Evaluating models of shortwave radiation below Eucalyptus canopies in SE Australia

Highlights

• Four transmission models were evaluated at 10 sites in temperate Eucalyptus forests.

• Extinction coefficients were derived from independent calibration at 4 sites.

• Transmission was spatially variable at hillslope, catchment and regional scales.

• Temporal variation in transmission is large due to variable path length.

• Including path length as a parameter therefore provides the most accurate predictions.

Abstract

In this study we examine the performance of four models that simulate radiation under forest canopies. The models are different in terms of how transmittance of radiation is conceptualised and the data sources used to obtain parameters. Two models (PAI_MS and PAI_NC models) use plant area index (PAI) to represent transmission. A third model (PL model) represents transmission as a function of the path length (L) of a directional beam as it crosses the canopy. The fourth model (LPI model) is based on a light penetration index obtained directly from lidar. The PAI_MS and PL models were calibrated using 6 months of radiation data at 4 independent sites. The LPI and PAI_NC models are uncalibrated. Performance was assessed using sub-daily and daily radiation measurements during summer (December–March) at 10 sites in forests ranging from open dry forests (PAI = 1.6) to tall temperate forests (PAI = 4.6). Mean annual precipitation ranged from 760 to 1750 mm across the domain. The PL model with a calibrated extinction coefficient (k₂ = 0.033) was the most accurate model within sites (R-square = 0.32–0.89 for sub-daily radiation) and across all sites (R-square = 0.82 for daily and sub-daily radiation). The LPI model performed well at most sites, but displayed some systematic bias in dense forests resulting in lower performance (R-square = 0.61 across all sites) while PAI_NC was negatively biased and a poor predictor across all sites (overall R-square = 0). The PAI_MS model, with a calibrated extinction coefficient (k₁ = 0.48), produced good results, but inspection of sub-daily radiation patterns show that the model tends to underestimate (overestimate) sub-canopy radiation during times of high (low) radiation. This is because transmittance is highest when the sun elevation is high (i.e. short path length), resulting in sub-canopy radiation that varies non-linearly with the intensity of above canopy radiation. Models that explicitly include path length in the transmission term therefore provide more flexibility for capturing sub-daily, seasonal and latitudinal variation due to sun position and vegetation structure. Other advantages of the path length approach include i) simple parameterisation using tree height as input and ii) explicit representation of diffuse and direct radiation, which can be important when accounting for terrain-effects on energy balance at the forest floor. We therefore recommend path length based modelling approaches for investigating hydrological processes below the canopy in temperate Eucalyptus forests.

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:

• Measure shortwave radiation in different landscape positions and in contrasting forest types.

• Calibrate shortwave radiation models using a subset of the experimental data.

• Test the performance of the model at daily and sub-daily timescales and evaluate the implications for landscape-scale applications.