Validation of a Swimming Direction Model for the Downstream Migration of Atlantic Salmon Smolts

: Fish swimming performance is strongly inﬂuenced by ﬂow hydrodynamics, but little is known about the relation between ﬁne-scale ﬁsh movements and hydrodynamics based on in-situ investigations. In the presented study, we validated the etho-hydraulic ﬁsh swimming direction model presented in the River Mandal from Southern Norway, using similar behavioral and hydraulic data on salmon smolts from the River Orkla in Central Norway. The re-parametrized model explained the variation of the swimming direction of ﬁsh in the Orkla system in same degree as the original model performed in the Mandal system (R 2 : 84% in both cases). The transferability of the model when using it from one river to predict swimming direction in the other river was lower (R 2 : 21% and 26%), but nevertheless relatively high given that the two localities differed in hydraulic conditions. The analyses thus provide support for the fact that the identiﬁed hydraulic parameters and their interaction affected smolt behavior in a similar way at the two sites, but that local parametrization of the base model is required. The developed etho-hydraulic models can provide important insights into ﬁsh behavior and ﬁsh migration trajectories and can be developed into prediction models important for the future development of behavioral downstream migration solutions.


Introduction
Habitat fragmentation due to the presence of hydropower plants, dams, and weirs is widespread in many rivers used as migratory routes by fish and is a major threat to worldwide aquatic biodiversity [1,2]. Maintaining or re-establishing longitudinal and lateral connectivity for fish in fragmented rivers is crucial to achieving environmental goals (e.g., the United Nations Sustainable Development Goals and the EU Water Framework Directive). Mitigation measures for upstream fish passage (such as fishways) are well-studied compared to measures for downstream fish passage. Based on the state of the art, the current best practice solution for small fishes in river systems with small to medium hydropower facilities consists of fined meshed (non-passable) racks with bypass facilities (e.g., [3] and references therein), although such a method is challenged by technical limitations, economic costs, the risks of fish impingement on racks [4], and predation. A major barrier for the development of alternative guiding systems is insufficient knowledge of how the hydrodynamics of the flow affect the behavioral choices of the migrating fish [5]. Due to technical limitations, links between hydraulics and fish behavior at fine spatial and temporal scales have mainly been explored under laboratory conditions (e.g., [6][7][8][9]), with inherent concerns regarding their relevance in natural systems. Recent advances in fish telemetry methods and computational fluid dynamics (CFD) modeling now allows the acquisition of fish position and properties of the flow field under natural conditions at high spatio-temporal resolutions and accuracy.
Previous research from North America [10] pioneered such an etho-hydraulic approach by combining CFD modeling and an individual-based behavioral model of juvenile Pacific salmon (Oncorhynchus spp.) to explore how downstream migrating fish navigate through dammed river sections by adjusting their direction, speed and depth according to the perceived conditions. Recently, an international research group in Scandinavia explored the effects of hydrodynamics on both swimming direction and swimming speed of downstream migrating Atlantic salmon (Salmo salar) smolts [11]. It studied in situ based on fish telemetry tracking and CFD modeling and developed explanatory etho-hydraulics models for the smolts. Such models are important tools for the understanding and prediction of fish swimming behavior, and for the development of mitigation measures. However, for development of predictive models, the transferability to other systems of such explanatory models needs to be explored. The aforementioned etho-hydraulics models were developed from tracking of downstream migrating salmon smolts in the River Mandal in southern Norway [11].
Here, we validate the model developed for swimming direction in River Mandal [11] from southern Norway using similar data from the Svorkmo hydropower plant intake on the River Orkla, in central Norway. This was done by parametrizing a similar explanatory model with the River Orkla data, and then by cross-validation of the two models.

Materials and Methods
In this study, datasets on smolt behavior and hydraulics from two river sites, at the River Mandal in southern Norway and the River Orkla in central Norway, were used to validate the swimming direction behavioral model for Atlantic salmon smolt developed on data from River Mandal [11] (hereafter the Mandal model). First, we re-parametrized the Mandal model, using the same dependent and explanatory variables and modeling procedures as those in the Mandal for data from the River Orkla (termed the Orkla Model) to explore the extent to which the model structure could explain smolt swimming direction at another site. Secondly, we explored how well the model parametrized for one site predicted behavior in the other site to examine the dependence of model transferability on parameter values.
Detailed information on the behavioral and hydraulic dataset and analyses from the River Mandal can be found in the cited study [11], whereas the River Orkla study is described below.

