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Developing an Effective Model for Predicting Spatially and Temporally Continuous Stream Temperatures from Remotely Sensed Land Surface Temperatures Kristina M. McNyset 1, *, Carol J. Volk 1 and Chris E. Jordan 2 Received: 8 October 2015; Accepted: 23 November 2015; Published: 4 December 2015 Academic Editor: Y. Jun Xu 1 2

*

South Fork Research, Inc., 44842 SE 145th St. North Bend, WA 98045, USA; [email protected] Northwest Fisheries Science Center, NOAA Fisheries 2725 Montlake Blvd E., Seattle, WA 98112, USA; [email protected] Correspondence: [email protected]; Tel.: +1-541-754-4807

Abstract: Although water temperature is important to stream biota, it is difficult to collect in a spatially and temporally continuous fashion. We used remotely-sensed Land Surface Temperature (LST) data to estimate mean daily stream temperature for every confluence-to-confluence reach in the John Day River, OR, USA for a ten year period. Models were built at three spatial scales: site-specific, subwatershed, and basin-wide. Model quality was assessed using jackknife and cross-validation. Model metrics for linear regressions of the predicted vs. observed data across all sites and years: site-specific r2 = 0.95, Root Mean Squared Error (RMSE) = 1.25 ˝ C; subwatershed r2 = 0.88, RMSE = 2.02 ˝ C; and basin-wide r2 = 0.87, RMSE = 2.12 ˝ C. Similar analyses were conducted using 2012 eight-day composite LST and eight-day mean stream temperature in five watersheds in the interior Columbia River basin. Mean model metrics across all basins: r2 = 0.91, RMSE = 1.29 ˝ C. Sensitivity analyses indicated accurate basin-wide models can be parameterized using data from as few as four temperature logger sites. This approach generates robust estimates of stream temperature through time for broad spatial regions for which there is only spatially and temporally patchy observational data, and may be useful for managers and researchers interested in stream biota. Keywords: land surface temperature; MODIS; stream temperature models

1. Introduction Stream water temperature is one of the most important factors influencing productivity, species composition, community structure, and life history expression of stream organisms. Timing of significant ecological events like invertebrate and fry emergence, onset and duration of photosynthesis, spawning, and migration are all determined in part by temperature (e.g., [1,2]). For example, fish growth and survival are optimized at particular temperatures (e.g., [3]) and these responses can be used in life cycle and bioenergetics modeling frameworks to incorporate fish activity and metabolic response to varied environmental conditions, such as climate change scenarios [4]. Therefore, the ability to track temperatures across multiple seasons and life stages becomes critical to accurately predicting fish response to changing conditions. Measures of daily, seasonal, and annual variation of stream temperature are ubiquitous in stream ecology research. Annual mean and maximum temperatures, such as seven-day running means and maximums, are commonly used as indicators of stream “health” or habitat quality for

Water 2015, 7, 6827–6846; doi:10.3390/w7126660

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Water 2015, 7, 6827–6846

aquatic species [5] and are also used as criteria for evaluation of adherence to the Clean Water Act [6,7]. Changes in the thermal regime of a given stream through human or natural alterations of the surrounding landscape (e.g., changes in riparian structure shading capacity, large-scale fire effects, physical changes to the stream channel either directly or through changes in other factors like sedimentation) are of particular concern to local, regional, and federal land managers [8]. Many aquatic organisms live for years and travel far during their life cycle. It is important for a complete understanding to be able to characterize stream temperatures not just at the local scale, but also across broad spatial and temporal scales, from reach to watershed to region [9]. Vagile species like salmon experience the temperature of hundreds to thousands of stream kilometers across years, and therefore population-level models need stream temperature estimates across regions. Similarly, life cycle models have benefited from inclusion of life-stage specific temperature estimates at these expansive spatial scales as well as through time [10–12]. Generating useful and accurate measures of water temperature requires monitoring. Digital thermographs (temperature loggers) are often placed in streams and can provide high temporal resolution data for a site, but only for the duration of their placement in the stream. There are also spatial limitations of temperature logger use, as the spatial structure of temperatures in streams can vary over short distances (e.g., within 10 m), such as when loggers are located close to tributary junctions [13]. Although digital thermographs are relatively inexpensive, the effort required to place and maintain the logger and retrieve the data is not. High implementation costs therefore can inadvertently affect logger placement within a watershed and even limit spatial extent, as some parts of many stream systems are almost entirely inaccessible to field crews. Conversely, spatially continuous surface water temperatures collected with remote sensing can illuminate spatial patterns at very fine resolutions over broad extents [14–16]. However, data are typically only available for snapshots in time at a handful of locations. Remote sensing based approaches can also be expensive due to the cost of flights and sensors and required expertise in image processing. Researchers have addressed the mismatch between the need for spatially and temporally continuous stream temperature data and the reality of the limited nature of almost all stream temperature datasets through a variety of estimation approaches with varying degrees of success. One of the most common methods for estimating temperature at large spatial scale is to develop models based on continuously available attributes. Air temperature is a relatively easy dataset to acquire for many localities and it has similar daily, seasonal, and annual variations to stream temperature, making it an obvious covariate choice in stream temperature models. However, the spatial patterns of variability in air and stream temperature are different and operate at different scales [17]. Thus, air temperature is not always a good predictor of stream temperature particularly when modeling across long time periods [18–20]. Complex heat budget models that include thermodynamic processes are able to improve temperature estimations in specific spatial contexts [21,22]. Other approaches use explicitly spatial methods of stream temperature estimation, such as inverse distance weighting and kriging, directly addressing spatial variability [23–25]. However, streams have unique spatial properties, like network connectivity and directionality of information flow, that are hard to capture using traditional spatial interpolation methods. In these models, predictions across time require new interpolations for each time step, making estimates into unmonitored time periods difficult [26]. Peterson et al. [26] recent model innovations that explicitly include the unique spatial properties of stream networks have been particularly successful in regions where spatially dense logger datasets are available. However, they are still limited by the temporal resolution and duration of observations used to parameterize models. Vatland et al. [16] were able to develop robust temperature estimates at high spatial (~100 m) and temporal (hourly) resolution over ~100 km of stream using thermal infrared imagery from a fixed wing aircraft mounted imaging system. Remotely sensed data from Earth orbiting satellites offer a potential data source of both temporally and spatially abundant temperature data and are often freely available [27]. For example,

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daily data are available from the U.S. National Aeronautics and Space Administration’s (NASA) Moderate Resolution Imaging Spectroradiometer (MODIS) sensors for 36 spectral bands and derivative products. Two MODIS platforms, Terra and Aqua, are in sun-synchronous, near-polar, circular orbits with 10:30 a.m. ascending and 1:30 p.m. descending nodes, respectively. One of the available MODIS products, Land Surface Temperature (LST), is produced using the generalized split-window LST algorithm [28,29]. It is available daily at 1 km2 spatial resolution for most of the planet and is a measure of thermal conditions at the Earth’s surface. These conditions are influenced by air temperature, climate, surface geology, vegetation, elevation, and physiography, among other factors, and these are the same factors that influence the temporal and spatial variation of temperature in many stream systems. In this paper, we provide examples of using public LST data to estimate stream water temperature in a spatio-temporally continuous manner in watersheds where we have a set of point-wise stream temperature observations from in-water sensors. We are not attempting to directly estimate water temperature from LST (like, for example, direct estimates of sea surface temperature [30]).Water Instead, we use LST as a covariate in linear models, first in the John Day River 2015, 7, page–page (JDR; a tributary to the Columbia River, USA) and then in other interior Columbia River (ICR) split-window LST algorithm [28,29]. It is available daily at 1 km spatial resolution for most of the basins (the Lemhi planet (LRB), (TRB),conditions Upperat Grande Ronde (UGR) and Wenatchee (WRB) Rivers and Tucannon is a measure of thermal the Earth’s surface. These conditions are influenced by air and temperature, climate, surface vegetation,and elevation, and physiography, (Figure 1)), at spatial temporal scalesgeology, of reaches days. We choseamong the other JDR basin for several factors, and these are the same factors that influence the temporal and spatial variation of reasons. First, it istemperature one of the longest undammed rivers in the continental United States [31], which in many stream systems. In this paper, we provide examples of using public LST data to estimate stream water temperature makes it an idealincandidate for elucidating spatially variable relationships between land surface a spatio-temporally continuous manner in watersheds where we have a set of point-wise stream and water temperature. Second,from thein-water Johnsensors. DayWeRiver habitat for water Endangered Species temperature observations are not provides attempting to directly estimate from LST (like, for example, direct estimates of sea surface temperature [30]). Instead, we use Act (ESA) listed temperature steelhead (Oncorhynchus mykiss) and bull trout (Salvelinus confluentus), as well LST as a covariate in linear models, first in the John Day River (JDR; a tributary to the Columbia River, USA)(O. and then in other interior Columbia River (ICR)trout basins (the Lemhi (LRB), Tucannon (TRB), as Chinook salmon tshawytscha) and several species (cutthroat (O.Upper clarkii) and redband Grande Ronde (UGR) and Wenatchee (WRB) Rivers (Figure 1)), at spatial and temporal scales of reaches (O. mykiss gairdnerii)). basin unique inreasons. thatFirst, there are nolongest hatchery released into and days.The We chose the JDRisbasin for several it is one of the undammedsalmonids rivers in United important States [31], whichhabitat makes it an for ideal candidate for elucidating spatially variable the JDR, and thusthe itcontinental provides wild fish populations. Moreover, the size, relationships between land surface and water temperature. Second, the John Day River provides habitat topology, and geographic extent Day basin makes deployment of temperature loggers for Endangered Species of Act the (ESA) John listed steelhead (Oncorhynchus mykiss) and bull trout (Salvelinus confluentus), as well as Chinook salmon (O. tshawytscha) and several trout species (cutthroat (O. clarkii) challenging, therefore modeling stream temperature using remote data sources is an appealing option and redband (O. mykiss gairdnerii)). The basin is unique in that there are no hatchery salmonids released for managers. Other basins, notimportant as large as for thewild JDR, also provide important fish habitat in a into ICR the JDR, and thuswhile it provides habitat fish populations. Moreover, the size, topology, and geographic extent of the John Day basin makes deployment of temperature loggers variety of landscape contexts. Our specific objectives were to: (1) estimate stream temperature using challenging, therefore modeling stream temperature using remote data sources is an appealing option for managers. Other basins, while not as(2) largeevaluate as the JDR, also provide important fish habitat in a variety remotely-sensed MODIS landICRsurface data; the predictive capability of models developed of landscape contexts. Our specific objectives were to: (1) estimate stream temperature using at site, subwatershed, and basin scales; and (3) assess how many sites in a basin remotely-sensed MODIS land surface data; (2) evaluate the predictive capability of models developed at are necessary to site, subwatershed, and basin scales; and (3) assess how many sites in a basin are necessary to develop develop robust temperature estimates. 2

