# Introduction

The MATLAB functions in the biogeochem-phi repository evaluate the different equations presented by Humphreys et al. (2018).

# Installation

Add all MATLAB functions from the biogeochem-phi repository to your MATLAB path.

## Dependencies

To work correctly, the biogeochem-phi functions also require that you download the MATLAB functions from oceancarb-constants, and add them to your MATLAB path.

# Functions

## bgc_isocap

Evaluates the isocapnic quotient (Q) following Eq. (8) of Humphreys et al. (2018); its approximation, following their Eq. (6); and the "released CO2:precipitated carbonate ratio" for calcification, of Frankignoulle et al. (1994).

### Usage

`[Q, Qx, Psi] = bgc_isocap(pco2, dic, temp, sal);`

### Inputs

 Variable Description Unit Type `pco2` Partial pressure of CO2 in seawater μatm double `dic` Dissolved inorganic carbon μmol/kg-sw double `temp` Seawater temperature °C double `sal` Practical salinity - double

### Outputs

 Variable Description Unit Type `Q` Isocap slope, i.e. ∂TA/∂DIC at constant seawater pCO2 - double `Qx` Approximation to the isocap slope - double `Psi` Special case of Φ for calcification (i.e. Ψ of Frankignoulle et al., 1994) - double

## bgc_phi

Calculates Φ, the amount of CO2 that must be released from or added to seawater after a change in TA and/or DIC in order to return back to the original seawater pCO2, following Eq. (10) of Humphreys et al. (2018).

### Usage

`Phi = bgc_phi(Q,Aq_Cq);`

### Inputs

 Variable Description Unit Type `Q` Isocap slope, i.e. ∂TA/∂DIC at constant seawater pCO2 - double `Aq_Cq` 1×2 vector of [ΔTA, ΔDIC] μmol/kg-sw double

### Output

 Variable Description Unit Type `Phi` Φ, of Humphreys et al. (2018) Eq. (10) μmol/kg-sw double

## bgc_normalise

Normalises an input vector to a magnitude of unity.

### Usage

`nCq_nAq = bgc_normalise(Aq_Cq);`

### Input

 Variable Description Unit Type `Aq_Cq` 1×2 vector of [ΔTA, ΔDIC] μmol/kg-sw double

### Output

 Variable Description Unit Type `nAq_nCq` Input vector normalised with a magnitude of unity μmol/kg-sw double