# Improving Land Surface Temperature Retrievals over Mountainous Regions

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Data

#### 2.1.1. Study Area

#### 2.1.2. Satellite Data

#### 2.1.3. Model Data

#### 2.2. LST Retrieval Algorithms

- Generalized Split-Windows (GSW) is based on the formulation by Wan and Dozier for the Advanced Very High Resolution Radiometer (AVHRR) and MODIS sensors [26] and later adapted for MSG/SEVIRI [22,27,28]; LST is computed using a semi-empirical expression involving top-of-atmosphere brightness temperature and surface emissivity in two thermal infrared channels (10.8 and 12 µm), the so-called split-window channels:$$\mathrm{LST}=\left({\mathrm{A}}_{1}+{\mathrm{A}}_{2}\frac{1-\mathsf{\epsilon}}{\mathsf{\epsilon}}+{\mathrm{A}}_{3}\frac{\mathsf{\Delta}\mathsf{\epsilon}}{{\mathsf{\epsilon}}^{2}}\right)\frac{{\mathrm{T}}_{10.8}+{\mathrm{T}}_{12}}{2}+\left({\mathrm{B}}_{1}+{\mathrm{B}}_{2}\frac{1-\mathsf{\epsilon}}{\mathsf{\epsilon}}+{\mathrm{B}}_{3}\frac{\mathsf{\Delta}\mathsf{\epsilon}}{{\mathsf{\epsilon}}^{2}}\right)\frac{{\mathrm{T}}_{10.8}-{\mathrm{T}}_{12}}{2}+\mathrm{C},$$
- Statistical Mono-Window (SMW) [11], where LST is computed based on an expression involving TOA brightness temperature and emissivity in a single thermal infrared channel (centered at 10.8 μm):$$\mathrm{LST}=\mathrm{A}\frac{{\mathrm{T}}_{\mathrm{c}}}{{\mathsf{\epsilon}}_{\mathrm{c}}}+\mathrm{B}\frac{1}{{\mathsf{\epsilon}}_{\mathrm{c}}}+\mathrm{C},$$
- Physical Mono-Window (PMW) [11,30], which is based on the direct inversion of the radiative transfer equation for one channel in the thermal infrared window (again centered at 10.8 μm):$$\mathrm{LST}\approx \left(\frac{{\mathrm{c}}_{2}{\mathsf{\nu}}_{\mathrm{c}}}{\mathrm{ln}\left(\frac{{\mathrm{c}}_{1}{\mathsf{\nu}}_{\mathrm{c}}^{3}{\mathsf{\tau}}_{\mathrm{c}}\left(\mathsf{\theta}\right){\mathsf{\epsilon}}_{\mathrm{c}}}{{\mathrm{L}}_{\mathrm{c}}\left(\mathsf{\theta}\right)-{\mathrm{L}}_{\mathrm{c}}^{\mathrm{up}}\left(\mathsf{\theta}\right)-{\mathrm{L}}_{\mathrm{c}}^{\mathrm{dn}}\left(1-{\mathsf{\epsilon}}_{\mathrm{c}}\right){\mathsf{\tau}}_{\mathrm{c}}\left(\mathsf{\theta}\right)}+1\right)}-\mathsf{\beta}\right)/\mathsf{\alpha},$$

#### 2.3. Orographic Correction of Atmospheric Profiles

- The exponential parametrization of Total Column Water Vapor. Assuming hydrostatic equilibrium, which is a good approximation for the vertical dependence of the pressure field in the real atmosphere, TPW decreases exponentially with height, where the rate of decay depends on the temperature lapse rate. As such, we tested a parametrization based on the exponential decrease of TPW with altitude [32,33], i.e.,$${\mathrm{TPW}}_{1}={\mathrm{TPW}}_{0}\mathrm{exp}\left(\frac{{\mathrm{H}}_{0}-{\mathrm{H}}_{1}}{\mathsf{\alpha}}\right)$$
- The Level reduction, which consists of using the surface pressure from COSMO and then, by linear interpolation, truncating the ERA-Int profile at that COSMO pressure level. This method is required for radiative transfer based LST retrieval algorithms (that use water vapor and temperature profiles as input). The method may also be used for statistically based algorithms with the drawback of introducing more variables to the models (thermodynamic profiles, where only TPW is required).

