Identify appropriate endmember compositions for hydrograph separation

Students will examine the various choices for new and old water endmembers for hydrograph separations.
Students will qualitatively consider the uncertainty associated with each possible endmember choice.
Students will recognize that choice of endmember affects the results of the hydrograph separation.

Students will calculate a weighted average.

45 minutes

7 selected data sets downloaded from Hydroclient in a previous step
Graphs of stream discharge and isotopes and precipitation isotopes created in a previous step

Calculated new water and old water endmember compositions

Calculator or Excel, R, Matlab, or any spreadsheet or data analysis program of the student's choice.

Choose a team: oxygen or hydrogen

If we are interested in defining isotopic endmembers for hydrograph separation, the first step is to choose the isotope system you are working with. You have all the data you need for both hydrogen and oxygen isotopes of water. Pick one of these and stick with it, but don't forget to consider how the opposite choice may alter your results.

Choose a new water endmember

In this step, we are going to focus on the storm event that happened April 3-6, 2014. For reasons that should become apparent later on, this event is the most straightforward to separate from the new water endmember point of view. The new water endmember represents precipitation falling on the catchment during the event of interest.

There were three rain samples taken during this event. Each rain sample represents a different amount of precipitation, and you can see these values in the odm_kentstate-koh_rain_gage_in_kent__ohio-precipitation.csv file that you downloaded from Hydroclient in the first step. As you should have discovered in the previous step, the isotopic value of precipitation varied over the course of the storm. This is pretty common, and is something that hydrologists doing hydrograph separation have had to grapple with. There is spatial variation in precipitation isotopes too, but that's beyond the scope of the quantitative analysis that you are doing here.

Let's consider the various options you have for deciding on the new water endmember. You could take an arithmetic average of the three rain samples, like this:



, where x with the subscripted number is the isotopic value of each sample.
But that would treat all of the rain samples as having equal importance to the stream, which might not be true given the differences in precipitation amount associated with each sample.

You could take a weighted average of the three rain samples, like this:



, where x with the subscripted number is the isotopic value of each sample and d with the subscripted number is the rainfall depth corresponding to each sample.
A weighted average is a better representation of the precipitation isotopes reaching the stream than a straight arithmetic average, but it also has problems. The isotopic value of rain falling late in the storm doesn't have any effect on the isotope values in the stream earlier in the storm. For example, rain falling on Wednesday at 6:00 pm can't be influencing the isotopes in the stream at Wednesday at 2:00 pm.

You could simply adopt the value of the first rain sample as the new water endmember, because that was the first rain to fall on the catchment. But then you ignore the changes in rainfall isotopes that happen later in the storm.

You could adopt the value of the first sample from the beginning of the storm to when it was collected, then use the second sample from that point until it was collected, and use the third value from then until the end of the storm. That solves problems of chronology, but it doesn't solve everything. Rain that fell early in the storm could still be moving through the watershed and stream and reaching the sampling point later in the storm, so we may not want to discount its influence entirely.

The above discussion should give you a sense that it's not unambiguous how to choose a new water endmember for hydrograph separation. There are more thorough discussions of these issues in the journal articles suggested with this unit, and there are more complicated approaches to this problem. And, again, here we are ignoring spatial variation in precipitation isotopes entirely.

Now that you've given this issue some thought, decide what approach you are going to use to pick a new water endmember for your hydrograph separation.

Choose an old water endmember

Choosing an old water endmember has its own issues. Ideally, this endmember represents all of the water that was stored in the catchment before rainfall began that might be available to move into the stream during the storm.
One common choice for the old water endmember is to take a baseflow sample in the stream before the storm begins. This strategy is based on the assumption that the stream is integrating all of the water in the watershed. There have been some criticisms of this approach in the literature, because baseflow might not be accessing all of the stored water volumes that might reach a stream during higher flows. In our data-driven example, a baseflow sample was collected on March 21, 2014. However, we are interested in a storm that begins April 3rd, and another storm occurred in between. Does baseflow from March 21 really represent old water in the catchment on April 3rd?

If you think that baseflow from 2 weeks earlier is not a sure-win choice, what other options might you have?

You could choose the last sample taken during the storm on March 29-31. Then you are making the assumption that the stream was returning to baseflow-like conditions when that was sample was collected. You might want to look at the hydrograph for that time and see how good an assumption you think that is.

Another choice is the first sample is collected on April 3, assuming that since the sample was taken quite early in the storm that no new water was in the stream at that time. Again, before making the decision to use that sample as your old water endmember, you should consider the hydrograph.

A fourth option for an old water endmember is to sample riparian groundwater (preferably before the storm of interest). However, it might be difficult to know how representative samples from one or a few wells are of the overall isotopic composition of old water. In our case, no riparian groundwater samples were available, so this is not an option for you.

As with new water, there has been a healthy discussion in the scientific literature about how to choose an old water endmember, and you can dig into that literature if you would like. When you feel as informed as you can be, choose an old water endmember.

Document your decision-making process

Before moving on, you should consider writing down not only what you choose for endmembers, but why you chose them. Contemplate the tradeoffs in information, complexity, and uncertainty that your choices involved. As you move into calculating the hydrograph separation, in the next step, you may decide to revisit your choices and see how they affect your final answers.