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Abstract
Simulation of thermal images plays an important role in the pre-evaluation of the data acquisition characteristics of sensors. This work addressed an operational method for the time-series thermal infrared (TIR) data of geostationary satellite simulated from polar-orbiting MODerate resolution Imaging Spectroradiometer (MODIS) sensors based on Radiative Transfer Model (RTM) under cloud-free conditions. The data procedure, including the land surface emissivity (LSE), time-series land surface temperature (LST), time-series atmospheric parameters, sensor performance, can be described as follows. Firstly, MODIS LST product filtering rules are developed due to its data quality. Then, a Diurnal Temperature Cycle (DTC) model with four parameters is used to acquire the time-series LSTs. The spatial and spectral matching method are adopted from MODIS LST&LSE product. A temporal interpolation method is used to obtain the time-series atmospheric parameters from the atmospheric profile provided by European Centre for Medium-Range Weather Forecasts (ECMWF). Then, the time-series TIR data at sensors were modeled using this method. Compared with the time-series TOA brightness temperature of MSG/ SEVIRI geostationary satellite, the results show that the modeling accuracy is achieved with root mean square errors (RMSEs) 2.39K, 2.81K, 1.06K, and 1.29K at MODIS overpass times, and the mean and RMSE are -0.09K and 1.61K for all cloud-free pixels at the UTC time spanning from 08:00 to 05:00, which can be well reconstruct the time-series real scenes using the proposed method.
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1. Introduction
Satellite remote sensing is a key way to extract long-term and large-scale land surface parameters [1–2]. Simulation of satellite images can be applied to validate the remote sensing mission, predict the imaging capability of remote sensing systems and to test the performance of algorithms [3–4], such as surface temperature and emissivity inversion [5–13], atmospheric compensation [14–15], and mineral identification [16], et al. Generally, the end-to-end image chain simulation for Earth Observation Satellites contains the landscapes, the atmospheric radiative transfer and the sensor performance [17–22]. Many end-to-end image simulation models were developed for remote sensing missions [23–24].
RTMs have been recognized as an important method to better understand the relationships between land surface and atmosphere characteristics and remote sensing observations [25]. Examples of the simulation of landscapes include the Suits model [26], the SAIL model [27], the SAILH model [28], the DART model [29–30], the PROSPECT + SAILH model [31], the DSMC model [32]. The atmospheric radiative transfer models, such as MODTRAN [33], 6S [34], RTTOV [35] have been used to simulate the influence of atmosphere. In generally, the current satellite image simulation method is to integrate several submodels, including the land surface, atmosphere, and the performance of sensor, within its simulation process. A four-stream surface-atmosphere radiative transfer theory was proposed by Verhoef and Bach [3] to calculate Sentinel-3 TOA radiances of optical and thermal domains, however, which doesn’t describe the simulation accuracy of thermal TOA radiance. A TOA radiance image simulation at 4.3-μm absorption bands was proposed by Liu et al. [36] and applied for target detection from MODIS products. Physically based multispectral image simulation consists of sensor system modeling, landscapes, and TOA image calculation [37]. For more realistic simulation data with the truth data, an alternative method is carried out by using the airborne/satellite collection of radiometric data to simulate target satellite imagery [38]. The existing methods seldom consider the problem of satellite data simulation when the land surface temperature varies with time.
The project of the geostationary satellite with high spatial and hyperspectral resolution has deployed in national Earth observation project of China. The geostationary satellite will provide a thermal infrared payload with spectrum spanning from 8 to 13μm to collect land surface thermal emission, which can observe the region of interest with a high frequency once a minute. Many of current studies are for specialized mission-based applications, and not suitable for general-purpose usage in Earth observation satellites [22]. Different from traditional methods, the objective of this study is to explore a geostationary satellite thermal infrared data simulation method to model the geostationary satellite TOA brightness temperature (BT) for supporting the evaluation of characteristics and algorithm of new thermal sensor. Since the thermal payload is still in the development stage, the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard the Meteosat Second Generation (MSG) satellite was used for analysis and validation.
