Publications in Radiation

Invited newsletter and book chapter
  1. Yang, K., T. Koike, G. Huang, and N. Tamai, 2007: Development and Validation of an Advanced Model for Estimating Solar Radiation from Surface Meteorological Data, Chapter 1 (pp.1-53), Recent developments in Solar Energy Research, Nova Science Publishers, Inc., New York, (ed. Hough T. P.), pp. 356.

    This chapter introduces the details of the development of a general model for estimating surface solar radiation from sunshine duration and other routinely measured parameters. Several independent works concluded this model is one of the best models in calculating surface direct solar radiation. The whole model or some formulas of the model are widely used in either practical applications or other models’ development. Additional references are Yang et al. (2001 Solar Energy) and Yang et al. (2006 AFM).

    介绍了一个简单通用的地表太阳辐射模型的细节。该模型计算简单,且考虑了大气中的辐射传输过程,无需局地校正,适用于不同海拔和气候区域。该模型被Springer和Elsevier出版的两本书全面介绍并收录源程序。该模型被数篇国际期刊论文评为计算太阳直射最好的模型之一。另外可参考Yang et al. (2001 Solar Energy) 和 Yang et al. (2006 AFM)。

Journal papers
  1. Tang, W., K. Yang, J. Qin, X. Niu, C. Lin, and X. Jing, 2017: A revisit to decadal change of aerosol optical depth and its impact on global radiation over China, Atmos. Env., 150, 106-115, doi:10.1016/j.atmosenv.2016.11.043.

    AOD is retrieved by combining visibility data and MODIS aerosol data. Aerosols have considerable effects on solar radiation climatology in China, but its direct effect is not adequate to explain the decadal variations of solar radiation.


  2. Tang, W., J. Qin, K. Yang, X. Niu, M. Min, and S. Liang, 2017: An efficient algorithm for calculating photosynthetically active radiation with MODIS products, Remote Sens. Environ, 194, 146-154, doi:10.1016/j.rse.2017.03.028.

    An efficient algorithm is developed to calculate surface PAR by combining a clear-sky PAR model and the parameterizations for cloud transmittances. The new algorithm is applied to estimate instantaneous PAR with inputs MODIS products onboard both Terra and Aqua platforms. The daily PAR is estimated from these two instantaneous values by an upscaling method. The instantaneous and daily PAR estimates were validated with in situ data collected in the USA and China and shows much better accuracy than those of previous studies.

    基于晴空 PAR 模型以及云天参数化方案发展了一个计算PAR的有效算法,将搭载在 Terra 和 Aqua 平台 上的 MODIS 产品为输入到该新算法得到了瞬时 PAR 值,并利用升尺度方案得到了日平均 PAR 值。反演的瞬时和日平均 PAR 值在美国和中国分别得到了有效验证,精度明显高于前人研究的反演精度。

  3. Tang, W., K. Yang, Z. Sun, J. Qin, and X. Niu, 2017: Global Performance of a Fast Parameterization Scheme for Estimating Surface Solar Radiation From MODIS Data, IEEE Trans. Geosci. Remote Sens, 55(6), 3558-3571, doi:10.1109/TGRS.2017.2676164.

    A fast parameterization scheme named SUNFLUX is first used in this study to estimate instantaneous surface solar radiation (SSR) based on products from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor onboard both Terra and Aqua platforms. The estimated instantaneous SSR is evaluated against surface observations obtained from seven stations of the Surface Radiation Budget Network (SURFRAD), four stations in the North China Plain (NCP) and 40 stations of the Baseline Surface Radiation Network (BSRN) and generally shows better accuracy than previous algorithms. Thus, this algorithm can be potentially applied on geostationary satellites for mapping high-resolution SSR data.

    本文首次将搭载在Terra 和 Aqua平台 上的MODIS产品代入一个快速算法来估算地表太阳辐射。反演的瞬时地表太阳辐射在美国7个SURFRAD站、中国北方4个站和全球40个BSRN站上进行了评估,精度高于以往算法,为未来利用静止卫星平台反演太阳辐射奠定了基础

  4. Tang, W., J. Qin, K. Yang, S. Liu, N. Lu, and X. Niu, 2016: Retrieving high-resolution surface solar radiation with cloud parameters derived by combining MODIS and MTSAT data, Atmos. Chem. Phys., 16, 2543-2557, doi:10.5194/acp-16-2543-2016.

