2.2. Data sources
This study used Landsat 7 Enhanced Thematic Mapper Plus (2000 and 2010) and Landsat 8 Operational Land Imager (OLI)/Thermal Infrared Sensor (TIRS) data of 2020. These Landsat images were obtained from United State Geological Survey (https://www.usgs.gov/products/data-and-tools/realtime-data/remote-land-sensing-and landsat), during dry season and cloud free in the months of January and December (Table 1). All the data were projected to UTM (Zone 32) and WGS 84 datum. The study area lies with 185 path and 57 raw reference system. The acquired data were used for LUM classification. Data category and its source are presented in Table 1.
The maximum and minimum air temperatures data used in this study are from CRU (Climate Research Unit) of the University of East Anglia in the United Kingdom. These data have been available since 1901 via the site https://climexp.knmi.nl/selectfield_obs2.cgi?id=2833fad3fef1bedc6761d5cba64775f0/ in NetCDF format, on a monthly time step and at a spatial resolution of 0.25° x 0.25 °. Precipitation and temperature data from CRU have been used to validate CMIP models in Logone basin which is a sub-basin of the Lake Chad basin (Nkiaka et al., 2018).
Table 1
Images
|
Path
|
Row
|
Pixel size
|
Acquisition date
|
Sources
|
Landsat ETM + of 2000
|
185
|
57
|
30*30
|
Jan. 2000
|
U.S. Geological Survey
|
Landsat ETM + of 2010
|
185
|
57
|
30*30
|
Dec. 2000
|
U.S. Geological Survey
|
Landsat OLI/TIRS of 2020
|
185
|
57
|
30*30
|
Jan. 2020
|
U.S. Geological Survey
|
2.3 Land‑Use/Land‑Cover Classification
Landsat images were classified using the supervised maximum likelihood classification, using the software Sentinel Application Platform (SNAP) which is made available to the general public free by the European Space Agency (ESA), via the site https://step.esa.int/main/download/snap-download/. This enabled us to perform a diachronic analysis of the evolution of land-use in the basin studied. This operation was preceded by operations of preprocessing and recognition of objects in the field by photography and GPS (Global Positioning System). Satellite images preprocessing refers to all the process applied to raw data to correct geometric and radiometric errors that characterize certain satellite images. These errors are generally due to technical problems with the satellites and interactions between outgoing electromagnetic radiation and atmospheric aerosols, also called “atmospheric noise”. The atmospheric disturbances are influenced by various factors that are present on the day of acquisition, including weather, fires, and other human activities. They affect all the images acquired by passive satellites including Landsat 4-5-7 and 8. The downloaded Landsat images being orthorectified, the preprocessing involved atmospheric correction of the images and reprojection into the local system (WGS_84_UTM_Zone_32N). For this, neo-channels were created, to increase the readability of the data by enhancing certain properties less obvious in the original image, thus showing more clearly the elements of the scene. Three indices are therefore created, namely: the Normalized Difference Vegetation Index (NDVI, Eq. 1), the brightness index (BI, Eq. 2) and the Normalized Difference Water index (NDWI, Eq. 3) (Ebodé et al., 2020). These indices respectively highlight vegetated surfaces, sterile (non-chlorophyllin) elements such as urban areas and water bodies. The formulae used in creating these indices are:
\(\mathbf{N}\mathbf{D}\mathbf{V}\mathbf{I}=\frac{\mathbf{N}\mathbf{I}\mathbf{R}-\mathbf{R}}{\mathbf{N}\mathbf{I}\mathbf{R}+\mathbf{R}}\) (Eq. 1)
\(\mathbf{B}\mathbf{I}={({\mathbf{R}}^{2}+{\mathbf{N}\mathbf{I}\mathbf{R}}^{2})}^{0.5}\) (Eq. 2)
\(\mathbf{N}\mathbf{D}\mathbf{W}\mathbf{I}=\frac{\mathbf{N}\mathbf{I}\mathbf{R}-\mathbf{M}\mathbf{W}\mathbf{I}\mathbf{R}}{\mathbf{N}\mathbf{I}\mathbf{R}+\mathbf{M}\mathbf{W}\mathbf{I}\mathbf{R}}\) (Eq. 3)
where NIR: ground reflectance of the surface in the near-infrared channel; R: ground reflectance of the surface in the red channel and MWIR: ground reflectance of the surface in the mid-wave infrared channel. The use of Google Earth, as well as the spaces sampled from the GPS, made it possible to identify with certainty the impervious areas (buildings, savannas, bare soils, and crops), water bodies (large rivers, lakes and ponds) and forest (secondary, degraded, non-degraded and swampy) of each mosaic. Before the classification, the separability of the spectral signatures of the sampled objects to avoid interclass confusion was assessed by calculating the “transformed divergence” index. The value of this index is between 0 and 2. A value > 1.8 indicates a good separability between two given classes. The different classes used in this study show good separability between them, irrespective of the image considered, with indices > 1.9. The validation of the classifications obtained was carried out using the confusion matrix, making it possible to obtain treatment details to validate the choice of training plots. After validating the land-use/land cover maps, the statistical and spatial differences of each class between studied periods were evaluated.
