A Comparison of Statistical Approaches for Predicting Stream Temperatures Across Heterogeneous Landscapes 1

Abstract:  Estimating stream temperatures across broad spatial extents is important for regional conservation of running waters. Although statistical models can be useful in this endeavor, little information exists to aid in the selection of a particular statistical approach. Our objective was to compare the accuracy of ordinary least-squares multiple linear regression, generalized additive modeling, ordinary kriging, and linear mixed modeling (LMM) using July mean stream temperatures in Michigan and Wisconsin. Although LMM using low-rank thin-plate smoothing splines to measure the spatial autocorrelation in stream temperatures was the most accurate modeling approach; overall, there were only slight differences in prediction accuracy among the evaluated approaches. This suggests that managers and researchers can select a stream temperature modeling approach that meets their level of expertise without sacrificing substantial amounts of prediction accuracy. The most accurate models for Michigan and Wisconsin had root mean square errors of 2.0-2.3°C, suggesting that only relatively coarse predictions can be produced from landscape-based statistical models at regional scales. Explaining substantially more variability in stream temperatures likely will require the collection of finer-scale hydrologic and physiographic data, which may be cost prohibitive for monitoring and assessing stream temperatures at regional scales.

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

[2]  S. Johnson,et al.  Factors influencing stream temperatures in small streams: substrate effects and a shading experiment , 2004 .

[3]  Arthur J. Lembo,et al.  Predicting stream temperatures: geostatistical model comparison using alternative distance metrics , 2003 .

[4]  Wayne A. Hubert,et al.  Fish Assemblages and Habitat Gradients in a Rocky Mountain–Great Plains Stream: Biotic Zonation and Additive Patterns of Community Change , 1991 .

[5]  A. Mackey,et al.  The prediction of water temperatures in chalk streams from air temperatures , 1991, Hydrobiologia.

[6]  J. Lyons.  Patterns in the species composition of fish assemblages among Wisconsin streams , 1996, Environmental Biology of Fishes.

[7]  P. Steen,et al.  Classification Tree Models for Predicting Distributions of Michigan Stream Fish from Landscape Variables , 2008 .

[8]  James H. Brown,et al.  Effects of size and temperature on developmental time , 2002, Nature.

[9]  Kevin E. Wehrly,et al.  Simulating effects of hydro‐dam alteration on thermal regime and wild steelhead recruitment in a stable‐flow Lake Michigan tributary , 2004 .

[10]  Edwin A. Roehl,et al.  Numerically Optimized Empirical Modeling of Highly Dynamic, Spatially Expansive, and Behaviorally Heterogeneous Hydrologic Systems – Part 1 , 2006 .

[11]  T. Thorslund,et al.  Effects of Constant Temperatures and Diel Temperature Fluctuations on Specific Growth and Mortality Rates and Yield of Juvenile Rainbow Trout, Salmo gairdneri , 1977 .

[12]  F. Rahel,et al.  Temperature mediation of competitive interactions among three fish species that replace each other along longitudinal stream gradients , 1998 .

[13]  Jay M. Ver Hoef,et al.  Geostatistical modelling on stream networks: developing valid covariance matrices based on hydrologic distance and stream flow , 2007 .

[14]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[15]  Steven C. Chapra,et al.  Temperature Model for Highly Transient Shallow Streams , 1997 .

[16]  Raymond Torres,et al.  Geomorphic analysis of tidal creek networks , 2004 .

[17]  P. Good.  Resampling Methods , 1999, Birkhäuser Boston.

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

[19]  T. Al Austin,et al.  Quantifying the effects of stream discharge on summer river temperature , 1998 .

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

[21]  Carol A. Gotway,et al.  Statistical Methods for Spatial Data Analysis , 2004 .

[22]  B. W. Sweeney,et al.  Geographic Analysis of Thermal Equilibria: A Conceptual Model for Evaluating the Effect of Natural and Modified Thermal Regimes on Aquatic Insect Communities , 1980, The American Naturalist.

[23]  E. Steel,et al.  Using wavelet analysis to detect changes in water temperature regimes at multiple scales: effects of multi‐purpose dams in the Willamette River basin , 2007 .

[24]  Patrick J. Sullivan,et al.  Spatial and temporal stream temperature prediction: Modeling nonstationary temporal covariance structures , 2004 .

[25]  J. Paruelo,et al.  How to evaluate models : Observed vs. predicted or predicted vs. observed? , 2008 .

[26]  Travis O. Brenden,et al.  A River Valley Segment Classification of Michigan Streams Based on Fish and Physical Attributes , 2008 .

[27]  Charles P. Hawkins,et al.  Channel Morphology, Water Temperature, and Assemblage Structure of Stream Insects , 1997, Journal of the North American Benthological Society.

[28]  R. Sponseller,et al.  Relationships between land use, spatial scale and stream macroinvertebrate communities , 2001 .

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

[30]  R. Peterman,et al.  A Science-Based Approach for Identifying Temperature-Sensitive Streams for Rainbow Trout , 2007 .

[31]  Paul W. Seelbach,et al.  Classifying Regional Variation in Thermal Regime Based on Stream Fish Community Patterns , 2003 .

[32]  J. R. Brett.  Energetic Responses of Salmon to Temperature. A Study of Some Thermal Relations in the Physiology and Freshwater Ecology of Sockeye Salmon (Oncorhynchus nerkd) , 1971 .

[33]  Scott P. Sowa,et al.  A GAP ANALYSIS AND COMPREHENSIVE CONSERVATION STRATEGY FOR RIVERINE ECOSYSTEMS OF MISSOURI , 2007 .

[34]  Orazio Giustolisi,et al.  A multi-model approach to analysis of environmental phenomena , 2007, Environ. Model. Softw..

[35]  Niyazi Kilic,et al.  Estimation of stream temperature in firtina creek (Rize-Turkiye) using artificial neural network model. , 2007, Journal of environmental biology.

[36]  Bernard A. Engel,et al.  Stream Temperature Dynamics in Upland Agricultural Watersheds , 2000 .

[37]  A GIS framework for collecting, managing, and analyzing multiscale landscape variables across large regions for river conservation and management , 2006 .

[38]  D. T. Crisp,et al.  Effect of air temperature upon mean water temperature in streams in the north Pennines and English Lake District , 1982 .

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

[40]  G. Helfman,et al.  MULTISCALE INFLUENCES ON PHYSICAL AND CHEMICAL STREAM CONDITIONS ACROSS BLUE RIDGE LANDSCAPES 1 , 2002 .

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

[42]  K. Rose,et al.  Model goodness-of-fit analysis using regression and related techniques , 1995 .

[43]  Heinz G. Stefan,et al.  Stream temperature dynamics: Measurements and modeling , 1993 .

[44]  F. Rahel,et al.  Potential habitat loss and population fragmentation for cold water fish in the North Platte River drainage of the Rocky Mountains : Response to climate warming , 1996 .

[45]  Michael Power,et al.  The predictive validation of ecological and environmental models , 1993 .

[46]  W. Hubert,et al.  A HYPOTHESIS ABOUT FACTORS THAT AFFECT MAXIMUM SUMMER STREAM TEMPERATURES ACROSS MONTANE LANDSCAPES 1 , 2001 .

[47]  Mysore G. Satish,et al.  Predicting river water temperatures using the equilibrium temperature concept with application on Miramichi River catchments (New Brunswick, Canada) , 2005 .