Increased utility of the Secchi disk to assess eutrophication in coastal waters with freshwater run-off

Journal of Marine Systems 60 (2006) 19 – 29 www.elsevier.com/locate/jmarsys

Increased utility of the Secchi disk to assess eutrophication in coastal waters with freshwater run-off Carina P. Erlandsson *, Anders Stigebrandt Go¨teborg University, Box 460, SE-405 30 Go¨teborg, Sweden Received 5 May 2005; received in revised form 27 October 2005; accepted 1 December 2005 Available online 19 January 2006

Abstract Changed local supply of nutrients in coastal waters can lead to changed content of phytoplankton. This influences the visibility, and thereby the water quality in the surface layers, which can be observed by e.g., the Secchi disk. However, the translation of Secchi depth observations to plankton content is complicated by the existence of light attenuating matter entering with run-off from land. To increase the utility of Secchi depth measurements to assess local eutrophication in coastal waters, a formula for calculating the Secchi depth in areas influenced by freshwater was developed. The study includes data analysis of Secchi depth, chlorophyll content, wind speed, and freshwater height estimated from salinity at two stations in the Gullmar Fjord in Sweden. The correlation coefficient between calculated and observed Secchi depths at the inner station close to the freshwater source increased from 0.63 using chlorophyll as the only dependent parameter, to 0.75 ( p b 0.001) including the accumulated freshwater in the surface layer from run off, and wind speed. At the outer station close to the mouth of the fjord it increased from 0.68 to 0.70 ( p b 0.001). The correlation between observed and calculated Secchi depth decreased considerably, if the restriction to observations made at sun elevations higher than about 308 above the horizon was relaxed. D 2005 Elsevier B.V. All rights reserved.

1. Introduction There is an environmental pressure on the coastal zone due to different kinds of human exploitation. The environmental response to a certain nutrient load varies among different coastal areas, therefore water quality models also accounting for water exchange, are used to quantify the local response. To be of value in water quality models, indicators used should be relatively easy and inexpensive to measure. In this paper we focus on the visibility of water, which is determined by the transmission of light and can be estimated e.g., through Secchi disk measurements. It is a * Corresponding author. E-mail address: [email protected] (C.P. Erlandsson). 0924-7963/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmarsys.2005.12.001

simple and cheap method used since the 1870s and for those reasons of great interest in the field of water quality. Relations between Secchi depth, Sd, and chlorophyll a, chl a content have been reported and discussed for open sea areas such as the central subtropical Atlantic ocean (e.g., Piazena et al., 2002) and the central subartic Pacific (e.g., Falkowski and Wilson, 1992; Kobari et al., 1999). Secchi depth measurements cannot be used to quantify the exact amount of chl a but give an opportunity to estimate short- and longterm changes of chl a content (Sande´n and Hakansson, 1996; Bjorkman and Smayda, 1998), see also Preisendorfer (1986) for fundamental aspects on the use of the Secchi disk. The clarity of the water column is determined by the vertical distribution of particulate and dissolved light attenuating matter, LAM. Bacterioplankton, phyto-

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plankton, dissolved organic matter (DOM), detritus, marine snow, sediments and the water itself compose the greatest impact on water column colour and clarity (Gordon et al., 1983; Mobley and Stramski, 1997; Stramski and Mobley, 1997). In areas with only small supplies of freshwater LAM (FLAM), changes in water quality as a result of changed local input of nutrients can be estimated from observations and calculations of the local Secchi depth (e.g., Megard and Bergman, 1989). The water quality model FjordEnv (Stigebrandt, 2001) calculates the changed Secchi depth, assuming that all nutrients entering the surface layer are transformed to phytoplankton that can be measured by chl a content. However, in an area where LAM enters with the freshwater, it will contribute to shallower Secchi depth, which impairs the possibility to relate Secchi depths solely to chl a (Megard and Bergman, 1989;

Conversi and McGowan, 1994). An increase of the chl a content caused by increased nutrient input will influence the Secchi depth less in areas with high content of FLAM (Bjorkman and Smayda, 1998; Portielje and Van det Molen, 1999). If one could separate the effects of FLAM and chl a on the Secchi depth readings, one could improve predictions of the environmental response to nutrient loading in areas with substantial supplies of FLAM. Except light attenuating matter in the water, which is our main concern in this paper, there are several other factors affecting the reading of the Secchi depth (Preisendorfer, 1986), but the uncertainty of Secchi disk measurements is relatively small (5–10%) (Preisendorfer, 1986; Megard and Bergman, 1989). The aim of this study was to construct a generally applicable formula for Secchi depth in eutrophicated

Fig. 1. Map of the Gullmar Fjord.

