New land surface temperature retrieval algorithm for heavy aerosol loading during nighttime from Gaofen-5 satellite data

Enyu Zhao; Enyu Zhao; Caixia Gao; Caixia Gao; Yuying Yao

doi:10.1364/OE.382813

1. Introduction

Land surface temperature (LST) is a fundamental factor that regulates most of the physical, chemical and biological processes of the earth and is controlled by the surface energy balance, atmospheric state, surface thermal properties, and subsurface mediums [1–11]. Remote sensing is certainly useful for understanding the spatial distribution and temporal evolution of land cover changes in response to the basic physical properties of surface radiance and emissivity [12–20]. Since the first launch of the Heat Capacity Mapping Mission (HCMM) in 1978, which provided thermal imagery, different thermal infrared sensors onboard various platforms have been developed such as Terra/Moderate Resolution Imaging Spectroradiometer (MODIS), NPP/Visible infrared Imaging Radiometer (VIIRS), Landsat8/Thermal Infrared Sensor (TIRS), NOAA/Advanced Along-Track Scanning Radiometer (AATSR), etc.

The Chinese Gaofen-5 (GF5) satellite, launched on May 9, 2018, is the world's first full-spectrum hyperspectral satellite that has achieved comprehensive observations of the atmosphere and land [21–26]. The satellite has two mid-infrared (MIR) channels, centered at 3.67 µm (channel 7: 3.50 ∼ 3.90 µm) and 4.89 µm (channel 8: 4.67 ∼ 5.05 µm), and four thermal infrared (TIR) channels centered at 8.20 µm (channel 9: 8.01 ∼ 8.39 µm), 8.63 µm (channel 10: 8.42 ∼ 8.83 µm), 10.80 µm (channel 11: 10.30 ∼ 11.30 µm), and 11.95 µm (channel 12: 11.40 ∼ 12.50 µm). The spatial resolution is 40 m for the TIR and MIR images and 20 m for the visible, near-infrared, and shortwave images [27].

After GF5 satellite was launched, several methods were proposed to retrieve LST from simulated GF5 TIR data, such as the temperature and emissivity separation (TES) algorithm [27], split-window (SW) algorithm [28,29], and the hybrid algorithm [30]. For example, Yang et al. proposed a TES algorithm for the simultaneous retrieval of land surface temperature and emissivity (LST&E) from the TIR GF5 satellite data. The results showed that the bias and root mean square errors (RMSE) in the retrieved LST were 0.47 K and 1.70 K, respectively. Ye et al. used the four GF5 TIR channels to retrieve LST, and the LST RMSEs at three field sites were 0.45, 0.81, and 0.58 K, respectively. Tang et al. estimated LST and sea surface temperature (SST) using a nonlinear SW method, and the results showed that the RMSEs of LST and SST were 0.7 K and 0.3 K, respectively. A hybrid algorithm was proposed by Ren et al. to estimate LST from GF5 TIR data simulated from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data, and the RMSEs of LST and LSE were less than 1 K and 0.015, respectively. However, most LST retrieval algorithms were developed with a default aerosol type (rural aerosol) and ﬁxed aerosol loading (ground horizontal visibility equivalent to 23 km).

Dust aerosols consist of mineral dust particles of different sizes and shapes. Liu et al. indicated that spring is the most active dust season, during which ∼20% and ∼12% of areas between 0° and 60° N are influenced by dust at least 10% and 50% of the time, respectively [31]. Dust aerosols in particular have a large influence on the observed radiances by infrared channels of satellites. During the daytime, aerosol presence causes a decrease in the shortwave radiative flux at the surface, which results in a temperature drop and a longwave emission decrease at the surface. In addition, the emitted radiance from the surface is further reduced during its transfer through the dust layer [32–36]. Paepe et al. analyzed the brightness temperature in the MSG/SEVIRI 8.7 µm and 10.8 µm channels and found that the satellite-measured radiance over desert decreased in the presence of aerosols [37]. Ruescas et al. quantified the magnitude of aerosol absorption on SST retrieval using in situ and satellite SSTs derived from the AATSR and observed an increase in residuals greater than −0.5°C with aerosol concentration (aerosol optical thickness: AOD) values greater than 1.2 [38]. Diaz et al. found a bias of −3 K for the retrieval of SST from AVHRR data under atmospheres with heavy dust aerosol loading; the average errors ranged from 0.34°C for aerosol index (AI) values between 0.5 and 1.0 to 1.74°C for AI ≥ 1.5 [39]. Wan et al. also found that the MODIS LST retrieved from the generalized split-window (GSW) algorithm would be underestimated if the quantity of aerosol loading was greater than the fixed aerosol loading [40].

