Modelling the inﬂuence of light on the biological characteristics of coastal waters

. Light is an important regulator of photo-chemical and photo-biological processes in coastal areas. However, understanding how the atmosphere-ocean interaction drives changes in the amount of light entering coastal waters and how changes in the underwater light environment inﬂuence the biological characteristic of coastal water can be challenging due to the complex oceanographic dynamics of these areas. Here, we empirically describe the seasonal relationships between meteorological and oceanographic variables over a three year period and quantify the effect light have on the productivity of a coastal area off 5 the Otago coast, New Zealand, through the application of an oceanographic-biological model. The model quantiﬁes changes in the production-biomass ratio (PP/B) (i.e. rate of production of organic matter from phytoplankton produced per unit of total organic biomass) using measurements of the underwater attenuation coefﬁcient, particulate organic carbon, chlorophyll-a and sea temperature. The sensitivity of the model to input data was estimated by comparing the PP/B ratio predicted from Chl a concentrations derived from ﬁeld measurements of the attenuation coefﬁcients of PAR light K d ( m − 1 ) and Chl a concentrations 10 derived from remote sensing data of K d ( m − 1 ) . The results presented here indicate a mild increment in solar radiation partially driven by increased wind speeds and reduction of cloud cover, ultimately producing small increments in the amount of solar radiation penetrating the water column, especially during summer. The model formulated, predict important seasonal shifts in the PP/B ratio. These shifts are driven by the rate at which light decays and likely modulated by the frequency of wind speeds that favour increments of the thermoclines depth and an increment of sea surface temperatures in the area. measurements of in situ ( λ ) comprehensive sampling to avoid erroneous measurements. In this obtained K d ( λ ) values during clear sky and sea conditions to minimize the effects of sea state on instrument deployment excessive lateral boat movements), yielded a strong correlation between remote sensing K d (490) and T (490) T( λ ) changed inversely proportional K d ( λ at different wavelengths, and there was a logistic correlation between T and K d that also changed with depths. m was steeper change, minor increments steep T

radiation is at its daily maximum, and when the zenith angle is between 24.6 -38.9°in summer and between 67.1 -75.0°in winter. For each wavelength, raw measurements from the spectroradiometer were calibrated using the following equation: acos · ucos I(λ) (1) 90 Where I(d z ) was the calibrated irradiance at different depths expressed in W m −2 . The variables a cos and u cos were the calibration values provided by the spectroradiometer supplier for each wavelength ( Table S1 in the Supplement), and I(λ) was the raw measured irradiance values for each wavelength between 300 − 700nm. The calibrated underwater light data was used to calculate K d (λ)(m −1 ) and the light transmittance, T (λ)(m −1 ), for each wavelength between 300 − 700nm, at each station between the surface and 5m using the following equations: T (λ) = I(λ 1 ) level of non-linearity, skewness, serial auto-correlation, self-similarity, and the periodicity of each time series. In addition, the seasonal and monthly averaged relationship between meteorological and oceanographic variables were analysed using principal component analysis (PCA) by combining remote sensing and all meteorological with the inferred values of the thermocline and pycnoclines.

