A comparative estimate of air temperature from modis land surface temperatures in Ghana

Abstract

This study is aimed at establishing a comparative estimate of air temperature (Tair) from Moderate Resolution Imaging Spectroradiometer (MODIS) Land Surface Temperature (LST) between 1 km and 6 km spatial resolutions and to investigate and quantify spatial variability of LST—Tair relationships. The test area is Republic of Ghana located in the sub-region of West Africa. The purpose of the research is to establish an optimal performance of Tair between two spatial resolutions. Arithmetic Mean method was employed for computation of the datasets. Seventy (70) pairs of composite LSTs consisting of Terra and Aqua MODIS observations which correspond to 70 meteorological stations were used. Due to problem of missing data and outliers, 277 pairs of LST data points per resolution were used. Application of Regression Analyses revealed a good direct correlation existing between values of Tair and LSTs in 1 km with coefficient of determination, R² = 0.8124 while, 6 Km resolution recorded R² = 0.8031. Hence, MODIS LST in 1 km is a better estimator of air temperature in Linear Regression study. Statistical indices of 1 km procedure were found to be lower than the 6 km procedure. The 1 km resolution registered a Root Mean Square Error (RMSE) of 1.97°C, Standard Error of regression, 1.14°C and Coefficient of Variation, CV of 10.19%. Meanwhile, 6 km resolution yielded a RMSE of 2.13°C, Standard Error of regression, 1.22°C and CV of 10.68% respectively. Therefore, 1 km resolution datasets show better accuracy and performance of air temperature estimation than 6 km data products. Hence, a good result would be achieved when 1 km datasets are processed.

Keywords:

• MODIS
• Land Surface Temperature products (LSTs)
• Air Temperature (Tair)
• regression statistics
• validation
• statistical indices
• Coefficient of Variation(CV)

PUBLIC INTEREST STATEMENT

One of the major limitations for monitoring and modelling of temperature variability is the sparse availability of meteorological station measurements coupled with the accuracy of various interpolation methods of air temperature estimation. This study is aimed at establishing a comparative estimate of air temperature from remotely sensed Land Surface Temperature (LST) between two spatial resolutions over Ghana and to investigate spatial variability of LST – Air temperature relationships. It was revealed that LST datasets show a very good performance of air temperature estimation. This study may provide practical information for urban planners, natural resources managers, environmental experts, extension officers, as well as farmers to manage natural landscapes to be sustainable and healthy.

1. Introduction

Satellite remote sensing can provide high spatio-temporal resolution data of land surface temperature (LST) at a global coverage. It might provide a feasible way to improve the spatiotemporal accuracy of estimating air temperature, because it is spatially contiguous and available on a regular basis, especially in regions where ground observations are too sparse to support reliable spatial interpolation. LST is defined as the “skin” temperature of the ground, which was detected by satellites via looking through the atmosphere to the ground (Haas, 2013; Youneszadeh et al., 2015).

LST is not equivalent to air temperature and their relationship is complex from a theoretical and empirical perspective. Most studies about estimating air temperature using remote sensing indexes are based on simple linear regression models. The US National Research Council and the Intergovernmental Panel on Climate Change (IPCC) expressed the need for long-term remotely sensed LST data in global warming studies to overcome the limits of conventional surface air temperature measurements (Colombi et al., 2007; Hadria et al., 2018).

National Aeronautics and Space Administration (NASA’s) earth observation satellites enable a comprehensive set of measurements to improve our understanding of the earth system. The Moderate Resolution Imaging Spectroradiometer (MODIS) is a satellite-based visible/infrared spectroradiometer on-board the Earth Observing System Satellites (Terra and Aqua) to sense radiation of terrestrial, atmospheric, and oceanic phenomena. They are polar-orbiting satellites and MODIS acquire data in 36 spectral bands, which provide important information for many research applications, including oceans and atmospheres (Dugord & Planning, 2013; Luo et al., 2018).

High temporal sampling of LST is achievable with geostationary satellites, but the spatial resolution is relatively coarse. Polar-orbiting satellites provide a more uniform global view of the earth, with similar or even better accuracy and higher spatial resolution in LST. Polar-orbiting thermal sensors pass twice over the same equatorial area and increase to more than 8 times over the polar region in each 24-hour period, covering a vast swath with a width of thousands of kilometers (Al, 2018; Basang et al., 2017). MODIS, an instrument platform on NASA’s Terra and Aqua polar-orbiting satellites, has successfully provided estimates of surface temperature for the past decades at a spatial resolution of 1000 m, a considerably higher resolution than that found in LST products from geostationary satellites (Al, 2018; Wang et al., 2013; Yamunadevi et al., 2017).

Land use is defined as “the arrangements, activities and inputs people undertake in a certain land cover type to produce, change or maintain it”. Land use should be matched with land capability and at the same time it should respect the environment, and global climate systems (Jalili, 2013). Land use land cover is converting over time and the most important driving force of the changes are the human needs. Human population is increasing and it causes transformation of natural ecosystems into human landscapes. Human settlements and especially, large urban and industrial areas significantly modify their environment. It is therefore critical to have detailed information of temporal and spatial land use land cover changes and its rate (Youneszadeh et al., 2015).

Colombi et al. (2014) examined the relationship between remotely sensed, in situ and modelled land surface temperature (LST) over a heterogeneous land-cover (LC) enclosed in alpine terrain. This relationship can help to understand to what extent the remotely sensed data can be used to improve model simulations of land surface parameters such as LST in mountainous areas.