Until now, several methods have been proposed to reduce the influences of volcanic and dust aerosols on SST or LST retrieval. Luo et al. proposed a new method to derive a night-time dust-induced SST difference index (DSDI) algorithm based on simulated brightness temperatures and principal component analysis (PCA) at infrared wavelengths of 3.8, 8.9, 10.8, and 12.0 µm. The retrieval accuracy was improved by 0.263 K, and the accuracy of SST retrieval would be improved by 1.2 K if the volcanic aerosol or dust aerosol was considered in the SST retrieval algorithms [41]. Moreover, Fan et al. estimated land surface temperature from three thermal infrared channels of MODIS data for dust aerosol skies; the RMSEs of actual and estimated LSTs were 1.8 K and 1.6 K for dry and wet atmospheres, respectively [42]. However, due to the uncertainty of land surface emissivity for LST retrieval, few methods have been proposed to reduce the influences of heavy dust aerosol loading on LST retrieval from GF5 satellite data.

Therefore, the objective of this study was to develop a new LST retrieval algorithm for heavy aerosol loading during nighttime for GF5 satellite data. Inspired by the idea of the two-channel algorithm, a four-channel LST retrieval method is proposed in this article. This article is organized as follows: Section 2 describes the details of the methodology for the four-channel LST retrieval method. The datasets used in this article are presented in Section 3. Section 4 shows the retrieval results and the sensitivity analyses. Conclusions are presented in Section 5.

2. Methodology

For a cloud-free atmosphere under local thermodynamic equilibrium, the radiative transfer equation (RTE) can be written as [9]:

(1)$${B_i}({T_i}) = {\tau _i}[{{\varepsilon_i}{B_i}({T_s}) + (1 - {\varepsilon_i})(R_{atm\_i}^ \downarrow + R_{atm\_i}^{s \downarrow }) + {\rho_{bi}}R_i^s} ]+ R_{atm\_i}^ \uparrow + R_{atm\_i}^{s \uparrow }$$

where ${B_i}(T)$ is the radiance in channel i corresponding to the emission of a blackbody at temperature T. ${T_i}$ is the brightness temperature at the top of the atmosphere (TOA) in channel i. ${\varepsilon _i}$ and ${T_s}$ are surface emissivity in channel i and surface temperature, respectively. ${\tau _i}$ is the transmittance of the atmosphere from the ground to the TOA along the viewing angle in channel i. $R_{atm\_i}^ \uparrow$ and $R_{atm\_i}^ \downarrow$ are the upward and downward atmospheric thermal radiance in channel i, respectively. $R_{atm\_i}^{\textrm{s} \uparrow }$ and $R_{atm\_i}^{\textrm{s} \downarrow }$ are the upward and downward solar diffusion radiance resulting from atmospheric scattering of the solar radiance in channel i. ${\rho _{bi}}$ is the spectral bidirectional reflectivity of the surface in channel i. $R_i^s$ is the solar radiance at ground level in channel i.

For the TIR data and night-time MIR data, the contribution of solar radiation can be neglected without loss of accuracy. Therefore, the RTE can be simplified as:

(2)$${B_i}({T_i}) = {\tau _i}[{{\varepsilon_i}{B_i}({T_s}) + (1 - {\varepsilon_i})R_{atm\_i}^ \downarrow } ]+ R_{atm\_i}^ \uparrow$$

According to the atmospheric radiation transfer theory, if an atmospheric equivalent temperature $T_a^ \uparrow$ is used, the upward atmospheric radiance $R_{atm\_i}^ \uparrow$ can be rewritten as [43]:

(3)$$R_{atm\_i}^ \uparrow \textrm{ = (1 - }{\tau _i}\textrm{)}{B_i}(T_a^ \uparrow )$$

Therefore, based on the radiative transfer theory with the Eq. (3) inserted, the TOA radiance ${B_i}({T_i})$ in channel i can be expressed as:

(4)$${B_i}({T_i}) = {\tau _i}{B_i}(T_i^{\prime}) + (1 - {\tau _i}){B_i}(T_a^ \uparrow )$$

where ${B_i}(T_i^{\prime})$ is the channel radiance observed at ground level with the brightness temperature $T_i^{\prime}$ at ground level.

