Remote-sensing reflectance and true colour produced by a coupled hydrodynamic, optical, sediment, biogeochemical model of the Great Barrier Reef, Australia: Comparison with satellite data

Environmental Modelling & Software 78 (2016) 79e96

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Remote-sensing reflectance and true colour produced by a coupled hydrodynamic, optical, sediment, biogeochemical model of the Great Barrier Reef, Australia: Comparison with satellite data Mark E. Baird a, *, Nagur Cherukuru a, Emlyn Jones a, Nugzar Margvelashvili a, Mathieu Mongin a, Kadija Oubelkheir a, Peter J. Ralph c, Farhan Rizwi a, Barbara J. Robson b, Thomas Schroeder a, Jennifer Skerratt a, Andrew D.L. Steven a, Karen A. Wild-Allen a a

CSIRO Oceans and Atmosphere, Hobart, Australia CSIRO Land and Water, Canberra, Australia c Plant Functional Biology and Climate Change Cluster, Faculty of Science, University of Technology Sydney, Sydney, Australia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 May 2015 Received in revised form 27 November 2015 Accepted 27 November 2015 Available online xxx

Aquatic biogeochemical models are vital tools in understanding and predicting human impacts on water clarity. In this paper, we develop a spectrally-resolved optical model that produces remote-sensing reflectance as a function of depth-resolved biogeochemical model properties such as phytoplankton biomass, suspended sediment concentrations and benthic reflectance. We compare simulated remotesensing reflectance from a 4 km resolution coupled hydrodynamic, optical, sediment and biogeochemical model configured for the Great Barrier Reef with observed remote-sensing reflectance from the MODIS sensor at the 8 ocean colour bands. The optical model is sufficiently accurate to capture the remote-sensing reflectance that would arise from a specific biogeochemical state. Thus the mismatch between simulated and observed remote-sensing reflectance provides an excellent metric for model assessment of the coupled biogeochemical model. Finally, we combine simulated remote-sensing reflectance in a red/green/blue colour model to produce simulated true colour images during the passage of Tropical Cyclone Yasi in February 2011. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Ocean colour Chlorophyll Sediment Water clarity Tropical cyclone Yasi

1. Introduction Coastal environments are often impacted by multiple natural and anthropogenic forcings, including nutrient and sediment runoff, ocean acidification and ocean warming (Parry et al., 2007). Despite these stressors being known for decades, even wellresourced coastal environmental agencies have in the past struggled to optimise resource management (Brodie and Waterhouse, 2012). The state of the art in the management of coastal environments is now looking to combined monitoring and prediction systems to provide near-real-time information (Schiller et al., 2014) and to develop optimal management strategies. This paper will focus on optical model developments to better integrate

* Corresponding author. E-mail address: [email protected] (M.E. Baird). http://dx.doi.org/10.1016/j.envsoft.2015.11.025 1364-8152/© 2015 Elsevier Ltd. All rights reserved.

biogeochemical modelling outputs and satellite ocean colour observations. The assessment of marine biogeochemical models presently relies primarily on either in-situ observations, that are generally sparse in space and often in time, or remotely-sensed ocean colour (Kidston et al., 2013; Jones et al., 2012, 2015). The observed in-situ biogeochemical quantities are often not direct analogues of model quantities. For example, phytoplankton biomass is typically represented in models using mass concentration of elements such as nitrogen contained within the cells, while the most cost-effective observations of phytoplankton are based on active fluorescence of cells (Earp et al., 2011). The frequency of satellite observations depends on latitude, cloud cover, orbit paths, glint etc., but, in general, they provide a vastly superior coverage to in situ observations of biogeochemical properties. Remotely-sensed ocean colour observations are more regular, but still do not correlate directly with model quantities

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M.E. Baird et al. / Environmental Modelling & Software 78 (2016) 79e96

except through imperfect remote-sensing reflectance to chlorophyll algorithms (Mobley et al., 2015). Thus what is lacking is a single quantity that can be calculated without unreliable assumptions from biogeochemical models, and that is routinely produced by remote-sensing teams with small errors. In this paper, the common quantity is the remote-sensing reflectance, Rrs, evaluated at multiple wavelengths. Remote-sensing reflectance is a measure of the water-leaving radiance normalized by the at-surface downwelling solar irradiance and has units of sr
1. Thus both model outputs and observations can be quantified as a remote-sensing reflectance. To avoid confusion, we will use the term observed remote-sensing reflectance to refer to satellite-derived Rrs, and simulated remote-sensing reflectance to refer to Rrs calculated from the outputs of the biogeochemical model. There is a long history of including optical calculations within an aquatic biogeochemical model (Jassby and Platt, 1976). Initially these models were based on simple exponential decay of scalar, spectrally-averaged irradiance with depth (Fasham, 1993; Taylor et al., 1997), and were developed primarily as a means of forcing light-limited phytoplankton growth functions. Later spectrallyresolved models were also considered (Gregg and Carder, 1990; Baird et al., 2007; Nerger and Gregg, 2007) as a means of providing better-constrained optical parameters values to improve predictive capabilities. It has also become apparent that with improved optical observations, such as in-situ radiometers, more sophisticated optical models facilitated a more complete comparison between model and observations (Fujii et al., 2007; Mobley et al., 2015). Recently a global biogeochemical model has been coupled to a spectrally-resolved optical model to produce remote-sensing reflectance values that can be compared with remotely-sensed observations (Dutkiewicz et al., 2015). The Dutkiewicz et al. (2015) model produced annually averaged patterns of remotesensing reflectance in 3 bands. Their simulated remote-sensing reflectances were similar to the Moderate-resolution Imaging Spectroradiometer (MODIS) composites, with a small positive bias. Being a global scale, blue water study, Dutkiewicz et al. (2015) were able to ignore the influence of the benthic reflectance and the scattering of suspended sediment, but these processes must be included for coastal waters such as considered in this paper. Nonetheless Dutkiewicz et al. (2015) is an important study that shows the utility of assessing biogeochemical models using remote-sensing reflectance calculated by an optical model from biogeochemical model output. Similarly, Mobley et al. (2015) presents simulated remote-sensing reflectance, although the study was idealised so no comparison with observations was possible. The GBR ecosystem, described as one of the seven natural wonders of the world, is under increasing pressure from local and global anthropogenic stressors (De'ath et al., 2009). Decreasing water clarity due to nutrient and sediment pollution is one of the most serious threats to the GBR ecosystem (Thompson et al., 2014), with the primary concern being the impact of lower benthic light levels on coral and seagrass communities (Collier et al., 2012; Petrou et al., 2013). In addition to water clarity being critical for the functioning of shallow-water systems, remote-sensing of water clarity is increasingly being used to manage shallow-water ecosystems. For example, Devlin et al. (2013) has categorised plumes into primary, secondary and tertiary extents using remotely-sensed ocean colour, and then used these estimates of extent as a means of determining the frequency of impact of river plumes on coral reefs on the GBR in the vicinity (~50 km) of large tropical rivers. The accurate simulation of remote-sensing reflectance by a coupled circulation, optical and biogeochemical model will allow it to be analysed using the

same technique to that developed for remotely-sensed ocean colour. Thus, a modelling system that produces remote-sensing reflectance as a model output will be better assessed on its skill at determining water clarity and will have improve utility for management planning than the biogeochemical models presently used in coastal applications. This paper describes a spectrally-resolved optical model for optically-complex coastal and open-ocean waters, detailing the calculation of inherent optical properties (IOPs) and apparent optical properties (AOPs), including remote-sensing reflectance. The model is sophisticated enough to provide realistic remote-sensing reflectance at any chosen wavelength, but computationally simple enough to be used within a ~4 km resolution, 47 layer, multi-year simulation of the 2000 km long Great Barrier Reef, with a 60 state variable biogeochemical model and 19 optically-significant components. The simulated remote-sensing reflectance fields are calculated from the biogeochemical model state and then compared to remotely-sensed observations. Finally, the simulated remote-sensing reflectances are used to produce simulated true colour images of the Great Barrier Reef at the time of Tropical Cyclone (TC) Yasi when the ocean surface was obscured by clouds, providing a new appreciation of the magnitude and spatial extent of changes in water clarity during an extreme event. 2. Methods A brief description of the modelling system is given in Appendix A. Here we concentrate on the bio-optical model. 2.1. Bio-optical model The optical model considers the processes of absorption and scattering by pure seawater, coloured dissolved organic matter (CDOM), non-algal particulates (NAP) and phytoplankton cells (Tables 1 and 2), as well as benthic reflectance. First the inherent optical properties (IOPs), such as total phytoplankton absorption at a specific wavelength, are calculated from the model state variables (e.g. phytoplankton chlorophyll biomass) and model parameters (e.g. cell radius, Table 3). The optical model then solves for the apparent optical properties (AOPs), such as the spectrally-resolved scalar irradiance, from the surface downwelling light field and the IOPs. Finally, the AOPs can be directly compared to remotely-sensed products such as remote-sensing reflectance and true colour images. 2.1.1. Inherent optical properties (IOPs) 2.1.1.1. Phytoplankton absorption. The absorption-cross section (a) of a spherical cell of radius (r), pigment-specific absorption coefficient (g), and homogeneous intracellular pigment concentration (ci), calculated using geometric optics (i.e., ray tracing) without considering internal scattering, is given by (Duysens, 1956; Kirk, 1975):

