It is well known that automatic speech recognition performs poorly in presence of noise or reverberation. Much research has been undertaken on model adaptation and speech enhancement to increase the robustness of speech recognizers. Model adaptation is effective to remove static mismatch between speech features and acoustic model parameters, but may not cope well with dynamic mismatch. Speech enhancement approaches can reduce dynamic perturbations, but often do not interconnect well with speech recognizer. There seems to be a lack of optimal way to combine these two approaches. In this paper we propose introducing the dynamic capabilities of speech enhancement into a static adaptation scheme. We focus on variance adaptation, and propose a novel parametric variance model that includes static and dynamic components. The dynamic component is derived from a speech enhancement pre-process, and the parameters of the model are optimized using an adaptive training scheme. An evaluation of the method with a speech dereverberation for preprocessing revealed that a 80 % relative error rate reduction was possible compared with the recognition of dereverberated speech, and the final error rate was 5.4 % which is close to that of clean speech (1.2%).