# 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

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**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 |

© 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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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