5 The UV, VIS and NIR environment of plants
Quantity, quality and timing in nature
This chapter discusses the light environment of plants. Plants themselves alter the light environment by selective absorption and reflection. In the case of terrestrial plants the air medium sourrounding the plants has little if any inpact on radiation within vegetation canopies. In the case of aquatic plants, the light received by submerged parts is affected in quality and quantity by the properties of water and solutes in addition to the effects of other plants. In the case of both terrestrial and aquatic plants the temporal dynamics of illumination are different than in the open.
Andreas Albert, Félix López Figueroa, Pirjo Huovinen
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5.1 Radiation in terrestrial plants’ environment
5.1.1 Attenuation of PAR
The attenuation of visible and radiation by canopies is difficult to describe mathematically because it is a complex phenomenon. The spatial distribution of leaves is in most cases not uniform, the display angle of the leaves is not random, and may change with depth in the canopy, and even in some cases with time-of-day. We start with one of the simplest approaches to the description of light attenuation with canopy depth: the use of an approximation based on Beer’s law as modified by Monsi and Saeki (1953), reviewed by Hirose (2005). Beer’s law (Equation [eq:Beer-Lambert]) assumes a homogeneous light absorbing medium such as a solution. However, a canopy is heterogenous, with discrete light absorbing objects (the leaves and stems) distributed in a transparent medium (air). \[I_z = I_0\cdot\mathrm{e}^{-K\,L_z} \label{eq:Monsi:Saeki}\] The equation above describes the radiation attenuated as a function of leaf area index (\(L\) or ) at a given canopy depth (\(z\)). The equation does not explicitly account for the effects of the statistical spatial distribution of leaves and the effects of changing incidence angle of the radiation. Consequently, the empirical attenuation (= extinction) coefficient (\(K\)) obtained may vary depending on these factors. \(K\) is not only a function of plant species (through leaf optical properties, and how leaves are displayed), but also of time-of-day, and season-of-year—as a consequence of solar zenith angle—and degree of scattering of the incident radiation. As the formula shown here is only a parametrization of Beer’s original equation for homogeneous media, as long as we assume that \(K\) does not change with depth in the canopy, it describes an exponential decay as Beer’s law does (Figure 3.7), except that we use leaf area index (LAI) in place of distance (\(l\)).
As the degree of scattering depends on clouds, sun elevation and on wavelength, the empirical attenuation coefficient (\(K\)) is different for UV and VIS radiation, time of day, seasons and state of the vegetation. Radiation attenuation in canopies has yet to be studied in detail with respect to UV radiation, mainly because of difficulties in the measurement of UV radiation compared to VIS radiation, a spectral region that has been extensively studied.
5.1.2 Spectrum wihtin vegetation
Ultraviolet radiation is strongly absorbed by plant surfaces, although cuticular waxes and pubescence on leaves can increase UV reflectance. The diffuse fraction of UV radiation in daylight is larger than that of visible light (Figure 4.18). In sunlit patches in forest gaps, the diffuse radiation fraction is smaller than in open areas because direct radiation is not attenuated while part of the sky is occluded by the surrounding forest. Attenuation with canopy depth is on average usually more gradual in tall vegetation like forests than in low vegetation, because of increased size of the area in penumbra.
The UV-B irradiance decreases with depth in tree canopies, but the UV-B:PAR ratio tends to increase (see Brown, Parker, and Posner 1994), as it also does when clouds occlude the solar disk (Figure 4.23). In contrast, Deckmyn, Cayenberghs, and Ceulemans (2001) observed a decrease in the UV-B:PAR ratio in white clover canopies with planophyle leaves. Allen, Gausman, and Allen (1975) modelled the penetration in plant canopies, under normal and depleted ozone conditions. Parisi and Wong (1996) measured doses within model plant canopies using dosimeters. The position of leaves affects exposure, and it has been observed that heliotropism can moderate exposure and could be a factor contributing to differences in tolerance among crop cultivars (Grant 1998, 1999a, 1999b, 2004).
Detailed accounts of different models describing the interaction of radiation and plant canopies, taking into account the properties of foliage, are given by Campbell and Norman (1998) and Monteith and Unsworth (2008).
