# Coefficient file formatΒΆ

The coefficients used in the model can be found in pyamps/coefficients/SW_OPER_MIO_SHA_2E_00000000T000000_99999999T999999_0101.txt.

Below is a description of the coefficient file. This information is not needed to use pyAMPS, but it can be useful if you want to do something more advanced and write new/modify the code.

The coefficient file is a .txt file with fixed width columns. It can be read with the Python pandas library by the following code:

```
>>> coeff_fn = 'SW_OPER_MIO_SHA_2E_00000000T000000_99999999T999999_0101.txt'
>>> names = ([x for x in open(coeff_fn).readlines() if x.startswith('#')][-1][1:]).strip().split(' ')
>>> coeffs = pd.read_table(coeff_fn, skipinitialspace = True, comment = '#', sep = ' ', names = names, index_col = [0, 1])
```

The first two columns contain the spherical harmonic wave numbers n and m. The other 76 columns are named

`tor_c_<param>`

`tor_s_<param>`

`pol_c_<param>`

`pol_s_<param>`

where `<param>`

refers to the 19 external parameters: `const`

, `sinca`

, `epsilon_cosca`

, `epsilon_sinca`

, `epsilon_cosca`

, `tilt`

, `tilt_sinca`

, `tilt_cosca`

, `tilt_epsilon`

, `tilt_epsilon_sinca`

, `tilt_epsilon_cosca`

, `tau`

, `tau_sinca`

, `tau_cosca`

, `tilt_tau`

, `tilt_tau_sinca`

, `tilt_tau_cosca`

, or `f107`

.

Here, `const`

refers to a constant term. `sinca`

and `cosca`

are *sin(IMF clock angle)* and *cos(IMF clock angle)*, respectively. `epsilon`

is the Newell coupling function divided by 1000 with inputs in nT and km/s. `tau`

is the Newell coupling function with *sin* replaced by *cos*. `f107`

is the F10.7 index in standard units (sfu). `tilt`

is the dipole tilt angle in degrees. Underscores in this list refer to multiplication, e.g.: `tilt_tau`

is the dipole tilt angle multiplied by tau.

The prefix of the column names (apart from `n`

and `m`

) denote the term in a real expansion of the poloidal and toroidal parts of the ionospheric magnetic field as described in Laundal et al. (2016). `tor`

and `pol`

refer to toroidal and poloidal, respectively. `_c`

and `_s`

refer to the *cos* and *sin* terms, respectively.

To get the spherical harmonic coefficients for a given set of external parameters, the coefficients should be multiplied by the corresponding external parameter (1 in the case of `const`

), and summed so that four columns remain, one for each `tor_c`

, `tor_s`

, `pol_c`

, and `pol_s`

.

There are several missing entries: The *(n, 0)* terms for the `_s`

coefficients are undefined, since *sin(m*x) = 0* for all *x* if *m = 0*. In addition, the toroidal expansion have more terms (higher spatial resolution) than the poloidal expansion, so that `pol_c_<param>`

and `pol_s_<param>`

are missing/undefined for *n > 45*.