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Predicting evaporation from mountain streams Szeitz, Andras Janos; Moore, Robert Daniel 2020-07-20

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Title PageTitle: Predicting evaporation from mountain streamsRunning title: Predicting evaporation from mountain streamsAuthors: Andras Janos Szeitz*, Robert Daniel MooreInstitutional affiliations: Department of Geography, University of British Columbia, 1984West Mall, Vancouver, BC, V6T 1Z4. Correspondence: aszeitz@gmail.comAcknowledgements: This research was funded by a Natural Sciences and EngineeringResearch Council (NSERC) Discovery Grant to R D Moore, and an NSERC CanadaGraduate Scholarship awarded to A J Szeitz. Anna Kaveney, Virgile Laurent and JohannesExler assisted with field data collection and instrument calibration. J Leach and twoanonymous reviewers provided constructive comments that helped us improve the manuscript.Accepted ArticleThis article is protected by copyright. All rights reserved.This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/hyp.13875  Predicting Evaporation from Mountain StreamsAbstract: Evaporation can be an important control on stream temperature, particularlyin summer when it acts to limit daily maximum stream temperature. Evaporation fromstreams is usually modelled with the use of a wind function that includes empirically derivedcoefficients. A small number of studies derived wind functions for individual streams; thefitted parameters varied substantially among sites. In this study, stream evaporation andabove-stream meteorological conditions (at 0.5 and 1.5 m above the water surface) weremeasured at nine mountain streams in southwestern British Columbia, Canada, covering arange of stream widths, temperatures, and riparian vegetation. Evaporation was measured ontwenty site-days in total, at approximately hourly intervals, using nine floating evaporationpans distributed across the channels. The wind function was fit using mixed-effects modelsto account for among-stream variability in the parameters. The fixed-effects parameters weretested using leave-one-site-out cross-validation. The model based on 0.5-m measurementsprovided improved model performance compared to that based on 1.5-m values, with RMSEof 0.0162 and 0.0187 mm h−1, respectively, relative to a mean evaporation rate of 0.06 mmh−1. Inclusion of atmospheric stability and canopy openness as predictors improved modelperformance when using the 1.5-m meteorological measurements, with minimal improvementwhen based on 0.5-m measurements. Of the wind functions reported in the literature, twoperformed reasonably while five others exhibited substantial bias.Keywords: stream temperature; evaporation; mass transfer model; wind function; latent heatflux2Accepted ArticleThis article is protected by copyright. All rights reserved.IntroductionStream temperature influences aquatic ecosystems through its effects on growth rates (Elliott& Hurley, 1997; Jensen, 1990), species distributions (Ebersole et al., 2001; Parkinson et al.,2016; Wichert & Lin, 1996), and nutrient availability (LeBosquet Jr. & Tsivoglou, 1950).Stream thermal regimes can be modified by natural disturbance such as forest fires (Friedet al., 2004; Isaak et al., 2010; Luce et al., 2014), land use such as forest harvesting (Brown &Krygier, 1970; Guenther et al., 2014), water withdrawals and impoundments (Gu et al., 1998;Hockey et al., 1982; Morse, 1972; Olden & Naiman, 2010), and climatic variability and change(Intergovernmental Panel on Climate Change, 2014; Isaak et al., 2016; Luce et al., 2014).Streams and rivers are exhibiting warming trends in many regions, and there is increasingconcern that this warming will have deleterious impacts on cold and cool-water species suchas salmon (e.g., Isaak et al., 2018). In response to these concerns, there has been a growth ofinterest in developing predictive tools to support management decisions using both empiricaland process-based approaches (e.g., Fabris et al., 2018; Null et al., 2013).Process-based stream temperature models provide the most rigorous approach for simulat-ing thermal response to environmental change. Process-based stream temperature modellingis a mature but still developing field. Much of the foundational work was conducted inthe 1960s and 1970s (Edinger et al., 1974, 1968). Models have been developed using La-grangian (Devkota & Imberger, 2012; Gu et al., 1998; Hockey et al., 1982; Vugts, 1974),semi-Lagrangian (Yearsley, 2009), and Eulerian frames of reference (Sinokrot & Stefan, 1993;Sridhar et al., 2004). Methods of solution have ranged from simple Euler integration forLagrangian models (Hockey et al., 1982; Leach & Moore, 2011) to sophisticated numericalsolutions of partial differential equations in a Eulerian framework that are capable of handlingunsteady flow (Kim & Chapra, 1997; Younus et al., 2000) and multiple-component transientstorage processes (Bingham et al., 2012; Buahin et al., 2019; Cardenas et al., 2014; Meieret al., 2003; Neilson et al., 2010; Westhoff et al., 2010). Even with the increasing complexityand sophistication of numerical schemes for modelling stream thermal processes, the accuracyof stream temperature simulations still depends on accurate modelling of stream surfaceenergy exchanges.Net radiation is often the dominant surface energy exchange, especially in summer duringperiods of low flow, when concerns about stream warming are often most acute (Khamis et al.,2015; Leach & Moore, 2010, 2019; Maheu et al., 2014; Morin et al., 1994; Webb & Zhang,1997). Substantial progress has been made in the development of methods for modellingboth shortwave and longwave radiation. For example, the effects of riparian vegetation onshading and the sky view factor can be estimated using hemispherical photographs (Moore3Accepted ArticleThis article is protected by copyright. All rights reserved.et al., 2005), geometric models (Chen et al., 1998; Li et al., 2012; Moore et al., 2014; Sridharet al., 2004), and canopy characteristics derived from light detection and ranging (LiDAR) orphotogrammetry (Dugdale et al., 2019; Loicq et al., 2018; Richardson et al., 2019). McMahon& Moore (2017) developed an empirical model for computing stream surface albedo as afunction of solar angles, turbidity, and aeration.Less attention has focused on the sensible and latent heat fluxes, despite the fact that latentheat transfer associated with evaporation can be an important heat loss mechanism; studies ofstream heat budgets have computed daily losses ranging up to 42 % of the net radiation for arange of sheltered streams (Caissie, 2016; Leach & Moore, 2010; Maheu et al., 2014; Webb &Zhang, 1997). Stream evaporation should increase at higher stream temperatures because ofthe approximately exponential dependence of surface vapour pressure on water temperature.Therefore, the role of latent heat transfer should become more important as streams andrivers continue to warm, especially in arid regions where streams are not sheltered by riparianforest (Mohseni & Stefan, 1999).In models for snow and glacier melt, the sensible and latent heat fluxes are commonlycomputed using semi-empirical bulk