Quantifying and modelling urban stream temperature: a ...

HYDROLOGICAL PROCESSESHydrol. Process. 30, 503–514 (2016)Published online 26 August 2015 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.10617

Quantifying and modelling urban stream temperature: acentral US watershed study

Sean Zeiger,1 Jason A. Hubbart,2* Stephen H. Anderson3 and Michael C. Stambaugh41 Water Resources Program, Department of Forestry, School of Natural Resources, University of Missouri, 203-T ABNR Building, Columbia, MO,

65211, USA2 Water Resources Program, Department of Forestry, School of Natural Resources, University of Missouri, 203-Q ABNR Building, Columbia, MO,

65211, USA3 Department of Soil, Environmental, and Atmospheric Sciences, University of Missouri, 302 ABNR Building, Columbia, MO, 65211, USA

4 Department of Forestry, University of Missouri, 203-C ABNR Building, Columbia, MO, 65211, USA

*CNa203E-m

Co

Abstract:

Hydrologic models that rely on site specific linear and non-linear regression water temperature (Tw) subroutines forced solelywith observed air temperature (Ta) may not accurately estimate Tw in mixed-use urbanizing watersheds where hydrogeologicaland land use complexity may confound common Tw regime assumptions. A nested-scale experimental watershed study designwas used to test Tw model predictions in a representative mixed-use urbanizing watershed of the central USA. The linearregression Tw model used in the Soil and Water Assessment Tool (SWAT), a non-linear regression Tw model, and a process-based Tw model that accounts for watershed hydrology were evaluated. The non-linear regression Tw model tested at a daily timestep performed significantly (P< 0.01) better than the linear Tw model currently used in SWAT. Both regression Tw modelsoverestimated Tw in lower temperature ranges (Tw< 10.0 °C) with percent bias (PBIAS) values ranging from �28.2% (non-linearTw model) to �66.1% (linear regression Tw model) and underestimated Tw in the higher temperature range (Tw> 25.0 °C) by3.2%, and 7.2%, respectively. Conversely, the process-based Tw model closely estimated Tw in lower temperature ranges(PBIAS= 4.5%) and only slightly underestimated Tw in the higher temperature range (PBIAS= 1.7%). Findings illustrate thebenefit of integrating process-based Tw models with hydrologic models to improve model transferability and Tw predictiveconfidence in urban mixed-land use watersheds. The findings in this work are distinct geographically and in terms of mixed-landuse complexity and are therefore of immediate value to land-use managers in similarly urbanizing watersheds globally.Copyright © 2015 John Wiley & Sons, Ltd.

KEY WORDS stream water temperature; experimental watershed study; urban heat island; storm water runoff; water quality;mixed-land use; discharge

Received 1 December 2014; Accepted 12 July 2015

INTRODUCTION

Water temperature (Tw) is an ecologically important waterquality parameter that is variously affected by indepen-dent and interacting natural and anthropogenic forces(Smith, 1972; Ward, 1985; Caissie, 2006; and Webb et al.2008). Caissie (2006) summarized naturally occurringinfluences of Tw regimes into four categories includingmeteorological influences (e.g. solar radiation and airtemperature), topographic influences (e.g. riparian vege-tation and latitude/altitude), stream discharge (e.g. volumeof water and inflow/outflow), and streambed interactions(e.g. groundwater input and hyporheic exchange).Anthropogenic influences of Tw are most often associated

orrespondence to: Jason A. Hubbart, University of Missouri, School oftural Resources Water Resources Program, Department of Forestry,-Q ABNR Building, 65211, Columbia, Missouri, USA.ail: [email protected]

pyright © 2015 John Wiley & Sons, Ltd.

with land use practices such as deforestation, streamwidening, thermal pollution from heated wastewater,increased impervious surfaces with urbanization, flowalteration, and greenhouse gas emissions (Caissie, 2006;Webb et al. 2008).The role of flow volume and timing on Tw variability

has long been recognized as a critical natural andanthropogenic influence on the thermal regime ofwaterways and aquatic ecosystem health. Ward (1985)showed that Tw was more dependent on meteorologicalconditions during baseflow periods, but as dischargeincreased Tw was more a function of flow volume.Sinokrot and Gulliver (2000) showed that the number ofdays Tw was above the 32.0 °C thermal maximum(threshold of potential mortality of North Americanfreshwater fishes) and the 35.0 °C critical thermalmaximum (threshold of potential death) increased asdischarge decreased in Central Platte River located inNebraska, USA. Stream water temperature was shown to

504 S. ZEIGER ET AL.

exceed 32.0 °C particularly during hot dry summermonths when incoming solar radiation is high andbaseflow is low (Sinokrot and Gulliver, 2000). In general,previous studies showed an inverse relationship betweendischarge and Tw attributed to the high heat capacity ofwater (Gu et al. 1999) and stream depth or flow volume(Sinokrot and Gulliver, 2000). Given the understoodrelationship between discharge and Tw, a considerableamount of research has been conducted to develop simplelinear and non-linear regression models to estimate Twusing relatively easily obtained air temperature (Ta) (referto literature review by Caissie (2006)). Regression Twmodels were shown to successfully estimate Tw whenthere is a strong correlation between Tw and Ta (Caissie,2006). Webb et al. (2003) used linear and non-linearregression modelling techniques to investigate Tw/Tamodulation and discharge in UK for two different flowclasses (above and below median discharge values).Results showed that Tw/Ta relationships were stronger forflow classes below median values, particularly in smallercatchments. This result was attributed to the effects ofdecreased discharge on thermal capacity. This observa-tion highlights that linear and non-linear models aregenerally easier to implement but often do not account forother variables that influence Tw such as watershedhydrologic processes (Ficklin et al. 2012). Despiteshortcomings, regression models are a well-acceptedmodality when requisite hydrometeorological data areunavailable (Stefan and Preud’homme, 1993). Due to theinherent ease of implementation, linear water temperaturemodels have been integrated with hydrologic models. Forexample, the Soil and Water Assessment Tool (SWAT)requires estimates of Tw to simulate in-stream biologicaland water quality processes (e.g. algal growth, bacterialdecay, and nutrient cycling). To estimate Tw, SWAT isequipped with a simple linear regression Tw subroutinemodel developed in the central USA by Stefan andPreud’homme (1993) that only requires average daily Tato predict Tw. While sufficient for many watersheds, themodel may not predict Tw accurately in mixed-useurbanizing watersheds where Tw processes may beconfounded by other factors including (though not limitedto) impervious surfaces. This observation supplies anexpressed need to test SWAT Tw model simulations incomplex urbanizing mixed-use watersheds.Ficklin et al. (2012) developed a process-based Tw

model that can be forced using SWAT model output. TheTw model accounts for Ta as well as the temperature andvolume of snowmelt, groundwater flow, soil water lateralflow, discharge, and surface water runoff in threecomponents including Tw and amount of the local watercontribution within the sub-basin, the temperature andvolume of inflows from upstream sub-basin(s), and heattransfer at the stream surface (refer to Equations (4)–(7) in

Copyright © 2015 John Wiley & Sons, Ltd.

