Considering the availability of both irrigated and unirrigated yield data of winter wheat, Bushland, TX and Clovis, NM were selected as the representative locations for the Llano Estacado region. Then, their winter wheat yield data generated through variety trials conducted in multiple years ( Table 1 ) under both irrigated and dryland conditions were obtained. The yields of all the winter wheat varieties used in the trials at each location in each year under each farming regimen (dryland or irrigated) were averaged to calculate the dryland and irrigated yields of a general winter wheat variety for these locations and years. Then, the relative yield of winter wheat for the corresponding location and year was calculated as the ratio of the dryland yield to the irrigated yield. The intent of using the relative yield was to reflect the effect of water only, while eliminating the effects of the other inputs involved, as both dryland and irrigated crops involved in each experiment had received the same amounts of other inputs, except the water.

Considering the availability of phase duration data and the approach used by [27] , five phenological phases were included in this study: 1) planting-emergence (PE); 2) emergence-tillering (ET); 3) tillering-booting (TB); 4) booting-anthesis (BA); and 5) anthesis-maturity (AM). Due to the lack of corresponding planting date data, representative planting dates from the literature were used (Bushland: 21 October, Clovis: 15 October). The duration of each phenological phase needed for splitting a growing season into several phases was estimated using the total thermal time (TTT; ˚C d) needed for each phase under dryland conditions ( Table 2 ) [28] - [32] . Once the planting date for each location and the duration for each phase in each year at each location were estimated, each wheat growing season at each location was split into the five phenological phases described above.

For each location, the daily values of ARID for each wheat growing season that had yield data were computed from the daily weather data, using the ARID equations described by [13] and the computational procedure (MATLAB program) provided by [10] . Once the daily values of ARID were computed for each year at each location, they were averaged by the phenological phase. The phasic values of ARID were then converted into the corresponding phasic values of “1 − ARID” as the yield model (Equation (1)) needs the latter.

For developing the ENSO phase-specific yield models, the years for which yield data were available ( Table 1 ) were assigned to a specific ENSO phase as categorized by the Japan Meteorological Agency (JMA) index [33] - [36] . The JMA index is a 5-month moving average of the sea surface temperature anomalies over the Equatorial Pacific (4˚S - 4˚N, 150˚W - 90˚W). An ENSO year, which starts from October through the following September, is categorized as El Niño, La Niña, or Neutral if the index values are ≥0.5˚C, ≤−0.5˚C, or between −0.5˚C and 0.5˚C, respectively, for 6 consecutive months, including October, November, and December [34] [36] . For ENSO characterization, the JMA index was used as it selects the ENSO events better than other similar indices [36] . According to this index, the total number of years for which the yield data were available in the Llano Estacado region (Bushland plus Clovis) under the El Niño, La Niña, and Neutral phases of ENSO were 28, 20, and 48, respectively ( Table 1 ).

Once the relative yield values of wheat and the phenological phasic values of (1 − ARID) were calculated for each year in each location under each ENSO phase, a matrix of dataset comprising 28 rows (years) and six columns was prepared for El Niño, that comprising 20 rows and six columns for La Niña, and that comprising 48 rows and six columns for the Neutral phase. The first column in the matrix contained the relative yields (dependent variable), and the remaining columns contained the corresponding phenological phasic values of (1 − ARID) for the five phases (independent variables).

For developing the ENSO phase-specific yield models, estimating the drought-sensitivity coefficient for winter wheat during the phenological phase p, denoted as λ_p, for each ENSO phase would be necessary. This would require regressing the linearized form (Equation (3)) of the ENSO phase-specific yield model (Equation (2)). Accordingly, all the values in the matrix prepared for each ENSO phase as explained above were converted to the natural logarithmic (ln) values. These transformed matrices, in turn, were used in the R-project software ( https://www.r-project.org/ ) to estimate the λ_p values through multiple linear regressions. The linearized yield model is as follows.