aerodynamic formulae, which use air temperature,humidity, and wind speed measurements at one height above the surface, and which explicitlyaccount for measurement height, surface roughness, and atmospheric stability (Conway et al.,2018; Moore, 1983). However, the fetch required to satisfy the underlying assumptionsof bulk aerodynamic formulae can be two or more orders of magnitude greater than themeasurement height (Oke, 1987). Consequently, these equations are not applicable to smalland medium-size streams. As an alternative, stream evaporation is often predicted usingempirical mass transfer equations, typically based on the following Dalton-style wind function:E = (a+ b · u) · (ew − ea) (1)where E is evaporation rate, u is wind speed, ew and ea are the vapour pressures of the watersurface and ambient air, respectively, and a and b are empirically determined coefficients.Many stream temperature modelling studies have used wind function models based onenergy-balance estimates of evaporation from lakes and ponds (e.g., Brady et al., 1969; King& Neilson, 2019). However, lake- and pond-derived mass transfer models may perform lesswell when used to estimate stream evaporation due to the lower fetch, especially for shelteredstreams (Gulliver & Stefan, 1986; Jobson, 1980). The model with coefficients reportedby Webb and Zhang (1997) has been applied with reasonable success to predict streamtemperature in a range of studies (e.g., Garner et al., 2014; Leach & Moore, 2011; Magnussonet al., 2012). The Webb-Zhang model appears to have been adapted from the wind functiondeveloped by Penman (1956) by applying unit conversions; thus, the Webb-Zhang model4Accepted ArticleThis article is protected by copyright. All rights reserved.has empirical support based on measurements over a range of “wet” surfaces. Althoughthe coefficients appear to have originated with Penman (1956), they will be called here the“Webb-Zhang” coefficients to avoid confusion with the Penman combination equation forwet-surface evaporation, and in recognition that Webb & Zhang (1997) is the commonlyreferenced source for those model coefficients.Empirical mass transfer functions for streams have been derived by energy-balance analysisin three studies focused on artificial or experimental channels (Fulford & Sturm, 1984; Gulliver& Stefan, 1986; Jobson, 1980) and by measuring evaporation using in-stream pans in fourstudies of natural streams (Benner, 2000; Caissie, 2016; Guenther et al., 2012; Maheu et al.,2014). Guenther et al. (2012), Maheu et al. (2014), and Caissie (2016) each focused on eitherone or two streams, all in forested catchments, while Benner (2000) focused on nine sitesalong an arid-land stream in Oregon.One challenge to comparing stream-derived wind functions is that Jobson (1980), Fulford& Sturm (1984) and Gulliver & Stefan (1986) used meteorological measurements over aland surface, whereas the other studies (i.e., Benner, 2000; Caissie, 2016; Guenther et al.,2012; Maheu et al., 2014) used meteorological measurements over the stream surface. Inaddition, meteorological measurements were made at different heights. Most studies usedmeasurements made 2 m above the surface, or, as in the case of Gulliver & Stefan (1986),wind speed was measured at 9 m but adjusted to represent measurements at 2 m. Benner(2000) used meteorological data measured 0.5 m above the surface and Guenther et al. (2012)used measurements at 1.5 m above the surface. Even just considering the most comparablestudies (Caissie, 2016; Guenther et al., 2012; Maheu et al., 2014), the fitted wind functionsvaried substantially. For example, the coefficient for wind speed ranged from 0.035 to 0.19mm h−1 s m−1 kPa−1. Although some of the variation in fitted wind functions may reflectmethodological differences among studies, it could also reflect the effects of site-specificconditions on boundary-layer development over the stream surface, such as atmosphericstability, fetch, and the effects of sheltering by riparian vegetation.The preceding review indicates that the lack of a robust, spatially transferable modelfor sensible and latent heat fluxes introduces an as-yet-unquantified source of uncertaintyinto stream temperature predictions. The broad goal of this study was to contribute to thedevelopment of a robust, transferable model of stream evaporation for inclusion in process-based stream temperature models. As a starting point, this research focused on nine forestedsites in a temperate mountain region. Evaporation was measured using instream pans overmultiple dates and wind functions were fit using above-stream meteorological data at twoheights to quantify the effect of measurement height. The candidate models included indicesof atmospheric stability and sheltering by forest canopy in order to account explicitly for5Accepted ArticleThis article is protected by copyright. All rights reserved.these site-specific controls on wind function parameters.MethodsStudy sitesField work was conducted at nine streams in southwest British Columbia, Canada (Figure 1).The streams were distributed between a coastal region and a region approximately 100 kminland (Figure 2). The coastal region has a typical maritime climate with cool, wet wintersand mild summers. Mean daily air temperatures at a climate station near the study streamsrange from 14.9 to 17.7 ◦C from June to August, with mean total precipition of 233 mm overthe same months. The inland region has relatively colder and drier winters, with warmer anddrier summers; mean daily air temperatures from June to August range from 16.3 to 19.2 ◦C,with a corresponding mean total precipitation of 112 mm. See Table S.1 for more detailedclimatic information.The study sites were selected to sample a range of stream widths, thermal regimes, andriparian vegetation conditions (see Table S.2 in supporting information). The sites wereprimarily located in coniferous forests, but three stream sites had deciduous trees dominantin their riparian vegetation.Bankfull width was measured and averaged across three transects at each study site usinga 30 m Sokkia/Eslon surveying tape, except at Rutherford Creek where an LTI Impulse 2000laser rangefinder was used. The transects were spaced such that they bounded the reach wherethe evaporation pans were deployed. The reach lengths ranged from 5 to approximately 20 m,with longer reaches corresponding to wider streams. Five to six mature trees representativeof the local species distribution were selected for tree height measurements; the average wasused to characterize each site. Tree height, ht (m), was calculated as follows:ht = HD × (tan θp − tan θn) (2)where HD is the horizontal distance from the measurement location to the tree (m), and θtand θb are the angles of inclination, in degrees, from the measurement location to the topand the bottom of the tree, respectively. The horizontal distance was measured using thesurveying tape and the angles of inclination were measured using a Suunto PM-5 inclinometer.Canopy openness, as a proportion, was estimated from a hemispherical photograph takenat each site using the image processing software, Gap Light Analyzer (GLA) following themethods detailed by Frazer