This paper is organized as follows: Section 2 gives the materials, including the satellite data and atmospheric parameters. Section 3 presents the details of the proposed method, including the theoretical basis and development. Section 4 describes the study area, the algorithm application, and its validation. The discussions and conclusions are presented in Section 5.
2. Materials
2.1 Satellite data
MODIS 1 km LST&E products [39] are used for the data source, because the accuracy of its LST is better than 1 K in the range from -10 to 50°C. Another important reason is the coverage at four times (10:30, 13:30, 22:30, and 01:30 local solar time) per day for Terra and Aqua, which can be used as the time-series geostationary satellite thermal infrared data simulation. The corresponding 1 km latitude and longitude data are stored in the MODIS geo-location product (MOD03). For accuracy analysis, the geostationary satellite SEVIRI/MSG sensor was used for comparison, which has 12 spectral channels covering from visible to infrared, and provides measurements every 15 minutes and 3.0 km at nadir for the infrared channels of the Earth-disc centered at 0 longitude and 0 latitude [40]. In TIR spectrum from 8 to 14μm, there are three channels located in atmospheric window, i.e., centered in 8.7μm, 10.8μm, and 12.0μm with the Noise Equivalent Delta Temperature (NEdT) of 0.10 K, 0.11 K and 0.15 K @ 300 K, respectively. For the convenience of analysis, the MSG/SEVIRI data with the center wavelength located in 10.8μm was used for geostationary satellite data simulation and validation.
2.2 Atmospheric Profiles
To require the geostationary satellite TOA radiance, the atmospheric parameters have to be obtained. In this paper, the ECMWF ERA5 dataset atmospheric profiles [41] were used to evaluate the atmospheric perturbations, which were covered the earth on a 30km grid and resolve the atmosphere using 137 levels from the surface up to a height of 80km. In this paper, the spatial resolution, vertical levels, height of the profile is 0.5° latitude/longitude, 37 levels, 48km height, respectively, for every 1-hour UTC time (Table 1).
Table 1. Description of the ECMWF ERA5 Atmospheric Profile Dataset
2.3 Study area
The study area is located in the Mediterranean region with longitude from 10°W to 4°E and latitude from 34°N to 44°N. This area has a Mediterranean climate, with mild, rainy winters and hot, dry summers. In general, the climate is dry and warm in the south, and the climate is relatively wet and cool in the north. In addition, there are a large amount MODIS and MSG/SEVIRI data in this region used for studies. The land cover types of the study area are generated from the Collections 5.1 MODIS Land Cover Type (MCD12Q1) product. To match the MSG-SEVIRI pixels, the MCD12Q1 pixels were aggregated to the MSG-SEVIRI pixel scale in terms of longitude and latitude. Only six general land cover classes over land at the MSG-SEVIRI pixel scale are displayed in Fig. 1.
Fig. 1. Study areas: Land cover types of the study area at the MSG-SEVIRI pixel scale aggregated from the MODIS MCD12Q1 product. Six selected pixels over different land cover types were used to evaluate the performance.
3. Method
In TIR domain, ignoring the scattering effect of atmosphere and assuming a local thermodynamic equilibrium, the at-sensors radiance measured by an instrument can be described by atmospheric radiative transfer equation (RTE) [42].
where $L(\lambda )$ is the radiance measured at-sensors at wavelength $\lambda$; ${L_g}(\lambda )$ is at-surface radiance; $\tau (\lambda )$ is atmospheric transmittance; $\varepsilon (\lambda )$ is the surface emissivity; $B(\lambda ,T)$ is the Planck’s function at wavelength $\lambda$ and temperature T; ${L_ \uparrow }(\lambda )$ and ${L_ \downarrow }(\lambda )$ are the atmospheric upwelling and downwelling radiances, respectively.
