Evapotranspiration Results from Bulrush and Mixed Vegetation Sites


Site Conditions Affecting Evapotranspiration


Peak vegetation heights typically were 1.9 to 2.3 m above land surface (fig. 8). Near-peak heights usually occurred from early July to early October, forming somewhat of a plateau of canopy height during the heart of the growing season. The bulrush and cattail typically senesce in late September, turning from green to brown, and then lodge over in October and November in response to wind and snow loading. The bent-over plants merge with and are supported by plants from previous years, creating a loosely woven mat of dead plants roughly 0.5 to 1 m in height, which becomes the understory of the next year’s live canopy (fig. 8). In the spring, new shoots sprout from the soil, up through the water column and understory, until they emerge into the open space above. Upon emergence, the plants grow rapidly to their peak height.


Water level typically fluctuates about 1.3 m annually in response to inflows and controlled outflow at the dam, resulting in water levels that vary both above and below land surface at both sites at times of the year (fig. 8). Minimum water levels usually occur in October, and maximum water levels occur from April through June. During the study period, maximum water level at the bulrush site was 0.89 m above land surface, and minimum water level was -0.63 m. Land surface is 0.15 m higher at the mixed site than at the bulrush site, so maximum and minimum water levels at this site were 0.15 m lower (fig. 8). During 2008 to 2010, the hydroperiods ranged from 7.2 to 5.2 months and from 5.9 to 3.5 months at the bulrush and mixed sites, respectively. Minimum hydroperiods occurred in 2010 due to unusually low water levels, and hydroperiods were substantially shorter than in 2008 and 2009.


Soil water content (θ; fig. 8) was measured using a 30-cm long time-domain reflectometer (TDR) installed vertically in the soil, which sensed the mean θ from the surface to a depth of 30 cm. The TDR probe was not specifically calibrated for this soil, so the absolute readings are approximate although differences should be qualitatively correct. At both sites, the probe was installed in mid-August 2008, about when the water level had receded to the land surface. During most of the study period, θ at the bulrush site was very steady at about 0.82 to 0.9 m³ m^-3, a value typical of saturated peat (Schedlbauer and others, 2011). During the coldest part of both winter periods, the apparent value dropped below this range (fig. 8), but this was very likely an artifact of freezing temperatures over at least part of the TDR measurement depth interval. The TDR responds to the dielectric constant of the surrounding (moist) medium, and the dielectric constant of ice is about 4 percent that of liquid water. The low readings probably were not caused by conditions of partial saturation because similarly low readings did not occur at the times of minimum water levels each year when partial saturation would be most expected (fig. 8). The apparently saturated soil (θ = 0.85) during the time of minimum water level (-0.63 m) in October 2009 suggests that the capillary fringe of the peat soil at this site is at least 0.63 m, an unusually high value. In contrast, the TDR probe at the mixed site appeared to indicate partial dewatering during all 3 years, beginning in August, when water level dropped below about 0.2 m below land surface (figs. 8D–F). Freezing soil water could not have been a factor at this time of year, and the declines in θ mirror declines in water level, suggesting a valid instrumental response and a more normal capillary fringe height of less than about 0.2 m. Soils were not sampled at the two sites, but these substantially different estimates of capillary-fringe height suggest that the soils differ greatly in mean particle size. In addition, while the saturated soil at the bulrush site indicates that the vegetation there was never stressed, the decrease in θ at the mixed site to values around 0.5 in September (figs. 8D–F) suggests that vegetation there may have experienced mild water stress toward the end of the growing season each year.


Source Areas and Fetch Considerations of Wetland Evapotranspiration Sites


A source-area model (Schuepp and others, 1990) was used to estimate the degree to which measured fluxes represent fluxes from the wetland surfaces (surfaces of interest) and to what extent they are affected (contaminated) by fluxes from the upwind open-water or other surfaces. Sensors used in the EC method must be placed at least 1.5 times the vegetation canopy height above the land (or water) surface to avoid measurement artifacts from underlying heterogeneities. Consequently, air passing by the EC sensors comes from upwind and, therefore, contains attributes (w, T_a, ρ_v) that correspond to fluxes from upwind surfaces. The source-area model describes the relative contributions to the measured flux signal from upwind surfaces as a function of upwind distance. The union of all contributing surfaces is known as the source area. The distance to the farthest upwind extent of uniform surface of interest is called the fetch.


At both wetland sites, sensor height, canopy height, and fetch were used to determine the percentage of the measured flux signal originating from the wetland surface. In this context, sensor and canopy heights refer to height above land surface or height above water surface if standing water is present. Canopy height measured at each site was assumed to be representative of the whole source area. Source areas are smallest in unstable conditions (H > 0, typically occur during daytime), somewhat larger in neutral conditions (H ≈ 0, typically occur in heavy overcast, high winds, or near sunrise and sunset), and largest in stable conditions (H < 0, typically occur during nighttime). Neutral conditions were assumed for these calculations to produce the most conservative (largest) daytime source areas. Nighttime (stable) conditions were not evaluated because very little ET occurs at night. Source areas also vary in size depending on the canopy roughness length (z_m) and displacement height (d). The values of z_m and d were calculated as 0.1 h and 0.65 h, respectively, where h is canopy height in meters (Campbell and Norman, 1998, p. 71). In general, source area decreases with increasing canopy height. At each site, the source-area model is used to compute the percentage of the measured flux signal originating from within the wetland in the minimum fetch direction and in the predominant wind directions for both the minimum and maximum source areas occurring during the study. From these bounding and predominant conditions, estimates are made of the mean percentage of flux signal originating from within the wetland.


Minimum fetch at the bulrush site was 2.0 km at azimuths of 360° and 180° (due north and due south, fig. 1). Maximum source area occurred during the first day of data collection (May 1, 2008) when canopy height (h) was 0.20 m above 0.80 m of standing water (fig. 8A). For these conditions, the source-area model indicated that 96.6 percent of the flux signal was contained within 2.0 km of the station. Near-maximum source areas typically occurred during the winter, when canopy height was low. The minimum source area occurred at maximum canopy height (2.3 m), typically in summer and early fall (figs. 8A–C). In these conditions, 99.0 percent of the flux signal was contained within 2.0 km of the station. Predominant daytime wind directions (both during the growing season and year-round) were 305°, 360°, and 135°, in decreasing order. Fetches in the 305° and 135° directions were 5.1 and 3.0 km (fig. 1), affording 98.6 and 97.7 percent containment of the maximum source area flux signal, and 99.6 and 99.3 percent containment of the minimum source area flux signal, respectively. Considering the range and likely prevalence of these containment values, the mean time-weighted containment of the flux signal by dense wetland bulrush is estimated to be about 98 to 99 percent.


