Okay, I'll bite. Maybe not exactly answering the question you ask, but possibly in a sort of roundabout way. First, a few basic statistics to help frame the answer. Inflow to Lake Powell (or before it existed, flow past Lees Ferry) going back in time goes like this. These are 20-year averages, all in maf:
1920-40: 14.9 maf
1940-60: 13.3
1960-80: 10.8
1980-00: 12.5
2000-20: 8.6
So the trend is generally down over the past century. Well understood, not news. And as noted previously, the 30-year average 1991-2020 is 9.55 maf.
Now in a perfect world of math, where the inflow equals the outflow, you would not expect the lake level to change. And yet that math somehow fails. Let's start with this:
1991-2020
Avg Annual Inflow = 9.55 maf
Avg. Annual Outflow = 9.16 maf
So based on that you might expect, assuming there's no other straws in the drink, for the lake to actually rise during that period. But of course it didn't. In 1991, the lake ranged from 3625-3639. And in 2020, the lake ranged from 3582-3610. That is to say, in spite of a net surplus of inflow vs. outflow during that period, the lake lost 30-40 feet.
Let that sink in for a second. Net inflow surplus. Lake level declines.
What accounts for that is a combination of evaporation, seepage, and some limited Lake Powell surface water use. Not sure what those numbers are exactly, but they are clearly enough to say that unless inflow substantially outstrips outflow in a given period, you're going to see the lake slowly decline.
Now going back to the original dataset I started with, let's look at three periods, just to provide context, and maybe a a closer view of what's going on...
1964-80
Avg Inflow - 11.1 maf
Avg Outflow - 8.9 maf
This was the period when the lake was filling. A net annual surplus of 2.2 maf was just enough to fill the lake in 17 years. So that suggests that much less than that net surplus would not result in much or any rise in the long term. Which brings us to...
1980-2000
Avg Inflow - 12.5 maf
Avg Outflow - 11.6 maf
In this period, the lake started full and ended full--essentially balanced. Average inflow was high, and of course outflow also had to be high in order to make sure the lake didn't spill over. But in the context of Trix's question, this 0.9 maf average annual surplus seems to be the sweet spot of sustainability, where you end up with the same lake level as where you start. Now let's look at the opposite scenario...
2000-2020
Avg Inflow - 8.65 maf
Avg Outflow - 8.72 maf
On the face of it, this suggests the lake level should be in balance, since input = output. But it's obviously not. In 2000, the lake was basically full. But in 2020, it hovered around 3600, a loss of 100 feet. So when input = output, you actually have a net loss. And if you divide 100 feet by 20 years, it comes to about 5 feet per year.
So back to Trix's question, this all suggests that since we need a 0.9 maf surplus to keep the lake from falling, given that outflow is set this year at 7.48 maf, we would need to see an inflow of 7.48 + 0.9 = 8.4 maf...
So there's your answer. This year, we need to see about 8.4 maf inflow to keep the lake from falling... And in years when releases are set at 8.23 maf, we would need 9.13 maf inflow just to stay even... which is more than the average annual average from 2000-20 (8.65 maf). And that is the problem.
For context, here was the inflow of the past 12 years:
2010 - 8.8 maf
2011 - 16.3
2012 - 6.1
2013 - 5.3
2014 - 9.3
2015 - 9.4
2016 - 9.9
2017 - 11.4
2018 - 5.4
2019 - 11.8
2020 - 6.5
2021 - 4.0
I'll let real modelers like drewsxmi take it from here, and really explain the underlying factors in more detail, but that's the layman's version of what we're facing...
Okay, I took a page from drewsxmi and decided to plot the data in order to create a formula that estimates how to correlate net volume change in a given water year with changes to the lake level. If I haven't lost you so far, read on. Geeks only.
The approach was simple enough. I compared the inflow to outflow in a given water year (Oct 1 - Sept 30) all the way back to 1964 and took the difference. As noted in my previous post, some huge inflow years such as 1983 were also huge outflow years, so the net increase wasn't that big in such years. Here were the top five and bottom five net inflow years during life of the lake:
Top Five
1979 +6.34 maf
1997 +5.77 maf
1973 +5.53 maf
1993 +5.09 maf
1983 +3.80 maf
Bottom Five
2021 -4.19 maf
2002 -4.17 maf
2018 -3.60 maf
2012 -3.36 maf
2013 -2.97 maf
So what you know from this is that even in a wildly good year, don't expect a net volume increase of more than about 5 maf. And a really bad year might be a 3-4 maf decrease.
That's the x axis.
The y axis is straightforward. It's the net change in the lake surface level when you compare Oct 1 to a year later. And here are the top and bottom five lake level changes when Oct 1 is the start and finish line:
Top Five
1973 +42.61 feet
1993 +39.50 feet
1965 +38.50 feet
1979 +37.96 feet
1995 +32.60 feet
Bottom Five
2021 -50.54 feet
2002 -38.18 feet
2018 -36.26 feet
2004 -32.92 feet
2012 -31.40 maf
Again, from this you can see the historic range of increases and decreases. Last year was by far the worst. And in the very best years, you might see something approaching 40 feet of net gain. But hard to see the trends from those charts, so I plotted everything back to 1964 on a chart, and here it is:
Each blue dot represents one year. The dotted line was generated by Excel to calculate the "best fit", or what we might expect in general. You'll see the data points on the outlying ends of the line tend to be the worst fit--where you get a higher variation in rise or lake fall from what you'd expect from the net volume change. Perhaps this has something to do with other factors such as soil moisture, which during extended droughts tends to decrease quite a bt and suppress lake rise, or exacerbate decreases, such as last year.
In any case, the data makes for a pretty clear trendline. One clear conclusion is that on average, if inflow = outflow, the lake drops by about 5.7 feet. The corollary to that is this: in order to keep the lake at the current level (or higher), the net inflow has to exceed 0.71 maf.
The equation is this:
y = 8.1x - 5.7
where
y = annual lake level change (feet)
x = annual lake volume change (maf)
[Oct 1 to Sept 30]
So what does this mean for this year?
Well, let's start with this: the lake level on Oct 1, 2021 was 3545.
We also know that BOR plans to release 7.48 maf in WY2022.
Here's the likely range of possible outcomes:
If WY 2022 inflow = 4.0 maf, net inflow = -3.48 maf.
Oct 1, 2022 water level = 3511
If WY 2022 inflow = 5.0 maf, net inflow = -2.48 maf.
Oct 1, 2022 water level = 3519
If WY 2022 inflow = 6.0 maf, net inflow = -1.48 maf.
Oct 1, 2022 water level = 3527
If WY 2022 inflow = 7.0 maf, net inflow = -0.48 maf.
Oct 1, 2022 water level = 3535
If WY 2022 inflow = 8.0 maf, net inflow = +0.52 maf.
Oct 1, 2022 water level = 3543
If WY 2022 inflow = 9.0 maf, net inflow = +1.52 maf.
Oct 1, 2022 water level = 3551
If WY 2022 inflow = 10.0 maf, net inflow = +2.52 maf.
Oct 1, 2022 water level = 3559
You get the idea from there...it's basically add 8 feet to the lake for every net increase of 1 maf, then subtract 5.7 feet...
Now given that total inflow since October 1, 2021 has only been 1.7 maf, we have a lot of ground to make up this spring and summer...
So there you have it... let's hope for more snow... but even if we have something huge happen from here on out, we're unlikely to exceed 3550 on October 1...more likely in the 3525-40 range...
www.usbr.gov
i think i'll have to make an alphabetical checklist or something so i don't miss something.
