  Adaptive optics (AO) system performance is improved using post-processing
techniques, such as point spread function (PSF) deconvolution. The PSF
estimation involves characterization of the different wavefront (WF) error
sources in the AO system. We propose a numerical error breakdown estimation
tool that allows studying AO error source behavior such as their correlations.
We also propose a new analytical model for anisoplanatism and bandwidth errors
that were validated with the error breakdown estimation tool. This model is the
first step for a complete AO residual error model that is expressed in
deformable mirror space, leading to practical usage such as PSF reconstruction
or turbulent parameters identification. We have developed in the computing
platform for adaptive optics systems (COMPASS) code, which is an end-to-end
simulation code using graphics processing units (GPU) acceleration, an
estimation tool that provides a comprehensive error breakdown by the outputs of
a single simulation run. We derive the various contributors from the end-to-end
simulator at each iteration step: this method provides temporal buffers of each
contributor. Then, we use this tool to validate a new model of anisoplanatism
and bandwidth errors including their correlation. This model is based on a
statistical approach that computes the error covariance matrices using
structure functions. A correlation analysis shows significant correlations
between some contributors, especially WF measurement deviation error and
bandwidth error due to centroid gain, and the well-known correlation between
bandwidth and anisoplanatism errors is also retrieved. The model we propose for
the two latter errors shows an SR and EE difference of about one percent
compared to the end-to-end simulation, even if some approximations exist.
