# Evaluating contributions of urbanization and global climate change to urban land surface temperature change: a case study in Lagos, Nigeria | Scientific Reports – Nature.com

### Intruduction to methods

The main objective of this study is to develop a general method to estimate the contributions of localized urbanization and global climate change on ULSTs and take Lagos as a case study to apply this method for estimations. It is well known that global warming and urbanization are the two key contributors to the higher LST in cities38. In addition, the interannual climate fluctuation also plays a role in the annual LSTs. In order to realize the objectives of this study, we have to separate the contributions of these three factors to the annual LSTs in a city.

It can be reasonably assumed that the annual (mean, min., or maximum) LSTs will fluctuate around a constant value due to interannual climate variations if there is no global warming or urbanization. It is also assumed that both global warming and urbanization contribute linearly to the LST increase in urban areas over the years. Therefore, a linear regression of the annual LST time series will remove the contribution of interannual climate variations to the annual LST, and the linear function obtained from regression represents the long-term systematic trend of the LST for a city area, which represents the combined contributions of both the urban expansion and local impact of global warming. Although the trend of temperature increase due to global warming varies globally, the trends for the two nearby areas within the same climate regime should be similar if not the same. That is why we select a nearby area, which has been neither subjected to urbanization nor experienced a large land use/land cover change, as the reference site for quantifying the contribution of global warming. The time series of annual LSTs and the linear regression are also calculated for the reference site. The linear function obtained from the regression on the reference site represents the trend of LST change due to global warming. The trend from the reference site can be used to approximate the trend of LST change due to global climate change in urban areas. Therefore, it can be assumed that the difference in the linear functions between the urban study area and the rural reference site can be attributed to the contribution of urbanization to ULST change.

Thus, the contributions of both localized urbanization and global warming can be quantified by the following steps: (1) calculating annual time-series LSTs for both the urban study area and the reference site; (2) using linear regressions to remove the interannual variation from the time series of both the study area and the reference site. The linear functions resulting from linear regression represent the long-time trends of LSTs in the study area and the reference site, respectively; (3) For the urban study area, calculating the systematic trend of LST contributed by the combination of urban expansion and local impact of global warming as shown in Eq. (1); and (4) deriving LST increase contributed by urbanization through removing the contribution of global warming from the systematic trend of LST in the reference site as shown in Eq. (2).

Based on the discussion above, ((Delta {T}_{U})) is the combination of the UHI effect caused by urbanization and the local impact of global warming. Thus,

$$Delta {T}_{U}=Delta {T}_{UHI}+{Delta T}_{G}$$

(1)

where (Delta {T}_{U}) denotes the overall systematic ULST change from the initial year to the final year, (Delta {T}_{UHI}) means the LST change due to the urbanization effect, and ({Delta T}_{G}) is the overall LST change due to global warming. The values of (Delta {T}_{UHI}) thus could be calculated by

$$Delta {T}_{UHI}={Delta T}_{U}-{Delta T}_{G}$$

(2)

Therefore, to derive (Delta {T}_{UHI}), we have to obtain ({Delta T}_{G}) first by finding a region that is not only close enough to the city so that the local impact of global warming is similar by being within the same or similar climatic zone, but also far enough from the city so that its LST is not impacted by the urbanization in the city. This region is called the reference site, which is usually selected from the nearby rural areas. Further, this site and its immediate neighbor should have no significant land use and land cover change (LULCC) over a long period of time. As such, the systematic LST change in this site is most likely to be linked to external atmospheric forcing, i.e., global climate change. The annual LST time series for the reference region then is calculated from the MODIS LST products and the linear regression on the time series is performed to remove the interannual variability. Then, ({Delta T}_{G}) can be obtained by

$${Delta T}_{G}={T}_{Rf}-{T}_{Ri}$$

(3)

where ({T}_{Rf}) and ({T}_{Ri}) are the LSTs of the reference region at the final time and the initial time of the time series, respectively, obtained through the linear regression equation.

Figure 6 provides the graphic description that explains the method in this study. In the figure, the curves represent the time series of annual specific LSTs for the urban study area (red) and the rural reference area (green). The straight dot lines are the minimum mean square error (MMSE) linear fitting obtained through linear regression as the trends of the LST time series for the urban (red) and rural areas (green). ({Delta T}_{U}) (in dark) is the systematic LST change during the study period for the urban area, which is the difference between the fitted value of ULST at the final time of the time series and that value at the initial time of the time series. ({Delta T}_{G})(in purple) is the contribution of global climate change to ({Delta T}_{U}). ({Delta T}_{G}) is calculated by the temperature difference between the fitted value of LST at the final time and that value at the initial time of the time series for the rural area. (Delta {T}_{UHI})(in red), the contribution of urbanization to long-term ULST change (boxtimes), is calculated by the difference between ({Delta T}_{U}) and ({Delta T}_{G}).

