Time and spatial variability of annual rainfall

The annual rainfall trend is determined as the Angular Coefficient (AC) of the least-square line for each rainfall time series in the MSP. The increasing trends or positive values of AC are typical only of 12 of the whole 126 series; the maximum observed slope is about 2.5 mm/a. Decreasing trends are observed for 114 series (90%); the minimum is about —9 mm/a. If a 5% significance level is considered for correlation coefficients, 60 negative trends are found versus only two positive trends.

There are 17 time series available before 1921 (three before 1829) and they are located in Campania and Apulia (Polemio & Casarano 2004). If the start of the study period is moved back with respect to the MSP, in Campania a downward trend in rainfall

is not evident while in Apulia a slight but almost continuous downward trend in rainfall is quite evident, even in the nineteenth century.

The results of the MSP are consistent with previous studies if average spatial values are considered (Brunetti 2002; Cambi et al. 2000; Piervitali & Colacino 2002). The higher density of gauges used in this study implies that the trend range is wider and the determination of extreme values is more accurate.

The spatial analysis of AC shows that 96.8% of the study area is affected by a negative trend (Fig. 3). Considering MAP and AC values as cell attributes, the spatial average of AC or the trend values for MAP class highlight the fact that the rainfall trend worsens or decreases as the MAP

Table 1. Regions or HCA and rainfall increases (Table 2). This figure is extremely worrying in the context of water management because high MAP areas are wide Apennine portions of the drainage basins of the artificial lakes which guarantee a relevant percentage of water supplies.

The reliability of detected rainfall trends has been evaluated by the Mann-Kendall test (Mann 1945; Kendall 1975). The Mann-Kendall variable S is:

where z¡ is the rainfall of the i-th year of the considered gauge z, and k is the number of data or dur-

Region Apulia Basilicata Calabria Campania HCA Apulia

Inner Basilicata Tyrrhrnian Calabria Calabria (transition) Ionian B.-C. Campania

644 893 1043 1118

650 986 1262 1054 865 1118

- 66 133 232 250 186 191

For each row the mean is determined considering the MSP: MAPR, MAP of a region; TR, precipitation trend; PVR, precipitation variation due to the trend and to the duration of MSP.

ation of the time series. S is distributed with null mean and variance s2 function only of k. This statistic, normalized to the respective standard deviation, highlights a negative trend with regard to 98% of the area, with the Mann-Kendall variable lower than average for more than one standard deviation over 75% of the area, and more than two standard deviations over 39%. It is clear that there is a relevant and generalized downward rainfall trend in the MSP.

The Mann -Kendall test has been improved taking into consideration three more detailed approaches (Douglas et al. 2000; Hirsch et al. 1982; Polemio et al. 2004a): pre-whitened series, trend estimator and spatial correlation calculation.

Pre-whitened series may be necessary since the Mann -Kendall test formulates the hypothesis that the data of a time series are independent and not autocorrelated. If the time series is autocorrelated a false trend could be detected. Each time series was then pre-whitened, obtaining a new series with null autocorrelation typical of a white process, and subjected to the Mann-Kendall test again. Widespread negative values of the

Mann -Kendall variable and downward rainfall trends were substantially confirmed.

An extension of the Mann-Kendall test also allows an alternative and independent estimate of the trend. It is defined, for each rainfall time series, as the median of the slopes dj — (zi — zj)/(i — j) of any combination with i and j equal to 1, 2, ... , k and i = j. This estimator, being based on a median, is more 'robust' with respect to extreme or anomalous values in the time series. The results are substantially similar to these obtained with the standard approach. The spatial correlation of the m rainfall time series allows the number of 'equivalent' independent rain time series to be estimated. It is useful to estimate the expected variance of a regional average for the Mann-Kendall variable, and then the significance of the trend over a wide area.

If Si is the Mann -Kendall variable value for the ith rain gauge and all the time series have the same length, then the variance is equal for all the Si, and a regional average S for the Mann-Kendall variable can be calculated. If the m time series are not correlated with each other, then the variance of 5 would

Table 2. Spatial average of angular coefficient (SAAC) of rainfall straight line trend for MAP class areas

MAP class (mm)

<600 600-750 750-900 900-1100 1100-1300 1300-1500 >1500 SAAC (mm/a) -0.64 -1.00 -1.89 -2.38 -2.64 -3.01 -4.74

Table 3. Distribution of the Mann-Kendall variable for the 41 temperature time series

Original series 21(51.2%) 16(39.0%) 11(26.8%) 20 (48.8%) 9(21.9%) 7(17.1%)

Pre-whitened series 24 (58.5%) 11(26.8%) 2(4.9%) 17(41.5%) 8(19.5%) 3(7.3%)

simply be s2/m. Since time series are actually correlated, with pij correlation coefficient between the rain gauges i and j, it is possible to define an 'equivalent' gauge number meq:

The variance of the regional average S will then u 2 2 be &s = s meq.

The selected rain gauges have been divided into three groups on the basis of HCAs and administrative boundaries: Campania (41 gauges), Apulia (28 gauges) and Calabria-Basilicata areas (56 gauges). If the original (not pre-whitened) series are considered, meq is 1.95 for the Campania group, 1.85 for the Apulian group and 2.54 for the Calabria-Basilicata group. The regional average 5 is, respectively, — 2.81 ss, —1.17 ss and —3.59 ss. For the pre-whitened series, meq is 1.84 for Campania, 1.85 for Apulia and 2.47 for Calabria-Basilicata, and S is, respectively, —2.26 ss, —1.18 ss and — 3.21 ss. It can be assessed that the negative trend is only slightly attenuated if the autocorrelation is considered, and thus the substantial statistical relevance of trend results is confirmed.