robust temperature estimates.

Figure 1. Interior Columbia River basins included in this analysis: JDR = John Day River, LRB = Lemhi River, TRBbasins = Tucannon River, UGR Upperanalysis: Grande Ronde, and = WRB = Wenatchee Figure 1. Interior Columbia River included in= this JDR John Day River, LRB = Lemhi River. The map area extends from 43°30′ N to 49°18′ N latitude and 112°24′ W to 121°48′ W longitude. River, TRB = Tucannon River, UGR = Upper Grande Ronde, and WRB = Wenatchee River. The map 3 112˝ 241 W to 121˝ 481 W longitude. area extends from 43˝ 301 N to 49˝ 181 N latitude and

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Water 2015, 7, page–page 2. Study Area

2. Study Area River basin covers ~668,000 km2 in the Pacific Northwest of North America. The Columbia The John The Day River River basinbasin includes over 15,000 kilometers ~20,000The km2 in the Pacific Northwest covering of North America. Columbia covers ~668,000 km2 instream 2 in north-central John DayOregon, River basin includes over streamin kilometers ~20,000 kmrange north-central USA (Figure 2).15,000 Elevations the Johncovering Day River basin from 82 to over Oregon, (Figure in the JohnElkhorn, Day Riverand basin range from mountain 82 to over 2700 m, and it 2700 m, and itUSA drains parts2).ofElevations the Ochoco, Blue, Strawberry ranges, ultimately drains parts of the Ochoco, Elkhorn, and Strawberry mountain ultimately ending the Day ending at the Columbia River.Blue, Notable natural features within theranges, watershed include theatJohn River. Notable natural features within the watershed include the John Day Fossil Beds Fossil Columbia Beds National Monument, parts of the Ochoco, Umatilla, and Malheur National Forests, and National Monument, parts of the Ochoco, Umatilla, and Malheur National Forests, and 237.4 km of 237.4 km of Wild and Scenic designated rivers [32]. The flora ranges from sage-steppe near the mouth Wild and Scenic designated rivers [32]. The flora ranges from sage-steppe near the mouth to high to high desert grasslands fir forests the mountains. is anatural single barrier naturaltobarrier desert grasslands and and pinepine and and fir forests in theinmountains. There isThere a single to anadromous fish forkofofthe theJDR, JDR, and otherwise mainstem, middle, anadromous fishpassage passage on on the the south south fork and otherwise the the mainstem, middle, and and north north forksforks are are entirely undammed andwinter winter and spring fluctuate based on precipitation entirely undammed and and spring flowsflows fluctuate based on precipitation and snowmelt. Stream structure and temperature in the JDR has been altered through historic and and snowmelt. Stream structure and temperature in the JDR has been altered through historic and contemporary mining, logging, grazing,and andwater water withdrawal throughout the basin [33]. [33]. contemporary mining, logging, grazing, withdrawalactivities activities throughout the basin

FigureFigure 2. John DayDay River basin. Green thelocation location temperature logger sites across 2. John River basin. Greendots dotsrepresent represent the of of all all temperature logger sites across all years. The yellow star is the site upstream of Camas Creek. all years. The yellow star is the site upstream of Camas Creek. The Lemhi River (LRB) is a tertiary tributary to the Columbia River located in SW Idaho, USA.

The Lemhi River (LRB) is a tertiary tributary to the Columbia River located in SW Idaho, USA. It is ~100 km long and drains parts of the Lemhi and Bitterroot ranges. The Tucannon River is a It is ~100 km long and to drains parts of River the Lemhi and Bitterroot Tucannon River is a secondary tributary the Columbia in SE Washington, USA.ranges. It flows The for ~80 km, draining 2 secondary to theButte Columbia in SE Washington, USA.Upper It flows for ~80 km, draining ~1300 tributary km of Oregon in the River Blue Mountain range [34]. The Grande Ronde River is part ofButte the Grande Ronde subbasinrange located in theThe NE corner Oregon, Ronde USA. It River ~1300watershed km2 of Oregon in the BlueRiver Mountain [34]. UpperofGrande drainsis~4248 of the Blue and Wallowa Mountains[35]. The Wenatchee River basinof is Oregon, the most USA. watershed partkm of2 the Grande Ronde River subbasin located in the NE corner 2 and is located in central Washington, USA. 2 northern basin included in this analysis and is ~3500 km It drains ~4248 km of the Blue and Wallowa Mountains [35]. The Wenatchee River basin is the most northern basin included in this analysis and is ~3500 4 km2 and is located in central Washington, USA. It drains portions of the eastern Cascade Crest. It has the broadest elevational range of the included watersheds (185–2870 m). 6830

