In analogy with the ultimate speed c, there is an ultimate acceleration β, nobody's acceleration can exceed this limit β, in the solar system, β=2.961520e+10(m/s2). Because this ultimate acceleration is large, any effect related to β will become easy to test, including quantum gravity tests. In this paper, an approach is put forward to connect the ultimate acceleration with quantum theory, therefore the ultimate acceleration has quantum effects. At the first, this approach is applied to sunspot problems, the sunspot cycle is calculated to be 10.93 years. Next, this approach is applied to the atmospheric circulations and European climate pattern. Constructive interference condition takes place at three latitudes on the northern hemisphere, that control overall wind fields around the earth. This quantum effect indicates that Europe suffers to a gust of cold streams from arctic regions per 2.24 years, this prediction agrees well with the observed cycles of the quasi-biennial oscillation in the equatorial lower stratosphere. The European climate pattern is under control of the four seasons and the cold streams per 2.24 years.