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Predicting Total Nitrogen, Total Phosphorus, Total Organic Carbon, Dissolved Oxygen and Iron in Deep Waters of Swedish Lakes

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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.

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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.

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Correspondence to Peter H. Dimberg.

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]

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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

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  • DOI: https://doi.org/10.1007/s10666-015-9456-4

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