3.1 Effect of sowing date on mustard yield
The mean mustard yield for cultivar “Varuna” varied from 2500 Kg/ha for first sowing date (SMW 40) to 344 Kg/ha for the last sowing date (SMW 49; Table 3). The decrease was greater in the case of crops sown in Standard meteorological week (SMW) 42 and onwards, with a minimum yield when sown during the sowing week SMW 49. The yield of mustard was highest with a mean of 2480 kg/ha and standard deviation of 714.6 kg/ha when mustard is sown in the first week of October. Table 3 indicates that yield reduction has been observed as the sowing is delayed from 1st week of October towards end of October and November. Also, the year-to-year variance, as represented by standard deviation (Table 3) was smaller in the case of late sown crops. Result of one-way ANOVA indicated that there was significant difference in yield between different sowing dates.
Table 3
Summary of the statistics of mustard yield data and mean values of weather variables experienced by crop at the time of sowing during corresponding sowing dates
Sowing date
|
Mustard yield (Kg/ha)
|
Mean values of weather variables
|
Mean
|
Median
|
Std. Deviation
|
Temperature 0C
|
R. Humidity %
|
Sun shine hrs.
|
Evap. (mm)
|
Wind Vel. (Kmph)
|
Rainfall (mm)
|
Max.
|
Min.
|
07:12 (am)
|
14:12 (pm)
|
Oct.01
|
2481
|
2400
|
715
|
32.4
|
21.9
|
87.8
|
59.6
|
6.8
|
3.5
|
2.6
|
1.8
|
Oct.08
|
2317
|
2387
|
746
|
32.5
|
19.4
|
85.7
|
53.5
|
7.9
|
3.4
|
2.7
|
7.6
|
Oct.15
|
1949
|
2000
|
700
|
31.1
|
17.4
|
87.2
|
53.0
|
7.3
|
3.2
|
2.4
|
3.8
|
Oct.22
|
1583
|
1658
|
564
|
30.5
|
14.6
|
88.5
|
45.9
|
7.4
|
3.1
|
2.4
|
0.0
|
Oct.29
|
1227
|
1133
|
448
|
29.3
|
13.8
|
88.9
|
45.1
|
5.9
|
2.6
|
2.1
|
0.8
|
Nov.05
|
991
|
913
|
439
|
28.2
|
12.5
|
90.3
|
44.1
|
6.6
|
2.4
|
2.3
|
0.2
|
Nov.12
|
899
|
803
|
383
|
27.8
|
11.3
|
91.3
|
42.5
|
6.8
|
2.4
|
2.2
|
0.0
|
Nov.19
|
689
|
573
|
412
|
26.4
|
10.1
|
92.4
|
43.1
|
7.0
|
2.4
|
2.2
|
0.0
|
Nov.26
|
474
|
492
|
169
|
25.8
|
9.8
|
92.5
|
47.5
|
6.3
|
2.2
|
2.4
|
2.7
|
Dec.03
|
339
|
319
|
150
|
24.5
|
9.6
|
93.8
|
51.4
|
5.2
|
1.9
|
2.2
|
0.3
|
*Calculated using 15 data points (1 data point in each year) corresponding to each sowing date
Wide variation has been observed in the mean maximum and mean minimum temperature at the time of sowing of mustard crops for different sowing dates (Table 3). Mean maximum (minimum) temperature ranges between 30 and 32.5oC (14.6 and 21.9 oC) for crops sown during 1st fortnight of October. Evaporation during this period is above 3 mm, bright sunshine hours is approximately 7 hours and more. However, when the sowing is delayed, both maximum and minimum temperature drops and reaches as low as 24.5 oC and 9.6 oC respectively during the SMW 49 (December 03). There is significant reduction in the sunshine hours i.e., of the magnitude of up to 2 hours and a slight reduction in the evaporative demand of atmosphere.
3.2 Cross comparison of models in the prediction of mustard yield at different sowing dates
The performance of each model was measured in terms of R2, RMSE, nRMSE, and MBE during calibration and validation stage (Table 4). As per the results obtained for ENET modelling approach, R2 values were very high (> 0.91 or higher) during calibration stage for all sowing dates. However, it ranged from 0.01 to 0.30 (except DOS 6 when R2 is 0.96) during validation stage. nRMSE values were excellent during calibration stage (except DOS 6) while they were poor at all sowing dates during the validation stage. Equations governing the prediction of mustard yield for different sowing dates by ENET modelling approach is given in Table 5.
