Ratio of photosynthetically active radiation to global solar radiation above forest canopy in complex terrain: measurements and analyses based on Qingyuan Ker Towers

Background Understanding of the ratio of photosynthetic photon flux density ( Q p ) to global solar radiation ( R s ) ( Q p / R s ) is crucial for applying R s to ecology-related studies. Previous studies reported Q p / R s and its variations based on measurements from a single observatory tower, instead of multi-site-based measurements over complex terrains. This may neglect spatial heterogeneity in the terrain, creating a gap in an understanding of how terrain affects Q p / R s and how this effect interacts with meteorological factors. Methods Here the Qingyuan Ker Towers (three towers in a valley with different terrains: T1, T2, and T3) were utilized to measure Q p and R s over mountainous forests of Northeast China. An airborne LiDAR system was used to generate a digital elevation model, and sky view factor of sectors (SVF s ) divided from the field of view of tower’s pyranometer was calculated as a topographic factor to explain the variations of Q p / R s . Results The results identified significant differences in Q p / R s of the three towers at both daily and half-hour scales, with larger differences on clear days than on overcast days. Q p / R s was positively correlated with SVF s of T1 and T3, while this correlation was negative with that of T2. The effect of SVF s on Q p / R s interacted with clearness index, water vapor pressure and solar zenith angle. Random forest-based importance assessment demonstrated that explanation ( R 2 ) on Q p / R s was improved when SVF s was included in the predictor variable set, indicating that incorporating terrain effects enhances the prediction accuracy of Q p / R s . The improvement in the R 2 values was more pronounced on clear days than on overcast days, suggesting that the effect of terrain on Q p / R s depended on sky conditions. Conclusions All findings suggested that Q p / R s is affected by terrain, and integrating terrain information into existing Q p / R s models is a feasible solution to improve Q p / R s estimates in mountainous areas.


Introduction
The solar radiation at the wavelength range of 400-700 nm, which can be absorbed by green plants to convert light energy into chemical energy in photosynthesis processes, is called photosynthetically active radiation (PAR) (Mayer et al. 2002;McCree 1972).PAR is quantified using either photon term in μmol m −2 s −1 or energy term in W m −2 .The former is used in this study and denoted by Q p .Q p is an indispensable input variable for modelling photosynthesis and primary productivity of terrestrial vegetation (Alados et al. 1996;Jacovides et al. 2007;Qin et al. 2018), and plays an important role in a variety of applications in ecology, forestry and agriculture (Alados et al. 1996;Akitsu et al. 2022;Proutsos et al. 2019).Therefore, accurate estimation of Q p is fundamental to understanding the exchange of CO 2 between the atmosphere and ecosystems.Unfortunately, Q p is measured not by most radiation stations particularly for a long term in the past due to problems with accuracy and availability of quantum sensors (Akitsu et al. 2017;Mizoguchi et al. 2010;Wang et al. 2015a, b).Alternatively, Q p is often converted from global solar radiation (R s ; W m −2 ) through a certain ratio of Q p to R s (Q p /R s ), since R s is more routinely monitored in more meteorological stations with a high better availability and accuracy (Akitsu et al. 2015).
Q p /R s values have been reported worldwide.The general idea of previous researches is to reveal how meteorological factors (e.g., clearness index, sky clearness, sky brightness, solar zenith angle and water vapor) affect Q p /R s (Foyo-Moreno et al. 2017;Wang et al. 2014;Yamashita and Yoshimura 2019;Zhu et al. 2015).For instance, Alados et al. (1996) developed different empirical models relating Q p /R s to sky condition, solar zenith angle and dew point temperature.Jacovides et al. (2007) suggested that the variability of Q p /R s was closely associated with local cloud conditions and aerosol content.Although some work has been conducted, yet few studies have addressed the interaction among meteorological factors especially in different sky conditions.For example, a lower clearness index is often accompanied by a higher water vapor pressure.It is unclear how their linkages affect their relationship to Q p /R s , and further affect Q p /R s modeling.
Q p /R s over a complex terrain may be altered by reflected radiation from the surrounding terrain.Generally, incident solar radiation at a point on the surface of complex terrain is the sum of three components: direct radiation from the sun to ground surface, diffuse radiation from the sky hemisphere, and reflected radiation from the hemisphere obstructed by surrounding terrain (Allen et al. 2006;Dubayah and Rich 1995).Pyranometers are commonly deployed in open areas without obstructions to measure solar radiation (Akitsu et al. 2017).In mountainous regions, however, complex terrain may alter the field of view (FOV) of pyranometers, resulting in reflected radiation from the surrounding mountains entering the pyranometer sensors (Li et al. 2016;Zhang et al. 2019).Different medias have different properties of absorption and reflection at different wavelength bands, resulting in differences in reflected Q p and reflected R s from both the unobstructed sky and surrounding terrain (Li et al. 2016;Zhang et al. 2019), which can further alter the Q p /R s entering FOV of pyranometers.Therefore, uncertainties in the measurements of the Q p /R s may generate if the topographical effect is not adequately considered (Wang et al. 2005(Wang et al. , 2006)).In addition, the redistribution of incident solar radiation dominated by terrain complicatedly interacts with solar position and sky conditions (Aguilar et al. 2010;Dubayah and Rich 1995;Zhang et al. 2019).For example, since diffuse solar radiation is lower in intensity and distributed more uniformly than direct solar radiation, the effect of terrain on the redistribution of incident solar radiation is less pronounced on cloudy days dominated by diffuse radiation than on clear days dominated by direct radiation.Previous studies have revealed that the solar radiation and its components over complex terrain have great spatio-temporal variation and heterogeneity due to the influence of terrain shading and clouds (Bosch et al. 2009;Wang et al. 2006;Zhang et al. 2019).However, understanding the effect of terrain on the Q p /R s is hampered by lacking multi-location-based measurement in complex terrain, which resulted in a gap in an understanding of how terrain influence Q p /R s , and how this influence interacts with sun position and sky conditions.
Here, we hypothesize that there is a difference in the R s and Q p received from the sky and reflected from the surrounding terrain within the FOV of pyranometer, which further alters Q p /R s above forest canopy.To validate the hypothesis, we measured Q p and R s at three observation sites with different terrain features in a valley, and compared the difference in Q p /R s of the three observation sites.We also analyzed how the interactive influence of terrain and meteorological factors on Q p /R s , and assessed the importance of both terrain and meteorological factors in explaining the variations in Q p /R s .This study provides new insights into the accurate modeling of Q p /R s in complex terrains.