Measurement of spectral irradiance within plant canopies is challenging because of the temporal dynamics and the spatial heterogeneity. One needs to measure all wavelengths within milliseconds and sample in a 3D space. The best tools are array spectrometers, which however, do not natively have a big enough signal to noise ratio to measure UV-B spectral irradiance in the presence of strong visible radiation, as is the case in sunlight and canopy light. Some broadband sensors are visible blind, but they do not resolve spectral irradiance but instead measure the irradiance integrated over a waveband. This technical limitations non-withstanding, progress since the first edition has been very significant in the characterisation of the light environment within different plant canopies.
5.1.3 Temporal dynamics and spatial heterogeneity
5.1.4 Spectral irradiance at the plant surface
Ray tracing models, etc.
5.1.5 Radiation within leaves
The same analysis as done for optical filters in section XXX with only two parallel air-glass interfaces, can in principle, be applied to an object with a heterogeneous internal structure, like a plant leaf with its multiple internal air-water interfaces. However, one would need to consider these multiple internal interfaces and their positions. The presence of these interfaces at different angles, plus small particles, cause strong scattering, and thus in this case \(\rho\) depends on both surface and internal properties of the leaf. We can still measure \(\rho\), \(\tau\) and \(\alpha\) but predicting them based on optical theory becomes daunting if at all possible. Simulation models based on a simplified description of leaves’ structure and pigments, such as PROSPECT can provide good approximations.
One way of demonstrating and/or measuring the role of air-water interfaces within leaf tissues on its optical properties is to infiltrate a leaf with water using a vacuum chamber so as to fill with water all air spaces within the leaf. The effect is most spectacular in a variegated leaf such as those from some clones of English ivy: after infiltration with water the green areas become translucent green and the white areas almost transparent. Obviously, the ability to greatly increase the number of photons absorbed with the same number of pigment molecules can greatly increase the efficiency of photosynthesis as well as the ability of photoreceptors to sense very low irradiances.
The internal structure of leaves has evolved to be extremely efficient at trapping light, to the point that it has been copied in a recent design for high efficiency solar cells (Yun et al. 2019). There is also evidence that shade leaves are better light traps per unit dry mass than sun leaves. On the other hand, modelling of the optical properties of leaves is still in its infancy. The optics of leaves, flowers and fruits are described in detail in the book (D. Lee 2007).
5.2 Radiation in aquatic plants’ environment
As solar radiation passes through a body of water, its spectrum changes with depth in a wavelength-dependent manner, determined by the optical characteristics of that water body. The penetration of UV radiation through water bodies can vary from only few centimetres in highly humic lakes (Kirk 1994a, 1994b; P. S. Huovinen, Penttilä, and Soimasuo 2003) to dozens of metres in the oceans (Smith et al. 1992; Kirk 1994a, 1994b). Some irradiance is reflected at the water surface, but the extent to which wavelengths in the UV to IR range penetrate water bodies depends mainly on (1) attenuation by water itself, (2) coloured dissolved organic matter (CDOM), and seston. Seston is the sum of living organic material (mainly phytoplankton) and non-living material (tripton). Non-living particles are further distinguished between organic material (detritus) and inorganic suspended matter. Each fraction has its own characteristic spectral absorption and scattering properties (reviewed by Dekker 1993; Kirk 1994a, 1994b; Hargreaves 2003; Wozniak and Dera 2007).
Particularly in coastal areas and shallow areas of lakes and streams, irradiance reflected from the ground or sea-bed beneath the water (henceforth bottom) influences the profile of radiation through the aquatic environment. This reflectance is described by a bidirectional reflectance distribution function (BRDF), which is wavelength specific and depends on the incident and reflected angle. If the reflectance is equally distributed in all directions, the bottom is a so called Lambertian reflector and the BRDF is constant. The bottom reflectance is greatly influenced by its slope and properties, i.e. whether the bottom is bare sediment or covered by algae and submersed vegetation (e.g. Maritorena, Morel, and Gentili 1994; Albert and Mobley 2003; Mobley and Sundman 2003; Mobley, Zhang, and Voss 2003; Pinnel 2007).
