Abstract
In many lakes, the physical and chemical characteristics are monitored for surface waters but not for deep waters. Yet, deep waters may be important for understanding the dynamics of lake water chemistry variables over the year. In this study, multiple regression models have been created for five different variables, total phosphorus, total nitrogen, total organic carbon, dissolved oxygen (DO) and iron, in the deep water for 61 Swedish temperate or subarctic lakes. The investigated season was February to October, depending on the data availability. Regressions used the corresponding variables from the surface water as well as different morphometric parameters as independent variables. It was possible to construct meaningful models (r 2 > 0.65; p < 0.05) for most of the variables and months. However, it was not possible to attain this criterion for some months regarding the DO concentration. Surface water concentrations were in general most important for predicting corresponding deep water concentrations. An exception was that during summer, DO differed considerably between surface waters and deep waters and voluminous lakes had particularly high DO concentrations in deep waters. No cross-systems relationship could be found between deepwater hypoxia and total phosphorus in deep waters during summer when phosphorus diffusion from sediments is most likely. A mass-balance modelling example was applied to illustrate the use of the produced models. These findings may provide a better understanding of the dynamics of these five variables in temperate or subarctic lakes.
Similar content being viewed by others
References
Bachmann, R. W., Bigham, D. L., Hoyer, M. V., & Canfield, D. E., Jr. (2012). Factors determining the distributions of total phosphorus, total nitrogen, and chlorophyll a in Florida lakes. Lake and Reservoir Management, 28, 10–26.
Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, 26, 211–252.
Carraro, E., Guyennon, N., Hamilton, D., Valsecchi, L., Manfredi, E. C., Viviano, G., Salerno, F., Tartari, G., & Copetti, D. (2012). Coupling high-resolution measurements to a threedimensional lake model to assess the spatial and temporal dynamics of the cyanobacterium Planktothrix rubescens in a medium-sized lake. Hydrobiologia, 698, 77–95.
Dalzell, D. J. B., & Macfarlane, N. A. A. (1999). The toxicity of iron to brown trout and effects on the gills: a comparison of two grades of iron sulphate. Journal of Fish Biology, 55, 301–315.
Diaz, R. J., & Breitburg, D. L. (2009). The hypoxic environment. Fish Physiology, 27, 1–23.
Dimberg, P. H., Hytteborn, J. K., & Bryhn, A. C. (2013). Predicting median monthly chlorophyll-a concentrations. Limnologica, 43, 169–176.
Håkanson, L. (1984). Lake bottom dynamics and morphometry: the dynamic ratio. Water Resources Research, 18, 1444–1450.
Håkanson, L., & Peters, R. H. (1995). Predictive limnology—methods for predictive modelling. Amsterdam: SPB Academic Publishers.
Håkanson, L., Blenckner, T., & Malmaeus, M. (2004). New, general methods to define the depth separating surface water from deep water, outflow and internal loading for mass-balance models for lakes. Ecological Modelling, 175, 339–352.
Håkanson, L., & Bryhn, A. C. (2008). A dynamic mass-balance model for phosphorus in lakes with a focus on criteria for applicability and boundary conditions. Water, Air, and Soil Pollution, 187, 119–147.
Hastie, T., Tibshirani, R., Friedman, J. (2009). The elements of statistical learning—data mining, inference and prediction, 2nd ed. Springer
Hoffman, A. R., Armstrong, D. E., & Lathrop, R. C. (2013). Influence of phosphorus scavenging by iron in contrasting dimictic lakes. Canadian Journal of Fisheries and Aquatic Sciences, 70, 941–952.
Hupfer, M., & Lewandowski, J. (2008). Oxygen controls the phosphorus release from lake sediments—a long-lasting paradigm in limnology. International Review of Hydrobiology, 93, 415–432.
Hutchinson, G. E., & Löffler, H. (1956). The thermal classification of lakes. Proceedings of the National Academy of Sciences USA, 42, 84–86.
Kortelainen, P. (1993). Content of total organic carbon in Finnish lakes and its relationship to catchment characteristics. Canadian Journal of Fisheries and Aquatic Sciences, 50, 1477–1483.
Lawen, L., Yu, H., Fieg, G., & Abdel-Wahab, A. (2013). New unstructured mesh water quality model for coastal discharges. Environmental Modelling & Software, 40, 330–335.
Phillips, G., Pietiläinen, O. P., Carvalho, L., Solimini, A., Solheim Lyche, A., & Cardaso, A. C. (2008). Chlorophyll-nutrient relationships of different lake types using a large European dataset. Aquatic Ecology, 42, 213–226. doi:10.1007/s10452-008-9180-0.
Prairie, Y. T. (1996). Evaluating the predictive power of regression models. Canadian Journal of Fisheries and Aquatic Sciences, 53, 490–492.
SLU, 2013. Swedish University of Agricultural Sciences. Database. http://www.slu.se/en/. Accessed 28 September 2013.
SMHI, 2008. Swedish Meteorological and Hydrological Institute. Lakes of Sweden. SMHI Fact Sheet 39. SMHI, Norrköping, 4 p (in Swedish).
SMHI. (2009). Swedish Meteorological and Hydrological Institute (p. 168). Norrköping: Lake depth and lake volume. SMHI (in Swedish).
Versteeg, H.K., Malalasekera, W. (2007). An introduction to computational fluid dynamics: the finite volume method. Pearson Education Limited
Vuorenmaa, J., Forsius, M., & Mannio, J. (2006). Increasing trends of total organic carbon concentrations in small forest lakes in Finland from 1987 to 2003. Science of the Total Environment, 365, 47–65.
Wetzel, R. G. (2001). Limnology (3rd ed., p. 1006). San Diego: Academic.
Acknowledgments
The authors would like to thank one anonymous peer-reviewer who greatly helped in improving this article. The Swedish University of Agricultural Sciences and the Swedish Meteorological and Hydrological Institute are also acknowledged for making their data publicly available.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Mass of TP in deep water
Month = Mod(TIME, 9)
(1.00, 2.00), (2.00, 3.00), (3.00, 4.00), (4.00, 5.00), (5.00, 6.00), (6.00, 7.00), (7.00, 8.00), (8.00, 9.00), (9.00, 10.0) [Moderator to activate different months]
TPdM = TPdM2 + TPdM3 + TPdM4 + TPdM5 + TPdM6 + TPdM7 + TPdM8 + TPdM9 + TPdM10 [The TP concentration in deep water; note that only one value can be above zero; μg/L]
TPdM2 = 10(0.57+0.84·log(TPs)−0.15·log(Alt)) IF Month = 2 ELSE 0 [Calculates TP concentration in deep water for February; μg/L]
TPdM3 = (−7.15 + 19.30 · log(TPs)) IF Month = 3 ELSE 0
TPdM4 = 10(0.36+0.71·log(TPs)) IF Month = 4 ELSE 0
TPdM5 = (0.02 + 3.31 · log(TPs))2 IF Month = 5 ELSE 0
TPdM6 = (1.55 + 0.20 · TPs)2 IF Month = 6 ELSE 0
TPdM7 = (4.62 + 0.10 · TPs − 0.34 · log(Volume))2 IF Month = 7 ELSE 0
TPdM8 = 10(0.45+0.67·log(TPs)) IF Month = 8 ELSE 0
TPdM9 = (−0.16 + 3.24 · log(TPs) − 0.83 · log(DR))2 IF Month = 9 ELSE 0
TPdM10 = 10(0.49+0.68·log(TPs)−0.09·log(Alt)−0.12·log(DR)) IF Month = 10 ELSE 0
TPpred_in_kg_in_deep_water = TPdM·VolumeDW·(10^−6) [calculates the TP mass in deep water; kg]
TPs = MOD(TIME, 9)
(1.00, 9.00), (2.00, 10.0), (3.00, 11.5), (4.00, 12.5), (5.00, 13.0), (6.00, 15.0), (7.00, 14.0), (8.00, 14.0), (9.00, 13.0) [Vector with surface water concentrations of TP; μg/L]
Sub-model for deepwater volume
A_areas = (1 − ET) · Area [Amount of accumulation area]
Dcrit = 1 IF DTA1 < 1 ELSE DTA1 [Boundary condition for the wave base; m]
DTA1 = Max_depth · 0.98 IF (45.7 · SQRT(Area · 10−6)/(21.4 + SQRT(Area · 10−6))) > Max_depth ELSE (45.7 · SQRT(Area · 10−6)/(21.4 + SQRT(Area · 10−6))) [Wave base; m]
ET = 0.99 IF ET_limit_3 > 0.99 ELSE ET_limit_3 [Boundary condition for ET; dim. less]
ET_limit_1 = 1 − ((Max_depth-Dcrit)/(Max_depth + Dcrit · EXP(3 − Form_factor1.5)))(0.5/Form_factor)
ET_limit_2 = 0.95 IF ET_limit_1 > 0.95 ELSE ET_limit_1
ET_limit_3 = 0.15 IF ET_limit_2 < 0.15 ELSE ET_limit_2
Form_factor = 3 · Dm/Max_depth [Form factor; dim. less]
VolumeDW = (Volume − VolumeSW) [Deep water volume; m3]
VolumeSW = (Area · (106) · Dm − A_areas · Form_factor · (Max_depth-Dcrit)/3) [Surface water volume; m3]
Constants and driving variables
Alt = 120.5 [Altitude; m]
Area = 0.17 · 106 [Lake area; in m2 for sub-model; in km2 for deepwater concentration]
DR = 0.12 [Dynamic ratio; dim. less]
Max_depth = 9.4 [Max depth; m]
Volume = 578,000 [Volume; m3]
Rights and permissions
About this article
Cite this article
Dimberg, P.H., Bryhn, A.C. Predicting Total Nitrogen, Total Phosphorus, Total Organic Carbon, Dissolved Oxygen and Iron in Deep Waters of Swedish Lakes. Environ Model Assess 20, 411–423 (2015). https://doi.org/10.1007/s10666-015-9456-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10666-015-9456-4