Improved empirical models for predicting nitrogen retention in lakes and reservoirs

Modelos empíricos aprimorados para prever a retenção de nitrogênio em lagos e reservatórios

ABSTRACT

Anthropogenic activities have significantly increased the movement of nitrogen (N) from land to freshwaters and to coastal waters and have led to severe environmental consequences. The flow of N is moderated by retention processes in terrestrial, freshwater and marine ecosystems. Freshwater ecosystems have the highest areal N retention rates. The proportion of N retained in aquatic ecosystems depends on the areal hydraulic load and is described by relatively simple semi-empirical or strictly empirical models. Here I compared the predictive power of several models, that predict the annual mean proportion of total N (TN) and dissolved inorganic N (DIN) retained in lakes and reservoirs and developed an improved version of the models currently in use by inclusion of additional relevant parameters. The study shows that models derived from mass balances describing the proportion of annual mean retention of TN and DIN as a sigmoid function of the areal hydraulic load can be approximated by a linear function on the logarithm of the areal hydraulic load. Stepwise multiple linear regression analyses identified the logarithm of the areal hydraulic load as the main explanatory variable for the proportion of retained TN, followed by the ratio between the DIN and the TN load and the ratio between in-lake concentrations of TN and total phosphorus (TP). The logarithm of the areal hydraulic load, the ratio between the DIN and the TN load and the logarithm of the in-lake concentration of TP explained the largest proportion of retained DIN. Addition of the second and third explanatory variable decreased the normalized root mean square deviation between the observed and predicted proportion of retained TN from 37%, to 31% and to 30% and between the observed and predicted proportion of retained DIN from 39%, to 35% and to 32%.

Keywords: empirical model, mass balance, nitrogen retention, lakes, reservoirs, multiple linear regression

RESUMO

As atividades antropogênicas aumentaram significativamente o movimento de nitrogênio (N) da terra para as águas doces e para as águas costeiras e levaram a consequências ambientais severas. O fluxo de N é moderado por processos de retenção em ecossistemas terrestres, de água doce e marinhos .Os ecossistemas de água docetêm as maiores taxas de retenção de N areal. A proporção de N retido em ecossistemas aquáticos depende da carga hidráulica areal e é descrita por modelos semi-empíricos ou estritamente empíricos relativamente simples. Aqui, comparei o poder preditivo de vários modelos, que preveem a proporção média anual de N total (TN) e N inorgânico dissolvido (NID) retidos em lagos e reservatórios e desenvolvi uma versão melhorada dos modelos atualmente em uso pela inclusão de parâmetros relevantes adicionais. O estudo mostra que os modelos derivados de balanços de massa que descrevem a proporção da retenção média anual de TN e DIN como uma função sigmoide da carga hidráulica areal podem ser aproximados por uma função linear no logaritmo da carga hidráulica areal. Análises de regressão linear múltipla por etapas identificaram o logaritmo da carga hidráulica areal como a principal variável explicativa para a proporção de TN retido, seguido pela razão entre DIN e a carga de TN e a razão entre as concentrações de TN no lago e fósforo total (PT). O logaritmo da carga hidráulica areal, a razão entre DIN e a carga de TN e o logaritmo da concentração de TP no lago explicaram a maior proporção de DIN retido. A adição da segunda e terceira variáveis ​​explicativas diminuiu o desvio quadrático médio normalizado entre a proporção observada e prevista de TN retido de 37% para 31% e para 30% e entre a proporção observada e prevista de DIN retido de 39% para 35% e para 32%.

Palavras-chave: empirical model, mass balance, nitrogen retention, lakes, reservoirs, multiple linear regression

Introduction

The global cycling of nitrogen (N) has almost doubled over the last century due to the large increase of anthropogenic N fixation through production of fertilizers, cultivation of legume crops, and combustion of fossil fuels (Galloway et al., 2004). Almost all N originating from land-based sources is retained from the three main ecosystem types: terrestrial (soils: 40%), freshwater (groundwater, lakes and reservoirs, rivers: 35%) and marine (estuaries, continental shelves, oxygen minimum zones: 25%); with rates per unit area in rivers/lakes that are up to 10 times higher than in soils (Seitzinger et al. 2006). Understanding and quantifying N retention processes is extremely important for managing and mitigating the severe environmental consequences associated with N pollution (Boyer et al., 2006). The main N retention processes are microbial-mediated emissions of N₂ gas, permanent storage in soils and sediments and uptake by primary producers. In aquatic ecosystems uptake of N by macrophytes and algae is usually only temporary as most nutrients assimilated during the growing phase are mineralized and released again in autumn (Clarke, 2002). The primary permanent N retention mechanism in aquatic systems is generally denitrification (Nixon et al., 1996; Saunders and Kalff, 2001a; Seitzinger, 1988), although more recently anaerobic ammonium oxidation (anammox) has been reported to contribute significantly to N retention (Lu et al., 2018). Denitrification occurs at oxic-anoxic interfaces. In aquatic systems these are located in the anaerobic layer of the sediments, in the suboxic bottom waters (Seitzinger et al., 2006) and in biofilms of submerged macrophytes or other substrates (Weisner et al., 1994). Nitrate can be supplied either from the overlaying water or produced in the sediment by nitrification of ammonium (coupled nitrification-denitrification). The first pathway may prevail in waters with a high external input of nitrate, the second when water column nitrate becomes limiting (de Klein, 2008). Measurements of denitrification rates in lakes show that nitrate concentration in the water above the sediment is the most important factor for predicting denitrification at variable geographical scales (McCrackin and Elser, 2012; Rissanen et al., 2013), but dependence on temperature (Ahlgren et al., 1994, Saunders and Kalff, 2001b, Veraart et al., 2011) and organic matter (Saunders and Kalff, 2001b) have also been reported. Because of the complexity of the N cycle, before N is finally retained from the aquatic ecosystem, it can undergo numerous reactions (assimilation, mineralization, nitrification, dissimilatory nitrate reduction to ammonium), that depend on a variety of environmental parameters such as concentrations of N, P, carbon (C) and oxygen, hydrology, morphology, and temperature. N occurs in different forms and oxidation states (nitrate, ammonium, nitrite, nitrous oxide, dinitrogen, organic nitrogen). Given this complexity, it is surprizing how well relatively simple empirical models are able to predict the proportion of TN retained in aquatic ecosystems (%R_TN). Most such models have been derived from N input-output budgets (Kelly et al., 1987; Alexander et al., 2002). Basically two main approaches for modelling %R_TN have been applied: models that predict directly %R_TN (Alexander et al., 2002; Jensen et al., 1990; Molot and Dillon, 1993) and models that are based on the assumption that most N is retained on account of the imported nitrate and estimate %R_TN indirectly from models that predict the proportion of retained dissolved inorganic nitrogen (%R_DIN) (Hindar et al., 2001; Seitzinger et al., 2002). Both %R_TN and %R_DIN correlate positively with the water residence time (τ) and negatively with the mean depth of the water column () (Molot and Dillon, 1993). τ and  affect the duration and the extent of the contact between the water column and the sediment surface influencing the N uptake by the sediment (Coppens et al., 2015).

Some of these relations have been used to make predictions of N retention rates at regional and global scales (Alexander et al. 2002; Beusen et al., 2016; Harrison et al., 2009; Seitzinger et al., 2010; Wollheim et al., 2008). Several studies suggested that parameters other than τ and  may significantly influence the proportion of N retained in lakes: in-lake concentration of P (Berge et al., 1997; Coppens et al., 2015; Kaste and Lyche-Solheim, 2005) and nitrate (Mulholland et al., 2008), the TN:TP ratio (Guildford and Hecky, 2000), temperature (Coppens et al., 2015; Rissanen et al., 2013), the presence of organic matter and the quality of the N loads (i.e. less easily recyclable inorganic N; Rissanen et al., 2013).

The aim of this study was to compare the predictive power of existing simple empirical annual mean TN and DIN retention models for lakes and reservoirs and to develop an improved version of the models currently in use by inclusion of other relevant parameters. The purpose is to predict the amount of annual mean TN and DIN that is retained.

Section snippets

Derivation and calibration of the models currently in use

Existing empirical N retention models can basically be divided into semi-empirical and strictly empirical models. Semi-empirical models are derived from N mass-balance equations of lakes or river sections, they are calibrated with measured environmental variables, and they describe the proportion of retained N as a function of τ and . Empirical models are a based on statistical relationships between %R_TN and τ, .

Results

As expected, %R_TN and %R_DIN increase with decreasing areal hydraulic load q, (Fig. 2). The calculated lake/reservoir specific settling velocities q_TN and q_DIN varied somewhat depending on the model used for their calculation. In general, q_TN and q_DIN calculated with the semi-empirical models derived from the mass balance of lake/reservoirs (Eqs. 3 and 4) were slightly higher than if calculated with the semi-empirical models derived from the mass balance of rivers sections (Eqs. 5 and 6).

Discussion

The analysis in this paper has shown that the areal hydraulic load q is the key variable for the prediction of both %R_TN and %R_DIN. This indicates that %R_TN and %R_DIN increase with increasing τ and with decreasing mean depth . Longer τ increases the chance of nutrients to the be transformed in the water column and lower  increases the chance of nutrients to be transformed at the sediment surface where most denitrification, the main N retention process occurs (Saunders and Kalff, 2001a; 

Conclusion

In summary, this study showed that empirical models derived from input-output mass balances of TN and DIN describing annual mean %R_TN and %R_DIN in lakes/reservoirs as a sigmoid function of q, can be approximated by a linear function on log₁₀q with little loss of information and can be significantly improved by focusing on the inorganic N load to the lakes. Nevertheless, the relatively low values of the adjusted R² of the models (0.5-0.7) suggests that the here presented models still deliver

Acknowledgments

This research did not receive any specific grant from founding agencies in the public, commercial, or not-for-profit sector. I’m very grateful to Dr. Richard Wright for controlling and editing the English language and for his very useful suggestions. Also very precious were the comments of two anonymous reviewers.

References (93)

• K.E. Havens et al.Nutrient dynamics and the eutrophication of shallow lakes Kasumigaura (Japan), Donghu (PR China), and Okeechobee (USA)Environ. Pollut.(2001)
• B. Kronvang et al.Nitrogen transport and fate in European streams, rivers, lakes and wetlands
• X. Lu et al.The relative importance of anammox and denitrification to total N₂ production in Lake ErieJ. Great Lakes Res.(2018)
• E. Mayorga et al.Global nutrient export from WaterSheds 2 (NEWS 2): Model development and implementationEnviron. Modell. Softw.(2010)
• G. Piñeiro et al.How to evaluate models: observed vs. predicted or predicted vs. observed?Ecol. Model.(2008)
• M.D. Rowe et al.A reactive nitrogen budget for Lake MichiganJ. Great Lakes Res.(2014)
• H.J. Salas et al.A simplified phosphorus trophic state model for warm-water tropical lakesWat. Res.(1991)
• D.L. Saunders et al.Denitrification rates in the sediments of Lake Memphremagog, Canada-USAWater. Res.(2001)
• I. Ahlgren et al.Nitrogen budgets in relation to microbial transformations in lakesAmbio(1994)
• R.B. Alexander et al.Estimating the sources and transport of nutrients in the Waikato River Basin, New ZealandWater Resour. Res.(2002)
• J.M. AndersenNitrogen and phosphorus budgets and the role of sediments in six shallow Danish lakesArch. Hydrobiol.(1974)
• D. Berge et al.Nitrogen retention in two Norwegian watercourses of different trophic statusAmbio(1997)
• H.W. Beusen et al.Global riverine N and P transport to ocean increased during the 20th century despite increased retention along the aquatic continuumBiogeosciences(2016)
• A.F. Bouwman et al.Nutrient dynamics, transfer and retention along the aquatic continuum from land to ocean: towards integration of ecological and biogeochemical modelsBiogeosciences(2013)
• E.W. Boyer et al.Modeling denitrification in terrestrial and aquatic ecosystems at regional scalesEcol. Appl.(2006)
• O. Broberg et al.External budgets for phosphorus, nitrogen and dissolved organic carbon for the acidified Lake GårdsjönArch. Hydrobiol.(1984)
• M.T. Cabrita et al.Seasonal variation in denitrification and dissolved nitrogen fluxes in intertidal sediments of the Tagus estuaryPortugal. Mar. Ecol. Prog. Ser.(2000)
• A. Calderoni et al.Phosphorus, nitrogen and silica budget in Lago MergozzoVerh. Internat. Verein. Limnol.(1978)
• S.J. ClarkeVegetation growth in rivers: influences upon sediment and nutrient dynamicsProg. Phys. Geogr.(2002)
• CLRTAPMapping critical loads for ecosystems, Chapter V of Manual on methodologies and criteria for modelling and mapping critical loads and levels and air pollution effects, risks and trends(2017)
• J. Coppens et al.The influence of nutrient loading, climate and water depth on nitrogen and phosphorus loss in shallow lakes: a pan-European mesocosm experimentHydrobiologia(2015)
• M.B. David et al.Denitrification and the nitrogen budget of a reservoir in an agricultural landscapeEcol. Appl.(2006)
• P.J. Dillon et al.The role of ammonium and nitrate retention in the acidification of lakes and forests catchmentsBiogeochemistry(1990)
• J.J.M. de KleinFrom Ditch to Delta, nutrient retention in running waters, PhD thesis(2008)
• P. Durand et al.Nitrogen processes in aquatic ecosystems
• G. Dudel et al.The nitrogen budget of a shallow lake (Grosser Müggelsee, Berlin)Int. Revue Ges. Hydrobiol.(1992)
• P. Ekholm et al.Internal and external loading as regulators of nutrient concentrations in the agriculturally loaded Lake Pyhäjärvi (southwest Finland)Hydrobiology(1997)
• C.J. Finlay et al.Human influences on nitrogen removal in lakesScience(2013)
• S. Fleischer et al.Nitrogen removal in created pondsAmbio(1994)
• T. Frisk et al.The effect of phosphorus on nitrogen retention in lakes
• J. Garnier et al.Biogeochemical mass-balances (C, N, P, Si) in three large reservoirs of the Seine Basin (France)Biogeochemistry(1999)
• M.M. Gibbs et al.Lake Horowhenua: a computer model of its limnology and restoration prospectsHydrobiologia(1994)
• J.N. Galloway et al.Nitrogen cycles: past, present, and futureBiogeochemistry(2004)
• C.E. Gibson et al.The nitrogen cycle in Lough Neagh, N. Ireland 1975 to 1987Int. Revue Ges. Hydrobiol.(1992)
• S.J. Guildford et al.Total nitrogen, total phosphorus, and nutrient limitation in lakes and oceans: Is there a common relationship?Limnol. Oceanogr.(2000)
• L. GraninaThe chemical budget of Lake Baikal: a reviewLimnol. Oceanogr.(1997)
• J.A. Harrison et al.The regional and global significance of nitrogen removal in lakes and reservoirsBiogeochemistry(2009)
• J. Hayward et al.1993. Nitrogen and phosphorus budgets in the Erne system, 1974-89Biol. Environ.(1993)
• A. Hindar et al.Effects of in-lake retention of nitrogen on critical load calculationsWater, Air, Soil Pollut.(2001)
• P. Höhner et al.Prediction of dissolved inorganic (DIN) concentrations in deep, seasonally stratified lakes based on rates of DIN and N removal processesAquat. Sci.(1993)
• H.M. Irfannullah et al.Low retention of nitrogen in a clear-water, shallow temperate lakeArch. Hydrobiol.(2008)
• ISE-CNR (Institute of Ecosystem Study – National Research Council), 1981–1990. Ricerche sull’evoluzione del Lago…
• ISE-CNR (Institute of Ecosystem Study – National Research Council), 1991-2000. Ricerche sull’evoluzione del Lago…
• ISE-CNR (Institute of Ecosystem Study – National Research Council), 2001-2009. Ricerche sull’evoluzione del Lago…
• IST-SUPSI (Institute of Earth Sciences-University of Applied Sciences and Arts), 2008-2012. Ricerche sull’evoluzione…
• J.P. Jensen et al.Relationships between nitrogen loading and in-lake nitrogen concentrations in shallow Danish lakesVerh. Internat. Limnol.(1990)

There are more references available in the full text version of this article.