Vonnisa et al. (2022) developed an algorithm to retrieve the vertical structure of the raindrop size distribution (DSD) of rain from simultaneous observations of 47 MHz Equatorial Atmosphere Radar (EAR) and 1.3 GHz Boundary Layer Radar (BLR) at Koto Tabang, West Sumatra, Indonesia (0.20°S, 100.32°E, 865 m above sea level). EAR is sensitive to the detection of turbulence, and BLR is susceptible to identifying precipitation echo. Results show that the precipitation spectrum obtained using the dual-frequency method is higher, more precise, and well-fitted than the single-frequency method. This means that the dual-frequency method has great potential to be used in observing the microphysical process and remote sensing application analysis of DSD at the study area.

Ekwueme and Agunwamba (2021) analysed trend and variability of air temperature and rainfall in regional river basins in five states of South-Eastern region of Nigeria. They examined variability of air temperature and rainfall in the area using the trend analysis approach. The results of Mann Kendall test showed that there was a trend of rainfall pattern in all the capital cities in South-East except Owerri and Awka. They also observed that the trend of rainfall was decreasing for all the study areas in South-East while, the trend of air temperature was increasing with the highest trend rate of 0.04698 ° C/year occurring in Enugu.

Jabal et al. (2022) studied the impact of Climate Change on Crops Productivity Using MODIS-NDVI Time Series in the Dukan Dam Watershed (DDW), Northern Iraq. In this study, an integrated approach of two methodologies, including MODIS Data and Normalized Difference Vegetation Index (NDVI), was employed to extrapolate the long-term changes in agronomic areas from 2000 to 2020. Three independent variables (rainfall, temperature, and agriculture area) were used in the multiple regression analysis to understand the impact of the main drivers affecting the production of crops in DDW. Obtained results showed an increasing trend in crop production as a result of the frequent use of groundwater and surface water sources along with the implementation of greenhouse cultivation.

The sparse availability of meteorological station measurements (density of the station network/number of station per unit area) is frequently insufficient to represent the spatial distribution of air temperature at detailed spatial scales due to lack of high-resolution data, especially in developing countries (Joshi et al., 2016; Lei, 2009).

The ground measurements of LST with widespread distribution of meteorological stations are costly and difficult, which justifies the need to derive these information from remotely sensed observations . In that respect, thermal infrared (TIR) remote sensing is the only cost effective and realistic source of data to retrieve LST in a regional to global scale with different spatial and temporal resolutions (Kestens et al., 2011; Lake, 2011).

Studies have shown that uncertainties exist in satellite-derived LST (Bahi et al., 2016). This implies that validation is a necessary step in order to determine the uncertainties of remotely sensed LST data and to understand their capabilities and limitations in the study area.

During the study period, certain meteorological stations may have encountered problems such as missing data resulting from cloud contaminations, change of measurement locations and update of instruments. A visit to the site revealed that some of the meteorological stations were not in operation at all. The Emena and Fomesua stations in particular were some of the non-operational stations while stations such as Akomadan, Abofour, Pretsea Abokobi, and Jamasi were having missing data. This adds to sparse availability of station networks in the area.

The primary objective of the current study is to establish a comparative estimate of air temperature from remotely sensed MODIS LST between 1 Km and 6 Km spatial resolutions over Ghana and to quantify the spatial variability of LST—Tair relations. We investigate these variations by exploiting Terra and Aqua observations of four LST day time and four LST night time from eight-day MODIS LST datasets. Spatial means of LST observations were computed based on spatial resolutions of 1 km and 6 km respectively. Average MODIS LSTs of these resolutions were each compared with the in-situ air temperature measurements recorded at Meteorological stations. Statistical analyses were employed to estimate the optimal performance of air temperature between the resolutions. Studies have been done to evaluate daily mean air temperature using average MODIS LST at various spatial resolutions. The bridging gap is to do a comparative estimation of air temperature from MODIS LST between 1 km and 6 km spatial resolutions over the study area.

2. Study area and data

2.1. Study area

Ghana, officially the Republic of Ghana, is a country located along the Gulf of Guinea in Atlantic Ocean to its south and in the sub-region of West Africa. Ghana spans an area of 238,535 Km² = (92,099 square miles), and has an Atlantic coastline that stretches 560 kilometers (350 miles) on the Gulf of Guinea. It lies between latitudes 4°45‘N and 11°N, and longitudes 1°15‘E and 3°15‘W. It is bordered by the Ivory Coast in the west, Burkina Faso in the north, Togo in the east and the Gulf of Guinea and Atlantic Ocean in the south (Council & Kingdom, 2018; Worqlul et al., 2019). Figure Figure 1 illustrates the physiological map of Ghana depicting its regional boundaries and location of meteorological stations. The Prime Meridian passes through Ghana, specifically through the industrial port town of Tema. Ghana is geographically closer to the “centre” of the Earth geographical coordinates than any other country; even though the notional centre (0°, 0°) is located in the Atlantic Ocean approximately 614 km (382 miles) off the south-east coast of Ghana on the Gulf of Guinea. Grasslands mixed with south coastal shrublands and forests dominate Ghana, with forest extending northward from the south-west coast of the country on the Gulf of Guinea in the Atlantic Ocean 320 kilometres (200 miles) and eastward for a maximum of about 270 kilometres (170 miles) with the Kingdom of Ashanti or the southern part of Ghana being a primary location for mining of industrial minerals and timber (Codjoe, 2006; Forkuo & Frimpong, 2012).

Figure 1. Physiological map of Ghana depicting regional boundaries and location of meteorological stations.

2.2. Data source

2.2.1. Meteorological data

Air temperature observations were obtained from 70 meteorological stations in the study area. The selected time period for the study ranged from February 2003 to January 2019 according to availability of meteorological station records and MODIS clear sky data. Daily maximum and minimum air temperatures were obtained from the Kumasi Meteorological Agency in Ashanti Region of Ghana.

