For the purpose of describing objectively the main characteristics of monthly mean circulation at 500rob level and thus establishing the correlation between the circulation at the same level of the middle and lower latitudes and the precipitation in the later part of the period over the basin of the lower Ghangjiang River, monthly mean 500rob height fields are expanded by use of mixed Chebyshev-Fourier polynomials, then the behavior of ultra-long waves is examined and finally these waves are classified in Fuzzy according to their expansion coefficients. The results thus obtained are:1) The ultra-long waves at 500rob level show remarkable seasonal variations, whose spectra in dry years are distinctly different from those in wet years; 2)Ultra-long waves at middle and lower latitudes during winter and spring, particularly the positions of ridge-trough ofwavenumber 1 and the intensity of the west wind in March, are well correlated with the precipitation over the basin of the lower Changjiang River in summer and with the summer circulation over East Asia as well.