# Annual Seasonality Extraction Using the Cubic Spline Function and Decadal Trend in Temporal Daytime MODIS LST Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data

#### 2.2.1. MODIS LST

#### 2.2.2. Meteorological Data

#### 2.3. Methods

#### 2.3.1. Cubic Spline Function

#### 2.3.2. Knots Selection

#### 2.3.3. LST Outlier Elimination

#### 2.3.4. Weighted Least Squares Regression

## 3. Results

#### 3.1. Placement and Number of Knots

#### 3.2. Annual Seasonal Patterns of LST Time Series

_{skin}) and the surface air temperature (T

_{air}) are different measures with regard to both their physical meaning and their magnitude (an absolute value of LST is usually higher than the surface air temperature), the two temperatures are complementary in their contribution of valuable information in climate study [41]. LST has been used for mapping and estimating surface air temperature in the different parts of the globe [42,43,44,45]. The seasonal curve resulting from the cubic spline function shows a similar pattern and trend to the local monthly average air temperature.

_{dry}) for the urban surface site is also higher than other locations. The ΔT

_{dry}of the urban site is around 6.03 °C, whereas the ΔT

_{dry}of the entire forest and agriculture land cover sites is around 4.03 and 4.89 °C, respectively. The urban and built-up land surface causes more variability of maximum and minimum surface temperature during the dry period. Figure 6b displays the ratio of surface temperature seasonality in urban and agricultural land cover area to the forest (S

_{urban}/S

_{forest}and S

_{agric.}/S

_{forest}). It highlights the impact of urbanization and agriculture land use on natural surface vegetation.

#### 3.3. Application to Daytime MODIS LST Data

#### 3.3.1. Spatial Distribution of Daytime LST Trends

#### 3.3.2. Trend of Daytime LST in Different LULC Types

^{2}LST pixel area. In the study area, there are 0.24 and 0.12 °C increases in the surface temperature in a decade for the 10:30 a.m. and 1:30 p.m. datasets, respectively, and those uprising trends are statistically significant. All diurnal surface temperature trends are warmer in all various land cover types and areas. The rising surface temperature trend in the morning is higher than in the afternoon. The overall LST trends, both 10:30 a.m. and 1:30 p.m. overpass-time, in the miscellaneous land (total 39 time series) increase more than in other areas. The second warming trend is found in the urban area (total of 62 time series), followed by the forest (total of 92 time series) and the agricultural (total of 389 time series) land cover areas. However, the afternoon LST trend in a cultivated area is more significant than in the forest area. Moreover, LST trends in Phuket City and Mueang Phuket districts, which have an extreme density of asphalt streets and concrete buildings, are higher than Thalang and Kathu districts, which are mainly para-rubber plantations and upland evergreen rain forest, respectively.

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Map of Phuket Island; (

**b**) map of Level-1 LULC classification of year 2009 with the location of three study sites.

**Figure 2.**Illustration of the cubic spline model with annual periodic boundary condition. $t$ is the time; $s\left(t\right)$ is the cubic spline function for $t>{T}_{0}$ and $t<{T}_{p}$; $s\left({T}_{0}\right)$ is the cubic spline function at $t<{t}_{1}$; and $s\left({T}_{p}\right)$ is the cubic spline function at $t>{t}_{p}$.

**Figure 3.**Adjusted r-squared and cross-validated error for three-sample 1:30 p.m. MODIS LST time series with varying number of knots and their placements.

**Figure 4.**Annual seasonality of three 1:30 p.m. MODIS LST time series with cubic spline fitting (red lines) using eight knots at “best practice” knots location (blue plus) at Julian Days 10, 35, 60, 90, 115, 310, 335 and 355. The green lines connect the average LST values within the Julian day. The “n” label displays the total number of observation used in the seasonal extraction process. The “missing” label indicates the percentage of missing values. The crosses indicate all the outliers excluded from the cubic spline fitting, and the total number of detached observations is displayed as “zero weighted”. The green bar presents the data distribution density. The “r-sq” label shows the adjusted r-squared value of the cubic spline function fitted to the data. The dark (black) dots indicate high-quality LST data, and the dots turn pale (grey) when the LST data are subjected to data quality control.

**Figure 5.**Trend comparison of seasonality produced from the proposed spline-based seasonality extraction method with the average MODIS LST and 2-m air temperature. The vertical black lines indicate the range of monthly average maximum and minimum temperature.

