Water temperature modelling: comparison between the generalized additive model, logistic, residuals regression and linear regression models

ABSTRACT Water temperature has a significant influence on aquatic organisms, including stenotherm fish such as salmonids. It is thus of prime importance to build reliable tools to forecast water temperature. This study evaluated a statistical scheme to model average water temperature based on daily average air temperature and average discharge at the Sainte-Marguerite River, Northern Canada. The aim was to test a non-parametric water temperature generalized additive model (GAM) and to compare its performance to three previously developed approaches: the logistic, residuals regression and linear regression models. Due to its flexibility, the GAM was able to capture some of the nonlinear response between water temperature and the two explanatory variables (air temperature and flow). The shape of these effects was determined by the trends shown in the collected data. The four models were evaluated annually using a cross-validation technique. Three comparison criteria were calculated: the root mean square error (RMSE), the bias error and the Nash-Sutcliffe coefficient of efficiency (NSC). The goodness of fit of the four models was also compared graphically. The GAM was the best among the four models (RMSE = 1.44°C, bias = −0.04 and NSC = 0.94).

[1]  J. C. Geyer,et al.  The Response of Water Temperatures to Meteorological Conditions , 1968 .

[2]  André St-Hilaire,et al.  Water temperature modelling in a small forested stream: implication of forest canopy and soil temperature , 2000 .

[3]  Bofu Yu,et al.  Transport Capacity of Overland Flow with High Sediment Concentration , 2015 .

[4]  Pavel Kabat,et al.  Global river temperatures and sensitivity to atmospheric warming and changes in river flow , 2011 .

[5]  Heinz G. Stefan,et al.  STREAM TEMPERATURE CORRELATIONS WITH AIR TEMPERATURES IN MINNESOTA: IMPLICATIONS FOR CLIMATE WARMING 1 , 1998 .

[6]  J. R. Manson,et al.  Temperature and the metabolic balance of streams , 2011 .

[7]  Taha B. M. J. Ouarda,et al.  Daily river water temperature forecast model with a k‐nearest neighbour approach , 2012 .

[8]  V. Acuña,et al.  Surface–subsurface water exchange rates along alluvial river reaches control the thermal patterns in an Alpine river network , 2009 .

[9]  Alan Y. Chiang,et al.  Generalized Additive Models: An Introduction With R , 2007, Technometrics.

[10]  Taha B. M. J. Ouarda,et al.  Predicting river water temperatures using stochastic models: case study of the Moisie River (Québec, Canada) , 2007 .

[11]  M. H. Quenouille.  Approximate tests of correlation in time-series 3 , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[13]  R. Enata.  Consequences of climatic change for water temperature and brown trout populations in Alpine rivers and streams , 2005 .

[14]  D. Isaak,et al.  Climate change effects on stream and river temperatures across the northwest U.S. from 1980–2009 and implications for salmonid fishes , 2012, Climatic Change.

[15]  Roger C. Bales,et al.  Estimating Stream Temperature from Air Temperature: Implications for Future Water Quality , 2005 .

[16]  L. Hansen,et al.  Potential impacts of global climate change on freshwater fisheries , 2007, Reviews in Fish Biology and Fisheries.

[17]  J. Armengol,et al.  Water temperature modeling in the Lower Ebro River (Spain): Heat fluxes, equilibrium temperature, and magnitude of alteration caused by reservoirs and thermal effluent , 2012 .

[18]  B. Webb,et al.  Changing UK river temperatures and their impact on fish populations. , 2004 .

[19]  R. D. Moore,et al.  Stream Temperature Patterns in British Columbia, Canada, Based on Routine Spot Measurements , 2006 .

[20]  Heinz G. Stefan,et al.  A nonlinear regression model for weekly stream temperatures , 1998 .

[21]  Pierre-André Cornillon,et al.  Régressión :: théorie et applications , 2007 .

[22]  A. Heath,et al.  Effects of temperature on aquatic organism sensitivity to selected chemicals , 1978 .

[23]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[24]  L. Crozier,et al.  Climate impacts at multiple scales: evidence for differential population responses in juvenile Chinook salmon. , 2006, The Journal of animal ecology.

[25]  J. Magnuson,et al.  Temperature as an Ecological Resource , 1979 .

[26]  M. Palmer,et al.  Stream Temperature Surges Under Urbanization and Climate Change: Data, Models, and Responses 1 , 2007 .

[27]  R. Tibshirani,et al.  Generalized Additive Models , 1986 .

[28]  R. Cunjak,et al.  Influence of water temperature and streambed stability on the abundance and distribution of slimy sculpin (Cottus cognatus) , 2007, Environmental Biology of Fishes.