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coastal areas by also accounting for effects of FLAM increasing the vertical attenuation of light. This would increase the utility of Secchi disk measurements to estimate plankton content as a measure of eutrophication. A description of the study area and data used are given first, followed by a short presentation of the theory behind the work. Then the results are presented and discussed, and finally, some conclusions are drawn. More detailed presentations of the optical and freshwater theories used in this paper are given in Appendix A and B. 1.1. Research area The analyses were performed on data from two stations in the Gullmar Fjord, situated at the west coast of Sweden (Fig. 1). The fjord is 28 km long and rather narrow (1–2 km), with a maximum depth of 120 m and a sill depth of 43 m. The waters in the fjord constitute four different water masses. The total mean freshwater input is about 21 m3 s 1 creating a thin (~ 0.5 m), fresh layer. The second layer, extending down to a strong pycnocline at about 15 m, is mainly Kattegat surface water with salinities of 22–31. This water is a mixture of water from the Skagerrak and the Baltic Sea. The water in the third layer, from about 15 m and down to the sill level, and the fourth layer below the sill depth are mainly Skagerrak water with higher salinities than the Kattegat water. The mean residence time of the water above the pycnocline is about 20 days (Arneborg, 2004). The relatively large exchange rates of the layers above sill level and the weak freshwater input result in similar conditions in and outside the fjord. The optic properties of the Kattegat and Skagerrak waters differ as the Kattegat water contains more yellow substances (Pettersson, 1936). The fjord has a primary production typical of temperate waters with a spring bloom triggered by light and a late summer/autumn bloom triggered by entrained nutrients caused by stronger wind mixing than during the summer period. The mean value of the annual gross primary production in the outer part of the fjord for 1985–1996 was 241 gC m 2 (Lindahl et al., 1998). 2. Data Monthly values of Secchi depth, wind speed, chl a, and salinity in the surface water were used from the station Inre Gullmaren in the inner part and from Sla¨ggo¨ in the outer part of the Gullmar Fjord (Fig. 1).

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The station Inre Gullmaren is included in a running monitoring program for the Swedish west coast that started in 1990, while the station Sla¨ggo¨ is included in a local monitoring program for the Gullmar Fjord. We used data from 1990 and onwards at both stations. The analysis of POC and its relationship to chl a is based on monthly data from Inre Gullmaren and Stretudden, situated about 7 km north of the fjord mouth (Fig. 1). 3. Theory A detailed presentation of the theory can be found in Appendix A and B. A short version is given below. The Secchi depth, Sd, is the depth where the sight of a white disk lowered into the water is lost. It may be expressed as a non-dimensional empirical constant, Cs, divided by k (m 1). Sd ¼

Cs k

ð1Þ

The attenuation coefficient of diffusive light, k, depends on the amount of light attenuating matter, LAM, of different origin in the water column, and can be expressed as: k ¼ x1 þ x2 chl a þ kb :

ð2Þ

Here x 1 is the contribution of light attenuating matter supplied by freshwater, FLAM. x 2d chl a is the contribution by particulate organic matter. Particulate organic carbon, POC, includes phytoplankton, zooplankton, other organism and detritus, all affecting the attenuation of light. Of these, phytoplankton, measured as chl a is the only parameter frequently measured in time and space. Observations in the Gullmar Fjord show that, chl a correlates well with POC (Fig. 2a,b). This justifies expressing the POC contribution to LAM by chlorophyll a observations. k b is the bbackgroundQ contribution, which includes, e.g., the attenuation of pure water which equals 0.03 m 1 (e.g., Kirk, 1983). The following expression for Sd is derived (Appendix A) for a case with a thin brackish layer on top of the seawater: Sd ¼