The first order of the Taylor’s expansion of the Planck function in the vicinity of temperature ${T_0}$ is as follows:

(5)$${B_i}(T) = {B_i}({T_0}) + \frac{{\partial {B_i}}}{{\partial T}}(T - {T_0})$$

After approximating the Planck functions ${B_i}(T_i^{\prime})$ and ${B_i}(T_a^ \uparrow )$ in Eq. (4) with the first Taylor’s expansion, the following expression is obtained:

(6)$$T_i^{\prime} = \frac{{{T_i}}}{{{\tau _i}}} - \frac{{1 - {\tau _i}}}{{{\tau _i}}}T_a^ \uparrow$$

Sobrino and Raissouni proposed a two-channel method to retrieve LST [44], which is expressed in this study as:

(7)$${T_s} = T_i^{\prime} + {a_1}(T_i^{\prime} - T_j^{\prime}) + {a_2}(1 - \varepsilon ) + {a_3}\Delta \varepsilon + {a_4}W(1 - \varepsilon ) + {a_5}W\Delta \varepsilon + {a_0}$$

where ${T_s}$ is the retrieved LST. $T_i^{\prime}$ and $T_j^{\prime}$ are the brightness temperature at ground level in channels i and j, respectively. $\varepsilon$ and $\Delta \varepsilon$ are the mean emissivity and emissivity difference, respectively. In addition, $\varepsilon = {{({\varepsilon _i} + {\varepsilon _j})} \mathord{\left/ {\vphantom {{({\varepsilon_i} + {\varepsilon_j})} 2}} \right.} 2}$ and $\Delta \varepsilon = ({\varepsilon _i} - {\varepsilon _j})$, where ${\varepsilon _i}$ and ${\varepsilon _j}$ are the emissivities in channels i and j, respectively. W is the water vapor content, and a₀ ∼ a₅ are the fitting coefficients.

Substituting Eq. (6) into Eq. (7), we obtain:

(8)$$\begin{array}{l} {T_s} = \frac{{{T_1}}}{{{\tau _1}}} + {a_1}(\frac{{{T_1}}}{{{\tau _1}}} - \frac{{{T_2}}}{{{\tau _2}}}) + [{a_1}\frac{{1 - {\tau _2}}}{{{\tau _2}}} - {a_1}\frac{{1 - {\tau _1}}}{{{\tau _1}}} - \frac{{1 - {\tau _1}}}{{{\tau _1}}}]T_a^ \uparrow \\ \;\;\;\; + {a_2}(1 - {\varepsilon _T}) + {a_3}\Delta {\varepsilon _T} + {a_4}W(1 - {\varepsilon _T}) + {a_5}W\Delta {\varepsilon _T} + {a_0} \end{array}$$

where ${T_1}$ and ${T_2}$ are the brightness temperatures in two TIR channels. ${\tau _1}$ and ${\tau _2}$ are the transmittances in two TIR channels. ${\varepsilon _T}$ is the mean emissivity, ${\varepsilon _T}\textrm{ = }{{({\varepsilon _1} + {\varepsilon _2})} \mathord{\left/ {\vphantom {{({\varepsilon_1} + {\varepsilon_2})} 2}} \right.} 2}$, where ${\varepsilon _1}$ and ${\varepsilon _2}$ are the emissivities in two TIR channels. $\Delta {\varepsilon _T}$ is the emissivity difference, $\Delta {\varepsilon _T} = {\varepsilon _1} - {\varepsilon _2}$.

To eliminate $T_a^ \uparrow$ in Eq. (8), another two-channel equation in two MIR channels is selected:

(9)$$\begin{array}{l} {T_s} = \frac{{{T_3}}}{{{\tau _3}}} + {b_1}(\frac{{{T_3}}}{{{\tau _3}}} - \frac{{{T_4}}}{{{\tau _4}}}) + [{b_1}\frac{{1 - {\tau _4}}}{{{\tau _4}}} - {b_1}\frac{{1 - {\tau _3}}}{{{\tau _3}}} - \frac{{1 - {\tau _3}}}{{{\tau _3}}}]T_a^ \uparrow \\ \;\;\;\; + {b_2}(1 - {\varepsilon _M}) + {b_3}\Delta {\varepsilon _M} + {b_4}W(1 - {\varepsilon _M}) + {b_5}W\Delta {\varepsilon _M} + {b_0} \end{array}$$

in which ${T_3}$ and ${T_4}$ are the brightness temperature in two MIR channels. ${\tau _3}$ and ${\tau _4}$ are the transmittances in two MIR channels. ${\varepsilon _M}$ is the mean emissivity, ${\varepsilon _M}\textrm{ = }{{({\varepsilon _3} + {\varepsilon _4})} \mathord{\left/ {\vphantom {{({\varepsilon_3} + {\varepsilon_4})} 2}} \right.} 2}$, where ${\varepsilon _3}$ and ${\varepsilon _4}$ are the emissivities in two MIR channels. $\Delta {\varepsilon _M}$ is the emissivity difference, $\Delta {\varepsilon _M} = {\varepsilon _3} - {\varepsilon _4}$, and b₀ ∼ b₅ are the fitting coefficients.

