Discussion


Currents through the delta are primarily wind driven. Winds typically exhibit an approximately diel pattern: light during morning and early afternoon and stronger during the evening and night. During periods of low wind speed, currents are slow across the delta and fastest in the river channel. When wind speeds are high, currents are slower in the northern delta than in the shallower southern delta. West-to-northwest winds generally cause water to enter the northern part of the delta from breaches in the levees along the Agency Lake side and to flow into Upper Klamath Lake through breaches in the levees on the Upper Klamath Lake side, or to flow across the river channel into the southern part of the delta (fig. 4A). In the shallow southern delta, strong currents enter at river breaches and take a nearly direct route south to exit through breaches in the levees on the Upper Klamath Lake side of the delta (figs. 2 and 4A; see also Wood, 2012). Our simulations were consistent with the overall understanding of how water moves through the delta, in that they showed that particle trajectories through the delta were affected by wind speed and direction, lake elevation, and shoreline configuration.


Outside the delta, the large-scale pattern of wind‑driven circulation transports particles south along the eastern shoreline of the lake. The eastern shoreline transport is part of a lakewide clockwise circulation in which water moves southeastward in a broad, shallow flow along the eastern side of the lake and returns in a narrow, deep, northwestward flow through the trench along the western shore (fig 1; see also Wood and others [2008]). Some of the southeastward flow continues to the south of Buck Island, and from there water can be recirculated to the north of Buck Island and back into the clockwise circulation, or it can exit the lake through the Link River outlet. Our simulations showed that after leaving the delta, particle travel time and retention were affected by wind speed and direction, and lake elevation, as well as simulated behavior.


In the delta, particle travel times were fast and particle pathways were direct across the southern delta, the Williamson River channel, and southeast along the shoreline of Upper Klamath Lake, whereas particle travel times were longer and pathways were more complex in the northern delta and Upper Klamath Lake and Agency Lake northwest of the river mouth (table 1). Strong west-northwest winds and higher lake elevation resulted in faster travel times of particles across the southern delta and into the lake. Weaker winds with more variable directions and lower lake elevation resulted in slower travel times, more complex pathways through the northern delta, and more variable points of entry into the lake. Different assumptions regarding dispersal (compare scenarios A–D in table 1) and swim speed (compare scenarios C-1.2, C and C-5.8 in table 1) resulted in differences of much less than 1 d in travel times to sites near the river channel and as much as 1.5 d to sites farther from the river channel and at the river mouth. Therefore, differences in travel time resulting from these various assumptions increased with distance from the upstream boundary, but were always small. Within the lake, swimming oriented to current direction resulted in faster downstream travel, a quicker exit of particles from the lake, and fewer particles in the domain than random swimming. When swimming was random, stronger swimming led to more dispersal, fewer particles leaving the lake, and more particles in the domain than with slower random swimming. Transport out of the lake, therefore, was determined by the speed of the eastern boundary current, which is a function of wind speed and lake elevation, and whether behavior enhanced that transport (aligning with currents) or countered that transport through greater dispersal (faster random swimming). The sensitivity of particle travel time and retention to different dispersal assumptions was small, however, in comparison to the sensitivity of these quantities to lake elevation and shoreline changes.


When the lake elevation was near full pool, prevailing wind-driven currents moved most particles directly and quickly, southeastward across the southern delta and into the lake, with few particles traversing the northern delta (fig. 6C). Relative to the 2009 elevation, particle travel times were shorter by as much as 2.6 d to sites southeast of the river mouth, but were longer by as much as 11.5 d to sites northwest of the river mouth (table 1, scenario C+). When the lake elevation was 0.25 m below the 2009 measured elevation (fig. 6A), fewer particles passed through the southern delta and more particles stayed in the river channel or traversed the northern delta. Relative to the 2009 elevation, particle travel times to most sites along the Upper Klamath Lake shoreline north, south, and offshore of the river mouth were faster, by as much as 4.6 d (table 1, scenario C-). When compared to the simulation at full pool, the simulations at the 2009 elevation and at a lower elevation showed that lake elevations lower than full pool retained more particles in the lake. There was evidence, however, that an intermediate “optimal” lake level that partially restricted transport into the southern delta, particularly close to the delta entrance, while still allowing the particles access to both the northern and southern sides of the delta farther downstream, would retain the most particles and result in the slowest travel times to the lake. 


Simulations with shorelines representing the changes in the delta between 2007 and 2009 provided insight into the changes in larval transport attributed to restoration (scenarios C-2007, C-2008, and C in table 1). Prior to restoration, the route to Upper Klamath Lake for all particles was fast and direct through the Williamson River channel. The reconnection of the northern delta in 2008 allowed particles to take long and complicated pathways into Upper Klamath Lake, effectively increasing travel time to all “downstream” sites in the lake, and increasing retention in the lake relative to the 2007 shoreline. When both sides of the delta were reconnected, prevailing winds created strong currents through the shallow southern delta, and more particles took a direct route through the southern delta to Upper Klamath Lake, so travel times to sites southeast of the river mouth decreased between 2008 and 2009, as did the retention of particles. However, both the 2008 and 2009 shorelines slowed the transport of particles and increased retention relative to pre-restoration conditions.


