Protecting Outmigrating Juvenile Spring-run Chinook—Part 3
Pete Nelson, PhD
Department of Water Resources
First… it’s been a while! I wrote two previous posts (Science for Salmon Part 1 and Part 2) about developing our annual forecast for the number of juvenile Spring-run Chinook salmon (“spring-run”) entering the Delta. Since then, the team developing this Juvenile Production Estimate (JPE) has been focused mainly on the modeling that uses various fish counts and environmental conditions to predict the number and timing of outmigrating spring-run. The modeling component is crucial because this is how we finally arrive at a forecast, but it’s a challenge to explain because it requires a lot of advanced mathematics.
Sometimes, scientists will point to a model into which the data are dumped and treat it as a bit of a “black box” from which emerges, sans further explanation, the answer (Figure 1). Our question—how many juvenile spring-run enter the Delta each year?—is a tough one, and we want to make the process used to determine our answer less opaque. So, this article is going to be a balancing act between that “black box” approach and an attempt to explain the beauty behind the math.
Figure 1. One way to find the answer! AI-generated illustration created with ChatGPT by OpenAI, based on user prompt.
Spring-run Chinook salmon have gone from being one of the most abundant Chinook runs in California to being one of the scarcest; consequently, they are listed as threatened under both the California and Federal Endangered Species Acts. The Sacramento-San Joaquin Delta is the Chicago O’Hare International for California Chinook, the hub for adult fish returning from the ocean to their natal streams to spawn, and for the juveniles migrating downstream back to the ocean. Salmon biologists, water managers, and fishermen worry about the gauntlet of threats these anxious travelers experience, including warm water, predators, and taking the “wrong turn” into water diversions. Managing the risk posed to the spring-run population by these diversions is the responsibility of the Department of Water Resources(DWR), and to do this we need to know when and how many salmon youngsters are entering the Delta each year.
The Modeling Architecture: More Than Just a Guess
A spring-run JPE isn't a single number pulled from thin air (or a fish pulled from a barrel); it is generated by a multi-model framework that combines several sophisticated statistical sub-models. To understand how we get to the final answer, we’re going to look at the four main challenges: counting out-migrating juvenile salmon, identifying which of those fish are actually spring-run, estimating their probability of surviving their journey to the Delta, and finally forecasting how many will actually reach that stage in their life-long journey.
Figure 2. Predicted abundance of outmigrating juvenile Chinook and their weekly capture probability (example from Lower Clear Creek, 2008). There’s a lot going on in these figures! See the text for details.
Challenge 1: Counting the Invisible (BT-SPAS-X)
The first step is estimating the total number of outmigrating juvenile salmon passing by sampling locations at sites like Knights Landing on the mainstem Sacramento River and on various tributaries. Figure 2, above, shows the expected abundance of outmigrating juvenile Chinook and their weekly capture probability using an example from Lower Clear Creek, 2008. There’s a lot going on in these figures: The upper graph shows weekly abundance estimates, and the lower graph shows weekly capture probabilities in a rotary screw trap. Both figures show the flow or discharge rate in green, the abundance estimates from a modified Peterson model in blue circles and the predicted fish numbers from the BT-SPAS-X model using vertical bars, gray when the estimates are based on trap captures and pink where no data were available. The thin black bars show the range around each weekly estimate within which we’re quite certain the “true” number lies; where that span is narrow, we think we’re close to reality, but where that span is broad our confidence is much reduced. There’s a bit more to the figure, but I’m going to leave it there. If you’re curious about every last detail (nice!), get in touch and I’ll help you out.
Anyway, all of this depends on Rotary Screw Traps which are floating funnels placed in the current, facing the outmigrating salmon as they travel downstream to catch a portion of the passing fish (see Figure 5 for a simplified illustration). We mark a bunch of the fish we catch and then release them upstream of the trap so they have to pass the trap again. We expect, then, to catch a mixture of a few those marked fish and more unmarked fish (i.e., not previously caught). The ratio of marked to unmarked fish tells us the trap “efficiency.” But trap efficiency is strongly affected by both the trap placement and stream conditions, giving results that are sometimes distressingly poor, catching as few as 5 in 2000 marked fish moving down the big mainstem river. These methods traditionally only look at one rotary screw trap at a time, and rely on regular sampling and efficiency tests, but the accuracy can be really poor if there are any interruptions in sampling.