    An artificial neural network (ANN) is applied to estimate cloud products from MTSAT geostationary satellite signals. The estimated cloud parameters are then used in an efficient parameterization model to map high spatiotemporal resolution surface solar radiation (SSR). The retrieved SSR has relatively high accuracy.


  5. Lin, C., K. Yang, J. Huang, W. Tang, J. Qin, X. Niu, Y. Chen, D. Chen, N. Lu, and R. Fu, 2015: Impacts of wind stilling on solar radiation variability in China, Sci. Rep., 5, 15135, doi:10.1038/srep15135.

    Long-term meteorological data at weather stations combined with short-term aerosol data were used to assess this hypothesis. It was found that surface solar radiation (SSR) decreased considerably (can be as high as 15%) with wind stilling in heavily polluted regions at a daily scale, indicating that wind stilling can considerably amplify the aerosol extinction effect on SSR. This effect is tiny in lightly polluted regions such the Tibetan Plateau. A threshold value of 3.5 m/s for wind speed is required to effectively reduce aerosols concentration. From this SSR dependence on wind speed, they further derived proxies to quantify aerosol emission and wind stilling amplification effects on SSR variations at a decadal scale. The results show that aerosol emission accounted for approximately 20% of the typical solar dimming in China, which was amplified by approximately 20% by wind stilling.

    本研究利用常规气象资料建立了地表太阳辐射和地表风速的统计关系,提供了地表风速减弱可降低地表太阳辐射的明确证据,该效应在污染较严重地区可以致使地表太阳辐射降低达15%,而在青藏高原以及其他污染较轻的地方该效应则可以忽略。当风速强于3.5 m/s,气溶胶基本可以通过扩散被清除,地表太阳辐射则不再随风速改变。利用这一统计关系,本研究首次建立了定量估计气溶胶直接辐射效应(包括排放增加的效应与风速减弱的放大效应)对地表太阳辐射长期变化的贡献。其结果表明,该贡献值大约为20%,而不是已有研究认为的主导因子。

  6. Niu, X. and R. Pinker, 2015: An improved methodology for deriving high-resolution surface shortwave radiative fluxes from MODIS in the Arctic region, J. Geophys. Res. Atmos., 120, 2382-2393, doi:10.1002/2014JD022151.

    This article develops an inference scheme to estimate the surface shortwave irradiance (SWR) for the Arctic at high resolution (5 km, hourly) based on the MODIS observations. Evaluation of the 5 km based SWR estimates against hourly ground observations at Barrow sites shows a mean bias of 7.9 W m-2 and a standard deviation of 58.2 W m-2 and a high correlation of 0.95. Information at this high resolution and good quality can lead to improved estimates of heat input into the complex Arctic domain.

    本文开发了一个用于估算地表短波辐射(SWR)的模型,基于 MODIS 观测估算了北极地区高分辨率太阳辐射( 5 公里,每小时)。基于 Barrow 观测站的小时尺度的地面观测评价了 5 公里的 SWR 估算,显示7.9 W m-2 平均偏差和 58.2 W m-2 标准偏差和 0.95 高相关。这种高分辨率和高质量的 SWR 估算可以提高对复杂北极地区热量输入的估计。

  7. Qin, J., W. Tang, K. Yang, N. Lu, X. Niu, and S. Liang, 2015: An efficient physically based parameterization to derive surface solar irradiance based on satellite atmospheric products, J. Geophys. Res. Atmos., 120, 4975-4988, doi:10.1002/2015JD023097.

    This paper develops a remote sensing model for surface solar irradiance that has full physical processes and meanwhile has a low computational cost. Estimated solar radiation with MODIS atmospheric products as input is validated widely. The model has high potential to be applied to radiation estimation from geostationary satellites.


  8. Pinker, R., X. Niu, and Y. Ma, 2014: Solar heating of the Arctic Ocean in the context of ice-albedo feedback, J. Geophys. Res. Oceans, 2014(119), 8395-8409, doi:10.1002/2014JC010232.

    Based on the latest development high quality surface solar radiation based on MODIS observations (2003-2009) and AVHRR (1984-2002) in the Arctic Ocean, this study find that the trend of the heat input into the Arctic open water for the period of 1984-2009 is positive in 0.3% year-1 and the trend of the open water fraction is positive in 0.8% year-2.

