I have CTD measurements at two stations (12 and 5 m depth) 700 meters apart from each other. I am wondering what is the best approach to estimate the cross-shore baroclinic pressure gradient using the density profiles. Some questions I've been struggling with are:
[1] How do I compensate the barotropic term since I do not have water elevation information?
[2] Should I correct for the bottom gradients? If so, how do I go about it?
[3] Is it valid to average the density values over depth before proceeding with the calculation?
Please refer to the attachment to see a sketch of the problem.
Any help in this matter is greatly appreciated.
It might help if you gave complete citations, because then someone could know what you've tried. Further to that, what is it that makes you say you've not had success? You may have more luck when you seek advice from a broader range of RG members than those who are familiar with two particular barely-cited papers, and when you explain what you have tried and why you judge the results unacceptable.
@Dan E Kelley, thanks for the tips. I've edited my answer and I hope it is more clear now. I would appreciate hearing your thoughts on this. =)
I'm still not clear on what you are trying to calculate, and why. For example, I don't see how the bottom gradient relates to this. Are you trying to calculate a force in an equation of motion?
I would not advise averaging density over depth.
Are the two profiles measured within a short time interval? If so, then the pressure offset in the CTD will be the same for each, and your data are (pressure, salinity, and temperature). From these you can calculate density. At that stage you can compute whatever you want to compute, given a formula. Bear in mind that two horizontally-separated points is the bare minimum for a lateral gradient.
I have just submitted a manuscript using a method to calculated geostrophic flow over a sloping bottom. If you are interested, please give me a private message.
In the meanwhile, the simplest method is Helland-Hansen's (1934). See Bingham and Hughes (2012, JGR 117 C1) for a review of this and other methods.
See Marchuk et al. (1973, Geophys. Astrophys. Fluid Dyn. pp.89-99) and Sheng and Thompson (1996, JGR, pp.25,647-25,659) for dynamically consistent methods of geostrophic calculation on a sloping bottom. But, these methods are complicated and not very easy to adopt. Alternatively, look at Bingham and Hughes (2012, JGR) for a survey of simpler methods.
Dear Saulo,
This can be done by the Steric Height Method, See my Pubs in RG
A note on the geostrophic velocity field referenced to a point. - for an explanation, and
A Discussion of the Northern Adriatic circulation aa computed from the ELNA data set. = for more explanation and results.
You don't have enough data with only two stations, but you can get a rough estimate by referencing to the deepest point, which should be ~1m from the bottom at the deep station. You should calculate the density using the in-situ CTD values of T & S, i.e. not the densities of the CTD instrument if it uses a standard ocean values.The method will give you both the baroclinic and barotrophic pressure gradients - and the transport through the section and a vertical profile of the parabathic mean velocity. This will only give the alongshore vector of the velocity. If you want offshore velocities, you will need to add stations along the coast. If more questions - contact me by email or on RG (but I might miss it here). GOOD LUCK
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