a ¼ pr 2 1


 ! 2 1
ð1 þ 2gci rÞe
2gci r ð2gci rÞ2

(1)

where pr2 is the projected area of a sphere, and the bracketed term is 0 for no absorption (gcir ¼ 0) and approaches 1 as the cell becomes fully opaque (gcir / ∞). The pigment-specific absorption coefficient (g) is wavelength-dependent (Fig. 1). The use of an absorption cross-section of an individual cell has two significant advantages. Firstly, the same model parameters used here to calculated absorption in the water column are used to

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Table 1 Optically-significant state variables. In the biogeochemical model there are 4 phytoplankton types (Table 2) which are specified as a concentration of nitrogen (mg N m
3) and pigment (mg chl a m
3). For the purpose of the optical model presented here, the critical quantities are number of cells, n, and intracellular pigment concentration, ci, which can be calculated directly from the biogeochemical state variables. Thus, in this paper the state variables representing phytoplankton are just n and ci. The other optically-significant state variables represent the concentrations of inorganic sediment, detritus and macrophytes. Description

Symbol

Units

Concentration of phytoplankton Intracellular pigment concentration of phytoplankton Concentration of mud particles Concentration of fine particles Concentration of sand particles Concentration of detritus at Redfield (C:N:P ¼ 106:16:1) Concentration of detritus at Atkinson (C:N:P ¼ 550:30:1) Concentration of refractory detritus Macroalgae biomass Zostera biomass Halophila biomass Coral host biomass Zooxanthellae biomass Zooxanthellae intracellular pigment concentration

n ci Mud Fine Sand DRed DAtk DC MA SG SGH CH CS ci

cell m
3 mg chl a m
3 kg m
3 kg m
3 kg m
3 mg N m
3 mg N m
3 mg C m
3 mg N m
2 mg N m
2 mg N m
2 mg N m
2 mg N m
2 mg chl a m
2

Table 2 Traits of suspended microalgae cells.a Values for Trichodesmium from Subramaniam et al. (1999). The two size classes allow larger phytoplankton with different traits to dominant in estuarine and coastal waters, and smaller phytoplankton to dominant in offshore waters.

Radius (mm) Ratio of xanthophyll to Chl a

Small

Large

benthic

phyto.

phyto.

phyto.

1 0.51

4 0.81

5 0.81

Trichodesmium

Symbol

Units

Ed,l Eo,l

W m
2 W m
2 rad sr
1 sr
1 m e m
1 m
1 m
1 m
1 e m2 cell
1 cell m
3

qSW rrs,l Rrs,l h wz,l Kl aT,l bT,l bb,l ul

al

n

determine photosynthesis in the biogeochemical model, including the effect of packaging of pigments within cells. Secondly, the dynamic chlorophyll concentration modelled in the biogeochemical model can be explicitly included in the calculation of phytoplankton absorption (Baird et al., 2013). Thus the absorption of a population of n cell m
3 is given by na m
1, while an individual cell absorbs aEo light, where Eo is the scalar irradiance. 2.1.1.2. Coloured dissolved organic matter (CDOM) absorption. The absorption of CDOM, aCDOM,l, is determined from a relationship with salinity in the region (Schroeder et al., 2012a):

aCDOM;443 ¼
0:0332S þ 1:2336

aCDOM;l ¼ aCDOM;443 expð
SCDOM ðl
443:0ÞÞ

(3)

where SCDOM ¼ 0.012 nm
1 is an approximate spectral slope for CDOM, with observations in the GBR ranging from 0.01 to 0.02 nm
1 for significant concentrations of CDOM. Lower spectral slope values generally occur at high concentrations of CDOM (Blondeau-Patissier et al., 2009) due to a greater influence of terrestrial-sourced organic matter.

5 a 0.50

Table 3 State and derived variables in the water column optical model.

Downwelling irradiance at wavelength l Scalar irradiance at wavelength l In-water azimuth angle Sub-surface remote-sensing reflectance Above-surface remote-sensing reflectance Thickness of model layer Optical depth weighting function Vertical attenuation coefficient Total absorption coefficient Total scattering coefficient Backscattering coefficient Fraction bb,l/(aT,l þ bb,l) Absorption cross-section Concentration of cells

salinity and 36. In some cases coastal salinities exceed 36 due to evaporation. The absorption due to CDOM at other wavelengths is calculated using a CDOM spectral slope for the region (BlondeauPatissier et al., 2009):

(2)

2.1.1.3. Absorption due to non-algal particulate material. In the model, optically-significant non-algal particulates (NAPs) include mineral particulates and detritus, with NAP absorption given by:

aNAP;l ¼ c1 NAP c2

(4)

where c1 and c2 are spectrally-resolved coefficients determined from in-situ observations in Gladstone Harbour at times when absorption was dominated by particles (Babcock et al., 2015). Spectrally-resolved values for c1 and a value of c2 ¼ 1 for all wavelengths was used (Fig. 2). The concentrations of NAPs, NAP, is given by:

 NAP ¼ Mud þ FineSed þ   106

550 12 106 12 D þ D þ DC 30 14 Atk 16 14 Red



(5) where NAP, Mud and FineSed are all quantified in kg m
3, DAtk and DRed are quantified in mg N m
3 and DC is quantified in mg C m
3. The conversion of dissolved and detritial carbon to mass is assumed to be 1:1, with carbon dominating the mass of detritus. 2.1.1.4. Total absorption. The total absorption, aT,l, is given by:

aT;l ¼ aw;l þ aNAP;l þ aCDOM;l þ

N X

nx ax;l

(6)

x¼1

where S is the salinity. In order to avoid unrealistic extrapolation, the salinity used in this relationship is the minimum of the model

where aw,l is pure seawater absorption (Fig. 1) and N is the number

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M.E. Baird et al. / Environmental Modelling & Software 78 (2016) 79e96

Fig. 1. Spectrally-resolved energy distribution of sunlight, pure seawater absorption, pure seawater scattering (Smith and Baker, 1981) and pigment-specific absorbance of Chl a and photosynthetic carotenoids (Ficek et al., 2004). The fraction of solar radiation between 400 and 700 nm for clear sky irradiance at the particular spectral resolution is given in the top left panel. The centre of each waveband used in the model simulations is identified by a cross on each curve, with values at 290 310 330 350 370 390 410 430 440 450 470 490 510 530 550 570 590 610 630 650 670 690 710 and 800 nm. The IOP curves include extrapolation to 300 nm and 800 nm. The light below 400 nm contributes a small fraction to the absorption of light by phytoplankton, and therefore photosynthesis, but does not impact on the AOPs used in this paper, as they are only calculated at 412 nm and above.

bT;l ¼ bw;l þ c3 NAP c4 þ bphy;l

N X

nx ci;x Vx

(7)

x¼1

where NAP is the concentration of non-algal particulates, bw,l is the scattering coefficient due to pure seawater (Fig. 1), c3 and c4 are two coefficients and phytoplankton scattering is the product of the chlorophyll-specific phytoplankton scattering coefficient, bphy;l , and the water column chlorophyll concentration of all classes, P nx ci;x Vx (where ci is the chlorophyll concentration in the cell, and V is the cell volume). The value for bphy;l is set to 0.2 (mg Chl a m
2)
1 for all wavelengths, a typical value for marine phytoplankton (Kirk, 1994). Similarly to absorption of NAPs, spectrallyresolved values for c3 and a value of c4 ¼ 1 for all wavelengths were based on field observations in Gladstone Harbour at times when absorption was dominated by particles (Babcock et al., 2015) (Fig. 2).

