E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

ava i l ab l e a t www.sc i enced i rec t . com

www.e l sev i e r. com/ loca te /eco l i n f

Computational uncertainty analysis of groundwater rechargein catchment

Nazzareno Diodatoa,⁎, Michele Ceccarellib

aMonte Pino Research Observatory on Climate and Landscape, GTOS\TEMS Network–Terrestrial Ecosystem Monitoring Sites(FAO–United Nations), 82100 Benevento, ItalybResearch Center on Software Technologies—RCOST, University of Sannio, via Port'Arsa, 11-82100 Benevento, Italy

A R T I C L E I N F O

⁎ Corresponding author.E-mail address: nazdiod@tin.it (N. Diodato

1574-9541/$ - see front matter © 2006 Elsevidoi:10.1016/j.ecoinf.2006.02.003

A B S T R A C T

Article history:Received 25 September 2005Received in revised form31 January 2006Accepted 15 February 2006

In this paper, a computational environinformatics (environmental informatics) operation formapping the groundwater climatological recharge in regional sub-basin is presented. It isbased on a soil–water balance (SWB) and spatial statistics integrated in a GIS environment.Mediterranean is a region with large demands for groundwater supplies. However, watercatchment data are affected by large uncertainty, arising from sampling and modelling,which makes predicting groundwater recharge difficult. Geostatistic tools for GIS are able toincorporate imput data (coverages, shape files, raster, grids) in water data processing,allowing formodeling spatial patterns, predictionatunsampled locations, andassessment ofthe prediction uncertainty in a meaningful way that can provide a more suitableinterpretation. An issue model of linear kriging, termed as lognormal kriging in form of aprobabilitymap (LKpm), is emphasized in this studybecauseasoftdescriptionof the rechargein terms of probability is consistent to mitigate the uncertainty of the SWB estimates. Theapproach was applied to a test site in the Tammaro agricultural basin (South Italy) for theincorporationof change of support inwater rechargedownscalingmodeling. So, the estimateof uncertainty at unsampled locations, via LKpm, was used to explain the probability ofexceeding a value range of the water recharge samples' distribution. In this way, theprobability of exceeding the median recharge (215 mm year−1) is low in the southeasternportion (48%) of the basin area and high in the northwestern remaining portion (52%).

© 2006 Elsevier B.V. All rights reserved.

Keywords:Soil–water balanceGroundwater rechargeGIS-geostatistcsProbability mapsSouthern Italy

Environmental modelling applications provide an impor-tant means by which scientists can interact with andinfluence policy at local, regional, national and interna-tional level. Wainwright, J., and Mulligan, M. (Eds.), 2004.Environmental Modelling. JohnWiley & Sons, Ltd., Chichester.

1. Introduction

In environmental conditions occurring in wet period of theyear, precipitation surplus is the most important water

).

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resource for natural groundwater recharge in mountainousareas and agricultural basins. Groundwater recharge is theaddition of water, via transmission through superficialmaterials, to the saturated sub-surface. Mountains hold keywater resources, especially in a Mediterranean environmentwhere precipitation is scarce or moderate, evapotranspirationis intense (Beguería et al., 2003), and where there is a strongdemand for groundwater supplies, such as resources key toeconomic development. Several efforts have been launched todevelop models and sustain water resource decision supportsystems. However, knowledge of the water reservoir in thefirst place must answer to the question expressed by Penman

.