et al. (1999). The photographs were taken using a Nikon Coolpix4500 digital camera with a Fisheye Converter FC-E8 lens attached. The camera was mounted6Accepted ArticleThis article is protected by copyright. All rights reserved.on a tripod and placed in the centre of the stream reach where evaporation and meteorologicalmeasurements were made, and levelled prior to taking a photograph. The photographs weretaken on days when the sky was uniformly overcast, or in the early morning on days withclear skies.Stream bankfull widths ranged from 3.1 m to 27.6 m, average tree heights ranged from 5.3m to 46.7 m, and canopy openness ranged from 9 % to 70 %. Study site elevations rangedfrom 52 to 1139 masl. The three streams in the interior region drain glacierized catchmentsand have higher snowmelt contributions, while the coastal region streams have hybrid rain-and snow-dominated hydrologic regimes.Stream evaporation measurementsStream evaporation was measured using the gravimetric approach developed by Maheuet al. (2014). Each evaporation pan consisted of a plastic container with dimensions of21.3× 21.3× 5.1 cm that was supported by a square wooden frame 34 cm wide, 1.9 cm thick,with an inner opening of 21.4×21.4 cm. The frame was painted white to minimize absorptionof solar radiation and warming, and was tethered to a concrete anchor to keep it in placewhen deployed in a stream.Evaporation measurements were made on 20 days between June 6th and August 17th,2018; field work was restricted to days without precipitation. On each sampling day, nineevaporation pans were deployed within the channel in pools or locations with low flow velocity.Three pans were placed along each of the left and right banks, and three in the centre of thechannel or pool (Figure 3). A preference was given to locations where the evaporation panscould be distributed across the width of the channel, or if that was not feasible, then acrossthe width of a pool.Each evaporation pan was initially filled with stream water to within about 2 cm of itsrim, and then weighed using an Ohaus Scout SPX2201 portable balance (resolution ± 0.1 g).The mass was measured approximately every 1 to 1.5 hours. The evaporation rate over eachmeasurement interval was computed asE = − ∆M · cfρw · A ·∆t (3)where E is evaporation rate (mm h−1) (positive for evaporation, negative for condensation),∆M is the change in mass over the measurement interval (kg), ρw is the density of water (kgm−3), ∆t is length of the measurement interval (s), A is the surface area of the water in thepan (m2), and cf is a conversion factor equal to 3.6·106, to convert E from m s−1 to mm h−1.The average evaporation rate over each measurement interval was computed from the nine7Accepted ArticleThis article is protected by copyright. All rights reserved.pans’ evaporation measurements.Stream temperature was recorded every 10 minutes with an Onset TidbiT v2 water temper-ature logger, which was housed in a white PVC radiation shield to reduce direct solar radiationeffects. The water temperature in each evaporation pan was measured approximately every20 minutes using an Omega Engineering HH-25TC thermocouple thermometer (resolution± 0.1 ◦C). Temperature measurements were made in the top 1 cm to represent, as closelyas possible, temperature at the water surface. A cross-calibration between the TidbiT andthe thermocouple was conducted, along with three other water temperature sensors. For therange of temperatures measured in the field, the thermocouple and TidbiT sensor agreedwithin ± 0.1 ◦C for 17 of 24 calibration measurements, and the maximum difference was 0.22◦C. Considering all five sensors, the range of contemporaneous measurements was less than orequal to 0.3 ◦C for 23 of 24 calibration measurements, with a maximum difference of 0.47 ◦C.A continuous record of pan water temperature was generated through linear interpolationfrom the manual measurements, using the approx() function in R (R Core Team, 2019).On days early in the study, when pan water temperature measurements were not madeconsistently at all pans, the average water temperature difference between the evaporationpans and the stream was used to adjust the recorded stream temperature.The evaporation pans had slightly curved sides. An empirical model was developed toestimate the surface area of water as a function of mass by setting up a pan on the same scaleused to make field measurements. The pan was filled with blue-dyed water in increments ofapproximately 0.025 kg. After each increment was added, a photograph was taken verticallydownward from a camera on a tripod. Surface area was determined for each photographusing the ImageJ software package (Schneider et al., 2012).Above-stream meteorological data collectionMeteorological conditions 1.5 m and 0.5 m above the stream surface were monitored duringevaporation measurements using a Campbell Scientific CR10X data logger. CampbellScientific HMP45C sensors measured air temperature and relative humidity (RH), with statedaccuracies of ± 0.2 ◦C and ± 2 to 3 % RH, respectively, at 20 ◦C. Wind speed was measuredwith MetOne 014A 3-cup anemometers, which have nominal starting threshold speeds of 0.45m s−1. Anemometers used in the field were calibrated against two that had been recentlyserviced by the manufacturer. See Szeitz (2019) for further details.All sensors were mounted on tripod cross-arms that extended the sensors over the centreof the stream (Figure 3), or in cases where the evaporation pans did not span the full streamwidth, the sensors were positioned over the centre of the evaporation pans’ distribution. The8Accepted ArticleThis article is protected by copyright. All rights reserved.meteorological sensors were scanned every 10 seconds, and 10-minute averages were loggedon a Campbell Scientific CR10X datalogger.The datalogger was programmed to compute wind speed as 0.80·x + 0.447, where x isthe pulse-count rate and 0.447 represents the anemometer’s stall speed in m s−1. An optionwas enabled such that, if the wind speed was equal to the threshold value (0.447) over ascan period, a value of 0 was returned. Therefore, over 10-minute intervals in which thewind speed was consistently below the threshold value, a value of 0 wind speed was returned.Alternatively, for 10-minute intervals in which there were periods with wind speed both aboveand below the stall speed, the program could return a wind speed between 0 and 0.447 m s−1.Calculation of meteorological variablesThe saturation vapour pressure, es(T ) (kPa), at a temperature T (◦C) was computed as:es(T ) = 0.611× exp( 17.27 · TT + 237.26)(4)The vapour pressure at the water surface, ew, was then computed as:ew = es(Tw) (5)where Tw is the water temperature of the pan or the stream. The vapour pressure of the air,ea, was calculated as:ea = es(Ta) · RH100 (6)where Ta is the air temperature and RH is the relative humidity (%). The vapour pressuredifference, ∆e, driving evaporation was then calculated as:∆e = ew − ea (7)Two atmospheric stability indices were calculated. For both indices, a value of zero indicatesneutral conditions and negative values indicate unstable conditions. One is the virtualtemperature difference between the stream