3.1 land surface scenes
3.1.1 Time-series LST
To simulate the time-series SEVIRI TOA brightness temperatures (BTs), the time-series SEVIRI LSTs are necessary to be known. Because at most four times MODIS observations are available per day, to solve this problem, the Diurnal Temperature Cycle model (DTC) is introduced to obtain the time-series SEVIRI LST. An improved 4-Parameter DTC model is used based on a semi-empirical DTC model to depict the diurnal variation of LST, and the RMSEs of the 4-parameter DTC model fitting the diurnal cycle of the time-series MSG/SEVIRI LSTs were less than 1.0 K [43].
where, ${T_0}$ is the residual temperature at sunrise; t is time; ${t_{sr}}$ is the sunrise time; ${t_m}$ is the maximum temperature time (h); ${t_s}$ is the temperature attenuation time (h); Ta is temperature amplitude; k is attenuation constant, $k = \omega /\pi \times [ta{n^{ - 1}}(\omega /\pi \times ({t_s} - {t_m}))] - \delta T/{T_a} \times {\sin ^{ - 1}}(\omega /\pi \times ({t_s} - {t_m}))$. $\omega = 4/3 \times ({t_m} - {t_{sr}})$;$\delta T$ is the temperature difference between ${T_0}$ and $T(t \to \infty )$, i.e., $\delta T = T(t \to \infty ) - {T_0}$. Assumed that ${t_s}$ is approximate to be 1 hour before the time of sunset, there are four unknown parameters, i.e., ${T_0}$, ${T_\textrm{a}}$, δT, ${t_m}$, in the DTC model.
3.1.2 LSE
LSE is one of the key input parameters for simulation of TOA radiance. MODIS MOD11_L2 LSE products by a classification-based look-up table according to land cover types are used for simulation. Because the four LSE images at four times a day from Terra and Aqua MODIS, the mean values are calculated by the four LSE images.
The invalid pixels can be filled with values at other times. In order to obtain the SEVIRI LSE, the spectral matching method of emissivity between TIR channels of SEVIRI and MODIS should be built. The emissivity spectra extracted from the ASTER Spectral Library, including water, ice, snow, vegetation, soil and mineral, are used to describe the spectral characteristics in TIR channels between SEVIRI and MODIS. The SEVIRI and MODIS emissivities were analyzed and built the emissivity linear relationship between SEVIRI and MODIS channels by using least square method. The spectral relationship of emissivity [44] is shown as: ε31 = 0.9492 × ε9 + 0.04916, ε32 = 0.9279 × ε10 + 0.02757. Where ε9 and ε10 are the emissivities of SEVIRI channels 9 and 10, respectively. The emissivities of MODIS channels 31 and 32 are ε31 and ε32, respectively.
3.2 Time-series atmospheric parameters acquisition method
ECMWF data have a higher temporal and spatial resolutions; however, they are still needed to be processed further. In this paper, a bilinear spatial interpolation method is used to obtain the atmospheric parameters by the MSG/SEVIRI coordinates. Furthermore, linear interpolation method using time-nearest ECMWF atmospheric parameter calculated by MODTRAN code is used to obtain the atmospheric parameters on finer time scales. We also analyze that the interpolation atmospheric profiles and the interpolation atmospheric parameters methods, the result is only a slight difference existing for the both methods, so the interpolation atmospheric parameters are used to speed up the data processing in this paper. Furthermore, to obtain the atmospheric parameters (atmospheric transmittance, upwelling and downwelling radiances) in SEVIRI channels, the spectral response functions of SEVIRI are needed to convolve the atmospheric parameters from MODTRAN.
3.3 MODIS product filtering rules
MODIS LST product filtering rules are necessary, which will affect the accuracy of data simulation. The product quality is mainly influenced by cloud cover and its retrieval algorithm. It should be noted that the correlation of LST at four times of the day. To better simulate the geostationary satellite data, the MODIS LST product filtering rules are as follow:
- a. According to the Quality Control (QC) criterion of the MODIS product, when QC is equal to zero, the pixel will be regarded as good data quality and cloud-free. The LST error is less than 1.0 K in the MOD11_L2 product. Thus, only the pixels of the MODIS product with the value of zero in QC flags are used for simulation.
- b. The temporal evolution of LST at four times of the day must be considered. In general, the Aqua LST at 13:30 UTC time is larger than the Terra LST at 10:30 UTC time due to the duration of the sun. If not, the reason may be that the long periods of cloud cover between 10:30 to 13:30 UTC times have cooled the land surface. Obvious, this pixel will be eliminated.