Study site and radiation measurements
The experimental site was located in the Qingyuan Forest CERN, National Observation and Research Station, Liaoning Province, Northeast China (124°54′E, 41°51′N, 500-1100 m a.s.l.).The area belongs to a temperate continental monsoon climate with a mean annual air temperature of 4.3 ºC and mean annual precipitation of 758 mm during 2010-2021.
The radiation sensors of the three towers were horizontally installed on 2 m south-facing arms at 46.5 m above the ground.R s was measured by means of CNR4 pyranometers (Kipp & Zonen, Delft, Netherlands) which were calibrated by factory before delivery.Q p was measured using PQS1 quantum sensors (Kipp & Zonen, Delft, Netherlands).To eliminate systematic errors among the quantum sensors of the three towers, we used a quantum sensor that was parallel with the routine quantum sensors at the original position (distance less than 1 m) and measured Q p for reference.The relationships of measured Q p between the reference sensor and the routine sensors of the three towers were fitted (T1: y = 1.1532x,R 2 = 0.998, P < 0.001; T2: y = 1.0554x,R 2 = 1, P < 0.001; T3: y = 1.0427x,R 2 = 0.995, P < 0.001).The radiation data used for fitting covered a range of radiation gradients and met requirements for radiometric calibration.The quantum sensors were multiplied by the corresponding correction coefficient to correct the systematic errors, respectively.Air temperature and relative humidity of the three towers were measured by the HMP155A sensors (Vaisala, Helsinki, Finland) installed 46.5 m above the ground.The sensors sampled every 5 s, and half-hourly averages of radiation and environmental factors were collected through CR1000X data-loggers and CR6 data-loggers, respectively, from January 2020 to December 2020.

