Results of Tracer Experiments


The wind observed at the Williamson River Delta was highly variable, in both speed and direction, between April 27 and September 29, 2008 (fig. 4). The 75th percentile of the east-west component was positive (indicating a westerly wind) on all dates, and generally ranged between about 1 and 6 m/s. The 75th percentile of the north-south component was positive and negative throughout the 5-month period and generally ranged between -3 and 4 m/s. The wind speed appears more visually correlated with the magnitude of the east-west wind component than with the north-south component, and this is confirmed with linear correlation analysis. The Pearson correlation coefficient R between the wind speed and the east-west component is 0.85, and the correlation between the wind speed and the north-south component is statistically insignificant (p<0.001).


The simulation of the Goose Bay tracer under strong northwest wind conditions as measured on May 22 (fig. 5A) shows that strong northwest winds push water in the southeast direction across Tulana and the Williamson River channel and then into Goose Bay. Water leaves Goose Bay through openings in levees on the south side and travels southward along the eastern shoreline with the prevailing clockwise circulation of Upper Klamath Lake. The simulation of the Williamson River tracer (fig. 5B) shows that most of the Williamson River flow is diverted through Goose Bay. The simulation of the Tulana tracer (fig. 5C) shows that northwest winds generate a complicated circulation pattern there. There is relatively less movement through the levee breaches on the south side of Tulana; primarily, water leaves through a breach just to the west of the mouth of the river channel. On the north side, water enters Tulana through the eastern breach and leaves through the western breach, creating an exchange with water from Agency Lake. 


Dependence of Flow through the Delta on Wind


The replacement rate in both Tulana and Goose Bay was highly variable between April and September when lake elevation and Williamson River inflow were held constant (fig. 6). When expressed as a fraction of the entire Goose Bay volume replaced in a single day, the total replacement rate in Goose Bay (with water from all sources) varied nearly 5-fold between the lowest value of 0.11 volume per day on September 19 and the higest value of 0.50 volume per day on May 22. This variability is attributable to the considerable changes in wind over the time period. Furthermore, the total replacement rate was moderately correlated with the 75^th percentile of wind speed (R=0.71, p<0.001), and several peaks in the total replacement rate coincided with peaks in the wind speed (May 7 and 22, June 6, and August 25); however, there were notable exceptions. In particular, total replacement rate minima occurred coincident with wind speed maxima on June 21, August 20, and September 19, and each of these dates was characterized by positive peaks in the north-south wind component (fig. 4), indicating southerly or southwesterly winds. 


Most of the water that left Goose Bay was replaced by water from the Williamson River, for the entire range of wind conditions (fig. 6). In contrast, water in Tulana was replaced largely by water from Agency and Upper Klamath Lakes, and less water as a fraction of the total came from the Williamson River (fig. 6). When expressed as a fraction of the entire Tulana volume replaced in a single day, the total replacement rate in Tulana varied nearly 3-fold between the lowest value of 0.08 volume per day on July 31 and the highest value of 0.30 volume per day on May 22. The replacement rate was correlated with the 75th percentile of wind speed (R=0.83, p<0.001). In contrast to Goose Bay, the total replacement rate in Tulana on June 21, August 20, and September 19, dates that were characterized by positive peaks in the north-south wind component, was either a small maximum or not an extreme value. The strong northwesterly winds on May 22 resulted in a peak in the total replacement rate of Tulana water, but almost none of that water was replaced with water from the Williamson River (fig. 6). 


The reciprocal of the volume replacement rates provides a theoretical replacement time for the replacement of all of the water in Goose Bay and Tulana (fig. 7). This calculation is not an estimate of the true water replacement time in Goose Bay or Tulana, because it is based on the conditions during only 1 day. It is not likely that replacement would occur at the same daily rate until the entire volume is replaced because conditions—wind conditions in particular—would not realistically remain constant over several days. Nonetheless, this theoretical replacement time provides another interpretation of the volume replacement rates (fig. 6), and the relative differences in theoretical replacement time between Goose Bay and Tulana are instructive. When expressed in this way, it is clear that water in Goose Bay has a shorter replacement time than water in Tulana, largely owing to the smaller volume in Goose Bay. At a lake elevation of 4,141.5 ft, for example, the volumes of Goose Bay and Tulana are approximately 5.3×10⁶ m³ and 2.4×10⁷ m³, respectively. The replacement time for water in Goose Bay varied from a minimum of 2.0 days during strong northwesterly wind conditions on May 22 to a maximum of 9.0 days during southwesterly wind conditions on September 19. The replacement time for Tulana water varied from a minimum of 3.3 days on May 22 to a maximum of 12.1 days during the relatively weak mid-summer winds on July 31. Under certain conditions, however, the replacement time for Tulana can approach or even be less than that in Goose Bay, as occurred on June 21, August 20, and September 19, all days characterized by a strong southerly wind component. In figure 7 it also is apparent that strong winds in April and May resulted in the shortest replacement times, whereas the weakest winds in July and August resulted in the longest replacement times. 