- c. There are some minor differences for the MODIS LSE product at four times of the day because of the difference of cloud coverage and the retrieval algorithm accuracy. The average emissivity is used as the input parameter for the data simulation, where QC is equal to zero and the emissivity error in MODIS Quality Assurance (QA) criterion should be less than 0.01.
In order to carry out the simulation, the TOA BT derived from the MSG/SEVIRI data and extracted from MOD11_L2 products were aggregated to the same spatial resolution using (4). In this work, the MOD11_L2 product (1 km) is aggregated to the spatial resolution at SEVIRI pixel scale (3 km at nadir). In this paper, the SEVIRI LST&LSE are aggregated using next Equation from MOD11_L1 LST&LSE product:
where, ${T_i}$ is the aggregated SEVIRI LST from MODIS LST ${T_j}$, ${\varepsilon _i}$ is aggregated SEVIRI LSE from MODIS LSE ${\varepsilon _j}$, ${\omega _j}$ is the area-weight of pixel j.
Simulation can only be completed with a high accuracy if the view time is accurately determined. Furthermore, to compare with the real image, the viewing zenith angle (VZA) of MSG pixel was obtained from the actual MSG images. Then the VZA as an input parameter of MODTRAN was used to simulate the TOA radiance. After the determination of the input parameters, the time-series TOA brightness temperature (BT) is calculated for each pixel using (1). Figure 2 shows the flowchart for time-series geostationary satellite thermal infrared data simulation. The atmospheric radiative transfer model, MODTRAN, was used to simulate the atmospheric downwelling radiance, atmospheric upwelling radiance, and atmospheric transmittance spectra for ECMWF atmospheric profiles. Then, the TOA BT can be modeled from (1). As well-known, the NEdT of the TIR sensor with instrument noise is key parameter. The NEΔT is set to 0.11 K@300 K for simulation.
4. Application
4.1 Results and discussion
4.1.1 Modeled time-series LST
MODIS Terra + Aqua MOD11_L2 LST&E products overpass four times per day have been used for simulation. The LSTs of MODIS MOD11_L1 product on 14/15 July 2004 are shown in Fig. 3. Figure 3 (a) and (c) are mosaicked using the two adjacent images at UTC times 11:20&11:25 and UTC times 22:25&22:30, respectively.
The LSTs at MSG/SEVIRI pixel scale are modeled using MODIS Product at four times on 14/15 July 2004 in Fig. 4. Figure 4 (a) and (c) are modeled using the two adjacent images at UTC times 11:20&11:25 and UTC times 22:25&22:30, respectively. Figure 4 (b) and (d) are modeled using only one image. The missing data can be seen in these images because the MOD11_L2 product is contaminated by cloud or affected by the retrieval algorithm. These missing data will not be used for modeling the TOA BT.
Fig. 4. Spatial distribution of the modeled LSTs at MSG/SEVIRI pixel scale using MODIS Product at four times.
When MODIS data acquired at four times each day are available, the MSG/SEVIRI LSTs can be directly calculated based on spatial aggregation method. For the LSTs at other times, there are no corresponding MODIS data available. As mentioned previously, the time-series MSG/SEVIRI LSTs are modeled based on the 4-parameter DTC model using four MODIS LSTs in daytime and night-time for each day. As an example, the time-series LSTs spanning from 08:00 to 05:00 UTC time of the next day with an increment of 15 min at the SEVIRI pixel scale over the six selected pixels (see Table 2) are shown in Fig. 5. In theory, the MODIS LSTs at four times should be normalized to the same view angle of MSG/SEVIRI before modeling the time-series LSTs. However, there is not any practical way to perform angular normalization of satellite-derived LST, because of the complexity of this normalization [47]. The accuracy of the modeled time-series MSG/SEVIRI LSTs depends on those of the MODIS LSTs.
Fig. 5. Time-series LSTs of MSG/SEVIRI are modeled based on the 4-parameter DTC model using four MODIS LSTs in the daytime and night-time on 14 July 2004 for the six selected pixels over different land cover types: (a) Savanna, (b) Grassland, (c) Forest, (d) Shrubland, (e) cropland, and (f) Barren land
Table 2. Detailed Information of the Six Selected Pixels
4.1.2 Modeled LSE
The LSEs of MODIS MOD11_L1 product are shown in Fig. 6. Figure 6 (a) and (c) are mosaicked using the two adjacent images at UTC times 11:20&11:25 and UTC times 22:25&22:30, respectively. Figure 6 (a) and (c) are extracted from Terra MOD11_L1 product, while Fig. 6 (b) and (d) are extracted from Aqua MYD11_L1 product. Obviously, there are some differences for the LSEs between Terra and Aqua, thus the mean emissivity has been adopted in the following sections (seen in Fig. 6 (e)).
4.1.3 Modeled time-series TOA BTs
The TOA BTs are modeled spanning from 08:00 to 05:00 UTC time of the next day with an increment of 15 min. The TOA BTs between 05:00 and 08:00 UTC time of the next day were not modeled due to large model error over these periods. The spatial distribution of the modeled TOA BTs at SEVIRI pixel scale at MODIS overpass times (10:30, 13:30, 22:30, and 01:30 local solar time) is shown in Fig. 7. These images show the actual MSG/SEVIRI TOA BTs and the modeled the MSG/SEVIRI TOA BTs at the SEVIRI pixel scale. Obviously, the spatial distribution of TOA BTs is consistent between the actual and modeled BTs.
4.2 Validation using the actual MSG/SEVIRI data
4.2.1 Validation for cloud-free pixels
As an example, all the results that follow are presented for the SEVIRI 10.8 μm channel. The validation of the model was performed by the intercomparison between the simulated and actual MSG/SEVIRI TOA BTs. All cloud-free pixels are used to evaluate the performance of the model proposed. Figure 8 shows the histograms of error between the modeled the TOA BTs and the actual MSG/SEVIRI TOA BTs. The modeling accuracy is achieved with root mean square errors (RMSEs) 2.39 K, 2.81 K, 1.06 K, and 1.29 K, standard deviations (STDs) 2.36 K, 2.77 K, 1.03 K, and 1.12 K at MODIS overpass times, respectively.
Fig. 8. Histograms of the Mean and RMSE between the actual and simulated time-series TOA BTs for all cloud-free pixels
In addition, all cloud-free pixels are used to statistically analyze the accuracy using the actual and modeled TOA BTs from 08:00 to 05:00 UTC time of the next day. The error histograms for the time-series modeled results are shown in Fig. 9. Except for cloud-free, the selected pixels also are needed to meet that the TOA BTs modeled from MODIS product at MODIS overpass times are less than 1.0 K compared to the SEVIRI TOA BTs. The mean, STD and RMSE are -0.09 K, 1.6 K and 1.61 K for these pixels in Fig. 9 (a). Meanwhile, the modeled accuracy was further analyzed using the data with the RMSE of MSG/SEVIRI TOA BTs fitted by DTC model less than 1.0 K shown in Fig. 9 (b). We can see that the mean, STD and RMSE are 0.11 K, 1.23 K and 1.24 K, respectively.
Fig. 9. Histograms of the Mean and RMSE between the actual and modeled time-series TOA BTs for all cloud-free pixels
As an example, the time-series TOA BTs are used for validation with the data from 08:00 to 05:00 of the next day at the SEVIRI pixel scale over the six selected pixels (see Table 2) on 14 July 2004. Figure 10 and Table 3 show the results and the RMSEs are 1.68 K, 0.43 K, 0.55 K, 0.75 K, and 0.91 K for savanna, grassland, forest, shrubland, and cropland, respectively. However, the RMSE is still as high as 2.59 K when the TOA BT below 285 K is excluded for Barren. The large error is mainly induced by cloud. It should be noted that the temperature variation is also described well using this model in Fig. 10 (f), especially for the cloud-free.
Fig. 10. Temporal distribution of the modeled TOA BTs at the SEVIRI pixel scale spanning from 08:00 to 05:00 UTC time of the next day with an increment of 15 min.