Combining Eq. (8) and Eq. (9), on the premise of $T_a^ \uparrow$ is the same in all channels, the $T_a^ \uparrow$ can be eliminated, and the new four-channel method can be obtained as follows:

(10)$$\begin{array}{l} {T_s} = {A_1}{T_1} + {A_2}{T_2} + {A_3}{T_3} + {A_4}{T_4} + {A_5}[{a_2}(1 - {\varepsilon _T}) + {a_3}\Delta {\varepsilon _T} + {a_4}W(1 - {\varepsilon _T}) + {a_5}W\Delta {\varepsilon _T}] + \\ \;\;\;\;\;\;{A_6}[{b_2}(1 - {\varepsilon _M}) + {b_3}\Delta {\varepsilon _M} + {b_4}W(1 - {\varepsilon _M}) + {b_5}W\Delta {\varepsilon _M}] + {A_0} \end{array}$$

where

(11)$${A_1} = \frac{{(1 + {a_1}){M_2}}}{{({M_2} - {M_1}){\tau _1}}}$$

(12)$${A_2} ={-} \frac{{{a_1}{M_2}}}{{({M_2} - {M_1}){\tau _2}}}$$

(13)$${A_3} ={-} \frac{{(1 + {b_1}){M_1}}}{{({M_2} - {M_1}){\tau _3}}}$$

(14)$${A_4} = \frac{{{b_1}{M_1}}}{{({M_2} - {M_1}){\tau _4}}}$$

(15)$${A_5} = \frac{{{M_2}}}{{{M_2} - {M_1}}}$$

(16)$${A_6} ={-} \frac{{{M_1}}}{{{M_2} - {M_1}}} = 1 - {A_5}$$

(17)$${A_0} = \frac{{{a_0}{M_2} - {b_0}{M_1}}}{{{M_2} - {M_1}}}$$

in which ${M_1}\textrm{ = }{a_1}\frac{{1 - {\tau _2}}}{{{\tau _2}}} - {a_1}\frac{{1 - {\tau _1}}}{{{\tau _1}}} - \frac{{1 - {\tau _1}}}{{{\tau _1}}}$ and ${M_2}\textrm{ = }{b_1}\frac{{1 - {\tau _4}}}{{{\tau _4}}} - {b_1}\frac{{1 - {\tau _3}}}{{{\tau _3}}} - \frac{{1 - {\tau _3}}}{{{\tau _3}}}$.

Figure 1 shows the relationship between the values of A₀, A₁, A₂, A₃, A₄, A₅ and the atmospheric WVC, where the coefficients a₀, a₁, b₀, b₁ are obtained by the statistical regression method from Eq. (7). From the figure, it can be seen that the values of A₀, A₁, A₂, A₃, A₄, A₅ depend on the WVC for the selected 380 atmospheric profiles (see Section 3) and that these values scatter when the WVC increases. Then, Eq. (10) can thus be expressed as:

(18)$${T_s} = {c_1}{T_{T1}} + {c_2}{T_{T2}} + {c_3}{T_{M1}} + {c_4}{T_{M2}} + {c_5}{\varepsilon _T} + {c_6}\Delta {\varepsilon _T} + {c_7}{\varepsilon _M} + {c_8}\Delta {\varepsilon _M} + {c_0}$$

where ${T_{T1}}$ and ${T_{T2}}$ are the TOA brightness temperatures in two TIR channels. ${T_{M1}}$ and ${T_{M2}}$ are the TOA brightness temperatures in two MIR channels. c₀∼c₈ are the coefficients of the four-channel method and are dependent on the WVC.

Fig. 1. The values of A₀, A₁, A₂, A₃, A₄, A₅ in Eq. (10) versus WVC. (a) for value of A₀; (b) for value of A₁; (c) for value of A₂; (d) for value of A₃; (e) for value of A₄; and (f) for value of A₅

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3. Simulation datasets

To develop the four-channel LST retrieval method, the at-sensor radiances should be simulated. For this purpose, the MODerate resolution atmospheric TRANsmission (MODTRAN) 4.0 computer code was used to predict the radiances for the GF5 TIR channels (channels 9, 10, 11, and 12) and the MIR channels (channel 7 and channel 8) in terms of the channel filter functions. MODTRAN was developed and continues to be maintained via a longstanding collaboration between Spectral Sciences, Inc. (SSI) and the Air Force Research Laboratory (AFRL). The MODTRAN software computes line-of-sight (LOS) atmospheric spectral transmittances and radiances over the ultraviolet through the long-wavelength infrared spectral regime (0-50,000 cm^-1; > 0.2 µm) [45]. The Thermodynamic Initial Guess Retrieval (TIGR) database, which was constructed by the Laboratoire de Meteorologie Dynamique (LMD) and represents a worldwide set of atmospheric situations (2311 radisoundings) from polar to tropical atmosphere with varying water vapor amounts ranging from 0.1 to 8 g/cm² [46], is used to analyze the atmospheric effects. In addition, there are 70 different surface emissivities obtained from the Johns Hopkins University (JHU) Spectral library (including soils, vegetation, and water, etc.) are taken into consideration in this study. Also, the Optical Properties of Aerosols and Clouds (OPAC) software is used to add the aerosol information for 10 aerosol types into the TIGR atmospheric profiles. The OPAC software easily provides optical properties in the solar and terrestrial spectral range of atmospheric particulate matter. The optical properties are the extinction, scattering, and absorption coefficients, the single scattering albedo, the asymmetry parameter, and the phase function [47].