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3. Materials and Methods 3.1. Geospatial Data Vector coverages of stream segments in the included basins were generated using a 10 m DEM [36] with the Functional Linkage of Waterbasins and Streams (FLoWs) toolbox in ArcGIS 9.3 [37,38]. FLoWs builds a flow-directed network from a DEM and partitions the landscape into land surface drainage areas. For example, the derived network for the John Day included 5532 stream reaches, defined as each confluence-to-confluence stream extent. The FLoWS toolbox was also used to generate reach-contributing area (RCA) polygons representing the non-overlapping land surface area draining into each stream segment. These RCAs were used as the working spatial resolution of analysis and prediction, and averaged in area about 3.7 km2 (standard deviation 3.28 km2 ) within the JDR. Elevation for each RCA was taken from a 10 m digital elevation model for the downstream boundary of the defining stream segment [39]. Elevation at each logger site was also determined. 3.2. Land Surface Temperature Data and Handling Data Gaps Daily Land Surface Temperature (LST) for 2000–2009 (MOD11A1 v005, 1 km2 spatial resolution rasters), and 8-day LST (MOD11A2 v005) for 2012 (also 1 km2 ), from the MODIS sensor were downloaded from NASA’s Earth Observing System Data and Information System [40]. The native Hierarchical Data Format (HDF) files are in a NASA-defined global sinusoidal projection. We extracted the “LST_Day_1 km” Scientific Data Sets, and converted them to Environmental Systems Research Institute (ESRI) raster format [41]. We reprojected the data to a user-defined Albers equal-area conic projection using a NAD83 datum. We clipped the daily data to the JDR extent, and the 8-day data to each basin extent, using the Marine Geospatial Ecology Tools (MGET) in ArcGIS [42]. Error estimates for MODIS v005 LST are 1 K were excluded from the analysis. Time series gaps sometimes occur in LST due to atmospheric conditions and satellite location and function. In the JDR, multi-day gaps in image availability often occur from dense cloud cover, obscuring sensing for hours to days, particularly in the winter months. Rarely, multi-day gaps due to sensor malfunction can also occur. The daily data was more likely than the 8-day data to have gaps, though occasional gaps did occur in the 8-day data. As a result, it was necessary to develop a gap-filling method such that predictions of water temperature would be spatially and temporally continuous throughout the basins. Gap-filling methods were developed on the daily LST data. Three approaches to gap-filling were considered: use of an alternate data source, temporal interpolation and spatial interpolation. We first tested an alternative remotely-sensed data source as a gap filler for the daily data: the Advanced Microwave Scanning Radiometer—Earth Observing System (AMSR-E) data, a passive microwave sensor that collects brightness temperature measurements (radiance of microwave radiation coming from the Earth’s surface). Microwave radiation is cloud penetrating, so this sensor offers a potential supplemental data source when MODIS LST is unavailable due to weather conditions [45,46]. Conveniently, the AMSR-E and MODIS sensors are both aboard the same satellite platform and therefore have a common spatial and temporal domain. We downloaded daily daytime descending pass AMSR-E brightness temperature for bands at 18, 23, 36, and 89 GHz (EASE grid format, 25 km2 spatial resolution) from the National Snow and Ice Data Center (NSIDC) [47]. Unfortunately, an artifact of the AMSR-E swath geometry and location of the JDR limits data availability in parts of the JDR every 5th day, so not all gaps could be filled using this method. Following Mao et al. [45], we parameterized and used the following polynomial structure to fill LST gaps: LST „ α ` β 89v ` β2 p36v ´ 23vq ` β3 p36v ´ 23vq2 ` β4 p36v ´ 18vq ` β5 p36v ´ 18vq2

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We also a temporal linear interpolation to estimate missing LST values using the timeSeries Water 2015,used 7, page–page package interpNA function in R [48] to fill gaps within the LST data. This function generates a We also used a temporal linear interpolation estimate missing values usingofthe timeSeries linear interpolation across any missing values in atotime series and isLST independent spatial location. package interpNA function in R [48] to fill gaps within the LST data. This function generates a linear Linear interpolations were done on each year’s daily LST data independently on a pixel-by-pixel interpolation across any missing values in a time series and is independent of spatial location. Linear basis. As this approach requires values on either side of data gaps in the time series, if the Julian day interpolations were done on each year’s daily LST data independently on a pixel-by-pixel basis. As 1 or 365(6) in any year had a missing value, an estimate for that value was made using a 4th order this approach requires values on either side of data gaps in the time series, if the Julian day 1 or 365(6) polynomial builthad on athe entirevalue, year’sandata. in any year missing estimate for that value was made using a 4th order polynomial Since spatial interpolation method are commonly used to generate spatially continuous data from built on the entire year’s data. patchy data [25], we tried filling method gaps with universal used kriging and inverse distance weighting (IDW) Since spatial interpolation are commonly to generate spatially continuous data from patchy data [25],after we tried filling review gaps with universal kriging and inverse distance (IDW) methods. However, the initial of these models, kriging and IDW wereweighting poor interpolators methods. thecover initialtended review of models, kriging and IDW poor interpolators for for LST, likelyHowever, because after cloud tothese be spatially continuous butwere temporally patchy, leaving LST, likely because cloud cover tended to be spatially continuous but temporally patchy, leaving little little data to interpolate from [49,50]. We therefore did not continue to pursue these methods. data to interpolate from therefore did not continue to pursue methods. To assess the utility of[49,50]. the twoWe remaining gap-filling methods wethese compared the predictive power To assess the utility of the two remaining gap-filling methods we compared the predictive power of unfilled vs. gap-filled daily LST for sites in each year that had a complete annual time series of Daily of unfilled vs. gap-filled daily LST for sites in each year that had a complete annual time series of Mean Water Temperature (DMWT) data. We used root mean squared error (RMSE) and the predicted Daily Mean Water Temperature (DMWT) data. We used root mean squared error (RMSE) and the residual sum ofresidual squaressum (PRESS) statistics as measures Once power. time-series predicted of squares (PRESS) statistics ofaspredictive measures power. of predictive Oncegaps were time-series filled usinggaps the linear method, area-weighted means of daily LST were calculated for each were filled using the linear method, area-weighted means of daily LST wereRCA by intersecting the RCA andby 1 intersecting km grid polygons ArcGIS (Figure 3). in ArcGIS (Figure 3). calculated for each RCA the RCAin and 1 km grid polygons

Figure 3. Example of LST gap-filling for one site in the JDR in 2003. Blue highlight is the original

Figure 3. Example of LST gap-filling for one site in the JDR in 2003. Blue highlight is the original unfilled LST data: pink lines and points are gap-filled using the AMSR-E method and the black line unfilled LST data: pink lines and points are gap-filled using the AMSR-E method and the black line is is gap-filling using a simple linear interpolation. gap-filling using a simple linear interpolation.

3.3. In-Stream Thermal Logger Data

3.3. In-Stream Thermal Logger Data

Daily summaries of hourly water temperature data from stream temperature loggers in the JDR were as dailyof model response and fordata model parameterization and validation. Daily used summaries hourly watermetrics temperature from stream temperature loggersWe in the utilized publically available logger data for sites where data had been collected between 2000 and JDR were used as daily model response metrics and for model parameterization and validation. 2009 bypublically tribal, state,available and federal organizations unique anddata opportunistic monitoring We utilized logger data forfor sites where had been collectedpurposes. betweenThese 2000 and data had been compiled as part of the Integrated Status and Effectiveness Monitoring Program [51] and 2009 by tribal, state, and federal organizations for unique and opportunistic monitoring purposes. were reviewed and filtered prior to generating summary metrics of daily mean and maximum These data had been compiled as part of the Integrated Status and Effectiveness Monitoring temperature (Figure 2). We utilized both automated data quality checks and a visual review of all Program and were reviewed and filtered to generating summary metrics dailyairmean data [51] to remove common anomalies in waterprior temperature data, such as leading and of tailing and maximum temperature (Figure 2). We utilized both automated data quality checks and a visual temperature readings, drying during low flow periods and burial in sediments [52]. Stream review of all data to remove common anomalies in water temperature data, such as leading temperature logger data sets were patchy in both space and time, as loggers were deployed by and tailingvarious air temperature drying during low flowtoperiods burialyears. in sediments [52]. Stream agencies in readings, different locations for less-than-one several and concurrent Most commonly, loggers were deployed from latepatchy spring in through early fall. temperature logger data sets were both space and time, as loggers were deployed by various Logger datalocations from 510 spatially unique JDR across all years were within models agencies in different for less-than-one to sites several concurrent years.included Most commonly, loggers (Figure 2). The number of sites varied across years ranging from 13 in 2005 to 215 in 2001 (Table 1). were deployed from late spring through early fall. Each site with at least 40 days of stream temperature measurements within a year was included in

Logger data from 510 spatially unique JDR sites across all years were included within models (Figure 2). The number of sites varied across years ranging from 13 in 2005 to 215 in 2001 (Table 1). 6 measurements within a year was included in the Each site with at least 40 days of stream temperature 6832

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dataset (the days did not have to be consecutive). The data set included 520 site-years (79,790 logger days) across all years (many sites had data from multiple years). Table 1. Number of temperature logger sites and days of data per year for the John Day River daily datasets included in these analyses. Year