## 3. Results

#### 3.1. Difference between ERA-Int and COSMO TPW

#### 3.2. Sensitivity Analysis

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Crago, R.D.; Qualls, R.J. Use of land surface temperature to estimate surface energy fluxes: Contributions of Wilfried Brutsaert and collaborators. Water Resour. Res.
**2014**, 50, 3396–3408. [Google Scholar] [CrossRef] - Trigo, I.F.; Viterbo, P.; Trigo, I.F.; Viterbo, P. Clear-sky window channel radiances: A comparison between observations and the ECMWF model. J. Appl. Meteorol.
**2003**, 42, 1463–1479. [Google Scholar] [CrossRef] - Trigo, I.F.; Boussetta, S.; Viterbo, P.; Balsamo, G.; Beljaars, A.; Sandu, I. Comparison of model land skin temperature with remotely sensed estimates and assessment of surface-atmosphere coupling. J. Geophys. Res. Atmos.
**2015**, 120, 12096–12111. [Google Scholar] [CrossRef] - Ghent, D.; Kaduk, J.; Remedios, J.; Ardö, J.; Balzter, H. Assimilation of land surface temperature into the land surface model JULES with an ensemble Kalman filter. J. Geophys. Res.
**2010**, 115, D19112. [Google Scholar] [CrossRef] - Reichle, R.H.; Kumar, S.V.; Mahanama, S.P.P.; Koster, R.D.; Liu, Q.; Reichle, R.H.; Kumar, S.V.; Mahanama, S.P.P.; Koster, R.D.; Liu, Q. Assimilation of satellite-derived skin temperature observations into land surface models. J. Hydrometeorol.
**2010**, 11, 1103–1122. [Google Scholar] [CrossRef] - Caparrini, F.; Castelli, F.; Entekhabi, D. Variational estimation of soil and vegetation turbulent transfer and heat flux parameters from sequences of multisensor imagery. Water Resour. Res.
**2004**, 40, 1–15. [Google Scholar] [CrossRef] - Kalman, R.E. A new approach to linear filtering and prediction problems. J. Basic Eng.
**1960**, 82, 35–45. [Google Scholar] [CrossRef] - Kalman, R.E.; Bucy, R.S. New results in linear filtering and prediction theory. J. Basic Eng.
**1961**, 83, 95–107. [Google Scholar] [CrossRef] - Kustas, W.P.; Norman, J.M. Use of remote sensing for evapotranspiration monitoring over land surfaces. Hydrol. Sci. J.
**1996**, 41, 495–516. [Google Scholar] [CrossRef] - Wan, Z.; Wang, P.; Li, X. Using MODIS land surface temperature and normalized difference vegetation index products for monitoring drought in the southern Great Plains, USA. Int. J. Remote Sens.
**2004**, 25, 61–72. [Google Scholar] [CrossRef] - Duguay-Tetzlaff, A.; Bento, V.; Göttsche, F.; Stöckli, R.; Martins, J.; Trigo, I.; Olesen, F.; Bojanowski, J.; da Camara, C.; Kunz, H. Meteosat land surface temperature climate data record: Achievable accuracy and potential uncertainties. Remote Sens.
**2015**, 7, 13139–13156. [Google Scholar] [CrossRef] - Siemann, A.L.; Coccia, G.; Pan, M.; Wood, E.F. Development and analysis of a long-term, global, terrestrial land surface temperature dataset based on HIRS satellite retrievals. J. Clim.
**2016**, 29, 3589–3606. [Google Scholar] [CrossRef] - Dee, D.P.; Uppala, S.M.; Simmons, A.J.; Berrisford, P.; Poli, P.; Kobayashi, S.; Andrae, U.; Balmaseda, M.A.; Balsamo, G.; Bauer, P.; et al. The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc.
**2011**, 137, 553–597. [Google Scholar] [CrossRef] - Good, E. Daily minimum and maximum surface air temperatures from geostationary satellite data. J. Geophys. Res. Atmos.
**2015**, 120, 2306–2324. [Google Scholar] [CrossRef] - Oyler, J.W.; Dobrowski, S.Z.; Holden, Z.A.; Running, S.W.; Oyler, J.W.; Dobrowski, S.Z.; Holden, Z.A.; Running, S.W. Remotely sensed land skin temperature as a spatial predictor of air temperature across the conterminous United States. J. Appl. Meteorol. Climatol.
**2016**, 55, 1441–1457. [Google Scholar] [CrossRef] - Mountain Research Initiative EDW Working Group. Elevation-dependent warming in mountain regions of the world. Nat. Clim. Chang.
**2015**, 5, 424–430. [Google Scholar][Green Version] - Lawrimore, J.H.; Menne, M.J.; Gleason, B.E.; Williams, C.N.; Wuertz, D.B.; Vose, R.S.; Rennie, J. An overview of the Global Historical Climatology Network monthly mean temperature data set, version 3. J. Geophys. Res. Atmos.
