Lidar data can be used to create raster datasets by selecting various attributes of lidar points within a defined spatial neighborhood around a raster cell. One of the most common raster products for assessing canopy structure is the light penetration index (LPI), the ratio of ground first return points (typically less than 2 m in elevation above ground) to the total number of lidar first return points within a given raster cell. This ratio has been shown to be useful for characterizing light extinction in canopies according to the Beer–Lambert law (Richardson et al., 2009) and thus has been explored as a predictor of understory light conditions (Musselman et al., 2013; Alexander et al., 2013; Bode et al., 2014). Solar radiation calculators in GIS software can also be used to compute solar insolation on a lidar-derived digital elevation model (DEM). Bode et al. (2014) combined an r.sun solar insolation model for the GRASS GIS software based on a DEM with LPI to produce estimates of ground-level solar insolation that showed high accuracy compared to pyranometer-collected field data in a mixed forest in northern California, USA.

Lidar point returns can be reprojected from the x, y, z Cartesian coordinate system in which they are most often delivered by a vendor into a spherical coordinate system which centers the point cloud around a specific location on the ground. This reprojection allows for a circular graph of the lidar point returns to be created around a point at ground level. Alexander et al. (2013) created a canopy closure metric from these projected point graphs based on gap fraction and found that this metric was correlated to Ellenburg indicator values (which relate plants to their ecological niche along an environmental gradient) of understory light availability. Moeser et al. (2014) created synthetic hemispherical photographs from reprojected lidar returns, and solar irradiance at ground level was calculated using traditional hemispherical photograph analysis software. The processed synthetic hemispherical photographs showed good correlation to pyranometer measured solar irradiance at three field sites in eastern Switzerland.

Because lidar point clouds are typically represented in a three-dimensional Cartesian coordinate system, it is possible to model the sun's position in relation to that three-dimensional space. The number of lidar returns that are reflected from a defined volume between the direction of the sun and the ground can then be calculated. These methods are computationally intensive, but have shown promise for providing the most direct measure of understory light availability. Lee et al. (2008) calculated the number of points within a conical field of view directed at the sun's location and created a model to relate this to ceptometer measurements of photosynthetically active understory solar radiation at specific times and locations in a pine forest in northern Florida, USA. This method is limited by its reliance on raw lidar point counts specific to the actual and relative point densities within their lidar acquisition. Raw point counts are affected by both changes in flight characteristics between missions and the patterns of flight line overlap within a mission. A different point cloud approach involves a linear tracing of the sun's rays along their path to the ground, and Martens et al. (2000) demonstrated how a ray-tracing algorithm could be used to characterize understory light conditions in a computer-simulated forest. Peng et al. (2014) combined a lidar-based ray tracing algorithm with field-collected canopy base heights to produce an estimate of understory solar insolation based on the Beer–Lambert law that compared well to field-collected pyranometer data but is limited in practical application because of its reliance on field-measured data in its model. Musselman et al. (2013) used a ray-tracing algorithm to produce highly detailed estimates of direct beam solar transmittance in 5-minute increments by voxelizing the lidar data and summing the number of voxels that a ray intercepted between the point of origin and the sun. The algorithm relied on site-specific pyranometer measurements to calibrate and adjust the beam transmittance, and therefore we were restricted from testing this method in this study.

Our objectives were to test the accuracy and precision of established methods of quantifying solar insolation from aerial lidar within areas of narrow, heavily forested streams. We utilized two raster approaches and one lidar point reprojection approach, three methodologies that had not been previously applied and tested using high-quality field data collected in heavily forested streams. We evaluated the three methodologies using simple linear regressions that compared lidar-derived metrics to field-based pyranometer measurements of solar insolation and hemispherical photograph-based measures of shade in western Oregon, USA. Further, we sought to apply this method to quantify solar insolation throughout a small headwater stream network.

All field locations were located within the wetted channel of Panther Creek and a tributary (Fig. 1) in narrow streams (1–6 m in width) located in the east side of the Coast Range of Oregon, USA, within a larger research area in which lidar has been used to quantify forest canopy structure (Flewelling and McFadden, 2011). All field sites were within a mature Douglas fir (Pseudotsuga menziesii) forest, with other dominant trees including red alder (Alnus rubra), western red-cedar (Thuja plicata), and western hemlock (Tsuga heterophylla). The elevation profile and description of the stream can be found in Richardson and Moskal (2014). The center of the channel was manually digitized as a polyline in ArcGIS using a combination of aerial imagery and the vendor-provided lidar DEM.