Csoð1 þ x3 W Þ  x1 Hf : x2 chl a þ kb

ð3Þ

Here we have included a dependence upon wind speed, W, with the proportionality constant x 3. The freshwater height, H f in the fjord can be calculated from the vertical salinity profile: Z 0 1 Hf ¼ ðSref  S ð zÞÞdz: ð4Þ Sref refdepth

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Combining Eqs. (3) and (5) we obtain the final expression for Sd: Sd ¼

Csoð1 þ x3 W Þ  x0 exp x2 chl a þ kb

 TT

d

Hf

:

ð6Þ

Advective and dispersive dilution of FLAM affects the Secchi depth via the value of H f. The reduction of FLAM content between the stations is therefore shown in the values of x 1, using Eq. (3). For instance, if x 1 is halved between the two stations, half of the FLAM present at Inre Gullmaren has been reduced through different processes when the freshwater reaches Sla¨ggo¨. 4. Results

Fig. 2. chl a versus POC content at a) Inre Gullmaren and b) Sla¨ggo¨.

Here S ref is the salinity at the reference depth, refdepth, and S(z) is the salinity at depth z. FLAM is often dominated by DOM (Kirk, 1983), and the fate of DOM after entering the marine environment has been studied by others. The visible part of DOM i.e., coloured (chromophoric) DOM (CDOM), decreases due to photo bleaching, sorption and sedimentation (Vodacek et al., 1995; Chen et al., 2002), but also through biological degradation (Moran et al., 2000; Boyd and Osburn, 2004). This suggests that the age of freshwater, T, should affect the amount of FLAM left in the surface layer. Including T, and the time-scale of the reduction of FLAM, T d, one can improve the Secchi depth formula (Eq. (3)) for applications further away from the freshwater source, using the following substitution: x1 ¼ x0 exp

 TT

d

:

ð5Þ

Here x 0 represents x 1 in the inner most part of a fjord. Biological degradation is temperature dependent, but the dominant processes involved in the decrease of FLAM in the fjord are unknown, why T d is assumed to be constant. The lowest content of FLAM is expected in the outer parts of the fjord, where T equals the residence time of the freshwater in the fjord, T f, see Appendix B. The decrease of FLAM may be neglected if T b T d, which results in x 16x 0.

For the calculations of H f, the reference depth was chosen to 5 m, so that the Kattegat water beneath the top layer became the reference water. We estimated k b from measurements of the maximum downward irradiance of light at 480 nm, in the Gullmar Fjord in Jerlov (1951), using the method described in Kirk (1983). Based on kb and the maximum Secchi depth observed in the Gullmar Fjord Cs was calculated to be 1.55, using Eq. (1). Using sets of simultaneous observations of Secchi depth, chl a, wind speed and salinity; x 1, x 2, x 3 were found solving Eq. (3) using the least squares method. Observations show that higher freshwater height corresponds to lower Secchi depth at both stations (Fig. 3a,b). For freshwater heights above 1 m, the Secchi depth never reached deeper than 5.0 m at Inre Gullmaren, while Secchi depths for lower freshwater heights varied to a great extent. The amount of freshwater decreased towards the outer part of the fjord. High chl a content at both Inre Gullmaren and Sla¨ggo¨ corresponds to shallower Secchi depth. The variation in Secchi depth for low content of chl a was high, and shallow Secchi depths were frequent also for low content (Fig. 3c,d). Using data observed during higher sun elevation, here defined as z 308 above the horizon, caused the correlation coefficient between observed and calculated Secchi depth to increase with 0.06 and 0.035 at Sla¨ggo¨ and Inre Gullmaren, respectively. We therefore concluded that the time of observation of Secchi depth is important. Our analyses were for that reason based only on data observed with the sun elevation z 308 above the horizon. With this restriction on sun elevation, the analysis was based on data from April to September. We also excluded one single occasion when H f was

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Fig. 3. Secchi depth versus freshwater height (a) and Secchi depth versus chl a content (c) at Inre Gullmaren. Secchi depth versus freshwater height (b) and Secchi depth versus chl a content (d) at Sla¨ggo¨. Data from Inre Gullmaren are from 1990–2002 and from Sla¨ggo¨ are from 1990–2002.

