A revisit of parametrization of summer downward longwave 1 radiation over the Tibetan Plateau from high temporal resolution 2 measurements 3

Abstract. The Tibetan Plateau (TP) is one of hot spots in the climate research due to its unique geographical location, high altitude, highly sensitive to climate change as well potential effects on climate in East Asia. Downward longwave radiation (DLR), as a key component in the surface energy budget, is of practical implications for many research fields. Several attempts have been made to measure hourly or daily DLR and then model it over the TP. This study uses 1-minute radiation and meteorological measurements at three stations over the TP to parameterize DLR during summer months. Three independent methods are used to discriminate clear-sky observations by making maximal use of collocated measurements of downward shortwave and longwave radiation as well as Lidar backscatter measurements with high temporal resolution. This guarantees a reliable separation of clear-sky and cloudy samples that favors for proper parameterizations of DLR under these two contrast conditions. Clear-sky and cloudy DLR models with original parameters are firstly assessed. These models are then locally calibrated based on 1-minute observations. DLR estimation is notably improved since specific conditions over the TP are accounted for by local calibration, which is indicated by smaller root mean square error (RMSE) and larger coefficient of determination (R2). The best local parametrization can estimate clear-sky DLR with RMSE of 3.8 W⸱m-2. Overestimation of clear-sky DLR by previous study is evident, likely due to potential residue cloud contamination on the clear-sky samples. Cloud base height under overcast conditions is shown to be intimately related to cloudy DLR parameterization, which is considered by this study in the locally calibrated parameterization over the TP for the first time.



Introduction
Downward longwave radiation (DLR) at the Earth's surface is the largest component of the surface energy budget, being nearly double downward shortwave radiation (DSR) (Kiehl and Trenberth, 1997).DLR has shown a remarkable increase during the process of global warming (Stephens et al., 2012).This is closely related to the fact that both a warming and moistening of the atmosphere (especially at the lower atmosphere associated with the water vapor feedback) positively contribute to this change.Understanding of complex spatiotemporal variation of DLR and its implication is essential for improving weather prediction, climate simulation as well as water cycling modeling.Unfortunately, uncertainties in DLR are considered substantially larger than that in any of the other components of surface energy balance, which is most likely related to scarce DLR measurements with high quality (Stephens et al., 2012).
The 2-sigma uncertainty of DLR measurement by using a well-calibrated and maintained pyrgeometer is estimated to be 2.5% or 4 W m -2 (Stoffel, 2005).However, the global-wide surface observations are very limited, especially in those remote regions.DLR is extensively estimated by proxy meteorological measurements of synoptic variables.It has been known for almost one century that the clear-sky DLR is determined by the bulk emissivity and effective temperature of the overlying atmosphere (Angstrom, 1918).Since these two quantities are not easily observed for a vertical column of the atmosphere, clear-sky DLR is alternatively parameterized as a function of air temperature and water vapor density, assuming that the clear sky radiates toward the surface like a grey body at a screen-level temperature (the standard level of meteorological measurements, generally 1.5 m above the ground).Dozens clear-sky DLR models have been developed by parameterization of different clear-sky effective emissivity (εc) to the screen-level temperature (Ta) and water vapor pressure (e).Exponential function (Idso, 1981) or power law function (Brunt, 1932) have been widely used to depict the relationship of εc to Ta and/or e.The coefficients of these functions are generally derived by a regression analysis of collocated measurements of Ta, e and DLR.Most of these proposed parameterizations are thus Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2019-397Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 May 2019 c Author(s) 2019.CC BY 4.0 License.empirical in nature and only specific for definite atmospheric conditions.Brutsaert (1975) was the first to develop a physically rigorous model of clear-sky atmospheric emissivity, which was based on the analytic solution of the Schwarzchild's equation for a standard atmospheric lapse rates of temperature and water vapor.Prata (1996) found that the precipitable water content (w) was much better to represent the effective emissivity of the atmosphere than e, which was loosely based on radiative transfer simulations.Dilley and O'Brien (1998) adopted this scheme but tuned empirically their parameterization using an accurate radiative transfer model.Given the fact that clear-sky DLR is impacted by water vapor and temperature profile (especially the inversion layer) and diurnal variation of Ta, a new model with two more coefficients considering these effects on DLR was developed (Dupont et al., 2008a).
