*2.4. Turfgrass Water Response Function (TWRF)*

A multiple linear regression model (with interactions and quadratic terms included) was used to develop TWRFs for hybrid bermudagrass and tall fescue species. The data for both years were combined. The primary input variables were the applied irrigation levels (%ETo), irrigation frequency restrictions, and cumulative ETo (since the beginning of the experiment for each particular year). The mean VR values for treatments were used as the output variable. The SAS 9.4 software (SAS Institute Inc., Cary, NC, USA) was used to develop and rank all possible regression equations based on correlation coefficients (with 0.7 as the minimum acceptable value). Multiple regression diagnostics, including the Shapiro–Wilk W statistic (to check the normality of the residuals), the condition index (to monitor the collinearity between the variables), and the first and second moment specification test (to check the equal residual variance) were used to finalize the list of input variables of the top model. The long-term mean daily ETo values were obtained from the CIMIS station #39 and used to estimate the response of tall fescue and hybrid bermudagrass to varying ET-based irrigation scenarios (60–100% ETo). The simulation was done for four months, from May to August, using the TWRFs.

The root mean square error (*RMSE*), mean absolute error (*MAE*), mean bias error (*MBE*), and correlation coefficient (*r*) were calculated to evaluate the TWRFs.

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (E\_i - M\_i)^2} \tag{2}$$

$$MAE = \frac{\sum\_{i=1}^{n} |E\_i - M\_i|}{n} \tag{3}$$

$$MBE = \frac{\sum\_{i=1}^{n} (E\_i - M\_i)}{n} \tag{4}$$

$$r = \frac{\sum\_{i=1}^{n} \left(E\_i - \overline{E}\right) \left(M\_i - \overline{M}\right)}{\sqrt{\sum\_{i=1}^{n} \left(E\_i - \overline{E}\right)^2 \sum\_{i=1}^{n} \left(M\_i - \overline{M}\right)^2}}\tag{5}$$

where *E* and *M* are estimated and measured visual rating values, respectively. *M* and *E* are the mean-measured and the mean-estimated visual rating values, respectively, and *n* is the total number of measured data points for the entire experiment (*n* = 162 for each species).
