Modelling Land Surface Temperature Variation in New Guinea Island from 2000 to 2019 Using a Cubic Spline Model

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Introduction
Land surface temperature (LST) represents the radiative skin of the Earth's surface, is primarily infuenced by solar radiation, and holds signifcant importance in climate research.LST serves as a crucial parameter in comprehending land surface dynamics across various scales, from local to global, within the realm of physics.Globally, it will impact ecosystems, living things, and human health [1,2].LST is a combination of vegetation and bare soil temperature.LST varies rapidly as a result of the two components' rapid responses to changes in incoming solar prominence.Variations in LST are also afected by changes in the quantity of clouds and aerosols in the atmosphere and by the intensity of daylight during the day.LST infuences the energy distribution between land and vegetation, resulting in the surface air temperature [3].Te increase in LST as an indicator of climate change has caused the melting of ice in the regions of the poles and areas of high elevation, which has resulted in rising sea levels and endangered several cities around the world [4].
Global LST has increased approximately 0.8 °C per century since 1880 and approximately 0.2 °C per decade since 1951 [5].In 2020, the global average temperature was 1.2 ± 0.1 °C above the 1850-1900 baseline [6].In Asia, the average temperature was 1.39 °C higher than the 1981-2010 average [7].In high-mountain Asia, the LST was signifcantly rising during 2001-2017 [8].Since 1910, annual and seasonal ocean surface and island air temperatures in the southern Pacifc region, including Papua and Papua New Guinea, have increased by 0.6 °C-1.0 °C per decade [9].By 2030, the projection for all emissions scenarios indicates that the annual average temperature in New Guinea will increase in the range of 0.4-1.0°C [10].However, the National Aeronautics and Space Administration moderateresolution imaging spectroradiometer database revealed no substantial increase in LST in New Guinea during 2000-2019, with an average temperature change of +0.012 °C per decade [11], whereas the nearby New Britain Island has a signifcant increase in LST with an average of 0.56 °C per decade [12].
Te purpose of this study is to examine at the pattern and variation of daytime LSTon New Guinea Island from 2000 to 2019 by extending the study of Munawar et al. [11], which reduces the distance between subregions and takes care of spatial correlation.Te cubic spline and a multivariate regression model were used to analyze the LST time series data.

Study Area and
Data.New Guinea is the world's secondlargest island, after Greenland.Politically, it is divided into two territories: Indonesia to the west and Papua New Guinea to the east.Te land use has changed from rainforests to oil palm plantations.Te climate in Papua New Guinea is predominantly tropical, characterized by rainfall throughout most seasons.However, signifcant changes in climate have been observed over recent decades, attributed to fuctuations in solar radiation, increased occurrences of volcanic eruptions, and heightened levels of greenhouse gas emissions [13].Te average maximum annual temperature ranges from 23 °C to 32 °C [14].During 2000 and 2019, the minimum, average, and maximum LSTs from all subregions in Figure 1 were 13.8 °C, 25.6 °C, and 32.8 °C, respectively.
New Guinea Island is located within the geographical coordinates of 130 °to 152 °East longitude and − 11 °to 0 °South latitude.Tis study took a sample of 90 subregions as shown in Figure 1.Te subregions were placed 105 pixels (95 km) apart in latitude and longitude.Te distance between each region's central point and its nearest neighbor is equal and contains 49 pixels in a 7 × 7 array, a layout that covers the whole island.Te frst analysis based on the previous study [11] focused only on 45 subregions (shaded circles in Figure 1) where the subregions were positioned at intervals of 210 pixels along the sample line widths, approximately 190 km apart.Tis analysis classifed the island into fve super-regions named super-regions A to E which represent north-west, central-north Papua Indonesia, central-south of the island between Indonesia and Papua New Guinea, north-east, and south-east of Papua New Guinea, respectively.
For the second analysis, all 90 subregions were included.Tis analysis divided each super-region of the frst analysis into two super-regions.For example, super-region A was divided into A1 and A2, yielding ten smaller super-regions.Te distance between each subregion is 105-pixels of latitude 95 km apart.
Te LST eight-day time data in Kelvin scale (then converted to Celsius) were downloaded from the NASA MODIS database, specifcally from NASA's Terra MODIS satellite, during 2000-2019 for each subregion [15].Te data are based on the sample points that have been determined on the island by avoiding placing points on the sea.If the point is placed on the sea, there will be no LST data from the satellite or considered as a missing value.MODIS LST data are obscured by clouds and other atmospheric disturbances and consequently infuence the data availability.Te R language and environment was used to analyze the data and to create the graphics [16].