larger than Sd, as Eq. (3) only applies if H f b Sd (see Appendix A). The mean least square solutions for x 1, x 2 and x 3 in Eq. (3) are shown in Table 1. The numbers of data sets were 60 and 41 at Inre Gullmaren and Sla¨ggo¨, respectively. The mean values are based on 100 runs, each with 90% randomly chosen observations from the two data sets. The standard deviations (std) at Inre Gullmaren were 15%, 4.5%, and 9% for x 1, x 2, and x 3, respectively. This indicates a greater need of more data for accurate determinations of x 1 and x 3 than of x 2, which shows the dominant role of chl a compared Table 1 Mean least square solutions for the attenuation coefficients for FLAM, x 1, plankton, x 2, and wind speed, x 3, estimated from Eq. (3) Station

x1

x2

x3

C. coef. ( p b 0.001)

I. Gullmaren Sla¨ggo¨

0.56 0.27

0.036 0.044

0.036 0.014

0.75 0.70

Also shown are the calculated correlation coefficients between observed and calculated values of Secchi depth for Inre Gullmaren and Sla¨ggo¨ using Eq. (3) with the values shown in the table.

to freshwater and wind speed on the Secchi depth in the fjord. The same pattern of std was found for Sla¨ggo¨. The mean value of x 1 was less in the outer than in the inner part of the fjord, as seen in Table 1. With a freshwater height of 1 m and 2.5 Ag chl a L 1, this difference would result in a Secchi depth of 4.7 m at Inre Gullmaren, and 6.1 m at Sla¨ggo¨. The difference in x 1 was interpreted as a reduction in the amount of FLAM from the inner to the outer part (by 50%). There was a small difference in x 2 between the two stations (Table 1). The spring bloom in the Gullmar Fjord occurs frequently in March, which was not included in the analysis period for the reason explained above in this section. The values of x 2 estimated here, are for that reason more representative for a summer situation with lower content of chl a. The mean value of Cs was expected to be lower (higher) if the wind coefficient, x3, was negative (positive), see Eq. (3). Different negative values of x3 were found at the two stations (Table 1), resulting in a mean value of Cs equal to 1.52.

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The general formula suggested for calculating Secchi depth for a certain place in the Gullmar Fjord, where the freshwater age equals T, is: T

Csoð1  0:02W Þ  0:56e21 Hf Sd ¼ : 0:04 chl a þ 0:11

ð7Þ

Using Eq. (B3), the mean age of the freshwater at Sla¨ggo¨ at the mouth of the fjord, T f was found to be 13.7 days, but is shorter for places further in. T d, was estimated using Eq. (5), and was found to be 21 days. The value of x 0 in Eq. (7) was chosen to be represented by x 1 at Inre Gullmaren (see Table 1) as this station is rather close to the freshwater source (T b T d). A round off mean value of the calculated x 3 shown in Table 1 was used in Eq. (7), as the differences estimated for the two stations did not show any difference in the resulting correlation coefficient. This was also the case with x 2, and a round off mean value of x 2 in Table 1 was applied. Observed and calculated Secchi depths (using Eq. (7)) at both stations are shown in Fig. 4a,b. It can be seen that the formula reproduces the Secchi depth reasonably well but fails to calculate especially greater Secchi depths correctly. The correlation coefficients between observed and calculated Secchi depth at Inre Gullmaren and Sla¨ggo¨ were 0.75 and 0.70 ( p b 0.001), respectively. This should be compared with the correlation coefficients of 0.64 and 0.68 ( p b 0.001) using only chl a, and thus excluding the effect of freshwater

run off and wind speed. The effect of freshwater was largest at Inre Gullmaren, close to the freshwater source, which was expected. The freshwater effect at Sla¨ggo¨, at the mouth of the fjord was rather small as a result of the decrease of FLAM content, but also due to a thinner freshwater layer (Fig. 2b). Eq. (A13) in Appendix A describes Secchi depth in a lake (Hf N Sd). We had observations from August 2003 to test this formula on the lake Ka¨rnsjo¨n, con¨ rekilsa¨lven, tributing with most of the water to the O the major freshwater contributor to the fjord. At this occasion the chl a content was 5.8 Ag chl a l 1 and the Secchi depth was 1.5 m. Using the values of x 0, x 2 and k b from Eq. (7), Eq. (A14) gave a Secchi depth of 1.7 m. The wind was in this case set to zero as we had no information about that. The difference of 0.2 m between the observed and estimated Secchi depth must be considered to be in the uncertainty interval of Secchi depth observations. Estimating x 0 from the other known parameters (x 2, k b, S) results in x 0 equal to 0.69, which is a bit higher than in the inner parts of the fjord. 5. Discussion Preisendorfer (1986) gave the advice of being careful in using Secchi depth measurements to distinguish between inherent optical properties, such as the spectral volume absorption and attenuation function. He con-