2.2.2. MODIS data—Terra and aqua satellites

In this study data derived from MODIS product were used. MODIS acquires data in 36 spectral bands onboard Terra and Aqua satellites. The LST product is derived from thermal infrared (TIR) observations in bands 31 (10.78–11.28 μm) and 32 (11.77–12.27 μm) using the generalized split window algorithm (Bahi et al., 2016; Grant, 2017; Parida, 2006; Zhang, 2014). Both sensors are aboard sun-synchronous polar orbiting satellites. The equatorial local solar overpass times of MODIS-Terra is 10:30 descending and 22:30 ascending (daytime/nighttime) and MODIS-Aqua is 13:30 ascending and 01:30 descending (daytime/nighttime). Terra and Aqua satellites are global operational datasets available from digital archives of the US NASA (Kang, 2018; Zhang, 2014; Zhou et al., 2017). MODIS-Terra was launched to the orbit on 18 December 1999 with a descending equatorial overpass time in the morning. Data acquisition from the sensor became available from early 2000. MODIS-Aqua was launched to the orbit on 4 May 2002 with an ascending equatorial overpass time in the afternoon. Data acquisition from this sensor became available since mid-2002. The data products were chosen to be used in this research due to its higher temporal frequency (four observations per day). The ease of access to data products through NASA’s online tools is an added advantage of this research. They have high frequency of global coverage with a large range of view angles spanning from −65° to +65° (Duan et al., 2014; Zhou et al., 2017).

2.2.3.

Supplementary data

In analyzing and evaluating original data, supplementary (extra) data becomes very essential in the research. To clip out the study area, a shapefile which covers the boundary of the study area was obtained from “extract by mask” icon embedded in the spatial analyst tools under ArcGIS environment. Moreover, new regions of Ghana shapefiles were employed in the research. These shapefiles were used to clip all images and data files required for this project. They were then projected into Geographic Coordinate Systems (GCS) WGS 1984, UTM Zone 30ºN with a projection type of transverse mercator (Basommi et al., 2015).

3. Methods

The methodology applied to achieve the research objectives is discussed and summarized in Figure Figure 2. First, 8-day MODIS LST in 1 km and 6 km resolutions were each compared with air temperatures from 70 meteorological stations spatially distributed in the study area (Figure Figure 1). The objective of this study is to do a comparative estimate of air temperature between MODIS LSTs in 1 km and 6 km spatial resolutions over Ghana and to quantify the spatial variability of LST—Tair relations.

Figure 2. Flow chart of research methodology.

3.1. Computation procedure

3.1.1. Computations of air temperature

In-situ (air) temperatures were compiled as follows; daily maximum and minimum temperatures of eight days corresponding to 8-day downloaded MODIS imagery were extracted. Average maximum and minimum air temperatures were then computed. The mean of these two averages was then computed for overall 8-Day average air temperature.

3.1.2. Retrieval of MODIS LST data values

Terra/Aqua MODIS LSTs and their products comprise the following: 1 km 8-day composite, MOD11A2/MYD11A2 (day and night) LSTs and 6 km 8-day composite, MOD11B2/MYD11B2 (day and night) LSTs (Figure Figure 3). In examining temporal variation of LST in relation to air temperature, the composite datasets from 2003 to 2019 were used. LST data values per pixel were extracted from the imagery by using meteorological station coordinates (Figure Figure 3 – (A), (B). (C) and (D)). This will result in an eight (8) LST data values—four (4) observations of Terra sensor and four (4) observations of Aqua sensor respectively (Figure Figure 2).

Figure 3. The spatial distribution of LST data values: (A) 2005 terra MODIS day and night in 1 km; (B) 2005 aqua MODIS day and night in 1 km; (C) 2005 terra MODIS day and night in 6 km; (D) 2005 aqua MODIS day and night in 6 km.

3.1.3. Computations of MODIS LSTs

The extracted MODIS values were entered into Excel spreadsheet format and were multiplied by the scale factor of 0.02 which convert them to degrees Kelvin. This scale factor is defined in MODIS LST product user guide (Al, 2018; Wan, 2013). Afterwards, LST values in Kelvin were subtracted by 273.15 to convert them from degrees Kelvin to degrees Celsius. Mean LSTs in 1 km and 6 km for Terra and Aqua observations were computed.

3.2. Statistical analysis methods

3.2.1. Arithmetic mean and standard deviation

The arithmetic mean value is found by adding together the values of the members of a set and dividing by the number of members in the set (Equation 1(1) $\bar{x}=\frac{1}{n}\sum _{\mathit{i}=1}^1{x}_i$(1) ). The population standard deviation, σ is the square root of population variance (Equation 2(2) $\mathit{\sigma }=\sqrt{\frac{{\sum }_{i=1}^n{\left(x_i-\bar{x}\right)}^2}{\mathit{N}}}$(2) ). and sample standard deviation, s is the square root of sample variance (Equation 3(3) $\mathit{s}=\sqrt{\frac{{\sum }_{i=1}^n{\left(x_i-\bar{x}\right)}^2}{\mathit{n}-1}}$(3) ).

(1) $\bar{x}=\frac{1}{n}\sum _{\mathit{i}=1}^1{x}_i$(1)

(2) $\mathit{\sigma }=\sqrt{\frac{{\sum }_{i=1}^n{\left(x_i-\bar{x}\right)}^2}{\mathit{N}}}$(2)

(3) $\mathit{s}=\sqrt{\frac{{\sum }_{i=1}^n{\left(x_i-\bar{x}\right)}^2}{\mathit{n}-1}}$(3)

Where, $x_i$ is the variable, $\bar{x}$ is the mean, $\mathit{\sigma }$ is population standard deviation, s is sample standard deviation, N is population number (number of population variables), n is the sample number (number of sample variables) (Walther & Moore, 2005;).