‘Methods’). The Ficklin et al. (2012) model was shown toproduce improved predictions relative to the simple linearregression Tw model currently used in SWAT in sevencoastal and mountainous regions of the western USA(Ficklin et al. 2012). For context, the linear Tw modelcurrently used in SWAT performed poorly in the westerncoastal and inland mountainous USA with average Nash–Sutcliffe efficiency (NSE) mean error (ME) values of�0.26 and 3.01 °C, respectively during validation. Poorperformance was attributed to the effects of complexmountainous hydroclimatological conditions (Ficklinet al. 2012). While outcomes of the Ficklin et al.(2012) model have been encouraging in uneven terrain,there is a need to test the model in mixed-use urbanizingwatersheds where hydrogeological complexity and landuse impacts may variably affect Tw regimes relative tothose described in previous studies.The objectives of the current work were to (i) evaluate

the Tw model used in SWAT (referred to as ‘the linearregression Tw model’), (ii) evaluate a non-linear regres-sion Tw model (referred to as ‘the non-linear regressionTw model’), and (iii) evaluate the Tw model developed byFicklin et al. (2012) (referred to as ‘the process-based Twmodel’) using 4 years of hydroclimate data collectedusing a five-site nested-scale experimental watershedstudy design in a mixed-land use urbanizing watershed.

SITE DESCRIPTION

This investigation took place in the Hinkson CreekWatershed (HCW, approximately 228km2) located in theLower Missouri Moreau River Basin in central Missouri(Figure 1). Elevation in HCW ranges from 274m abovemean sea level at the headwaters to 177m above mean sealevel at the watershed outlet (Hubbart et al. 2010). Basedon a 20-year climate record (1992 to 2012) averageannual total precipitation was 1082mm and averageannual Ta was 14 °C (Hubbart and Zell, 2013). Soils inthe headwater portion of HCW are loamy loess with anunderlying claypan, while soils in the lower reaches ofHCW are composed of silty and sandy clay (Hubbart andZell, 2013). Floodplain alluvial soils in the lower reacheshave infiltration rates that vary dramatically fromagricultural sites (porosity = 0.5 cm3/cm3, bulkdensity =1.33 g/cm3) to bottom land hardwood forestsites (porosity=0.51 cm3/cm3, bulk density=1.31g/cm3)ranging from 0.1 to 126.0 cm/h, respectively (Hubbart et al.2011). Soils outside of the alluvium in the lower reaches arecomposed of a cherty clay solution residuum correspondingto the Weller–Bardley–Clinkenbeard association (Hubbartand Zell, 2013). Land uses in the headwaters of HCW areapproximately 57% agricultural, 36% forested, and 5%urban, while land use in the lower reaches is approximately

Hydrol. Process. 30, 503–514 (2016)

Figure 1. Location of hydroclimate monitoring sites and respective sub-basins in the Hinkson Creek Watershed, central Missouri, USA. Star

denotes Sanborn Field meteorological monitoring station

505QUANTIFYING AND MODELLING URBAN STREAM TEMPERATURE: A CENTRAL US STUDY

41% agricultural, 36% forested, and 23% urban. Thesedistinctions are important for understanding of the effects ofland use onTw. Approximately 60%of the City of Columbiacontaining 27.74km2 of impervious surface (Zhou et al.2012) drains to Hinkson Creek. The population ofColumbia, Missouri, was estimated to be 113225 as per2012 census results (USCB, 2012).The HCW was instrumented with a nested-scale exper-

imental watershed study design in 2009 (Hubbart et al. 2010)that made possible this investigation. The study designincluded partitioning the watershed into five sub=basins,each with different dominant land uses (e.g. site no. 1 drains43.9km2 agricultural, while site no. 5 drains 47.4km2 urban)

Table I. Cumulative contributing area of sub-basins

Sub-basinTotal

area (km2)Stream

length (km)Average stream

width (m)

Site no. 1 77 20 12.2Site no. 2 101 27 16Site no. 3 114 32 13.4Site no. 4 180 40 18.4Site no. 5 206 49 14.1

Percent areas are shown in parentheses.


(Table I and Figure 1). Site no. 5 was near the watershedoutlet, while sites nos.1–4 are nested within. The currentwork utilized data collected at the nested-scale hydroclimatestations that included such data as stream stage, solarradiation, Tw, Ta, and a suite of additional meteorologicalvariables (Hubbart et al. 2010; Hubbart et al. 2013).

METHODS

The study period included four water years (WYs) (1October 2009 to 30 September 2013). Data were sensed ateach climate station every 10 s and averaged and stored(Campbell Scientific CR-1000 data loggers) every 5min(Table II). Stage was monitored at each hydroclimatestation using a Sutron Accubar® constant flow bubbler.Streamflow velocities were manually measured using aFLO-MATE™ Marsh McBirney flow meter and a wadingrodwhen stagewas less than 1-m deep, and aUSGeologicalSurvey (USGS) Bridge Board™ during stormflows. Stage-discharge rating curves were developed for each site usingthe incremental cross section method to estimate streamdischarge as per the methods of Dottori et al. (2009). Anymissing or erroneous climate data were modelled using datarecorded at Sanborn Field meteorological monitoringstation located onUniversity ofMissouri campus (Figure 1).

