The dependence of the consumption of dissolved oxygen on lake morphology in ice covered lakes

The consumption of oxygen in ice-covered lakes is analyzed and related to biological oxygen demand and sediment oxygen demand. An approach for computing dissolved oxygen concentration is suggested assuming horizontally mixed waters and negligable vertical dispersion. It is found that the depletion of dissolved oxygen is mainly due to the transfer of oxygen at the water/sediment interface. The morphology of a lake is very important for how fast the dissolved oxygen concentration is reduced during winter. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/nh.2020.150 s://iwaponline.com/hr/article-pdf/doi/10.2166/nh.2020.150/650379/nh2020150.pdf Lars Bengtsson (corresponding author) Osama Ali-Maher Water Resources Engineering, Lund University, Box 117, 221 007 Lund, Sweden E-mail: lars.bengtsson@tvrl.lth.se


INTRODUCTION
The water quality in lakes is much dependent on the dissolved oxygen (DO) in the water. In lakes, which are ice covered during long winters, the dissolved oxygen concentration may decrease to very low values. In shallow lakes, anaerobic conditions may develop, as was already discussed by Greenbank (). The ice cover isolates the water from the atmosphere and thus there is no gas exchange between air and water. Solar radiation is weak and does not penetrate through the ice and the snow on the ice. Therefore, there is no photosynthesis and no primary production contributing to oxygen production. Instead, DO decreases, when oxygen is consumed by bacterioplankton in the water through organic matter mineralization and by diffusion of dissolved oxygen. The oxygen concentration is reduced faster in the deep parts of a lake than near the ice. In a state-of-the-art paper, Bengtsson () points to the importance of increased knowledge about dissolved oxygen in winter lakes. A short review on DO in ice covered lakes is given by Terzhevik & Golosov (). Kirillin et al. () in their review on ice-covered lakes also discussed DO in ice-covered lakes, as did Golosov et al. () with emphasis on climate change. Primary production can proceed some time after ice formation prior to when there is snow on the ice. At high altitudes, at modest latitudes, and snow free ice cover, primary production can be due to rather intense solar radiation continuing throughout the winter, as shown in a study from Mongolia by Song et al. (). The DO is prevented from decreasing to low values.
In regions where the ice covered period extends into April or even May (Northern Globe), the solar radiation is intense, when the lakes are still ice covered. After the snow has melted, some solar radiation can penetrate through the ice into the water. Radiative-driven convection is initiated under There are many reported observations of DO concentrations in ice-covered lakes. When describing the depletion of oxygen, the lakes are mostly treated as wellmixed units (e.g., Hargrave ), but Golosov et al. () accounted for vertical distribution of DO. In studies of found that the consumption of DO was related to the depth of a lake and thus to the morphology; the shallower lake, the more oxygen consumption and the lower DO concentration. Mathias & Barcia () stressed the importance of the extension of littoral zones and the oxygen depletion during winter. Chambers et al. ()  The paper is structured so that after the introduction with objectives, the two observation sites are described, followed by a section reporting literature data of observed DO consumption in different ice-covered lakes. The theory on which this paper is based is given, directly followed by applications on the two lakes. The applications are divided into separate sub-sections for each lake, and a sub-section dealing with convection under ice. The results of the applications are summarized followed by discussion.

STUDY SITES Lake Velen
Lake Velen is situated in south-western Sweden in a boreal forest-type basin. The lake has a glacial origin. The lake basin is elongated, 6.3 km long, and rather narrow, with a maximum width of 1.1 km. The lake area is 2.8 km 2 and the mean depth 6.5 m. The maximum depth is 17 m. The western shoreline is rather steep. The river inflow is minor and almost zero during the ice-covered period. Ice usually forms in

Lake Vendyurskoe
Lake Vendyurskoe is situated in Russian Karelia. The lake is similar to Lake Velen. It has a glacial origin. There is almost no inflow in winter. The lake is situated in the same type of landscape as Lake Velen. The lake is shallow, with a mean depth of 5.3 m and maximum depth 13.5 m. The surface area is 10.5 km 2 , and thus larger than the area of Lake Velen. The morphology is given in detail in Maher et al. The ice-covered period is usually from early or mid-November until late April. Temperature and DO were measured in situ using an oxygen sensor in many verticals during several week-long campaigns mainly in late winter. Barcia & Mathias ()  year over three months showed the same value for middepth water but a higher value 0.048 g/m 3 /d for deep water.

OBSERVATIONS OF OXYGEN CONSUMPTION FROM THE LITERATURE
The consumption rate within the water in ice-covered lakes seems to change rather slowly with depth except near the sediments (Pulkanen & Salonen ). However, very near bottom sediments, also at shallow water, the DO concentration drops to low values, as observed during measurements in Lake Vendyurskoe (Maher et al. ), and from the referred Finnish studies.

METHODS -THEORY
Oxygen is consumed within the water and in the sediments.
The consumption of oxygen within the water is, when there is no aeration, directly related to the consumption of bacterioplankton, the biological oxygen demand (BOD), as: L is biological oxygen demand. The decay coefficient k L has unit 1/day, t is time. Also L reduces, so that dL/dt is proportional to k L * L: Thus, The concentration reduces exponentially. L 0 is the initial value of L. The solution to Equation (3) is: with index 0 for initial value. This is the classical Streeter-

Phelps analysis (Streeter & Phelps ).
Since there is no turbulence in the ice-covered lake water, much of the phytoplankton sinks towards the bottom. Therefore, the biological oxygen demand near the ice and at mid-depth reduces at a rate that is less than what can be expected from Equation (2) sinking, reaches 10 m depth in ice-covered lakes within a month after ice has formed on the lake. This indicates that, at least after a month, the reduction of DO in ice covered lakes may be more dependent on processes near the bottom than the consumption within the lake water. This is also in line with the findings by Barcia & Mathias (, ) that the DO reduction is faster the shallower a lake is.
As seen from Equation (3), the DO concentration reduces at a slower rate as time goes on. Thus, the consumption rate reduces when the concentration reduces. This led Terzhevik et al. () to suggest that the DO consumption could be given as, now with notation k w instead of k L : with a decay coefficient k w . The solution to Equation (5) is of course: The sediments consume oxygen, sediment oxygen demand (SOD). The absorption into the sediments is a transport process over a diffusive boundary layer, in principle: where k is diffusivity, d thickness of boundary layer and c B is oxygen concentration at the sediment surface. Instead of using k/d, a parameter, transfer coefficient, unit velocity, Assuming horizontally well-mixed water and neglecting advective terms, the decrease of dissolved oxygen is described by the diffusion equation: where c is DO concentration, t is time, z is vertical direction, and D is diffusion coefficient. The consumption term includes consumption within the water as well as loss to the sediments. Malm () found in a study of Lake Vendyurskoe that the vertical mixing is determined solely by molecular processes. As already discussed, the consumption rate per unit volume is of the order 0.1 g/m 3 /d. This consumption rate can be compared with the first term on the right-hand side of Equation (8). The scaling is, excluding the area, Dc/H 2 , where H is a depth scale. The oxygen diffusion coefficient in cold water is about 10 À4 m 2 /d, so when c is 10 g/m 3 and the depth scale is 5 m, this scaled diffusion term is only 4 × 10 À5 g/m 3 /d, and thus much smaller than the consumption rate. This was discussed already by Golosov et al. (). Therefore, what is left of the diffusion equation is only The consumption within the water is following Terzhevik et al. () taken as k w *c. It will be shown later that this consumption is minor compared to the oxygen uptake by sediments. The consumption due to transport of oxygen into the bottom sediments is per unit exposed bottom area, SOD, or k b * (c À c B ). The volume of an increment dz at level z is A(z) * dz, A(z) being the lake area at distance z from the deep part of the lake. The exposed bottom area at that level is the wetted perimeter * dz, which is A(z) À A(z À dz). The wetted perimeter is δA/δz. Integrating over the area at a given level z gives: with z directed upwards. When SOD is restricted by the transfer through the boundary layer, the equation is after division by A(z): Since there is no direct mixing between different z-layers, c(z) is simply replaced by c in the formulas below.
The consumption, right-hand side of Equation (11), at a certain level can be described as: or after introducing a parameter K(z) The introduced parameter K, unit 1/time, is dependent on the depth distribution and since the area reduces with depth, the coefficient K increases with depth.
Lake area is a function of depth, see the hypsographic curves in Figures 1 and 2. Often a simple expression can be used: with A s , as the surface area and H as the maximum depth and z distance from deep bottom. Then: When the oxygen concentration in the sediment drops to zero, the solution of the consumption equation, is simply with c 0 as the initial DO with K being dependent on the considered depth (level), either from Equation (16)  Equation (17), but adjusted for different columns within a lake.
The character of sediments at deep water are, in most lakes, different from those near the shores. While the sediments at shallow water are more of mineral character, the deep water sediments are muddy and organic. The organic content increases with depth. Therefore, the sediment oxygen transfer coefficient can be assumed to increase from a surface value to higher value at large depth. A linear increase is assumed: with constant value k bdeep below the depth H s ; y ¼ H À z is measured from the surface.
Pulkanen & Salonen (), when measuring the oxygen consumption in bottles, found that the DO decrease was faster in the bottles with deep water compared to in the bottles with water from mid-depth. Therefore, it can be expected that also the decay coefficient k w increases with depth. However, as will be shown, the oxygen consumption within the water is small compared to the flux to the sediments.

RESULTS -APPLICATIONS
The approach was first tested on Lake Velen for two years and then for Lake Vendyurskoe using data from three years.

Lake Velen
The DO measurements from Lake Velen are from the 1970s.
Two processes are considered, the biological oxygen demand within the water, and the diffusion of dissolved oxygen into the sediments. There are two parameters in the suggested theory, k w and k b , but they can be depth dependent. It is assumed that the oxygen content in the sediments is very low. The oxygen content in mg/L was calculated from values given in mole (Falkenmark ).
Prior to freeze-up in late December 1970December (winter 1970December -1971) the DO concentration varied in the vertical between 12.8 and 12.4 mg/L, but with lower value at 12 and 14 m.
12.8 mg/L was set as initial value through the entire water column.
The measurements under ice were carried out about 80 days after ice formation (March 1971). The total content of oxygen in the water had decreased by about 9,000 kmol, which corresponds to an average decrease of DO concentration by 1.7 mg/L.
Originally, it was thought to account for the consumption of bacterioplankton within the water. However, already during the first computation, it was found that to get a good fit k w had to be given very low values. A good fit was obtained when k w was given an increasing depth The dissolved oxygen in the water was measured prior to freeze-up. The dissolved oxygen was then measured from given as about 11.5 mg/L, which is chosen as initial value.
The oxygen consumption was first computed using the same parameters as for Lake Velen. However, the DO consumption was computed to be too intense when those parameters were used. By decreasing the k bdeep from 0.02 to 0.017 m/d a good fit was obtained, as seen in Figure

Convection in Lake Vendyurskoe
In early spring, the snow disappears from the ice on winter lakes and solar radiation can penetrate the ice. Convection occurs. A homothermal layer develops near the ice. An example from Lake Vendyurskoe is shown in Figure 8, showing the temperature prior to convection (or when convection had just begun) and during convection. The homothermal layer extends about 4 m down from the underside of the ice. There are 4 days in between the observations. Some convection may have occurred also before the first observations. When solar radiation penetrates into the water, primary production can start, which means that there is a source for oxygen. However, when convection is initiated, it also means that due to the motions the transfer of dissolved oxygen into the shallow sediments increases.
When studying DO profiles in Lake Vendyurskoe prior to convection and 4 days after convection began in April 2000, using data from Maher () (Figure 9), it is seen that the DO concentration is homogeneous over the homothermal layer, but also that the DO concentration in the water close to the ice has decreased.
The oxygen consumption considering only the bottoms above 4 m, where there are considerable water movements due to convection, is about 12 g/m 2 , which is a loss rate of   Later, as the solar radiation through the ice increases, the primary production will start and a source for oxygen production is available.
However, the more intense observations in Lake Ven-

DISCUSSION AND SUMMARIZING RESULTS
The results from the DO studies in Lake Velen and Lake Vendyurskoe show that the reduction of DO in these icecovered lakes can be estimated accounting only for the sediment oxygen demand. The same parameters, although slightly different for the two lakes, can be used for different years. Biological oxygen consumption within the water may probably still occur early after ice formation and at deep parts of the lakes, but seems to be minor. Even when it is included in the computations, the sediment uptake parameter is only reduced by 10% to get the same fit as when not accounting for the biological oxygen consumption.
The morphology is important for how DO develops throughout the winter. When the sediment uptake of DO dominates, the ratio exposed bottom area/water volume at given depths determines how fast the water becomes depleted in oxygen. Shallow lakes may be depleted in oxygen, and DO concentration can decrease to very low levels in depressions within a lake.
The initial DO concentration prior to ice formation determines how the DO profile develops during the winter. The initial concentration must be known for the simulations.
The two investigated lakes are similar in size and situated in similar environments. There are no major inflows.
The approach of determining DO assuming that the decrease of DO is mainly due to the loss to the sediments can probably be applied also to very shallow lakes. The minor aeration at open water at inlets may have some influence if the lake volume is very small. Reeds along the shores may have some effect on DO.
It ought to be possible to use the suggested approach also in lakes larger than Lake Velen and Lake Vendyurskoe. At very large depths there may remain oxidizable organic matter for rather a long time, but this can be accounted for in the approach, although it would be difficult to put a value on the coefficient. In a very large lake, the water may not be horizontally homogeneous, especially if there are large inflows from rivers. Ice may form at different times over such lakes.
When solar radiation penetrates the ice in early spring, convection is initiated. During a few days before biological activity commences, water with high DO content mixes with water at lower level with lower DO content at the same time as the motions of the water masses give rise to increased oxygen loss to shallow sediments. In very shallow lakes, where the convective motions reach close to the bottoms, there is a risk of low DO concentrations also near the ice.

CONCLUSIONS
The important finding of the simulations performed in this study is that the major part of oxygen consumption in icecovered lakes is the uptake and consumption of DO in the bottom sediments. This explains the much faster decrease of DO concentration at deep water than at near-surface water. The lake morphology is important for how the DO concentration develops in winter lakes. The development of DO at different depth in a winter lake can be simulated accounting only for the DO loss to the sediments. For individual lakes, the same parameters can be used for consecutive years. Since there is no source of oxygen once a lake is ice covered, the initial conditions very much determine the DO concentration throughout the ice-covered period. What is new in the study is that the DO concentration profile can be determined from the hypsographic curve of the lake, once the initital conditions are known.
Another finding is that in early spring, when solar radiation penetrates the ice and induces convection resulting in homothermal conditions near the ice, the induced motion apart from creating homogenous DO concentration over the homothermal layer also results in a faster transfer of oxygen to the shallow bottom sediments. Until biological activity starts under the ice, the DO concentration near the ice reduces.