**Figure 1.**
Land cover types of the study area at the MSG-SEVIRI pixel scale aggregated from the Collection 5.1 MODIS land cover type product MCD12Q1. Six selected pixels over different land cover types were used to evaluate the performance of the 4-parameter diurnal temperature cycle (DTC) model.

**Figure 1.**
Land cover types of the study area at the MSG-SEVIRI pixel scale aggregated from the Collection 5.1 MODIS land cover type product MCD12Q1. Six selected pixels over different land cover types were used to evaluate the performance of the 4-parameter diurnal temperature cycle (DTC) model.

**Figure 2.**
Illustration of the DTC model parameters.
${T}_{s}^{d}$ and
${T}_{s}^{n}$ are the land surface temperatures (LSTs) of the daytime and night-time parts, respectively, t is the time, T_{0} is the residual temperature around sunrise, T_{a} is the temperature amplitude, ω is the width over the half-period of the cosine term, t_{m} is the time at which the temperature reaches its maximum, t_{sr} is the time of sunrise, t_{ss} is the time of sunset, t_{s} is the start time of free attenuation, δT is the temperature difference between T_{0} and T(t→∞), and k is the attenuation constant.

**Figure 2.**
Illustration of the DTC model parameters.
${T}_{s}^{d}$ and
${T}_{s}^{n}$ are the land surface temperatures (LSTs) of the daytime and night-time parts, respectively, t is the time, T_{0} is the residual temperature around sunrise, T_{a} is the temperature amplitude, ω is the width over the half-period of the cosine term, t_{m} is the time at which the temperature reaches its maximum, t_{sr} is the time of sunrise, t_{ss} is the time of sunset, t_{s} is the start time of free attenuation, δT is the temperature difference between T_{0} and T(t→∞), and k is the attenuation constant.

**Figure 3.**
Histograms of the differences between t_{s} obtained from model fitting (i.e., t_{s} treated as a free parameter) and t_{s} estimated from t_{ss}−1 for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 3.**
Histograms of the differences between t_{s} obtained from model fitting (i.e., t_{s} treated as a free parameter) and t_{s} estimated from t_{ss}−1 for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 4.**
Fitting the 4-parameter DTC model to the diurnal cycle of the MSG-SEVIRI-derived LST on 31 July 2010 for the six selected pixels over different land cover types: (**a**) forest, (**b**) shrubland, (**c**) woodland, (**d**) grassland, (**e**) cropland, and (**f**) unvegetated land. Fitting errors of LST are also shown.

**Figure 4.**
Fitting the 4-parameter DTC model to the diurnal cycle of the MSG-SEVIRI-derived LST on 31 July 2010 for the six selected pixels over different land cover types: (**a**) forest, (**b**) shrubland, (**c**) woodland, (**d**) grassland, (**e**) cropland, and (**f**) unvegetated land. Fitting errors of LST are also shown.

**Figure 5.**
Histograms of the RMSE values of the 4-parameter DTC model fitting the diurnal cycle of the MSG-SEVIRI-derived LST for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 5.**
Histograms of the RMSE values of the 4-parameter DTC model fitting the diurnal cycle of the MSG-SEVIRI-derived LST for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 6.**
Histograms of the RMSE values of the 5-parameter DTC model fitting the diurnal cycle of the MSG-SEVIRI-derived LST for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 6.**
Histograms of the RMSE values of the 5-parameter DTC model fitting the diurnal cycle of the MSG-SEVIRI-derived LST for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 7.**
Fitting the 4-parameter DTC model to only four MSG-SEVIRI-derived LSTs on 31 July 2010 for the six selected pixels over different land cover types: (**a**) forest, (**b**) shrubland, (**c**) woodland, (**d**) grassland, (**e**) cropland, and (**f**) unvegetated land. Fitting errors of LST are also shown. Filled squares represent the LSTs corresponding to the MODIS overpass times (10:30, 13:30, 22:30, and 01:30 local solar time).

**Figure 7.**
Fitting the 4-parameter DTC model to only four MSG-SEVIRI-derived LSTs on 31 July 2010 for the six selected pixels over different land cover types: (**a**) forest, (**b**) shrubland, (**c**) woodland, (**d**) grassland, (**e**) cropland, and (**f**) unvegetated land. Fitting errors of LST are also shown. Filled squares represent the LSTs corresponding to the MODIS overpass times (10:30, 13:30, 22:30, and 01:30 local solar time).

**Figure 8.**
Histograms of the RMSE values of the 4-parameter DTC model fitting only four MSG-SEVIRI-derived LSTs for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 8.**
Histograms of the RMSE values of the 4-parameter DTC model fitting only four MSG-SEVIRI-derived LSTs for all cloud-free pixels on (**a**) 28 January, (**b**) 9 April, (**c**) 31 July, and (**d**) 1 October 2010.

**Figure 9.**
Fitting the 4-parameter DTC model to four MODIS LSTs (filled squares) on 31 July 2010 for the six selected pixels over different land cover types: (**a**) forest, (**b**) shrubland, (**c**) woodland, (**d**) grassland, (**e**) cropland, and (**f**) unvegetated land.

**Figure 9.**
Fitting the 4-parameter DTC model to four MODIS LSTs (filled squares) on 31 July 2010 for the six selected pixels over different land cover types: (**a**) forest, (**b**) shrubland, (**c**) woodland, (**d**) grassland, (**e**) cropland, and (**f**) unvegetated land.

**Figure 10.**
Spatial distribution of the modeled LSTs at the MODIS pixel scale spanning from 07:00 to 05:00 local solar time of the next day with an increment of 2 h.

**Figure 10.**
Spatial distribution of the modeled LSTs at the MODIS pixel scale spanning from 07:00 to 05:00 local solar time of the next day with an increment of 2 h.

**Table 1.**
Detailed information of the six selected pixels.

**Table 1.**
Detailed information of the six selected pixels.
**Site** | **Latitude** | **Longitude** | **Elevation** | **Land Cover Type** |
---|

A | 43.909°N | 0.235°E | 153.1 m | Forest |

B | 34.161°N | 1.677°W | 1134.2 m | Shrubland |

C | 40.030°N | 7.166°W | 381.7 m | Woodland |

D | 33.941°N | 0.769°W | 1080.4 m | Grassland |

E | 37.405°N | 4.326°W | 746.2 m | Cropland |

F | 30.642°N | 3.564°E | 347.6 m | Unvegetated |