3.2.2. Some statistical indices

In addition, some statistical indices were computed to assess the accuracy of the predicted air temperature. These indices were: root mean square error (RMSE), mean bias error (MBE) and mean absolute error (MAE) (Equation 4(4) $\mathit{RMSE}=\sqrt{\frac{1}{\mathit{n}}\mathit{\hspace{0.17em}}\sum _{\mathit{i}=1}^{\mathit{n}}{\left(\mathit{T}\mathrm{\_}\mathit{obs}-\mathit{T}\mathrm{\_}\mathit{est}\right)}^2}\mathit{\hspace{0.17em}}$(4) , Equation 5(5) $\mathit{MBE}=\sum _{\mathit{i}=1}^{\mathit{n}}\left(\frac{\left(\mathit{T}\mathrm{\_}\mathit{obs}-\mathit{T}\mathrm{\_}\mathit{est}\right)}{\mathit{n}}\right)\mathit{\hspace{0.17em}}$(5) and Equation 6(6) $\mathit{MAE}=\sum _{\mathit{i}=1}^{\mathit{n}}\left|\frac{\left(\mathit{T}\mathrm{\_}\mathit{obs}-\mathit{T}\mathrm{\_}\mathit{est}\right)}{\mathit{n}}\right|\mathit{\hspace{0.17em}}$(6) ) (Al, 2018).

(4) $\mathit{RMSE}=\sqrt{\frac{1}{\mathit{n}}\mathit{\hspace{0.17em}}\sum _{\mathit{i}=1}^{\mathit{n}}{\left(\mathit{T}\mathrm{\_}\mathit{obs}-\mathit{T}\mathrm{\_}\mathit{est}\right)}^2}\mathit{\hspace{0.17em}}$(4)

(5) $\mathit{MBE}=\sum _{\mathit{i}=1}^{\mathit{n}}\left(\frac{\left(\mathit{T}\mathrm{\_}\mathit{obs}-\mathit{T}\mathrm{\_}\mathit{est}\right)}{\mathit{n}}\right)\mathit{\hspace{0.17em}}$(5)

(6) $\mathit{MAE}=\sum _{\mathit{i}=1}^{\mathit{n}}\left|\frac{\left(\mathit{T}\mathrm{\_}\mathit{obs}-\mathit{T}\mathrm{\_}\mathit{est}\right)}{\mathit{n}}\right|\mathit{\hspace{0.17em}}$(6)

Where, n is the number of records in validation datasets used in this study, T_obs is the observed variable (Air Temperature) and T_est is the estimated variable (MODIS LST). The RMSE indicator represents the mean deviation between any estimated values and their equivalent observed. Lower values indicate better performance (Bahi et al., 2016; Hadria et al., 2018). The MBE shows the direction of the error bias with zero indicating unbiased estimation of a model. Another indicator used in this research is MAE. The MAE shows the error magnitude, and lower values mean better performance (Sun et al., 2014; Xiao et al., 2018).

3.2.3. Standard error of regression

Standard error of regression estimates how accurate the mean of any given sample represents the true mean of the population. A larger standard error indicates that the means are more spread out, and thus it is more likely that your sample mean is an inaccurate representation of the true population mean. A low standard error shows that sample means are closely distributed around the population mean, which means that your sample is representative of your population. In total, standard error investigates how varying the sample statistic is when numerous samples are extracted from the same population (Equation 7(7) $\mathit{Standard}\mathit{Error}\mathit{of}\mathit{Regression}=\left(\sqrt{1-\mathit{Adjusted}{R}^2}\right)\mathbf{\ast }\mathit{STDEV}\left(\mathit{Y}\right)\mathit{\hspace{0.17em}}$(7) ) (Frey, 2018).

(7) $\mathit{Standard}\mathit{Error}\mathit{of}\mathit{Regression}=\left(\sqrt{1-\mathit{Adjusted}{R}^2}\right)\mathbf{\ast }\mathit{STDEV}\left(\mathit{Y}\right)\mathit{\hspace{0.17em}}$(7)

STDEV(Y) = Standard Deviation of Y-axis (MODIS LST)

3.2.4. P—value

Probability value (P-value) helps to determine the significance of results. The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (>0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis. P-values very close to the cutoff (0.05) are considered to be marginal (could go either way) (Rajagopalan, 2000; Youneszadeh et al., 2015).

3.2.5. Chi-Square test statistic

A chi-square statistic is one way to show a relationship between two categorical variables (Orékan, 2007; Were, 2008) (Equation 8(8) $X_c^2=\sum _{\mathit{i}=1}^k\frac{{\left(O_i-E_i\right)}^2}{E_i}$(8) ). The formula for chi-square statistic used in the chi square test is:

(8) $X_c^2=\sum _{\mathit{i}=1}^k\frac{{\left(O_i-E_i\right)}^2}{E_i}$(8)

The subscript “c” is the degree of freedom. “O” is observed variable (Air Temperature), E is expected variables (MODIS LST) and “i” is the “ith” position in the contingency table. A very small chi square test statistic means that your observed data fits your expected data extremely well. In other words, there is a relationship. A very large chi square test statistic means that the data does not fit very well. In other words, there isn’t a relationship. In theory, if your observed and expected values were equal (“no difference”) then chi-square would be zero—an event that is unlikely to happen in real life.

3.2.6. Regression analysis

3.2.6.1. Linear regression

The least squares regression line (the line of best fit) was employed. If a plot of “n” pairs of data (x, y) for an experiment appears to indicate a “linear relationship” between y and x, then the method of least squares may be used to write a linear relationship between x and y variables (Holderness, 2012; Muzein, 2010).

3.2.6.2. Pearson’s coefficient of correlation (r)

The amount of linear correlation between two variables is expressed by a Pearson’s correlation coefficient, r (Faculty et al., 2014; Holderness, 2012). The smaller the value of r, the less is the amount of correlation which exists. Generally, values of r which are in the range of 0.7 to 1 and −0.7 to − 1 show that a fair amount of correlation exists.

