All-sky longwave downward radiation from satellite measurements: General parameterizations based on LST, column water vapor and cloud top temperature

ISPRS Journal of Photogrammetry and Remote Sensing 161 (2020) 52–60

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All-sky longwave downward radiation from satellite measurements: General parameterizations based on LST, column water vapor and cloud top temperature

T

Tianxing Wanga,b, , Jiancheng Shib, Ya Mac, Husi Letub, Xingcai Lid ⁎

a

School of Geospatial Engineering and Science, Sun Yat-Sen University, Zhuhai, Guangdong 519082, China State Key Laboratory of Remote Sensing Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing Normal University, Beijing 100101, China c Chinese Academy for Environmental Planning, Beijing 100012, China d School of Physics and Electronic-electrical Engineering, Ningxia University, 750021, China b

ARTICLE INFO

ABSTRACT

Keywords: Surface longwave downward radiation Land surface temperature Column water vapor Cloud-top temperature CERES Cloudy-sky

Remotely sensed surface longwave downward radiation (LWDR) plays an essential role in studying the surface energy budget and greenhouse effect. Most existing satellite-based methods or products depend on variables that are not readily available from space such as, liquid water path, air temperature, vapor pressure and/or cloudbase temperature etc., which seriously restrict the wide applications of satellite data. In this paper, new nonlinear parameterizations and a machine learning-based model for deriving all-sky LWDR are proposed based only on land surface temperature (LST), column water vapor and cloud-top temperature (CTT), that are relatively readily available day and night for most satellite missions. It is the first time to incorporate the CTT in the parameterizations for estimating LWDR under the cloudy-sky conditions. The results reveal that the new models work well and can derive all-sky global LWDR with reasonable accuracies (RMSE < 23 W/m2, bias < 2.0 W/ m2). The convenience of input data makes the new models easy to use, and thus will definitely expand the applicability of remotely sensed measurements in radiation budget fields and many land applications.

1. Introduction Surface longwave downward radiation (LWDR) is an essential parameter for studying the surface radiation and/or energy balance. It plays a key role in the greenhouse effect of the Earth system (Wang and Dickinson, 2013; Stephens et al., 1994), and thus is an essential variable for understanding the global warming. In addition, it is also a very important driving data in many land, hydrology and climate models. Compared to the ground-based measurements and the reanalysis data, remote sensing provides a unique opportunity to globally map surface LWDR with high spatio-temporal resolutions considering its ability of global coverage and routine monitoring. Therefore, during the past decades, the satellite-based data, such as Clouds and the Earth's Radiant Energy System (CERES) (Wielicki et al., 1998), Moderate Resolution Imaging Spectroradiometer (MODIS) (Masuoka et al., 1998; Justice et al., 1998, 2002) and Atmospheric Infrared Sounder (AIRS) (Sun et al., 2010) etc., are frequently used to derive LWDR (Zhou et al., 2019; Cheng et al., 2019; Wang et al.,2018; Yan et al.,2016; Wang et al.,2012; Kato et al., 2011; Bisht and Bras, 2010, 2011; Wang and Liang, 2009, ⁎

2010; Gupta et al., 2010; Tang and Li,2008; Zhou et al., 2007; Bisht et al., 2005; Kato et al., 2005; Pinker et al., 2003;Zhou and Cess, 2001; Gupta, 1989; Gupta et al., 1992). Although tremendous attempts have been carried out for deriving surface LWDR based on remote sensing measurements, most of those methods are mainly focus on clear-sky conditions, only a few studies were dedicated to derive LWDR under cloudy conditions (Wang et al., 2018; Kato et al., 2011; Gupta et al., 2010; Bisht and Bras, 2010; Forman and Margulis.2009; Zhou et al., 2007; Zhou and Cess, 2001; Gupta et al., 1992; Gupta, 1989). The spatial and temporal discontinuity of the derived LWDR products from remotely sensed measurements severely impede their wide applications. This, for a long time, is a big problem in radiation budget community. In most existing literatures, the clear-sky LWDR were frequently derived using air temperature and vapor pressure or relative humidity at screen-level which are usually estimated from the atmospheric profiles based on empirical formula (Wang et al., 2018; Bisht and Bras, 2010; Lhomme et al., 2007; Carmona et al., 2014; Iziomon et al., 2003; Crawford and Duchon.1999; Prata, 1996). In reality, these parameters