Minimum fetches at the mixed site were about 0.97 km at 90° (or due east) and 1.03 km at 240° (fig. 1) and these azimuths also corresponded to the two equally predominant wind directions. Minimum fetch is, therefore, estimated as the average of these two, or 1.0 km. Maximum source area occurred during the first day of data collection (May 1, 2008) when canopy height (h) was 0.20 m above 0.65 m of standing water (fig. 8D). Near-maximum source areas typically occurred during the winter, when canopy height was low. For these conditions, the source-area model indicated that 92.4 percent of the flux signal was contained within 1.0 km of the station. The minimum source area occurred at maximum canopy height (2.30 m; figs. 8D–E). In these conditions, 97.8 percent of the source area was within 1.0 km of the station. During average growing season conditions, 95.6 percent of the source area was within 1.0 km of the station. In addition, wind directions that afforded 1.5 km or more of fetch occurred during about 23 percent of the growing season, which provided 97.0 percent or greater containment of the source area. Considering the range and likely prevalence of these containment values, the mean time-weighted containment of the source area by dense wetland mixed vegetation is estimated to be about 95 to 96 percent.


The above estimates of flux-signal containment by the bulrush and mixed vegetation types indicate that the measured fluxes overwhelmingly originated from the surfaces of interest—and not from other, dissimilar surfaces farther upwind. In addition, the surfaces upwind of the study sites in the minimum-fetch directions consisted of open water at the mixed site and open water to the south or intermittently flooded wetland to the north at the bulrush site. The hydroperiod of the wetland to the north was similar to that of the bulrush site. During the growing season, ET from these surfaces is roughly equal to ET from the surfaces of interest, and therefore would have an insignificant effect on measured ET. The greatest potential for contrast in ET occurs in the fall and early winter, when the wetland vegetation is dormant and standing water (from rising lake level) is not yet present at the study sites. If the adjacent lake surface is unfrozen during this time, it would slightly inflate the measured ET at the sites. However, because the measured winter-time ET is about 10 percent of its annual mean value and the lake surface was frozen during part of this time, the net effect on the annual mean is very small. In summary, contamination of the measured ET from surfaces surrounding the wetland surfaces of interest is very small and probably much smaller than the inherent accuracy of the EC method.


Energy-Balance Closure and Trends


A single value of EBR was used to correct H_m and LE_m in this report to avoid the occurrence of unrealistic EBR values that can occur over shorter time periods. Correction on a 30-minute, daily, or biweekly basis is problematic because the smaller signal-to-noise ratio can produce very large or small values of EBR at times when TF and AE are small (near sunrise, sunset, and at night for 30-minute values, during overcast winter periods for daily and biweekly values), potentially producing unreliable final values of H and LE. For example, if EBR is small and values of H_m and LE_m are of similar magnitude and of opposite sign, they will both be inflated to very large numbers; and if H_m exactly equals –LE_m, division by zero will occur. To compare the use of a single EBR with shorter-period EBR, a biweekly EBR value was computed, and is shown along with biweekly AE, uncorrected TF, and the mean EBR at the bulrush site in figure 9. Biweekly EBR is relatively constant during the high-flux time of year: March 1 to October 31. During this time, biweekly EBR ranges from 16 percent greater than, to 12 percent smaller than the mean EBR (equal to 0.730), and averages 0.753, or 3.2 percent greater than the mean EBR. This high-flux EBR follows a subtle but consistent pattern from year to year, resembling the letter m, with maxima around mid-May and early September, and minima around mid-March, early July, and late October.


During low-flux times of the year, biweekly EBR is more variable, unpredictable, and tends to be smaller than the mean EBR (fig. 9). Over half are smaller than 60 percent, and one value drops as low as -332 percent in December, 2008, when AE > 0 and TF < 0. In addition, inter-annual variability is much greater than during high-flux times. The unpredictable and large variation of EBR during low-flux times probably is caused by a low signal-to-noise ratio in the AE and TF measurements, because those fluxes are small; less than 70 W m^-2, and averaging around 32 W m^-2. Because the low signal-to-noise ratio creates somewhat random variations in EBR, biweekly correction of TF to satisfy these EBR values is considered questionable.


The m pattern evident during the high-flux times extends into the low-flux times, although with less definition and more variability. The reason for this pattern was investigated using graphical and regression analyses, but no significant relations to other variables were found. The value of EBR has frequently been related to friction velocity, u* = (τ/ρ_a)^0.5, citing reduced turbulence at low wind speeds as a cause of low EBR (for example, Wilson and others, 2002; Aubinet and others, 2012, ). However, EBR is virtually unrelated to u* in this study. Using all biweekly data, EBR is not significantly related to u* (r = -0.318, a negative correlation, opposite to that observed elsewhere, and p = 0.21). After removing the outlier point at EBR = -332 percent, r equals 0.187, and p equals 0.14, still an insignificant relation. All biweekly EBR results for the mixed site (data not shown) are very similar to those for the bulrush site.


Considering the relatively small errors incurred during the high-flux times by the use of a single, mean EBR, and the difficulty and questionable validity of using a biweekly EBR during low-flux times, a single, mean value of EBR was chosen to correct the TF in this study. Although ET computed this way may be slightly overestimated or underestimated at times compared to the use of a biweekly EBR, the study‑period averages are identical.


Values of EBR also were computed for six different but overlapping full 2-year periods during the study to explore whether the EBR calculated for the whole study period (2.41 years) was representative of an annual average value. The first 2-year period began on the first day of the study, and each subsequent 2-year period began 4 weeks later the preceding one. The EBRs of the six 2-year periods varied by less than ± 1 percent, and the means were within 0.25 percent of the full-study period EBR at both sites (data not shown), indicating that the full-study period EBR adequately approximated the annual EBR, and the annual EBR was relatively constant during the study period.