3.2.6.3. Coefficient of determination (?)

R squared (R) or Coefficient of determination shows percentage variation in two variables. The higher the better and it’s always between 0 and 1. It can never be negative—since it is a squared value. Multiplying two r’s results in R squared (R²) value (Forkuo & Frimpong, 2012; García et al., 2005).

3.2.7. Outliers

In statistics, an outlier is an observation point that is distant from other observations. An outlier can cause serious problems in statistical analyses (Eswaramoorthy, 2017; Kang, 2018). Two categorical steps were used to remove outliers. The first step involves using standard deviation method for each dataset and secondly using influential points method. Every step is followed by the calculation of new R and r respectively.

3.2.8. Coefficient of variation

The coefficient of variation (CV) is a widely used quantity to assess the reproducibility of measurement methods or equipment. It is the ratio of the standard deviation to the mean. The higher the value of CV, the greater the level of dispersion around the mean. The lower the value of CV, the more precise the estimate and the better the methods or equipment’s precision. CV is a dimensionless non-negative quantity, usually expressed in percentage, which makes it quite easy to interpret in practice (Equation 9(9) $\mathrm{CV}=\frac{\mathit{\sigma }}{\mathit{\mu }}\ast 100$(9) ) (Traore, 2015; Ã & Zhang, 2010). Consider a random variable, X with mean, μ > 0 and variance $\mathit{\sigma }{\mathit{\hspace{0.17em}}}^2$ assumed to be normally distributed. By definition, CV is given by the expression;

(9) $\mathrm{CV}=\frac{\mathit{\sigma }}{\mathit{\mu }}\ast 100$(9)

4. Results

4.1. Spatial distribution of daytime and nighttime LSTs

Figures Figure 4 (A) and (B) illustrates spatial distribution of Terra and Aqua MODIS daytime and nighttime observations of 1 km LSTs for 2005 images. Visual inspection shows that during daytimes, LST tends to be higher in the northern parts of the study area and lower in the southern sector. A reverse pattern was recognized during night time observations whereby the northern parts of the country were recording lower LSTs and the southern sector was experiencing higher night LSTs. At the same period, water bodies were recording a very higher observation.

Figure 4. (A) spatial distribution of 1 km terra MODIS daytime, and nighttime LSTs of 2005. (B) Spatial Distribution of 1 km Aqua MODIS Daytime, and Nighttime LSTs of 2005 in degrees Celsius

4.2. Spatial distribution of average LSTs

Figures Figure 5 (A, B, C and D) illustrates average LSTs of MODIS image of 2005 and 2019 in two spatial resolutions. It was observed that the highest average LSTs were mainly found in the Northern regions of the country. Moderate average LSTs were basically concentrated around the middle parts of the study area with some patches observed in water body catchments and wetland environments—in the case of 2005 images. Meanwhile, minimum average LSTs were observed in the middle and the southern parts of the country. Visual inspection from Figure Figure 5 reveals a decreasing trend in average LSTs from northern part of the country to southern part. There was also an increase in average LSTs over the years (from 2005 to 2019).

Figure 5. (A to D): the spatial distribution of mean LSTs in °C (2005 and 2019).

4.3. Dealing with outliers

We tested how the removal of possible outliers in the measurements will improve correlation results from regression analysis. A scatter plot by itself is a nonparametric test for the existence of outliers (Haas, 2013). Outliers were removed in batches followed by the calculation of new R² and regression line equation. The first step is using standard deviation method for each dataset and the second step is application of influential point method. The red line in Figure Figure 6 represents the cutoff margin of 2 standard deviations from the mean.

Figure 6. Scatter plots of standardized datasets revealing outliers in air temperature and MODIS LSTs (a 2 standard deviation of the mean was applied).

4.4. Regression statistics

Application of regression analysis to the datasets reveals a significant positive relationships between air temperature measurements and MODIS-derived LSTs (Table 1). The analyses recorded a coefficient of correlation, r of 0.9013 for 1 km spatial resolution while, 6 km resolution registers $\mathit{r}=0.8962$ respectively. In 1 km procedure and with no outlier removed, the coefficient of determination, R² was 0.5494 and increased to 0.6018 with application of standard deviation method. Influential points method further increased it to 0.8124 considerably. With respect to 6 km resolution and with no outlier removed, R² was equal to 0.5714. Application of standard deviation method increased it to 0.6330 while influential points method further increased it to 0.8031 respectively. The Regression analysis revealed output of Probability value (P-value). P-value was at level of significance, α = 0.05, α = 0.01and α = 0.001respectively.

Table 1. Regression statistics from spatially averaged data, with and without outliers

Methods	1 Km			6 Km
	R^2	R	P-Values at $\mathit{\alpha }$ = 0.05 $\mathit{\alpha }$ = 0.01 $\mathit{\alpha }$ = 0.001	R^2	R	P-Values at $\mathit{\alpha }$ = 0.05 $\mathit{\alpha }$ = 0.01 $\mathit{\alpha }$= 0.001
No Outlier Removed	0.5494	0.7412	1.07E-49	0.5714	0.7560	1.21E-60
Standard Deviation Method	0.6018	0.7758	1.94E-53	0.6330	0.7956	1.16E-68
Influential Point Method	0.8124	0.9013	1.13E-70 Statistically Significant	0.8031	0.8962	3.53E-78 Statistically Significant

4.5. Linear regression analysis between air temperature and LST

In this study, 70 pairs of composite LSTs consisting of Terra and Aqua observations which correspond to 70 meteorological stations for each year were used. Due to problems of non-operational stations, missing data resulting from cloud contaminations, change of measurement locations and update of instruments, 321 pairs of LST data points (consisting of 1 km and 6 km MODIS LSTs) were used. Possible outliers in the measurements were removed resulting in 277 pairs of LST data points. They were each plotted against air temperature data from 2003 to 2019 (Figures 7 and 8). The blue points indicate evaluation results for Tair compared with LSTs based on 1 km spatial resolution. The pink circle points on the other hand indicate evaluation results for the 6 km spatial resolution. The red linear fit corresponds to Tair vs LST in 1 km plots while the black linear fit corresponds to Tair vs LST in 6 km plots.

