Evaluating models of shortwave radiation below Eucalyptus canopies in SE Australia
Introduction
Shortwave radiation is a major component of the energy budget below forest canopies and is an important factor in the water balance and associated biogeochemical processes on the forest floor. Snowpack dynamics, fuel moisture, and decomposition processes in the litter layer are all strongly influenced by shortwave radiation below the canopy (Hinckley et al., 2014, King et al., 2012, Matthews, 2006, Niu and Yang, 2004, Ossola and Nyman, 2017, Reid et al., 2014, Schaap et al., 1997, Schiks et al., 2015, Sicart et al., 2004, Thompson et al., 2015). More generally in forest hydrology, the shortwave radiation flux has been found to be a major driver of evapotranspiration in understory and ground components (Baldocchi et al., 2000, Barbour et al., 2005, Black et al., 1989, Kelliher et al., 1992, Scott et al., 2003, Silberstein et al., 2001). Below the canopy, and on the forest floor, the shortwave radiation is a function of transmittance, which depends on 1) the density and thickness of the vegetation layer, 2) the terrain and 3) the position of the sun. Complex terrain and spatial variation in vegetation give rise to large spatial variation in transmittance due to geometric interactions with the sun beam. The magnitude of this spatial variation is also dependent on time, with seasonality and time of day both affecting how a beam is transmitted though vegetation.
Terrain and vegetation are not acting independently because the slopes with low radiation tend to support denser vegetation, a feature common to most water-limited systems (Gutiérrez-Jurado and Vivoni, 2013, Huxman et al., 2005, Kirpatrick and Nunez, 1980, Nyman et al., 2015, Yetemen et al., 2015, Zhou et al., 2013). Differences in evaporative demand as a result of aspect results in a positive feedback whereby wetter conditions on polar aspects results in more vegetation, which further reduces solar radiation on the forest floor (Gutiérrez-Jurado and Vivoni, 2013, Nyman et al., 2015). The combination of complex terrain and heterogeneous vegetation can result in poor predictions of sub-canopy processes across a landscape if models are parametrised at coarse scales or missing key processes in their conceptual representation of radiation. How models perform to resolve such topographic related variation in forest structure is unclear. In temperate forest of southeast (SE) Australia there are no studies that set out specifically to evaluate model performance in terms of accuracy and capacity to represent complex terrain, heterogeneous vegetation and the interactive effects of these at a landscape scale. Yet, the shortwave radiation is known to be a key control on eco-hydrological processes that determine hydrological partitioning, litter and soil moisture dynamics, and decomposition.
Below canopy (or sub-canopy) transmittance of shortwave radiation is commonly modelled with Beer’s law, whereby the amount of radiation penetrating the vegetation canopy decays exponentially depending on vegetation structure (Campbell and Norman, 1998, Hellström, 2000, Liston and Elder, 2006, Niu and Yang, 2004, Seyednasrollah and Kumar, 2014, Sullivan and Matthews, 2013, Wigmosta et al., 1994). According to Beer’s Law the transmittance through a medium is a function of three parameters; the path length of the beam as it passes through the medium, the concentration (or density) of the medium and its absorptivity. In forests applications of Beer’s law there is some aggregation of these parameters because the concentration, absorptivity and path length are problematic to represent explicitly in the parametrisation. Monsi and Saeki (2005), for instance, express the transmittance as a function of plant area index (PAI) and an extinction coefficient (k). This variant of Beer’s law assumes that path length and density are both represented in PAI and that the extinction coefficient is the absorptivity, which varies with vegetation type. This variant of Beer’s law has been used to estimate shortwave radiation on the forest floor in various environments (Hellström, 2000, Liston and Elder, 2006, Sullivan and Matthews, 2013), and it is probably the most commonly used model of light transmittance in forests. However, because path length is bundled up with vegetation density in PAI, the effects of sun position on transmittance is not represented, which is a limitation in applications to sub-daily time scales or in cases where transmittance is subject to spatial-temporal effects due to terrain, seasonality, or latitude.