5.2.1 Refraction
The refraction of incoming (downwelling) radiance at the water surface can be determined by Snell’s law, which describes the angular refraction of the incident beam. The radiation passes the first medium with a refractive index \(n_1\) and then the second medium with a refractive index \(n_2\). If the incoming direction of the radiation is given by the angle \(\theta_1\), the beam is refracted to the angle \(\theta_2\). Snell’s law is \[n_1 \cdot \sin\theta_1 = n_2 \cdot \sin\theta_2\] For the case of radiation arriving from the air under the incident angle \(\theta_i\) and going into the water with the transmitted angle \(\theta_t\), this yields a refractive index for the air of \(n_a=1\) and for the water of \(n_W=1.33\) \[\theta_t = \arcsin \left( 0.75\cdot \sin\theta_i \right)\]
Theoretically, \(n_W\) is not constant but depends on temperature, wavelength and salinity, as described by Quan and Fry (1995). In principle, the shorter the wavelength, the higher the refractive index of water, but in practice the wavelength-dependent difference in refraction is unimportant. For example comparing the values at 400 and 800 nm for 20and no salinity produces a difference of \(<\) 0.5%. If the wind speed is high, the slope of surface waves also has to be taken into account. A rough surface reflects and transmits the incoming radiation beam in more directions and makes the radiation field more diffuse than a smooth surface.
5.2.2 Absorption and scattering by pure water
Water itself absorbs and scatters radiation. The optical properties of the water in the visible and ultraviolet (UV) spectrum are not precisely known, since no theoretical model exists which exactly describes the absorption and scattering properties of pure water. Therefore, it is necessary to rely on laboratory measurements to approximate the values of these parameters. Investigations into absorption by water \(a_W\) were initially documented by Morel (1974), Smith and Tyler (1976), Smith and Baker (1981), Pegau and Zaneveld (1993) and more recently by Buiteveld, Hakvoort, and Donze (1994) and Hakvoort (1994). The absorption properties of water also depend on temperature. The influence of temperature is weak below 700 nm, but its effect increases with increasing wavelength; so, for example, a temperature increase of 10 K produces a \(\approx\)7% change in the absolute value of \(a_W\) at 740 nm.
The scattering of radiation by molecules in liquids has been modelled theoretically by Smoluchowski (1908) and Einstein (1910). This approach is based on statistical thermodynamics and is called the theory of fluctuation. Theoretically, the scattering function is wavelength-dependent and follows the \(\lambda^{-4}\) law. Experiments show a slight deviation from the model, giving a better correlation with \(\lambda^{-4.32}\) (Morel 1974) due to the effects of isothermal compressibility, the refractive index of water, and the pressure derivative of the refractive index of water (Hakvoort 1994).
The wavelength dependency of the absorption and scattering coefficients of pure water are shown in Figure [fig:Water:Abs_Scat] using data from Hakvoort (1994). Water mainly contributes to the attenuation of PAR and IR wavelengths, since absorption by pure water increases from around 550 nm towards longer wavelengths.
5.2.3 Absorption and scattering by water constituents
Absorption and scattering by water constituents is the sum of (1) absorption by CDOM, sometimes also called yellow or humic substances, gilvin or gelbstoff, (2) absorption and scattering by living material like phytoplankton, and (3) absorption and scattering by dead organic and inorganic particles. The influence of each constituent on the scattering process depends on wavelength, particle size, concentration, and refractive index. Theoretical details are explained in, for example, Hulst (1981).
