysis produced by the European Center for Medium Range Weather Forecasts (ECMWF). ERA5 is generated using the Integrated Forecasting System (IFS) and a four-dimensional variation (4D-VAR) data assimilation scheme. It provides globally consistent atmospheric, land, and ocean variables at an hourly temporal resolution and a native horizontal resolution of approximately 31 km, with 137 vertical levels extending from the surface to 0.01 hPa. ERA5 covers the period from 1940 to the present and assimilates a wide range of satellite andin situ observations, offering substantial improvements over earlier ECMWF reanalysis in terms of spatial resolution, temporal continuity, and representation of physical processes ([14])

MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) is produced by NASA’s Global Modeling an Assimilation Office using Goddard Earth Observing system Model, Version 5 (GEOS-5), and an incremental analysis update assimilation scheme. MERRA-2 covers the period from 1980 to the present and has a native horizontal resolution of approximately 0.5˚ × 0.625˚, with 72 vertical levels extending from surface to 0.01 hPa. A distinctive feature of MERRA-2 is its explicit assimilation of aerosol observations, with improves the representation of radiative processes and their influence on atmospheric temperature ([12]).

JRA-55 (The Japanese 55-year Reanalysis) is produced by the Japan meteorological Agency using a state-of-the-art global spectral model and four-dimensional variations data assimilation system. JRA-55 spans the period from 1958 to the present and is provided at a horizontal resolution of approximately 55 km with 60 vertical levels. A key strength of JRA-55 is the consistent assimilation of historical satellite observations using modern retrieval algorithms, which improves temporal homogeneity across the entire record. JRA-55 has demonstrated good performance in representing large scale atmospheric circulation and temperature variability, particularly in the free troposphere ([16]).

For each reanalysis dataset, monthly mean air temperature fields at standard pressure levels (100, 250, and 500 hPa) were extracted for the Central African Republic domain. To ensure inter dataset consistency, all data were interpolated onto a common regular grid of 0.5˚ × 0.5˚. The CAR domain is given by the geographic mask 14˚E-27˚E, 2˚N-11˚N, with the restriction that only land points are considered. The bilinear interpolation brings all the data to the common 0.5˚ grid. The area-weighted spatial averaging uses cosine latitude weighting. Months with less than 20 valid data points are set to missing and not interpolated. Less than 0.5% of the data points are set to missing in any of the data sets over the period 2000-2020.

Spatial averaging was then applied to generate regional mean time series for each pressure level and dataset.

To ensure methodological transparency and reproducibility, this section explicitly presents the mathematical formulations used for linear and nonlinear trend estimation.

2.3.1. Temperature Anomalies

Monthly temperature anomalies are calculated by removing the mean seasonal cycle from the original temperature time series. Let T m ( y ) denote the monthly mean air temperature for month m in year y . The climatological mean for month mean over the analysis period is defined as:

where N is the total number of years in the study period (2000-2020). The temperature anomaly is then computed as:

2.3.2. Seasonal Averaging

Seasonal mean temperature anomalies are computed by averaging monthly anomalies over the two dominant climatic seasons of the Central African Republic: the dry season and the rainy season. For a given season s, consisting of M s months, the seasonal anomaly is defined as:

This approach explicitly reflects the bimodal seasonal structure of the CAR climate and avoids the use of boreal-standard seasons (e.g., DJF, JJA), which are not physically representative of the region.

2.3.3. Linear Trend Estimation

Let T(t) denote the monthly mean air temperature anomaly at time t, where t = 1, 2, ∙∙∙, N resents the time index in months overs the study period (2000-2020). The linear trend is estimated using ordinary least squares regression.

where α is the intercept, β(t) is the linear trend coefficient (˚C month⁻¹) and ε is the residual term representing internal climate variability and observational noise. The statistical significance of the trends can be evaluated by a two-tailed Student’s t-test. Serial autocorrelation is addressed by using the effective sample size N e f f = N ( 1 − r ) / ( 1 + r ) , where r is the lag-1 autocorrelation of the OLS residuals. The standard error is multiplied by N / N e f f prior to the calculation of confidence intervals. All trends in Table 1 are statistically significant at p < 0.05 after this correction.

2.3.4. Nonlinear Trend Estimation Using Ensemble Empirical Mode Decomposition (EEMD)

To better understand the mechanisms driving climate warming, we need more than just average warming rates, we also need to look at how those rates change over time. Linear trend analysis gives a basic idea of long-term changes, but it assumes the warming rate stays the same, which isn’t always true. This means it can miss periods when warming speeds up, slows down, or even shifts in a big way. More and more, scientists are seeing that warming in the atmosphere, especially over land, doesn’t follow a straight path. It can change because of factors like shifts in heat absorption, interactions between land and air, and natural climate swings ([29]). Spotting these changes is especially important in places like the Central African Republic, where faster warming could make heat worse, hurt farming, and damage ecosystems.

