Spatial Dependence of Geochemical Elements in a Semiarid Agricultural Field: I. Scale Properties Akissa Bahri,* Ronny Berndtsson, and Kenji Jinno ABSTRACT Information on the spatial structure of soil chemical elements in field soils is needed to evaluate potential environmental hazards. Basic spatial properties of total soil contents of 20 major and trace elements were investigated for three different scales in a soil in northern Tun- isia. In total, 314 soil samples were taken on two adjacent 40 by 40 nr plots (one plot sludge-amendedand one without sludge). Theoret- ical lognormal probability distributions best, fit the empirical distri- butions for most of the elements. Assuming complete randomness, a relative error margin of 10%, and a probability level of 0.05, average values for the sampled scales can be estimated with a minimum num- ber of samples, which are 25 for Cd and Cr, 10 for Al, Be, Ca, Fe, Mg, and Pb, and five for other elements. The elements Al, Ca, and Fe can be sampled irrespective of scale and location (sludge vs. no sludge) with a resulting similar variance. Elements like Cd, Cr, Mg, Na, Ni, Sr, and V have a variance independent of location but are dependent on scale. Other elements, Ba, Be, Co, Cu, K, Mn, P, Pb, S, and Zn, have a variance that depends on both scale and location. I NFORMATION on the spatial structure of soil chemical elements in agricultural lands is needed to evaluate possible crop uptake effects, to calculate soil-water chemical and leaching characteristics of the soil, and to predict groundwater quality (McBratney et al., 1982; Bresler et al., 1981; Webster and Nortcliff, 1984; Archer and Hodgson, 1987). In spite of this and a documented large spatial variability of most soil chemical elements (e.g., Beckett and Webster, 1971), there have been few studies published on this topic. For practical applications as well as for theoretical modeling work, information is needed on the spatial dependence of major and trace element content and what mechanisms are governing this spatial depend- ence. Wopereis et al. (1988) studied the spatial variability of heavy metals in nonpolluted soil on a 1-ha scale. They found no spatial structure of heavy metal con- tents in the soil on this scale. Thus, they concluded that spatial variability is due to heterogeneity at a mi- croscopic scale. They also found, however, that by accepting a relative error margin of 10% and a prob- ability level of 0.05, mean values of Pb, Zn, Ni, Cu, and Cd could be estimated by sampling 4, 7, 7, 16, and 121 samples, respectively. Thus, Cd was the most difficult element to evaluate on a field scale, because of its high spatial variance. Soil properties are, however, usually spatially de- pendent (Webster and Nortcliff, 1984). Therefore, it is believed that soil-texture-dependent variables, such as trace elements, are also spatially dependent. The problem is, however, to find the scale of variability A. Bahri, Rural Engineering Research Center, Ministry of Agri- culture, B.P. no. 10, Ariana 2080, Tunis, Tunisia; R. Berndtsson, Dep. of Water Resources Engineering, Univ. of Lund, Box 118, S-221 00 Lund, Sweden; K. Jinno, Dep. of Civil Engineering (SUIKO), Kyushu Univ., 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812, Japan. Received 7 Dec. 1992. 'Corresponding author. Published in Soil Sci. Soc. Am. J. 57:1316-1322 (1993). and coupled mechanisms governing the dependence. Webster and Nortcliff (1984), accordingly, found that there is substantial spatial dependence for Fe and Mn, rather less for Zn, and little for Cu. As for the example above for heavy metals, by accepting a relative error margin of 10% and a probability level of 0.05, a mean value of Fe could be estimated by sampling about 25 samples on a 1-ha plot. Similarly, because of the greater spatial variability for Zn and Cu, these metals would need a much greater number of samples. With the above studies as a general background on element occurrence in soils, extensive soil sampling was planned and executed in two adjacent field plots at the Cherfech agricultural field research station in northern Tunisia. The objective of the sampling was to investigate total contents of major and trace ele- ments in sludge-applied vs. no-sludge soils and the spatial variability patterns at different scales. We de- scribe the soil, sampling strategy, and basic statistical properties of the 20 elements analyzed. Thus, our con- tribution is partly to introduce a geochemical data base specifically collected for spatial variability patterns of major and trace elements that have previously not been presented and partly to characterize the overall spatial variability of these elements depending on sludge ap- plication and the scale of the sampled soil area. We also used a geostatistical approach for characterizing the spatial dependence (Berndtsson et al., 1993). MATERIALS AND METHODS The experiments were done at the Cherfech agricultural field research station located at Cherfech, 25 km north of Tunis in the Lower Medjerda Valley. The Lower Medjerda Valley cli- mate is Mediterranean, characterized by mild winters receiving the major part of the annual rainfall (450 mm on average) and by dry and hot summers. Average annual potential evapotran- spiration calculated by the Penman (1948) equation is 1370 mm and water deficit is particularly important from May to October. During the 1988-1989 cropping season, rainfall was 195 mm and less than average (374 mm on average). During the following cropping season (1989-1990), rainfall was 362 mm. The soil conditions found at Cherfech in terms of texture and chemical composition are representative for the region (Research Center for the Utilization of Saline Water in Irri- gation, 1970). The USDA classification of the soil is Vertic Xerofluvent. The topography is a plane and nearly level and the microtopography in the two experimental plots was, at the sampling time, almost level. The soils are of fluvatile origin with a water table at rather shallow depth (average of 1.5 m). They have been formed on alluvial sediments of the Medjerda River and are alternately fine and coarse textured. Three ho- rizons may be distinguished in the soil profile: an upper layer (0-0.40 m) with a high content of clay and silt (70-85%), a second layer (0.40-0.90 m) of silty clay loam and silt loam with a prismatic structure, and a third one (1.0-1.3 m) of loam and sand. The soil bulk density varies between 1.33 in the upper layers to 1.62 Mg m~ 3 in the deeper ones. The upper 0.20 m of the soil profile appeared spatially rather homoge- Abbreviations: BEC, background emission concentration; DM, dry matter; CV, coefficient of variation; pdf, probability distri- bution function. 1316 Published September, 1993