Data preprocessing
Gaps in R s and Q p of the three towers were filled using measurements from the adjacent towers (e.g., gaps in T1 were filled with measurements from T2). Daily R s and Q p values were calculated by summing the halfhourly R s and Q p values recorded for daytime when Q p > 1 μmol m −2 s −1 .The percentage of missing R s data were 2.6%, 1.7%, and 3.6% for T1, T2 and T3, respectively.The percentage of missing Q p data were 0.6%, 0.3%, and 1.4% for T1, T2 and T3, respectively.All gap filling data of R s and Q p were used to calculate the values of annual or monthly radiation but not to perform any statistical analysis (e.g., correlation analysis).
Prior to analyzing the half-hourly Q p /R s and its influencing factors, it is necessary to perform quality control on half-hourly Q p /R s to remove erroneous data.Q p /R s value outside the range from 1.3 μmol J −1 to 2.8 μmol J −1 were excluded for analysis (Proutsos et al. 2019;Wang et al. 2014).To eliminate the problem caused by cosine response, data with solar zenith angle greater than 78° were also excluded (Akitsu et al. 2015;Proutsos et al. 2019).Additionally, data were eliminated when R s values exceeded the extraterrestrial shortwave radiation, as well as when both of R s and the extraterrestrial shortwave radiation are less than 5 W m −2 .

Clearness index (Kt) and water vapor pressure (e)
Clearness index (K t ) refers to the ratio of the global solar radiation incident on the horizontal plane to the extraterrestrial global solar radiation R a (W m −2 ) (Tsubo and Walker 2005), which represents the cloud and aerosol content in the atmosphere (Jacovides et al. 2007).R a is determined as follows (Ham 2005): where G sc is the solar constant (1367 W m −2 ); J is the calendar day that counts from January 1; θ is the solar zenith angle.
According to half-hourly K t , the sky condition was classified: K t ≤ 0.3, overcast day; 0.3 < K t < 0.7, partially cloudy days; K t ≥ 0.7, clear days (Yu et al. 2015).According to the grading standards of K t , overcast days, partially cloudy days and clear days of the three towers accounted for 24.1 ± 1.2%, 44.8 ± 0.5%, and 31.2 ± 1.4%, respectively (data not shown).
Water vapor pressure (e) is used to represent the water vapor content in the atmosphere (Papaioannou et al. 1996).We directly used the half-hourly e collected by the data-logger according to air temperature and relative humidity (Tetens 1930).

Solar zenith angle (cosθ)
The cosine value of the solar zenith angle (cosθ), which is used to relate the path length of solar radiation passing through the atmosphere (Allen et al. 2006;Bosch et al. 2009).cosθ is calculated as following equation (Ham 2005): where Φ is the latitude of the location; t is time; δ and t 0 are the solar declination angle and the solar time, respectively, given by Campbell et al. (1998): where LC is the longitude correction, to the east of the standard meridian of the local time zone: every 1° plus 4 min (1/15 h); west: every 1° minus 4 min.ET is the equation of time difference: f is calculated as the following: The cosine of the solar azimuth angle (cosψ) is used to determine the solar azimuth with respect to a specific location on Earth.The solar azimuth is defined based on the south meridian, where the counterclockwise direction is considered positive (0° to 180°), and the clockwise direction is considered negative (− 180° to 0°).cosψ is calculated as following equation (Ham 2005):

Sky view factor
Sky view factor (SVF), defined as a ratio of the unobstructed sky area to the total hemisphere sky area (Dubayah and Rich, 1995), was introduced to represent the sky visibility within the FOV of the observation location.We quantified the SVF by the following four steps.First, an airborne LiDAR system (Riegl VUX-1UAV) was used to generate a digital elevation model by point cloud from ground with a spatial resolution of 0.5 m (Chen et al. 2022).Second, we used the Solar Analyst in ESRI© ArcGIS 10.4 to generate a sky shed with a dimension of 200 × 200 grid, which spatially corresponds to the towers (2) et al. 2019).Third, we partitioned the FOV of each tower's pyranometer into 36 sectors with an interval of 10°.Fourth, we employed color statistics analysis in Adobe Photoshop CS6 to calculate the numbers of pixels representing the terrain surface and sky, respectively.The ratio of sky coverage pixels to the total number of pixels within each sector was calculated and denoted as SVF s .