Corresponding author. E-mail address: [email protected] (T. Wang).

https://doi.org/10.1016/j.isprsjprs.2020.01.011 Received 24 April 2019; Received in revised form 16 December 2019; Accepted 9 January 2020 0924-2716/ © 2020 Published by Elsevier B.V. on behalf of International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS).

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(air temperature, vapor pressure etc.,) are not readily available from the satellite signals. In contrast, the land surface temperature (LST) and the column water vapor (CWV) are relatively easy to estimate from space under clear-sky conditions (Wan and Dozier. 1996; Li and Becker. 1993; Duan et al., 2014a, 2014b; Duan et al, 2019; Kaufman and Gao. 1992; Gao and Kaufman.2003; Ma et al., 2017), moreover, they are closely correlated with the screen-level temperature and humidity. Therefore, parameterizations that only rely on the readily available LST and CWV would be very attracting for the community and can definitely widen the range of applications of remotely sensed LWDR products. Unlike the clear-sky data, the estimation of cloudy-sky LWDR from space is very complicated and challengeable. For cloudy-sky LWDR, the thermal contribution consists of two parts. Except for the thermal radiation from the atmosphere under the cloud layers (sub-cloud atmosphere, see Fig. 2 in Wang et al.,2018), the radiation originated from the cloud layers is another contributor that cannot be ignored, especially under the conditions with lower CWV and colder air temperatures (Stephens et al.,2012). Many studies pointed out that, in cloudy case, the height and temperature of the cloud-base are controlling factors for the LWDR estimation (Kato et al., 2010, 2011; Stephens et al.,2012; Wild et al., 2001; Zhang et al.,2004). For instance, Gupta (1989) and Gupta et al. (1992,2010) derived LWDR by parameterizing cloud-base temperature and sub-cloud atmospheric CWV using CERES measurements. Forman and Margulis (2009) suggested a method to estimate cloud-coupled LWDR using air temperature, vapor pressure and cloud-base temperature. Wang et al. (2018) also derived a high resolution LWDR by combining AIRS/AMSU and MODIS based on the cloud base information. Although the cloud-based temperature or height is directly related to the cloudy thermal contribution (Zhou and Cess.2001), it is not easy to directly estimate from the satellites, because the optical remote sensing can only provide the cloud top characteristics due to the opacity of the clouds (Nakajima and Nakajma, 1995; Letu et al., 2019). The cloud-based temperature needed by those above-mentioned methods are usually empirically estimated based on the cloud optical parameters (Minnis et al., 2011; Gupta, 1989). For this point, some researches tend to use surrogated parameters, such as cloud fraction (Lhomme et al., 2007; Carmona et al., 2014; Iziomon et al., 2003; Crawford and Duchon.1999), liquid water path (LWP) or ice water path (IWP) (Crawford and Duchon.1999; Duarte et al.2006; Zhou and Cess.2001; Zhou et al.,2007) to quantify the cloud contribution. Although the LWP or IWP can be directly derived from satellite data compared with the cloud base parameters, it is still unavailable for most optical sensors at nighttime, such as widely used MODIS, VIIRS and Himawari-8 etc. In contrast, the cloud top temperature (CTT) can be retrieved at both daytime and nighttime for most remote sensing missions, and many cloud top height products are currently readily available for the public. It is a promising way if the CTT can be used as an indicator for quantifying the cloud thermal contribution in a proper manner. This is the motivation of this study. We intend to propose general schemes to derive all-sky LWDR from satellite measurements based only on the readily available variables of LST, CWV and CTT. With these new parameterizations, all-sky LWDR can be easily mapped by the common users at regional and even global scales by making full use of currently available space-based data and products. Specifically, the purpose of this paper is twofold: (1) to provide a general parameterization for deriving clear-sky LWDR with the inputs of LST and CWV; (2) to propose a parameterization for deriving cloudy-sky LWDR with the inputs of LST, CWV and CTT.

