The deepwater in many areas with restricted water exchange suffers from low oxygen concentrations due to degradation of organic matter. The objective of this study was to investigate how topography may influence the vertical transport, Fc, of particulate organic matter, POM, to the deepwater. A conceptual/analytical model for Fc was developed covering the combination of the three possible sources of POM/nutrients to an enclosed area; the coastal water, local supply, and nutrient rich local deepwater. The mathematical formulation of the conceptual model includes several factors describing to which degree various physical mechanisms in the fjord are influencing Fc. The model consists of submodels for the different sources of POM/nutrients. A one-dimensional process oriented numerical model was used to test the conceptual model. Restricted water exchange with the coastal water led to decreased import of POM and thereby decreased vertical transport, Fc, of coastal POM. The contribution to Fc by local input of nutrients to the surface layer was described by a function of the residence time of the water above sill level, Tsw and the time Tp it takes for POM produced in the surface layer to settle below sill level. The recirculation of POM produced due to basin water renewals was shown to be a function of several factors: The relation between the depth of photic zone, Hp and the sill depth, Ht, the vertical velocity of the rising nutrient rich water mass versus the settling velocity of POM, etc. The results based on the conceptual submodels agreed well with the results from the process oriented numerical model. Methods to identify the trophic state of coastal waters, and also simple models to calculate the effect of a local point source, can be found in literature. However, using the model developed in this paper the effects of nutrient enrichment from different sources can be quantified in a simple and more efficient way than earlier. The model can thus be used to categorise areas with respect to sensitivity to local and large scale eutrophication, which is an important step towards better management and more sustainable exploitation of the coastal zone.
 Increased primary production in the surface layer due to eutrophication may increase the concentration of particulate organic matter (POM) and affect the water quality of the surface layer of the fjord measured by, e.g. chlorophyll a concentrations and the visibility in the water column. At deeper depths, increased vertical transport of POM, Fc, and an increased consumption of oxygen due to degradation of POM may deteriorate the water quality through decreased oxygen concentrations [e.g., Skei et al., 2000; Wu, 2002; Erlandsson et al., 2006]. A review on how our conceptual model of the eutrophication problem has developed is given by Cloern . How different coastal systems respond to changed loads of nutrients is still an important water quality issue. Semienclosed systems such as fjords might be especially sensitive to eutrophication [Wassman, 1991]. The characterizing feature of a fjord is the sill, preventing an efficient exchange of the so-called basin water below sill level. Particulate organic matter, POM, settling from the water above sill level is trapped in the basin water, where it is consumed by various organisms. Intermittent low oxygen concentration and high nutrient concentrations in the basin water are therefore naturally occurring in many fjords [Wassman, 1991].
 Basin water renewals lifting the resident nutrient rich water above sill level end stagnation periods. Uplift of nutrient rich basin water can in some fjords with relatively shallow sills and long residence time be the dominating source of nutrients. An example of a system with strong pelagic-benthic coupling is the Baltic Sea, where the water exchange with the Kattegat is very restricted resulting in a residence time of the water of about thirty years. Therefore Kattegat does not act as an important sink or source of POM/nutrients for the Baltic Sea. The local sources of nutrients dominate this system, i.e. supply by deepwater uplift and freshwater runoff, and the seasonal loss of POM/nutrients from the surface layer is dominated by the vertical transport of POM, Fc [Wulff and Stigebrandt, 1989]. The topography is of significant importance for the flux of carbon and sedimentation in fjords [Farmer and Freeland, 1983; Håkanson et al., 1986; Aure and Stigebrandt, 1989a, 1989b]. If the sill reaches well up in the photic zone, a fraction of the POM produced due to the uplift of nutrients may be produced below sill level. This POM might then be trapped in the fjord. If the sill depth is well below the photic zone on the other hand, the uplifted nutrients may escape to the coastal water without being exposed in the photic zone resulting in a decoupling between the photic zone and deeper parts of the fjord.
 Water quality models are used to predict changes in the environment, such as changed chlorophyll concentrations due to change in nutrient input and changed minimum oxygen concentration due to a changed transport of POM to the basin water [Stigebrandt, 2001; Tett et al., 2003]. Several formulas to estimate the vertical transport Fc of POM have been developed [e.g., Berger and Wefer, 1990; Aure and Stigebrandt, 1990]. The formula by Aure and Stigebrandt  was developed for coastal waters and describes a downward exponential decrease of the flux of organic matter due to pelagic remineralization. They found that Fc in fjords was equal to the vertical transport of POM in the coastal water in systems with short residence time of the surface water, i.e. short compared to the time it takes for organic matter from the surface layer to settle at sill level, Tp. The formula can thereby be applied to compute the transport of coastal POM into the basin water of fjords with short residence time of the surface water [Aure and Stigebrandt, 1990].
 Based on theoretical budgets of POM, Stigebrandt  further developed the formula for Fc, including the effects of local sources of nutrients. Inspired by this work, we are here further developing the conceptual model and we explore the fate of POM also through modelling to increase our understanding of POM dynamics in inshore waters, and to further develop the formula for use in water quality models.
 The paper is organized as follows. A conceptual model of POM dynamics is developed in the second section. The numerical model used to validate the conceptual model is described in Appendix A. The results are presented in the third section, and in the forth and fifth sections we discuss and conclude our results. A list of abbreviations used in this paper is given in the Notation section.
2. Conceptual Model of the Dynamics of Particulate Organic Matter
 The dynamics of POM is sketched in Figure 1. POM in the surface water of an inshore area with concentration c is produced locally or may be imported from the coastal water. The exchange of water between the inshore and coastal areas is determined by external driving forces and topography. A narrower entrance will restrict the exchange of water and POM, and increase the residence time of the surface water in the area, Tsw.
 Possible local sources of nutrients are by freshwater runoff, so-called point sources and in case of a fjord basin water renewals lifting nutrient rich water to the photic zone (Figure 1). POM is removed from the surface water by water exchange with the coastal water and through sedimentation.
 POM in the sea can be measured as particulate organic carbon, POC and includes both living and dead organic matter, with living POM dominating during the productive season. In this paper POM and POC are used synonymously, and POC is equal to the nutrient concentration times the Redfield carbon-nutrient ratio. The most important scope of the model is to estimate the most important sources of POM/nutrients and not the exact amount of input, which allows us to make some useful simplifications. In this simplified model of POM dynamics we do not consider how it is formed, but regard all nutrients entering the photic zone as potential living POM. The nutrient concentrations of the local sources and the coastal water can then be expressed as POM concentrations. The fact that POM can only be produced during the productive season, i.e. when the basic need for light is satisfied, should be considered though, and is here accounted for by the production factors, f5f and f5d. They describe how large part of the nutrients from point/freshwater sources (f5f) and the uplifted nutrients from the local deep water (f5d) that will be available during the productive season. The length of the productive season increases with decreasing latitude and the range of f5f and f5d is typically between 0.5 and 1.0. In this paper f5f and f5d equal one for simplicity. The depth, Hp, of the photic zone can be estimated by e.g. Secchi disc measurements, the depth varies during the productive season but for the analysis in this paper it can be assumed constant. For simplicity we will assume vertical walls in the fjord.
 Steady state dynamics of POM in a fjord can be described by a balance of sources and sinks within the system.
The source terms of POM appear on the left side. (1) the flow of water from the coastal area, Q, with the POM concentration cc, (2) the potential contribution of POM from the freshwater input, f5f · Qf, with the concentration cf, with point sources included, and (3) the potential contribution of POM, cb, due to a nutrient uplift through basin water renewal by new deepwater inflow, Qd. The terms on the right side show the sinks; (4) the export of POM to the coastal water and (5) the POM settling below sill level in the fjord, here wp is the settling velocity. During the time of stagnation, Tstag, nutrients are enriched below the photic zone in the basin water, and are then lifted above sill level during the time of renewal, Tfill. The time Te of a full cycle of water exchange, Tstag + Tfill, can be days or in some fjords many years. Tfill is given by the following expression:
Here Vb is the volume of the basin. Qd is determined by the transport capacity of the entrance and can be assumed to be about equal to Q as described by Stigebrandt . The possibility of recirculation of exported water and POM/nutrients may be important especially in areas where the water exchange is dominated by tidal circulation, even though not consider in this paper. But it is included in the model of water exchange presented by Stigebrandt  which may be used to calculate Q in the conceptual model developed here. The results in the present paper are based on the assumption of a total renewal of the basin water, i.e. that the basin water is lifted just above sill level, but we also briefly discuss the effect on the result when it is not.
 The nutrient concentration expressed as POM, cb, in the basin water below the photic zone at the end of a stagnation period of length Tstag is given by:
The value of cstag gives the mean concentration of POM at sill level during the stagnation period, At the horizontal surface area at sill level and Vp is the volume of the basin water below the photic zone. It can be assumed that the amount of uplifted nutrients is only a fraction, υ (≤1), of the nutrients once transported to the deep water as POM. The remainder, 1 − υ, is retained in the sediment, or in case of nitrogen, transferred to the gas state. Note that υ has different values for phosphorous and nitrogen. The value of υ is local and should then also include potential release of phosphorus from anoxic sediments, which may be important in some places. Values of υ reported in literature are about 0.8 [Hall et al., 1991; Wulff and Stigebrandt, 1989], but should possibly vary between areas. The nutrient concentration below sill level but above the depth of the photic zone can be assumed to be low due to primary production.
2.1. Import of POM From the Coastal Water
 Without a local nutrient source, the coastal water is the only source of POM. The water exchange is in that case the factor influencing the concentration of POM in the inshore area. If the water exchange is restricted, so is the import of POM. Removing the terms describing local contributions by setting Qf = 0 and Qd = 0 in equation (1), a budget for POM emanating from the coastal water can be expressed as:
 Here c has been replaced by ccs, the concentration of coastal POM in the surface layer in the fjord above sill level due to the exchange with the coastal water. As seen in equation (4), the concentration of POM at sill level in the fjord will be less than in the coastal water because of the loss through sedimentation in the fjord. Using equation (4), the vertical transport of coastal POM (gC m−2 s−1) to the basin water in the fjord is:
The vertical transport of POM at sill level in the coastal water is Fc0 = cc · wp. Fcc is generally less than Fc0, but in situations when there are practically no restrictions on the flow and/or the sinking speed wp is very small such that Q ≫ At · wp, Fcc will be close to Fc0.
2.2. Local Supply of Nutrients to the Surface Layer
 Local input of nutrients will contribute to POM in the fjord. For simplicity we assume that the concentration of POM in the coastal water vanishes. Excluding the third term on the left side in equation (1) describing a nutrient uplift by setting Qd = 0 and rearranging, a POM budget in the surface layer above sill level in the fjord due to local input of nutrients by freshwater runoff/point sources results:
This expression assumes well mixed water down to sill level. However, possible freshwater input may together with wind mixing create a fresher, well mixed surface layer above sill level (Figure 2) and an estuarine circulation. The nutrients will remain in the surface layer until utilised through production of POM or flushed out of the fjord. The locally produced POM, cfs, may settle in the fjord and thus contribute to the vertical transport of POM at sill level. But the residence time, Tsw, of the intermediary water between the surface layer and the sill depth must then be sufficiently long to allow POM generated in a thin surface layer to sink down below sill level instead of being flushed out of the fjord. In many places though, Tsw is short compared to the time, Tp, it takes for POM to sink to sill level, and the locally produced POM is then flushed out of the fjord.
 From results based on investigations of 29 Norwegian fjords, Aure and Stigebrandt [1989a, 1989b] concluded in essence that the local primary production did not end up in the basin water of these fjords due to short residence times of the surface waters compared to the sinking time, thus Tsw < Tp. Instead the concentration of POM at sill level was found to be a function of the primary production in the coastal area outside the fjords, as in section 2.1 above. To refine the analysis of this case, we make a partition of the water above sill level, in a surface layer and an intermediary layer (see Figure 2).
 The sources of POM to the surface layer include freshwater input and/or point sources and recirculation of POM from the intermediary layer due to the entrainment flow Qe into the surface layer (see Figure 2). The sinks are loss of POM to the coastal water and sedimentation to the intermediary layer. The only source of POM to the intermediary layer is the sedimentation of POM from the surface layer. The sink terms are loss to the coastal and surface water, cfi Q, and sedimentation out of the intermediary layer at sill depth, cfi · wp · At. An expression for POM in the intermediary layer, cfi due to a local source of nutrients in the surface layer can be found from budgets for POM in the surface and the intermediary layers. We find that:
 The quotient in equation (7) can be rewritten in terms of the time scales Tp and Tsw, and is a water/POM time ratio factor, f3, determining the part of cfs remaining in the fjord after the time Tp:
Equation (7) shows that the concentration of POM at sill level is about equal to the concentration in the surface layer (cfi ≈ cfs) when Q is small, i.e. when Tsw ≫ Tp as shown by equation (8).
 Finally, using equations (7) and (8) and the budgets for POM in the intermediary layers, we may express the transport of POM at sill level due to freshwater input of nutrients.
Here the production factor f5f has been included for completeness. The entrainment flow in the estuarine circulation, Qe can be calculated from conservation of salt and volume. The resulting formula above showing that for Tsw ≪ Tp (f3 ≪ 1), most locally produced POM will leave the fjord before settling in the basin water, agrees with the findings in the Møre and Romsdal area in Norway by Aure and Stigebrandt [1989a, 1989b]. The settling velocity between different species included in POM obviously varies a lot, and the mean settling velocity should be used to estimate Tp. Aure and Stigebrandt [1989a] estimated the mean settling velocity of POM in Møre and Romsdal area to be 1.5 m d−1. A fjord with a sill depth of 30 m would then have Tp equal to 20 days, and if Tsw would equal 10 days only a third (f3 = 0.33) of the locally produced POM would settle in the fjord according to equation (8).
2.3. Deepwater Inflow-Recirculation of POM
 During periods of basin water stagnation, increasing concentrations of nutrients are due to the supplied organic matter being mineralized; see equation (3). Basin water renewals end stagnation periods, lifting the resident nutrient rich water above sill level. The contribution to the vertical transport of POM by the nutrient rich basin water during a full cycle of stagnation and renewal is considered here, with the basin water lifted just above sill level. The analysis in this paper does thus not consider inflow of new basin water larger than the volume of the basin. But the effect of such events compared to the circumstances in our analysis is discussed for each case. Furthermore, the analysis does not consider the possible mixing between old and new basin water that might occur during inflow of new deepwater.
 If the concentration outside the fjord, c0 is assumed to vanish and if the local supply to the surface layer vanishes, i.e. Qf = 0, then the third source term in equation (1), f5d · Qd · cb, describing the POM contribution from nutrient uplift during basin water renewal is balanced by the two sink terms, thus:
Here cb is the concentration of potential POM in the basin water below the depth of the photic zone, defined by equation (3), the water below sill level but above the photic zone is assumed to be depleted of nutrients due to primary production. cba is the concentration of “basin water” POM above sill level in the fjord.
 The steady state description of POM recirculation to the basin water in equation (10) is not very practical since the water exchange occurs during a relatively short time and a time dependent description is called upon. The time, Tfill, it takes for the basin water volume, Vb, to be exchanged is determined by the flow capacity of the mouth, Qd, see equation (2). The total contribution of POM to the basin from basin water renewal, i.e. the recirculation of POM to the basin water can be found integrating the vertical transport of POM across the surface area, Ap, at the depth of the photic zone, Hp, during the time, Tfill plus the mean time, Ta, it takes for all organic matter produced by the uplifted nutrients above sill level to settle at Ht. The maximum height to which POM is lifted above sill level is the depth Ha, defined later in 2.4.3. The total amount of POM sinking back to the basin water equals the total amount of POM that is lifted above sill level minus the amount of POM that is exported to the coastal water, thus:
The first term on the right hand side in equation (11) represents the maximum contribution from the resident nutrient rich basin water. Vp can be either smaller than, or equal to the volume of the basin water, Vb (Figures 3a and 3b). The second term represents that part of the POM originating from the uplift that is flushed out of the fjord. The total amount of potentially available POM (cb · Vp) is a known quantity. Qd is also known, but the concentration of POM in the out flowing water, cba is not known and will vary during the time Tfill + Ta.
 To find out how much of the uplifted POM/nutrients that will return to the fjord basin we make a stepwise development to come up with something more practical than equation (11). The amount of POM left in the fjord due to the deepwater inflow is influenced by three different conditions: (1) the depth of the sill, (2) the speed, w, of the rising old basin water relative to the sinking speed wp of POM, and (3) the residence time above sill level of the uplifted water, in relation to the time it takes for the POM to settle below sill level. To express these three conditions we will develop three factors f6, f1, and f4, varying between zero and one. The depth of the sill may obviously vary from very shallow to far below the photic zone. The velocity of the rising water mass depends on the water exchange in the entrance and the horizontal surface area of the fjord at different depth, where an increasing area at shallower depths will lead to decreasing speed of the lifted water. A water exchange of 1000 m3 s−1 and a mean surface area of 30 km2 would then result in a speed of the old basin water of about 3 m d−1. The residence time of the water above sill level in such fjord with a sill depth of 30 m is about 10 days. In this application we assume vertical walls of the basin though.
 1. The escape factor f6 tells how large part of the nutrients in the old basin water that will be lifted up in the photic zone resulting in production of POM. 1 − f6 is then the part of the nutrients leaving the fjord below the photic zone, not contributing to Fc. Figure 3a shows a fjord with Hp > Ht, where all uplifted nutrients will reach the photic zone during the uplift (f6 = 1), and Figure 3b shows a fjord for which f6 would be below one, allowing nutrients to escape the fjord below the photic zone.
 2. The vertical advection factor f1 tells how large part of the POM produced by the uplift that will remain below sill level, between Ht and Hp (see Figure 3a).
 3. The water/POM time ratio factor, f4 tells how large part of the produced POM lifted above sill level (1 − f1) that will remain in the fjord and not be flushed out by the water exchange.
2.3.1. Effect of the Sill Depth, Ht: Escape Factor f6
 For a maximum potential contribution of POM, Ht should be shallower than the production depth, i.e. nutrients from the basin water can in that case not escape the fjord without passing through the photic zone (Figure 3a). If Ht > Hp some or all nutrients may escape the fjord without being exposed in the photic zone (Figure 3b). To describe this case, we define the sill factor, f6, being equal to one when Ht ≤ Hp. When Ht > Hp (Vp = Vb) and the volume between Hp and Ht is larger than Vp all nutrients are assumed to escape the fjord below the photic zone (f6 = 0). There is a gradual change of f6 between the two extremes.
 In the Introduction we stated that the Baltic Sea is an example of a system with a strong benthic-pelagic coupling and f6 is therefore equal to one for that area, while it would equal zero for an area lacking a benthic-pelagic coupling.
 A larger volume exchanged than that of the basin would in this case make no difference for the result if f6 equals one. In a fjord with 0 ≤ f6 < 1, it would possibly result in that a larger part of the nutrient rich volume was lifted up in the photic zone, and the f6 value would then be higher than the value estimated by equation (12).
2.3.2. Effect of the Velocity of the Rising Water Due to the Deepwater Inflow: Vertical Advection Factor f1
 For a maximum potential contribution of POM, the velocity w of the water mass lifted should be less than the settling velocity, wp, of POM. In that case all POM will sink back into Vp below Hp, see Figure 3a, thus no POM will be lifted above sill level. When the velocity, w, of the lifted water is larger than wp, POM will move upward at a lower velocity, w − wp, than that of the rising water mass, which means that all POM will not be lifted above sill level during the time Tfill, here equal to the time of a complete exchange the basin water.
 The time, Tpt it takes for POM to be lifted from Hp where it is produced to Ht is; Tpt = (Hp − Ht)/(w − wp). The time during which POM is lifted above sill level is then:
 If Tpt ≥ Tfill, all POM will remain in the basin water and Tup = 0. The total amount of POM lifted above sill level during Tup is; Fup = cbVpTup/Tfillp. Tfillp is the time needed for all POM to be lifted above sill level, and it is also the time during which POM is generalized at the level Hp. Tfillp is a function of the height, Hfillp, of the water mass below sill level containing POM as a result of the uplift. This height is smaller than H − Hp due to the different vertical velocity of nutrients (water) and POM. From continuity we obtain the following relationship; Hfillp = (H − Hp)(w − wp)/w, and Tfillp = (H − Hp/w).
 We express the effect of the velocity w upon the transport of POM above sill level with the advection factor, f1, where f1 = 1 if all POM is retained below sill level. f1 is defined as follows:
Note that equation (14) is valid only when the two following conditions are fulfilled: (i) w > wp (if w < wp all POM will remain below sill level and f1 = 1), and (ii) Ht < Hp (if Ht ≥ Hp the nutrients must be lifted up above sill level to be utilized and no POM can therefore be produced below sill level, and f1 = 0). And f1 becomes:
All POM will remain in the basin water if Tup = 0, while some POM is lifted up above sill level if Tup > 0. It should be pointed out that the sill level has to be less than the depth of the productive zone to enable POM to be produced and trapped below sill level (f6 = 1). Summarising the results above, the vertical advection factor f1 may be expressed as follows:
If the exchanged volume is larger than the volume of the basin and w < wp all POM will remain in the fjord no matter of exchanged volume and the analysis above is then correct also in a general sense. If w > wp, Tpt has to be larger than the time of the inflow for all POM to remain below sill level. The expression for f1 in equation (15) was developed for the case when the exact volume of the basin is exchanged. However, it might apply also for larger volumes of exchange, and one may then let Tfill in equation (13) be the actual time of inflow. A longer time of exchange than Tfill, increases Tup, and will decrease the value of f1, see equation (15), i.e. the amount of POM lifted above sill level will increase.
2.3.3. Effect of the Water Exchange on the Part of POM Lifted Above Sill Level: Water/POM Time Ratio Factor f4
 The fate of the part of the produced POM lifted above sill level (1 − f1), depends on the relation between the residence time of the old basin water above sill level after the deepwater inflow, and the time it takes for POM to settle below sill level (the value of f6 must be larger than zero). And can be described by a water/POM time ratio factor, f4, which is similar to f3 developed in section 2.2. The water/POM time ratio factor f3 is defined in equation (8) and depends on the residence time of water Tsw and the time Tp it takes for POM to settle from the sea surface where it is produced to sill level. But in the case of a deepwater exchange, water containing POM may not be lifted all the way to the surface but to the height Ha above Ht, and POM may occupy the whole water column from Ha down to Ht, where we define Ha as; Ha = Tup(w − wp), where Tup is defined by equation (13). We therefore have to define the relevant settling time Ta, which is here taken as the mean time for POM to settle at sill level from the water column of height, Ha, above sill level, thus; Ta = Hawp−1.
 The residence time of the lifted water mass containing the “basin water” POM can be assumed to equal Tsw [see Stigebrandt, 2001]. We therefore suggest that the water/POM time ratio factor f4 in case of a deepwater inflow can be expressed as follows:
Here f4 = 1 when all POM remain in the fjord. This factor is affected if the volume of the exchange exceeds the basin volume. The time Tup, POM is lifted above sill level will in that case increase, see equation (13), resulting in a longer settling time Ta for POM. f4 would then decease for increasing time of inflow larger than Tfill. The part of POM lifted (1 − f1) may also increase as discussed in 2.3.2 above, and both effects work to decrease the amount of POM settling in the fjord.
2.3.4. Summary of the Effect of Deepwater Inflow Upon Nutrient Recirculation
 With both f6 and f1 (equations (12) and (16)) equal to one, all of the potentially available POM (cb · Vb) remains in the fjord below sill level, and nothing is lost permanently to the coastal water or temporarily to the water above sill level. A necessary circumstance for any POM remaining below sill level (f1 > 0) is that the sill depth is shallower than the depth of the production layer (f6 = 1). If f1 is smaller than one, a part, 1 − f1, is lifted above sill level, and this part will be affected by the water exchange and then possibly lost to the coastal water. The fraction of (1 − f1) that will remain in the fjord is described by the value of f4 (equation (17)). This means that if f1 is less than one and f4 is equal to one, all POM will still remain in the fjord and the part lost to the surface (1 − f1) water will settle back into the basin water. All the different factors used to quantify the vertical transport of POM are explained in Table 1.
Table 1. Definitions of the Different Factors Used in the Conceptual Model of POM Dynamics in Fjord Basins
vertical advection factor; the part of POM produced from basin water nutrients, that remains below sill level after the water exchange.
0 ≥ f1 ≤ 1
water/POM time ratio factor; the part of the POM locally produced in the surface layer that settles in the fjord basin.
0 ≥ f3 ≤ 1
water/POM time ratio factor in case of a deepwater inflow; the part of the POM lifted above sill level that settles in the fjord basin.
0 ≥ f4 ≤ 1
the production factor; on/off season.
0 ≥ f5 ≤ 1
escape factor; the fraction of basin water nutrients that enters the photic zone.
0 ≥ f6 ≤ 1
 The expression for the total transport of POM to the basin water below the photic zone due to uplift of nutrients from the basin water covering all cases in 184.108.40.206.2–2.3.3 is then:
Here the production factor f5d has been included for completeness. Note that this expression describes the total contribution from this nutrient source during a full cycle of stagnation and renewal (Tstag + Tfill). The right hand side of equation (18) is equal to the right hand side of equation (11), where the sink term in equation (11) is now expressed with the factors f1 and f4.
2.4. Adding the Three Nutrient Sources
 The contribution of nutrients (potential POM) from basin water renewal in equation (18) was expressed as the contribution of POM during a full cycle of stagnation and renewal (Tstag + Tfill), while the contributions from the coastal water and from fresh water run off/point sources were considered on daily basis as these are continuous sources of nutrients and POM. Our goal here was to be able to estimate the pressure of different sources on the consumption of oxygen in the basin water, i.e. the contribution of POM, consuming oxygen when degraded.
 The oxygen condition in the basin water of a fjord depends on the length of the stagnation period Tstag during which new oxygen is supplied only by turbulent diffusive processes, and oxygen is consumed due to degradation of POM. It also depends on the time it takes for the oxygen concentrations in the basin water to reach critical levels, which depends on the vertical transport of POM, estimated here and the total amount of oxygen at the beginning of the stagnation period. The influence of low oxygen concentrations (<2 ml L−1) on the pelagic and benthic fauna is described by, e.g., Baden et al. . The total vertical transport to the basin water at sill level, Fc (gC m−2 d−1), of POC in a fjord can be expressed combining equations (5), (9), and (18):
 From the description of the two sources of POM given above in sections 2.2 and 2.3 one finds that the vertical transport of POM, Fc, due to local sources to a large extent depends on the residence time of the water above sill level and the time it takes for POM to settle down to sill level. But as shown in section 2.4 other important conditions also affect Fc. If POM produced from old basin water is trapped below sill level or not. If trapped, POM will not be influenced by the conditions above sill level and all will settle in the fjord. Another important condition is whether or not the basin water may escape the fjord below the photic zone. Fjords with Tsw ≪ Tp are not sensitive to nutrient input in the surface layer as seen in section 2.2, where equation (8) shows that f3 describing the part of the locally produced POM remaining in the fjord is equal to 0.1 (10%) when Tsw = 0.1 · Tp (f3 = 0.5 (50%) when Tsw = Tp). But one realizes from the results in section 2.3, that such fjords may be more sensitive to nutrient uplifted by basin water exchange as Ta may be less than Tp because the “basin water” POM may not be lifted all the way to the surface and the “basin water” POM from this source will thus have a larger chance to settle in the fjord (described by the factor f4). How high (Ha) the “basin water” POM will be lifted above sill level depends on the velocity of the uplift, which is determined by the rate of water exchange and the topography of the fjord.
3. Testing the Conceptual Model
 The conceptual model was tested for defined cases by comparing the results with results from a transient numerical model, which is described in Appendix A. We used the same strategy to investigate the flow of POC from each of the three sources: With constant depths of the sill, the model was run for different widths of the entrance to obtain different rates of water flow through the entrance and different residence times of water above sill level, but keeping the volume above sill level in the fjord constant.
 The water exchange above sill level in the numerical model was forced by a harmonically varying density field outside the entrance creating an intermediary circulation with a period of 5 days. The model was for all cases run until quasi steady state was obtained for POC, i.e. until the vertical transport of POC at sill level did not change over time.
3.1. Changed Import of POC From the Coastal Water
 The concentration, c0, of POC outside the entrance was held constant down to the sill depth. In this case there was no local source of POC in the fjord. To calculate the theoretical concentration of POC due to the transport through the entrance in the fjord, see equation (4), we used Q calculated by the numerical model. The theoretical expression for ccs was compared to the concentration of POC at sill level calculated by the numerical model, because the concentration at this level determines the flux of POC into the basin water.
 The results (not shown) from runs with five different sill depths with varying entrance widths show that the flow of water, and POC, was strongly restricted for narrow entrances (<1000 m) and for shallow sills (<20 m), and less restricted for wider and deeper entrances. The conceptual model estimate the import of POM from the coastal water to be 100% to 120% of what was calculated by the numerical model. The largest overestimation occurring for the most restricted cases. The model runs show that a restricted flow trough the entrance leads to less POC in the fjord, and that the theoretical description in equation (4) fits well with the numerical results.
3.2. Local Supply of Nutrients to the Surface Layer
 An estuarine circulation in the numerical model was generated by a freshwater input of 20 m3 s−1 and the thickness of the wind mixed layer was fixed to 4 m. The entrainment flow, Qe, was calculated from conservation of salt and volume. The concentration of POC in the freshwater was set to 6.4 gC m−3, which corresponds to 0.08 mol N m−3 (700 ton N yr−1) using Redfield ratio. The concentration of POC in the coastal water was set to zero. The concentration of POC developed due to the input of POC from the freshwater source, and the export to the coastal water and the basin water.
 The maximum theoretical value of the concentration of POC in the wind mixed surface layer due to the local nutrient input occurs with Qe = 0. It is 0.147 gC m−3, and was nearly achieved by the model for the most narrow entrance (Figure 4a). The estuarine circulation increases with wider entrance width, which is reflected in the concentration of POC in the surface layer, cfs, showing decreasing concentration with increasing entrance widths (Figure 4a).
 The amount of local POC exported to the basin water, cfi · wp · At, in a fjord is a function of the concentration of POC in the surface layer, cfs, and of the time it takes for POC to reach down to sill level, Tp, from the bottom of the surface layer, and the residence time of the water in the intermediary layer, Tsw, as discussed in section 2.2. With narrower entrance widths, the concentration of POC in the model at sill level, cfi, increased in relation to the concentration in the surface layer, cfs, as shown in Figure 4b. This is due to a constant Tp for the same sill depth, but an increasing Tsw and thereby an increasing value of f3 = Tsw/(Tsw + Tp) with decreasing entrance width, allowing more POC to settle below sill level instead of being flushed out of the fjord.
 The theory for the factor f3 developed here is based on the assumption of the same concentration of POC, cfi, at the top and the bottom of the intermediary layer (below the surface layer but above the basin water). Figures 4a and 4b show the concentration of POC in the surface layer, cfs, and at sill level, cfi, calculated by the model and with the theoretical expressions developed here and for cfi earlier by Stigebrandt . From the results in Figure 4a, one may conclude that the “new” theory reproduces the model results well. The entrainment flows, Qe, used in the “new” theory where the same for all sill depths, except for the shallowest sill where the decreased entrainment flow resulted in a somewhat fresher mixed layer. The concentrations at sill depth, cfi, are well described by both theories (Figure 4b).
3.3. Deepwater Inflow-Nutrient Uplift
 The depth of the fjord was 40 m, with a surface area of 25 km2. The deepwater inflow in the numerical model was driven by dense water residing above sill level outside the fjord entrance (4 m below the surface). The concentration of POC in the coastal water was zero, and there was no local input (Qf = 0). The implication of removing the estuarine circulation is discussed later. The initial concentrations of nutrients below and above Hp were 7 mmol N L−1 = 0.55 gC m−3 and 0 mmol N l−1, respectively. A minimum “seed” concentration of POC (0.001 gC m−3) was prescribed in the top 1 m. The initial concentration of POC in the rest of the water column water was zero. The concentrations of POC and nutrients developed due to production, sinking and advection. The depth of the photic zone Hp was 30 m. The duration of the uplifts were kept equal to Tfill, i.e. long enough to just refill the whole basin volume, Vb. Both start and ending of the uplift were initiated during one time step, which means that there were abrupt changes in the salinity stratification in the coastal water.
Figure 5 shows the total vertical transport of POC back to the basin water due to the uplifted nutrients. The theory generally overestimates the vertical transport, Fc (Figure 5). If all POC are transported back, the transport integrated over the period Tstag + Tfill equals 5.5 gC m−2. In Table 2 it shows that the advection factor, f1 was one for the 6 m (not shown), and the 10 m sill depth and all POC were thereby retained below sill level giving a maximum vertical transport. This was also true for the narrowest entrance with a sill depth of 14 m (Table 2). The factor f4 describes the fraction of POC lifted above sill level (1 − f1) that is recirculated to the basin water.
Table 2. Values of the Advection Factor, f1; and the Time Ratio Factor for Deepwater, f4 for the Different Runs Shown in Figure 4a
Entrance Width, m
Sill Depth, m
Sill Depth, m
The escape factor, f6 is equal to one since Ht < Hp.
 The resulting values of f6, f1 and f4, in Figure 5 are given in Table 2 and show that the results from the conceptual and numerical models correspond relatively well, but some uncertainties due to the setup of the numerical model will be discussed later.
 The conceptual model of the vertical transport of POM, Fc, in a fjord consists of submodels for three sources of POM/nutrients, and is a development of the model presented by Stigebrandt . The theory for coastal water exchange was found to give a satisfying description compared with the results from the numerical model and was not developed further. In the submodel for local freshwater input/point sources in Stigebrandt  it was assumed that all POC settles in the fjord if the time it takes for POC to settle below sill level, Tp, is half the time of Tsw. And that no POC will reach below sill level if Tp is more than 1.5 times longer than Tsw. This theory does also fit rather well with the model results (see Figure 4b). However, the theory developed here does not include guessed values even though qualified, which is a clear improvement compared to the old theory. The effect of nutrient uplift from the local deepwater, caused by basin water renewal, was shown to be a function of several factors, and was also rather well predicted by the submodel including; (i) the relation between the depth of photic zone, Hp and the sill depth, Ht, (ii) the vertical velocities of the rising water mass and the sinking POM, (iii) the volume of the basin above sill level and below Hp, (iv) the residence time of the water above Ht. This submodel was extensively developed in this paper and the new conceptual model was found to reproduce the result of the numerical model rather well.
 The objective was to study the effect of topography, e.g. residence times and velocities of the water, on the transport of organic matter in inshore waters. Atmospheric input was not considered. The simplistic formulation of the POC dynamics due to biological processes used in the paper was considered a necessity to be able to interpret the results. The effect of grazing on the vertical transport of POM, Fc, is complex and works both to increase and decrease the vertical transport [e.g., Noji, 1991] and would impair the interpretation of the resulting transport of POM due to topography. Grazing and degradation of POC were therefore not included in the model and nutrients were assumed to be totally utilized as they enter the photic zone, only withdrawal in the basin water by permanent inclusion in sediment and/or by denitrification. The assumption of total utilisation of nutrients in the photic zone works to potentially increase the local Fc. The depth of the photic zone (30 m) may seem deep compared to the photic zone in many coastal waters but was chosen for the possibility run several different cases, i,e., several sill depths shallower than the photic zone.
 The shading effect on the primary production of POM and yellow substances from freshwater discharge was not considered in the submodel for deepwater even though a freshwater input might influence the photic zone [Erlandsson and Stigebrandt, 2006] and thereby the effect of an uplift of nutrient rich basin water.
 In the conceptual submodels we introduced several factors influencing Fc. Especially in the submodel of deepwater uplift of nutrients to the photic zone three different factors were introduced to resolve the different processes involved. A number of different time scales were introduced due to the different vertical velocities of water and POM, being important to understand the fate of POM. While the water mass is lifted a certain vertical distance, the contained POM will be partly left behind due to its settling velocity preventing POM to be lifted at the same speed. The settling velocity of POM is important for the result from the conceptual model, and is probably the largest weakness, using it to calculate the dominating sources of POM to an area, and this must be considered using the model for this purpose. Studies of settling velocity of POM show a large variation depending on particle size, shape, and density [e.g., Bienfang, 1980; Dagg and Walser, 1986]. The conceptual model considers the mean settling velocity of the local population. From sedimentation studies, Wassman  estimated the specific settling velocity in five Norwegian fjords and polls with very different characteristics to between 0.15 and 1.04 m d−1. The settling velocity of POM is affected by stratification as it is a well known fact that the concentration of POM often increases at density surfaces. This may decrease the sedimentation of POM at deeper depth due to remineralisation in the pycnocline. During bloom situations that may occur due to occasional nutrient input, high concentrations of POM may lead to coagulation and thereby increased settling velocity [e.g., Kørboe et al., 1994]. The mean settling velocity 1.5 m d−1 [Aure and Stigebrandt, 1989a] used in this paper was based on an investigation of 29 different fjords in Møre and Romsdal area in Norway and was calculated as the mean settling velocity needed to support the deepwater basins with a sufficient amount of POM to explain the oxygen concentration and consumption found in the fjord basins. The submodel for deepwater exchange was developed for the special case where the time of exchange equals Tfill defined in equation (2). It is a fact that knowledge about the duration of deepwater exchange is more or less always lacking, and a short discussion in the end of each sections 2.3.1–2.3.3 of the effect of shorter and longer deepwater inflows was included. The estimated sensitivity of a fjord or other enclosed areas to POM/nutrient input using the model developed in this paper must be carefully interpreted taking the above weaknesses into account. But doing so, we believe that our analytical/conceptual model might be an important contribution to the understanding of the effects of local input of POM/nutrients.
 The production factors, f5, describing the likelihood that, nutrients discharged from freshwater and point sources (f5f), and deepwater (f5d), may be utilised by primary producers were assumed to equal one in this paper, but depend partly on the length of the productive season i.e. on latitude [see, e.g., Cushing, 1975; Strass, 1990] and in case of a deepwater renewal if it occurs during the productive season or not. If the residence time, Tsw, is long compared to the unproductive season, one may assume that nutrients uplifted during this season have the potential of being left in the surface layer until the production starts. The uplifted nutrients may then be utilised in the beginning of the productive season. This is the case in the Baltic Sea for example, where Tsw is many years. All nutrients from freshwater and point sources will then be utilized and f5f = 1 in the Baltic Sea.
 To test the conceptual model a numerical model was used (see Appendix A). The depth of the pycnocline created by the estuarine circulation was held fixed. This was done to create similar stratification in the different runs, but it means de facto that in this case we prescribed the (wind) mixing to increase with increasing entrance width and this might have an effect on the resulting concentrations of POC in the model.
 The initiation of the start and ending of the deepwater inflow during one time step ( hour) led to transient high pressure gradients above sill level between the fjord and coastal area and we therefore used Qd calculated by the numerical model in the conceptual model. This set up was not considered to influence the result. One complication in the numerical model is the estimate of Ha, the greatest distance POM is lifted above sill level (defined in section 2.3.3). The theory assumes that nutrients are transformed to POC as soon as they reach the photic zone, Hp. In case of short and fast uplifts, the nutrients are lifted a small distance above Hp in the numerical model before being transformed to POC due to the configuration of the model. This results in those cases in a larger Ha since nutrients are lifted with the velocity w, while POM is lifted with the velocity w − wp. The difficulty to define when the resident water has left the fjord in the numerical model causes together with the complication mentioned above uncertainties in the numerical model results and may possibly explain some of the differences between the theory and the model results shown in Figure 5.
5. Conclusions and Implications
 A conceptual/analytical model for Fc was developed covering the combination of the three possible sources of POM/nutrients to an enclosed area; namely, the coastal water, local supply in the surface water, and nutrient rich local deepwater. The mathematical formulation of the model includes several factors (Table 1). The factors vary between 0 and 1 and give an opportunity to quantify the effect of the most important physical conditions on the vertical flux of POM, such as the light conditions, i.e. the length of the productive season; the sill depth; the residence time of the surface water; and the mean velocity of the rising water mass, the settling velocity of POM, and the maximum height to which POM is lifted during basin water renewal. The vertical transport of POM, Fc, to the basin water can be estimated from the values of the factors and the sensitivity to different sources of POM/nutrients can thus be established. This is a complement to methods to identify the trophic state of coastal waters found in literature [e.g., Vollenweider et al., 1998, and references therein; Tett et al., 2003], and is an important step towards better management and more sustainable exploitation of the coastal zone. The conceptual/analytical model for the vertical flux of POM into the basin water of inshore areas may be used in integrated water quality models like the FjordEnv model [Stigebrandt, 2001].
 In the work of Erlandsson et al. , Skagerrak water was identified to be the dominant source of POC to the vertical transport of organic matter to the basin water of Gullmar Fjord, which suggests that the factors developed in this paper are all closer to zero than to one, i.e.; short residence time of the surface water (f3 ≪ 1, f4 ≪ 1), sill depth substantially below the photic zone (f6 < 1, f1 = 0). Since many of the deepwater exchanges occur off the productive season, and the residence time of the intermediary water above sill level is rather short 40 days [Arneborg, 2004], f5f and f5d are also below one. One realizes that Gullmar Fjord is not very sensitive to local eutrophication, but may respond negatively to large scale eutrophication since the minimum oxygen concentrations has shown to decrease [e.g., Erlandsson et al., 2006]. With Tp = 1.5 [Aure and Stigebrandt, 1989a, 1989b] and Tsw = 40 result in f3 = 0.57, and with Tp = 0.5 [Wassman, 1991] and Tsw = 40 results in f3 = 0.27, i.e. 57% or 27% of the local primary production settle in the fjord basin depending on settling velocity, where the last estimate fits best with the results of Erlandsson et al. . The reason is probably that the strong pycnocline in the Gullmar Fjord separating the less saline Kattegat water from the Skagerrak water beneath enhance the sedimentation below the pycnocline. This elucidates the need for a better parameterisation of the mean settling velocity of POC.
 The model may for example be used to establish if the much used technique of discharging and interleaving nutrient rich waste water beneath the photic zone is suitable or not. The idea is to avoid an increased primary production in the photic zone, but the results in this paper indicate that in some areas this technique may result in the unwanted effect of increased vertical transport of POM to the basin water. In a fjord with the sill at or above the depth of the photic zone, POM produced from nutrient rich basin water may to a large extent settle in the area if the vertical advection speed w is less than wp or if the residence time of the surface water is long compared with the time it takes for POM to settle below sill level. One example of this may be the inner part of the Oslo Fjord, with a relatively shallow sill depth of 20 m and a long residence time of the water above sill level [Gade, 1968]. To escape the fjord all nutrients have to be lifted up in the photic zone and the value of the escape factor f6 is then about one. To be safe, discharging and interleaving of nutrient rich waste water should be done only in basins where the escape factor f6 equals zero. This should secure that the nutrients does not reach the photic zone in the fjord. Another more obvious application of the model is to establish if an area is suitable for development of aqua culture, where the model tells if the area is sensitive to local input of nutrients from, e.g., a fish farm or not, which then is given by the value of f3.
Appendix A:: Numerical Model
 To test of the conceptual model we used a one-dimensional numerical transient model with 1 m thick layers. The physical part of the model is described by Stigebrandt  and has been tested in, e.g., Himmerfjärden [Engqvist and Omstedt, 1992]. The physical and biological states of each level are calculated for each time step, e.g., the salinity and temperature, giving the density of the layers, and the concentration of particulate organic carbon and dissolved inorganic nitrogen. The numerical model is run for a steady state solution of the POC concentration in each case studied. In the present paper it describes a fjord with vertical walls and horizontal area A (km2). The water exchange in the model was forced by density fluctuations in the coastal water causing so-called intermediary circulation. The salinity in the coastal water increased downward (from 27 psu at the sea surface to 29 psu at 22 m depth) with a superposed synchronous variation of 1 psu in each layer, while the temperature was constant. The POM concentration was estimated as particulate organic carbon, POC, for each layer and time step ( hour). The description of the ecosystem was kept simple. The amount of POC in the model was regulated by sinking, by addition of POC from different sources, and by export to the coastal water. The nutrient concentration was calculated only in the deepwater case, were deepwater nutrients were utilised when lifted up into the photic zone. The input of nutrients was in the other two cases expressed as POC assuming total utilisation.
 Effects of the Coriolis force were neglected which should be a good approximation as long as the width of the entrance is less than the internal Rossby radius. Estuarine circulation was generated by constant wind and freshwater input in the case with input of POC from a freshwater source. The depth of the wind mixed layer was fixed at 4 m depth. The tidal amplitude was zero. The surface area of the fjord, equal to the area at sill level At, was 25 km2.
 The physical part of the model is described in more detail by Stigebrandt , and a short version is given below. The flow trough the entrance, Q, at the level z, for each time step, is given by:
Were Bm (z) is the width of the entrance at z and dz is the thickness of the layer.
Here DPI and DPS are the pressure difference between the fjord and the coastal water due to density differences and different surface elevation, respectively. ρ = 1000 is the reference density, and α = 0.3 is the fraction of the pressure difference used for forcing [Stigebrandt, 1990]. The inflowing coastal water will flow to the level of equal density in the fjord. The change in temperature, salinity, and the concentration of POC and nutrients due to water exchange are calculated at depth z in the fjord for each time step as shown in equation (A3) for temperature T1:
A(z) being constant in this application, is the surface area at level z. Tin is the temperature of the inflowing water, Qin [m3 s−1], and Qout is the rate of out flowing water. The direction of the vertical velocity, w is upward in equation (A3). A buoyancy term due to freshwater input Qf is added at the sea surface, and Tf is the temperature of the freshwater. The first two terms are only valid for the basin water when there is a deepwater intrusion. The two last terms in equation (A3) are only valid for the water above sill level. Diffusion is not an important process during deepwater renewal when advective process dominates and was therefore not included in the model. We have assumed no mixing with the ambient water during deepwater inflow since this is not crucial for our analysis. The vertical velocity, w, of the water during inflow at z is defined positive flowing into and negative flowing out of the layer and is expressed:
 The concentration of phytoplankton, expressed as particulate organic carbon, POC in the model, depends solely on physical processes such as advection and sinking in the two cases considering coastal exchange and freshwater input. The assumption of total transformation of nutrients to POC was handled by input of POC instead of nutrients from those sources.
 The third case differs in this matter and is discussed below. In the case of nutrient uplift from the basin water, the numerical model was configured to convert all nutrients to be totally utilized once they entered the photic zone.
The change in the concentration of POC due to advection, Adv(z), is defined in equation (A3). The depth of the photic zone was assumed to be at the depth were only 1% of the incident light were still available. The intensity of light at the surface, Qs, was calculated based on latitude and day. In this application we used latitude 58 N and day 200. The light intensity varied over 24 hours though. The intensity of light at level z is expressed:
About 50% of the light is absorbed at the top of the ocean and Io is Qs. The vertical attenuation constant, kd, was calculated from a background value plus the concentration of POC, in the water:
Here the light limiting term LTLIM is equal to one above and zero below the depth of photic zone, and Gmax = gr · expgt·temp, is configured to create a rapid transformation of nutrients to POM by a high value of the growth factor gr. The nutrient limitation is defined according to Michaelis-Menten equation.
Here KN is the half saturation constant for nitrate. The sink term in equation (A5) was calculated from an assumed constant sinking velocity, wp of POC equal to 1.5 m day−1 [Aure and Stigebrandt, 1989a]
surface area at the depth of the photic zone, m2.
surface area at sill level, m2.
concentration of POC in the fjord, gC m−3.
concentration of POC in the coastal water, gC m−3.
concentration of POC in the surface layer of the fjord due to the exchange with the coastal water, gC m−3.
concentration of DIN in the basin water below the photic zone, expressed as POC, gC m−3.
concentration of POC originating from the basin water that is flushed out of the fjord, gC m−3.
concentration of POC in the freshwater, gC m−3.
concentration of POC in the surface layer of the fjord due to freshwater input of nutrients, gC m−3.
concentration of POC at sill depth in the fjord due to freshwater input of nutrients, gC m−3.
concentration of POM at sill level during the stagnation period of the basin water, gC m−3.
dissolved inorganic nitrogen, mmol l−1.
vertical advection factor.
time ratio factor.
time ratio factor in case of a deepwater inflow.
the production factor (on/off season) for freshwater discharge.
the production factor (on/off season) for basin water uplift.
vertical transport of POC in the coastal water, gC m−2 s−1.
vertical transport of POC in the fjord, gC m−2 s−1.
vertical transport of POC in the fjord due to water exchange, gC m−2 s−1.
vertical transport of POC in the fjord due to freshwater input, gC m−2 s−1.
vertical transport of POC in the fjord due to basin water uplift, gC m−2 s−1.
the depth of the photic zone, m.
the hight above Ht to where POM is lifted during the basin water uplift, m.
the sill depth, m.
the total depth, m.
the height of the water mass containing POM, m.
particulate organic carbon, gC m−3.
flow through the entrance, m3 s−1.
deepwater inflow, m3 s−1.
entrainment flow, m3 s−1.
freshwater input, m3 s−1.
residence time of the basin water, s.
filling time of the basin, i.e. all basin water lifted above sill level, s.
settling time of POC from the mixed layer down to sill depth, s.
The time it takes for POM to be lifted from Hp to Ht, s.
The time POC is lifted above sill level.
the time of Tup needed to lift all POC above sill level, s.
the time it takes for POM to settle at sill level from the height Ha, s.
residence time of the water above sill level, s.
volume of water above sill level, m3.
volume of the basin water, m3.
volume of the basin water below Hp, m3.
mean vertical velocity during a deepwater inflow, m s−1.
settling velocity of POC, m s−1.
the recirculated fraction of the nutrients once transported to the deep water as POC.
 This work has been supported by the EU project ECASA. I want to thank my supervisor Anders Stigebrandt for valuable discussions and critics of the manuscript.