SWAT modelling

To force the SWATmodel and acquire necessary forcingfor the Ficklin et al. (2012) Tw model, a SWAT 2012project was created using ArcSWAT 2012. Calibrationparameters were set to reflect physically realistic values forthe watershed as per SWAT model calibration methodsproposed by Arnold et al. (2012). Hydrologic ResponseUnits (HRU’s) files (format .hru) were edited to show landuse practices realistic for HCW. Agricultural HRU’s wereset to a corn-soybean rotation with three fertilizationoperations (anhydrous ammonia, elemental nitrogen, andelemental phosphorus) and tandem disc tillage. PastureHRU’s were set to a grazing operation. Urban HRU’s wereset to a fescue growing operation. Lawn fertilization andstreet sweeping operations were scheduled by keying in aschedule into SWAT management operations tab.

and land use types in Hinkson Creek Watershed

Urban(km2)

Pasture/crop(km2)

Forested(km2)

Wetland/water (km2)

3.9 (5) 43.9 (57) 27.7 (36) 1.5 (2)6.1 (6) 56.6 (56) 36.4 (36) 2.0 (2)12.5 (11) 58.1 (51) 41.0 (36) 2.3 (2)28.8 (16) 82.8 (46) 64.8 (36) 3.6 (2)47.4 (23) 84.5 (41) 70.0 (34) 4.1 (2)

Hydrol. Process. 30, 503–514 (2016)

Table II. Instrumentation installed at gauging sites on HinksonCreek, Missouri, USA

Instrument Measurement and units

TE525WS Rain Gauge Precipitation (mm)LICOR 200X Pyrometer Solar radiation (W/m2)MET1 034B Anemometer Wind speed/direction

(m/s) (deg)Sutron Accubar® ConstantFlow Bubbler

Stage (mm)

HMP45C Temperature andHumidity Probe

Air temperature (°C), relativehumidity (%)

107-L Temperature Probe Water temperature (°C)


SWAT was manually calibrated and validated for flowusing a split-time method (Gassman et al. 2007) at a dailytime step using discharge data from the five Hinkson Creekgauging sites. Water years 2010, 2011, and 2012 were usedfor calibration, and WY 2013 was used for validation. Toenhance the reliability of SWAT model calibration andvalidation results, SWATwas calibrated at site no. 5 nearestthe watershed outlet as well as the site no. 4 nested sub-basins similar tomethods used byArnold et al. (2012). Eachsub-basin was calibrated in order of increasing downstreamdistance from site no. 1 in the headwaters to site no. 5 nearestthe watershed outlet. During manual calibration of SWATseveral parameters were adjusted including curve number(CN), alpha base flow (ALPHA_BF), SURLAG, andESCO. The parameters were chosen for adjustment duringcalibration because they were among the most significantfollowing a sensitivity analysis using SWAT-CUP, softwareused for automatic calibration of the SWAT model (Arnoldet al. 2012). All CNs (CN2 and CNOP) were increased by amaximum of 5 simultaneously using the SWAT manualcalibration helper tool. ALPHA_BF was increased from thedefault value of 0.048 to a value of 0.448 in the groundwaterinput files (.gw). The SURLAG value was set to 1.0 in thebasin input files (.bsn). ESCO was set to 1.0 using theSWAT manual calibration helper tool. Other SWAT modelparameters were set to default settings.

Modelling stream water temperature

The following sub-section includes methods used totest the linear regression Tw model used in SWAT and the

Twlocal ¼T snowsub_snowð Þ þ Tgwsub_gw

� �þ λTair;lag� �

sub_surqþ sub_latqð Þsub_wyld

(4)

process-based Tw model developed by Ficklin et al.(2012). The linear regression Tw model used in SWAT2012 was forced with Ta data from each gauging site asper Stefan and Preud’homme (1993) to predict Tw:


Tw tð Þ ¼ 5:0þ 0:75Ta (1)

where Tw is the stream water temperature (°C), Ta is theair temperature (°C), and t is the time (daily).A non-linear regression Tw model was forced with Ta

data collected from each corresponding gauging site(Figure 1). Non-linear regression Tw models are usefulto account for other variables of importance in Twincluding the effects of latent heat exchange at the streamsurface. Mohseni et al. (1998) developed the followingmodel:

Tw ¼ μþ aþ μ1þ eγ β � Tað Þ (2)

where Tw is the stream water temperature, Ta is the airtemperature, α is the maximum Tw, μ is the minimum Tw, βis Ta at the inflection point of the function, γ is the steepestslope of the function, and e (Euler’s number) is 2.71828.The non-linear regression equation is an S-curve functioncharacterized by two curves. The inflection pointseparates the two curves in the function. Below theinflection point, the positive curvature increases as theslope increases from left to right. Above the inflectionpoint, the negative curvature decreases as the slopedecreases from left to right. The parameter γ is calculatedusing the following equation:

γ ¼ 4 tanθa� μ

(3)

where γ is a function of the slope tanθ at the point ofinflection, α is the maximum Tw, and μ is the minimum Tw.Ficklin et al. (2012) proposed a process-based Tw

model that accounts for Ta, snowmelt, groundwater flow,soil water lateral flow, discharge, and surface waterrunoff. Three components considered in the process-based Tw model include the local water contributionwithin the sub-basin, the temperature and volume ofinflows from upstream sub-basin(s), and heat transfer atthe stream surface during the streamflow travel time in thesub-basin. Stream water temperature and the amount oflocal water contribution within the sub-basin are derivedusing the following equation:

where sub_snow is the snowmelt volume (m3 d�1),sub_gw is the groundwater flow (m3 d�1), sub_surq isthe surface water runoff (m3 d�1), sub_latq is the soilwater lateral flow (m3d�1), and sub_wyld is the total

Hydrol. Process. 30, 503–514 (2016)


water yield within the sub-basin. Lambda (λ) is acalibration coefficient relating Tair.lag and sub_latq, andsub_surq. Tair.lag is the average daily Ta with lag (°C).Decreasing λ decreases model output dependency on thetemperature and volume of surface water runoff and soilwater lateral flow. The temperatures of surface water runoffand soil water lateral flow are dependent on Ta. Lag is acalibration parameter that adjusts the number of previousdays; Ta was averaged to estimate the temperature ofsurface water runoff and soil water lateral flow. Tsnow is thetemperature of inflows from snowmelt (0.1 °C), and Tgw isthe groundwater temperature (°C) (Ficklin et al. 2012).The temperature and amount of inflow from upstream

sub-basin(s) were derived using the following equation:

Twinitial ¼ Twuptream Qoutlet � sub_wyldð Þ þ Twlocalsub_wyldQoutlet

(5)

where Twupstream is water temperature of streamflowentering the sub-basin (°C) and Qoutlet is discharge at theoutlet (m3 d�1). For headwater streams Twinitial equalsTwlocal (Ficklin et al. 2012).The heat transfer at the stream water surface during the

streamflow travel time in the sub-basin is derived usingthe following equations:

Tw ¼ Twinitial þ Tair � Twinitialð ÞK TTð Þ if Tair > 0;

(6)

Tw ¼ Twinitial þ Tair þ εð Þ � Twinitial½ �K TTð Þ if Tair < 0;

(7)

where Tair is the mean daily temperature (°C), K (1/h) is abulk coefficient of heat transfer ranging from 0 to 1, TT istravel time (hourly) of water through the sub-basin, and εis a coefficient that accounts for Tw pulses when Tair isless than 0 °C (Ficklin et al. 2012). A decreased value ofK reduces the dependency of Tw on Ta and travel timewithin a given sub-basin. Ta is used as a proxy forradiative forcing (Ficklin et al. 2012).Input data for the process-based Tw model were

obtained from SWAT model output files as per Ficklinet al. (2012). SWAT 2012 was manually calibrated andvalidated for streamflow at daily time steps using mean

Table III. Ratings used to quantitatively evaluate mod

Rating RSR

Very good 0.00 ≤RSR ≤ 0.50Good 0.50<RSR ≤ 0.60Satisfactory 0.60<RSR ≤ 0.70Unsatisfactory RSR> 0.70


discharge data from each gauging site. Data from theSanborn Field meteorological station (Figure 1) provided7years of weather input data used to ‘warm-up’ the SWATmodel for calibration. Water years 2010, 2011, and 2012(wet, average, and dry years, respectively) were used forcalibration, and WY 2013 was used for validation incompliance with SWAT model calibration and validationguidelines proposed by Moriasi et al. (2007). Thisprocedure was used for all five gauging sites. After SWATwas successfully calibrated and validated for streamflow,the process-based Tw model developed by Ficklin et al.(2012) was forced using the SWAT model output.Moriasi et al. (2007) suggested the use of three model

evaluation criteria with corresponding performance rat-ings (Table III) to assess hydrologic model performanceincluding NSE, ratio of root mean square error to thestandard deviation of observed data (RSR) and percentbias (PBIAS). The suggested performance ratings wereestablished at monthly time steps by generalizing reportedperformance ratings based on published literature.Moriasi et al. (2007) noted that monthly model evaluationguidelines should be properly adjusted for hydrologicmodel evaluation at a daily time step because modelsimulation results are often poorer for shorter time stepsthan longer time steps throughout the published literature.Therefore, in the current work, streamflow simulationswere evaluated at daily time steps. In addition to the threemodel evaluation criteria suggested by Moriasi et al.(2007), two commonly used error indices were used toevaluate model efficiency in the current work includingmean absolute error (MAE) and root mean squared error(RMSE) (Wehrly et al. 2009; Moriasi et al. 2007).

RESULTS

Climate data recorded at Sanborn Field meteorologicalmonitoring station and the five hydroclimatic monitoringsites in HCW (Figure 1) indicated average total annualprecipitation ranging from 744 (WY 2012) to 1600mm(WY 2010) with a mean of 1032mm for the 4-year studyperiod (Table IV). Average total annual precipitation of1032mm recorded during the 4-year study period wasapproximately 50mm less than the 20-year record of1082mm. Mean Ta ranged from 12.1 °C at site no. 1 to

el efficiency (recreated from Moriasi et al. (2007))

NSE PBIAS

0.75<NSE≤ 1.00 PBIAS<±100.65<NSE≤ 0.75 ±10 ≤PBIAS<±150.50<NSE≤ 0.65 ±15 ≤PBIAS<±25NSE ≤ 0.50 PBIAS ≥ ±25

Hydrol. Process. 30, 503–514 (2016)

Table IV. Daily climate statistics during the study period (WY 2010–2013) for six climate stations located in Hinkson CreekWatershed, Missouri, USA

Climate data Daily statistic Site no. 1 Site no. 2 Site no. 3 Site no. 4 Site no. 5 Sanborn Field

P (mm)a Max 1590 1567 1610 1578 1602 1651Mean 1026 1012 1057 1044 1026 1028Min 708 678 784 754 751 739

Q (m3/s) Max 60.3 69.2 117.7 145.0 217.7 --Mean 0.9 1.1 1.6 2.3 3.6 --Min 0.0 0.0 0.0 0.0 0.0 --St. Dev. 4.5 4.2 5.3 6.2 10.0 --

Ta (°C) Max 42.8 41.6 43.0 41.9 41.6 40.8Mean 12.1 12.8 13.3 12.9 12.9 13.7Min �30.8 �30.4 �26.6 �26.7 �29.0 �20.6St. Dev. 10.6 10.7 10.7 10.5 10.6 10.6

Tw (°C)b Max 32.1 34.7 36.1 33.9 32.9 --Mean 13.7 14.2 14.2 14.4 14.2 --Min 0.0 0.4 0.2 0.1 0.1 --St. Dev. 8.6 9.7 9.5 9.5 9.4 --

RH (%) Max 97.7 98.0 98.0 97.1 99.4 98.0Mean 71.8 70.3 67.5 70.8 70.0 65.4Min 33.6 33.0 32.3 33.5 32.5 32.7St. Dev. 11.4 11.3 12.1 10.8 11.0 13.4

V (m/s) Max 5.2 3.8 4.1 3.0 4.1 5.3Mean 1.3 1.1 1.2 0.8 1.3 2.0Min 0.0 0.0 0.0 0.0 0.0 0.0St. Dev. 0.7 0.6 0.6 0.4 0.6 0.7

Rs (MJ/m2)c Max 30.1 31.5 29.2 28.3 29.3 29.3Mean 13.8 14.8 13.4 12.9 13.9 14.1Min 0.4 0.6 0.8 0.5 0.3 0.5St. Dev. 7.8 8.3 7.8 7.3 7.6 7.8

Precipitation (P), discharge (Q), air temperature (Ta), stream temperature (Tw), relative humidity (RH), wind speed (V), and solar radiation (Rs), and St.Dev. is standard deviation.a Precipitation data are average annual totals.b Stream temperature data range from WY 2011 to WY 2013.c Solar radiation data are daily totals.


