Extract daily data from sub-daily tidal data

[galengorski]

This was converted from a discussion into an issue, I have copy and pasted the replies below:

Based on 2/15/22 meeting (notes here) trying to extract data from sub-daily tidal data so that it is usable on the daily time step seems like a more tractable approach.

One suggestion for capturing a sub-daily temporal signal in daily water level data from @aappling-usgs:

• split the hourly water level data into 24 different "daily" datasets, so we would have water level at 1:00am, 2:00am etc at a daily time step. This seems like it might be worth a shot for modeling, but it will be less interpretable from an "analysis of the drivers" point of view
• @ted80810 is looking into some daily summary statistics of tidal fluctuations that we might be able to use

Originally posted by @galengorski in #50 (comment)

[galengorski]

From Salme:

I really want to caution against using any sort of daily mean of tidal data. The major tidal frequencies are at 12, 12.42 hourly frequencies, and that signal will be aliased into other frequencies.

Taking a look at the NOAA tides and currents station at Lewes, DE: https://tidesandcurrents.noaa.gov/harcon.html?unit=0&timezone=0&id=8557380&name=Lewes&state=DE

The higher the amplitude, the more important the constituent is in representing the total tidal signal. Let's take the first 6 tidal constituents and their frequencies:

M2 - 12.42 hours
S2 - 12 hours
N2 - 12.62 hours
K1 - 23.93 hours
M4 - 6.21, a harmonic of M2, generated from nonlinearities when tide approaches shallow water (ie continental shelf)
O1 - 25.81 hours
M6 - 4.14 hours, a second harmonic of M2, generated from nonlinearities when tide approaches shallow water (ie continental shelf), and interacts with itself

This is why we use hourly signals in tidal time series analysis - we can identify these harmonic frequencies, and a lot of them hover around the 12 hour or 1 day frequency. I can answer more questions on this at today's (2/17) meeting.

[galengorski]

From Galen:

Based on discussion from our meeting on 2/22, it seems like we might be able to pull out some daily statistics from the water level data based on the differences between the predicted and observed water level. For example in the plot below is water level data for Lewes, the blue line shows predicted water level while the green line shows observed. From 1/14-1/18 the observed water level is above the predicted likely due to an offshore storm event. This results in a net influx of water into the estuary. While the period from 1/18-1/20 observed < predicted indicating a net outflow from the estuary. @salme146 please correct me if I am misrepresenting the interpretations. A couple of ideas for daily statistics to pull out of this record:

• sum(obs - predicted) water level indicative of flow into our out of the estuary
• daily max water level - daily min water level: highs would indicate spring tides associated with the break up of salt front dynamics while lows would indicate neap tides associated with more stable behavior

@ted80810 I know you are working on developing some daily summaries of tidal data, maybe this could be a place to start?

[galengorski]

I did a quick analysis to see what it would look like to extract some of these daily metrics on a chunk of tidal data. Here is the hourly data, I put gray dotted lines to show day markers:

Here is the same period with the daily metric overlaid:

One thing to think about is that the min-max is so much larger than the fluctuations in the tidal data because it is summed over the entire day. This might be something to think about changing, I'm not sure