The Penman-Monteith equation is often used to estimate transpiration, but an important limitation to this approach, especially for mountainous forested sites, is an accurate estimate of canopy conductance averaged over the area of interest (Gs). We propose a method for estimating watershed-scale transpiration using estimates of Gs derived from measurements of stable isotopes. To estimate Gs, we first determined the isotopic composition of ecosystem respiration (δ13CER) as derived from the 12C:13C ratio of respired CO2 entrained within nocturnal cold air drainage flows exiting the base of the watershed. An isotope-derived estimate of recent canopy conductance over the entire watershed (Gs-I) was derived using biophysical models. To estimate daily average transpiration, we applied Gs-I and other measured environmental variables to the Penman-Monteith equation. The results were compared with an independent measure of transpiration using the heat dissipation method at four locations within the watershed. Considering the large number of assumptions required for both estimates of transpiration, the two estimates were remarkably similar. The relationship between the values derived by the two techniques was statistically significant (p value < 0.01), the slope of the line (slope = 1.7) was not statistically different from 1 (p value > 0.1), but the standard error was large (SE = 0.48). The results demonstrate that this technique holds promise, but the effects of potential limitations require further attention. The future research necessary to fully demonstrate the validity of this potentially promising method is discussed.
 Transpiration is a large component of the hydrological budget, often accounting for well over half of the water that exits annually from closed-canopied ecosystems [Hewlett, 1982]. It is therefore of great interest to hydrologists to measure and monitor rates of transpiration. In many analyses, evapotranspiration (the combination of both free evaporation from wet surfaces and transpiration) is inferred from a simple mass balance approach as difference between total precipitation and all other measured outputs. However, this approach cannot differentiate between transpiration and evaporation, and it may also be seriously in error if net changes in water storage or leakage through bedrock are not assessed. Evaporation is usually a very small component of evapotranspiration when closed canopies are dry [e.g., Blanken and Rouse, 1995; Schaap and Bouten, 1997]. Evapotranspiration may be estimated from microclimatological measurements by applying the Penman-Monteith equation, which elegantly incorporates the biological and physical controls over transpiration and provides a more accurate estimation of transpiration than other empirical models as it is based on sound biophysical principles [Monteith and Unsworth, 2007]. However, the Penman-Monteith equation requires an accurate estimate of canopy conductance (Gs). This term may vary greatly in response to variations in vegetation structure and function as well as microclimate. Accurate estimation of stomatal conductance is not an issue in low-stature vegetation, like grasslands, because transpiration in these systems is relatively insensitive to changes in Gs; that is., short canopies are relatively uncoupled from the atmosphere [Jarvis and McNaughton, 1986; Monteith and Unsworth, 2007]. In tall, coniferous forest canopies, however, Gs exerts strong control over transpiration [Jarvis and McNaughton, 1986; Monteith and Unsworth, 2007], and is highly variable over daily, weekly and annual time scales [e.g., Bond and Kavanagh, 1999; Marshall and Waring, 1984]. Therefore, using a mean value for Gs derived for a particular species or vegetation type [e.g., Kelliher et al., 1995] can lead to significant errors when the Penman-Monteith equation is used to estimate transpiration of forests [Mackay et al., 2007].
 To understand why carbon isotopes might be used to monitor transpiration, one must first understand how carbon isotopes are fractionated during photosynthesis and respiration by plants. During photosynthesis C3 plants (almost all woody plants and most temperate herbaceous plants are C3 plants) preferentially assimilate 12CO2 over 13CO2. This fractionation is caused by differences in diffusion rates when CO2 enters the stomata and by discrimination by the enzyme ribulose-1,5-bisphosphate carboxylase/oxygenase (rubisco), which preferentially accepts 12CO2 during the carboxylation process [Farquhar et al., 1989]. When plants are water stressed because of low soil moisture availability and/or high atmospheric vapor pressure deficit (VPD), plants often close their stomata, thereby limiting the availability of CO2 for fixation. When CO2 becomes limited, rubisco accepts more 13CO2. Therefore, the stomatal conductance of a leaf is one of the two major influences that affect the ratio of 13C to 12C in sugars resulting from photosynthesis because stomata control the supply of CO2 to rubisco. The other major influence is carboxylation capacity. Farquhar et al.  mathematically described the relationship between carbon isotope fractionation during photosynthesis (Δ13C), the concentration of CO2 within the leaf (Ci) of C3 plants, and the concentration of CO2 in the atmosphere (Ca):
where a is the fractionation against 13C due to the diffusion of CO2 into the stomata and b is the net fractionation due to carboxylation. On the basis of both theoretical and empirical analysis, the values of a and b are commonly assumed to be 4.4‰ and 27.7‰, respectively [Farquhar et al., 1989]. Subsequent to carboxylation, the sugars are transported to various parts of the plant, and from the roots to the soil. Cells in growing shoots, and microorganisms in the soil, use the sugars for respiration, releasing CO2. Recent research suggests that a large portion of CO2 respired from entire ecosystems (both plants and soils) is produced from sugars that were created 0–4 days earlier [Andrews et al., 1999; Bowling et al., 2002; Ekblad et al., 2005; Ekblad and Högberg, 2001; Horwath et al., 1994; Steinmann et al., 2004]. Because a large portion of the CO2 comes from recently manufactured sugars, the isotopic signal of the respiration can be used to explore ecosystem-scale responses to plant water stress.
