The SPAC Analytics fitting tool enables the user to look for piecewise or linear curve fits between two parameters, and to display the fits of individual plants or groups.
In drought experiments, the main use of the piecewise linear fit is to detect the critical theta (Ɵcrit) point at which soil water content becomes a limiting factor for plant transpiration. Ɵcrit is an important parameter for examining the water-balance behavior of plants and the ability of roots to take full advantage of any available water. See Gosa, S.C. et. al., 2019 for more details.
The piecewise linear fit formula in use is the following:
In which, E represents the Y-axis value, b represents the slope of the curve (in the relevant part of the curve), and Ɵ represents the X-axis value, which is the soil water content in Ɵcrit as mentioned above.
The piecewise curve fit could be adjusted by restricting the fit boundaries:
The recommended method to find the Ɵcrit is to place a transpiration-related parameter (Daily transpiration, Transpiration rate, E, Gs canopy) on the Y-axis and a soil water content parameter (VWC from a soil sensor or VWC calculated based on weight) on the X-axis during the drought treatment period only (adding points outside the drought period will give excess weight to the first part of the formula, where Ɵ≥Ɵcrit).
See the following screenshot for a piecewise fit plot example:
*Group 1 is composed of 7 plants over 12 days (84 points).
The fit output:
All results can be exported to CSV by clicking the export button at the top right corner of the plot. Two separate files will be downloaded: the fit data points and the fit output.
Linear regression fit can also be calculated and displayed. The plot is straightforward:
A basic output is presented also for the linear fit:
