A simple model for predicting oxygen depletion in lakes under climate change

Figures & data

Table 1. Empirical estimates of VHOD rates obtained from literature for corresponding lakes, years, and trophic status.

Method	Lake name	Year	VHOD (mg L^−1 d^−1) (TREF = 4°C)	Trophic status	Source
A	Twin City South	1989	0.0148	eutrophic	(Axler et al. 1992)
	Sherman	1989	0.0109	oligotrophic
	Twin City South	1990	0.0374	eutrophic
	Sherman	1990	0.0304	oligotrophic
	Twin City South	1991	0.0436	eutrophic
	Sherman	1991	0.0374	mesotrophic
	Lower Crystal Springs	1999	0.0296	oligotrophic	(Beutel 2003)
	Lafayette	1967–1968; 1998–1999	0.1145	eutrophic
	Mathews	1997–1999	0.0265	oligotrophic
	Upper San Leandro	1997–1999	0.0787	mesotrophic
	San Antonio	1999–2000	0.0273	mesotrophic
	Muskegon	2011	0.222	mesotrophic	(Biddanda et al. 2018)
	Muskegon	2012	0.1651	mesotrophic
	Muskegon	2013	0.2072	mesotrophic
	Eerie	2005	0.0658	eutrophic	(Conroy et al. 2011)
	Otisco	2002	0.109	eutrophic	(Denkenberger et al. 2007)
	Onondaga	2002	0.1511	eutrophic
	Otisco	2003	0.1106	mesotrophic
	Otisco	2004	0.0974	mesotrophic
	Onondaga	2004	0.1768	eutrophic
	Blelham Tarn	1968–2008	0.2555	eutrophic	(Foley et al. 2012)
	Borabey	2013	0.0888	mesotrophic	(Göncü and Albek 2019)
	Porsuk	2013	0.1846	eutrophic
	Borabey	2014	0.0569	mesotrophic
	Porsuk	2014	0.1838	eutrophic
	Zurich	2003	0.1116	eutrophic	(Jankowski et al. 2006)
	Greifensee	2003	0.0857	eutrophic
	Rotorua	—	0.4518	eutrophic	(Rutherford et al. 1996)
	Rotorua	—	0.4673	eutrophic	(Vant 1987)
	Rotoiti	1981–1982	0.3505	eutrophic	(Vincent et al. 1984)
B	Sammamish	1965	0.0439	eutrophic	(Bella 1970)
	Clarke	1968	0.0112	oligotrophic	(Cornett 1982)
	Brewer	1968	0.0157	oligotrophic
	Costello	1968	0.0163	oligotrophic
	Kearney	1968	0.0179	mesotrophic
	Bob	1976	0.0327	oligotrophic
	Brompton	1978	0.0165	oligotrophic
	Central	1978	0.041	oligotrophic
	Lyster	1978	0.0203	oligotrophic
	Stukley	1978	0.0162	oligotrophic
	Lovering	1978	0.0169	oligotrophic
	Brompton	1979	0.021	oligotrophic
	Lovering	1979	0.0175	oligotrophic
	Lyster	1979	0.0207	oligotrophic
	North	1979	0.0274	oligotrophic
	Orford	1979	0.0254	oligotrophic
	Stukely	1979	0.0178	oligotrophic
	Truite	1979	0.0255	oligotrophic
	Central	1979	0.0279	oligotrophic
	Fitch	1979	0.021	mesotrophic
	Massawippi	1979	0.0499	oligotrophic
	Magog	1979	0.0239	eutrophic
	Brompton	1980	0.0209	oligotrophic
	Petite Brompton	1980	0.038	oligotrophic
	Lovering	1980	0.0205	oligotrophic
	Lyster	1980	0.0248	oligotrophic
	Orford	1980	0.0326	oligotrophic
	Stukely	1980	0.0212	oligotrophic
	Truibe	1980	0.0237	oligotrophic
	Central	1980	0.0376	mesotrophic
	Fitch	1980	0.0297	mesotrophic
	Massawippi	1980	0.0599	oligotrophic
	North	1980	0.0277	oligotrophic
	Magog	1980	0.0317	eutrophic
	Esrom	1969	0.0269	eutrophic	(Jónasson et al. 1974)
	Michin	1969	0.0293	oligotrophic	(Kerekes 1974)
	Bluehill	1969	0.0065	oligotrophic
	Skeleton	1969	0.0192	oligotrophic	(Michalski et al. 1973)
	Dudley	1969	0.0209	oligotrophic
	Gravenhurst	1969	0.0244	eutrophic
	Gravenhurst	1970	0.0173	eutrophic
	Gravenhurst	1973	0.0183	eutrophic
	Gravenhurst	1974	0.0281	eutrophic
	Harp	1973	0.0329	mesotrophic	(Nicholls 1976)
	Jerry	1973	0.0437	mesotrophic
	Stoney	1971	0.028	mesotrophic
	Washington	1957	0.0244	eutrophic	(Shapiro 1960)
	Washington	1958	0.025	eutrophic
	Kamloops	1974	0.0047	oligotrophic	(St John et al. 1976)
	Lake Lucerne, Horwer Bucht	1969	0.0259	eutrophic	(Stadelmann 1971)
	Walensee	1972	0.0138	oligotrophic	(Von Zimmermann and Suter-Weider 1976)
	Walensee	1973	0.0307	mesotrophic
	Walensee	1974	0.0269	mesotrophic
	Lake Lucerne, Horwer Bucht	1966	0.0259	mesotrophic	(Von Zimmerman 1969)
	Lake Lucerne, Horwer Bucht	1967	0.0301	mesotrophic
C	Aegerisee	1950–1951	0.0115	mesotrophic	(Livingstone and Imboden 1996)
	Aegerisee	1968–1983	0.0159	mesotrophic
	Constance	1977–1987	0.0334	eutrophic	(Rhodes et al. 2017)
	Constance	1988–1999	0.0285	mesotrophic
	Constance	2000–2010	0.028	oligotrophic

