Aquatic Carbon Export and Dynamics in Mountain Headwater Streams of the Western U.S.

Mountain headwater streams actively cycle carbon, receiving it from terrestrial landscapes and exporting it through downstream transport and gas exchange with the atmosphere. Although their importance is now widely recognized, aquatic carbon fluxes in headwater streams remain poorly characterized. In this study, aquatic carbon fluxes were measured in 15 mountain headwater streams and were used in a geostatistical analysis to determine how landscape characteristics influence aquatic carbon fluxes. In‐stream sensors were used to measure fluorescent dissolved organic matter (fDOM) (a surrogate for dissolved organic carbon (DOC)) at a subset of sites to characterize dynamic responses to hydroclimatic events. Wetlands have a positive influence on aquatic carbon fluxes, whereas perennial snow/ice has the opposite effect, reflecting differences in soil organic matter content in these landscapes. Mean annual temperature (MAT) has a complex influence on DOC, with peak DOC exports in basins with MAT of 0–2°C. Precipitation has a strong positive influence on aquatic carbon fluxes, and declining snowpacks in the western United States may reduce future aquatic carbon exports. fDOM (and by implication DOC) and HCO3‐ ${{\text{HCO}}_{3}}^{\mbox{-}}$ showed strong dynamic responses to snowmelt and rain events, with fDOM increasing and HCO3‐ ${{\text{HCO}}_{3}}^{\mbox{-}}$ decreasing during events. Combining results from this study with those from a companion study on CO2 exchange yielded total aquatic carbon fluxes of 7.2–15.7 g C m−2 yr−1 (median = 12.22), similar to those from forests and peatlands. Given net ecosystem production (NEP) of similar magnitude, NEP calculations that do not account for losses via the aquatic pathway can substantially overestimate terrestrial carbon sequestration.


Introduction
Despite their small size, headwater streams are disproportionally important in the global carbon cycle (Drake et al., 2018;Schneider et al., 2020).Small headwater streams account for 89% of total global stream length (J.A. Downing et al., 2012), and they are areas of active carbon cycling, receiving organic and inorganic carbon from the surrounding landscape and exporting it through downstream transport and gas exchange with the atmosphere (Drake et al., 2018;Horgby, Gomez-Gener, et al., 2019;Wallin et al., 2010).Although their importance in the global carbon cycle has been recognized (Aufdenkampe et al., 2011;Battin et al., 2009), a paucity of observations in mountain headwater streams has contributed to large uncertainty in flux estimates for them (Dinsmore et al., 2013;Drake et al., 2018).The scarcity of data is largely because of the difficulty of measuring transient, but potentially large, aquatic carbon fluxes in remote mountain areas, particularly during storms and seasonal snow cover (Drake et al., 2018).
Many headwater streams (first-third order) drain seasonally snow-covered mountains, which, like high-latitudes, are highly sensitive to effects of climate change (Dettinger, 2014;Rangwala et al., 2013).Mountains cover 25 percent (%) of global land area, and in the western United States (U.S.), mountains have experienced substantial declines in snowpack during the last several decades, largely driven by increasing air Abstract Mountain headwater streams actively cycle carbon, receiving it from terrestrial landscapes and exporting it through downstream transport and gas exchange with the atmosphere.Although their importance is now widely recognized, aquatic carbon fluxes in headwater streams remain poorly characterized.In this study, aquatic carbon fluxes were measured in 15 mountain headwater streams and were used in a geostatistical analysis to determine how landscape characteristics influence aquatic carbon fluxes.In-stream sensors were used to measure fluorescent dissolved organic matter (fDOM) (a surrogate for dissolved organic carbon (DOC)) at a subset of sites to characterize dynamic responses to hydroclimatic events.Wetlands have a positive influence on aquatic carbon fluxes, whereas perennial snow/ice has the opposite effect, reflecting differences in soil organic matter content in these landscapes.Mean annual temperature (MAT) has a complex influence on DOC, with peak DOC exports in basins with MAT of 0-2°C.Precipitation has a strong positive influence on aquatic carbon fluxes, and declining snowpacks in the western United States may reduce future aquatic carbon exports.fDOM (and by implication DOC) and  HCO3showed strong dynamic responses to snowmelt and rain events, with fDOM increasing and  HCO3decreasing during events.Combining results from this study with those from a companion study on CO 2 exchange yielded total aquatic carbon fluxes of 7.2-15.7 g C m −2 yr −1 (median = 12.22), similar to those from forests and peatlands.Given net ecosystem production (NEP) of similar magnitude, NEP calculations that do not account for losses via the aquatic pathway can substantially overestimate terrestrial carbon sequestration.
Plain Language Summary Small mountain streams play an important role in the global carbon cycle, receiving carbon from the surrounding landscape and exporting it via streamflow and gas exchange with the atmosphere.In this study, we quantified downstream transport of aquatic carbon in 15 headwater streams in the western United States and characterized temporal dynamics at a subset of sites in Rocky Mountain National Park.Snowmelt was the main driver of aquatic carbon fluxes in the study basins, and future changes in snowpacks could have a substantial effect on carbon cycling in them.Rainstorms caused sharp changes in aquatic carbon concentrations, reflecting dynamic responses to major hydroclimatic events.The amount of carbon exported from mountain streams by streamflow and gas exchange is large and can have an important influence on net ecosystem carbon budget estimates.temperatures (Clow, 2010;Meybeck et al., 2001;Mote et al., 2018).Changes in the duration and extent of seasonal snowpacks is likely to have a profound effect on aquatic carbon cycling (Laudon et al., 2012;Meingast et al., 2020).Refining flux estimates and how they respond to variations in temperature and runoff is essential to improving our understanding of climate feedbacks on the aquatic carbon cycle (Balathandayuthabani et al., 2023).
Most previous studies of freshwater aquatic carbon fluxes have relied on discrete sampling, which can capture seasonal patterns, but often fails to capture rapid changes in chemistry during storms, resulting in potentially large uncertainty in flux estimates (Dyson et al., 2011;Hoffmeister et al., 2020;Marcé et al., 2016).Recent advances in sensor technology have opened new opportunities for measuring key aquatic carbon components at high frequency, enabling measurements at the time scale of hydrologic and biogeochemical processes that drive rapid changes in concentrations in streams (Kirchner et al., 2004;Rode et al., 2016).In situ optical measurements of fluorescent dissolved organic matter (fDOM) have shown promise as a proxy for DOC (Boix Canadell et al., 2019;B. D. Downing et al., 2012;Pellerin et al., 2012;Wymore et al., 2018), and direct measurement of CO 2 in streams is now possible using in-stream sensors (Clow et al., 2021;Johnson et al., 2010).
In this study, we made year-round measurements of the major components of the aquatic carbon budget in seven high-elevation, seasonally snow-covered mountain catchments in Rocky Mountain National Park (RMNP), Colorado.Our objective was to gain a better understanding of aquatic carbon export and dynamics and the processes that drive them in mountain headwater streams.Measured components included lateral export of DOC,  HCO3 -, PC, and CO 2 , as well as CO 2 exchange between streams and the atmosphere.In-stream sensors were used to measure fDOM (as a surrogate for DOC) and CO 2 , enabling calculation of daily fluxes and characterization of diel patterns and dynamic responses to snowmelt and storm events.In addition, weekly to bimonthly discrete sampling for DOC,  HCO3 -, and PC was performed to directly quantify their export at seasonal and annual time scales.DOC,  HCO3 -, and PC also were measured in eight additional mountain headwater streams in the western U.S., and data from all 15 sites were used in a geostatistical analysis to determine how landscape characteristics (e.g., hypsography, soil, vegetation, geology, and climate) influence annual aquatic carbon fluxes.
To address our objectives, we sought to answer the following research questions: • How do aquatic carbon concentrations and fluxes vary spatially and temporally in mountain headwater streams?• How do the relative importance of DOC,  HCO3 -, PC, and CO 2 fluxes vary by season and in relation to landscape characteristics?
• What processes drive aquatic carbon fluxes at annual, seasonal, daily, and sub-daily time scales?
We hypothesize that climate, hypsography, soil, vegetation, and geologic attributes of mountain headwater catchments can impart strong signals on aquatic carbon concentrations and that these signals may manifest as spatial and temporal variations in fluxes of aquatic carbon.
CO 2 exchange results were presented in Clow et al. (2021); thus, the focus of the present paper is on lateral export and temporal dynamics of DOC,  HCO3 -, PC, and CO 2 .All data used in this work are published and freely available in Clow et al. (2023) and the U.S. Geological Survey (USGS) National Water Information System (NWIS) database (U.S. Geological Survey, 2023b).

