pagos 0.3.0

Python Analysis of Groundwater and Ocean Samples

PAGOS

Python Analysis of Groundwater and Ocean Samples (PAGOS) is a Python toolkit for creating and testing hydrological gas exchange models. Datasets from field campaigns containing data for a number of gas tracers can be used to optimise the parameters of gas exchange models, expressed as Python functions. These can be PAGOS' built-in models or user-defined.

Installation

Use the package manager pip to install PAGOS. PyPi link here.

pip install pagos

Usage

This is a relatively abridged version of the information you can find in example scripts.

How quantities are defined in PAGOS

This package is designed with a number of "numerical safeguards". Datapoints used in PAGOS may contain units, and a future implementation of PAGOS should also include uncertainties. Although many of the functions in PAGOS will work with other types, they are designed for use with Quantity objects from Pint. The following code produces such a quantity representing the speed 11.2 m/s.

from pagos import Q
mySpeed = Q(11.2, 'm/s')
print(mySpeed)
# -> 11.2000 meter / second

Those familiar with Pint will recognise Q() as a shortcut for pint.UnitRegistry.Quantity().

Water property calculations

The properties of seawater and various gases can be calculated with the water and gas modules. For example, calculating the density of, kinematic viscosity of and vapour pressure over water at a given temperature and salinity:

from pagos import water as pwater
from pagos import Q

myTemp1 = Q(10, 'degC')
mySal1 = Q(30, 'permille')

myDensity1 = pwater.calc_dens(myTemp1, mySal1)
myDensity2 = pwater.calc_dens(10, 30) # <- default units of degC and permille assumed

print(myDensity1)
print(myDensity2)
# -> 1023.0511189339445 kilogram / meter ** 3
# -> 1023.0511189339445 kilogram / meter ** 3

We can see that the water property function have default, assumed units for any given float arguments. PAGOS will also automatically convert units of a different kind:

myTemp2 = Q(283.15, 'K')
mySal2 = Q(3, 'percent')

myDensity3 = pwater.calc_dens(myTemp2, mySal2)

print(myDensity3)
# -> 1023.0511189339445 kilogram / meter ** 3

Other properties available to be calculated for water are vapour pressure over the water and kinematic viscosity of the water, given temperature and salinity:

myVapourPres = pwater.calc_vappres(myTemp1)
myKinVisc = pwater.calc_kinvisc(myTemp1, mySal1)
print(myVapourPres)
print(myKinVisc)
# -> 12.272370555643239 millibar
# -> 1.3516218130144556e-06 meter ** 2 / second

Gas property calculations

Much like the bulk water properties, properties of gases dissolved in water can also be calculated, namely the equilibrium concentration and the Schmidt number at given temperature, salinity and overlying pressure. Also like the functions in the water module, the gas module functions have default assumed units which may be overriden by the user. See how all of the following calculations return the same result:

from pagos import gas as pgas
myTemp, myTempC, myTempK = 20, Q(20, 'degC'), Q(293.15, 'K')
mySal, mySalpm, mySalpc = 32, Q(32, 'permille'), Q(3.2, 'percent')
myPres, myPresatm, myPreshPa = 1, Q(1, 'atm'), Q(1013.25, 'hPa')

Ceq1 = pgas.calc_Ceq('Ne', myTemp, mySal, myPres)
Ceq2 = pgas.calc_Ceq('Ne', myTempC, mySalpm, myPresatm)
Ceq3 = pgas.calc_Ceq('Ne', myTempK, mySalpc, myPreshPa)
Sc = pgas.calc_Sc('Ne', myTemp, mySal)

print('Ceq1(Ne):', Ceq1)
print('Ceq2(Ne):', Ceq2)
print('Ceq3(Ne):', Ceq3)
print('Sc(Ne):', Sc)
# -> Ceq1(Ne): 1.5676847690725347e-07
# -> Ceq2(Ne): 1.5676847690725347e-07
# -> Ceq3(Ne): 1.567684769072535e-07
# -> Sc(Ne): 300.07687253959057 dimensionless

Multiple gas properties may be calculated all at once:

Ceqs = pgas.calc_Ceq(['Ne', 'Ar', 'N2', 'CFC12'], 20, 32, myPreshPa)
print('Ceq(Ne, Ar, N2, CFC12) =', Ceqs, 'ccSTP/g')

Note how calc_Ceq returns only a float by default, not a unit-bound Quantity. This is in contrast to most other functions in PAGOS, including calc_Sc, and is set up this way to increase speed when performing inverse modelling. The float returned is the value of the equilibrium concentration in units of cc/g, but without the units explicitly returned with it. The unit can be changed, and optionally returned, using the unit and ret_quant arguments:

Ceqsmolkg = pgas.calc_Ceq('Ne', 20, 32, myPreshPa, 'mol/kg')
Ceqsmolcc = pgas.calc_Ceq('Ne', 20, 32, myPreshPa, 'mol/cc', ret_quant=True)
print('Ceq(Ne) =', Ceqsmolkg)
print('Ceq(Ne) =', Ceqsmolcc)
# -> Ceq(Ne) = 6.9908309248701225e-09
# -> Ceq(Ne) = 7.147959263640384e-12 mole / cubic_centimeter

Creating and fitting models

The real power of PAGOS is in its gas exchange modelling capabilities. PAGOS allows for simple user-definition of gas exchange models. Say we wanted to implement a simple unfractionated excess air model (that is, equilibrium concentration "topped up" with an excess air component):

C_\mathrm{gas}^\mathrm{eq}(T, S, p, A) = C_\mathrm{gas}^\mathrm{eq}(T, S, p) + A*z,

where $A$ is in the units of $C^\mathrm{eq}_\mathrm{gas}$ and $z$ is the atmospheric abundance of the gas. We can implement it very simply like this:

from pagos import gas as pgas
from pagos.modelling import GasExchangeModel, gas_exchange_model
def ua_model(gas, T, S, p, A):
    Ceq = pgas.calc_Ceq(gas, T, S, p)
    z = pgas.abn(gas)   # <- pagos.gas.abn(G) returns the dimensionless atmospheric abundance of G
    return Ceq + A * z
UAModel = GasExchangeModel(ua_model, ('degC', 'permille', 'atm', 'cc/g'), 'cc/g')

The arguments to GasExchangeModel() are the user-defined function describing the model (ua_model above), a tuple of default input units (('degC', 'permille', 'atm', 'cc/g') above) and one default output unit ('cc/g' above). The default input units correspond to the assumed units of the arguments of the model function ((T, S, p, A) above). The output units are those in which the result of the model is expressed. To calculate the result of a model for a given gas, use the run() method of GasExchangeModel. Note that they are default units, but can be overridden:

myResult1 = UAModel.run('Ne', 10, 30, 1, 5e-4) # no given units, default units assumed
myResult2 = UAModel.run('Ne', Q(10, 'degC'), Q(30, 'permille'), Q(1, 'atm'), Q(5e-4, 'cc/g')) # units manually given but are the same as the defaults
myResult3 = UAModel.run('Ne', Q(283.15, 'K'), Q(3, 'percent'), 1, 5e-4) # non-default units included, default units of degC and permille overridden

print('Result with no given units:', myResult1)
print('Result with given units matching defaults:', myResult2)
print('Result with overridden units:', myResult3)
# -> Result with no given units: 1.7903293005762066e-07 cubic_centimeter / gram
# -> Result with given units matching defaults: 1.7903293005762066e-07 cubic_centimeter / gram
# -> Result with overridden units: 1.7903293005762066e-07 cubic_centimeter / gram

If messing around with the Q() constructor isn't to your liking, one can also override units with the units_in argument thus:

myResult4 = UAModel.run('Ne', 283.15, 3, 1, 5e-4, units_in=('K', 'percent', 'atm', 'cc/g'))
print('Result using units_in kwarg:', myResult4)
# -> Result using units_in kwarg: 1.7903293005762066e-07 cubic_centimeter / gram

The returned units may also be altered with the units_out keyword argument. Additionally, note in the example below that the 'percent' in units_in is overridden by the explicit Quantity object with its already given 'permille' unit. This is a nice safeguard, but also a good reason not to use the units_in argument along with Q()-based model arguments, as units_in will always be silently overridden.

myResult5 = UAModel.run('Ne', 10, Q(30, 'permille'), 1, 5e-4, units_in=('degC', 'percent', 'atm', 'cc/g'), units_out='m^3/kg')
print('Result in using units_out kwarg:', myResult5)
# -> Result in using units_out kwarg: 1.790329300576207e-10 meter ** 3 / kilogram

Inverse Modelling

Parameters of a GasExchangeModel's function can be fitted using data. A better walkthrough can be found in the example scripts folder, but here is a brief explanation. The GasExchangeModel.fit() method can be used to fit a number of parameters of a gas exchange model using a least-squares minimisation. Here is an example using the Belgium data (from Jung and Aeschbach 2018) taken from the example scripts/example data folder:

from pagos.modelling import fitmodel

# Data import
# These data are from Jung and Aeschbach 2018 (https://www.sciencedirect.com/science/article/pii/S1364815216307150)
gases_used = ['Ne', 'Ar', 'Kr', 'Xe']
pangadata = pd.read_csv('example scripts/Example Data/Complete_Input_Data_Samples_Belgium.CSV', sep=',')
print('Data from Jung and Aeschbach 2018:')
print(pangadata)

def ua_model(gas, T_recharge, S, p, A):
    Ceq = pgas.calc_Ceq(gas, T_recharge, S, p)
    z = pgas.abn(gas)
    return Ceq + A * z
UAModel = GasExchangeModel(ua_model, ('degC', 'permille', 'atm', 'cc/g'), None)

fit_UA = UAModel.fit(pangadata,                                             # the data as a Pandas DataFrame
                     to_fit=['T_recharge', 'A'],                            # the arguments of the model we would like to fit
                     init_guess=[Q(1, 'degC'), 1e-5],                       # the initial guesses for the parameters to be fit
                     tracers_used=gases_used,                               # the tracers used for the fitting procedure
                     constraints={'T_recharge':[-10, 50], 'A':[0, 1e-2]},   # any (optional) constraints we might want to place on our fitted parameters
                     tqdm_bar=True)                                         # whether to display a progress bar
print('Fit of UA model:')
print(fit_UA[['Sample', 'T_recharge', 'A']])

# -> Fit of UA model
#            Sample                   T_recharge                                           A
#    0     BE_TB532     7.1+/-0.9 degree_Celsius     0.0023+/-0.0006 cubic_centimeter / gram
#    1     BE_MW901     5.0+/-0.4 degree_Celsius   0.00348+/-0.00029 cubic_centimeter / gram
#    2     BE_VZELE     5.0+/-0.4 degree_Celsius   0.00098+/-0.00022 cubic_centimeter / gram
#                                               .
#                                               .
#                                               .

The arguments are explained in the method docstrings and on the right hand side above. Note here that the init_guess arguments do NOT have to be Quantity objects, although they can be for clarity/safety, if you want. When units are omitted, the default_units_in passed to the GasExchangeModel() constructor are used. So in this case, 1e-5 becomes 1e-5 cc/g.

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Feel free to contact the author Stanley Scott at [e-mail].

License

BSD-3-Clause, see LICENSE file.
PAGOS was developed for Python 3 by Stanley Scott and Chiara Hubner.