In the presence of clouds, the total effective emissivity of the sky is remarkably modulated by clouds.The existing clear-sky parameterization should be modified according to the cloud fraction (CF) and other cloud parameters.CF is generally used to represent a fairly simple cloud modification under cloudy conditions.Many equations with cloudiness correction have been developed and evaluated by the DLR measurements across the world (Crawford and Duchon, 1999;Niemela et al., 2001).
CF is widely obtained from surface human observations (Iziomon et al., 2003) that is subjective in nature.CF can also be derived from DSR (Crawford and Duchon, 1999) and/or DLR measurements (Durr and Philipona, 2004).Moreover, DSR or DLR measurements with very high temporal resolution (for example, 1-min) can also provide cloud type information (Duchon and Malley, 1999), and thereby allowing to consider the effects of cloud types on DLR (Orsini et al., 2002).This indicates that 1-min DSR and DLR measurements are beneficial to the DLR parameterization.
With an average altitude exceeding 4 km above the sea level (a.s.l.), Tibetan Plateau (TP), the largest mountain area in the world, exerts a huge influence on regional and global climate through mechanical and thermal forcings (Wu et al., 2007).TP is the region with very high sensitivity to climate change.The most rapid warming rate over the TP occurred in the latter half of the 20 th century was likely associated with relatively large DLR increase.Duan and Wu (2006) indicated that increase in low level nocturnal cloud amount and thereby DLR can partly explain the increase in the minimum temperature, despite decreases in total cloud amount during the same period.By using observed sensitivity of DLR to change in specific humidity for the Alps, Rangwala et al. (2009) suggested that increase in water vapor appeared to be partly responsible for producing the large warming over the TP.Since the coefficients of these empirical models and their performances showed spatiotemporal variations, establishment of localized DLR parameterizations over the TP is of highly significance.Given the importance of DLR to climate change, further studies on the DLR parameterization as well as DLR sensitivity to atmospheric variables are desirable, which would expected to improve our understanding of climate change over the TP (Wang and Dickinson, 2013).DLR measurements with high temporal resolution using high quality radiometer over the TP are quite scarce.So it is not surprising that there have been very few studies on DLR and its parameterization.Wang and Liang (2009) evaluated clear-sky DLR parameterizations of Brunt (1932) and Brutsaert (1975) at 36 globally distributed sites, in which DLR data at two TP stations were used.Yang et al. (2012) used hourly DLR data at 6 stations to study the major characteristics of DLR and the all-sky parameterization of Crawford and Duchon (1999) was assessed.More recently, Zhu et al. (2017) evaluated 13 clear-sky and 10 all-sky DLR models based on hourly DLR measurements at 5 automatic meteorological stations over the TP.Note that the CG3 pyrgemeters (Kipp & Zonen), the second class radiometer according to the International Organization for Standardization (ISO) classification, were used to measure DLR in these previous studies.The parameterization would thus be impacted by a large measurement uncertainty (roughly 10% according to the CG3 manual).
Clear-sky and CF were determined with relative low temporal resolution, for example, subjectively by human observer every 3 or 6 hours, which would also impact the parameterization.One would expect that these previous methods developed for daily or longer-term averages were usually less accurate at shorter time intervals.
In order to further our understanding of DLR and DSR over the TP,
Simultaneous 1-min averages of Ta and e are taken from the automatic meteorological stations.CG4 is designed for the DLR measurement with high reliability and accuracy due to its specific material and unique construction.Window heating due to absorption of solar radiation in the window material is the major error source of DLR measurement, which is strongly suppressed by a unique construction conducting away the absorbed heat very effectively.The shading and un-shading experiment of CG4 measurements show a window heating offset of less than 4 W⸱m -2 (Meloni et al., 2012), as a comparison, it can reach 25 W⸱m -2 for CG3 since it is always not shaded (Wang and Dickerson, 2013).An installation of the CG4 on the Kipp & Zonen CV2 ventilation unit is able to prevent dew deposition on the window.The radiometers are calibrated before and after field measurements through comparison to the reference radiometers operated by the national metrological standards of meteorology that is A Micropulse Lidar (MPL-4B, Sigma Space Corporation, United States) was installed site-by-site with radiometers.The Nd:YLF laser of the MPL produces an output power of 12 μJ at 532 nm.The repletion rate is 2500 Hz.The vertical resolution of the MPL data is 30 m and the integration time of the measurements is 30 s.The MPL backscattering profiles are used to identify the cloud boundaries and derive the CBHs (He et al., 2013).The dataset contains about 700 hours of coincident DLR, DSR, Lidar and meteorological measurements.