CDOM mainly refers to coloured dissolved humic materials and consists of humic and fulvic acids, originating from decomposed plant material suspended in the water or entering from the surrounding catchment area. The pigments in humic and fulvic acids absorb strongly in the blue and UV wavelengths and are dissolved and therefore do not scatter irradiance. Kalle (1966) recognised that CDOM absorption decreases exponentially with increasing wavelength in the visible part of the spectra. Following the study of Morel and Prieur (1976), Bricaud, Morel, and Prieur (1981) expressed this relationship in the following model: for a known absorption at a wavelength \(\lambda_0=440\) nm, the CDOM absorption \(a_Y\) can be determined by \[a_Y(\lambda) = a_Y(\lambda_0)\cdot {\rm e}^{-s_Y(\lambda-\lambda_0)} \label{equ_ay}\] Although the exponential coefficient \(s_Y\) is variable, a standard value of \(s_Y=0.014\) nm\(^{-1}\) is commonly used. Bricaud, Morel, and Prieur (1981) compared the value of \(s_Y\) across many data sets and reported a standard deviation of only \(\Delta s_Y=\pm 0.003\) nm\(^{-1}\). The amount of CDOM in water is determined by filtration using membrane filters of 0.2 \(\mu\)m pore size. The filtrate is collected into a quartz cuvette with length \(l\) and put into a (double beam) spectrophotometer to measure its absorbance (optical density) \(A(\lambda)\). Then, \(a_Y(\lambda)=2.303\cdot\frac{A(\lambda)}{l}\) (Kirk 1994a). The absorption coefficient at 440 nm has been used as an indication of optical colour (Kirk 1994a), while size of humic molecules has been estimated from the ratio \(\frac{a_Y(\lambda=250{\rm nm})}{a_Y(\lambda={\rm 365 nm})}\), with increasing size indicated by smaller ratios (Haan 1972, 1993; Haan, Boer, and T 1987). To determine \(a_Y\) from clearer (e.g. oceanic) waters, a cuvette with a 10 cm path-length is generally needed due to their low values of absorption.
Phytoplankton can contribute to the attenuation of PAR through absorption by their photosynthetic pigments such as chlorophyll and pheophytin, but they can also cause scattering. The absorption by phytoplankton \(a_P\) is the sum of absorption by each pigment multiplied each by their concentrations. Due to the fact that many species of phytoplankton occur in aquatic environments and every species contains more than one pigment, it is more practicable to calculate the absorption by mean specific absorption coefficients for each different algal species separately. This has been done by Gege (1998) for freshwater Lake Constance in Germany and by Prieur and Sathyendranath (1981) for an oceanic environment. Besides these examples, there are other models for oceanic waters that use the specific in vivo absorption coefficient and concentration of chlorophyll-a, \(a_{chl}^*\) and \(C_{chl}\), respectively. Morel (1991) found that the power law \(a_P = 0.06\, a_{chl}^*\, [C_{chl}]^{0.65}\), which was first proposed by Prieur and Sathyendranath (1981), provided the best estimate of the absorption coefficient for his data set. \(C_{chl}\) is the concentration of chlorophyll-a in units of \(\mu\)g l\(^{-1}\). Figure [fig:Phyto:Abs] shows the specific oceanic chlorophyll absorption coefficient from Morel (1991) normalized to maximum absorption at 440 nm. Figure [fig:Phyto:Abs] also shows laboratory measurements of chlorophyll-a and chlorophyll-b absorption1 after Frigaard, Larsen, and Cox (1996). Spectra for chlorophyll absorption, and that of various other photochemically-relevant substances, are also available in computer software such as PhotochemCAD2 (Du et al. 1998; Dixon, Taniguchi, and Lindsey 2005). The empirical model of Bricaud et al. (1995) parameterises the specific absorption coefficient from \(C_{chl}\). This model draws on extensive studies of more than 800 spectra to give \(a_P^*(\lambda) = A(\lambda)[C_{chl}]^{-B(\lambda)}\) with positive empirical coefficients \(A\) and \(B\) depending on wavelength. The model incorporates both the package effect of phytoplankton cells and the effect of the varying pigment composition on absorption.