Estimation of chlorophyll-a from attenuation coefficients
To derive Chl a concentrations from K d (λ) values, two different attenuation coefficients, K bio and K W (λ) were used following a well established approach to characterize optically complex waters (Morel and Maritorena, 2001;Morel et al., 2007;Giddings et al, 2021) ( Figure 2). K bio , includes the contribution of all biogenic components of the water column, its calculation was approximated by using an χ(λ) coefficient that changes with wavelength and the theoretical exponent e(λ). Both, statistically 155 derived functions described by Mobley (1994) and first used on a bio-optical model given by Morel (1988) to describe optically complex waters with Chl a values < 30 mg m −3 . The approach described χ(λ) and e(λ) function values from 400 to 800 nm.
Thus, values for UV-wavelengths < 400nm were obtained by fitting a third order polynomial model to the regression between χ(λ) and e(λ) (R core team, 2019) (Table B2). Together, equations (6) and (7) were used to estimate Chl a concentration (mg m −3 ) from K d (λ). However, K bio was approximated from in situ measurements of K d (490) following equation (6) 160 thought its relationship with the water decay constant K W . Theoretically, K W represents the spectral values of the diffuse attenuation coefficient of pure sea water. K W was best approximated by its lower values limits, which are expressed by equation (7): Where a W (λ) and b W (λ) represented the absorption and molecular scattering for optically pure sea water. The validity of this formulation has been discussed in detail by Smith and Baker (1981), and values used in this study for K W where those from Smith and Baker (1981) (Table B1). Using equations (6) to (8), the estimation of Chl a from K d (λ) values was obtained as follow: between the ocean surface and 5mt depth. Both models, however, used POC (mg C m −3 ) data from satellite observations to calculate the effect of light on the PP/B ratio following the formulation listed in equations (9) to (11).
With PP being primary production (mg C m −3 ) and B the phytoplankton stock (mg Chl a m −3 ). The terms on the right of the equation represented the light and nutrient limitation: with V mT the temperature dependant maximum growth rate function at light saturation, calculated using equation (10); where α is the initial slope of the production/irradiance curve; I Z (W m˘2) at depth z(m); [N] the nitrogen concentration for New Zealand coastal areas, calculated converting POC data using equation (11); in the two models, to level the amount of input variables between the two models and also due the lack of data for the study area. Therefore, the fix values were based on derived values of Chl a from remote sensing and field obtained data and values reported by other authors (Cloern et al., 1995).
The values form the dimensionless function V mT were calculated following equation (10), where "t" was the in situ temper-195 ature taken from the CTD profiles, "a" was the maximum growth rate at 0 • C set to 0.8 d −1 , and "b" an specific phytoplankton growth parameter set to 1.06 following (Oschilies and Garçon, 1999;Koné et al., 2005).
Because the implementation of the model followed a less complex approach, which its primary focus was to assess the capability to track changes in the PP/B ratio in time, here values of [N] were assumed constant with depth and the calculations of the nutrient concentration were made using surface POC values obtained from remote sensing measurements. The transformation 200 assumed a C:N ratio of (5:6) according to equation (11), where "b" is the molar weight of N.

Seasonal changes in meteorologic-ocean conditions
Maximum surface levels of solar radiation between 11:00 -14:00hrs during the austral summer were between two to three times higher than values during the austral winter when few to no clouds were present. During summer, solar radiation and cloud cover displayed larger daily temporal variability. However, the periods of peak solar radiations during winter were longer compared to summer months (Table 3). For instance, during summer, only 26.5% of the time the sky presented NCD conditions, while the remaining 74% of the time clouds conditions varied from FEW to OVC conditions. As a result, cloud cover produced a significant reduction of the incident solar radiation levels (two-way ANOVA; F (4,2379) = 19.78; p < 0.05).
With OVC conditions decreasing the mean intensity of solar radiation between 34 to 37%. While, SCT produced a reduction 210 21.3% and BKN cloud conditions produced an overall reduction of 34% in solar radiation reaching the surface of the ocean.
In contrast, during winter months, all cloud conditions had significant effects on the total mean values of solar radiation, with OVC conditions reducing solar radiation levels between 55 to 66.4%, an average reduction 1.5 times higher than other clouds conditions (Table 3).
Average atmospheric temperature during the three year period were 10 ± 4.7 ºC higher in summer than in winter and higher 215 temperature were positively associated with an increment of the meridional wind velocity, that pushed important reductions in the amount of clouds during summer months, time of the year when total wind speeds were stronger (summer = 7.68 ± 5.04 kt and winter = 5.15 ± 4.46 kt). Time series analysis of solar radiation showed a small increment of solar radiation during summer months with a mild seasonal component (Table A1), while cloud cover time series show a mild decrease of clouds cover in time (Fig.A1). The Lyapanuv exponent for both time series, which dictated the rate of separation, was similar between 220 solar radiation (∼0.56) and cloud index (∼0.51) time series (Table A1). This suggested the existence of a similar behaviour between cloud cover and solar radiation (Fig.A1).
The oceanographic conditions for the study area followed a trend similar to the atmospherical data, with ocean water temperature higher in summer compared to winter values and salinity values ranging from 34.2-34.6 PSU in summer and 33-34.9 PSU in winter ( Table 3). Observations of remote sensing data and field data showed an increment in time of ocean temperatures 225 (3). However, observations of k d (490) and remote sensing and observations of k d (320) showed opposite trends (Table 3) but a similar coast-offshore gradient with overall higher values of K d closer to the coast (Fig.C5). This gradient was most evident at the beginning and the end of the summer months but was less apparent during winter, when values of Chl a across the study area remained relatively unchanged (Fig.C3).
Results from PCA analysis showed that although values of POC were significatively different during summer compared to 230 winter months (ANOVA, F (1,58) = 4.401; p = 0.04)( Table 3), with concentration generally decreasing with distance from the coast (Fig.C2), the main drivers of differences in the characteristic of the water column are seasonal (Fig.4a). With higher Chl a and K d (490) driving most of the variation in summer (Fig.4b) and higher k d (320) in combination with a shallower halocline driving most of the variation in winter (Fig.4c). For instance, significant differences in mean K d values between summer and winter months (ANOVA, F (1,58) = 4.401; p = 0.04) were found with lower values during winter compared to 235 summer (Table 3). Therefore, more light is able to reach deeper layers of the water column during winter months. Full analysis of the K d from 300 -700 nm showed statistical differences between values of K d at surface and values of K d at 5m depth for all stations (ANOVA, F (11,60) = 2859; p ≤ 0.05) (Fig. 3) and seasonal differences in the K d (300 − 700) between summer and winter (ANOVA, F (1,75) = 134.1; p ≤ 0.05).
wavelengths into deeper waters. These high concentrations result from the predominant wind conditions that create a shallow thermo-and pycnocline, especially during summer months. Ultimately, retaining POM influx from the Clutha river s run-off in shallower layers of the water column.

