Designing “liveable” cities as climate change effects are felt all over the world has become a priority to city authorities as ways are sought to reduce rising temperatures in urban areas. Urban Heat Island (UHI) effect occurs when there is a difference in temperature between rural and urban areas. In urban areas, impervious surfaces absorb heat during the day and release it at night, making urban areas warmer compared to rural areas which cool faster at night. This Urban Heat Island effect is particularly noticeable at night. Noticeable negative effects of Urban Heat Islands include health problems, air pollution, water shortages and higher energy requirements. The main objective of this research paper was to analyze the spatial and temporal relationship between Land Surface Temperature ( LST) and Normalized Density Vegetation Index (NDVI) and Built-Up Density Index ( BDI) in Upper-Hill, Nairobi Kenya. The changes in land cover would be represented by analyzing the two indices NDVI and BDI. Results showed the greatest increase in temperature within Upper-Hill of up to 3.96 °C between the years 2015 and 2017. There was also an increase in impervious surfaces as indicated by NDVI and BDI within Upper-Hill and its surroundings. The linear regression results showed a negative correlation between LST and NDVI and a positive correlation with BDI, which is a better predictor of Land Surface Temperature than NDVI. Data sets were analyzed from Landsat imagery for the periods 1987, 2002, 2015 and 2017 to determine changes in land surface temperatures over a 30 year period and it’s relation to land cover changes using indices. Visual comparisons between Temperature differences between the years revealed that temperatures decreased around the urban areas. Minimum and maximum temperatures showed an increase of 1.6 °C and 3.65 °C respectively between 1987 and 2017. The comparisons between LST, NDVI and BDI show the results to be significantly different. The use of NDVI and BDI to study changes in land cover due to urbanization, reduces the time taken to manually classify moderate resolution satellite imagery.
One of the important parameters in urban climate is Land Surface Temperature (LST), which directly controls the Urban Heat (UH) effect [
Data about the earth’s surface over a wide area can be extracted from satellite imagery at high temporal and spatial resolutions. Changes in land cover, specifically vegetation health, have been carried out using near infra-red as the vegetation portion reflects highly in this range [
The aim of the paper is to investigate what impact these changes in land cover have had on the land surface temperature in Upper-Hill using indices derived from satellite products. Another aim is to analyze which indices would be a better predictor for land surface temperature. The hottest months in Kenya are February and March while the coldest is in July until mid-August. The research was carried out during the months of January and February due to availability of cloud-free imagery.
Upper Hill, is approximately 4 Km from the city center of Nairobi and it has seen rapid developments over the years.
Landsat imagery acquired on February 13th 1987, February 10th 2002, January 5th 2015 and January 26th 2017 were used as the primary data source for deriving the land surface temperature and indices that would be used to determine the land cover changes. Data sets were acquired during the hot- season but due to cloud cover, imagery within the same month was not available. Data analysis involved using spatial metrics to determine the relationship with land surface temperatures derived from Landsat time-series imagery. Statistical modeling using ordinary linear regression to obtain this relationship was used. The study area is approximately 15 Km2. A buffer of one kilometer from Upper-Hill boundary was
defined and used to demonstrate the aforementioned relationship. Wu et al. [
Level 1T Imagery acquired from Landsat 5 TM, Landsat 7 ETM+ and Landsat 8 sensors were downloaded as L1T data from the USGS [
D N 7 = ( slope λ ∗ D N 5 ) + intercept λ (1)
where DN 7 is Landsat 7 ETM+ and DN 7 is Landsat 5 TM equivalent DN data. The slope and intercept are the inverse of those described by Vogelmann et al. [
The values obtained were then used to calculate the Top-of-Atmosphere using Equation (2).
Spectral information is in digital number (DN), which has to be converted to reflectance values for analysis. Landsat 5 and 8 use the same formula for their bands which is different from Landsat 7. ArcGIS 10.4 was used to compute the Land Surface Temperature for both day and night time imagery.