Acquisition of VHOD rate involved (A) literature searches, (B) conversions from AHOD, and (C) conversions from the oxygen consumption rate associated with the pelagic (J_V) and benthic (and J_A) zones.

Figure 1. Study lakes in Germany (black points) denoting where stratification duration and mean hypolimnion temperature data were observed. Points for Breiter Luzin, Schmaler Luzin, and Feldberger Haussee overlap.

Table 2. Mean hypolimnion temperature, stratification duration, and model-based VHOD estimates in 13 German lakes.

Trophic state	Name	Year	Hypolimnion temperature (°C)	Stratification duration (d)	VHOD (mg L^−1 d^−1)
Oligotrophic	Titisee	2019	4.40	221	0.0216
	Titisee	2020	4.50	235	0.0218
	Rappbode	2016	4.09	224	0.0211
	Rappbode	2017	4.19	213	0.0212
	Rappbode	2018	3.99	223	0.0209
	Rappbode	2019	4.06	229	0.0210
Mesotrophic	Laacher See	2017	4.51	257	0.0344
	Laacher See	2018	4.30	248	0.0338
	Tollensesee	2021	7.09	191	0.0427
	Groß Glienicker See	2018	9.35	176	0.0516
	Groß Glienicker See	2019	10.50	183	0.0567
	Schmaler Luzin	2021	5.52	227	0.0375
	Illmensee	2018	5.87	225	0.0386
	Illmensee	2019	6.28	228	0.0399
	Breiter Luzin	2003	4.72	225	0.0350
	Breiter Luzin	2004	4.33	224	0.0339
	Breiter Luzin	2005	4.46	230	0.0343
	Breiter Luzin	2006	4.06	250	0.0332
	Breiter Luzin	2010	4.41	223	0.0341
	Breiter Luzin	2011	4.61	228	0.0347
	Breiter Luzin	2012	4.86	225	0.0355
	Breiter Luzin	2015	4.64	232	0.0348
	Breiter Luzin	2016	4.44	231	0.0343
	Breiter Luzin	2018	4.39	228	0.0341
	Breiter Luzin	2019	4.49	251	0.0344
	Breiter Luzin	2020	5.08	239	0.0361
Eutrophic	Arendsee	2013	4.29	217	0.0422
	Arendsee	2014	5.07	243	0.0451
	Arendsee	2015	5.17	225	0.0455
	Arendsee	2016	5.06	230	0.0450
	Arendsee	2017	4.86	239	0.0443
	Arendsee	2018	4.50	224	0.0430
	Arendsee	2019	4.87	243	0.0443
	Arendsee	2020	5.52	233	0.0468
	Arendsee	2021	5.43	218	0.0464
	Scharmützelsee	2020	7.72	220	0.0562
	Scharmützelsee	2021	8.71	191	0.0610
	Feldberger Haussee	2018	8.08	195	0.0579
	Feldberger Haussee	2019	9.37	193	0.0645
	Feldberger Haussee	2020	9.08	190	0.0629
	Feldberger Haussee	2021	10.11	165	0.0686
	Großer Plöner See	2021	5.99	223	0.0486
	Tegeler See	2018	8.95	198	0.0623
	Tegeler See	2019	10.99	174	0.0738
	Tegeler See	2021	10.80	153	0.0726

Figure 2. Mean (black lines) VHOD rates as a function of hypolimnetic temperature for different trophic status. The shaded regions illustrate the 99% confidence interval of each trophic state VHOD mean.

Figure 3. Validation of predicted O₂ concentrations from our model with in situ measured O₂ concentrations from 5 German lakes (Arendsee, Feldberger Haussee, and Tegler See are eutrophic; Breiter Lutzin and Groß Glienicker See are mesotrophic). The regression line (red) is shown with 95% confidence interval (shaded grey area). Blue and dotted line indicates the 1:1 line.

Figure 4. Contour plots displaying the predicted O₂ concentration (color scale) in (a) oligotrophic, (b) mesotrophic, and (c) eutrophic lakes as a function of stratification and hypolimnion temperature. Points denote separate years in a respective lake. Isolines represent O₂ concentrations.

Figure 5. Stratification duration for a lake of a specific trophic state at a given hypolimnetic temperature to reach critical O₂ biological and ecological thresholds; anoxia = 0.5 mg L⁻¹ (solid line), hypoxia = 2 mg L⁻¹ (long dash), uninhabitable by cold dwelling fish species = 5 mg L⁻¹ (dot dash). Our reference temperature of 4°C is denoted by the black dotted line.

Axler RP, Larsen C, Tikkanen CA, McDonald ME, Host GE. 1992. Limnological assessment of mine pit lakes for aquaculture use. NRRI Technical Report, NRRI/TR-92-03. Duluth (MN): University of Minnesota, Natural Resources Research Institute.

 Google Scholar

Beutel MW. 2003. Hypolimnetic anoxia and sediment oxygen demand in California drinking water reservoirs. Lake Reservoir Manag. 19(3):208–221.

 Web of Science ®Google Scholar

Biddanda BA, Weinke AD, Kendall ST, Gereaux LC, Holcomb TM, Snider MJ, Dila DK, Long SA, VandenBerg C, Knapp K. 2018. Chronicles of hypoxia: time-series buoy observations reveal annually recurring seasonal basin-wide hypoxia in Muskegon Lake—a Great Lakes estuary. J Gt Lakes Res. 44(2):219–229.

 Web of Science ®Google Scholar

Conroy JD, Boegman L, Zhang H, Edwards WJ, Culver DA. 2011. “Dead zone” dynamics in Lake trie: the importance of weather and sampling intensity for calculated hypolimnetic oxygen depletion rates. Aquat Sci. 73(2):289–304.

 Web of Science ®Google Scholar

Denkenberger JS, Driscoll CT, Effler SW, O’Donnell DM, Matthews DA. 2007. Comparison of an urban lake targeted for rehabilitation and a reference lake based on robotic monitoring. Lake Reservoir Manag. 23(1):11–26.

 Web of Science ®Google Scholar

Foley B, Jones ID, Maberly SC, Rippey B. 2012. Long-term changes in oxygen depletion in a small temperate lake: effects of climate change and eutrophication. Freshw Biol. 57(2):278–289.

 Web of Science ®Google Scholar

Göncü S, Albek E. 2019. An integrated approach to assess the ecological and chemical status of lakes with HOD/AHOD: a case study of two lakes. J Oceanol Limnol. 37(1):146–159.

 Web of Science ®Google Scholar

Jankowski T, Livingstone DM, Bührer H, Forster R, Niederhauser P. 2006. Consequences of the 2003 European heat wave for lake temperature profiles, thermal stability, and hypolimnetic oxygen depletion: implications for a warmer world. Limnol Oceanogr. 51(2):815–819.

 Web of Science ®Google Scholar

Rutherford J, Dumnov S, Ross A. 1996. Predictions of phosphorus in Lake Rotorua following load reductions. N Z J Mar Freshw Res. 30(3):383–396.

 Web of Science ®Google Scholar

Vant W. 1987. Hypolimnetic dissolved oxygen: survey and interpretation. Wellington (New Zealand): Lake Managers Handbook NWASCA.

 Google Scholar

Vincent W, Gibbs M, Dryden S. 1984. Accelerated eutrophication in a New Zealand lake: Lake Rotoiti, central North Island. N Z J Mar Freshw Res. 18(4):431–440.

 Web of Science ®Google Scholar

Bella DA. 1970. Dissolved oxygen variations in stratified lakes. J Sanit Eng Div. 96(5):1129–1146.

 Google Scholar

Cornett JL. 1982. Prediction and interpretation of rates of hypolimnetic oxygen depletion [dissertation]. Montreal (QC): McGill University.

 Google Scholar

Jónasson P, Lastein E, Rebsdorf A. 1974. Production, insolation, and nutrient budget of eutrophic Lake Esrom. Oikos. 25(3):255–277.

 Web of Science ®Google Scholar

Kerekes JJ. 1974. Limnological conditions in five small oligotrophic lakes in Terra Nova National Park, Newfoundland. J Fish Res Board Can. 31(5):555–583.

 Google Scholar

Michalski M, Johnson M, Veal D, Brydges T. 1973. Muskoka lakes water quality evaluation. Rpt. No. 3, Eutrophication of the Muskoka Lakes. Toronto (ON): Ontario Ministry of the Environment, Water Resources Branch.

 Google Scholar

Nicholls KH. 1976. Comparative limnology of Harp and Jerry Lakes, adjacent cottaged and uncottaged lakes on southern Ontario's Precambrian Shield. Toronto (ON): Ontario Ministry of the Environment, Water Resources Branch.

 Google Scholar

Shapiro J. 1960. The cause of a metalimnetic minimum of dissolved oxygen 1. Limnol Oceanogr. 5(2):216–227.

 Web of Science ®Google Scholar

St. John B, Carmack E, Daley R, Gray C, Pharo C. 1976. The limnology of Kamloops Lake, British Columbia. Vancouver (BC): Environment Canada: Inland Waters Directorate Pacific and Yukon Region.

 Google Scholar

Stadelmann P. 1971. Stickstoffkreislauf und primärproduktion im mesotrophen Vierwaldstättersee (Horwer Bucht) und im eutrophen Rotsee, mit besonderer berücksichtigung des nitrats als limitierenden factors [Nitrogen cycle and primary production in the mesotrophic Lake Lucerne (Horwer Bucht) and the eutrophic Rotsee, with special consideration of nitrate as a limiting factor]. Schweiz Z Hydrol. 33(1):1–65.

 Google Scholar

Von Zimmermann U, Suter-Weider P. 1976. Beiträge zur limnologie des walen-, zürich-ober-und zürichsees [Contributions to the limnology of Lake Walen and Lake Zurich]. Schweiz Z Hydrol. 38(2):71–96.

 Google Scholar

Von Zimmerman U. 1969. Okologische und physiologische untersucnungen un der plaktiaehen blaralge Oseillatorla rubescens D. C. inter besonderer berucksichtigung von lieht und temperatur [Ecological and physiological studies on the plaktiae algae Oseillatorla rubescens D. C. with special consideration of light and temperature]. Schweiz Z Hydrol. 38:71–96.

 Google Scholar

Livingstone DM, Imboden DM. 1996. The prediction of hypolimnetic oxygen profiles: a plea for a deductive approach. Can J Fish Aquat Sci. 53(4):924–932.

 Web of Science ®Google Scholar

Rhodes J, Hetzenauer H, Frassl MA, Rothhaupt K-O, Rinke K. 2017. Long-term development of hypolimnetic oxygen depletion rates in the large Lake Constance. Ambio. 46(5):554–565.

 PubMed Web of Science ®Google Scholar