 Recent research has used the “Keeling plot” approach to monitor how changing environmental variables affect the ratio of 13C to 12C in respiration [Keeling, 1958, 1961]. The Keeling plot is a two end-member mixing model that assumes there are two sources of CO2 in air collected in the canopy air space, ambient CO2 and respired CO2 [Keeling, 1958, 1961]. By using regression analysis to relate the ratio of 13C to 12C (y axis) to the inverse of the CO2 concentration (x axis) of multiple air samples collected during the course of one night, one can determine the isotopic composition of the respiration by extrapolating to the y intercept. To reduce the uncertainty, this method requires the samples to have a wide range of CO2 concentrations [Pataki et al., 2003]. When using the Keeling plot approach, the 13C:12C ratio is usually standardized by comparing the 13C:12C of the air sample (R) to a standard (Vienna Peedee belemnite (Rstd)) in order to express the carbon isotope ratios as δ13C (‰):
In recent reports, we demonstrated that the very conditions that complicate many micrometeorological studies in mountainous regions may offer an opportunity for an entirely different approach for studying processes at the ecosystem scale [Pypker et al., 2007a, 2007b]. In a deeply incised watershed (20 to 33° slopes) in western Oregon, we estimated that more than 90% of the respired CO2 from the entire ecosystem can be flushed from the watershed by nocturnal cold air drainage [Pypker et al., 2007b]. We also found that, on most clear nights, the range of CO2 concentrations in drainage air over a single night was sufficient to use the Keeling plot approach to determine the carbon isotope composition of ecosystem-respired CO2 (δ13CER) [Pypker et al., 2007a]. Using this technique we demonstrated that changes in δ13CER may be used to predict changes in Gs [Pypker et al., 2008]. If this finding holds up to further scrutiny in other watersheds, and the measurement techniques are improved, it may be possible to quantify the main control on transpiration of forests in mountainous ecosystems. Furthermore, by combining the deduced Gs and locally measured meteorological data in a standard transpiration model, such as the Penman-Monteith equation [Monteith and Unsworth, 2007], it may be possible to predict watershed-scale transpiration. However, questions remain.
 For δ13CER to be used to predict Gs using the technique outlined by Pypker et al.  the only significant source of isotope variability must be due to fractionation during recent carbon fixation. If significant postassimilation fractionation [e.g., Badeck et al., 2005; Bowling et al., 2008; Duranceau et al., 1999, 2001; Ghashghaie et al., 2001, 2003; Hymus et al., 2005; O'Leary, 1981; Prater et al., 2006; Xu et al., 2004] occurs in Douglas fir forests, we would be unable to predict transpiration using δ13CER unless this additional term could be quantified. In addition, we assume the isotopic signal from respiration remains constant throughout the night. If these or other assumptions defined in the methods are violated, then we would be unable to predict transpiration. The goal of this paper is to determine whether δ13CER has the potential to be used as a tool to estimate the transpiration of an entire watershed using the isotope-derived Gs in combination with locally measured meteorological data.
2. Materials and Methods
2.1. Study Site
 The study area was a 96 ha watershed (“watershed 1”), located in the H. J. Andrews Experimental Forest in the western Cascades of central Oregon, USA (44.2 °N, 122.2 °W) (Figure 1). The watershed is predominately covered by young Douglas fir replanted following clear-cut harvesting in the late 1960s. Smaller components of the tree basal area consist of western hemlock (Tsuga heterophylla (Raf.) Sarg), bigleaf maple (Acer macrophyllum Pursh), vine maple (Acer circinatum Pursh) and red alder (Alnus rubra Bong.); the angiosperm populations are greatest within the riparian area [Moore et al., 2004]. The canopy was between 25 and 28 m tall [Moore et al., 2004]. The soil has Andic properties, is seasonally reduced, and has loamy to gravelly clay loam texture [Swanson and James, 1975]. The site has wet mild winters and warm dry summers with a mean annual precipitation of 2300 mm, about 80% of which falls during the winter months [Rothacher et al., 1967]. In the warm dry summers, cold air drainage occurs on most nights [Pypker et al., 2007a].
