Introduction

The great challenge of the agricultural sector is to produce more food from less water. With rapidly growing population, the pressure on limited fresh water resources increases. Estimation of water requirement of crop is essential for crop planning on farm and, for designing and monitoring irrigation projects. Prediction methods for crop water requirements are used owing to difficulty of obtaining accurate field measurements. Food and Agriculture Organisation (FAO) has given guidelines to calculate crop water requirements of crop under different climatic and agronomic conditions. Methods often need to be applied for such climatic and agronomic conditions, which are different from those under which they were originally developed. Testing the accuracy of methods under a new set of conditions is laborious and time consuming. Therefore, use of available computer software with appropriate modifications to suit the site conditions may be a better option.

Small-scale irrigation initiatives are expanding rapidly in Maharashtra. However, in many cases optimal yields are not being obtained despite the available water and required nutrient applications. Local stakeholders need an easy-to-use decision-support tool to assess irrigation water use and its impact on yield. A very powerful option to identify potential yields and possible crop cultivation constraints of particular areas are crop modeling tools [7]. Use of models can assist in evaluating and reducing time intensive and expensive field tests [19]. Model results with regard to crop performance, management, and yield estimates will help decision makers to decide which management system is suited best for a particular field, by estimating the yield and crop water productivity optimum. Frequently applied crop yield models are: CropSyst, CERES, DSSAT, EPIC, CropWat, SWAP/WOFOST, and AquaCrop [11].

AquaCrop simulates crop yield response to water and is particularly suited to address conditions where water is a key limiting factor in crop production. AquaCrop is developed from revision of ‘FAO Irrigation and Drainage Paper No. 33 Yield Response to Water’ (Doorenbos and Kassam 1979, [5]. AquaCrop attempts to balance accuracy, simplicity, and robustness. AquaCrop is the successor of CropWat featuring new adjustment options to reproduce crop environment in more detail. The capacity of AquaCrop model in simulating the yield in response to water is proved by various researchers [1, 3, 4, 8, 10, 16, 18], etc. Cabbage (Brassica oleracea var. capitata) is one of the important vegetable crops in Maharashtra State. Average annual production of cabbage in India is 8395.01 thousand tons and in Maharashtra is 421.00 thousand tons [National Horticulture Board (NHB) [14]. Productivity of cabbage in India, Maharashtra, and Vidarbha region is 22.04, 21.10, and 20.00 t ha−1, respectively. It is clear that the productivity in Vidarbha region is too less as compared to national level. Conventionally, cabbage is irrigated with flood irrigation method. The effect of drip irrigation on yield of cabbage under mulch and non-mulch condition is studied. Higher yield was obtained for drip irrigation with black plastic mulch 111.72 t ha−1 as compare to 106.68 t ha−1 for full volume of irrigation met with drip. Use of drip irrigation either alone or in combination with mulch can increase cabbage yield significantly over furrow irrigation to tune of 65 %. The highest yield per unit quantity of water used was 427.04 kg ha−1 mm−1 for the treatment 60 % of full water requirement with black mulch. The cost–benefit ratio is 8.17 for furrow irrigation treatment with full volume followed by 6.99 for 60 % of full volume of irrigation met with drip [17].

Taking into account the importance of water productivity, this research project was undertaken with following objectives. To calibrate and validate AquaCrop model for cabbage and to predict the response of cabbage to different irrigation schedules using validated model.

Materials and Methods

Data Collection

Meteorological Data

Meteorological data for the period November 2013 to February 2014 was obtained from Agro-meteorological Observatory, Department of Agronomy, Dr. P.D.K.V., Akola. It comprised of maximum and minimum temperature (°C), mean daily relative humidity (%), daily sunshine hours (hr), wind speed (ms−1), rainfall (mm), and evaporation (mm day−1) (Fig. 1).

Fig. 1
figure 1

Variation of maximum and minimum temperature

Crop Data

Crop-specific parameters required by AquaCrop model are plant density, yield, biomass, harvest index (HI), effective rooting depth, crop growth stages and green canopy cover (CC), while user-specific parameters required are crop cultivar, timing of crop cycle, water management, and agronomic practices.

The required data such as was obtained from a field experiment conducted in the Department of Irrigation and Drainage Engineering, Dr P.D.K.V Akola, India during the year 2013–2014 (Fig. 2).

Fig. 2
figure 2

Experimental plot of cabbage

The experiment consists of following treatments.