surface and the air above it, ∆θ (◦C), whichrepresents the vertical variation in air density above the stream (Gulliver & Stefan, 1986).The virtual temperature, θ (K), of a fluid parcel is calculated as:θ = T + 273.151 + 0.378 · e/p (8)where p is the atmospheric pressure (kPa), e is the vapour pressure (kPa) and T is the9Accepted ArticleThis article is protected by copyright. All rights reserved.temperature (◦C) of the fluid, namely the stream or the overlying air. As p was not measured,a standard pressure, P , for each field site’s elevation was estimated using the U.S. StandardAtmosphere, 1976, atmosphere model (USS, 1976) as follows:P = Pb ·(TbTb + Lb · (h− hb)) g·MaR∗·Lb × kp (9)where h is the elevation of the field site (m), and Pb, Tb, Lb, and hb are the standard pressure(101.325 kPa), temperature (288.15 K), temperature lapse rate (0.0065 K km−1), and referenceelevation (0 m) where 0 < h ≤ 11, 000 m; g (m s−2) is gravitational acceleration, Ma (kgmol−1) is the molar mass of air, R∗ (J mol−1 K−1) is the universal gas constant, and kpis a conversion factor equal to 1 × 10−3 to convert from units of Pa to kPa. The virtualtemperature difference was then calculated as:∆θ = θw − θa (10)where θw is the virtual temperature at the water surface, and θa is the virtual temperature ofthe air above the water.The second stability index used was the buoyant force, γ (m s−2), which relates buoyantdifferences to temperature differences between two fluid parcels. It was calculated as:γ = g(Tw + 273.15Ta + 273.15− 1)(11)Both stability indices were evaluated as predictors. They performed similarly as predictors,with the buoyant force providing slightly superior performance, so subsequent reference to astability index will refer solely to the buoyant force.Evaluation of models from the literatureWe used the data collected in this study to evaluate the performance of wind function modelsderived in four previous stream-based studies (Benner, 2000; Caissie, 2016; Guenther et al.,2012; Maheu et al., 2014) and two non-stream-based wind functions commonly used in streamtemperature models (Brady et al., 1969; Webb & Zhang, 1997). When applying the windfunctions of Maheu et al. (2014), Caissie (2016), Brady et al. (1969), and Webb & Zhang(1997) using meteorological data from this study, wind speed data for 1.5 m above the streamwere adjusted to 2 m (7 m for the Brady et al. (1969) wind function) using a power-lawrelation (Sutton, 1953). No adjustments were made to the vapour pressures. For the Benner(2000) model, meteorological measurements made at 0.5 m above the stream were used as10Accepted ArticleThis article is protected by copyright. All rights reserved.input to be consistent with the measurements in that study.For comparison to the literature models, we fit a “base” model of the form of Eq. 1 to ourdata. Whereas previous studies fit wind function models separately by site, models were fit inthis study to the full data set using mixed-effects statistical models. Mixed-effects models arebased on the assumption that there is a set of fixed-effects coefficients that apply throughoutthe population of sites to which the model is intended to apply, and that the coefficients atany given site exhibit random deviations from the fixed-effects values. As applied in thisstudy, the goal of mixed-effects models is to derive the best model that could be appliedto new sites with no additional calibration. Mixed-effects models are common in biologicalscience and ecology, but have had fewer applications in hydrology; some hydrological examplesinclude Booker & Dunbar (2008), Kasurak et al. (2011), Ploum et al. (in press) and Howieet al. (2020).When framed as a mixed-effects model, the base wind function model can be expressed asEik = (a+ αk) · (ew,ik − ea,ik) + (b+ βk) · wik · (ew,ik − ea,ik) + ik (12)where the subscript k indicates a specific site; the subscript i indicates the ith observation atsite k; a and b are fixed effects that are assumed to apply to the entire population of sites;αk and βk are deviations from the fixed-effects coefficients for site k, assumed to be drawnfrom normally distributed populations; and ik is a random error term. If the model wereapplied to a new site, only the fixed-effects coefficients (a and b) would be used. If the modelwere applied to new observations from one of the original sites, then both the fixed effectsand the random effects for that site (αk and βk) would be used.The performance of the fitted models was evaluated using leave-one-site-out cross-validation.In each iteration of the cross-validation, all data for one site were withheld; the model was fitusing data for the remaining sites and then applied using the fixed-effects coefficients to datafor the withheld site. Model performance was determined by computing the root-mean-squareerror (RMSE, mm h−1) and the Nash-Sutcliffe efficiency (NSE), as follows:RMSE =√√√√ 1nn∑i=1(Eˆi − Ei)2(13)NSE = 1−∑ni=1(Eˆi − Ei)2∑ni=1(Ei − E¯)2 (14)where Eˆi is the modelled evaporation rate, and E¯ is the mean observed evaporation rate fromthe nine pans for a given measurement interval.11Accepted ArticleThis article is protected by copyright. All rights reserved.To evaluate the sensitivity of the results to uncertainties in the pan temperatures, themodel comparison was conducted using both the recorded ambient stream temperature andthe interpolated pan water temperature to determine ew.Evaluation of extended models and effect of measurement heightIn addition to applying the base model, we tested the performance of extended models thatincluded additional predictors. Specifically, canopy openness (φ) and buoyant force (γ) wereincorporated as additional model predictors in various combinations to form a total of 12candidate models as listed in Table 1.Separate models were fit for each of the two measurement heights (0.5 m and 1.5 m). The12 expanded models listed in Table 1 were fit using the mixed-effects approach described above,and with surface vapour pressure computed using the interpolated pan water temperatures.In the first round of model testing, the mixed-effects models allowed each model parameter,(a, b, and if present, c and d), to vary by site. Any model that had one or more insignificantestimated fixed-effects coefficients (p-value > 0.05) was dropped from further consideration.ResultsEvaporation pan water temperatureFor eight of the nine streams, water in the evaporation pans averaged between 0.51 and 1.64◦C warmer than stream temperature. The exception was Marion Creek, however, which hadconsistently lower pan water temperatures with an average difference of -0.66 ◦C (Figure 4).The trend in the water temperature difference typically followed the stream temperaturetrend, but there was variability among pans depending on their exposure to solar radiation(Figure S.1). Individual openings in the canopy provided localized pools of sunlight to thestream, which increased the water temperature of any evaporation pans they crossed overthe course of a day. The full daily time series of stream and evaporation pan temperaturescan be found in the Supporting Information (Figure S.2).Meteorological conditions and evaporation ratesThe distributions of measured and derived meteorological conditions, and the measuredevaporation rates, are presented in Figure 5. The meteorological and stream temperaturedata are at 10-minute intervals, and the evaporation rate measurements are at approximately1- to 1.5-hour intervals. Time series of meteorological data are provided in the Supporting12Accepted ArticleThis article is protected by copyright. All rights reserved.Information (Figure S.3).As seen in Figure 5 (top panel) and in the supporting information (Figure S.3), airtemperatures were typically greater than stream temperature, and increased with heightabove the stream surface (Figure 6, top panel). Exceptions to this trend were observed atMarion Creek and Blaney Creek (Lower), as the former had higher stream temperatures thanair temperatures at almost all times, and the latter experienced several hours of nearly equalstream and air temperatures on July 5th. Both of these study sites are downstream of lakesthat are subject to substantial warming.Measured wind speeds often increased with height above the stream surface but notconsistently (see Figure 6, middle panel, and supporting information, Figure S.3). A generallynegative relation exists between the average difference in wind speeds, the local canopyopenness, and the sheltering ratio. As seen in Table 2, both of the Blaney Creek sites andSpring Creek have sheltering ratio values > 4 and canopy openness values < 0.25, and theyexperienced the greatest average wind speed differences, ranging from 0.12 to 0.22 m s−1.Conversely, Alouette River and Miller Creek have low sheltering ratios (< 1) and greatercanopy openness values (> 0.50), and they experienced average wind speed differences ofapproximately 0.02 m s−1.The vapour pressure at 0.5 m was greater than the vapour pressure at 1.5 m for 95 % ofthe observations (Figure 6, bottom panel); see also Supporting Information (Figure S.3). Thegreatest vapour pressure differences were associated with the highest stream temperatures,as observed at Marion Creek and Alouette River (Figure 5).Conditions were generally stable, with unstable conditions indicated for only 12 to 14 %of the time at heights of 1.5 and 0.5 m, respectively. The exception to this trend was MarionCreek; it was dominated by unstable conditions, which occurred > 97 % of the time, at bothheights.Evaporation rates ranged from -0.01 to 0.20 mm h−1 with a mean evaporation rate of0.06 mm h−1 (Figure 5). As expected, evaporation rates generally increased with increasingvapour pressure differences and/or higher wind speed (e.g. comparing Alouette River toMarion Creek, Figure 5 panel 4).An error analysis indicated that the mean uncertainty in the measured evaporation ratefor an individual pan measurement was 0.004 mm h−1 (see Supporting Information). Theuncertainty in the mean evaporation rate, as represented by a statistical confidence intervalaround the mean, was greater than the measurement uncertainty for an individual pan.Indeed, for three observations of low evaporation rates, the 95 % confidence intervals weregreater than the magnitude of the observations (Figure S.4). This result indicates thatsampling variability was often substantially greater than the uncertainty of an individual pan13Accepted ArticleThis article is protected by copyright. All rights reserved.measurement. The median relative uncertainty in mean evaporation was 13 %.Literature wind function comparisonFitted model coefficients vary substantially among studies (Table 3). Relative model perfor-mance was consistent regardless of whether the ew, and by extension the ∆e, was computedusing the stream or the pan water temperature (Figure 7). However, performance of thefitted models, and those of Brady et al. (1969) and Webb & Zhang (1997), was slightly betterwhen using the interpolated pan temperatures.As seen in Figure 7, the models of Benner (2000) and Maheu et al. (2014) consistentlyoverestimated evaporation, the model of Caissie (2016) overestimated on average but had highvariability, and the model of Guenther et al. (2012) consistently underestimated evaporation.Both the Brady et al. (1969) and Webb and Zhang (1997) models performed similarly to thisstudy’s base model (Figure 8).Effects of additional predictors and measurement heightOf the model forms in Table 1, no model that expanded upon the base mass transfer modelwith a stability index alone was significant. Models that expanded upon the base modelwith a canopy openness variable alone were only significant when the canopy variable wasan interaction term on the wind speed. Models that included both a stability and canopyvariable often had multiple forms that were fully significant.The results of the cross-validation of the significant models are summarized in Table 4.Model performance was considered on the basis of the root-mean-square error, and the bestperforming models’ estimated coefficients are provided in Table 5. The base model performedwell under cross-validation for both the 0.5-m and 1.5-m measurements; the 0.5-m model hada root-mean-square error (RMSE) of 0.0162 mm h−1 and a Nash-Sutcliffe efficiency of 0.897,while the 1.5-m model had respective values of 0.0187 mm h−1 and 0.862.Of the models based on 1.5-m measurements that had significant coefficients, 72 % improvedupon the performance of the base model under cross-validation compared to 29 % for thefiltered 0.5-m models. The best performing expanded model fit to the 0.5-m measurements,Model 9, provided a 2 % reduction in the RMSE from the base model. The best performingexpanded model fit to the 1.5-m measurements, Model 11, provided an 11 % reduction in theRMSE. The cross-validated model predictions for the selected models in Table 1 are shownin Figure 8. While the expanded 0.5-m model had better goodness-of-fit indicators than theexpanded 1.5-m model, they both had similar site-specific residual error distributions, withthe exception of the streams draining glacierized catchments (Cayoosh Creek, Miller Creek,14Accepted ArticleThis article is protected by copyright. All rights reserved.Rutherford Creek) as seen in Figure 9.While the fixed-effects coefficients are used during model cross-validation and whenapplying the models to external datasets, the magnitudes of the site-specific adjustments for agiven model provide information on how much site-specific variability is not accounted for bythe fixed-effects terms in the model. The base model’s site-specific adjustments ranged from0.4 to 37 % of the fixed-effect coefficient value for the 1.5-m model, and between 1 and 25 %for the 0.5-m model. This result indicates that there was site-specific variability unaccountedfor by the base model predictors, especially for the 1.5-m model. However, the expandedmodels’ site-specific adjustments were less than 0.001 % of the fixed-effect coefficient valuefor both the 1.5-m and 0.5-m models. That is, explicitly incorporating canopy openness andstability predictors into the model effectively accounted for the site-specific variability thatwas otherwise accounted for through site-specific random-effects adjustments to the windfunction.DiscussionAssessment of evaporation pan methodologyOverall uncertainty in the mean