The study area (approximately 500 km²) is the southern

sector of the wider Campania Plain, a structural depression on the Tyrrhenian Coast (Figure 2(a)). This area, located between Naples (40˚50' North, 14˚15' East) to the East, Somma-Vesuvius (40˚49' North, 14˚25' East) to the South, and the mountains of Sarno (40˚49' North, 14˚37' East) to the North, occupies the south-eastern part of the Campania Plain (Figure 2(b)).

Climate is very variable in spring and autumn and more stable in winter and summer. Dry season, from May to September, not enable to recharge the soil before of November-December, in order to inter-annual variability. A typical seasonal trend of different terms of water balance is illustrated in Figure 3, where the climogram for the Campania Plain describes the humid period (October-March) followed by the dry-summer season (June-August). Transitional periods (April-May and September) are the growing seasons where vegetation is green.

The graben system of the area began to form during the Pliocene, between Mesozoic carbonate sequence outcropping to the east and south of the plain. During the Pleistocene this structural depression was filled with pyroclastic deposits (ashes, pumice, scoriae and tuffs) of Neapolitan volcanoes (Phlegraean Fields and SommaVesuvius) and alluvial (mainly sandy and partly clayey) and marine (mainly silt) sediments to a thickness of some thousands of metres. The first few hundred metres beneath the soil of the circumvesuvian plain, the zone of the most active groundwater circulation, are made up of the pyroclastic deposits (ashes, pumice and scoriae) and alluvial deposits interposed with marine sediments marshy layers and paleosols. The tuff aquitards divide the flow into two overlapping levels (Figure 4).

Travertine, debris and conglomerates lie at the base of the limestone mountains, while approaching the SommaVesuvius volcano lava flows prevail, interbedded with pyroclastic deposits.

The carbonate aquifers are the most important aquifers located at the boundaries of the plain. The Somma-Vesuvius volcano has a radial water table. Groundwater flows towards the sea and also feeds the aquifer of the surrounding plain. The aquifer of the Campania Plain is characteristically extremely heterogeneous due to granulometric variation in the unconsolidated sediments, the degree of fissuring of rock and complex stratification of deposits.

The map (Figure 5(a)) shows that the aquifer of the Campania Plain flows from NE to SW and highlights the presence of one axe of groundwater drainage to the East of Naples. There are two groundwater divides: the first is between San Giuseppe Vesuviano and Palma Campania (in SE of the map) and the second is between Cancello and Caivano (in NW of the map).

The hydraulic gradient varies from a few units per thousand to a few units per hundred. In particular, the highest values of the piezometric gradient found at the foot of Lattari mountains, may be related to high transmissivity from carbonate aquifers (10⁻¹ - 10⁻² m²∙s⁻¹) compared with values in other areas the plain (10⁻² - 10⁻⁴ m²∙s⁻¹).

The main contributions to aquifer recharge are provided by direct infiltration and groundwater inflow from the nearby volcanic and carbonate aquifers. The mean annual effective infiltration is of 59.6 × 10⁶ m³∙yr⁻¹ [23]. In the Figure 5(b) is shown the map of land-use, with the urban and agricultural activity covering most of the study area. The urban areas are developed, however, in the absence of infrastructure networks. Therefore, we assume a deep percolation of organic waste in the aquifer.

Groundwater pollution sampling was initiated since 1992

in Campania Plain and continued in 2001 and 2006 years [24,25]. However, only in 1992 a wide and resolute sampling was conducted covering a surface of about 500 km².

In 158 wells used for the reconstruction of the paper in the aquifer isopiezometric curves were also collected water samples for the determination of nitrate concentrations. The analysis refers to the period of low water of the aquifer. Nitrate in water samples was colorimetrically measured [26,27]. The wells were managed by one of the leading institutions of central-southern aqueduct (ARIN, Naples Water Resources Company, http://www.arin.na.it).