Eddy-covariance sensors functioned correctly during 84 percent of the study period (table 4), substantially better than in higher rainfall locations such as Florida, where EC sensors were operational only 51 percent of the time during a recent study (Schedlbauer and others, 2011). The energy‑balance ratio (EBR) was calculated from equation 8 using only data collected when all energy-balance sensors functioned correctly, constituting 63.0 and 70.8 percent of the study period at the bulrush and mixed sites, respectively (table 4). The EBRs of 0.730 and 0.781 at the bulrush and mixed sites, respectively, are slightly below the mean observed EBR of about 0.8 (Twine and others, 2000; Wilson and others, 2002; Foken, 2008), but are well within the range typically seen in many studies (Dugas and others, 1991; McCaughey and others, 1997; Twine and others, 2000; Mauder and others, 2006; Foken, 2008). Measured values of turbulent flux (H_m and LE_m) were divided by these ratios to obtain final values, designated as H and LE. Regressions between 30-minute available energy and final turbulent flux yielded RMSEs of 71.9 and 63.7 W m^-2 which, when compared to a range in available energy of about 1000 W m^-2, resulted in reasonably large r ² values of 0.878 and 0.905 (table 4). Daily and biweekly r ² values (using both measured and gap-filled data) increased substantially (table 4), illustrating that much of the error in 30-minute energy-balance data is random, and decreases over longer periods.


Daily values of the main energy-balance components (R_n, H, and LE) are shown in figure 10. G is not shown because the daily mean value (0.9 W m^-2) and standard deviation (17 W m^-2) are both quite small and G contributes little to the seasonal changes in energy-balance partitioning. A high degree of correlation can be seen between equivalent fluxes at the two sites, substantiating the field measurements, which were made independently of each other. The upper envelope of R_n corresponds to clear skies and displays the usual sinusoidal shape, with intermittent excursions downward caused by the occurrence of clouds. Occasionally, R_n exceeds the upper envelope sine curve when clouds are near, but not obscuring, the direct solar beam arriving at the site. These clouds can forward-scatter short-wave radiation (Monteith and Unsworth, 1990), raising R_n above clear-sky values.


The available energy delivered to the surface is partitioned between H and LE, and this partitioning varies considerably during the year as the wetland progresses through its annual life cycle (fig. 10). Partitioning is described in terms of the ratio of H to LE, known as the Bowen (1924) ratio, β. At the beginning of the year, the vegetation canopy is dormant and water level is below land surface. The loosely woven mat of dead stalks forms a complex surface, at times partially covered with snow and ice and partially bare, and at other times entirely bare. Snow and ice-covered surfaces contribute to LE, whereas bare stalks contribute to H. On average, H and LE are roughly equal during winter (β ≈ 1), alternating positions of dominance as precipitation coats the surfaces, then is redistributed and removed by evaporation and sublimation (fig. 10). During March, April, and early May, water level rises but is mostly shaded by the mat of dead stalks, and therefore has a minor effect on the equal partitioning. Both H and LE steadily grow in response to increasing R_n. The new vegetation begins to emerge from the dead stalk mat in May or June (fig. 8), which begins to shift the partitioning toward LE, reducing β (fig. 10). By mid-June, H begins to decrease (even though R_n is still approaching peak values) due to increased transpiration from the vigorously growing canopy. This shift toward greater LE was somewhat delayed in 2010, a year of unusually low water levels early in the growing season. Because ample root-zone water was available for transpiration during this time, a possible alternate mechanism for the delay in 2010 is discussed in Daily Evapotranspiration and Crop Coefficients.


By midsummer, energy is partitioned overwhelmingly to LE (fig. 10), with typical daily values of β near 0.26 (bulrush site) and 0.13 (mixed site). This wholesale shift over to LE at the expense of H is largely a result of transpiration by the growing or mature vegetation, creating an obvious gulf between H and LE values in the energy-balance graphs (fig. 10). The tendency toward even lower β at the mixed site is somewhat unexpected, given the shallower water levels there, and suggests either greater partitioning toward LE by cattail and wocus transpiration at that site, or toward evaporation from areas of open shallow water associated with the wocus.


In early September, plants begin to senesce and turn brown, initiating a shift back toward equal partitioning between H and LE. During this time, H actually increases even though R_n rapidly decreases (fig. 10). During most of October, H is substantially greater than LE (β ≈ 2) primarily because October is dry (precipitation is discussed in Daily Evapotranspiration and Crop Coefficients) and above freezing. Therefore, what little precipitation falls is rainfall, which penetrates through the mostly vertical stalks to the lower stalk mat and the soil, where it is effectively decoupled from R_n and the overlying atmosphere. During November and December, the dead canopy lodges over, making a more supportive surface for the substantial snowfall during those months and providing a better exposure of the snow to R_n. As a result, β again approaches 1, which persists for the rest of the winter months.


Daily Evapotranspiration and Crop Coefficients


Daily values of ET and ET_r at both wetland sites during the study period (May 1, 2008, to September 29, 2010) are shown in figure 11. This study period brackets three growing seasons, from 2008 to 2010. A generally sinusoidal pattern in ET and ET_r can be seen during all 3 years, superimposed with daily variations above and below the mean pattern. The mean sinusoidal pattern is largely determined by the R_n input (fig. 10), modified somewhat by water level and vegetation properties, discussed in this section, below. The daily variations are also closely related to variations in R_n (fig. 10), and to precipitation, discussed in this section, below. A high degree of correlation can be seen between bulrush and mixed site ET, and between ET_r and ET at both sites. Both short term (daily) and longer term (weekly to monthly) variations in ET_r are reflected in the measured ET at both sites. On a daily basis, ET and ET_r alternate relative magnitudes to some degree, although on average ET_r > ET. Periods when ET is noticeably less than ET_r tend to be in the spring (May 2008; parts of April and May 2009; and parts of March, April, May, and June 2010) and fall (most of September and October 2008; late August through early October 2009; and parts of September 2010). During much of winter and late summer, ET is often indistinguishable from ET_r at the daily time step shown in figure 11.


