The UV radiation data were obtained from a national-scale network, CERN, which was the first standard network established to measure solar radiation for investigating the radiation budget and its spatial and temporal variations over China. CERN consists of 40 stations that provide in situ measurements of UV radiation, covering almost all typical ecosystems. Two stations are in grassland ecosystems, there is one urban station, three for bays, two for lakes, six for deserts, fifteen for agriculture, ten for forests, and one for marshland. The spatial distribution of the 40 CERN stations in China is shown in Fig. 1, and the geographical locations, altitudes and ecosystem types of the stations are provided in Table 1. The urban station, in Beijing, which is located at the Institute of Atmospheric Physics of the Chinese Academy of Sciences, is the center of data collection, quality control and instrument calibration for the entire radiation observation system.
CUV3 broadband radiometers (Kipp & Zonen, The Netherlands), which have an accuracy of 5%, have been installed at all CERN stations to make observations of UV radiation (290-400 nm). This level of accuracy meets the World Meteorological Organization's (WMO) measurement standards. UV pyranometers are calibrated using standard lamps with a known spectroradiometer, and this calibration system is at the forefront of UV radiation research in China. A spectrometer measures a standard lamp spectral irradiance and then retrieves the spectral sensitivity under standard lamp conditions (K c). Using the same method, the spectral sensitivity under sunshine conditions (K s) can be deduced. The K c is considered equal to K s in narrow wavebands. For each narrow waveband, K c can be obtained by using the lamp spectral irradiance, and the spectroradiometer can then be used to measure solar irradiance. The UV radiation can be derived by integrating the solar spectral irradiance between 290 and 400 nm. At the same time, the calibrated UV pyranometers measure the response voltage. All CUV3 pyranometers are calibrated and inter-compared at the beginning and the end of data collection to ensure the accuracy of the calibration. Daily checks are made to ensure that the radiometers are free of dirt and positioned horizontally to guarantee the data quality. M520 (Vaisala) data collectors are used to collect the data. All radiation data are recorded at 1-min intervals, and hourly values are derived from the 1-min values through integration.
The UV radiation observation system in China started relatively late compared to similar systems elsewhere around the world. Most of the observed UV datasets described above begin in 2005, and the observation sites are very sparse. To obtain high spatial resolution and long records of historical UV radiation data, either empirical and semi-physical methods or satellite inversion algorithms can be used. In this study, daily UV radiation datasets for the period before the use of instrumentation were obtained from solar radiation measurements through an all-sky UV estimation model. However, in the CMA radiation network, only around 120 sites can provide daily solar radiation. Moreover, due to the retrofitting of many of the radiation instruments before 1993, the accuracy of the observed solar radiation data was relatively low during that period (Tang et al., 2011). Instead of using these data, solar radiation amounts reconstructed with a hybrid model were used to calculate the UV radiation.
2.3.1. Reconstructing solar radiation using a hybrid model
The hybrid model put forward and improved by Yang et al. (2001, 2006) was applied to estimate solar radiation using the AOD and total column ozone measurements retrieved from satellite data and routine meteorological observations obtained from the CMA. The details of this hybrid model have been described by (Yang et al., 2006), so only a brief description is given here. Physical processes, such as Rayleigh scattering, aerosol extinction, ozone absorption, water vapor absorption, permanent gas absorption, and the effects of clouds, which are represented by the transmittance functions τ r, τ a, τ oz, τ w and τ c, respectively, are considered, and the simplicity of the Ångström correlation is also maintained in the hybrid radiative transfer model. The solar beam radiative transmittance (τ d) and the solar diffuse radiative transmittance (τ d) under clear skies can be calculated using Eqs. (3) and (4): \begin{eqnarray} \label{eq2} \tau_{\rm b}&=&\tau_{\rm r}\tau_{\rm a}\tau_{\rm oz}\tau_{\rm w}\tau_{\rm g} ;\ \ (2)\\ \label{eq3} \tau_{\rm d}&=&0.5[\tau_{\rm oz}\tau_{\rm g}\tau_{\rm w}(1-\tau_{\rm a}\tau_{\rm r})] .\ \ (3) \end{eqnarray} Solar radiation reaching the surface of the Earth can be obtained using the following equation: \begin{equation} \label{eq4} R_{\rm s}=\tau_{\rm c}\int_{\Delta t=24}(\tau_{\rm b}+\tau_{\rm d})R_0{\rm d}t , \ \ (4)\end{equation} where R0 is the solar radiation at the top of the atmosphere, t is time, and ∆ t is the integration period.
More detail on the methods for calculating τ r, τ a, τ oz, τ g and τ c can be found in the paper by (Yang et al., 2006). The data required by the model as the input, including surface pressure, surface relative humidity, air temperature, and sunshine duration, which were obtained from routine observations at 724 weather stations (Fig. 2) with specified latitudes and longitudes, underwent quality control by the CMA. Other input values, such as the AOD and total column ozone at the 724 stations, were interpolated from satellite retrievals. The column ozone concentrations were obtained from the Solar Backscatter Ultraviolet Merged Ozone Data Set, Version 8.6 (http://acd-ext.gsfc.nasa.gov/Data_services/merged/index. html). The AOD was obtained from a MODIS data product (MOD08-M3, level 3, Collection 5.1) (http://ladsweb. nascom.nasa.gov/data/search.html) with a spatial resolution of 1°× 1°. As no AOD data were available before 2000, and no ozone data before 1970, climatic mean AOD and ozone values were used in the hybrid model.