13.7 °C at Sanborn Field with a six site mean of 13.0 °C.Mean relative humidity ranged from 65.4% at SanbornField to 71.8% at site no. 1 with a six site mean of 69.3%.Mean daily total solar radiation ranged from 12.9MJ/m2

at site no. 4 to 14.8MJ/m2 at site no. 2 with a six sitemean of 13.8MJ/m2. Mean discharge ranged from 0.9m3/sat site no. 1 to 3.6m3/s at site no. 5 with a five site mean of1.9m3/s (Table IV). Average daily Tw at rural site no. 1 inthe headwaters was lower than all other gauging sites by0.5–0.7 °C. Conversely, urban site no. 4 average daily Twwas higher than all other gauging sites by 0.2–0.7 °C.Whiledifferences between sites noa. 2–5 were at times within theaccuracy limitations of the sensor (±0.2 °C), observedincreased Tw at urban sites are at least partially attributableto urban land use effects on stormwater heating (e.g. increasedimpervious surfaces and flow regime alteration).

SWAT modelling

The SWAT model was successfully calibrated andvalidated for streamflow at a daily time step using observeddischarge data from each of the nested gauging sites. Model


evaluation results during the calibration period (WYs2010–2012) for the five gauging sites showed NSE valuesranging from 0.50 at site no. 1 to 0.66 at site no. 4 with afive site mean of 0.57 (Table V). Model evaluation resultsduring the validation period for the gauging sites showedNSE values ranging from0.48 at site no. 5 to 0.67 at site no. 4with a mean five site value of 0.53.


Unlike the linear regression Tw model, the non-linearregression Tw model required parameterization using non-linear regression analyses. Results from non-linear regres-sion analyses of Ta and Tw showed that Ta and Tw departedfrom linearity at a daily time step. For example, Taaccounted for greater than 90% of the explained variance inTw with coefficients of determination (r2) values rangingfrom 0.91 at site no. 5 to 0.93 at site no. 3 with a mean r2

value of 0.92 (Figure 2). Departures from linearityoccurred at temperatures above 20 °C and when Tadecreased to sub-zero temperatures, although Tw did notdecrease below the approximate freezing point of water.

Hydrol. Process. 30, 503–514 (2016)

Table V. SWAT model calibration and validation results showing six model evaluation criterion for daily streamflow at five gaugingsites in Hinkson Creek, USA

Statistic Site no. 1 Site no. 2 Site no. 3 Site no. 4 Site no. 5 All sites

CalibrationNSE 0.50 0.51 0.60 0.66 0.56 0.57PBIAS (%) �4.2 �8.5 14.7 0.4 24.2 5.3RSR 0.7 0.7 0.6 0.6 0.7 0.7MAE (m3/s) 0.8 1.1 1.2 1.6 0.8 1.1RMSE (m3/s) 2.7 3.3 4.3 4.9 2.7 3.6ValidationNSE 0.49 0.49 0.52 0.67 0.48 0.53PBIAS (%) 3.9 5.8 22.0 4.5 45.0 16.2RSR 0.7 0.7 0.7 0.6 0.7 0.7MAE (m3/s) 1.0 1.3 1.5 1.7 3.3 1.7RMSE (m3/s) 3.6 4.7 5.8 5.4 11.3 6.2

NSE is Nash–Sutcliffe efficiency, PBIAS is percent bias, RSR is ratio of root mean square error to the standard deviation of observed data, MAE is meanabsolute error, and RMSE is root mean square error.

Figure 2. Coefficients of determination (r2) non-linear (red curve) regression analyses are shown using a daily time step for five gauging sites located inHinkson Creek Watershed, USA


Copyright © 2015 John Wiley & Sons, Ltd. Hydrol. Process. 30, 503–514 (2016)


The process-based Tw model developed by Ficklin et al.(2012) required calibration of model parameters includingλ, lag, K, and ε (refer to Equations (4–7) in ‘Methods’).Calibration parameter λwas set to a value of 1, and lag wasset to a default value of 7 similar to the methods used byFicklin et al. (2012). The parameter K is the bulkcoefficient of heat transfer that adjusts the relationshipbetween Ta and Tw (Ficklin et al. (2012). For example, a Kvalue of 1 would be Ta=Tw when Ta is greater than 0 °C.Ficklin et al. (2012) found that K was the most sensitiveparameter duringmodel calibration, as was observed in thisstudy during model calibration. In the current work, therewas a general trend for K values to increase with streamdistance from the headwaters likely attributable toincreased influence of atmospheric conditions on streamtemperature with increasing travel time and streamdistance. Parameter K ranged from 0.90 at site no. 1 to0.99 at site no. 4 with a mean K of 0.96. Parameter ε rangedfrom 2 at site no. 2 to 5 at site no. 1 with amean ε value of 3.Model evaluation tests showed that every Tw model

performed well in the current work with NSE valuesgreater than 0.88 and RMSE values less than 3.2 °C.However, despite generally positive model performances,ANOVA showed that the non-linear regression Tw modelperformed significantly better (P<0.01) than the linearregression Tw model used in SWAT. Significant differ-ences (P>0.05) were not found between the non-linearregression Tw model and process-based Tw modeldeveloped by Ficklin et al. (2012) and for the modelevaluation tests considered during the validation period(WY 2013) (Table VI). The process-based Tw modelaccounted for watershed hydrology, but the variance wasnot significantly (P>0.05) lower relative to the linear and

Table VI. Summary of average model evaluation results from allfive gauging sites in Hinkson Creek Watershed, USA

StatisticNonlinearregression SWAT

Ficklinet al. (2012)

CalibrationNSE 0.92 0.90 0.91PBIAS (%) �0.6 �4.6 3.0RSR 0.3 0.3 0.3MAE (°C) 2.0 2.3 2.0RMSE (°C) 2.6 3.0 2.8ValidationNSE 0.91 0.88 0.89PBIAS (%) �0.1 �5.0 5.6RSR 0.3 0.4 0.3MAE (°C) 2.0 2.5 2.2RMSE (°C) 2.7 3.2 2.9

NSE is Nash–Sutcliffe efficiency, PBIAS is percent bias, RSR is ratio ofroot mean square error to the standard deviation of observed data, MAE ismean absolute error, and RMSE is root mean square error.


non-linear regression Tw models tested. There was lessvariability in Tw results in the higher temperature range(Tw>20.0 °C) presumably attributable to lower flow(Mohseni and Stefan, 1999). The mean PBIAS valuesfor all five sites ranged from �4.6% for the linearregression Tw model used in SWAT to 3.0% for theprocess-based Tw model developed by Ficklin et al.(2012) during the calibration period. The mean PBIASvalues for all five sites ranged from �5.0% for the linearregression Tw model to 5.6% for the process-based Twmodel during the validation period.