Table 1 CERES products used for building the training database. Products

Year

Instrument

Resolution

Parameters

CER-SSF_Terra-FM1MODIS Edition4A CER-SSF_Aqua-FM3MODIS Edition4A

2015 2016 2018

FM1

Footprint ~ 20 km nadir

LST CWV CTT LWDR- “model B” LWDR- “model C”

FM3

sources. First, three years (2015, 2016, 2018) of CERES products over the globe were used to build the database. CERES is one of the few missions that release the global all-sky surface LWDR products with about 20 km resolutions (SSF product). The CERES LWDR products are widely verified and show a good performance (Yu et al., 2019; Wang et al., 2018; Stephens et al.,2012; Kratz et al., 2010; Gupta et al., 2010; Zhou et al.,2007). Specifically, the product information of CERES used in this study is listed in Table 1. Considering the good consistence, in CERES SSF product, the average of LWDR generated from “model B” (hereafter referred to as LWDR_B) (Gupta et al. 1992; 2010) and “Model C” (hereafter referred to as LWDR_C) (Zhou and Cess, 2001; Zhou et al., 2007) are used as the final cloudy-sky LWDR in our database and only the CERES samples with cloud fraction greater than 0.98 were retained to train. For clear-sky LWDR, existing studies showed that the LWDR_B is low biased in some regions (Zhou et al., 2007), and our previous analysis also show similar conclusion, thus the LWDR_C was chosen as the final clear-sky radiation in our database. To further strengthen the representativeness of the training database, a comprehensive simulation based on a radiative transfer (RT) model was conducted. The used RT model is MODTRAN 6.0 (Alexander et al., 2015) and the corresponding settings for the simulation is listed in Table 2. During simulations, the atmosphere was generated by combing the MODIS profile product (https://doi.org/10.5067/MODIS/ MOD07_L2.006) and TIGR profiles (Chedin et al., 1985; Chevallier et al., 1998) which was described in Wang et al. (2012). Finally, a training database with about 55,664 records for cloudy-sky and 62,806 for clear-sky conditions were built respectively, by combing the CERES products and the RT simulations. Please note that, although the MODIS and TIGR profiles are utilized in this study during the simulation, other profile databases such as, GAPRI (Mattar et al.,2015) and other databases used in literatures (Jiménez-Munoz et al., 2010; Jiménez-Munoz et al., 2016), can also be employed. 2.2. Non-linear regression modeling For clear-sky conditions, the LWDR controlling variables in the training database are the LST and CWV which are used to approximate the air temperature and the humidity at screen-level, respectively. Considering that, many studies revealed that the LST shows a reasonable relationship with the air temperature (Benali et al., 2012; Zhu et al., 2017; Zhou et al.,2017), the following non-linear form is adopted to derive the clear-sky LWDR after many experiments. Compared to air Table 2 Settings of MODTRAN parameters when simulating the all-sky LWDR.

2. Method 2.1. Generation of training database for parameterizing the all-sky LWDR

Parameters

Setting/Values

Aerosol loading LST

Default Rural, VIS = 23 km Surface air temperature ± 20 K with an increment of 3K [0.05, 5] with an increment of 0.2 g/cm2 Cumulus, Altostratus, Stratus, Nimbostratus [0.5,8] above the surface with an increment of 1 km 0,1,2,3,4,5 (Km)

Water vapor Cloud types Cloud Top height(km) Surface altitude

To develop the new schemes for deriving all-sky LWDR, a representative database which at least include the variables of LST, CWV, CTT and LWDR should be built. In this study, this is conducted in two 53

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temperature, the LST is relatively easy to derive from the satellite data with better accuracy. The substitution of LST for the air temperature will greatly expand the applications of remote sensing measurements in estimating the global LWDR.

