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Abstract
Studies indicated that a root mean square error (RMSE) of 3.7 K was found if dust aerosol was not considered in the traditional land surface temperature (LST) retrieval algorithm. To reduce the influence of dust aerosol on LST estimation, a three-channel algorithm is proposed using MODIS channels 29, 31, and 32 with model coefficients irrelevant to the aerosol optical depth (AOD). Compared with actual and estimated LSTs, the RMSEs are 1.8 K and 1.6 K for dry and wet atmospheres, respectively, when the AOD is 1.0. Sensitivity analyses considering instrument noise, land surface emissivity uncertainties, and the algorithm error itself show that the LST errors are 2.5 K and 1.7 K for dry and wet atmospheres, respectively, when the AOD is 1.0. Finally, some in situ measured LSTs at the Jichanghuangmo, Huazhaizi, and Yingke sites in northwest China are taken as referenced LST values and compared with the MODIS LST products MOD11_L2/MYD11_L2 and those estimated with the proposed method. The results show that the proposed method can improve the LST retrieval accuracy from 1.4 K to 2.2 K in dust aerosol atmospheres.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is widely recognized that land surface temperature (LST) is a key parameter for many applications such as evapotranspiration [1–3], soil moisture [4, 5], climate change [6], and environmental studies [7–9]. To retrieve LST from satellite infrared radiometers, the single channel algorithms [10], multichannel algorithms [11–13], and multiangle algorithms were proposed [14]. A default aerosol type (rural aerosol) and a fixed aerosol loading (ground horizontal visibility equal to 23 km) have commonly been used in the development of those algorithms [15–18]. However, numerical simulations showed that a significant bias up to −3 K with a root mean square error (RMSE) of 3.7 K was found in the nadir view if dust aerosol was not considered in the LST retrieval algorithm [19]. Wan [20] also found that the Moderate-Resolution Imaging Spectroradiometer (MODIS) LST product is underestimated if the quantity of aerosol loading is greater than the fixed aerosol loading used in the development of the generalized split-window (GSW) LST retrieval algorithm. In addition, dust aerosol can also impact the estimates of sea surface temperature (SST), and some studies have indicated that a bias of greater than −3 K has been reported for the retrieval of SST from Advanced Very High Resolution Radiometer (AVHRR) data under atmospheres with heavy dust aerosol loading [21].
Spring is the most active dust season, and 20% of the global areas between 0° N and 60° N are influenced by dust at least 10% of the time [22]. Thus, some LST and SST retrieval algorithms have been proposed to reduce the influence of dust aerosol. There are two main algorithm categories to eliminate the influence of dust aerosol on SST retrieval: one is adding the terms of aerosol optical depth (AOD) in the SST retrieval algorithm [23, 24]. This showed that the accuracy of SST retrieval would be improved by 1.2 K if the dust aerosol was considered in the SST retrieval algorithms [25]. Another is using the channels that are relatively insensitive to dust aerosol [26]. For the LST retrieval, Fan et al. [19] proposed an LST retrieval algorithm for dust aerosol skies based on the GSW algorithm by adding a linear function of AOD. However, because of the difficulty related to the acquisition of reliable dust aerosol AOD estimates, especially at night [27], there are no available nighttime LST retrieval algorithms for dust aerosol conditions. Besides that, an original method that generates all-weather LST products combining thermal infrared and passive microwave satellite measurements was developed [28]. As we mainly focus on LST retrieval based on satellite thermal infrared data, it is not detailed discussed in this study.
Thus, the objective of this study is to develop an LST retrieval algorithm for dust aerosol areas (i.e., those frequently affected by dust aerosol) during the day and at night without the AOD as an input parameter. Considering that the two-channel algorithm proposed by Sobrino and Raissouni [29] is one of the most commonly used methods to estimate clear-sky LST from thermal remotely sensed data with considering the influences of atmosphere and land surface emissivity (LSE), a three-channel method based on the two-channel algorithm is proposed in this study. As MODIS is widely used to retrieve LST, this study uses MODIS as an example to develop the methodology. This paper is organized as follows: Section 2 provides the data used in this study; Section 3 describes the methodology for LST retrieval and the results; a sensitivity analysis is provided in Section 4; and Section 5 presents the results from evaluating the proposed algorithm using in situ measurements and MODIS satellite data. The discussion is in Section 6. The conclusions are presented in the last section.
2. Data
2.1 Simulated data
The atmospheric radiative transfer code Moderate Resolution Atmospheric Transmission version 4 (MODTRAN4.0) [30] is used to simulate the MODIS data needed to develop the methodology as a substitute for field measurements. In this study, 180 atmospheric profiles, 54 LSEs (including 41 soils, 4 vegetation, and 9 water/snow/ice), and the dust aerosol optical properties of transported mineral aerosol types were selected from the radiosonde observation database – the Thermodynamic Initial Guess Retrieval (TIGR) database [31] (http://ara.abct.lmd.polytechnique.fr/index.php?page=tigr), the Advanced Spaceborne Thermal Emission Reflection Radiometer (ASTER) spectral library [32, 33] (http://speclib.jpl.nasa.gov/), and the Optical Properties of Aerosols and Clouds (OPAC) software [34], respectively. These data are inputted into MODTRAN4.0 to produce the simulated data set.
Figure 1 is a plot of the atmospheric water vapor content (WVC) as a function of the temperature (T0) in the first layer of the 180 selected atmospheric profiles in TIGR; this plot shows that T0 varies from 233 K to 310 K, and the atmospheric WVC changes from 0.01 g/cm2 to 3.0 g/cm2. As dust aerosol mainly occurred in arid or semiarid regions during spring [35] with relatively low atmospheric WVC, only atmospheric profiles in TIGR with WVC of less than 3.0 g/cm2 are used in this study. In addition, because the accuracy of the LST retrieval algorithm is dependent on the atmospheric WVC, the WVC of those 180 atmospheric profiles are evenly distributed between 0.01 g/cm2 to 3.0 g/cm2 to make the simulated data set representative of all possible actual conditions.
Fig. 1 Atmospheric WVC as a function of the temperature (T0) in the first layer of the 180 selected atmospheric profiles from TIGR.
The extinction coefficient, single scattering albedo, and asymmetry parameter of MODIS thermal infrared window channels 29, 31, and 32 (centered at 8.5, 11.0, and 12.0 μm, respectively), with the extinction coefficient normalized to 1.0 at 0.55 μm, are given in Fig. 2. The LST retrieval method proposed in this study is used for both daytime and nighttime; thus, only thermal infrared window channels are considered. In Fig. 2, channel 29 shows the lowest extinction coefficient, which indicates that the atmospheric transmittance should be larger than that of the other channels in dust aerosol conditions.
Fig. 2 Dust aerosol extinction coefficient, single scattering albedo, and asymmetry parameter of MODIS channels 29, 31, and 32. The extinction coefficients are normalized to 1.0 at 0.55 μm.
Using the atmospheric profiles, LSEs, and dust aerosol optical properties from TIGR, ASTER, and OPAC, respectively, the top of the atmosphere (TOA) radiances of the three MODIS thermal infrared window channels 29, 31, and 32, including the influence of dust aerosol, are produced. In addition, to increase the representativeness of the simulations, the LST varied over a wide range from T0 minus 6 K to T0 plus 18 K with a step of 3 K. Considering the angular dependence of the TOA radiance, six different viewing zenith angles (VZAs) with VZA = 0°, 33.56°, 44.42°, 51.32°, 56.25°, and 60° (Secant(VZA) = 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0) are used in the simulations. After integrating the simulated TOA radiances and the channel response functions of MODIS channels 29, 31, and 32, the TOA brightness temperatures are calculated with the inversion of the Planck function and named Data-simu. The procedure for generating the Data-simu is shown in Fig. 3.
Fig. 3 Procedures for generating the Data-simu simulated data sets and the calculation of the coefficients for the proposed three-channel LST retrieval algorithm.
In addition, two categories of brightness temperatures measured at 3 km above the ground in the satellite direction are produced similarly to how Data-simu was produced for the methodology development. One category uses the complete vertical atmospheric profiles from the ground to the satellite elevation in the simulation (Data-whole); the other category truncates the atmospheric profiles at 3 km, and no atmospheres above this height are included (Data-truncated).
2.2 Satellite data
To evaluate the accuracy of the proposed LST retrieval method in this study, the actual MODIS data are acquired. Six MODIS products are used in the study: (1) the 5-min calibrated TOA radiance in 1-km resolution MOD021KM/MYD021KM, (2) the geolocation data in 1-km resolution MOD03/MYD03, (3) the 5-min aerosol product in 10-km resolution MOD04_L2/MYD04_L2, (4) the 5-min atmospheric WVC product in 1-km resolution MOD05_L2/MYD05_L2, (5) the 5-min LST and LSE products in 1-km resolution MOD11_L2/MYD11_L2, and (6) the 8-day global LST and LSE products in 0.05°-resolution MOD11C2/MYD11C2.
The observed radiances of channels 29, 31, and 32 in MOD021KM/MYD021KM are used to calculate the corresponding TOA brightness temperatures. Based on the radiances in MOD021KM/MYD021KM and the effective central wavenumber of the corresponding channels, the TOA brightness temperatures are acquired by inversion of the Planck function. Then, the TOA brightness temperatures are inputted into the three-channel algorithm to estimate the LST in this study.
The geodetic latitude and longitude in MOD03/MYD03 are used to perform the geometric corrections for MOD021KM/MYD021KM, MOD05_L2/MYD05_L2, and MOD11_L2/MYD11_L2. The satellite VZA in MOD03/MYD03 is taken as the input parameters of the proposed algorithm.
The AOD and aerosol type products in MOD04_L2/MYD04_L2 are applied to select the dust aerosol skies in this study. As the spatial resolution of the AOD and aerosol type products are 10 km, which is different from the spatial resolution of MOD021KM/MYD021KM, the AOD and aerosol type are first resampled to 1-km. Then, the pixels labeled as dust aerosols for the aerosol type with an AOD greater than 0.05 [36] are taken as the dust aerosol pixels in this study.
The atmospheric WVC in MOD05_L2/MYD05_L2 is used to select the coefficient groups of the proposed three-channel algorithm. There are two atmospheric WVC products in MOD05_L2/MYD05_L2 for the daytime: one is in 1-km resolution produced with near-infrared algorithm, another is 5-km resolution produced using infra-red algorithm. The 1-km resolution atmospheric WVC product is used in this study.
To evaluate the improvement of the proposed algorithm for LST retrieval in dust aerosol skies, the LST products in MOD11_L2/MYD11_L2 [37] produced by the GSW algorithm are compared with the results of the proposed algorithm. MOD11C2/MYD11C2 provides LSEs in channels 20, 22, 23, 29, 31, and 32 over a time interval of 8 days. The LSEs, resampled to 1 km for channels 29, 31, and 32, are used as the input parameters for the proposed method. Because MODIS aerosol products are not available at night, only daytime MODIS data are used in the validations. However, this algorithm can be used for the daytime and nighttime.
2.3 In situ measurements
The accuracy evaluation of the LST retrieval algorithm in this study uses three meteorological sites: the Jichanghuangmo (JCHM) (38.778°N, 100.696°E), Huazhaizi (HZZ) (38.765°N, 100.318°E), and Yingke (YK) (38.851°N, 100.401°E) sites. Those three sites are located in the Heihe River Basin in northwest China and are frequently affected by dust aerosol in the spring. The land surface type of the JCHM and HZZ sites is large and flat desert steppe, which consists of bare soil and a ground cover fraction of A. sparsifolia of approximately 0.1. The YK site is covered by a large and homogeneous corn field.
Two Apogee SI-111 thermal infrared radiometers are used at the JCHM site to measure the radiometric temperatures with a sample interval of 5 s; one observes the surface at nadir from a 4-m height with a footprint of 8 m2, and the other views the sky at an effective angle of approximately 55° from the zenith to measure the atmospheric downward radiance. The spectral range of the SI-111 radiometer is 8-14 μm, and the instrument accuracy used at the JCHM site is ± 0.2 K at temperatures from 238 K to 338 K (http://www.apogeeinstruments.com/infraredradiometer).
The HZZ and YK sites are equipped with Kipp & Zonen CNR1 net radiometers, which observe the surface at nadir from heights of 6 m and 4 m, respectively. The 30-min interval downward and upward longwave radiations that are integrated with 30-s sample records measured by CNR1 are used in this study. The spectral range of CNR1 net radiometers is 4.5-42 μm, and the accuracy is approximately 8 W/m2 during the day.
Those in situ measurements were collected from June, 8th 2012 to October, 17th 2012, from June, 1st 2008 to August, 29th 2009, and from November, 5th 2007 to August 28th, 2009 for the JCHM, HZZ, and YK sites, respectively, to calculate the in situ measured MODIS pixel scale LST in this study.
3. Methodology
3.1 Radiative transfer in dust aerosol skies
To develop the new LST retrieval algorithm, the vertical atmospheric column profile is divided into two layers: the lower-layer (from ground level to approximately 3 km in height) that is affected by dust aerosol and the upper-layer (above 3 km in height) that is not affected by dust aerosol [22]. Notably, 90-99% of the atmospheric water vapor is located below 10 km above the ground and most of the vapor is at less than 3 km [38]. Assuming that the upper-layer is isothermal, the upper-layer radiation in the satellite direction can be taken as the radiance emitted by a temperature Tatm-u with an emissivity of εiu. i is the channel number (i = 29, 31, or 32). Based on Kirchhoff’s law, the upper-layer emissivity can be expressed as:
where τiu is the transmittance of the upper-layer atmosphere in the satellite direction. Thus, based on the radiative transfer theory [14], the TOA outgoing radiance Bi(Ti) in the thermal infrared channel i can be expressed as:where Bi(Ti0) is the radiance in the direction of the satellite at the interface of the two atmospheric layers, Bi is the Planck function weighted with the spectral response function of channel i; Ti and Ti0 are the brightness temperatures in channel i measured at the TOA and the top of the lower-layer atmosphere in the direction of the satellite, respectively.To retrieve the LST using brightness temperatures rather than radiances, the first-order Taylor series expansion of the Planck function Bi(T) with respect to Ti is commonly used in the two-channel LST retrieval algorithms [39]:
After approximating the Planck functions Bi(Ti0) and Bi(Tatm-u) in Eq. (2) with the first-order Taylor series expansion with respect to Ti, we can obtain:Equation (4) indicates that the TOA brightness temperature Ti is the summation of Ti0 and Tatm-u weighted by τiu and 1-τiu.
To retrieve the LST in dust aerosol skies using the TOA measured brightness temperature Ti, the relationship between the LST and Ti0 needs to be clarified. The radiation at the interface of the two atmospheric layers, Bi(Ti0), is composed of four parts:
where the first part is the land surface radiation emitted by a temperature Ts with LSE equivalent to εi, while τi is the transmittances of the lower-layer atmosphere; the second is the ground-reflected downward radiation from the lower-layer atmosphere, in which R↓iatm-l is the hemispheric value of the downward atmospheric radiance; the third part R↑iatm-l is the upward radiation from the lower-layer atmosphere; the fourth is the downward radiations from the upper-layer atmosphere that are reflected by the ground, in which R↓iatm-u is the hemispheric value of the upper-layer downward atmospheric radiance; ri is the product of lower-layer atmosphere transmittances in the downward and upward directions. All of the parameters in Eq. (5) except Ts are weighted by the channel spectral response function in channel i.3.2 The three-channel algorithm
Assuming that the atmospheric profile is truncated at the top of the lower-layer atmosphere and no absorption or emission is assumed in the upper-layer atmosphere, then Bi(Ti0) is reduced to the sum of the first three parts in Eq. (5) and is labeled Bi(Ti’) in this study. Using Data-whole and Data-truncated, the differences between Ti0 and the corresponding Ti’ when the VZA is equivalent to 0° and 60° are calculated and named δ(Ti0) (i = 29, 31, and 32). The maximum values of δ(T320) as VZA equivalent to 0° versus the atmospheric WVC and LSE are shown in Fig. 4. The mean, maximum and standard deviations (STDs) of δ(Ti0) in the three MODIS thermal infrared window channels when the VZA is equivalent to 0° and 60° are given in Table 1.
Fig. 4 δ(T320) values versus atmospheric WVC and land surface emissivity in channel 32. δ(T320) is the brightness temperature difference between the T320 that is measured at the top of the dust aerosol and the corresponding values of T32’ with the atmospheres truncated above the top of the dust aerosol height.
Table 1. The mean, maximum, and STD of δ(Ti0) (i = 29, 31, or 32) in the three MODIS channels.
As shown in Fig. 4, the maximum value of δ(T320) is 0.32 K. The value of δ(T320) tends to increase in atmospheres with higher WVCs or when the LSE values are lower. This is because the atmospheric emissivity is larger in infrared window channels when the atmosphere is wet. Another reason is that the downward atmospheric radiance reflected by the ground is larger when LSE decreases (land surface reflectance increases). As shown in Table 1 for the conditions with VZA = 0° or 60°, the total maximum values of δ(Ti0) are less than 1 K. The mean values are less than 0.06 K, which is similar to the noise-equivalent temperature difference (NETD) of the MODIS thermal infrared channels. Table 1 indicates that the δ(Ti0), which is composed of the fourth part of Eq. (5), can be ignored. Thus, the fourth part of Eq. (5) are eliminated in further analysis of this study.
To determine an accurate estimate of the LST, many LST retrieval algorithms have been proposed to reduce the influences of the second and third parts of Eq. (5) under clear-sky conditions [40]. Sobrino and Raissouni [29] proposed a two-channel algorithm with separate terms for the atmospheric and LSE corrections to retrieve the LST. In this study, this algorithm can be written as:
where Ts is the retrieved LST; Ti0 and Tj0 are the brightness temperatures measured at the top of the lower-layer atmosphere in channels i and j, respectively; ε1 is the mean channel emissivity ε1 = (εi + εj)/2; Δε1 is the emissivity difference Δε1 = εi-εj; W is the total atmospheric water vapor content; and ai (i = 0-5) is the numerical coefficient of the two-channel algorithm.To study the possibility of using the two-channel algorithm to estimate the LST in dust aerosol skies with the data measured at the top of the lower-layer atmosphere, the simulated Data-truncated is used. With the LSTs set in MODTRAN and the corresponding simulated brightness temperatures in Data-truncated, the coefficients in Eq. (6) are determined using the statistical regression method. Table 2 shows the RMSEs between the given LSTs and the estimated LSTs using Eq. (6) for different MODIS channel combinations.
Table 2. RMSEs of LST estimated using Eq. (6) for different MODIS channel combinations.
Table 2 indicates that some of the MODIS channel combinations can be employed to retrieve LST in dust aerosol skies using the brightness temperatures measured at the top of the dust aerosol with a minimum RMSE of 1.1 K. In addition, the RMSE of channel combination 31 and 32 is less than the channel combinations of 29 and 31 or 29 and 32, although the dust aerosol extinction coefficient in channel 29 is lower than channels 31 and 32. This is because the retrieval accuracy of two-channel algorithms is significantly dependent on the LSEs [41]. The mean values of those 54 LSEs using in this study are 0.94, 0.97, and 0.98 for MODIS channels 29, 31, and 32, respectively, with STDs of 0.04, 0.01, and 0.01. Thus, the errors caused by the LSE are lower when using channels 31 and 32 than when using other channel combinations.
Considering the influence of the upper-layer atmosphere, Eq. (4) in channels i and j is used to eliminate Ti0 and Tj0 in Eq. (6), respectively. Thus, with changing the formation of Eq. (4) as the function of Ti0, the following equation is acquired by substitute Ti0 in Eq. (6) with the function of Ti0:
where τju is the upper-layer atmospheric transmittance in channel j. To eliminate Tatm-u in Eq. (7), another two-channel algorithm in channels i and k is selected:where Tk is the brightness temperature measured at the TOA in channel k; τku is the upper-layer atmospheric transmittance in channel k; ε2 is the mean channel emissivity ε2 = (εi + εk)/2; and Δε2 is the emissivity difference Δε2 = εi-εk. Combining Eqs. (7) and (8), the three-channel LST retrieval algorithm is proposed as follows:where
here, and .As i = 31, j = 29, and k = 32, Fig. 5 shows the values of A1, A2, A3, and A0 versus atmospheric WVC with the upper-layer atmospheric transmittance acquired from MODTRAN and the coefficients of ai (i = 0-5) and bi (i = 0-5) acquired by the statistical regression method based on Data-truncated. The values of A1, A2, A3, and A0 are dependent on atmospheric WVC for the 180 selected atmospheric profiles, and the variations in A1, A2, A3, and A0 are approximately 2.5, 1.5, 1.0, and 1.0, respectively. As the total atmospheric WVC increases, A1, A2, A3, and A0 tend to be more scattered. Considering the influence of atmospheric WVC on the coefficients of Eq. (9) and to improve the accuracy of the retrieved LST, the three-channel LST retrieval algorithm for dust aerosol atmosphere in this study is divided into three groups based on the atmospheric WVC with an overlap of 0.5 g/cm2: [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2. For each group, the coefficients are constant values. In addition, because any one of ε1, ε2, Δε1, or Δε2 can be determined by the other three, ε1 is eliminated and Eq. (9) is finally expressed as follows:
where Ti, Tj, and Tk are the TOA brightness temperatures in channels i, j, and k, respectively; Δε1 is the LSE difference in channels i and j; ε2 and Δε2 are the LSE mean and difference in channels i and k, respectively; and ci (i = 0-5) is the numerical coefficient of the three-channel algorithm. For different atmospheric WVC groups, the ci (i = 0-5) values are different.
3.3 LST retrieval
Considering that when satellite VZA increases, the optical path increases and the atmospheric attenuation increases, a VZA correction term Secant(VZA)-1 is added to Eq. (15). For MODIS, with i = 31, j = 29, and k = 32, the three-channel LST retrieval algorithm for dust aerosol areas is expressed as:
where T29, T31, and T32 are the TOA brightness temperatures of MODIS channels 29, 31, and 32; Δε1 = ε31-ε29, ε2 = (ε31 + ε32)/2 and Δε2 = ε31-ε32; here, ε29, ε31, and ε32 are the LSEs in MODIS channels 29, 31, and 32, respectively; and ci (i = 0-6) is the numerical coefficient of the three-channel algorithm. The simulated data set Data-simu is used to determine the coefficients in Eq. (16) using the statistical regression method. Additionally, the RMSEs between the actual LSTs (LSTs set in MODTRAN) and the LSTs estimated using Eq. (16) are 1.37 K, 1.17 K and 1.18 K for the atmospheric WVC groups of [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2, respectively. The ci (i = 0-6) coefficients for the three WVC groups are shown in Table 3.Table 3. Coefficients of ci (i = 0-6) in Eq. (16) for different WVC groups.
To estimate the improvement in the proposed three-channel algorithm for LST retrievals under dust aerosols, the LST is recalculated using the two-channel algorithm (Eq. (6)). As the factors including W are eliminated in the three-channel algorithm, the factors of a4W(1-ε1) and a5WΔε1 in Eq. (6) are also eliminated and the correction term of Secant(VZA)-1 is added in the two-channel algorithm, which is named as the revised two-channel LST retrieval algorithm in this study:
Similar as the three-channel algorithm, the two-channel algorithm is also divided into three groups according to the atmospheric WVC. Using MODIS channels 31 and 32, as well as the corresponding LSEs, the coefficients of Eq. (17) are determined with Data-simu. Fig. 6 shows the RMSEs of the two-channel algorithm (hollow symbols) and the three-channel algorithm (solid symbols) that estimated the LST versus the AOD for WVC ranges of [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2.Fig. 6 RMSEs of the LST estimated from the proposed three-channel algorithm versus the AOD for different atmospheric WVC ranges: [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2. The hollow symbols represent the two-channel algorithm and the solid symbols represent the three-channel algorithm.
As shown in Fig. 6, for both the two-channel algorithm and the three-channel algorithm, the RMSEs decrease as AOD increases from 0 to 0.5; then, the RMSEs increase when the AOD is greater than 0.5. The differences between different atmospheric WVC groups are less than 0.2 K for a given AOD condition. In addition, it is clear from this figure that the RMSE of the proposed three-channel algorithm is less than the traditional two-channel algorithm when the AOD is less than 0.3 or greater than 0.6. The RMSEs are 2.9 K and 1.6 K for the two-channel algorithm and the three-channel algorithm, respectively, when AOD = 1 and WVC is [1.0, 2.5] g/cm2. The RMSEs of the three-channel algorithm are 1.7 K and 1.2 K for the dry and wet atmospheric groups, respectively, when AOD = 0; and those RMSEs are 1.8 K and 1.6 K when AOD = 1. When AOD is between 0.3 and 0.6, the RMSE of those two algorithms are nearly the same. This indicates that the proposed three-channel algorithm can improve the LST retrieval accuracy under dust aerosol skies.
4. Sensitivity analysis
To determine the accuracy of the LST retrieval, the error theory was applied to Eq. (16). Typical errors are considered to be 0.05 K for the NETD of MODIS channels 29, 31, and 32, and 0.01 for the Δε1, Δε2 and ε2 estimations. Thus, the total errors can be calculated according to the following expression:
where δ(T29), δ(T31), δ(T32), δ(Δε1), δ(Δε2), and δ(ε2) are the errors resulting from the uncertainties of T29, T31, T32, Δε1, Δε2 and ε2, respectively, and δ(alg) represents the error from the three-channel LST retrieval algorithm itself. These errors are given in Fig. 7.Fig. 7 LST errors δ(T29), δ(T31), δ(T32), δ(Δε1), δ(Δε2), and δ(ε2), and δ(alg) caused by the uncertainties of T29, T31, T32, Δε1, Δε2, and ε2 and the algorithm error itself, and the total LST errors δ(LSTtotal) versus different atmospheric WVC groups.
Figure 7 shows the total LST errors and the errors caused by the uncertainties of the input parameters in Eq. (16) for different atmospheric WVC groups. The LST errors caused by the uncertainties of T29, T31, T32, Δε1, Δε2 and ε2 are less than 0.4 K, and the errors in the uncertainty of Δε2 are approximately 1.9 K for dry atmospheric conditions with WVC from 0 to 1.5 g/cm2. This result indicates that to obtain an accurate LST using the proposed three-channel LST retrieval algorithm, relatively high-quality emissivities in channels 31 and 32 are necessary, which is consistent with the requirement of other split-window algorithms [41]. Considering all the LST errors caused by the uncertainties of the input parameters and the model error itself, the total LST errors are 2.5 K, 2.0 K, and 1.7 K for atmospheric WVC groups of [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2, respectively.
5. Validations
5.1 Result
The LST (Ts) at the JCHM site is calculated as follows:
where Tu and Td are the radiometric temperatures measured by the downward- and upward-heading radiometers, respectively; B is the Planck function weighted for the spectral response function of the SI-111 radiometer; and ε is the land surface emissivity of the SI-111 radiometer channels. Considering the land cover types of JCHM are bare soil and A. sparsifolia, Li et al. [42] calculated the LSE based on the vegetation cover method. During the field experiment, the emissivities of bare soil and A. sparsifolia at the JCHM sites were measured using the ABB BOMEM MR304 spectroradiometers based on the Iterative Spectrally Smooth Temperature and Emissivity Separation (ISSTES) algorithm. With nine and five valid emissivity samples obtained for bare soil and A. sparsifolia, respectively, ε is calculated as 0.970 ± 0.002. Thus, the ε value at the JCHM site is set to 0.97 in this study. The 1-min interval values of Tu and Td that are averaged by the 5-s records are used to calculate Ts in this study.The 30-min interval downward and upward longwave radiations that are integrated with the 30-s sample records measured by CNR1 are used to calculate the LST at the HZZ site (Ts) as follows:
where L↑ and L↓ are the upward and atmospheric downward longwave radiations at the surface, respectively; εb is the broadband emissivity (BBE) over the entire infrared region, and σ is the Stefan-Boltzmann constant (5.67*10−8W/m2/K4). The HZZ and JCHM sites exhibit the same land cover types, and Li et al. [42] indicated that the ASTER thermal infrared data used to calculate the BBE values of the HZZ and JCHM sites were approximately the same; the εb is equivalent to 0.97 in this study. The maximum time interval between the MODIS and in situ measurements is 15 minutes at the HZZ site, and the error caused by the time inconsistency is ignored in this study. The Ts at the YK site is calculated using the same method as HZZ site [19], and it is not declared in this study; in which εb is acquired from Global LAnd Surface Satellite broadband emissivity product (GLASS BBE) provide by University of Maryland Global Land Cover Facility (http://glcf.umd.edu/).Using the brightness temperatures from MOD021KM/MYD021KM and the LSEs in MOD11C2/ MYD11C2 that are associated with the observation times and coordinates of the in situ measurements, the daytime LST in a dust aerosol sky is retrieved by employing Eq. (16). As MOD11C2/MYD11C2 are only available with a time interval of 8 days, the LSEs close to the day of the in situ measurements are used. In addition, as some of the optically and physically thin clouds can be ignored by the cloud mask products [43]. To eliminate the influence of cloud contamination, only the pixels identified as confident clear sky are selected based on the quality control data in the MOD11_L2/MYD11_L2. Using the estimated Ts values from Eq. (19) and (20) as the MODIS pixel-scale LST at the evaluation sites, the difference between the LST retrieved from the satellite data (LSTsate) and the corresponding Ts is the LST retrieval error in this study.
Figure 8 shows the LST retrieval errors between the LSTs extracted from MOD11_L2/MYD11_L2 and the Ts calculated from in situ data (solid circles) and between the LST retrieved from the three-channel algorithm proposed in this study and the Ts (hollow circles) versus AOD for the three test sites. Figure 8 (a) and (b) show the results for the JCHM site with MOD11_L2 and MYD11_L2, respectively; Fig. 8(c) and (d) describe the results for the HZZ site with MOD11_L2 and MYD11_L2, respectively; and Figs. 8(e) and 8(f) are the results for the YK site with MOD11_L2 and MYD11_L2, respectively.
Fig. 8 The differences between the LSTs extracted from MOD11_L2/MYD11_L2 and the Ts calculated from in situ data versus AOD for different test sites (solid circles); the differences between the LSTs retrieved from the new three-channel algorithm and Ts are also shown in this figure (hollow circles). (a) and (b) show the JCHM site with MOD11_L2 and MYD11_L2 data, respectively, (c) and (d) show the HZZ site with MOD11_L2 and MYD11_L2 data, respectively, and (e) and (f) show the YK site with MOD11_L2 and MYD11_L2 data, respectively.
Figure 8 shows that the RMSEs of the LST estimated by the proposed three-channel algorithm are less than those of the MODIS LST products for the JCHM, HZZ, and YK sites in dust aerosol skies. The improvements in the accuracy for MOD11_L2 and MYD11_L2 at the JCHM site are 1.4 K and 1.7 K, respectively; that for MYD11_L2 at the HZZ site is 1.6 K; and for MOD11_L2 and MYD11_L2 at the YK site are 2.2 K and 1.4 K, respectively; however, the declines in the RMSEs are approximately 0.1 K for MOD11_L2 at the HZZ site, which may be because the validation data are less than 10 days. In addition to the RMSEs, the biases of the LST retrieved using the proposed three-channel algorithm are all closer to 0 than the biases of the MODIS LST products.
5.2 Analysis
In addition to the influences discussed in the sensitivity analysis, the evaluation of the three-channel LST retrieval algorithm also depends on the accuracy of Ts (δ(Ts)), namely, the differences between the Ts calculated from the in situ data and the actual MODIS pixel-scale LST at the evaluation sites. The Ts error mainly comes from the instrument error, the uncertainties associated with the spatial thermal inhomogeneity of the evaluation sites, and the uncertainty of the emissivity in the SI-111 channels and the longwave broadband emissivity.
The accuracy of the SI-111 radiometer δ(Tinstru) used at the JCHM site is ± 0.2 K at temperatures from 238 K to 338 K (http://www.apogeeinstruments.com/infraredradiometer), and the accuracy of the CNR1 net radiometers used at the HZZ and YK sites are approximately 8 W/m2 during the day, which is associated with an LST error of approximately 1.0 K [19].
Using twelve ASTER LST products from May 30, 2012 to September 28, 2012, the LSTs for the 11 × 11 pixels (1 km2) centered on the JCHM and HZZ sites were extracted and the STD was calculated for each scene by Li et al. [42]. The average STD of the twelve ASTER scenes was considered to be an estimate of the spatial uncertainties associated with the use of in situ LSTs to evaluate the satellite LST product due to the spatial dissimilarity problem δ(Tspatial). Average values of 0.52 K and 0.68 K were obtained for the JCHM and HZZ sites, respectively. Assuming that there are no significant differences in the land coverage at the HZZ site, the δ(Tspatial) is also taken as 0.68 K for the HZZ site in this study. Fan et al. [19] used TIR data (band 6) of the Landsat-5 Thematic Mapper to analyze the thermal homogeneity of the YK site. The δ(Tspatial) is 0.62 K at the YK site.
Assuming an uncertainty of 0.01 for both the emissivity of the SI-111 channels and the longwave broadband emissivity, the LST error (δ(Temi)) caused by this uncertainty is 0.3 K.
Thus, the Ts errors can be expressed as follows:
The δ(Ts) values are 0.63 K, 1.24 K, and 1.21 K for the JCHM, HZZ, and YK sites, respectively.6. Discussion
The total error of the extended GSW LST retrieval algorithm for dust aerosol skies proposed by Fan et al. [19] is 2.2 K for AOD equal to 1.0 and VZA equal to 60°, considering the errors from instrument noise, emissivity uncertainties of the GSW channels, the uncertainty of AOD, the errors of the GSW algorithm, and the extension algorithm itself. However, the total LST errors of the proposed three-channel algorithm are 2.5 K, 2.0 K, and 1.7 K for the atmospheric WVC groups of [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2, respectively. This indicates that the three-channel LST retrieval method is more accurate for wet atmospheres and less accurate for dry atmospheres compared with the extended GSW LST retrieval algorithm for dust aerosol conditions. In addition, one of the advantages is that the three-channel algorithm is independent of the AOD as an input parameter, which is important for nighttime dust aerosol atmospheres, when reliable AOD data are difficult to acquire.
Note that we only evaluated the daytime algorithm to determine the performance of the proposed three-channel LST retrieval algorithm in dust aerosol atmospheres in this study because we needed to select the dust aerosol atmospheres using MODIS aerosol products. However, in practical applications, the three-channel LST retrieval algorithm, which is not dependent on dust aerosol AOD as an input parameter, can be directly used for the daytime and nighttime LST retrieval. As only the atmospheric profiles with WVC less than 3.0 g/cm2 are used in the algorithm development, thus this algorithm mainly used for the arid or semiarid regions in the spring when dust aerosol is a frequent influence. In addition, as the 10 km resolution AOD and aerosol type products are resampled to 1 km in this study, the influence of the 1 km aerosol products resampled from 10 km resolution can also impact the accuracy of field validations. As the final algorithm proposed in this study is not dependent on the dust aerosol AOD as input parameter, this influence can be ignored for actual applications.
7. Conclusions
We developed a three-channel LST retrieval algorithm based on a widely used two-channel algorithm for clear-sky conditions to acquire the LST in dust aerosol skies. To improve the retrieval accuracy, the algorithm is divided into three groups based on the atmospheric WVC with an overlap of 0.5 g/cm2: [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2. Using a simulated data set from MODIS channels 29, 31, and 32 that considered the influence of dust aerosol, the LST was estimated with RMSEs of 1.7 K and 1.2 K for dry and wet atmospheres, respectively, when the AOD is 0, and those RMSEs are 1.8 K and 1.6 K when AOD is 1. This result indicates that the proposed three-channel algorithm can be used to estimate LST not only for dust aerosol skies but also for clear-sky conditions, namely, in areas frequently affected by dust aerosol.
In addition, a sensitivity analysis of the algorithm was performed to assess the LST errors caused by instrument noise and LSE uncertainties as well as the total LST errors. The analysis showed that the LST errors from instrument noise and the emissivity errors in the mean and difference of MODIS channels 32 and 29 are less than 0.4 K. However, the errors from the uncertainty of the emissivity difference between MODIS channels 31 and 32 were approximately 1.9 K for dry atmospheres with WVC from 0 to 1.5 g/cm2. Considering the total errors from the uncertainties of the input parameters and the algorithm error itself, the total LST errors are 2.5 K, 2.0 K, and 1.7 K for the atmospheric WVC groups of [0, 1.5], [1.0, 2.5], and [2.0, 3.0] g/cm2, respectively.
Finally, to test the performance of the proposed LST retrieval algorithm in dust aerosol skies, in situ measurements from the JCHM, HZZ, and YK sites in northwest China were used to calculate the LST to represent the true LST values at the MODIS pixel scale. The TOA brightness temperatures obtained from MOD021KM/MYD021KM, emissivities extracted from MOD11C2/MYD11C2, atmospheric WVC from MOD05_L2/MYD05_L2, and VZAs from MOD03/MYD03 were used to retrieve the LSTs at the three sites. The results showed that compared with the MODIS LST products, MOD11_L2/MYD11_L2, the proposed LST retrieval method improves the LST retrieval accuracy from 1.4 K to 2.2 K in dust aerosol atmospheres.
Funding
Director Foundation of the Institute of Geology, China Earthquake Administration (IGCEA1522); National Natural Science Foundation of China (41601390); Key Programs of Large and Medium-sized Urban Earthquake Disaster Scene Building (2016QJGJ14); China Earthquake Administration Special Project Surplus Fund (High Resolution Rapid Post-earthquake Assessment Techniques); Innovation Project of LREIS (O88RA801YA).
Acknowledgments
The authors would like to thank Laboratoire de Meteorologie Dynamique for the distribution of the latest version of the Thermodynamic Initial Guess Retrieval database, Jet Propulsion Laboratory for providing the ASTER spectral library data, and Heihe Plan Science Data Center for providing the field data.
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