    本文应用最新发展的基于 MODIS(2003-2009年)和基于 AVHRR(1984-2002年)的高质量的地表太阳辐射的时间序列数据,发现北极地区海洋的太阳热量输入在 1984-2009 年的趋势是正向的 0.3% 每年,开放水域的范围的趋势也是正向的 0.8% 每年。

  9. Tang, W., J. Qin, K. Yang, X. Niu, X. Zhang, Y. Yu, and X. Zhu, 2013: Reconstruction of Daily Photosynthetically Active Radiation and its Trends over China, J. Geophys. Res. Atmos., 118(23), 13,292-13,302, doi:10.1002/2013JD020527.

    A PAR model is utilized to estimate daily PAR from routine meteorological parameters at CMA stations. The estimate is evaluated against measurements at ten Chinese Ecosystem Research Network (CERN) stations. Comparison with a locally-calibrated model indicates that the estimate has a comparable or even higher accuracy than the local model calibrated. Finally, a 50-year dataset of daily PAR at 716 CMA stations over China is reconstructed by the validated model, and its climatology and long-term variations over China are analyzed.


  10. Tang, W., K. Yang, J. Qin, and M. Min, 2013: Development of a 50-year daily surface solar radiation dataset over China, Sci. China Ser. D, 56(9), 1555-1565, doi:10.1007/s11430-012-4542-9.

    We developed a 50-year dataset of daily surface solar radiation at 716 CMA stations. The data quality is better than previous estimates by locally calibrated Ångström-Prescott models. Spatial variation and temporal trend of solar radiation were presented.


  11. Niu, X. and R. Pinker, 2012: Revisiting satellite radiative flux computations at the top of the atmosphere, Int. J. Remote Sens., 33(5), 1383-1399, doi:10.1080/01431161.2011.571298.

    to be available soon


  12. Qin, J., K. Yang, S. Liang, and W. Tang, 2012: Estimation of daily photosynthetically active radiation under all-sky conditions from sunshine duration data, J. Appl. Meteor. Climatol., 51(1), 150-160, doi:10.1175/JAMC-D-10-05018.1.

    In this study, the parameterization for broadband transmittance in the PAR band is established. On the basis of this parameterization, the scheme is built for estimation of ground PAR under clear-sky condition. At the same time, the sunshine duration is used to be an indicator of cloud, parameterize its influence on the ground PAR, and then estimate the PAR under all-sky condition.


  13. Yang, K., B. Ding, J. Qin, W. Tang, N. Lu, and C. Lin, 2012: Can aerosol loading explain the solar dimming over the Tibetan Plateau?, Geophys. Res. Lett., 39, L20710, doi:10.1029/2012GL053733.

    Solar dimming and cloud cover deceasing were observed simultaneously in many places, and this paradox was also found over the Tibetan Plateau, one of the cleanest regions in the world. Aerosol loading is usually used to explain this phenomenon, but we show this is not the case over the Tibetan Plateau. By contrast, due to the air warming and moistening in this region, CAPE enhanced while CIN weakened over last 30 years; accordingly, deep cloud cover increased, which led to the solar dimming. In fact, no robust evidence supports the increase in aerosols over this region during this period.


  14. Lu, N., J. Qin, K. Yang, and J. Sun, 2011: A simple and efficient algorithm to estimate daily global solar radiation from geostationary satellite data, Energy, 36(5), 3179-3188, doi:10.1016/

    In this study, the geo-stationary satellite observations at all channels during one day are compressed through the singular value decomposition. Then, the mathematical relationship between these compressed information and the ground global solar radiation is constructed by training the artificial neural network. This relationship is used to estimate the surface solar radiation in China, showing this method performs both rapidly and accurately.


  15. Niu, X. and R. Pinker, 2011: Radiative fluxes at Barrow, Alaska: a satellite view, J. Clim., 24(21), 5494-5505, doi:10.1175/JCLI-D-11-00062.1.

    Based on the surface observation at the Barrow North Slope of Alaska site, this paper evaluates the newly developed surface solar radiation based on MODIS observation (UMD_MODIS) and the international famous radiation products: NASA/LaRC, AVHRR, UMD-D1, NCEP; the results show that UMD_MODIS is the best estimation model (the average error is -3.6 W m-2 and the standard deviation is 22.6 W m-2), and the average errors of the international radiation products are: 7, 9.5, 10.9, 51.8 W m-2, and the standard deviations are 46.8, 51, 42.2, 51.4 W m-2.