LWDR _clr = A0 + A1 × LST a0 × ln(1 + CWV )a1 + A2 × ln(1 + CWV ) a2 + A3 × ln(1 + CWV ) a3

3. 3.Results 3.1. Performance of the nonlinear and RF models Fig. 1 demonstrate the fitting performances of the nonlinear and RF models for the clear-sky and cloudy-sky LWDR estimations. It shows that, for the nonlinear model, the RMSE for the training database is 17.9 W/m2 and 10.7 W/m2 for the clear-sky and cloudy-sky models, respectively. The bias is nearly 0 for both models. Compared with the nonlinear models, the accuracy of the RF models is relatively better with RMSE < 10 W/m2 for both the clear- and cloudy-sky LWDR. This proves that both the nonlinear and the RF models can properly fit the samples of in the training databases.

(1)

Where, LWDR _clr is clear-sky LWDR; A0 , A1, A2 , A3, a0 , a1, a2 and a3are fitting coefficients (see Table 3). Under cloudy conditions, except the downward thermal contribution of the sub-cloud atmosphere (LWDR _atm ), the radiation contribution from the cloud layers should also be accounted for. The longwave radiation originated from the cloud layer is inevitably attenuated by the underlying atmosphere which is closely related to the loadings of CWV. Considering the water vapor absorption, a new parameterization for cloudy-sky LWDR derivation from space is proposed (Eq. (2)) based on existing parameterizations. Then, the all-sky surface LWDR is modelled as equation (3).

3.2. Comparison with the CERES products In this section, the CERES product that cover the globe and in the whole year of 2011 (instrument Terra-FM1) (different from the data used in the training stage) was used as an independent data source to examine the performance of the new models and then compare them with the two algorithms employed in the CERES product. The results indicate that the proposed new models have satisfactory accuracies in term of estimating both the clear- and cloudy-sky LWDR based on LST, CWV and CTT (Fig. 2). For both the clear- and cloudy-sky conditions, the RMSE and bias for the nonlinear model are less than 11 W/m2 and 0.5 W/m2, respectively; and for the RF based model, the accuracy is even better, the RMSE and bias are less than 3 W/m2 and 0.2 W/m2, respectively. In addition, the consistence between the results from the new models and that of the LWDR_B and LWDR_C were also test (Fig. 3). The analysis reveals that, in general, the new models have a very good consistence with the two datasets in the CERES product for both the clear and cloudy-sky conditions. Specifically, for clear-sky days, the bias for the all four methods are very similar (< 1.5 W/m2), while, the RMSE of the new models versus the LWDR_B (15.5 W/m2 and 12.8 W/ m2) is relatively larger than that of LWDR_C (5.9 W/m2 and 1.2 W/m2). A similar situation is detected for the cloudy-sky conditions with the exception of that our new methods are low biased against LWDR_B but over biased against LWDR_C by about 7 W/m2. This is logically reasonable because the new models take the average value of the LWDR_B and LWDR_C as the cloudy LWDR, thus the derived LWDR based on the new models have a balance accuracy. As a whole, the above comparison analyses demonstrate that the proposed models can generate very similar LWDR to the CERES products in terms of accuracy although they only utilize the readily available parameters from space, i.e., LST, CWV and CTT.

