Table 1 shows the condensed results of the hypothesis test for wind velocity. For each climate zone, we calculated the frequency of months/stations where wind was stronger during rainy and dry days, as well as no significant difference.

In most regions, there is no difference between wind velocity during rainy and dry days. In the semi-arid and coastal northeast, stronger wind occurs slightly more frequently during dry days. In the more temperate south, it is the other way round. In general, it was observed that coastal stations showed stronger wind during dry weather, while stations in hillier regions have stronger winds more frequently during rainy days.

Wind velocity influences E/ETP by removing moisture from the surface, bringing less saturated air. Thus, higher velocities result in higher E/ETP. As seen, dry days, more often than not, show stronger wind velocity, which also helps to explain the negative relationship between rainfall and E/ETP.

Statistical analyses were performed considering minimum, maximum and mean daily temperature. Table 2 shows the analysis for the maximum temperature. In almost 90 % of the cases, maximum temperature was significantly higher during dry days than during rainy days, more so in the temperate south and less so in the equatorial amazon. It confirms the intuitive notion, also stated by Allen (1998), that dry days have maximum temperatures higher than rainy days.

For minimum temperatures, aggregate results are shown in Table 3. Its results show that the assumption by Allen (1998), that rainy/cloudy days have higher minimum temperatures, is valid for temperate climates, but not necessarily for tropical/equatorial regions. Here, very often minimum temperatures were higher in dry days.

In the average, results shown in Table 4 allow the conclusion that dry days tend to be warmer in all regions of the country. As seen, this is in part due to higher maximum temperatures, as expected, but in some parts also due to higher minimum temperatures even in dry days, contrary to some literature, notably Allen et al. (1998).

This also helps to explain the negative relationship between rainfall and E/ETP, since, as seen, temperature is positively correlated with E/ETP.

In the case of sunshine duration (used here to estimate incoming radiation), the correlation is quite intuitive, and is confirmed by the statistical analysis: in almost 100 % of the months/stations, mean sunshine duration was higher in dry days, as seen in Table 5. This is the main factor explaining the inverse relationship between rainfall and E/ETP.

The same happens for relative humidity. Table 6 shows that in 100 % of the cases, relative humidity is higher during rainy days. Since relative humidity is negatively correlated with E/ETP, this also explains the inverse relationship investigated in this paper.

Finally, results for atmospheric pressure are shown in Table 7. For higher latitudes, there is a positive correlation between dry weather and atmospheric pressure, as expected. In regions closer do the Equator; however, this correlation is no longer valid, since there is no statistical difference between pressure during dry and rainy days. The variability of atmospheric pressure also plays a minor role in the variability of ETP; for one side, higher pressure increases the specific weight of air, allowing more moisture to be retained in the surrounding air; on the other hand, it increases the psychrometric constant, which comes into the denominator of the Penman-Monteith equation, thus decreasing ETP.

Figure 1 shows an example of the resulting regressions, for the meteorological station of Brasilia (tropical Brasil central zone), for the month of January. It can be observed that, as expected, rainfall variability is in general much higher than that of ETP. In this case, while rainfall varied between 29 and 577 mm month-1, ETP varied between 85 and 145 mm month-1. The negative slope shown in this example was also obtained for all remaining regressions, emphasizing the inverse relationship between rainfall and ETP.

Although data dispersion is relatively high (also expressed in the low coefficient of determination R2, it should be remembered that these regressions are an alternative for the use of long-term averages of ETP for hydrological simulation, i.e. when no time series are available.

This kind of regression is particularly useful during transition months between the dry and rain seasons in tropical regions (typically April/May and September/October in the Southern Hemisphere), which can be either very rainy or very dry, depending on the year. It is also useful in regions where the rain season presents periodical breaks, or periods of 10 to 15 days without rainfall. These periods, usually between December and March, can have very high ETP given the higher extraterrestrial radiation during summer months.

Only during very dry months, like July and August, ETP can have a higher variability, since rainfall is hardly larger than zero. In this case, the regressions are less useful, and the use of ETP averages seem to be more practical.

Figure 2 shows the spatialized values of the R2 coefficient for the regression in two months of transition between rainy and dry seasons.

As can be seen, the higher values for the coefficient were obtained in the tropical zone. In the temperate and equatorial zones, the inverse relationship between rainfall and ETP is not so clear, perhaps because of a higher frequency of cloudy, but not necessarily rainy days.

Finally, Table 8 shows the average of R2 statistics for each zone and month.

As mentioned, the winter months in the Southern Hemisphere (June to August) showed the lowest average regression performance, because of the low variability of rainfall during these months in most regions of Brazil.

The statistical analysis performed over the meteorological variables explaining the evapotranspiration process supported the comprehension of the mechanisms behind the inverse relationship between rainfall and ETP. Incoming radiation, which is the main driver of ETP, is clearly higher during dry days than in rainy days. Relative humidity, which also strongly influences ETP, is clearly higher during rainy days. Both results are intuitive and are supported by the statistical analysis.

Mean air temperature, which is also positively correlated with ETP, is generally higher during dry days, in comparison to rainy days. The results also showed that minimum temperatures very often were higher during dry days, mostly in the tropics. This result shows that one very popular premise of hydrometeorology is not necessarily true for tropical regions, namely the belief that minimum temperatures should be lower during clear weather due to less heat retention in the lower atmosphere.

For wind velocity and atmospheric pressure, results were less clear. In most cases, null hypothesis of equal means could not be rejected, thus not allowing further conclusions. One singular fact that was observed is a tendency for stronger wind during dry days in coastal places, while in hilly locations wind was stronger in rainy days.

Thus, the inverse relationship between rainfall and ETP is explained mostly by the higher incoming radiation (or sunshine duration) and lower relative humidity in dry days, and by a lesser part, by higher mean air temperature in these conditions.

In general, the results of the regressions confirmed the inverse relationship between rainfall and ETP, since regression slopes were negative in most cases.

Although the numerical values of the coefficient of determination R2 were low, it must be remembered that these regressions are an alternative to the use of ETP averages, i.e. monotonical ETP values, in order to take at least a share of temporal variability into account. Thus, while the obtained regressions explain around 50 % of ETP's variability, the usage of long-term averages would explain 0 %.

The obtained relations are particularly useful in tropical regions, during months of transition between rain and dry seasons, which can be either very wet or very dry, thus showing varying ETP.

These indirect estimates of ETP can be useful, for example, for extending ETP series into the past, in regions or periods where rainfall data is more abundant than meteorological data. As mentioned, the Brazilian hydropower network is planned and operated to supply energy demand, at a low risk, even in the case of a repetition of a critical hydrological period occurred in the 1950s, when hydrometeorological data was scarce nationwide (and even more so in low-populated areas like the amazon, where hydropower was expanded in recent years). More accurate ETP estimates would be helpful both for a better assessment of inflows during that period (given the need of proper rainfall-runoff modelling) and for a better estimation of evaporation losses.

Other potential areas of usage are reservoir design and reservoir yield estimation, where long-term ETP averages are still widely used, leading to an overestimation of reservoir yields. Irrigation management would also be an area for application, through a better estimation of crop water needs, based only on rainfall measurements and the regressions obtained. Finally, assessment of future hydrological conditions would also benefit, since ETP conditions could be easily estimated based only on rainfall predictions.