Daily values of K_c at both wetland sites and precipitation (P) at the Klamath Falls weather station (KFLO) during the study period are shown in figure 12. The KFLO record is only an approximate indicator of timing and amount of P at the Upper Klamath NWR because the KFLO station is 44 km from the study sites. The most obvious feature in these plots is that daily K_c is generally predictable and well behaved from June through September, whereas K_c is quite variable (noisy) the rest of the year. The noisy periods consist of somewhat sustained intervals when K_c is generally small, punctuated with short-lived spikes in K_c, usually during and just after days of P (this relation between K_c and P is only approximate because of the distant KFLO location). This seasonal dependence of K_c variability is caused by (1) the seasonal change in the magnitude of ET_r; (2) the seasonal change in the amount and frequency of P; and (3) the seasonal change in sensitivity of canopy energy partitioning to inputs of P. During the growing season, larger ET_r provides a more stable denominator in the calculation of K_c (K_c = ET/ET_r), whereas measurement and modeling uncertainty in ET_r has a greater proportional effect on K_c when fluxes are small, during the non-growing season. Coincidentally, very little P falls between mid-June and the end of September, but P is instead heavily skewed toward the winter months. Therefore, the potential for K_c to spike in response to P intercepted by the canopy occurs more frequently during the non-growing season. Lastly, interception has little effect on energy partitioning during the growing season, because (1) transpiration is already large, nearly satisfying the atmospheric demand; and (2) the live leaves are nearly vertical, shunting the water to lower canopy layers where it is less available for evaporation.


During the non-growing season, the bent over, more nearly horizontal leaves intercept more rain and snow and provide better exposure of the intercepted water to incoming radiation and better aerodynamic transport back to the atmosphere. This process shifts energy partitioning away from H toward LE, causing K_c to spike. For example, note the subdued response of K_c to P of 3 mm or more during the growing season on August 6, 2008, June 15 and 30, 2009, August 6-7, 2009, and July 25, 2010. In contrast, when the canopy is dormant, interception greatly enhances the ET rate, causing K_c to spike to values well above 1 for short periods, while the intercepted water evaporates (numerous examples in fig. 12). A reasonable correlation can be seen between the magnitude of daily P (measured at KFLO) and K_c during the non-growing season (fig. 12).


Daily values of K_c greater than about 2 require some explanation, considering the proximity of the study sites to the AGKO weather station (and the concomitant similarity in weather), and the high degree of water availability occurring at the study sites and assumed in the computation of ET_r using AGKO data. At the bulrush site, all days of K_c > 2 (n = 45) occurred either before May 6 or after October 3. At the mixed site, all days of K_c > 2 (n = 32) occurred either before May 11 or after November 5. These periods correspond to times before the emergence of new growth from the dead canopy litter layer in the spring, or after senescence in the fall (that is, roughly during the non-growing season). Probably the main cause of high K_c values is the assumption of a 45 s m^-1 surface resistance in the computation of ET_r. During or just after precipitation, when the surface is wet, the actual surface resistance approaches zero. During the non-growing season, when the canopy is lodged over, the nearly horizontal leaf surfaces retain precipitation longer, sustaining high ET rates for one to a few days, depending on the amount of interception and the ensuing atmospheric demand. Once the canopy dries out, K_c typically returns to values well below one, reflecting dormancy and the lack of transpiration. This mechanism probably is compounded by a low signal-to-noise ratio in measured wetland ET and in computed ET_r, which are both relatively small at this time of year. Although K_c appears to be rather intractable during the non-growing season, its value is relatively unimportant because little ET occurs during this time. In addition, aggregation into biweekly periods reduces noise through averaging, as seen in the next section, Biweekly Evapotranspiration and Crop Coefficients.


An expanded view of daily K_c during the growing season of all 3 years is shown in figure 13. During the middle of the growing season, daily K_c follows a simple pattern rather consistently from year to year. From mid-June through mid‑September, K_c is relatively well behaved and follows a concave-downward curve. Although the canopy begins growing in early May, K_c values in May and early June are still somewhat noisy because the new growth has not fully emerged from the dead stalk mat and interception causes spikes in K_c. During late September, canopy senescence has progressed sufficiently that interception again begins to cause spikes in K_c. A base value of K_c (analogous to base flow in a stream) can be established during these periods, using the lowest values as a guide to estimate dry-canopy K_c. Combining this base value with the mean behavior during the middle of the season leads to simple piecewise linear descriptions of K_c at both sites—as shown in figure 13 and quantified in table 5, that approximate the concave‑downward curves. These piecewise linear approximations were determined by eye (visual examination). Based on spikes occurring from May 1 through about June 20, and after about September 15, a suggested value of K_c = 1.5 could be used on days of rainfall > 3 mm during these periods (superseding the piecewise calculation), or on days following rainfall, if the rainfall occurs in the afternoon or evening.


This modeling scheme of daily K_c and ET was tested by assuming that all precipitation recorded at the KFLO AgriMet station occurred early in the day, triggering the specified value of K_c = 1.5 on the day of precipitation. A comparison of modeled and measured ET is shown in figure 14, and associated statistics are presented in table 6. These models are only marginally successful, as indicated by large scatter about the one-to-one line (fig. 14), small slope, r ², and coefficient of efficiency (CE) values, and large intercept and RMSE values (table 6). The CE is similar to r ², except it ranges from 1 to -∞, is more rigorous, and requires equality as well as correlation between two variables to approach 1 (Nash and Sutcliffe, 1970). Model performance may improve if the actual timing of precipitation were known, allowing the use of K_c = 1.5 on the day following precipitation when precipitation occurs late in the day. Further, if atmospheric demand on the day following precipitation is especially low (overcast conditions), the use of K_c = 1.5 could be extended to the next sunny day, possibly creating further improvement. However, model accuracy is limited by the 44-km distance between the KFLO precipitation measurement and the wetland sites (and concomitant decoupling of precipitation), and by the simplistic treatment of the complicated interactions between canopy structure, interception, and subsequent atmospheric demand and evaporation. While these models may provide an approximate estimate of daily ET at the wetland sites, much of the random variability can be removed by considering biweekly time steps, as in the following section.