The River Orkla
The River Orkla, located in Central Norway (63 • 03 N, 9 • 40 E), has a mean annual discharge of 72 m 3 s −1 and a total of five hydropower plants operating within the watercourse. The lowermost Svorkmo hydropower plant (HPP; Figure 1) is located in the main migratory route of anadromous Atlantic salmon and is a challenge for the downstream migration of Atlantic salmon smolts and kelts in the river [12]. As an attempt to prevent the movement of smolts (and ice and debris) towards the HPP, a concrete wall with two identical submerged openings (1.5 × 25.8 m, each at 2-2.5 m depth) was installed at the intake entrance during the construction of the HPP facility (in operation from 1983). The water withdrawal towards the Svorkmo HPP typically varies between 20 and 55 m 3 s −1 . The water level at the intake of the Svorkmo HPP is controlled by the Bjørset dam 100 m downstream of the intake, which comprises two pool and weir fishways along the two riverbanks (one in operation during the study) and four spillway gates. To meet the requirements of a minimum flow at 20 m 3 s −1 during summer, one of the gates is opened (usually Gate 1 is used, next to the operating fishway) from May 1 (when almost all smolts have passed). During winter and until the gate opening, a minimum flow of 4 m 3 s −1 is spilled through the fishway.
Water 2021, 13, 1230 3 of 10 with two identical submerged openings (1.5 × 25.8 m, each at 2-2.5 m depth) was installed at the intake entrance during the construction of the HPP facility (in operation from 1983). The water withdrawal towards the Svorkmo HPP typically varies between 20 and 55 m 3 s −1 . The water level at the intake of the Svorkmo HPP is controlled by the Bjørset dam 100 m downstream of the intake, which comprises two pool and weir fishways along the two riverbanks (one in operation during the study) and four spillway gates. To meet the requirements of a minimum flow at 20 m 3 s −1 during summer, one of the gates is opened (usually Gate 1 is used, next to the operating fishway) from May 1 (when almost all smolts have passed). During winter and until the gate opening, a minimum flow of 4 m 3 s −1 is spilled through the fishway.

Telemetry
During the smolt migration period from late April to early June, 100 Atlantic salmon smolts were caught using a floating rotary trap. The smolts were surgically tagged with acoustic transmitters (Lotek, 200kHz, model M-626, 7.5 × 17 mm, Lotek Wireless Inc., Newmarket, ON, Canada, with 2 s burst interval) following the methodology used in River Mandal [11], in accordance with the Norwegian regulations for animal welfare and treatment (Permit ID: 7636).
A two-dimensional telemetry array comprising 27 hydrophones (Lotek 200kHz WHS 3050, Lotek Wireless Inc., Newmarket, ON, Canada) was deployed at the intake area of the Svorkmo HPP, covering the area from 150 m upstream of the intake facility to 100 m downstream to the Bjørset dam ( Figure 1). Due to the shallow water depth at the study site (≈1.5-2.5 m), only a 2D setup could be deployed, in contrast to Laudal HPP on the River Mandal [11], where the depth in front of the intake allowed for a 3D telemetry array.
Fish positional signals of those 91 individuals that were detected in the study area (others were either lost to predation, or had not reached the site during the study period) were processed using the YAPS method [13] to determine location and the concomitant estimated positional error. The tracks were further processed to remove periods when either fish had scattered estimated positions or they were stationary (high number of