Effects of path length can be represented implicitly by modelling the extinction coefficient as a function of sun position (i.e. incident angle) (Hellström, 2000, Nijssen and Lettenmaier, 1999, Norman and Campbell, 1989, Sicart et al., 2004). In doing so the diffuse and direct shortwave radiation are treated separately, with only the direct fraction having a transmittance model that depends on incident angle. Another application of Beer’s law assumes that the transmittance of the direct component is a function of the path length (L) of the solar beam as it traverses foliage and wood in the forest canopy (Link et al., 2004, Seyednasrollah and Kumar, 2014). In this approach the density of the vegetation and the extinction coefficients are combined into a single parameter (with units of m−1), which describes the rate of absorption per unit path length. Path length of the direct beam is a function of tree height, solar incident angle and terrain. A more data intensive approach to modelling transmission is to use airborne light detection and ranging (lidar) to calculate a light penetration index (LPI) (Bode et al., 2014, Moeser et al., 2014). LPI is estimated from the number of ground returns relative to the total number of returns and is a measure of canopy density. Lidar based models rely less on assumptions of canopy shapes and dimensions, but can be computationally intensive (Moeser et al., 2014, Musselman et al., 2013).
In models of fuel moisture (e.g. Matthews, 2006), snowmelt (e.g. Pomeroy et al., 2016) or near surface soil moisture dynamics (e.g. Ebel, 2013) the prediction errors in radiative forcing may be large relative to the variation that hydrological models are aiming to resolve, particularly in landscape-scale applications where vegetation and terrain are highly variable. Errors in radiation predictions are introduced in the functioning of the model and in the derivation of parameters that can be applied across the landscape. Much of the existing work on sub-canopy radiation has been done on deciduous or boreal forests in context of snowcover energetics (Hardy et al., 2004, Link et al., 2004, Seyednasrollah and Kumar, 2013, Sicart et al., 2004). The hydrological context for our study is moisture dynamics in surface fuels below canopies in fire prone Eucalyptus forests. This surface fuel component is an important control on fire spread and ignition probability (Gould et al., 2011, McArthur, 1967) and there has been much research dedicated to predicting its moisture status (Matthews, 2014). Incoming shortwave radiation is known to be a key control on surface temperature and evaporation from fuels (Byram and Jemison, 1943, Gibos, 2010, Nyman et al., 2015, Sharples, 2009, Walsh et al., 2017). However, little effort has gone into evaluating how transmission models perform. Uncertainty in the radiative forcing is unaccounted for, which presents a major constraint on efforts to develop, refine and test models of fuel moisture dynamics across variable landscapes.
In this study the objective is therefore to evaluate the performance of sub-canopy radiation models when applied across landscapes with contrasting vegetation and complex terrain. The study is situated in SE Australia in eucalyptus forest ranging from dry open forest to tall temperate forest. The region is prone to wildfire and the context of the study is set in terms of the capacity to predict fuel moisture dynamics at high resolution across large areas where terrain and vegetation are variable. The specific aims are to:
- 1.
Measure shortwave radiation in different landscape positions and in contrasting forest types.
- 2.
Calibrate shortwave radiation models using a subset of the experimental data.
- 3.
Test the performance of the model at daily and sub-daily timescales and evaluate the implications for landscape-scale applications.
Section snippets
Overview
We compare four shortwave radiation models that simulate the transmittance of shortwave radiation through forest canopies; PAIMS, PAINC, PL and LPI models (Table 1). Two models (PAIMS and PAINC) calculate transmission using plant area index (PAI). PAIMS (Monsi and Saeki, 2005) is independent of zenith angle (z) and represent the canopy effects on radiation without partitioning diffuse (Rbc,dif) and direct radiation (Rbc,dir) into separate components. PAINC (Norman and Campbell, 1989) separates
Model calibration
The calibrated extinction coefficients, k1 and k2, were 0.48 ± 0.0026SE (R2 = 0.92, RMSE = 0.53 MJ m−2day−1) and 0.033 ± 0.00015SE (R2 = 0.67, RMSE = 75.1 W m−1), respectively, for the PAIMC and PL models. In the calibration of k1 for the daily PAIMS model there was relatively little scatter, but some bias with respect to the site located on the east aspect (Fig. 2). With the 30-min radiation used to calibrate the PL model there is more scatter which is expected given that 1) the tree canopy is not a
Model evaluation
The path length model (PL) (Eq. (8)) with a calibrated extinction coefficient (k2 = 0.033 ± 0.00015SE) was the most accurate radiation model in terms of RMSE, bias and R-square (Fig. 6, Fig. 7). RMSE was 25.9 W m−2 and 1.26 MJ m−2 day−1 for daily and sub-daily radiation. The calibrated extinction coefficient, which can be considered representative of a wide range of Eucalyptus forests, is within the range of values (0.019 − 0.038 m−1) reported for boreal forest and temperate rainforest in North America (
Conclusions
Four canopy transmission models were evaluated in terms their capacity to produce accurate predictions of shortwave radiation below forest canopies. Models vary in terms of how transmission is conceptualised and how parameters are derived (Table 1). We calculated extinction coefficients (k) for two sub-canopy radiation models; one based on plant area index (PAIMS model: k1 = 0.48) and another based on path length of the sun beam (PL model: k2 = 0.033). The extinction coefficients are representative
Acknowledgement
Research funding was provided by Natural Disaster Resilience Grants Scheme (NDRGS) and the Victorian Department of Environment, Land, Water and Planning (DELWP). We are grateful for being able to collect field measurements on land managed by Melbourne Water. Craig Baillie helped establish field sites and provided ongoing field support. Insightful comments from reviewers helped improve the quality of the manuscript.
