Analysing variability and trends in different sources of irrigation in India: A time series perspective

Introduction

Agriculture is the most important sector of Indian economy, where more than 58% population depends on agriculture. Irrigated agriculture has made a major contribution to food production and food security throughout the world. The farmers get water for their crops either from rainfall or from artificial irrigation such as wells, tanks and canals. The importance of irrigation for agricultural production growth in India hardly wants any emphasis. Improved reliability of facility of water supply through canals, tanks or through groundwater (wells) has significantly contributed to the increase in agricultural productivity in India. Recent studies show that the irrigation needs to play a bigger role towards a goal of achieving a better agricultural productivity and also the national food security. (Persaud and Stacey, 2003;Kumar 1998, GOI 1999; Bhaduri et al., 2012) [9, 8, 6, 2] . India's irrigation covered crop area was about 22.6 million hectares in 1951, and it increased to a potential of 90 million hectares at the tip of 1995, integral of canals and wells. The irrigation infrastructure includes a network of canals from rivers, ground (well) water, tanks and various rain water harvest merchandise for agriculture activities. As per the land use statistics 2018-19, the total geographical region of the country is 328.7 million hectares, of which reported net sown area is 139.3 million hectares and the net irrigated area is 71.6 million hectares. (Ministry of Agriculture and farmers Welfare, Annual Report, 2022-23). In India, there is three major sources of Irrigation: Canals, Tanks and Wells. Canals: Canals are the main source of irrigation in India, especially in northern part i.e. Uttar Pradesh, Andhra Pradesh, Punjab and Haryana of India. Canals are big water channels taken out from rivers to carry water to places which are pretty much far away from the river. Tanks: Tank irrigation is a natural or man-made spring included as part of a structure. It is mainly known for harvesting and preserving the local rainfall and water from streams and rivers for later use, primarily for agriculture and drinking water. It is commonly used in southern part of India viz. Andhra Pradesh, Karnataka, Tamil Nadu and Maharashtra.

Well: Well irrigation is a principal method of irrigation used in India. Underground water is tapped for drinking purposes and at the same time it is also tapped for irrigating the cultivated land. It is also found that in such areas, production of crops done with the usage of well water is quite rewarding. Uttar Pradesh leads in well irrigation and is followed by Punjab, Haryana, Bihar, Gujarat and Andhra Pradesh. Two types of wells: Open wells and tube-wells.

Materials and Methods

Materials

All the data are used in the study relies on secondary data compiled from various published sources. Data with respect to net irrigated area by different sources of irrigation in India are selected from the period of 1950-1951 to 2021-22 from Ministry of Agriculture & Farmers Welfare, Govt. of India. Canal, tank and well are the major sources of irrigation in India on which the time series analysis is done.

Methodology

This present paper is attempting to analyse the various time series models and to estimate the best fitted models for net irrigated area under different sources. Also, to examine the nature of each series which has been subjected to get various descriptive statistical measures and trend models is also considered for study.

Descriptive Statistics

Descriptive statistics offer simple summaries about the data and the measures. The descriptive statistics study that used for study are maximum, minimum, mean, median, skewness, kurtosis etc. to describe the pattern of the series and draw a consensus under consideration.

Trend models

Box-Jenkins models

It is that methodology which assess the present value of the series is any way related with its past values. Box -Jenkins (1970) analysis is a mathematical method of identifying, estimating, fitting, checking, and using integrated autoregressive, moving average (ARIMA) time series models. The method is appropriate for time series of medium to long length (at least 30 observations). It is used for forecasting which is technically known as the ARIMA methodology.

Autoregressive Integrated Moving Average Model (ARIMA)

ARIMA models are the most general class of models for forecasting a time series which can be made stationary by transformation or differencing. In fact, the easiest way for ARIMA models is as fine-tuned versions of random walk and random trend models: the fine-tuning consists of adding lags of the differenced series or lags of the forecast errors to the prediction equation, as needed to remove any last traces of autocorrelation from the forecast errors. Lags of the differenced series appearing in the forecasting equation are called "auto-regressive" (AR) terms, lags of the forecast errors is defined as "moving average" (MA) and a time series which needs to be differenced to be made stationary is said to be an "integrated" which is a stationary series. A non-seasonal ARIMA model can be classified as an "ARIMA" i.e. p,d,q model, where:  p is the number of autoregressive terms,  d is the number of non-seasonal differences, and  q is the number of lagged forecast errors for prediction.

ARIMA in general form is as follows

Where ∆ denotes differences operator like

Here, Z t-1 … Z t-p are values of past series with lag 1… p respectively.

ARIMA consists of following steps are as follows Identification:

The problem is to find out the appropriate values of p, d and q. One of the important tools for identification are the autocorrelation function (ACF), the partial autocorrelation function (PACF), and the resulting correlograms, which are simply the plots of ACF and PACFs against the lag length.

Estimation: After identifying the appropriate values of p and q the next step is to estimate the parameters of the autoregressive and moving average terms included in the model. Sometime this calculation can be done by simple least squares.

Diagnostic checking:

In this step one can see the whether the chosen model fits the data reasonably well.

Stationarity test:

For stationarity test, two test is used i.e. Augmented-Dickey-Fuller (ADF) test and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests are used to check whether the data series is stationary or not.

Model Formulation

The It is given by LB = n (n+2)∑

Results

Table-1 displays descriptive statistics with respect to NIA by different sources of irrigation in India from 1951 to 2022. The descriptive statistics demonstrates the mean, maximum and minimum values along with other statistical properties. It is noticed that since 1951 the net irrigated area by canal has increased from 8.30 to 19.22 million hectares, registering a simple growth rate of almost 1.48% per annum with an average of 14.42. In case of tank, the net irrigated area has been increased from 1.59 to 4.78 million hectares registering a simple growth rate of almost -0.81% per annum with an average of 3.15, while in case of wells, the net irrigated area has been increased from 5.98 to 47.33 million hectares, registered with a simple growth rate of almost 9.66% per annum with an average of 23.40. It is observed that in case of total NIA has increased from 20.85 to 77.91 million hectares with an average of 44.83 and registered a simple growth rate of almost 3.75% per annum. It has been observed that the simple growth rate of well source of irrigation is much higher than other sources of irrigation. In case of well and total NIA has registered positive skewness and negative kurtosis, which means that there has been increasing order during early half of the study period and it's for a long time. The standard deviation of total net irrigated area is comparatively higher than well, tank and canal. The lowest standard deviation is observed in case of tank. In case of canal and tank, negative skewness and negative kurtosis has been registered which reveals that there is marginal and consistent in net irrigated area during the later phase of investigation. As per JB test result, it is confirmed that all three data series are normally distributed as canal, well and total NIA are significant but tank are nonsignificant. It has been concluded that data series of well was better balanced as compared to other sources.

Trend model fitting regarding net irrigated area by different sources in India

Various parametric regression models are applied to all dataset for path of movement of the series from knowing the above per se performance. All estimated parameter and goodness of fit by those models are presented in table-2. For testing parametric models, linear model is fitted best for canal, tank, well and total NIA on the basis of following criteria: significance of parameters at 5% level, maximum R 2 value and minimum value of RMSE. The coefficients of linear model are negatively significant in nature with maximum R 2 value and thereby indicating the tendencies of the series to decline in recent past. This is clearly a major concern towards irrigation sources. In case of canal, linear model is best fitted based on the parameter estimate and goodness of fit, it is found that that in canal, all parameters are significant with the value of R 2 (0.76) and minimum values of RMSE (1.32).While in tank, linear model is significant with the value of R 2 (0.83) and minimum values of RMSE (0.36).It is observed that in well irrigation, linear model is fitted with positively significant with the value of R 2 (0.98) and minimum values of RMSE (2.05) and for total NIA, negatively significant with the value of R 2 (0.99) and minimum values of RMSE (1.66). From figure-1, it seems that net irrigated area by wells among all other sources increases rapidly; due to this reason showing highest simple growth rate (table-2) among all other sources. But in case of tank, the figure-1 revealed that the net irrigated under tank decreased rapidly by the time that's why its simple growth rate was in negative value. For applying the most time series models, the dataset must be checked of its stationarity. Augmented Dickey Fuller (ADF) test and KPSS test are applied for testing the stationarity. From table-3, it is observed that all the dataset are presented as non-stationary which is insignificant at 5% level of significance as the null hypothesis is not rejected as the p-value is greater than 0.05 that means the null hypothesis is not stationary. The ACF and PACF graphs of the original series also clearly indicates that none of the series is stationary in nature and first order differencing is sufficient to make these stationary i.e., d=1. As per autocorrelation and partial autocorrelation consideration, the best fitted ARIMA (p, q, q) models are selected for different sources of irrigation in India and compared to each other as depicted in table-4. All the best fitted models are selected based on maximum R 2 value and minimum values of RMSE, MAPE, MAE, MaxAPE, MaxAE. Ljung Box test are done for randomness. It is found that ARIMA (0, 1, 4) are fitted best for canal, for tank ARIMA (1, 0,1) is fitted best and for total NIA ARIMA (1, 0, 3) whereas (1, 0, 2) is selected best fitted model for well source of irrigation due to high R 2 (0.997) and low values of RMSE (0.521), MAPE (1.583) and MAE (0.466). Residuals of this model also satisfied both the normality and randomness assumptions. All the estimated parameters are significant at 5% level of significance. From residual ACF and PACF plots of ARIMA models for all sources of irrigation and its total, it is as shown in figure -2. From this it is also confirmed that the 'good fit' for selected models.

Model validation and forecasting

Among the selected models, ARIMA models fit well for all dataset and finally used to forecast for corresponding variables. There are two kinds of forecast i.e. in sample forecast and out sample forecast. From table-5, it clearly observes that in sample forecast are from 2020 to 2022 and out sample forecast are from 2023 to 2029. In case of in sample forecast, the predicted values are for all dataset are almost close to actual values. The net irrigated area by canal is forecasted as 18.48 million hectares for the year 2027 and 18.74 million hectares for the year 2029. It is found that the net irrigated area by tank will be decreased 1.58 million hectares in the year 2029. In case of well, the net irrigated area will be increased 49.46 million hectares and 50.56 million hectares for the year 2027 and 2029 respectively. It is observed that the total NIA will be increased 78.36 in the year 2029. From figure-3, it is observed that the net irrigated area by canals, wells and total NIA are forecasted as increasing order except tank which is forecasted as decreasing order. The net irrigated area by wells has showed a definite increasing from 1951 to 2029.

Discussion and Conclusion

In our study, we examined that the use of well source of irrigation has been increasing since 1951, as compared to other sources of irrigation i.e. canal and tank and becoming an important source of irrigation. There is a positive relationship between agriculture and well (groundwater) source of irrigation. After forecasting the data, it has been observed that in future there would be more demand of well source of irrigation for growing crops. Groundwater based irrigation allowed farmers to cultivate crops throughout the year, even during the dry season, resulting in increasing agricultural productivity and reduced vulnerability to weather fluctuations. Demand of tank and canal source of irrigation has been reduced because of irregularity of rainfall.

References

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