Site Description
The 15 streams in this study drain mountain headwater catchments of the western U.S. (Figure 1).In Figure 1, sites 1-10 are in the Rocky Mountains, 11 and 12 are in the Cascade Range, and 13-15 are in the Sierra.All the sites are in protected areas, such as national parks or national forest wilderness, and are upstream from any major water diversions, development, or agricultural land use (Mast & Clow, 2000).Streamflow and water chemistry data were collected during 2011-17 at seven sites in RMNP, Colorado and at eight additional sites in the western U.S. (Figure 1).Landscape characteristics are described in Clow et al. (2018), M. L. Clark et al. (2000), and Mast and Clow (2000), and are summarized in Table S1 in Supporting Information S1.The study basins range in size from 1.6 to 468 km 2 , although most (13 of 15) are within the 5-200 km 2 size range.Mean elevations are high, ranging from ∼2,000 to 3,500 m, except for Lookout Creek (Cr.), which has a mean elevation of ∼1,000 m.All the basins were glaciated during the late Pleistocene and have thin patchy soils in high alpine zones, with thicker and more well-developed soils in forested zones at lower elevations.Soils are classified predominantly as Inceptisols, Cryosols, and Mollisols, except at Sagehen Cr. and Lookout Cr., where soils are primarily Alfisols.The dominant bedrock geology in most basins is granitic or metamorphic gneiss, with volcanic rocks in two basins (Sagehen Cr. and Lookout Cr.).Limited areas of limestone occur at two sites (Swiftcurrent Cr. and Vallecito Cr.).Topography is steep, with mean slope ranging from 30% to 66%, except at Sagehen Cr., where mean slope is 14%.Climate is warm and dry during summer, and cold and wet during winter.Long-term (1971Long-term ( -2000) ) mean annual air temperatures range from 0.3 to 8.6°C, with Lookout Cr., Sagehen Cr., and Merced River notably warmer than the other sites.Mean annual precipitation ranged from 0.88 to 2.27 m during 1971-2000, and the wettest sites were Swiftcurrent Cr. and Lookout Cr.Typically, 55-87% of precipitation falls as snow, except at the lowest elevation site (Lookout Cr.), where snow accounts for one-third of annual precipitation.All sites, except Lookout Cr., develop deep seasonal snowpacks that accumulate beginning in November and persist until spring snowmelt (usually May-June); the accumulation and melting of the seasonal snowpack usually is the major hydrologic event of the year, although summer thunderstorms can cause large transient spikes in discharge and chemistry.Major vegetation classes include evergreen forest (primarily conifer >5 m tall), herbaceous grassland (primarily mountain meadow and tundra), shrub (shrubs and trees <5 m tall), and barren terrain (bare rock and talus).Stream water chemistry typically is dilute (specific conductance (SC) <50 uS/cm) with circumneutral pH between 6 and 8.

Field Measurements
Depth-integrated stream samples were collected weekly to bimonthly from high-velocity zones of the stream (U.S. Geological Survey, 2023a), with frequency tailored to the seasonal hydrograph.The highest frequency was during snowmelt, when streamflow and stream chemistry typically change quickly, and the lowest frequency was during the winter low-flow period (mid-October through March), when streamflow and chemistry usually are relatively stable.At some of the high-elevation sites in RMNP, deep seasonal snowpacks prevented access to the streams during mid-winter (December-February).Samples were analyzed for DOC,  HCO3 -, and PC using USGS methods designed for low-ionic strength waters (Fishman et al., 1994).
At the sites in RMNP, fDOM, turbidity, water temperature, SC, and water depth were measured at high frequency to provide information on short-term concentration dynamics.All high-frequency measurements were made at 10-15 min intervals using in-stream sensors connected to Campbell Scientific CR1000 dataloggers, which logged the data and were powered by solar panels and deep-cycle batteries.Sensors were calibrated in the laboratory prior to installation and rechecked annually according to manufacturer's specifications.fDOM and turbidity concentrations were measured using Turner Designs C3/C7 sensors equipped with an automated anti-fouling wiper to maintain clean optics.The fDOM measurement was made by optical fluorescence with an excitation wavelength of 325 nm and emissions wavelength of 470 nm (Saraceno et al., 2017).Raw fDOM values were adjusted for temperature and turbidity to obtain corrected fDOM (fDOM T,t ) as described in Clow et al. (2023), based on recommendations in B. D. Downing et al. (2012) and Saraceno et al. (2017).Water temperature and SC were measured using in-stream sensors from Campbell Scientific (CS547).Water depth was measured using vented, submersible pressure transducers (Campbell Scientific CS450).Discharge measurements were made each year over the range of hydrologic conditions, and statistical relations were developed between water depth and discharge; these relations were used to calculate discharge from the high-frequency water depth data (Rantz, 1982).Dissolved CO 2 was measured hourly using Vaisala GMP-222 sensors that were modified for use in streams; for details, please see Clow et al. (2021) and Johnson et al. (2010).