Fig. 4. Time plots of data (solid line) and calculated, using Eq. (7) (dotted line) Secchi depth at Inre Gullmaren (a) and Sla¨ggo¨ (b).

C.P. Erlandsson, A. Stigebrandt / Journal of Marine Systems 60 (2006) 19–29

siders bthe problem of how to extract from the disk readings quantitative estimates of certain apparent optical properties of natural watersQ to be the active centre of todayTs research on Secchi disk science. The research displayed in the present paper is completely within this field of research. The effect of wind speed and sun elevation on the uncertainty of Secchi disk observations were investigated by Preisendorfer (1986), and Megard and Bergman (1989). They concluded that the uncertainties due to these and other parameters are small (5–10%). It is not clear if the analyses included the effect of wind speed for low sun elevations (b 308). Our finding that the correlation coefficient increased with 0.06 and 0.035 ( p b 0.001) at Sla¨ggo¨ and Inre Gullmaren with a sun elevation restriction of higher than about 30 degrees, indicates that the elevation of the sun is of importance at low angles. This is supported by the description of the effect of waves on reflection of incident light in Jerlov (1968). Cox and Munk (1956) showed that the effect of wind speed on the reflection of the sun light increases rapidly with decreasing sun elevation (b 308). As many stations are included in monitoring programs, the Secchi depth is generally not observed at noon, but when the ship arrives at the station according to a time table. In areas situated at higher latitudes such as the Gullmar Fjord (588 N), this might be a factor to consider as the sun is below 308 during a large part of the year. The sun elevation is above 308 over the horizon at noon, from the mid of March to the end of September. In the dataset we found several occasions during winters when the observations had been performed even before sun rise, probably using a working light. Due to the sun elevation restriction, we were able to use only 25% of the observations at Sla¨ggo¨ from March to September and 40% at Inre Gullmaren for the same period. For applications of the formula to other areas, Eq. (A14) should give a representative value of x 0 using a known value of the Secchi depth in the freshwater source. Doing so in our case resulted in a higher value than the estimated value at Inre Gullmaren, indicating reduction of FLAM on its way to the sea, and in the area of freshwater discharge. The value of T d, found here is hard to validate, and may be different in other areas, due to different composition of FLAM. Substituting POC with chl a did probably decrease the correlation between observed and calculated Sd, but was a necessary step to increase the utility of the formula as there are many more observations of chl a than of POC content. The validity of the value of x 2 for

25

other areas can be discussed. It cannot be compared to the specific attenuation coefficient for phytoplankton as it is related to the quotient between chl a and POC. Phytoplankton species occurring in the Gullmar Fjord are described in Lindahl (1987). The mean value of x 2 found here is probably valid in areas with phytoplankton communities similar to those found in the Gullmar Fjord. The value of the correlation coefficient between calculated and observed Secchi depth increased including wind speed in the formula at Inre Gullmaren, which had the highest negative value of x 3, indicating decreasing visibility with increasing wind speed. Only a minor increase in the correlation coefficient was found for Sla¨ggo¨ including the effect of the wind. The most plausible explanation of the wind effect we can think of is resuspension of LAM in the inner, shallower parts of the fjord at higher wind speeds. This should give a larger influence in the inner than in the outer part, resulting in different values of x 3 at the two stations. The value of Cs found in this paper fits well with the value estimated by Aure and Stigebrandt (1989), using published data from the Norwegian and the Barents Seas. The relatively short residence time of the surface layer (second layer) in the Gullmar Fjord (20 days) is coupled to an effective transport of water, which evens out the differences in content of the bbackgroundQ matter between the different parts of the fjord. The background attenuation coefficient, k b, should therefore have about the same value at both stations. Jerlov (1951, 1968) has classified marine waters into a number of categories on the basis of the curve of percent transmittance of downward irradiance against wavelength. He recognised three basic types of oceanic water; I, II and III, and nine types of coastal water. The coastal water types should not be valid in the present case, as kb in this paper is a background value excluding the effects of freshwater discharge and phytoplankton (chlorophyll). Our estimated kb fits with oceanic water III, thus representing Kattegat water. Another method determining kb for an area, than that used in this paper, is described in Holmes (1970), where he uses the relation between the beam attenuation and Secchi depth to establish the value of the attenuation coefficient of diffusive light, k b. The content and composition of matter in the surface layer influencing the Secchi depth can in our case possibly be affected by up-welling or down-welling along the coast, as the optic properties of the Kattegat and the Skagerrak waters differs. One might think that

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Fig. 5. POC versus salinity at Inre Gullmaren and Stretudden. Circles indicate winter values (November to February).

such a signal should be found including salinity of the water at 5 m depth, in the formula, as salinity is a good indicator for the different water masses. As seen in Fig. 5a–b, higher content of POC tend to coincide with lower salinity but the picture is scattered and there is no clear relation. However, our analyses (not shown) showed that the salinity need not be included in the formula, suggesting that up-and down-welling along the coast are of little importance to the Secchi depth in the Gullmar Fjord. 6. Conclusions We have derived a formula of the Secchi depth in a fjord, as a function of chlorophyll content, freshwater height and wind speed. The inclusion of freshwater in the formula extends the utility of Secchi depth measurements in assessing eutrophication in coastal waters. The Secchi depths calculated by the formula showed good correlation with observed Secchi depths, excluding occasions when data had been sampled at low sun elevations. The mean value of the plankton coefficient, x 2, found here is suggested to be valid in areas with phytoplankton communities similar to those found in the Gullmar Fjord. The value of the wind coefficient, x 3, for different areas should vary due to the extent of resuspension of sediments during periods with strong wind. The value of T d, the time-scale of reduction of FLAM may also vary between areas due to different compositions of FLAM. It was found that the FLAM content decreased by 50% from the inner to the outer part of the fjord, excluding the effect of dilution. This gave T d equal to 21 days in this particular fjord.

Acknowledgements This work was performed as a part of the EU project ECASA. Data were provided by the Swedish Meteorological and Hydrological Institute (SMHI). Appendix A. Optical theory Based on BeerTs law, Poole and Atkins (1929), proposed that the light intensity, I, in water decreases exponentially with depth. I ð zÞ ¼ I ð0 þ Þexpkz

ðA1Þ

Here I(0+) (Wm 2) is the intensity of light penetrating the sea surface, k (m 1) the diffusive vertical attenuation coefficient and z the depth. The Secchi depth, Sd, is the depth where the sight of a white disk lowered into the water is lost. Using Eq. (A1), the intensity of light falling on the Secchi disk at depth Sd equals. I ðSdÞ ¼ I ð0 þ ÞexpkSd :

ðA2Þ

If all light falling on the disk is reflected, the intensity of the beam from the disk at the sea surface I(0) becomes: I ð0  Þ ¼ I ðSdÞexpaSd :

ðA3Þ

Here a is the beam attenuation coefficient. The ratio between the intensities of the penetrating light and the, from the disk returning light then equals: I ð0  Þ ¼ expðkþaÞSd : I ð0 þ Þ

ðA4Þ

C.P. Erlandsson, A. Stigebrandt / Journal of Marine Systems 60 (2006) 19–29

Eq. (A4) can be written: Sd ¼

CsV kþa

27

Here k 1 = x 1 + x 2d chl a + k b. The light intensity at the Secchi depth level (Sd), equals: ðA5Þ I ðSdÞ ¼ I ðHf Þexpk2 ðSdHf Þ :

ðA10Þ

where CsV ¼  ln

I ð0  Þ I ð0 þ Þ

ðA6Þ

In practice, Cs’ should depend on the sensitivity of the human eye and the amount of bbackgroundQ light coming from other scatters and reflections in the water column and at the sea surface e.g., due to roughening of the sea surface by wind. It is often justified to assume that the beam attenuation is proportional to the diffusive attenuation, see Holmes (1970). One may then write Eq. (A5) in the following way: Sd ¼