Table 4
Statistical measures derived for different models in predicting actual yield of mustard as affected by weather and mustard diseases
DOS
|
Model
|
R2cal
|
RMSEC
|
nRMSEC
|
MBEC
|
R2val
|
RMSEV
|
nRMSEV
|
MBEV
|
1
|
ENET
|
1
|
0.25
|
0.96
|
0
|
0.16
|
9.77
|
46.25
|
6.37
|
Ridge
|
0.86
|
2.66
|
10.13
|
0
|
0.27
|
8.48
|
40.12
|
4.59
|
LASSO
|
0.79
|
3.93
|
15.85
|
0
|
0.92
|
5.64
|
26.67
|
2.94
|
ANN
|
1
|
0.06
|
0.23
|
-0.03
|
1
|
0.07
|
0.31
|
0.01
|
2
|
ENET
|
1
|
0.19
|
0.76
|
0
|
0.11
|
8.26
|
45.27
|
4.70
|
Ridge
|
0.86
|
2.74
|
10.82
|
0
|
0.45
|
7.99
|
43.74
|
5.23
|
LASSO
|
0.93
|
2.05
|
8.80
|
0
|
0.96
|
2.71
|
14.87
|
1.76
|
ANN
|
1
|
0.09
|
0.35
|
-0.05
|
1
|
0.11
|
0.60
|
0.04
|
3
|
ENET
|
1.00
|
0.19
|
0.85
|
0
|
0.13
|
8.30
|
54.56
|
6.11
|
Ridge
|
0.92
|
2.78
|
12.40
|
0
|
0.13
|
8.61
|
56.63
|
6.53
|
LASSO
|
0.90
|
2.47
|
12.13
|
0
|
0.97
|
3.48
|
22.91
|
1.60
|
ANN
|
1
|
0.08
|
0.34
|
-0.03
|
1
|
0.08
|
0.54
|
0.01
|
4
|
ENET
|
1
|
0.18
|
1.06
|
0
|
0.30
|
3.39
|
23.40
|
0.78
|
Ridge
|
0.93
|
2.55
|
15.15
|
0
|
0.26
|
3.75
|
25.89
|
1.67
|
LASSO
|
1
|
0.23
|
1.45
|
0
|
1
|
0.32
|
2.20
|
0.05
|
ANN
|
1
|
0.06
|
0.38
|
-0.03
|
1
|
0.10
|
0.70
|
0.00
|
5
|
ENET
|
1
|
0.33
|
2.84
|
0
|
0.14
|
4.25
|
29.96
|
-1.42
|
Ridge
|
0.92
|
2.07
|
17.53
|
0
|
0.25
|
3.23
|
22.75
|
-1.69
|
LASSO
|
0.88
|
1.98
|
15.88
|
0
|
0.32
|
2.13
|
15.00
|
-1.09
|
ANN
|
1
|
0.01
|
0.05
|
0
|
1
|
0.00
|
0.02
|
0.00
|
6
|
ENET
|
0.91
|
1.93
|
21.94
|
0
|
0.96
|
3.59
|
26.34
|
-3.51
|
Ridge
|
0.91
|
1.93
|
21.94
|
0
|
0.96
|
3.59
|
26.34
|
-3.51
|
LASSO
|
0.91
|
1.63
|
15.97
|
0
|
0.96
|
1.79
|
13.14
|
-1.75
|
ANN
|
1
|
0.03
|
0.37
|
0.02
|
1
|
0.04
|
0.30
|
-0.01
|
7
|
ENET
|
1
|
0.23
|
2.75
|
0
|
0.05
|
4.26
|
34.71
|
-2.76
|
Ridge
|
0.90
|
1.66
|
19.57
|
0
|
0.06
|
3.96
|
32.29
|
-2.39
|
LASSO
|
0.89
|
1.55
|
16.23
|
0
|
0.71
|
2.35
|
19.16
|
-0.99
|
ANN
|
1
|
0.18
|
2.08
|
0.03
|
1
|
0.27
|
2.19
|
-0.09
|
8
|
ENET
|
1
|
0.13
|
1.93
|
0
|
0.01
|
5.28
|
56.08
|
-1.00
|
Ridge
|
0.92
|
1.71
|
24.84
|
0
|
0.00
|
5.22
|
55.37
|
-0.52
|
LASSO
|
0.70
|
3.40
|
44.74
|
0
|
0.49
|
4.48
|
47.55
|
-1.19
|
ANN
|
1
|
0.11
|
1.57
|
0.01
|
1
|
0.43
|
4.57
|
-0.03
|
ENET = Elastic Net, LASSO = Least absolute shrinkage and selection operator, ANN = Artificial neural network, R2cal = coefficient of determination at calibration stage, RMSEC = root mean square error at calibration stage, nRMSEC = normalized root mean square error at calibration stage, MBEC = Mean biased error at the calibration stage, which indicates the tendency of the model to overestimate or underestimate the value of the predicted variable, R2val = coefficient of determination at validation stage, RMSEV = root mean square error at validation stage, nRMSEV = normalized root mean square error at validation stage, and MBEV = Mean biased error at the validation stage. 56 Weather indices were used as the independent variable. DOS1 to DOS8: First to eight sowing dates (October 1, October 8, October 15, October 22, October 29, November 5, November 12, and November 19, respectively).
