dRHOds units used in the eos calculation

[andersy005]

From an offline email conversation with @islasimpson

Can someone advise me what the units are of dRHOds in the eos calculation. The code is setting it to kg/m^2/degC but I suspect this is incorrect as it seems like instead of degC it should be per some form of salinity unit. I assumed it would be in PSU's but I'm having to divide by 1000 to get it to make sense. It's also possible that it should be in degC and I don't really understand what I'm doing which is why I'm raising this in discussion rather than an issue.

pop-tools/pop_tools/eos.py

Lines 104 to 110 in f8dc20b

	if return_coefs:
	RHO, dRHOdS, dRHOdT = _compute_eos_coeffs(salt, temp, pressure)
	dRHOdS.name = 'dRHOdS'
	dRHOdS.attrs['units'] = 'kg/m^3/degC'
	dRHOdS.attrs['long_name'] = 'Haline contraction coefficient'

Ccing @matt-long,@mnlevy1981, @dcherian, @klindsay28, @ALDepp who know more about POP than I do :)

[matt-long]

@andersy005, you are correct. S is salinity, so degC is incorrect. Correct alternatives to consider:

• g/kg
• PSU

I think I would go with PSU.

[islasimpson]

Thanks. I realize now why I couldn't comment yesterday - I hadn't put a category. Anyway, makes sense it should be in some salinity units. Are you sure it's in PSU? When I calculate the anomalous density component associated with salinity using dRHOdS*SALT where SALT is in g/kg I had to divide it by 1000 for the salt and temperature components to add up to the total. Is it possible that the rate of change with salinity is in kg/m3/kg/kg instead of kg/m3/g/kg? Or maybe I've just done something weird...

[mnlevy1981]

@islasimpson There is a factor of 1000 in the computation of dRHOdS in _compute_eos_coeffs():

pop-tools/pop_tools/eos.py

Line 326 in f8dc20b

DRHODS = (WORK3 - WORK1 * DENOMK * WORK4) * DENOMK * 1000.0

I always bungle things when I try to write out salinity units, and the added complication of having the salinity in the denominator would only exacerbate the problem... but it makes sense to me that (WORK3 - WORK1 * DENOMK * WORK4) * DENOMK would be kg/m3/(g/kg) and then multiplying by 1000 g / kg converts it to (kg/m3)/(kg/kg)

[mnlevy1981]

I should add that I tried to figure out the units of DENOMK, but even after comparing the coefficients defined in

pop-tools/pop_tools/eos.py

Lines 242 to 255 in f8dc20b

	# *** these constants will be used to construct the denominator
	mwjfdp0s0t0 = 1.0
	mwjfdp0s0t1 = 7.28606739e-3
	mwjfdp0s0t2 = -4.60835542e-5
	mwjfdp0s0t3 = 3.68390573e-7
	mwjfdp0s0t4 = 1.80809186e-10
	mwjfdp0s1t0 = 2.14691708e-3
	mwjfdp0s1t1 = -9.27062484e-6
	mwjfdp0s1t3 = -1.78343643e-10
	mwjfdp0sqt0 = 4.76534122e-6
	mwjfdp0sqt2 = 1.63410736e-9
	mwjfdp1s0t0 = 5.30848875e-6
	mwjfdp2s0t3 = -3.03175128e-16
	mwjfdp3s0t1 = -1.27934137e-17

to what's in MJWR (2003) I couldn't figure it out. In section 2, the paper says

Note that while salinity is a dimensionless quantity, we use the common terminology of 35 psu (standing for practical salinity units) to describe a sa- linity of 0.035 because it tells the reader exactly how the salinity has been calculated

But that could mean that the units of S are in psu or that the units of S are in kg/kg but they write things like "Using a million random points drawn from the (S– T–p) cube (0 psu, 40 psu) x (-3 C, 40 C) x (0 db, 104 db)" to make it easier for the reader to understand the ranges

[islasimpson]

Thanks for looking into it. This is not something I know about at all I'm afraid. All I know is that I had to divide the SALT part by 1000 to get the SALT and TEMP anomalies to add up to the total, which suggests to me it's in kg/m3 per kg/kg. But since this is all new to me, it's possible I am doing something else wrong.