Maize crop yield forecast using discriminant function analysis of weather parameters for Udham Singh Nagar district of Uttarakhand

Introduction

Maize is a vital crop for food security and sustainable agriculture, with over 90% of global production used for food, feed, and biofuel (FAO, 2020) [1] . Accurate yield prediction is crucial for farmers, policymakers, and stakeholders to make informed decisions. Weather variables significantly impact maize yield, but analyzing multiple weather variables can be challenging. Climate change is one of the most pressing issues of our time, with far-reaching consequences for global food security, sustainable agriculture, and ecosystem resilience. Maize, a staple crop for over 50% of the global population, is particularly vulnerable to climate change impacts. Rising temperatures, changing precipitation patterns, and increased frequency of extreme weather events can significantly affect maize yields, leading to reduced food availability, economic losses, and social instability. Weather variables significantly impact maize yield, but analyzing multiple weather variables can be challenging. Understanding the relationships between climate change and maize yields is crucial for developing effective mitigation and adaptation measures. This research aims to contribute to the existing body of knowledge on climate change and agriculture, providing insights for policymakers, researchers, and practitioners to ensure food security and sustainable agriculture in the face of climate change. Researchers have previously attempted to develop statistical models for predicting agricultural yield prior to harvest, utilizing time series data on crop yield and meteorological variables.

Early attempts by Fisher (1924) [2] , Hendricks and Scholl (1943) [3] , Agrawal et al. (1980) [4] , Agrawal et al. (1983) [5] , Agrawal et al. (1986) [6] , and Agrawal et al. (2001) [7] , and Jain and Singh (1980) [8] employed regression models. Later, Rai and Chandrahas (2000) [9] , Agrawal et al. (2012) [10] , Sisodia et al. (2014) [11] , Azfar et al. (2014) [12] , Azfar et al. (2015) [13] , and Yadav et al. (2016) [14] explored the use of discriminant function analysis, incorporating weather indices and weekly weather data, to forecast agricultural yield. Notably, the application of discriminant function analysis has yielded promising results, demonstrating its potential as a valuable tool for agricultural yield prediction. In this research, we utilized discriminant function analysis (DFA) to investigate the relationship between weather indices and maize yields in the Udham Singh Nagar district of Uttarakhand. By applying DFA to various weather variables, our objective was to identify the most critical weather factors that impact maize yield and develop robust statistical models for predicting yields in this region, thereby enabling datadriven decision-making for agricultural planning and management.

Materials and Methods

Description of the study area

The study area for constructing Yield forecast models encompasses the Udham Singh Nagar district in Uttarakhand state, particularly focusing on kharif maize crop yield data (kg/ha) and corresponding weather data. The study area located in the Kumaon Division's Terai region, this district spans across 78° 45' E to 80° 08' E longitude and 28° 53' N to 29° 23' N latitude. The region experiences a sub-tropical to sub-humid climate, characterized by three distinct seasons: summer, monsoon, and winter. The soil profile is predominantly shallow, with a texture ranging from sandy to loamy.

Description of the data

Software used

The analysis and modeling in this study were carried out using two software tool: SPSS (Statistical Package for the social Sciences) and Microsoft Excel.

Statistical procedure

Out of the 21-year data, 17-year data were used for training the model while remaining 4 years data were used for testing the model. Weekly data on weather variables was used to create weather indices (Agrawal et al., 1983) [5] . In this study five models were created with discriminant function analysis as independent variables which also include time trend and maize yield as dependent variable. Discriminant analysis is a multivariate technique concerned with separating distinct sets of objects (or sets of observations) and allocating new objects (or observations) to the previously defined groups. The technique of discriminant function analysis is used to identify an appropriate function that discriminates best between set of observations from two or more groups and classifying the function observations into one of the previously defined groups. Observations are classified into k non-overlapping groups on the basis pvariables.

Development of weather indices using correlation coefficient as weight

This is based on the method given by (Agrawal et al., 1983) [5] for developing forecast using weather indices. In this procedure, the entire 15 weeks data have been utilized for constructing weighted and un-weighted weather indices of weather variables along with their interactions. In all, 72 indices (36 weighted and 36 unweighted) consisting of 8 weighted weather indices and 28 weighted interaction indices; 8 un-weighted indices and 28 un-weighted interaction indices have been obtained. These weather indices and interaction indices have been computed by using the following formula:

Where, j = 0, 1 (where, '0' represents unweighted indices and '1' represents weighted indices) n = Number of weeks considered in developing the indices r iw = Correlation coefficient between de-trend crop yield and i th weather variable in w th week r ii'w = Correlation coefficient between de-trend crop yield and the product of i and i' th weather variable in w th week X iw and X i'w are the i and i' th weather variable in w th week respectively

Determination of number of discriminant scores

Consider that observations are classified into k (=3) nonoverlapping groups on the basis p (=8) variables. The technique identifies linear functions where the coefficients of the variables are determined in such a way that the variation between the groups gets maximized relative to the variation within the groups. The maximum number of discriminant function that can be obtained is equal to minimum of (k-1) and p (Sharma, 1996) [15] .