2000

2001

2002

Sites Days

50 6200

64 72 11,470 10,869

2003

2004

2005

2006

2007

2008

2009

Total

46 7667

54 5705

24 4658

31 4494

45 7195

45 9991

89 520 11,541 79,790

Analyses were conducted in other ICR basins to assess 3 things: model sensitivity to data density, the relationship between LST and stream temperature in basins other than the JDR, and model quality effects of coarser temporal partitioning. Four other ICR basins were selected (the Lemhi, Tucannon, Upper Grande Ronde, and Wenatchee), along with the JDR, to represent the geomorphic and topological variability across the ICR. These basins are included in the Columbia Habitat Monitoring Program (CHaMP), and have temperature data collected following CHaMP protocols as part of a systematic, cross-agency effort to standardize fish habitat characterization methods across the interior Columbia River basin (champmonitoring.org). We utilized publically available 2012 logger data from CHaMP. 2012 had the most data available across all the basins. Eight-day summaries of hourly water temperature data from stream temperature loggers in the included basins were used as 8-day model response metrics and for model validation. Logger data were reviewed and filtered in a similar fashion as the daily data. CHaMP program data collection utilizes a spatially balanced survey design [53] and loggers are left instream year-round, with some sites visited annually and others on a 3-year rotating cycle. Sites are visited and logger data downloaded mid-year, so some sites only had logger data from either the first or second halves of the year, but those time-series were complete. While the 2000–2009 daily data were temporally patchy, the 2012 CHaMP temperature logger data were temporally continuous within each half of the year with few data gaps. 3.4. Model Development We developed simple fixed-effects linear models for a 10-year period (2000–2009) in the JDR. Mean elevation, stream gradient, and upstream catchment area are spatially continuous variables that have been shown to correlate with stream temperature (e.g., [54]) and were also considered as model predictor variables. Because there is spatial structure in the LST data, and the spatially continuous variables are correlated with each other, we used a simple linear regression of each candidate predictor variable on LST for the entire basin for all years to elucidate predictor variable correlation, and reviewed residuals before considering predictor inclusion in the LST model. Annual, 4th order polynomial models were briefly considered to model the annual temperature curve, but they yielded no better results than simple linear models and had less spatial predictive power due to over-fitting effects and were therefore excluded from the model development process. We used a cross-correlation function (CCF) (Time Series Analysis (TSA) package in R) [55] to test for any significant time lags in the correlative relationships between LST and water temperature which would occur if land surface warming or cooling events detected in the LST were not reflected in concurrent water temperatures but instead lagged, and vice versa. We developed a CCF for data from 10 randomly selected sites around the basin. Daily mean water temperature and LST have shared time series structure, so a time series model for LST was parameterized using autoregressive [AR(1)] models. Residuals from this model were used to filter DMWT. This created a “white noise” series for input into the CCF from which significant lags can be identified. This process is known as prewhitening and differencing [56]. This was done to each time series included and significant lags were identified through significant cross-correlations.

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It was necessary to review the possible effects of using a land-surface based temperature with no limit in range to predict water temperature data, which have a floor of possible values. For example, no water temperatures below ´0.5 ˝ C were observed in our data while land surface temperatures do fall below ´0.5 ˝ C in winter months. We used censored regression (“tobit” models [57,58]) which sets a limit on the possible values of the dependent variable in one or both directions: in this case, a floor of ´0.5 ˝ C was set (VGAM R package) [59]. We compared these results to Ordinary Least Squares (OLS) models that we truncated a posteriori, so any predicted water temperature values below ´0.5 ˝ C were truncated to ´0.5 ˝ C. The tobit models may result in less prediction bias if the censored results are meaningful. However, because the tobit models include a latent variable which can complicate interpretation, the OLS approach would be preferred if censoring bias is not present. Both spatial and temporal factors were tested during model development. Models were built at three spatial scales: individual models for each logger site (“site-specific models”); four models for each year built on aggregate datasets for each of the four 6th-field Hydrologic Units [60] in the basin (“HUC” models, for “Hydrologic Unit Code”); and a basin-wide model using all available logger data within the JDR (“global model”). We used the site-specific models to evaluate the utility of LST as a model covariate to estimate stream temperature. The HUC and global models were developed as broad spatial scale models that might be more attractive products to conservation managers, but may have lower predictive accuracy. Models were developed at three temporal scales since the relationship between model predictor variables and LST may vary annually and seasonally. We developed a global model using all data across all years, and a global model including year and seasonal terms. Initial modeling efforts indicated that the model parameter estimates differed between the first and second halves of the year, so semi-annual models should be considered. So, we developed models at each spatial scale for each year, splitting data into two sets based on the date of the maximum DMWT and developed separate models for each half of the year. We predicted daily mean stream temperature for every reach in the JDR for the 10 year period and then compared estimates to observed stream temperature logger data for validation. We assessed model quality and predictive power using two data-subsetting techniques to parse out data used for validation: (1) comparing Predicted Residual Sums of Squares (PRESS) produced from a leave-one-out (LOO) cross-validation on the daily data and (2) goodness of fit metrics from a leave-one-out jackknife by site. In each jackknife iteration (n = 100), data were sampled without replacement, such that data from N-1 sites were used to parameterize the models. The parameterized models in each iteration were used to estimate daily mean stream temperature across the basin, and data from the excluded site (“validation data”) was used to test predictive accuracy. Predicted Root Mean Squared Errors (RMSEPs) were calculated for the validation data and used as model quality metrics. Root Mean Squared Errors (RMSEs) were also calculated for models at all spatial scales to assess goodness-of-fit and predictive power. Final model structure selection within years was made using Akaike information criterion (AIC) [61]. Eight-day models were developed as fixed-effects linear models for each basin with no spatial partitioning using aggregated logger data for that basin. Similar to the daily models, the data were split into first and second halves of the year. LST, LST2 , Julian day, and elevation were included as candidate variables. Potential model structures that were considered included: a b c d e

Temp ~ LST Temp ~ LST + LST2 Temp ~ LST + JulianDay Temp ~ LST + JulianDay + Elevation Temp ~ LST + LST2 + JulianDay + Elevation

Final model structure for each half of the year in each basin was determined using PRESS statistic and AIC. Area under the curve (AUC) was calculated for some sites for estimated annual time series to provide a metric to compare inter-annual variation at a site. 6834

Water 2015, 7, 6827–6846

3.5. Sensitivity Analysis Once final model structure was determined, the 8-day data were subjected to a jackknife approach to generate test statistics of model quality with decreasing sample size. In each jackknife iteration (n = 100), data were sampled without replacement, such that data from i sites were used to parameterize the models. The data were also bootstrapped (n = 100) to generate standard errors of the parameter estimates. The parameterized models in each iteration were used to estimate 8-day stream temperature across the basin, and data from N-i excluded sites (“validation data”) were used to test predictive accuracy. RMSEPs and p2 s (r2 analogue from the validation data) were calculated for the validation data and used as model quality metrics. This process was repeated for each basin for each i of 2 . . . N-(N/2) where “N” is the total number of sites for each half year within a basin. Water 2015, 7, page–page

4. Results

iteration (n = 100), data were sampled without replacement, such that data from i sites were used to parameterize the models. The data were also bootstrapped (n = 100) to generate standard errors of 4.1. Estimating the Missing Land Surface Data in each iteration were used to estimate 8-day parameter estimates. TheTemperature parameterized models stream temperature across the basin, and data from N-i excluded sites (“validation data”) were used Linear interpolation AMSR-E gapp2sfilling methods produced adequate proxies for to test predictiveand accuracy. RMSEPs and (r2 analogue from the both validation data) were calculated for the validation data and used as model quality metrics. This process was repeated for each basin interpolation daily LST data as RMSE and PRESS statistics were similar yet low, though the linear for each i of 2…N-(N/2) where “N” is the total number of sites for each half year within a basin.

performed marginally better. The AMSR-E approach also still left some gaps in the data that Results 3). Although the AMSR-E alternative data source approach was successful, required filling4. (Figure the data processing, computational time, and management overhead necessary were intensive and 4.1. Estimating Missing Land Surface Temperature Data much greater thanLinear theinterpolation simple linear approach. We therefore concluded a simple temporal linear and AMSR-E gap filling methods both produced adequate proxies for daily LST data as RMSE and PRESS statistics were similar yet low, though the linear interpolation interpolation was most effective for filling in cloudy-day gaps in the LST for use in our models. performed marginally better. The AMSR-E approach also still left some gaps in the data that required filling (Figure 3). Although the AMSR-E alternative data source approach was successful, the data 4.2. Predictor Variable Selection and Temporal Lag Analyses processing, computational time, and management overhead necessary were intensive and much

greater than the simple linear approach. We therefore concluded a simple temporal linear We reviewed the residuals from linear regressions of potential predictor variables and stream interpolation was most effective for filling in cloudy-day gaps in the LST for use in our models. temperatures to determine the most informative and least correlated physiographic variables to include 4.2. Predictor Variable Selection and Temporal Lag Analyses in the LST model. Gradient, catchment area, stream order, an estimate of mean annual flow, and reviewed the residuals from linear regressions of potential predictor variables and stream elevation were allWe considered. Though all the physiographic variables were significantly correlated temperatures to determine the most informative and least correlated physiographic variables to with stream temperature andmodel. LST,Gradient, they were alsoarea, significantly each flow, other. There was a include in the LST catchment stream order,correlated an estimate of with mean annual and elevationnegative were all considered. Though all the the physiographic variables significantly slight though significant relationship between residuals from awere linear model and elevation, correlated with stream temperature and LST, they were also significantly correlated with each other. so elevation was included as though the representative physiographic candidate variable. The final models used There was a slight significant negative relationship between the residuals from a linear model elevation, so elevation was includedvariables as the representative physiographic candidateas variable. The LST, Julian day,and and elevation as predictor and water temperature the response variable. final models used LST, Julian day, and elevation as predictor variables and water temperature as the A cross-correlation analysis on prewhitened and differenced annual time series of DMWT and response variable. LST showed a zero lag with theanalysis highest cross-correlation function coefficient for all A cross-correlation on prewhitened and differenced annual time series of DMWT and included sites showed lag with the highest cross-correlation coefficient for all included sites4). Therefore, indicating thatLST LST anda zero water temperature data were function aligned temporally (Figure indicating that LST and water temperature data were aligned temporally (Figure 4). Therefore, we we used a direct temporal alignment for building. used a direct temporal alignment formodel model building.