Figure 7. Scatter plot of air temperature versusMODIS LST in 1 km spatial resolution for all meteorological stations.

Figure 8. Scatter plots of air temperature versusMODIS LST in 6 km spatial resolution for all meteorological stations.

4.6. Validation results for combined Stations

Statistical Analysis was employed on the datasets, in order to identify the best estimator of air temperature (Table 2, Figure Figure 9). The procedure for 1 km LST yielded a RMSE of 1.97°C, MAE of 1.56°C, MBE was estimated as 0.72°C and Chi-Square Statistic ($X_c^2$) computed as 42.96 with Standard Error of regression being 1.14°C respectively. Meanwhile, 6 km LST procedure reveals a RMSE of 2.13°C, MAE of 1.77°C, MBE of 1.18°C and $X_c^2$ of 51.25 with Standard Error of regression equals to 1.22°C respectively. Moreover, in the case of 1 km LST method, the mean and standard deviation were equals to 26.90°C and 2.74°C, while the 6 km LST were 26.44°C and 2.82°C respectively. Since the means and standard deviations of the two procedures were nearly equivalent, we therefore rank the two methods by using coefficient of variation (CV) which is defined as the ratio of standard deviation to its mean value. CV of 1 km procedure was equivalent to 10.19% while 6 km was 10.68% respectively.

Table 2. Validation results for combined stations

Resolution (N = 277)	Statistical 1ndices							Coefficient of Variation (%) $\left[\mathit{CV}=\frac{\mathit{Std}\mathit{Dev}}{\mathit{Mean}}\mathbf{\ast }100\right]$
	Mean	Std Dev	Std Error	RMSE	MAE	MBE	Chi-Square Statistic (N = 277)
1 km	26.90	2.74	1.14	1.97	1.56	0.72	42.96	10.19
6 km	26.44	2.82	1.22	2.13	1.77	1.18	51.25	10.68

Figure 9. Validation results for Tair—LST distribution of combined stations (without Mean and Chi-Square Statistic).

4.7. Time-series of temperature datasets

Table 3 illustrates spatially averaged time-series of three temperature datasets in this study while Figure 10 shows trend lines of temperature datasets from 2003 to 2019. Air temperature is shown in blue. MODIS-derived LST in 1 km resolution shown in Red, while MODIS-derived LST in 6 km is shown in black. Comparison of these datasets reveals differences in temperature variability at different dates.

Table 3. Spatially averaged temperature of three datasets

8 Day	T_air			LST
				1 Km			6 Km
	Mean	Std Dev	CV	Mean	Std Dev	CV (%)	Mean	Std Dev	CV (%)
2003	29.02	1.86	0.06	28.61	2.85	10.0	28.09	2.87	10.2
2005	26.90	1.34	0.05	26.01	2.07	8.0	25.52	1.98	7.8
2007	26.10	1.21	0.05	24.71	1.48	6.0	24.25	1.43	5.9
2009	27.65	1.21	0.04	26.99	1.64	6.1	26.42	1.83	6.9
2011	29.28	1.68	0.06	29.40	2.98	10.1	28.09	3.22	11.5
2013	26.42	1.30	0.05	25.69	2.13	8.3	25.19	2.14	8.5
2015	25.51	0.93	0.04	24.66	1.69	6.9	23.85	1.49	6.2
2017	28.51	0.95	0.03	27.35	1.42	5.2	27.02	1.38	5.1
2019	30.30	1.42	0.05	30.10	2.06	6.8	29.51	2.34	7.9

Figure 10. Trend lines of temperature datasets: Air temperature (Tair), 1 km MODIS LST and 6 km MODIS LST, 2003 to 2019.

5. 5. Discussions

5.1. Spatial distribution of daytime and nighttime LSTs

Spatial Distribution of LST observations revealed that the northern sector of the study area recorded higher LSTs during daytimes, while southern parts experience lower LSTs. A reverse pattern was recognized during night time observations whereby the northern parts of the study area experienced lower LSTs and southern sector recorded higher night LSTs. At the same period water bodies were recording a very higher LSTs which tends to be distributed around volta lake catchments and marshy areas of the country. This may be due to the specific heat capacities of various land cover types and climatic conditions experienced in various regions of the country This is in consonant with Yang et al. (2017) who revealed that land covers had noticeable influences on estimating air temperatures. Water has a high specific heat capacity of 4182 J/kgºC (Youneszadeh et al., 2015). Hence, it can be considered as a cooler land use during daytimes and hotter during night times. These findings seem to be consistent with research of Jalili (2013) who reported that inland water and offshore areas have higher night LSTs.

5.2. Spatial distribution of average LSTs

Figures Figure 5 (A, B, C and D) reveal a decreasing trend in average LSTs from the northern part of the country to the southern part. This may be attributed to climatic conditions experienced in various regions of the country and the specific heat capacities of various land cover types. This is because northern part of Ghana is located in the savanna zone characterized by tropical grasslands. This area experiences warm temperatures all year round. It has dispersed trees and there is enough sunlight for undergrowth which is mostly grass and shrubs. The southern part of Ghana is dominated by rain forest zone having high mean annual rainfall of up to 2,200 mm. Moreover, the coastal savannah zone is characterized by convectional rainfall due to the nearness to the water body (sea). The reason could also be attributed to the uni-modal rainfall pattern experience in the northern sector of Ghana indicating a single rainy season in a year, while it is bi-modal in the southern sector indicating a double rainy season in a year (Amekudzi et al. 2015; Council & Kingdom, 2018).