The rising trend in daily K_c during April through mid‑July is noticeably delayed at both sites in 2010, a year of substantially lower water levels (fig. 8). During this period in 2010, ET is also noticeably smaller than in 2008 and 2009 (fig. 11). The lower K_c values in early 2010 probably were not caused by canopy stress because water levels were at or above land surface by late February at the bulrush site and by early April at the mixed site, well before new growth began. The major meteorological variables affecting ET were averaged for the period April 1–June 30, and a comparison of these averages for 2009 and 2010 is given in table 7. Wind speed is not included because its effect on ET is small and variable depending on other environmental conditions (Campbell and Norman, 1998). Spring 2010 was more overcast, humid, and cool, but less rainy than spring 2009. These variables all contributed to lower ET in 2010, but the reduced solar radiation, vapor pressure deficit, and temperature do not account for the small K_c because they affect ET_r to about the same proportion as they affect ET. The similar reduction in ET_r and ET from these environmental conditions can be seen by comparing figures 11B, C, E, and F. The reduced rainfall in 2010 probably did contribute to smaller K_c through reduced evaporation of intercepted rainfall, but as discussed earlier in this section, the effect of rainfall is short-lived, causing upward spikes in K_c, and even the base values of K_c (during dry periods between rainfall) are substantially lower in 2010 than in 2009 and 2008 (fig. 12). Apparently some other factor contributed to the reduction in ET during spring 2010 without a corresponding reduction in ET_r, leading to consistently smaller values of K_c.


A mechanism for a relation between K_c and standing water level has been proposed by German (2000), who measured ET at multiple sites in the Florida Everglades—vegetated with sawgrass, spike rush, muhly grass, and cattail; vegetation similar to that at the present study site. If canopy biomass is distributed evenly in the vertical direction, light penetration from above decreases with depth into the canopy approximately according to Beer’s law. Conversely, the amount of light reaching an underlying water surface increases as water-surface elevation increases. At the Everglades site, the density of plant material (primarily the dead stalk understory) was greatest near the land surface and decreased with distance above land surface (Carter and others, 1999). German reasoned that this canopy architecture would enhance the extinction effect compared to that of an evenly distributed canopy, greatly increasing the proportion of water surface receiving solar radiation at higher water levels. Greater radiation input to the water surface causes greater partitioning to LE. At lower water levels, a greater proportion of dead plant material per unit horizontal area is exposed to sunlight, generating greater H at the expense of LE. We expand on German’s (2000) observation by noting that lower water levels also increase the aerodynamic resistance from the water surface to the free atmosphere, further shifting the energy exchange away from the water surface, toward the upper, dead canopy. At the current study site, canopy architecture is similar to that documented in the Everglades, and although detailed measurements were not made, many photographs taken during site visits substantiate the greater density of dead plant material near the ground. This dependence of energy partitioning on water level very likely occurs at the present study site, and the unusually small value of K_c during spring 2010 probably was at least partially related to the unusually low water levels during that time.


Biweekly Evapotranspiration and Crop Coefficients


Biweekly ET_r and measured ET at both sites are shown by year in figure 15. A reasonable correlation can be seen between the two sites and between measured ET and ET_r. On average, ET_r exceeds ET, although some exceptions can be seen. Bulrush site ET tends to exceed mixed site ET, also with notable exceptions (for example, midsummer, 2008). Although the timing of the relation between ET and ET_r changes from year to year, ET tends to approach ET_r most reliably from mid‑July to mid-August. During the winter, when fluxes are small, ET approaches and even substantially exceeds ET_r, but no consistent patterns are apparent. In December 2009, ET at both sites exceeds ET_r by more than a factor of 2.


Biweekly K_c values were computed from the biweekly ET and ET_r rates, and the K_c values are shown in figure 16, along with biweekly precipitation (P) totals. As with daily K_c, values are somewhat predictable during the growing season (May through September) and are quite variable during other times of the year. Values of daily K_c that spike to 5 or 6 in November through January (fig. 12) are somewhat moderated by aggregation into biweekly periods, but values still exceed 2 in December 2009 due to the small values of ET_r during that time. On a biweekly basis, K_c is less correlated with P than on a daily basis (fig. 16). For example, relatively large P in early June 2009 and mid-April 2010 did not result in large values of K_c; in fact, K_c was smaller in December 2008 than in December 2009—although P was greater in 2008. This lack of correspondence between P and K_c probably is related to: (1) the timing and frequency of P; (2) the tendency for P to be sequestered by the lower canopy understory and soil; and (3) the abundant soil water content during the growing season. During the non-growing season, rainfall amounts that exceed the interception capacity of the dormant canopy drain to lower layers and the soil, where evaporation is reduced due to shading and decreased aerodynamic transport. A greater percentage of drainage occurs from a few large rainfalls than from many small rainfalls of equal total depth, reducing the percentage available for evaporation. This mechanism reduces the correlation between biweekly K_c and P, instead making K_c more dependent on the number of rainfall events during the period. Snowfall tends to remain more elevated in the canopy than rainfall, but wind redistributes the snow to lower levels, and solar radiation melts the snow on warmer days, causing some drainage and obscuring the linkage between K_c and P. During the growing season, evaporation of interception is comparable to transpiration due to the ample soil moisture, reducing the impact of interception on ET. While interception of P causes noticeable spikes in daily K_c, this effect becomes masked by other processes on a biweekly basis. Therefore, the biweekly magnitude of P does not appear to be useful in predicting the biweekly value of K_c.


Ensemble averages of ET and ET_r were computed using data from all 3 years and were parsed into 26 biweekly periods to create a 1-year average record. Ensemble average K_c for each biweekly period was then calculated as the ratio of average ET to average ET_r. By averaging fluxes from the corresponding biweekly periods each year, the non-linear effects of averaging unusually large or small K_c values are removed. Due to the start (May 1, 2008) and end (September 29, 2010) of the study period, averages are computed from 3 years during the growing season (May through September), and 2 years otherwise. The resulting time series of ensemble average biweekly K_c is reasonably predictable during the growing season and somewhat more erratic otherwise (fig. 17). Values of ensemble average K_c during the growing season are listed in table 8.


