Rivers and streams within the study area were delineated using the 1:100000-scale National Hydrography Dataset (NHD; http://www.horizon-systems.com/NHDPlus/index.php, last access: 2 December 2018; McKay et al., 2012), which was attributed with mean annual flow values from data at the Western U.S. Stream Flow Metrics website (http://www.fs.fed.us/rm/boise/AWAE/projects/modeled_stream_flow_metrics.shtml, last access: 2 December 2018; Wenger et al., 2010). To highlight the perennial subset of the network where temperature monitoring occurred, reaches with annual flows less than 0.03 m3s-1 were removed from the network, as were reaches with channel slopes >15 %, and those coded as intermittent in the NHD (Fcode=46003). Filtering reduced the original network extent from 58 000 to 29 600 km with streams flowing at elevations of 221–3105 m. To visualize thermal heterogeneity in the network, a scenario representing mean August temperatures for a baseline climate period of 1993–2011 was downloaded from the Northwestern Stream Temperature website (NorWeST: https://www.fs.fed.us/rm/boise/AWAE/projects/NorWeST.html, last access: 2 December 2018; Isaak et al., 2016a) and linked to the NHD reaches (Fig. 1). Several large rivers drain the area in a generally westerly direction, the largest of which is the Salmon River with a mean annual discharge of 315 m3s-1 and a basin that comprised 44 % of the study area. Six large dams and reservoirs are in downstream portions of the network (three in the Boise River basin, two in the Payette River basin, and one in the Clearwater River basin), but these affect thermal conditions in less than 300 km of river and no temperature data were used from these sections. Spatial attributes and environmental characteristics of the study area network are summarized in Table 1.

To obtain a water temperature data set for analysis, we intersected the filtered network with the NorWeST database of daily temperature summaries (Chandler et al., 2016) and extracted data for sites that had mean daily temperature values on at least 70 % of the days from 1 December 2010 to 30 November 2015. We started the thermal year on 1 December because temperatures usually reach their annual lows by this date and the 3-month period thereafter constituted a logical winter season (i.e., December, January, February). Subsequent 3-month periods were considered to be spring (March, April, May), summer (June, July, August), and fall (September, October, November) seasons. NorWeST temperature records were supplemented with additional data solicited from hydrologists and fisheries biologists employed by the Idaho Department of Fish and Game and the U.S. Forest Service, and we also downloaded data from online databases maintained by the Columbia Habitat Monitoring Program (https://www.champmonitoring.org/Home/Index, last access: 2 December 2018) and the NOAA Northwest Fisheries Science Center (https://www.webapps.nwfsc.noaa.gov/WaterQuality/, last access: 2 December 2018). Geographic gaps in monitoring were identified using geospatial analysis (e.g., Jackson et al., 2016) and additional sensors were strategically deployed where needed (Isaak et al., 2010, 2013). Data from the different sources were recorded at a variety of sub-daily intervals, so records were summarized to mean daily temperatures for standardization. Data were collected using different sensor models (TidbiT, Stowaway, and Pendant models from Onset Computer Corporation, Pocasset, Massachusetts, USA; Temp101a model from MadgeTech, Warner, New Hampshire, USA), which had measurement accuracies of ±0.2 to ±0.5 ∘C and resolutions of 0.02 to 0.14 ∘C based on manufacturer specifications and calibration tests we performed. Sensors were deployed using underwater epoxy or steel cables for connection to large boulders and other immobile channel structures and were shielded from direct sunlight (Isaak et al., 2013; Stamp et al., 2014). Temperature records were subject to standard quality assurance–quality control measures as described elsewhere (Chandler et al., 2016).