378 E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

(1961), “What happens to the rain?” Monitoring of waterbudget components is useful for comparing the fate of waterinputs among ecosystems (Brye et al., 2000), and theirmodelling is an effective technique to assist managers anddecision-makers in the assessment of soil–water balance(SWB). Greater emphasis is being placed on the use ofconceptual and physically based models for the prediction ofgroundwater recharge (Ragab et al., 1997; Lohmann et al., 1998;Arnold et al., 2000; Grismer et al., 2000; George et al., 2001;Chen et al., 2002; Drécourt and Madsen, 2002; Jones andBanner, 2003; Wang et al., 2004). However, quantitative spatialdescriptions of the phase of the hydrologic cycle remainalways very complicated and subject to a great deal ofuncertainty (Sophocleous, 1991; Singh and Woolhiser, 2002).A large number of papers have been attributed to some extentto the spatial variability in basin of environmental propertieswhich in turn influence predictions of groundwater climato-logical recharge models, such as rainfall (Pardo-Igúzquiza,1998; Chaubey et al., 1999; Campling et al., 2001; Deirasme etal., 2000; Gómez-Hernández and Cassiraga, 2000; Goovaerts,2000; Diodato and Ceccarelli, 2005a), evapotranspiration(Martinez-Cob, 1996; Dalezios et al., 2002; Moges et al., 2002;Szilagyi, 2002), runoff (Woods et al., 1997; Olivera andMaidment, 1999; Hernández et al., 2000; Carey and Woo,2001; Jetten et al., 2003; Sankarasubramanian and Vogel, 2003;Leblois et al., 2004) and hydrogeological features (Triantafiliset al., 2003; Vermeulen et al., 2004) data.

Catchment have been recognized as natural units for waterresourcesmanagement (Heathcote, 1998), in which hydrologicprocesses and their spatial non-uniformity are defined byclimate, topography, geology, soils, vegetation and land use,and are related to the basin size (Singh and Woolhiser, 2002).The assessment of the environmental condition in watercatchment requires integration of information and analysis tofurther decision-making, a requirement that can be addressedusing the data-management facilities of geographical infor-mation system (GIS) (Aspinall and Pearson, 2000). However, itoften deals with data sets which are relatively small andaffected by sampling gaps and errors. Processes of expoundingcomplex geographical phenomena into a distinct elementaryarea require therefore a change of scale towards a finerscaling, referred to as downscaling (Bernert et al., 1997; Stein etal., 2001; Renschler, 2003). Regional-scale sub-basin arecharacterized typically by natural variability in climatic andland-surface features (Wooldridge and Kalma, 2001). Especial-ly, hydroclimatological features are usually known only at thelocations of observations. To estimate it at unsampledlocations over the whole basin (and the expected waterreservoir input by precipitation recharge), a procedure isrequired for downscaling and so to predict the variability ofspatial hydroclimatological groundwater recharge. Someresearches proved that uncertainty assessment in geographicdata and its consequences for water resource decisions madeusing GIS is very incomplete (Wilson et al., 2000). Instead, themutual benefits of linking GIS, statistics and geostatisticsshould be mostly appreciated. In particular, the methods ofgeostatistics use the stochastical theory of spatial correlationboth for scale change and for apportioning uncertainty(Journel and Huijbregts, 1978; Isaaks and Srivastava, 1989;Goovaerts, 1997; Burrough, 2001). The application of geosta-

tistics in the geosciences has spread from the original metalmining applications to energy resource and industrial mineralwith contributions of the French engineer Georges Matheronin the early 1960s. The applications to many other areas ofearth science and environmental, hydrogeological and geo-technical applications, successively occurred with the adventof high-speed computers (Houlding, 2000). Although the scopeof geostatistics has included hydrogeological processes, gen-erally the infiltration rate and groundwater recharge geosta-tistical downscaling modelling is not the unique problem thatappears in practice. There are issues where the explicitestimation of the drift (Gelhar, 1993; Márkus et al., 1999),gradients and patterns at meso- and or random patterns atlocal scales (Fortin et al., 2002; Makkawi, 2004), multivariatespatial processes (Stein et al., 1991; Ersahin, 2003), and outliervalues (Nolan et al., 2003) are important. For example,universal kriging was developed for problems of spatialinterpolation if a drift seemed to be justified to model theexperimental data (Cressie, 1993a,b). But its use has beenquestioned in relation to the bias of the estimated underlyingvariogram (Pardo-Igúzquiza and Drowd, 1998; Wackernagel,2003). A related major area of interest and application ofnonparametric estimation of conditional distribution is theindicator kriging techniques, that is seen as mainstream andconventional the predictable refuge of those who simply needrobust interpolations of erratic spatial phenomena (Srivas-tava, 1997). However, indicator kriging systemdoes not alwaysguarantee that probability estimates satisfy 0≤F[Z(u)]≤1 ormay not follow the order relations of a conditional cumulativedistribution function (Vargas-Guzman and Dimitrakopoulos,2003). Alternatively, when the assumption of multivariatenormality is satisfied, variants of linear kriging algorithms canbe used to create probability and quantilesmaps (Krivoruchko,2001).