Statistical analysis
One-way ANOVA was used to assess the differences in Q p /R s of the three towers at half-hourly and daily scales and under different sky conditions.Further, we compared the differences in Q p /R s of the three towers on typical overcast and clear days.Considering the influence of atmospheric water vapor content on Q p /R s , we selected several typical overcast and clear days in the dry season and the wet season respectively to compare the differences in Q p /R s .Specifically, we first calculated the differences in Q p /R s between each pair of towers on typical overcast and clear days in the dry and wet seasons, and since we are concerned with the magnitude of the differences in Q p /R s , we took the absolute values of these differences.Then we used the T-test to test the differences in Q p /R s between each pair of towers on typical overcast and clear days in both the dry and wet seasons.One-way ANOVA and T-test were performed using the "stats" R package.
Pearson's correlation coefficient (r) was introduced to examine the effect of K t , e, cosθ and SVF s on Q p /R s in different sky conditions.Considering that the potential correlation among variables may affect the relationship analysis, we conducted a partial correlation analysis to exclude the mutual influence of variables.By controlling the influence of K t , e, cosθ and SVF s on Q p /R s respectively, the relationship between other variables and Q p /R s was analyzed.To distinguish two types of correlation analysis, correlation analysis without controlling the influencing factors was expressed as zero-order correlation (Li et al. 2020).Correlation and partial correlation analysis were performed using the "Hmisc" R package and the "ppcor" R package, respectively.
A random forest (RF) model (Breiman 2001) was used to determine the contribution of terrain to the variation in Q p /R s and the importance for predicting Q p /R s .RF models are highly interpretable and non-parametric, and are suitable for constructing nonlinear relationships between Q p /R s and both meteorological and topographic factors (Breiman 2001).The number of regression trees (ntree) per group was set to 300, and the number of variables (mtry) per node building the regression tree was set to 2. Four datasets were generated (the whole year and the three types of sky conditions).Each dataset contained two groups of variables: one group included K t , e and cosθ; the other included K t , e, cosθ and SVF s .We assessed the variable importance in predicting Q p /R s using the mean square error (MSE) and the explained percentage of variance (R 2 ).These analyses and the significance tests of variables were performed using the "randomForest" R package and the "rfPermute" R package, respectively.

Variation in daily and half-hourly Q p /R s Temporal variation in daily Qp/Rs
Daily Q p and R s of the three towers presented a generally similar seasonal pattern (Fig. 2a, b), showing an increase from winter (16.953 ± 0.538 mol m -2 d −1 for Q p and 9.105 ± 0.464 MJ m −2 for R s ; standard deviation was calculated from the values of the three towers and thereinafter) to summer (42.615 ± 0.578 mol m -2 d −1 for Q p and 19.705 ± 0.246 MJ m −2 for R s ).The annual averaged Q p and R s values of the three towers were 29.499 ± 0.182 mol m -2 d −1 and 14.447 ± 0.235 MJ m −2 , respectively.Daily Q p /R s also presented seasonality (Fig. 2c).The Q p /R s was higher in summer (2.186 ± 0.015 mol MJ −1 ) and lower in winter (1.910 ± 0.043 mol MJ −1 ), with intermediate values observed in spring (2.049 ± 0.035 mol MJ −1 ) and autumn (2.037 ± 0.006 mol MJ −1 ) (Fig. 2c).The seasonality of Q p /R s generally showed a similar response to seasonal variation in water vapor pressure (e) (Fig. 2c, d).
Although the seasonal variations of Q p /R s of the three towers were generally comparable, significant differences were observed in their daily Q p /R s (F = 5.19, P < 0.01; Table 1).

Diurnal variation in half-hourly Qp/Rs
Q p /R s of T1 and T2 showed a similar diurnal variation during the growing season with remarkable fluctuations at near sunrise and sunset, as well as showed a slight increase at noon (Fig. 3a-g).Differently, the diurnal variation in Q p /R s of T3 increased in April (slope = 0.022, P < 0.001) and May (slope = 0.008, P < 0.001), with lower Q p /R s values at sunrise and higher Q p /R s values at sunset (Fig. 3a, b).The diurnal variations in Q p /R s of T3 generally exhibited a U-shaped pattern from June to October (Fig. 3c-g).
Figure 4 showed diurnal variations of Q p /R s on typical clear and overcast days in the peak growing season (additional information for other months can be found in Additional file 1: Figs.S1, S2).The diurnal variation of Q p /R s differed between clear and overcast days (Fig. 4, Additional file 1: Figs.S1, S2).Significant differences in the half-hourly Q p /R s were observed among the three towers in the different sky conditions (P < 0.001; Table 1).The significantly higher difference in the half-hourly Q p /R s was exhibited on clear days than on overcast days (Fig. 5).

