Sverdrup critical depth and the role of water clarity in Norwegian Coastal Water

The critical depth concept was first recognized by Gran and Braarud (1935). During summer, in the Bay of Fundy, they observed an unexpected no bloom situation. Their interpretation was that high amounts of detritus of terrestrial origin caused too murky water and insufficient light for the tidally mixed phytoplankton. Almost 20 years later, this was elaborated by Sverdrup (1953) into a hypothesis for the initiation of the spring bloom in the North Atlantic Water (NAW) masses. Since then, variations in mixed layer depth have been a key in phytoplankton modelling. As illustrated by the study of Gran and Braarud, variation in the non-phytoplankton light attenuation coefficient is also a key to understand phytoplankton bloom conditions. Due to lack of accurate parameterizations, however, non-phytoplankton light attenuation is often assumed invariant in phytoplankton modelling. Here, I report spatial variation in a proxy for the pre-bloom light attenuation in Norwegian Coastal Water (NCW). It is shown that this variation can be partially accounted for by variations in salinity and dissolved oxygen. The light attenuation coefficient at 440 nm increased by 0.041 and 0.032 m with drops in salinity and dissolved oxygen of 1PSU and 1 ml O2 l , respectively. Consequences for the euphotic depth, Sverdrup critical depth, and the nutricline depth are discussed. I conclude that phytoplankton modelling, particularly across coastal and oceanic waters, such as NCW and NAW, needs to account for variations in the non-phytoplankton light attenuation and that salinity might be a useful proxy for regional parameterizations.


Introduction
Sverdrup's "critical depth" is commonly associated with the initiation of the spring bloom in clear oceanic water.This concept originated, however, from observations made in a murky inshore location, the Bay of Fundy (Gran and Braarud, 1935).There, elevated non-phytoplankton light attenuation, in combination with strong tidal mixing, was likely responsible for a no bloom situation at a time when both nutrients and incoming irradiance were at high levels (Figure 1).Based on a detailed study of phytoplankton and hydrography in the Gulf of Maine and the Bay of Fundy, Gran and Braarud (1935) concluded: "Although our material is insufficient for accurate calculations, we have come to the conclusion that for these reasons the extraordinary turbulence and turbidity conditions of the Bay of Fundy waters are the main factors for limiting their production of phytoplankton.No other explanation could be found, as the surface waters at the least productive seasons, as in June, contain a surplus of nutrient salts, and the zooplankton feeding upon the phytoplankton is not as rich in the Bay of Fundy as in the gulf of Maine".This reasoning was translated (Sverdrup, 1953) into a mathematical expression for the critical depth (Z cr ) that has become a cornerstone, although questioned by some (e.g.Behrenfeld, 2010), in biological oceanography: where, in modern notation, K is the attenuation coefficient for downwelling irradiance, E 0 and E c the average daily (24 h) irradiances, respectively, below the surface and at the compensation depth, i.e. the depth where photosynthetic production equals "all" losses, not just respiration, during a 24-h cycle (see clarification by Chiswell, 2011).From Equation (1), we see that all coefficients in the critical depth formulation are associated with light and that the critical depth is particularly sensitive to variations in K.The frequently used phytoplankton bloom condition of Sverdrup (1953) can be formulated: if there exists a thoroughly mixed top layer of thickness D, D must be shallower than Z cr in order for a bloom to develop.Gran and Braarud (1935) noted that the high turbidity of the Bay of Fundy was due to detritus washed out by rivers at the head of the bay.They refer to an experiment on photosynthesis and respiration indicating that the compensation depth (Z c ) was not deeper than 10 m.If this depth, often equated with the euphotic depth, equals 1% light depth (i.e.Z c ¼ 2ln(0.01)/K), it can be seen that K must have been higher than 0.46 m 21 .This value indicates a critical depth shallower than 50 m, and it seems plausible that the lack of bloom in the Bay of Fundy indeed was in accordance with the critical depth hypothesis, i.e. that the mixed layer depth was deeper than the critical depth.Nevertheless, the observations of Gran and Braarud (1935) emphasize that natural variations in the non-phytoplankton light attenuation are critically important to phytoplankton bloom conditions.Sverdrup (1953) chose an oceanic test location, at Weather Ship M in the Norwegian Sea, with much higher water clarity than the Bay of Fundy.One challenge with this location, however, was the lack of observations of the pre-bloom light attenuation coefficient and Sverdrup had to assume values for this coefficient.Lack of accurate parameterizations of the non-phytoplankton light attenuation coefficient is still a challenge in ecosystem modelling in general as well as in coastal and oceanic areas off Norway (e.g.Schrum et al., 2006;Hjøllo et al., 2012;Samuelsen et al., 2014).
Here, I quantify variations in the pre-bloom light attenuation in water masses along the coast of Norway (Table 1, Figure 2).These water masses spanned salinities from 16.6 to 35.2.Norwegian Coastal Water (NCW) is transported with the Norwegian Coastal Current (NCC) from south to north (Figure 2) along the Norwegian coast (Saetre, 2007).NCW, characterized by salinity ,34.5 (Saetre, 2007), forms a wedge between the coastline and the North Atlantic Water (NAW, salinity .34.5).Both NCW and NAW, which are located below the NCW, extend into the many deep fjords situated along the Norwegian coast on its way towards the Barents Sea.The freshwater content of the NCW originates from the brackish Baltic Sea, the rivers entering the North Sea, and drainage from Norway (Saetre, 2007).Many previous studies have shown that Chromophoric Dissolved Organic Matter (CDOM) of terrestrial origin is an important light absorber in the Baltic Sea, Kattegat, Skagerrak, and Danish coastal waters.This light absorption correlates negatively with salinity (e.g.Højerslev et al., 1996;Stedmon et al., 2000;Kowalczuk et al., 2005), and as also reviewed by Nelson and Siegel (2013), CDOM absorption decreases linearly with increasing salinity if the mixing of offshore and terrestrial end-member water masses is the only process affecting CDOM.Based on this concept, I estimate an empirical model where salinity, but also dissolved oxygen (see below), serve as proxy for the non-phytoplankton NCW light attenuation.

