Update README.md

Addition of description of error propagation.

README.md

@@ -1,6 +1,6 @@
-Here you can find a set of models describing the atmospheric refraction and dispersion. 
+*Here you can find a set of models describing the atmospheric refraction and dispersion.*
 
-Contents:
+**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
@@ -12,7 +12,8 @@ Contents:
 
 
 
-On the dispersion model:
+**On the dispersion model:**
+
 Dispersion model from Ciddor, 1996, calculates the index of refraction of air using the following parameters:
 - Temperature
 - Pressure
@@ -22,13 +23,14 @@ Dispersion model from Ciddor, 1996, calculates the index of refraction of air us
 
 
 
-On the atmospheric refraction / atmospheric dispersion models:
+**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 ( A*tan(z) + B^*tanˆ^3(z) )
+- Oriani's theorem ( Atan(z) + Btan^3(z) )
-- Oriani's theorem expanded ( A*tan(z) + B*tanˆ^3(z) + C*tan^5(z)  )
+- Oriani's theorem expanded ( Atan(z) + Btan^3(z) + Ctan^5(z)  )
 - Error function refraction model
 
 
@@ -43,3 +45,42 @@ Input parameters for the spherical atmosphere models (all but the first):
 - 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 |
+