2.2. Environmental Variables
 A 37 m tower located at the base of the watershed was instrumented in May 2005 with ten shielded thermistors (Model 107 temperature probe, Campbell Scientific, Inc., Logan, Utah), a net radiometer (Q7 REBS, Campbell Scientific, Inc.), a shielded temperature/RH probe (HMP45c, Campbell Scientific, Inc.), eight 2-D sonic anemometers (WS425, Vaisala, Helsinki, Finland) and two 3-D sonic anemometers (81000, R. M. Young, Traverse City, Michigan). The 2-D and 3-D sonic anemometers were measured at 0.1 and 1 Hz, respectively, and values were averaged over 1 min intervals. The remaining instruments were recorded every 1 s and averaged over 15 min intervals (using CR10X and CR23X data loggers, Campbell Scientific, Inc.).
 Perpendicular to the axis of the valley, a transect of eight plots (four on each slope) was established in the spring of 2005 (Figure 1). At each plot, air temperature/relative humidity was measured at midcanopy (HMP45c, Campbell Scientific, Inc.) and soil moisture (Echo-20, Decagon Devices, Pullman, Washington) and soil temperature (model 107 temperature probe, Campbell Scientific, Inc.) were measured at 5, 30 and 100 cm depth. Calibration equations that were specific to HJA soils were used to convert the millivolt signal from the soil moisture sensors to volumetric water content [Czarnomski et al., 2005]. Observations were recorded by a data logger (CR23X, Campbell Scientific, Inc.) every 15 s and averaged over 15 min intervals.
2.3. Sample Collection and Analysis
 Air samples for isotopic analysis were collected using methods outlined by Pypker et al. . Air samples were collected on 11 nights from 8 May to 25 October 2006 for isotope analysis using an automated air collection system [Hauck, 2006] at three heights (3, 10, 30 m above ground) on the tower (Figure 1). Air was pumped at ∼1.5 L min−1 (model UNMP30KNDC, KNF Neuberger, Inc.) through tubing from one of the three heights as selected by a six position stainless steel valve (Valcon M, Valcon Instruments, Houston, Texas), then passed through a 200 cc cylinder containing magnesium perchlorate to absorb water vapor before entering a 16 position sample valve (Valcon M, Valcon Instruments). At each position on the valve, a 15 mL coiled sample loop of stainless steel was connected, so that sampled air passed through one of the 16 loops prior to exiting. The air was then directed to an infrared gas analyzer (IRGA) (LI-6252, LI-COR, Inc., Lincoln, Nebraska, USA). The valves, pumps and IRGA were controlled by a data logger (CR10X, Campbell Scientific, Inc.), which recorded the sampling time and CO2 concentration of the air passing through the system. One hour after sunset, sampling began at 5-min intervals. To ensure a broad range of CO2 concentrations the samples were collected only if their concentrations differed from previous samples by a value set a priori [Lai et al., 2005]. If the concentration of CO2 in the current sample loop exceeded that of past samples by >4 ppm, the valve moved to the next position and a new sampling height on the tower was selected. If the concentration difference was ≤4 ppm, the system continued to sample from the same tower height and sample valve position and attempted to take a sample 5 min later. This process continued until either all 15 sample loops filled (the 16th sample loop could not be used to collect a sample because it remained open to the atmosphere after the system finished collecting samples) or it was 1 h before sunrise. If the sample loops were full the system shut down. If all the sample loops were not full 1 h prior to sunrise, the system collected samples every 5 min until the remaining sample loops were filled [Hauck, 2006].
 Air samples were analyzed in the laboratory within 24 h of collection. For δ13C analysis, we used a Finnigan/MAT DeltaPlus XL isotope ratio mass spectrometer interfaced to a GasBench II automated headspace sampler at the College of Oceanic and Atmospheric Sciences, Oregon State University [Hauck, 2006]. The GasBench-II is a continuous flow interface that allows injections of several aliquots of a single gas sample into a mass spectrometer for automated isotope determinations of small gas samples. The sample valve was directly plumbed into the mass spectrometer. Helium pushed the sample air out of the sample loops and into the mass spectrometer with each aliquot being 250 μL. A typical analysis consisted of three gas standards (tank CO2-He mixtures), five sample replicates and an additional two gas standards for every sample loop. The CO2 concentration [CO2] of each sample was calculated from the peak volt area produced by the mass spectrometer analysis of each sample loop [Hauck, 2006]. To calibrate the system, each of the sampling containers was filled with a gas of a known CO2 concentration (403 and 958 ppm; as determined by NOAA). The air was passed from the loops into the mass spectrometer in the same manner as the air samples from the field. A linear relationship between peak volt area and CO2 concentration was generated. This CO2 calibration was performed independently for each sampling date.