To retrieve LST, only clear-sky conditions were considered. Consequently, the profiles whose relative humidity at one of the levels is greater than 90% in the TIGR database were discarded since this seldom happens under clear-sky conditions [48]. In this study, 380 representative atmospheric situations were extracted from the TIGR database. Figure 2 shows a plot of WVC as a function of the atmospheric temperature in the first layer above the surface of these selected atmosphere profiles. As shown, the atmospheric bottom temperature (T₀) varies from 250 to 310 K and the WVC changes from 0.1 to 5.39 g/cm².

Fig. 2. Plot of the atmospheric water vapor content as function of atmospheric temperature

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To simulate TOA radiances, for each atmospheric profile, five values of surface temperature were considered, from T_a -5 K to T_a +15 K with a step of 5 K. Moreover, the view zenith angles (VZAs) were set to 0°, 33.56°, 44.42°, 51.32°, 56.25° and 60°, corresponding to 1/cos(VZA) values of 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0, respectively; 1/cos(VZAs) could thus be sampled with a step of 0.2. Additionally, the AOD was set to the range 0.1 to 1.0 with a step of 0.1 in the MODTRAN software. In total, 79,800,000 groups of simulated data could be obtained for the algorithm development (380 atmospheric profiles × 5 LSTs × 70 emissivities × 6 VZAs × 10 AODs × 10 OPAC aerosol types).

4. Results and sensitivity analyses

4.1 Four-channel algorithm coefficients

To improve the accuracy of the retrieved LST, for each AOD and VZA, the WVC was divided into five sub-ranges with an overlap of 0.5 g/cm²: [0, 1.5], [1.0, 2.5], [2.0, 3.5], [3.0, 4.5], and [4.0, 5.5] g/cm². Then, the coefficients c₀ ∼ c₈ in Eq. (18) could be obtained via the statistical regressions method for each VZA and AOD sub-range. Since there are four TIR channels on the GF5 satellite, the question is how to select the channels, that is, how to combine the two MIR channels with two adjacent TIR channels to obtain the LST. In this paper, two channel combinations are compared, combination 1 (channels 7, 8, 9, and 10), denoted as CC1, and combination 2 (channels 7, 8, 11, and 12), denoted as CC2.

Figures 3(a)–3(h) display the coefficients of the two channel combinations as functions of the secant VZA for the sub-ranges with dry atmosphere (WVC: 0 ∼ 1.5 g/cm²), wet atmosphere (WVC: 4 ∼ 5.5 g/cm²) and AODs of 0.1 and 1.0. As shown in these figures, the coefficients c₀∼c₈ can be linearly interpolated in functions of the secant VZA for both channel combinations. Similar results are obtained for the other sub-ranges.

Fig. 3. Coefficients for the sub-ranges of dry and wet atmospheres. (a) for CC1, WVC: 0∼1.5 g/cm², AOD: 0.1; (b) for CC1, WVC: 0∼1.5 g/cm², AOD: 1.0; (c) for CC1, WVC: 4∼5.5 g/cm², AOD: 0.1; (d) for CC1, WVC: 4∼5.5 g/cm², AOD: 1.0; (e) for CC2, WVC: 0∼1.5 g/cm², AOD: 0.1; (f) for CC2, WVC: 0∼1.5 g/cm², AOD: 1.0; (g) for CC2, WVC: 4∼5.5 g/cm², AOD: 0.1; and (h) for CC2, WVC: 4∼5.5 g/cm², AOD: 1.0.

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4.2 LST Estimation

Figure 4 displays the histograms of the difference between the actual T_s and the T_s estimated using the four-channel algorithm with the coefficients corresponding to the sub-ranges WVC: 1∼2.5 g/cm² and VZA = 0° and for the AODs of 0.1 and 1.0, respectively. The RMSEs between the actual and estimated T_s are 0.28 K for the CC1 group with an AOD of 0.1 and 1.94 K for the other group with an AOD of 1.0. The RMSEs are 0.28 K for the CC2 group with an AOD of 0.1 and 2.54 K for an AOD of 1.0. Similar results were obtained for the other groups.