Modelled
Chlorophyll-a values and K d values.

375
The modelling approach implemented in this study, although based on similar core equations and principles, did not require the use of extensive computational routines, as it can be the case when using other well-established radiative transfer models (Mobley, 2001;Emde et al., 2016). For instance, derived Chl a and modelled K d (λ) values were a function of the absorption and scattering coefficients of pure water, this differed from values previously reported (Barrot, 2006) and change from study to study depending the experimental approach used, which could lead to small differences in results from the model. However, 380 this remains an active area of research in optics and physics. Using these parameters plus others previously described in the methodology section, the model has a consistent behaviour, and modelled parameters have the expected correlations with field measurements. For instance, modelled and field K d values displayed a positive lineal correlation and wavelength-dependent differences in the modelled quantities. As two different approaches were followed, one calculating a K bio , which values depended either on the Chl a concentration or the dimensionless function χ; and the second one, following a theoretical K bio 385 which values were the sum of K w and empirical measurement's of K d . In both cases, a linear relationship was found between both modelled quantities and field K d values.
A similar relationship between modelled values of K d obtained using different parameterizations, and field values of K d has been described by Kim et al. (2015), who found a correlation between (≈ 0.47 to 0.70) depending on the region of the world, and an overall correlation of (≈ 0.02) between Chl a concentrations and K d values. The Chl a values from this study were 390 derived from a function that incorporates field K d measurement, the χ function, and the water decay constant. The derivation of Chl a values from this equation has been empirically proved by Morel and Maritorena (2001) and tested using remote sensing measurements of K d and SeaWIFS reflectance by Barrot (2006). In both cases Chl a decline with increasing attenuation coefficients and different reflectance ratios. Here, the modelled Chl a values were below the maximum values obtained from satellite data but fell within the range reported for the area by other authors (Murphy et al., 2001;Ramadyan, 2017). The 395 approach followed in this study, from which Chl a were derived from field K d values, adds to the evidence that within certain boundaries, it is possible to use remote sensing data to study coastal systems. The complexities and biases involved in the use of remote sensing data solely to this purpose has been extensively discussed in the literature (? Pan and Zimmerman, 2010;Cao et al., 2014;Liang et al., 2019). From this perspective, integrative studies that utilise remote sensing data and field measurements to produce a complementary model approach that fill gaps in data might be an appropriate way of dealing with issues regarding 400 patchiness of remote sensing data in coastal areas.

Biological production to biomass (PP/B) model
No data of PP/B has been previously reported for coastal areas around the Otago Peninsula, which made the validation of our

Appendix A: Atmospheric data analysis
The weather in Otago NZ is highly variable, for this reason we had to first investigate if any weather patterns was observable in 425 the environmental variables. We chose to use time series analysis over the three year period of hourly observations from 2016 to 2018 using the R package "Openair" that uses a non-parametric method to calculate time series trends using a Generalized Additive Model (GAM) to find the linearity in the data. Statistical trends are presented in data table (Table S4).
Appendix B: Relationship between spectral values of K d , field obtained values K d and light transmittance.
We use the specific absorption (a w ) and scattering (b w ) coefficients for pure sea water proposed by Smith and Baker (1998) 430 (Table B2). But first, we needed to know the behaviour of these coefficients in order to accurately parameterize K w , whose values showed an increase with wavelength and differed substantially at wavelengths above 600 nm (Fig. A3) Simultaneously, when comparing field Kd(λ) with modelled K d (λ) values (which is dependent on Kw values), a strong positive lineal correlation was found at all wavelengths ( Fig A4) (See Tables B1 to B3, Appendix B for values of (a w ) and (b w ), and for the values of the functions χ(λ) and e(λ) used to calculate some of the parameters of the model).     Temperature (C) T emp 1h 20km * a, b