3.1. Input weather parameter
Figure 2 presents the annual fluctuations of input parameters including R, Tmean, S and U2 in different climates during 1981–2020. In very dry climate, the R was less than 200 mm y− 1. In the very dry climate, the fluctuation of R values was noticeably less than humid climates during the study period. According to Fig. 2a, the values of R in the humid climates located on the north coast of Iran was much higher than very dry, dry, and semidry climates. Based on Fig. 2b, the fluctuation of Tmean in the dry climate was higher than other climates. The fluctuation of Tmean (Fig. 2b) in very dry climate depended on the land cover, the sea level elevation, and the difference between day and night Tmean (Sharafi and Ghaleni, 2022). According to Fig. 2c, solar radiation in the humid climate was much less than other climates. Primary analysis showed that the average number of sunny days was 244, 289, 322, and 344 days in the humid, semidry, dry, and very dry climates, respectively. The average number of sunny days was least in the humid climate. Also, the difference in the S among drier climates was not significant. The maximum and minimum of U2 were observed in very dry and humid climates, respectively (Fig. 2d). The frequency of U2 had a higher value in the third quarter in very dry, dry, and semidry climates and reversely, this item was reported in the first quarter in the humid climate. The decrease of cover land and relative humidity in drier climates was more effective in the increase of wind speed. The fluctuation among climate variables (U2, R, Tmean, and S) in humid climate was more moderate. This item can be more effective in the increase in rainfed crop yield.
3.2. R trend
Figure 3a-d represent the changing trend of R in the very dry, dry, semidry, and humid climates across Iran. The results (Fig. 3d) showed that the maximum decrease in R occurred in the humid climate with a very negative slope (-3.72 mm y− 1) and has also resulted in unpredictable damages to the neighbor regions. Also, the lowest variations (-0.31 mm y− 1) in R were observed in very dry climate (Fig. 3a). The slope values of R trends in dry and semidry were − 1.11 and − 1.98 mm y− 1, respectively (Fig. 3b and c).
According to the results of Fig. 3a-d, all different climates had negative trends at 95% confidence level. The results were similar to the findings of (DehghaniSanij et al., 2004) and (Bannayan and Eyshi Rezaei, 2014) in Karaj and Khorasan provinces of Iran, respectively. Sharafi and Mir Karim, 2020 verified the negative trend for R in Iran. In other words, the semi dry and humid climates have been most affected by the negative impacts of decrease in R, and this could lead to major problems for the future of agriculture in these climates.
3.3. Association of R and yield
Figure 4 shows the AAR (mm y− 1) and yield (kg ha− 1) of rainfed wheat and barley in different climates across Iran. The AAR in very dry climate was lower than 101 mm (Fig. 4a). The AAR varied in very dry, dry, semi dry, and humid climates between 18.3–356 mm (Fig. 4a), 81.3–468 mm (Fig. 4b), 134–456 mm (Fig. 4c), and 1237–2662 mm (Fig. 4d), respectively.
The average yield of rainfed wheat and barley in very dry (592 and 609 kg ha− 1, Fig. 4a), dry (669 and 677 kg ha− 1, Fig. 4b), semidry (488 and 623 kg ha− 1, Fig. 4c), and humid (1651 and 1054 kg ha− 1, Fig. 4d) climates was obtained. These results exhibited a clear association trend between R and the yield of rainfed crops. Many researches confirmed that in most of the cases, the increase or decrease in the crop yield corresponds to climatic fluctuations (Almeida-Dias et al., 2010). Bannayan et al., 2011 also showed that there was a significant correlation between different crops yield with climatic factors in dry climates of northeast Iran.
The changes trend of the yield of rainfed wheat was similar to barley during studied years in dry climates, but, it was different in humid climate because of the fluctuations of R during those years. The yield of rainfed wheat extremely increased in comparison with barley because R fluctuations were very low during 1981–2000 in the humid climate. Reversely, due to the intensity of R fluctuations, the yield of rainfed wheat and barley decreased during 2001–2020, but, this decrease in the yield of rainfed wheat was more than rainfed barley. These results showed that the rainfed barely had a more suitable reaction to drought in these years. Barley is usually very sensitive to very humid conditions and it is threatened by invasive pathogens (Jalli et al., 2020; Velásquez et al., 2018). It is mentioned in humid climate, the most fertile lands allocate to cash crops and rainfed crops cultivate in the rough lands.
