Multi-level mixed modeling for crop yield prediction in Haryana State (India)

U. Verma1, H. P. Piepho2, J. O. Ogutu2 and M. H. Kalubarme3

1Department of Mathematics and StatisticsCCS Haryana Agricultural University Hisar, Indiae-mail: vermas21@hotmail.com Mob. No. 9416926933

2Bioinformatics UnitUniversity of Hohenheim, Stuttgart, Germany

3Bhaskaracharya Institute for Space Applications and Geo-Informatics Department of Science and Technology, Govt. of Gujarat, Gandhinagar, India

AbstractAbstract

Forecasting of crop yield is one of the most important aspects Forecasting of crop yield is one of the most important aspects of agricultural statistics system in India. Such predictions of agricultural statistics system in India. Such predictions before harvest are needed by the national and state before harvest are needed by the national and state governments for various policy decisions relating to storage, governments for various policy decisions relating to storage, distribution, pricing, marketing, import-export, etc. In this distribution, pricing, marketing, import-export, etc. In this paper, therefore, a methodology for pre-harvest crop yield paper, therefore, a methodology for pre-harvest crop yield estimation is developed for major mustard growing districts in estimation is developed for major mustard growing districts in Haryana (India). Zonal yield models using agro-Haryana (India). Zonal yield models using agro-meteorological parameters were generated using regression meteorological parameters were generated using regression based analyses and mixed model procedures. The percent based analyses and mixed model procedures. The percent deviation(s) of district-level yield forecasts from the real time deviation(s) of district-level yield forecasts from the real time yield(s) data show a preference for using linear mixed yield(s) data show a preference for using linear mixed models. The common weather-based approach to yield models. The common weather-based approach to yield forecast is linear regression with constant coefficients over forecast is linear regression with constant coefficients over time. time.

This may be restrictive and of limited prediction power since This may be restrictive and of limited prediction power since it does not account for the year-to-year dependence in the it does not account for the year-to-year dependence in the yield variable. A mixed model procedure provided a flexible yield variable. A mixed model procedure provided a flexible way to fit a multi-level model for crop yield prediction. The way to fit a multi-level model for crop yield prediction. The key idea followed in this paper is to borrow strength across key idea followed in this paper is to borrow strength across districts. districts. The The linear mixed effects models with the linear mixed effects models with the usefulness of the mixed model framework for pre-harvest usefulness of the mixed model framework for pre-harvest crop yield forecasting and to provide some empirical crop yield forecasting and to provide some empirical evidence for the superiority of mixed models over the evidence for the superiority of mixed models over the classical regression-based analyses.classical regression-based analyses.

Key words:Key words: Multiple linear regression, linear mixed model, Multiple linear regression, linear mixed model,

weather variables, pre-harvest crop forecast and percent relative weather variables, pre-harvest crop forecast and percent relative deviation.deviation.

IntroductionIntroduction

India is one of the largest rapeseed-mustard growing countries in India is one of the largest rapeseed-mustard growing countries in the world, occupying the first position in area and the third the world, occupying the first position in area and the third position in production after the EU27 and China, and contributing position in production after the EU27 and China, and contributing around 11% of the world’s total production. India’s contributions to around 11% of the world’s total production. India’s contributions to the world acreage and production are 28.3 and 19.8 per cent, the world acreage and production are 28.3 and 19.8 per cent, respectively. Rapeseed is a major crop in India, grown on nearly respectively. Rapeseed is a major crop in India, grown on nearly 13% of the cropped land. Rapeseed and mustard crops are 13% of the cropped land. Rapeseed and mustard crops are adapted to tropical as well as temperate environments and adapted to tropical as well as temperate environments and require relatively cool temperatures for optimal growth. It is require relatively cool temperatures for optimal growth. It is basically a winter crop and is grown in the rabi season from basically a winter crop and is grown in the rabi season from September-October to February-March. The crop grows well in September-October to February-March. The crop grows well in areas receiving 25 to 40 cm of rainfall and this is provided by the areas receiving 25 to 40 cm of rainfall and this is provided by the monsoon rains during the sowing season of the crop in India. monsoon rains during the sowing season of the crop in India. Brassica (rapeseed-mustard) is the second most important edible Brassica (rapeseed-mustard) is the second most important edible oilseed crop in India after groundnut and accounts for nearly 30% oilseed crop in India after groundnut and accounts for nearly 30% of the total oilseeds produced in the country. of the total oilseeds produced in the country. The major rapeseed-The major rapeseed-mustard growing states of India comprise Haryana, M.P., mustard growing states of India comprise Haryana, M.P., Rajasthan and U.P. and collectively represent 81 percent of the Rajasthan and U.P. and collectively represent 81 percent of the national acreage and contribute 82.9 per cent to the total national acreage and contribute 82.9 per cent to the total rapeseed-mustard production. rapeseed-mustard production.