Fig. 2. Spectrally-resolved non-algal particulate (NAP) specific absorption and scattering coefficient, based on data from Gladstone Harbour WIT1 site in September 2013, with measured NAP concentration 33 g m
3, and absorption and attenuation coefficients measured with a Wetlabs acs. Coefficient values are assumed to be constant below 400 nm.

of phytoplankton classes (see Table 2).

2.1.1.5. Scattering. The total scattering coefficient is given by

2.1.2. Apparent optical properties (AOPs) AOPs can be calculated from IOPs and the surface irradiance forcing. The optical model is forced with the downwelling shortwave radiation just above the sea surface, based on remotelysensed cloud fraction observations from an atmospheric forcing product (ACCESS-R, Bureau of Meteorology 6 hourly, 0.11 spatial resolution, reanalysis product) and calculations of top-of-theatmosphere clear sky irradiance and solar angle at 1 hourly time intervals. The downwelling irradiance just above the water interface is split into wavebands using the weighting for top of atmosphere, clear sky irradiance (Fig. 1). Snell's law is used to calculate the

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83

azimuth angle of the mean light path through the water, qsw, as calculated from the atmospheric azimuth angle, qair, and the refraction of light at the air/water interface (Kirk, 1994):

backscattering and absorption coefficients for the whole water column, ul, is:

sinqair ¼ 1:33 sinqsw

ul ¼

(8)

0

Calculation of in-water light field. Given the IOPs determined above, the exact solution for AOPs would require a radiative transfer model (Mobley, 1994), which is too computationallyexpensive for a complex ecosystem model such as developed here. Instead, the in-water light field is solved by using empirical approximations of the relationship between IOPs and AOPs from coastal waters (Kirk, 1991; Mobley, 1994). The vertical attenuation coefficient at wavelength l when considering absorption and scattering, Kl, is given by:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aT;l bT;l 1 þ ðgi þ gii cosqsw Þ Kl ¼ cosqsw aT;l

(10)

where mC is the carbon content of the cells, here in pg cell
1. The total backscatter then becomes:

bb;l ¼ e bw bw;l þ bbphy;l n þ e bb;NAP;l c3 NAP c4

wl;z

(11)

ew , is 0.5, n is the where the backscatter ratio of pure seawater, b concentration of cells, and for particulate matter (NAP, detritus, microalgae), e bb;NAP;l , is variable (Vaillancourt et al., 2004), but takes a value of ~0.02 (Table 4), c3 NAP c4 is described above for total scattering. To account for a greater backscatter ratio, and therefore backscatter, at low wavelengths (Fig. 4 of Vaillancourt et al. (2004)), we linearly increased the backscatter ratio from 0.02 at 555 nm to 0.04 at 470 nm. Above and below 555 nm and 470 nm respectively the backscatter ratio remained constant. To calculat the remote-sensing reflectance at the surface, we need to consider the light returning from multiple depths and the bottom. The ratio of the backscattering coefficient to the sum of

(12)

0 z 1 Z1 Zz0    0  0 1 @ ¼ exp
2Kl;z0 dz
exp
2Kl;z0 dz A z1
z0 0

0

(13)

wl;z

2.1.3. Remote-sensing reflectance In addition to the IOPs calculated above, the calculation of remote-sensing reflectance uses a backscattering coefficient, bb, which has a component due to pure seawater, and a component due to particulates. The particulate component for phytoplankton is strongly related to cell carbon (and therefore cell size) and the number of cells (Vaillancourt et al., 2004):

wl;z0 bb;l;z0 dz0 al;z0 þ bb;l;z0

where wl;z0 is a weighting representing the component of the remote-sensing reflectance due to the absorption and scattering at depth z', and z is the bottom depth. The weighting fraction is given by:

(9)

The term outside the square root quantifies the effect of absorption, where aT,l is the total absorption. The term within the square root of Eq. (9) represents scattering as an extended pathlength through the water column, where gi and gii are empirical constants and take values of 0.402 and 0.180 respectively (Kirk, 1991; Mobley, 1994). The values of gi and gii depend on the average cosine of scattering. For filtered water with scattering only due to water molecules, the values of gi and gii are quite different to natural waters. But for waters ranging from coastal to open ocean, the average cosine of scattering varies by only a small amount (0.86e0.95, Kirk (1991)), and thus uncertainties in gi and gii do not strongly affect Kl. In the biogeochemical model, Kl is used to determine the downwelling and scalar irradiance for the purposes of providing a light field for the photosynthetic processes. As this component of the optical model is not used in this paper, the description is left to Baird et al. (2014).

 R2 ¼ 0:97 bbphy;l ¼ 5  10
15 m1:002 C

Zz

1 ¼ z1
z0

Zz1

  exp
2Kl;z0 dz0

(14)

z0

where Kl is the vertical attenuation coefficient at wavelength l (Eq. (9)), and the factor of 2 accounts for the pathlength of both downwelling and upwelling light. The integral of wl,z to infinite depth is 1. In areas where light reaches the bottom, the integral of wl,z to the bottom is less than one, and benthic reflectance is important (see Sec. 2.1.4). Note that the weighting of the surface expression of an IOP based on twice the vertical attenuation rate has been used in shallow-water semi-analytical reflectance models to consider the relative impact of water column and benthic constituents (Lee et al., 1998) and for considering the surface expression of depth-varying chlorophyll concentration (Moline and
zelin, 2000). Pre The calculation of the vertical attenuation coefficient (Eq. (9)), and its use to weight (Eq. (14)) the effect of the three dimensional IOPs on remote-sensing reflectance (Eq. (12)) represents an approximation of the more complex radiative transfer calculation of remote-sensing reflectance. Nonetheless the above algorithms are computationally cheap, allowing the simulated remote-sensing reflectance fields to be calculated efficiently. The sub-surface remote-sensing reflectance, rrs, is given by:

rrs;l ¼ g0 ul þ g1 u2l

(15)

where g0 ¼ 0.0895 and g1 ¼ 0.1247 are coefficients for the nadirview in oceanic waters that vary with wavelength and other optical properties (Morel, 2002), but can be approximated as constants (Lee et al., 2002). The constants result in a change of units from the unitless u to a per unit of solid angle, sr
1, quantity rrs,l. The above-surface remote-sensing reflectance is given by (Lee et al., 2002):

Rrs;l ¼

0:52rrs;l 1
1:7rrs;l

(16)

2.1.4. Benthic reflectance of macrophytes, benthic microalgae and sediment types In order to calculate the importance of benthic reflectance, the integrated weighting of the water column must be calculated (Sec. 2.1.3), with the remaining component being ascribed to the benthic reflectance. Thus, the weighting of the benthic reflectance as a component of remote-sensing reflectance is given by:

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M.E. Baird et al. / Environmental Modelling & Software 78 (2016) 79e96 Table 4 Constants and parameter values used in the optical model. using an average cosine of scattering of 0.924 (Mobley, 1994). . Constants

Symbol

Value

Chl-specific total scattering coef. of phytoplanktona Azimuth-independent scattering coefficientb Azimuth-dependent scattering coefficientb CDOM-specific absorption coefficient at 443 nmc Spectral slope of CDOM absorptionc Linear surface reflectance coefficientd Quadratic surface reflectance coefficientd Backscatter ratio of non-algal particlese Nitrogen-specific projected area of macroalgaef Nitrogen-specific projected area of Zosterag Nitrogen-specific projected area of Halophilah Nitrogen-specific projected area of coral skeletonsi

bphy gi gii kCDOM;443 SCDOM g0 g1 e bb;NAP

0.2 (mg Chl a m
2)
1 0.402 0.180 0.02 m2 mg C
1 0.012 nm
1 0.0895 0.1247 0.02 1.0 m2 g N
1 1.9 m2 g N
1 1.5 m2 g N
1 2.0 m2 g N
1

a b c d e f g h i

UMA USG USGH UCH

Kirk (1994). Kirk (1991). Blondeau-Patissier et al. (2009). Morel (2002); Brando et al. (2012). Vaillancourt et al. (2004). Generic value. Kemp et al. (1987); Hansen et al. (2000). Vermaat et al. (1995). (Gustafsson et al., 2013).