Visual inspection of Figure Figure 5 also revealed that average LSTs increases considerably over the years (from 2005 to 2019). Locally, this may be due to the specific heat capacities of various land cover types and climatic conditions experienced in various regions of the country. But globally, it could be attributed to global warming resulting from increasing surface temperatures which has been predicted over the years. The findings is consistent with the research of Global and Ecology (2017) who reported that the world’s leading scientists has warned of rising temperatures and increasing frequency and intensity of extreme events over the years. Also, El-Magd et al. (2016) stated that global warming has obtained more attention because of increasing global mean surface temperature since the late 19th century.

5.3. Regression statistics

Regression Analyses results revealed that 1 km resolution procedure recorded R² = 0.8124 which was greater than that of 6 km resolution (R² = 0.8031) respectively. The two scatter plots revealed a good direct correlation existence between values of Air Temperature at weather stations and MODIS derived LSTs. But, the 1 km resolution dataset was showing a better accuracy of air temperature estimation than the 6 km data product. Hence, a good result would be achieved when 1 km datasets are processed in Linear Regression study. Moreover, the analysis also revealed output of P-value (Probability value) and the smaller the p-value, the more significant the relationship. Since all P-values in the regression analyses fall below the level of significance, α (p < 0.05, P < 0.01, and p < 0.001) (Table 1)(. Therefore, we reject the null hypothesis and conclude that all the correlations are statistically significant for α = 0.05, α = 0.01and α = 0.001respectively.

5.4. Validation analyses

Validation analyses employed on the datasets revealed the following indices; The 1 km LST procedure recorded a RMSE of 1.97°C and MAE of 1.56°C while, 6 km procedure yielded a RMSE of 2.13°C and MAE of 1.77°C respectively. RMSE is an indicator which represents the mean deviation between any estimated values and their equivalent observed with lower values indicating better performance (Bahi et al., 2016; Hadria et al., 2018). Also, MAE shows the error magnitude and lower values mean better performance. Its value is used to express the long-term mean difference in degrees Celsius between two variables (Sun et al., 2014; Xiao et al., 2018). In these two cases, better performance was recognized in 1 km MODIS LST datasets (Table 2, Figure Figure 9). The MBE was estimated as 0.72°C for 1 km LST and 1.18°C for 6 km LST which is quite higher. MBE is an index which shows the direction of the error bias with zero indicating unbiased estimation. The positive values of MBE indicate that MODIS LST datasets were underestimated compared with the Tair measurements. Chi-Square Statistic ($X_c^2$) was computed for the two resolutions. From Table 2, $X_c^2$ for 1 km LST was estimated as 42.96 while 6 km LST was 51.25 respectively. Since a low value of chi-square statistic is an indication of a high correlation existence between two sets of data, the 1 km dataset shows an optimal and a better performance of air temperature estimation than 6 km resolution. Moreover, the mean and standard deviation of 1 km method were equal to 26.90°C and 2.74°C respectively. While, the 6 km resolution method recorded a mean value of 26.44°C and a standard deviation value of 2.82°C. The closer and smaller the standard deviation value beside its mean value, the better the performance and vice versa. Therefore, 1 km LST resolution would have a better accuracy of air temperature estimation in these analyses. In addition, Standard Error of regression index yielded a value of 1.14°C with respect to 1 km LST resolution while that of 6 km procedure index was 1.22°C respectively. A larger standard error of regression indicates that the means are more spread out, and thus it is more likely that the sample mean is an inaccurate representation of the true population mean. A low standard error shows that the sample means are closely distributed around the population mean, which means that the sample is a representative of the population. On account to this, optimal performance is seen in 1 km dataset. This study is consistent with the research of Colombi et al. (2014) who revealed that Inverse Distance method shows a RMSE of 2.23°C, while remote sensing procedure shows a RMSE of 1.89°C and therefore better results are achieved by processing remotely sensed data. They further reported that their results are satisfactory since the obtained RMSE, approximately 2°C, can be considered acceptable for the purposes of providing daily mean air temperature values as an input for distributed and semi-distributed models.

Coefficient of Variation (CV) of 1 km procedure was equivalent to 10.19% while 6 km was 10.68%. The higher the value of CV, the greater the level of dispersion around its mean and the lower the value of CV, the more precise the estimate. Therefore, 1 km spatial resolution with smaller CV value would have a better performance of air temperature estimation.

Various statistical indices employed in this research revealed that 1 km LST datasets were lower than the 6 km data products. Therefore, 1 km LST dataset shows an optimal performance and a better accuracy of air temperature estimation than the 6 km resolution. Hence, 1 km MODIS LST data products is the best estimator of air temperature measurements and therefore better results would be achieved when its datasets are processed.

5.5. Time-series of temperature datasets

Time-series of temperature datasets used in this study; consisting of Air temperature, 1 km MODIS-derived LSTs and 6 km MODIS-derived LSTs revealed differences in temperature variability at different dates (Table 3, Figure Figure 10). Visual inspection of Figure Figure 10 reveals that ground-based air temperature values were found to be higher than 1 km and 6 km MODIS-derived LSTs. This would be the case as surfaces were less warm than adjacent air masses during those periods. Moreover, 1 km LST dataset were found to be higher than the 6 km LSTs and also observed to be closer to the Tair dataset. Therefore, better precision is achieved with the 1 km resolution. This adds to the optimal and a better performance of 1 km MODIS LST dataset for air temperature estimations which have been explained above.

