Abstract
From harmonic analysis of the 500mb height data obtained from 20°N to 80°N at intervals of 10° latitude during the thousand day period of the ten winters from 1947/48 to 1956/57, some statistical features of amplitudes and phase angles of the 500mb heights are derived for wave number one to six and the results are presented. The symbols adopted in this paper are given in Section 2.
The negative correlation between zonal mean 5-day mean surface pressures at 70°N and 35°N has been discussed by Willett (1960) and Lorenz (1951). This applies also to the daily 500mb heights, giving the maximum negative correlation coefficient -0.568 between Δz (40°N) and Δz (70°N) as shown in Table 1. This correlation coefficient varies from year to year with the range about 0.2 around the mean value -0.568 as shown by the full line in Fig. 1. The dotted line in Fig. 1 is the correlation coefficient between the 5-day mean surface pressures p(35°N) and p(70°N) in winter half year obtained by Willett (1960). The parallelism of the two curves shows that the negative correlation for the 500mb heights is related to the meridional shift of the atmospheric mass in the northern hemisphere.
The meridional distribution of the amplitudes and the standard deviation of their anomaly are shown in Fig. 2 and Fig. 3 for n=1 to 6 respectively. The maximum of both of them shifts to the lower latitudes with increasing wave number.
Correlation coefficients between the anomalies of amplitudes at each latitudes are pre-sented in Table 1 and partly in Fig. 4. It is seen from the table that the correlation is generally poor at two latitudes 20 degrees or more apart except for n=2 and 3. The maximum of correlation coefficient between the amplitudes at two latitudes 10 degrees apart shifts to the low latitudes with increasing wave number as can be seen in Fig. 4.
The frequency distribution of phase angles is shown in Fig. 5. The distribution of φ1 indicates that the maximum frequency shifts eastward with increasing latitude, as already shown by Barrett (1958) for the 300mb height and the project AROWA for the 500mb height. The distribution of φ2 shows also the shifts of the maximum frequency, but in this case, two homogeneous zones in the higher and the lower latitudes are recognized. That is to say, the phase angle in the higher latitudes is about 180 degrees out of the one in the lower latitudes. This is reflected in the fact that the frequency distributions of φ2 are different at high, normal and low index stages of ΔU55N as shown in Fig. 6. At the high index stage two homogeneous zones in the higher and the lower latitudes are significant. At the low index stage, however, the shift of φ2 is clearly seen. On the other hand, the frequency distributions for n_??_4 are rather flat compared with those for n_??_3 as can be found in Fig. 5.
In Fig. 7, the distributions of phase velocities, defined by the phase difference in con-secutive two days, are presented at 50°N for n=1 to 6 at high (dotted line), normal (thin full line) and low index (heavy full line) stages of U50N. The linear relationship does not exist between the phase velocities and U50N for n_??_3, but it is more pronounced for the higher wave number and most significant for n=6.
The result described above indicates that the ultra long waves n_??_3 predominate to the
north of the middle latitudes and the long waves n_??_5 in the middle or low latitudes, with the critical wave number four. This statistical fact may be taken into consideration in the theoretical studies such as model researches.
