The importance of 1.5°C warming for the Great Barrier Reef

Materials and Methods
Downscaling model data. 
Our semi-dynamic downscaling method applies the S2P3-R v2.0 model (Halloran et al., 2021), driven by surface air temperature, winds, air pressure, humidity and net longwave and shortwave radiation, as simulated by the fully coupled global climate models. The atmospheric forcing’s are used in conjunction with high resolution bathymetry (Beaman, 2010) and tidal forcing (Egbert & Erofeeva, 2002) to simulate water column properties in the vertical dimension. The S2P3-R v2.0 model has been applied over the domain 142.0 W, 157.0 E, 30.0 S, 10.0 S from 4-50m water depth, at a 10km horizontal resolution and 2m vertical resolution. We drive the model with surface level atmospheric data from the CMIP6 models, MRI-ESM2-0 (#2) (Adachi et al., 2013), EC-Earth3-Veg (#3) (Döscher et al., 2021), UKESM1-0-LL (#4) (Sellar et al., 2019), CNRM-ESM2-1 (#5) (Séférian et al., 2019), IPSL-ESM2-0 (#6) (Boucher et al., 2020). Sea surface temperature data were output daily from 1950-2100 (inclusive) and masked to contain values just within the Great Barrier Reef Marine Park Authority Boundary (GBRMPA, 2004).

The S2P2-R v2.0 physical component is driven by tides and winds to simulate vertical profiles of temperature, turbulence, and currents. A tidal slope is calculated from M2, S2, N2, O1, and K1 ellipses to then calculate the water’s velocity 1m above the seabed. The bottom stress is calculated as a function of this velocity and a prescribed bottom drag coefficient (Sharples et al., 2006). Wind stress is calculated as a function of the surface drag coefficient, air pressure and wind speed and direction with respect to tides (Smith & Banke, 1975). Mixing profiles are then calculated from these in a turbulence closure scheme as a function vertical density (Canuto et al., 2001). Importantly, temperature is considered the only factor in the density calculation, with salinity variability being considered second order. We would expect this model to fail in areas where 1.) the horizontal controls, i.e. advection, exceed vertical controls, i.e. atmospheric forcing, and 2.) where density variations are strongly dependent on salinity (Halloran et al., 2021; Marsh et al., 2015; Sharples et al., 2006).

Coral stress metrics. 
To calculate coral stress, two metrics were applied to the sea surface temperature output: DHW, and the frequency of severe bleaching years. The DHW values are a potential trigger for coral bleaching and have been strongly correlated to bleaching events in the past (Bozec et al., In press; Hughes et al., 2017; Hughes et al., 2018; Skirving et al., 2020), but do not necessarily provide evidence of coral bleaching. The DHW values were calculated using the National Oceanic and Atmospheric Administration (NOAA) Coral Reef Watch methodology described below (Heron et al., 2014; Skirving et al., 2020). Importantly, prior to the calculation of annual maximum DHW, calendar years were modified to be centred on the austral summer (e.g., August 1, 2014 – July 31, 2015) to avoid double counting severe bleaching events that cross from one calendar year to the next (Skirving et al., 2019). 

Maximum Monthly Mean Climatology
For each grid point, the monthly mean climatology was calculated. The monthly mean is a set of 12 temperature values that represent the average temperature at each point for each month calculated over the period 1985 to 2012, adjusted to 1988.2857. This is the average of the years used in the original NOAA Coral Reef Watch climatology, i.e., 1985–1990 and 1993 (the missing years were originally necessary due to aerosol contamination from the Mt. Pinatubo eruption, modern satellite data now account for this contamination but, the climatology remains adjusted). The daily sea surface temperature values in each month were averaged to produce 12 mean sea surface temperature values for each of the 28 years from 1985 to 2012. Next, a least squares linear regression was applied to each month, e.g., the 28 values for each of the January values were regressed against the years, and the temperature value corresponding to X = 1988.2857 was assigned as the monthly mean value for January for each point separately. This was repeated for each month until each point had a set of 12 monthly mean values, representing the monthly mean climatology. This method maintained a similar monthly mean value to the original Coral Reef Watch climatology while increasing the number of years that contributed to the climatology. (Skirving et al., 2020)

Degree Heating Week Calculation
Using the maximum monthly mean, a warm sea surface temperature anomaly was created called a ‘HotSpot’. The ‘HotSpot’ (Skirving et al., 2020) is calculated by subtracting the maximum monthly mean from daily sea surface temperature values. To select only warm anomalies, all negative values were reset to zero, so ‘HotSpot’ ≥ 0. The DHW product is a daily summation of ‘HotSpot’ values over an 84-day running window which represents the summer duration. Since thermal stress is considered to begin at maximum monthly mean + 1, the DHW is an accumulation of all ‘HotSpot’ values greater than or equal to 1. (Skirving et al., 2020) The median DHW value was then taken annually across the spatial domain for each model in each scenario. Then the median DHW value was further averaged using all models within each scenario resulting in an ensemble mean per scenario. 

Frequency of Severe Bleaching per Decade Calculation
The maximum DHW was extracted for each reef cell, from each year of the 2014-2100 time series (exclusive) for each model and each scenario. For each reef cell, the frequency of severe bleaching (>=8 DHW) was determined over an 11-year moving average giving a near decadal projection. The median frequency value was then taken annually across the spatial domain for all models and scenarios. The timeseries was then averaged using all models within each scenario resulting in an ensemble mean per scenario and scaled to a decade.