The Haryana state, located in northern India, has a The Haryana state, located in northern India, has a total geographical area of total geographical area of 4.42 m ha4.42 m ha. Like most of the . Like most of the other states in India, the principal occupation in the other states in India, the principal occupation in the villages of Haryana is agriculture. About 70% of the villages of Haryana is agriculture. About 70% of the total population of Haryana are dependent upon total population of Haryana are dependent upon agriculture to earn their livelihood and this has made agriculture to earn their livelihood and this has made the state self-sufficient in food grains production. the state self-sufficient in food grains production. There are two major types of crops namely Rabi and There are two major types of crops namely Rabi and Kharif cultivated in the villages of Haryana, depending Kharif cultivated in the villages of Haryana, depending on the two cultivation seasons. The Haryana state is on the two cultivation seasons. The Haryana state is one of the top contributors of food grains to the Indian one of the top contributors of food grains to the Indian market. In fact, Haryana together with Punjab are market. In fact, Haryana together with Punjab are called the `Grain Bowl` of India. called the `Grain Bowl` of India.

Climate change is a major concern today and Climate change is a major concern today and

researchers are engaged in understanding its impact researchers are engaged in understanding its impact on growth and yield of crops. Changes in seasonal on growth and yield of crops. Changes in seasonal temperatures affect crop yield, mainly through their temperatures affect crop yield, mainly through their effect on phenological and developmental processes. effect on phenological and developmental processes. Winter crops are especially vulnerable to high Winter crops are especially vulnerable to high temperatures during the reproductive stages and their temperatures during the reproductive stages and their differential responses to rising temperatures can have differential responses to rising temperatures can have important consequences for crop yield. important consequences for crop yield.

In many previous studies, yield forecasting models have In many previous studies, yield forecasting models have incorporated a series of weather predictors (Hoogenboom incorporated a series of weather predictors (Hoogenboom 2000, Kandiannan et al. 2002, Verma et al.2003, Dadhwal 2000, Kandiannan et al. 2002, Verma et al.2003, Dadhwal et al.2003). et al.2003). Models developed by Mehta et al. (2000), Models developed by Mehta et al. (2000), Agarwal et al. (2001) and Ramasubramanian et al. (2004) Agarwal et al. (2001) and Ramasubramanian et al. (2004) were successfully used for forecasting yields of various were successfully used for forecasting yields of various crops at district as well as agro climatic zone level in crops at district as well as agro climatic zone level in different states of India. As well; Bazgeer et al., 2007, different states of India. As well; Bazgeer et al., 2007, Andarzian,, 2008, Esfandiary et al., 2009, Xingjie et al., Andarzian,, 2008, Esfandiary et al., 2009, Xingjie et al., 2010, Ahmad and Kathuria, 2010, Mehta et al., 2010, 2010, Ahmad and Kathuria, 2010, Mehta et al., 2010, Adrian, 2012 Adrian, 2012 and Verma et al.(2011) have developed and and Verma et al.(2011) have developed and used agromet indices in context of crop yield prediction. used agromet indices in context of crop yield prediction.

Several mixed models have also been developed and Several mixed models have also been developed and

used to forecast crop yield. Hall and Clutter (2004) have used to forecast crop yield. Hall and Clutter (2004) have proposed the use of multivariate multilevel nonlinear proposed the use of multivariate multilevel nonlinear mixed effect models for timber yield predictions. Hebel et mixed effect models for timber yield predictions. Hebel et al. (1993) have applied shrinkage estimators to the al. (1993) have applied shrinkage estimators to the prediction of French winter wheat yield. prediction of French winter wheat yield. A study on crop A study on crop yield modelling under a mixed modelling framework has yield modelling under a mixed modelling framework has been conducted by Lenny et al. (2006). been conducted by Lenny et al. (2006).