To improve our abundance estimates, we’ve started using a model with penalized splines—mathematical curves that act like a flexible ruler—to smooth out the trends in outmigration, allowing us to predict the trap efficiency when the trap wasn't even in the water, or when efficiency tests didn’t happen. The model "borrows" information from all the other years at that site when the traps were running, and across other sites, as well as using current environmental conditions like stream flow to help fill in the gaps. It also accounts for "process error," recognizing that there will always be some unexplained variation in efficiency.
Challenge 2: Who is Who? (The PLAD Model)
The next challenge is that multiple runs of Chinook salmon—fall, late-fall, winter, and spring—all use the Sacramento River watershed and, based on appearance, the juveniles are indistinguishable. Traditionally, biologists used Length-at-Date (LAD) criteria, which basically assumed that if a fish was a certain size on a certain day, it belonged to a specific run. However, using length-at-date for run assignment is notoriously inaccurate, often misidentifying half of the fish it tries to categorize.
To fix this, our colleague, Noble Hendrix, developed the Probabilistic Length-at-Date (PLAD) model. Instead of a "yes or no" assignment, PLAD uses genetic data from a subset of fish to build a "mixture model.” This model looks at the distribution of fish sizes from a genetically-determined sample of juvenile salmon and calculates the probability that a juvenile is a spring-run based on its length, when it was caught, and where it was caught (Figure 3). It’s like a more accurate version of a growth chart that acknowledges that some "late bloomers" or "early birds" from different runs might overlap in size, and allows us to assign each fish captured a probability regarding its run-type (e.g., 60% likelihood spring run and 40% winter run). By using this probabilistic approach, we can assign run types even to fish that weren't genetically tested, while being honest about how certain we are in that assignment.
Figure 3. An example of run-type probability curves for juvenile Chinook; unique to a specific location and time of year. Different colors denote different run-types.
Challenge 3: Estimating Survival (Smolt Survival)
The previous models help us to estimate the abundance and timing of juvenile spring-run produced each year in the Sacramento River watershed, but before these fish reach the Delta they must survive something of a gauntlet as they migrate from smaller, higher elevation streams to the confluence of the Sacramento and the San Joaquin rivers. This passage is fraught with danger, ranging from potentially poor water conditions to hungry predators, and estimating the probability of their survival is critical to developing our ultimate estimate (Figure 4).
Figure 4. Release location to Sacramento River survival rates. Red are dry year releases; blue are wet year releases.
Our survival model uses fish detection data from acoustic telemetry studies to estimate survival rates for juvenile salmon migrating from their natal tributaries, down the Sacramento River or the Feather River, and eventually to the Delta. Fish tagged with tiny sound-emitting devices are detected as they pass a series of underwater listening devices along the migration path, and each detection is logged as an individual fish of known origin at a specific date and time. So, yes, the government is listening. Just not to you. A sequence of detections provides a measure of downstream passage speed, and a failure of detection suggests the likely demise of that fish somewhere upstream. The primary determinants of survival in the model are fish size (bigger fish have an improved probability of success) and environmental conditions, such as flow or water temperature. For this reason, survival probabilities vary from year to year and from fish to fish, and the model integrates newly acquired data with the previous results each year.
Challenge 4: Predicting the Future (Stock-Recruit and In-Season Models)
Now that we have a decent idea of how many juvenile salmon are moving from their rearing habitat high in the watershed and we have an estimate of their survival probabilities for different flow conditions and fish sizes, we can use models to forecast how many of those are likely to make it to the Delta. We have two general ways of doing this:
First, we can use Spawner-Outmigrant Stock-Recruit models to predict how many outmigrating juveniles that today’s parents will produce over the coming year. This is like trying to guess how many apples an orchard will produce based on how many trees were planted and what the weather is expected to be like. We include environmental conditions in our forecast models, like water temperature and peak flows during spawning and rearing. Our findings show that cooler water and higher flows generally lead to more productive salmon populations.
As the migration season begins, we switch to the other way of forecasting the expected number of outmigrants, using an In-Season Outmigrant Model. This is similar to how a GPS updates your expected arrival time as you drive. Basically, at any given date during the outmigration season, the In-season Outmigrant Model counts how many outmigrants have passed a rotary screw trap and then uses the outmigration timing recorded from previous years to forecast how many more outmigrants we expect to pass by season’s end. Early in the season (say, late December), very few outmigrants have passed most of the rotary screw trap sites, so the forecast is broad and uncertain. But as more fish pass the traps, say by the end of February or March, the model "learns" more about the current season’s migration and environmental conditions, and the forecast becomes much more precise.
Bringing it All Together: The Integrated JPE
The final "answer" comes from the integrated JPE model, which stitches all these pieces together. It takes the spawner counts, expands the rotary screw trap catch counts to estimate outmigrant abundances with BT-SPAS-X, identifies the spring-run among those outmigrants with PLAD, forecasts total season outmigrant numbers with Stock-Recruit and In-season Outmigrant models, and then uses survival models to forecast how many of those expected outmigrants will make it as they swim from their natal creeks down the mainstem Sacramento River to the legal boundary of the Delta where the river flows under the I-Street bridge in the city of Sacramento (Figure 5).
Figure 5. JPE schematic: From data collection to cloud storage, and from analyses to implementing management decisions. The JPE depends on understanding the ecology of the Sacramento River and its tributaries which derive much of their water from Sierra snowmelt, water regulated by dams and other infrastructure. Central Valley Chinook salmon adults leave the ocean and return to natal streams where they spawn and die, their offspring rearing in freshwater before migrating to the ocean. State resource agencies, including DWR, gather data on these salmon, including their numbers, size and genetics. The JPE relies particularly heavily on RSTs to monitor juveniles. Biologists throughout the Central Valley upload these data to the cloud where they are collated, checked and made available to scientists who use the models described in this essay to assess Chinook runs every year. These assessments, including the JPE, are provided to resource managers and policy-makers in the State capital who, in turn, make decisions regarding water diversions and storage in near real-time, providing that water for human uses as well as the ecological systems that depend on that resource. Please see table 1 below for an explanation of the icons.
This modeling process relies on a massive "field-to-cloud" effort that pipes data from over 40 different information streams overseen by dozens of data stewards to ensure that the data we put into the models are reliable and updated on a weekly basis for real time management decisions. Well…that’s the system that’s being built and should be in place by the end of 2026. Because each step—from counting a single egg to tracking a juvenile past a trap—has some uncertainty, our models propagate that error throughout the entire process. This means we won’t just give management teams a single JPE number wrought in stone (the answer!); we will give them a distribution of possible JPEs centered on a highest probability estimate that expresses our degree of confidence in the JPE forecast. And we can update that forecast through the season as more data roll in and our confidence in the forecast increases.
Patience truly does lead to beauty. By moving away from simple guesses and toward these sophisticated, probabilistic tools, we are creating a more transparent and robust way to protect our threatened spring-run Chinook salmon. For us, the answer to how many juvenile spring-run are entering the Delta is going to be different every year, each time generating additional, challenging questions: What was the effect of rainfall this time? How did ocean conditions affect the health of returning adults? And how should we ensure that there are sufficient water resources for this incredible fish every year?
Table 1. This table displays each of the icons used in Figure 5, a schematic of the spring run JPE, accompanied by text describing what each icon represents.
| Image |
Explanation |
 |
Sacramento River and its tributaries |
 |
Sierra Nevada mountains with snowpack
|
 |
Dams and other diversions give us the means to store and regulate water use |
 |
Chinook salmon are an anadromous fish, juveniles hatching and rearing in freshwater but completing most of their growth in the ocean; adults return to freshwater to spawn |
 |
Pacific Ocean offers salmon abundant food, vast space and rapid growth potential
|
 |
Data: numbers, size, genetics and more; this information is crucial to understanding salmon ecology, determining fisheries policy, and making water use decisions |
 |
Rotary Screw Trap: these capture juvenile salmon as they migrate downstream, holding them so that we can count and measure them before releasing them back into the river |
 |
Scientists collect data in the field, analyze samples in the lab, enter those data into the system, and develop and run the models to understand the patterns |
 |
Cloud storage for the data provides a central repository accessible to all
|
 |
Models, including the response of salmon production to positive environmental conditions, help to make sense of lots of data
|
 |
State capital where policy is developed, such as that determining how water use decisions are made |
 |
Decisions like a mandatory reduction in water exports to prevent drawing migrating juvenile salmon into pumping plants, for example |
Note: Dr. Josh Korman, who led the technical team developing these models, died on 25 May 2026. Josh was one of the rare quantitative ecologists who also spent major amounts of time in the field—with a mask and snorkel, pulling nets and counting fish—and his keen enthusiasm for the challenge of understanding threatened fish populations was inspiring. We lost Josh before the completion of this project, but we were lucky to work with him. As we finish, I trust that we’d have made Josh proud.