Four transects were installed in late June 2015 using a Leica Builder Total Station and georeferenced using a Javad Maxor GPS unit. The locations of the transects can be seen in Fig. 1, with the 19 point locations used for capturing field data denoted by black dots surrounded by white circles (A contains 3 points, B and C contain 4 points, and D contains 8 points). Transect locations were chosen manually in order to maximize variability in forest shade while allowing for safe access by the field crew. Each point location was located within the stream channel and marked by driving rebar into the substrate until only 1 m was exposed above the water surface. Point locations were approximately 15 m apart within a transect in order to allow data from multiple point locations to be collected by a single datalogger.

Two datasets were collected at each point location during the last 2 weeks of June in 2015. A hemispherical photograph was collected using a Nikon CoolPix 4500 digital camera leveled on a tripod 1 m above the ground under uniform sky conditions (Fig. 2) utilizing a method to find the optimum light exposure (Zhang et al., 2005). Each hemispherical photograph was analyzed using the Gap Light Analyzer (GLA) program (Frazer et al., 1999) in order to produce estimates of percent transmittance for diffuse and direct sunlight. An Apogee Instruments SP-110 self-powered silicon-cell pyranometer, leveled and mounted to the rebar pole at 1 m height (Fig. 3), was used to collect a full day's solar output at each point location using the datalogger. The raw voltage values collected by the datalogger were calibrated to solar irradiance using the closest publicly available meteorological data. All pyranometer datasets were collected on cloudless days, except for transect A, and pyranometer data from transect A were not used in this study. The calibrated pyranometer data from a point location from transect D are shown in Fig. 4. Note that the silicon-cell photodiodes, such as the SP-110 can, produce erroneous readings under conifer canopies. A black body thermopile pyranometer would have been more appropriate for this study but was not available to the authors.

Airborne discrete-return lidar was acquired in June of 2015 according to the specifications described in Table 1. The vendor provided processed discrete lidar point returns as well as a lidar DEM and highest hit model at a pixel resolution of 1 m. The highest hit model was subtracted from the DEM to create a canopy height model (CHM) describing the vegetation height normalized to the ground surface. In addition, FUSION (McGaughey, 2009) was used to subtract the elevations of the raw lidar points from the ground elevation in the DEM to produce a normalized point cloud dataset (NPCD). Note that the perspective of the lidar analyses is in reference to ground height while the field data were collected at 1 m above the ground. While this is a small difference, it could be a source of error in comparisons, especially at low solar angles.

LPI was computed as follows: 1LPI=Rg/Rt. LPI was computed in ArcGIS using a circular buffer with radius 10 m around each field point location mirroring the radius used in Richardson et al. (2009). LPI was also computed using a shifted square buffer modified from the method of Bode et al. (2014) where the buffer side length (s) was calculated based on the following: 2s=htan⁡θ, where h is equal to the modal tree height across all our plots (34 m), and θ is equal to the maximum lidar scan angle subtracted from 90∘ (75∘), resulting in a buffer side length of 9.12 m. The square buffer was shifted south to account for the seasonal solar angle in the Northern Hemisphere according to the following: 3shift=s1+cos⁡σ-s, where σ is equivalent to the solar angle at noon on the date of interest. A solar angle of 68∘ was used in this study, resulting in a southern shift of 3.42 m. The buffer tool, zonal statistics tool, and move command were used to achieve the shift in ArcGIS. We also computed topographically influenced solar radiation using the lidar DEM and the solar radiation function in ArcGIS, but found that there was no significant difference across the plot locations and thus did not use these results in subsequent analysis.

Synthetic hemiphotos were created in MATLAB using the method of Moeser et al. (2014) and analyzed for diffuse and direct light transmittance in GLA. All statistical analyses were performed in R (version 3.4).

Longitudinal profiles of stream shading were created in ArcGIS in 1 m increments based on the intersections of the stream polyline center line with the raster output of modeled solar insolation.

Figure 5 shows the correlation between field-collected pyranometer data and processed hemispherical photographs, with data from transect A removed. These data are highly correlated (r2=0.87), but these data are also not equally distributed across a range of solar insolation. Many more plot locations were at low levels of solar insolation than in areas of relatively low shade. This is very typical of the heavily forested streams in northwestern North America. Note that none of our plot locations contained transmittance greater than 40 %.