Study region and statistical methodologyStudy region and statistical methodology

The Haryana state comprised of 21 districts The Haryana state comprised of 21 districts (geographical area: 4.42 m ha)(geographical area: 4.42 m ha) is situated between 74° is situated between 74° 25’ to 77° 38’ E longitude and 27° 40’ to 30° 55’ N 25’ to 77° 38’ E longitude and 27° 40’ to 30° 55’ N latitude. latitude. A time-series of state Department of Agriculture A time-series of state Department of Agriculture (DOA) mustard yield data spanning (DOA) mustard yield data spanning 1966-67 to 2008-09 1966-67 to 2008-09 and weather data from 1980-81 to 2008-and weather data from 1980-81 to 2008-09(09(Source:Source:esaharyana.gov.in/StateStatisticalAbstract/) esaharyana.gov.in/StateStatisticalAbstract/) and different meteorological observatories in Haryana) and different meteorological observatories in Haryana) were collected for the purpose. The major mustard were collected for the purpose. The major mustard growing districts; Rohtak, Mahendergarh, Rewari, growing districts; Rohtak, Mahendergarh, Rewari, Faridabad, Gurgaon, Bhiwani, Sirsa and Fatehabad Faridabad, Gurgaon, Bhiwani, Sirsa and Fatehabad were grouped into different zones based on their were grouped into different zones based on their physiographic/soil or agroclimatic conditions.physiographic/soil or agroclimatic conditions.

Multiple linear regression and linear mixed model Multiple linear regression and linear mixed model procedures incorporating different alternative procedures incorporating different alternative variance-covariance structures were used for the variance-covariance structures were used for the development of zonal weather-yield models. The development of zonal weather-yield models. The predictive abilities of the models were compared predictive abilities of the models were compared by fitting the zonal models using weather by fitting the zonal models using weather variables namely average maximum temperature, variables namely average maximum temperature, average minimum temperature and accumulated average minimum temperature and accumulated rainfall calculated over different fortnights, as rainfall calculated over different fortnights, as covariates. Since, the weather variables affect the covariates. Since, the weather variables affect the crop differently during different phases of its crop differently during different phases of its growth period. Thus, to integrate the weather growth period. Thus, to integrate the weather variables over different growth phases, the crop variables over different growth phases, the crop growth period (growth period (September to February) September to February) was was divided into 12 fortnights and daily weather data divided into 12 fortnights and daily weather data summarized on a fortnightly basis (summarized on a fortnightly basis (1980-81 to 1980-81 to 2006-07)2006-07) were used for the model building and were used for the model building and model testing period(s).model testing period(s).

Modeling procedures Modeling procedures

Multiple linear regressionMultiple linear regression The multipleThe multiple linear regression model was used to relate crop linear regression model was used to relate crop

yield(s) to the average maximum temperature, average minimum yield(s) to the average maximum temperature, average minimum temperature calculated for 10 fortnights covering the period temperature calculated for 10 fortnights covering the period October to February, and accumulated rainfall for 12 fortnights October to February, and accumulated rainfall for 12 fortnights over the period September to February.In this method, a over the period September to February.In this method, a dependent (response) variable is regressed with a set of dependent (response) variable is regressed with a set of independent (explanatory) variables which may or may not be independent (explanatory) variables which may or may not be inter-related among themselves. inter-related among themselves.

The standard linear regression model considered may be written The standard linear regression model considered may be written in the form in the form Y=Xb+Y=Xb+εε;; where, where,

YY is an (n×l) vector of observations (DOA yields), is an (n×l) vector of observations (DOA yields),XX is an (n×p) matrix of known form (weather variables & trend is an (n×p) matrix of known form (weather variables & trend yield),yield),bb is a (p×l) vector of parameters, is a (p×l) vector of parameters,εε is an (n×l) vector of errors, is an (n×l) vector of errors,

and Eand E((εε)=0)=0, V, V((εε))= = IIσσ22,, so the elements of so the elements of εε are uncorrelated. are uncorrelated. Since ESince E((εε)=0,)=0, an alternative way of writing the model is an alternative way of writing the model is EE(Y)= Xb,(Y)= Xb, The normal equations The normal equations (X’X)(X’X)-1-1 bb = = YY are fitted by least squares are fitted by least squares

technique (here technique (here YY, , X X & & bb are same as above and are same as above and (X’X)(X’X)-1-1 is the is the dispersion matrix) providing the solution. dispersion matrix) providing the solution.

Data for the last one month of the crop season Data for the last one month of the crop season were excluded, as the idea behind the study is were excluded, as the idea behind the study is to predict yield(s) about one month before the to predict yield(s) about one month before the actual harvest. actual harvest. The best subsets of weather The best subsets of weather variables were selected using a stepwise variables were selected using a stepwise regression method (Draper and Smith, 1981) in regression method (Draper and Smith, 1981) in which all variables are first included in the which all variables are first included in the model and eliminated one at a time with model and eliminated one at a time with decisions at any particular step conditioned by decisions at any particular step conditioned by the result of the previous step. The best the result of the previous step. The best supported weather variables were retained in supported weather variables were retained in the model if they had the highest adjusted Rthe model if they had the highest adjusted R2 2

and lowest standard error (SE) of yield at a and lowest standard error (SE) of yield at a given step. The predictive performance(s) of the given step. The predictive performance(s) of the zonal yield equations were compared on the zonal yield equations were compared on the basis of adj-Rbasis of adj-R22, percent deviations of yield , percent deviations of yield estimates from the real-time yields. estimates from the real-time yields.