Dependence of Flow through the Delta on Inflow and Elevation


To examine the flow of water through the Delta as a function of Williamson River inflow and lake elevation, the volume fraction of water replaced per day was converted to a volume rate per second, in order to provide a convenient means of putting the movement of water through the Delta into perspective for comparison to the Williamson River inflow. The replacement rate of water in both Goose Bay and Tulana had a strong dependence on inflow from the Williamson River, such that replacement rates were higher at higher inflows (fig. 8). That dependence tended to be diminished at higher wind speeds, particularly in the case of winds with a strong northerly component. During the strong northwesterly winds on May 22, the Goose Bay replacement rate varied from 33.1 to 38.2 m³/s, whereas during the low winds on July 31 the Goose Bay replacement rate varied from 9.1 to 31.7 m³/s. In Tulana, the replacement rate varied from 82.0 to 96.3 m³/son May 22 and from 18.8 to 59.0 m³/son July 31. The replacement rate also had a strong dependence on lake elevation (fig. 9), but the dependence tended to increase at higher wind speeds. Goose Bay replacement rate varied from 6.8 to 50.4 m³/s on May 22 and from 4.4 to 14.8 m³/s on July 31; Tulana replacement rates varied from 53.8 to 113 m³/s on May 22 and from 13.5 to 29.6 m³/s on July 31. In Goose Bay, the replacement rate of water appeared to meet a lower threshold of 4–5 m³/s that was relatively insensitive to wind speed at a lake elevation between 4,141.5 and 4,140.5 ft. 


The partial replacement rate of water in Goose Bay or Tulana with Williamson River water depended on Williamson River inflow, such that it increased at higher inflows (fig. 10). At the lowest flows, the exchange between the Williamson River and Tulana was cut off on May 22, during strong northwest winds. The partial replacement rate of water in Goose Bay or Tulana also increased at higher lake elevation (fig. 11). The dependence of the partial replacement rate in both sides of the Delta on lake elevation was subject to a threshold between elevations of 4,140.5 and 4,141.5 ft. Below this threshold, the partial replacement rate was not strongly influenced by wind, but rather was controlled primarily by the levee openings around the river channel (fig. 11) and, based on the results in figure 10, on the Williamson River inflow. 


Wood River inflows were calculated as 0.3 times the flow in the Williamson River. This ratio of the Wood River flow to the Williamson River flow is, however, highly variable, both within a single year and in a given month between years, and the value of 0.3 is at the low end of the observed values. For this reason, sensitivity to this ratio was investigated. An additional model simulation was done with boundary conditions at the Wood River defined as 0.6 times the flow in the Williamson River; for this model simulation lake elevation was set to 4,141.5 ft and the Williamson River flow was set to 25 m³/s. Doubling the flow in the Wood River relative to the Williamson River had a small effect (median values differed by less than 2 percent) on the replacement rate in Tulana, and an even smaller effect on the replacement rate in Goose Bay (median values differed by less than 1 percent). The minimum, median, and maximum Tulana replacement rates when the ratio of Wood to Williamson flows was set to 0.3 was 22.6, 33.8, and 80.3 m³/s, whereas the same statistics were 23.6, 34.4, and 79.7 m³/s when the ratio of Wood to Williamson flows was set to 0.6. The minimum, median, and maximum Goose Bay replacement rates when the ratio of Wood to Williamson flows was set to 0.3 was 7.01, 14.5, and 29.2 m³/s, whereas the same statistics were 7.08, 14.6, and 29.3 m³/s when the ratio of Wood to Williamson flows was set to 0.6.


First posted March 29, 2012