LWDR _cld = B 0 + B1 × LWDR _atm + B 2× CTT b0 [ln(1 + CWV )b1 + ln(1 + CWV )b2 + ln(1 + CWV )b3] (2)

LWDRAll

sky

= (1

(3)

cf ) × LWDR _clr + LWDR _cld × cf

where, LWDR _cld is the cloudy-sky LWDR; B0 , B1, B2 , b0 , b1, b2 andb3are fitting coefficients (see Table 3). LWDR _atm is the thermal contribution from the sub-cloud atmosphere. Considering the fact that the thermal contribution is mainly from the lower layers of the atmosphere, in this study, LWDR _atm is calculated using the same equation LWDR _clr (Eq. (1)), i.e., and coefficients as that of LWDR _atm =LWDR _clr . LWDRAll sky is the all-sky LWDR; cf is cloud fraction of a pixel. 2.3. Machine learning-based modeling As a statistical technique, the machine learning-based methods are widely used in the geoscience modelling fields (El Naqa et al., 2018; Wang et al.,2012; Wang et al., 2009). Its good fitting ability is attracting more and more attention, especially the deep learning method (Zhu et al., 2017; Zhang et al.,2016; Cheng et al.,2016). Considering its good accuracy and high efficiency, in this study, the random forest (RF) method (Breiman, 2001) is adopted to model the clear-sky and cloudysky LWDR, respectively for comparison purpose. The inputs of the random forest model are the same as that of the non-linear models mentioned above. During the training phase, the number of trees was set to 28, and other parameters are kept as the default. Our test shows that, the performance of the RF model is very similar when the tree number change from 20 to 30 for the present study. Note that, although RF is tested here, the readers could also employ other types of machine learning methods, such as artificial neuron network, support vector machine etc.

3.3. Verification against the ground-based measurements To examine the absolute accuracies of the newly proposed models, the LWDR measurements of 2012(both Terra-FM1 and Aqua-FM3) at seven SURFRAD sites (Augustine et al., 2000). were selected as the true data for validation. The SURFRAD data are available at http://www. srrb.noaa.gov/surfrad/. During analysis, the SURFRAD 1-min measurements located in the range of ± 5 min from the CERES overpass time were averaged as the final ground-based LWDR values, and no spatial consideration is conducted, just using the nearest CERES pixels at each site. The validation reveals that both the nonlinear and RF models show reasonable consistence with the ground measurements, the RMSE and bias are 22.5 W/m2 and −1 W/m2, respectively for the nonlinear model under all-sky conditions (Fig. 4(a)). The RF model shows similar accuracy to that of the nonlinear model with RMSE and bias are 22.7 W/m2 and 0.01 W/m2, respectively (Fig. 4(b)). To better understand the performance of the new models, the LWDR_B and LWDR_C are also verified against the ground measurements (Fig. 4(c) and (d)). It indicates that all these four methods show very similar accuracies for all-sky LWDR. For clear-sky situation, all of these

Table 3 Coefficients of the new parameterizations for deriving all-sky LWDR from space. Clear-sky Coefficients

A0 A1 A2 A3 a0 a1 a2 a3

52.382621 0.0001694 11.587137 28.739175 2.484027 0.188556 1.310620 1.279775

Cloudy-sky Coefficients

B0 B1 B2 b0 b1 b2 b3

−16.688367 1.058278 1.253816e-006 3.305942 −0.038784 3.08312 −0.037125

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Fig. 1. Fitting performances of the nonlinear and RF models for clear-sky and cloudy-sky LWDR estimations based on the training database (Left: nonlinear model; right: RF model).

retrieval accuracy. In this section, we further examine the spatial distribution of LWDR maps of the new methods and other products. The Himawari-8 LWDR data (Bessho et al., 2016) collected on September 13, 2018 ranging 2:00 to 3:00 UTC, CERES SYN1deg hourly product (Ed4A) and the corresponding ERA5 reanalysis (Copernicus Climate Change Service (C3S) (2017): ERA5: Fifth generation of ECMWF atmospheric reanalyses of the global climate. Copernicus Climate Change Service Climate Data Store (CDS), 2019. https://cds.climate. copernicus.eu/cdsapp#!/home) data were randomly selected to compare. It covers a region of 60°S-60°N, 80°E-160°W. The Himawari-8 LWDR was calculated at each 10-min scales using the proposed parameterizations and finally averaged to the hourly product. The different LWDR maps are shown in Fig. 5. It reveals that, on the whole, these maps show similar spatial patterns of LWDR with the exception that both CERES and ERA5 show low bias over the Tibet plateau and the