To characterize time varying and nonlinear temperature, this study applies the Ensemble Empirical Mode Decomposition (EEMD) technique to monthly temperature anomaly time series, following the methodology of ([29]). The only authoritative EEMD parameters used throughout the study are as follows: The number of ensemble members = 100, the amplitude of the white noise = 0.2 × σ of the original series, and the standard EMD stopping criterion of “residual monotone or <= 1 extremum” as recommended by [38] and consistent with the findings of [29]. The erroneous sentence stating 400 ensemble members has been deleted EEMD is an adaptive, data driven decomposition method designed to separate non stationary and nonlinear signals into physically meaningful components without prescribing any basis functions.

Given a temperature anomaly time series T ( t ) , it is decomposed as

where ( C k ( t ) ) denotes the intrinsic mode functions (IMFs) representing oscillatory components from high to low frequency, and ( R ( t ) ) is the residual component representing the nonlinear trend.

The decomposition proceeds iteratively as follows:

1) Identify all local maxima and minima of the current residual ( R k − 1 ( t ) ) .

2) Construct upper and lower envelopes using cubic spline interpolation.

3) Compute the local mean m k ( t ) of the two envelopes.

4) Extract the IMF:

5) Update the residual:

The EEMD decomposition process will continue in an iterative manner until the residual is either a monotonic function or has at most one extremum, to ensure that there are no more oscillatory components that can be extracted. In this research, the EEMD algorithm was carried out with 100 ensemble members, with the amplitude of the added white noise set to 0.2 times the standard deviation of the original time series, as suggested by ([38]). For each ensemble member, the intrinsic mode functions (IMFs) were extracted in a sequential manner, and the ensemble mean of the corresponding IMFs was computed to remove mode mixing caused by noise.

After removing the first k = 13 IMFs representing oscillatory components from high to low frequency. The EEMD decomposition was performed with 400 ensemble members and a noise amplitude of 0.2 times the standard deviation of the input series, with 10 sifting iterations per IMF.

During the dry season, i.e., from November to March, the temperature of the atmosphere in the CAR is determined by the combined effects of diminished cloudiness, weakened convection, and enhanced surface heating resulting from the southward shift of the Intertropical Convergence Zone (ITCZ). As the sky is clear, solar insolation is enhanced, resulting in an increase in sensible heat flux, especially over the northern savanna regions, where the vegetation cover is meager. On the other hand, surface heating is moderated in the southern part of the CAR, where the tropical forest is denser, along with enhanced evapotranspiration.

Figure 2. Spatial distribution of temperature at 100, 250, and 500 hPa for satellite data (left panels) and ERA5 (right panels) on dry season.

Figure 2 presents the spatial distributions of temperature at various levels over Africa during the dry season across different datasets. As precipitation effects are minimal during the dry season, temperatures exhibit predominantly zonal patterns, with extensive high-temperature regions covering the equatorial zone. The dry season shows a meridional temperature gradient characterized by lower temperatures in the north and higher temperatures in the south, indicating that temperature at these altitudes is primarily determined by insolation. Although the spatial structures are broadly similar among the different datasets, discrepancies exist in the location of high-temperature regions; At 100 hPa, the AMSU-A data show an additional high-temperature center in the southern part of the region. In the lower troposphere, although the AMSU-A data can also well reproduce the meridional temperature gradient, the land-sea thermal contrast is relatively pronounced.

Figure 3. Spatial distribution of temperature at 100, 250, and 500 hPa for JRA-55 (left panels) and MERRA-2 (right panels) on dry season.

Differences in spatial structure are also evident among the reanalysis products (Figure 3). At 100 hPa, JRA-55 exhibits a distinctly different warm region compared to the other two reanalysis datasets, resembling more closely the AMSU-A data, with the maximum temperature occurring in the northern part of the region, whereas ERA5 and MERRA-2 center their warm anomalies over the tropics. At 500 hPa, ERA5 displays a more pronounced zonal temperature distribution, while JRA-55 and MERRA-2 show two extrema on either side of the equator, a pattern more consistent with the satellite observations.

During the rainy season (April-October), the northward migration of the Intertropical Convergence Zone (ITCZ) intensifies cloud cover, deep convection, and strong-scale moisture convergence in the Central African Republic (CAR). More cloud cover reduces the surface net shortwave radiation because of increased cloudiness, and latent heating from convection also modifies the vertical temperature profile. As a result, the horizontal temperature gradients are reduced and the spatial homogeneity of the atmospheric temperature field is increased compared to the dry season.