Statistical Methods. Several statistical techniques have
been used in a number of studies to examine trends and patterns in surface temperature such as least-squares linear regression [17][18][19] and cubic splines [20].However, the distribution of LST varies considerably in both time and space.Data that are related to each other in terms of time lags and between two nearby places will infuence one another, which can afect the results of inferential analyses [21].
Te seasonal pattern of the LST for the 90 subregions was examined and seasonally adjusted.Te seasonally adjusted LST is given by where Y a is a seasonally adjusted time series of LST, Y is the observed LST per day over 18 years, S f is a vector of spline ftted values that are calculated from the cubic splines, and x is the average LST per year.Te seasonally adjusted LST was then ftted using a second-order autoregressive model to account for the autocorrelation.Te pattern of seasonally adjusted LST data was examined using cubic spline and a multivariate regression model [22].Cubic spline functions are defned as piecewise polynomials with degree r where knots are the chosen positions that join the pieces.A spline function of degree r is a continuous function with r − 1 continuous derivative [23,24].Te cubic spline function approach is given by [25] and x + � max (x, 0).Tese splines are a linear function of p parameters a, b, and c 1 , c 2 and c p− 2 to ft the data by using a linear model.
Te position and number of knots used to smooth the data are critical for cubic spline ftting.Some studies have selected the positions of knots based on the season [20,26,27].Te diference in LST may be associated with heatwaves in the tropical area during April and May and rainfall during June-September [28].Tis study used eight knots, four of which were placed at the start of the year and four at the end, in accordance with the seasons that are typical of tropical regions.