Clear-sky discrimination
Clear skies should be discriminated from cloudy conditions before performing clear-sky DLR parametrization, which is achieved by the synthetical analysis of DSR, DLR, and CBH from MPL.The term clear sky or cloud-free in this paper means a sky without any condensed liquid or ice water for all classes of altitude.
Following the method initiated by Crwford and Duchon (1999), we calculate two quantities reflecting DSR magnitude and variability based on 1-min observed DSR (DSRobs) and calculated clear-sky DSR (DSRcal) values.DSRcal is calculated by the model C of Iqbal (1983) in which direct and diffuse components of DSR on a horizontal surface are parametrized separately.Direct DSR is first calculated by multiplying transmittance due to Rayleigh scattering, aerosol attenuation and absorption by water vapor, ozone and the uniformly mixed gases.Diffuse DSR is estimated as the sum of the Rayleigh and aerosol scattering as well as the multiple reflected irradiance between surface and atmosphere.The terrain reflection is estimated according to Dozier and Frew (1990).The precipitable water is calculated from e according to a linear relationship that was developed based on collocated e and radiosonde (in AL) or GPS (NQ and NC) -based precipitable water measurements .
Climatological value of aerosol optical depth and single scattering albedo are from the reference (Che et al., 2015).Mean surface albedo values of 0.22 at NQ, 0.18 at NC, and 0.25 at AL were from Liang et al. (2012).Malley, 1999;Long and Ackerman, 2000;Orsini et al., 2002).The mean and standard deviation of the scaled DSRobs in a 21-min moving window (±10-min) centered on the time of interest are then calculated to discriminate clear-sky.Selection of the width of 21-min is empirical but a consequence of having a reasonable time span for estimating the mean and variance (Duchon and Malley, 1999).Clear-sky DSR should satisfy the followed three requirements: 1) ratio of DSRobs to DSRcal is within 0.95 to 1.05, 2) difference between scaled DSRobs and DSRcal is less than 20 W⸱m -2 , and 3) standard deviation of scaled DSRobs is less than 20 W⸱m -2 .Temporal variability of DLR is also used to separate cloudy sky from cloud-free situations.Based on analysis of the standard deviation of scaled DLR (scaled to 500 W⸱m -2 ) for a ±10-min period, clear-sky periods are detected if the standard deviation is less than 5 W⸱m -2 .Given the fact that DSR and DLR experience difficulties in detecting clouds in the portion of the sky far away from the sun (Duchon and Malley, 1999) or high-altitude cirrus clouds (Dupont et al., 2008b), coincident MPL backscatter measurements are used to strictly select clear-sky samples.We can be sure that there is a cloud element somewhere in the sky when the MPL identifies a cloud, we require that no clouds are detected by the MPL within the ±10-min period, otherwise it is defined as cloudy condition.
These two different methods are complementary to each other to some extent (Dupont et al., 2008b), one would expect that a combined analysis of both passive and active remote sensing instruments can precisely detect clear sky periods.We hence

Cloud fraction estimation
Given synoptic cloud observations are very limited and temporally sparse, various parameterizations using DSR or DLR data have been developed to estimate the cloud fraction (CF) or called cloud modulate factor (CMF) (e.g., Deardorff, 1978;Marty and Philipona, 2000;Durr and Philipona, 2004;Long et al., 2006;2008).Because of the good agreement between clear-sky DSRobs and DSRcal calculated by the Iqbal C calculations (Iqbal, 1983), with mean bias of 1.7 Wm -2 and root mean square error (RMSE) of 10.7 Wm -2 , we use Deardorff 's method to calculate CF from DSRobs and DSRcal.The method is based on a fairly simple cloud modification to DSR as follows.
To avoid the error caused by abrupt DSR variation, 21-min DSR samples rather than its instantaneous measurements are used to calculate CF here.