In this paper a geostatistical approach, called lognormalkriging (Dowd, 1982) in the form of a probability map (LKpm),was applied to a test site in the Tammaro agricultural basin(South Italy) for a spatial uncertainty assessment of ground-water climatological recharge based on long-term SWBmodel.Modeling of SWB in wet climate forms the basis to determinegroundwater recharge. In this way, SWB model involve ameasurement and georeference of some hydroclimatologicaland land-cover variables at a single n locations; which, in thecase study, equal to 31 observation points randomly distrib-uted. Afterwards, LKpm, incorporating change of support inuncertainty modeling, was used to map a water reservoirrange set of the distribution.

2. Research design for modelling and spatialanalysis

2.1. Point groundwater recharge estimates

Groundwater recharge is the rate at which infiltrating watermoves across the water table. The range of recharge rates at asite can be estimated using different approaches, such asSWB, one-dimensional soil water flow, groundwater levelfluctuation, groundwater balance and isotope and soluteprofile techniques (Kommadath, 2000; Scanlon et al., 2002).

379E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

Among these we use the SWB method which was guided bythe available data, economy and objectives of the study. In ageneral form, the long-term SWB of a particular location in thebasin can be written, following Finch (2001), as:

P−AET−ðQon þ QoffÞ−R ¼ DS ð1Þ

where P is precipitation; AET is actual evapotranspiration; Qon

and Qoff are, respectively, surface runoff and sub-surface flow;R is recharge; and ΔS is the change in storage. All componentsare given as rates in mm year−1. Eq. (1) can be rearranged tosolve for recharge:

R ¼ P−AET−ðQon þ QoffÞFDS ð2Þ

Sub-surface flow and change in storage are difficult tomeasure and are not used in this study. Sub-surface flow is aquantity small and in first approximation can be ignored. For amean annual water budget over a long period of years, ΔS≈0 isnot an unreasonable assumption, especially under a Mediter-ranean climate, and has been a standard procedure used inother studies (Roads et al., 1994; Louie et al., 1994). Therefore,simplifying the Eq. (2) we obtain:

R ¼ P−AET−Qon ð3Þ

Thus, the main variables that control hydroclimatologicalgroundwater recharge in a typical basin, as the one understudy, are: precipitation, actual evapotranspiration and sur-face runoff (Fig. 1). These factors are closely related to changesin climate, land-use/plant cover and soil permeability.

2.1.1. Evapotranspiration estimateIn the SWB model, actual evapotranspiration AET is deter-mined on the basis of the relations derived from long-term

Fig. 1 –Spatial soil–water balance model showing the river landscthe Tammaro basin (after Beekman and Xu, 2003).

hydrologic water budget data from over 250 watershedsaround the world (Zhang et al., 2001):

AET ¼1þ w

PET0

P

� �

1þ wPET0

P

� �þ P

PET0

� �26664

37775d P ð4Þ

where, w is the plant-available water coefficient which canobtained from tables (Lu et al., 2003) and reflects the relativedifferences of water use for transpiration; P is the annualprecipitation amount; and

PET0 is annual reference evapo-

transpiration amount.Many methods exist for estimating reference evapotrans-

piration, which can be found in Allen et al. (1998). However, itis recognized that the more complicated formula in notnecessarily the best one (Droogers and Allen, 2002). Indeveloping countries, as in the land under study, whereaccurate data collection is difficult, the account of Hargreavesmethod (Hargreaves et al., 1985) is desirable, rather thanattempting to set up a complex weather data collectionsystem. The Hargreaves method (HG), using as predictorsonly mean air temperature, mean daily temperature rangeand extraterrestrial radiation, has been tested using somehigh quality lysimeter monthly data representing a broadrange in climatological conditions (Hargreaves, 1994). Howev-er, it is possible that the accuracy of this model can beimproved by adjusting the parameters to local conditions. Inthis way, the result was the following form for the HG (Diodatoand Ceccarelli, 2005b):