2.4. Data Analysis
 A two end-member mixing model (“Keeling plot”) was used to estimate δ13CER [Buchmann and Ehleringer, 1998; Flanagan and Ehleringer, 1998; Keeling, 1958; 1961]. Prior to inclusion in the Keeling plot, all data points were screened for accuracy using methods outlined by Pypker et al. . If the standard deviation of the replicates of the δ13C of the reference gas or sample gas was greater than 0.2, the point was removed. This procedure ensured that only reliable data points were included in the analysis. The δ13C of the air samples from the sample loops were plotted against corresponding 1/[CO2] values. We used ordinary least squares regression to relate 1/[CO2] to δ13C as it has been found to be the best method for Keeling plot analysis [Zobitz et al., 2006]. Standard errors of the intercepts were estimated using a bootstrap method. After the Keeling plot was generated, the regression was visually checked for nonrandom residuals. If the Keeling plot had nonrandom residuals the data collected on that date were not used in the analysis as this indicated that there was likely a problem with the data set. Data from only two dates (24 April and 31 July) were rejected using this protocol.
2.5. Transpiration-Heat Dissipation Method
 From April to October, 2006, we used heat dissipation sensors [Granier, 1985, 1987] to measure the water flux of 10 trees per plot in four plots along the transect (Figure 1 and Table 1). The measured trees represented the range of tree diameters in each plot. In each tree, a 2 cm sensor was inserted into the xylem at the 0–2 cm depth interval at 1.4 m above ground so that the outside edge of the sensor was flush with the outer edge of the xylem. In addition, in 3 dominant trees per plot, 1 cm sensors were installed at two additional xylem depth intervals (2–3 cm and 3–4 cm) to account for radial flux profiles [Phillips et al., 1996]. Sapwood depth measurements, visually inspected from increment cores, indicated that none of the sensors crossed the heartwood boundary. Measurements were recorded by a data logger (CR23X, Campbell Scientific, Inc.) every 15 s and averaged over 15 min intervals. Measurements from all pairs of probes were converted to sap flux density (g H2O m−2 sapwood s−1) using empirical equations [Granier, 1985, 1987]. Sap flux in the inner (>2 cm depth) xylem of trees that were not equipped with inner sap flow probes was estimated from a ratio between the outer 0–2 cm flux and the inner 2–3 cm or 3–4 cm fluxes from the measured trees. We assumed that there was no change in flux between the depth of the 3–4 cm sensor and the heartwood boundary.
Table 1. Site Characteristics for Each of the Four Sapflow Plotsa
Provided are the site totals and the total represented by Douglas fir (PSME) for stem density (all trees only), basal area, sapwood depth, and leaf area index (LAI).
Standard error is given in parentheses.
 We scaled measurements from individual sensors to mean transpired water flux per unit ground area (mm d−1). First, for each plot, diameter at 1.4 m was measured for all trees. Xylem depth for each tree was calculated using a diameter to xylem depth relationship developed from over 200 tree cores taken across the watershed (equation (3) (R2 = 0.77, p < 0.01); T. Woolley, unpublished data, 2005):
where dbh is depth at breast height. For each tree, the total xylem area at each depth interval (0–2 cm, 2–3, and >3 cm) was calculated.
 The flux within each depth interval of xylem was calculated as the product of the area of that interval and the measured or predicted flux; we then summed the fluxes for each xylem depth interval to estimate total flux per tree. Last, we summed the fluxes of all the trees on each plot and divided by the ground area to estimate mean transpiration flux per unit ground area. Recent work demonstrates that trees often transpire at night when the VPD is above 600 Pa [Ewers and Oren, 2000]. Within the study watershed VPD was greater than 200 Pa on less than 30% of the sample nights (H. Barnard, unpublished data, 2006). Even on the nights with VPD greater than 200Pa, the effect on Gs is likely minimal, as past research demonstrates that nocturnal transpiration by Douglas fir trees is only 1–7% of daytime transpiration [Dawson et al., 2007].