Landsat 7 ETM+ consists of two thermal bands, 6a and 6b, obtained at 120 m and resampled to 30 m. Band 6a was employed since it has low radiometric variance and used in areas where vegetation cover is present. Equation (2) shows the conversion from DN to Top of Atmosphere (TOA) radiometric values for Landsat 7 and the results are shown in
L λ = ( L max − L min Q calmax − Q calmin ) ∗ ( Q c a l − Q calmin ) + L min (2)
Band | Slope | Intercept |
---|---|---|
1 | 0.943 | 4.21 |
2 | 1.776 | 2.58 |
3 | 1.538 | 2.50 |
4 | 1.427 | 4.80 |
5 | 0.984 | 6.96 |
7 | 1.304 | 5.76 |
Satellite Date | LMAX | LMIN | QCALMAX | QCALMIN |
---|---|---|---|---|
LS5 13-02-1987 | 15.303 | 1.238 | 255 | 1 |
LS7 10-02-2002 | 12.650 | 3.200 | 255 | 1 |
where,
Lλ: spectral radiance,
Qcalmin: minimum quantized calibrated pixel value in DN,
Qcalmax: maximum quantized calibrated pixel value in DN,
Qcal: DN value of the pixel,
Lmin: minimum radiance detected by the sensor,
Lmax: maximum radiance detected by the sensor.
Landsat 8 consists of two thermal bands, band 10 and 11. USGS [
L λ = M L Q c a l + A L (3)
where:
Lλ is Top of Atmosphere (TOA) radiance in (Watts/m2*um),
ML is Band-specific multiplicative rescaling factor (RADIANCE_MULT_BAND_x where m is the band number),
Qcal is the digital number,
AL is the band specific additive rescaling factor (RADIANCE_ADD_BAND_x where x is the band number).
To obtain the at-satellite brightness, Equation (4) was used for the analysis:
Satellite Date | ML | AL | K1 (Wm−2∙sr1∙μm−1) | K2 (Kelvin) |
---|---|---|---|---|
LS8_05-01-2015 | 3.3420 E-04 | 0.10000 | 774.8853 | 1321.0789 |
LS8_26-01-2017 | 3.3420 E-04 | 0.10000 | 774.8853 | 1321.0789 |
T B = K 2 / ln ( K 1 L λ + 1 ) (4)
where:
TB is the satellite brightness temperature in degrees Celsius,
K1 is the band specific thermal conversion constant (K1_CONSTANT_BAND_x, where x is band 10),
K2 is the band specific thermal conversion constant (K2_CONSTANT_BAND_x, where x is band 10).
Data outputs were exported as Geotiff imagery from ERDAS IMAGINE to ArcGIS 10.4 for further data analysis.
To determine the Land Surface Emissivity (LSE), NDVI was first computed using the reflectance values of red and near infra-red (NIR) bands of the Landsat image. The 16-bit integer values in Landsat 8 were converted to Top of Atmosphere reflectance as shown in Equation (5) [
ρ λ ′ = M K Q c a l + A K (5)
where:
ρ λ ′ = Top of Atmosphere (TOA) planetary spectral reflectance without solar angle correction and is unitless,
MK = band-specific multiplicative rescaling factor (REFLECTANCE_MULT_BAND_x where x is the band number),
Qcal = the digital number of band_x,
AK = the band specific additive rescaling factor (REFLECTANCE_ADD_BAND_x where x is the band number).
ρ λ ′ does not have the solar elevation angle correction hence it is not the true TOA. Using the solar elevation angle from the metadata, conversion to the true TOA is done using Equation (6) [
ρ λ = ρ λ ′ sin θ (6)
Satellite Date | MK | AK | 𝞱 (degrees) |
---|---|---|---|
LS8_05-01-2015 | 2.000E−05 | −0.10000 | 55.23001491 |
LS8_26-01-2017 | 2.000E−05 | −0.10000 | 55.75141661 |
where:
ρ λ = top of atmosphere (TOA) planetary reflectance and is unitless,
θ = solar elevation angle obtained from the metadata.
NDVI was then calculated using reflectance values of the red and infra-red bands using Equation (7)
N D V I = N I R − R N I R + R (7)
Equation (8) calculates the vegetation portion to obtain the LSE as shown in Equation (9).
P v = ( N D V I − N D V I min N D V I max + N D V I min ) 2 (8)
where:
P v = vegetation portion,
N D V I = normalized difference vegetation index,
N D V I min = minimum NDVI,
N D V I max = maximum NDVI,
where the minimum NDVI is the value for pure soil normally given as 0.2 and maximum NDVI is the value of pure vegetation given as 0.5.