$\ln \left({\tilde{Y}}_{i,j,k}\right)=\underset{p=1}{\overset{P}{{\displaystyle \sum }}}\left\{{\lambda }_{i,p}\times \ln \left(1-{\text{ARID}}_{i,j,k,p}\right)\right\},$(3)

where ${\tilde{Y}}_{i,j,k}$ is the relative yield; P is the total number of phenological phases of winter wheat considered (5); and the subscripts i, j, k, and p stand for the i-th ENSO phase, the j-th location, the k-th year, and the p-th phenological phase, respectively.

Given the limited number of years available, especially for the El Niño and La Niña phases, the leave-one-out technique of cross-validation was used to evaluate the yield model. Following this technique, the available dataset (the transformed matrix) for each ENSO phase was divided into two parts: one for parameterization and the other for evaluation. That is, of the total 28 input-output combinations for El Nino, for instance, the first 27 combinations (rows) were used as the parameterization set for estimating the λ_p values through the regression of Equation (3) and the last one combination (row) as the evaluation set for yield estimation through the use of the just estimated λ_i,p values in the yield model (Equation (2)). Leaving one combination out and adding one combination in, both parameterization and the evaluation sets were moved forward 27 times. Each movement created a new parameterization set and a new evaluation set, which, in turn, produced a set of new λ_p values through regressions (using Equation (3)) and, finally, a yield estimate (using Equation (2)). This process, consequently, provided 28 relative yield estimates for El Niño, 20 for La Niña, and 48 for the Neutral phase. Finally, using the mean absolute error, the root mean square error (RMSE), the Nash-Sutcliffe Index [37] , and the Willmott Index [38] as the measures of fit, the estimated relative yields using Equation (2) for the years for which the observed yields were available under each ENSO phase were compared with the corresponding observed relative yields to evaluate the performance of an ENSO phase-specific winter wheat yield model.

Table 3 shows the phenological phase-specific drought sensitivity coefficients estimated for the ENSO phase-specific winter wheat yield model (Equation (2)) for the Llano Estacado region of the United States. Using these coefficients in Equation (2) resulted in the following ENSO phase-specific relative yield models for winter wheat.

${\tilde{Y}}_E=1.21\times {\left(1-\text{ARID}\right)}_{E,\text{PE}}^{0.03}\times {\left(1-\text{ARID}\right)}_{E,\text{ET}}^{0.082}\times {\left(1-\text{ARID}\right)}_{E,\text{TB}}^{0.443}\times {\left(1-\text{ARID}\right)}_{E,\text{BA}}^{0.043}\times {\left(1-\text{ARID}\right)}_{E,\text{AM}}^{0.039}$(4)

${\tilde{Y}}_L=0.67\times {\left(1-\text{ARID}\right)}_{L,\text{PE}}^{0.037}\times {\left(1-\text{ARID}\right)}_{L,\text{ET}}^{0.066}\times {\left(1-\text{ARID}\right)}_{L,\text{TB}}^{0.165}\times {\left(1-\text{ARID}\right)}_{L,\text{BA}}^{0.075}\times {\left(1-\text{ARID}\right)}_{L,\text{AM}}^{0.023}$(5)

${\tilde{Y}}_N=0.99\times {\left(1-\text{ARID}\right)}_{N,\text{PE}}^{0.03}\times {\left(1-\text{ARID}\right)}_{N,\text{ET}}^{0.167}\times {\left(1-\text{ARID}\right)}_{N,\text{TB}}^{0.263}\times {\left(1-\text{ARID}\right)}_{N,\text{BA}}^{0.154}\times {\left(1-\text{ARID}\right)}_{N,\text{AM}}^{0.019}$(6)

where ${\tilde{Y}}_E$, ${\tilde{Y}}_L$, and ${\tilde{Y}}_N$ are the relative yields of winter wheat for the El Niño (E), La Niña (L), and Neutral (N) phases of ENSO, respectively; and the five phenological phases are represented by subscripts PE, ET, TB, BA, and AM.