Clear-sky DLR parameterization evaluation and localization
Eleven clear-sky DLR (DLRclr) parameterizations (Table 2) are evaluated based  Brutsaert (1975), Greenland in Konzelmann (1994) and Australian desert in Prata (1995).The climate in those areas is likely similar to that in TP, so one would expect the coefficients in those parameterizations are also suitable in TP.The higher RMSE (>37 W m -2 ) and the lower R 2 (~0.7) for Swinbank (1963) and Idso and Jackson (1969).Both used T as the sole parameter.The essential point was that the screen temperature is a better indicator of the mass of radiatively active water vapor than the surface vapor pressure.However, previous studies have suggested that these methods would produce substantially large RMSE (>37.5 W⸱m -2 ) and low R 2 (<0.75) (Duarte et al., 2006).The reason is that the atmospheric effective emissivity is more sensitive to the water vapor profile than the mass of radiatively active water vapor when the surface layer is dry compared to the whole column (Dupon et al., 2008).Furthermore, DLRclr is more much sensitive to variation of water vapor content over the TP than humid environment.Careful consideration of water vapor effect on DLR is obviously required over the TP.
The coefficients in eleven parameterizations (Table 2) were originally calibrated and determined in different geographical locations; therefore, they may not be the optimal values for the usage in the TP.Thus we take use of 1-min clear-sky DLR samples to locally calibrate the parameters of these parametrizations.We used k-fold cross-validation method to determine the local parameters.This method has two main advantages：i)less error rate because it repeatedly fits the statistical learning method using training data sets,.ii ) decreasing the error rate by using random training/validation data sets for multiple times (James et al., 2013).Here, all data was randomly divided into 10 groups of approximately equal size, the coefficients are computed by using 9 groups as training set, and the remained one as validation.This The non-linear least-squares fitting of the DLRclr parameterizations (Table 2) resulted in the coefficient values in Table 3.For each fitted parameterization, we calculated RMSE and R 2 and the results are shown in Fig. 2(b).When using the parameterizations with the locally fitted parameters (Fig. 2(b)), the accuracy of the parameterization relative to the published values is substantially improved.Most RMSEs are less than 10 W⸱m -2 except the parameterization proposed by Swinbank (1963) and Idso and Jackson (1969) that still produced the worst results (with R 2 of 0.71 and RMSE of 15 W•m -2 ) even the parameters are locally calibrated.The Dilley and O'Brien's parameterization, which was initially developed by considering the adaptation of climatological diversities, is expected to be able to fit the measurements in tropical, mid-latitude and Polar Regions.This expectation is verified by its wide deployment in DLRclr estimations in different climate regimes and altitude levels, for example, in the tropical lowland (eastern Pará state, Brazil) and the mild mountain area (Boulder, the United States) (Marthews et al., 2012;Li et al., 2017).The present study also confirmed that Dilley and O'Brien is the best clear-sky parameterization over the TP.This parameterization was also proved to be the most reliable estimates of DLRclr in the TP (Zhu et al., 2017).The locally calibrated equation is as follows.(2) The RMSE and R 2 of Eq.( 2) are ~3.8W⸱m -2 and > 0.98 respectively, which are substantially lower than those in previous studies in the TP, for example, the RMSE was 9.5 W•m -2 in Zhu et al. (2017).Note that the parameters here differ quite a lot from those in the reference (Zhu et al., 2017) that is shown in Eq. (3).DLR is always overestimated by Eq. ( 3).Note that Eq. ( 3) was derived from 1-hour DLR measurements, which was discriminated to be taken under clear-sky or cloudy conditions based on human observation at even lower resolution (every 3-6 hours).
Both factors are likely to introduce potential cloud contamination on clear-sky discrimination due to rapid variations of cloud.The presence of clouds would lead to a larger DLR value relative to that in clear sky, which is most likely cause for the overestimation of Eq. ( 3).Significant impacts on the monthly and yearly radiation budget of the same magnitude are not avoided as a result of persisting overestimation of DLR by Eq. (3).

Parameterization of cloudy-sky DLR
The parameterizations of cloudy-sky DLR (DLRcld) are based on estimated DLRclr coupled with the effect of cloudiness or cloud emissivity, which depends primarily on CF, and some other cloud parameters, like CBH and cloud type (Arking, 1990;Viúdez-Mora et al., 2014).Four parameterizations (Table 4), which modifies the bulk emissivity depending on CF, are assessed and locally calibrated in this section.
DLRclr is estimated according to Eq. ( 2) with the locally fitted coefficients.The fitted values of the coefficients (using k-Fold Cross-Validation) of the four parameterizations are presented in Table 5, and the RMSE and R 2 of original and locally fitted parameterizations in TP are presented in Fig. 4.
