Statistical Analysis of Crop Yield‐Soil Water Relationships in Heterogeneous Soil under Trickle Irrigation

Field data of bell pepper ( Capsicum frutescens ‘Maor’) yield ( Y ), soil water pressure potential ( P ), and salinity (EC) obtained under trickle irrigation, and of two soil hydraulic parameters ( K 1 and α), were used to analyze spatial variability of these properties and its impact on relationships between crop yield and soil properties. Both conventional statistical analysis methods and spatial structure analysis methods were used. With the conventional methods, observations of each property were considered as statistically independent regardless of their spatial position in the field. Results of multiple regression analysis suggest the variability in K 1 and α is responsible for about 25% of the variabilities in both P and EC, which in turn, are responsible for < 25% of the variability in Y , when experimental data from the entire field are considered. With the spatial structure methods, a variogram was used to investigate spatial structure of different properties, and a cross‐variogram was used to investigate spatial dependence of P and EC on K 1 and α and spatial dependence of Y on P and on EC. Results show field spatial structure affects the relationships between different properties over distances which were related to the respective ranges of direct variograms of pertinent properties. The characteristic length of field spatial structure (in terms of integral scale, J ) varied between J = 25 m ( K 1 ) and J =78 m (α) with an average of J =43 m . The direct variograms of properties were used to calculate kriging estimates of pertinent properties, which in turn, were used for two subsequent analyses. In the first analysis, kriging estimates obtained for a square domain (43 by 43 m in size) moving over the entire field were used to calculate the correlation between different properties at different parts in the field. The analysis showed that in some parts of the field variability in K 1 and α was responsible for about 90% of the variabilities in both P and EC, which in turn, were responsible for about 90% of the variability in Y . In the second analysis, kriging estimates of Y , P and EC obtained for regions in the field which are associated with a constant saturated zone in the vicinity of the trickle emitter (in terms of its radius r u = r u ( K 1 , α; Q ); Q being trickle emitter discharge) were used to analyze the dependence of Y on P and on EC. The analysis showed that in regions which were associated with relatively small values of r u ( r u < 0.05 m) the variability in P and EC is responsible for > 0.8 of the variability in Y . In regions which were associated with relatively large values of r u ( r u >0.08 m) and a relatively large leached zone, it was not soil water pressure or salinity, but other factors that most influenced yield.