Methods
During the unproductive winter season, locations along the Norwegian coast with bottom depth of several hundred meters (Table 1) contain relatively small amounts of organic and inorganic particles in the water column.Under these conditions, spectrophotometric measurements of light absorption in unfiltered samples have been used as proxy for the light attenuation of downwelling irradiance (Aksnes et al., 2009).A benefit is that measurements can be obtained regardless of sunlight conditions and from large depths.All together, 375 measurements were obtained from 40 different locations along Figure 1.Birth of the critical depth concept.This concept originates from observations in the Bay of Fundy (Gran and Braarud, 1935), a location with high non-phytoplankton light attenuation and consequently a critical depth that might have been shallower than 50 m (see text).Compared with the Gulf of Maine, the Bay of Fundy was characterized by less stability (as indicated by s t ), high nutrients and low oxygen saturation (i.e.low photosynthesis) throughout the water column.Gran and Braarud (1935) concluded that the phytoplankton in Bay of Fundy was limited by tidal mixing below a shallow compensation depth caused by limited light penetration.The observations for Gulf of Maine and Bay of Fundy are from June at station 24A and 37, respectively, and are taken from the tables in Gran and Braarud (1935).the Norwegian coast (Table 1, Figure 2) between 588N and 688N during a cruise with RV "Ha ˚kon Mosby" in the period from 6 November to 16 December 2008.This period of the year was chosen to minimize the effect from phytoplankton on light attenuation.Depending on the bottom depth (Table 1), 6-12 water samples were collected between the surface and 700-m depth with rosette mounted Niskin water collectors attached to a CTD system (Seabird SBE 911).Absorbance on the unfiltered water samples (A un ) was measured at 400,420,440,450,460,480,500, and 550 nm with a spectrophotometer (UV/VIS Spectrometer Lambda 2, Perkin Elmer).Absorbance readings were made for four subsamples placed in a 10-cm quartz cuvette that was acclimatized to room temperature.Distilled freshwater purified with a Millipore Simplicity 185 Water Purification System was used as blank control.As in studies of light absorption (e.g.Højerslev et al., 1996), I calculated a quantity (in units of m 21 ) from the absorbance readings; a un (l) = 2.303A un (l)/0.1,where l is the wavelength.I fitted the exponential function, a un (l) ¼ Ce 2kl , to the observations by log-linear regression (Bricaud et al., 1981).Here, C is a constant and k is the spectral slope factor.Throughout the present study, I use a un at 440 nm, which was obtained by insertion of l ¼ 440 in the estimated regression equations.This wavelength was chosen because it is approximately the midpoint of the waveband peak that most classes of algae have in their photosynthetic action spectrum (Kirk, 2011).Similar to the attenuation of downwelling irradiance, K, the a un measurements are affected by scattering and absorption from potential particles, such as phytoplankton, as well as from dissolved matter of the water samples.Thus, below I avoid to use the notation of absorption (a) and instead use K p to emphasize that the measurements are used as an "approximation" for the attenuation coefficient (K) for downwelling irradiance (at 440 nm), i.e.K ≈ K p ¼ a un (440).This approximation ignores that K is an apparent optical property that depends on the angular distribution of the underwater light field.The ability of the proxy, K p , to predict measured light penetration is tested for a NAW and a NCW location (see below).
Dissolved oxygen was determined from the water samples by a standard Winkler technique, and salinity was obtained from the CTD system simultaneously with the collection of water.Water samples (100 ml) were also filtered through 0.45 mm Sartorius filters, and the filters were frozen for later determination of Chl a by the use of acetone extraction (Holm-Hansen et al., 1965).