ET0ðmÞ ¼ qRa

kðTavg þ 17:8Þd

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif ðDTRÞ

qð5Þ

where ET0(m) is the monthly reference evapotranspirationamount (mm); Ra is average daily extraterrestrial radiation (MJ

ape grid system (right) and modeling elementary area (left) of

380 E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

m−2 d−1) which can obtained from tables (Allen et al., 1998);λ=(2.501− (2.361·10−3) ·Tavg), which is the latent heat of thevaporization (MJ kg−1); Tavg is average daily air temperature(°C) defined as the average of the mean daily maximum(Tmax) and mean daily minimum (Tmin) temperature;f ðDTRÞ ¼ Tmax− 19d 1−cos m−1

12−m

� �� � −wddwet is the daily tempera-

ture range function in that Tmin (term in brace brackets) wascorrected for the mth month; dwet is the rainy days' numberin a month with rainfall per day≥1.0 mm; empiricalcoefficients ρ and w, equal to 0.00143 and 0.1, respectively,were calibrated for Italian Apennines climate on monthlycalculations of ETo by regression analyses (r2=0.95 significantat p=0.01) versus evapotranspiration measured from modi-fied Atmometer and Penman–Monteith jointed dataset. Themodified Atmometer was recently compared with Penman–Monteith ET in southern Italy (Magliulo et al., 2003) and avery close agreement has been observed. So that annualreference evapotranspiration amount may be simply com-puted as:

PET0 ¼

X12m¼1

ET0ðmÞd dm ð6Þ

where m=1 (January) to 12 (December), and d is the daysnumber in a month.

2.1.2. Surface runoff estimateNumerous field studies have indicated that surface runoffin wet regions is mainly produced by saturation excessrunoff (Hernández et al., 2000; Carey and Woo, 2001; Ao etal., 2003; Melesse et al., 2003). This means that the spatialdistribution of soil moisture storage will result in a differentsurface runoff production. For a large area, the saturationexcess runoff will occur in a certain portion of the largearea where there is no soil moisture deficit (Liang and Xie,2001; Sun and Deng, 2004). The key science question is howthe long-term hydrologic response of the basin can bederived purely from auxiliary climate and pedologic data. Toanswer to question, Vandewiele et al. (1992) have intro-duced a parsimonious but robust rainfall–runoff model forhumid basins, including the split sample technique whichhas been applied for demostrating the model's abilitytowards extrapolation and its insensitivity to calibrationperiod. The variables included precipitation (P), actualevapotranspiration (AET), effective wetness ratio (P /AET),and soil moisture (s). According to these results, we

Fig. 2 –River basin (a), and discretized river

estimate surface runoff (Qon) utilizing the approach pro-posed by the Authors, as:

Qon ¼ adsbd P−AETd 1−exp −P

AET

� �� � �ð7Þ

where coefficient b was placed equal to 0.5 according toVandewiele et al. (1992) and coefficient awas arranged equal to0.065 on long-term runoff data of the Tammaro basin; s is thetotal available soil water in the root zone (mm), which can befounded in Diodato and Ceccarelli (2004). The disaggregationapproach towards finer-scale hydrological modeling, usingaveraged parameter values, should be inadequate for repre-senting runoff processes at a small scale. However, in theTammaro basin runoff ratio is significant only during theyear's wet periods. In these conditions runoff was not affectedby grid size, according to Kuo et al. (2002).

2.2. Theory review on support change within geostatisticaldownscaling

Given a river basin of areaA in Fig. 2(a) that is approximately inclose hydraulic contact with the aquifer, the expected annualinput water reservoir (WR) by precipitation recharge is givenby:

WR ¼ZARðsÞdds ð8Þ

where R(s) is the value of the hydroclimatological groundwaterrechargemean at spatial location s (s denoting the coordinatesof a point in the plane); R(s) is only known at those pointswhere meteorological and hydrogeological observations areavailable, and then it must be estimated at the non-sampledpoints. In practice, the integral (8) is evaluated using thediscrete sum approximation:

WR ¼XNj¼1

RBd ðsjÞ ð9Þ

where the area A of the river basin has been discretized in Ncells of equal area B in Fig. 2(b); and RB(sj) is the areal averagehydroclimatological groundwater recharge mean over cell Bwith centroid sj. It is clear that RB(sj) is an areal averageestimate:

RBd ðsjÞ ¼1B

ZBðsjÞ

RðsÞd ds ð10Þ

basin (b) (after Pardo-Igúzquiza, 1998).