Treatment

Specifications

T1

Irrigation scheduling at 50 % moisture depletion of available water capacity under black polyethylene mulch with drip irrigation

T2

Irrigation scheduling at 50 % moisture depletion of available water capacity under silver polyethylene mulch with drip irrigation

T3

Irrigation scheduling at 50 % moisture depletion of available water capacity with drip irrigation

T4

Irrigation scheduling at 100 % crop evapotranspiration under black polyethylene mulch with drip irrigation

T5

Irrigation scheduling at 100 % crop evapotranspiration under silver polyethylene mulch with drip irrigation

T6

Irrigation scheduling at 100 % crop evapotranspiration with drip irrigation

Soil Data

To characterize the soil at experimental plot, soil profile study was carried out. Soil samples were collected from respective soil horizons for physicochemical analysis and results are presented in Table 1.

Table 1 Physical properties and soil moisture constants for soil at experimental site

Brief Description of Model

The complexity of crop responses to water deficits led to the use of empirical production functions as the most practical option to assess crop yield response to water. Among the empirical function approaches, FAO Irrigation and Drainage Paper No. 33 [6] represented an important source to determine the crop yield response to water through the following equation:

$$\left( { 1 { - }\frac{\text{Ya}}{\text{Yx}}} \right){\text{ = ky}}\left( { 1 { - }\frac{\text{ETa}}{\text{ETx}}} \right)$$
(1)

where

\({\text{Yx}}\) and \({\text{Ya}}\)—Maximum and actual yield, \({\text{ETx}}\) and \({\text{ETa}}\)—Maximum and actual evapotranspiration, and \({\text{ky}}\)—Crop yield factor

Calibration and Validation of Model

Part of the obtained field data, i.e., data for full irrigation treatment (100 % ETc under non-mulch—T6) was used for calibration of the model, while the remaining data were used to validate the model. AquaCrop version 4.0 was used in the study.

The model was calibrated by varying parameters such as canopy cover, water productivity, and harvesting index.

Model Performance

Nash–Sutcliffe coefficient and a dimensionless statistical measure, i.e., coefficient of residual mass were used to judge the performance of the model.

Nash–Sutcliffe Coefficient of Efficiency

Nash–Sutcliffe coefficient of efficiency (\({\text{R}}_{\text{NS}}^{ 2}\)) is used to assess predictive power of hydrological models. \({\text{R}}_{\text{NS}}^{ 2}\) is described by following formula [13].

$$R_{\text{NS}}^{2} = 1 - \frac{{\sum {(Q_{\text{O}} - Q_{\text{S}} )^{2} } }}{{\sum {(Q_{\text{O}} - Q_{\text{av}} )^{2} } }}$$
(2)

where, Qo—observed values; Qs—simulated values; Qav—mean of observed values.

Coefficient of Residual Mass (CRM)

CRM is a dimensionless statistical performance criterion as described below.

$${\text{CRM = }}\frac{{\left[ {\sum\limits_{\text{i = 1}}^{\text{n}} {{\text{O}}_{\text{i}} } { - }\sum\limits_{\text{i = 1}}^{\text{n}} {{\text{S}}_{\text{i}} } } \right]}}{{\sum\limits_{\text{i = 1}}^{\text{n}} {{\text{O}}_{\text{i}} } }}$$
(3)

where

\({\text{O}}_{\text{i}}\)—observed value at time i; \({\text{S}}_{\text{i}}\)—simulated value at time i.

Formulation of Irrigation Schedules

Daily reference ETo was estimated using modified Penman–Monteith equation [2]. Crop evapotranspiration was computed on daily basis using values of crop coefficients, for cabbage referred from [9, 15]. Ten schedules were formulated considering various levels of water application and mulch in combination as follows (Table 2).

Table 2 Formulated irrigation schedules

Effectiveness of Formulated Schedules

The calibrated model was used to evaluate the impacts of different irrigation schedules on performance of cabbage. Water use efficiency (WUE) refers to the ratio between the total yield of irrigated cabbage and total irrigation water applied [12].

$${\text{WUE}} = \frac{{{\text{Total}}\;{\text{irrigated}}\;{\text{cabbage}}\;{\text{yield}},{\text{kg}}}}{{{\text{Total}}\;{\text{irrigation}}\;{\text{water}}\;{\text{applied}},{\text{m}}^{3} }}.$$
(4)

Results and Discussion

Calibration and Validation of AquaCrop Model

Calibration and validation of FAO crop water productivity model, i.e., AquaCrop in terms of canopy cover, biomass and yield. Model performance and effectiveness of developed alternative delivery schedules was also evaluated based on water use efficiency.

Calibration of AquaCrop Model

AquaCrop model was calibrated for the period from November 27, 2013, to February 20, 2014, i.e., crop period, using field data for full irrigation treatment (i.e., irrigation scheduling at 100 % ETc under non-mulch—T6). To judge the performance of model, observed values of model parameters, i.e., canopy cover (CC), biomass and yield of cabbage were compared with simulated outputs. The performance of model is discussed in the following sections (Fig. 3).