Daily Exports
Daily exports (lateral fluxes) of aquatic carbon were calculated as the product of daily concentration and daily average discharge.Daily concentrations were calculated two ways.The first method, which we refer to as the interpolation method, was used for DOC,  HCO3 -, and PC at all sites and was by simple linear interpolation between sampling events.In the second method, which we refer to as the high-resolution (hi-res) method, fDOM T, t was used as a surrogate to estimate DOC at fine temporal resolution (daily and sub-daily); this method was used only in RMNP, where we collected high-frequency fDOM data.Surrogate relations were established by simple linear regression of fDOM T, t against DOC.As mentioned, data gaps existed for winter periods when ice cover prevented operation of fDOM sensors.A continuous record of daily fDOM T, t concentrations was developed by estimating concentrations during data gaps using stepwise multiple linear regression (MLR; see next section for details).Potential explanatory variables in the MLR included discharge, sine and cosine of the day of the year (to account for seasonality and hysteresis), water temperature, SC, and snow depth.The gap-filled daily fDOM T, t record was converted to DOC concentrations, which were multiplied by daily average discharge to obtain daily aquatic carbon exports.Daily exports were summed to obtain total monthly and annual exports.Annual volume-weighted mean (AVWM) concentrations were calculated by dividing annual exports by total annual discharge.
Uncertainties in flux estimates stem from a variety of sources.For the interpolation method, sources of uncertainty included laboratory measurements of aquatic carbon concentrations, field measurements of discharge, and errors associated with interpolation of concentrations between sampling events.For DOC fluxes estimated using the hi-res method, additional sources of uncertainty stem from use of linear regressions to fill data gaps and to convert fDOM T, t to DOC.Quality control data indicate that errors in concentration and discharge measurements are likely less than 10% (U.S. Geological Survey, 2023b).Uncertainty in linear regression estimates were quantified based on the root mean square error (RMSE) of the regressions, which are shown on relevant figures.Errors associated with interpolation of concentrations are difficult to quantify because we lack knowledge of what "true" concentrations were on any given day; however, a qualitative assessment was done by comparison of time-series plots of concentrations estimated using the interpolation and hi-res methods.Overall uncertainties in annual exports were assessed by comparing annual fluxes calculated using concentrations estimated from the interpolation and hi-res methods on bivariate plots.

Spatiotemporal Statistical Analyses
Spatial and temporal variability in concentrations and exports were evaluated using a MLR approach, with landscape characteristics and annual precipitation and air temperature as potential explanatory variables (Table S1 in  Supporting Information S1).The objective of the geospatial analysis was to determine the influence of landscape characteristics on annual exports of individual aquatic carbon species.The temporal analysis was performed to elucidate how concentrations of aquatic carbon species respond to climatic and hydrologic drivers at diel, event, and seasonal time scales.It is recognized that landscape variables and climate do not control solute concentrations themselves, but rather are proxies for processes that influence flow paths, mixing of source waters, and biogeochemical reactions.
In our stepwise MLR procedure, equations were fit using maximum likelihood methods with the potential explanatory variable that explained the most variance entering the regression equation first (Clow et al., 2021).Residual variance was calculated, and the variable that explained the most residual variance entered the equation next.This procedure was repeated until the minimum Akaike information criteria was obtained (Akaike, 1981).Potential colinearity among variables was evaluated using the variance inflation factor, with a criteria for exclusion of 5 (Hair et al., 2005).All statistical analyses were performed in JMP v.17 (SAS, 2023).
Climate and landscape characteristics used in the geostatistical analyses were extracted from the Geospatial Attributes of Gages for Evaluating Streamflow II (GAGES-II) data set (Falcone, 2011), as described in Clow et al. (2018).Several sites in RMNP were missing from the GAGES-II data set, so basin attributes for those sites were quantified in ArcGIS v. 10.8.1 (ESRI, 2023), as described in Clow et al. (2021).

Time-Series Patterns
Previous studies of fDOM and CO 2 using high-frequency in-stream measurements have revealed strong variations in concentrations and exports at hourly, daily, and seasonal times scales, as well as in response to storm events (Boix Canadell et al., 2019;Clow et al., 2021;Crawford et al., 2016;Tunaley et al., 2016).By relating these variations to climatic and hydrologic data, it is possible to gain insight into driving processes, both physical and biological (Kirchner et al., 2004;Rode et al., 2016;Whitmore et al., 2021;Zarnetske et al., 2018).In the present study, we examined time-series patterns in hourly fDOM T, t (and by analogy, DOC) using time-series plots and continuous wavelet transform (CWT) analysis.Time-series plots enable qualitative assessment of patterns and are useful for hypothesis development.CWT analysis enables statistical detection of periodicity in time series, similar to Fourier analysis (Crawford et al., 2016), and can aid hypothesis testing.Statistically significant (p ≤ 0.05) spectral power at a period of 24 hr, for example, would be indicative of strong diel variation, whereas spectral power at a period of 8760 (1 year) would indicate strong seasonal variation at the annual time scale.The CWT analysis was performed in the statistical software package R using the "biwavelet" routine (R Core Team, 2022).

Precipitation and Runoff
Annual precipitation varied widely among sites and among years, ranging from 0.28 to 3.06 m, with a median of 1.17 m (Figure S1, Table S2 in Supporting Information S1).Lookout Cr. and Swiftcurrent Cr. were notably wetter than the other sites, and sites in the Sierra (sites 13-15) showed the most inter-annual variability, with coefficients of variation of 45-49% for precipitation.The Sierran sites experienced drought conditions during 2013-15 and relatively wet conditions during 2017.In western Colorado, 2011 was wet, and 2012 was exceptionally dry.Precipitation was less variable at the other sites.
Annual runoff patterns followed those of precipitation, ranging from 0.09 to 2.12 m (median 0.73 m), with greater runoff at Lookout Cr. and Swiftcurrent Cr. than at the other sites (Figure S1, Table S2 in Supporting Information S1).Sites in the Sierra had CVs of 59-99% for runoff, with very low runoff during 2013-15, and greater than average runoff during 2017.In the southern Rockies (sites 1-8), runoff was higher than average during 2011 and much lower than normal during 2012.

