110
Chapter 6: Analysing the Boreal Summer Relationship
method see Nicholson, 1985; adapted for grid-box time-series in Ward, 1994).
The time-series for the two regions (Figure 6.5b,c) have been filtered and are
used in the analysis below.
6.5.3 High Frequency Sahel Rainfall Variations
a) Field Significance
Plots have been made of the correlation between the high-frequency
« 11 years; HF) Sahel rainfall series and each grid-box series of HF SST
(Figure 6.6a) and HF SLP (Figure 6.6b). There are many correlations that
are locally statistically significant. However, one would expect on average 5%
of the correlations in each figure to be significant at the 5% level by chance
(cf. Section 9.2.1). So to assess the null hypothesis ofno association between
Sahel rainfall and the marine fields, it is necessary to assess the prob ability
of achieving the number of statistically significant boxes in Figures 6.6a,b
by chance. This test is called testing "Field Significance" (Section 9.2.1).
The SST and SLP time-series contain strong spatial correlations. This raises
the likelihood of achieving by chance a large fraction of statistically significant correlations. To assess field significance in this situation, a Monte Carlo
method has been used, as recommended by Livezey and Chen (1983). Alternative approaches are permutation procedures discussed in Chapter 9 .
• Sea-Surface Temperature
Following Livezey and Chen (1983), 500 random normal rainfall series,
each oflength 40, have been simulated using a random number generator.
These 500 simulated rainfall series were used to create 500 correlation
maps like the one in Figure 6.6a using the observed SST data. Table 6.2
shows the fraction of occasions in the Monte Carlo simulation on which
the area covered by locally significant 10° lat x 10° long SST boxes
exceeded the significant area in the Sahel-SST correlation map (Figure
6.6a).
For all available regions, 32.2% of the sampled ocean area is covered
by significant correlations between Sahel rainfall and SST (Figure 6.6a).
Such a coverage was achieved in less than 0.2% of the Monte Carlo
simulations i.e. none of the 500 correlation maps contained more area
covered with significant correlations. So field significance is very high
indeed, and the null hypothesis of no association between Sahel rainfall
and SST can be rejected with great confidence. Sub-domains of the
global ocean were also tested and found to be highly field significant,
including the extratropics .
• Sea-Level Pressure
The field significance analysis was repeated for the SLP correlations in
Figure 6.6b. Again, field significance is very high for the whole analysis domain. The correlations north of 30° N are field significant at the
Chapter 6: Analysing the Boreal Summer Relationship
method see Nicholson, 1985; adapted for grid-box time-series in Ward, 1994).
The time-series for the two regions (Figure 6.5b,c) have been filtered and are
used in the analysis below.
6.5.3 High Frequency Sahel Rainfall Variations
a) Field Significance
Plots have been made of the correlation between the high-frequency
« 11 years; HF) Sahel rainfall series and each grid-box series of HF SST
(Figure 6.6a) and HF SLP (Figure 6.6b). There are many correlations that
are locally statistically significant. However, one would expect on average 5%
of the correlations in each figure to be significant at the 5% level by chance
(cf. Section 9.2.1). So to assess the null hypothesis ofno association between
Sahel rainfall and the marine fields, it is necessary to assess the prob ability
of achieving the number of statistically significant boxes in Figures 6.6a,b
by chance. This test is called testing "Field Significance" (Section 9.2.1).
The SST and SLP time-series contain strong spatial correlations. This raises
the likelihood of achieving by chance a large fraction of statistically significant correlations. To assess field significance in this situation, a Monte Carlo
method has been used, as recommended by Livezey and Chen (1983). Alternative approaches are permutation procedures discussed in Chapter 9 .
• Sea-Surface Temperature
Following Livezey and Chen (1983), 500 random normal rainfall series,
each oflength 40, have been simulated using a random number generator.
These 500 simulated rainfall series were used to create 500 correlation
maps like the one in Figure 6.6a using the observed SST data. Table 6.2
shows the fraction of occasions in the Monte Carlo simulation on which
the area covered by locally significant 10° lat x 10° long SST boxes
exceeded the significant area in the Sahel-SST correlation map (Figure
6.6a).
For all available regions, 32.2% of the sampled ocean area is covered
by significant correlations between Sahel rainfall and SST (Figure 6.6a).
Such a coverage was achieved in less than 0.2% of the Monte Carlo
simulations i.e. none of the 500 correlation maps contained more area
covered with significant correlations. So field significance is very high
indeed, and the null hypothesis of no association between Sahel rainfall
and SST can be rejected with great confidence. Sub-domains of the
global ocean were also tested and found to be highly field significant,
including the extratropics .
• Sea-Level Pressure
The field significance analysis was repeated for the SLP correlations in
Figure 6.6b. Again, field significance is very high for the whole analysis domain. The correlations north of 30° N are field significant at the