**2011**, 116, D19121. [Google Scholar] [CrossRef] - Qin, J.; Yang, K.; Liang, S.; Guo, X. The altitudinal dependence of recent rapid warming over the Tibetan Plateau. Clim. Chang.
**2009**, 97, 321–327. [Google Scholar] [CrossRef] - Li, Z.-L.; Tang, B.-H.; Wu, H.; Ren, H.; Yan, G.; Wan, Z.; Trigo, I.F.; Sobrino, J.A. Satellite-derived land surface temperature: Current status and perspectives. Remote Sens. Environ.
**2013**, 131, 14–37. [Google Scholar] [CrossRef] - Masiello, G.; Serio, C.; De Feis, I.; Amoroso, M.; Venafra, S.; Trigo, I.F.; Watts, P. Kalman filter physical retrieval of surface emissivity and temperature from geostationary infrared radiances. Atmos. Meas. Tech.
**2013**, 6, 3613–3634. [Google Scholar] [CrossRef] - Masiello, G.; Serio, C.; Venafra, S.; Liuzzi, G.; Göttsche, F.; Trigo, I.F.; Watts, P. Kalman filter physical retrieval of surface emissivity and temperature from SEVIRI infrared channels: A validation and inter-comparison study. Atmos. Meas. Tech.
**2015**, 8, 2981–2997. [Google Scholar] [CrossRef] - Freitas, S.C.; Trigo, I.F.; Bioucas-Dias, J.M.; Göttsche, F.M. Quantifying the uncertainty of land surface temperature retrievals from SEVIRI/Meteosat. IEEE Trans. Geosci. Remote Sens.
**2010**, 48, 523–534. [Google Scholar] [CrossRef] - Derrien, M.; Gléau, H. MSG/SEVIRI cloud mask and type from SAFNWC. Int. J. Remote Sens.
**2005**, 21, 4707–4732. [Google Scholar] [CrossRef] - Trigo, I.F.; Dacamara, C.C.; Viterbo, P.; Roujean, J.-L.; Olesen, F.; Barroso, C.; Camacho-de-Coca, F.; Carrer, D.; Freitas, S.C.; García-Haro, J.; et al. The satellite application facility for land surface analysis. Int. J. Remote Sens.
**2011**, 32, 2725–2744. [Google Scholar] [CrossRef] - Baldauf, M.; Seifert, A.; Förstner, J.; Majewski, D.; Raschendorfer, M. Operational convective-scale numerical weather prediction with the COSMO model: Description and sensitivities. Mon. Weather Rev.
**2011**, 139, 3887–3905. [Google Scholar] [CrossRef] - Wan, Z.; Dozier, J. A generalized split-window algorithm for retrieving land-surface temperature from space. IEEE Trans. Geosci. Remote Sens.
**1996**, 34, 892–905. [Google Scholar] - Trigo, I.F.; Monteiro, I.T.; Olesen, F.; Kabsch, E. An assessment of remotely sensed land surface temperature. J. Geophys. Res.
**2008**, 113, D17108. [Google Scholar] [CrossRef] - Trigo, I.F.; Peres, L.F.; DaCamara, C.C.; Freitas, S.C. Thermal land surface emissivity retrieved from SEVIRI/Meteosat. IEEE Trans. Geosci. Remote Sens.
**2008**, 46, 307–315. [Google Scholar] [CrossRef] - Martins, J.P.A.; Trigo, I.F.; Bento, V.A.; da Camara, C. A Physically constrained calibration database for land surface temperature using infrared retrieval algorithms. Remote Sens.
**2016**, 8, 808. [Google Scholar] [CrossRef] - Yu, X.; Guo, X.; Wu, Z. Land surface temperature retrieval from Landsat 8 TIRS—Comparison between radiative transfer equation-based method, split window algorithm and single channel method. Remote Sens.
**2014**, 6, 9829–9852. [Google Scholar] [CrossRef] - Matricardi, M.; Chevallier, F.; Tjemkes, S. An improved general fast radiative transfer model for the assimilation of radiance observations. ECMWF Tech. Memo.
**2001**, 345, 153–173. [Google Scholar] [CrossRef] - Basili, P.; Bonafoni, S.; Mattioli, V.; Ciotti, P.; Pierdicca, N. Mapping the atmospheric water vapor by integrating microwave radiometer and GPS measurements. IEEE Trans. Geosci. Remote Sens.
**2004**, 42, 1657–1665. [Google Scholar] [CrossRef] - Morland, J.; Mätzler, C. Spatial interpolation of GPS integrated water vapour measurements made in the Swiss Alps. Meteorol. Appl.
**2007**, 14, 15–26. [Google Scholar] [CrossRef]

**Figure 4.**Scatterplot of the ratio of COSMO total precipitable water (TPW) at each grid point with respect to its surrounding neighbors, TPW

_{i}, versus differences in height ΔH (grey dots). The black curve represents an exponential fit to the data. Circles and whiskers represent the mean and standard deviation of TPW/TPW

_{i}, respectively, considering classes ΔH in steps of 100 m.

