Hi my friend

Full modeling of the ionosphere is hard and complex. Perhaps this data to help you: height integrated Hall conductivity,height integrated Pedersen conductivity or current of ionosphere. you can obtain this data from Internet or calculate it.

In fact modeling the ionosphere is not as such easy. Simplest approach is try to understand MHD combines gas dynamic equations with the Maxwell equations and   treat plasma as single species and collision-less fluid. Then you need to solve density magnetic field , momentum, Total energy

Hi,

You could try the NeQuick2 model (good for modelling ground-to-satellite links), or for general TEC mapping try the International Reference Ionosphere (see links).  Note that these models (and also the IONEX files Andrew mentioned) don't have the fine resolution you need to model the very largest gradients in TEC, and the models may only be appropriate for 'average' conditions, not extreme events.

- Neil Rogers

http://www.igs.org/assets/pdf/Workshop%202014%20-%20PY08%20-%20Nava%20-%202270%20-%20The%20NeQuick%20model%20characteristics%20and%20uses.pdf

http://iri.gsfc.nasa.gov/

Dear  Andrew Mazzella,  Gebregiorgis Fikade, Mahlagha Bajelan and  Neil Christopher Rogers, thank you very much for the detail explanation and help given. Basically, as what you all mentioned above, obviously, I can take the data from IRI, IONEX, or even NeQuick. But my concern, as what we all aware of, its not easy and practical to model the ionosphere again. But as a preliminary study before I can model the ionosphere over the Malaysia region (future research plan), I wish to determine the ionospheric gradient effect to GPS signals. Indeed, it can be physics-based model for the ionosphere gradients, or a representation from observational data, as was mentioned by Andrew. Previously I had use very the manual kind of method to model the ionosphere using some simple gradient method. However, I am not sure how accurate is that. So, that's why Im curious to know if there any method or by using any mathematical approach (i.e. statistical approach) to determine the gradient of the ionosphere using either the physics-based data or from observation data. 

Dear Andrew Mazzella, your answer seems to be mermerizing, Im just speechless as I didn't expect such a long respond from you. However, it is totally awesome to have someone like you to assist people like me. Your ideas are great. Let me do 1 by 1 and will try to get back to you asap. Many thanx again Andrew.

Karthi

Dear Karthigesu,

In the following paper:

Wanninger, L., The occurrence of ionospheric disturbances above Japan and their effects on precise GPS positioning, Proc. of the CRCM, '93, p.175, Kobe, December, 1993.

you can find in Section 2 the description on how to account for the horizontal gradients in the electron distribution. Basically, you have to take the differences of two VTEC observations to one particular satellite at consecutives epochs, dVTEC, that you will then normalized to a distance of 100km as Equation 7 does in such paper. For such normalization you will need to calculate the distance between the two corresponding ionospheric pierce points (for the two epochs you are considering), when considering a single-layer approach for the ionosphere.

Angela