During the growing season, ensemble average K_c rises almost monotonically from a value near 0.75 on May 1, to a peak near 1.0 in mid-August, then declines monotonically to a value near 0.5 by late September. The only substantial perturbation in this pattern is during late May-early June, when K_c is greater than the subsequent 2 or 3 values. This boost in ET at both sites may be related to fortuitous timing and amounts of rainfall, primarily in 2008 and 2009 (fig. 12). On the rising limb of K_c, values at the two sites are nearly equal, with the bulrush K_c slightly greater than the mixed site K_c on average. On the descending limb, the bulrush K_c is substantially and consistently greater than the mixed site K_c. The tabled values of ensemble average K_c are used to model biweekly ET during the 3 growing seasons, as discussed later in this section.


During the non-growing season, ensemble average K_c varies somewhat unpredictably; large variations occur between adjacent periods and between sites (fig. 17). In particular, the very large (> 2) values in late December 2009 (fig. 16B) have been somewhat moderated by the 2008 data, but the 2-year average still stands out from the rest, especially at the bulrush site. In addition, K_c values in October are unusually small compared to values during the rest of the non-growing season. During the study, October precipitation at the Klamath Falls KFLO station was 52 percent of the average for 1999 through 2011. Part of the random variability in K_c is probably related to the small sample size (n = 2 years) during the non-growing season, combined with the small ET_r values as described in Daily Evapotranspiration and Crop Coefficients. It is therefore suggested that the extreme values of K_c (mostly during October and December) are not representative of the long-term, and that a single mean value of K_c can adequately characterize the whole non-growing season. Consequently, ET and ET_r were averaged from October through April, and a single non-growing season K_c was computed for each site. These values are 0.758 and 0.683 at the bulrush and mixed sites, respectively, and are listed in table 8.


Ensemble average values of K_c from the growing season (fig. 17; table 8) and mean values from the non-growing season (table 8) were multiplied by biweekly values of ET_r to test the adequacy of the average K_c values to reproduce the measured ET values at both sites during the entire study, consisting of 63 biweekly periods. The results of this comparison are shown in figure 18, and associated statistics are presented in table 9. Overall, performance of the average K_c approach is very good, with r ² values greater than 0.96, RMSE values less than 0.4 mm d^-1, and slopes and intercepts of best-fit lines near 1 and 0, respectively. This is not the most stringent test of the method, because the seasonal K_c values were determined from the test data rather than from an independent data set. However, a fair amount of variability in K_c occurred from year to year (during the same biweekly period) at both sites (fig. 16), and the ability of the model to reproduce the measured ET is still quite good. For example, water levels were about 0.5 to 0.2 m lower in 2010 than in 2008 and 2009 (fig. 8) during the first half of the year. As a result of this or other factors, K_c values were noticeably lower during the early 2010 growing season (fig. 16), and inclusion of these data lends some generality to the K_c model by averaging in the unusual year. The resulting model only slightly overestimates ET in 2010 (the red squares in fig. 18), while still maintaining relatively good accuracy overall.


As an alternative to the discrete values of biweekly growing season ensemble average K_c in table 8, fourth-order polynomials were fit to the biweekly values and the resulting curves are shown in figure 17. Information for computing K_c in this manner is given in table 10. This approach provides a more generalized and automated computation of growing season K_c, but undoubtedly sacrifices accuracy in modeling ET during the study period compared to the K_c table approach (fig. 18; table 9). However, over periods of many years, this approach may perform equivalently to the K_c table approach.


Study-Period and Annual Evapotranspiration


On average during the study period, R_n at the bulrush and mixed sites was 126.4 W m^-2 and 113.9 W m^-2, respectively. The smaller mixed site R_n of about 10 percent probably is related to differences in cloudiness, water depth, or vegetation type. The 4-component measurements of R_n indicate that this 10 percent difference is partitioned as follows: 3.8 percent to incoming solar, 4.3 percent to reflected solar, 1.5 percent to outgoing long-wave, and 0.4 percent to incoming long‑wave. The smaller incoming solar at the mixed site is likely associated with the predominant south-westerly winds at that site, issuing from the Cascade Range through the mouth of Fourmile Creek at Pelican Bay (fig. 1), entraining montane cloudiness preferentially over the mixed site. The bulrush site is more removed from the mountains and from the Fourmile Creek air stream, as indicated by its more evenly distributed wind directions, and the site should experience sunnier skies as a result. Mean reflectivity of the bulrush site during the study was 0.128, compared to 0.156 at the mixed site. This greater retention of solar radiation at the bulrush site was the largest factor in the R_n difference and is consistent with the deeper water at that site (Sumner and others, 2011). But the R_n difference also could be related to differences in vegetation color. Deeper water at the bulrush site also would tend to keep the surface cooler and account for the reduced outgoing long-wave radiation at that site. Although the mixed site was located among large patches of open water associated with wocus, wocus patches were distant enough from the station that they did not affect the measured R_n, but probably did affect the measured turbulent fluxes.


Average ET during the study period, during each year of study, and during a 3-year period was computed for both sites and is presented along with ET_r in table 11. The 2008 and 2010 annual values were computed by filling in the missing parts of 2008 (January 1–April 30) and 2010 (September 30–December 31) with data from the equivalent times in 2009. The 3-year period is the mean of the 3 study years. This 3-year period was synthesized because the study-period average combined 3 growing seasons with 2 non-growing seasons and, therefore, is biased high compared to an annual average. Little uncertainty is introduced by the substitutions because ET is small during the non-growing season. As seen in table 11, study period ET was about 5 percent greater at the bulrush site than at the mixed site. Because the EC data were corrected to close the energy balance, the two factors affecting this 5 percent difference are mean values of available energy, AE, and how that energy was partitioned between H and LE, or the Bowen ratio, β. Mean values of AE during the study period were 127.0 and 115.1 W m^-2 at the bulrush and mixed sites respectively. (These values differ slightly from the R_n means cited in the previous paragraph by the amounts of mean Q_x + G, which were -0.6 and -1.2 W m² at the bulrush and mixed sites, respectively.) Although AE is about 10 percent greater at the bulrush site than at the mixed site, a greater proportion of AE was partitioned into LE at the mixed site, reducing the LE (and ET) site difference to about 5 percent. As noted earlier, the greater proportion of open water associated with stands of wocus at the mixed site possibly resulted in a lower mean β at the mixed site (0.450) than at the bulrush site (0.525) despite the 0.15-m higher land surface and resulting shallower water depths at the mixed site.