[29]  Roger D. Peng,et al.  Statistical Methods for Environmental Epidemiology with R: A Case Study in Air Pollution and Health , 2008 .

[30]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[31]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[32]  Matthias Schmid,et al.  Developing and testing temperature models for regulated systems: A case study on the Upper Delaware River , 2014 .

[33]  M. Lapointe,et al.  Climate change and resilience of tributary thermal refugia for salmonids in eastern Canadian rivers , 2015 .

[34]  M. M. Cox,et al.  A spatially explicit network-based model for estimating stream temperature distribution , 2007, Environ. Model. Softw..

[35]  D. Caissie.  The thermal regime of rivers : a review , 2006 .

[36]  Veerasamy Kothandaraman,et al.  Analysis of Water Temperature Variations in Large River , 1971 .

[37]  Heinz G. Stefan,et al.  Stream temperature/air temperature relationship : a physical interpretation , 1999 .

[38]  Nassir El-Jabi,et al.  Estimation de la température de l'eau de rivière en utilisant les réseaux de neurones et la régression linéaire multiple , 2005 .

[39]  W. Connor,et al.  Temperature during Incubation as One Factor Affecting the Distribution of Snake River Fall Chinook Salmon Spawning Areas , 2003 .

[40]  B. Langbein,et al.  Long-Term Changes , 2016 .

[41]  Tyler Wagner,et al.  A regional neural network ensemble for predicting mean daily river water temperature , 2014 .

[42]  Gene E. Likens,et al.  Rising stream and river temperatures in the United States , 2010 .

[43]  H. Stefan,et al.  Sensitivity of stream temperatures in the United States to air temperatures projected under a global warming scenario , 1999 .

[44]  Desmond E. Walling,et al.  Water–air temperature relationships in a Devon river system and the role of flow , 2003 .

[45]  D. Hannah,et al.  Recent advances in stream and river temperature research , 2008 .

[46]  F. Moatar,et al.  Water temperature behaviour in the River Loire since 1976 and 1881 , 2006 .

[47]  O. Hoegh‐Guldberg,et al.  Ecological responses to recent climate change , 2002, Nature.

[48]  S. Hinch,et al.  Effects of rapid experimental temperature increases on acute physiological stress and behaviour of stream dwelling juvenile chinook salmon , 2006 .

[49]  Agnès Ducharne,et al.  Importance of stream temperature to climate change impact on water quality , 2007 .

[50]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[51]  Patricia Burkhardt-Holm,et al.  Consequences of climatic change for water temperature and brown trout populations in Alpine rivers and streams , 2006 .

[52]  G. Smoot,et al.  Water temperature--influential factors, field measurement, and data presentation , 1975 .

[53]  Pierre Legendre,et al.  Development and validation of numerical habitat models for juveniles of Atlantic salmon (Salmo salar) , 2000 .

[54]  K. Bhaskaran,et al.  Time series regression studies in environmental epidemiology , 2013, International journal of epidemiology.

[55]  Travis O. Brenden,et al.  A Comparison of Statistical Approaches for Predicting Stream Temperatures Across Heterogeneous Landscapes 1 , 2009 .

[56]  G. Sun,et al.  A model to predict stream water temperature across the conterminous USA , 2015 .

[57]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[58]  J. M. Elliott,et al.  A functional model for maximum growth of Atlantic Salmon parr, Salmo salar, from two populations in northwest England , 1997 .

[59]  S. Wood.  mgcv:Mixed GAM Computation Vehicle with GCV/AIC/REML smoothness estimation , 2012 .

[60]  Lao Juan,et al.  Development and Validation of a Scale for Measuring Instructors' Attitudes toward Concept-Based or Reform-Oriented Teaching of Introductory Statistics in the Health and Behavioral Sciences , 2010, 1007.3219.

[61]  Robert M. Scheller,et al.  Effects of climate warming on fish thermal habitat in streams of the United States , 1996 .

[62]  Cynthia L. Lowney,et al.  Stream temperature variation in regulated rivers: Evidence for a spatial pattern in daily minimum and maximum magnitudes , 2000 .

[63]  W. Marszelewski,et al.  Long-term changes in temperature of river waters in the transitional zone of the temperate climate: a case study of Polish rivers , 2016 .

[64]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[65]  Taha B. M. J. Ouarda,et al.  Utilisation des réseaux de neurones et de la régularisation bayésienne en modélisation de la température de l’eau en rivière , 2008 .

[66]  Heinz G. Stefan,et al.  STREAM TEMPERATURE ESTIMATION FROM AIR TEMPERATURE , 1993 .