In the case of Ridge modelling approach, R2 values were again high (range between 0.86 and 0.93) during calibration stage for different sowing dates. However, it ranged between 0.13 and 0.46 (except DOS 6 when R2 is 0.96) during validation stage. nRMSE values were good to fair during calibration stage, while they were fair to poor during the validation stage. Similar to ENET, Ridge models were also not able to capture variation in the dataset, especially during late sowing dates (DOS 7 and 8) when R2 values were less than 0.10 and nRMSE fall under poor category. Ridge modelling approach retains all predictor in the final model, which makes the table bulky to reproduce. Therefore, we have omitted the equations governing yield prediction by this approach.
Wide variation in model performances was found with respect to prediction of mustard yield by LASSO at different sowing dates. R2 values at calibration were in nearly all cases high (between 0.70 and 1) for different sowing dates. Unlike ENET and Ridge, R2 values at validation were comparatively much higher (greater than 0.92) for most of the sowing dates (except DOS 5 and 8 for which it was less than 0.50). nRMSE values were good to poor at most of the sowing dates (except DOS 4 when model performance was excellent in terms of the nRMSE). Equations governing the prediction of mustard yield for different sowing dates by LASSO modelling approach is given in Table 6.
The cross comparison of different models showed that none of the models yielded satisfactory results for late sowing dates (DOS7 and DOS8), except ANN. Nevertheless, ANN followed by LASSO showed better performance for early to normal sown crops. In case of ANN, R2 values at calibration as well as validation were in nearly all cases very high (R2 ≈ 1.00). nRMSE values were excellent at all sowing dates for the ANN model.
Table 5
Equation for predicting mustard Yield derived from ENET during different dates of sowing
DOS
|
Equation
|
DOS1
|
22.3798139 + 0.054*Z141–0.036*Z240 + 0.110*WR
|
DOS2
|
31.948544 + 0.052*Z141–0.037*Z240–0.692*Time
|
DOS3
|
307.365313 + 0.845*Z51–0.137*Z20
|
DOS4
|
132.808309 + 0.366*Z51 + 0.005*Z151–0.094*Z20 + 0.006*Z451
|
DOS5
|
-103.797291 + 0.539*Z51–0.001*Z370
|
DOS6
|
-70.488054 + 0.184*Z51 + 0.064*Z241 + 0.001*Z160
|
DOS7
|
45.2612648 + 1.456*Z41–0.132*AB_Pod + 0.008*Z271–0.004*Z671–0.085*WR − 0.063*Z20
|
DOS8
|
53.8857635 + 1.129*Z41–0.175*Z20
|
Table 6
Equation for predicting mustard Yield derived from LASSO during different dates of sowing
DOS
|
Equation
|
DOS1
|
24.8073 + 2.642602*Z141 + 0.828641*Z151–0.82604*Z250
|
DOS2
|
23.31466 + 1.822084*Z51 + 1.406353*Z151 + 0.66581*Z11 + 0.406386*Z150 + 0.263659*WR − 0.43487*Z260–1.44853*Time − 2.18401*Z20
|
DOS3
|
20.3432 + 4.559278*Z51 + 0.64148*Z141 + 0.194844*Z451 + 0.174859*Z151 + 0.131922*WR − 1.10105*Z250
|
DOS4
|
16.18449 + 2.06555*Z51 + 1.864982*Z451 + 1.502912*Z151 + 0.477153*Z171 + 0.398134*Z670 + 0.048264*Z141–0.25058*Time − 0.30608*Z250–0.41483*Z20–1.10351*Z240
|
DOS5
|
12.48117 + 0.289997*Z471 + 0.526567*Z121 + 0.56469*Z271 + 0.748257*Z131 + 1.407286*Z51
|
DOS6
|
10.19678 + 1.071268*Z51 + 0.956943*Z241 + 0.938593*Z471 + 0.893505*Z341 + 0.266219*Time + 0.105854*Z251
|
DOS7
|
9.55631 + 1.279748*Z461 + 1.065818*Z121 + 0.668448*Z161 + 0.644006*Z271 + 0.258772*Z160 + 0.207597*Z141 + 0.129609*Z460 + 0.057392*Z471 -0.12559*AB_Pod
|
DOS8
|
7.603926 + 0.618974*Z41 + 0.603584*Z461 + 0.581344*Z271
|
Weighted and unweighted weather indices have been used as the predictors
DOS1 to DOS8: First to eight sowing dates (October 1, October 8, October 15, October 22, October 29, November 5, November 12, and November 19, respectively), WR: White rust (Albugo candida), AB_Pod: Alternaria blight infection on pods