    本文基于北极阿拉斯加北坡的一个综合观测站点 Barrow 的地表观测数据综合评价了作者团队基于 MODIS 观测最新估算的地表太阳辐射产品 (UMD_MODIS) 以及国际著名的辐射产品:NASA/LaRC, AVHRR, UMD-D1, NCEP,结果显示 UMD_MODIS 是最好的估算模型(平均误差为 -3.6 W m-2,标准偏差为 22.6 W m-2),国际辐射产品的平均误差分别为:7.0, 9.5, 10.9, 51.8 W m-2,标准偏差分别为:46.8, 51.0, 42.2, 51.4 W m-2

  16. Qin, J., Z. Chen, K. Yang, S. Liang, and W. Tang, 2011: Estimation of monthly mean daily global solar radiation based on MODIS and TRMM products over the Tibetan Plateau and its surroundings, Appl. Energy, 88(7), 2480-2489, doi:10.1016/j.apenergy.2011.01.018.

    In this study, the artificial neural network is used to construct the mathematical relationship between in-situ global solar radiation measurements and multiple types of MODIS and TRMM products. After the stability of this relationship is validated, it is implemented to map the global solar radiation over the entire Tibetan Plateau.


  17. Qin, J., K. Yang, S. Liang, H. Zhang, Y. Ma, X. Guo, and Z. Chen, 2011: Evaluation of surface albedo in GEWEX-SRB and ISCCP-FD data against validated MODIS product over the Tibetan Plateau, J. Geophys. Res. Atmos., 116, D24116, doi:10.1029/2011JD015823.

    In this study, in-situ measurements are used to validate the fine-resolution MODIS albedo product over the Tibetan Plateau. Then, they are aggregated on the coarse-resolution grid boxes of GEWEX-SRB and ISCCP-FD products and implemented to validate their albedo. The results indicate that they are overestimated in the southeastern Tibetan Plateau. The possible reason for this is that the cloud is judged as the snow in both of these two products.


  18. Tang, W., K. Yang, J. Qin, C. Cheng, and J. He, 2011: Solar radiation trend across China in recent decades: a revisit with quality-controlled data, Atmos. Chem. Phys., 11, 393-406, doi:10.5194/acp-11-393-2011.

    This paper presents a new evaluation of the long-term variation of surface solar radiation over China by combining quality-controlled observed data and two radiation models. The new trend estimate is different from previous ones in two aspects. First, the magnitude of solar radiation over China decreased by about −0.23Wm−2 yr−1 between 1961 and 2000, which is greatly less in magnitude than trend slopes estimated in previous studies (ranging over −0.41 ~ −0.52Wm−2 yr−1). Second, the "From Dimming to Brightening" transition in China during the late 1980s ~ the early 1990s was addressed in previous studies, but this study indicates the solar radiation reached a stable level since the 1990s and the transition is not noticeable. Finally, an obvious transition from brightening to dimming around 1978 is found over the Tibetan Plateau, where aerosol loads are very low, indicating that the importance of cloud changes in altering solar radiation may be comparable to that of the aerosol changes.

    结合可靠的观测资料和两个辐射模型,本文重新评估了中国区域地表太阳辐射的长期变化趋势。新的评估主要有两点和以前的研究不一样。第一,中国区域太阳辐射在1961-2000间平均下降幅度大约0.23Wm−2,这个数值远远低于以前研究的结果。 第二,以前研究得出90年代初太阳辐射在中国存在一个所谓“由暗变亮的”转变,而本研究发现自90年代初太阳辐射趋于平稳,至少这个转变并不明显。最后,我们发现在青藏高原地区1978年前后太阳辐射存在一个明显的“由亮变暗”的转变,而青藏高原地区气溶胶浓度非常低,这一点暗示云的改变和气溶胶浓度的改变对太阳辐射的变化同等重要。

  19. Niu, X., R. Pinker, and M. Cronin, 2010: Radiative fluxes at high latitudes, Geophys. Res. Lett., 37, L20811, doi:10.1029/2010GL044606.