2.6. Estimates of Canopy Conductance (Gs)
 To test the feasibility of simulating the response of canopy average stomatal conductance to changing environmental variables using δ13CER measurements, we estimated canopy average stomatal conductance by calculating the canopy average stomatal conductance necessary to produce the δ13CER measured on the tower using Farquhar equations (Gs-I) (equations (6)–(7)) [Farquhar et al., 1980, 1989].
 We estimated a hypothetical value for canopy average stomatal conductance (Gs-I) that would be expected if recent photosynthate were the only source of carbon in ecosystem respiration and fractionation during respiration was negligible. To do this, we used the methods outlined by Pypker et al. . In brief, we assumed that the difference between δ13CER and δa (the isotopic ratio of the source air) is equal to photosynthetic discrimination (Δ13C). This assumption allowed us to estimate Gs-I by using a combination of biophysical models for leaf level photosynthetic isotopic discrimination (equations (4) and (5)) [Farquhar et al., 1989] and carbon assimilation/internal CO2 curves (equation (6)) [Farquhar et al., 1980]. We used the following steps when estimating Gs-I. First, carbon discrimination (Δ13C) was estimated using
where δa is the isotopic ratio of the source air. We assumed δa to be −8.2‰. Then, the internal CO2 concentration [Ci] was estimated using
On the basis of the Ci values, the assimilation of CO2 (A) was estimated using
where Vcmax (μmol m−2 s−1) is the maximum rate of rubisco-mediated carboxylation; Kc and Ko (μmol mol−1) are the Michaelis-Menten coefficients for CO2 and O2 binding to rubisco, respectively; Ox (μmol mol−1) is the intercellular partial pressure of oxygen; τ (μmol mol−1) is the CO2 compensation point; and Rd (μmol m−2 s−1) is the daytime respiration rate. Values of Vcmax, τ and Rd (46 μmol m−2 s−1, 27.5 μmol m−2 s−1 and 42 μmol m−2 s−1, respectively) were estimated from A/Ci curves measured on Douglas fir trees of similar age at Wind River, Washington, approximately 150 km north of our site (B. J. Bond et al., unpublished data, 2002). For Douglas fir trees, Vmax regulates photosynthesis when Ci is below 400 ppm [Ethier et al., 2006]. For our analysis, Ci ranged from 174 to 253 ppm. The variables Kc, Ko, Ox were treated as constants with assumed values of 21 μmol mol−1, 2.32 μmol mol−1 and 1.5 μmol mol−1, respectively. We ignored potential temperature effects on Kc, Ko, Ox and τ (Figure 2). Canopy average stomatal conductance was then estimated using
where Ca is the atmospheric concentration of CO2 (assumed to be 380 μmol mol−1), and the factor 1.6 converts from CO2 conductance to water vapor conductance [Taiz and Zeiger, 1991].
2.7. Estimates of Transpiration From Isotope Measurements
 Transpiration for the watershed was estimated by inserting Gs-I and the average weather conditions measured 3–5 days earlier into the Penman-Monteith [Monteith and Unsworth, 2007]. The Penman-Monteith equation was run on a 15 min time step for each of four plots (501, 505, 507, and 510; see Figure 1) and the total transpiration was calculated for each day. The totals from each plot were then averaged, thereby providing an estimate of transpiration for the entire watershed. To estimate the 3–5 day lagged transpiration from the watershed we used
where E is transpiration (kg m−2 s−1), Δ is the rate change of saturation vapor pressure with temperature (Pa K−1), Rn is net radiation measured in the tower at the base of the watershed (W m−2), G is the ground heat flux (W m−2), ρ is the density of air (kg m−3), cp is the heat capacity of air (J kg−1 K−1), ra is the aerodynamic resistance of the canopy (s m−1), λ is the latent heat of evaporation (J kg−1), and VPD as measured in each plot (Pa). Relative to E and the sensible heat flux, G is usually small in forested ecosystems [Oke, 1992]. We assumed G was only 10% of Rn. The aerodynamic resistance (ra) was estimated using
where z is the height of the canopy (m), d is the height of the zone of zero displacement (m), k is von Karman's constant (0.41), zo is the roughness length (m) and u(z) is the wind speed at 33 m on the base tower (m s−1). In using equations (8) and (9) we assumed that d = 0.65 h, where h is canopy height (h = 28 m), zo = 0.1 h, the relative humidity and temperature measured at canopy height at four plots in the watershed (Figure 1) were representative for the entire watershed and atmosphere was neutrally stable [Campbell and Norman, 1998; Monteith and Unsworth, 2007]. The average isotope-derived estimates of evapotranspiration for each plot with sap flow measurements were compared to the average transpiration measurements from the four plots for dates when both methods provided data (n = 10). Two dates with isotopic measurements were not included in the analysis because one or more of the sites measuring transpiration using the heat dissipation method were not in operation.