Fig. 3. Observed end-member benthic reflectance from 400 to 700 nm from Heron Island. Photos of the substrates, and the data, are available in Roelfsema and Phinn (2012). The line colour is calculated from the MODIS true colour algorithm (Gumley et al., 2010), giving the colour of the substrate lit by a spectrally-flat light source. Green algae appears almost black as there is low reflectance across all wavelengths, while sand is the whitest. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

wl;bot ¼ 1


1 zbot

Zzbot

  exp
2Kl;z0 dz0

(17)

0

where Kl is the attenuation coefficient at wavelength l described above. The benthic reflectance between 400 and 700 nm of ~100 substrates have been measured on Heron Island, Coral Sea, Australia (Roelfsema and Phinn (2012); Leiper et al. (2012), Fig. 3) and similar spectra have been measured for muds in the region of the Whitsunday Islands (Fig. 4). When the bottom is composed of mixed communities, the remote-sensing reflectance is weighted by the fraction of the end members substrates (such as sand, mud, coral

Fig. 4. Observed end-member benthic reflectance from terrestrial muds in the region of the Whitsunday Islands. The line colour is calculated from the MODIS true colour algorithm, giving the colour of the substrate lit by a spectrally-flat light source. Benthic reflectance is measured as p [sr sr
1] Lu [W m
2 nm
1 sr
1] divided by Ed [W m
2 nm
1]. The brown spectra with a value at 400 nm of 0.08 sr
1 is the value used in the model simulations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

skeleton etc.) visible from above, with the assumption that the substrates are layered from top to bottom by macroalgae, seagrass (Zostera then Halophila), corals (zooxanthellae then skeleton), benthic microalgae, and then sediments. Zostera and Halophila are representative of functionally distinct shallow-water perennial and deep-water transient species and are also the dominant genera on the GBR. Implicit in this formulation of benthic reflectance is that the scattering of one substrate type (i.e. benthic microalgae) does not contribute to the reflectance of another (i.e. sand). This will hold true if the substrates are spatially segregated on the bottom. In terms of an individual photon, it implies that if it first intercepts substrate A, then it is only scattered or absorbed by A. While this is an approximation (for example, light reflected by sediments may be further scattered by a coral skeleton), secondary scattering is too

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85

complex to consider in this paper.

ubot;l ¼ wl;bot fMA rMA;l þ fSG rSG;l þ fSGH rSGH;l 2.1.4.1. Calculation of benthic reflectance. The fraction of the bottom taken up by a benthic plant (or coral) of biomass B is Aeff ¼ 1
exp(
UBB), where UB is the nitrogen-specific projected area (Table 4), with exp(
UBB) uncovered (Babcock et al., 2015). Thus the fraction of the bottom covered by macroalgae, seagrass (Zostera and Halophila) and corals polyps is given by:

fMA ¼ 1
expð
UMA MAÞ

(18)

fSG ¼ ð1
fMA Þð1
expð
USG SGÞÞ

(19)

fSGH ¼ ð1
fMA
fSG Þð1
expð
USGH SGHÞÞ

(20)

fpolyps ¼ ð1
fMA
fSG
fSGH Þð1
expð
UCH CHÞÞ

(21)

where MA, SG, SGH and CH are the biomass of macroalgae, Zostera, Halophila and corals respectively. Of the fraction of the bottom taken up by the coral polyps, fpolyps, zooxanthellae are first exposed. Assuming the zooxanthellae are horizontally homogeneous, the fraction taken up by the zooxanthellae is given by:



p 2 fzoo ¼ min fpolyps ; pffiffiffi nzoo przoo 2 3

(22)

where pr2 is the projected area of the pffiffiffi cell, nzoo is the concentration of zooxanthellae cells, and p=ð2 3Þ  0:9069 accounts for the maximum packaging of spheres. Thus the zooxanthellae can take up all the polyp area. The fraction, if any, of the exposed polyp area remaining is assumed to be coral skeleton:

fskel ¼ fpolyps
fzoo

(23)

The benthic microalgae overlay the sediments. Following the zooxanthellae calculation above, the fraction taken up by benthic microalgae is given by:

fMPB ¼ min



 p 2 1
fMA
fSG
fSGH
fpolyps ; pffiffiffi nMPB prMPB 2 3 (24)

where rMPB is the radius of the benthic microalgae. Finally, the sediment fractions are assigned relative to their density in the surface sediment layer:

M¼

X ðSand þ Mud þ FineSedÞ

Sand  fSand ¼ 1
fMA
fSG
fSGH
fpolyps
fMPB M

(25)

(26)

bMPB;l bzoo;l þ fskel rskel;l þ fMPB azoo;l þ bb;zoo;l aMPB;l þ bb;MPB;l !

þ fSand rSand;l þ fMud rMud;l þ fFineSed rFineSed;l (29) where the absorption and backscattering are calculated as given in Sec. 2.1.1, and r is the measured benthic reflectance of each end member (Dekker et al., 2011). 2.2. Observed remote-sensing reflectance The simulated remote-sensing reflectance is compared to the observed remote-sensing reflectance from MODIS-Aqua. Accurate atmospheric correction (AC) is a prerequisite for quantitative ocean colour remote-sensing and remains a challenge above optically complex coastal waters due to the difficulty of separating the atmospheric path radiance from the water-leaving radiance. AC is the process of removing the effects of Rayleigh and Mie scattering as well as absorption of atmospheric gases and certain types of aerosols from remotely-sensed imagery. These contributions have to be removed from the imagery to enable multi-temporal image analysis and to obtain the remote-sensing reflectance. In this study we applied an Artificial Neural Network (ANN) approach trained by a radiative transfer model to invert the top of atmosphere (TOA) signal measured by MODIS-Aqua. Aqua is a sunsynchronous polar-orbiting satellite that views sections of the study region up to twice a day with a spectroradiometer recording in the visible and near infra-red. The ANN algorithm was adapted to an approach previously developed for the MEdium Resolution Imaging Spectrometer (MERIS) sensor but on the basis of a different learning algorithm (Schroeder et al., 2007a, b). In contrast to atmospheric correction algorithms based on the Black-Pixel assumption (negligible water-leaving radiance in the nearinfrared (NIR) spectral region >700 nm, Siegel et al. (2000)) - the ANN method applied here does not attempt to decouple atmospheric and oceanic light fields. Rather, it performs the correction directly from the full TOA spectrum. Algorithm performance is described in detail in Goyens et al. (2013) and King et al. (2014). SeaDAS-provided Level-2 flags were used to quality control the observed remote-sensing reflectance and to exclude erroneous and out-of-range pixels. We filtered the data for land and severe sun glint affected pixels, cloud contamination including cloud shadows and rejected pixels with observing and solar zenith angles above 52 and 70 , respectively. For the comparison with model output, the observed remote-sensing reflectance at the centre of the 4 km grid cell is obtained through interpolation from the 1 km observations. 2.3. Simulated true colour

Mud  ¼ 1
fMA
fSG
fSGH
fpolyps
fMPB M

(27)

FineSed  fFineSed ¼ 1
fMA
fSG
fSGH
fpolyps
fMPB M

(28)

fMud

þ fzoo

with the porewaters not being considered optically-significant. Now that the fraction of each bottom type has been calculated, the fraction of backscattering to absorption plus backscattering for the benthic surface as seen just below the surface, ubot,l, is given by:

True colour images can be generated from remote-sensing reflectance in the red, green and blue wavebands. True colour images created using MODIS output are typically generated from wavebands 1, 3 and 4 (645, 470, 555 nm respectively). In this paper, because wavebands 1, 2 and 4 do not have regional atmospheric corrections available, we used the 667, 547 and 488 nm bands for which the ANN atmospheric-corrections were available. It is worth noting that while the observations represent remotely-sensed reflectance measured by a sensor with a response across a