Dependence of meteorological factors on Q p /R s Dependence of Qp/Rs on Kt
Q p /R s of the three towers was negatively correlated with K t in the whole year (the zero-order correlation, Pearson's r = − 0.636 ± 0.039, P < 0.001) (Fig. 6a-c).Correlations between Q p /R s and K t was significant (r were − 0.66 5 ± 0.033, − 0.570 ± 0.040 and − 0.625 ± 0.023, respectively, P < 0.001), even though effects of cosθ, e, and SVF s were excluded (Fig. 6a-c).The correlations between Q p /R s and K t were − 0.457 ± 0.096 on overcast days, − 0.264 ± 0.032 on partially cloudy days and − 0.392 ± 0.067 on clear days, respectively (Fig. 6d-l).Correlations between Q p /R s and K t remained significant and stable when the effects of cosθ, e, and SVF s on Q p /R s were excluded (except on clear days) (Fig. 6d-i).

Dependence of Qp/Rs on e
Q p /R s of the three towers was positively correlated with e in the whole year (r = 0.559 ± 0.046, P < 0.001) (Fig. 6a-c).The correlations were weakened (r were 0.467 ± 0.068, 0.513 ± 0.046 and 0.538 ± 0.066, respectively), when effects of K t , cosθ, and SVF s were excluded (Fig. 6a-c).The correlations also depended on sky conditions.The correlations were weaker on overcast days (r = 0.350 ± 0.057, P < 0.001) than on partly cloudy (r = 0.589 ± 0.092, P < 0.001) and clear days (r = 0.756 ± 0.075, P < 0.001) (Fig. 6d-l).For a given sky condition, the correlations of Q p /R s and e were still significant when the effects of the other factors were excluded (Fig. 6d-l).Differently, the correlations decreased when the effect of cosθ was removed (r were 0.322 ± 0.056 on overcast days, 0.516 ± 0.106 on partially cloudy days and 0.612 ± 0.094 on clear days; P < 0.001) (Fig. 6d-l).

Dependence of Qp/Rs on solar zenith angle
Q p /R s of the three towers was positively correlated with cosθ in the whole year (r = 0.274 ± 0.035, P < 0.001) (Fig. 6a-c).The correlations were significant when effects of K t , e and SVF s were excluded, respectively (Fig. 6a-c).The correlations between cosθ and Q p /R s were observed to increase along a K t gradient (r were 0.172 ± 0.020 on overcast days, 0.395 ± 0.053 on partly cloudy days, and 0.643 ± 0.080 on clear days; P < 0.001) (Fig. 6d-l).When effect of K t was excluded, the correlations between Q p /R s and cosθ increased on partially cloudy days (r = 0.424 ± 0.045, P < 0.001) while decreased on clear days (r = 0.599 ± 0.083, P < 0.001) (Fig. 6d-l).
The correlations did not change on overcast days (r = 0.174 ± 0.032, P < 0.001).The effect of cosθ on Q p /R s was significantly weakened when effect of e was excluded (r were 0.095 ± 0.022 on overcast days, 0.227 ± 0.050 on partially cloudy days, and 0.377 ± 0.097 on clear days; P < 0.001), but was slightly enhanced when effect of SVF s was excluded (r were 0.203 ± 0.024 for overcast days, 0.443 ± 0.077 for partially cloudy days, and 0.663 ± 0.071 for clear days, respectively; P < 0.001) (Fig. 6d-l).

Dependence of Q p /R s on SVF s
The azimuthal variations of sky view factor of sectors SVF s of the pyranometers of the three towers showed different variation trends at − 180° to 180° azimuth (Fig. 7ac).SVF s of T1 showed a comparable W-shaped variation trend at − 180° to 180° azimuth (Fig. 7a).The variation trend of SVF s of T2 was different from that of T1, showing an M-shaped variation trend at − 180° to 180° azimuth (Fig. 7b).The variation trend of SVF s of T3 was similar to that of T1 (except − 180° to − 80° azimuth), showing a roughly symmetrical V-shaped variation trend at − 180° to 180° azimuth (Fig. 7c).