 All statistical analyses were performed in S-PLUS (S-PLUS® 8.0 for Windows, Insightful Corp., Palo Alto, California).
3.1. Environmental Variables
 The weather in 2006 followed a common pattern for the Pacific Northwest; the summer was dry, with increasing atmospheric vapor pressure deficit during the summer months (Figure 3). The soil moisture declined throughout the summer as there was very little rain during the summer at the site. The wind speeds near the top of the forest canopy were usually below 1 m s−1, but occasionally exceeded 3 m s−1.
3.2. Seasonal Changes in δ13C of Ecosystem Respiration (δ13CER) and Transpiration
 The δ13CER ranged between −23.4 ± 0.8 to −27.6 ± 0.5 ‰ from 8 May to 25 October 2006 (Figure 4). In the spring, δ13CER remained relatively unchanged until mid-July. After this time, changes in VPD and soil moisture resulted in an increase in the δ13CER because the shifts in environmental variables likely reduced canopy average stomatal conductance [Pypker et al., 2008]. When the VPD and Gs measured and modeled 5 days earlier are compared to changes in δ13CER, there is a significant correlation [Pypker et al., 2008].
 Average transpiration, as estimated using the heat dissipation method, was highly variable both seasonally and daily. Within a single season the average transpiration rates ranged from 0.1 (SE = 0.03) to 1.7 (SE = 0.17) mm d−1, with the highest values typically occurring in late June to mid-July (Figure 5). After late July average transpiration steadily declined. Spatially, transpiration also was variable, as the plots near the top of the slopes (501 and 510) typically had greater transpiration rates relative to those located near the bottom of the deeply incised valley (plots 505 and 507). Not surprisingly, plot 507 had the lowest transpiration rates as it was near the bottom of the valley and was on a north facing slope (Figure 1).
3.3. Estimates of Canopy Average Transpiration Using the Penman-Monteith Equation
 Average daily transpiration, as estimated by the heat dissipation method, was similar to the mean transpiration predicted by the Penman-Monteith equation in combination with the isotope derived Gs-I (Figure 6). The slope of the fitted line relating the heat dissipation method derived and isotope derived transpiration was significant (slope = 1.69; SE = 0.48; p value < 0.01; R2 = 0.60); the slope was not statistically different from a slope of 1 (p value > 0.1) and the intercept was not statistically different from zero (intercept = −0.17; SE = 0.45; p value > 0.7). The lack of statistical difference between the regression slope and the 1:1 line was likely due, in part, to the large standard error. The isotope-derived transpiration measurements were considerably greater than the sap flow measurements at transpiration rates above 0.8 mm d−1.
4.1. Contrasting the Two Methods for Estimating Transpiration
 Measured transpiration in this forest was more variable than the observed changes in δ13CER. During the growing season the sap flow, as measured by the heat dissipation method, varied considerably in the late spring and early summer, yet the δ13CER did not. This is possibly because stomatal conductance is only one variable that controls transpiration from a forest; other significant drivers include vapor pressure deficit, net radiation and aerodynamic resistance (equation (8)). Therefore, it is possible for stomatal conductance (and d13CER) to mildly vary, while transpiration experiences large changes.
 The significant correlation between the two measurement methods suggests that measurements of δ13CER can be used in combination with biophysical models to estimate transpiration. The δ13CER derived estimates of transpiration were usually greater than the average heat dissipation method measurements although the difference between the slope of the fitted line and the 1:1 line was not statistically different. The lack of statistical difference resulted because estimated slope had a large standard error (SE = 0.48). The results demonstrate that there is a correlation between the two results, but it is likely that confounding factors do not allow them to agree at high transpiration rates. The offset between the two methods may result from many factors as there are errors in each method.
 The difference in the transpiration estimated by the two methods could result from different estimates of canopy average stomatal conductance. When comparing Gs-I with estimates of Gs from the heat dissipation method, Pypker et al.  found the two were significantly correlated (p value < 0.05; R2 > 0.51) but Gs-I was on average 0.00024 m s−1 greater (for values ranging between 0.0012 and 0.0036 m s−1). When applied to the Penman-Monteith equation, this results in greater estimates of transpiration.