All the sensitivity coefficients under each ENSO phase had positive values, indicating that the water stress during any phenological phase of winter wheat would have negative impacts on yields under any ENSO phase. This result was in agreement with the findings of several previous studies. In a similar study conducted in the Llano Estacado region, but without considering the ENSO effect, [22] also found that water stress during any phase could be detrimental. In an experiment carried out in Arizona, USA, [39] observed that wheat grain yields were reduced by the water stress that occurred at any growth stage. In a review study, [27] demonstrated that wheat yields could be impacted by water stress during any phenological phase, depending on the weather conditions. Reference [40] also exhibited through a review paper that winter wheat yield is vulnerable to drought at any growth stage. Reference [41] promulgated that water stress occurring at any particular stage would result only in high yield losses, not crop failure, whereas that occurring during the entire growing season would result in crop failure.

Under each ENSO phase, the TB phenological phase had the largest value of the drought sensitivity coefficient of all the phenological phases of winter wheat considered ( Table 3 ), implying that this phenological phase was the most sensitive to drought. This implication was consistent with those of several other studies [22] [27] [39] [41] [42] . The likely reasons for the greatest sensitivity of winter wheat yields to drought during the TB phase were as follows. The crop water demand during this phenological phase is high [43] . The water stress during this phase reduces the number of stems and heads by increasing the senescence of tillers and stems and reduces yields by reducing the number of grains through fewer spikelets per head, fewer grains per spikelet, or both [27] [39] [44] [45] .

The ET phase was the second most sensitive phase to drought under El Niño and Neutral and the third most sensitive phase under La Niña. The following phenomena were possible causes for high drought sensitivity during this phase. Plant water stress during the ET phase drastically limits leaf growth and tiller development [44] [46] - [50] . Under severe water stress, tillering may decrease by about 50% [47] [49] , and leaf area index (LAI) development is severely hampered [27] . Water stress just before floral initiation decreases the number of spikelet primordia [51] .

In drought sensitivity, the BA phase followed the ET phase under El Niño and Neutral and the TB phase under La Niña. The sensitivity of wheat yields to drought during the BA phase was likely due to the following phenomena. Plant water stress during this phase reduces the availability of carbon and nitrogen, both of which are critical for spike growth [27] . When water stress occurs during spike growth and emergence, the kernel number decreases sharply, leading to a decrease in wheat yields at a maximum rate [52] . Water stress at heading increases the number of sterile spikelets and florets and that around anthesis affects pollination and fertilization, thus reducing the seed setting rate and, eventually the grain yield [50] . Water stress during this phase reduces yields also through insufficient assimilates [53] .

As the sensitivity coefficients under all ENSO phases showed, the PE phase was less sensitive to drought than ET, TB, and BA phases. References [22] and [41] also found similar results. The sensitivity of wheat yields during PE was likely because an early drought in the growing season may have affected wheat germination and crop establishment [54] . Severe water stress during PE and ET prevents crop development [27] .

The smaller values of the drought sensitivity coefficients during the AM phase relative to other phenological phases under all ENSO phases indicated that winter wheat yields were the least sensitive to drought that occurred during this phenological phase in any ENSO year. The scientific documentation also shows that, of all the phenological phases of wheat, water stress during the AM phase had the smallest yield impacts [39] [42] . The detrimental effect of drought on wheat yields during this phase was likely because the water stress around anthesis decreased carbohydrate accumulation in the stem by accelerating development [55] [56] and during grain-filling shortened the grain-filling period by accelerating senescence [52] [57] . The terminal part of the grain-filling period in the Llano Estacado region is generally hot and dry, which tends to terminate grain-filling early. Under these conditions, more grains may be more important than a greater grain-filling rate during the AM phase for high yields [44] . The larger sensitivity coefficients for TB and BA phases relative to the AM phase well reflected this phenomenon ( Table 3 ). The rational values of the sensitivity coefficients suggested that the yield models (Equations (4) to (6)) were able to express the ENSO phase-specific relationship between ARID and the relative yields of winter wheat in the Llano Estacado region accurately.

