Introduction

Accurate estimation of crop water requirement is an important aspect of agricultural planning. The water requirement varies widely from crop to crop and also during the period of growth of individual crops. Water use efficiency which is essentially governed by crop evapotranspiration (ETc) can be improved by proper irrigation planning, scheduling and decision making on a regional scale based on estimated ETc, which in turn depends on the crop coefficient (Kc). ETc is calculated by multiplying reference evapotranspiration (ET0) with Kc to account for the differences in the crop canopy under given climatic conditions. The FAO-56 [1] reported crop coefficients at different stages of growth for various agricultural crops and suggested the adjustment for different wetting frequencies, climatic, agronomic and water management conditions. However, it has been emphasized in the literature that there is a strong need for local calibration of crop coefficients under given climatic conditions.

The researchers have [2] developed crop coefficients for a number of crops grown under different climatic conditions and suggested the use of these values at locations where local data are not available. However, they emphasized the strong need for local calibration of crop coefficients since the climatic conditions encountered in the field differ from the standard conditions. Earlier, the researchers have worked out on crop coefficient values and crop coefficient curves for different crops [3–5]. The investigators have derived crop coefficient curves as a function of day past planting for different crops using fifth order polynomial [6]. Shah and Edling crop coefficients for rice crop for the vegetative, flowering, and yield formation stages using Penman–Monteith (daily) ET0 and recommended a second order polynomial to moderately fit to the interval-wise Kc data [7]. The researchers have developed crop coefficients for wheat and sorghum crops from ETc measurements and weather data at Karnal and, observed that Kc values for these crops at the four crop growth stages are significantly different from those suggested in UN FAO indicating the need for generating these values at the local/regional level [8]. The values of Kc have been estimated at different stages for potato crop using lysimeter measured ETc at sub- humid Kharagpur region and compared stage- wise Kc values estimated by various methods [9]. The Kc value at the maturity stage was found to be considerably higher than the corresponding FAO recommended Kc value. It was also observed that the Penman–Monteith method is the best method to estimate daily and stag-wise Kc using the lysimeter measured ETc. The investigators have [10] estimated Kc in AL- Hassa for the fourth growth stages of wheat crop. Jeetendra Kumar and Singh developed crop. It has been developed by earlier investigators the crop coefficient models for wheat and maize in the Gandak command area in Bihar and a polynomial model was fitted to the Kc values [11]. Alkaeed et al. emphasized the need for local calibration of Kc by indicating the necessary adjustment of Kc to the field conditions under the environmental effects [12]. The researchers have developed crop coefficients and relationships for cotton, sorghum and millet crops [13]. It was also reported that Kc values for cotton crop in the late stage, for sorghum crop in the mid and late stages and for millet crop in all stages were significantly different from FAO suggested Kc values.

The present study compares the crop coefficients computed using ET0, estimated from Penman–Monteith equation and, lysimeter measured ETc with those recommended by FAO-56. It also attempts to develop crop coefficient models for different crops in the study area for estimating ETc with reasonable degree of accuracy.

Materials and Methods

The lysimeter measured ETc and the climatic data during the crop period at Tirupati (Rayalaseema region), Nellore, Rajahmundry and Anakapalli (Coastal region) and Rajendranagar (Telangana region) meteorological centers in Andhra Pradesh collected from the India Meteorological Department (IMD), Pune, India were used in the data analysis and model development. The data was divided into training and testing sets for the purpose of model development and its verification respectively. The closeness of the statistical structure in terms of mean, variance and skewness of the calibration and validation data sets was ensured while making the division. The location of the meteorological centers is shown in Fig. 1 and a brief description of these centers is presented in Table 1. The crop details and the period of data collected are given in Table 2.

The crop coefficients for various crops were calculated as the ratio of lysimeter measured ETc to ET0 estimated from Penman–Monteith equation and compared with the adjusted Kc values. The adjusted FAO-56 Kc curve was constructed with mean values at different crop growth stages after suitably modifying the table values of crop coefficients for average wetting events and climatic conditions using the following expressions.

$$ {\text{K}}_{{{\text{c}}\;{\text{ini}}}} = {\text{K}}_{{{\text{c}}\;{\text{ini}}\; ( {\text{FAO)}}}} + \left[ {({\text{I}} - 10)/(40 - 10)} \right] \times \left[ {{\text{K}}_{{{\text{c}}\;{\text{ini}}\; ( {\text{heavy}}\;{\text{wetting)}}}} - {\text{K}}_{{{\text{c}}\;{\text{ini}}\; ( {\text{light}}\;{\text{wetting)}}}} } \right] $$
$$ {\text{K}}_{{{\text{c}}\;{\text{mid}}}} = {\text{K}}_{{{\text{c}}\;{\text{mid}}\; ( {\text{FAO)}}}} + \left[ {0.04({\text{u}}_{2} - 2) - 0.004({\text{RH}}_{ \hbox{min} } - 45)} \right]({\text{h}}/3)^{0.3} $$
$$ {\text{K}}_{{{\text{c}}\;{\text{end}}}} = {\text{K}}_{{{\text{c}}\;{\text{end}}\; ( {\text{FAO)}}}} + \left[ {0.04({\text{u}}_{2} - 2) - 0.004({\text{RH}}_{ \hbox{min} } - 45)} \right]({\text{h}}/3)^{0.3} $$
Fig. 1
figure 1