Fig. 3
figure 3

Observed and simulated canopy cover for calibration period

Canopy parameters, i.e., initial canopy cover, canopy size of transplanted seedling, number of days to recover; maximum canopy cover and canopy cover decline, were adjusted manually during the calibration process.

Figure 4 shows that there is close match between observed and simulated canopy cover. It is supported by high value of \(R_{\text{NS}}^{ 2}\) (0.96). Another statistical parameter, i.e., CRM having value as −0.067, indicates that the model overestimates the canopy cover. From Fig. 4 it is clear that the canopy cover was overestimated by model particularly during 36–64 DAT, i.e., during development stage. But, the scatter plot clears that as the canopy cover lie on both sides of 1:1 line, there is no consistent over or under estimation.

Fig. 4
figure 4

Comparison between observed and simulated canopy cover for calibration period

Figure 5 shows that the model overestimate biomass though the value of \({\text{R}}_{\text{NS}}^{ 2}\) is high as 0.96. It is supported by another statistical criterion, i.e., CRM with value of −0.122 indicating model overestimate the biomass, in general. From Fig. 5 it is clear that the biomass was overestimated by model particularly during 30 to 75 DAT.

Fig. 5
figure 5

Comparison between observed and simulated biomass for calibration period

Cabbage head yield was observed as 14.31 t ha−1 for calibration period. For harvesting index of 80 %, the model predicted yield was 14.27 t ha−1. Nash–Sutcliffe coefficient as 0.98 indicates that the observed and simulated yields were in close match. Coefficient of residual mass as 0.084 indicates that the model slightly underestimates the yield.

Above results showed that the model calibration was satisfactory as the observed and simulated values of canopy cover, biomass, and cabbage yield matched well. Also \(R_{\text{NS}}^{ 2}\) and CRM statistics were acceptable. Hence, the AquaCrop model setup was considered as calibrated (Fig. 6).

Fig. 6
figure 6

Comparison between observed and simulated yield for calibration period

Model Validation

Model validation is in fact the extension of calibration process. Thus validation was carried out without any further adjustments to the calibrated model parameters. The model was validated for the period November 27, 2013 to February 20, 2014 for the remaining treatments, i.e., T1 to T5. The cumulative yield and biomass for validation period for each treatment were simulated with model, and Table 3 presents the results of statistical tests for validation period.

Table 3 Statistical analysis of validated results for biomass and yield

The biomass varied between 13.50 and 17.10 t ha−1, whereas yield of cabbage varied between 9.90 and 13.46 t ha−1. The average variation between observed and simulated biomass is −1.79 %, while average variation in yield is found to be −1.35 %.

Nash–Sutcliffe coefficient \(\left( {{\text{R}}_{\text{NS}}^{ 2} } \right)\) values are found as 0.96 for biomass and 0.93 for cabbage yield which shows close match between observed and simulated biomass and yield, respectively. Coefficient of Residual Mass (CRM) is found as −0.018 and −0.013 for biomass and yield, respectively, indicates that model overestimates the biomass and yield, likewise during calibration.

The comparison of observed and simulated values of biomass and yield for validation period are presented in Fig. 7.

Fig. 7
figure 7

Comparison between observed and simulated yield and biomass for validation

As simulated values lie on both side of 1:1 line, it is cleared that the model does not overestimate or underestimate the parameters consistently. Considering overall acceptability of validation results, it is concluded that the model performs well with relatively high validity.

Effectiveness of Developed Alternative Irrigation Schedules

To optimize irrigation schedule, water use efficiency (WUE) for different developed irrigation schedules was calculated (Eq. 4) using water applied and simulated yield; presented in Table 4.

Table 4 Water use efficiency for different schedules

In case of first set of irrigation schedules, i.e., from S1 to S5, WUE varied from 5.02 to 5.55 kg m−3. Schedule S5 resulted in maximum WUE, i.e., 5.55 kg m−3, while schedule S1 resulted in the lowest WUE, i.e., 5.02 kg m−3.

In second set of irrigation schedules, i.e., from S6 to S10, WUE varied from 5.16 to 6.91 kg m−3. Schedule S10 resulted in maximum WUE, i.e., 6.91 kg m−3, while schedule S6 resulted in the lowest WUE, i.e., 5.16 kg m−3. In general, water use efficiency increases as the water applied decreases.

Figure 8 shows the variation of yield against water applied for developed schedules.

