Migratory birds can utilize the geomagnetic field for orientation and navigation through a widely accepted radical-pair mechanism. Although many theoretical works have been done, the available experimental results have not been fully considered, especially the temporary disorientation induced by the field which is increased by 30% of the geomagnetic field and the disorientation of the very weak resonant field of 15 nT. In this paper, we consider the monotonicity of the singlet yield angular profile as the prerequisite of direction sensitivity, and find that for some optimal values of the hyperfine coupling parameters (that is, the order of 10^{-7}∼10^{-6} meV) the experimental results available so far can be satisfied. We also investigate the effects of two decoherence environments and demonstrate that, in order to satisfy the available experimental results, the decoherence rate should be lower than the recombination rate. Finally, we investigate the effects of the fluctuating magnetic noises and find that the vertical noise destroys the monotonicity of the profile completely, but the parallel noise preserves the monotonicity perfectly and even can enhance the direction sensitivity.