Linear mixed modelingLinear mixed modeling

The approach we adopted under the linear mixed modeling The approach we adopted under the linear mixed modeling procedure differs from other studies (Hall & Clutter 2004, Hebel et procedure differs from other studies (Hall & Clutter 2004, Hebel et al. 1993, Lenny et al. 2006 etc.) in that the hierarchical structure of al. 1993, Lenny et al. 2006 etc.) in that the hierarchical structure of the data at the geographical level is exploited. For mixed the data at the geographical level is exploited. For mixed modeling,modeling, the hierarchical data structure of yield is represented as the hierarchical data structure of yield is represented as

where, where, yyijtijt = yield in the = yield in the j j-th district within -th district within ii-th zone in the -th zone in the tt-th year-th year sstt = general state effect in the = general state effect in the tt-th year-th year zzitit = effect of the = effect of the ii-th zone within state in the -th zone within state in the tt-th year-th year ddijtijt = effect of the = effect of the jj-th district within -th district within ii-th zone in the -th zone in the tt-th year-th year

For each of the three effects (state: For each of the three effects (state: sstt, zone: , zone: zzitit, district: , district: ddijtijt), we ), we have set up a time-series model with three components: have set up a time-series model with three components: Regression + Time Trend + White noise. Regression + Time Trend + White noise.

RegressionRegression is a fixed part comprising regression on timeis a fixed part comprising regression on time as well as well as on the meteorological covariatesas on the meteorological covariates. .

Time TrendTime Trend is is comprised of a random part comprised of a random part for serial correlation for serial correlation with AR(1) type covariance structure and regression splines with AR(1) type covariance structure and regression splines (Ruppert et al. 2003). (Ruppert et al. 2003).

White noiseWhite noise is an additional independently distributed random is an additional independently distributed random error term.error term. To exemplify the modeling framework, we considered To exemplify the modeling framework, we considered the simple form illustrated below.the simple form illustrated below.

ijtittijt dzsy

A hierarchical mixed model for crop yield estimationA hierarchical mixed model for crop yield estimation

State-level Zone-level District-levelState-level Zone-level District-level

Regression:Regression:

Time Trend: Time Trend:

White noiseWhite noise: :

ttt hets

t tijij

tii

)1(~ ARet )1(~ ARf it )1(~ ARg ijt

2,0~ ht Nh 2,0~ kit Nk 2,0~ tijt Nm

ititiiit kftz ijtijtijijijt mgtd

So, the linear mixed effects models with random time/weather effects at district, zone and state level with AR(1) type covariance structure werefittedfor crop yield estimation.

Results and DiscussionResults and Discussion

The objective of the agromet yield modeling was to The objective of the agromet yield modeling was to assess the predictive accuracies of the contending assess the predictive accuracies of the contending models for estimating district-level crop yields and how models for estimating district-level crop yields and how the accuracies are influenced by grouping the districts the accuracies are influenced by grouping the districts into zones. Hence, the crop growth period was split into into zones. Hence, the crop growth period was split into 12 fortnights and the fortnightly weather variables were 12 fortnights and the fortnightly weather variables were used as covariates in the models and then the same used as covariates in the models and then the same were used to estimate pre-harvest crop yields. were used to estimate pre-harvest crop yields. Data for Data for the last one month of the crop season were excluded, the last one month of the crop season were excluded, as the idea behind the study is to predict yield(s) about as the idea behind the study is to predict yield(s) about one month before the actual harvest. one month before the actual harvest. The best The best supported weather variables were retained in the supported weather variables were retained in the model if they had the highest adjusted Rmodel if they had the highest adjusted R2 2 and lowest and lowest standard error (SE) of yield at a given step. standard error (SE) of yield at a given step.

