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Edited by: David Koweek, Carnegie Institution for Science (CIS), United States

Reviewed by: Derek Roberts, San Francisco Estuary Institute, United States; Wei Fan, Zhejiang University, China; Alessandra Larissa Fonseca, Federal University of Santa Catarina, Brazil

This article was submitted to Ocean Solutions, a section of the journal Frontiers in Marine Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The phosphorus (P) concentration ^{3} year^{−1} and ^{−2} year^{−1}. With these parameter values, the model gives a quite good description of the observed evolution of

The eutrophication of the Baltic proper, the salt-stratified part of the Baltic Sea, continues to worsen, despite large cuts in the land-based P (phosphorus) source ^{−3} in 1958 (Stigebrandt,

The observed winter surface concentration

The Baltic Sea is the second largest (373,000 km^{2}) brackish water system in the world. The Baltic proper (251,000 km^{2}), located south of the Gulf of Bothnia (^{−1}. A halocline separates the surface layer from the deepwater of salinity 12–20, with the highest salinity in the Arkona Basin closest to the mouth (e.g., Leppäranta and Myrberg,

Topographic map of the Baltic proper showing the partition into deep basins. The Gulf of Riga is included in the Eastern Gotland Basin. Hydrographical data come from the stations marked in the map, see the section Data.

Due to extensive entrainment of overlying water into the dense bottom current, the highest salinity of the deepwater of the East Gotland Basin is only 12–13 despite the inflowing water from Kattegat may have salinities in the interval 20–30 (e.g., Stigebrandt et al.,

The annual biological production of organic matter in the Baltic proper is determined by the P concentration _{4} and DIN at the sea surface in

The mean seasonal cycles of PO4 and DIN/16 at the sea surface (0 m) at BY 15 in the East Gotland Basin in the period 2004–2018. Data from SMHI (

The long-term (1968–2018) evolution of the volume-weighted NP ratio, here (NO3 + NH4)/PO4 in winter in the 60 m thick surface layer and in the deepwater of the Baltic proper. Data from SMHI (

The total phosphorus supply ^{−1} (Stigebrandt,

It is well-known that anoxic conditions in the bottom water permit an internal P source, ^{−1}. This formulation implies that

Following Van Nes et al. (

Using the P budget model described in the section Model, we compute ^{2}) is known from observations and the parameter ^{−2} year^{−1}) is the specific P flux. The model is also forced by the internal and external sinks that are computed from ^{3} year^{−1}) carrying P to the sinks. Using the method of least squares, we determine the best estimate of the parameters

Nutrient load compilations are carried out by all HELCOM countries to evaluate and quantify the amount of nutrients annually discharged from land into the sea. The data are obtained from national monitoring programs and reporting from industries and municipal water works. Data for the annual land-based supply of phosphorus

The total area ^{−1} (Stigebrandt, ^{−1} during the whole period. From their

In anoxic water in the Baltic proper, ammonia has been measured about 6 times more frequently than hydrogen sulfide as estimated from the hydrographical database Shark (SMHI, _{2}S of hydrogen sulfide from the concentration NH_{4} of ammonium as follows; H_{2}S = 4.18·NH_{4} −5.89 if NH_{4} > 1.41 and O_{2} = 0; otherwise H_{2}S = 0. The oxygen debt is defined as the amount of oxygen needed to oxidize all hydrogen sulfide and ammonium present in the anoxic water column. The “concentration” of oxygen debt _{2}d_{2}S_{4}^{−3}), e.g., Reed et al. (_{2}_{2}

We apply a time-dependent model of the total amount of phosphorus P in the water column of the Baltic proper (Stigebrandt,

Essential features of the phosphorus model. Phosphorus fluxes from sources and to sinks are shown by red arrows and water fluxes by blue arrows. Red bottoms indicate possible locations of phosphorus storage.

P will accumulate in the deepwater due to the several-years-long residence time of the deepwater in the Baltic proper, which is due to the salinity stratification. We account for this by the introduction of two layers in the model. In a two-layer context, the total amount of P in winter in the water column V

Here ^{3}. The lower layer, beneath 60 m depth, has the volume V2 = 3,990 (km^{3}) (Stigebrandt,

The total amount of P in the water column of the Baltic proper changes with time

The term on the left side is the rate of change of P stored in the water column and the terms on the right side are the total P source

The total sink

Here the parameter ^{3} year^{−1}), carrying P to the internal and external sinks. In the present application we can estimate the parameter

The nature of the internal P source

Here ^{2}) is the area of anoxic bottoms in the Baltic proper and the parameter ^{−2} year^{−1}) the specific P flux from anoxic bottoms.

For simplicity, the following empirical relationship between

Here the empirical parameter α equals the average ratio between the amounts of P in winter in the lower and upper layers, respectively. The value of α is determined by the residence time of the lower layer and α should be stable in time if the long-term mean vertical circulation does not change. Using this relationship simplifies the model and implies that we replace two equations, one for each layer, by one equation for the upper layer.

Using observed annual values of the total P content in winter in the upper and lowers layers,

Here the summation index i runs from 1968 to 2018 for which period interval P has been observed regularly in the Baltic proper, see the section Data. It is found that α for that period equals 1.15. Using Equation (6), it follows that as an average there are 15% more P in the lower than in the upper layer and

In the model, the ratio α occurs only in the combination

The evolution of

Using Equations (1), (4), and (6), we can rewrite Equation (2) as follows

From this follows that the lower layer, through the parameter α, increases the inertia and thus the spin-up time of the system. Equation (8) shows that

The equilibrium concentration

The equilibrium concentration

Analytical solutions of the time-dependent model for two cases, Case 1 and Case 2 were discussed by Stigebrandt (

For Case 2, the two-layer case, Stigebrandt (

The time-scale

Stigebrandt (

In the present application of the model,

Here

We first apply the method of least squares to find the pair of values of the parameters ^{−3} at the start of the computations in 1950, Equation (8) was integrated to compute the year to year evolution of the P concentration ^{3} year^{−1}) and values of ^{−2} year^{−1}). We found that the least value of the sum of squared residual ^{−3})^{2}. It occurs for the pair ^{3} year^{−1}) and ^{−2} year^{−1}). Before plotting

Model results showing the normalized sum of the squared residual ^{3} year^{−1} and ^{−2} year^{−1}.

The analysis gives the total sink flow ^{3} year^{−1}. This solution does not depend upon the partition between different kinds of sinks. If needed, partition of the total sink into the two main sink components, ^{3} year^{−1} according to Wulff and Stigebrandt (^{3} year^{−1} and the (fix) ratio between the external and internal sinks,

Due to lack of observational data, the initial value ^{−3} to study the importance of the initial value for the result of the computations. From Equation (10) and using ^{3} year^{−1}, one finds that the time constant

Computational results ^{−2} year^{−1} and ^{3} year^{−1}. Three different initial concentrations

The long-term evolution of ^{3} year^{−1} and ^{−2} year^{−1}, mimics the observed concentration quite well and this comparison provides a successful test of the model (

The evolution of the total sink ^{−1} which is about two times larger than present time ^{−1} after year 2000. The curve

Sources and sinks in the Baltic proper in the period 1950–2014. Computational results from the model with ^{−2} year^{−1} and ^{3} year^{−1}.

We recall that ^{−1}. The export to the ocean ^{−1}.

To further elucidate the effect of

Computational results from the best fit model for the period 1950–2014 (2014 marked by vertical line) with the internal source ^{−3}.

The computed curves ^{−3} in 1958 and we adopt this value for ^{−1} when the threshold value ^{−1}. For larger supplies we expect that

To predict the future evolution of ^{−1} for the subsequent years from the value in 2014 which is consistent with the Baltic Sea Action Plan (HELCOM,

The result of the computation for the period 2014–2050 is shown on the right-hand-side of

During the oxygenation process, most of the P that is removed from the water column (about 500 ktons) will end up in the internal sink ^{−1} for the whole period after 2014, see the section Data, and therefore

The specific flux ^{−2} year^{−1}, is only about 53% of the flux estimated by Stigebrandt et al. (

The results from our model may be compared to results obtained from more complex biogeochemical models. Almroth-Rosell et al. (^{−1}. For the same period the present model computes a mean ^{−1}.

In the section Results, it was shown that the internal P supply

Self-amplifying eutrophication due to

Hydrogen sulfide and ammonium from anaerobic decomposition of organic matter in the sediment may accumulate in anoxic bottom water and thereby contribute to an oxygen debt

The evolution of the oxygen debt

As shown by the model in the present paper, anoxia and the accompanying

The threshold value

The present management strategy to reduce the eutrophication of the Baltic Sea, here called the “business-as-usual” scenario, is to reduce

In the “business-as-usual” scenario one may expect increased annual production of cyanobacteria (Vahtera et al.,

Since ^{−1} in the section The Baltic Proper Response to

Only systems fulfilling the following requirements can be restored by sustained oxygenation of the bottoms: (i) the

The first proposal to oxygenate the deepwater of the Baltic proper to reduce ^{3}s^{−1} of winter water into the deepwater (Stigebrandt et al., ^{3} s^{−1} of well-oxygenated surface water of often low salinity into the deepwater were investigated in a pilot experiment in the small anoxic By Fjord (Stigebrandt et al.,

A recent publication investigating the legal aspects of sea-based engineering measures to combat the eutrophication of the Baltic Sea concludes that the legality of any sea-based measure depends on the risks they present balanced against their benefits (Ringbom et al.,

The specific internal P source ^{−2} year^{−1} from anoxic bottoms and the total sink flow ^{3} year^{−1}, estimated in the present paper are temporal system averages, determined using 47 years of data on input and response of the Baltic proper to the P loading. There are numerous ^{−2} year^{−1}.

The values of ^{−1} (

Finally, more research is needed to describe the nature of the internal P source

The original contributions presented in the study are included in the article/

AS designed the study and wrote the manuscript. AA prepared data, made the calculations, prepared the figures. AS and AA discussed the results. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviews led to improvements of the quality of the paper.

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