The existence of relevant rainfall variations in periods shorter than MSP can be better highlighted with the moving average analysis: the deviation from MSP average of moving averages of decreasing duration (5, 3 and 2 years) is considered (Fig. 4).

The 5-year duration allowed the evaluation of significant deviations from the average over long periods. Dry periods were recorded in Apulia for 1942-1950, 1988-1992 and 1997-2001; the last two periods were almost the driest periods in Basilicata, Calabria and Campania.

The 5-year average deviation has been continuously negative since 1978 in Basilicata and Calabria and since 1983 in Campania, whereas the negative deviation in Apulia was observed from 1980 to 1995. The analysis of 3-year and 2-year moving averages shows the drought duration of 2 or 3 years is longest from 1980 as from this year the minimum rainfall has been reached and has been exceeded one or more times in each considered region, particularly with the latest drought of 1999-2001. In Apulia and Campania, some dry periods of the late 1920s and 1940s were as dry as the latest droughts.

The decade's average analysis also highlights a persistent succession of low-rainfall years and drought periods from about 1980; the results are consistent with those of other authors, obtained using different time series and lower data density (Brunetti et al. 2004). It can be hypothesized that the observed downward trend in rainfall is strongly influenced by low rainfall observed after 1980. On a

HCA basis, the 1981-2001 average is lower than the 1921-1980 average of 10% in Apulia, 14% in Basilicata-Calabria and 16% in Campania.

The Student i-test is used to assess whether each time series of 1921-1980 and 1981-2001 can be considered part of the same population. The 1981-2001 average is lower than the 1921-1980 average for 98% of the time series. The 5% and 1% significance level is, respectively, found for 75% and for 53% of the time series: the rainfall of the latest 20 years can be considered anomalously low.

Monthly data have been utilized to characterize the rainfall seasonal trend. The most important contribution to the annual negative trend is due to the winter (the months from December to February, which is the rainiest season) rainfall trend (Fig. 5). The precipitation deficit of the last 20 years is mostly due to a reduced contribution of winter rainfall. Spring (March-May) and autumn (September-November) also show negative trends, although much less evident. A positive trend appears for summer, the arid season: the effect is null in terms of water resources availability.

Monthly temperature series are available from 1924 onwards. To fill the residual monthly gaps the time series were grouped into HCA. A different approach, based on gap filling and homogenization, was necessary for 15 time series of gauges located in Campania due to the abundance of very anomalous values, in particular for the last 20 years (the homogeneity evaluation is based on the Craddock (1979) test).

The linear trend analysis shows the temperature trend is not as homogeneous as the rainfall trend both in the whole study area and in each HCA (Tables 3 and 4). A prevailing increasing trend is observed in Campania but is weak in Apulia and is substantially absent in the remaining area.

To apply the Mann-Kendall test, pre-whitening of the temperature series is necessary due to their significant autocorrelation. The Mann-Kendall S distribution is close to Gaussian; there is a slight prevalence of increasing trends in the Campania region where an increase of temperature starting from about 1980 is observed, as shown in Figure 4. However, this is not enough to assess a significant and generalized temperature trend over the whole area in MSP, since this behaviour is not so evident elsewhere. These results are thus quite different from those by other authors (Brunetti et al. 2004; Cambi et al. 2000), probably due to the strong difference of data set length and spatial density of examined gauges.

The real or actual evapotranspiration Er was calculated using Turc's formula (Turc 1954) with the correction suggested by Castany (1968), using temperature and rainfall monthly data. In this way an approximate but simple evaluation of the annual variation of actual evapotranspiration can be obtained.

The average annual net rainfall (ANR) of a time series ranges from 52 to 1565 mm for the whole group of 41 available time series in the period 1924-2001. The AC of net rainfall (ACNR) is strongly negative everywhere. The absolute value of ACNR is directly correlated to MAP: it increases or gets worse as MAP increases. ACNR ranges from — 0.4 to —4.3 mm/a, grouping the time series by

re o

Dec-Feb Mar-May Jun-Aug Sep-Dec

Dec-Feb Mar-May Jun-Aug Sep-Dec

1 | ||

□ Basilicata Fig. 5. Spatial average of seasonal rainfall trends of the main study period. Fig. 5. Spatial average of seasonal rainfall trends of the main study period. □ Basilicata Table 4. Number of time series as percentage of the total for each HCA and classes of angular coefficient of temperature trend (ACT, "C/100 years) HCA ACT < -1 - 1 < ACT < - 0.5 + 0.5 < ACT < +1 ACT > +1 Apulia 7 7 20 7 Calabria-Basilicata (all) 17 25 8 8 ## Campania 7 0 13 27MAP (Table 5). In the whole period, the reduction of net rainfall can be roughly assessed as from 27% to 33% of ANR: this percentage is everywhere higher than that calculated for actual rainfall. This dramatic situation is due to different phenomena. First of all, the downward rainfall trend is more relevant during winter, when generally net rainfall reaches maximum levels and actual evapotranspiration minimum levels. The entire winter decrease in actual rainfall becomes a decrease in net rainfall. The summer is arid everywhere and the actual evapotranspiration is less than the potential one due to low rainfall. The increase in summer rainfall is completely 'burned' by actual evapotranspiration. The recent trend towards a rise of annual temperature and the regime variation amplify the effect of rainfall variations. |

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