    This paper evaluates the newly developed surface solar radiation estimates based on MODIS observations, against the surface observations including the land ground observations of 6 BSRN stations and 1 stations in Greenland and 4 unique ocean buoy measurements; the results show that the estimates are in good agreement with surface observations , and this product is useful for providing information in formulating energy budgets at high latitudes.

    本文应用北极地区的地面观测数据评估了基于 MODIS 观测估算的地表太阳辐射产品,地面观测包括陆地上的 6 个 BSRN 观测站和 1 个格林兰岛观测站以及 4 个海洋上独特的浮标观测数据;结果显示估算的太阳辐射与地面观测有很好的一致性,该产品有助于提供高纬度地区能源预算的信息。

  20. Tang, W., K. Yang, J. He, and J. Qin, 2010: Quality control and estimation of global solar radiation in China, Sol. Energy, 84(3), 466-475, doi:10.1016/j.solener.2010.01.006.

    A set of quality-check procedures were implemented to control the quality of the solar radiation measurements at 97 stations in China. A hybrid model for estimating global solar radiation was then evaluated against the controlled data. The results show that the model can estimate the global radiation with good accuracy over most of China.


  21. Yang, K., J. He, W. Tang, J. Qin, and C. Cheng, 2010: On downward shortwave and longwave radiations over high altitude regions: Observation and modeling in the Tibetan Plateau, Agric. For. Meteorol., 150(1), 38-46, doi:10.1016/j.agrformet.2009.08.004.

    This paper presented the major characteristics of SWD and LWD over the Tibetan Plateau (TP). The results showed that LWD received by TP is much lower than that of its surrounding areas and their monthly-mean differences can be up to 100Wm-2. On the contrary, SWD over TP is significantly higher than that over its surrounding areas, due to low extinction rate of airmass, water vapor, and aerosol occurred in TP. It is found that the surface data-based estimate, though not calibrated locally, shows a good agreement with the measurements and has an advantage of producing less root-mean-square errors and higher correlation coefficients than the satellite estimates. Under this condition, it is suggested to combine both the surface data-based estimate together with the satellite estimates in order to improve the accuracy of the SWD and LWD data.

    本文揭示了青藏高原地区地表下行短波辐射和长波辐射的主要特征。结果表明青藏高原地表接收到的下行长波辐射要比周边地区小很多,他们之间月平均的差值可以达到100 Wm-2。相反,青藏高原地表接收到的下行短波辐射却要比周边地区大很多,这主要由于青藏高原较低的大气质量,水汽和气溶胶对太阳辐射较弱的衰减造成的。分析结果表明基于地表辐射模型虽然没有用当地辐射观测资料标定,但是它的估算和辐射观测值有很好的一致且其精度要优于卫星反演结果。因此,在这种情况下联合地表辐射模型和卫星反演将是提高地表下行短波辐射和长波辐射估算精度的一个有效方法。

  22. Qin, J., S. Liang, X. Li, and J. Wang, 2008: Development of the Adjoint Model of a Canopy Radiative Transfer Model for Sensitivity Study and Inversion of Leaf Area Index, IEEE Trans. Geosci. Remote Sens., 46(7), 2028-2037, doi:10.1109/TGRS.2008.916637.

    In this study, the auto-differential technique is used to obtain the adjoint model of a radiative transfer equation for the vegetation canopy at the level of source code. Then, the adjoint model is coupled with a global trust region optimization algorithm to retrieve leaf area index. This method is implemented with ETM+ data as input and the inversion results are validated against the ground measurements.


  23. Yang, K., R. Pinker, Y. Ma, T. Koike, M. Wonsick, S. Cox, Y. Zhang, and P. Stackhouse, 2008: Evaluation of satellite estimates of downward shortwave radiation over the Tibetan Plateau, J. Geophys. Res. Atmos., 113, D17204, doi:10.1029/2007JD009736.

    This study evaluated four satellite products of downward shortwave radiation (GEWEX-SRB V2.5, GEWEX-SRB V2.81, ISCCP-FD, and UMD-SRB) for the elevated Tibetan Plateau. It showed that the high-resolution UMD-SRB data are more favorable than the coarse resolution data (ISCCP-FD and GEWEX-SRB). Discrepancies among the satellite products are larger in highly variable terrain and smaller for nonvariable terrain. Attention should be also given to the quality of input parameters besides cloud properties, as there are large discrepancies among the satellite products for clear-sky radiation.