DISCUSSION

Climate during the study period (WY 2010–2013) washighly variable ranging from a very wet year inWY 2010 to‘extreme’ to ‘exceptional’ (D3 to D4) drought conditionsin WY 2012 (National Oceanic and Atmospheric Admin-istration, 2012). Mean discharge at site no. 4 during the3-year study period was 0.18m3/s less than the historic(1967–1981, 1986–1991, and 2007–2013) annual averagedischarge of 1.78m3/s recorded at USGS gauging station#06910230. The observed climatic variability during thestudy supplied novel data that were well suited for SWATmodel calibration and validation for streamflow andinvestigation of the effects of hydrology on Tw modeloutput.

SWAT modelling

The SWAT model was successfully calibrated andvalidated for streamflow at a daily time step with NSEvalues ranging from 0.50 to 0.66 (Table V). These resultsare comparable with the results of Ficklin et al. (2012)who reported mean NSE values during calibration andvalidation periods of 0.68 and 0.61, respectively. Ingeneral, observed daily stormflows were underestimatedusing SWAT, especially during the spring when largerstorms were observed (Figure 3). A review by Borah andBera (2004) indicated that SWAT underestimatesstreamflow during larger events, especially at a dailytime step. Arnold et al. (2000) reported that SWATunderestimations of spring stormflows may be because ofproblems associated with simulating snowmelt, evaporation/transpiration, and antecedent soil moisture conditions.Accurate streamflow estimations during larger storms areimportant when simulating Tw with process-based modelsdependent on discharge. These observations supplyimpetus for future model improvements.


The departure of linearity shown by results from thenon-linear regression technique showed the effects of

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Figure 3. Time series SWAT simulated and observed discharge data collected during the validation period (WY 2013) recorded at five gauging siteslocated in Hinkson Creek Watershed, USA


evaporative cooling on daily average Tw. Mohseni et al.(1998, 1999) and Webb et al. (2003) also showed a non-linear relationship between Ta and Tw. Mohseni et al.(1998) found non-linear regression analyses betweenaverage weekly Ta and Tw resulted in an average r

2 value of0.93 (n=584). Mohseni et al. (1999) showed weekly non-linear regression analyses resulted in r2 values greater than0.80 for 91% of gauging stations tested (n=993). Webbet al. (2003) showed r2 values greater than 0.84 associatedwith daily non-linear regression Tw models dependent onTa (n=4). While the non-linear Tw model performed betterin the south central USA, the air–water temperaturerelationship has been shown to be better described by alinear relationship inMinnesota where evaporative coolingeffects on Tw are not as prominent as in the work presentedby Mohseni et al. (1998).In the current work, the linear Tw model used in SWAT

estimated daily Tw well, but the non-linear regression Twtechnique significantly improved Tw estimates. Morril


et al. (2005), Webb et al. (2003), and Mohseni et al.(1998) also showed that non-linear regression Twtechniques improved Tw estimates. Morrill et al. (2005)showed NSE values from linear and non-linear regressiontechniques ranging from 0.54 to 0.93 and 0.77 to 0.95,respectively. RMSE values ranged from 3.3 to 1.5 °C and3.0 and 1.5 °C, respectively (Morrill et al., 2005). Webbet al. (2003) showed non-linear regression techniques,significantly improved, which explained variance betweenTa and Tw by 0.8 to 1.3%. Mohseni et al. (1998) showedmean NSE values of 0.93 with a standard deviation of 0.1(n=584), and RMSE values ranged from a mean 1.6 °Cwith a standard deviation of 0.5 °C for Tw models createdusing non-linear regression techniques. Thus, the non-linear regression Tw model evaluation results from thecurrent research were comparable to previously publishedresearch.Ficklin et al. (2012) showed that the linear regression

Tw model, currently used in SWAT, did not perform well

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Figure 4. Results showing observed stream water temperature (Tw) versussimulated Tw data for each of the three Tw models tested at a daily time

step in Hinkson Creek Watershed, USA


in the mountainous and coastal regions of the westernUSA, mainly because of the hydroclimatological effectson Tw. Conversely, the process-based Tw model publishedby Ficklin et al. (2012) performed well in the morerugged western terrain. The successful previous results ofFicklin et al. (2012) and the current research show thatthe linear regression Tw model used in SWAT does notperform satisfactory in all regions. However, the process-based Tw model developed by Ficklin et al. (2012) hasbeen shown to perform well in the mountainous andcoastal regions of the western USA (mean NSE=0.82).The current work shows that the linear Tw model used inSWAT and the process-based Tw model may be effectivein surface runoff dominated streams of the central USA(mean NSE>0.88; RMSE<3.2 °C). However, thereremains a need for both models to be tested in low-ordergroundwater dominated streams of the central USA wheregroundwater contributions can dominate Tw regimes.The linear Tw model used in SWAT was originally

developed in the central USA by Stefan and Preud’homme(1993) where landscape physiography is distinct fromother regions. Therefore, it is reasonable that Ficklin et al.(2012) showed that the linear regression Tw model used inSWAT produced NSE values less than 0 for three of sevenstudy sites in the mountainous region of the western USA,considering that site-specific empirical models are nothighly transferable in particular to mountainous regions.SWAT overestimated Tw overall indicated by negativePBAIS values. Ficklin et al. (2012) showed negative PBIASvalues for the linear regression Twmodel used in SWAT thatranged from�14.9 to�73.6%. However, the PBIAS valuesin the current work were within 5% of the observed Tw.The linear Tw model used in SWAT showed the