Fig. 4. Histogram of the difference between the actual and estimated T_s for the sub-range with VZA being 0°, and WVC from 1.0 g/cm² to 2.5 g/cm². (a) for CC1, AOD: 0.1; (b) for CC1, AOD: 1.0; (c) for CC2, AOD: 0.1; and (d) for CC2, AOD: 1.0

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The RMSEs between the actual and estimated T_s are given as functions of AOD for different WVC sub-ranges in Fig. 5. The RMSE increases with increasing VZA, and the same rule appears with the increase of AOD. The RMSEs are less than 1 K in all sub-ranges with AOD less than 0.2 for CC1 and CC2. The minimum RMSE is 0.28 K when the WVC varies from 0 to 1.5 g/cm², AOD is 0.1 and VZA is 0° for both channel combinations. The maximum RMSEs are 3.59 K and 4.72 K with WVC varying from 4 to 5.5 g/cm², an AOD of 1.0 and a VZA of 60° for CC1 and CC2, respectively. The differences between RMSE for CC1 and CC2 increase with the increase of AOD. The biggest difference appears in the sub-range of WVC varying from 4 to 5.5 g/cm², an AOD of 1.0, and a VZA of 60°.

Fig. 5. RMSEs between the actual and estimated T_s are given as functions of AOD for different sub-ranges of WVC for CC1and CC2.

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4.3 Sensitivity analysis

The accuracy of LST retrieval can be affected by the instrumental noises, uncertainties of LSEs and atmospheric properties, and the uncertainty of the method and some other factors. In this study, the instrument noises (noise equivalent temperature difference, NEΔT), the uncertainties of LSEs, WVCs, and AODs are taken into account.

4.3.1 Sensitivity analysis for instrumental noises

The expected NEΔT in GF5 TIR and MIR channels is less than 0.2 K. In this part, a Gaussian random distribution error of 0.2 K was added to the TOA brightness temperatures of the four channels in Eq. (18) to analyze the impact of NEΔT on the LST retrieval. In addition, the errors between the LSTs retrieved from the noise-added brightness temperatures and those determined from the noise-free brightness temperatures for AOD sub-ranges of 0.1 and 1.0 in the five WVC sub-ranges are shown in Fig. 6. It is seen that a NEΔT of 0.2 K produces an error of approximately within 0.4 K when AOD is 0.1 and within 2.0 K when AOD is 1.0 for CC1; the error is less than 0.4 K when AOD is 0.1 and within 1.7 K when AOD is 1.0 for CC2.

Fig. 6. LST retrieval error caused by NEΔT. (a) for CC1, AOD: 0.1; (b) for CC1, AOD: 1.0; (c) for CC2, AOD: 0.1; and (d) for CC2, AOD: 1.0.

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4.3.2 Sensitivity analysis for LSEs

A 1% uncertainty of LSEs was added to the averaged $\varepsilon$ and the emissivity difference $\Delta \varepsilon$. The effects of the emissivity uncertainty on LST retrieval are displayed in Table 1 and Table 2 for the condition of VZA = 0° for CC1 and CC2, respectively. The values in the two tables are the RMSEs which were obtained from the LSTs retrieved from LSE-uncertainty-added conditions minus those determined from no-LSE-uncertainty conditions. Note that the RMSEs vary from 0.31 to 1.01 K, with a mean error of 0.70 K for CC1, and the errors increase with the increase of AOD in Table 1. The same results can be found in other sub-ranges of VZAs.

Table 1. Effect of the emissivity uncertainty (0.01) on LST retrieval for CC1

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Table 2. Effect of the emissivity uncertainty (0.01) on LST retrieval for CC2

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From Table 2, it can be seen that the LST retrieval errors vary from 0.32 to 3.08 K with a mean error of 1.14 K for CC2; errors decrease with the increase of WVC and errors increase with the increase of AOD. The same results can be found for other VZA sub-ranges.

4.3.3 Sensitivity analysis for WVC

The LST retrieval accuracy is influenced significantly by the accuracy of atmospheric data. In this study, the WVC was divided into different sub-ranges to improve the LST retrieval accuracy as mentioned in Section 4.1. In this work, a 20% uncertainty of WVC was added to the true WVC, and the new WVC is then used to select the coefficients in Eq. (18) to retrieve the LST [49].

Figures 7(a)–7(h) show the RMSEs between the LSTs retrieved from the atmospheres with no WVC errors and the LSTs derived from the atmospheres with 20% uncertainty of WVC. From Fig. 7, it can be seen that for the dry atmospheres (WVC: 0∼1.5 g/cm²), when the AOD is 0.1, the RMSEs are 0.08 K and 0.11 K for CC1 and CC2, respectively; when the AOD is 1.0, the RMSEs are 0.26 K and 0.70 K for CC1 and CC2, respectively (see Figs. 7(a)–7(d)). For the wet atmospheres (WVC: 4∼5.5 g/cm²), when the AOD is 0.1, the RMSEs are 0.14 K and 0.11 K for CC1 and CC2, respectively; when the AOD is 1.0, the RMSEs are 0.60 K and 0.52 K for CC1 and CC2, respectively [see Figs. 7(e)–7(h)].