Annual-Scale Concentrations and Exports From Discrete Sampling
Discrete (grab) sampling can provide valuable information on seasonal and annual patterns in solute concentrations and export, which can be compared to landscape characteristics to elucidate driving mechanisms.In our study, AVWM concentrations of DOC,  HCO3 -, and PC varied widely among sites, and inter-site variability was much greater than interannual variability (Figure S2, Table S2 in Supporting Information S1).In RMNP, where a subset of sites occurs on an elevation transect, DOC concentrations were lower in the alpine/subalpine zone (0.5-2 mg C L −1 , sites 1-3) than in the montane zone (3-6 mg C L −1 , sites 4-7), reflecting greater soil development and a prevalence of wetlands at lower elevations.At the other western U.S. sites, DOC concentrations ranged from ∼1 to 3 mg C L −1 , similar to those reported for other mountain headwater streams in the western U.S. and the Swiss Alps (Boix Canadell et al., 2019;Boyer et al., 1997).These concentrations are lower than annual mean DOC values reported for most peatland streams, reflecting likely differences in the organic carbon content of soils in the study areas (e.g., Dinsmore et al., 2013;Laudon et al., 2011).Like DOC,  HCO3concentrations were quite low (0.2-2 mg C L −1 ), except at Sagehen Cr. and Swiftcurrent Cr., where AVWM concentrations ranged from approximately 4-7 mg C L −1 .
At most sites, DOC concentrations exceeded  HCO3concentrations, with the highest DOC:  HCO3in RMNP (Figure S2, Table S2 in Supporting Information S1).Notable exceptions occurred at Swiftcurrent Cr. and Vallecito Cr., which are underlain in part by limestone, and at Sagehen Cr. and Lookout Cr., which have deep soils developed on volcanic bedrock.These geologic characteristics are conducive to enhanced chemical weathering, and thus, high  HCO3concentrations (Berner, 1978).PC concentrations were much less than either DOC or  HCO3 -, likely reflecting the lack of physical disturbance common at the study sites (Tables S1 and S2 in Supporting Information S1).
Landscape characteristics exerted strong control on AVWM concentrations.Our MLR analysis indicated that the strongest predictors of AVWM DOC concentrations were %wetlands (positive influence), mean topographic slope (negative), and mean annual air temperature (negative) in the basins (Figure 2a).The positive influence of wetlands on DOC concentrations reflects the high organic carbon content of wetland and riparian soils, combined with flushing of DOC from those soils during snowmelt and rainstorms (Boyer et al., 1997;Burns et al., 2016;Creed et al., 2008;Laudon et al., 2012;Strohmeier et al., 2013).The negative influence of basin slope is consistent with a paucity of organic-rich soils and short hydrologic residence times in basins with steep relief (Clow et al., 2018;Strohmeier et al., 2013).The MLR identified a strong negative relation between air temperatures and AVWM DOC concentrations; however, previous studies have suggested the relation is more complex.In a regional, multi-year analysis of relations between catchment characteristics, climate, and mean annual DOC concentrations, Laudon et al. (2012) found that mean annual temperature (MAT) was a primary control on DOC concentrations in catchments in Finland, but the relation was non-linear.In their study, DOC concentrations were highest in catchments with MATs between 0 and 3°C.At lower temperatures, soil organic matter (SOM) decomposition rates are depressed, resulting in low DOC production and low stream DOC concentrations.And at higher temperatures, SOM mineralization may exceed SOM production, again resulting in low DOC concentrations (Laudon et al., 2012).In the present study, a simple linear regression of DOC against MAT indicated concentrations and exports were greatest in basins with MAT of 0-2°C, similar to the findings of Laudon et al. (2012).Many of our study basins in the Rocky Mountains fall within this temperature range and have experienced significant warming during the last few decades (Clow, 2010).Projections for continued regional warming (Overpeck & Udall, 2020) suggest streams in the Rocky Mountains may experience declines in DOC export in the future.
Annual export of DOC at the study sites ranged from 0.18 to 4.95 g C m −2 yr −1 (median 1.35 g C m −2 yr −1 , Figure 1, Table S2 in Supporting Information S1; all exports normalized to basin area).Controls on DOC exports were similar to those for DOC concentrations, with %wetland exerting a positive influence, and air temperature exerting a negative influence (Figure 2b).Annual precipitation also had a strong, positive influence on DOC exports, but little relation to DOC concentration, indicating chemostatic behavior.This type of behavior occurs when concentrations in soil water and streams are buffered from change by processes in soils, limiting the dilution effect of snowmelt and rain (Boix Canadell et al., 2019;Clow & Mast, 2010;Godsey et al., 2009;Zarnetske et al., 2018).The positive relation between DOC export and annual precipitation may have important implications for feedbacks between climate and aquatic C cycling.The feedbacks are likely to be complex; however, our results indicate that an increase (decrease) in annual precipitation may lead to an increase (decrease) in DOC export.This is consistent with previous studies that documented positive relations between precipitation, runoff, and DOC export in streams draining northern peatlands and forests (Dinsmore et al., 2013;Meingast et al., 2020;Räike et al., 2012).Drivers may include increased flushing of DOC from soils and increased DOC production during wet years in ecosystems that normally are water limited, as many are in the western U.S. (Dinsmore et al., 2013;Räike et al., 2012;Tank et al., 2018;Zarnetske et al., 2018).In the western U.S., there have been widespread declines in snowpack driven largely by increasing air temperatures (Clow, 2010;Mote et al., 2018;Woodhouse et al., 2016); results from this study suggest that if these trends continue, we could expect substantial declines in DOC export from mountain streams in the region.
Geology plays a dominant role in determining  HCO3concentrations at the study sites, reflecting the importance of mineral weathering as a source of  HCO3in natural waters (Berner et al., 1983;Drever & Clow, 1995).Concentrations of  HCO3were greatest at Swiftcurrent Cr., Sagehen Cr., and Lookout Cr., which are underlain by limestone and volcanic bedrock that weather quickly (Campeau et al., 2017), and were lowest at sites underlain by slow-weathering granitic bedrock in the Rockies and southern Sierra (Figure S2, Tables S1 and S2 in Supporting Information S1).Sagehen Cr. and Lookout Cr. also have deep soils that promote release of  HCO3through enhanced water-rock interaction (Clow et al., 2018;Rademacher et al., 2005).Results from our MLR analysis confirm that carbonate bedrock and contact time have a positive influence on AVWM  HCO3concentrations, whereas soil permeability and herbaceous grassland (%herbaceous grassland) and ice/snow (%ice/snow) in the basins have a negative influence (Figure 2c).Long contact times (water transit times) provide for greater interaction between water and bedrock, promoting the release of weathering products.A previous study using data from a subset of our study sites found strong relations between transit times and AVWM concentrations of silicate mineral weathering products (e.g., silica and sodium; Clow et al., 2018).High soil permeability has the opposite effect by facilitating rapid hydrologic flushing through soils.Herbaceous grassland (i.e., tundra) and ice/snow are associated with alpine environments, where mineral weathering rates tend be slow because of cold temperatures and short snow-free seasons (White & Blum, 1995;White et al., 1999).
Annual export of  HCO3ranged from 0.11 to 10.56 g C m −2 yr −1 (median 0.45 g C m −2 yr −1 ), with the lowest rates at Merced River and Marble Fork in the southern Sierra, which have minimal soil and are underlain by resistant granitic bedrock (Figure 1, Table S2 in Supporting Information S1).The highest  HCO3export rates were at Swiftcurrent Cr. due to the enhancing effect of limestone on weathering and  HCO3release.The MLR results indicate that landscape controls on  HCO3export were similar to those for  HCO3concentrations, except that annual precipitation was a positive influence on exports (Figure 2d).The combined influence of high  HCO3concentrations and high annual precipitation on  HCO3export is best exemplified by Swiftcurrent Cr., which had the greatest  HCO3concentrations, second greatest precipitation, and greatest  HCO3exports among the study sites.These results are consistent with previous studies that have documented positive relations between precipitation, runoff, and solute export at a wide range of basin scales (Drever & Clow, 1995;Raymond & Oh, 2007).
Positive relations between annual precipitation and export of  HCO3 -(and other weathering products, such as silica) supports the interpretation that chemostatic behavior is a key influence on aquatic carbon exports.A previous study at the Andrews Cr., CO, study site identified several mechanisms for chemostatic behavior (Clow & Mast, 2010).Flushing of high-concentration water from the subsurface by snowmelt and rain through advective transport contributes directly to chemostatic behavior, and there are secondary effects as well.By diluting water stored in the subsurface, hydrologic flushing causes mineral saturation indices to shift farther from equilibrium, enhancing weathering rates (Steefel, 2008).Additionally, when snowmelt and rain infiltrate the subsurface, they increase soil wetness and reactive mineral surface area, which further increases weathering rates (Clow & Mast, 2010).A key implication is that variations in precipitation are likely to have a significant effect on aquatic carbon exports and CO 2 consumption by mineral weathering (Berner, 1992;Clow & Mast, 2010).
Like DOC, AVWM PC concentrations were greatest in basins with abundant wetlands.Results from the MLR analysis (not shown for brevity) indicate that %wetland and %herbaceous grassland had a positive influence on PC concentrations, and %ice/snow had a negative influence.These relations largely reflect the organic matter percentage (OM%) of soils in each landscape, with high OM% in wetland and herbaceous grassland environments, and low OM% in glacial terrain.The relatively low AVWM PC concentrations at the study sites resulted in low PC export, which ranged from 0.01 to 2.91 g C m −2 yr −1 (median 0.13 g C m −2 yr −1 ; Table S2 in Supporting Information S1).One caveat about our estimate of PC export is that, although we had hoped to develop useful surrogate relations between PC and high-frequency turbidity measurements to improve estimates of PC export during storms, we were largely unsuccessful; regressions between PC and turbidity explained less than 17% of the variance in PC.Thus, PC export during storms remains poorly quantified at our study sites.
Lateral exports of CO 2 are available only for the sites in RMNP, where they ranged from 0.09 to 0.47 g C m −2 yr −1 (median 0.26 g C m −2 yr −1 ; Table S2 in Supporting Information S1).There are few published data on lateral exports of CO 2 for comparison; however, Dawson et al. (2002) and Dinsmore et al. (2013) reported lateral CO 2 exports of 0.26-1.27g C m −2 yr −1 for peat-dominated systems in the United Kingdom.
This study is one of the first to document all the major components of lateral exports of aquatic carbon in mountain streams.Lateral exports were dominated by DOC and  HCO3 -, with lesser contributions from PC and CO 2 (Table S2 in Supporting Information S1).Variations in climate had a substantial effect on aquatic carbon concentrations and fluxes (Figure 2), and if recent warming and drying trends continue, commensurate declines in aquatic carbon fluxes may be expected.