All the calculations involved in the hybrid model were conducted using the FORTRAN 90 program. Using this hybrid model, daily solar radiation values from 1961 to 2014 were obtained and could be used to reconstruct the daily UV radiation.
2.3.2. Reconstructing UV radiation by combining the hybrid model results with an all-sky UV estimation model
As UV radiation is highly correlated with solar radiation, most published experimental results use measured solar radiation to calculate UV radiation by considering the ratio of UV radiation to solar radiation as an empirical constant (Calbó et al., 2005; Podstawczynska, 2010). (Long and Ackerman, 2000) used a power law equation to describe the dependence of solar radiation on the cosine of the solar zenith angle under clear-sky conditions. The clearness index (Kt) is defined as the ratio of the solar irradiance reaching the surface of the Earth to the extraterrestrial solar irradiance, and it provides a general indication of scattering and absorption processes due to aerosols, gases, clouds, etc. Earlier studies of the effects of Kt and the solar zenith angle on UV radiation have been analyzed and confirmed under different sky conditions (Hu et al., 2010; Wang et al., 2013; Liu et al., 2016). To develop the estimation model, the entire hourly dataset from Lhasa Station under all weather conditions was studied. Figure 3a displays the UV radiation plotted against the cosine of the solar zenith angle (μ). Different colors represent different Kt values. For a given specific Kt interval, it is recommended that the relationship between UV radiation and the cosine of the solar zenith angle is calculated with the following power law equation: \begin{equation} \label{eq5} {\rm UV}={\rm UV}_0\mu^e , \ \ (5)\end{equation} where UV0 indicates the UV radiation for one unit of μ, and e determines how UV varies with μ. Unfortunately, it is not straightforward to obtain direct measurements of UV0, as that requires the solar zenith angle to be zero.
Kt was first allocated as 0.03, with a step size of 0.01. The relationship between UV and μ was fitted using the power law equation [Eq. (6)] within each specific Kt interval. The relationship between UV0 and Kt was then analyzed (Fig. 3b). The dependence of UV0 on Kt is described by Eq. (7): \begin{equation} \label{eq6} {\rm UV}_0=a+bK_t+cK_t^2+dK_t^3 , \ \ (6)\end{equation} where the units of a, b, c and d are W m-2.
The long-term observed daily values of Rs could be easily obtained from the hybrid model, but long-term hourly values of Rs were not obtainable. Therefore, Eqs. (6) and (7) were modified to calculate daily UV radiation amounts using the daily values of R s, as follows: \begin{equation} \label{eq7} {\rm UV}_{\rm daily}=(A+B\overline{K}_t+C\overline{K}_t^2+D\overline{K}_t^3)\bar{\mu}^Et_{\rm d} ,\ \ (7) \end{equation} where UV daily is the daily amount of UV radiation; the units of this quantity are MJ (m2 d)-1. \(\overline{K}_t\) is the ratio of daily R s to daily extraterrestrial solar irradiance; \(\bar\mu\) is the average of the cosine of the solar zenith angle from sunrise to sunset; t d is the daily sunshine duration (hours); and A, B, C, D and E are parameters that differ between climatic zones. Therefore, China was divided into eight climatic zones, and the UV radiation data were reconstructed using the corresponding values of the parameters A to E, given in Table 2, and combined with the solar radiation estimates obtained from the hybrid model.
2.3.2. Validation of the reconstructed UV radiation estimates
To validate the accuracy of the UV radiation reconstruction model, the UV radiation amounts measured in situ at 40 CERN stations from 2005 to 2014 were chosen for comparison with the reconstructed UV radiation data obtained by applying the hybrid model and an all-sky UV estimation model to the nearest CMA station. Statistical estimators, such as the correlation coefficient (R), the mean bias error (MBE), the mean absolute bias error (MABE), and the root-mean-square error (RMSE) were used as benchmarks for the radiation products. These metrics are defined as follows: \begin{eqnarray} \label{eq8} R&=&\frac{\sum_{i=1}^{i=N}(E_i-E_{\rm ave})(M_i-M_{\rm ave})}{\sqrt{\sum_{i=1}^{i=N}(E_i-E_{\rm ave})^2\cdot \sum_{i=1}^{i=N}(M_i-M_{\rm ave})^2}} ;\ \ (8)\\[1mm] \label{eq9} {\rm MBE}&=&\frac{100}{M_{\rm ave}}\left(\frac{\sum_{i=1}^{i=N}(E_i-M_i)}{N}\right) ;\ \ (9)\\[1mm] \label{eq10} {\rm MABE}&=&\frac{100}{M_{\rm ave}}\left(\frac{\sum_{i=1}^{i=N}|E_i-M_i|}{N}\right) ;\ \ (10)\\[1mm] {\rm RMSE}&=&\frac{100}{M_{\rm ave}}\left(\frac{\sum_{i=1}^{i=N}(E_i-M_i)^2}{N}\right)^{0.5} . \ \ (11)\end{eqnarray} Here, Ei is the estimated value (ith number), Mi is the measured value, E ave is the average of the estimated values, M ave is the average of the measured values, and N is the number of observations.
Table 3 shows the four statistical parameters calculated using the CERN-observed UV radiation and the calculated UV radiation at the nearest CMA stations. The correlation coefficient is larger than 0.8 for all stations except BNF and MXF. The MBE values are negative at 35 of the stations, which indicates that the reconstructed UV radiation values represent slight underestimates compared with the observations. Only MXF and THL have MABE values larger than 25% and RMSE values larger than 30%. All of the statistical results show that the reconstructed UV radiation values are reliable.