Fig. 3 –Geographic location, area and data map collection of the Tammaro basin.

381E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

where B is called the support of the estimate, being:

A ¼XNj¼1

BðsjÞ ð11Þ

the whole region, and B(sj) denotes the support B at grid-pointsj. The change-of-support problem remains a major challengeto geostatisticians. According to Pardo-Igúzquiza (1998), blockkriging provides estimates of Eq. (10) from the experimentaldata with punctual support (for example data measured inobservation sites):

RB⁎ ðsjÞ ¼

Xna¼1

kadRðsaÞ ð12Þ

with R(sα) being the climatological groundwater rechargemeanat the point-station sα. The result is that, at each point regular

lattice (sj), the expected value (ordinary linear kriging esti-mate), R⁎B(sj) is obtained. If a soft interpretation of the results isof interest (as in the case under study), a particular extention ofordinary linear kriging model, such as Lognormal Kriging inform of probability map (LKpm), must be adopted in order toestimate the mean value rather than the probability ofexceeding a threshold value.

2.3. Lognormal Kriging approach — LKpm

Most geostatistical researches in hydrogeological science aimat estimating soilwater properties at unsampled places andmapping them. Kriging is a generic name adopted by thegeostatisticans for a family of generalized least-squaresregression algorithms (Webster, 1996). There are different

Fig. 4 –Histograms for the recharge original data (a), and afterlog-transformation (b).Tab

le1–Orininal

andtran

sfor

med

data

forso

il–water

balance

values

Original

data

[z]

137

139

263

273

288

159

100

236

198

3917

033

233

929

176

682

122

5741

714

958

123

109

239

247

9722

328

145

421

529

2Lo

g-tran

sfor

med

data

[ln(z)]

4.9

4.9

5.6

5.6

5.7

5.1

4.6

5.5

5.3

3.7

5.1

5.8

5.8

5.7

6.6

4.4

4.8

4.0

6.0

5.0

4.1

4.8

4.7

5.5

5.5

4.6

5.4

5.6

6.1

5.4

5.7

382 E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

kriging algorithms, andmost of themare reviewed in Kitanidis(1997), with references to hydrogeological applications, inGoovaerts (1997), with references to soil applications and inChilès and Delfiner (1999), with references to Earth sciences.

For some kriging models only a deterministic estimateper cell is needed; for others, as in decision-making, oneneeds to know the local uncertainty associated to theestimates (Burrough and McDonnell, 1998). To achieve thisgoal, a type of linear kriging, called lognormal kriging (Dowd,1982; Cressie, 1993a,b) in form of probability map (LKpm),can be adopted. In this way, the data z(s1), z(s2),…, aretransformed to their corresponding natural logarithms, sayy(s1), y(s2),…, which represent a sample from random variableY(s)= ln Z(s). Since log-transformated recharge variable hasapproximately a normal distribution (see Section 4.1) we canassume that recharge lognormally distributed. The variogramof Y(s) is computed and modelled and then used thetransformed data for estimate Y at target points by ordinarykriging (OK). If we denote the kriged estimate at s0 as Y⁎(s0) andits variance as σ2(s0), then the formulae for the back-transformation of the estimate is, for OK (Webster and Oliver,2001, p. 180):

ZOK⁎ ðs0Þ ¼ exp YOK

⁎ ðs0Þ þ r2OKðs0Þ2

−w

)(ð13Þ

Fig. 5 –Voronoi map for mean (a) and standard deviation (b).

Fig. 6 –Examination of bivariate data distribution after logtransformation: indicator covariances for 0.2 (a), 0.4 (b), 0.6 (cand 0.8 (d) quantiles.

383E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

where ψ is the Lagrangemultiplier in the ordinary kriging. Theestimation variance of Z(s) is (Olea, 1999, p. 44):

r2OKðs0Þ ¼Xni¼1

kiCðsi−s0Þ þXnj¼1

kjCðsj−s0Þ−Xni¼1

Xnj¼1

kikjCðsi−sjÞ

ð14Þwhere λi and λj are weight vectors associated with thedistance i=h and j= i+h respectively, and calculated bysolving of the kriging simultaneous equation system (John-ston et al., 2001); C is the covariance function of Z(s). In thiswork, spatial patterns are described in terms of averagesimilarity between data separated by a vector h (seeGoovaerts, 1997 p. 86 for formulas), which is measured bythe experimental covariane function C(h). As expected, C(h)quantifies the commonly observed relationship between thevalues of the samples and the samples' proximity (Glackenand Blackney, 1998).