**Figure 6.**Seasonality of 1:30 p.m. MODIS LST time series. (

**a**) The seasonal profiles of forest, agricultural and urban land cover classes; (

**b**) relation of seasonal profiles in agricultural and urban land cover to the natural forest.

**Figure 7.**Spatial distribution of MODIS LST trends for the (

**a**) 10:30 a.m. and (

**b**) 1:30 p.m. datasets, including the p-value distribution of their trends, (

**c**,

**d**) for the 10:30 a.m. and 1:30 p.m. datasets, respectively.

**Figure 8.**Overall decadal surface temperature trend (error bars denote 95% confidence intervals) in five LULC types and four areas of Phuket Island for 10:30 a.m. and 1:30 p.m. MODIS LST datasets.

**Figure 9.**Plot of cross-correlation function among the seasonality of the three selected study sites. The blue dashed lines represent a 95% confidence interval at ±0.3

District | Area: km^{2} | Lowland: km^{2} (%) * | LULC 2009: km^{2} (%) | ||||
---|---|---|---|---|---|---|---|

F | A | U | M | W | |||

Phuket City | 13.6 | 12.6 (92.6) | 0.7 (5.2) | 1.2 (8.8) | 10.8 (79.4) | 0.6 (4.4) | 0.3 (2.2) |

Mueang Phuket | 151.8 | 102.6 (67.6) | 37.5 (24.6) | 41.4 (27.3) | 58.6 (38.6) | 12.6 (8.4) | 1.6 (1.1) |

Kathu | 80.2 | 26.0 (32.4) | 28.0 (34.9) | 22.7 (28.3) | 23.8 (29.7) | 4.5 (5.6) | 1.2 (1.5) |

Thalang | 284.4 | 212.8 (74.8) | 53.8 (18.9) | 165.7 (58.3) | 40.3 (14.2) | 19.7 (6.9) | 4.9 (1.7) |

Total | 530.0 | 354.0 (66.8) | 120.0 (22.6) | 231.0 (43.6) | 133.5 (25.2) | 37.5 (7.1) | 8.0 (1.5) |

Site | Average Elevation | LULC 2009 | MODIS Sinusoidal Project Tile System | Latitude, Longitude (Middle of Pixel) |
---|---|---|---|---|

1 | 275.2 m | Forest (F) | V: 8, H: 27, S: 800, L: 233 | 8.054167, 98.374528 |

2 | 53.1 m | Agricultural (A) * | V: 8, H: 27, S: 881, L: 232 | 8.062500, 98.317638 |

3 | 14.6 m | Urban and built-up (U) | V: 8, H: 27, S: 895, L: 253 | 7.887500, 98.393357 |

Cross-Correlation | Lag | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

−6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |

Forest vs. Agric. | 0.047 | 0.182 | 0.333 | 0.492 | 0.645 | 0.778 | 0.877 | 0.929 | 0.933* | 0.892 | 0.819 | 0.724 | 0.618 |

Forest vs. Urban | 0.225 | 0.366 | 0.520 | 0.674 | 0.810 | 0.910 | 0.960* | 0.939 | 0.870 | 0.765 | 0.641 | 0.514 | 0.395 |

Urban vs. Agric. | 0.101 | 0.241 | 0.397 | 0.560 | 0.714 | 0.843 | 0.931 | 0.963* | 0.936 | 0.859 | 0.744 | 0.607 | 0.462 |

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**MDPI and ACS Style**

Wongsai, N.; Wongsai, S.; Huete, A.R.
Annual Seasonality Extraction Using the Cubic Spline Function and Decadal Trend in Temporal Daytime MODIS LST Data. *Remote Sens.* **2017**, *9*, 1254.
https://doi.org/10.3390/rs9121254

**AMA Style**

Wongsai N, Wongsai S, Huete AR.
Annual Seasonality Extraction Using the Cubic Spline Function and Decadal Trend in Temporal Daytime MODIS LST Data. *Remote Sensing*. 2017; 9(12):1254.
https://doi.org/10.3390/rs9121254

**Chicago/Turabian Style**

Wongsai, Noppachai, Sangdao Wongsai, and Alfredo R. Huete.
2017. "Annual Seasonality Extraction Using the Cubic Spline Function and Decadal Trend in Temporal Daytime MODIS LST Data" *Remote Sensing* 9, no. 12: 1254.
https://doi.org/10.3390/rs9121254