Pyranometer-based solar insolation and hemispherical photograph percent diffuse and direct radiation transmittance calculated at all point locations except transect A were compared to three lidar predictors using simple linear regression. These results are shown in Fig. 6. The LPI calculated using a 10 m circle centered on the point location explained about 55 % of the variability in both response variables, but the prediction accuracy improved when LPI was calculated using the shifted square buffer. Shifted LPI explained 74 % of the variability in solar insolation and 64 % of the variability in percent transmittance. Synthetic hemispherical photographs explained 77 % of the variability in solar insolation and 60 % of the variability in percent transmittance. Figure 6 shows comparisons between transects B and D to make interpretation easier, but Table 2 shows the results of linear regressions between predicted variables and hemispherical photograph transmittance for all plot locations resulting in small reductions in the amount of variability explained. Table 3 gives parameters of slope and intercept resulting from the simple linear regression.

While both the raster-based shifted LPI approach and the lidar point reprojection synthetic hemispherical photograph approach explained more than 60 % of the variability in the field data, the limited range of solar insolation conditions at the point locations in our study may limit some of the conclusions that can be drawn. Excluding transect A, 14 of the 16 point locations received less than 0.8 kWh m-2 d-1, leading the other two point locations to exert a large degree of leverage on the results. Note that these two point locations received less than 35 % of the maximum solar insolation. The three points in transect A all received less than 0.8 kWh m-2 d-1 and their inclusion in Table 2 did not improve coefficients of determination, suggesting that all methods are not as effective at predicting field-measured values in areas of high canopy cover. The constraints of the study design requiring point locations to be located in the stream made it impossible to achieve a greater range in solar insolation. It is reasonable to expect that including more point locations receiving larger amounts of insolation would have led to improved accuracy and greater coefficients of determination, as previous studies have shown that accuracy increases as canopy cover decreases (Moeser et al., 2014; Musselman et al., 2013; Richardson and Moskal, 2014).

One explanation of the decrease in variability at high canopy cover in regressions E and F shown in figure is demonstrated in Fig. 7. Here, a synthetic hemispherical photograph from transect D is compared to a field-captured hemispherical photograph with the GLA modeled sun path superimposed. This sun path is critical for determining the quantity of direct light, but very small differences in the center location of the two images can produce large differences in the modeled direct light. The sun path passes through a modeled canopy gap near solar noon on the synthetic hemispherical photograph, while it intersects only canopy and misses the gap on the field-collected hemispherical photograph. Very small registration errors can cause differences in transmittance at low light levels, and we suggest that these errors are likely to cause the errors observed in the regressions. The daily pyranometer output for the same point location is shown in Fig. 8 to further aid comparison. The pyranometer is only briefly exposed to full sunlight, highlighting the contribution of small gaps in the canopy.

Understory vegetation is another likely cause of observed errors, as airborne lidar is inherently limited in its ability to fully sample multi-layered canopies (Richardson and Moskal, 2011). We noticed several points with differences between lidar predictors and field data that contained understory vegetation in close proximity to the field instruments. The ideal scenario would be for the lidar scan angles to precisely match the range of potential solar angles at each plot location, but this is currently impractical, leading to an incomplete sample of the canopy light environment which contributes to the observed errors.

The correlations between lidar predictors and field data were strongest in Fig. 6c and e, and these lidar predictors are both appropriate to use as the basis for estimating solar insolation across the study area. Implementation of shifted LPI was the simplest and least time-intensive method, and we chose to model solar radiation by multiplying shifted LPI by the maximum above-canopy solar insolation for 20 June 2015 and then computing a non-intercept linear regression (Fig. 9). Removing the intercept from the model lowered the coefficient of determination but provided a model that did not estimate negative values of solar insolation. Figure 10 shows the model applied across the study area. The graphs show the pattern of solar insolation across the two reaches in the study, highlighting the utility of these methods for predicting solar insolation in heavily forested streams across wide spatial extents. Figure 11 shows the relative frequency of binned solar insolation values, highlighting the dominance of heavily shaded areas (note that a dammed reservoir, point D on the map, contributes the majority of the points in full sun).

The relatively unbiased results shown in Fig. 9 show that field calibration is not required to produce accurate estimates of solar insolation. However, information is still needed on local above-canopy meteorological conditions, which can either be modeled from known solar outputs or collected from a nearby meteorological station. Little bias was observed in comparisons between synthetic hemispherical photograph transmittance and field-based hemispherical photograph transmittance (Table 3). Therefore, both approaches tested in this study should not require field calibration.