Fig. 7
The azimuthal variations of sky view factor of sectors (SVF s ) of the pyranometers of the three towers at − 180° to 180° azimuth.The dashed gray line indicates that the value of SVF s is 1.T1: Tower 1; T2: Tower 2; T3: Tower 3 Dependence of Qp/Rs on SVF s SVF s were positively correlated with Q p /R s of T1 (r = 0.153, P < 0.001) and T3 (r = 0.258, P < 0.001), and were weakly and negatively correlated with Q p /R s of T2 (r = − 0.039, P < 0.001) in the whole year (Fig. 6a-c).
Except for T1, no correlation between SVF s and Q p /R s was found on overcast days (Fig. 6d-f ).SVF s were positively correlated with Q p /R s of T1 and T3 and were negatively correlated with Q p /R s of T2 on partially cloudy and clear days (Fig. 6g-l).The relationship between SVF s and Q p /R s was influenced, to some extent, by the interaction between SVF s and meteorological factors in different sky conditions (Fig. 6g-l).When the effect of K t or e was excluded, the correlations between Q p /R s and SVF s were weakened and partially insignificant on partially cloudy and clear days (Fig. 6g-l).When the effect of cosθ was excluded, differently, correlations were significantly enhanced on partially cloudy days (r = 0.129 for T1, − 0.241 for T2, 0.353 for T3) and clear days (r = 0.259 for T1, − 0.109 for T2, 0.424 for T3) (Fig. 6g-l).In summary, correlations between SVF s and Q p /R s were found and were influenced by meteorological factors.

Importance assessment of variables
Including SVF s as an input variable of RF model can improve the predictive performance of Q p /R s .For the whole year, the R 2 value was improved by 5.04%, 3.65% and 7.36% for T1, T2 and T3, respectively, when including SVF s as the input variable (Fig. 8).For different sky conditions, the improvements in R 2 values were greater on clear and partially cloudy days than on overcast days (Fig. 8).For example, when SVF s was included, the R 2 values increased by 16.07% for T1, 8.95% for T2, and 20.79% for T3 on partially cloudy days, while increased by 2.84% for T1, 3.56% for T2, and 1.93% for T3 on overcast days (Fig. 8).
The variable importance varied depending on sky conditions.In non-SVF s groups, K t was the most important, followed by e and cosθ in the whole year (Fig. 8).Along a K t gradient (from clear days to overcast days), the importance of cosθ and e gradually increased (Fig. 8).e was the most important factor driving Q p /R s on partially cloudy and clear days (Fig. 8).
The SVF s importance varied among the three towers in different sky conditions.SVF s of T3 explained more Q p /R s than that of T1 and T2 in the whole year (Fig. 8).SVF s explained more to the changes in Q p /R s on partially cloudy and clear days than that on overcast days (Fig. 8).Note that SVF s was the most important factor affecting Q p /R s of T3 on partially cloudy and clear days (Fig. 8).

Analysis of daily and half-hourly Q p /R s
The seasonal patterns of daily Q p /R s were generally similar among the three towers.Daily Q p /R s values were higher in summer than in winter (Fig. 2c), which was consistent with results reported by Akitsu et al. (2015), Hu and Wang (2012), and Wang et al. (2014).One possible explanation for the seasonal variation is associated with a high-water vapor content in summer, which can strongly absorb near-infrared radiation, whereas its effect on PAR is weak (Fig. 2c and d) (Alados and Alados-Arboledas 1999;Jacovides et al. 2007;Li et al. 2010).
Significant differences in Q p /R s were observed among the three towers at both daily and half-hour scales, supporting the hypothesis that topography alters Q p /R s above forest canopy.Since meteorological conditions, such as sky clearness index, water vapor pressure and solar zenith angle, were nearly consistent among the three towers, the differences in Q p /R s induced by meteorological factors are expected to be excluded.Note that the differences in Q p /R s of the three towers were larger on clear days than on overcast days (Fig. 5).Clear sky is dominated by direct beam, while overcast sky is dominated by diffuse radiation.The effect of topography on direct solar beam is significantly greater than that on diffuse solar radiation (Whiteman et al. 1989).We therefore conjectured that the differences in Q p /R s among the three towers may be related to the differences in reflected solar radiation from the surrounding terrain that enters the field of view of pyranometer.The effect of terrain on Q p /R s is discussed in Section "Effect of topography".