Finally, lognormal kriging in form of probabilitymap can beadopted for a soft description of climatological recharge, used

in this study to mitigate the uncertainty of the SWB estimates.In this way, the practice of LKpm involves calculating andmodeling covariance function at a range of threshold valuesarranged in order of increasing magnitude. In this paper, theyare the set of recharge data arranged from the small to thelarge data corresponding to zk=(100, 150, 215median, 250, 300

)

Table 2 – Parameters of covariogram models ofgroundwater recharge data

Nuggeteffect

Structure model

Partial sill Range (m) Function

0.0617 0.358 34,821 Hole effect

384 E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

and 350 mm y−1), where for 215median we mean that themedian of distribution of zk is 215.

3. Case study: data collection and areadescriptions

The demonstration site (Tammaro basin) is a rural moun-tainous region of the southern Italy (Fig. 3), whose primaryeconomic resource is agriculture. The basin of Tammaroriver flow down into the great basin of Volturno river,occupying its surface in a ratio of about 12% (about 675 on5600 km2). Its aquifer has a horizontally almost homoge-neous geological structure, being covered by a soil layervariable between 0.0 and 1.3 m. The highly permeablematerial is organized in localized areas connected with themain calcareous relief. Altitudes range from 128 to 1429 m a.s.l., with average spatial slope of about 3%; only the 19% ofthe area has a slope mean great ranging from 13% to 15%.The raingauge stations indicate a moderate rainfall regime:annual precipitation is around 900 mm in the part south ofthe basin, ranging from 1000 to 1400 mm in the remainingpart, while exceeds 1400 mm only on northwestern water-shed line. Rainfall is concentrated above all between mid-autumn and end of spring, but most intense precipitation, asshower and thunderstorm, happened in the cold season. Therainfall, high evapotranspiration losses and mild slopesenable a moderate infiltration, whereas have a limitingeffect on the surface runoff in this watershed. Meteorologicaland hydrogeological data used in the work were sampled at31 observation sites in a 60,000 by 55,000 m rectangular area

Fig. 7 –Experimental variogram cloud after log-transformationwianisotropic search ellipse with weights (in %) that are showed fotarget point (c).

covering the basin (Fig. 3). The meteorological data corre-spond to the averages of the monthly data from 1955 to 1994recorded from stations of the former network of the ServizioIdrografico and Mareografico Nazionale (SIMN, 1955-1999),and from additional UCEA-RAN network.

The natural vegetation of these zones of the ItalianApenninic inland is that typical of the Mediterranean mountain-ous and sub-mountainous sector. The combination of wet winterand dry summers produce a termophyla vegetation, such asQuercus pubescens, Colutea arborescens, Acer campestre and, forhigh-mountainous sector, Fagus sylvatica, Acer obtusatum andIlex aquifolium (Blasi et al., 1988).

4. Results

4.1. Exploratory data analysis and management

Exploratory data analysis is an important statistic support toinspect and explore data before deciding to transform themfor analysis and illustrates what can be achieved by takinglogarithms of single variates and by principal componentanalysis of multivariate data (Webster, 2001). Then, the firststep in spatial analysis is checking the raw data for drifts andoutliers (Szlilágyikishné et al., 2003) and, eventually, forbivariate normal distribution. Outliers and skewed data inspatial sense can be detected by frequency distribution andthird moment (g) about the mean and the standard deviation.