methods show a negative bias, but the new models show a relatively smaller bias. In contrast, the LWDR_B demonstrates a larger bias for clear-sky conditions (-12.1 W/m2). At present version, the accuracies of the new models are better than or at least comparable to most existing algorithms (Wang et al.,2019; Cheng et al.,2019; Zhou et al.,2019; Wang et al.,2012; Bisht and Bras, 2010,2011; Wang and Liang,2009; Tang and Li. 2008; Zhou et al.,2007; Zhou and Cess.2001; Gupta et al.,1992; Gupta et al., 2010). The above comparison and analysis prove that the new models work well in deriving all-sky LWDR from space at present form. 3.4. Spatial comparison with existing LWDR products In the above sections, we compared the proposed parameterizations with CERES SST product and ground-based measurements in terms of

Fig. 2. Comparison of the derived all-sky LWDR based on the new models versus the CERES product in the year of 2011 (Terra-FM1) over the globe (Left: the nonlinear model; right: the RF model, blue and red colors indicate clear- and cloudy-sky, respectively). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 3. Comparison of the derived all-sky LWDR based on the new models versus two algorithms (LWDR_B and LWDR_C) embedded in CERES product in the year of 2011 (Terra-FM1) over the globe (Left: model B; right: model C, blue and red colors indicate clear- and cloudy-sky, respectively). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

ocean areas southwest of the Oceania. On the one hand, this discrepancy is probably attributed to the different grid scales of these two datasets compared with the relatively high resolution Himawari-8 data (5 km); on the other hand, the calculated Himawari-8 LWDR data incorporate more detailed cloud contributions by parameterizing the CTT. This is why the Himawari-8 LWDR demonstrates more details of spatial variation than that of other two products, implying the improved ability in analyzing the spatio-temporal variations of longwave radiation over the Intertropical Convergence Zone (ITCZ). Finally, an interesting finding is that, unlike the other two products, some regular streaks are occurred in ERA5 data, which should be further examined.

noteworthy advantages of these new models include: (1) The driving data are relatively easy to collect compared to existing algorithms; thus, the new models are easy to use by the common users. For clear-sky conditions, the only needed inputs of the new models are readily available LST and CWV from satellite, instead of requiring the air temperature, vapor pressure etc., as the existing methods; For cloudysky cases, instead of using cloud-base temperature, cloud-base height (cannot be direct observed by optical sensors), or the surrogated parameters such as, LWP and IWP which currently are not available for most satellite at nighttime, the CTT was employed in the new model. Compared with other cloud parameters used in existing algorithms, the CTT can be directly sensed by both optical and microwave sensors and theoretically easy to derive. Moreover, currently, the CTT is a routine operational product for most satellite missions. Therefore, the new models are general and can be applied to most optical remote sensing data; and (2) Because the only inputs for these models are readily available LST, CWV and CTT, the proposed new methods provide potential ability to map global LWDR with good accuary by making full

4. Discussion and conclusions In this paper, new parameterizations for deriving the space-based all-sky surface LWDR are proposed. Meanwhile, machine learningbased RF models are also provided with the same inputs setting as the nonlinear parameterizations. Compared to other existing methods, the