### LST data acquistition

One effective method to measure LST is thermal remote sensing. In this study, we use two daily MODIS Land Surface Temperature & Emissivity products, MOD11A1 (version 6) and MYD11A1 (version 6), from the National Aeronautics and Space Administration (NASA). The MOD11A1 daily LST product, available from February 24, 2000, is derived from the MODIS sensor onboard the Terra satellite. And the MYD11A1 daily LST product, available from July 04, 2002, is derived from the MODIS sensor onboard the Aqua satellite. Thereby, the MODIS LSTs are compiled from January 01, 2003 to December 30, 2021. Both Terra and Aqua MODIS products provide daily global coverage (http://modis.gsfc.nasa.gov). They have different local overpass times, i.e., Terra descending around 10:30 and ascending around 22:30 at local time, Aqua descending around 01:30 and ascending around 13:30 at local time, which allow the two MODIS sensors to observe the Earth surface four times per day at 01:30, 10:30, 13:30, and 22:30 local time. Clouds and other atmospheric disturbances often obscure parts of or even the entire observation scene, which is a significant obstacle to continuously monitor or predict LST changes, especially in tropical regions23. The Terra and Aqua MODIS LST products are only captured under cloud-free conditions32. Therefore, data availability of LSTs may influence the accuracy of the accumulated annual LST estimations23,39.

Google Earth Engine (GEE) platform is used to access daily LST time series, convert LSTs units, and calculate the regional average LSTs for the urban study area and rural reference site. Specifically, the daily daytime and nighttime LSTs (LST_Day_1km and LST_Night_1km) are selected firstly from MOD11A1 and MYD11A1, respectively. Next, the LST values are converted from Kelvin to Celsius units using the following formula:

$${T}_{c}=0.02{T}_{k}-273.15$$

(4)

where ({T}_{c}) is the temperature in Celsius (°C), ({T}_{k}) is the scaled absolute temperature in Kelvins (K) stored in the MODIS LST products, and 0.02 is a scale factor. And then an existing GEE function is applied to calculate a single cumulative value of the mean/max./min. LSTs during the study time period. Lastly, the boundary polygons that determined the urban study area and rural reference region are uploaded to clip the corresponding LST values and then export these LSTs to Google Drive.

### LST data availability

When deriving meteorological parameters from remote-sensing time series, those satellite observations are expected to be presented in good quality40. Due to cloud cover and weather conditions, the remotely sensed LST time-series products, especially in the tropical regions, contain both spatial and temporal gaps and missing values, which could cause undesirable uncertainties in the analysis. To increase the spatial/temporal coverage of LST in the Lagos area, combined daily diurnal MODIS LSTs from both Terra and Aqua satellites are derived in this study to generate the daytime and nighttime LST time series. Because the MYD11A1 product is available from July 2002, which is later than the available date of MOD11A1, the time period of data collection for this study is thus set to the time period from the first day of 2003 to the last day of 2021. Since the entire temporal period covers a total of 6940 days (19 years) as well as four observation times each day, the amount of remotely sensed LST images is huge to be processed and calculated. Therefore, the Google Earth Engine (GEE) (https://earthengine.google.com/platform/), which is a cloud-based platform for a variety of geospatial analyses, is performed to collect and process time-series daily mean, maximum and minimum ULSTs and RLSTs from daytime and nighttime MOD11A1 and MYD11A1 products.

As introduced above, Lagos is located within a tropical climate zone characterized by high year-round temperatures and abundant seasonal precipitation. Due to frequent cloud cover in this region, satellite-observed LST data are not available for each day. Particularly during the wet seasons, LST images are only available for a few days each month. Statistics from LSTs of those few days are hardly representative of the LSTs of the month, which could result in inaccurate LSTs in month or year and further estimations41. To verify and validate this issue, we further count the specipic numbers of cloud-free LST images from MODIS at four observation times for each day in the years 2003–2021 for both study sites. Figure 7 depicts the total numbers of LSTs collected at four observation times for each month of the year throughout the study period across the urban area (left plots) and the rural reference site (right plots), respectively. The higher collections can be found in Jannuary, December, and November. Although satellite remote sensing is an excellent data source for monitoring the Earth surface characteristics on a large scale42. It is still challenging to retrieve the satellite-observed land surface characteristics in the tropics. Therefore, for this study, we only compile daily time-series LSTs in January, November, and December for the urban and reference sites to calculate the annual dry-season LSTs. For simplicity, we use the annual LSTs to represent the annual dry-season LSTs in this study. The data processing and results acquisition are in accordance with the methods discussed above.

All raw data used in this study, including MOD11A1 (v6), MYD11A1 (v6), and MCD12Q1 (v6), are freely available and online accessible from the following links: