Modelling phosphorus and suspended particulate matter in Ringkøbing Fjord in order to understand regime shifts

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Journal of Marine Systems 68 (2007) 65 – 90 www.elsevier.com/locate/jmarsys

Modelling phosphorus and suspended particulate matter in Ringkøbing Fjord in order to understand regime shifts Lars Håkanson a,⁎, Andreas C. Bryhn, Jenny M. Eklund a

Department of Earth Sciences, Uppsala Univ., Villav. 16, 752 36 Uppsala, Sweden

Received 23 March 2006; received in revised form 30 October 2006; accepted 30 October 2006 Available online 22 December 2006

Abstract The focus in this work is on the conditions in Ringkøbing Fjord (Denmark), where there have been major regime shifts during the last 30 years. The regime shift in the 1990s is discussed in this paper and concerns reductions in nutrient input from land and changes in salinity. The changes in these abiotic have drastically influenced the structure and functioning of the ecosystem [e.g., in phytoplankton production, water clarity, macrophyte cover and biomass of clams]. This work concerns the modelling and understanding of such changes and the aim is also to consider patterns in variability in the data that may explain the regime shift. The model used is a general, dynamic process-based mass-balance model for total phosphorus (TP) and suspended particulate matter (SPM). The model uses ordinary differential equations (the ecosystem scale). The calculation time is 1 month to reflect seasonal variations. We quantify, e.g., sedimentation, resuspension, diffusion, mixing and retention. The model has previously been tested for coastal areas of different character and shown to predict TP, SPM, Secchi depth, chlorophyll and the oxygen saturation in the deep-water zone very well (within the uncertainty bands of the empirical data). We show that the model, with new calculation routines for macrophytes and clams, also describes the conditions in Ringkøbing Fjord well, which means that the model is a useful general tool for interpretations of changes in coastal ecosystems. The model is simple to apply in practice since all driving variables may be readily accessed from maps or regular monitoring programs. © 2006 Elsevier B.V. All rights reserved. Keywords: Modelling; Phosphorus; Suspended particulate matter; Chlorophyll; Secchi depth; Regime shifts; Macrophytes; Clams; Predictive power; Ringkøbing Fjord

1. Introduction and aim This work has a focus on dynamic mass-balance modelling of suspended particulate matter (SPM), total phosphorus (TP), Secchi depth (a measure of water clarity), salinity, chlorophyll-a concentrations (a standard measure of phytoplankton biomass) and the changes that have taken place concerning nutrient inflow, salinity and macrophyte cover and biomass of ⁎ Corresponding author. E-mail address: [email protected] (L. Håkanson). 0924-7963/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmarsys.2006.10.010

clams in Ringkøbing Fjord (Jutland, Denmark; see Pedersen et al., 1995; Nielsen et al., 2004; Petersen et al., 2006). A previous work from our group related to Ringkøbing Fjord concerned general patterns in variability and uncertainty in a set of key water variables, variations in data from different time periods, correlations and regressions between coastal water variables, and confidence intervals for empirical mean values (Bryhn et al., 2006). Another work from our group also related to this paper concerns mass-balance modelling of phosphorus in coastal areas in general (Håkanson and Eklund, in press) and yet another work deals with

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strategies to set management goals for Ringkøbing Fjord and avenues to reach and maintain such goals for coastal areas (Håkanson and Bryhn, in press). The regime shift in Ringkøbing Fjord which occurred in the 1970s is not well documented by empirical data but concerned marked increases in nutrient concentrations and eutrophication effect variables (such as increases in primary production and decreases in water clarity). The regime shift, which occurred in the lagoon in the 1990s will be discussed and modelled in this paper and concerns major reductions in nutrient input from land and changes in salinity and the consequences these abiotic changes have for the structure and functioning of the ecosystem of Ringkøbing Fjord. According to Rasmussen (2003) and Petersen et al. (2006), the improved water quality after the latter regime shift may to a great extent be attributed to clams that have cleared the water from nutrient-rich particles. Regime shifts is a “hot” topic in aquatic sciences. It is discussed in many books and papers (see, e.g., Scheffer, 1990; Scheffer et al., 2000; Carpenter, 2003, for a compilation) and it is also the target of the Thresholds project (see http://www. thresholds-eu.org/). This paper will first discuss data from Ringkøbing Fjord (from Bryhn et al., 2006), then we will briefly discuss the question of limiting or regulating nutrient and explain why we have not modelled nitrogen in this work, then we will give basic information about the dynamic mass-balance model used in this work (key structures, equations and results from validations; from Håkanson and Eklund, in press) and finally we will demonstrate

how the model works for Ringkøbing Fjord, how it is complemented with new calculation algorithms for production and biomass of clams and macrophytes, and how it can be utilised as a tool to understand the changes that has taken place in this lagoon. 2. Methods and data 2.1. Data from Ringkøbing Fjord Basic data on Ringkøbing Fjord are given in Table 1. The lagoon is connected to the open sea (North Sea) through a sluice, so in many ways this system may also be regarded as a lake close to the sea. The area of the lagoon is about 300 km2, the mean depth 1.9 m and the maximum depth 5.1 m. The regime shift may be demonstrated in many ways. Fig. 1 shows two key types of uncertainties or error bars related to the regime shift in focus in this work. Fig. 1A gives the 95% confidence intervals for individual data for chlorophyll-a concentrations within a year and the error bars for the mean annual values (that the error in the mean value with a 95% probability is smaller than the L-value, as calculated from the sampling formula, see Eq. (1) later). Fig. 1B, C and D give error bands for the mean chlorophyll values for different time periods (3-months, monthly data and daily data). From Fig. 1, one can note that the error in the mean value (L) depends on the time scale because the error in the mean value (L) is calculated from the number of data (n) used in calculating the mean value and 12 times as many data

Table 1 General description of Ringkøbing Fjord Variable

1990–1993

2000–2003

Area (km2) Volume (V, km3) Maximum depth (Dmax, m) Mean depth (Dm, m) Temperature (°C) Freshwater inflow from land (Q, km3/year) Salinity (Sal, ‰) Total phosphorus (TP) (μg/l) Total nitrogen (TN) (μg/l) TP load from land (t/year) TN load from land (t/year) Suspended particulate matter (SPM, mg/l) Secchi depth (Sec, m) Chlorophyll-a (Chl, μg/l) Biomass, clams, Mya arenaria (g dw/m2) Biomass, other benthic fauna (g dw/m2) Macrophyte cover (% of lagoon area)

300 0.57 5.1 1.9 9.5 1.6 7.8 130 1,700 140 6,500 43 0.6 52 0.1 6 9

300 0.57 5.1 1.9 10.0 1.7 9.6 56 1,200 140 5,300 19 1.6 9.1 150 13 2

Mean annual values for two periods before and after the change in ecosystem regime (see also Bryhn et al., 2006).

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Fig. 1. Illustration of the uncertainties in the empirical data on chlorophyll-a concentrations calculated from annual data, data from 3-month periods, monthly data and daily data (when at least 3 samples are available) from Ringkøbing Fjord for the given time period. The figure gives the error for the mean values (L) and for comparative purposes also the wide 95% confidence intervals for the individual data.

are generally used to calculate the annual mean values compared to the monthly means values.

modelling and they are all related to substance-specific questions related to the behaviour of nitrogen in aquatic systems:

2.2. On nitrogen modelling and limiting nutrients It should be noted that we have not done any dynamical modelling for nitrogen, as we have for phosphorus and SPM. This is regrettable, especially since many parts of the model used for TP and SPM are general and could also be applied for total nitrogen (TN), e.g., the parts concerning resuspension of particulate nitrogen, mixing, inflow and outflow. There are several reasons why we have not done nitrogen

• Nitrogen fixation. Today there are no algorithms which could be used within the framework of the existing general mass-balance model that could quantify nitrogen fixation from the atmosphere and from sources within a given coastal systems in a general manner. Studies have shown (see Rahm et al., 2000) that atmospheric nitrogen fixation may be a very important process in contexts of mass-balance calculations, but at present we do not have any

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empirically well-tested algorithms to quantify atmospheric and internal nitrogen fixation for Ringkøbing Fjord or in general for coastal areas in this modelling. The particulate fraction. In this mass-balance modelling, it is imperative to have a reliable algorithm for the particulate fraction of nitrogen, since the particulate fraction (PF) is the only fraction that by definition can settle out due to gravity. So, for this modelling one must define the particulate fraction for TN in the same manner as it is defined for TP and in the way in which SPM is defined, i.e., from filtration (see Håkanson, in press). So, PF for TN should be determined in this way and the factors that may affect the PF-value for TN in different coastal ecosystems need to be clarified. Denitrification. From previous modelling work for nitrogen (see, e.g., Floderus, 1989), one can conclude that denitrification depends on sediment red-ox conditions, i.e., on sedimentation of degradable organic matter and the oxygen concentration in the deep-water zone, but also on the frequency of resuspension events, on the presence of mucusbinding bacteria, on the conditions for zoobenthos and bioturbation. Given this complexity, it is easy to understand that empirically well-tested algorithms to quantify denitrification on a monthly basis (which could be used in this modelling) do not exist to the best of our knowledge. N-uptake and retention in biota. It has been demonstrated that the uptake and retention of phosphorus in the aquatic foodweb is very important for the understanding and modelling of P (see Håkanson and Boulion, 2002). Since biota contains more N than P, one can assume that this is even more important for N. It is well established (see Redfield et al., 1963) that plankton cells have a typical atomic composition of C106, N16P, which means that 16 times as many atoms of N are needed than of P. But so far, we have not seen any modelling taking these matters into account in the same manner as for P. This means that there is also an uncertainty regarding these fluxes for N. The atmospheric wet and dry deposition of nitrogen may be very large (in the same order as the tributary inflow) and patchy (see Wulff et al., 2001), which means that for large coastal areas and for relatively smaller coastal areas far away from measurement stations, the uncertainty in the value for the atmospheric deposition can be very large. The modelling scale. If the modelling (of N and/or P) is done at short time steps (hours to days) and at specific sites in coastal areas, it is important to

consider the influence of varying winds (speed, direction and duration), temperature and chemical forms of the studied nutrients. This means that models designed to quantify short-term variations tend to be large with many driving variables and many uncertain rates and model variables. It also implies that the accumulated uncertainties in the model predictions may be very large (see Håkanson and Peters, 1995) and that such models (when properly calibrated) can give good descriptive power but generally only poor predictive power since the predictions depend on the weather conditions, and it is not possible to predict the weather conditions well for more than a few days ahead. The modelling we have used in this work is based on monthly calculations and a basic underlying assumption, which has also proven to be valid by the good validation results, is that for monthly predictions, one can make important simplifications in the model (thus reducing accumulated uncertainties) and remove weather as a driving variable. Evidently, this does not mean that this process resolution is an optimal one for all objectives. In this paper, we do not specifically address the very interesting and much debated issue on limiting or regulating nutrient. Total phosphorus is since long recognised as the most crucial limiting nutrient for lake primary production in most but not all lakes (Schindler, 1977, 1978; Bierman, 1980; Chapra, 1980; Boers et al., 1993; Wetzel, 2001). Nitrogen is regarded as a key nutrient in some marine areas (Redfield, 1958; Ryther and Dunstan, 1971; Nixon and Pilson, 1983; Howarth and Cole, 1985; Howarth, 1988; Hecky and Kilham, 1988; Ambio, 1990; Nixon, 1990; Livingston, 2001). It has been suggested that several other brackish waters do not follow the general N versus P pattern related to “limiting” or “regulating” nutrient for the primary phytoplankton production/biomass and chlorophyll-a concentrations, as demonstrated by Guildford and Hecky (2000); for a review, see Labry et al. (2002). Savchuk and Wulff (1999) argued that P controls the Baltic Proper, while N controls the adjacent and less saline Eastern Gulf of Finland. In Ringkøbing Fjord, where the salinity is between 5 and 15‰ and where one might expect nitrogen to limit or regulate primary production and chlorophyll-a concentrations, the data do not support the nitrogen hypothesis (Bryhn et al., 2006). According to the basic theory related to the Redfield ratio, one would have expected that there would have been higher concentrations of bluegreen algae during periods when the Redfield ratio is lower than 7.2, since this would have favoured algae

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which can take up and utilise atmospheric nitrogen (Sellner, 1997; Gruber and Sarmiento, 1997). Curve 3 in Fig. 2 shows that there is no clear relationship between the TN/TP-ratio and empirical chlorophyll concentrations or concentrations of cyanobacteria (curve 4) and that the TN/TP-ratio is never lower than 7.2 (curve 1). However, the summer values for the ratio between dissolved inorganic N and P changed from below 7.2 to above 7.2 with the regime shift. So, this ratio may be a better explanatory factor of the variations in cyanobacteria than the TN/TP-ratio in Ringkøbing Fjord. Chlorophyll concentrations calculated from regressions based on empirical TN-data correspond rather poorly to measured chlorophyll data (Fig. 2B), whereas empirical regressions based on measured TP-data or modelled TPconcentrations describe the variations in chlorophyll much better. One should note that there is also a rather

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strong correlation between TN- and TP-concentrations in Ringkøbing Fjord (Bryhn et al., 2006). From this, one can conclude that in Ringkøbing Fjord, quantitative statistical analyses based on empirical data indicate that phosphorus may regulate primary production all years in the entire trophic gradient from very eutrophic conditions during the period 1985 to 1995 and also during the period from 1998 to the present. However, this does not contradict observations conveying that short-term nitrogen limitation occurs in Ringkøbing Fjord (Bryhn et al., 2006). 2.3. Basic structure of the mass-balance model and results from earlier model validations The idea here is not to repeat what has been presented before, but to highlight the specific features and structures

Fig. 2. A. Empirical data illustrating the question on limiting nutrient in Ringkøbing Fjord. A. Gives the TN/TP-ratio (curve 1), the Redfield ratio (7.2; based on concentrations), median annual values on chlorophyll (curve 3; note that there was a change in the analytical method for the chlorophyll determinations in 1985 and the values before that are represented here by a constant) and median annual data on cyanobacteria (= bluegreens; there are no data before 1989). B. Gives modelled chlorophyll-a concentrations (based on modelled TP-concentration), modelled chlorophyll-a concentrations from a regression based on empirical TN-data, and the error bands for the empirical monthly chlorophyll data.

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of this dynamic modelling so that these modelling results can be understood. There are some specific parts of this modelling approach, which are essential to understand and they will be mentioned below: • The definition of the coastal area and of coastal morphometric parameters (such as area, volume, mean depth, etc.) is generally done using the topographical bottleneck method (see Pilesjö et al., 1991; Håkanson, 2000), but this is not important for Ringkøbing Fjord, where the water exchange between the lagoon and the sea is regulated by a sluice. • There is a general sub-model to calculate the exchange of water and matter between the coast and the sea which is explained by Håkanson (2000) and Håkanson et al. (2004a). • The sub-models to define surface-water and deepwater volumes and hence also mixing between surface water and deep water have been presented by Håkanson et al. (2004b). This approach is not based on water temperatures but on sedimentological criteria (the wave base concept; see Fig. 3). • There is also a sub-model to quantify the relationships between SPM, salinity and water clarity (Secchi depth; from Håkanson, in press), which will be used in this work. These relationships are shown in Fig. 4. The basic structures of the SPM-model and the TPmodel are very similar and illustrated in Fig. 5 for TP.

This modelling quantifies inflow to surface water and deep water (from the sea, point source emissions, tributaries and precipitation), outflow from surface water and deep water and internal transport processes, such as sedimentation from surface water to deep water and to ET-areas (areas of fine sediment erosion and transport; these are the areas where resuspension occurs), resuspension from ET-areas back to surface water and to deep water, sedimentation from deep water to accumulation areas (A-areas, with continuous sedimentation of fine particles), diffusion of phosphorus from A-sediments to deep water and upward and downward mixing between the surface water and deep water compartments and land uplift (which does not occur in Ringkøbing Fjord). The dynamic SPM-model and the TP-model have been validated and shown to predict very well. The key question in this work is: Does this modelling also work well in Ringkøbing Fjord? The r2-value (r2 = coefficient of determination) when empirical data on sedimentation (from sediment traps) were compared to modelled values in 17 Baltic coastal areas was 0.89 using the SPM-model and it is not really possible to obtain better predictions due to limitations and uncertainties in the available empirical data. The mean error (MV) is 0.075 and the median error −0.05; the standard deviation was 0.48, which should be compared to the 95% confidence interval for the uncertainty in the empirical data used to measure sedimentation, which is 1.0. One can also note that also Secchi depths are predicted close to the

Fig. 3. The ETA diagram (Erosion-Transportation-Accumulation; for more information, see Håkanson and Jansson, 1983) illustrating the relationship between effective fetch, water depth and bottom dynamic conditions. The wave base (Dwb) separating areas of transport (T ) from areas of continuous sedimentation (A) have been used as a general criterion to differentiate between the surface water and the deep water volumes. Note that since the area of Ringkoebing Fjord is 300 km2 (or Lef ≈ 17.3 km), the ETA-diagram gives the theoretical wave base to 20.3 m, which is much lower than the maximum depth of 5.1 m.

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Fig. 4. Illustration of the relationship between Secchi depth, SPM in surface water and salinity in surface water (for further information, see Håkanson,

uncertainty given by the empirical data. This is also true for the oxygen saturation in the deep water (O2Sat; see Håkanson, in press). The dynamic TP-model works well when tested for 21 Baltic coastal areas (see Håkanson and Eklund, 2006). The mean error was 0.0028, the median error 0.005 and the standard deviation for the error 0.18, which should be compared to the standard deviation related to the uncertainty in the empirical data, which is 0.16. This means that the model predicts as well as these empirical data permits. It is the uncertainty in the empirical data that restricts further model improvements. It should be stressed that this modelling is meant to apply for coastal areas in general and that it should account for all important processes regulating the transport of TP and SPM to, within and from a given system. It is also crucial to use a technique that provides an ecologically meaningful and practically useful definition of the coastal area. Arbitrary borderlines can be drawn in many ways and the morphometric parameters of such areas would be devoid of meaning in contexts of mass-balances modelling. The approach used in this modelling comes from Håkanson et al. (1984) and Pilesjö et al. (1991) and assumes that the borderlines are drawn at the topographical bottlenecks so that the exposure (Ex; defined by the ratio between the section area, At, and the enclosed coastal area, A) of the coast from winds and waves from the open sea is minimised. From Fig. 5, one can note that there are four main compartments: surface water, deep water, areas where processes of fine sediment erosion and transport dominate the bottom dynamic conditions (ET-areas)

and the areas with continuous sedimentation of fine particles, the accumulation areas (A-areas). The limit between the surface and deep water compartments are calculated not in the traditional way from water temperature data but from the water depth separating transportation areas from accumulation areas, the “critical” depth (= the wave base, Dwb, see Fig. 3). There are four basic inflows of TP: 1. Inflow of TP to coastal surface water from the sea (FinSW; regulated by a sluice in Ringkøbing Fjord). 2. Inflow of TP to the deep water from the sea (FinDW); this is set to zero for Ringkøbing Fjord. 3. Land uplift (FLU). Land uplift is a special case for the Baltic (see Håkanson et al., 2004a) and land uplift is set to zero in this work for Ringkøbing Fjord. 4. Tributary inflow (FinQ). 5. Direct fallout (Fprec). The amount of particulate TP deposited on ET-areas may be resuspended by, e.g., wind/wave action or slope processes, so resuspension is an important internal process influencing the TP-flux in coastal areas in general, but especially so in Ringkøbing Fjord, which is very large and shallow. The resuspended matter can be transported either back to the surface water (FETSW) or to the deep water (FETDW). How much that will go in either direction is regulated by a distribution coefficient calculated from the form factor (Vd) of the coastal area. Other internal processes are mixing, i.e., the transport from deep water to surface water (FDWSWx) or from

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Fig. 5. A general outline of the structure of the dynamic coastal model for phosphorus. SW and DW are abbreviations for surface water and deep water, respectively.

surface water to deep water (FSWDWx) and diffusion (FADW), i.e., the transport of dissolved TP from Asediments to the deep-water compartment. When there is a partitioning of a flow from one compartment to two or more compartments, this is handled by a distribution (= partitioning = partition) coefficient. This could be a default value, a value derived from a simple equation or from an extensive sub-model. There are four such distribution coefficients (DCs) in this TP-model: 1. The DC regulating the amount in particulate and dissolved fraction. A default value for the particulate fraction, PF = 0.56, has been used in all these simulations for phosphorus, as motivated by Håkanson and Eklund (2006).

2. The DC regulating sedimentation either to areas of erosion and transport (ET-areas) above the wave base (Dwb; FSWET) or to the deep-water areas beneath the wave base (FSWDW, see fig. 8). 3. The DC describing resuspension flux from ET-areas back either to the surface-water compartment (FETSW) or to the deep-water areas (FETDW). 4. The DC describing how much of the TP in the water that has been resuspended (DCres) and how much that has never been deposited and resuspended (1 − DCres). The model has also been extensively tested by means of sensitivity and uncertainty tests (using both uniform and characteristics uncertainties for driving variables, sub-models and fluxes; see Håkanson, in press) and the

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Table 2 A compilation of the differential equations for the coastal model for phosphorus (from Håkanson and Eklund, 2006) Surface water (SW) MSW(t) = MSW(t − dt) + (FinSW + Fprec + FinQ + FPS + FETSW + FDWSWx − FoutSW − FSWDW − FSWDWx − FSWET)dt = 0.001·CTPsea·VSW / TSW [data on CTPsea = TP-conc. in the sea outside the coast, μg/l; VSW = SW volume; TSW = theoretical FinSW SW retention time; inflow to SW from the sea] Fprec = Prec·Area·CTPprec·0.001·0.001 / 12 [Prec = annual precipitation in mm; CTPprec = 5 μg/l; direct fallout from precipitation] FinQ = 60 60 24 30 CTPin Q [CTPin = conc. in river water; Q = mean monthly river water discharge; river inflow] = [TP from other point sources = 0 in these simulations] FPS FETSW = MET(1 / TET) (1 − Vd / 3) [Vd = the form factor = 3·Dm / Dmax; resuspension ET to SW] FDWSWx = MDW Rmix VSW / VDW [VSW = SW volume; VDW = DW volume; mixing DW to SW] = Q CTPSW·0.001 + MSW(1 / TSW) [outflow from SW] FoutSW FSWDW = MSW(1 − DF) (vSW / DSW)·(1 − ET)(1(1 − DCresSW) + Yres·DCresSW) [sedimentation SW to DW] FSWDWx = MSWRmix [mixing SW to DW] FSWET = MSW(1 − DF)(vSW / DSW)ET(1(1 − DCresSW) + YresDCresSW) [sedimentation SW to ET] Deep water (DW) MDW(t) = MDW(t − dt) + (FSWDW + FETDW + FADW + FinDW + FSWDWx − FDWSWx − FDWA − FoutDW)·dt FSWDW = MSW(1 − DF)(vSW / DSW)(1 − ET)(1(1 − DCresSW) + YresDCresSW) [sedimentation SW to DW] FETDW = MET(1 / TET)(Vd / 3) [Vd = the form factor = 3·Dm / Dmax; resuspension ET to DW] = MARdiff [diffusion] FADW FinDW = 0.001·(CTPsea·1.25)·QDW [data on CTPsea = 25 μg/l; CTP set 25% in DW than in SW; inflow of TP to DW from the sea] FSWDWx = MSWRmix [mixing SW to DW] = MDWRmixVSW / VDW [VSW = SW volume; VDW = DW volume; mixing DW to SW] FDWSWx FDWA = MDW(vDW / DDW)(1 − DF)YT(1(1 − DCresDW) + YresDCresDW) [sedimentation DW to A] FoutDW = MDW(1 / TDW) [outflow from DW to sea] ET-areas (ET): MET(t) = MET(t − dt) + (FSWET − FETDW − FETSW)dt FSWET = MSW(1 − DF)(vSW / DSW)ET(1(1 − DCresSW) + YresDCresSW) [sedimentation SW to ET] FETDW = MET(1 / TET)(Vd / 3) [Vd = the form factor = 3·Dm / Dmax; resuspension ET to DW] FETSW = MET(1 / TET)(1 − Vd / 3) [Vd = the form factor = 3·Dm / Dmax; resuspension ET to SW] A-areas (A): MA(t) = MA(t − dt) + (FDWA − Fbur − FADW)dt FDWA = MDW(vDW / DDW)(1 − DF)YDW(1(1 − DCresDW) + YresDCresDW) [sedimentation DW to A] Fbur = if TA N 48 then MA(1/48) else MA(1 / TA) [TA = the age of active A-sediments; burial] = MARdiff [diffusion; Rdiff = the diffusion rate] FADW Where DF = 1 − PF = 1 − 0.56 = 0.44 DDW = (Dmax − Dwb) / 2 [Dwb = the depth of the wave base, m] DSW = Dwb / 2 DCresSW = FETSW / (FETSW + Fprec + FinSW + FPS + FinQ + FfarmSW) DCresDW = FETSDW / (FETDW + FinSDW + FSWDW) = if ABS(SWT − DWT) b 4 °C then Rmix = 1 else Rmix = 1 / ABS(SWT − DWT) Rmix Rdiff = 0.0003 / 12·YO2; if O2Sat N 50%, YO2 = (2 − 1·(O2Sat / 50 − 1)) else YO2 = (2 − (CTPsed / 1)·3000·(O2Sat / 50 − 1)) SecSW = 10^(− (z+ 0.5)·(log(SPMSW) + 0.3) / 2 + z); z = (10^(0.15·log(1 + SalSW) + 0.3) − 1) SPMsea = 10^(− 0.3 − 2·(log(Secsea) − (10^(0.15·log(1 + Salsea) + 0.3) − 1)) / ((10^(0.15·log(1 + Salsea) + 0.3) − 1) + 0.5)) = AreaAVd(Dmax − Dwb) / 3 VDW VSW = (V − VDW) vdef = 6 m/month = (vdef)YSPMDWYsalDWYDRYDW((1 − DCresDW) + YresDCresDW) vDW vSW = (vdef)YSPMSWYsalSWYDRYZMT((1 − DCresSW) + YresDCresSW) YZMT = If Q N Qsea then YZMT = (Salsea / SalSW)(Qsea + Q) / Q) else YZMT = (Salsea / SalSW)(Qsea + Q) / Qsea) [Q-values in m3/month; calculates sedimentation effects related to the “zone of maximum turbidity”] = (1 + 0.75(CSW / 50 − 1)) [calculates how changes in SPM (CSW) influences sedimentation] YSPMSW YSPMDW = (1 + 0.75(CDW / 50 − 1)) [calculates how changes in SPM (CDW) influences sedimentation] YsalSW = (1 + 1(SalSW / 1 − 1) = 1·SalSW / 1 [calculates how changes in salinities N1‰ influence sedimentation] YsalDW = (1 + 1((SalSW + 3) / 1 − 1)) [calculates how changes in deep-water salinities influence sedimentation] = If DR b 0.26 then 1 else 0.26 / DR [calculates how changes in DR/turbulence influence sedimentation] YDR Yres = ((TET / 1) + 1)0.5 [calculates how much faster resuspended sediments settle out] YDW = If TDW b 7 (days), YDW =1 else YDW =(TDW /7)0.5 [calculates how changes in deep-water turbulence influence deep-water sedimentation]

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most important factor regulating model predictions of TP-or SPM-concentrations in coastal water is generally (but not for Ringkøbing Fjord, see later) the value used for the TP- or SPM-concentration in the sea outside the given coastal area. The obligatory driving variables include four morphometric parameters (coastal area, section area, mean and maximum depth), salinity (these simulations use empirical salinities) and measured TP-concentrations or Secchi depths (calculated into SPM-concentrations) in the sea outside the given coastal area and, for estuaries, in major tributaries. All basic equations are compiled in Table 2. Many of the structures in the model are general and could be, and have been, used for coastal areas other than those included in this study, e.g., for open coasts, estuaries or areas influenced by tidal variations and for other substances than phosphorus and SPM (see Håkanson, in press). 2.4. Variations, uncertainties and confidence intervals for the empirical data Fig. 6 shows the modelled values (which will be explained in detail in the following text) in relation to the uncertainty bands for the median monthly and median annual empirical data (the L-values, i.e., the error in the empirical data accounting for the number of analyses and the standard deviations). One cannot verify a model with better accuracy than permitted by the uncertainty related to the observations. The uncertainty bands for the empirical data in Fig. 6 inform about the inherent uncertainty in the empirical data from Ringkøbing Fjord. Had this modelling been done at finer time-scales (say on a daily or weekly basis), the inherent uncertainties in the empirical data would have been very large (see Bryhn et al., 2006). So, instead of comparing modelled values to empirical data in Fig. 6, we compare modelled values to the uncertainty bands in the empirical data. This is done for TP-concentrations, SPM, Secchi depth and chlorophyll-a concentrations. Calculated data on TP-concentrations in sediments (from areas of fine sediment accumulation; see Fig. 6E) are compared to the uncertainty bands related to the TP-

concentrations in sediments. Fig. 6F gives vital background information of the changes in macrophyte cover and biomass of clams in the lagoon. Note the very marked changes in all these variables from the period 1990/1993 to 2000/2004. In this paper, we will address the causal reasons for these changes. These uncertainty bands in Fig. 6 should be seen as reference bands and a good model would produce predictions within the domain given by these to error bands for the empirical data. Table 3 gives a compilation of CV-values for salinity, TN, TP, chlorophyll, Secchi depth, SPM and water temperature based on daily, weekly, monthly and yearly sampling. From this table, one can note that the CVvalues are higher for TP than for TN, highest for SPM and lowest for salinity. The error bands for the monthly and annual data used in this work (see Fig. 6) are based on these CV-values. If the variability within an ecosystem is large, many samples must be analyzed to obtain a given level of certainty in the mean value. There is a general formula, derived from the basic definitions of the mean value, the standard deviation and the Student's t value, which expresses how many samples are required (n) in order to establish a lake mean value with a specified certainty (Håkanson, 1984): n ¼ ðtCV=LÞ2 þ 1

ð1Þ

where t = Student's t, which specifies the probability level of the estimated mean (usually 95%; strictly, this approach is only valid for variables from normal frequency distributions), and CV = coefficient of variation within a given ecosystem. L is the level of error accepted in the mean value. For example, L = 0.1 implies 10% error so that the measured mean will be expected to lie within 10% of the expected mean with the probability assumed in determining t. Since one often determines the mean value with 95% certainty ( p = 0.05), the corresponding t-value is 1.96 (from statistical tables). If the CV is 0.35, about 50 samples are required to establish a lake-typical mean value for the given variable provided that we accept an error of

Table 3 Coefficients of variation (CV) for salinity, TN, chlorophyll, Secchi depth, TP, water temperature and SPM based on daily, weekly, monthly and annual data from Ringkøbing Fjord for the period 1980 to 2004

Daily Weekly Monthly Yearly

Salinity

TN

Chlorophyll

Secchi

TP

Temperature

SPM

0.08 0.08 0.08 0.24

0.07 0.11 0.12 0.47

0.18 0.29 0.30 0.56

0.11 0.20 0.20 0.42

0.15 0.25 0.27 0.62

0.03 0.09 0.10 0.53

0.20 0.37 0.38 0.70

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Fig. 6. Illustration of the uncertainties in the empirical data for TP-concentrations (A), SPM-concentrations (B), Secchi depth (C), chlorophyll (D; note that the data before 1985 are represented by one value), TP-concentration in accumulation area sediments (E) and changes in macrophyte cover and biomass of clams (F). Figures A to D show the error (L) in the monthly and yearly median values (L) related to the median value of the coefficient of variation (CV) calculated from all available empirical data (n) from the period 1980 to 2004. These L-values are shown in figures A to D and they are used as the reference bands against which the modelled values should be compared. The bolded lines show model-predicted values and one cannot expect a model to predict better than the domain given by these uncertainty bands in the empirical data.

L = 10%. It one accepts a larger error, e.g., L = 20%, fewer samples would be required. The CV-values in Table 5 are calculated for different time periods using data from Ringkøbing Fjord from 1980 to 2004. Given the fact that there are typically about 8 samples available for each month and about 88 samples for annual data, one can see that the mean or median annual values may be determined with less statistical certainty than the mean/median monthly values in spite of the fact that the CV-values are higher for the annual data. For example, for chlorophyll, we have: For monthly data, CV = 0.30, n = 8 gives that the mean value can be estimated with an error (L) less than

21% of the mean (with a 95% certainty). For annual data, CV = 0.56, n = 88 gives that the error (L) around the mean value is 12% of the mean. So, given the marked variability in most of these water variables, and the relatively few monthly data available, it becomes important to focus on large-scale changes by either using median or mean values on a monthly, 3-monthly or yearly basis. 2.5. Regressions Bryhn et al. (2006) have presented many regressions between chlorophyll and Secchi depth (as y-variables)

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and potential x-variables From those results, one may note: • The results depend very much on the season; the best results are generally obtained for data from the summer period. • Better correlations are obtained for median values than for mean values because most frequency distributions for most variables are not normal, so medians reflect typical conditions better than means. • There are major differences among the x-variables in how they correlate to these two effect variables (or operational bioindicators). Total phosphorus concentration (TP) is by far the best predictor both for chlorophyll and Secchi depth in Ringkøbing Fjord. • Nitrogen or ratios based on nitrogen or different forms of nitrogen generally co-vary with these two operational bioindicators poorly or very poorly. The empirical model to predict chlorophyll-a concentration (Chl in μg/l) in this work comes from a regression given in Fig. 7D1 based on empirical median TPconcentrations (CTP in μg/l) from annual data from Ringkøbing Fjord (r2 = 0.96; n = 21). In the following simulations, we will replace (CTP) in this regression by modelled monthly values on CTP and use Eq. (2) to calculate monthly chlorophyll-values. Chl ¼ ððSWT þ 0:1Þ=9Þ101 ð1:72logðCTP Þ−1:86Þ

ð2Þ

where ((SWT + 0.1) / 9) is a dimensionless moderator based on the ratio between measured median monthly surface water temperatures (SWT) divided by a surface water temperature of 9 °C related to the duration of the growing season and a mean annual water temperature (see Håkanson and Boulion, 2002). The constant 0.1 is added since there is also primary production in the winter if the temperature approaches zero. This expression will give a simple seasonal variability pattern to the chlorophyll values using the basic regression (10^(1.72·log(CTP) − 1.86)). Fig. 7 also addresses some important methodological issues related to regressions, uncertainties in data and models and identifications of thresholds. The regressions in Fig. 7 use chlorophyll as y-variable and TP as x-variable, but we would like to stress that the figure is meant to illustrate general aspects of regression analyses. The first figure (Fig. 7A) gives results based on daily data. Generally, there are 1 to 3 data per day and a total of 623 data in this regression, which gives an r2 of 0.55, which is well below the threshold r2-value of 0.75 for practical

usefulness (see Prairie, 1996; Håkanson, 1999). Fig. 7A also gives the 95% confidence intervals for individual data. From this figure, one can note the wide scatter, the low r2value and that the slope is 1.08. Fig. 7A2 gives two box-and-whisker plots (showing medians, quartiles, percentiles and outliers) for the CVvalues for the chlorophyll concentrations for all daily data based on 3 samples, since it is not meaningful to determine the standard deviation, SD, if n is not ≥ 3. One can note, that the median CV is 0.18. This figure also gives the L-value (the error for the mean values from the sampling formula). One can see that L is 25% if n is 3 and all individual CVs are accounted for. The next figure (B1) gives the same thing as A1 but for monthly data. Fig. 7B2 gives box-and-whisker plots for CV and L based on monthly data; the median values are 0.29 and 0.28, respectively. Fig. 7C1 shows the results for data from 3-month periods; one can note that the slope is 1.43 and the r2-value 0.71. Fig. 7C2 indicates that the median CV for these 86 median values based on data from 3 months (generally from 24 samples) is 0.44; the corresponding L-value is 0.22. Fig. 7D2 gives the results for the 21 annual median values (generally based on 88 samples); the slope is 1.72 and the r2-value 0.96. The median CV is 0.56, and the corresponding L-value is 0.078. From Fig. 7, one can specifically note: • The CV-values increase from daily to annual sampling periods (median values change from 0.18 to 0.56). This is valid not just for chlorophyll, but for most water variables in most coastal areas (see Håkanson, in press). • The median L-values decrease from 0.25 to 0.078 in spite of the fact that the CV-values increase; this is because the increase in CV is more than compensated for by the increase in number of data for each median (or mean value), from 3 to 88. • The slopes increase in a logical and steady way from 1.08 to 1.72. This means that the interpretation of how changes in nutrient concentrations (here TP) influence primary production changes drastically if different regressions are used without due consideration to the presuppositions. The main reason for this change in slopes is that chlorophyll-values in relation to nutrient concentrations are higher during the summer because the water temperatures and the light conditions favour a higher primary production, and that there are more samples from the summer period than from the winter period in this monitoring. • The r2-values increase in steps from 0.55, 0.63, 0.71 to 0.96. The regime shift in the lagoon related to

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Fig. 7. Regressions between chlorophyll and TP using data from Ringkøbing Fjord (data from 1984 to 2004). A1. Gives results (regression line, r2 and n) based on daily median data; generally there are 1 to 3 data per day and a total of 623 data in this regression, which gives an r2 of 0.55; the slope is 1.08. A2. Gives a box-and-whisker plot for the CV-values for the chlorophyll concentrations for all daily data based on 3 samples. A2 also gives a similar plot for the L-value (the error in the mean from the sampling formula). B1. Gives the same thing as A1 but for monthly data. B2. Gives the box-and-whisker plots for CV (based on monthly data) and L; the median values are 0.29 and 0.28, respectively.

the changes in chlorophyll concentrations (shown in Fig. 1) can best be identified using the annual data (Fig. 7D1), and this is mainly because those median values have a small inherent uncertainty, an L-value of 0.078. One way to estimate the highest possible r2 of a predictive model is to compare two empirical samples since one can generally not expect models to predict better than empirical data (see Håkanson, 1999). Two parallel series of data on TP-concentrations where 3 data have been randomly selected in the series called Emp1 and 3 other samples used for Emp2; these two samples represent monthly median values and should represent the same thing. The r2-value calculated from 181 samples taken within one month is 0.31, which is rather low but highly significant ( p b 0.0003) since the

number of data (n) is so large (181). This variability includes analytical and methodological uncertainties but mainly depends on the significant monthly variability for TP (and most other water variables) in this lagoon (and other coastal bays). The higher the CVvalue, the more difficult it will be to establish representative and reliable empirical mean or median values of the given variable. One can note that very significant improvements in predictive power can be expected from median annual values, as compared to median monthly values (r2 = 0.87 versus r2 = 0.31). The main reason for this significant increase in the r2-value has to do with the fact that 12 times as many empirical data have been used in the regression for the annual data and that one would have obtained an even higher r2 if we have had accesses to 12 times as many data for the monthly data, but this is not the case. So, in this

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modelling, depending on the accessibility and variability of the data, we will focus on either median values for 3-months periods and/or on the annual time scale.

Fig. 8 illustrates how modelled monthly values are smoothed for (A) TP-concentrations and (B) Secchi depth.

2.6. Annual data calculated from monthly data

2.7. Changes in clams and macrophytes

We have demonstrated the great uncertainty in monthly mean or median values and motivated why this modelling will not focus on short-term predictions. In all the following presentations, we will use a smoothing function to create more reliable monthly values. So, a first-order exponential smooth (SMTH) of the input (the modelled monthly values for TP-and SPM-concentrations, etc.) will be used. The smoothing function is written as: SMTH(input, average time, initial value), or, using a differential equation (see also Håkanson, 1999):

Two groups of organisms that have gone through major changes in the lagoon during recent years are clams and macrophytes (see Table 1). The dominating clam, the soft-shelled Mya arenaria, is also abundant along the North Sea coast outside Ringkøbing Fjord. It is sensitive to low salinity and does not exist in waters with a mean salinity of less than 4–5‰ (Strasser, 1999). Eggs are probably even more sensitive than larvae and adults and have a salinity optimum of about 16–32‰ (Stickney, 1964). It is therefore most likely that it was the change in salinity from 7 to 13‰ (median values) in Ringkøbing Fjord between 1994 and 1996 (see Fig. 9) that had highly beneficial effects on the clam community, which surged in 1996 and has increased in biomass since then (see Fig. 10 and Table 1). Similar changes were observed in 1910, when a canal was dug between the lagoon and the sea and the salinity increased from about 5–10‰ to 15–25‰ (Petersen et al., 2006).

SIðtÞ ¼ SIðt−dtÞ þ CIdt

ð3Þ

where SI CI

Smooth of input (a time series of data). Change in smooth; CI = (IN − SI) / AT, where IN = input, AT = average time, set to 12 months in all the following simulations.

Fig. 8. Modelled monthly values for (A) TP-concentrations in water and (B) Secchi depths compared to smoothed monthly values (using an exponential smoothing function with an “average time” of 12 months; see Håkanson, 1999).

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Lat

Dmax

A1 Fig. 9. The regime shift in Ringkøbing Fjord exemplified by empirical data for the change in macrophyte cover (%), as compared to macrophyte cover predicted by a lake model (from Håkanson and Boulion, 2002) and used for Ringkøbing Fjord for the period 1980 to 2003, and compared to empirical median annual salinities.

The salinity also affects the macrophytes as different macrophyte species prefer different salinities (Boston et al., 1989; King and Garey, 1999) and have different tolerances to changes in salinity (Rout and Shaw, 1998, 2001). This means that in order for macrophytes to abound, a relatively constant salinity is desirable. Fig. 9 indicate that there may have been detrimental effects on the macrophyte cover from drastic salinity changes in Ringkøbing Fjord during the last 20 years. However, no obvious structural changes in species composition have been documented within this functional group. How would these changes in macrophytes and clams influence the mass-balance for TP and SPM? Is it possible to compare and rank the fluxes of TP and SPM to and from macrophytes and clams with other fluxes, and the roles that these changes in two functional species play in the overall reaction of Ringkøbing Fjord to the changes in nutrient inflow and salinity? This is what this modelling aims to discuss and quantify. As a background to the discussion, Fig. 9 compares the changes in macrophyte cover to modelled values for lakes (because such models are not available, or known to us, for coastal areas), using the following empirical model from Håkanson and Boulion (2002): MðMaccov Þ¼ 10:49 þ 1:502ðSec=Dm Þ −1:993 90=ð90−LatÞ−0:422ðMDmax Þ þ logðA1Þ ðr2 ¼ 0:84; n ¼ 19Þ

ð4Þ

Where Sec / Dm The ratio between Secchi depth (m) and the mean depth (Dm in m); the greater this ratio, the

79

larger the macrophyte cover; this is the most important factor regulating macrophyte cover in lakes. Latitude (°N); the lower the latitude, the larger the macrophyte cover; this is related to increased temperatures at lower latitudes. The maximum depth (Dmax in m); systems with great depths generally have a lower macrophyte cover. The area shallower than 1 m (in km2), as calculated using the algorithm in Fig. 6; the larger this area, the larger the macrophyte cover.

Fig. 9 shows that one would have expected a significantly higher macrophyte cover in Ringkøbing Fjord had this been a lake and that the macrophyte cover would normally increase when the Secchi depth increases. The opposite thing has happened in Ringkøbing Fjord, so the regime shift is actually greater than one would see just from looking at the changes from the 1980s. This empirical model Eq. (4) does not include salinity or extinction of species related to changes in salinity, but it is interesting to note that if the system will reach a new steady-state at a mean annual salinity of 10 to 12‰, one can expect that the macrophyte cover would increase significantly. But macrophytes need space on the bottom and they will compete with the clams for this space. This means that it will be very interesting to follow the situation in Ringkøbing Fjord and see what kind of balance will appear between the clams and the macrophytes. 3. Results 3.1. Initial results and adjustments of the model The first modelling results were shown in Fig. 2, which gave a comparison between modelled values using the modified general mass-balance models for TP and SPM. Fig. 11 compares empirical data (median annual values) to modelled data using the basic model (which do not consider macrophytes or clams), and also modelled data from the modified model (which will be explained in this section). One can note that the basic model gives good predictions for TP- and SPMconcentrations in water when smoothed values are compared to median annual empirical data for the entire period up till the changes in macrophyte cover and clams. For the period after 1996, one can see that the model gives too high TP-concentrations and hence also too high chlorophyll-values, too high SPMconcentrations, and hence too low Secchi depths.

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Fig. 10. Illustration of the conditions related to chlorophyll and biomass of clams during the threshold period (the invasion of the clams) between 1994 and 1998. A. Gives modelled values of the biomass of clams and the uncertainty in the median empirical annual chlorophyll values (L). B. Gives all actual chlorophyll data. One can note the great scatter in the data before the threshold period in relation to after the threshold and also a slight seasonal temperature dependence of the chlorophyll values.

It should be noted that to produce the curves related to the basic model, there has been no tuning of the model, i.e., no changes in any model equations, except for the evident changes in the obligatory driving variables. The following data have been used in this modelling: (1) Median monthly empirical data on salinity and water temperature have been used in all the following simulations. (2) Median monthly data for tributary water discharge (Q; and not modelled values) have been used for the entire period (1980 to 2004). (3) These calculations have also used empirical median monthly values for tributary inflow of TP (i.e., water

discharge times tributary concentration; see curve 1 in Fig. 12B). (4) The water exchange between the sea and the lagoon has not been modelled by the standard algorithms included in the basic dynamic model (since there is a sluice regulating the water exchange between the lagoon and the sea in this case), but has been calculated by a simple mass-balance for salt, given by: Qsea ¼ Salemp Q=ðSalsea −Salemp Þ Qsea

ð5Þ

The requested water flow from the sea into the lagoon (m3/month); these values are also used

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Fig. 11. A. Empirical data (median annual values) compared to modelled values using the dynamic TP-model with (modified version) and without (basic model) considerations to changes in macrophyte cover or clams in Ringkøbing Fjord for the period between 1980 and 2004. B. A comparison between empirical data (median annual values) compared to modelled values using the dynamic SPM-model with (modified version) and without (basic model) considerations to changes in macrophyte cover or clams in Ringkøbing Fjord.

Salemp Q Salsea

to calculate the inflow of TP and SPM from the sea. Empirical data on the salinity in the lagoon (‰; such data are at hand). Tributary water discharge (m3/month; empirical data on Q are available). Salinity in the sea outside the coast; set to 33‰, as a general default value.

(5) The tributary inflow of SPM has been calculated from the tributary inflow of TP by assuming that the TP-concentration on SPM in tributaries is a factor of 2 higher than the maximum median values from recent sediments in the lagoon (see Håkanson, in press). This means that the TP-concentration on tributary SPM has been set to 2 mg/g dw. (6) The wave base in Ringkøbing Fjord is at 20 m (calculated from Fig. 3) and the maximum depth is 5.1 m. This means that the entire lagoon is dominated by resuspension events. However, functionally, one can expect that there will be topographical deepholes and sheltered areas that will function as

accumulation areas and in this modelling these areas have been estimated by the following boundary condition: If the default wave base (Dwb0 =20 m from Fig. 3)N 0.95·Dmax then Dwb =(0.95/(1+0.05·((Dmax /Dwb0)−1))) Dwb0 ¼ ð45:7MArea=ð21:4 þ MAreaÞÞ; ðArea in km2 Þ

ð6Þ

For Ringkøbing Fjord, this gives that the functional wave base (Dwb) is at a water depth of 0.99·Dmax = 5.0 m and that 6% of the area would function as an accumulation area and the rest as ET-areas with resuspension. (7) Since the lagoon is so dominated by resuspension, the sediment water content and organic content is lower than in more “normal” coastal areas and the bulk density higher. The default, “normal” water content in A-sediments (0–10 cm) is generally set to be 75% in this model, but empirical data from Ringkøbing suggests that 65% would be more

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Fig. 12. A. TP-amount in ET-sediments (curve 1), in A-sediments (curve 2), in surface water (curve 3), in macrophytes (curve 4) and in clams (curve 5); data from Ringkøbing Fjord for the period 1980 to 2004. B. TP-fluxes from land (curve 1; scale 0-30 t/month), from the sea (curve 2; scale 0-3 t/month), TP-uptake in clams (curve 3; scale 0-30 t/month); and TP from surface water to macrophytes (curve 4; scale 0-3 t/month) and return flow from macrophytes to surface water (curve 5; scale 0-3 t/month). C. Internal TP-fluxes, sedimentation from surface water to ET-areas (curve 1), resuspension from ET-areas to surface water (curve 2), mixing from surface water to deep water (curve 3), outflow from the fjord to the sea and burial (curve 5). Note the scale on the y-axis. The internal fluxes are very important in this large and shallow fjord; modelled values for Ringkøbing Fjord for the period 1980 to 2004.

appropriate in this lagoon, so 65% has been used. This value influences the TP-concentration in sediments. In the following, we will explain how the basic model has been modified and how the roles of the macrophytes and the clams have been quantified. 3.2. Fluxes, amounts and biomasses It is not possible to understand the roles of the changes in macrophytes and clams without due

considerations to TP-amounts (where can the TP be found?) and TP-fluxes (how much TP comes from various sources and from internal transport processes?). Fig. 12 is meant to give important background information on this. From Fig. 12A, one can note that after the regime shift most TP is found on ET-areas (curve 1) and in the clams (curve 5), less TP are in Asediments (curve 2), macrophytes (curve 4) and even less in surface water (SW, curve 3). In Section 3.2.1 below, we will explain how these calculations have been done for TP in clams and macrophytes. Fig. 12B gives the key fluxes, TP inflow from land (note the scale for

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TP-inflow and TP-uptake in clams; these are the most important fluxes); TP inflow from the sea (this is generally the second most important external, driving, flux; note the scale) and TP uptake in clams and macrophytes. Fig. 12C shows how important the internal fluxes (sedimentation, resuspension, mixing, burial and outflow) are (note the scale on the y-axis) compared to the external (driving) TP-fluxes. To quantify these internal fluxes makes it also possible to understand the roles that the macrophytes and the clams play in the ecosystem not just for biouptake and retention of nutrients but also for sedimentation, sediment entrapment in macrophyte beds and clams, retention of matter on ET-areas and consumption of SPM (plankton, etc.) by clams from the water. 3.2.1. Calculations of changes in macrophytes and clams 3.2.1.1. Macrophytes. Fig. 13 shows the calculated changes in macrophyte biomass. In this modelling, the changes in macrophytes will influence the system in two ways, (1) SPM and TP bound in macrophytes will be released when the macrophytes are reduced due to variations in salinity and bound again when the macrophytes expand; all the following calculations relate to the initial conditions with a macrophyte cover of 9% of the lagoon area, and (2) the macrophytes will influence the retention of SPM and TP since particulate matter entrapped in macrophytes beds will stay a longer time, as compared to bottom areas with less macrophytes. Macrophyte biomass (BMmacemp in g dw) has been calculated from empirical data on macrophyte cover (Maccov in %) in the following way (from macrophyte

83

production in g ww/m2·year; from Håkanson and Boulion, 2002): BMmacemp ¼ ð1=6:6Þð365=300ÞðAreaÞ101 ð2:472

þ 1:028logðMaccov Þ−0:516ð90=ð90−LatÞÞÞ ð7Þ

Where (1/6.6) transforms g ww to g dw, (365/300) is the number of days per year divided with the characteristic turnover time for macrophytes (T = 300 days; by definition T = BM / PR; BM = biomass in g; PR = production in g per month), Area is the coastal area in m2 and latitude (Lat) is 56 °N. The biomass calculated in this way is shown by the curve “BMmacemp” in Fig. 13 (recalculated from g dw to t dw). The change in biomass, as related to the initial conditions, is also given in Fig. 13 (dBMmac), as well as the increase in macrophyte biomass (dBMmacs). The macrophytes will bind TP (as long as the macrophytes live, TP will be retained in their biomass) and the macrophytes will influence the retention/ resuspension of TP and SPM. This has been quantified in the following manner. MTPmac ðtÞ ¼ MTPmac ðt−dtÞ þ ðFTPSWmac þ FTPETmac −FTPmacET −FTPmacSW Þdt

ð8Þ

Where FTPSWmac The TP-flow from surface water (SW) to macrophytes (mac); MTPSW · Rupmac · 0.5 · (BM macemp / BM macref ) [M TPSW = the TPamount in SW; Rupmac = uptake rate of TP in macrophytes = 0.0075 per month; (BM macemp / BM macref ) = a dimensionless

Fig. 13. Empirical and calculated changes in macrophyte biomass (curve marked “Empirical biomass” gives calculated changes based on empirical data on macrophyte cover), calculated changes in biomass relative to initial conditions (macrophyte cover = 9%) and calculated increases in salt-water species; Ringkøbing Fjord for the period 1980 to 2004.

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moderator describing the ratio between the macrophyte biomass calculated from empirical changes in macrophyte cover, from Eq. (7), and related to a reference value when the macrophyte cover is 9% in Eq. (7); 0.5 = a distribution coefficient regulating the TPuptake in macrophytes from either from surface water, 0.5 (50%) or from ET-sediments (1–0.5 = 0.5]. FTPETmac The TP-flow from ET-areas to macrophytes; MET ·Rupmac ·0.5·(BMmacemp /BMmacref) [MTPET =the TP-amount on ET-areas]. FTPmacET The TP-flow from macrophytes to ET-areas; 0.9 · MTPmac / Tmac[Tmac = the turnover time for TP in macrophytes set to 24 months as a default value; 90% of the TP in dead macrophytes is set to return to ET-areas]. FTPmacSW The TP-flow from macrophytes to surface water; 0.1 · MTPmac / Tmac [10% of the TP in dead macrophytes is set to return to the SWcompartment]. The mean TP-concentration in macrophytes is assumed to be 0.4% dw (from Håkanson and Boulion, 2002). This means that the changes in TP-amounts and TP-fluxes related to the changes in macrophyte biomass can be calculated (see Fig. 12). From Fig. 12A, one can note that relatively small amounts of TP are bound in the macrophytes, even when the macrophyte cover attain values higher than 9% of the area; from Fig. 12B, one can see that the TP-fluxes to (and from) the macrophytes are also relatively small compared to most other major fluxes. This means that the main role the macrophytes play for the massbalances of TP and SPM concerns how they entrap and retain particulate TP and SPM (see Eq. (9)), and hence also influence resuspension and water clarity (see also Fig. 15, later). From Fig. 13, one can note the good correspondence between modelled biomasses of macrophytes using Eq. (8) (from modelled TP-concentrations) and macrophyte biomasses calculated from empirical data on macrophyte cover using Eq. (7). When the macrophytes die, the amount of matter bound in the plants is added to the ET-areas as SPM. The macrophytes (and the clams) also entrap and retain SPM and particulate phosphorus and influence the age of SPM and particulate TP on ET-areas (TET). This has been quantified in the following way for the macrophytes. Ymac ¼ ðMaccov =9Þ

ð9Þ

Ymac is a dimensionless moderator influencing TET. If the macrophyte cover is 9% (the reference conditions), Ymac is 1 and there is no change in TET, as compared to calculations using the general modelling set-up without considerations to macrophyte and clams. If the macrophyte cover is 4% (see Fig. 9), Ymac is 0.54 and TET is a factor of 0.54 lower and resuspension higher. 3.2.1.2. Clams. The clams will also influence the mass-balance for TP and SPM; the clams will bind TP (TP will be retained in the clam biomass) and the clams will influence the retention/resuspension of TP and SPM. But the clams also have to eat and in this modelling they consume plankton and organic matter included in SPM mainly in the water phase. This has been quantified in the following manner. The fluxes of TP to and from the clams area given by (F for flow as in Eq. (8)): MTPclam ðtÞ ¼ MTPclam ðt−dtÞ þ FTPSWclam þ FTPETclam −FTPpredclam −FTPclamSW −FTPclamET Þdt ð10Þ Where FTPSWclam TP-uptake in clams from SW; MTPSW · Rupclam · YSalclam · DC1 [MTPSW = TP-amount in SW; R upclam = uptake rate of TP in clams = 0.03 per month; YSalclam =a dimensionless moderator describing the influence of salinity on the TP-uptake in clams (see Eq. (11)); DC1 = a distribution coefficient regulating the TP-uptake in clams from either surface water or from ETsediments; DC1= 0.9; i.e., 90% from the water phase as a default value]. FTPETclam TP-uptake in clams from ET-areas; MTPET · Rupclam · YSalclam·(1 − DC) [MTPET = TP-amount on ET-areas]. FTPpredclam Predation on clams by birds, fish, etc. MTPclam · Rpred · [MTPclam = TP-amount in clams; Rpred = predation rate on clams as a measure of TP removal from the system via clams; set to 1% = 0.01 per month, as a default value]. FTPclamSW DC2·MTPclam / Tclam [DC2 = a distribution coefficient quantifying the return flow of TP from clams either to either ET-areas or to the SW-compartment; DC2 = 0.1, as a default value, i.e., 10% to the SW-areas; Tclam = the turnover time for TP in clams set to 36 months as a default value].

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FTPclamET (1 − DC2)·(MTPclam / Tclam) If SalM50 b9:5x then YSalclam ¼ 0 else YSalclam ¼ SalM50 ð11Þ

Using this sub-model to calculate TP-uptake in clams, and from information on the TP-concentration in clams, one can also calculate the clam biomass (BMclam). This is done in the following manner: • BMclam = MTPclam / 0.0027 [BM clams in g dw; the TP-concentration in clams is set to 0.27% P per g dw; from Håkanson and Boulion, 2002]. If the biomass of clams is calculated per area unit, we have: • BMclam = BMclam / Area [BM clams in g dw per m2]. The clams also consume SPM in the water phase, entrap and retain SPM and particulate phosphorus and influence the age of matter on ET-areas (TET). This has been quantified in the following way. Sediment entrapment is given by: If BMclam ðin g dw=m2 ÞbBMnormclam then Yclam ¼ 1 else Yclam ¼ ðBMclam =BMnormclam Þ1

ð12Þ

Yclam is a dimensionless moderator influencing TET. If the actual clam biomass (BMclam) is lower than the normal biomass (BMnormclam), Yclam = 1. If this ratio between the actual and the normal biomass is higher than 1, more SPM and particulate phosphorus is retained on ET-sediments and the age of these sediments (TET) becomes longer and the resuspension lower. Eq. (11) means that the default threshold salinity is set to 9.5‰ (median annual value). Fig. 14 gives results from tests to find the proper value for the

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threshold salinity. Four different values have been tested in this example (8.5, 9.5 and 10.5‰) and the figure illustrates how well empirical biomasses of clams are modelled in these cases. These results (and several similar tests) motivate the use of 9.5‰ as a default value in the following simulations. At lower median annual salinities, there will be less TP-uptake in clams and less clams than what the empirical data suggest; if the salinity is 19‰, YSalclam is 19 and the TP-uptake 2 times higher than at a salinity of 9.5‰. It means that if one would like to have a high water clarity, a high production of macrophytes and clams, then the mean or median annual salinity should not be lower than 9.5‰. One can also note from Fig. 14 that this modelling gives biomasses of clams that agree well with empirical data, and since the TP-concentration in clams is known (at least in terms of order of magnitude values), one can assume that the modelling of TPuptake and retention in clams is fairly accurate. Note that value for the normal biomass (BMnormclam) should represent a normal biomass of zoobenthos in the system. We have tested various values and can conclude that a value of 25 g dw/m2 gives the best predictions and hence, this value should represent a typical, normal zoobenthos biomass in the lagoon. Higher values means a higher consumption of SPM, lower SPM-values in the water and a higher Secchi depth. The consumption of SPM (plankton and organic matter included in SPM) by clams is given by: FSWclam ¼ MSPMSW RSWclam If ðBMclam =BMnormclam Þ b1 then RSWclam ¼ 0 else RSWclam ¼ ðBMclam =BMnormclam Þ

ð13Þ

Where MSPMSW is the mass of SPM available for the clams in the surface water; the organic fraction of SPM,

Fig. 14. Empirical data on biomass of clams versus modelled values at three different threshold salinities (for mean annual data; the default value used in this modelling is 9.5‰); Ringkøbing Fjord for the period 1980 to 2004.

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which includes the food eaten by the clams such as living and dead plankton, is set to be 33% (or 0.33; see Håkanson and Jansson, 1983); and the TP-fraction of SPM is set to be 2 mg/g dw (as mentioned before); RSWclam is the uptake or consumption rate of clams consuming SPM (per month). If the actual clam biomass (BMclam) is lower than the normal biomass (BMnormclam), Rclam is zero. If this ratio (BMclam/BMnormclam) is higher than 1, more SPM is lower from the surface water due to consumption by clams. This is a net flux of SPM from the surface water mass. This also means that the role of the macrophytes and the clams may be quantified using the dynamic model with its associated sub-models for Secchi depth and chlorophyll. The results are given in Fig. 15 where the actual modelled situation (curve 1) is compared to a situation when there is no change in macrophyte cover of biomass (the basic model, curve 2). This

simulation is meant to demonstrate the roles of the macrophytes and the clams (SPM and TP is added when the macrophytes are reduced and SPM and TP is more retained when the macrophytes and clams increase). Curves 3 in Fig. 15 illustrate a situation when the salinity has been kept constant at 5.5‰. The difference between curves 2 and 3 illustrates the role of the salinity. The higher the salinity, the higher the flocculation and aggregation, the higher the sedimentation, the clearer the water and the lower the TPconcentration and the lower the chlorophyll-values. Curves 4 show the role of the changes in TP-inflow (from tributaries). The lower the TP-inflow, the lower the TP-concentration in the lagoon and hence also the chlorophyll concentrations. Curves 5 demonstrate the role of the macrophytes. One can note that the macrophytes do play an important role, especially in situations with relatively low biomasses of clams. For

Fig. 15. Simulations to illustrate the role of different factors influencing the regime shift in Ringkøbing Fjord. Curves 1 in gives modelled values for (A) TP-concentrations, (B) chlorophyll, (C) SPM and (D) Secchi depth using the modified model (which predicts close to the empirical data); curves 2 compares the output from the modified model with that of the basic model (macrophyte cover = 9%; no invasion of clams); curves 3 show the results if the salinity is constant at 5.5‰ (using the basic model); curves 4 gives the results if the TP-inflow is constant (at 20.4 t/year using the basic model); curves 5 compared to curves 2 illustrate the role of the changes in macrophyte cover (using the basic model); curves 6 compared to curves 2 illustrate the role of the changes in clams (using the basic model); one can note that for the last years (2001–2004), the situation in the lagoon depends very much on the invasion of the clams, which depend very much on the salinity being higher than 9.5‰.

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the TP-concentration, one can see higher concentrations in the actual situation around 1996 when the macrophytes begin to disappear and lower TPconcentration after 1998 when they begin to reappear. The changes in TP-concentrations are reflected in the changes in chlorophyll (Fig. 15B). The most marked changes appear for Secchi depth (Fig. 15D) — during the 1990s, the water clarity would have been significantly lower (and the SPM-concentrations higher; Fig. 15C) had there been no changes in macrophytes (i.e., if the macrophyte cover is set to 9% for the entire period). This simulation is theoretical in the sense that the results given by the curves in Fig. 15 include changes in salinity and no changes in clams. The important role of the clams is shown by curve 6 in Fig. 15. Evidently, the clams do not influence the conditions in the lagoon when there are only small amounts of them, but they play a decisive role when

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the biomass of the clams increase above the normal value of 1 g dw/m2 ; the higher the biomass of the clams, the more TP will be retained in the clam biomass, and the greater the influence on the TPretention in the sediments. When the clam biomass reaches values higher than 100 g dw/m 2 , they dominate the conditions in the lagoon (Secchi depth, chlorophyll, TP and SPM). In a following paper, we will address different remedial scenarios for Ringkøbing Fjord, such as how changes in inflow of nutrients and salinity, influence the system (see Håkanson and Bryhn, 2006). 3.3. Sensitivity analyses The basic dynamic model for TP and SPM has been tested extensively by sensitivity and uncertainty analyses using both uniform and characteristic uncertainties

Fig. 16. Sensitivity analyses to illustrate the role of different values for nine model factors of minor importance for the predictions of (A) TPconcentrations, (B), chlorophyll concentrations, (C) SPM-concentrations and (D) Secchi depths. The tested changes are given in the figure. Note that in these nine simulations each factor has been changed and all else have been kept unchanged; data from 1980 to 2004.

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for fluxes, driving variables and different model components (see Håkanson, in press; Håkanson and Eklund, 2006), and those tests will not be repeated here, where we will instead focus on the new parts related to the conditions in Ringkøbing Fjord and the role of the clams and macrophytes. Fig. 16 presents results from 9 sensitivity analyses. Curve 1 gives the default conditions, as a reference. Curve 2 gives results when there is no uptake, no consumption of SPM by the clams. Evidently, there are uncertainties regarding the approach to quantify how the clams influence SPM and if this processes is disregarded, there will be more SPM in the water, and a lower Secchi depth (Fig. 15D). Of all the tested 9 uncertainties, this is one of the most important one, and it is specifically marked in Fig. 15D. Note that all 9 curves (except for curve 7) are close for TP (Fig. 15A), chlorophyll (Fig. 15B), SPM (Fig. 15C) and Secchi depth (Fig. 15D). The only curves which clearly depart are for the Secchi depth for the last period related to the introduction of the clams. The next test concerns the return flow of SPM to ET-areas when the macrophytes die (curve 3). If this small flux (see the results in Fig. 12B) is not accounted for, the SPM-concentrations will only increase very little. Curve 4 gives results if the Secchi depth in the sea outside Ringkøbing Fjord is not set to 5 m (which is the default value), but to 4 m. This value is used to calculate the SPM-concentration in the sea, and hence also the inflow of SPM from the sea to the lagoon. Since this flow is not so dominating in this lagoon, this uncertainty is not so important. The calculation related to curve 5 concerns the inflow of TP from the sea. In this case, the TP-concentration in the outside sea is set to 30 μg/l and not to 25 μg/l, which is the default value. Also this uncertainty is of less importance. There are new aspects related to the age of the ETsediments, which regulates resuspension, concerning the role of the clams and the macrophytes to entrap and retain SPM and particulate phosphorus. But if the age of the ET-sediments is increased by 25% for TP, it does affect the predictions very much, as shown by curve 6 (one of the lumped curves). Test 7 concerns the factor regulating sediment entrapment and retention of SPM and TP by clams. This uncertainty affects the predictions relatively much. The next test concerns the proper value for the SPM-transport from land. This is calculated from empirical data on TP-transport (see curve 1 in Fig. 12B). The question is if the TPconcentration on suspended particles in the tributaries is 2 mg/g dw (which is the default value) or 2.2 mg/g dw? Also this uncertainty is of little importance (curve

8). Test 9 concerns to uncertainties related to the SPMconsumption of the clams and the organic fraction of SPM (curve 9). One can set the organic fraction to be 25% or 33% but this does not affect the predictions very much. In summary, we may conclude from these sensitivity tests that these uncertainties do not influence the main results very much concerning the changes in the bioindicators (Secchi depth and chlorophyll) and the corresponding changes in modelled TP-and SPMconcentrations or the main conclusions about the relative roles and interactions of the macrophytes and the clams in Ringkøbing Fjord and how this modelling approach describe these interesting interactions in the lagoon. 4. Conclusions This work has used a general dynamic massbalance model, including a sub-model for SPM and another for TP and connected empirically-based models to predict Secchi depth and chlorophyll-a concentrations, for the conditions in Ringkøbing Fjord for the period 1980 to 2004, when there was a major regime shift. There have been reductions in the nutrient loading to the lagoon and changes in salinity, which have caused marked variations in macrophytes and clams. How well can these changes be understood, quantified and modelled? This is the key question in this work and the answer is that this modelling can describe the changes very well. For the initial phase (from 1980 to 1995), this modelling give good predictions without any tuning, modifications or calibrations of the model for TP-concentrations in water and accumulation area sediments, SPM-concentrations in water, Secchi depths and concentrations of chlorophyll-a. For the second phase (1996 to 2004), the modelling gives good results after considerations to the changes in macrophyte cover/biomass and biomass of clams. Basically, the macrophytes and clams compete for the same space on the bottom, they both take up and retain phosphorus (and nitrogen) and they both entrap and retain SPM and particulate phosphorus and reduce resuspension. For the future, it will be very interesting to follow the situation in the lagoon and see whether a new dynamic steady-state will develop, how the macrophyte cover and the clam biomass will adjust to the nutrient loading and salinity, and what the competition between clams and macrophytes will lead to. The reductions in nutrient input cannot fully explain the improved water quality, which should also, and to a

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