Figure 4. Spatial distribution of temperature at 100, 250, and 500 hPa for satellite data (left panels) and ERA5 (right panels) on rain season.

Figure 5. Spatial distribution of temperature at 100, 250, and 500 hPa for JRA-55 (left panels) and MERRA-2 (right panels) on rain season.

During the rainy season, atmospheric temperatures at all levels over Africa exhibit a gradual decrease from north to south, which may be attributed to the greater oceanic coverage in the southern part of the region. The AMSU-A data faithfully reproduce the characteristic pattern of higher temperatures in the north and lower temperatures in the south, and accurately capture the vertical structure over CAR, with colder temperatures in the upper troposphere and warmer temperatures in the lower troposphere. However, certain discrepancies exist between the two datasets. The spatial structure of brightness temperatures from AMSU-A appears notably smoother across all channels. Additionally, AMSU-A channel 9 (approximately 100 hPa) reveals a warm region in the southern part of the domain, which contrasts markedly with the ERA5 reanalysis. Similarly, the warm region in the southern domain identified in AMSU-A channel 5 (approximately 500 hPa) is shifted noticeably northward compared to that in ERA5.

Temperatures during the rainy season generally exhibit a gradual increase from south to north, which is opposite to the dry season, indicating that solar radiation exerts a dominant influence on the spatial distribution of temperature. Similarly, the AMSU-A dataset can well reproduce the atmospheric spatial structure in the reanalysis data, including the local high-temperature zone in the northeastern part of the region at 100 - 250 hPa. The characteristic that the high-temperature zone expands to the entire latitudinal belt at 500 hPa is also well captured. However, the land-sea contrast in the AMSU-A brightness temperature data is more pronounced, which may be an important factor responsible for its failure to adequately reproduce the low temperatures in the southeastern part of the region at 500 hPa (Figure 4).

There are also certain differences among different reanalysis datasets, as illustrated in Figure 5. At 100 hPa, the JRA-55 dataset shows an abnormally strong high-temperature zone in the southeastern part of the region. At 250 hPa, neither JRA-55 nor MERRA-2 exhibits an obvious zonal high-temperature zone near 10˚S. The temperature structure in this region from ERA5 is more similar to that from AMSU-A data.

Figure 6. Vertical cross section for dry season (a) Satellite; (b) ERA5; (c) JRA-55; and (d) MERRA-2.

Figure 6 presents vertical cross-sections along the equator for different datasets during the dry season. All datasets exhibit a characteristic decrease in temperature with altitude, as well as a gradual decline in temperature from the equator toward higher latitudes on both sides. As the dry season coincides with winter in the Northern Hemisphere, the warm region is shifted predominantly toward the Southern Hemisphere, while temperatures in the Northern Hemisphere decrease rapidly with increasing latitude. The AMSU-A data faithfully reproduce the latitudinal temperature variations in the lower troposphere; however, at higher altitudes, the AMSU-A brightness temperatures display markedly different latitudinal patterns, even exhibiting a reversed structure with colder temperatures over the tropics and warmer temperatures on both sides. Examination of the AMSU-A weighting functions reveals that channel 9 brightness temperature is influenced not only by upper-tropospheric temperatures but also by lower-stratospheric temperatures. Given that the tropopause height is higher over the tropics than at higher latitudes, this vertical structural difference likely contributes to the higher brightness temperatures on the northern and southern flanks relative to the equatorial region at these altitudes.

Figure 7. Vertical cross section for rainy season (a) Satellite; (b) ERA5; (c) JRA-55; and (d) MERRA-2.

During the rainy season, temperatures at all levels similarly decrease with altitude; however, the latitudinal temperature variation differs markedly from that of the dry season, as illustrated in Figure 7. Although the overall pattern remains one of warmer tropics and cooler extratropics, the low-level warm region shifts distinctly northward into the Northern Hemisphere due to the boreal summer timing of the rainy season. Additionally, a bimodal temperature structure emerges, with a temperature minimum occurring near 5˚N in the Northern Hemisphere—likely associated with the northward migration of the Intertropical Convergence Zone (ITCZ). The ITCZ maintains intense convective cloud bands year-round, where high albedo reflects solar radiation and evaporative cooling from precipitation creates a “cold trough” in temperature. This equatorial cloud-rain cooling, alternating with subtropical desert heat, produces the characteristic “cool center, warm flanks” bimodal structure of African summer temperatures. The AMSU-A data likewise capture the northward displacement of the low-level warm region and reproduce the corresponding bimodal structure in the lower troposphere. However, at higher altitudes, the AMSU-A brightness temperatures exhibit an increase with latitude toward both northern and southern flanks—a pattern distinctly different from the reanalysis products. This discrepancy likely contributes to the notable differences in climatic trends between AMSU-A brightness temperatures and reanalysis products at upper levels.