When particle ages were converted to lengths, field data agreed modestly with simulations though larvae usually were longer than predicted from particle ages, particularly for the largest size class (lengths ≥16 mm and ≤19 mm) (table 3). Correlations with field data among all gear types, species (as determined by date of entry into the lake), and size classes were consistently positive for three of our dispersal scenarios (all but oriented swimming) and provided an additional, moderate level of corroboration for four model (table 4). Overall, the highest correlations with field data were obtained with the assumption of passive dispersal (Pearson R between 0.23 and 0.76, depending on how data were parsed), but the assumption of active dispersal throughout the day also resulted in moderate R values (0.27–0.49) and slightly less bias in the simulated lengths of fish. There was no compelling evidence, however, that any scenarios for active dispersal through swimming resulted in a better or worse description of larval dispersal than the assumption of passive dispersal. The correlation with field data was higher for those particles inserted after June 2 than for those inserted before June 2. Lost River sucker larvae usually enter the delta 2–4 weeks before shortnose sucker larvae, and June 2 provided an approximate demarcation date between entry of the two species, based on our 2009 boundary samples. This suggests that the particle simulation was better at describing dispersal of shortnose sucker larvae, that the field sampling was worse at measuring Lost River sucker larvae in the system, or both. 


Most biophysical models have disconnects with field data (Leis, 2007), and this model was no exception. The extent to which these disconnects are a result of model assumptions or the inability of the empirical data to describe conditions in the environment with sufficient accuracy is unknown. For example, the simulated lengths generally were smaller than the measured lengths of fish captured in nets. This bias was not uniform across gear types, however, and was greatest for pop net catches, less for larval trawl catches, and smallest for plankton net catches.


Intra- and inter-gear differences in efficiencies are seldom mentioned in larval dispersal modeling (Leis, 2007); most researchers simply acknowledge that different gears deployed in different ways in the same place sometimes give different results (Overton and Rulifson, 2007). For this study, all nets were assumed maximally efficient for the smallest larvae and analyses were restricted to larvae less than 19 mm, but there were obvious spatial and gear differences. Small larvae (10–13 mm) constituted 87 percent of all larvae at plankton net sites, 36.2 percent at pop net sites, and 34.1 percent at larval trawl sites. However, at the larval trawl site closest to the larval source at the mouth of the Williamson River (OSU U6), the small size class constituted 59.4 percent of the catch and was more similar to plankton net samples. Therefore, the gear‑specific differences may be attributed partly to site location as well, such that sites closest to the river source, where pop and plankton nets were the predominant types used, had the smallest larvae. A better understanding of the size efficiency of nets (Millar and Fryer, 1999) is needed to distinguish between spatial and gear-specific differences in the size of the catches. The gear-specific differences also are due to sampling different parts of the water column, where ontogenetic shifts in larval sucker behavior could also account for some of the variation. For example, a diet study of sucker larvae and juveniles from Upper Klamath Lake suggested that the approximate 50 percent surface-50 percent benthic diet transition occurs at a standard length of about 20 mm. However, individuals vary greatly and benthic foods can constitute 25 percent or more of the diet in a 15-mm, standard‑length larva (Markle and Clauson, 2006), which indicates that a gradual and variable vertical transition in orientation is a likely cause for some of the observed differences in catches. In addition, our catches were made during the day, and the occupation of different parts of the water column by larval suckers for feeding or other reasons could have a diel dependence.


Our focus on an endangered species present in low densities adds an additional problem not found in typical studies that focus on the most abundant species. Density simulations (Wood and others, 2012) showed that larvae at our initial concentrations of between 20 and 50 fish/m³ at the Modoc Point Road Bridge would have concentrations less than 1 fish/m³ when dispersed passively to sites more than a few kilometers away from the Williamson River channel. If fish are uniformly distributed, these densities are close to a density detection limit for the gear types used. For example, at one larva per net, the larval trawl detection limit was between 0.14 and 2 fish/m³, the pop net detection limit was between 0.37 and 3.0 fish/m³, and the plankton net detection limit was between 0.012 and 3.7 fish/m³. Given the low simulated densities in areas far from the Williamson River channel, many zero catches in the field samples should be expected, particularly because larval fish are not expected to be uniformly distributed within a 75-m radius around a sample site, but instead are expected to be clustered. Therefore, the rarity of the target species may have further added imprecision to the larval catch densities and the length distributions obtained from those catches.


Many simplifying assumptions were made in the model. With regard to swimming, larvae were assumed to be passive, to have active random swimming behavior, or to have active swimming with simple current orientation behavior, and had simple day-night drift behavior that was constrained to occur everywhere within the Williamson River channel but nowhere outside the channel. Descriptions of swimming behavior were based on descriptions of the behavior of similar elongate larvae in the literature, and were designed primarily to test the sensitivity of the dispersal patterns to some swimming behaviors. Most routine measures of swimming performance, critical speed and burst speed, are not suitable for use in models of larval dispersal (Irisson and others, 2009), for which a routine, sustainable speed is required. Cues that trigger changes in swimming are unknown, whereas the suite of potential cues (age, size, temperature, or detection of shorelines, currents, or chemicals [Trnski, 2002; Leis and Carson-Ewart, 2003]) is large.


The better performance of the model in simulating particles during the period when shortnose sucker larvae rather than Lost River larvae should have been most abundant may be due to behaviors not included in the model. For example, some evidence shows that Lost River sucker early juveniles are found preferentially in open water, whereas shortnose sucker juveniles are found closer to the shoreline (Simon and others, 2009). Most of our field samples were collected close to shore, close to the delta, or in the transit path that any larva would need to travel from the river to the lake, rather than in open water. In 2009, even though the density of Lost River suckers in the drift in the Williamson River was greater than that of shortnose suckers (Wilcoxon test, p<0.05), Lost River suckers were five times less likely to be in our nets (0.81 percent of our samples compared to 4.21 percent for shortnose suckers; table 2), suggesting that the field samples might be biased in favor of the collection of shortnose suckers. Markle and others (2009) found that Lost River sucker larvae, aged 17–42 days, dispersed more quickly out of the lake and speculated that they were more dependent on gyre retention than shoreline retention. The present analysis included only one site (OSU U8) that appeared to be influenced by gyre retention, so this hypothesis remains largely untested.


Other simplifying assumptions in the model regarded entry age and mortality. The age of larvae at the upstream boundary was a single age rather than a true age distribution, and age and size relations were assumed to be linear across the larval size range, with no seasonal adjustments. Mortality was modeled as spatially uniform and independent of age, a common compromise (Helbig and Pepin, 1998). Of these assumptions, the assumption of spatially uniform, age-independent mortality was the most critical because of its effect on the model and its biological improbability. Mortality is an important variable to include in biophysical models (Hare and others, 2002), but details are needed in addition to the crude estimates generally available. One potential driver of spatial patterns that is not investigated in biophysical models is that aggregations of larvae could be a result of spatially non-uniform mortality. Estimating site-specific mortality requires determination of the confounding effects of migrations (Helbig and Pepin, 1998). In one attempt, Markle and others (2009) found as much as an order of magnitude difference in apparent mortality for different ages of sucker larvae and different sites in Upper Klamath Lake. The success of our correlation analysis suggests that our simulation of the advection and dispersal of larvae can replicate the spatial and temporal variability of fish lengths of the field data, but that simulated lengths were almost uniformly biased low, and adding spatial- and age-dependent mortality to the model could be an important improvement.


This study supports the hypothesis that advection trajectories of larval fish are a product of interactions of ontogeny and behavior with hydrography (Bradbury and others, 2006; Leis and others, 2006). Our simulations identified temporal patterns determined by the timing of larval pulses in the Williamson River and spatial patterns resulting from complex interactions of wind-driven currents with the bathymetry of the delta and remnants of the levees around it.


These simulations were done to help describe the effects of a major delta restoration project on larval dispersal, to help interpret field data, and to evaluate management options for retaining more larvae in the lake. Restoration projects commonly end when on-the-ground work is completed, with no detailed evaluation of the initial assumptions and actual effects of the project. This model is a tool to aid understanding of the effect that restoration of the Williamson River Delta has on the dispersal of larval suckers and the ability of the project to increase retention of larvae in Upper Klamath Lake.


The simulations show that transit through the delta is dependent on wind speed and that strong prevailing winds cause more particles to take a route through the southern delta. The simulations also suggest that lake elevation might be used to optimize the tradeoff between keeping lake elevation low enough to maximize the number of larvae that are transported to the northern delta, which tends to result in slower travel times overall to the lake, but high enough to minimize the number of larvae that are sent down the Williamson River channel, which results in faster travel times to the lake. Bathymetry and vegetation are expected to change as the delta matures, and the model can be used to predict the response in travel times to those changes. The model also can be used as a tool to visualize dispersal tracks and to highlight conflicts with field data. Dispersal tracks can be used to establish more efficient sampling protocols by weighting areas based on predicted sizes and abundance. Conflicts with field data can be used to focus on biologically meaningful questions such as species differences, behavioral cues to swimming and settlement, and spatial patterns in mortality. All of these analyses can lead to better hypotheses about the importance of larval dispersal in year class formation.


First posted January 31, 2014