Table 3. Results of BT for Six Selected Pixels over Different Land Cover Types
4.2.2 Validation for partly cloudy pixels
In addition, the modeled TOA BTs at the SEVIRI pixel scale has also been analyzed under the condition of partly cloudy or atmospheric instability. Figure 11 shows the temporal distribution of the modeled results when the modeled TOA BTs at MODIS four times are less than 1.0 K compared to MSG/SEVIRI TOA BTs. Figure 11 (a) and (b) show the results for partly cloudy, obviously except for the data covered by cloud, the model can be well simulated the diurnal trend of temperature. Figure 11 (c) and (d) show the results for atmospheric instability, it can be seen that the time-series TOA BTs can also be well simulated. Thus, the model proposed in this paper can perform well for the data acquired under these conditions.
Fig. 11. Temporal distribution of the modeled TOA BTs at the SEVIRI pixel scale under the condition of partly cloudy spanning from 08:00 to 05:00 UTC time of the next day with an increment of 15 min.
5. Conclusions
A method for simulation of geostationary satellite time-series thermal infrared data under cloud-free condition was developed to simulate the realistic environments in this paper. In order to analyze the feasibility, the MSG/SEVIRI data was used. A DTC model with four parameters is used to acquire the time-series LST with the interval of 15 min from the MODIS Terra + Aqua LST&LSE products four times per day. The area-weighted spatial matching method and spectral matching method are adopted for MODIS LST&LSE product and MSG/SEVIRI data. Then, a temporal interpolation method is proposed to obtain the time-series atmospheric parameters from the ECMWF 1-hour profile at 0.5° latitude/longitude spatial resolutions.
The time-series TOA BTs at MSG/SEVIRI pixel scale are modeled using the proposed method. The spatial distribution of the modeled TOA BTs shows the temperature trend between the actual MSG/SEVIRI and the modeled TOA BTs is consistent. The diurnal cycle of the modeled TOA BTs describes the temporal evaluations of the TOA BTs at MSG/SEVIRI pixel scale. The validation results show that the time-series thermal infrared data for geostationary satellite can be well simulated using the proposed method. The modeling accuracy is achieved with root mean square errors (RMSEs) 2.39 K, 2.81 K, 1.06 K, and 1.29 K at MODIS overpass times, respectively. In addition, all cloud-free pixels were used to statistically analyze the accuracy using the actual and modeled TOA BTs at the UTC time spanning from 08:00 to 05:00. The mean and RMSE are -0.09 K and 1.61 K for cloud-free pixels. Meanwhile, the modeled accuracy was further analyzed using the data with the RMSE of MSG/SEVIRI TOA BTs fitted by DTC model less than 1.0 K. The mean and RMSE are 0.11 K and 1.24 K, respectively.
The geostationary satellite thermal infrared data simulation is affected by many factors, such as land surface scene (temperature and emissivity), atmospheric parameter, DTC model, cloud coverage. In addition, the viewing zenith angle, DEM, the angular heterogeneity of emissivity are also key factors. In this paper, it can be seen that MODIS LST will directly affect the DTC model parameters, including the temperature amplitude, the width over the half-period of the cosine term, and the time of the maximum temperature, which will lead to the inaccurate simulation. In addition, the modeled TOA BTs has also been analyzed under the condition of partly cloudy or atmospheric instability. The temporal distribution of TOA BTs can be well simulated when the modeled TOA BTs are less than 1.0 K compared to MSG/SEVIRI TOA BTs at MODIS overpass times.
Compared to the models published before, such as the combined PROSAIL and MODTRAN model, DART model, et al., the proposed operational method in this paper can better describe the realistic environments, especially for the time-series diurnal temperature cycle. More comparative analysis with the geostationary satellites, such as GEOS, GMS, CHINESE FENGYUN, will be done in the future work.
Funding
National Key Research and Development Program of China (2016YFB0500400); National Natural Science Foundation of China (41871221).
Acknowledgment
The authors would like to appreciate the editor and anonymous reviewers for their constructive comments and suggestions on this study.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data availability. Data underlying the results presented in this paper are available in Ref. [39–41]. The authors would like to thank EUMETSAT for providing the MSG/SEVIRI data, MODIS Science Team for providing LST/LSE products, and ECMWF for providing atmospheric data.
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