production and soil salinity in the field production and soil salinity in the field A common way to present crop – salinity data is according to the
Maas–Hoffman model (see above figure): initially a horizontal line connected to a downward sloping line. The breakpoint is also called threshold or tolerance. For field data with random variation the tolerance level can be found with
segmented regression. As the Maas-Hoffman model is fitted to the data by the method of
least squares, the data at the tail-end influence the position of the breakpoint. Another method was described by Van Genuchten and Gupta. It uses an inverted S-curve as shown in the left-hand figure. This model recognizes that the tail-end may have a flatter slope than the middle part. It does not provide a sharp tolerance level. Using the Maas–Hoffman model in situations with a flat trend in the tail-end may lead to a breakpoint with a low ECe value, owing to the employment of the condition to minimize the deviations of the model values from the observed values over the entire domain (i.e. including the tail-end). Using the
logistic sigmoid function for the same data applied in the van Genuchten-Gupta model, the curvature becomes more pronounced and a better fit is obtained. A third model is based on the method of partial regression, whereby one finds the longest horizontal stretch (the range of
no effect) of the yield-ECe relation while beyond that stretch the yield decline sets in (figure below). With this method the trend at the tail-end plays no role. As a result, the tolerance level (breakpoint, threshold) is larger (4.9 dS/m) than according to the Maas-Hoffman model (3.3 dS/m, see the second figure above with the same data). Also a better fit is achieved. ==Augmenting tolerance==