Kriging and its derivatives have been recognized as the main spatial interpolation techniques from 1970s. Kriging is a method for making optimal, unbiased estimates of regionalized variables at unsampled points. It is possible to have a good estimation of the selected variable using the values collected in the surrounding stations and a structural analysis [28]. Probability kriging (PK) is a specific method belonging to the family of kriging, introduced by as a non-linear and non-parametric method using indicator variables [29]. PK represents an effort for calculating estimates that are less sensitive than indicator kriging to the choice and number of cut-offs (thresholds) and estimates better reflecting local variability [30]. PK is a composite kriging of the indicator data using the rank-order transform as additional variable [31]. Replacing the values of the primary variable in PK by indicator data and using the rank-order transform data, the indicator code, , is assigned as the pollutant variable [32,33]. A vector-based GIS software package ArcGIS 9.2 was used to map, query, and analyze the data in this study.

In the present paper, environmental risk assessments related to nitrate pollution are derived from the probability that a pollutant leaching rate can migrate from sub-surface to groundwater. The selected thresholds or the action level often determine the introduction or not of certain measures. The concentration in natural water is less than 10 mg∙L⁻¹. Water containing more than 100 mg∙L⁻¹ is bitter to taste and causes physiological distress. Water in shallow wells containing more than 50 mg∙L⁻¹ causes methemoglobinemia, the so-called blue baby syndrome in humans [34].

Availability of the regionalization between indicator pollutant at nitrate threshold concentrations for each location s_α within the study area would allow a grid layer α(s_α) referring to “probable hydrogeological effectiveness” of the nitrate pollutant on the basis of the estimate when actually. The European Commission suggested two limits for nitrates: a first threshold, z_k1 = 25 mg∙L⁻¹, which represents the minimum concentration needed to overcome the drinking groundwater quality, and the second, z_k2 = 50 mg∙L⁻¹, which represents the maximum values for the drinking groundwater quality.

The presence of nitrates is considered an indicator of pollution in the Campania Plain because of the intensive agricultural land use, urbanization and industrial practices throughout the area. In several wells, nitrate concentrations exceed the maximum allowable concentration (50 mg∙L⁻¹) as set by the Italian law. The statistics of nitrate data collected in October 1993 are summarized with mean and median values equal to 57 mg∙L⁻¹, and 43 mg∙L⁻¹, respectively. The maximum value is 239 mg∙L⁻¹. Figure 6(a) shows a strong skewed distribution. This is why a Box-Cox transformation (with 0.4 transformation parameter) was adopted. The transformation results in a quasinormal distribution (Figure 6(b)).

A two-stage model of regionalization was fitted using an iterative procedure [31]. Stage 1 assumes an isotropic model and executes a first run of the experimental spatial structures on the scaled data, , where z(s_α) is used to denote the j^th measurement of a variable at the α^th spatial locations s_α, and σ is the sample standard deviation. With stage 2, numbers such as lag (assumed equal 7), lag size h (assumed equal to 2000 m), and range (a) are set to represent the limit of spatial dependence, while nugget is set to represent the unexplained spatial variability, calibrated interactively. Also at, this stage it has been assumed an isotropic semivariogram model for the pollutant indicator spatial pattern. In this way, Figure 7 shows the experimental semivariogram (dots) computed from 158 nitrate data, with spherical permissible models fitted (blue curves).

Semivariogram values increase with the separation distance, reflecting the assumption that nearby nitrate-pollutant data tend to be more similar than data that are farther apart. The modelled variograms have been tested by the cross-validation method. The semivariograms reach 2000 to 10,000 m before dipping around a sill value.

In particular, while unidirectional semivariograms in Figure 7(a) was modelled as a combination of two distinct spatial structures-nugget variance and a spherical structure for z_k1—the semivariogram in Figure 7(b) was composed by nugget plus two spherical structures for z_k2 (Figure 6(b)) (see also Equations (3) and (4)).

The three spatial structures for high nitrate concentration lead us to believe that there are different sources of pollution resulting from the landscape overlying the aquifer. At the local level the presence of nitrates may result from direct leakage into the groundwater of organic waste. At larger range, instead, nitrate may have derived from non-point source as agricultural manures.

The symbolic term in Equations (3) and (4), , is the spherical correlation function equal to

.