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waveband with a centre wavelength, the simulated remotelysensed reflectance is based on just the centre wavelength. Otherwise, the remotely-sensed and simulated true colour images in this paper have identical processing. The true colour images will look slightly different to those produced by, for example, the NASA SeaDAS software which uses wavebands 1, 3, and 4, and potentially different stretches. We have adopted the processing techniques used to produce MODIS true colour images described in Gumley et al. (2010): true colour image brightness (on a scale of black ¼ 0, white ¼ 1) is adjusted by linearly mapping remote-sensing reflectance at each of the three wavelengths to a brightness that approaches 1 in the brightest of the three bands (see Results). Additionally, a piece-wise linear scaling is used to brighten dark components. Thus, simulated true colour is determined from combining simulated remotesensing reflectance using the techniques developed for processing remotely-sensed true colour. Further processing is undertaken using the CIE (International Commission on Illumination) 1931 colour space at 10 nm resolution. This removes the approximation of using a centre wavelength at just 3 bands. 2.4. Study site The Great Barrier Reef (GBR) stretches 2000 km along the northeast Australian coast, and includes an estimated 3860 reefs. The region (which in this paper extends to 29 S) has been the site of an extensive set of remote and in-situ optical studies (BlondeauPatissier et al., 2009; Schroeder et al., 2012a; Oubelkheir et al., 2006, 2014). These studies have characterised the in-situ properties of the GBR water using spectrally-resolved absorption and scattering observations, showing waters with a range of optical properties varying from sediment-dominated river plumes, CDOM and phytoplankton-dominated shelf waters through to relatively clear marine waters. 2.5. Model configuration This section briefly describes the model configuration (eReefs GBR4 BGC v918), with an emphasis on the optically-significant components. More details on the model grid and hydrodynamic configuration are given in Herzfeld and Gillibrand (2015), Herzfeld (2015) and Schiller et al. (2015). The model is forced using flow and concentrations of dissolved and particulate constituents from 21 rivers along the Queensland coast (north to south: Normanby, Daintree, Barron, combined Mulgrave þ Russell, Johnstone, Tully, Herbert, Haughton, Burdekin, Don, O'Connell, Pioneer, Fitzroy, Burnett, Mary, Calliope, Boyne, Caboolture, Pine, combined Brisbane þ Bremer, and combined Logan þ Albert) and the Fly River in Papua New Guinea (Herzfeld, 2015). To determine river concentrations, sediment and nutrient observations were statistically evaluated over 10 years (Furnas, 2003). Separate analysis was undertaken for wet- (the Fly, and the northern most 6 rivers in Queensland) and dry- (remainder) catchment rivers. Volume-averaged wet season export coefficients based on this observed dataset were derived for wet- and drycatchment river types, and mean flow-weighted concentrations determined. These constant concentrations are multiplied by higher frequency (daily) observed discharge data to calculate the flux of constituents at the river mouths. The eReefs BGC and sediment model has 3 open ocean boundaries. Nutrient concentrations flowing in from the boundaries were obtained from the CSIRO Atlas of Regional Seas (CARS) 2009 climatology (Ridgway and Dunn, 2003) and empirical nutrienttemperature relationships. The initial conditions are specified by

a generalised empirical relationship and scaled nutrient profiles on the model density profile specifying top and bottom water column values from CARS ocean atlas. Surface NO3 is usually low (< 3 mg m
3). In deeper waters nutrient concentrations increase from 0 to 1500 m depth and then remain constant down to the ocean floor (4000 m depth, 500 mg m
3). The initial conditions for most other tracers were not spatially resolved, since observations for the outer reef and Coral Sea are limited temporally and spatially. 3. Results 3.1. Simulated remote-sensing reflectance A hindcast of the coupled model was run from 1 Sep 2010 to near present, producing 3 dimensional distributions of opticallysignificant water column constituents and spatially- and temporally-varying benthic substrates. We use the above-described optical model to produce simulated remote-sensing reflectance from the hindcast biogeochemical output at midday each day. We focus on 2011 as it contained an extremely wet summer (Oubelkheir et al., 2014) and a severe tropical cyclone (Great Barrier Reef Marine Park Authority, 2011). The optical properties of the GBR in 2011 were highly variable, providing a more thorough test of the optical model than would a less extreme year. The mean simulated remote-sensing reflectance, based on 365 midday values for 2011 for each of the 8 MODIS ocean colour bands, was calculated (Fig. 5). For comparison, text on each panel of Fig. 5 gives the remote-sensing reflectance at each wavelength calculated using the optical model for an infinitely deep water column of pure seawater, Rrs,clear. As expected, offshore simulated remote-sensing reflectance at short wavelengths (412, 443 nm) is up to 0.015 sr
1 (compared to a pure seawater value at 412 nm of 0.014 sr
1), and generally decreases at longer wavelengths as the impact of greater absorption by pure seawater reduces reflectance (Fig. 5). At the shorter wavelengths (<600 nm), the shallow outer reefs have anomalously high remote-sensing reflectance (visible as light-blue to red speckles) due to reflection of light from the ocean bottom. At longer wavelengths higher absorption prevents light from reaching the bottom, and no bottom signal is seen in the remotesensing reflectance. High remote-sensing reflectance (up to 0.04 sr
1) is seen in bands from 443 to 667 nm where scattering particles were commonly present in 2011, due to benthic resuspension and river discharges. The effect of CDOM absorption, which has highest concentrations close to the coast, can be seen in reduced remote-sensing reflectance particularly in the 412 and 443 nm bands. The remote-sensing reflectance was observed from 599 MODISAqua swaths in 2011 (not shown). The error in the simulated remote-sensing reflectance was calculated as the midday simulated remote-sensing reflectance minus the observed remote-sensing reflectance of the same day. Along the Queensland coast, MODISAqua orbits occur between 1230 and 1505 h. The 2011 mean mismatch between simulated and observed remote-sensing reflectance, and spatial averages of bias and root mean square (rms) error for each of the 8 MODIS ocean colour bands, are shown in Fig. 6, and tabulated in Table 5. Across all bands the spatially-averaged bias (Table 5, 8th data row) is less than the spatial variability of the observations (Fig. 5). For example, at 531 nm the mean error at any one location over the entire year can be large (
10
2 to 10
2 sr
1) due to, for example, the prediction of persistent phytoplankton blooms when in fact they are rare at that location. In contrast, the spatially-averaged bias is relatively small (
2.9  10
3 sr
1). Thus the optical model does not have large, domain-wide, systematic biases that would obscure

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Fig. 5. Spatially-resolved temporal mean for 2011 of the simulated remote-sensing reflectance at the centre of the 8 MODIS ocean colour bands. For reference, the model calculated remote-sensing reflectance of pure seawater at each band is given. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 5 Spatially- and temporally-averaged mean absolute percent error (MAPE), bias [10
3 sr
1] and root mean square error (RMSE) [10
3 sr
1] statistics for the 8 ocean colour bands in 2011. ANN - in situ: atmospherically-corrected remote-sensing reflectance minus in-situ surface radiometry within ± 3 h in complex coastal waters from European coastal and the GBR (Schroeder et al., 2012b; Goyens et al., 2013); SIM - ANN: simulated remote-sensing reflectance at midday minus observed atmospherically-corrected remotesensing reflectance from MODIS-Aqua on the same day; shelf: depth <200 m; all: domain wide. Region MAPE

RMSE

BIAS

ANN e in situ SIM-ANN SIM-ANN ANN e in situ SIM-ANN SIM-ANN ANN e in situ SIM-ANN SIM-ANN

all shelf all shelf all shelf

412

443

488

531

547

667

678

748

26 52 77 6.1 2.7 2.9
2.9 0.5 0.9

23 41 62 6.5 2.9 3.5
3.1 0.8 1.1

17 19 43 4.8 3.6 5.0
0.7
0.7
1.0

16 12 52 4.6 4.9 6.9 0.7
2.9
4.1

15 13 57 5.0 5.6 7.9
0.2
3.9
5.3

28 10 77 4.0 3.7 4.9
1.9
3.3
4.4

29 98 78 3.8 4.0 5.3
1.8
3.7
4.8

43 119 155 1.5 0.9 1.2 0.7
0.8
1.0

the errors in the biogeochemical model state for which this analysis is being undertaken. However, even averaged over a full year, the mean error in some locations is as large as the signal (e.g. along the northern coast at 531 and 547 nm, Fig. 5). The larger errors are linked to poor skill in the coupled biogeochemical model, and in particular its prediction of total suspended sediments. To analyse the sources of the errors in the biogeochemical model, it is most instructive to look at one time and region in detail.

Fig. 7 shows a comparison of the observed atmosphericallycorrected 1 km, and the simulated 4 km, remote-sensing reflectance at 3 ocean colour bands in the region of the Burdekin River on 25 Jan 2011. The images are falsely-coloured, with intensity ranging between 0 (blue) - 0.03 (red) sr
1 for the 488 and 547 nm bands, and 0e0.01 sr
1 for the 667 nm. The offshore simulated and remotely-sensed reflectances are similar. Along the coast, high reflectance of 470 nm can be seen in shallow waters, except in the

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Fig. 6. Spatially-resolved temporal mean rms error (simulated remote-sensing reflectance at midday minus observed atmospherically-corrected remote-sensing reflectance) for 2011 at the centre of the 8 MODIS ocean colour bands. Within each panel the spatial mean of the rms error of the temporal mean, and the spatially- and temporally-averaged model bias is given. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

high CDOM waters of the Burdekin River plume. The simulated CDOM absorption exceeds that observed resulting in anomalously low simulated reflectance at 470 nm (~0 sr
1) compared to the observations (~0.01 sr
1), and this is repeated at 547 nm. The remote-sensing reflectance at 667 nm is well captured, except for missing peaks slightly downstream of the mouth of the Burdekin River.

3.2. Simulated true colour True colour images can be generated from individual red, green and blue (RGB) wavelengths (see Methods). Fig. 8 is composed by combining the data from the three wavelengths in Fig. 7 in an additive colour model, and brightening the image by a factor of 10 (Fig. 8). The significance of the date chosen is that it is 1 week before TC Yasi impacted the region (Great Barrier Reef Marine Park Authority, 2011), and this image has been analysed in detail by Devlin et al. (2013) and Petus et al. (2014). The large-scale colour features visible on the remotely-sensed image are evident in the simulated image, namely: a deep-blue open-ocean, light-blue coral reefs, and river-derived plume waters that vary from brown to deep green. In agreement to the

findings from the 1-year quantitative analysis on individual wavelengths above, the good representation of broad-scale features demonstrates the optical model is generally capturing the remotesensing reflectance of the region. Thus, model-observation mismatch primarily occurs in locations where the coupled hydrodynamic - biogeochemical model poorly estimates the observed state of optically-significant components. The remotely-sensed true colour image (Fig. 8) shows a plume of brownish green water extending northward from the mouth of the Burdekin River in a series of billows, with the darkest waters in the northern part of the image surrounding Hinchinbrook Island. The simulated image also captures the brownish water at the mouth of the Burdekin River, and darker waters to the north, but the sections of the plume north of the Burdekin River are darker in the model, and extend further offshore. In the region of Hook Reef the model shows light-blue waters, with individual reefs clear in both remotely-sensed and simulated images. Surrounding the reefs, in both observed and simulated images, is a greenish tinge that in the model corresponds to elevated water-column chlorophyll concentrations. In the simulated image, the greenish tinge obscures individual reefs off Dingo Reef, due to a combination of the 4 km model poorly representing depth of individual reefs, and higher

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Fig. 7. Comparison of atmospherically-corrected remotely-sensed 1 km (left) and simulated 4 km (right) remote-sensing reflectance at 488 (top), 547 (middle) and 667 (bottom) nm. The white pixels in the remotely-sensed images are clouds, grey is land. The location of the image is given as a box in Fig. 9.

suspended particulate matter. At the southern extent of the image the model shows a slightly darker coastal region than the observations. The model hindcast produced a biogeochemical state from which a realistic image of true colour was generated. Thus, it is reasonable to assume that the images produced by the simulation during TC Yasi, when clouds obscured the entire region (Great Barrier Reef Marine Park Authority, 2011), give an indication of the scale of the impact of the cyclone on the water clarity of the GBR. Fig. 9 shows the simulated true colour image before, during, and after the cyclone. The coastal waters in the middle of the images show enhanced scattering, a result of the combination of resuspension of sediment and river discharge. The sediments have settled by 8 Feb 2011, but enhanced mixing in deep waters outside the reef has mixed a deep chlorophyll maximum and nutrients to the surface, resulting in some regions of high chlorophyll in the centre of the domain. The response to TC Yasi was dominated by

sediment resuspension, due to the extreme waves, with water clarity returning to pre-cyclone values relatively quickly. In contrast, later in the month (not shown) a larger rainfall event had a longer-lasting impact on coastal waters due to the duration of elevated river flows. Finally, we combine the comparison of simulated and observed true colour and reflectance spectra. Fig. 10 shows both simulated and observed remote-sensing reflectance at the 8 MODIS wavelengths at 4 co-incident points on the 25 Jan 2011, representative of 4 different water types (Types 2, 3, 4 and 6 of Moore et al. (2009), representing a gradient from brown to blue waters). The line colours in Fig. 10 are calculated from the remote-sensing reflectances at 488, 551 and 667 nm, thus similarity in line colour indicates a similarity of the spectra. Close to the Burdekin River the match-up is almost perfect across all wavelengths (Fig. 10, olive green waters). The darker green coastal waters, which are highly influenced by CDOM, diverge, with the simulated spectra (Fig. 10,  ) showing up

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Fig. 8. Comparison of atmospherically-corrected observed 1 km (left) and simulated 4 km (right) true colour images. In order to use observed atmospherically-corrected remotesensing reflectance, the RGB wavelengths used were 667, 551 and 488 nm, and this was done for both simulated and remotely-sensed images. The white pixels in the remotelysensed images are clouds, grey is land. The location of the image is given as a box in Fig. 9, which also shows simulated true colour for the whole model domain on 25 Jan. The pink symbols show the location of spectra plotted in Fig. 10. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 9. Simulated true colour image of the Great Barrier Reef 1 week before (25 Jan) Tropical Cyclone Yasi struck the northeast Australian coastline, the day of impact (2 Feb) and 1 week after (8 Feb). The box shows the model domain on the Australian coastline. The box within the image of 25 Jan shows the region rendered in Fig. 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to 20% greater reflectance than observed at 488, 531 and 547 nm. Offshore of the O'Connell River, above a reef, the simulated (Fig. 10, ) and remotely-sensed (Fig. 10, +) reflectances at all wavelengths are within 0.001 sr
1, although a slight overestimate occurs in the simulated reflectance at 412, 443 and 488 nm. In the blue open-ocean waters the simulated and remotely-sensed reflectance diverge at 412 and 443 nm. The remotely-sensed reflectance is close to the pure seawater values, so the simulation must contain a small over-estimation of quantities of blueattenuating substances. In general the spectra are well

represented in the simulation, leading to natural-looking true colour images (Fig. 8). The simulated true colour images were constructed from remote-sensing reflectances at 488, 551 and 667 nm so that they could be compared directly with atmospherically-corrected observations. To further consider the rendering of true colour images, we produced true colour images using remote-sensing reflectance resolved every 10 nm (Fig. 11). We convert the 10 nm resolved remote-sensing reflectance to a RGB image using the mean human photoreceptor response specified by the Commission

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4. Discussion

Fig. 10. Comparison of atmospherically-corrected remotely-sensed 1 km (,þ,*,symbols with dashed lines) and simulated 4 km (+,,,◊,△ symbols with solid lines) spectra at four different locations on 25 Jan. Line colour is determined using the MODIS true colour algorithm, brightened by a factor of 20. The location of the model and simulated points are given in Fig. 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

A spectrally-resolved optical model has been developed to calculate remote-sensing reflectance from biogeochemical state in order to assess the performance of the biogeochemical model. Thus, the success of this study relies on the optical model being more accurate than the biogeochemical model's ability to predict the distribution and concentration of optically-significant constituents, such that when a mis-match occurs between observed remote-sensing reflectance and simulated remote-sensing reflectance the origin of error lies in the biogeochemical model. Simple inspection of the outputs shows that the largest errors in remotesensing reflectance occur where the model biogeochemical state is poorly predicted. Thus the optical model has achieved its primary goal - to use remote-sensing reflectance as a quantitative measure of the performance of the biogeochemical model. In addition to improved model assessment, model-generated remote-sensing reflectance fields introduce the possibility of implementing data assimilation based on the mismatch between observed and simulated remote-sensing reflectance, as has been undertaken for terrestrial forest canopies (Quaife et al., 2008). Recent studies by Ciavatta et al. (2014) and Shulman et al. (2013) have shown that assimilating the IOPs (diffuse attenuation coefficient at 443 nm and phytoplankton absorption at 488 nm, respectively), outperforms the assimilation of satellite-derived chlorophyll-a (MODIS OC3M). However, there are still many marine biogeochemical data assimilation studies that assimilate satellite chlorophyll products assuming a direct correspondence with model phytoplankton chlorophyll concentrations (Kidston et al., 2013; Xiao and Friedrichs, 2014). As Ciavatta et al. (2014) and Shulman et al. (2013) point out, there are many sources of error in the MODIS OC3 chl-a and this is especially true in complex coastal waters. Therefore, for assimilation purposes, it is desirable to assimilate products that have as few assumptions as possible (e.g. estimates of IOPs have less assumptions than estimates of chlorophyll concentration), and therefore the associated error budget is better understood. By comparing identical observed and model quantities (remote-sensing reflectance at each of the MODIS bands ocean colour and true colour bands), it is anticipated that biogeochemical data assimilation will therefore be more effective. 4.1. Limitations of the optical model