2.3. LST Retrieval
The LST is influenced by topography, landscape composition, land cover, urbanization and global change (Hamstead et al., 2015; Feng et al., 2018). It is affected by albedo; the vegetation covers and the soil moisture (Chibuike et al., 2018). The ETM + and TIRS thermal band calibration constants in this study are presented in Table 2. The LST using Landsat ETM + and Landsat 8 Operational Land Imager has been calculated (Chibuike et al., 2018) in many steps.
Table 2
ETM + and TIRS thermal band calibration constants
|
Constant 1-K1 Watts/(m2*ster*µm)
|
Constant 2- K2 Kelvin
|
Landsat 7
|
666.09
|
1282.71
|
Landsat 8
|
774.8853
|
1321.0789
|
2.3.1. Step I: Conversion of the digital number (DN) into spectral radiance (L)
In the present study, digital numbers were converted to at-sensor radiances sensor, prior to calculating brightness temperature. The ETM + DN values ranges between 0 and 255 (Eq. 4).
\(\text{L}{\gamma }=\frac{\text{L}\text{M}\text{A}\text{X}{\gamma }-\text{L}\text{M}\text{I}\text{N}{\gamma }}{\text{Q}\text{C}\text{A}\text{L}\text{M}\text{A}\text{X}-\text{Q}\text{C}\text{A}\text{L}\text{M}\text{I}\text{N}}\times \left(\text{D}\text{N}-\text{Q}\text{C}\text{A}\text{L}\text{M}\text{I}\text{N}\right)+\text{L}\text{M}\text{I}\text{N}{\gamma }\) (Eq. 4)
where \(\text{Q}\text{C}\text{A}\text{L}\) is the quantized calibrated pixel value in Digital Number \(\text{D}\text{N}\), \(\text{L}\text{M}\text{I}\text{N}{\gamma }\) is the spectral radiance that is scaled to \(\text{Q}\text{C}\text{A}\text{L}\text{M}\text{I}\text{N}\) in ( Wm2ster− 1µm− 1 ), \(\text{L}\text{M}\text{A}\text{X}{\gamma }\) is the spectral radiance that is scaled to \(\text{Q}\text{C}\text{A}\text{L}\text{M}\text{A}\text{X}\) in ( Wm2ster− 1µm− 1 ), \(\text{Q}\text{C}\text{A}\text{L}\text{M}\text{I}\text{N}\) is the minimum quantized calibrated pixel value corresponding to \(\text{L}\text{M}\text{I}\text{N}{\gamma }\) in \(\text{D}\text{N}\), and \(\text{Q}\text{C}\text{A}\text{L}\text{M}\text{A}\text{X}\) is the maximum quantized calibrated pixel value corresponding to \(\text{L}\text{M}\text{A}\text{X}{\gamma }\) in \(\text{D}\text{N}=255\).
At first, digital numbers were converted from Landsat 8 Operational Land Imager to spectral radiance, then brightness temperature was extracted from Thermal Remote Sensing Data (Kayet et al., 2016). In The Landsat 8 data on Radiance Multiplier (ML) and Radiance Add (AL), the thermal infrared (TIR) band was converted into spectral radiance \(L\gamma\) using the approach provided by Chander & Markhan (2003) and used by Chibuike et al. (2018) as indicated in (Eq. 5).
