Description and discussion of the indexing methodology

The documentary source used in this work provides information about the presence o absence of rainy in Zafra at the quasi-weekly temporal scale. The reports rarely inform about the number of rainy days. Therefore, we are not able to construct daily indices or even a weekly index series referring to the number of rainy days. In this regard, although we consider useful and highly informative, we can only construct monthly series that refer to frequency of rainy weeks. The methodology used to construct the rainy indices consisted in establishing two categories of indices: value 0: indicates the absence of rainfall during the days (i.e. one week without rainfall). Value 1: indicates presence of rainfall during some of the days (i.e. one week with rainfall).

The index value was assigned to each individual day of one report. From those indices series, the monthly percentage of rainy weeks was calculated. However, we identified some problems:

  • There were weeks with two weather reports. The index values were assigned to the days referring to each report. So, we took into account the indices values in these weeks to calculate the monthly percentages of rainy weeks.
  • There were dayswith absence of weather information. In this case, we took into account only the number of days in each month with weather information to estimate the monthly percentages of rainy weeks.
  • There were months with less 50% of the days with weather information (two weekly reports or less). Theses months were deleted of data series. In total 64 months were removed.
  • There were months with 50% or more of the days with weather information. In this case, theses months were not removed of data series.

Therefore, we considered that 50% or more of the days in the month is enough to indicate is rained or not in this month. This hypothesis was checked in the current period (1960-1990). For this purpose, we performed an additional statistical analysis for the precipitation in the current period deleting one or two weeks with data in each month.Then we applied the same methodology used for the older period (1750-1840), i.e. we constructed for the current period (1960-1990) weekly indices which indicate presence or absence of rainfall, without taking into account the intensity or the number of rainy days in each week. Value 0: indicates the absence of rainfall during the days (i.e. one week without rainfall). Value 1: indicates presence of rainfall during some of the days (i.e. one week with rainfall).

For each month, in all period 1960-1990, we removed one week of data and we calculated the monthly percentage of rainy weeks. The anomalies with respect to monthly percentage of rainy weeks without deletingany week of data were estimated as follows:

WherePAjirefers to monthly rainfall anomalies in the month i of the year j.PIji is the percentage of rainy weeks in the month i of the year j removing one week of data and PITjiis the percentage of rainy weeks in the month i of the year j without removing any week of data.

The monthly anomalies were estimated removing one week at a time of the 4 weeks per month: first week, second week, third week and fourth week. The mean and standard deviation of the anomalies obtained of the four possibilities for each month were calculated (see Table 1).The results show that the means of the anomalies are around 0 and the standard deviationsare <10% (except in June and September when the rainfall is more sporadic in Zafra region).

Afterwards this approach was performed removing two weeks of data.The possibilities of delete two weeks were: first and second weeks, first and third weeks, first and fourth weeks, secondand third weeks, and second and fourth weeks.

We calculated the mean of the anomalies obtained from the six possibilities for each month (see Table 1). The results show that the means of the anomalies are around 0 and the standard deviations are <17% except in June and September again.

Therefore, we are confident to reaffirm that the use of the 50% or more of the days in the month is sufficient to construct the monthly index within anaverage mean error less than 20%.

On the other hand, it is necessary to indicate that only 0.72% of the months (6 months) in all the study period (1750-1840) have 2 weeks without data and 4% of the months (33 months) have 1 week without data.

Table 1.Mean and standard deviation of the anomalies.

Month / Deleting one week / Deleting two weeks
Mean / Standard deviation / Mean / Standard deviation
January / -0.464 / 8.610 / 0.037 / 14.347
February / 0.006 / 9.337 / 0.018 / 16.041
March / 0.272 / 9.362 / 0.768 / 15.528
April / -0.058 / 9.539 / -0.168 / 15.993
May / 0.129 / 9.796 / 0.367 / 16.268
June / -0.158 / 11.180 / -0.454 / 18.675
July / -0.042 / 7.788 / -0.121 / 12.867
August / 0.237 / 6.802 / 0.649 / 11.101
September / 0.228 / 10.734 / 0.657 / 17.897
October / -0.051 / 9.083 / -0.354 / 14.873
November / -0.046 / 9.570 / -0.132 / 15.994
December / -0.046 / 8.759 / -0.130 / 14.543