Fig. 11. Simulated true colour using the CIE convention for scaling RGB intensity with human photoreceptor response (Dierssen et al., 2006), obtained from a 10 nm resolution simulated remote-sensing reflectance between 300 and 800 nm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

^ Internationale de l0 Eclairage (1991) ISO/CIE 10527 (Fig. 3 of Dierssen et al. (2006)). Subjectively, using the CIE protocol the CDOM plume in Fig. 11 looks less ’metallic’ or greyish than in Fig. 8, although hue saturation has also occurred, with some pixels appearing grey. The benefit in colour representation using the CIE methods is marginal, and a direct comparison of model-generated CIE true colour with observed true colour is not possible due to limited bands of the MODIS observations. Thus, for comparison with the MODIS sensor at least, we find true colour images based on remote-sensing reflectances at 488, 551 and 667 nm most useful.

While the greatest error in the calculation of remote-sensing reflectance lies in the estimate of the biogeochemical state by the model, it is worth considering the most likely source of errors in the optical model itself. The semi-empirical, single-scattering equation used to calculated vertical attenuation (Eq. (9)) does not include directional multiple scattering, or inelastic processes such as fluorescence or Raman scattering. Representing these processes requires a radiative transfer model such as HydroLight (Sequoia Scientific, Inc; background theory in Mobley (1994)). Additionally errors are introduced in the calculation of IOPs. The most significant limitation in the calculation of IOPs is the consideration of only two inorganic particle types, which are given identical optical properties determined from Gladstone Harbour. Gladstone Harbour is in the southern third of the model domain where an intensive optical study was undertaken (Babcock et al., 2015). Sediment optical properties from Gladstone Harbour are likely to be a good representation of river-derived particles, and appear to capture the brown-ish colour of, for example, the Burdekin River plume. However, it is likely that suspended carbonate sediments will appear more white than terrestrial muds. Thus the image of the GBR as TC Yasi passes (Fig. 9), which is dominated in the coastal zone by resuspended particles due to large waves,

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Fig. 12. Palette of true colours from IOP relationships. The true colours are produced from the MODIS algorithm and IOP relationships in Sec. 2.1.1. The centre box is the colour produced by pure seawater absorption and scattering alone. From the centre, moving right is increasing CDOM (as quantified by salinity), down is increasing NAP, and left and up are increasing chlorophyll in cells package by 0.35 and 0.73 respectively. The line contours in the top left panel are 0.5, 1, 1.5 and 2 mg Chl m
3. Note that packaged chlorophyll is not plotted with NAP and unpackaged is not plotted with CDOM. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

shows a long light brown strip, whereas it is likely that in reality this strip was more light-blue in appearance. Another significant limitation in the optical model is the consideration of CDOM absorption. The biogeochemical model only resolves the effect of terrestrially-derived CDOM. Furthermore, we have chosen to use a constant CDOM absorption/salinity relationship (Eq. (2)). Thus CDOM absorption is decoupled from any dissolved organic matter fluctuations that are not captured by freshwater/open ocean mixing. Other optical modellers have used a relationship between CDOM absorption and dissolved organic matter concentrations (Dutkiewicz et al., 2015). While this is relatively simple for the open-ocean, the multiple sources of CDOM, and the optical complexity of the waters, made such an approach difficult for the GBR region, and we have therefore left this to future work. Finally, the calculation of backscatter is inherently difficult due to the differing backscatter ratios of various phytoplankton types (Whitmire et al., 2012). Further, we assumed a linear relationship between scattering (both total and backscatter) and concentration of NAP, based on limited observations from Gladstone Harbour (Babcock et al., 2015) in our model domain, when others find a nonlinear relationship in different regions (Antoine et al., 2011). Thus, uncertainty in backscatter values, an important component of the optical-depth weighted reflectance calculations, are a limitation on the prediction of remote-sensing reflectance. 4.2. Comparison of simulated and remotely-sensed errors The observed remote-sensing reflectance contains errors,

primarily due to errors in atmospheric correction, which are given in Table 5 for the ANN algorithm in coastal waters. Unfortunately the errors in the ANN algorithm have been quantified for locations and time periods outside the simulation domain. Nonetheless, the error estimates can be assumed to be typical of coastal waters. It is to be expected that the estimated error in the simulated remote-sensing reflectance (SIM-ANN in Table 5), root mean square error (RMSE) and percentage error (MAPE), will be greater than the ANN algorithm alone, since the error estimates contain the errors of the ANN algorithm. But should the errors be similar, then the optical model is performing at least as well as can be achieved. Domain-wide (which is about 75% water > 200 m depth) the RMS errors (SIM-ANN) are actually less than the coastal estimates of errors in the ANN algorithm. The most likely explanation for this somewhat surprising result is that the estimated errors in the ANN algorithm, based on coastal observations, overestimate the errors in the open ocean. The small errors in the open ocean for SIM-ANN give confidence in the clear water absorption and scattering, and the calculation of remote-sensing reflectance from sub-surface reflectance. In the more complex shelf waters, the simulated errors as a percentage of the signal (MAPE) are approximately three times the estimate of the observational error, with the largest errors being in the 412, 667, 678 and 748 nm bands. That is, the observations are sufficiently accurate to quantify real errors in the model biogeochemical state. Obviously this condition is necessary for the observations to be useful for either model assessment or data assimilation. The assessment of the optical model (Eq. (12)) itself, which requires translation of errors in remote-sensing reflectance

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to biogeochemical properties, is left to future work.

4.3. Interpretation of true colour images To aid in the interpretation of true colour images, and as an assessment of the parameterisation of the model, it is possible to produce true colour representations of individual, opticallysignificant components of the models. For the benthic reflectance data given in Figs. 3, 4 and 10 the line colour of benthic substrate end members were calculated using the true colour algorithm applied to the remote-sensing reflectance fields above. Thus we see sand as white (highly reflective across all optical bands, Fig. 3) and mud as brown (Fig. 4). True colour rendering can be further used to interpret mixtures of optically-significant constituents (Figs. 12 and 13). For the values of remote-sensing reflectance for sand and mud from Heron Island (Roelfsema and Phinn, 2012; Leiper et al., 2012), and microalgal optical properties calculated as per Sec. 2.1, a ternary plot can be used to visualise the changes in true colour with sediment composition (Fig. 13). While true colour has many advantages, Fig. 12 shows that different combinations of optically-significant constituents can produce similar colours. A further limitation of true colour images lies in the different rendering systems (i.e. computer screens, printers etc., Dierssen et al. (2006)), and, to some extent, on the eye of the beholder. Published true colour images are often tailored, through, for example, altered brightness, to emphasise the phenomenon being

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considered. Our approach here has been to be use the same processing from remote-sensed reflectance to true colour for both observations and simulations. And to use true colour images as a powerful qualitative tool, leaving the quantitative comparison to remote-sensing reflectance. 4.4. Concluding thoughts The simulated true colour images, constrained using a quantitative assessment with remotely-sensed reflectance fields at multiple bands, provides a new means to view biogeochemical model output. From one true colour image we can comment on the ability of the biogeochemical model to represent circulation, river plumes and sediment resuspension, bottom light quality and benthic reflectance. Simulated true colour images are not falsely coloured, thus do not require a colour map, nor are they 2D as they have a depth of field, being based on reflectance from multiple depths and the bottom. Thus simulated true colour can be considered a photograph of the optical state of the model, and, like observed true colour, a powerful and intuitive visualisation tool. In producing model-generated remote-sensing reflectances, and from these simulated true colour images, this paper has worked towards unifying how ocean colour observations and models can be analysed. For the managers of water quality, such as those managing the GBR, being able to compare exactly two sources of information for the purpose of management decisions should prove to be an important step. For example, present systems for identifying plume extents from observed true colour images (AlvarezRomero et al., 2013) can be applied, without alteration, to simulation outputs. For modellers, the exact comparison improves the robustness of the model assessment, and, it is anticipated, will improve the ability of data assimilation techniques to improve model predictions. Finally, while producing identical model outputs and observations quantities, it is worth emphasising that model and observed remote-sensing reflectances cannot substitute for each other, but remain distinct, independent sources of information whose value is increased by the availability of the other. Acknowledgements