LSE is then computed using:
L S E = 0.004 ∗ P v + 0.986 (9)
Using the at-satellite brightness temperature and the Land Surface Emissivity, LST was computed in degrees Celsius as shown in Equation (10).
L S T = [ T B 1 + ( λ ∗ T B ρ ) ∗ ln ( L S E ) ] − 273.15 (10)
where:
LST = land surface temperature,
TB = at-satellite brightness temperature,
λ = wavelength of emitted radiance (λ = 11.5 µm),
ρ = h*c/σ (1.438*10−2 m∙K),
σ = Bolzmann’s constant (1.38*10−23 J∙K−1),
h = Planck’s constant (6.26*10−34 J∙s),
c = velocity of light (2.998*10−8 m∙s−1).
This was calculated as indicated in Equation (7). This was reclassified into two classes, vegetated and non-vegetated, where values of more than 0.2 were classified as vegetated. This was used as a mask to visually analyze land surface temperature within the study area as well as validate results obtained by calculating BDI as shown in Equation (12).
The Normalized Density Building Index (NDBI) density index is analyzed using the difference between reflectivity within the mid-infra-red (MIR) range and near infra-red (NIR) band range as in Equation (11). This is a dimensionless value where bright values indicate high density of built-up areas. NDBI was developed by Zha et al. [
N D B I = M I R − N I R M I R + N I R (11)
Built-up density index (BDI) is a novel method that was developed by Lee et al. [
B D I = N D B I − N D V I (12)
LST, NDVI and BDI analysis was initially undertaken at a resolution of 30 meters. Values were averaged to obtain 90 × 90 meter pixel cells, which were then converted to point data in each cell. Averaging was done to obtain the average value of each of the indices amongst nine pixels to increase processing speed and easier interpretation of results statistically and visually over the study area.
Land surface temperature was analyzed from different months due to availability of data. In 1987, cloud cover in some parts of the study area affected the land surface temperatures recorded after the analysis.
Results from Figures 2(a)-(d) showed that land surface temperatures increased from February 1987 to February 2002, reaching a maximum of 38.86˚C within the CBD in 2002. LST was also observed to have increased in 2002, thereby decreasing in 2015 and 2017 respectively. Changes in temperature occurred in areas having concentrations of vegetation and impervious surfaces as shown in
An analysis was undertaken to determine areas where LST increased or decreased by subtracting two raster images as shown in
The three figures namely Figures 3(a)-(c) show land surface temperature differences calculated between the years 1987-2002, 2015-2002 and 2017-2015 respectively. The 1987 raster image was subtracted from the 2002 raster image. Areas that had negative values indicated a decrease in temperature i.e. temperatures in 1987 were higher than in 2002. The same was done where 2002 and 2015 images were subtracted from 2015 and 2017 imagery respectively. Areas that had positive values implied an increase in temperatures while areas with negative values implied a decrease in temperature. In 1987, areas that had cloud cover recorded temperature differences of between 10.69˚C - 19.99˚C, and these were excluded from the analysis. However, temperature differences between the highest and lowest recorded difference were highest between 2002 and 2015 with
17.79˚C, and the lowest occurring between 1987 and 2002 with 12.22˚C. Overall temperatures had increased during the years, with the greatest temperature increase in parts of Upper-Hill and surrounding areas towards the north and western areas. However in the Central Business District that is located east of the study area showed a decrease in temperature. These changes in land surface temperature could be as a result in an increase in impervious surfaces which absorb heat during the day. Night-time land surface temperature in this period would need to be analyzed to determine whether there is an expected increase in temperature in these urban areas as they radiate absorbed heat.
Normalized Difference Vegetation Index (NDVI) indicates the health of vegetation at any given time during observation while built-up density index enhances built-up areas more than normalized difference built-up index (NDBI). These two indices were used to examine temperature variations and also determine their relationship with LST.
NDVI values range between −1 to 1 with very low NDVI values of −0.1 to 0.1 indicating presence of rocks, sand or impervious surfaces. Higher NDVI values of 0.2 indicate presence of vegetation, with denser vegetation having values of 0.6 to 0.9, and deep water having a value of −1. In
Figures 4(a)-(d) show results from analyzing NDVI values in the year 1987, 2002, 2015 and 2017. Results showed an increase in minimum values and a decrease
in maximum values from 1987 to 2002. This is an indicator that the amount of impervious surfaces had increased from 1987. By visually inspecting the results, it was observed that the central part of the study area where Upper-Hill is situated had transformed and with values being indicative of a decrease in vegetation due to urbanization.
BDI values range between −2 and +2 as NDVI and NDBI ranges are between −1 and +1. Since BDI is calculated by the difference between NDVI and NDBI, the values obtained that are indicative of clusters of built-up areas are dependent on the values obtained in each. In
Figures 5(a)-(d) show BDI results for the years 1987, 2002, 2015 and 2017 respectively. Concentrations of built-up densities are shown in the north-western part of the study area, and gradually increase within the central part of the study area though the years.
Minimum | Maximum | Mean | |||||||
---|---|---|---|---|---|---|---|---|---|
LST(˚C) | NDVI | BDI | LST(˚C) | NDVI | BDI | LST(˚C) | NDVI | BDI | |
13 Feb 1987 | 22.22 | −0.20 | −0.49 | 32.37 | 0.42 | 0.52 | 27.27 | 0.09 | 0.06 |
10 Feb 2002 | 23.44 | −0.38 | −0.57 | 38.35 | 0.41 | 0.81 | 32.09 | −0.09 | 0.30 |
5 Jan 2015 | 24.24 | −0.12 | −0.95 | 36.88 | 0.50 | 0.19 | 30.77 | 0.20 | −0.33 |
26 Jan 2017 | 23.82 | −0.09 | −0.67 | 36.02 | 0.46 | 0.13 | 30.70 | 0.16 | −0.18 |
cluded in the values indicated. The table shows that minimum values in LST, NDVI and BDI had increased which applied also to the maximum value, which had resulted from a change in land cover. LST minimum temperature had increased by 1.6˚C (6.7%) while maximum temperature increased by 3.65˚C (10.13%) between 1987 and 2017. This was affected by changes in land cover where vegetated areas were replaced by impervious surfaces. These areas are a great storage of heat hence absorbing heat during the day and releasing this heat at night.
LST, NDVI and BDI raster imagery were aggregated to 90 × 90 meter cells for statistical analysis in ArcGIS. In 1987 due to the presence of cloud cover, the data values were excluded from the analysis as these values were outliers and would have affected the model. Linear regression was carried out for all years, with LST as the dependent variable and NDVI, BDI as the independent variables.
The scatter plot showed a negative correlation between LST and NDVI and a positive correlation with BDI in each of the four years. A histogram of the residuals indicated they had a normal distribution.
The R2 values for each of the years indicate that BDI is a better predictor of LST compared to NDVI. Adjusted R2 for NDVI was the lowest at 26.1% in 1987, increasing in 2002 to 49.3% which was the highest and reducing to 48.1% and 15.5% in 2015 and 2017 respectively. For BDI, 1987 had the lowest R2 value at 41.4%, increasing to 58.1% in 2002 and reducing to 53.1% and 28.9% in 2015 and 2017 respectively. Values from
Year | Feb 1987 | Feb 2002 | Jan 2015 | Jan 2017 | ||||
---|---|---|---|---|---|---|---|---|
Indices | NDVI | BDI | NDVI | BDI | NDVI | BDI | NDVI | BDI |
R2 | 0.26 | 0.41 | 0.49 | 0.58 | 0.48 | 0.53 | 0.16 | 0.29 |
Cloud cover and cloud shadows within the data set may have affected the output results as areas that were covered by cloud were omitted in the analysis. These areas could have had important information that would have changed the ranges in temperature, vegetation or built-up indices. Minimum and maximum land surface temperature has increased indicating a change in climate as the study was taken over a 30 year period. Linear regression indicates that BDI is a better predictor of LST than NDVI, however the model values also reduced with the decrease in temperature, indicating that there were other factors that were affecting land surface temperature. Results showed that understanding effects of changing land cover over a specific area enables mitigative measures to be determined, rather than analyzing a large area that has different geographical conditions. Future work will focus at comparing night-time and day-time land surface temperature to determine the aspect of surface urban heat islands.
Mwangi, P.W., Karanja, F.N. and Kamau, P.K. (2018) Analysis of the Relationship between Land Surface Temperature and Vegetation and Built-Up Indices in Upper-Hill, Nairobi. Journal of Geoscience and Environment Protection, 6, 1-16. https://doi.org/10.4236/gep.2018.61001