  24. Yang, K., T. Koike, and B. Ye, 2006: Improving estimation of hourly, daily, and monthly solar radiation by importing global data sets, Agric. For. Meteorol., 137(1-2), 43-55, doi:10.1016/j.agrformet.2006.02.001.

    This study developed a model to estimate solar radiation from sunshine duration. It can explicitly account for radiative extinction processes in the atmosphere. Moreover, global data sets that describe the spatial and temporal distribution of ozone thickness and Angström turbidity were introduced in the model to enhance its universal reliability and applicability. The model was calibrated in lowland and humid sites and validated at a number of sites in various climate and elevation regions. The new model shows overall better performances than three Angström-Prescott models.


  25. Yang, K., T. Koike, P. Stackhouse, C. Mikovitz, and S. Cox., 2006: An assessment of satellite surface radiation products for highlands with Tibet instrumental data, Geophys. Res. Lett., 33, L22403, doi:10.1029/2006GL027640.

    This study presents results of comparisons between instrumental radiation data in Tibet and two satellite products: the Global Energy and Water cycle Experiment - Surface Radiation Budget (GEWEX-SRB) and International Satellite Cloud Climatology Project - Flux Data (ISCCP-FD). Severe and systematic errors were found in monthly-mean SRB shortwave radiation (SW) and FD longwave radiation (LW). The large errors in SRB SW were caused by neglecting elevation effects, but the errors in FD LW were mainly due to significant errors in input data.

    本文利用青藏高原上的辐射观测资料验证了两个卫星产品(GEWEX-SRB和ISCCP-FD)。月平均SRB 短波辐射(SW)和FD长波辐射(LW)存在着严重的系统误差。月平均SRB 短波辐射巨大的误差是由于忽略了高程对其影响,而月平FD长波辐射的误差主要是由于输入参数存在巨大误差造成的。

  26. Yang, K. and T. Koike, 2005: A general model to estimate hourly and daily solar radiation for hydrological studies, Water Resour. Res., 41, W10403, doi:10.1029/2005WR003976.

    In this study, a simple model that can explicitly account for radiative transfer processes in the atmosphere is developed to estimate hourly and daily solar radiation.The radiation model is compared with the Food and Agricultural Organization radiation model and globally and locally calibrated Angström -Prescott models at a number of sites in various climate and elevation regions, and it is suggested that the new model is more general and more accurate, especially for estimating hourly solar radiation.

    本文发展了一个简单的能估算小时平均和日平均的太阳辐射模型,该模型明确的考虑了大气中的辐射传输过程。在各种不同气候和不同海拔地区的观测站上,通过比较该模型和粮农组织模型、全球标定以及当地标定的Angström -Prescott模型,我们发现该新的模型是一个更普实且更精确的模型,尤其是估算小时辐射时更是如此。

  27. Yang, K. and T. Koike, 2002: Estimating surface solar radiation from upper-air humidity, Sol. Energy, 72(2), 177-186, doi:10.1016/S0038-092X(01)00084-6.

    A numerical model is developed to estimate global solar irradiance from upper-air humidity. Model inter-comparisons at 18 sites in Japan suggest (1) global solar radiation strongly depends on the sky clearness indicator, (2) the new model generally gives better estimation to hourly-Y. M.mean solar irradiance than the other three methods used in numerical weather predictions, and (3) the new model may be applied to estimate long-term solar radiation.


  28. Yang, K., G. Huang, and N. Tamai, 2001: A hybrid model for estimating global solar radiation, Sol. Energy, 70(1), 13-22, doi:10.1016/S0038-092X(00)00121-3.

    This study developed a hybrid model to estimate global radiation. This model suggested that H = (a + b S/S0)Hb + (c + d S/S0)Hs , Hb and Hs are effective beam radiation and effective diffuse radiation, which imply latitude, elevation and seasonal effect on radiation. Hb and Hs are calculated by an arithmetic model derived from spectral model.

    本文发展了一个用于估算太阳总辐射的混合模型。该模型的形式为:H = (a + b S/S0)Hb + (c + d S/S0)Hs,Hb和Hd分别是有效直接辐射和散射辐射,它们考虑了纬度、高程和季节对辐射的影响。Hb和Hd可以通过基于谱模型得出的算术模型计算得到。