The Pearson correlation coefficients (r) were also determined for the observed and predicted yield by different modelling approaches. Wide variation in the model performance was found in terms of r values as well (Table 7). In case of ANN, r value ranged between 0.91 and 1.00, except for the late sowing dates (DOS6 and onwards). Among shrinkage modelling approaches, LASSO performed well for majority of the sowing dates (except for the late sowing dates (DOS7 and DOS 8). The r values for other two approaches showed varying performance: Ridge (0.38–0.91); and ENET (0.46–0.92). These correlation coefficient values also showed ANN as the best performing model followed by LASSO, ENET, and Ridge. Small values of r correspond to the late sowing dates DOS 6 and onwards.
Table 7
Correlation coefficient between observed and predicted values at eight sowing dates by different modelling approaches
Sowing date
|
ENET
|
Ridge
|
LASSO
|
ANN
|
DOS1
|
0.68
|
0.75
|
0.71
|
0.98
|
DOS2
|
0.82
|
0.83
|
0.82
|
1.00
|
DOS3
|
0.72
|
0.75
|
0.74
|
0.90
|
DOS4
|
0.92
|
0.91
|
0.92
|
0.97
|
DOS5
|
0.85
|
0.38
|
0.84
|
0.98
|
DOS6
|
0.85
|
0.85
|
0.84
|
0.63
|
DOS7
|
0.59
|
0.59
|
0.62
|
0.85
|
DOS8
|
0.46
|
0.46
|
0.47
|
0.82
|
As per the evaluation performed based on R2, RMSE, nRMSE, and MBE, the application of ANN modelling approach generated the most accurate model among all the statistical methods and machine learning techniques considered in this research. The ANN outperformed the others demonstrating the highest R2, and lowest RMSE, and nRMSE at all sowing dates. The R2 value of the ANN model was close to 1 and MBE values were very close to zero at all sowing dates, compared to the other techniques. The plot of predicted versus actual yield suggested least dispersion from the line of best fit in case of ANN modelling approach (except late sowing dates, DOS6 onwards; Fig. 5) which is in line with the earlier findings of this study.
3.3 Contribution of input variables as obtained by the best performing model
Figure 6 presents the relative contribution of predictors (weather variables and disease severity) to the prediction of mustard yield, obtained by the PaD method. The vertical axis represents top ten input variables (weather variables and disease severity), plotting the highest contributing variable (largest sum of square derivative SSD value) at the top and other variables below in their decreasing order of contribution to prediction of a given variable. The scale of the horizontal axis varies with the different sowing dates. The contribution term is relative which depends on SSD values corresponding to each input variable for a given sowing date. The variable having the highest SSD value (i.e., the highest contribution) is assigned a value of 100%. Other variables are assigned this value (in %) based on their SSD values in comparison to the SSD value of the highest contributing variable.
The predictors that have significant contributions to the yield prediction are disease severity as well as weather variables (Fig. 6). Results indicate that the severity of white rust, followed by the morning relative humidity (which is a function of minimum temperature) are important determinants of yield for early sown crops. However, in late sown crops, Alternaria blight becomes the major yield-influencing (i.e., yield-reducing) variable. The relative contribution of disease severity of Alternaria blight exceeds 90%. This is especially true for sowing dates DOS 4 and beyond. Among the weather indices, the weighted weather indices of temperature and humidity have significant contribution in yield prediction. The afternoon relative humidity (a function of solar radiation) and rainfall are important predictors for very late sowing dates (DOS7 and DOS8).