The particulate structure of phytoplankton cells causes scattering. The influence of phytoplankton on the total scattering coefficient depends on the other constituents of the water body. For water containing a low concentration of inorganic suspended sediment scattering is driven by the concentration of phytoplankton (as occurs in the open ocean). Gordon and Morel (1983) developed an empirical model, which directly correlates scattering with the pigment concentration of chlorophyll-a \(C_{chl}\) in units of \(\mu\)g l\(^{-1}\). The scattering coefficient of phytoplankton \(b_P\) in units of m\(^{-1}\) is given by \[b_P(\lambda) = B \cdot [C_{chl}]^{0.62} \cdot \left(\frac{\lambda_0}{\lambda}\right) \label{equ_bp_emp}\] with \(\lambda_0=550\) nm and \(B=0.3\) as mean values for oceanic waters dominated by phytoplankton. The equation ([equ_bp_emp]) is valid for a range of phytoplankton concentrations from 0.05 to 1 \(\mu\)g l\(^{-1}\). Gordon and Morel (1983) found that oceanic waters have a value of \(B\le 0.45\). Higher values are used for other aquatic environments, for example turbid coastal waters. In coastal regions, Sathyendranath, Prieur, and Morel (1989) proposed that the scattering coefficient is indirectly proportional to absorption by phytoplankton: \(b_P(\lambda) \propto 1/a_P(\lambda)\). The proportionality factor depends on the concentration of chlorophyll-a in the same manner as the scattering coefficient of equation ([equ_bp_emp]). Dekker (1993) investigated the contribution to scattering of each water constituent in inland waters3. He found that the composition of scattering particles was more variable in inland waters than in the ocean and it depended on the trophic state of the water and therefore on the distribution of organic and inorganic particulate matter. The scattering and backscattering coefficient of phytoplankton can be determined by \(b_P(\lambda)=b_P^*(\lambda) \cdot C_P\) where the specific scattering coefficient of phytoplankton is \(b_P^*\). For lakes Dekker (1993) reported that the specific scattering coefficient of phytoplankton ranges from 0.12 to 0.18 m\(^2\)mg\(^{-1}\) at a wavelength of 550 nm. The specific scattering coefficients can be obtained by integrating the scattering phase function of the observed matter, here, phytoplankton. Extensive and commonly used measurements were done by Petzold (1977). Other functions can be found for example in Mobley (1994).
Particulate matter in water bodies consists of organic and inorganic material. The organic constituents are contained in phytoplankton cells or are fragments of dead plankton and faecal pellets of zooplankton. These parts are often called detritus. Inorganic particles include suspended mineral coming from inflows or resuspension at coastal regions. They mainly consist of quartz, clay, and calcite. There are only a few published values of the specific absorption coefficients of suspended particles in water from aquatic environments because they are difficult to separate into their individual constituent parts. A comparison of these values is given by Pozdnyakov and Grassl (2003). In general, absorption by all suspended particles in most water bodies is very low and it is negligible for inorganic particles. Roesler, Perry, and Carder (1989) produced the following relationship for absorption by detritus in coastal waters which is very similar that of CDOM: \[a_X(\lambda) = a_X(\lambda_0) \cdot {\rm e}^{-s_X(\lambda-\lambda_0)} \label{equ_adet}\] with a mean value of \(s_X=0.011\) nm\(^{-1}\) and \(a_X(\lambda_0)=0.09\) m\(^{-1}\) at \(\lambda_0=400\) nm for their data. Particulate matter in general causes more scattering of irradiance than it absorbs. In coastal waters and freshwater, scattering is higher than in oceanic waters due to the additional presence of particles not related to phytoplankton. These particles come from suspended inorganic sediments of different sizes. Scattering is caused by differences in the refractive indices of the two materials (the water medium and the material of the particles) and are due to the ratio of particle size to wavelength. Different functions of scattering coefficients and phase functions are, for example, described by Mobley (1994). Especially turbid and coastal waters, or rivers and lakes, are dominated by large particles (\(>1\) \(\mu\)m and a refraction index of 1.03). Therefore, the scattering coefficient of non-living particles \(b_X\) can be estimated while neglecting their size distribution and wavelength dependence. Thus, \(b_X\) is derived from \(b_X(\lambda) = b_X^* \cdot C_X\), with the concentration of the total suspended matter \(C_X\) and the specific scattering coefficients \(b_X^*\). Dekker (1993) gave example specific scattering coefficients of 0.23 to 0.79 m\(^2\) g\(^{-1}\) for different trophic states in lakes.
5.2.4 Results and effects
In summary, after considering all the components that absorb radiation, in very clear non-productive oceanic waters blue-green wavelengths in the PAR spectrum dominate, whereas in highly-coloured, humic inland waters blue wavelengths are rapidly attenuated. In humic lakes, CDOM largely governs UV attenuation (e.g. Kirk 1994a, 1994b; Scully and Lean 1994; P. S. Huovinen, Penttilä, and Soimasuo 2003)), whereas in oceans (Smith and Baker 1979) and clear lakes containing low CDOM concentrations the contribution of phytoplankton to UV attenuation can be significant (Sommaruga and Psenner 1997). If very turbid water contains a large amount of inorganic particles, CDOM is bonded by calcium carbonate contained in the particles, and consequently the colour of the water returns to blue.