Location map of the meteorological centers in Andhra Pradesh

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Table 1 Brief description of the meteorological centers
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Table 2 Crop details and period of data
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A polynomial Kc model as a function of x (number of days from sowing of the crop) is expressed as:

$$ {\text{K}}_{\text{c}} = {\text{C}}_{ 1} {\text{x + C}}_{ 2} {\text{x + C}}_{ 3} {\text{x}}^{ 2} + \ldots $$

where C1, C2, C3,… are empirical constants.

The Kc models were developed using calibration data set and verified using validation data set. The performance of Kc models is verified by comparing ETc computed from ET0 estimated from Penman–Monteith equation and Kc, calculated using the models developed with that of lysimeter measured ETc using the validation data set. The validity of the models is evaluated based on numerical and graphical performance indicators. The numerical performance indicators include correlation coefficient, RMSE [14], and efficiency coefficient [15]. The scatter and comparison plots are graphical indicators.

Results and Discussion

The daily crop coefficients calculated at different stages of growth were compared with mean adjusted values as recommended in FAO-56 manual by fitting the mean curve with the trend similar to the one recommended in FAO-56 as shown in Fig. 2. It may be noted that the table values suggested in FAO-56 were adjusted to the climatic conditions and wetting frequencies of the study area for the construction of the FAO-56 Kc curve. The variation of Kc at different stages of crop growth (Fig. 2) indicates that FAO-56 mostly overestimates daily Kc values at all stages of groundnut crop at Tirupati and of tobacco crop at Rajahmundry. It almost coincides with the proposed mean daily Kc curve of castor crop at Rajendranagar at initial and development growth stages but overestimates at mid and late stages. It underestimates at initial, development and mid stages and overestimates at late stage of sugarcane crop at Anakapalli. It almost coincides with mean daily Kc at all stages of paddy crop at Nellore. A significant deviation of the curve (Fig. 2) at most of the stages of crop growth of crops selected for the present study from that suggested by FAO-56 may be due to different agronomic, soil, climate and water management conditions. This suggests the need for the development of Kc models at the centers in order to reasonably estimate ETc in the study area.

Fig. 2
figure 2

Comparison of Kc curve derived from PMM ET0 and lysimeter measured ETc with that of FAO-56 curve

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The variation of Kc with time during crop period is shown in Fig. 3. Differences in leaf anatomy, stomata characteristics, aerodynamic properties and albedo caused ETc of different crops to differ under the same climatic conditions. It may be observed from these plots that Kc values showed an increasing trend with the advancement in the crop growth up to physiological development and after that started declining. A dual third order polynomial model each for raising and falling trends of Kc curve was therefore fitted to the data as presented in Table 3.

Fig. 3
figure 3

Variation of daily Kc values

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Table 3 Polynomial regression Kc models
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It may be noted that the variation of Kc with crop canopy and other crop parameters is not dealt with in the present study because of limited crop data available. However, the empirical coefficients in the model may, to a certain extent, implicitly take care of the effect of various crop parameters for the commonly grown crops and their varieties in the study area. The ETc has been estimated using Kc values obtained from these models and compared with ETc measured. Figures 4 and 5 respectively present the scatter diagrams and comparison plots between measured ETc and estimated ETc. The performance indicators in the ETc estimates are given in Table 4. The values of R2 and EC indicate that ETc values estimated using the Kc models developed are fairly good. The RMSE found is also low. The slope (m) and intercept (c) respectively close to one and zero of scatter plots and, closeness of computed ETc with ETc measured in the comparison plots, indicate the satisfactory performance of the models. Therefore, the Kc models proposed may be adopted in the reasonable ETc estimation for the crops commonly grown in the study area.

Fig. 4
figure 4

Scatter plots of daily ETc observed with ETc estimated. A Training period, B testing period

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Fig. 5
figure 5

Comparison of daily ETc observed with ETc estimated during testing period

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Table 4 Performance indicators
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Conclusion

The crop coefficient values, computed for various crops using lysimeter measured ETc and, Penman–Montieth ET0 were compared with adjusted Kc values suggested in FAO-56 manual. These values deviated significantly from the adjusted FAO-56 values. A third order polynomial model has been developed to determine Kc values at different stages of growth for the crops commonly grown in the study area. The ETc values computed using Kc estimated from the models proposed are comparable with those lysimeter measured ETc. The Kc models proposed for different crops in the study area may therefore be adopted in the ETc estimates with reasonable degree of accuracy.