A two-sided paired-t test was conducted to determine whether daily ET values from the two sites during the study period are statistically different at the α = 0.05 probability level. Site ET differences are normally distributed. This test yielded a t-value of 2.067 (p = 0.0369), indicating that the null hypothesis can be rejected and ET values from the two sites are statistically different, but not conclusively. The accuracy of EC data is typically given as ±5 to 10 percent under ideal conditions (Foken, 2008) such as found here, and the corresponding precision (or ability to distinguish differences under similar conditions) should be substantially smaller than the accuracy, on the order of ±1 to 2 percent. Therefore it seems likely, although not conclusively, that ET was slightly and significantly greater from the bulrush site than from the mixed site.


Variability between years (about ± 8.5 percent) was substantially greater than variability between sites (about ± 2.5 percent). The years of 2008 and 2009 were very similar overall; bulrush ET was slightly greater in 2009 than in 2008, whereas mixed site ET was slightly greater in 2008 than in 2009 (table 11). In 2010, ET at both sites was about 14 to 15 percent less than during the previous 2 years. Available energy at the bulrush site was 1 percent greater in 2010 than in 2008 through 2009. Available energy at the mixed site was 2 percent less than in 2008 through 2009, and therefore it cannot account for the lower ET in 2010. As discussed earlier, unusually low water levels in the first half of 2010 probably reduced evaporation from the standing water by decoupling the water surface from incoming radiation. In addition, synthesized precipitation (P) was 16 percent lower in 2010 than in 2008–2009 and may have reduced evaporation of intercepted water, especially during the non-growing season. (Although the last 3 months of the synthesized 2010 data are borrowed from 2009, the substitution was made for ET as well as P and should preserve any correlation between ET and P.) Therefore, lower water levels and precipitation probably were the main factors causing the lower ET in 2010.


Maximum annual ET occurred in 2009 at the bulrush site and in 2008 at the mixed site. Differences between the maximum annual value and the next lower value are small (1.8 and 4.0 percent at the bulrush and mixed sites, respectively), and the year reversal could be caused either by site differences in climate and surface response to climate, or simply by random error in the EC method. However, the most likely causative climatic variable, available energy, was greater at both sites in 2009, suggesting the year reversal may be a result of random error.


Overall, the 3-year synthesized average ET values at the bulrush and mixed sites are 0.953 m/yr and 0.903 m/yr, respectively. The corresponding 3-year synthesized average ET_r from the Agency Lake weather station is 1.145 m/yr, resulting in average annual K_c values of 0.832 and 0.789 at the bulrush and mixed sites, respectively. These annual values fall near the middle of the range of ensemble average biweekly K_c values given in figure 17 and table 8. Based on our estimate that 70 percent of the Upper Klamath NWR is typified by the bulrush site and 30 percent by the mixed site, the 3-year average ET value for the whole NWR is 0.938 m/yr. The 3-year synthesized average precipitation at the Klamath Falls weather station (KFLO) is 0.233 m/yr, equal to about 25 percent of 3-year average measured ET.


The relation of the 3-year synthesized ET values to expected values of long-term ET can be partially investigated by comparing relevant climatic variables during the 3-year period to their long-term means. In a water-limited system, precipitation (P) is probably the most important variable, whereas in an energy-limited system, solar radiation (R_s) and temperature assume that role. Although the most relevant temperature is that of the evaporating surface, air temperature (T_a) is commonly used because it is highly correlated with surface temperature and is more readily available. During the heart of the growing season, the NWR wetland clearly is energy-limited, but at other times of the year, P influences ET through evaporation of intercepted water. Long-term means of R_s, P, and T_a are calculated using data from the nearby Agency Lake (AGKO) and Klamath Falls (KFLO) weather stations (fig. 1) and are compared to 3-year synthesized study period means in table 12. Long-term means are calculated from water years 2001–2011 (11 years) and the 3-year values are synthesized from the same months and years used to compute measured ET, to be consistent with those data. The closer AGKO station is used when possible (for R_s and T_a), but only the KFLO station has a reliable precipitation record during the winter, so those data are used to compute P. Although the KFLO station record begins in 1999, the first 2 years are not used, to be consistent with the full period of record at the AGKO station (2001–2011). Solar radiation during the study period was about 9.5 percent lower than the 11-year mean, which should reduce the study period ET compared to the long term. Interestingly, P also was about 17 percent less during the study period than its long-term average. Often, reduced P is associated with greater R_s, but the frequency, duration, and intensity of P, as well as the distance between the AGKO and KFLO stations, can alter this relation. In this wetland setting, reduced P should have little effect on growing-season ET, and a mildly inhibiting effect on non-growing season evaporation of intercepted water. Finally, the study-period T_a is slightly cooler than the long-term mean, which also should slightly reduce ET. Overall, the study period was less sunny, drier, and cooler than the 11-year average, all of which should reduce the study-period ET compared to the norm. While this result indicates that the study-period ET given in table 11 probably is smaller than the long-term average, the smaller ET should have little or no effect on the accuracy of the K_c approach developed in this study. The effects of R_s and T_a on ET are explicitly included in the Penman-Monteith expression for ET_r, and the effects of P on annual ET from this well-watered wetland are small.


Comparison of Wetland Evapotranspiration with Evapotranspiration of Local Crops


A comparison of our measured wetland ET with ET of crops in the area can be made using data from the Bureau of Reclamation AgriMet Web site. Computation of ET_r is based on an assumption that the alfalfa crop is full sized and green year-round, as indicated by an assumed surface resistance (r_s) of 45 s/m at the daily time step, regardless of time of year (Allen and others, 2005). In the region of the current study, actual alfalfa ET is somewhat less than ET_r due to reduced green leaf area during the non-growing season and multiple cuttings during the growing season. The Bureau of Reclamation AgriMet Web site computes and posts values of estimated ET for alfalfa and other crops. These ET values are computed using the 1982 Kimberly‑Penman equation to compute ET_r, with appropriate values of K_c. Although this ET_r equation is slightly different than the ASCE equation, the K_c values were developed to provide best estimates of crop ET using the 1982 ET_r equation (the AgriMet Web site does not provide estimates of crop ET using the more recent ASCE ET_r equation). The Web site posts crop ET for each growing season, the duration of which is established by local conditions and expert opinions year by year. We computed wetland ET using our measured data during the 2008 through 2010 growing seasons, and the 70 percent to 30 percent weighting (for bulrush versus mixed vegetation) used earlier in Study-Period and Annual Evapotranspiration. We obtained alfalfa and pasture growing-season ET data for 2008 through 2010 from the Klamath Falls (KFLO) AgriMet Web site because crop ET is not computed for the closer AGKO station. A comparison of growing-season ET (table 13) shows that wetland ET was about 9 percent less than alfalfa ET, and about 18 percent greater than pasture ET during 2008 through 2010.