Since the recharge data were still skewed (Fig. 4a) withg=1.826, square root and lognormal transformations wereconsidered. Logarithm transformation provided a less skeweddata (Fig. 4b and Table 1) than square root transformation,−0.361 and 0.650, respectively. Drift analysis has shown theexistence of a nonrandom (deterministic) component inspatial distribution of data: the moderate gradient of therecharge data occurs along the northwest to southeastdirection. The northwest to sutheast drift in recharge datacan be attributed to persistent rainfall on themountains of theCampania Apennines (Diodato, 2005). Visual inspection of theVoronoimapwith non-constantmean and standard deviation

th Hole effect model black curve (a), variogram surface (b), andr data control points (in dark grey) used for estimation at the

385E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

values (Fig. 5), provide additional evidence of non-stationarityin the data. Nevertheless, we felt that the stationarityhypothesis does not hold for the whole region, but onlylocally. In this way, to make a robust assumption ofhomogeneity of variances, the concept of process stationarityis replaced by a stationarity of the governing influence relatingthe local hydrology processes and the local anisotropyneighbor (see also the end of the Section 4.2). In similarsituation, Ordinary kriging is recommended for interpolation(Journel and Rossi, 1989).

Ordinary kriging can be easily extended to probabilitymapsif a consistent set of bivariate distribution can bemodeled (seeJohnston et al., 2001 pp. 206–207). The Fig. 6 shows thattheoretical curve (dark gray line) is similar to the logarithmdata transform (light yellow curves) leading to a distributionwhich is closer to the bivariate normal distribution.

Fig. 8 –Kriged probability map of groundwater recharge correspodata.

4.2. Spatial structural modeling

A model of regionalization was fitted using an iterativeprocedure developed by Johnston et al. (2001), and composedby two stage. Stage 1 begins by assuming an isotropic model,and it executes a first run of the experimental spatialstructures on the scaled data z(sα)= (z(sα)−z¯) ·σ−1, where z(sα)is used to denote the jth measurement of a variable at the αthspatial locations sα, and σ is the sample standard deviation.With stage 2 any parameter, such as number of lag (assumedequal 7), lag size h (assumed equal 5000meters), range awhichrepresent the limit of spatial dependence, nugget (equal to0.0617) and partial sill (0.358) is calibrated interactively. Alsoat this stage it has been assumed a isotropic covariogrammodel (Table 2). However, this is critical subject as it was notpossible to verify the contrary because of small sample size.

nding to 100, 150, 215, 250, 300 and 350 mm year−1 threshold

Fig. 9 –Coverage of the Tammaro basin for high probability(P>0.5) of a range of recharge threshold data.

386 E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

In this way, Fig. 7a shows the experimental covariogramcomputed from the 31 data of recharge, with Hole effectpermissible models fitted. Covariogram values decrease withthe separation distance, reflecting the assumption thatrainfall recharge data nearby tend to be more similar thandata that are farther apart. The covariogram reaches from34,821 m, before dipping and fluctuating around a sill value.Unidirectional covariograms were modelled as a combina-tion of two distinct spatial structures: nugget variance and aHole effect structure:

CðhÞ ¼ 0:0617 h ¼ 00:0617þ 0:358dHoleEffectðjhj;aÞ h > 0

ð15Þ

where HoleEffect(|h|,a) represent a dimensional Hole effectvariogram of unit sill with practical ranges given by thecircle with a=34,821 m.

The function Hole effect equal to (Johnston et al., 2001):1−sin 2Pjhj

að Þsin 2Pjhj

að Þ �

.Because covariance function is used for mapping, we must

instruct the program how to gather and use the control pointduring interpolation. With the surface covariogram support(Fig. 7b), we designed a search anisotropic neighborhood (Fig.7c), and specified the lenght of the ellipse search radius (min:10,000 and max: 14,000 m, respectively), the angle with majordirection of anisotropy (10°), the number of sector (four), andthe number of data points for sector (two).

4.3. Spatial pattern of groundwater recharge estimation

Fig. 8 shows kriged probability maps based on the threshold ofrecharge 1000×1000 m grid. The maps indicated that thephenomenon accounted by LKpm is not smooth (i.e., rechargeindicator values change strongly with the distance). In thisrespect the covariogram with nugget effect was selected asthe base model for calculations, so that covariogram modelsestimations which differ significantly from the known valueeven at short distances. Spatial pattern reaches highprobability of recharge values in the northwestern of theTammaro basin. Because in this basin portion precipitationvalues are two times higher than the actual evapotranspi-ration values, in the period October–May, there is aconsiderable moisture in the soils. In this way, the coverageof the Tammaro basin for a probability range of exceeding aset of recharge threshold values were displayed in Table 3.For the median recharge value (215 mm year− 1) thehistogram of Fig. 9 showed that it is high in the northwest-