There is marked variation in the penetration of UV radiation among water bodies, and within a water body during the year. Global changes, such as climate warming and acidification (Schindler et al. 1996; Yan et al. 1996; Donahue et al. 1998) can lead to increased underwater UV penetration, likewise UV-B radiation itself which can positively affect its own penetration through the photodegradation of CDOM (Morris and Hargreaves 1997). Variation in the absorption properties of dissolved organic compounds with the seasons and according to their origin and molecular weight (Stewart and Wetzel 1980; Hessen and Tranvik 1998; Lean 1998), interferes with our estimation of UV penetration based on CDOM concentrations. Temporal changes in the absorption characteristics of CDOM have also been reported, with fresh CDOM being photochemically more active than older CDOM (Lean 1998). It is also notable that UV radiation has been shown to penetrate deeper in saline prairie lakes than in fresh waters of corresponding CDOM concentrations (Arts et al. 2000).
Estimations of CDOM are relatively easy to perform and therefore often used for in situ and remote sensing measurements of optical properties. However, another parameter called dissolved organic carbon (DOC, in units of mg l\(^{-1}\)) is also useful to measure, since it is more interpretable for studies of carbon cycling and in the context of global change research. Kowalczuk et al. (2010), report that CDOM contributes approximately 20% to the total DOC pool in the open ocean and up to 70% in coastal areas. Unfortunately, on a global scale it has not yet been possible to make a direct link between CDOM and DOC due to the heterogeneous organic composition of CDOM. Until that connection is made, estimation of the universal bulk carbon-specific CDOM absorption coefficient, defined as the ratio of CDOM absorption to DOC concentration, remains almost impossible (Wozniak and Dera 2007), but at least there are good correlations between \(a_Y\) and DOC concentrations in coastal areas (Kowalczuk et al. 2010).
Aquatic organisms can be affected not only directly but also indirectly through UV-dependent changes in the surrounding water, e.g. through increased formation of photochemical reaction products such as singlet oxygen and hydrogen peroxide. Especially in lakes with low DOC concentrations, photoenhanced toxicity of some environmental contaminants or release of complexed metals into the water can occur due to the photodegradation of organic matter (Zepp 1982; Palenik, Price, and Morel 1991; Hessen and Donk 1994; Arfsten, Schaeffer, and Mulveny 1996; Scully et al. 1997). Despite the potential for detrimental effects, the final impact of UV radiation on organisms may be mitigated by their protective and repair mechanisms (Karentz, Cleaver, and Mitchell 1991; Mitchell and Karentz 1993; Vincent and Roy 1993), which somehow also depend on certain wavelengths of irradiation. When evaluating the exposure of seaweeds to UV radiation, it should be taken into account that other factors, such as kelp canopies, can markedly reduce the PAR and UV radiation reaching their understorey. Furthermore, the underwater radiation received by seaweeds can be significantly altered depending on the tidal range (P. Huovinen and Gómez 2011). Phenolic compounds released from large brown algae into the surrounding water can also locally attenuate UV radiation.
Classifications of water bodies based on their optical characteristics have been developed as general tools in order to allow comparisons between different water bodies. Jerlov (1976) traditional and widely-used classification of marine waters, based on their transmittance of irradiance at different wavelengths, recognizes three oceanic (I–III) and nine coastal (1–9) types of water body (Figure [fig:Jerlov]). Morel and Prieur (1977) classified ocean waters into two types based on their optically dominant components: (i) phytoplankton and their products dominate case-i waters, (ii) particles and dissolved coloured material dominate case-ii waters. The classification proposed by Kirk (1980) is principally suited to inland waters and is based on the spectral absorption of the soluble and particulate fractions. Kirk (1980) defined type G waters, in which CDOM is the dominant light-absorbing component, compared with type T, W and A waters, where tripton, water itself and phytoplankton dominate respectively. Beyond these scales, various other optical classifications have also been proposed (reviewed by Kirk 1994a; Hargreaves 2003).