Figure 4. Cross-correlation function for pre-whitened and differenced time series of DMWT and LST

Figure 4. Cross-correlation function pre-whitened series of DMWT and LST for one site in the JDR showingfor the highest correlation atand lag 0.differenced Blue dotted linetime indicates significance threshold of p < 0.05. for one site in the JDR showing the highest correlation at lag 0. Blue dotted line indicates significance 9 threshold of p < 0.05.

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4.3. Daily Model Performance Across Temporal 4.3. Daily Model Performance Across TemporalScales Scalesin in the the JDR JDR a strong correlative relationshipbetween between DMWT across all all sitessites and and yearsyears ThereThere is a is strong correlative relationship DMWTand andLST LST across (Figure (Figure 5). 5).

Figure 5. Relationship betweenDaily Daily Mean (°C)(˝and Surface Temperature (K) Figure 5. Relationship between MeanWater WaterTemperature Temperature C) Land and Land Surface Temperature for all sites, 2000–2009 in the John Day River basin. The black line and r2 are from a simple linear (K) for all sites, 2000–2009 in the John Day River basin. The black line and r2 are from a simple linear regression (DMWT ~ LST). regression (DMWT ~ LST).

There was no significant difference in global models including all data across years from a tobit or OLSwas model 2). This is likely due to the fact that the censoredall aspect the water data is not There no (Table significant difference in global models including dataofacross years from a tobit a sampling error,2). butThis actually representative thethat true the population of aspect water temperatures, so there or OLS model (Table is likely due to theoffact censored of the water data is not a is noerror, bias but for actually which to correct. Truncating the population DMWT predictions from the OLSsomodels sampling representative of the true of water temperatures, there is no a posteriori allowed for direct interpretation of the model coefficients without biasingathe results.allowed All bias for which to correct. Truncating the DMWT predictions from the OLS models posteriori models generated for spatial scale comparisons were built using simple linear regressions. for direct interpretation of the model coefficients without biasing the results. All models generated for spatialTable scale2.comparisons were built using simple linear RMSEs (in °C) and r2 from OLS and Tobit models builtregressions. using all data for the JDR across years. Models using LST only and LST + year and seasonal terms are included.

Table 2. RMSEs (in ˝ C) and r2 from OLS and Tobit models built using all data for the JDR across years. N = 79,790 Days Models using LST only and LST + year and seasonal terms are included. Model Fixed Effects r2

OLS

Model

OLS

DMWT ~ LST

Fixed Effects

DMWT ~ LST + year

RMSE

N = 79,790 Days 0.76 2.74 2

r 0.77

RMSE 2.85

OLS DMWTDMWT ~ LST + ~ year + season 0.77 2.85 OLS LST 0.76 2.74 OLS DMWT ~ LST + year 0.77 2.85 Tobit DMWT ~ LST 0.76 2.80 OLS DMWT ~ LST + year + season 0.77 2.85 Tobit DMWT ~ LST + year 0.77 2.75 Tobit DMWT ~ LST 0.76 2.80 Tobit DMWT ~ LST + year season 0.76 2.80 Tobit DMWT ~ LST + +year 0.77 2.75 Tobit DMWT ~ LST + year + season 0.76 2.80 The basin-wide model including all variables across all sites and all years (2000–2009) had reasonable goodness-of-fit metrics (r2 = 0.77, RMSE 2.85) (Table 2). Global models across all sites and The basin-wide including all variables sites halves and all (2000–2009) all years includingmodel a year term, a “season” term (i.e., across first andallsecond of years the year split by the had reasonable metrics (r2 a=year 0.77,and RMSE 2). Global across all sites highestgoodness-of-fit DMWT in the year), and both season2.85) term,(Table performed no bettermodels than global models with no temporal terms. However, separate individual global models for each season’s data and all years including a year term, a “season” term (i.e., first and second halves of the year split 2 = 0.82, RMSE = 2.33) (Table 3). performed (“Spring” = 0.82,a RMSE = 2.63;season “Fall” rterm, by the highest significantly DMWT in better the year), andr2both year and performed no better than seasonal data together the utility of including Julian day inmodels the models, as Julian globalLumping models the with no temporal terms.negates However, separate individual global for each season’s day is positively correlated with temperature2(both water and land surface) in 2the first half of the data performed significantly better (“Spring” r = 0.82, RMSE = 2.63; “Fall” r = 0.82, RMSE = 2.33) year, and negatively correlated in the second. Model quality improved even more when models were (Table 3). Lumping the seasonal data together negates the utility of including Julian day in the models, built on each year’s data using the seasonal split (mean across years r2 = 0.83, RMSE = 2.24). All as Julian day is positively correlated with temperature (both water and land surface) in the first half of subsequent modeling included models by year and the seasonal split in the data.

the year, and negatively correlated in the second. Model quality improved even more when models 10 were built on each year’s data using the seasonal split (mean across years r2 = 0.83, RMSE = 2.24). All subsequent modeling included models by year and the seasonal split in the data.

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Table 3. Model comparison of global models built including all sites across all years, those including Water 2015, 7, page–page year and season terms, and those split into two datasets based on the highest DMWT across each year (“Spring” “Fall”). “Year” models are the metrics foracross models builtthose on each year’s data Table 3.and Model comparison of global models builtmean including all sites all years, including (including a and seasonal year seasonsplit). terms, and those split into two datasets based on the highest DMWT across each year (“Spring” and “Fall”). “Year” models are the mean metrics for models built on each year’s data (including a seasonal split). Model Fixed Effects RMSE r2 Fixed Effects GlobalModel DMWT ~ LST GlobalGlobal DMWT ~ LST + year DMWT ~ LST GlobalGlobal DMWTDMWT ~ LST~+LST year + season + year Global DMWT ~ LST + LST2 + Elev Global DMWT ~ LST + year + season Spring DMWT ~ LST + LST2 + Elev + JulDay Global DMWT ~ LST + LST2 + Elev Fall DMWT ~ LST + LST2 + Elev + JulDay + Elev DMWT ~ LST LST22 + Year Spring DMWT ~ LST + +LST Elev++JulDay JulDay

RMSE 2.74

r2 0.76

2.85 2.74 2.85 2.85 2.83 2.85 2.63 2.83 2.33 2.63 2.24

0.76 0.77

0.77 0.82 0.77 0.82 0.82 0.83

0.77 0.77 0.77

Fall

DMWT ~ LST + LST2 + Elev + JulDay

2.33

0.82

Year

DMWT ~ LST + LST2 + Elev + JulDay

2.24

0.83

4.4. Annual, Daily Model Performance across Spatial Scales in the John Day River Basin Model as Performance acrossusing SpatialAIC Scales in each the John Dayand River Basin spatial partitions most Best4.4. fitAnnual, modelDaily structure determined for year across 2 Best fit model structure determined AIC Day for each year and across spatial partitions often took the form of DMWT ~ as LST + LST using + Julian + Elevation. Elevation was notmost significant 2 + Julian Day + Elevation. Elevation was not significant in often took the form of DMWT ~ LST + LST in the global models in 2003. As elevation does not vary at a site, site-specific models took the form the global models in 2003. As elevation does not vary at a site, site-specific models took the form DMWT ~ LST + LST2 + 2Julian Day. Site-specific models had a mean RMSE across all sites and all DMWT LST + LST + Julian Day. Site-specific models had a mean RMSE across all sites and all years ˝ ~ (sd: years of of 1.28 0.11)(Figure (Figure 1.28 C °C (sd: 0.11) 6).6). 2 The p The across all sites andand all all years validation forsite-specific the site-specific p2 across all sites yearsfor forthe the leave-one-out leave-one-out validation datadata for the models had a mean of 0.86. TheThe site-specific almost in prediction, while the models had a mean of 0.86. site-specificmodels models showed showed almost no no biasbias in prediction, while the global andmodels HUC models showed slight bias towardunder-prediction under-prediction at high temperatures (Figure(Figure 7). global and HUC showed slight bias toward at high temperatures 7). This bias was also evident when the validation data were compared to estimated values. This bias was also evident when the validation data were compared to estimated values.

Root Mean Squared Errors from site-specific models for all years. Green dots are median values Figure 6.Figure Root6. Mean Squared Errors from site-specific models for all years. Green dots are median for the year; blue boxes are the first–third quartiles and the whiskers are the min and max values. values for the year; blue boxes are the first–third quartiles and the whiskers are the min and max values. HUC model quality varied from HUC to HUC and year to year, as did the number of sites and

days of data in each year. HUC and global models performed similarly across years. HUC models hadmodel a meanquality RMSE across all HUCs and allto years of 2.3 °C (sd: Global hadnumber a mean RMSE HUC varied from HUC HUC and year0.45). to year, asmodels did the of sites and across all years of 2.5 °C (standard deviation 0.26). HUC models performed slightly better than global days of data in each year. HUC and global models performed similarly across years. HUC models models in years with sufficient data in each HUC, but global models performed better than HUC ˝ C (sd: 0.45). Global models had a mean RMSE had a mean RMSE across HUCs alloryears 2.3 Of models in years withall little data and in one more of HUC. course, global models were necessary when ˝ C (standard deviation 0.26). HUC models performed slightly better than global across allthere years ofno 2.5data was in a HUC in a year. An example of ten yearsdata of temperature estimates one sitemodels is shownperformed in Figure 8. The site than is in HUC models in years with sufficient in each HUC, butforglobal better the North Fork John Day River above the confluence with Camas Creek (elevation 826 m). when models in years with little data in one or more HUC. Of course, global models were necessary

there was no data in a HUC in a year. 11 An example of ten years of temperature estimates for one site is shown in Figure 8. The site is in the North Fork John Day River above the confluence with Camas Creek (elevation 826 m). Temperature logger data at this site were available for about half the years included in this analysis, 6837

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Temperature logger data at this site were available for about half the years included in this analysis, Temperature logger data at this site were available aboutThere half the includedvariation in this analysis, complete timefor series. is years considerable but estimates were generated for the complete time series. between but in estimates were generated for the complete time series. There is considerable variation between and thethe shape of each annual curve. Though yearsyears 2003, 2003, 2006, years in both boththe themaximum maximumtemperature temperature and shape of each annual curve. Though years in both the maximum temperature and the shape of each annual curve. Though years 2003, 2006, and 2007 have very similar annual maximum daily means (AMDM) for the year (24.3, 24.0, 24.4 °C, 2006, and 2007 have very similar annual maximum daily means (AMDM) for the year (24.3, 24.0, and 2007 have very similar annual maximum daily means (AMDM) for the year (24.3, 24.0, 24.4 °C,˝ ˝ respectively), the AUCsthe forAUCs each year’s temperature profile differ: 2919,differ: 2849, and 3024 °C,and respectively 24.4 C, respectively), for each year’s temperature profile 2919, 2849, 3024 C, respectively), the AUCs for each year’s temperature profile differ: 2919, 2849, and 3024 °C, respectively (Table 4). Though 2007 was cumulatively warmer across the across entire the year, 2003year, was2003 bothwas warmer respectively (Table 4). Though 2007 was cumulatively warmer entire both (Table 4). Though 2007 was cumulatively warmer across the entire year, 2003 was both warmer sooner in the first half of the year and cooler sooner in the second half of the year than both 2006 and warmer in the first halfyear of the and cooler in the second theboth year2006 thanand both soonersooner in the first half of the andyear cooler sooner insooner the second half of the half year of than 2007.and Similarly, though 2004 had a2004 lower AMDM and lower and annual AUC at thisAUC site than either 2006 2006 2007. Similarly, though had a lower AMDM lower at this site than 2007. Similarly, though 2004 had a lower AMDM and lower annual AUCannual at this site than either 2006 or 2007, the AUC for 1 January–15 April is higher for 2004 (Table 4). either 2006the or AUC 2007, for the1AUC for 1 January–15 April higher for 4). 2004 (Table 4). or 2007, January–15 April is higher foris2004 (Table

Figure 7. Stream temperature predicted from the global, site-specific, and HUC models for Figure 7.7.Stream temperature predicted fromfrom the global, site-specific, and HUC models formodels 2000–2009 predicted the and HUC for 2000–2009Stream vs. the temperature observed values. The validation dataglobal, plot is site-specific, the jackknife-by-site, leave-one-out vs. the observed values. The validation data plot is the jackknife-by-site, leave-one-out validation 2000–2009 vs. the observed values. The validation data plot is the jackknife-by-site, leave-one-out validation data for all years vs. the predicted temperatures for those sites from the global models for data foryear. alldata years vs.allthe predicted for regression those sites from the global models forobserved each year. validation years vs. predicted for between those sites from the global models for each Thefor solid black linethe is temperatures the simple temperatures linear the predicted and The solid line regression between predicted andrelationship. observed and temperatures each year.black The solid linerelationship). islinear the simple linear regression between the predicted observed forsimple that The dashed line the is the one-to-one temperatures (withisblack r2the (with r2 for that relationship). The dashed line the one-to-one relationship. Theisdashed line is the one-to-one relationship. temperatures (with r2 for that relationship).

Figure 8. 8.Example daily mean meanstream streamtemperature temperaturefrom fromone one site across Figure Exampleofofobserved observed and and predicted predicted daily site across 10 10 years (2000–2009). The site is located on the North Fork John Day River above the confluence with years (2000–2009). The site is located on the North Fork John Day River above the confluence with Camas Creek. Blue dots are daily stream temperature andthe thegray gray line estimated Figure 8. Creek. Example of observed and predicted daily mean stream temperature from one site across Camas Blue dots areobserved observed daily mean mean stream temperature and line is is estimated daily stream temperature from site-specific models in years where data are available, and the black 10 daily years (2000–2009). The site is located on the North Fork John Day River above the confluence with stream temperature from site-specific models in years where data are available, and the black line is from HUC-based models. Camas Creek. Blue dots are observed daily mean stream temperature and the gray line is estimated line is from HUC-based models. daily stream temperature from site-specific models in years where data are available, and the black line is from HUC-based models. 12

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Table 4. Annual summary metrics for a site located in the North Fork John Day above the confluence TableCamas 4. Annual summary for daily a site mean located in the North Day confluence with Creek. Annual metrics maximum (AMDM), totalFork AreaJohn Under theabove Curvethe (AUC) in °C, with Camas AnnualApril, maximum daily mean (AMDM), total Area the AUC for Creek. 1 January–15 January–June, and July–December areUnder given.the Curve (AUC) in ˝ C, the AUC for 1 January–15 April, January–June, and July–December are given. Year

AMDM

2000

22.3

Year

2001 2002 2003 2004 2005 2006 2007 2008

AUC January-April

AMDM

22.9

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

2009

21.1 24.3 23.1 15.3 24.0 24.4 22.0

AUC January–June

290 AUC

AUC 1209

January–April 392

January–June 1332

290 392 244 376 267 63 218 225 132 395

1209 1068 1332 1270 1068 1270 839 839 431 431 1037 1037 1175 1175 660 660 998

22.3 22.9 21.1 24.3 23.1 15.3 24.0 24.4 22.0 18.3

244 376 267 63 218 225 132

18.3

395

AUC July–December

AUC 2281 July–December 1899

3491

AUC Total

3232

2281 1621 1899 1649 1621 1649 2128 2128 1148 1148 1812 1812 1849 1849 1887 1887 1919

998

AUC Total

3491 3232 2688 2919 2967 1579 2849 3024 2547 2917

1919

2688 2919 2967 1579 2849 3024 2547 2917

4.5. Eight-Day Model Performance and Sensitivity Analysis across Basins 4.5. Eight-Day Model Performance and Sensitivity Analysis across Basins The number of sites per season per year varied across basins, ranging from 0 in the spring in the The number of sites per season per year varied across basins, ranging from 0 in the spring in the Lemhi to 52 in the fall in the Upper Grande Ronde. Final model structure for the eight-day models for Lemhi to 52 in the fall in the Upper Grande Ronde. Final model structure2 for the eight-day models all basins took the same form as the daily models: 8DMWT ~ LST + LST + Julian Day + Elevation. for all basins took the same form as the daily models: 8DMWT ~ LST + LST2 + Julian Day + Elevation. Eight-day model quality metrics varied from basin to basin, with mean model metrics across all basins Eight-day model quality metrics varied from basin to basin, with mean model metrics across all of: r2 = 0.91 (sd: 0.02), RMSE 1.29 ˝ C (sd: 0.45) (Figure 9). Root mean squared prediction errors ranged basins of:˝r2 = 0.91 (sd: 0.02), RMSE 1.29 °C (sd: 0.45) (Figure 9). Root mean squared prediction errors from 1.2 C in the Wenatchee to 2.74 ˝ C in the Upper Grande Ronde (Table 5). ranged from 1.2 °C in the Wenatchee to 2.74 °C in the Upper Grande Ronde (Table 5).

Figure 9. 9. Eight-day Eight-day mean mean stream stream temperature temperature predicted predicted vs. observed observed for the leave-one-out validation Figure data for for all basins. The The solid solid black black line line isis the the simple simple linear linear regression regression between between the the predicted predicted and and data 2 for that relationship). The dashed line is the one-to-one relationship. 2 observed temperatures (with r observed temperatures (with for that relationship). The dashed line is relationship. ˝ C. RMSE ==1.29 1.29°C. RMSE 2 are Table 5. 5. Model Modelmetrics metricsfor for eight-day models all basins. RMSEP p2from are leave-one-out from leave-one-out Table eight-day models forfor all basins. RMSEP and pand cross cross validation. JDR =Day John Day LRB River, LRB = River, LemhiTRB River, TRB = Tucannon River, UGR =Grande Upper validation. JDR = John River, = Lemhi = Tucannon River, UGR = Upper GrandeWRB Ronde, WRB = Wenatchee Ronde, = Wenatchee River. River.

BasinBasin JDR LRB TRB UGR WRB

JDR LRB TRB UGR WRB

N Sites

N Sites

“Spring” “Spring” RMSE RMSEP r22

RMSEP

p2

p

N Sites

RMSE

r

11 11 0 0 10 31 10 9

1.70 1.70 1.32 1.80 1.32 0.81

0.91 0.91 0.91 0.88 0.91 0.95

2.38 2.38 1.962.66 1.96 1.20

0.91 0.91 0.90 0.88 0.950.90

31 9

1.80 0.81

0.88 0.95

2.66 1.20

0.88 0.95 13 6839

2

RMSE

N Sites

18 18 20 52 8

18 18 20 52 8

“Fall”“Fall” RMSEP r2 2

RMSE

1.56 1.22 0.97 1.65 0.90

r

2

p RMSEP

p2 0.92 0.91 0.96 0.92 0.94

0.93 1.560.91 1.220.96 0.92 0.970.94

2.33 0.93 2.32 1.97 0.91 2.74 0.96 1.75

0.92 2.33 0.91 0.96 2.32 0.92 1.97 0.94

1.65 0.90

0.92 0.94

2.74 1.75

Water 2015, 7, 6827–6846 Water 2015, 7, page–page

Results Results of of the the sensitivity sensitivity analysis analysis were were remarkably remarkablyconsistent consistentacross acrossbasins. basins. Model Model quality quality metrics for models parameterized using only two sites were not good for any basin, but improved metrics for models parameterized using only two sites were not good for any basin, but improved significantly significantlywith withincreasing increasingsample samplesize, size,stabilizing stabilizingat atapproximately approximatelyNN==44(Figure (Figure10). 10). Results Results were were similar similar for foreither eitherspring springor orfall fallmodels modelswithin withinaabasin. basin.

Figure 10. 10. Sensitivity squared errors errors (and (and standard standard deviation deviation of of those those Figure Sensitivity analysis analysis mean mean root root mean mean squared means) from the N-i site jackknife for all basins. Mean Root Mean Squared Errors on the Y-axis, and means) from the N-i site jackknife for all basins. Mean Root Mean Squared Errors on the Y-axis, and the number of included sites on the X-axis for all graphs. “Spring” indicates data from the first half of the number of included sites on the X-axis for all graphs. “Spring” indicates data from the first half thethe year (and across the the year. year. of year (and“Fall” “Fall”the thesecond secondhalf) half)asasdetermined determinedby bythe the peak peak mean mean temperature temperature across (a)Tucannon TucannonRiver River basin; (b) Upper Grande River (c) basin; (c) Wenatchee River basin; (a) basin; (b) Upper Grande RondeRonde River basin; Wenatchee River basin; (d) Lemhi (d) Lemhi (f) John Day River basin. River basin;River (e,f) basin;(e) John Day&River basin.

5. Discussion 5. Discussion We have have demonstrated demonstrated that that remotely-sensed remotely-sensed LST LST can can be be used used in in linear linear regression regression models models to to We generaterobust, robust,spatially spatiallyand andtemporally temporallycontinuous continuousestimates estimatesof of stream streamtemperature. temperature. The The strongest strongest generate relationship was between DMWT and LST, though the inclusion of Julian day did improve predictive relationship was between DMWT and LST, though the inclusion of Julian day did improve predictive power. Elevation Elevation was was not not included included in in the the site-specific site-specific models, models, and and itit was was not not always always significant significant in in power. the HUC HUC and and global global models. models. This This approach approach does does not not attempt attempt to to explicitly explicitly model model spatial spatial variation variation or or the network structure. Instead, we leverage the spatial structure inherent in the LST datasets to facilitate network structure. Instead, we leverage the spatial structure inherent in the LST datasets to facilitate the development development of of estimates estimates over over large large geographic geographic regions regions and and across acrossyears. years. We We found found that that other other the commonly used spatial variables often related to stream temperature did not increase model quality when included along with LST. The spatial structure inherent in the LST seems to captures that 6840 14

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commonly used spatial variables often related to stream temperature did not increase model quality when included along with LST. The spatial structure inherent in the LST seems to captures that spatial variation at the RCA scale; changes in the thermal profile on the landscape mirror changes in the thermal profile of the water. This is not to say that only near-stream local factors influence local Water 2015, 7, page–page temperatures, only that the patterns are co-variable. Model the scale; dailychanges JDR models was relatively consistent across spatial partitions. spatial performance variation at theofRCA in the thermal profile on the landscape mirror changes in thermal profile of thewhen water.the Thisdata is not to say that only near-stream influence localThis Modelthe quality did improve were partitioned into annuallocal andfactors seasonal subsets. the patterns are co-variable. could temperatures, be the resultonly of athat number of factors related to climate variation, or inter-annual variation in Model performance of the daily JDR wasof relatively consistent spatialin partitions. Model the data. For example, the number andmodels location sites with dataacross available each year varied quality did improve when the data were partitioned into annual and seasonal subsets. This could the out. considerably. A consistent dataset from the same sites across years could be used to teasebethis result of a number of factors related to climate variation, or inter-annual variation in the data. For example, This inter-annual variation could also be indicative of the broad climate difference between years the number and location of sites with data available in each year varied considerably. A consistent dataset (e.g., cold and dry, warm and wet) and bears further investigation. If broad climate categories can be from the same sites across years could be used to tease this out. This inter-annual variation could also be identified, models could potentially be generalized for future predictions basedand on expected changes indicative of the broad climate difference between years (e.g., cold and dry, warm wet) and bears in climate. further investigation. If broad climate categories can be identified, models could potentially be generalized The final predictions site-specific, HUC, and global models generally performed well regardless of site or for future based on expected changes in climate. The site-specific, HUC, HUC-level and global models performed well regardless of asite or job year, except infinal a few notable cases. modelsgenerally for the Middle Fork John Day did poor year, except a few notable cases. HUC-level modelslows for the Middle Fork though John Daythe didpost-snowmelt a poor job of estimating the in summer high, fall cool-off, or winter in some areas, estimating the summer high, fall or winter lows some 11). areas,The though post-snowmelt springofincrease is well represented (ancool-off, example is given in in Figure Johnthe Day River is almost spring increase is well represented (an example is given in Figure 11). The John Day River is almost entirely rain and snowmelt fed, with few known springs in the basin. However, sites located at entirely rain and snowmelt fed, with few known springs in the basin. However, sites located at Phipps Meadow on the Middle Fork indicate a nearby spring influencing in-stream temperature in Phipps Meadow on the Middle Fork indicate a nearby spring influencing in-stream˝temperature in that segment. In every year the winter daily mean temperature hovers around 10 C, dropping to as that segment. In every year the winter daily mean temperature hovers around 10 °C, dropping to as low aslow 2 ˝C for few weeks during snowmelt, to aa summer summerhigh high slightly cooler other as 2 °Cafor a few weeks during snowmelt,then thenrising rising to slightly cooler thanthan other sites in the area, and dropping throughout the fall back to winter lows (Figure 11). sites in the area, and dropping throughout the fall back to winter lows (Figure 11). HUC HUC and global models diddid notnot estimate profile;however, however, site-specific models and global models estimatethis thisannual annual profile; site-specific models did did produce temperature estimates (Figure 12). produce goodgood temperature estimates (Figure 12).

11. Observed (blue dots) and estimated (black lines) daily mean stream temperature from a FigureFigure 11. Observed (blue dots) and estimated (black lines) daily mean stream temperature from a site in the Middle Fork John Day River near Phipps Meadow. Estimated stream temperature is from site in the Middle Fork John Day River near Phipps Meadow. Estimated stream temperature is from models built using all the data for the HUC 4 encompassing the Middle Fork. models built using all the data for the HUC 4 encompassing the Middle Fork.

The JDR models built using data from typical sites can be applied generally in the basin, but this suggests that LSTbuilt modeling could produce robust temperature estimates in forthe other typesbut of this The JDR models usingmethods data from typical sites can be applied generally basin, stream In addition, systems with produce mixed inputs would require more spatial partitioning for of suggests thatsystems. LST modeling methods could robust temperature estimates for other types model results. If some subset of mixed reachesinputs are known to be springmore fed, data from spring-fed for streamoptimal systems. In addition, systems with would require spatial partitioning sites can be used to parameterize models used to estimate temperature for those reaches selectively. optimal model results. If some subset of reaches are known to be spring fed, data from spring-fed Our approach generates temporally robust, continuous estimates of temperature, allowing sites can be used to parameterize models used to estimate temperature for those reaches selectively. inter-annual variation evaluation at single sites or across multiple sites or watersheds. These Our approach generates temporally robust, continuous estimates of temperature, allowing estimates also allow the development of summary metrics that characterize the in-stream thermal inter-annual variation evaluation at as: single sitesmetrics, or across multiple or watersheds. These regime for each stream reach such seasonal growing seasonsites thermal inputs, counts of estimates also allow the development of summary metrics that characterize the in-stream thermal days above minima and maxima, and the timing of thermal milestones [62]. Aquatic organisms regimeexperience for eachthe stream reach such regime as: seasonal metrics,notgrowing season seasonal thermalevents. inputs, counts of complete thermal in their habitat, just the extreme Extreme metrics have their utility, but the cumulative effects of temperature on growth and development are also potentially important. Terrestrial biologists use Growing Degree Days (GDD) to anticipate insect

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days above minima and maxima, and the timing of thermal milestones [62]. Aquatic organisms experience the complete thermal regime in their habitat, not just the extreme seasonal events. Extreme metrics have their utility, but the cumulative effects of temperature on growth and development Water 2015, 7, page–page are also potentially important. Terrestrial biologists use Growing Degree Days (GDD) to anticipate insect emergence or bud break [63,64] and continuous stream temperature estimates could be used emergence or bud break [63,64] and continuous stream temperature estimates could be used to develop to develop similar aquatic-based metrics to estimate the timing of significant events for in-stream similar aquatic-based metrics to estimate the timing of significant events for in-stream biota. For example, biota. For example, daily temperature estimates for a single site (above Camas Creek in the North daily temperature estimates for a single site (above Camas Creek in the North Fork John Day River) are Fork shown John Day River) are shown in Figure Not only are dodifferent annualrates maxima vary,and butcooling there are in Figure 8. Not only do annual maxima8. vary, but there of warming different rates of warming and cooling across years. For example, the earlier spring warm-up suggests across years. For example, the earlier spring warm-up suggests temperature-dependent events (like temperature-dependent events (like invertebrate emergence) would occur earlier in 2004 even invertebrate emergence) would occur earlier in 2004 even though it was cooler than 2006 and 2007though in of than summer maxima. it wasterms cooler 2006 and 2007 in terms of summer maxima.

Figure 12. Observed (blue dots) and estimated (black lines) daily mean stream temperature from a Figure 12. Observed (blue dots) and estimated (black lines) daily mean stream temperature from a site in the Middle Fork John Day River near Phipps Meadow. Estimated stream temperature is from site in the Middle Fork John Day River near Phipps Meadow. Estimated stream temperature is from models built using site-specific data. models built using site-specific data.

Many aquatic managers and biologists work with weekly summaries of stream temperature. Estimates from eight-day in this analysis were more accurate than daily model estimates. For Many aquatic managersmodels and biologists work with weekly summaries of stream temperature. 2 and p2 for eight-day models for 2012 in the JDR were >0.9 and RMSEs were below 1.8 °C example, r Estimates from eight-day models in this analysis were more accurate than daily model estimates. (Table 5). rPart of the improvement model quality may to were having>0.9 longer serieswere in 2012 2 and For example, p2 for eight-dayinmodels for 2012 in be thedue JDR andtime RMSEs below for the eight-day models, but likely also because the eight-day models are averaging across the daily ˝ 1.8 C (Table 5). Part of the improvement in model quality may be due to having longer time series in fluctuations in both water and land surface temperature. These fluctuations may just be noise and 2012 for the eight-day models, but likely also because the eight-day models are averaging across the thus uninformative over long time series, where the eight-day means better represent the actual trend daily through fluctuations both water land surface temperature. These fluctuations be noise time. inModel qualityand across basins varied, with the highest error in the may UGRjust models and thus uninformative over long time series, where the eight-day means better represent the actual (mRMSE = 1.7 °C) and the lowest in the Wenatchee (mRMSE = 0.86 °C). This variation in model trendquality through time.due Model quality basins the highest error in the UGR models is likely to factors that across vary across the varied, basin butwith are uncoupled from surface temperature ˝ C)example, ˝ C). but (mRMSE = 1.7 For and thethere lowest Wenatchee (mRMSE Thisnotvariation dynamics. mayin bethe groundwater influx in parts=of0.86 the UGR others. in model results sensitivity analysis werethe surprising. Models parameterize with data from only quality is The likely due of tothe factors that vary across basin but are uncoupled from surface temperature two sites were not good, but model quality quickly improved with the inclusion of 3–4 sites and then dynamics. For example, there may be groundwater influx in parts of the UGR but not others. stabilized at full dataset levels. There was still variability in model quality across basins, but the only The results of the sensitivity analysis were surprising. Models parameterize with data from models for a basin got as good as they were going to get when including data for 4–5 sites, and did two sites were not good, but model quality quickly improved with the inclusion of 3–4 sites and not improve with the inclusion of more sites (Figure 10). The same pattern was seen in models for then stabilized at full dataset levels. There was still variability in model quality across basins, but both halves of the year (“spring” and “fall” models for the JDR are shown in Figure 10). These results the models forthat a basin got aseffort goodin as terms they were goingplacement to get when for 4–5 sites, and indicates sampling of logger can including shift fromdata putting as many did not improve loggers with the more (Figure 10). The pattern inand models temperature as inclusion feasible in aofbasin to sites having fewer loggers in same place for longerwas timeseen series, for both halves of the year (“spring” and “fall” models for the JDR are shown in Figure 10). These then focusing logger placement in specific streams that may not be well-characterized by the results indicatesmodel that sampling effort in springs, terms of logger placement can shift from putting as many basin-wide (like streams fed by groundwater influx, etc.). We loggers did not examine temporal modelto sensitivity in theseloggers analyses. would informative temperature as feasible in a basin having fewer in Itplace forbelonger time to series, knowfocusing how many (or few) observations in a time streams series arethat necessary for robust estimates, and also by if the and then logger placement in specific may not be well-characterized when loggers are in place effects annual model quality. That is, there is a strong bias toward short basin-wide model (like streams fed by springs, groundwater influx, etc.). (1–3 month) summer time series in extant logger datasets, perhaps these models would be better served by having shorter time series but in the spring and fall instead, or as well. These questions

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We did not examine temporal model sensitivity in these analyses. It would be informative to know how many (or few) observations in a time series are necessary for robust estimates, and also if when loggers are in place effects annual model quality. That is, there is a strong bias toward short (1–3 month) summer time series in extant logger datasets, perhaps these models would be better served by having shorter time series but in the spring and fall instead, or as well. These questions remain open to future investigations. There is a trade-off with this modeling approach between resolution (both spatial and temporal) and generality. The 1 km2 spatial resolution may be too coarse for some applications, such as locating thermal refugia, for example. However, the ability to generate reasonable estimates of daily or weekly stream temperature across entire basins or regions should prove useful in many research and management applications. Acknowledgments: This study was supported by Bonneville Power Administration projects: 2003-017 and 2011-006, and funding provided by the American Reinvestment and Recovery Act and USDA Forest Service, Pacific Northwest Research Station. Data used in this analysis were collected by numerous research and natural resource monitoring programs across the Columbia River basin and graciously made available to us by these parties. Author Contributions: Kristina McNyset was primarily responsible for conceiving of the methods, conducting the analyses, and writing the paper. Chris Jordan contributed to the conception and analysis. Carol Volk assisted in data collection, analysis, and writing. Conflicts of Interest: The authors declare no conflict of interest.

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