greatest underestimation of Tw in the higher temperaturerange (Tw>20.0 °C) in the current research with a PBIASvalue of 7.2% (Figure 4). Underestimations of Tw whenTw is greater than 20.0 °C could lead to underestimationsof algal growth, nutrient cycling, biochemical oxygendemand, and many other biological and ecologicalaquatic ecosystem functions. This information may beimportant to urban land managers that may wish to useSWAT to develop best management practices or totalmaximum daily load estimates (Borah et al., 2006). Forexample, nutrient transformations in SWAT are depen-dent on Tw (Neitsch et al., 2005).In the current work, the linear regression Tw model used

in SWAT and the non-linear regression Tw models tendedto greatly overestimate Tw in the lower temperatures (0.0 to10.0 °C) with PBAIS values of �28.2 and �66.1%,respectively. Conversely, the Ficklin et al. (2012) Twmodel tended to underestimate Tw in the lower ranges (0.0to 10.0 °C) with a PBIAS value of 4.5%. All modelsshowed increased variation in results below 20 °C. Highflow rates and snowmelt can affect Twwhen Ta is between 0


to 20 °C (Mohseni and Stefan, 1999). The linear and non-linear regression Tw models did not simulate Tw estimatesgreater than 30.0 °C, but Tw greater than 32.0 °C wasobserved at each gauging site, and Tw greater than 35 °Cwas observed at site no. 3. Mohseni et al. (1998) foundnon-linear regression Tw model parameter α (parameterestimating maximum Tw) was at times underestimated,which could lead to inaccurate estimations of Tw in theupper temperature range (i.e. Tw>30.0 °C). The linearregression Tw model currently used in the SWAT and non-linear regression Twmodels do not account for a number ofhydrological processes (e.g. surface water runoff, soilwater lateral flow, ground water, and snowmelt) andtherefore may not estimate Tw accurately during snowmeltor storm events in urban areas. The process-based Tw

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model developed by Ficklin et al. (2012) may producemore conservative estimates of Tw in particular in highertemperature ranges (i.e. Tw>20.0 °C). Estimates of Tw inthe higher temperature ranges may be important when Twmodels are used to investigate suitable thermal habitat forfish species. For example, results from the current studyindicated that Tw estimates generated using a linear or non-linear Tw model may show suitable thermal habitat whenobserved Tw is greater than maximum temperaturetolerance for warm water fish species (i.e. Tw>32 °C).

Implications for model development

Direct measurement of Tw may not always be practicalbecause of costs associated with instruments (e.g. sensorsand data loggers) and labor (e.g. installation and mainte-nance). Choosing an appropriate Tw model alternative is apivotal decision and is dependent on the objectives andspatial and temporal scale of the management or researchgoals (Rivers-Moore and Lorentz, 2004). If the goal is tomake predictions given specific land use scenarios, a bestestimate of Tw using regression models dependent on Tafrom nearby weather stations may be a viable option forhydrologic models like the SWAT model. However, theSWAT model Tw predictions may be strengthened byimplementing options for Tw model input. For example,possible options would be to input directly measured Tw orto choose differentTwmodelling platforms such as the linearregression Tw model currently used in SWAT, a non-linearregression Tw model, or the process-based Tw modeldeveloped by Ficklin et al. (2012). Linear regression Twmodels may be better suited for regions where high airtemperatures (Ta>25.0 °C) do not causeTw to level off (e.g.higher latitudes of the USA) (Erickson and Stefan, 2000),whereas the non-linear regression Tw models have beenshown to provide more reliable predictions in the southernlatitudes of the USA (Mohseni et al. 1998). The process-based Twmodel developed by Ficklin et al. (2012) has beenshown to work well in a number of regions; however, Twestimates generated using the process-based Tw modeldeveloped by Ficklin et al. (2012) are highly dependent on awell-calibrated hydrologic model. Further, process-basedTw models require multiple meteorological and hydrologicinputs that may not be available for robust hydrologicmodels. Therefore, futuremodel development should includeflexible parameterization schemes that can use available datawhile balancing the simplicity of air temperature-based andmore complex process-based models.

CONCLUSIONS

Anthropogenic impacts on Tw variability in a mixed landuse urbanizing watershed in the central USA wereinvestigated to improve Tw model predictive confidence


and better inform management decisions in mixed-useurbanizing watersheds. Without directly measured Tw,best estimates of Tw using deterministic or statistical/stochastic modelling techniques are required. Thus,model output from different Tw models must be evaluatedbefore use. This research took advantage of four WYs ofTw data collected using a nested-scale experimentalwatershed study design approach. Three daily Tw modelswere tested, including the linear Tw model used in thecurrent version of SWAT, a non-linear regression Twmodel, and a process-based Tw model that accounted forTa and multiple hydrologic quantities generated bySWAT. The linear Tw model produced satisfactoryestimates of Tw at a daily time step (NSE>0.88;RMSE<3.2 °C). The non-linear regression Tw modelstested at a daily time step performed significantly(P<0.01) better than the linear Tw model currently usedin SWAT in this study. However, both linear and non-linearregression Tw models tended to overestimate Tw less than5 °C and underestimate Tw greater than 20°C. The process-based Twmodel developed by Ficklin et al. (2012) producedmore accurate estimates of Tw when Tw was greater than20 °C. Additionally, the processed-based Tw model wasmore transferrable relative to regression Tw models andtherefore may be a better Tw model to incorporate intoprocess-based hydrologic models like SWAT.Results from this research show that regression-based Tw

models should be used with caution in streams (particularlyurban) where Tw exceeds 30 °C to avoid underestimatingsuitable thermal conditions for warm water biota. Addi-tionally, simulations of water quality processes dependenton Tw including, but not limited to, algal growth rates,nutrient cycling rates, and biochemical oxygen demandmay be underestimated. This information is critical tourban land managers wishing to use SWAT or othermodels to develop total maximum daily load estimates andimprove management practices for swiftly developingmixed-land use watersheds.