Based on Fig. 4a-c, simultaneously with R fluctuations, the average yield of rainfed barley was reported more than wheat in dry climates. This issue is related to its tolerate of barley to drought conditions (Jalli et al., 2020). According to these results, in crop pattern planning, it is suggested to farmers that allocated more lands to rainfed barley in drought years. These results confirmed by other studies (Bannayan et al., 2011; Bannayan and Eyshi Rezaei, 2014; DehghaniSanij et al., 2004; Nassiri et al., 2006; Sabziparvar, 2008; Shamsnia and Pirmoradian, 2013).
The R and Tmean proved to be the limiting and determining factor for crop yields; R variability resulted in crop yield variability of rainfed wheat and barley in the study area.
3.4. Performance analysis of MLR
Table 3 presents the MLR equations developed for the four climates for the training dataset. The values of a1, a2, a3, a4 are the coefficients of R, Tmean, S, and U2 during the crop growing season of rainfed crops and a0 is the constant coefficient for the equation of crop yield. After the coefficients of MLR were obtained, the crop yield was estimated for rainfed wheat and barley for each climate for the testing dataset and was evaluated and compared with the observed yield values (Table 3).
Table 3
Equations derived from the MLR models for estimation yield of rainfed wheat and barley in different climates across Iran
Crop
|
Climate
|
models
|
Wheat
|
Very Dry
|
Y=-663.1 (R) + 1.21 ( Tmean) + 3.35(S) + 0.39(U2) + 3.89
|
Dry
|
Y = 331.15 (R)-0.253 ( Tmean) + 3.3(S) + 0.141(U2)-44.8
|
Semi Dry
|
Y = 145.96 (R) + 0.47 ( Tmean)-20.8(S) + 0.28(U2)-18.7
|
Humid
|
Y = 3856.1 (R)- 1.015 (Tmean)- 93.1(S) + 0.065(U2) + 121.6
|
Barley
|
Very Dry
|
Y=-845.3 (R) + 0.4 ( Tmean)-+12.5(S) + 0.39(U2) + 5.42
|
Dry
|
Y = 648.7 (R)-0.11 ( Tmean)-1.5(S) + 0.064(U2)-34.4
|
Semi Dry
|
Y = 49.1 (R)-0.68 ( Tmean) + 0.5(S) + 0.188(U2)-14.7
|
Humid
|
Y = 559.3 (R)-0.47 ( Tmean)-227.8(S) + 0.038(U2) + 26.36
|
Y = a1R + a2Tmean + a3S + a4U2 + a0
|
Table 4 shows the regression analysis (Tstat and p-value) to determine if the independent variables have significant effects on yield at 95% confidence level. It is observed that the absolute values of the independent variables’ Tstat for all MLR models were greater than 1.97 which confirm the p-values. The p-value of independent variables given in Table 6 indicated that R and U2 were the most significant variables in the MLR models with the highest Tstat. The coefficients associated with the R and U2 were larger than the coefficients associated with other variables indicating that the R and U2 had more contributions to the yield estimation of rainfed wheat and barley than other variables. When Tmean data were no longer included in the model (i.e., semidry and humid climates), S was found to be more significant on the yield estimations than U2.