 The differences between the estimates of Gs and Gs-I could occur because the heat dissipation method provides a canopy average estimate of Gs for the dominant tree type, Douglas fir, whereas the isotope method provides a flux weighted estimate of Gs-I. In this paper we assume that Gs-I represented average canopy conductance, but in actuality, it is weighted to the locations where photosynthesis is fixing the most carbon. These locations in the canopy with greater carbon fixation have subsequently greater stomatal conductance relative to the estimates from the heat dissipation method. Hence, at high transpiration rates, it is likely that estimates of Gs-I will be greater than Gs.
 The differences between the two methods could be further increased because the Penman-Monteith equation estimates transpiration from the soil and understory up to the top of the forest canopy, whereas the heat dissipation method only provides estimates for the dominant trees. The understory can supply approximately 10 to 20% of whole canopy transpiration [Black and Kelliher, 1989]. Therefore, the Penman-Monteith equation may exceed the transpiration estimates of only overstory trees, particularly when the soils are relatively moist.
 The difference in transpiration rates could also occur because of errors associated with the heat dissipation method caused by scaling from only four locations in the watershed. With only four plots, one plot could have unreasonable influence on the average. For example, one of the four plots was located in a shady region near the base of a north facing slope (plot 507). Its inclusion in the analysis weakened the relationship between the two methods used to derive transpiration. If the plot is removed, the relationship between the two methods for estimating transpiration is improved (slope = 1.4; SE = 0.39, p value < 0.01, R2 = 0.61 and intercept = 0.001; SE = 0.39; p value > 0.95) (data not shown). However, more work is needed to determine if this plot is representative of areas of extremely low transpiration rates that occur elsewhere in this watershed. For this reason this plot remained in the analysis. In short, both methods for estimating transpiration have many sources of errors and uncertainty that needs further attention in future research needs. Discussion of some needed research follows.
 The use of the linear Farquhar model currently requires many assumptions that can lead to inaccurate estimates of Gs [Seibt et al., 2008]. For example, the equations we used do account for internal transfer of CO2 and photorespiration [Farquhar and Sharkey, 1982; Ghashghaie et al., 2003; Wingate et al., 2007], and this can lead to inaccurate estimates of Ci [Seibt et al., 2008]. To apply our simple method for estimating transpiration, we needed to make numerous assumptions as outlined in our methods. Each of these assumptions must be reviewed, and its effect quantified, if this technique is to be used to estimate transpiration in complex terrain. For example, we assumed that the δ13CER signal was constant throughout the night. However, recent research has shown that the signal can shift as the evening progresses [e.g., Hymus et al., 2005; Prater et al., 2006; Werner et al., 2006]. These shifts could result from changing temperatures in combination with changing substrates consumed during respiration [Kodama et al., 2008]. In our watershed the temperature is variable both spatially and temporally [Pypker et al., 2007b]. Two key assumptions that are central to this paper were that fractionation after assimilation was negligible and the carbon respired at night was recently fixed. These two assumptions must be better explored if this technique is to be applicable.
 The significance of fractionation that occurs after assimilation needs to be assessed and other possible sources of fractionation should be explored. Past research suggest that the difference between the δ13C of sucrose in the leaf and respired CO2 can range between ±0–10‰ [e.g., Duranceau et al., 1999; Duranceau et al., 2001; Ghashghaie et al., 2003; Ghashghaie et al., 2001; Hymus et al., 2005; O'Leary, 1981; Prater et al., 2006; Xu et al., 2004]. For example, a shift in the δ13CER may result because plants might switch the substrate they are metabolizing (e.g., from glucose to lipids) and alter the proportion of sucrose being converted to CO2 and lipids during respiration [Ghashghaie et al., 2003]. These shifts will alter the isotopic ratio of respired CO2, because, as the portion of respired CO2 that is derived from lipids increases, the 13C content of the respiration decreases. Research demonstrates that the difference found between the δ13C of the sucrose in the leaf and the respired CO2 can change over the course of an evening if a plant changes the substrate being metabolized [e.g., Barbour et al., 2007; Mortazavi et al., 2006]. Differences between the δ13C of ecosystem respired air and the bulk leaf is believed to be common, resulting in the ecosystem respired air to be on average 1.7‰ enriched (greater 13C) relative to the bulk leaf [Bowling et al., 2008]. While it is accepted that postassimilation fractionation occurs, it is not known whether size of this fractionation is significant in all species and in all environments [Bowling et al., 2008]. For example, past research demonstrates that difference between the δ13C of ecosystem respiration and the sugars in the leaf is highly variable; enrichment of the respired air relative to the bulk leaf can range from approximately −0.75‰ to 4.5‰ [Bowling et al., 2008].