5.2.5 Modelling of underwater radiation
Following Beer’s law (Equation [eq:Beer-Lambert]), for deep water (no reflection from bottom), radiance \(L(\lambda)\) decreases exponentially with depth \(z\) in the water column: \[L(z,\lambda) = L(z=0,\lambda)\cdot\mathrm{e}^{-\frac{a\cdot z}{\cos\theta}} \label{equ_beer}\] alternatively written as \[\cos\theta\,\frac{{\rm d}L(z,\lambda)}{{\rm d}z} = -a\cdot L(z,\lambda) \label{equ_dbeer}\] \(\theta\) is the zenith angle of the incoming (downwelling) radiance in water. Note that Eqs. [equ_beer] and [equ_dbeer] are only valid if the water column is homogeneous with depth and there are no scattering particles and internal sources of light in the water, i.e. no fluorescence, raman scattering, nor bioluminescence. Thus, calculation of actual radiative transfer in water (not under idealised conditions) is much more complicated and can only be solved approximately by using empirical, semi-analytical or computational models (Dekker 1993; Mobley 1994; Z. P. Lee, Carder, and Arnone 2002; Albert and Gege 2006).
The radiative transfer equations [equ_beer] and [equ_dbeer] are valid for radiance \(L\), which represents the collimated beam from one specific direction. Due to their construction, radiance detectors do not measure a beam from an infinitely small solid angle, they have an aperture of typically one or two degrees. Other types of detectors sense light from more than one direction, they measure the entire sphere or hemisphere (for details see also section [sec:basic:concepts] on page ), by integrating the incoming radiance over all directions. Another useful relationship between irradiance and fluence rate can be obtained using the Gershun equation: \[\frac{\rm d}{{\rm d}z} E(z,\lambda) = -a \, E_0(z,\lambda) \label{equ_gershun}\] If, for example, only the downwelling irradiance \(E_d(z,\lambda)\) is measured or necessary for calculating radiative transfer, Equation [equ_dbeer] yields \[\frac{{\rm d}E_d(z,\lambda)}{{\rm d}z} = -K_d\cdot E_d(z,\lambda) \label{equ_downirr}\] giving the diffuse attenuation coefficient for downwelling irradiance, \(K_d\). \(K_d\) is related to the total absorption \(a\) and scattering \(b\) as well as to \(\theta\) and also the solar zenith angle \(\theta_s\) (Kirk 1991; Albert and Mobley 2003). A practical and often-used method to estimate \(K_d\), and therefore the transparency of the water, is the Secchi disk test. The visibility of a submerged white disk can be correlated to downwelling diffuse attenuation (Tyler 1968). This and also the penetration depth \(z_d\) give useful information about the water body. The penetration of irradiance important for photosynthesis (primary production) is often expressed as the depth at which, for example, 1% or 10% of the value just below the water surface is reached. The depth, where 1% of PAR is reached, separates the euphotic zone from the aphotic zone. After Kirk (1994a), \(z_d\) can be obtained from \(K_d\): \(z_d(1\%) = 4.6/K_d\) and \(z_d(10\%) = 2.3/K_d\). In Figure [fig:Valdivia], an example of spectral attenuation of solar radiation at different depths, as well as the penetration depths of UV-B, UV-A radiation and PAR are given for coastal waters of the south-eastern Pacific Ocean (off the coast of Chile).
A very useful tool to simulate spectral radiance and irradiance under water, depending on different concentrations of the water constituents or bottom depth and type, is called WASI (water colour simulator, (Gege 2004)). The software includes different analytical parameterisations and it can also be used for inverse calculations, i.e. for estimating optical properties and concentrations of water constituents from (remote sensing) measurements. The software program including the manual is available free of charge using an anonymous login at the ftp server ftp://ftp.dfd.dlr.de/pub/WASI. Other models, which include angular distributions of radiation under water are, for example, the Monte Carlo method (Prahl et al. 1989; Wang, Jacques, and Zheng 1995)4, HydroLight (technique described by (Mobley 1994)), or EcoLight-S (Mobley 2011).
Data available from Frigaard’s website at the University of Copenhagen at http://www.bio.ku.dk/nuf/resources/scitab/chlabs/index.htm.↩︎
Latest software version available at the PhotochemCAD website at http://photochemcad.com. Data available at the PhotochemCAD data site at http://omlc.ogi.edu/spectra/PhotochemCAD/index.html.↩︎
Inland waters include rivers, streams and lakes.↩︎
Program available from the website of the Oregon Medical Laser Center at http://omlc.ogi.edu/software/mc/↩︎