Table 4
Tstat and p-value of independent variables for MLR models
Crop
|
Climate
|
Intercept
|
Independent Variable
|
R
|
Tmean
|
S
|
U2
|
Wheat
|
Very Dry
|
Tstat
|
5.46
|
4.98
|
2.106
|
2.206
|
3.07
|
p-value
|
2.15 ×10− 20
|
1.65 ×10− 18
|
1.4 ×10− 5
|
4.5 ×10− 10
|
4.5 ×10− 16
|
Dry
|
Tstat
|
-68.36
|
4.016
|
2.088
|
2.03
|
3.04
|
p-value
|
1.25 ×10− 53
|
2.15 ×10− 19
|
1.24 ×10− 7
|
2.5 ×10− 5
|
1.5 ×10− 12
|
Semi Dry
|
Tstat
|
-22.16
|
4.03
|
2.33
|
3.35
|
2.42
|
p-value
|
6.15 ×10− 33
|
1.55 ×10− 17
|
3.74 ×10− 6
|
3.1 ×10− 8
|
2.4 ×10− 7
|
Humid
|
Tstat
|
256.34
|
3.98
|
2.11
|
3.46
|
2.26
|
p-value
|
1.23 ×10− 78
|
4.24 ×10− 12
|
9.2 ×10− 6
|
3.5 ×10− 15
|
2.3 ×10− 11
|
Barley
|
Very Dry
|
Tstat
|
8.67
|
4.67
|
2.243
|
2.116
|
3.27
|
p-value
|
4.32 ×10− 32
|
2.42 ×10− 14
|
7.2 ×10− 7
|
2.5 ×10− 5
|
7.5 ×10− 12
|
Dry
|
Tstat
|
-45.32
|
3.97
|
2.123
|
1.96
|
3.13
|
p-value
|
4.25 ×10− 22
|
1.23 ×10− 18
|
5.2 ×10− 6
|
4.6 ×10− 4
|
7.3 ×10− 11
|
Semi Dry
|
Tstat
|
-26.86
|
3.53
|
2.21
|
3.12
|
2.62
|
p-value
|
2.15 ×10− 23
|
1.35 ×10− 15
|
4.14 ×10− 9
|
3.1 ×10− 7
|
2.3 ×10− 8
|
Humid
|
Tstat
|
53.74
|
3.12
|
2.02
|
3.34
|
2.45
|
p-value
|
4.21 ×10− 63
|
3.22 ×10− 14
|
7.1 ×10− 6
|
4.3 ×10− 14
|
6.1 ×10− 10
|
Tstat t statistic, p value probability
|
The yield of rainfed wheat and barley were estimated for the testing phase using eight models in different climates across Iran. The comparison between the estimated yield values by MLR models and observed yield values during the training and testing phases is illustrated in Table 5. The R2, MBE, and CRM values for MLR models in Table 5 showed that the MLR models had unbalanced performance of in different climates. These statistical criteria for drier climates (very dry, dry and semi dry) were higher than the humid climate. These criteria reported that the performance slightly varied for MLR models with humid climate than those for dry climate (Table 5). The results showed that the values of R2 and CRM in the MLR models in drier climates are close to one during the training process. The R2 values falling between 0.74–0.85 and 0.64–0.79 for rainfed wheat and barley for testing data set, in these climates, respectively. While the MLR model for humid climate showed a bad correlation with observed yield, the R2 values were 0.61 and 0.53 for wheat and barley, respectively. Shamsnia and Pirmoradian, 2013 revealed the correlation coefficient of 0.91 between the simulated yields by AquaCrop model and observed yields of rainfed wheat in Shiraz station. The values of R2 between observed and estimated yields by the MLR of rainfed wheat showed that the MLR was more accurate in the drier climates (R2 = 0.85 − 0.74) than the humid climate (R2 = 0.53). The lowest correlation was obtained for rainfed wheat (R2 = 0.61) and rainfed barley (R2 = 0.53) in the humid climate region. The values of MBE for the very dry climate during both training and testing processes decreased to about the half of values recorded for humid climate. There was a good agreement between the yield observed and estimated by MLR models in very dry, dry and semi dry climates, whereas the R2, MBE, and CRM values were moderately few for humid climate. This implies that the R and U2 (importance ratio of 43.52% and 20.16%, respectively) data are more effective in estimating the yield of rainfed wheat and barley. The MBE (1.25–1.4 for wheat; 1.36–1.55 for barley), and CRM (0.77–0.83 for wheat; 0.86–0.91 for barley) values for MLR models indicated that the MLR models tend to overestimate in all climates for the training and testing data set. This overestimate was higher from drier to humid climate and the accuracy of model was decreased. The MLR models behaved well given that there were no significant differences in the statistical criteria values given by the training and testing data sets in different climates.