It represents a dimensional semivariance of unit sill with ranges given by the circle with a₁ = 10000, z_k1 = 25 mg∙L⁻¹, and a₂ = 3000 a₃ = 10000 meters, for z_k2. Ideally, the value of the semivariogram should reach a minimum value when the separation vector h is zero. In the case study, this is not true firstly because the measurement error exists in nitrate sampling data, and secondly because the distribution and number of wells could be poor. The range relative to the large threshold, z_k2 = 50 mg∙L⁻¹, has a minor nugget than with z_k1 = 25 mg∙L⁻¹ but the nugget/total sill ratio is roughly the same (0.46 - 0.47)which indicates moderate spatial correlation for both the thresholds.

Figures 8(a) and (b) show probability-kriged maps, based on 500 m by 500 m grid across Campania Plain. In kriged model pattern area of Figure 8(a), it is possible to observe a distinct separation between East (minor) and West (major) zone of nitrate map, which is consistent with the pattern of groundwater flow outlined in par. 2.1. The areas having probability of 50% that the nitrate concentration exceeded 25 and 50 mg∙L⁻¹ are narrow, intermediate bands (in light blue). This indicates that nitrate concentration is characterized by high gradient when its concentration is near the threshold values.

Especially in the map of Figure 8(a), it appears a distinct separation between little free zone at East (blue) and a large polluted area at West (red-orange-yellow) including Naples metropolitan area. This map accounts for areas exceeding 25 mg∙L⁻¹ for about 70% of the total surface.

In Figure 8(b), it is mapped the probability that nitrate concentration exceeded the 50 mg∙L⁻¹, with high probability that remains at West, although not all areas are strongly polluted. In this case, areas with very high probability are aligned along a diagonal line crossing Maddaloni, Acerra, Lufrano and Naples municipalities.

As already outlined [24], this trend takes into account the groundwater inflow that is carried out in correspondence of the foothills (cf. par. 2.1), but also the concentration of the pollutant that originates from the surface and effective infiltration. Due to the source of surface contamination, the pollutant load in the vicinity of the foothills is not particularly high, when compared to that of more central areas of the plain. This is due both to the limited extension of the foothills, on which the effective infiltration of rain takes place, and to a major capacity of denitrification of the plain subject to agricultural manure. In the most central part of the plain, there has been a general increase in the spread of nitrates due to the flow of water and potential pollution. Comparing land-use chart and nitrate probability maps, we can see an increase in hazard only where intensive agriculture mixes with more urbanized areas.

At the time of sampling, the only areas remaining free from high concentrations can be individuated between the surrounding of Palma Campania, Nola, Marigliano and Roccarainola municipalities. Local patterns with high nitrate concentration were also founded in Somma Vesuviana and Palma Campania, especially in PK [>50 mg∙L⁻¹].

However, no spatial pattern variability can be detected below 2000 m, due to nugget effect. This represents unexplained or random variance, which is either caused by variability of data that cannot be detected at the scale of sampling, or measurement errors within Campania Plain. Although the monitoring phase refers to the period of lean ground when less effective infiltration is present, the maps presented here suggest a dramatic pattern with still high probability of exceeding the above limits. Therefore, it is suspected that nitrate concentrations in well water can be high during any month of the year and the issue of nitrate contamination and health effects should not be ignored.

The error involved on the expansion of the information from point to landscapes through probability kriging es-

timation can be assessed through a quantitative estimation standard error of indicator and cross-validation [36].

The result of the cross-validation is presented within the statistical errors and scatter diagram (above and below panels in Figure 9, respectively). Mean is minor of 0.01 for PK [(a) and (b)] showing lack of systematic error. Since Root Mean Square Error is close to the Average Standard Errors (second and third row, respectively, in Figures 8(a) and (b)), mean is correctly assessing the variability in prediction. Root Mean Square Standardized error (RMSS) compare the error variance with the same theoretical variance such as kriging variance. Therefore, it should be close to 1, as resulting from the fifth row, where RMSS is 1.01.

If we consider OK experiment, measurements versus the predicted values of nitrate are in disagreement (see the scatter diagram of Figure 9(c)). Also, mean error is greater than 0.01, although the other errors are comparable with PK approach. However, a large bias remains in the relative scatter plot, indicating that OK is not suitable for interpreting spatial pattern in Campania Plain.