Zonal trend- agromet yield relationships based on Zonal trend- agromet yield relationships based on multiple linear regression analysismultiple linear regression analysis Zone-1 (Rohtak)Zone-1 (Rohtak)

YieldYieldest est = = -1105.84+79.43 TMX-1105.84+79.43 TMX33+54.89 TMN+54.89 TMN11-20.06 ARF-20.06 ARF77-82.82 -82.82

TMXTMX44+.951Tr+.951Tr RR22 = 0.85 , Adj. R = 0.85 , Adj. R22 = 0.82 & SE = 148.8 = 0.82 & SE = 148.8

Zone-2 (Bhiwani, Sirsa, Fatehabad)Zone-2 (Bhiwani, Sirsa, Fatehabad)

YieldYieldestest= = -950.23-10.94 ARF-950.23-10.94 ARF33-51.32 TMN-51.32 TMN1010+35.74 TMX+35.74 TMX99+ 29.77 TMX+ 29.77 TMX77 - -

21.44 TMX21.44 TMX66+1.55 Tr+1.55 Tr

RR22 = 0.82 , Adj. R = 0.82 , Adj. R2 2 = 0.80 & SE = 150.2= 0.80 & SE = 150.2 Zone-3 (Faridabad, Gurgaon, Mahendergarh, Rewari)Zone-3 (Faridabad, Gurgaon, Mahendergarh, Rewari)

YieldYieldest est = = TMXTMX77+49.27 TMN+49.27 TMN55+163.47 TMN+163.47 TMN99- 16.79 ARF- 16.79 ARF44-51.65 2327.83--51.65 2327.83-

78.17 TMX78.17 TMX22 -103.92 -103.92 TMXTMX88-9.55 ARF-9.55 ARF99+ 93.52 TMX+ 93.52 TMX44

RR2 2 = 0.75 , Adj. R= 0.75 , Adj. R2 2 = 0.72 & SE = 168.0= 0.72 & SE = 168.0

where where YieldYieldestest - Model predicted yield (q/ha) - Model predicted yield (q/ha)

Tr - Linear time-trend based yieldTr - Linear time-trend based yield

TMX - Av. maximum temperature TMX - Av. maximum temperature

TMN - Av. minimum temperatureTMN - Av. minimum temperature

ARF - Accumulated rainfall ARF - Accumulated rainfall

(1,2,3,…,10/12 are different fortnights (1,2,3,…,10/12 are different fortnights covering the crop growth period) covering the crop growth period)

SE - Standard error of the yield estimateSE - Standard error of the yield estimate

The predictive accuracies of the zonal regression The predictive accuracies of the zonal regression models and linear mixed models expressed in terms of models and linear mixed models expressed in terms of the per cent deviations of the estimated yields from the the per cent deviations of the estimated yields from the observed yields, differed markedly between the three observed yields, differed markedly between the three zones. zones. Though, all the weather variables were Though, all the weather variables were statistically significant as predictors of crop yield, statistically significant as predictors of crop yield, however, the percent relative deviations of the however, the percent relative deviations of the estimated yields from the observed yields were too wide estimated yields from the observed yields were too wide for practical purposes for the sample period itself in for practical purposes for the sample period itself in case of regression models. The yields estimated had case of regression models. The yields estimated had rather wide percent deviations from the observed yields, rather wide percent deviations from the observed yields, sometimes too wide than considered acceptable for sometimes too wide than considered acceptable for reliable yield prediction purposes. We attempted to reliable yield prediction purposes. We attempted to improve the predictive accuracy of the zonal yield improve the predictive accuracy of the zonal yield models by using linear mixed modeling and the linear models by using linear mixed modeling and the linear mixed models substantially improved the predictive mixed models substantially improved the predictive accuracy and produced what we consider to be accuracy and produced what we consider to be satisfactory district-level yield(s) estimation. Hence, satisfactory district-level yield(s) estimation. Hence, based on this empirical study, we recommend the use based on this empirical study, we recommend the use of linear mixed models for pre-harvest crop yield of linear mixed models for pre-harvest crop yield forecasting to enhance the predictive accuracy of the forecasting to enhance the predictive accuracy of the zonal models. zonal models.

This study has demonstrated the utility of understanding This study has demonstrated the utility of understanding and quantifying the relationships between mustard yield and quantifying the relationships between mustard yield and weather variables. The relationships can be and weather variables. The relationships can be employed in studies that explore the impact of climate employed in studies that explore the impact of climate change on probable future crop yields at regional scales. change on probable future crop yields at regional scales. It is worth emphasizing that the weather variables and It is worth emphasizing that the weather variables and linear time trend we considered may not always suffice linear time trend we considered may not always suffice as a basis for routine reliable mustard crop yield(s) as a basis for routine reliable mustard crop yield(s) prediction. It is therefore useful to explore and identify prediction. It is therefore useful to explore and identify additional suitable agronomic/ biometrical variables that additional suitable agronomic/ biometrical variables that may further enhance the predictive accuracies of the may further enhance the predictive accuracies of the models. It would also be worthwhile exploring if other models. It would also be worthwhile exploring if other summaries of the weather variables using alternative summaries of the weather variables using alternative time windows besides the fortnight summary we used, time windows besides the fortnight summary we used, may further improve the performance of the models. may further improve the performance of the models.