The stream temperature data set consisted of records from 226 sites across a range of elevations, stream sizes, and reach slopes (Fig. 1; Table 1). Although we set the minimum threshold for record completeness at 70 % during the 5-year period, the average completeness of records was higher at 88 %. Missing daily values were imputed using the MissMDA package (Missing Values with Multivariate Data Analysis; Josse and Husson, 2016) in R (R Development Core Team, 2014) because temporal covariation among proximate stream temperature sites is usually strong. That was confirmed in our data set by the high correlations between observed daily temperatures and predictions from the imputation technique, which ranged from r=0.98 to 0.99. All temperature records at the 226 sites were complete after imputation and consisted of 1826 mean daily temperatures from 1 December 2010 to 30 November 2015. Climatological variation during the same period was described using discharge data downloaded from the National Water Information System database (https://waterdata.usgs.gov/usa/nwis/nwis, last access: 2 December 2018) for a high-elevation gage site at 1850 m and a low-elevation gage site at 294 m and air temperature data from monitoring stations in the Cooperative Observer Network (https://www.ncdc.noaa.gov/data-access, last access: 2 December 2018) that were near the gage sites (Fig. 1).

Prior to calculating metrics for thermal characteristics, mean daily temperatures for 365 days were calculated from the 5 years of data at each site to provide representative values. Twenty-eight temperature metrics were then calculated to describe aspects of those annual records based on five categories associated with magnitude, variability, frequency, timing, and duration (Tables 2 and 3). Metrics were similar to those used in previous studies of thermal regimes (Arismendi et al., 2013; Chu et al., 2010; Rivers-Moore et al., 2013; Steel et al., 2016) and in studies assessing the effects of peak summer temperatures on the distribution and abundance of aquatic organisms (Dunham et al., 2003; Huff et al., 2005; Isaak et al., 2017b). A wide range of variability occurred among sites where mean annual temperatures ranged from 3.1 to 10.3 ∘C and annual standard deviations ranged from 2.51 to 7.40 ∘C (Table 3). Relationships among the thermal metrics were described by conducting PCA on a data matrix in which columns represented the 28 metrics and rows were the 226 monitoring sites. Linear combinations of the data were estimated with coefficients equal to the eigenvectors of their correlation matrix, which were the principal components (PCs; Pearson, 1901; Sergeant et al., 2016). The first principal component accounted for the largest possible variance in the data set and succeeding components accounted for the largest portions of the remaining variance while being orthogonal (i.e., uncorrelated) to the preceding components. Correlations, or loadings, between each metric and the PCs were also calculated to assist in subsequent interpretations. The Princomp procedure in SAS (SAS Institute Inc., 2015) was used to conduct the PCA. To describe geographical relationships, PC scores were mapped to the 226 temperature sites and bivariate correlations were calculated with descriptors of network conditions such as elevation, reach slope, and discharge summarized in Table 1.

To assess the consistency of spatial temperature patterns among monitoring sites, a T-mode PCA (Richman, 1986) was done on a data matrix of mean daily temperatures in which the columns were the 365 days starting on 1 December and the rows were the 226 monitoring sites. In this analysis, the number of principal components explaining significant variation indicates the number of distinct spatial phases that occur throughout the year (Gallacher et al., 2017). Eigenvector loadings on the dominant PCs were plotted for each day of the year to describe when each phase occurred, and mean daily temperatures were mapped during these periods for visualization.

To assess temporal covariance among sites, an S-mode PCA (Richman, 1986) was done by transposing the T-mode data matrix so that monitoring sites were columns and the time-ordered daily mean temperatures were rows. Because hydroclimatic conditions among years could have affected the results, the S-mode PCA was done not only for the 5-year averages of daily water temperatures, but also on the disaggregated time series of 1826 daily values at the 226 monitoring sites. Concordance between the S-mode PC scores, air temperature, and discharge was examined post hoc by plotting standardized time series and calculating bivariate correlations.

