*Here you can find a set of models describing the atmospheric refraction and dispersion.*

**Contents:**
- atmosphericModel.py           : Python model that can be used to calculate the atmospheric refraction and dispersion
- refractionModel.py            : Python script that compares the output of the different rerfraction models. 
                                  Can be used as an example on how to use atmosphericModel.py
- 1976USSA.txt                  : Table with temperature, pressure, density and more as a function of altitude.
                                  Values derived from the 1976 U.S. Standard Atmosphere.
- manual.pdf                    : Manual for using atmosphericModel.py
- atmospheric refraction example: jupyter notebook example
- [Tech note]...models.pdf      : Tech note describing the models.



**On the dispersion model:**

Dispersion model from Ciddor, 1996, calculates the index of refraction of air using the following parameters:
- Temperature
- Pressure
- Relative humidity
- CO2 density




**On the atmospheric refraction / atmospheric dispersion models:**

Available models:
- Full integration using the refractive integral (requires detailed information about the atmosphere, e.g. 1976USSA.txt)
- Plane-parallel atmosphere refraction model
- Cassini's homogeneous atmosphere refraction model
- Oriani's theorem ( Atan(z) + Btan^3(z) )
- Oriani's theorem expanded ( Atan(z) + Btan^3(z) + Ctan^5(z)  )
- Error function refraction model




Input parameters for the spherical atmosphere models (all but the first):
- Temperature               [K]
- Pressure                  [Pa]
- Relative humidity
- CO2 density               [ppm]
- Latitude                  [deg]
- Height above sea level    [m]
- Wavelength(s)             [um]
- Zenith angle              [deg]


**Analytical error propagation**

Full analytical error propagation is available for the Ciddor dispersion model (Observatory.dn_tph( ) ), for the Cassini refraction model (refraction.cassiniError( ) ) and for the Cassini dispersion model (dispersion.cassiniError( ) ).
The results agree well with a Monte Carlo simulation, suggesting that if additional errors have not been considered, they are of neglible importance.

Uncertainties that are considered:

Ciddor dispersion model:

| Param. | Description | Unit |
| ------ | ------ | ------ |
| dl | Wavelength | um |
| dT | Temperature | K |
| dP | Pressure | Pa |
| dRH | Relative Humidity |  |
| dCO2 | CO2 density | ppm |
 

Cassini refraction model:

| Param. | Description | Unit |
| ------ | ------ | ------ |
| dn | Refractive index |  |
| dz | Zenith angle | deg |

Cassini dispersion model:


| Param. | Description | Unit |
| ------ | ------ | ------ |
| dl1, dl2 | Wavelength(s) | um |
| dT | Temperature | K |
| dP | Pressure | Pa |
| dRH | Relative Humidity |  |
| dCO2 | CO2 density | ppm |
| dz | Zenith angle | deg |