Fig. 7. Histogram of the difference between the estimated LST_WVC obtained from atmospheres with no WVC errors and estimated LST_ΔWVC retrieved from atmospheres with 20% uncertainty of WVC for the dry and wet atmospheres. (a) for CC1, AOD = 0.1, WVC∈[0.0, 1.5] g/cm²; (b) for CC2, AOD = 0.1, WVC∈[0.0, 1.5] g/cm²; (c) for CC1, AOD = 1.0, WVC∈[0.0, 1.5] g/cm²; (d) for CC2, AOD = 1.0, WVC∈[0.0, 1.5] g/cm²; (e) for CC1, AOD = 0.1, WVC∈[4.0, 5.5] g/cm²; (f) for CC2, AOD = 0.1, WVC∈[4.0, 5.5] g/cm²; (g) for CC1, AOD = 1.0, WVC∈[4.0, 5.5] g/cm²; and (h) for CC2, AOD = 1.0, WVC∈[4.0, 5.5] g/cm².

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4.3.4 Sensitivity analysis for AOD

The retrieval of AOD from space is generally challenging over land. To numerically analyze the sensitivity of the LST retrieved using the four-channel algorithm [Eq. (18)] to AOD uncertainty, the AOD was increased by 0.1 in this section [50].

Figures 8(a)–8(h) show the RMSEs between the LSTs retrieved using the coefficients in the sub-range of original AOD and the LSTs obtained using the coefficients in the sub-range with AOD larger by 0.1 due to the AOD error. From Fig. 8, it can be seen that for the dry atmospheres, when the AOD (whose original value is 0.1) was increased by 0.1, the RMSEs are 0.26 K and 0.29 K, the BIASs are 0.13 K and 0.14 K for CC1 and CC2, respectively; when the AOD (whose original value is 0.9) was increased by 0.1, the RMSEs are 0.11 K and 0.14 K, the BIASs are 0.05 K and 0.09 K for CC1 and CC2, respectively [see Figs. 8(a)–8(d)]. For the wet atmospheres, when the original AOD is 0.1, the RMSEs are 0.23 K and 0.25 K, the BIASs are 0.09 K and 0.10 K for CC1 and CC2, respectively; when the original AOD is 1.0, the RMSEs are 0.13 K and 0.16 K, the BIASs are 0.06 K and 0.11 K for CC1 and CC2, respectively [see Figs. 8(e)–8(h)].

Fig. 8. Histogram of the LST error due to the uncertainty of AOD for the dry and wet atmospheres. (a) for CC1, original AOD = 0.1, WVC∈[0.0, 1.5] g/cm²; (b) for CC2, original AOD = 0.1, WVC∈[0.0, 1.5] g/cm²; (c) for CC1, original AOD = 0.9, WVC∈[0.0, 1.5] g/cm²; (d) for CC2, original AOD = 0.9, WVC∈[0.0, 1.5] g/cm²; (e) for CC1, original AOD = 0.1, WVC∈[4.0, 5.5] g/cm²; (f) for CC2, original AOD = 0.1, WVC∈[4.0, 5.5] g/cm²; (g) for CC1, original AOD = 0.9, WVC∈[4.0, 5.5] g/cm²; and (h) for CC2, original AOD = 0.9, WVC∈[4.0, 5.5] g/cm².

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5. Conclusions

A new four-channel algorithm was proposed to fully utilize the information from the four infrared window channels of GF5 visual and infrared multispectral image (VIMS) measurements to reduce the heavy dust aerosol effect on LST retrieval during nighttime. To develop the four-channel LST retrieval method, the simulated dataset was generated with the aid of the atmospheric radiative transfer model MODTRAN 4.0. The numerical values of the algorithm coefficients were obtained using a statistical regression method from numerically simulated GF5 TIR and MIR data under different atmospheric, surface and AOD conditions.

The simulation results showed that the proposed four-channel algorithm based on the combination of channels 7, 8, 9, and 10 (denoted as CC1) performed better than that based on channels 7, 8, 11, and 12 (denoted as CC2) and that the RMSEs between the actual and estimated LSTs were 0.28 K for CC1 with an AOD of 0.1 and 1.94 K with an AOD of 1.0. Sensitivity analyses related to instrument noise, the uncertainty in the LSEs, atmospheric WVC, and AOD were performed. The results showed that the LST retrieval errors increased as AOD increased. Compared with LST retrieval without NEΔT, adding a NEΔT of 0.2 K resulted in an error within 0.4 K when AOD was 0.1 and within 2.0 K when AOD was 1.0 for CC1; the error range was 0.4 K when AOD was 0.1 and within 1.7 K when AOD was 1.0 for CC2. Assuming that a 1% uncertainty of LSEs was added to the averaged $\varepsilon$ and the emissivity difference $\Delta \varepsilon$, the influence on the LST retrieval error for CC1 increased with increased AOD in the same WVC sub-range, and the error changed slightly as the WVC increased in the same AOD sub-range, with a maximum RMSE of 1.01 K. However, the influence for CC2 was relatively significant, particularly for the dry atmospheres with a maximum RMSE of up to 3.08 K. The uncertainty of WVC could cause the LST retrieval errors to be approximately 0.6 K and 0.7 K for CC1 and CC2, respectively. The uncertainty of AOD could cause the LST retrieval errors to be approximately 0.3 K for both CC1 and CC2, respectively.

This paper provides a valuable algorithm for retrieving LSTs from GF5/VIMS measurements under heavy aerosol conditions. However, due to the paper length limits, the method has not been validated by GF5 observations, which will be addressed in the next research step.

Funding

National Natural Science Foundation of China (41671370, 41801231, 61601077, 61971082); Fundamental Research Funds for the Central Universities (3132019208, 3132019341).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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AOD WVC	0-1.5 g/cm²	1-2.5 g/cm²	2-3.5 g/cm²	3-4.5 g/cm²	4-5.5 g/cm²
0.1	0.35	0.32	0.32	0.32	0.31
0.2	0.40	0.38	0.36	0.34	0.35
0.3	0.49	0.55	0.48	0.42	0.45
0.4	0.63	0.73	0.64	0.54	0.60
0.5	0.74	0.85	0.77	0.65	0.72
0.6	0.81	0.92	0.85	0.74	0.80
0.7	0.86	0.96	0.90	0.80	0.86
0.8	0.88	0.99	0.94	0.84	0.90
0.9	0.90	1.00	0.96	0.87	0.92
1.0	0.91	1.01	0.98	0.89	0.94

AOD WVC	0-1.5 g/cm²	1-2.5 g/cm²	2-3.5 g/cm²	3-4.5 g/cm²	4-5.5 g/cm²
0.1	0.68	0.56	0.41	0.33	0.32
0.2	0.52	0.37	0.39	0.36	0.36
0.3	1.10	0.69	0.66	0.45	0.45
0.4	1.66	1.02	0.89	0.54	0.55
0.5	2.11	1.33	1.09	0.60	0.61
0.6	2.44	1.59	1.26	0.65	0.65
0.7	2.68	1.82	1.42	0.70	0.68
0.8	2.86	2.01	1.55	0.76	0.71
0.9	2.99	2.17	1.67	0.81	0.74
1.0	3.08	2.29	1.76	0.85	0.75

AOD WVC	0-1.5 g/cm²	1-2.5 g/cm²	2-3.5 g/cm²	3-4.5 g/cm²	4-5.5 g/cm²
0.1	0.35	0.32	0.32	0.32	0.31
0.2	0.40	0.38	0.36	0.34	0.35
0.3	0.49	0.55	0.48	0.42	0.45
0.4	0.63	0.73	0.64	0.54	0.60
0.5	0.74	0.85	0.77	0.65	0.72
0.6	0.81	0.92	0.85	0.74	0.80
0.7	0.86	0.96	0.90	0.80	0.86
0.8	0.88	0.99	0.94	0.84	0.90
0.9	0.90	1.00	0.96	0.87	0.92
1.0	0.91	1.01	0.98	0.89	0.94

AOD WVC	0-1.5 g/cm²	1-2.5 g/cm²	2-3.5 g/cm²	3-4.5 g/cm²	4-5.5 g/cm²
0.1	0.68	0.56	0.41	0.33	0.32
0.2	0.52	0.37	0.39	0.36	0.36
0.3	1.10	0.69	0.66	0.45	0.45
0.4	1.66	1.02	0.89	0.54	0.55
0.5	2.11	1.33	1.09	0.60	0.61
0.6	2.44	1.59	1.26	0.65	0.65
0.7	2.68	1.82	1.42	0.70	0.68
0.8	2.86	2.01	1.55	0.76	0.71
0.9	2.99	2.17	1.67	0.81	0.74
1.0	3.08	2.29	1.76	0.85	0.75

New land surface temperature retrieval algorithm for heavy aerosol loading during nighttime from Gaofen-5 satellite data

Abstract

1. Introduction

2. Methodology

3. Simulation datasets

4. Results and sensitivity analyses

4.1 Four-channel algorithm coefficients

4.2 LST Estimation

4.3 Sensitivity analysis

4.3.1 Sensitivity analysis for instrumental noises

4.3.2 Sensitivity analysis for LSEs

4.3.3 Sensitivity analysis for WVC

4.3.4 Sensitivity analysis for AOD

5. Conclusions

Funding

Disclosures

References

Cited By

Figures (8)

Tables (2)

Equations (18)

Optics Express