Thermal regimes in the mountain river networks we studied were simple and responded relatively coherently to climatic variability across a geomorphically consistent area with few reservoirs. Strong seasonal patterns in water temperatures characteristic of temperate latitudes were apparent in response to the primary signal set by the annual air temperature cycle and accompanying changes in solar radiation. Not surprisingly given the pronounced elevational gradients in the study landscape, the dominant regime aspect represented by PC1 in the metric-based PCA was associated with magnitude. Less expected was that many of the variability metrics also loaded heavily on the first PC because variation has been treated as a distinct element of thermal regimes (e.g., Steel et al., 2012; Kovach et al., 2018). The concurrence of magnitude and variability metrics probably also relates to elevation and changes in the importance of groundwater buffering, which both cools streams and dampens diurnal and seasonal variations (Caissie and Luce, 2017). For example, the coldest streams at the highest elevations are usually strongly buffered by groundwater inputs derived from large annual snowpacks in mountain environments and often show limited thermal variability (Luce et al., 2014b; Isaak et al., 2016b). Downstream from the headwaters, the proportional inputs of groundwater decrease and streams are more coupled to climatic variability even as their average temperatures increase due to solar gains over longer flow distances (Caissie, 2006). In contrast to the metrics associated with PC1, metrics that described the winter period and the extent of the growing season largely defined PC2. This “winter” PC is probably common to stream thermal regimes in mountain landscapes where subzero air temperatures are frequent and result in prolonged periods with water temperatures near 0 ∘C. The orthogonal nature of PC1 and PC2 suggests that streams with otherwise similar magnitude and variance structures will sometimes differ substantially with regards to their winter and growing seasons – a distinction that could have important implications for biological communities or stream physicochemical processes.

Our results also suggest that important local nuances in water temperature dynamics like the differences in timing of spring warming and peak temperatures may emerge from the interactions among annual climate cycles, basin geomorphology, and hydrology. Because precipitation, air temperatures, snowpack, runoff volume, and runoff timing are all evolving in response to climate change in mountain environments across the study region (Mote et al., 2005; Luce et al., 2013) and globally (Stewart, 2009), better understanding of these connections is needed. In particular, more insight into the relationship of water temperatures with annual unit-area runoff and whether the underlying mechanisms relate to changes in snowpack accumulation (Luce et al., 2014a; Lute and Luce, 2017), snowmelt timing and rate (Musselman et al., 2017), the volume of water stored in groundwater (e.g., Tague et al., 2007), or the outcomes of extreme low flows (e.g., Kormos et al., 2016; Luce and Holden, 2009) could lead to better predictions about water temperatures and the evolution of thermal regimes in response to expected changes in air temperatures and precipitation.

Water temperature models are often developed for use in ecological assessments and to understand how habitat degradation or restoration efforts may affect thermal regimes (Benyahya et al., 2007; Gallice et al., 2015; Dugdale et al., 2017). Our results, like several previous studies that have compared multiple temperature metrics (Isaak and Hubert, 2001; Rivers-Moore et al., 2013; Steel et al., 2016), confirm that numerous metrics are strongly correlated and provide redundant information. The specific choice of a metric, therefore, may not be critical as long as it represents an important aspect of a thermal regime and is suited to the goals of a study. Metrics associated with temperature magnitude and variability, which have been the focus of most modeling efforts, are good choices because they represent significant portions of the information about thermal regimes and have been shown on many occasions to be important determinants of ecological attributes such as species distributions and abundance or physical processes in streams and rivers (Isaak et al., 2017b; Webb et al., 2008). Our preferred metrics in previous research have been mean August or mean summer temperatures because the data records for their calculation are typically available at the largest number of sites in mountain environments, which maximizes sample sizes and minimizes the distances over which interpolations are made when developing and applying network-scale temperature models (e.g., Detenbeck et al., 2016; Isaak et al., 2017a). Metrics based on longer-term means rather than short-term daily or weekly maxima are also more stable and easier to predict (Isaak et al., 2010; Turschwell et al., 2016), although a focus on the latter metrics is often mandated within regulatory environments and may negate these considerations (Todd et al., 2008; McCullough, 2010).