Fig. 8
figure 8

Variation of yield against water applied

From Fig. 8, it is clear that if water applied decreases by 41.70 %, the yield of cabbage decreased by 44.14 %. It is cleared that as water applied decreases, the rate of reduction in the yield decreases gradually. From the table it is also clear that the cabbage is very sensitive to water applied.

It is also clear that in case of second set of developed schedules, i.e., schedules for mulched condition, as water applied decreases, yield of cabbage also decreases, but the rate of decrease in the yield is less as compare to Set I schedules. Table 4 also confirms that the yield of cabbage is increased under mulch condition as compare non-mulch condition, irrespective of schedule.

Maximum WUE was observed for schedule S10. Schedule S10 saved 41.70 % of water, but yield of cabbage reduced by 21.20 %. Schedule S8 saved 25.19 % water and resulted in only 4.63 % reduction in the yield as compared to control treatment. In case of schedule S7, with saving of 10 % water over control treatment, yield was increased by 1.41 %. Though yield was increased, water use efficiency decreased. Taking into account these facts, a soil moisture status in the soil was studied with output of calibrated model. The model generated transpiration, canopy cover, and soil moisture in the rootzone for schedule S8 and S10 are depicted in Figs. 9 and 10, respectively.

Fig. 9
figure 9

Model generated transpiration, canopy cover, and soil moisture in the rootzone for schedule S8

Fig. 10
figure 10

Model generated transpiration, canopy cover, and soil moisture in the rootzone for schedule S10

Figure 9 shows that up to first 30 days, soil moisture in the rootzone is at field capacity. Afterward it gradually decreases till the end of crop period. Throughout the crop period soil moisture is within available water capacity. The transpiration matched with that for full irrigation schedule (i.e., 100 % ETc) during first 60 days. Later on transpiration decreases during last 30 days as compare to that for full irrigation schedule and that’s why yield reduced by 4.63 %. The canopy cover matched with that for full irrigation schedule.

Figure 10 shows that up to first 20 days, soil moisture in the rootzone is at field capacity. Afterward it gradually decreases from 20 to 40 days after transplanting, and then it is more or less constant. Throughout the crop period soil moisture is within available water capacity. The transpiration matched with that for full irrigation schedule (i.e., 100 % ETc) during first 35 days. Later on transpiration decreases gradually till end of crop period as compared to that for full irrigation schedule and that is why yield reduced by 21.20 %. The canopy cover also decreases from 35 to 90 days after transplanting.

Thus it is clear that for schedule S8 soil moisture status in rootzone canopy cover and transpiration is better as compared to that for schedule S10.

As schedule S8 (mulch + Irrigation schedule at 80 % ETc) saved 25.19 % water with only 4.63 % reduction in the yield of cabbage head as compared to control, it should be used for cabbage production.

Summary and Conclusions

Irrigated agriculture is the largest water-consuming sector, and it faces competing demands from other sectors, like industrial and domestic. Increasing demand and scarcity of water makes it important to use available water in most economic ways. Since land is a shrinking resource for agriculture, the pathway for achieving this goal has to be higher productivity per unit of arable land and water. Thus, the objective of irrigation in the present era is not only to provide supplementary water for crop production but also to increase crop per drop of water. As such, the question of improving the present level of water use efficiency in general and for irrigation in particular assumes a great significance in perspective water resource planning.

AquaCrop model proved its capability in simulating canopy cover, biomass and yield. The AquaCrop model was calibrated for daily irrigation schedule at 100 % ETc. The calibrated model parameters, i.e., initial canopy cover, harvesting index, and water productivity, were observed as 0.67, 80 %, and 21 g m−2, respectively.

Ten alternative irrigation schedules were formulated for mulch and non-mulch condition. These alternative irrigation schedules were optimized on the basis of water use efficiency. Simulations were carried out with calibrated AquaCrop model for the period November 27, 2013 to February 20, 2014. WUE efficiency is found maximum for schedule S10 with high reduction in the yield as 21.20 %, while schedule S8 saved 25.19 % water, with only 4.63 % reduction in the yield of cabbage head. Therefore, it is suggested to undertake cabbage production under polyethylene mulch with drip irrigation having daily irrigation schedule fixed at 80 % of ETc.

Implications

Among the developed alternative irrigation schedules, the schedule S8, which can explained as irrigation scheduling at 80 % of crop evapotranspiration (ETc) under polyethylene mulch with drip irrigation, was observed to be the best as compared to existing schedule in terms of WUE. By implementing the selected schedules for cabbage, increase in water productivity as well as water saving can be achieved.

As performance of delivery schedule was assessed based on water use efficiency estimated using the computer software tool AquaCrop, it needs to be validated on field scale to confirm the actual variation in observed values of this study.