Table 3 – Statistics of the coverage (%) of the Tammarobasin for a set of probability of a range of rechargethreshold data: 100…350 mm

Probability values range

0.0–0.1

0.1–0.2

0.2–0.3

0.3–0.4

0.4–0.5

0.5–0.6

0.6–0.7

0.7–0.8

0.8–0.9

0.9–0.10

100 1 3 4 13 2 4 15 3 5 70150 28 8 2 1 1 2 16 4 4 44215 34 6 3 2 3 3 10 5 9 25250 40 7 6 5 3 2 8 13 7 8300 45 6 4 3 2 10 9 7 7 7350 54 6 7 10 8 5 3 2 3 1

ern area (48%) and low in the southeastern of the basinremaining portion (52%).

Hole effect model implies that the variations of precipita-tion recharge reflects possibly cyclic hydrogeological phe-nomena, due to the presence of topographic characteristics(e.g. relief and land-cover), according to Journel and Huijbregts(1978). This finding suggest that increasing variability intopographic properties, producing a mosaic pattern of sourceand sink area, may prove to be an effective difficulty in themanagement for groundwater recharge control.

4.4. Error assessment and cross-validation results

The major limitation of the SWB-residual approach is that theaccuracy of the recharge estimate depends on the accuracywith which other components in the water budget equationare measured. In the our study this limitation not is criticalbecause the magnitude of the recharge rate is moderaterelative to that of the other variables, resulting equal 23% (R /Pratio), 49% (R /AET ratio), and 81% (R /Qon ratio).

The error involved on the expansion of the informationfrom point to landscapes through indicator kriging estimationat fine grid can be assessed through a quantitative estimationstandard error of indicator and cross-validation. The result ofthe cross-validation is presented within the statistics of theexperimental errors and scatter diagram. In accordwith Isaaksand Srivastava (1989) and Johnston et al. (2001), the cross-validation removes each data location, one at a time, andpredicts the associated data value. In prediction standard error

Table 4 – Statistics of the experimental errors computedfrom recharge 31-data

Threshold values(mm year−1)

100 150 215 250 300 350

Prediction standard errorMean (LK) 0.04 0.00 0.00 −0.01 −0.01 −0.02Root-mean-square

(LKpm)0.35 0.30 0.26 0.31 0.31 0.30

Root-mean-square(IK)

0.31 0.40 0.35 0.41 0.31 0.28

For Root-Mean-Square error are compared Lognormal kriging(LKpm) and Indicator Kriging results (in bold are reported the bestvalues).

Fig. 10 –Cross-validation scatter diagram of recharge 31-data a with range of cut-offs values zk=100 (a), 150 (b), 215 (c), 250 (d),300 (e) and 350 mm year−1 (f).

387E C O L O G I C A L I N F O R M A T I C S 1 ( 2 0 0 6 ) 3 7 7 – 3 8 9

of the Table 4, mean value equal to (−0.004)− (+0.089), showinglack of systematic error. Analyst integrated in ArcMap-GISsoftware, had showed that LKpm performed better than thetypically used, such as indicator kriging (Table 4, rows 4 and 5).Also in the scatter diagram of Fig. 10, actual values of rechargeversus the predicted probability indicators are in good accord.

5. Conclusions

Water percolation and surplus are normal recurring hydro-geoclimatological phenomena that vary in space, time, andintensity. They may interest basin at local scales for shortperiods or cover broad regions for more months, moving fromsoil surface to ground water in agricultural landscape thatneeded of water reservoir. This paper has presented aprobabilistic approach to assess the level of recharge in asub-regional basin of south Italy. It is based on use of thegeostatistical technique to yield a series of stochastic images,which represent equally probable spatial distributions of thegroundwater recharge across the site. Thismodel can calculatethe probability of exceeding some specified recharge thresh-olds values and the resulting probability map can be used toquantificate water reservoir. The novelty of the proposedapproach consists in the lognormal linear kriging probabilisticassessment of recharge, which means recognizing explicitlyand to incorporate uncertainty in site characterization.

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