Fig. 13. Modelled true colour for mixed sand, mud and microalgae sediment composition. The number of cells, n, required to fill the fraction without sand and mud, fMPB, is pffiffiffi calculated as n ¼ fMPB =ðp2 r 2 =ð2 3ÞÞ (from Eq. (24)). The ternary plot shows cells of 5 mm radius with two internal concentrations of pigment (and therefore absorption). The generic parameter for the effect of cell pigment concentration on the reflectance is the packaging effect, al =ðpr 2 Þ, which varies between 0 and 1. A value of zero is a transparent cell with no self-shading, and a value of 1 is fully opaque at the specified wavelength. The upward pointing triangles, D, show the effect of cells with a package effect at 470 nm of 0.73, while the downward pointing triangles, V, show the effects of cells with a package effect at 470 nm of 0.35. Sand reflectance is based on observations from Heron Island (Roelfsema and Phinn, 2012), and mud reflectance from the Whitsunday Islands (pers. comm. Janet Anstee). To read the counterclockwise ternary plot: At each point in the triangle the sum of sand, mud and microalgal fractions equals 1. Follow the grid in a SE direction from the sand axis, a NE from the mud axis, and W from the microalgae axis. Thus, the bottom left corner is 100% light yellow sand, the bottom right corner is 100% brown mud, and the top corner is 100% green algal cells. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The model simulations were developed as part of the eReefs project, a public-private collaboration between Australia's leading operational and scientific research agencies, government, and corporate Australia. Atmospherically-corrected MODIS products were sourced from the Integrated Marine Observing System (IMOS) e IMOS is supported by the Australian Government through the National Collaborative Research Infrastructure Strategy and the Super Science Initiative.We thank the many colleagues involved in developing the eReefs model, particularly Mike Herzfeld, John Andrewartha, Philip Gillibrand and Richard Brinkman. Thank you also to Chris Roelfesema, Stuart Phinn and Janet Anstee for providing benthic reflectance data, and Lesley Clementson for determining water column IOPs from Gladstone Harbour. Mark Baird was additionally funded by the CSIRO Wealth from Oceans Flagship, the Gas Industry Social & Environmental Research Alliance (GISERA) and the CSIRO Coastal Carbon Cluster. A Brief description of the modelling system The CSIRO Environmental Modelling Suite (EMS) has been developed over 20 years to model coupled physical, optical, sediment, chemical and biogeochemical processes in marine and estuarine environments (Wild-Allen et al., 2010; Robson et al., 2013; Baird et al., 2014). The model contains 19 opticallysignificant constituents: pure seawater, dissolved organic matter,

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two categories of non-algal particulate matter (detritus), four classes of phytoplankton, two size classes of inorganic particles, three types of benthic plants, coral skeletons and zooxanthellae, benthic microalgae and three types of bottom substrates. Spectral irradiance

Biogeochemical model (water column / porewater) Carbon chemistry Gas (O2,CO2) exchange

Hydrodynamic and wave models

Spectral irradiance

Meteorology

Trichodesmium

Microzooplankton

1 μm phytoplankton

Macrozooplankton

4 μm phytoplankton Benthic microalgae

Labile detritus

(each with N, P, energy and Chl reserves)

(benthic and pelagic sourced)

Refractory detritus (POC, PON, POP)

DIC

DIN

DIP

(NO3 NH4 N2)

River nutrients, par culates and flows

Sediment model

DOC

PIP / IPIP

DON DOP

Coral Host / symbiont (calcifica on and dissolu on)

Seagrass

Macroalgae

Leaves & roots (Halophila / Zostera)

Biogeochemical model (macrophytes) Fig. A.1. Schematic of CSIRO Environmental Modelling Suite, illustrating the model forcing (circulation, waves and meteorology), sediment and carbon chemistry models, and the biogeochemical quantities and processes in the water column, epipelagic and sediment zones.

The hydrodynamic model is a fully three-dimensional finitedifference baroclinic model based on the three dimensional equations of momentum, continuity and conservation of heat and salt, employing the hydrostatic and Boussinesq assumptions (Herzfeld, 2006; Schiller et al., 2015). The equations of motion are discretized on a finite difference stencil corresponding to the Arakawa C grid. In the vertical z-coordinate scheme, there are 47 fixed zlevels. The atmospheric forcing products (wind, pressure, heat fluxes) are supplied by the Bureau of Meteorology (BOM) reanalysis products. A tidal signal was superimposed on the low frequency sea level oscillation provided by BRAN2.3 on the regional grid open boundary. This tidal signal was introduced via a local flux adjustment. The OTIS tidal model was used to generate the tidal signal from amplitude and phase information for 8 constituents. The local grid open boundary was forced with temperature, salinity and velocity (with local flux adjustment) derived from the regional grid. A mass conserving flux-based advection scheme is used to transport biogeochemical tracer. The sediment transport model (Margvelashvili, 2009) is initialised with the observed distribution of 3 classes of sediment. Sediment particles are resuspended whenever the bottom friction exceeds the critical shear stress of resuspension and settle on the seabed otherwise. The bottom friction under combined waves and currents is estimated through the nonlinear bottom boundary layer model (Madsen, 1994). The biogeochemical model is organised into 3 zones: pelagic, epibenthic and sediment. The epibenthic zone overlaps with the lowest pelagic layer and the top sediment layer, sharing the same dissolved and suspended particulate material fields. The sediment is modelled in multiple layers with a thin layer of easily resuspendable material overlying thicker layers of more consolidated sediment.

Dissolved and particulate biogeochemical tracers are advected and diffused throughout the model domain in an identical fashion to temperature and salinity. Additionally, biogeochemical particulate substances sink and are resuspended in the same way as sediment particles. Biogeochemical processes are organized into pelagic processes of phytoplankton and zooplankton growth and mortality, detritus remineralisation and fluxes of dissolved oxygen, nitrogen and phosphorus; epibenthic processes of growth and mortality of macroalgae, seagrass and corals, and sediment based processes of phytoplankton mortality, microphytobenthos growth, detrital remineralisation and fluxes of dissolved substances (Fig. A.1). The biogeochemical model considers four groups of microalgae (small and large phytoplankton, Trichodesmium and microphytobenthos), three macrophytes types (seagrass types corresponding to Zostera and Halophila, macroalgae) and coral communities. Photosynthetic growth is determined by concentrations of dissolved nutrients (nitrogen and phosphate) and photosynthetically active radiation. Autotrophs take up dissolved ammonium, nitrate, phosphate and inorganic carbon. Microalgae incorporate carbon (C), nitrogen (N) and phosphorus (P) at the Redfield ratio (106C:16N:1P, Redfield et al. (1963)) while macrophytes do so at the Atkinson ratio (550C:30N:1P, Atkinson and Smith (1983)). Microalgae contain two pigments (chlorophyll a and an assessory pigment), and have variable carbon:pigment ratios determined using a photoadaptation model (described in Baird et al. (2013)). Micro- and meso-zooplankton graze on small and large phytoplankton respectively, at rates determined by particle encounter rates and maximum ingestion rates. Of the grazed material that is not incorporated into zooplankton biomass, half is released as dissolved and particulate carbon, nitrogen and phosphate, with the remainder forming detritus. Additional detritus accumulates by mortality. Detritus and dissolved organic substances are remineralised into inorganic carbon, nitrogen and phosphate with labile detritus transformed most rapidly (days), refractory detritus slower (months) and dissolved organic material transformed over the longest timescales (years). The production (by photosynthesis) and consumption (by respiration and remineralisation) of dissolved oxygen is also included in the model and depending on prevailing concentrations, facilitates or inhibits the oxidation of ammonia to nitrate and its subsequent denitrification to di-nitrogen gas which is then lost from the system.

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