6. Conclusions

The study seeks to bridge the gap by analyzing a comparative estimate of air temperature from MODIS LST between 1 km and 6 km spatial resolutions over Ghana. Various studies have been done to evaluate mean air temperature using average MODIS LST at various spatial resolutions. The results of this study confirm that there was a good direct correlation existence between values of Air Temperature at weather stations and MODIS derived LSTs. But, 1 km resolution datasets shows a very strong performance of air temperature estimation than the 6 km datasets. All P-values revealed that correlations are statistically significant. The 1 km LST dataset reveals various parameters (R² = 0.8124, P-value = 1.13E–70 P<α at a significant level, α = 0.05, 0.01 and 0.001 respectively). While at the same period, 6 km LST relation yielded the following parameters (R² = 0.8031, P-value = 3.53E–78, P < α at α = 0.05, 0.01 and 0.001 respectively). Hence, 1 km resolution datasets is a better estimator of air temperature in linear regression study.

Statistical indices employed in this study revealed that values of 1 km procedure were lower than the 6 km method. The 1 km resolution procedure registered a Root Mean Square Error (RMSE) of 1.97°C, Standard Error of regression of 1.14°C and Coefficient of Variation, CV = 10.19%. Meanwhile, 6 km resolution yielded a RMSE of 2.13°C, Standard Error of regression = 1.22°C and CV = 10.68% respectively. Therefore, 1 km resolution datasets shows a better accuracy and performance of air temperature estimation than the 6 km datasets. Hence, a good result would be achieved when 1 km datasets are processed. Also, results are satisfactory since the obtained RMSE, approximately 2°C, can be considered acceptable for the purpose of providing mean LST values as an input for air temperature measurements.

Average LSTs increase considerably over the years and may be attributed to global warming resulting from increasing surface temperatures which had been predicted in the past. It was revealed that climatic conditions experienced in various regions of the country and specific heat capacities of land cover types were having a noticeable influence on LST estimates. Another knowledge being added to archival literature is the fact that air temperature estimation (LST measurements) is better in smaller resolutions than higher ones.

Further developments will consider mainly three topics. At first, calibrations of LST datasets could also be performed using different spatial and temporal resolutions within a differing topography. This could be greatly helpful in areas where meteorological stations are sparse or non-existent. Secondly, different satellite datasets could be employed for air temperature estimation and validation. In addition, further studies could investigate specific heat capacities of various land cover types of the study area. Furthermore, one of the major requirements of air temperature estimations would be the use of cloud-free images. However, it might not be possible to have images completely free from such contaminations. Therefore, cloud infilling algorithms might be useful in such cases.

Acronyms used

Table

Aqua MODIS 8-Day Land Surface Temperature and Emissivity 1 kilometer level 3 gridded product (MYD11A2)	9
Aqua MODIS 8-Day Land Surface Temperature and Emissivity 6 kilometer level 3 gridded product (MYD11B2)	9
Coefficient of Variation (CV)	13
Estimated Variable (MODIS LST) (T_est)	11
Geographic Coordinate Systems (GCS)	7
Intergovernmental Panel on Climate Change (IPCC)	3
Land Cover types (LC types)	3
Land surface temperature (LST)	3
Mean Absolute Error (MAE)	11
Mean Bias Error (MBE)	11
Moderate Resolution Imaging Spectroradiometer (MODIS)	3
National Aeronautics and Space Administration (NASA)	3
Observed Variable (Air Temperature) (T_obs)	11
Probability value (p-value)	12
Root Mean Square Error (RMSE)	11
Root Mean Squared Deviation (RMSD)	11
Standard Deviation (Std Dev)	18
Standard Error (Std Error)	18
Terra MODIS 8-Day Land Surface Temperature and Emissivity 1 kilometer level 3 gridded product (MOD11A2)	9
Terra MODIS 8-Day Land Surface Temperature and Emissivity 6 kilometer level 3 gridded product (MOD11B2)	9
Thermal Infrared (TIR)..,	6
Universal Transverse Mercator (UTM)	7
World Geodetic System (WGS)	7

Acknowledgments

I offer my sincerest gratitude to my supervisors Prof. Eric K. Forkuo and Prof. E. M. Osei Jnr. for their great knowledge, support, patience and help in building this research structure. Their insightful ideas, encouragements and ability to keep me on track were helpful throughout the duration of this work. They always provide useful advice and comments on how best to improve my work. We also acknowledge the esteemed lecturers in Geomatic Engineering Department of KNUST for regular preliminary thesis presentations. In fact, their time, inputs, suggestions and constructive criticisms have helped improve this work. Many thanks to Mr Tieku, the director of Kumasi Meteorological Agency, Ghana for providing us with free climate data. In fact, his persistent help in field experiments was very remarkable and memorable. In addition, we are also thankful to NASA for access to their websites for free datasets. In addition, I am very grateful to my mother who have just demised and I’m dedicating this thesis to her for her support and encouragement. I would also like to extend my thanks to my children for their support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Adubofour Frimpong

Adubofour Frimpong is a lecturer and a research scholar in the Department of Civil Engineering, Koforidua Technical University, Koforidua, Ghana. His main research areas include Geographic Information Systems (GIS) and Remote Sensing. Prof. E. M. Osei Jnr, PhD, FGhIS, MAARSE, MIEEE, MFIG, LS. Geomatic Engineering Department College of Engineering KNUST Kumasi Email: [email protected], [email protected], [email protected], Tel: [phone]. https://www.researchgate.net/profile/EdwardOseiJnrscholar.google.com

The two professors are broadly interested in geospatial data analysis with particular emphasis on developing GIS/Remote Sensing (RS) models, change detection, land use/land cover change dynamics, etc. Our current research work is focused on estimation of air temperature from remotely sensed land surface temperatures in Ghana.

Eric Kwabena Forkuo

Eric Kwabena Forkuo is a professor and a research scholar in the Department of Geomatic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana. His main research areas include Geoinformatics (GIS) and Remote Sensing.