As Table 3 shows, the order of phenological phases with diminishing sensitivity to drought under a given ENSO phase was as follows. El Nino: TB > ET > BA > AM > PE. La Niña: TB > BA > ET > PE > AM. Neutral: TB > ET > BA > PE > AM. However, the coefficient values, especially between ET and BA phases, were not significantly different under each ENSO phase. Also, the coefficient difference between PE and AM phases was not significant under each ENSO phase. These patterns suggested that in terms of drought sensitivity, the five phenological phases studied could be classified into three groups: 1) highly sensitive: TB; 2) moderately sensitive: ET and BA; and 3) slightly sensitive: PE and AM.

The values of the various metrics used to evaluate the performance of the ENSO phase-specific winter wheat yield models for the Llano Estacado region of the southern United States are presented in Table 4 . The RMSE value ranged from 0.07 to 0.10 (dryland yield per unit of irrigated yield), whereas the mean absolute error value ranged from 0.06 to 0.09. The percentage error of the yield model, computed as the ratio of RMSE to the mean observed relative yield, ranged from 20 to 26. The value of the Willmott index fell between 0.82 and 0.89, whereas that of the Nash-Sutcliffe index lay between 0.54 and 0.67. As the values of these metrics indicated, each ENSO phase-specific winter wheat yield model performed reasonably well at predicting the relative yields and, thus, the yield losses due to drought.

The Willmott index values indicated that the relative yields of winter wheat estimated by the yield model agreed fairly closely with those calculated from the observed data. The Nash-Sutcliffe index values also indicated that the agreements between the model-estimated and observed values were acceptable for the winter wheat yield model, and thus the predictive power of the yield model was relatively good. As the positive values of this index indicated, the model predictions were more accurate than the means of the observed data. The mean values of both observed and relative yields were the same and ranged from 0.32 to 0.52 across the ENSO phase-specific models. The percentage error, if computed as the absolute difference between the predicted and the observed values relative to the observed value, would be almost zero, an indication of a small error. Under El Niño, the range of the predicted relative yields was 0.27 to 0.68, and that of the observed relative yields was 0.25 to 0.78. That is, the width of the range of the predicted yields (0.41) relative to that of the observed yields (0.53) was about 0.77, which indicated that the model error based on this statistic was about 23%. Similarly, the errors of this kind under La Niña and Neutral were 24% and 14%, respectively. These values were also an indication for a relatively low modeling error. All the above metrics indicated that each ENSO phase-specific yield model was able to reflect the phenomenon of water stress decreasing the yields of winter wheat in the Llano Estacado region fairly well ( Figure 1 ).

The performance of each ENSO phase-specific yield model was significantly better than that of the generic yield model [22] , which did not consider the ENSO effects ( Table 4 vs. Table 5 ). Compared with the generic model, the ENSO phase-specific models increased the Willmott index by 0% to 9% and the Nash-Sutcliffe index by 14% to 28%, depending on the ENSO phase. Similarly, the ENSO-specific yield models reduced the mean absolute error by 5% to 11% and the percentage error and the root mean square error by 11% to 12%.

Relative to the generic yield model, the ENSO phase-specific yield models better reflected the impacts of the interannual variability of weather conditions during the winter wheat growing season in the Llano Estacado region. The following phenomena were the likely reasons for this outcome. The precipitation or drought patterns during a given phenological phase of winter wheat were different across the ENSO phases. For instance, the weather conditions during late fall through early spring in El Niño years were wetter and cooler than the normal years, whereas the La Niña winters were drier and warmer than the normal years [23] - [25] . Accordingly, a phenological phase of wheat occurring during this period may have different responses to drought in El Niño and La Niño years. The sensitivity of wheat yields to water stress under a given ENSO phase was also different across the phenological phases. Because of these phenomena, therefore, the phenological phase-specific drought sensitivity coefficient value was custom-made for a particular ENSO phase, which eventually led to better results.