**Figure 5.**Histogram representing the relative frequency of ERA-Int TPW departures from COSMO reference TPW (in blue) for classes of 0.25 cm over the Alps for 2014. Median, 25th, and 75th percentiles of differences of height between ERA-Int and COSMO are shown in black lines.

**Figure 6.**Contingency tables of the COSMO and ERA-Int TPW (in mm) for the April to September period (only cases with height differences between models greater than 1000 m are used) (

**a**) uncorrected ERA-Int; (

**b**) ERA-Int with exponential correction.

**Figure 7.**Scatterplots of corrected versus original values of retrieved LST for the four different classes of ΔH (yellow, red, green and blue dots) when PMW (

**left panels**), SMW (

**middle panels**), and GSW (

**right panels**) retrieval algorithms are applied during extended summer (

**top panels**) and extended winter (

**bottom panels**).

**Table 1.**Land surface temperature (LST) root mean square difference (RMSD) (K) when comparing LST derived with COSMO profiles (reference) and LST derived with ERA-Int original profiles (Orig) and ERA-Int corrected with the different methods (Corr), for a physical mono-window (PMW) (

**a**), statistical mono-window (SMW) (

**b**), and generalized split-windows (GSW) (

**c**). N represents the number of profiles in a determined class of altitude difference and season. The seasons are extended winter (November–March) and extended summer (April–September).

LST (K) (RMSD) | 1000 < $\mathbf{\Delta}\mathbf{H}$ < 1250 | 1250 < $\mathbf{\Delta}\mathbf{H}$ < 1500 | 1500 < $\mathbf{\Delta}\mathbf{H}$ < 1750 | $\mathbf{\Delta}\mathbf{H}$ > 1750 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Orig | Corr | N | Orig | Corr | N | Orig | Corr | N | Orig | Corr | N | |

(a) PMW | ||||||||||||

November–March | 0.3 | 0.0 | 16,544 | 0.4 | 0.0 | 7230 | 0.5 | 0.0 | 2762 | 0.6 | 0.0 | 1126 |

April–September | 1.0 | 0.2 | 9091 | 1.2 | 0.2 | 4132 | 1.3 | 0.1 | 1582 | 1.8 | 0.1 | 629 |

(b) SMW | ||||||||||||

November–March | 0.1 | 0.0 | 16,544 | 0.0 | 0.0 | 7230 | 0.0 | 0.0 | 2762 | 0.0 | 0.0 | 1126 |

April–September | 0.5 | 0.2 | 9091 | 0.5 | 0.2 | 4132 | 0.5 | 0.1 | 1582 | 0.4 | 0.0 | 629 |

(c) GSW | ||||||||||||

November–March | 0.1 | 0.0 | 16,544 | 0.0 | 0.0 | 7230 | 0.0 | 0.0 | 2762 | 0.0 | 0.0 | 1126 |

April–September | 0.4 | 0.1 | 9091 | 0.4 | 0.1 | 4132 | 0.4 | 0.1 | 1582 | 0.3 | 0.0 | 629 |

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**MDPI and ACS Style**

Bento, V.A.; DaCamara, C.C.; Trigo, I.F.; Martins, J.P.A.; Duguay-Tetzlaff, A. Improving Land Surface Temperature Retrievals over Mountainous Regions. *Remote Sens.* **2017**, *9*, 38.
https://doi.org/10.3390/rs9010038

**AMA Style**

Bento VA, DaCamara CC, Trigo IF, Martins JPA, Duguay-Tetzlaff A. Improving Land Surface Temperature Retrievals over Mountainous Regions. *Remote Sensing*. 2017; 9(1):38.
https://doi.org/10.3390/rs9010038

**Chicago/Turabian Style**

Bento, Virgílio A., Carlos C. DaCamara, Isabel F. Trigo, João P. A. Martins, and Anke Duguay-Tetzlaff. 2017. "Improving Land Surface Temperature Retrievals over Mountainous Regions" *Remote Sensing* 9, no. 1: 38.
https://doi.org/10.3390/rs9010038