[67]  C. Krueger,et al.  Behavioral Thermoregulation of Brook and Rainbow Trout: Comparison of Summer Habitat Use in an Adirondack River, New York , 2003 .

[68]  K. Smith,et al.  The prediction of river water temperatures / Prédiction des températures des eaux de rivière , 1981 .

[69]  S. E. Adlouni,et al.  Generalized Additive Models in Environmental Health: A Literature Review , 2012 .

[70]  André St-Hilaire,et al.  Stochastic modelling of water temperatures in a small stream using air to water relations , 1998 .

[71]  G. Morin,et al.  Comparaison des performances relatives à un modèle déterministe et à un modèle stochastique de température de l'eau en rivière , 1986 .

[72]  Jan de Leeuw,et al.  Statistical Methods for Environmental Epidemiology with R , 2009 .

[73]  R. Haggerty,et al.  The paradox of cooling streams in a warming world: Regional climate trends do not parallel variable local trends in stream temperature in the Pacific continental United States , 2012 .

[74]  B. Webb.  Trends in stream and river temperature , 1996 .

[75]  H. Stefan,et al.  Global Warming and Potential Changes in Fish Habitat in U.S. Streams , 2003 .

[76]  Marijana Hadzima-Nyarko,et al.  Modelling river temperature from air temperature: case of the River Drava (Croatia) , 2015 .

[77]  J. Olden,et al.  Incorporating thermal regimes into environmental flows assessments: modifying dam operations to restore freshwater ecosystem integrity , 2010 .

[78]  Heinz G. Stefan,et al.  LINEAR AIR/WATER TEMPERATURE CORRELATIONS FOR STREAMS DURING OPEN WATER PERIODS , 2000 .

[79]  P. Heuberger,et al.  Calibration of process-oriented models , 1995 .

[80]  G. Russell,et al.  Modeling changes in summer temperature of the Fraser River during the next century , 2007 .

[81]  Robert M. Scheller,et al.  A field information-based system for estimating fish temperature tolerances , 1995 .

[82]  E. Maurer,et al.  Effects of climate change on stream temperature, dissolved oxygen, and sediment concentration in the Sierra Nevada in California , 2013 .

[83]  Balaji Rajagopalan,et al.  Forecasting river temperatures in real time using a stochastic dynamics approach , 2013 .

[84]  C. Frissell,et al.  Thermal heterogeneity, stream channel morphology, and salmonid abundance in northeastern Oregon streams , 2003 .

[85]  André St-Hilaire,et al.  Temporal variability of thermal refuges and water temperature patterns in an Atlantic salmon river. , 2013 .

[86]  Balaji Rajagopalan,et al.  Regression Model for Daily Maximum Stream Temperature , 2003 .

[87]  Anna B. Neuheimer,et al.  The growing degree-day and fish size-at-age : the overlooked metric , 2007 .

[88]  G. Yohe,et al.  A globally coherent fingerprint of climate change impacts across natural systems , 2003, Nature.

[89]  Mysore G. Satish,et al.  Modelling of maximum daily water temperatures in a small stream using air temperatures , 2001 .

[90]  Balaji Rajagopalan,et al.  Statistical Modeling of Daily Water Temperature Attributes on the Sacramento River , 2015 .

[91]  M. Secondat.  Les variations de la température et de la concentration en oxygène dissous des eaux lacustres et des eaux courantes. Leur retentissement sur la distribution des poissons , 1952 .

[92]  Steven C. Walker,et al.  Empirical modelling of lake water-temperature relationships: a comparison of approaches , 2008 .

[93]  Mysore G. Satish,et al.  Predicting water temperatures using a deterministic model : Application on Miramichi River catchments (New Brunswick, Canada) , 2007 .

[94]  Bernard Bobée,et al.  A Review of Statistical Water Temperature Models , 2007 .

[95]  Taha B. M. J. Ouarda,et al.  Feasibility study of a geostatistical modelling of monthly maximum stream temperatures in a multivariate space , 2009 .

[96]  Taha B. M. J. Ouarda,et al.  Comparison of non-parametric and parametric water temperature models on the Nivelle River, France , 2008 .

[97]  D. Cluis,et al.  RELATIONSHIP BETWEEN STREAM WATER TEMPERATURE AND AMBIENT AIR TEMPERATURE , 1972 .

[98]  Miyuki Ono,et al.  Statistical analyses on the effects of air temperature fluctuations on river water qualities , 2003 .

[99]  Daniel Caissie,et al.  Stream temperature modelling using artificial neural networks: application on Catamaran Brook, New Brunswick, Canada , 2008 .

[100]  G. Minshall,et al.  The River Continuum Concept , 1980 .