AcknowledgementAcknowledgement The weather data received from Haryana Space The weather data received from Haryana Space

Applications Centre, Hisar and Department of Agro-Applications Centre, Hisar and Department of Agro-meteorology, CCS HAU, Hisar, India are gratefully meteorology, CCS HAU, Hisar, India are gratefully acknowledged.acknowledged.

ReferencesReferences

[1] D. Adrian, A model-based approach to forecasting corn and soybean yields. [1] D. Adrian, A model-based approach to forecasting corn and soybean yields. USDAUSDA, , National Agricultural Statistics Service, Research & Development National Agricultural Statistics Service, Research & Development Division (2012).Division (2012).

[2] R. Agarwal , R.C. Jain and S.C. Mehta, Yield forecast based on weather [2] R. Agarwal , R.C. Jain and S.C. Mehta, Yield forecast based on weather variables and agricultural inputs on agroclimatic zone basis. Indian J. of variables and agricultural inputs on agroclimatic zone basis. Indian J. of Agril. Sci. 71(7)Agril. Sci. 71(7) (2001)(2001), , 487-490.487-490.

[3] T. Ahmad and O.P. Kathuria, Estimation of crop yield at block level. Adv. Appl. [3] T. Ahmad and O.P. Kathuria, Estimation of crop yield at block level. Adv. Appl. Res. 2(2)Res. 2(2) (2010), 164-172. (2010), 164-172.

[4] B. Andarzian, A.M. Bakhshandeh, M. Bannayan, Y. Emam, G. Fathi and S. [4] B. Andarzian, A.M. Bakhshandeh, M. Bannayan, Y. Emam, G. Fathi and S. Alami, Wheat Pot : a simple model for spring wheat Yp using monthly Alami, Wheat Pot : a simple model for spring wheat Yp using monthly weather data. Biosyst. Eng. 99(2008), 487–495.weather data. Biosyst. Eng. 99(2008), 487–495.

[5] S. Bazgeer, Gh. Kamali, and A. Mortazavi, Wheat yield prediction through [5] S. Bazgeer, Gh. Kamali, and A. Mortazavi, Wheat yield prediction through agrometeorological indices for Hamedan, Iran. Biaban 12agrometeorological indices for Hamedan, Iran. Biaban 12 (2007), 33-38.(2007), 33-38.

[6] V. K Dadhwal, V. K., Sehgal, R. P. Singh, and D.R. Rajak, Wheat yield [6] V. K Dadhwal, V. K., Sehgal, R. P. Singh, and D.R. Rajak, Wheat yield modeling using satellite remote sensing with weather data; recent Indian modeling using satellite remote sensing with weather data; recent Indian experience. Mausamexperience. Mausam 5454 (2003), 253-262.(2003), 253-262.

[7] N. Draper, and H. Smith, Applied Regression Analysis. 2nd edition[7] N. Draper, and H. Smith, Applied Regression Analysis. 2nd edition .. New New York: Wiley (1981).York: Wiley (1981).

[8] F. Esfandiary, G. Aghaie, and A. D. Mehr, Wheat yield prediction through agro [8] F. Esfandiary, G. Aghaie, and A. D. Mehr, Wheat yield prediction through agro meteorological indices for Ardebil district. World Academy of Science, meteorological indices for Ardebil district. World Academy of Science, Engineering and Technology 49(2009), 32-35.Engineering and Technology 49(2009), 32-35.

[9 D.B. Hall and M. Clutter Multivariate multilevel nonlinear mixed effects models [9 D.B. Hall and M. Clutter Multivariate multilevel nonlinear mixed effects models for timber yield predictions. Biometrics 60 (2004), 16-24.for timber yield predictions. Biometrics 60 (2004), 16-24.

[10] P. Hebel, R. Faivre, B. Goffinet, and D. Wallach, Shrinkage estimators applied [10] P. Hebel, R. Faivre, B. Goffinet, and D. Wallach, Shrinkage estimators applied to prediction of French winter wheat yield. Biometrics 49 (1993), 281-293.to prediction of French winter wheat yield. Biometrics 49 (1993), 281-293.

11] G. Hoogenboom, Contribution of agrometeorology to the simulation of crop 11] G. Hoogenboom, Contribution of agrometeorology to the simulation of crop production and its applications. Agricultural and Forest Meteorology production and its applications. Agricultural and Forest Meteorology 103(2000), 137-157.103(2000), 137-157.