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Fig. 4. Validation of the derived all-sky LWDR from the four models against SURFRAD ground-based LWDR measurements in the year of 2012 (both Terra-FM1 and Aqua-FM3) ((a): Nonlinear model; (b): RF model; (c): CERES model B; (d): CERES model C. blue and red colors indicate clear- and cloudy-sky, respectively). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

use of various satellite products both at daytime and nighttime. This will further expand the applicability of remotely sensed measurements in surface energy balance studies. The only limitation of the new methods is the dependence on LST under cloudy skies. As is known to all, it is difficult to estimate cloudysky LST from thermal infrared remote sensing data due to the opacity of the clouds. In fact, this is a challenging problem that is faced by the remote sensing community for a long time. How to derive LST based on traditional remotely sensed measurements is still a big topic in the community although tremendous work has been conducted. The issue regarding to the LST estimation under cloudy skies is beyond the scope of this study. Here, considering the lack of easy-to-use scheme in terms of input variables in existing methods, we mainly focus on the problem of how to conveniently derive all-sky LWDR from space on the assumption that the surface temperature under both clear and cloudy conditions are provided. The main contribution of this study is to alleviate the current predicament that it is not a trivial work to derive all-

sky LWDR even if the all-sky surface temperature is given for most common users, and that currently, the applications of remotely sensed products in estimating LWDR is highly limited due to the demanding inputs of the existing methods. But then again, it is not completely impossible to derive cloudy-sky LST from remotely sensed data. Many attempts have been conducted to estimate such LST based on solarcloud-satellite geometry (Wang et al., 2019), microwave data (Mao et al., 2007), fusion of microwave and thermal infrared data (Duan et al., 2017; Wang et al., 2014; Kou et al., 2016; Shwetha and Kumar, 2016) or statistical approaches (Yang et al., 2019; Sun et al., 2017; Zeng et al., 2018). Moreover, some reanalysis LSTs are also frequently used in remotely sensed products, such as MODIS and CERES etc. These could provide useful data sources for approximating the cloudy-sky surface temperatures. The validation and inter-comparison reveal that the new methods work well, the RMSE of the derived LWDR under all-sky conditions is less than 23.0 W/m2 for both ones, and the bias is less than 2.0 W/m2.

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Fig. 5. LWDR maps of Himawari-8, CERES SYN1deg hourly product and the corresponding ERA5 reanalysis on September 13, 2018. ((a): Himawari-8 true color image, bands 3,2, and 1 for RGB; (b): Himawari-8 LWDR derived using the proposed parametrizations; (c): CERES SYN1deg hourly product; (d): ERA5 reanalysis).

Unlike existing algorithms where the direct variables (such as, air temperature, vapor pressure, LWP, IWP, sub-atmosphere water vapor etc.,) that control the all-sky LWDR are utilized, the new models only employ three indirect variables (LST, CWV and CTT), but show comparable and even better accuracy than existing methods. The comparison regarding the LWDR spatial distribution also reveals the effectiveness of the proposed parameterizations in characterizing the global LWDR variations. The authors must admit that, the new methods still have many spaces to improve at present version. For instance, (1) the training database should be further strengthened by including more CERES or

other satellite data and the ground-based measurements; (2) adding more simulated samples given more representative atmospheric and surface conditions with wide ranges; and (3) new forms and/or updated coefficients of Eqs. (1) and (2) with better fitting accuracy are also expected in the future. In Section 3.3, the new methods are validated against the ground measurements at seven sites of SURFRAD in the whole year of 2012, other validation versus measurements at different climatic regions is also required. All these are our main work in the next investigations. However, we are sure that this do not affect our conclusion considering the comparison analysis in Section 3.2 where the used CERES data are globally distributed.