Table 5
Performance statistics of the MLR models for estimation yield of rainfed wheat and barley in the training and testing periods in different climates across Iran
Crop
|
Climate
|
Training data
|
Testing data
|
R2
|
MBE (%)
|
CRM
|
R2
|
MBE (%)
|
CRM
|
Wheat
|
Very Dry
|
0.96
|
1.25
|
0.001
|
0.85
|
1.4
|
-0.01
|
Dry
|
0.88
|
1.34
|
-0.004
|
0.79
|
2.1
|
-0.02
|
Semi Dry
|
0.87
|
1.4
|
-0.005
|
0.74
|
4.5
|
-0.03
|
Humid
|
0.66
|
2.6
|
-0.008
|
0.61
|
7.9
|
-0.025
|
Barley
|
Very Dry
|
0.9
|
1.36
|
-0.002
|
0.79
|
2.7
|
-0.019
|
Dry
|
0.83
|
1.45
|
-0.005
|
0.71
|
3.6
|
0.03
|
Semi Dry
|
0.81
|
1.55
|
-0.008
|
0.69
|
5.4
|
-0.055
|
Humid
|
0.69
|
2.9
|
-0.01
|
0.53
|
8.7
|
-0.069
|
Figure 5 shows SI for predicted models of MLR in rainfed wheat and barley in different climates of Iran. In general, the results of the present study confirmed that MLR model had the accuracy. Similar results were also reported by Bannayan and Eyshi Rezaei, 2014. Their results cleared that the MLR model generally has had similar SI values in dry climate. This might show the importance of climatic parameters on yield estimating in the very dry and dry climates, as well as humid climate. The impact of input climatic parameters seems to be very low in Tabass and Zabol stations gave the undesirable results in these stations (Fig. 5). However, this situation should be used with cautiousness because a comprehensive study should be conducted to determinate the portion of each parameter on the MLR model magnitudes, which is beyond the scope of this research (Fig. 5).
Figure 6 shows the Taylor's diagram for MLR models in different climates across Iran during the test phase. Three statistical measures including R2, SD, and RMSD determined the degree of compliance of rainfed yield behavior between the observed and estimated values. According to Figs. 6 the highest (0.9 for wheat and 0.95 for barley) and lowest (0.6 for wheat and 0.4 for barley) proximity to the SD line in the observed values were related to the MLR models for very dry and humid climates, respectively. The accuracy of model in humid climate (Fig. 6a) was lower than drier climates (Fig. 6b-d). Findings shows fit and accuracy of the MLR models to estimate the yield of rainfed wheat was better than rainfed barley in all climates (Fig. 6).
Three additional indices of uncertainty (U95), Tstat test and the GPI were used for better assessment of the MLR models. Figure 8 shows the values of U95 and Tstat of the MLR models in different climates. According to the Fig. 7, it can be clearly seen that the MLR model in very dry climate has the smallest value of the U95 index to estimate the yield of rainfed wheat and barley that confirms its excellent performance over the MLR models in other climates. These models presented 61% and 55% reductions of U95 index, compared to the MLR model to estimate the yield of rainfed wheat and barley in humid climate, respectively. All models in different climates were significant at 95% level in the Tstat index, confirming the significant differences between the estimated and observed yield of rainfed wheat and barley.
Finally, various statistical indices may have different results in determining the accurate model because each index shows the performance of the model at a unique level. Choosing appropriate model based on different indices cannot be a reliable solution. Therefore, a standard statistical index is required to combine the overall effect of statistical indices (Maroufpoor et al., 2019). The GPI was used as a 5-agent index (Eq. 9) which was a combination of five indices including RMSE, MBE, Tstat, U95, and R2. It is expected that the model with the first rank (when GPI value is close to zero) is both better in performance and accuracy (Behar et al., 2015; Gueymard, 2014; Maroufpoor et al., 2019; Stone, 1994). Figure 8 shows the GPI values for train MLR models of yield estimation of wheat and barley based on the ranking in different climates. Based on Fig. 8, the absolute superiority of the test MLR model in very dry climate is found in the estimation of the yield of rainfed wheat and barley. Although MLR models in other climates showed similar performance to the MLR model in this climate based on Table 2 and Fig. 6 the GPI showed a significant difference in terms of modeling quality and accuracy of the results in estimating yield. The GPI of the MLR model in very dry climate was reduced up to 89% and 90% compared to the MLR model in humid climate in estimation of yield for rainfed wheat and barley, respectively. Estimating the yield of rainfed wheat and barley with MLR models with high accuracy levels can be useful in agricultural studies. MLR models can be used to predict the yield of rainfed crops by climate factors. Therefore, these models can be to identify yield gap and help to decrease of damages of drought to rainfed crops in different climates.