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Results and Discussion
Super-region A (north-west) was selected to describe the results of New Guinea Island for the northwest region.Te results of the frst analysis revealed that the LST has a seasonal pattern with two summer peaks (Figure 2).During the rainy season, the lowest LST occurred on day 210 (the end of June), and the highest LST occurred on day 324 (the end of October).Subregion 9 has the highest average LST (27.7 °C).
Figures 3 and 4 show the results of the second analysis for the northwest area of two super-regions A1 and A2.Te LST patterns in each subregion showed only minor seasonal changes.Even though each subregion has diferent coordinates (latitude and longitude), the seasonal patterns are very similar.In general, the local minima for LST occurred in January corresponding to the rainy seasons.
As shown in Figures 3 and 4, LST increased from October to November (days 286-305) in subregions 1, 2, 3, 5, 7, and 8. On the other hand, LST increased from October to December (days 286-363) in subregions 4, 6, and 9, with stability toward the end of the year.Regarding the seasonal pattern, LSTdecreased on approximately days 172-210 (June to July), corresponding with the rainy season.Tis is due to the fact that land is covered with wet vegetation [29].Tese fndings showed that seasonal patterns were not clear in the subregions of New Guinea Island.
Figures 5-7 display the patterns and trends of seasonally adjusted LSTfor super-region A (north-west) of New Guinea island.Te estimated coefcients of autoregressive ar 1 and ar 2 were small, indicating that the time series of seasonally adjusted of daytime LST are independent.Te black lines denote the ftted lines from the linear model, and red curves denote the natural cubic splines.Figure 5 shows that the LST was signifcantly increasing in subregion 4 and decreasing in subregions 7 and 9.However, the results of cubic spline model showed that the LSTs in subregions 7 and 9 were signifcantly changing.Figures 6 and 7 reveal that more subregions in the northwest super-regions had LSTs that were signifcantly changing.
Te z value statistics displayed in the bottom-right panel of Figures 5-7 are based on statistical testing; there is no average daytime LST increase in a super-region, assuming that increases in subregions of the same super-region are the same.Te average daytime LST for super-region A (north-west) of − 0.11 °C per decade was statistically signifcant with a z value of − 2.098 and 95% confdence interval of (− 0.21, − 0.01) (Figure 5).As shown in Figure 6, the mean daytime LST for super-region A1 was 0.058 °C with a 95% confdence interval of (− 0.048, 0.164), with a nonsignifcant z value of 1.077.As shown in Figure 7, the average daytime LST for super-region A2 was − 0.121 °C with 95% confdence interval of (− 0.226, − 0.018), showing signifcant z value of − 2.293.Te variations in LST varied by super-region.
Figure 8 shows 95% confdence interval of average daytime LST variations for 45 subregions (top panel) and for all 90 subregions (bottom panel) together with the overall average LST.Te 45 subregions showed a nonsignifcant increase of an overall average daytime LST with 0.012 °C (95% confdence interval: − 0.052, 0.077), while the overall average daytime LST for the 90 subregions was a statistically signifcant increase, with 0.086 °C per decade (95% confdence interval: 0.028, 0.144).
Tere were variations in the overall daytime LST for each super-region with fve super-regions containing 45 subregions.Te average daytime LST changed per decade in super-regions A (north-west), B (central-north), C (south), D (north-east), and E (south-east) by − 0.116 °C, 0.0026 °C, 0.206 °C, − 0.076 °C, and 0.046 °C, respectively.However, only Advances in Meteorology analysis indicates a clear upward trajectory.Without intervention to address the current pace of climate change, the upward trends in both rainfall and temperature are expected to persist [30].
Te rise in LSTon New Guinea Island can be an indicator of climate change due to its association with frequent fuctuations in weather patterns [31].Changes in LST could be caused by urbanization LU/LC change as a human efort to fulfll the population's needs [32].Te West of New Guinea Island has 2% of forest lost since 2001 as an efect of the development of industrial plantation, mining, and building of facilities [33].Te environmental damage, mainly due to reduced rainforest or green open space as the result of massive human activities, would have a substantial efect on global warming.Te increase in LST would afect the reduction of crops and fshing yield, which can lead to a reduction in the quality of life of the people living on the island.6 Advances in Meteorology

Conclusions
On New Guinea Island, many regions were found to have an increase in daytime land surface temperature.Tere was not signifcant increase of overall average LST in 45 subregions.However, when the number of subregions was increased for 90 subregions by reducing the distance between subregions, the overall average LST was signifcantly increased with +0.086 °C per decade (confdence interval: 0.028, 0.144).LST increased signifcantly in the central-north, central-south of the island (super-regions B1, C1, and C2) and the southern part of Papua New Guinea (super-region E2), whereas it decreased in the middle part of the Indonesian territories (super-region A2).Te LST variation also occurs at the subregion level.Tis fnding was part of the study by Munawar [34].Tis study chose a distance between each region's central point of 105-pixels (95 km in latitude and longitude), which    Advances in Meteorology is reasonable to use as a representative sample and to minimize spatial correlation.However, it is important to take into account the optimal spacing between subregions on the smaller islands.New Guinea Island consists of many mountains and vegetation, which is typical of tropical areas in general.Tis result is only based on the LSTeight-day time from Terra MODIS; further investigation should compare the LST variation data obtained from MODIS Terra and Aqua.Future research should take into account additional elements connected to LST, such as land elevation, land use/ land cover, and the Normalized Diference Vegetation Index.

Figures 2 -
4 show the seasonal patterns after ftting a natural spline function with eight knots, denoted by solid red curves.Te eight knots' locations in the model are indicated by the blue crosses.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :
Figure 1: New Guinea Island located at longitude 130 to 152 °East and latitude − 11 to 0 °South.Letters A-E represent super-regions, each split into two smaller regions; all the numbers represent the 90 subregions.