Seasonal Variations in Exports
Seasonal exports of aquatic carbon largely reflect seasonal patterns in runoff (Figure 3).In most study basins, aquatic carbon exports were greatest during the snowmelt period (May-June); for DOC and  HCO3 -, they accounted for 65-89% and 49-69% of annual export, respectively.During some years, such as 2013-15, peak exports occurred much earlier in the Sierra than in the Rocky Mountains because of abnormally warm and dry winter/spring weather in the far west (Hidalgo et al., 2009;Stewart, 2009).Previous studies have documented strong shifts in the timing of snowmelt in the western U.S., with early melt associated with abnormally shallow snowpacks and warm springtime weather (Cayan et al., 2001;Clow, 2010;Stewart et al., 2004).Our results from the Sierran sites suggest that a regional shift in timing toward earlier melt is likely to induce earlier, and perhaps smaller, peaks in aquatic carbon export in the future.
Seasonal patterns in aquatic carbon exports were different at Lookout Cr. than in the other study basins, where annual hydrographs are dominated by winter accumulation and springtime melting of seasonal snowpacks (Figure 3).At Lookout Cr., precipitation, runoff, and aquatic carbon exports were greatest during the winter period (November-February) when most precipitation occurs, rather than during spring and early summer.Results from Lookout Cr. may provide a preview of how the seasonality of aquatic carbon fluxes in seasonally snow-covered catchments may shift in the future, as they transition from snow dominated to rainfall dominated precipitation regimes.

Daily and Sub-Daily Variations
Although discrete sampling can provide useful information for quantifying seasonal and annual exports and how they are influenced by landscape characteristics, higher-frequency data enable characterization of aquatic carbon dynamics and the hydrologic and biogeochemical processes that drive them at fine temporal scale.
Seven years of high-frequency discharge and fDOM T, t data from the North Inlet study site shows strong periodicity at multiple time scales (Figure 4a).Each year, the main discharge event is driven by the accumulation and melting of the seasonal snowpack, with the magnitude of peak discharge reflecting the maximum snowpack water content (Figures 4b and 4c).Discharge typically is low during winter, when the snowpack is accumulating, and it increases sharply during May-June, when the snowpack begins to melt.This is followed by a gradual recession in discharge through the summer period, interrupted occasionally by summer and fall rainstorms (Figure 4c).fDOM T, t follows a similar pattern, with low concentrations during winter, a broad annual peak on the rising limb of snowmelt runoff (April-May), and sharp transient spikes in response to storm events.Interestingly, although fDOM T, t peaks prior to peak discharge during snowmelt, transient fDOM T, t and discharge peaks usually are nearly synchronous during storm events (Figure 4c).We interpret this to indicate that although flushing of DOC from catchment soils is important during both types of events (snowmelt and storms), the pool of available DOC in soil water is depleted during snowmelt because of the magnitude and duration of the event.Depletion typically does not occur during individual storm events because flushing is of smaller magnitude and duration than during snowmelt.
The influence of seasonal cycles and storms on fDOM T, t can be seen in the CWT plot as areas of strong spectral power highlighted in red (Figure 4a).Each year, there is strong spectral power at a period of 8760 during April-May, reflecting the influence of snowmelt on fDOM T, t at the annual time scale.Strong spectral power also was evident during storm events that occurred sporadically through the summers, such as in 2014.Each year, fDOM T, t displayed strong periodicity at the diel time scale (24) beginning in April and tapering off through the summer (Figures 4a, 4c-4e).This pattern is similar to that of discharge, except diel fluctuations in discharge tapered off much sooner than those of fDOM T,t (Figures 4c-4e) The diel pattern in fDOM T,t during snowmelt may reflect mixing of dilute snowmelt with shallow, organic-rich soil water (Boyer et al., 1997;Tank et al., 2018); however, other processes are likely important during late summer, when diel variability in discharge is minimal (Figure 4e).These processes might include aquatic metabolism and photo-oxidation of dissolved organic matter (DOM) during daylight hours (Nimick et al., 2011).
The periodicity in fDOM T,t shown for North Inlet in Figure 4 is present at all of the study sites in RMNP; the accumulation/melting of the seasonal snowpack drives seasonal variations, storms induce transient spikes, and a variety of processes contribute to diel variability in fDOM T, t .One important difference among sites is in the magnitude and duration of diel variability, which is greater at the lower-elevation sites than at the higher-elevation sites.This is consistent with observations in previous studies that diel cycles tend to be greatest in highly productive, clear, and slow-moving streams (Nimick et al., 2011).By using high-frequency data from in-stream sensors,  results from this study expand our understanding of multi-scale temporal variability in aquatic carbon in mountain streams.