evaporation rate for a given measurement interval, asexpressed in the confidence limits around the mean, is a combination of random measurementerror and sampling variability. Given the design of the pans and their mode of deployment inthis study, each pan was able to provide an estimate of evaporation with a mean uncertaintyof 0.004 mm h−1, relative to mean and maximum measured rates of 0.06 and 0.20 mmh−1, respectively. However, the confidence limits for the mean evaporation were generallygreater than the uncertainty in an individual pan measurement, suggesting that samplingvariability was the dominant source of uncertainty. Sampling variability arises because thepans experienced variable conditions caused, for example, by differences in pan water heatingdue to sunlight infiltrating canopy gaps, or differences in wind exposure due to in-streamboulders or overhanging vegetation. While the overall uncertainty increased with increasingmean evaporation rates, its relative magnitude decreased. For example, the mean overalluncertainty was 27 % of the mean evaporation rate at Miller Creek (0.006 mm h−1 and 0.022mm h−1, respectively), while the mean overall uncertainty at Rutherford Creek was 7.6 %of the mean evaporation rate (0.010 mm h−1 and 0.136 mm h−1, respectively). Consideringall streams, the results indicate that an overall uncertainty of approximately 18 % of themean measured value can be achieved for typical conditions by deploying nine evaporationpans. This result highlights the need for replication of pans to achieve an appropriate level of15Accepted ArticleThis article is protected by copyright. All rights reserved.accuracy.The water temperature in the evaporation pans often differed substantially from that ofthe stream, ranging from 1.4 ◦C lower to 4.5 ◦C higher than stream temperature. The timeseries of pan water temperatures show that frequent temperature fluctuations occurred withinmeasurement intervals, and warming occurred within 10 to 20 minutes of pan deployment onnumerous occasions (Supporting Information, Figure S.2). If this temperature difference werenot accounted for, the vapour pressure difference used in the wind function would often beunderestimated, potentially leading to an overestimate of the fitted wind function coefficients,as seen in Table 3.Given the observed rates of pan warming, it is recommended that future users of thismethodology measure the surface temperature of the water in the evaporation pans with hightemporal resolution (e.g., every 10 minutes). In addition, it may be useful to experiment withalternative materials. The pans used in this study were made from plastic with a recyclingcode of 5, indicating polypropylene. Published thermal conductivities for polypropylene rangefrom 0.10 to 0.22 W m−1 ◦C−1 (Engineering Toolbox, 2003). For comparison, aluminum hasa thermal conductivity of approximately 240 W m−1 ◦C−1 (Engineering Toolbox, 2003).It was only possible to deploy the pans at sites with placid flow, and the water in the panswas not moving. Based on a limited set of experiments, Benner (2000) found that evaporationfrom moving water was greater than that for still water at low wind speeds with low vapourpressure differences. However, these conditions are associated with low evaporation; Benner(2000) found minimal difference in evaporation from still and moving water for conditionsconducive to higher evaporation. A more serious limitation relates to the potential effect ofaeration on evaporation. Aerated water has a greater effective surface area than water withplacid flow, which could enhance sensible and latent heat exchanges. Therefore, there is somequestion about the applicability of the fitted wind functions to steep streams, especially athigher flows when aeration becomes stronger.Meteorological data measurement height and instrument sensitiv-ityPrevious studies used measurement heights of 1.5 or 2 m, with the exception of Benner(2000), who used a measurement height of 0.5 m. In this study, the a coefficient for the0.5 m measurement height (0.0815 mm h−1 kPa−1) was higher than that for the 1.5 mmeasurement height (0.0663 mm h−1 kPa−1), while the b coefficient was similar between thetwo measurement heights. The increased value of a with decreased measurement height isconsistent with the fact that the vapour pressure difference driving evaporation should decrease16Accepted ArticleThis article is protected by copyright. All rights reserved.with decreasing measurement height, as was the case for the majority of measurements.Model performance was better when using meteorological measurements from 0.5 m ratherthan 1.5 m above the stream surface, producing a 13 % reduction in root-mean-square errorfor the base model. This superior performance could result from the fact that measurementsat a lower height would be closer to being in an internal boundary layer adjusted to the watersurface. Although this result might encourage the use of lower measurement heights, animportant consideration is that stream stage varies with discharge; this point is particularlyrelevant for proglacial streams, which experience significant diel fluctuations in discharge.As a consequence, wind functions derived from measurements at a specific height would notbe accurate when applied to streams with varying stages with meteorological measurementsat a fixed height. As the gradients of wind speed and vapour pressure tend to decreasewith increasing height above a surface, this source of error would be greatest for windfunctions derived from measurements at a low height. A further consideration relates toinstrument precision. Because wind speed and surface-to-air vapour pressure differencesgenerally increase with height above a stream, these measured values should be subject toless relative uncertainty when measured at a greater height above the stream surface.Given the starting-speed limitations of the cup-type anemometers often employed formeteorological measurements, low wind speeds are likely to be under-reported for shelteredstreams. In cases where the wind-function intercept is non-zero, the model implicitly adjustsfor the effect of the anemometer’s stall speed on the estimated coefficient values. However,if these models were applied using wind speed data obtained from a sensor with increasedaccuracy (lower starting/stalling speed), the predictions would be biased for low wind speeds.Empirically derived wind functions must be applied with consideration of the accuracy ofthe instruments used to obtain the fitting data in order to produce reliable and unbiasedestimates.Effects of additional predictor variablesFor both meteorological measurement heights, the addition of a stability variable alone waseither not significant or did not improve model predictions. For measurements made at 1.5 m,the addition of canopy and stability variables together provided modest model improvement,with an 11 % reduction in root-mean-square error and an increase in the Nash-Sutcliffeefficiency from 0.862 to 0.891. However, for measurements made at 0.5 m, the addition of acanopy variable alone outperformed the addition of both variables, but provided marginalimprovements over the base model (2 % reduction in root-mean-square error, increasedNash-Sutcliffe efficiency from 0.897 to 0.900).17Accepted ArticleThis article is protected by copyright. All rights reserved.The relatively minor improvement associated with the expanded models suggests thatstability played a minor role compared to the forced convection influence of wind on vapourtransfer for these small, relatively sheltered streams. However, the limited range of stabilityconditions observed in the current study may have been insufficient to comprehensivelyevaluate its influence. The benefit of adding stability and/or canopy openness predictors forboth measurement heights is that they account for the site-to-site variability that could notbe accounted for by the base model. While the stability index can be computed from air andstream temperatures, canopy openness is not typically available. Where field measurementsare not available, canopy openness could be estimated using satellite imagery (Carreiraset al., 2006), LiDAR data (Korhonen et al., 2011) or photogrammetry (Dugdale et al., 2019).Given these concerns and those discussed in the previous section, it is recommended that theexpanded 1.5 m model be used if canopy openness measurements are available, or reliableestimates can be obtained, given its superior performance over the base model.Comparison of wind function coefficients among studies and scopeof applicationMost studies of stream evaporation focused on one or at most two streams and producedsite-specific estimates of the wind function coefficients (Table 3). Interestingly, the modelsdeveloped using stream evaporation measurements performed relatively poorly when applied toour data, with both consistent overestimation (Benner, 2000) and underestimation (Guentheret al., 2012). On the other hand, both the Brady et al. (1969) and Webb & Zhang (1997)models came close to matching the performance of this study’s base model, despite not beingbased on stream evaporation measurements.Based on the cross-validation results, the models developed in this study can provideestimates of evaporation with a typical error of less than 0.02 mm h−1 or, in energy fluxunits, about 14 W m−2. The cross-validation results indicate that the models can be appliedwith reasonable confidence to model water temperature for small- to medium-size streams intemperate forested landscapes. However, the model developed by Benner (2000) overestimatedevaporation for our field sites, which suggests that the models developed in this study wouldunderestimate evaporation at the field sites studied by Benner (2000), which were located ina warmer, drier environment. It is recommended that future research on stream evaporationapply a consistent methodology to streams representing a broad range of thermal regimes,physiography, and hydroclimate.A challenge in applying wind functions for computing the sensible and latent heat fluxesfor streams is generating suitable meteorological data. Above-stream conditions differ from18Accepted ArticleThis article is protected by copyright. All rights reserved.those over land, typically being cooler and moister during daytime in summer and lesswindy for sheltered sites (Benyahya et al., 2010; Guenther et al., 2012; Leach & Moore,2010). Consequently, if wind functions derived using above-stream meteorological data wereapplied using land-based meteorological measurements, the simulated sensible and latentheat fluxes would be biased. On the other hand, if wind functions are fit using land-basedmeteorological data (e.g., Fulford & Sturm, 1984; Gulliver & Stefan, 1986; Jobson, 1980), thenthe fitted coefficients implicitly incorporate the effects of sheltering and internal boundarylayer development over the surface of the study stream, which could limit the applicability ofthe wind function to other sites.In most applications of stream temperature models, meteorological data are measured atland-based stations. There have been attempts to develop empirical approaches for usingland-based meteorological data to predict evaporation as a function of fetch or surfacearea (Granger & Hedstrom, 2011; McJannet et al., 2012). While these approaches may bereasonable for lakes and ponds, they may be less applicable for streams, given their distinctivelinear geometry and the influences of stream banks and riparian vegetation on boundary-layerdevelopment.Future research should focus on developing approaches to adjust such land-based measure-ments to make them consistent with above-stream conditions to reduce bias. As a startingpoint, it may be useful to scale temperature and vapour pressure as (xa − xw)/(xl − xw),where x represents one of air temperature or vapour pressure, and the subscripts a, w, andl indicate conditions above the stream, at the water surface and at a land-based weatherstation, respectively. For wind speed, an appropriate scaling could be ua/ul. These scaledvariables could then be related to variables such as stream width and vegetation height.Considering the current paucity of above-stream meteorological data, there is a need forfurther field work to collect relevant data over a range of streams to support the developmentof empirical scaling relations. This field work should be supported by theoretical work thatexpands upon earlier lake- and pond-focused studies by Weisman & Brutsaert (1973) andHipsey & Sivapalan (2003), but which explicitly accounts for distinctive features of streams.ConclusionEvaporation rates were measured using floating evaporation pans at nine streams with a rangeof widths (3.1 to 27.6 m), temperature regimes, and degrees of sheltering. The evaporationrates ranged from -0.01 to 0.20 mm h−1, with a mean rate of 0.06 mm h−1. Generalized windfunctions were derived using these measurements and meteorological conditions measured 1.5and 0.5 m above the stream surface, and had respective root-mean-square errors of 0.018719Accepted ArticleThis article is protected by copyright. All rights reserved.and 0.0162 mm h−1 under cross-validation, and respective Nash-Sutcliffe efficiencies of 0.862and 0.897. The cross-validation results support the application of the fitted models for small-to medium-size streams in temperate forested regions.Canopy openness and a stability index, the buoyant force, were incorporated as additionalmodel predictors. The addition of a stability predictor alone did not improve model predictions.The wind function had consistent performance under cross-validation, and the addition ofcanopy openness and stability predictors reduced site-specific variability in evaporationpredictions. The reductions in prediction error achieved with these additional variables weregreater for measurements at 1.5 m rather than 0.5 m. The wind function models presented byBrady et al. (1969) and Webb & Zhang (1997) performed similarly to models fit specificallyto our data set.Future research should investigate stream evaporation using a consistent methodologyacross a broader range of conditions (stream temperatures, widths, degrees of sheltering, andstability conditions), as well as examining the nature of wind, temperature, and humidityprofiles above streams. This would advance our understanding of stream evaporation incomplex micrometeorological environments and the variability in wind function coefficients,and would aid the development of more robust, generalized wind functions applicable to abroader range of streams. 