Telemetry
During the smolt migration period from late April to early June, 100 Atlantic salmon smolts were caught using a floating rotary trap. The smolts were surgically tagged with acoustic transmitters (Lotek, 200 kHz, model M-626, 7.5 × 17 mm, Lotek Wireless Inc., Newmarket, ON, Canada, with 2 s burst interval) following the methodology used in River Mandal [11], in accordance with the Norwegian regulations for animal welfare and treatment (Permit ID: 7636).
A two-dimensional telemetry array comprising 27 hydrophones (Lotek 200 kHz WHS 3050, Lotek Wireless Inc., Newmarket, ON, Canada) was deployed at the intake area of the Svorkmo HPP, covering the area from 150 m upstream of the intake facility to 100 m downstream to the Bjørset dam ( Figure 1). Due to the shallow water depth at the study site (≈1.5-2.5 m), only a 2D setup could be deployed, in contrast to Laudal HPP on the River Mandal [11], where the depth in front of the intake allowed for a 3D telemetry array.
Fish positional signals of those 91 individuals that were detected in the study area (others were either lost to predation, or had not reached the site during the study period) were processed using the YAPS method [13] to determine location and the concomitant estimated positional error. The tracks were further processed to remove periods when either fish had scattered estimated positions or they were stationary (high number of successive observations occurring over short distances). This resulted in a total of 21,062 observations (median standard error of estimated positions:~0.80 m) originated from 74 individuals (out of the 91 fish tracked successfully in the system).

Hydraulic Modeling
During the period when smolts were tracked within the study area (25 April-21 May), the flow regime in River Orkla varied highly from late-spring flood events to a one-week low-flow period. As the entire flow-series during the telemetry study could not be modeled due to heavy computational effort, ten flow scenarios were selected to represent the hydrological conditions experienced by the smolts (specified by hourly recorded hydrological and operational parameters, e.g., water elevation, discharge diverted to the HPP, spilled water through the gates, etc.). Each smolt was allocated to one of these scenarios based on the time of their positional signals ( Table 1). The hydrological conditions of the ten selected scenarios together with the bathymetry data from Acoustic Doppler Current Profiler (ADCP, SonTek M9) mapping were used to characterize the hydrodynamics of the flow at the vicinity of the Svokmo HPP intake and the Bjørset dam (Table 1) using the computational fluid dynamics model OpenFOAM (release 4.1.0, [14]). Structural elements (dam with spillway gates and intake channel with submerged wall and two openings) were digitalized based on technical drawings and RTK GPS measurements (Leica Viva CS15). Ten hexahedra-dominant computational mesh were then generated by the snappyHexMesh utility of OpenFOAM with grid elements comparable to the size of smolts (0.15-0.3 and 0.1 m in horizontal and in vertical directions, respectively), creating in total approximately 18 million cells per scenario. Table 1. The scenarios for CFD modeling (A-J) with water surface elevation (W elev (m above sea level (m a.s.l.)), inlet discharge (Q in (m 3 s −1 )), discharge through the dam (Q dam [m 3 s −1 ]) and through the intake (Q intake (m 3 s −1 )). The dimensionless ratio between the two outlets (Q dam /Q intake ) is also presented. The gate openings (G1-G4) indicate the percentage (%) of the actual opening of the gates. Note that below 16%, the gate was considered closed (TronderEnergi, personal communication). The number of fish (Nr fish ) sorted into each scenario is also shown. The ten scenarios were simulated by the pimpleFoam one-phase solver from the Open-FOAM software, which uses the PIMPLE algorithm [15] for pressure-velocity coupling and allowed modeling of the 3D transient flow on the discretized domain by solving the Reynolds-averaged Navier-Stokes equations. Turbulence was modeled using the widely validated standard k-ε turbulence model [16]. Detailed description on the numerical modeling process, including model calibration and validation, can be found in one of the previous studies of the authors [17]. The transient scenarios were set up to simulate 10 min of river flow upon reaching developed flow patterns, in correspondence with the observed average passage time of the smolts (<10 min). The following modeled variables were stored accordingly over the 10 consecutive minutes of each simulation at a 60 s time interval: the three components of flow velocity (u, v, and w, Cartesian velocity directions in streamwise, transversal, and vertical directions, respectively) and the turbulent kinetic energy (TKE). These data were further processed in combination with the smolt trajectories.

Combining Fish Positioning and Hydraulics
To analyze the effects of hydrodynamics on the swimming direction of smolts in the River Orkla, described as angular difference (minimum angular difference at time t; in degrees) between the resultant flow vector and the ground direction of fish between times t − 1 and t + 1, following the study in River Mandal [11], estimated fish positions (YAPS, [13]) were combined with the averaged (in time and depth) modeled hydraulic variables, following the 2D etho-hydraulic model developed for the "main watercourse" at the Laudal HPP intake on the River Mandal [11]. Two depths (0.4 and 0.6 m below the water surface) were selected to cover the water depth that Atlantic salmon smolts were expected to migrate [18].

Fish Swimming Direction Models
A generalized linear mixed model using the template model builder [19] with a betadistribution technique was used to parameterize the explanatory angular difference model for the Orkla site (Orkla model). Angular difference was defined as the absolute difference between the ground direction of the fish (the direction in which the fish is moving, in degrees) and the flow direction (in degrees) and indicates the swimming direction of the fish relative to the flow direction. The angular difference ranges from 0 • (the fish is moving in the same direction as the flow) through 90 • (the fish is moving perpendicular to the flow) to 180 • (the fish is moving in an opposite direction to the flow). The model setup followed the model developed in River Mandal [11] in which angular difference was explained by hydraulic explanatory variables, the u and v velocity components, and TKE, as well as the swimming speed of the smolt (SwimSpeed). The swimming speed was calculated as S 2 x + S 2 y , where S x and S z are swimming speeds in x and y directions and calculated as S x = G x − u and S y = G y − v. Here, G x and G y are the ground speed of the fish in x and y dimensions, and u and v are the water velocity components in the same dimensions. Ground speed and swimming speed of a fish in time (t) were calculated as displacement from time t − 1 to time t + 1. Next, we cross-validated the models by comparing predictions from the Mandal model with those observed in the Orkla site and the predictions from the Orkla model with observations in the Mandal site.
All model selections were based on the Akaike's information criterion (AIC; [20]) provided by the bbmle-library [21], and model performance was evaluated by examining the correlation (Pearsons R 2 ) between the predicted and the observed values.

Results
Among the ten modeled scenarios (Table 1), five exhibited higher flow discharge through the intake towards the HPP (Q intake ) than the spilled discharge over the dam (Q dam ). Out of the 91 detected fish, 42 smolts were detected under these conditions, whereas 49 fish were detected in the other five scenarios where Q dam > Q intake (30 and 44 fish, respectively, among the 74 smolts used in further analysis). The latter hydraulic scenarios emerged as the result of two longer flood events (scenario G and I, Table 1) and one short flood peak (scenario J, Table 1). The design of the intake and dam area as well as the floods caused larger variation of the hydraulic condition in the Orkla site compared to the Mandal site conditions (Figure 2), and distributions were skewed towards higher values, particularly for transversal velocities (v) and turbulent kinetic energy (TKE). Using the same statistical modeling procedures as in the study on River Mandal [11], the most parsimonious model obtained for the Orkla site included the same main effects and interactions as the Mandal model (M.org model from Table 2). Turbulent kinetic energy, horizontal velocity components, and swimming speed of the fish and concomitant interactions significantly explained angular differences in the Orkla site (R 2 = 0.84, Table  3), with similar explanatory power as for the Mandal site (R 2 = 0.84). The estimated gradients differed somewhat between the models, but the direction of the effects (signs) was the same. The ability of the models to explain angular difference in the other river system was similar, with the Orkla model tested at the Mandal site performing slightly better (R 2 = 0.26) compared to the Mandal model tested at the Orkla site (R 2 = 0.21). Using the same statistical modeling procedures as in the study on River Mandal [11], the most parsimonious model obtained for the Orkla site included the same main effects and interactions as the Mandal model (M.org model from Table 2). Turbulent kinetic energy, horizontal velocity components, and swimming speed of the fish and concomitant interactions significantly explained angular differences in the Orkla site (R 2 = 0.84, Table 3), with similar explanatory power as for the Mandal site (R 2 = 0.84). The estimated gradients differed somewhat between the models, but the direction of the effects (signs) was the same. The ability of the models to explain angular difference in the other river system was similar, with the Orkla model tested at the Mandal site performing slightly better (R 2 = 0.26) compared to the Mandal model tested at the Orkla site (R 2 = 0.21). Table 2. Investigated combination of the variables for best model selection of angular difference parameterized for the River Orkla site. The model candidates were tested with different parameter setups for the fixed effect, while the same dispersion structure was used for all of them as for the River Mandal site [11]. The degree of freedom (df ) in addition to the AIC values and the difference in the AIC values (∆AIC) were calculated by the bbmle R package [21].

Candidates
Parameter Set up for Fixed Effect AIC ∆AIC df  Table 3. Estimated parameters of the best models for angular difference parameterized for the River Orkla site and for the River Mandal site [11]. Parameter estimates are presented for the fixed effect only, with the standard error in parentheses. All R 2 are calculated by comparing observed values vs. predicted values for the models, and R 2 own70% is calculated by parameterizing the model on 70% of the individuals and compare the observed vs. predicted for the remaining 30% of the individuals. R 2 own is the R 2 of angular difference when the model was parameterized and tested on the same river site, while the R 2 cross is the R 2 for the models parameterized on one site and tested in the other site.

Dependent Variables per Sites:
Orkla

Discussion
Etho-hydraulic models that can explain fish movement are important for future development of guiding systems that ensure safe two-way passage of migrating riverine fish at anthropogenic structures such as hydropower facilities and dams [5,10]. Statistical explanatory models for the effects of hydraulic variables on fish swimming, such as the model developed in River Mandal [11] for the swimming direction of Atlantic salmon smolts, are important steps towards predictive models that can be used in design of guiding systems. The explanatory models inform the hydraulic variables involved and how they interact to influence the behavior of the fish. However, the generality of the identified links between smolt movement and hydraulic variables needs to be assessed.
The model, developed from smolt tracking and hydraulic modeling in the River Mandal [11], performed well when re-parameterized to similar data from the River Orkla. The most parsimonious model from both sites included the same main and interaction effects, affecting angular difference in the same directions. The Orkla model explained 84% of the variation in angular difference of the 74 tracked smolts at this site, a prediction rate that matched the performance of the original model (84%-73 smolts, [11]). The correspondence of the modeling results from the two sites occurred despite the generally higher velocities, larger range of the hydraulic parameters, and generally higher swimming speeds in the Orkla than in the Mandal site (see Figure 2). Thus, the results provide support for how the hydraulic variables and concomitant interactions identified in the River Mandal [11] influence the swimming direction of Atlantic salmon smolts during their downstream migration, and that general behavioral mechanisms were indeed identified.
The more challenging cross-validation yielded lower explanatory powers. The Mandal model explained 21% of the angular difference of salmon smolts in the Orkla site, whereas the Orkla model explained 26% of the angular difference in the Mandal site. Interestingly, the Orkla model performed somewhat better in the cross validation than the Mandal model, probably due to the wider range of the hydraulic parameters estimated for the Orkla site. Indeed, the Mandal model predictions for the Orkla site represent extrapolation to hydraulic conditions not found at the Mandal site. Developing representative and transferable etho-hydraulic models is challenging, in particular due to their limitation in quantifying and studying all the possible exogenous and endogenous factors and associated interactions that would likely contribute to the complex decision-making process of fish swimming performance [10]. Such limitations may explain the moderate explanatory power of the cross validations.
In both models in this study, the interplay among the hydraulic variables emerges as more important for angular difference than the effect of single variables. This result corroborates the finding from River Mandal [11] and stresses the importance of considering the interaction of multiple hydraulic variables when assessing the effects of hydraulics on fish swimming performance, which has so far been the typical laboratory approach.
The models presented here were developed for Atlantic salmon smolts and can be used to develop predictive trajectory models for this species and life-stage. We recognize that due to the specific biomechanical, physiological, and morphometric attributes of each fish species and associated life-stages, these models cannot be generalized and used for other species. Thus, we advocate that future research focuses on the development of etho-hydraulic models targeting umbrella fish species representing different swimming modes [22][23][24].
Etho-hydraulic behavioral models are powerful tools and highly relevant for the future progress of river management and engineering solutions for safe fish migration past barriers [2,5,10].