Model used in estimation
The chlorophyll concentrations were generally low (see below), but chlorophyll (Chl) will nevertheless affect the proxy for light attenuation K p .I apply the following model: where K non is the non-phytoplankton light attenuation and f (Chl) the attenuation from algal cells (see Table 2 for a summary of symbols).I assume that the water samples of NCW are a mixture of two end-member water masses; oceanic water (NAW) and freshwater (FW).Furthermore, it is assumed that K non is determined by the mixing ratio of the two water masses and the respective nonphytoplankton attenuations, K NAW and K FW , according to: where g and 1 2 g are the fractions of NAW and FW, respectively (as given by salinity, see below).This model is similar to conservative mixing of, e.g.CDOM of two end-member water masses, which gives rise to a negative linear relationship between CDOM absorption and salinity (Aarup et al., 1996;Kowalczuk et al., 2003;Stedmon and Markager, 2003;Nelson and Siegel, 2013).Equation (3) is a simplification since the freshwater sources and their content of persistent light attenuating substances are diverse and include many different riverine inputs to the Baltic Sea, the North Sea, as well as directly to the NCW.The third term of Equation (3), K loc , is introduced to reflect locally produced non-phytoplankton light attenuating substances from heterotrophic activity.Previous oceanic (Yamashita and Tanoue, 2008;Nelson and Siegel, 2013) and fjord (Aksnes et al., 2009) studies suggest that heterotrophic consumption of dissolved oxygen, i.e. apparent oxygen utilization (AOU, Nelson and Siegel, 2013), might serve as proxy for light absorption in some areas.The present study includes hypoxic fjord basins and it is hypothesized that bacterial degradation of particulate organic matter produces local light attenuating DOM in proportion with the removal of dissolved oxygen.Such relationship between light attenuation and AOU is parameterized as follows: for a water mass high in dissolved oxygen (Oxy ¼ Oxy max ), K loc ¼ 0 is assumed.When Oxy , Oxy max , K loc is assumed to increase linearly with the decrease in Oxy, i.e.K loc ¼ (1 2 h)K Oxy¼0 , where h ¼ Oxy/Oxy max and K Oxy¼0 is the hypothetical non-phytoplankton light attenuation of water without dissolved oxygen.Equation (3) then becomes:

Estimation of model parameters
The salinity of the NAW end-member is set equal to the highest salinity (35.2) observed in the present study and the salinity of FWendmember is set to zero.Then, g ¼ Sal/35.2,where Sal is the salinity of the water sample in question.Similarly, Oxy max is set equal to the highest dissolved oxygen concentration in the dataset (7.1 ml l 21 ) and consequently h ¼ Oxy/7.1.The water samples were collected during a period of presumably low biological productivity (November and December), but Chl a was present (average 0.23 and s.d.0.49 mg m 23 ) particularly in the southernmost locations (see the "Results" section).Out of the 375 samples, 324 contained concentrations less than 0.5 mg m 23 and 26 samples had concentrations on the range 1 -3.6 mg m 23 .The effect of chlorophyll on K is known to be nonlinear (Morel and Maritorena, 2001).To keep the number of parameters to be estimated low, however, I assume that the effect of chlorophyll (Chl) on K p is linear and Equation (2) becomes K p ¼ K non + k 3 Chl.Combination with Equation ( 4) and elimination of where k 0 , k 1 , and k 2 are: Estimates of k 0 , k 1 , k 2 , and k 3 were obtained by fitting Equation (5a) to the observations of K p , Sal, Oxy, and Chl.This equation corresponds to a linear multiple regression model and the software Statistica was applied.Estimates of K NAW , K FW , and K Oxy¼0 were obtained by solving Equations ( 5b) -(5d).
Observed and predicted light penetration in pre-bloom NAW and NCW Measurements of underwater irradiance (Trios RAMSES ACC hyperspectral radiometer), salinity, dissolved oxygen, and fluorescence in NCW and NAW were available from two field studies.In the first, measurements were taken at a coastal location (60.418N 5.108E, 9 February 2010) during a cruise with RV "H.Mosby".
The second included measurements from a cruise with RV "G.O.Sars" at a station in the Norwegian Sea (65.038N 0.518W, 7 May 2013).The observed light penetration was compared with that predicted from the proxy, K p .Values for K p as a function of depth were obtained from Equation (5a) by use of observed depth distributions of salinity, dissolved oxygen, and chlorophyll as input.The predicted irradiance, E, as a function of depth (z) was calculated: Here, E 0 is the irradiance just below the surface and s is an integration variable accounting for the observed non-uniform depth distributions of K p (being a function of salinity, dissolved oxygen, and chlorophyll).

Results
The variations in salinity, oxygen, and chlorophyll accounted for 62% (R ¼ 0.79) of the observed variation in the light attenuation proxy, K p , and the statistical effects of all three variables were significant (Figure 3 and Table 3).Increases of 0.041 + 0.003 and 0.032 + 0.004 m 21 in K p are associated with a 1 PSU drop in salinity and a 1 ml l 21 drop in dissolved oxygen, respectively (Table 3).The estimated effect of chlorophyll corresponds to an increase of 0.073 + 0.011 m 21 for an increase of 1 mg Chl a m 23 (Table 3).The estimated non-phytoplankton light attenuation of the freshwater source was K FW ¼ 1.47 + 0.05 m 21 .The corresponding value for the North Atlantic source water was K NAW ¼ 0.03 + 0.07 m 21 .Overall, the observed K p tends to decrease with latitude and depth (Figure 4), and this pattern is also well reflected by the model predicted K p (Figure 5a). Figure 5b -d illustrates how the predicted K p is associated with variations in chlorophyll, salinity, and dissolved oxygen, respectively.Except for the surface water of the southernmost locations, chlorophyll concentrations were generally low and therefore accounted for a small part of the variations in K p in the model (Figure 5b).The variations in salinity accounted for the largest variations in K p (Figure 5c), except for some intermediate and large depths where variations in oxygen, particularly in the south, accounted for the largest part of the variations in K p (Figure 5d).
The derived model was verified by measurements obtained at an NCW and an NAW location (Figure 6).Light penetrations, standardized as the fraction of observed irradiance at 2-m depth, are shown in Figure 6a.The sensitivity of the radiometer allowed irradiance measurements down to 80 m at the NCW location and to 170 m in the clearer NAW location.Linear regression analysis on the ln-transformed irradiances (not shown in Figure 6a) gave attenuation coefficients (K) of 0.182 m 21 (s.e.¼ 0.002, r 2 ¼ 0.99, n ¼ 17) and 0.0600 m 21 (s.e.¼ 0.0007, r 2 ¼ 0.99, n ¼ 22) for the NCW and the NAW location, respectively.
Table 3. Statistical effects of salinity, oxygen, and chlorophyll on K p (440 nm) estimated with multiple regression analysis according to the model in Equation ( 5).
This provides K non values of 0.183 m 21 and 0.054 for the NCW and the NAW location, respectively.The average salinity was 35.12 and 32.55 for NAW (upper 170 m) and NCW (upper 80 m), respectively (Figure 6b).According to the proxy model, 80% of the elevated K non at the NCW location was associated with the lower salinity, whereas the remaining 20% was associated with lower dissolved oxygen at this location (Figure 6c).
The effect of chlorophyll on K has been estimated by Morel and Maritorena (2001) and for 440 nm this effect corresponds to K Chl ¼ 0.11 Chl 0.67 .It should be noted that this expression also includes effects of constituents other than chlorophyll like CDOM produced by algal cells.Subtraction of this effect (insertion of average chlorophyll of the observed profiles in Figure 6d) from the measured K values provides K non values of 0.168 and 0.032 m 21 for the NCW and NAW location, respectively, which is lower than those indicated by the proxy.