Hysteresis
Concentration-discharge (C-Q) relations can provide additional insight into mechanisms driving variations in stream concentrations at various time scales.A plot of fDOM T, t against discharge at North Inlet for 2014 shows strong clockwise hysteresis at the seasonal time scale, with much higher fDOM T, t concentrations on the rising limb of the snowmelt hydrograph than on the falling limb (Figure 5).This supports the hypothesis that fDOM T, t that accumulates in the soil during winter through partial decomposition of soil carbon is flushed into the stream by percolating snowmelt (Boyer et al., 1997;Brooks et al., 1999).Lower concentrations on the falling limb and a shift toward a much weaker C-Q relation at peak snowmelt runoff reflect depletion of a finite pool of DOM in soil water (Brooks et al., 1999;Pellerin et al., 2012;Winnick et al., 2017).The implication is that fDOM T, t concentrations in the stream shift from being transport limited during winter/spring to supply limited at peak snowmelt as the pool of DOM in soil water is depleted.Hysteresis was much weaker at diel and event time scales, and variations in fDOM T, t at those times could be the result of simple mixing between shallow soil water and groundwater (Winnick et al., 2017).

Temporal Dynamics
Temporal variations in fDOM T, t concentrations are controlled by complex interactions between hydrologic and biogeochemical processes.Regression coefficients in MLR equations used to reproduce temporal variations in aquatic carbon concentrations can provide insight into the relative importance of those processes.A comparison of regression coefficients for sites in RMNP shows similarities and differences among sites (Table S3 in Supporting Information S1).
At most sites, discharge had a strong, positive influence on fDOM T,t concentrations, consistent with flushing of DOM from shallow catchment soils during snowmelt and rain events (Table S3 in Supporting Information S1, see Figure 6a for an example of temporal MLR results).Exceptions occurred at the two highest elevation sites (sites 1 and 2, Table S1 in Supporting Information S1), where the fDOM T, t -discharge relations were weak or undetectable (Table S3 in Supporting Information S1).The weak fDOM T, t -discharge response at the high-elevation sites may reflect a small soil DOM pool in those basins due to a paucity of well-developed soils.One commonality in the MLR results among sites was inclusion of sine and/or cosine of the day of the year, indicating that seasonal-scale hysteresis occurred at all the sites.This implies that DOM flushing during snowmelt was ubiquitous as well.Most sites showed a negative relation between fDOM T, t and water temperature, which might reflect higher mineralization and photobleaching rates of DOM when temperatures are warm (Laudon et al., 2012;Nimick et al., 2011).Most sites also showed a positive relation between fDOM T, t and SC, consistent with derivation from a common source, that is, shallow soil water.Deeper soil water and groundwater have high SC, but low DOM, thus they are unlikely to be the main fDOM T, t source (Clow & Mast, 2010;Tank et al., 2018).
The time-series MLR equations that were used to fill gaps in the fDOM T, t record explained 74-90% of the temporal variance in observed fDOM T, t during the 2011-2017 study period and had RMSEs of 0.07-0.14ppb quinine sulfate equivalents (Table S3 in Supporting Information S1; Figure 6a).Figures 7a and 7d show observed and estimated fDOM T, t for North Inlet.The agreement between observed and estimated fDOM T, t indicates the MLR equations can be used to reliably estimate fDOM T, t during periods of missing data and to replicate fDOM T, t temporal dynamics.By implication, the MLRs also can be used to reproduce DOC dynamics, provided there are strong relations between fDOM T, t and DOC.
Concentrations of fDOM T, t and DOC were strongly correlated at all the sites in RMNP, and in most cases, the relations were linear (r 2 > 0.85, Figure 8).At several sites, the relation was slightly non-linear, and using the natural log of DOC improved the fit.The slight non-linearity is consistent with the inner filter effect, in which high concentrations of DOC interfere with fDOM measurements (Saraceno et al., 2017).The gap-filled fDOM T, t records were combined with the DOC-fDOM T, t relations shown in Figure 8 to make estimates of daily DOC concentrations for each site in RMNP.A time-series plot of DOC concentrations for North Inlet shows strong seasonal variations in response to snowmelt, as well as strong increases in DOC in response to storms, such as the event during September 2013 (Figures 7b and 7e).Measured DOC concentrations usually fell within the 95% confidence interval of DOC estimates; however, interpolated DOC concentrations sometimes did not (Figure 7e).This indicates that the high-frequency fDOM T,t record was able to capture dynamic responses to storm events, such as those that occurred during July-September 2014 at North Inlet.In contrast, DOC concentrations estimated by linear interpolation between discrete measurements failed to capture those responses.
Like DOC,  HCO -3 concentrations estimated using MLR show strong seasonal patterns; concentrations increased through winter until the beginning of snowmelt, when they rapidly declined due to dilution and acid neutralization reactions, reaching a minimum near peak runoff (Figures 7c and 7f).
HCO3concentrations gradually recovered through the summer and fall, except for sharp downward spikes during storm events.As with DOC, the high-resolution estimates for  HCO3captured rapid changes in chemistry during storms, whereas interpolation of concentrations between discrete measurements did not (Figure 7f).These results confirm the utility of using high-frequency data and time-series models to better understand dynamic responses to storm events.
The time-series MLR equations explained 72%-91% of the temporal variance in  HCO3concentration, indicating they are useful tools for representing  HCO3dynamics (Table S3 in Supporting Information S1, Figures 7c  and 7f).The regressions generally were stronger at sites in the larger basins (sites 4-7), reflecting greater consistency in  HCO3response to events like snowmelt and storms at larger basin scale.There was a positive relation between  HCO3and SC in the time-series MLRs, as expected given that  HCO3usually is the dominant anion in RMNP stream water (Figure 6b, Clow et al., 2018).Unlike fDOM T, t ,  HCO3had a negative relation with discharge, reflecting dilution of  HCO3as flows increased.The slope of the  HCO3 --discharge relation was greater in the larger basins, indicating the dilution effect was stronger in those basins.We hypothesize that the dilution effect is a result of soil water and groundwater mixing with dilute snowmelt and rain, and greater dilution occurs in larger basins because they have higher baseline  HCO3concentrations.