Although AgriMet does not compute non-growing-season crop ET, a rough comparison of annual wetland and crop ET can be made by assuming ET from all vegetated surfaces is equal during the non-growing season. This assumption is supported by the similar weather and existence of dormant vegetation at the locations involved. Although wetland ET probably exceeds crop ET in late winter and early spring due to the presence of standing water at the wetland, crop ET probably exceeds wetland ET during fall and early winter (when standing water is absent) because of the greater mulching effect of the more massive dormant canopy at the wetland. We compute mean 2008 through 2010 non-growing season wetland ET using the same synthesis methods used in Study-Period and Annual Evapotranspiration to estimate early 2008 and late 2010 water use. Non-growing season crop ET is assumed equal to wetland ET, and annual ET is computed as the sum of growing-season and non-growing-season ET of both wetland and crops. On an annual basis, wetland ET during 2008 through 2010 is estimated to be about 6 percent less than alfalfa ET and about 14 percent greater than pasture ET (table 13).


Comparison of Wetland Evapotranspiration with Previous Studies


Bidlake (2000) conducted a field campaign to characterize ET at a site about 200 m northwest of the bulrush site during the growing season of 1997. He deployed EC sensors during four 1- to 2- day periods (May 29–30, July 10–12, August 23–25, and October 11–13), and a recording weather station at the same location continuously from May 29 to October 13. The EC fluxes were used to calibrate a Penman-Monteith (PM) model (similar to the one used in the present study to compute ET_r at the AGKO AgriMet site) by solving for the average surface resistance, r_s, during each EC deployment, and interpolating r_s between site visits. The Penman-Monteith model was then used to compute daily ET during the entire growing season, and the daily values were aggregated into weekly values. Bidlake’s EC data were not corrected to force energy-balance closure and, therefore, neither were the modeled ET values because they were calibrated to match the EC data. For comparison with the current study, we divided Bidlake’s ET data by the average energy budget ratio (EBR) measured during that study (0.88) to force energy-balance closure and improve comparability with the current study.


Bidlake’s 1997 adjusted weekly ET (Bidlake, 2000) is plotted along with our 2008 through 2010 biweekly bulrush ET in figure 19. Compared to our 2008 and 2009 ET data, the 1997 ET was somewhat lower in June, nearly equal in July, somewhat greater in August, and nearly equal thereafter, resulting in very similar growing season totals. June and August differences may be attributable to: interpolation of r_s to compute the 1997 ET; the use of relatively short periods (29–35 hours) to compute each r_s interpolation endpoint; or to climatic differences between years. Worthy of note is that in 1997, June appeared to be cloudier, and August clearer, than the corresponding months during the current study (fig. 10; Bidlake, 2000, fig. 1), which is consistent with the ET differences during those periods. Interestingly, ET magnitudes during all 4 years are similar from late August to early October, a time when the canopy is tall and beginning to senesce. Overall, the 1997 growing season ET data are in general agreement with the ET measured in the current study and help support our results.


During the growing season of 2000, Bidlake (2002) measured ET from three fallowed agricultural fields in the Tule Lake National Wildlife Refuge in northern California, about 83 km southwest of the present study site. During the previous year (1999), the three sites were sown to barley and irrigated, and had variously evolved into a patchwork of harvested, unharvested, and burned (by wildfire) areas by spring 2000. One of the sites was tilled and sown to rye in February 2000 to simulate a dry-land cover crop that might be used during future fallowing. During the growing season of 2000, surface coverage consisted of a mixture of stubble and other crop residues, weedy volunteer species, small grain plants sprouted from the seeds of previous crops, bare soil, and rye (at the one site planted with rye). All sites were un-irrigated during 2000. Water table depths averaged about 1.1 m below land surface during the growing season, ranging from about 0.7 to 1.4 m. Evapotranspiration was measured or estimated from May 1 to October 31 (184 days, designated as the growing season) using the Bowen-ratio method, supplemented with modeling during data gaps. The Priestley-Taylor method (with variable α) was used during short (< 2 hr) gaps, and a reference ET (ET_r) method was used for longer gaps. Daily ET_r was obtained from a University of California weather station about 8 km north, and daily K_c values were computed by interpolation between, or extrapolation beyond periods when Bowen-ratio sensors were operational. Extended gaps occurred at the beginning and end of the growing season, approximately the first half of May, and the last two-thirds of October, at all 3 sites. Because ET at these times was small, little error in the seasonal totals was incurred by the use of the ET_r model. Although timing of peak ET varied substantially between the fields, the growing-season totals were quite similar, ranging from 0.426 to 0.444 m, and averaging 0.435 m.


We computed 2008 through 2010 wetland growing‑season ET using our measured data from the same growing season as in Bidlake (2002), again weighting the bulrush and mixed site ET 70 percent-30 percent, respectively. Growing‑season ET data from October 2009 were substituted for the October 2010 period, which occurred after the study period. Wetland growing-season ET was about 65 percent greater than ET from the fallowed cropland (table 14). Although Bidlake did not compute non-growing season ET at the fallowed crop sites, a rough comparison of annual wetland and fallowed-crop ET can be made by assuming ET from both vegetated surfaces is equal during the non-growing season, as was assumed for alfalfa and pasture. We compute mean 2008 through 2010 non-growing season wetland ET using the same synthesis methods used in Study Period and Annual Evapotranspiration to estimate early 2008 and late 2010 water use. Non-growing season fallowed-crop ET is assumed equal to wetland ET, and annual ET is computed as the sum of growing-season and non-growing-season ET of both wetland and fallowed crops. On an annual basis, wetland ET during 2008–2010 is estimated to be about 43 percent greater than fallowed-cropland ET during 2000 (table 14).


First posted March 4, 2013