Development of the forecast model using discriminant function analysis

The crop years have been divided into three groups based on crop yield adjusted for trend effect in order to apply discriminant function analysis for modeling yield using weather variables. These three groups' meteorological data were utilized to create linear discriminant functions, and each year's discriminant scores were calculated. The forecast models are fitted by taking the discriminant scores and the trend variable as the regressors and crop yield as the regressand. The models are developed using stepwise regression procedure. Since there are three groups and eight meteorological variables in the current study, only two discriminant functions are necessary to classify a crop year into one of the three categories. These are the three groups of crop years, namely adverse, normal, and congenial: Let y and s represent the average and range of agricultural production after adjusting for n years. Adjusted crop yields less or equal to y-s would be in the adverse group, those between y-s and y+s would be in the normal group, and those above or equal to y+s would be in the congenial group.

Model 1

In this approach, all 72 indices (weighted and unweighted including interaction indices) served as discriminant variables in a discriminant function analysis. This yielded two sets of discriminant scores, which were subsequently utilized as regressor variables in a forecasting model. The model was fitted with untrended yield as the dependent variable (regressand) and the two sets of discriminant scores, along with the trend variable (T), as independent variables (regressors). The resultant model takes the form as follows: Y= ꞵ 0 + ꞵ 1 ds 1 + ꞵ 2 ds 2 + ꞵ 3 T + ԑ Where, y = crop yield ꞵ 0 = intercept of the model ꞵ i ʹs (i=0, 1, 2, 3) = the regression coefficients ds 1 and ds 2 are the two discriminant scores. T is trend variable (T=1,2,3,….,n) and ԑ is error term assumed to follow independently normal distribution with mean 0 and variance σ 2 .

Model 2

In this approach, 16 weather indices (8 weighted and 8 unweighted) derived from 8 weather variables served as discriminant variables in a discriminant function analysis. This yielded two sets of discriminant scores, which were subsequently utilized as regressor variables in a forecasting model. The model was fitted with untrended yield as the dependent variable (regressand) and the two sets of discriminant scores, along with the trend variable (T), as independent variables (regressors). The resultant model takes the form as follows: Y= ꞵ 0 + ꞵ 1 ds 1 + ꞵ 2 ds 2 + ꞵ 3 T + ԑ Where the notations represent the same variables as defined in Model 1.

Model 3

In this approach, 36 unweighted weather indices (8 primary indices and 28 interaction terms) served as discriminant variables in a discriminant function analysis. This yielded two sets of discriminant scores, which were subsequently utilized as regressor variables in a forecasting model. The model was fitted with untrended yield as the dependent variable (regressand) and the two sets of discriminant scores, along with the trend variable (T), as independent variables (regressors). The resultant model takes the form as follows:

Where the notations represent the same variables as defined in Model 1.

Model 4

This approach utilizes 36 weighted weather indices (8 primary indices and 28 interaction terms) as discriminant variables in a discriminant function analysis. This yielded two sets of discriminant scores, which were subsequently utilized as regressor variables in a forecasting model. The model was fitted with untrended yield as the dependent variable (regressand) and the two sets of discriminant scores, along with the trend variable (T), as independent variables (regressors). The resultant model takes the form as follows: Y= ꞵ 0 + ꞵ 1 ds 1 + ꞵ 2 ds 2 + ꞵ 3 T + ԑ Where the notations represent the same variables as defined in Model 1.

Model 5

This approach utilizes 28 weighted weather interaction indices and 28 unweighted weather interaction indices as discriminant variables in a discriminant function analysis. This yielded two sets of discriminant scores, which were subsequently utilized as regressor variables in a forecasting model. The model was fitted with untrended yield as the dependent variable (regressand) and the two sets of discriminant scores, along with the trend variable (T), as independent variables (regressors). The resultant model takes the form as follows:

Where the notations represent the same variables as defined in Model 1. All the aforesaid models have been fitted with the data pertaining to the years 2001 to 2017 and the data pertaining to the year 2018 to 2021 were used for validation of the forecast models.

Testing the Performance of the Model

Finally the performance of the developed models was evaluated on the basis of Coefficient of determination (R 2 ), Adjusted Coefficient of determination (Adj.R 2 ), Root Mean Square Error (RMSE) and Percentage Error (PE). R 2 &Adj.R 2 towards 1 and RMSE towards 0 indicate better performance of the developed models. Also least range of PE indicates better performance.

Results and Discussion

Yield forecast models were constructed using maize crop yield data (kg/ha) and weather data of maize for a period of 21years (2001-2021). 17 years data for training the model, from 2001 to 2017 were used and 4 years data for testing the model, from 2018 to 2021 were used. Training set establishes the relationship between predictors and dependent variable. Testing dataset determine the prediction accuracy of forecasted models. In this study five models were created with discriminant scores as independent variables which also include time trend and maize crop yield as dependent variable.

Conclusion

Discriminant function analysis is a powerful statistical technique for predicting outcomes based on multiple variables. In this case, it's been used to develop forecast models for maize crop yield in Udham Singh Nagar district of Uttarakhand using weekly data on eight weather variables. One of the five developed models, model 4 which includes all the 36 weighted weather indices (8 primary indices and 28 interaction terms) has been identified as the best performers based on various evaluation criteria such as coefficient of determination, Root Mean Square Error (RMSE) and percentage error. This model can provide a reliable forecast of maize crop yield which is incredibly valuable for farmers, agricultural planners, and policymakers. This kind of predictive insight can help inform decision-making related to crop management, resource allocation, and market preparation.

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