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Journal of Environmental Engineering 126: 518–526.27Accepted ArticleThis article is protected by copyright. All rights reserved.Table 1: The base wind function (Model 0) and 11 expanded model forms incorporatingcanopy openness and stability variables. The models were fit to meteorological measurementsmade 0.5 and 1.5 m above the stream surface.# Model0 E = (a+ b · u) · ∆e1 E = (a+ b · u+ c · φ) · ∆e2 E = (a+ b · u+ c · γ) · ∆e3 E = (a+ b · u+ c · φ · u) · ∆e4 E = (a+ b · u+ c · γ · u) · ∆e5 E = (a+ b · u+ c · φ+ d · γ) · ∆e6 E = (a+ b · u+ c · φ · u+ d · γ) · ∆e7 E = (a+ b · u+ c · φ+ d · γ · u) · ∆e8 E = (a+ b · u+ c · φ · u+ d · γ · u) · ∆e9 E = (a+ b · φ · u) · ∆e10 E = (a+ b · φ · u+ c · γ) · ∆e11 E = (a+ b · φ · u+ c · γ · u) · ∆eAccepted ArticleThis article is protected by copyright. All rights reserved.Table 2: Stream physiography, average wind speeds, and differences in wind speed. Thesheltering ratio is computed as tree height ÷ stream width, and uh refers to wind speed in ms−1 measured h metres above the stream surface. The streams are arranged by decreasingvalues of wind speed difference.Stream CanopyOpen-nessShelteringRatiou1.5 u0.5 ∆uBlaney Ck. (Lower) 0.09 8.41 0.61 0.39 0.22Blaney Ck. (Upper) 0.24 4.21 0.30 0.16 0.14Spring Ck. 0.16 10.55 0.38 0.26 0.12Rutherford Ck. 0.70 0.29 1.63 1.53 0.10Marion Ck. 0.11 7.88 0.45 0.38 0.07Miller Ck. 0.57 0.97 0.48 0.42 0.05Alouette R. 0.45 1.83 1.27 1.25 0.02Cayoosh Ck. 0.50 0.86 1.19 1.17 0.02North Alouette R. 0.15 4.19 0.17 0.18 -0.01Accepted ArticleThis article is protected by copyright. All rights reserved.Table 3: A comparison of wind function coefficients, a and b, derived from stream evaporationmeasurements, and two commonly cited in stream temperature modelling studies. In the seventhcolumn, Tp indicates the evaporation pan water temperature. The units of a and b are mm h−1kPa−1 and mm h−1 s m−1 kPa−1, respectively.Source Site Wind Function Measurement Stream TpDescription (a + b · u) height (m) width (m) measured?This study Forestedstreams0.0663 + 0.0449·u 1.5 3.1 to 27.6 yes(ew,pan) 0.0815 + 0.0437·u 0.5This study Forestedstreams0.0699 + 0.0549·u 1.5 3.1 to 27.6 yes(ew,stream) 0.0699 + 0.0661·u 0.5Benner(2000)Streams in mead-ows and forest0.144 + 0.085·u 0.5 2.7 to 19.5 yesGuenther etal. (2012)Forested stream 0.0424·u 1.5 1.5 yesMaheu et al.(2014)Forested stream 0.11 + 0.122·u 2 8 noForested stream 0.123 + 0.035·u 2 80 noForested stream 0.047n + 0.074n · u 2 80 noCaissie et al.(2016)Forested stream 0.19·u 2 1.7 noBrady et al.(1969)Powerplant cool-ing lake0.101 + 0.005∗·u2 7 - -Webb andZhang(1997)Streams in pas-ture and wood-land0.055 + 0.059·u 2 - -n wind function coefficients derived from night-time measurements∗ coefficient units of mm h−1 s2 m−2 kPa−1Accepted ArticleThis article is protected by copyright. All rights reserved.Table 4: Goodness-of-fit statistics computed from leave-one-out cross-validated model pre-dictions for a selection of models. The root-mean-square error (RMSE, mm h−1) and theNash-Sutcliffe efficiency (NSE) are the model goodness-of-fit statistics provided.# Model RMSE NSE1.5 m 0 E = (a+ b · u) · ∆e 0.0187 0.86211 E = (a+ b · φ · u+ c · γ · u) · ∆e 0.0166 0.8910.5 m 0 E = (a+ b · u) · ∆e 0.0162 0.8979 E = (a+ b · φ · u) · ∆e 0.0159 0.900Accepted ArticleThis article is protected by copyright. All rights reserved.Table 5: The population-level estimated coefficients and coefficient standard errors for theselected models.Estimated coefficient value [standard error]# a (mm h−1 kPa−1) b (mm h−1 s m−1 kPa−1) c (mm h−1 s3 m−2 kPa−1)1.5 m 0 0.0663 [0.0079] 0.0449 [0.0069] -11 0.0837 [0.0033] 0.1201 [0.0169] 0.0766 [0.0234]0.5 m 0 0.0815 [0.0049] 0.0437 [0.0072] -9 0.0944 [0.0034] 0.0684 [0.0069] -Accepted ArticleThis article is protected by copyright. All rights reserved.For Peer Review Figure 1: Photographs of the nine study sites. 199x218mm (300 x 300 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved.For Peer Review Figure 2: The locations of the study streams, indicated by red dots, in southwest British Columbia. The climate stations providing data of the regional hydroclimate are indicated by white dots and labelled with their Environment and Climate Chanage Canada climate station ID. Figure 1 provides the stream names that correspond to the stream numbers. The inland streams are numbered 4, 6, and 8, and the remaining streams are the coastal streams. The base map source is the Stamen Terrain tile set © OpenStreetMap contributors. 462x524mm (600 x 600 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved.For Peer Review Figure 3: The evaporation pans and meteorological station set up at Spring Creek. The TidbiT water temperature logger is submersed near the meteorological station. This demonstrates the ideal distribution of evaporation pans in a stream and the location of the meteorological station with respect to the pans; individual stream characteristics resulted in deviations from this ideal. 103x138mm (600 x 600 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved. Figure 4: The stream-averaged distributions of water temperature difference between the evaporation pans and the stream. 179x79mm (600 x 600 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved.For Peer Review Figure 5: The distributions of meteorological conditions at each stream during stream evaporation measurements, arranged by increasing mean stream temperature. 199x279mm (600 x 600 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved. Figure 6: The distributions of meteorological conditions measured 0.5 and 1.5 m above the stream surface, arranged by increasing mean stream temperature. 199x169mm (600 x 600 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved.For Peer Review Figure 7: Comparison of the evaporation rates estimated by applying seven literature wind functions to this study’s dataset. The wind function coefficients and the study references are provided in Table 3. The two panels for Maheu correspond to the wind functions for Catamaran Brook (CB) and the Little Southwest Miramichi River (LSWM). The panels are ordered from 1 to 7 by decreasing model root-mean-square error, and the Nash-Sutcliffe efficiency is provided in the top-left corner of each panel. 149x260mm (300 x 300 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved. Figure 8: Cross-validated model predictions for the base mass transfer model and the two best expanded models, Models 9 and 11, for meteorological measurements made 0.5 m and 1.5 m above the stream surface, respectively. 260x169mm (300 x 300 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved. Figure 9: The site-specific residual error distribution for the base and expanded 0.5-m and 1.5-m models. The residuals were computed from cross-validated model predictions. 199x159mm (300 x 300 DPI) Accepted ArticleThis article is protected by copyright. All rights reserved.

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