Effect of meteorological factors
Q p /R s is closely related to sky conditions and atmospheric water vapor.Previous investigations identified that the effect of cloud attenuation on solar radiation at nearinfrared band includes absorption and scatter, whereas the attenuation on solar radiation at PAR band mainly involves the scatter (Alados and Alados-Arboledas 1999;Jacovides et al. 2007).A decrease in K t has a pronounced impact on solar radiation at near-infrared band, leading to an increase in Q p /R s (Foyo-Moreno et al. 2017;Proutsos et al. 2019;Yu et al. 2015).Another reason may be that a low K t is often along with overcast days.A high content of water vapor absorbs more solar radiation at near-infrared band than at PAR band, resulting in a higher PAR fraction (Alados and Alados-Arboledas 1999;Jacovides et al. 2007).The effect of K t on Q p /R s remained significant and consistent when the effect of other factors (except on clear days) was excluded, indicating that K t independently plays a crucial role in affecting Q p /R s .Along a K t gradient (from clear days to overcast days), the effect of water vapor pressure on Q p /R s gradually weakens (Figs.6d-l, 8), probably due to the difficulty of solar radiation penetrating the atmosphere in conditions of water vapor saturation (Proutsos et al. 2019).The reduced sensitivity of Q p /R s to water vapor pressure may introduce uncertainty in the estimation of Q p /R s on overcast days.
Q p /R s increased with cosθ.The medium in the atmosphere mainly absorbs the near-infrared band and scatters the PAR band.As the path length of solar radiation penetrates through the atmosphere decreases, light absorption at the near-infrared wavelength is stronger than light scattering at the PAR wavelength (Alados et al. 1996).As a result, solar radiation loses more at the near-infrared wavelength than at the PAR wavelength during the light transmission process, leading to an increase in Q p /R s (Jacovides et al. 2003).The effect of cosθ on Q p /R s was greater on clear days than on overcast days (Figs.6d-l,  8).One possible explanation is that, on a clear day, solar radiation penetrating the atmosphere is mainly related to the penetrating path length, while other factors, such as clouds and water vapor in the atmosphere, can be negligible.On an overcast day, the transmission of solar radiation penetrating the atmosphere involves various factors and complex interaction effect.For example, the effect of cosθ on Q p /R s was significantly weakened when the effect of water vapor pressure was excluded (Fig. 6).This is probably due to an inherent link between the distance of radiation transmission and water vapor content.The variations in Q p /R s in response to changes in cosθ can be Fig. 8 Random forest model-based importance assessment of the two groups of variables on Q p /R s .Non-SVF s groups include K t , cosθ, and e, and SVFs groups include K t , cosθ, e, and SVF s .Increase of the mean square error is the percentage of variance explained by the two groups of variables for Q p /R s .The variable importance was normalized to a scale of 0 to 1. Significance levels are: *P < 0.05, **P < 0.01, and ***P < 0.001.T1: Tower 1; T2: Tower 2; T3: Tower 3 partially attributed by water vapor pressure.Differently, we noticed that the effect of cosθ on Q p /R s was enhanced, when effect of SVF s was excluded (Fig. 6), which may be due to the interaction between solar zenith angle and topography on solar radiation (further discussed in Section "Effect of topography").