Relative to that under clear-sky conditions, cloudy parameterizations using the given parameters produced larger RMSE (generally exceeding 35 W•m -2 ) except that developed by Jacobs (1978) (RMSE of 18 W•m -2 ).R 2 was generally smaller than 0.9.RMSE decreased significantly in Maykut and Church (1973) and Sugita and Brutsaert (1993) as locally calibrated parameters were used.Relative smaller and almost no RMSE improvements were found for the methods developed by Konzelmann (1994) and Jacobs (1978).
Eq. ( 4  The RMSE and R 2 are ~18 W⸱m -2 and ~0.89.RMSE here is close to 15 W m -2 obtained at different altitudes in Swiss (Gubler et al., 2012), and slightly lower than 23 W m -2 in mountain area in Germany (Iziomon et al., 2003).Comparing to previous studies over the TP (RMSE of 22 W m -2 in Zhu et al., 2017), our cloudy model also produces better results.

Effect of CBH on DLR under Overcast Conditions
Since clouds behave approximately as a blackbody, the most relevant cloud parameter (besides CF) to DLR under overcast skies (DLRovc) is the temperature of its lower boundary (CBH).Radiative transfer model simulation has suggested that CBH under overcast conditions is an important modulator for the DLR.The cloud radiation effect (CRE), the difference between DLRobs and DLRclr, decreases with increasing CBH at a rate of 4~12 W•m -2 that depends on climate profiles (Viúdez-Mora et al., 2014).This indicated that cloudy DLR parameterization can be improved if CBH effect is considered.
The statistical relationship between CRE and CBH under overcast conditions in the TP is presented in Fig. 5, a box plot of CBH versus CRE.The peak and median values of CRE decrease with the increase of CBH.With the increase of CBH, the variation range of the CRE rises, ranging from 25 to 50 W•m -2 , as a result of the specific meteorological and cloud conditions.Compared to that at Girona, Spain, a low altitude mid-latitude site (Viúdez-Mora, et al., 2014), CRE in the TP is generally lower by 5~10 W•m -2 .This is likely associated with the fact that clouds in the TP with the same CBH as that in Girona have relatively lower temperature, thereby producing lower radiative effect on DLR.It is interesting that the decreasing tendency of CRE with CBH is apparent.CRE is about 70 W•m -2 for clouds < 1 km and decreases to ~40 W•m -2 for clouds at 3~4 km in the TP.The decreasing rate of CRE with CBH is estimated to be -9.8W•m -2 km -1 in the TP that is within the model simulations To consider CBH effect under overcast conditions, we introduced a modified parameterization similar as that in Viúdez-Mora et al. (2014).
The bias and RMSE of Eq.( 5) between measurements and calculations is 1.3 W•m -2 and 16.5 W•m -2 , respectively, which are significantly lower than that of Eq.( 4 Overcast DLR is highly sensitive to CBH.The parameterization in this case can be substantially improved by consideration of CBH effect.The bias between model calculations and measurements decreases from 10.3 W m -2 to 1.3 W m -2 when CBH effect is introduced A broadly representative of existing DLR parameterizations with good performance was assessed over the TP, while this did not imply that our sample of techniques was either exhaustive or optimal in all applications.We only focused on daytime DLR parameterization in TP since DSR is used in the cloud-screening method.Given a significant role of DLR played in the surface energy budget during nighttime, it is highly desirable to perform further study on the nighttime DLR parametrization in future.These results are based on summer DLR measurements in TP, so the conclusions here need to be tested in other seasons, especially in winter when DLR has been observed to increase in the TP (Rangwala et al., 2009).These further study would shed new light on how DLR is related to temperature and water vapor and why DLR has changed in the TP.
Author contributions.XD and XA designed the experiments and MQ carried them out.
MQ and JQ prepared the manuscript with contributions from all co-authors.
Competing interests.The authors declare that they have no conflict of interest.
Data availability.The data can be obtained from the corresponding author upon request.
Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2019-397Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 May 2019 c Author(s) 2019.CC BY 4.0 License.measurements of 1-min DSR and DLR at 3 stations over the TP using state-of-the-art instruments have been performed in summer months since 2011.These data provide us opportunity to evaluate clear-sky DLR models and quantitatively assess how cloud properties impact DLR.This study makes progress in the following aspects.Clear-sky discrimination and CF estimation are based on 1-min DSR and DLR measurements that are objective in nature.Misclassification of cloudiness into cloud-free skies would be minimized by adopting strict cloud-screening procedures based on not only 1-min DSR and DLR measurements but also coincident Lidar backscattering measurements.Potential effects of cloud-base height (CBH) on overcast DLR are investigated.Locally calibrated parameterizations of clear-and cloudy-sky DLRs are finally achieved.
Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2019-397Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 May 2019 c Author(s) 2019.CC BY 4.0 License.1-min DSRcal are first scaled to a constant value of 1400 W⸱m -2 , which is used to normalize the DSRobs by multiplying the same set of scale factors (Duchon and Fig. 1 shows how our method determines clear-sky conditions.DSRobs presents a smooth temporal variation from sunrise to about 14:00, August 19, 2016 (LST), being consistent with DSRclr.Similarly, DLR also varies very smoothly during this period and standard deviations of 21-min DLRs are generally less than 5 W m -2 .Both facts suggest that the sky is sunny and cloudless.This inference is supported by MPL backscatter measurements that do not detect any clouds overhead.Contrarily, an abruptly changes of 1-min DSRobs and DLR are evident and we can see DSRobs occasionally exceeds the expected DSRclr, indicating occurrence of thin or fair weather cumuli clouds.MPL detect a persistent cloud layer at 3 km above ground during 14:00-17:00 LST, which agrees with DSR and DLR measurements very well.Two-layer clouds are observed by MPL until to sunset, which is accompanied by highly variation of observed DSR and DLR.
Fig.3shows the comparison of instantaneous clear-sky DLR measurements as a function of calculations by Eq. (2) and by Eq. (3).It is seen that measurements are in good agreement with calculations of Eq. (2), as shown by an overwhelmingly large number of data points falling along or overlap the 1:1 line.By contrast, clear-sky ) shows the best cloudy-sky parameterization over TP by combining the clear-sky parameterization of Dilley and O'Brien (1998) with the cloud modulation Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2019-397Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 May 2019 c Author(s) 2019.CC BY 4.0 License.correction scheme of Jacobs (1978).
)(10.3 W m -2 and 21.4 W m -2 ) in overcast conditions.This result indicates a remarkable improvement in the estimation of DLR under overcast conditions by introducing CBH to the DLR parameterization.5 Discussion and conclusionsThe parameterization of clear-sky DLR requires a well-defined distinction between clear-sky and cloudy-sky situations that commonly depends on human cloud observations 4~6 times each day.Human observations are subjective in nature and have a very limited temporal resolution that obviously cannot capture dramatic variations of clouds.Furthermore, synoptic(human cloud observations show the tendency to stronger weight the horizon that DLR is not highly sensitive(Marty and     Philipona).Therefore, parameterization of clear-sky DLR based on synoptic sky observations is hence very likely biased as a consequence of improper selection of clear-sky measurements.This issue should be considered cautiously because it is essential to precisely quantify aerosol and cloud radiative effects that rely on precise identification of cloud free references(Dupont et al., 2008b).Using 1-min DSR and DLR at 3 stations over the TP, DLR parameterizations are evaluated and localized parameterizations have been developed.Potential CBH effect on overcast DLR is experimentally determined.Major conclusions are as follows.Among 11 clear-sky DLR parameterizations tested in this study, these two methods using only atmospheric temperature largely deviated from other parameterizations.DLR estimation can be improved by localization of these parameterizations.The best method suitable for the TP is the parameterization Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2019-397Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 May 2019 c Author(s) 2019.CC BY 4.0 License.developed by Dilley and O'Brien (1997).The locally calibrated Dilley and O'Brien model can produce clear-sky DLR with a RMSE of 3.8 W•m -2 .

*Brutsaert
Fig. 1.Time series of one-day sample on 2016.8.19 transited from clear-skies to cloudy-skies: (a) measured (black line) and calculated (dotted black line) downward shortwave radiation and its 21-min standard deviation (grey line), (b) measured downward longwave radiation and 21-min standard deviation and (c) MPL backscattering coefficient (color bar) and the cloud base height (white dots).
Fig. 5. Scatter plot of cloud radiative effect against MPL derived cloud base height are represented by box plot (the blue box indicates the 25th and 75th percentiles, the whiskers indicate 5th and 95th percentiles, the red middle line is the median).The black circles line and the black triangles is mean values of cloud radiative effect over TP in this study and in Girona, Spain (Viúdez-Mora et al., 2014).

Table 2 .
11 clear-sky DLR parameterizations and associated specific conditions