Groundwater levels can vary with so many things, including those mentions.  Soils, tree and plant types, geology, rainfall amount, intensity, duration, days since rainfall, hydrologic modifications, etc.  If you have several types of peatlands or soils mapped associated with the peatlands, set up some wells with transducers to monitor water depth with time.  Global and Hobo are a couple companies that make water level transducers that I know about.  Some transducers are atmospheric pressure adjusted and some need adjusting to barometric pressure.  I do not know if there a models already available to do what you want, but if so these would be based on information collected and analyzed in detail, and validated with time.  If there are already well or pieziometer records for these, perhaps that will help develop a model.  Soils may have varying depths of organic accumulations, vegetation types of varying ages, densities and transpiration rates add to complexity and ability to generalize from primarily atmospheric and climactic data obtained remotely.. 

Dear William, thank you very much for your answer, yes we have already installed transducers equipment to monitor water depth with time (Global weather station and Hobo). We will check different types and depths of peat soils in the field.

Since GW mechanisms are complex, numerical modelling is always preferable. However, you can go for data-driven approach since you have several interdependent datasets as you mentioned. First, try to figure out the significant variables related with the groundwater level in your area and then develop your desired GW level model using different data-driven methods such as ANN, GP, SVM, ARIMAX etc. and so on.

Before constructing a groundwater flow model which generates groundwater levels, a groundwater recharge model should be built up using weather, soil, land-use and DEM data. 

There is a easy-to-use GIS groundwater flow model that allows you to construct model, calibrating the model, and visualizing the  modelled groundwater levels all in GIS:

http://www.bgs.ac.uk/gisgroundwater/

Dear Colleague, based on the previous answers, I suggest that you get also information on the underground medium. Are there heterogeneities ? At which lengscale ? I agree that the upper boundary condition are  the main source of uncertainties in numerical groundwater modeling. However, you may also be interested in lateral boundary conditions which are generally to be found from regional groundwater studies. 

How about satellite data GRACE? 

Primero que nada y para entenderte explícame en forma precisa : ¿Que entiendes y para que es el modelar el nivel de aguas subterráneas? La forma tradicional es medirlo en captaciones existentes o hechas ex profeso. ¿Y lo más importante cuál es el problema que debes resolver?

Dear All,

How to modelling of steamflood performance through fiber optic temperature sensing.

Best Regards