Effect of topography
The two lines of evidence suggest that terrain affects Q p /R s , supporting our hypothesis.The surrounding terrain alters the field of view of the pyranometer, affecting the measured Q p /R s .Although three towers with different terrain features were used, fully comprehending the effect of terrain on Q p /R s is difficult.For statistical purposes, we partitioned the field of view of each observation into 36 sectors, which exhibits various terrain features (sky view factor in this case).The incident solar radiation azimuthally corresponding to a given sector may interact with terrain and generate special situation of reflection from the surrounding terrain, which can help us to understand the effect of terrain on Q p /R s .
The joint decreasing trends in sky view factor and Q p /R s may be related to a lower proportion of the sky in the sector that azimuthally corresponding to incidence solar radiation.The absorption of PAR is stronger by forested surface than by the sky.Therefore, the PAR that reflected from forested surface and then entering the pyranometer is lower than the PAR directly entering pyranometer from the sky, resulting in a decrease in Q p /R s of T1 and T3.Differently, the effects of SVF s of the pyranometer of T2 on Q p /R s were contrary to that of T1 and T3 (Fig. 6ac), which may be attributed to the azimuthal SVF s feature of the pyranometer of T2, which was generally opposite to that of T1 and T3 (Fig. 7).
Another evidence arises from analyzing the interaction between terrain and sky condition.The effects of terrain on Q p /R s were greater on clear days than on overcast days, which was mainly attributed to the effect of terrain, since the effect is greater on direct solar beam than on diffuse radiation (Whiteman et al. 1989).The terrain effects also interacted with the meteorological factors.When the influence of solar zenith angle was excluded, the effects of terrain on Q p /R s were enhanced on clear days (Fig. 6g-l).Since the effects of terrain on redistribution of solar radiation are closely related to the geometric relationship between the sun position and the terrain, and the effects were partially masked when the solar zenith angle is low (Wang et al. 2006;Zhang et al. 2019).Differently, the terrain effects were weakened on clear days, when the influence of sky condition or water vapor pressure was excluded (Fig. 6j, k).Variations in Q p /R s are partly contributed by meteorological factors, and the terrain effect may be enhanced by the coupled interaction between meteorological factors and terrain factors.The performance of RF model improved when the terrain effect was included for prediction of Q p /R s (Fig. 8).This indicates that including terrain factors for the prediction of Q p /R s can improve the prediction accuracy.Moreover, we found that the importance of terrain effect increases as the sky condition changes from overcast to clear (Fig. 8), which is consistent with the expectations.In summary, the results suggest terrain can explain the observed variation in Q p /R s , indirectly supporting the finding that topography alters Q p /R s above the forest canopy.
Here, despite our efforts to explore the relationship between Q p /R s and complex terrain, there are still some limitations.First, we only used the sky view factor azimuthally corresponding to incidence solar radiation to represent the terrain feature, while the contribution of the other sectors of non-solar incidence azimuths was not included for analysis.Second, our analysis was based on field-observation, which cannot explain the mechanism of radiation-terrain interaction.For example, amount of solar radiation and its components reflected from the surrounding terrain cannot be quantified.Third, pyranometers were placed at a relatively high position to measure incoming solar radiation into the forest ecosystem.If the pyranometers are relocated to a low position, the influence of terrain on Q p /R s may strengthen, as the surrounding terrain and vegetation would exert a larger obstructing effect on the field of view of the pyranometer.

Conclusion
We validated the proposed hypothesis that topography alters Q p /R s above forest canopy through measurements of solar radiation and photosynthetic photon flux density at three sites in a valley.We found the significant differences in both daily and half-hour Q p /R s among the three sites, which were more pronounced on clear days than on overcast days.Q p /R s decreased with the increase of clearness index, while increased with water vapor pressure and the cosine of the solar zenith angle.Specially, the effects of water vapor pressure or solar zenith angle on Q p /R s were weakened when the influence of other meteorological factors was excluded, indicating that the effects of water vapor and solar incident path length on Q p /R s were not independent.Notably, sky view factor of sectors significantly influenced Q p /R s .Compared with using meteorological factors alone, the explanation of Q p /R s was improved when sky view factor was included in the predictor variables set, and the improvement in the explanatory power was greater on clear and partially cloudy days than on overcast days.These results imply that the surrounding terrain may affect Q p /R s .To develop accurate models for predicting Q p /R s in mountainous areas, the influence of topography on Q p /R s should be investigated under various sky conditions.

Fig. 3 Fig. 4
Fig. 3 Diurnal variations of the half-hourly Q p /R s during the growing season.Shaded regions represent the standard error of the half-hourly Q p /R s average.T1: Tower 1; T2: Tower 2; T3: Tower 3. The diurnal variation of Q p /R s in the non-growing season may fluctuate greatly due to the interference of snowfall and snow cover on the mountain surface.Here we only showed the diurnal variations of Q p /R s in the growing season (from April to October)

Table 1
Comparison of Q p /R s monitored by the three towers For the daily Q p /R s , it is difficult to categorize the exact sky conditions and to ensure sufficient data availability for statistical analysis in a given sky condition, so we only compare the differences in Q p /R s among the three towers on a halfhour scale in different sky conditions