Cs : k

Here k 2 = x 2d chl a + k b, since there is no FLAM in the lower sub-layer. Combining Eq. (A9) and (A10) we find that: I ðSdÞ ¼ expk1 Hf expk2 ðSdHf Þ : I ð0 þ Þ Using (A8) we then find that: k1 Hf þ k2 ðSd  Hf Þ ¼ Cs:

ðA7Þ Sd ¼ I ðSdÞ : I ð0 þ Þ

ðA8Þ

Values of Cs have been estimated in different Atlantic waters; from data in the English Channel, Poole and Atkins (1929) found a value of 1.7. The same value was found for the Caribbean region and south of the Bermuda region (Clark, 1941). Holmes (1970) found Cs equal to 1.44 in the turbid waters of Goleta Bay in California. Using published data from the Norwegian and the Barents Seas, Aure and Stigebrandt (1989), estimated Cs to 1.54. The assumption that the beam attenuation is proportional to the diffusive attenuation implies that the Secchi depth can be related to the relative light intensity at the level of the Secchi depth. If Cs = 1.55, for instance, Sd is the depth where the irradiation equals 21% of the surface value, I(0+). The assumption simplifies the derivation below, of a formula for Secchi depth including the presence of POC and freshwater FLAM. FLAM is only contained in the brackish layer which is often shallower than the Secchi depth. Optically, the upper layer may then be thought of as two separate sub layers. In the present application we consider the upper sub layer to consist of pure freshwater of thickness H f, as defined by Eq. (4), and its content of FLAM. The light intensity at depth H f then equals: I ðHf Þ ¼ I ð0 þ Þexpk1 Hf

ðA9Þ

ðA12Þ

Rewriting Eq. (A12) and also letting Cs be a function of wind speed, W, i.e., Cs = Cso(1 + x3W), give us the following equation for the Secchi depth, Sd.

Here Cs = k / (k+a)CsV. Using Eq. (A2) we find that: Cs ¼  ln

ðA11Þ

Csoð1 þ x3 W Þ  x1 Hf : x2 chl a þ kb

ðA13Þ

The assumption that the beam attenuation is proportional to the diffusive attenuation does not weaken our analysis since x 1, x 2, x 3 are estimated from Eq. (A13), by adaptation to data on W, H f, chl a, and Sd, using the least square method. One may note that maximal Sd is obtained when there is no freshwater and chlorophyll and only the background matter attenuates the light. We recall that Eq. (A13) requires that H f b Sd. If the depth of Hf is larger than or equal to Sd, as for example in a freshwater lake, but possibly sometimes also in the sea, the formula above becomes: Sd ¼

Csoð1 þ x3 W Þ : x1 þ x2 chl a þ kb

ðA14Þ

If H f on the right hand side in Eq. (A13) is replaced by Sd, Eq. (A13) becomes identical to Eq. (A14). There is thus a smooth transition in Secchi depth when the freshwater height becomes deeper than the Secchi depth. Appendix B. Freshwater layer theory The residence time (age) of the freshwater layer in a fjord, T f, can be estimated from the spatial mean freshwater height, the surface area of the fjord, A , and the freshwater input, Q f. Tf ¼

Hf A Qf

ðB1Þ

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Under the condition of hydraulic control at the mouth and a passive underlying watermass Stigebrandt (1981) derived the following relationship between H f and Q f: 3

Qf ¼

Hf 2 Bm

pffiffiffiffiffiffiffiffiffiffiffiffiffi gbSref 3

U2

:

ðB2Þ

The empirical constant U is estimated to 4.0 from the spatial mean value of Hf and data of the freshwater flow, Q f. Bm is the fjord width at the mouth, g = 9.81(m s 2) the gravity and b = 8 d 10 4 the linearized contraction coefficient of salt. Eq. (B2) expresses the theoretical relationship between the freshwater height and the freshwater supply. The formula has been tested on Holandsfjord, see Green et al. (2004). In the present paper, Eq. (B2) is used to include the variation of T f, caused by variation in H f. Combining Eqs. (B1) and (B2), the residence time of freshwater in a fjord can be estimated from: 3

Tf ¼

U2 A pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : Bm gbSref Hf

ðB3Þ

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