ACKNOWLEDGEMENTS

Funding was provided by the US Environmental Protec-tion Agency Region 7 through the Missouri Department ofNatural Resources (P.N: G08-NPS-17) under Section 319of the Clean Water Act, and the Missouri Department ofConservation. Results presented may not reflect the viewsof the sponsors, and no official endorsement should beinferred. Collaborators include (but are not limited to)Boone County Public Works, City of Columbia, Univer-sity of Missouri, and the USGS. Special thanks are becauseof many Interdisciplinary Hydrology Laboratory scientistsfor field assistance and multiple reviewers whose con-structive comments greatly improved the article.

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REFERENCES

Arnold JG, Moriasi DN, Gassman PW, Abbaspour KC, White MJ,Srinivasan R, Santhi C, Harmel RD, van Griensven A, Van Liew MW,Kannan N, Jha MK. 2012. SWAT: model use, calibration, andvalidation, American Society of Agricultural and Biological Engineers55 (4): 1491–1508.

Arnold JG, Muttiah RS, Srinivasan R, Allen PM. 2000. Regionalestimation of base flow and groundwater recharge in the UpperMississippi river basin, Journal of Hydrology 227: 21–40.

Borah DK, Bera M. 2004. Watershed-scale hydrologic and nonpoint –source pollution models: review of applications. Transactions of theASAE 47(3): 789–803.

Borah DK, Yagow G, Saleh A, Barnes PL, Rosenthal W, Krug EC, HauckLM. 2006. Sediment and nutrient modeling for TMDL developmentand implementation, American Society of Agricultural and BiologicalEngineers 49(4): 967–986.

Caissie D. 2006. The thermal regime of rivers: a review. FreshwaterBiology 51: 13891406.

Dottori F, Martina MLV, Todini E. 2009. A dynamic rating curveapproach to indirect discharge measurement. Hydrology Earth SystemSciences 13: 847–863.

Erickson TR, Stefan HG. 2000. Linear air/water temperature correlationsfor streams during open water periods. Journal of HydrologicEngineering 5(3): 317–321.

Ficklin DL, Lou Y, Stewart IT, Maurer EP. 2012. Development andapplication of a hydroclimatological stream temperature modelwithin the Soil and Water Assessment Tool, Water ResourcesResearch 48: 116.

Gassman PW, Reyes MR, Green CH, Arnold JG. 2007. The Soil andWater Assessment Tool: historical development, applications, andfuture research directions. Transactions of the American Society ofAgricultural and Biological Engineers 50: 1211–1250.

Gu R, McCutcheon S, Chen C. 1999. Development of weather dependentflow requirements for river temperature control. EnvironmentalManagement 24(4): 529–540.

Hubbart JA, Muzika R-M, Huang D, Robinson A. 2011. Improvingquantitative understanding of bottomland hardwood forest influence onsoil water consumption in an urban floodplain. The Watershed ScienceBulletin 03: 34–43.

Hubbart JA, Zell C. 2013. Considering streamflow trend analysesuncertainty in urbanizing watersheds: a baseflow case study in thecentral United States. Earth Interactions 17(5): 1–28.

Hubbart JA, Holmes J, Bowman G. 2010. Integrating science baseddecision making and TMDL allocations in urbanizing watersheds. TheWatershed Science Bulletin 01: 19–24.

Hubbart JA, Kellner E, Freeman G. 2013. A case study considering thecomparability of mass and volumetric suspended sediment data.Environmental Earth Science 71: 4051–4060.


Mohseni O, Stefan HG. 1999. Stream temperature/air temperature relation-ship: a physical interpretation, Journal of Hydrology 218: 128–141.

Mohseni O, Stefan HG, Erickson TR. 1998. A nonlinear regression modelfor weekly stream temperatures. Water Resources Research 34(10):2685–2692.

Mohseni O, Erickson TR, Stefan HG. 1999. Sensitivity of streamtemperatures in the United States to air temperatures projected under aglobal warming scenario.Water Resources Research 35(12): 3723–3733.

Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, VeithTL. 2007. Model evaluation guidelines for systematic quantification ofaccuracy in watershed simulations. American Society of Agriculturaland Biological Engineers 50(3): 885–900.

Morrill JC, Bales RC, Asce M, Conkin MH. 2005. Estimating streamtemperature from air temperature implications for future water quality.Journal of Environmental Engineering 131(1): 139–146.

Neitsch SL, Arnold JG, Kiniry JR, Williams JR, King KW. 2005. Soil andWater Assessment Tool theoretical documentation: version 2005, TexasWater Resources Institute, College Station, TX.

NOAA National Climatic Data Center, State of the Climate: Drought forAnnual. 2012. published online December 2012, retrieved on July 10,2014 from http://www.ncdc.noaa.gov/sotc/drought/2012/13.

Rivers-Moore NA, Lorentz S, 2004. A simple, physically-based statisticalmodel to simulate hourly water temperatures in a river. South AfricanJournal of Science 100: 331–333.

Sinokrot BA, Gulliver JS. 2000. In-stream flow impact on river watertemperatures. Journal of hydrologic research 38: 339–349.

Smith K. 1972. River water temperature – an environmental review.Scottish Geographical Magazine 88: 211–220.

Stefan HG, Preud’homme EB. 1993. Stream water temperature estimationfrom air temperature. Water Resources Bulletin 29(1): 27–45.

United States Census Bureau (USCB). 2012. U.S. Census Bureau: Stateand County Quick Facts. Available on line at: http://quickfacts.census.gov/qfd/states/29000.html

Ward JV. 1985. Thermal characteristics of running waters. Hydrobiologia125: 31–46.

Webb BW, Clack PD, Walling DE. 2003. Water-air temperaturerelationships in a Devon River system and the role of flow.Hydrological Processes 17: 3069–3084.

Webb B, Hannah D, Moore R, Brown L, Nobilis F. 2008. Recentadvances in stream and river temperature research. HydrologicalProcesses 22: 902–918.

Wehrly KE, Brenden TO, Wang L. 2009. A comparison of statisticalapproaches for predicting stream temperatures across heterogeneouslandscapes, Journal of the American Water Resources Association45(4): 986–979.

Zhou B, He HS, Nigh TA, Schulz JH. 2012. Mapping and analyzingchange of impervious surface for two decades using multi-temporalLandsat imagery in Missouri, International Journal of Applied EarthObservation and Geoinformation, 18: 195–206.

Hydrol. Process. 30, 503–514 (2016)

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