Comparatively little effort has gone towards modeling temperature metrics associated with growing season length or the dates of spring and winter season onset, despite the significant information these metrics provide about thermal regimes and their relevance to the phenology and life histories of organisms that constitute aquatic communities (Huryn and Wallace, 2000; Neuheimer and Taggart, 2007). These aspects of thermal regimes, as well as magnitude and variability characteristics, are also likely to be evolving in response to climate change, so new models are needed to provide forecasting abilities about changes later this century. Rather than focusing on individual metrics, researchers could also instead use PCA to efficiently summarize multiple temperature metrics and then model the eigenvector loadings that define one or more of the principal components. This approach would maximize the amount of thermal information represented by a response metric, but would yield results that were more ambiguous to interpret.

The growth of new stream and river temperature monitoring and data collection activities has been remarkable in recent years. Although optimization of those efforts ultimately depends on local considerations, some general guidelines emerge from this work that may be applicable to other areas. For example, the coherent behavior we observed among temperatures at many sites suggests that a limited number of monitoring stations will often be sufficient to represent the temporal dynamics of thermal regimes. Those stations would need to be spread geographically and along major environmental gradients and replicated to mitigate against sensor losses, but 20–30 stations might prove sufficient at scales comparable to our study area. Given low sensor costs and the availability of standardized data collection protocols (Isaak et al., 2013; Stamp et al., 2014), monitoring arrays could also be crowd-sourced effectively if site locations were coordinated and chosen strategically using geospatial analyses to describe and stratify networks for sample allocation (Jackson et al., 2016). Monitoring networks might also be supplemented by incorporating data from sites established for other purposes such as documenting thermal responses to habitat restoration efforts (Nichols and Ketcheson, 2013) or disturbances associated with land management, wildfires, or livestock grazing (Mahlum et al., 2011; Nusslé et al., 2015). In fact, those factors motivated collection of many of the data sets compiled for this analysis, although supplementation with additional sites was needed to ensure adequate coverage within the study area.

If one of the goals of temperature data collection efforts is to develop accurate prediction maps that show spatial variation in one or more thermal metrics (e.g., Isaak et al., 2017a; Steel et al., 2016), monitoring sites may need to be established more densely than the temporal considerations discussed above otherwise suggest. Spatial autocorrelation in temperature metric values is minimal in mountain river networks beyond distances of 10–100 km (Isaak et al., 2010; Zimmerman and Ver Hoef, 2017), so this level of sensor spacing would be required to generate the most accurate maps. Given the extent of many river networks, that could translate into a large number of sites, but most of these could be monitored for short periods while temporal dynamics were represented by a subset of long-term sites because temporal covariance among sites would be strong. Costs associated with numerous sensor deployments could be prohibitive, so aggregation of existing data sets from multiple natural resource agencies into a centralized database often becomes an attractive option. Moreover, if those central databases are made publicly accessible, professionals from the contributing agencies may begin to coordinate data collection activities more consistently and effectively across larger areas (e.g., Isaak et al., 2018b).

As new data collection and database development efforts proceed, it is commonly the case that temperature records have inconsistent period lengths or missing values. Usually it is desirable to have complete records for analysis, so missing values are sometime imputed based on the correlations between two monitoring site records that strongly covary (e.g., Rivers-Moore et al., 2013). However, the process can be tedious if required at more than a few sites, so an efficient improvement is offered by the imputation technique described by Josse and Husson (2012) that is easily used in the MissMDA software package (Josse and Husson, 2016) for the R statistical program (R Development Core Team, 2014). This technique examines and uses correlations among multiple site records simultaneously to estimate missing values by first applying standard PCA to the incomplete data set where missing values are replaced with the respective record mean. Data are then reconstructed from the PCs, and the initial analysis step is repeated but with missing values replaced using estimates from the reconstructed data. The process is repeated until convergence, and the missing values in the original data records are ultimately replaced with estimates from the last PCA reconstruction (Josse and Husson, 2012). Care should be taken against overreliance on the technique to impute particularly sparse records, but the MissMDA package provides a useful tool for addressing gaps when working with large temperature data sets or time series of other measurements common to hydrology such as gage discharge records (e.g., Isaak et al., 2018a).