References (62)
- et al.
On measuring and modeling energy fluxes above the floor of a homogeneous and heterogeneous conifer forest
Agric. Forest Meteorol.
(2000) - et al.
Empirical modeling of hourly direct irradiance by means of hourly global irradiance
Energy
(2000) - et al.
Subcanopy Solar Radiation model: predicting solar radiation across a heavily vegetated landscape using LiDAR and GIS solar radiation models
Remote Sens. Environ.
(2014) - et al.
Computing diffuse fraction of global horizontal solar radiation: a model comparison
Sol. Energy
(2012) - et al.
Simplified expressions for radiation scattering in canopies with ellipsoidal leaf angle distributions
Agric. For. Meteorol.
(2007) - et al.
Quantifying fine fuel dynamics and structure in dry eucalypt forest (Eucalyptus marginata) in Western Australia for fire management
For. Ecol. Manage.
(2011) Solar radiation transmission through conifer canopies
Agric. Forest Meteorol.
(2004)Evaporation, xylem sap flow, and tree transpiration in a New Zealand broad-leaved forest
Agric. Forest Meteorol.
(1992)Estimation of leaf area index in eucalypt forest with vertical foliage, using cover and fullframe fisheye photography
For. Ecol. Manage.
(2007)- et al.
Canopy closure, LAI and radiation transfer from airborne LiDAR synthetic images
Agric. Forest Meteorol.
(2014)
Estimation of solar direct beam transmittance of conifer canopies from airborne LiDAR
Remote Sens. Environ.
Determination of mean tree height of forest stands using airborne laser scanner data
ISPRS J. Photogramm. Remote Sens.
Spatial and temporal distribution of solar radiation beneath forest canopies
Agric. Meteorol.
Estimation of leaf area index and covered ground from airborne laser scanner (Lidar) in two contrasting forests
Agric. Forest Meteorol.
Forest floor water content dynamics in a Douglas fir stand
J. Hydrol.
The understory and overstory partitioning of energy and water fluxes in an open canopy, semiarid woodland
Agric. Forest Meteorol.
Energy balance of a natural jarrah (Eucalyptus marginata) forest in Western Australia: measurements during the spring and summer
Agric. Forest Meteorol.
A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation
Sol. Energy
Determining landscape fine fuel moisture content of the Kilmore East ‘Black Saturday’ wildfire using spatially-extended point-based models
Environ. Modell. Softw.
Factors controlling evaporation and energy partitioning beneath a deciduous forest over an annual cycle
Agric. Forest Meteorol.
Canopy radiative transfer models for spherical and known leaf inclination angle distributions: a test in an oak-hickory forest
J. Appl. Ecol.
Components of ecosystem evaporation in a temperate coniferous rainforest, with canopy transpiration scaled using sapwood density
New Phytol.
Processes controlling understorey evapotranspiration [and discussion]
Philos. Trans. R. Soc. London B Biol. Sci.
Solar radiation and forest fuel moisture
J. Agric. Res.
An Introduction to Environmental Biophysics. [electronic Resource]
The distribution and abundance of ground-dwelling mammals in relation to time since wildfire and vegetation structure in south-eastern Australia
Wildl. Res.
Simulated unsaturated flow processes after wildfire and interactions with slope aspect
Water Resour. Res.
Effect of Slope and Aspect on Litter Layer Moisture Content of Lodgepole Pine Stands in the Eastern Slopes of the Rocky Mountains of Alberta
Ecogeomorphic expressions of an aspect-controlled semiarid basin: II. Topographic and vegetation controls on solar irradiance
Ecohydrology
Forest cover algorithms for estimating meteorological forcing in a numerical snow model
Hydrol. Processes
Aspect control of water movement on hillslopes near the rain-snow transition of the Colorado Front Range
Hydrol. Processes
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