Discussion
The present study provides a model to estimate variations in the non-phytoplankton light attenuation in coastal waters of Norway in relation to the variations in salinity and dissolved oxygen.
Because the largest salinity variation is generally found in upper water, salinity appears to be a useful proxy for K non in the euphotic zone.The largest variation in dissolved oxygen is normally found at intermediate and large depths, i.e.where hypoxia is common, and has been applied as proxy for the light conditions in the mesopelagic zone (Aksnes et al., 2009).Salinity has previously been applied as proxy for non-phytoplankton light attenuation in phytoplankton modelling, e.g. in Florida shelf water (Walsh et al., 2003) and in the Gulf of St Lawrence (Mei et al., 2010).These studies report salinity coefficients, which corresponds to k 1 ¼ 20.041 + 0.003 m 21 PSU 21 (Table 3), on the ranges 20.095 to 20.003 (for 443 nm) and 20.02995 to 20.01392 m 21 PSU 21 (for PAR).The present study suggests that salinity also might be a useful proxy for K non in phytoplankton modelling in coastal waters of Norway.Below, I discuss some implications of variation in K non on the euphotic depth, the critical depth, and the nutricline depth spanning a salinity range from 28 to 35 (Figure 7).

Implications of variation in the non-phytoplankton light attenuation of NCW
If the depth of the euphotic zone is defined as the depth where 1% of the surface light penetrates, the euphotic depth of NCW 28 (i.e.salinity is 28) is 98 m shallower than in NAW 35 (14 and112 m, respectively, Figure 7) for a water column devoid of chlorophyll and with a dissolved oxygen concentration of 7 ml l 21 .According to the assumptions underlying Figure 7 (see legend), the deepening of the critical depth associated with a move from NCW 28 to NAW 35 is 427 m (from 61 to 488 m).Note, however, that the actual shoaling in a bloom situation will also be affected by the phytoplankton shading.
Elevated non-phytoplankton attenuation shoals the euphotic zone and consequently also the phytoplankton and nutrient distributions (Urtizberea et al., 2013).This optical effect is strong and can be quantified by the analytical expression for the steady-state nutricline depth (Z n ); Z n ¼ 2ln(cK)/K [Equation (3) in Aksnes et al., 2007], where c is a scaled quantity reflecting biological nutrient uptake rate, vertical transport of the nutrient, and the actual definition of the nutrient concentration at Z n .For c ¼ 0.014 m (Figure 1 in Aksnes et al., 2007), nutricline depths corresponds to 16 and 182 m for the K non values calculated for NCW 28 and NAW 35 , respectively (Figure 7).This calculation is based solely on the change in K non and ignores the effect of phytoplankton self-shading.Nevertheless, it illustrates that spatial variations in K non are likely to have large implications for the vertical distribution of nutrients in NCW during the productive season.
The simple analytical sensitivity analysis in Figure 7 illustrates that the largest variations (in meters) in euphotic depth, critical depth, and nutricline depth are to be expected at salinity variations in the upper range (i.e. between 34 and 35).This is in line with previous sensitivity analyses involving numerical ecosystem models (e.g.Fasham et al., 1990;Urtizberea et al., 2013) showing that the outcome of these models, particularly at small values of K non (i.e.close to pure water), is very sensitive to variation in K non .This can be illustrated by assumptions made by Sverdrup (1953).He assumed values in the range 0.075 -0.10 m 21 for his critical depth estimates for the Norwegian Sea.A value of 0.05 m 21 , which appears realistic for the NAW pre-bloom situation (see above), provides critical depths that are 50 -100% deeper than those indicated by Sverdrup and will, for a given mixed layer depth, indicate earlier spring bloom initiation than in Sverdrup (1953).

Salinity as proxy for non-phytoplankton attenuation in ecological modelling
According to Sarmiento and Gruber (2006) and Fujii et al. (2007), most ecosystem models that have been developed to study the ocean's biogeochemical properties use simple formulations to describe light penetration.In such formulations (Sarmiento and Gruber, 2006), K is often a function of the simulated phytoplankton concentration added to the contribution from clear water (K w ) and non-phytoplankton constituents (K x ), i.e.K ¼ K w + K x + k p P, where k p P is the contribution from phytoplankton (K w + K x here corresponds to K non ).The effect of pure water is often set close to 0.04 m 21 for PAR, while, according to Sarmiento and Gruber (2006), K x is generally ignored.Some ecological modelling studies do include the optical effects (and thereby K x ) of constituents such as CDOM (Bissett et al., 1999;Fujii et al., 2007;Mouw et al., 2012;Alver et al., 2014).A reason why the more advanced bio-optical approaches are underrepresented in ecosystem models is likely due to the difficulty and uncertainties in translating model outputs accurately into optical properties.Given that there exists a robust relationship between non-phytoplankton light attenuation and salinity for certain areas (e.g.Walsh et al., 2003;Mei et al., 2010), salinity proxies for non-phytoplankton attenuation are likely to be useful.This is particularly true if assumption of invariant K non is the alternative.It should be noted, however, that there is no universal relationship between the non-phytoplankton light attenuation and salinity and that Equation (7) has been derived specifically for the pre-bloom situation in Norwegian coastal areas.

Latitudinal variations in non-phytoplankton light attenuation
A large fraction (38%) of the variation in the light attenuation proxy is not accounted for by the variations in salinity, oxygen, and chlorophyll (Table 3 and Figure 3).The measurements were obtained between the surface and 700-m depth along a coastline that spans 2000 km (Table 1).Variation in attenuation properties of the  different freshwater sources along this coastline is likely to have affected the observations, but also variations in the oceanic waters that mix in along the coast.Such effects have not been accounted for in the present analysis and have likely increased the error term of the estimation model.If the distance along the coast from south to north (Table 1) is included ad hoc in Equation (5a), this effect, as well as the other three, becomes statistically significant (p , 10 25 ), and the unexplained fraction drops from 38 to 33%.The distance effect is negative, 20.058 m 21 per 1000 km.This might indicate that the non-phytoplankton light attenuation of the freshwater and/or the oceanic sources drops northward along the coast.This suggestion, however, needs to be addressed in studies where the optical properties of these sources are targeted.

Effects of terrestrial CDOM on non-phytoplankton light attenuation in NCW
CDOM has received increased attention in the last decades due to its role in the global carbon budget, but also because it changes the colour (brownification) and light conditions in rivers and streams (Roulet and Moore, 2006), in lakes (Larsen et al., 2011), and in coastal waters (Branco and Kremer, 2005;Frigstad et al., 2013).Increased amounts of organic carbon in Scandinavian lakes have been related to increased precipitation, warming, and associated changes in the terrestrial vegetation (Larsen et al., 2011).Long-term Secchi depth shoaling off Southern Norway, in the North Sea, and in the Baltic Sea has been reported (Fleming-Lehtinen and Laamanen, 2012;Dupont and Aksnes, 2013) and associated with long-term ecosystem changes (Haraldsson et al., 2012), but it is unclear to what extent this shoaling has been caused by increased phytoplankton or CDOM of terrestrial origin.Predictions based on climate change scenarios suggest future increase in organic carbon in lakes and rivers in Scandinavia (Larsen et al. 2011) and consequently to an increase in the coefficient K FW of the mixing model.In that case, K non increases and is likely to cause shoaling and narrowing of NCW photic zones in the coming years.In the words of Gran and Braarud (1935): "The amount was so considerable that it seemed obvious that the detritus essentially must lower the light supply of subsurface localities"., where E 0 /E c ¼ 20 (see text).K was derived from salinity according to the proxy equation ( 7) where dissolved oxygen was set constant (Oxy ¼ 7 ml l 21 ).

