change GET query string

Hi,

I search page which gets filter using GET method. in some cases I can get  ?brand=&model=2   this kind of query where brand is empty. 
When I get this kind of get string I want remove 'brand'  from get field so it will be ?model=2 . 
In other words when user make query url ?brand=&model=2 as a response url I want to be it ?model=2

I dont know how to do it.

Thanks in advance