 The correlation between the isotope-derived transpiration and the transpiration estimated using the heat dissipation method suggests that fractionation that occurs after assimilation might be negligible in this Douglas fir forest during the summer of 2006. If fractionation after assimilation in this forest was indeed substantial, the estimates of Gs-I and transpiration using δ13CER would not be expected to be close to the values on the basis of direct transpiration measurements (heat dissipation method). If there was a small shift in the isotopic ratio from respiration relative to the isotopic ratio of the photosynthate, equations (4)–(7) would not accurately predict the correct Gs. Modeling, field and laboratory experiments suggest that there is indeed an offset between isotopic composition of respiration and photosynthate [see reviews by Bowling et al., 2008; Ghashghaie et al., 2003]. Hence, it is important that future research quantify the effect of postassimilation fractionation on the isotopic ratio of respiration. However, in the current study, the two estimates of transpiration were not very different, which suggests that there was either little fractionation after assimilation in this forest or there were other processes (e.g., offsetting fractionation shifts in the sources of ecosystem respiration) that were offsetting. In the future, the magnitude of fractionation after assimilation for Douglas fir forests must be determined if stable isotopes are to be reliably used to estimate watershed-scale transpiration.
4.3. Other Requirements for Using Carbon Isotopes to Derive Canopy Average Stomatal Conductance
 To successfully use seasonal changes in δ13CER to estimate ecosystem transpiration one must know the size and stability of the source area for CO2. In the study watershed, the cold air drainage patterns are ideal for monitoring seasonal changes in δ13CER [Pypker et al., 2007b]. Nocturnal cold air drainage in this watershed is persistent and occurs on greater than 80% of summer nights [Pypker et al., 2007a]. Because a strong inversion forms above the canopy, respired CO2 is effectively trapped within the watershed [Pypker et al., 2007b]. Below the inversion layer, the air is well mixed, resulting in an integrated δ13C signal. Over the course of an evening the range of CO2 concentrations is sufficient to use the Keeling plot approach to estimate δ13CER [Pypker et al., 2007a]. Trace gas experiments have indicated that the source area probably encompasses the entire watershed [Pypker et al., 2007b]. However, other watersheds may not have a well-defined source area, suitable range in CO2 concentrations or be as decoupled from the synoptic flow. Researchers should determine if the wind patterns and range of CO2 concentrations in their watershed are appropriate prior to attempting this method.
 Despite some challenges in using this method, the use of stable isotopes to derive watershed-scale transpiration has some benefits over direct transpiration measurements using the heat dissipation method. It can be challenging and labor intensive to measure direct transpiration from a sufficient number of trees to accurately estimate transpiration in a mountainous watershed. Douglas fir is conservative when using water, regulating its stomata to prevent leaf water potential from dropping below −2.1 MPa [Bond and Kavanagh, 1999; McDowell et al., 2002]. Thus, the stomatal conductance of Douglas fir is nonlinearly correlated to changes in vapor pressure deficit and soil moisture availability [Bond and Kavanagh, 1999]. In mountainous regions, the microclimate is highly variable because changes in elevation, aspect and soil depth will directly affect incident radiation, VPD and soil moisture [Geiger, 1965]. This variability requires researchers to monitor a large number of trees to accurately represent transpiration in the watershed. In contrast, the air sampled at the base of the watershed requires only one measurement location and provides an integrated signal of the CO2 respired from the entire watershed [Pypker et al., 2007b]. More frequent sampling of atmospheric isotopes is now possible with portable tunable diode lasers [Bowling et al., 2003]. These systems could provide values of δ13CER for each night with suitable weather, thereby providing a dynamic estimate of Gs. Such and advance would help us to understand how the different ecosystem processes affect the δ13CER signal.
 The observed shifts in δ13CER during the summer resulted from recent changes in discrimination during photosynthesis. The measurement of these shifts allowed realistic estimates of Gs [Pypker et al., 2008] and transpiration using δ13CER in combination with biophysical and hydrological models. However, isotope derived estimates of transpiration were consistently greater than the sap flow estimates. This indicates that further research is needed to quantify the sources of the respired CO2 within the watershed and the effect of all of the assumptions on the δ13CER signal.
 We thank J. Moreau, T. Cryer, A. Padilla, J. Mandrick, and C. Czarnomski for their help with site construction, fieldwork, and data collection; A. Schauer for help with data logger programming; and C. Tarasoff for her helpful comments on the manuscript. Last, we wish to thank the anonymous reviewers for their very helpful comments. Funding for this project was provided by the National Science Foundation (grants DEB-0132737 and DEB-0416060).