[12] K. Kandiannan, K.K. Chandaragiri, N. Sankaran, T.N. [12] K. Kandiannan, K.K. Chandaragiri, N. Sankaran, T.N. Balasubramanian and C. Kailasam, Crop-weather model for Balasubramanian and C. Kailasam, Crop-weather model for turmeric yield forecasting for Coimbatore District, Tamil Nadu, India. turmeric yield forecasting for Coimbatore District, Tamil Nadu, India. Agricultural and Forest Meteorology 112Agricultural and Forest Meteorology 112 (2002), 133- 137.(2002), 133- 137.

[13] W. Lenny L. Denis and ML Pierre, The early explanatory power of a [13] W. Lenny L. Denis and ML Pierre, The early explanatory power of a satellite based measure in crop yield modelling. Les Cahier du satellite based measure in crop yield modelling. Les Cahier du CREF 06-15 (2006),CREF 06-15 (2006), 1-251-25..

[14] S.C. Mehta, R. Agarwal and V.P.N. Singh, Strategies for composite [14] S.C. Mehta, R. Agarwal and V.P.N. Singh, Strategies for composite forecast. J. Ind. Soc. Agril. Statistforecast. J. Ind. Soc. Agril. Statist.. 53(3) (2000), 262-272. 53(3) (2000), 262-272.

[15] S.C. Mehta, S. Pal and V. Kumar, Weather based models for [15] S.C. Mehta, S. Pal and V. Kumar, Weather based models for forecasting potato yield in Uttar Pradesh. Project Report No. forecasting potato yield in Uttar Pradesh. Project Report No. IASRI/P.R.-01(2010)IASRI/P.R.-01(2010), , IASRI, New DelhiIASRI, New Delhi..

[16] V. Ramasubramanian and R.C. Jain, Use of growth indices in Markov [16] V. Ramasubramanian and R.C. Jain, Use of growth indices in Markov Chain models for crop yield forecasting. Biom. JChain models for crop yield forecasting. Biom. J . . 41(1) (1999), 99- 41(1) (1999), 99-109.109.

[17] D. Ruppert, M.P. Wand and R.J. Carroll, Semiparametric regression. [17] D. Ruppert, M.P. Wand and R.J. Carroll, Semiparametric regression. Cambridge University Press, Cambridge(2003).Cambridge University Press, Cambridge(2003).

[18] U. Verma, D.S. Ruhal, R.S. Hooda, M. Yadav, A.P. Khera, C.P. Singh, [18] U. Verma, D.S. Ruhal, R.S. Hooda, M. Yadav, A.P. Khera, C.P. Singh, M.H. Kalubarme and I.S. Hooda, Wheat yield modelling using M.H. Kalubarme and I.S. Hooda, Wheat yield modelling using remote sensing and agrometeorological data in Haryana State. J. remote sensing and agrometeorological data in Haryana State. J. Ind. Soc. Agric. Statist. 56, 2Ind. Soc. Agric. Statist. 56, 2 (2003), 190-98.(2003), 190-98.

[19] U. Verma, D.S. Dabas, M.S. Grewal, J.P. Singh, R.S. Hooda, M. Yadav, [19] U. Verma, D.S. Dabas, M.S. Grewal, J.P. Singh, R.S. Hooda, M. Yadav, M.H. Kalubarme, M.P. Sharma and R. Prawasi, Crop yield M.H. Kalubarme, M.P. Sharma and R. Prawasi, Crop yield forecasting in Haryana: 1986 to 2010. Summary Report,forecasting in Haryana: 1986 to 2010. Summary Report, Department of Soil Science, CCS HAU, Hisar (2011), pp.1-148Department of Soil Science, CCS HAU, Hisar (2011), pp.1-148 ..

[20] Ji. Xingjie Yu Yongqiang and Wen Zhang The Harvest Index Model of [20] Ji. Xingjie Yu Yongqiang and Wen Zhang The Harvest Index Model of Winter Wheat in China based on meteorological data. Scientia Winter Wheat in China based on meteorological data. Scientia Agricultura Sinica 43, 20 (2010), 4158-68. Agricultura Sinica 43, 20 (2010), 4158-68.