\(\text{L}{\gamma }=\left({M}_{L}\text{*}{Q}_{cal}\right)+{A}_{L},\) (Eq. 5)
where \(\text{L}{\gamma }\) is the top of atmosphere spectral radiance (Wm2ster− 1µm− 1), \({M}_{L}\) is the band-specific multiplicative rescaling factor from the metadata (RADIANCE_MULT_ BAND\(\_x\), where \(x\) is the band number), \({A}_{L}\) is the bandspecific additive rescaling factor from the metadata (RADIANCE_ ADD_BAND\(\_x\), where \(x\) is the band number) and \({Q}_{cal}\) is the quantized and calibrated standard product pixel values (DN).
2.3.2. Step II: Conversion to Brightness Temperature
Brightness temperature and average atmospheric temperature were used to calculate LST based on land surface emissivity (Yang et al., 2017). The specific formula for mono-window algorithm for retrieving LST was used (Li et al., 2005). The black body temperature was obtained from the spectral radiance using Plank’s inverse functions. Spectral radiance values for band 6 and 10 were converted to radiant surface temperature under assumptions of uniform emissivity using pre-launch calibration constants (Chibuike et al., 2018). The Landsat satellite imagery was converted from spectral radiance to more physical useful variable (Kumar, 2017). The conversion formula is presented in (Eq. 6).
\(\text{T}=\frac{{K}_{2}}{\text{l}\text{n}(\frac{{K}_{1}}{L\gamma }+1)},\) (Eq. 6)
where \(\text{T}\) is effective at satellite temperature in Kelvin, \({K}_{2}\) is calibration constant 2, \({K}_{1}\) is calibration constant 1, and \(L\gamma\) is spectral radiance in Wm2ster− 1 µm− 1.
2.3.3. Step III: Land Surface Emissivity Estimation
The land surface emissivity estimation was performed (Chibuike et al., 2018) and computed using Eq. 7.
$$\text{Ƹ}=0.005*{P}_{v}+0.986 \left(\text{E}\text{q}\text{u}\text{a}\text{t}\text{i}\text{o}\text{n} 7\right)$$
where \({P}_{v}\) is the vegetation proportion obtained (Carlson and Ripley, 1997) using Eq. 8.
$$\text{P}\text{V}={\left[\frac{\text{N}\text{D}\text{V}\text{I}-\text{N}\text{D}\text{V}\text{I}\text{m}\text{i}\text{n}}{\text{N}\text{D}\text{V}\text{I}\text{m}\text{a}\text{x}-\text{N}\text{D}\text{V}\text{I}\text{m}\text{i}\text{n}}\right]}^{2} \left(\text{E}\text{q}\text{u}\text{a}\text{t}\text{i}\text{o}\text{n} 8\right).$$
In this study, the calculated radiant surface temperature was corrected for emissivity (Chibuike et al., 2018) using Eq. 9.
$$LST=\frac{TB}{1\left(\gamma \frac{TB}{P}\right)\text{l}\text{n}\text{Ƹ}} \left(\text{E}\text{q}\text{u}\text{a}\text{t}\text{i}\text{o}\text{n} 9\right)$$
where LST is land surface temperature (in Kelvin), TB is radiant surface temperature (in Kelvin), \({\gamma }\) is the wavelength of emitted radiance (10.8 µm), \(P\) is \(h*c/\sigma\)(1.438*10− 1 mK), \(h\) is Planck’s constant (6.26*1010−34 Js), \(c\) is the velocity of light (2.998*108 m/s), \(\sigma\) is Stefan Boltzmann’s constant (1.38*10− 23 J K− 1), and \(\text{Ƹ}\) is land surface emissivity.
Finally, LST result from Landsat ETM + and OLI/TIRS was converted into degree Celsius, by subtracting 273.15. To convert temperature, the degree Kelvin to degree Celsius (Eq. 6).
2.3.4. Analysis of annual maximum and minimum air temperatures
The Mann-Kendall test at the 95% significance level was used to analyze mean annual maximum and minimum air temperatures. This test is based on the test statistic “S” defined as follow:
$$\text{S}=\sum _{\text{i}=1}^{\text{n}-1}\sum _{\text{j}=\text{i}+1}^{\text{n}}\text{s}\text{g}\text{n}\left(\text{x}\text{j}-\text{x}\text{i}\right) \left(\text{E}\text{q}\text{u}\text{a}\text{t}\text{i}\text{o}\text{n} 10\right)$$
Where the xj are the sequential data values, n is the length of the data set, and sgn = (θ) if θ > 1, 0 if θ = 0 and − 1 if θ < 0. There is no significant trend in the series analyzed when the calculated p-value is above the chosen significance level.