Based on snowpack and baseflow conditions as of March 1, predicted natural streamflows for the upcoming April 1 - June 30 time period are:

- Henry's Lake: 121% of average
- Henry's Lake to Island Park Dam: 91% of average
- Henry's Fork upstream of Ashton: 88% of average
- Fall River: 115% of average
- Teton River at St. Anthony: 139% of average

Full results are shown in the table below. The text explains methods and inteprets the output.

# "Natural streamflow"

## What is it?

Like all streams in the Snake River basin, the Henry's Fork and its tributaries are highly managed for irrigation and hydroelectric power generation. Water is stored in and released from reservoirs, diverted from streams, pumped from aquifers, recharged into aquifers, and returned to streams after passing through irrigation systems and power plants. Thus, streamflow on any given day in most of our rivers differs from what it would be in absence of reservoirs, diversions, power plants, etc. However, the water supply that flows into the managed river/reservoir system is still the product of natural hydrologic processes that start with precipitation on the watershed and include snow accumulation and melt, runoff, natural aquifer recharge, and aquifer outflow. This water is what I term *natural streamflow*. Other synonyms are *unregulated streamflow*, *natural watershed inflow*, or simply *water supply*.

## Why predict it?

Because knowledge of water supply forms the scientific basis for managing the river/reservoir system, predicting natural streamflow is the starting point for predicting reservoir storage and delivery and hence regulated streamflows. In the case of the Henry's Fork upstream of Ashton for example, the prediction of natural streamflow removes the effects of storage in and delivery from Henry's Lake and Island Park Reservoir. Natural streamflow in Fall River removes the effects of storage in and delivery from Grassy Lake and the effects of irrigation diversion of water from the river.

## Issues specific to the Teton River

For the purposes of these predictions, the Teton River is handled slightly differently. Upstream of the St. Anthony gage on the Teton River, its flow is affected by irrigation diversion and return flow and by delivery of Island Park storage water to the Teton River via the Crosscut Canal, which diverts water from the Henry's Fork at Chester Dam. For these predictions, I have removed the effect of delivery of water from the Crosscut Canal, but I have not accounted for upstream irrigation diversion. Thus, my definition of "natural" flow in the Teton River at St. Anthony still includes effects of upstream diversions and return flow. I have not removed these effects from the calculation for four reasons.

- Unlike diversions from Fall River, the mainstem Henry's Fork and the lower Teton River, few of the uppper Teton River irrigation diversions are measured in real time and reported in readily available electronic format. Thus, a large amount of manual data entry and statistical modeling are required to account for these diversions. Because of the large amount of work required, I do this accounting in a large, concentrated effort only once every 5 or 10 years. I did this in 2004 and again in 2011. I'll probably do it again after the 2018 water year.
- Calculation of return flows requires running a complicated groundwater-surface water model for Teton Valley, which I do at the same time as the diversion accounting. Check back in 2019.
- The effects of upstream diversion and return flow on Teton River flow at St. Anthony are relatively small, especially during April, May and June.
- Although effects of these diversions and return can have large ecological effects in Teton Valley and in specific tributaries, the amount of "regulated" flow that reaches the Crosscut Canal outflow point is the primary factor determining when and how much Island Park storage water is diverted from the Henry's Fork and delivered through the Crosscut Canal. Thus, from the standpoint of managing Island Park Reservoir and the entire Henry's Fork watershed irrigation system, the "natural" flow I use here--observed Teton River flow minus the Crosscut Canal input--is most relevant.

If you are interested in learning more about water supply and use in the Teton River, as well as about ecological effects of water use and management in the upper Teton River watershed, see my Henry's Fork water budget, our report on hydrologic alteration, and the master's thesis of Kimberly Peterson, one of my former graduate students. Of course, a wealth of information on the Teton River is available from our good friends and colleagues at Friends of the Teton River.

# How do we predict streamflow?

## Statistical methods

I use a standard statistical technique known as linear regression, which considers a response variable, in this case streamflow, as a function of various predictor variables. The two most important features of regression modeling are selection of an optimal set of predictors, and verifying that the underlying mathematical assumptions of the final model are met. I use a modern model-selection approach based on information theory to select the optimal predictors. This approach maximizes the accuracy of the model in making future predictions, minimizes error in estimating model parameters, and minimizes bias associated with including too many predictors. Some like to say that this approach is the most "parsimonious." I also apply appropriate mathematical relationships among the variables to make sure that the proper probability distributions apply. This ensures that the predictions are unbiased and that our prediction uncertainties are honestly reported. For example, when we report that a given flow will occur with a given probability, that probability is accurate.

## What predictor variables are used?

The model-selection process indicated that for each of the predictive models we developed, the best predictors of April-June streamflow, given information available to us on March 1, are

- previous winter's baseflow and
- March 1 snow-water-equivalent (SWE) index.

I define winter baseflow as mean natural streamflow over the period November 1 through February 28. Specifically, if I am predicting streamflow for April 1 through June 30 of 2017, I consider the previous winter's baseflow as natural streamflow from November 1, 2016 through February 28, 2017. The SWE index values I use are the same ones I have been reporting all winter. See my latest snowpack blog for details. In particular, the upper Henry's Fork index is used as an input for prediction of natural streamflow at Henry's Lake, Henry's Lake-to-Island Park, and Henry's Fork at Ashton. The Fall River index is used to predict Fall River natural flow, and the Teton River index is used for the Teton River prediction. Well, almost. The Teton River is again an exception. The Grand Targhee site, while included in my daily SWE updates, was not used in this analysis because its data record goes back less than 10 years.

## How many years of data are used in the analysis?

Statistical precision is maximized by using the largest possible number of data points. For the three locations in the upper Henry's Fork watershed, data sufficient for back-calculation of natural flow, as well as SWE data at all four relevant snow-survey sites, go back to water year 1972. Thus, the upper Henry's Fork models use water years 1972-2016, a solid data set of 45 years. SWE data at the Fall River and Teton River sites is available over a shorter period of record; models for those subwatersheds use water years 1981-2016, still a good data set of 36 years.

## How precise are the models?

One measure of model precision is the fraction of sum-of-squares explained by the predictors in the model. This is known as R^{2}, which ranges from 0 for a model with no precision at all (you would do no better at predicting the response from the model than from simply drawing a random value from a hat containing all of the streamflows observed in previous water years) to 100% for a model that perfectly predicts the response every time. In natural systems, R^{2} values typically range between 40% and 80%, with values at the lower end of this range more typical of biological systems and values at the higher end more typical of physical systems. An R^{2} value of 70%, for example, indicates that 70% of the squared deviations in the response variable relative to its mean is explained by the predictive model. You can think of this as 70% of the variability explained by the predictive model. The other 30% remains unexplained by the predictors; this is the component we refer to as "random variation." Even given our knowledge of the predictors, the observed value can still deviate from the prediction due to other variables not included in the model, but this deviation is limited to only 30% of the total variation in the data (only 30% of the variation gets drawn from the hat).

In addition to calculating R^{2} for the whole model, we can calculate R^{2} for individual predictor variables, thereby learning what fraction of the variability in the response is explained by each predictor. The table below shows R^{2} values for each predictor, for the model as a whole, and for the random component. Notice that R^{2} is highest in the two subwatersheds with the highest groundwater influence--Henry's Lake to Island Park (includes Big Springs) and the Henry's Fork above Ashton (includes Big Springs, Buffalo River and Warm River). In addition, baseflow explains a larger fraction of variability in these two subwatersheds than in the others. This shows that groundwater-dominated systems are more predictable than snowmelt-dominated systems. Groundwater inputs are much more stable from year to year, depending on accumulated aquifer recharge over previous years, decades, and centuries. Snowmelt-dominated systems depend to a much larger degree on how much snow falls in that particular year. However, the actual streamflow response to a given snowpack in these systems is more highly influenced by variables such as spring-time temperature, how fast the snow melts, and rain during the spring. All of these variables influence streamflow, but we don't know anything about these variables at the time we make the prediction. Thus, we have to live with lower predictability in the snowmelt-dominated systems than in the groundwater-dominated systems.

# How do I interpret the table?

## Predictor variables

The first two columns of the output table shown at the top of the blog give the values of the two predictor variables as a percent of the period-of-record average. Remember that the periods of record are 1972-2016 for the Henry's Fork and 1981-2016 for Fall River and Teton River. Also, these are reported as means, so they are a little lower than the percentages of 1981-2010 medians NRCS and I use in the daily SWE reporting. Notice that the baseflow inputs are very low for the mainstem Henry's Fork because of the effect of a four-year drought on the deep Yellowstone Plateau aquifers that supply the majority of water between Henry's Lake and Ashton. Baseflow values in the other subwatersheds are average to above average in response to the record-high precipitation we received last October and to rain-on-snow events in mid-February. That precipitation quickly made its way into the runoff-dominated streams, where as we need to wait another 6-18 months to realize that precipitation in the groundwater streams.

## Predicted flow

The third and fourth columns of numbers give the model-predicted natural streamflow, expressed as a mean in cubic feet per second (cfs) over the April 1-June 30 time period. Of course, the actual streamflow will not be uniformly distributed over that time period; it will be lower early in the spring, highest during the peak of snowmelt, and lower again in June. So, for example, we expect an average of 117 cfs inflow to Henry's Lake, but streamflow may be as high as 200 or even 300 cfs during the peak of snowmelt. I have also expressed the predicted flow as a percent of the period-of-record mean, for ease in intepretation. Notice that above-average SWE will translate into above-average water supply in the runoff-dominated streams but not in the mainstem Henry's Fork, which is dominated by groundwater. Expected April-June water supply in these subwatersheds is only around 90% of average because of well-below average baseflows inherited from the preceeding four drought years as well as the larger fraction of the response predicted by baseflows versus SWE.

## Exceedance probabilities

Columns five and six give the predicted natural streamflow that will be exceeded with 90% probability. For example, there is a 90% chance that inflow to Henry's Lake will be at least 83 cfs, given the information we have on March 1 and all of the unexplained random variables that could affect actual streamflow. Again, these are expressed both as mean flow in cfs and as a percent of average. The predicted value on the Teton River is so high that we are 90% certain that flow there will be well above average. On the other hand, the 90% exceedance flow on the Henry's Fork at Ashton is only around 70% of average; that is, there is still a 10% chance that mainstem Henry's Fork water supply will be lower than 70% of average.

## What happened last year?

The good news in all five subwatersheds is that the 90% exceedance flow is well above last year's values. This is shown in the last two columns of the table. Clearly, runoff last spring was dismal in the upper Henry's Fork and Fall River subwatersheds, albeit somewhat better in the Teton River. These predictions show that with 90% certainty, 2017 will be better than 2016 throughout the entire watershed.

# What's next?

As I have been saying in my snowpack updates all winter, amount of water in the snowpack is only part of the story. If that snow melts early over a short period of time, natural streamflow will still be very low in the mid- to late-summer, even with well-above average SWE on the ground right now. Early runoff and another long, hot summer could result in streamflow conditions similar to last year's by July or August, which were characterized by very low flows in Fall River and lower Henry's Fork and very high irrigation delivery from Island Park Reservoir.

Over the next few weeks, I will be developing predictions of timing of snowmelt and streamflow to give us some idea of how long into the summer streamflows will be supported by melt of this year's above-average snowpack. Shortly after April 1, I will update predictions of streamflow amount and timing and then use these to simulate some possible scenarios for regulated flows in the mainstem Henry's Fork and Fall River.

I know that some of you are already planning your fishing trips to the Henry's Fork and surrounding rivers, but if you can hold off a few weeks, I will be able to provide a lot more certainty at that time in predictions of river conditions through July.