Figure 2 .
Figure 2. The Norwegian Atlantic Current (NWAC) transports saline NAW into the Norwegian Sea, whereas the NCC transports less-saline NCW northwards along the Norwegian coast.The shaded area indicates the area covered by the stations listed in Table1.
21 (ml O 2 l 21 ) 21 20.032 + 0.004 20.27 + 0.03 k 3 m 21 (mg Chl a m 23 ) 21 0.073 + 0.011 0.27 + 0.04 K Oxy¼0 m 21 0.23 + 0.03 K FW m 21 1.47 + 0.05 K NAW m 21 0.03 + 0.07 All effects were statistically significant (p , 10 25 ).The multiple R was 0.79.The b is the regression coefficient that is obtained when all variables are standardized to a mean of 0 and an s.d. of 1.This coefficient compares the relative contribution of each independent variable (salinity, dissolved oxygen, and Chl a) in the prediction of K p .The indicated uncertainties are + standard error.The estimates are based on 375 records where the ranges of the variables were K p 0.03-1.4m 21 (mean 0.18), salinity 16.6-35.2(mean 33.4), chlorophyll 0.0-3.6 mg Chl a m 23 (mean 0.23), and dissolved oxygen 0.1 -7.1 ml l 21 (mean 5.21).(Figure 6c), and fluorescence (Figure 6d) is shown by the lines in Figure 6a.The average of the predicted attenuation coefficients (i.e.K p ) are 0.185 and 0.064 m 21 for NCW (0 -80 m) and NAW (0-170 m), respectively, which are close to the measured values.The fluorescence measurements (Figure 6d) indicate chlorophyll concentrations below 0.05 and 0.22 mg Chl a m 23 at the NCW and the NAW location, respectively.An estimate of the nonphytoplankton attenuation, K non , is obtained by setting Chl ¼ 0 in Equation (5a):

Figure 4 .
Figure 4. Observations of K p at 440 nm as a function of latitude and depth.One observation, K p ¼ 1.38 m 21 (Figure 3), is outside the scale and not shown.

Figure 5 .
Figure 5.The model predicted K p values at 440 nm [Equation (5a), estimated coefficients in Table 3] as a function of latitude and depth (a), and how much of these values that could be accounted for by chlorophyll (b), salinity (c), and dissolved oxygen (d).

Figure 6 .
Figure 6.Observed and model predicted light penetration (a) in NAW (65.038N 0.518W on 7 May 2013) and in NCW (60.418N 5.108W on 9 February 2010).Light penetration is given as a fraction; E(z)/E(2), where E(z) and E(2) are the observed downwelling irradiance at depth z and 2 m, respectively.The model predicted light penetration was obtained by using Equation (5a) (estimated coefficients in Table 3) and the observed distributions of salinity (b), dissolved oxygen (c), and chlorophyll (d).

Figure 7 .
Figure7.Predicted variations in euphotic, nutricline, and critical depth as a function of salinity in a gradient from NCW 28 to NAW 35 .Euphotic depth was calculated according to 2ln(0.01)/K,nutricline depth according to 2ln(0.014K)/K (see text), and critical depth according to Equation (1), where E 0 /E c ¼ 20 (see text).K was derived from salinity according to the proxy equation (7) where dissolved oxygen was set constant (Oxy ¼ 7 ml l 21 ).

Table 1 .
Sampling locations along the Norwegian coast in 2008.

Table 2 .
Symbols used in the text.
D. L. Aksnesg and h by insertion of g ¼ Sal/ 35.2 and h ¼ Oxy/7.1 provide the following model: