# Great way to visualize Great Lakes water budgets

Via Matthew Garcia, this infographic by Kaye LaFond of glerl.noaa.gov is pretty rad.

The bars on the left represent Precipitation onto the lake, Runoff into the lake, and Evaporation out of the lake, in thousands of cubic meters per second. To convert to cubic kilometers per year, multiply by 31.5. The bars on the right indicate flow between lakes.

We have a paper in review right now about how a change from seasonal to ephemeral snow in this area would greatly impact Lakes Michigan & Huron. Interesting to think about the runoff in this context, which would sort of change seasonality. Does the runoff from the relatively small watersheds of these lakes add up to a lot in comparison to the other fluxes in and out of the lakes?

The water balance for Michigan-Huron is that the mass balance of the lake from the left-hand side + that from the right-hand side must equal zero, or rearranging:

$P+R-E = Q_{out}-Q_{in}$

The values of those quantities are defined in the table below:

Quantity Value [ $\text{ km}^3/\text{year}$ ]
$P$ 97.7
$R$ 85.1
$E$ 59.9
$Q_{in}$ 69.3
$Q_{out}$ 170.1

So the left-hand side of the equation gives $97.7+85.1-59.9 = 122.9 \text{ km}^3/\text{year}$. And the right-hand side of the equation gives $170.1-69.3 = 100.8 \text{ km}^3/\text{year}$. Note that the two do not match, which is noted explicitly in the infographic:

You may find that the numbers listed here do not always balance … which speaks to the uncertainty of some of these values… However, the values here are the best available, and generally give a good representation of the relative contribution of each of the water budget components.

The imbalance is relatively large, however. The fluxes out of the lake total 230 km3/year, and the error is about 22 km 3/year, a difference of nearly 10 %. Props to the authors for drawing attention to the uncertainty. Assuming that the flow between lakes is relatively well known, then the value of $P+E-R$ of 122.9 km 3/year is only known to ~18 %. This is arguably problematic in trying to detect how changes such as those I mentioned above about earlier snowmelt will impact lake levels. We still have a lot to learn about the water cycle! Our ability to characterize large-scale hydrology is still not where it needs to be.

However, as stated in the quote, this mass balance is of great value in thinking about changes in the snowmelt runoff entering the lake during the winter. It helps to show that the runoff coming into the lakes is a huge component of the annual budget, forming a total of ~1/3 of the total inflow to Michigan-Huron. So a dramatic change in the timing of the inflow could have huge impacts on overall lake levels. Seasonality would also have to be considered.