Comparison of Exports From Discrete Sampling and High-Frequency Measurements
Multiplying daily concentrations of DOC and  HCO3estimated using the hi-res (MLR) method by daily discharge yielded high-resolution estimates of DOC and  HCO3export.Linear regression of annual exports calculated using the sample-interpolation method against those calculated using the hi-res method indicates good agreement, with r 2 s ≥ 0.93 and RMSEs of 0.33 g C m −2 yr −1 for DOC and 0.03 g C m −2 yr −1 for  HCO3 -(Figure 9).Uncertainty in the estimates is indicated by shading in Figure 9.For DOC, the slope of the regression was 0.95, indicating the sample-interpolation method yielded slightly lower estimates than the hi-res method, indicating a possible bias of approximately −5% for the interpolation method.Differences are at least partly due to the inability of the interpolation method to account for heightened DOC exports during storm events (Birkel et al., 2014).For  HCO3 -, the slope of the regression was 1.05, indicating the sample-interpolation method yielded higher estimates than the hi-res method with a possible bias of +5% for the interpolation method.As with DOC, the difference may be attributed to inaccurate estimates by the interpolation method during storms; in this case, the interpolation method failed to account for declines in  HCO3that occur during storms.
The relatively good agreement between exports estimated using the two methods is noteworthy given previous studies that indicated storms often account for large fractions of annual DOC exports, with the implication that high temporal-resolution measurements are essential to accurately quantifying aquatic carbon exports (Birkel et al., 2014;J. M. Clark et al., 2007;Raymond & Saiers, 2010).Birkel et al. (2014), for example, found that exports from northern peat-dominated catchments calculated using high-resolution time-series models were more than double those calculated from weekly sampling, and they attributed the difference to coarser resolution sampling "missing important DOC flushing events."Raymond and Saiers (2010) estimated that 86% of annual DOC export from temperate forest streams in the eastern U.S. occurred during storms.And at a small upland peat catchment in the United Kingdom, J. M. Clark et al. (2007) noted that coarse-scale monitoring could either under-or over-estimate exports, depending on time of year.One commonality among the sites in the previous studies was that most precipitation fell as rain.At our study sites, which are snow dominated, exports during storms accounted for a relatively small fraction of annual exports.At North Inlet for example, storms accounted for 0.7-9.8% of annual DOC export, and 1.3-14.1% of annual  HCO3export.In contrast, the snowmelt period accounted for 65-89% and 49-69% of annual export of DOC and  HCO3 -, respectively.These results for snowmelt-period exports are consistent with previous studies in the Rocky Mountains (Boyer et al., 1997;Brooks et al., 1999), and indicate that the importance of storm events for aquatic carbon exports varies strongly with the dominant hydroclimatic regime.Capturing storm events using high-frequency measurements is likely to be more important in rainfall-dominated catchments than in seasonally snow-covered catchments.As precipitation in seasonally snow-covered catchments transitions from snow to rain, we might expect the importance of storm-driven aquatic carbon exports to increase as well.

Aquatic Carbon Budgets for Mountain Headwater Streams
A full aquatic carbon budget was calculated for the study sites in RMNP by combining lateral export data from this study with data on CO 2 exchange in Clow et al. (2021).For CO 2 exchange, fluxes were estimated and summed for all perennial stream reaches in a given basin and normalized to basin area for consistency with lateral flux estimates (Clow et al., 2021).Median total lateral exports during 2011-17 for sites in RMNP ranged from 1.44 g C m −2 yr −1 in the alpine zone (sites 1-3 in Table S1 in Supporting Information S1) to 3.76 g C m −2 yr −1 in the montane zone (Figure 10; sites 4-7 in Table S1 in Supporting Information S1).DOC was the dominant species, accounting for two-thirds to three quarters of total lateral exports.HCO 3 − and lateral export of CO 2 also were important, accounting for 10-15% and 5-24% of lateral exports, respectively.PC was the smallest component, accounting for 4-8% of lateral exports.CO 2 evasion fluxes were substantial, ranging from 3.71 to 12.13 g C m −2 yr −1 (median = 9.15; Clow et al., 2021), 1-5 times as large as lateral exports (Figure 10; Table S2 in Supporting Information S1).The CO 2 evasion fluxes are larger than those previously estimated for most natural systems (Dinsmore et al., 2013;Huotari et al., 2013;Peter et al., 2014;Schelker et al., 2016), but are similar to those reported for steep mountain headwater streams in the Swiss Alps (Horgby, Segatto, et al., 2019).The high evasion fluxes in Clow et al. (2021) and Horgby, Segatto, et al. (2019) were attributed to inflows of high-CO 2 groundwater into streams, which rapidly evaded CO 2 along turbulent reaches (Horgby, Boix Canadell, et al., 2019).Summing lateral exports and CO 2 exchange for the study sites in RMNP yields estimates of total aquatic carbon fluxes of 7.2-15.7 g C m −2 yr −1 (median = 12.22; Figure 10; Table S2 in Supporting Information S1).To our knowledge, this is the first complete, multiyear aquatic carbon budget for seasonally snow-covered mountain headwater streams.
Comparisons with aquatic carbon budgets for other undisturbed freshwater landcover types, such as forests and peatlands, indicate that aquatic carbon fluxes from mountain headwater streams are comparable in magnitude to those from other systems, contrary to the findings in Crawford et al. (2015).A meta-analysis of local-scale studies indicated that the median annual aquatic carbon flux from forests is 9 g C m −2 yr −1 (range 1-20), primarily through lateral export (Webb et al., 2019 and references therein).Peatlands tend to have larger fluxes, with median fluxes of 37 g C m −2 yr −1 (range 3-54, excluding one outlier), and again lateral exports dominate (Webb et al., 2019 and references therein).DOC usually is the largest component of lateral exports from peatlands, but in forested systems, dissolved inorganic carbon exports can dominate if underlying bedrock contains carbonate.CO 2 evasion fluxes can be important as well (Horgby, Segatto, et al., 2019).In a larger-scale meta-analysis for the conterminous U.S., Butman et al. (2016) reported aquatic carbon yields of 17.3 g C m −2 yr −1 for the upper Colorado River Basin, a mountainous region of the western U.S., and 86% of the flux was from CO 2 evasion.For the conterminous U.S., the average aquatic carbon yield was 18.8 g C m −2 yr −1 , with CO 2 evasion accounting for 65% of the total aquatic flux (Butman et al., 2016).Continuing up in scale, global lateral export in streams and rivers is estimated at 6.0 g C m −2 yr −1 (Battin et al., 2009;Cole et al., 2007), and CO 2 evasion is estimated to be 12.1 g C m −2 yr −1 (Raymond et al., 2013), for a total global aquatic carbon flux of 18.1 g C m −2 yr −1 .As others have noted (Argerich et al., 2016;Webb et al., 2019), this is similar in magnitude to global average terrestrial net ecosystem production (NEP) of 17.6 g C m −2 yr −1 (Koffi et al., 2012).Accurate NEP estimates need to account for transport of carbon from terrestrial to aquatic systems; however, this is not commonly done (Casas-Ruiz et al., 2023;Webb et al., 2019).Doing so can reduce NEP estimates substantially, sometimes changing estimates of NEP from indicating ecosystems are net sinks to indicating they are net sources of carbon to the atmosphere.Development of methods to integrate terrestrial and aquatic carbon budgets is a key research need for the future (Butman et al., 2016;Casas-Ruiz et al., 2023).

Conclusions
In this study, lateral exports of DOC,  HCO3 -, and PC were quantified for 15 mountain headwater streams in the western U.S. Lateral exports were compared to hypsography, vegetation, soil, geology, annual precipitation, and temperature to determine the influence of basin characteristics and climate on aquatic carbon budgets.Climate plays a key role influencing interannual variations in aquatic carbon fluxes, with higher fluxes during wet years than during dry years and large seasonal variability in fluxes that are controlled by the timing and magnitude of snowmelt runoff.Temperature has a strong influence on DOC, but the relation is complex and may be non-linear; results indicate DOC exports peak when MAT is between 0 and 2°C, consistent with previous research in Finland (Laudon et al., 2012).These results indicate that changes in climate can have a strong influence on aquatic carbon exports in the future.In mountain catchments with seasonal snowpacks, declining snowfall and warming temperatures may result in shifts in the timing and magnitude of aquatic carbon fluxes.
Basin characteristics have a strong influence on aquatic carbon.In our study, DOC had a strong negative relation to average basin slope, reflecting short contact times and thin, patchy soils in basins with high relief.Wetlands had a positive effect as flow through organic-rich wetland soils enhanced DOC concentrations during snowmelt and storms.Contact time and the presence of carbonate minerals had a positive influence on  HCO3concentrations and exports, reflecting enhanced weathering and water-rock interaction in basins with deep soils and reactive bedrock.
High-frequency monitoring revealed dynamic responses in DOC and  HCO3concentrations at diel and event time scales.Strong diel cycles in DOC were observed, likely due to sub-daily variations in flow paths and water sources (snowmelt and shallow soil water), aquatic metabolism, and photo-degradation.Summer rainstorms elicited transient spikes in DOC and transient depressions in  HCO3 -, reflecting flushing of dilute rainwater through shallow soils rich in organic matter.As in many temperate and boreal systems, accounting for dynamic fluxes during storm events is essential for accurate aquatic carbon flux estimates.
Aquatic carbon fluxes from mountain headwater streams are comparable in magnitude to those from forests, peatlands, and to the global average.They also are comparable to global average NEP estimates; however, NEP calculations that do not account for losses via the aquatic pathway can substantially overestimate terrestrial carbon sequestration.This has important implications for global carbon budget estimates, which may need to be revised to better account for transport of carbon from terrestrial to aquatic systems.

Figure 1 .
Figure 1.Map of study sites in western United States with Rocky Mountain National Park expanded on right.Graphs show annual exports of dissolved organic carbon and bicarbonate (  HCO3 -) (0-5 g C m −2 yr −1 , except Swiftcurrent, which is 0-11 g C m −2 yr −1 ) by year for 2011-2017.Sites 1-10 are in the Rocky Mountains, 11-12 are in the Cascade Range, and 13-15 are in the Sierra Nevada.Cr. = Creek.Vertical datum is NAVD88.

Figure 2 .
Figure 2. Results from multiple-linear regression analysis of landscape factors influencing Annual volume-weighted mean concentrations and export of dissolved organic carbon (DOC; (a) and (b)), and bicarbonate (  HCO3 -; (c) and (d)) in 15 mountain headwater streams of the western U.S. In plots on the left, red line indicates slope of the regression line, shaded area indicates 95% confidence interval of regression line, and RMSE is root mean square error.Scaled parameter estimates are beta coefficients centered by the mean, scaled by range/2, and show the relative influence of parameters in the regression equation.Data source: (Clow et al., 2023; U.S. Geological Survey, 2023b).

Figure 3 .
Figure 3. Monthly runoff and exports of dissolved organic carbon, bicarbonate (  HCO3 -), and particulate carbon at study sites during 2015.Data source: (Clow

Figure 6 .
Figure 6.Results from multiple-linear regression analysis of dynamic factors used to reproduce temporal patterns in fDOM T, t and  HCO3concentrations at North Inlet, 2011-17 water years.In plots on the left, red line indicates slope of the regression line, shaded area indicates 95% confidence interval of regression line, and RMSE is root mean square error.Scaled parameter estimates are beta coefficients centered by the mean, scaled by range/2, and show the relative influence of parameters in the regression equation.Data source: (Clow et al., 2023; U.S. Geological Survey, 2023b).

Figure 7 .
Figure 7. Observed and estimated fDOM T, t , dissolved organic carbon (DOC), and  HCO3concentrations at North Inlet; a-c shows 2011-17 water years, and d-f show expanded view of 2014.Gray lines indicate 95% confidence intervals for estimated DOC and  HCO3 -.Light gray shading indicates periods of snow cover.Data source: (Clow et al., 2023; U.S. Geological Survey, 2023b).

Figure 8 .
Figure 8. Scatter plots showing relations between fDOM T, t and dissolved organic carbon at sites in Rocky Mountain National Park.Data source: (Clow et al., 2023; U.S. Geological Survey, 2023b).

Figure 9 .
Figure9.Annual exports calculated using sample interpolation method plotted against annual exports calculated using high-resolution concentration estimates from multiple-linear regression analysis.Dark gray shading indicates uncertainty in the slope of the regression.Light gray shading indicates uncertainty in individual annual export estimates.Data source:(Clow et al., 2023; U.S. Geological Survey, 2023b).

Figure 10 .
Figure 10.Median annual fluxes of aquatic carbon from stream in Rocky Mountain National Park in g C m −2 yr −1 .Two pies are shown for each site.CO 2 exchange and total lateral exports are shown in the pie on the left; individual lateral export components are shown in the pie on the right.Data source: (Clow et al., 2023; U.S. Geological Survey, 2023b).