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Although the improvement is needed, at least, our study proved the feasibility to use these readily available variables from the satellite to derive all-sky global LWDR. We believe the framework and findings presented in this study can provide new ideas for the remote sensing community, especially in the areas of radiation and/or energy balances, climate change and environmental monitoring.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The work in this paper is jointly supported by the National key research and development program of China (2018YFA0605401), National Natural Science Foundation of China (No. 41571364, 41771387), and the Key Research and Development Program of Ningxia province of China (2018BFH03004). The CERES SSF and SYN1deg-1Hour Ed4A products used in this work are downloaded from https://eosweb.larc.nasa.gov/project/ceres/ceres_table, which are provided by the NASA Langley Research Center's (LaRC) ASDC DAAC and are managed by the NASA Earth Science Data and Information System (ESDIS) project. The MODIS data used in this study are downloaded from https://search.earthdata.nasa.gov/. The ERA5 reanalysis datasets are downloaded from https://cds.climate.copernicus.eu/ cdsapp#!/dataset/reanalysis-era5-single-levels?tab = form; The SURFRAD data are available at http://www.srrb.noaa.gov/surfrad/. All other data used are listed in the references. We are grateful to the three anonymous reviewers for their valuable comments on our manuscript. References Augustine, J.A., DeLuisi, J.J., Long, C.N., 2000. SURFRAD - A national surface radiation budget network for atmospheric research. Bull. Am. Meteorol. Soc. 81, 2341–2357. Benali, A., Carvalho, A.C., Nunes, J.P., Carvalhais, N., Santos, A., 2012. Estimating air surface temperature in Portugal using MODIS LST data. Remote Sens. Environ. 124, 108–121. Berk Alexander, Patrick Conforti, and Fred Hawes, “An accelerated line-by-line option for MODTRAN combining on-the-fly generation of line center absorption with 0.1 cm-1 bins and pre-computed line tails,” Proc. SPIE 9471, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXI, 947217 (May 21, 2015). Bessho, K., Date, K., Hayashi, M., Ikeda, A., Imai, T., Inoue, H., Okuyama, A., 2016. An introduction to Himawari-8/9—Japan’s new-generation geostationary meteorological satellites. J. Meteorolog. Soc. Japan. Ser. II 94 (2), 151–183. Bisht, G., Bras, R.L., 2010. Estimation of net radiation from the MODIS data under all sky conditions: Southern Great Plains case study. Remote Sens. Environ. 114, 1522–1534. Bisht, G., Bras, R.L., 2011. Estimation of net radiation from the moderate resolution imaging spectroradiometer over the continental United States. IEEE Trans. Geosci. Remote Sens. 49, 2448–2462. Bisht, G., Venturini, V., Islam, S., Jiang, L., 2005. Estimation of the net radiation using MODIS (moderate resolution imaging spectroradiometer) data for clear sky days. Remote Sens. Environ. 97, 52–67. Breiman, L., 2001. Random forests. Mach. Learn. 45, 5–32. Carmona, F., Rivas, R., Caselles, V., 2014. Estimation of daytime downward longwave radiation under clear and cloudy skies conditions over a sub-humid region. Theor. Appl. Climatol. 115, 281–295. Chedin, A., Scott, N.A., Wahiche, C., Moulinier, P., 1985. The improved initialization inversion method - a high-resolution physical method for temperature retrievals from satellites of the tiros-N series. J. Climate Appl. Meteorol. 24, 128–143. Cheng, G., Zhou, P.C., Han, J.W., 2016. Learning rotation-invariant convolutional neural networks for object detection in VHR optical remote sensing images. IEEE Trans. Geosci. Remote Sens. 54, 7405–7415. Cheng, J., Yang, F., Guo, Y., 2019. A comparative study of bulk parameterization schemes for estimating cloudy-sky surface downward longwave radiation. Remote Sens. 11, 528. Chevallier, F., Cheruy, F., Scott, N.A., Chedin, A., 1998. A neural network approach for a fast and accurate computation of a longwave radiative budget. J. Appl. Meteorol. 37, 1385–1397. Crawford, T.M., Duchon, C.E., 1999. An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling longwave radiation. J. Appl. Meteorol. 38, 474–480. Duan, S.B., Li, Z.L., Li, H., G?ttsche, F.M., Wu, H., Zhao, W., Coll, C., 2019. Validation of collection 6 MODIS land surface temperature product using in situ measurements.

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