SAS code:SAS code:Proc glimmix data=mustard Noclprint Method=RSPL;Proc glimmix data=mustard Noclprint Method=RSPL;class district zone;class district zone;Model Yield=Zone*district Zone*district*time /noint dist=normal link=identity Model Yield=Zone*district Zone*district*time /noint dist=normal link=identity

ddfm=kr solution; ddfm=kr solution; random time/sub=intercept type=pspline knotmethod=equal(20);random time/sub=intercept type=pspline knotmethod=equal(20);random time/sub=zone type=pspline knotmethod=equal(20); random time/sub=zone type=pspline knotmethod=equal(20); random time/sub=zone*district type=pspline knotmethod=equal(20); random time/sub=zone*district type=pspline knotmethod=equal(20); output out=mustard_yld_pred Pred(ilink)=mu LCL(ilink)=lower UCL(Ilink)=Upper; output out=mustard_yld_pred Pred(ilink)=mu LCL(ilink)=lower UCL(Ilink)=Upper; nloptions tech=NEWRAP Maxiter=1000 maxfunc=1000; nloptions tech=NEWRAP Maxiter=1000 maxfunc=1000; run;run;Proc glimmix data=mustard Noclprint Method=RSPL itdetails;Proc glimmix data=mustard Noclprint Method=RSPL itdetails;class district zone;class district zone;Model Yield=Zone*district Zone*district*time / dist=normal link=identity ddfm=kr Model Yield=Zone*district Zone*district*time / dist=normal link=identity ddfm=kr

solution htype=1; solution htype=1; random time/sub=intercept type=pspline knotmethod=equal(10);random time/sub=intercept type=pspline knotmethod=equal(10);*/random time/sub=district type=pspline knotmethod=equal(10) */; */random time/sub=district type=pspline knotmethod=equal(10) */; random time/sub=zone type=pspline knotmethod=equal(10); random time/sub=zone type=pspline knotmethod=equal(10); random time/sub=zone*district type=pspline knotmethod=equal(10) knotinfo ; random time/sub=zone*district type=pspline knotmethod=equal(10) knotinfo ; random RF1-RF12/ sub=intercept type=ar(1) s; /*rr for mx*/random RF1-RF12/ sub=intercept type=ar(1) s; /*rr for mx*/random Tmx1-Tmx10/ sub=intercept type=ar(1) s; /*rr for mn*/random Tmx1-Tmx10/ sub=intercept type=ar(1) s; /*rr for mn*/random Tmn1-Tmn10/sub=intercept type=ar(1) solution; /*rr for rf*/random Tmn1-Tmn10/sub=intercept type=ar(1) solution; /*rr for rf*/output out=mustard_yld_pred Pred(ilink)=mu LCL(ilink)=lower UCL(Ilink)=Upper; output out=mustard_yld_pred Pred(ilink)=mu LCL(ilink)=lower UCL(Ilink)=Upper; nloptions tech=NEWRAP Maxiter=10000 maxfunc=10000; nloptions tech=NEWRAP Maxiter=10000 maxfunc=10000; run;run;

Table 1. District-specific estimated mustard yields (Est. yield) based on zonal models and their associated percentage deviations (RD (%) = 100 (Est. yield –observed yield)/ observed yield).

i) Weather variables and trend yield were used as regressors

Districts/ Years Fatehabad Faridabad Gurgaon Mahendergarh Rewari

Est. Yield (q/ha)

RD(%) Est.Yield(q/ha)

RD(%) Est.Yield(q/ha)

RD(%) Est.Yield (q/ha)

RD(%) Est.Yield

(q/ha)

RD(%)

2004-05 13.93 21.83 11.08 -6.01 11.08 -4.64 11.08 -7.27 11.08 -20.79

2005-06 16.61 17.02 6.52 -57.50 6.52 -47.68 6.52 -44.19 6.52 -57.24

2006-07 16.45 12.56 14.52 -2.75 14.52 14.24 14.52 2.76 14.52 -0.42

Av. abs. dev 17.13   22.08 22.18 18.07 26.15

 Districts/Years

Rohtak Bhiwani Sirsa

Est.Yield(q/ha)

RD(%) Est.Yield (q/ha)

RD(%) Est.Yield (q/ha)

RD(%)

2004-05 14.11 12.34 12.86 18.73 13.63 18.12

2005-06 13.09 48.78 15.26 36.36 16.10 32.63

2006-07 13.81 2.27 14.82 15.13 15.73 19.35

Av. abs. dev   21.12 23.40 23.36

ii) Linear mixed model for yield with spline smoothing of time trend

 Districts/Years

Fatehabad Faridabad Gurgaon Mahendergarh Rewari

Est. Yield (q/ha)

RD(%) Est.Yield(q/ha)

RD(%) Est.Yield(q/ha)

RD(%) Est.Yield(q/ha)

RD(%) Est.Yield

(q/ha)

RD(%)

2004-05 13.81 17.26 14.56 19.05 12.42 6.43 13.22 9.61 14.77 5.28

2005-06 14.01 -1.25 14.69 -4.47 12.51 0.31 13.31 12.19 14.97 -1.91

2006-07 14.21 -2.78 14.82 -0.73 12.60 -0.89 13.40 -5.41 15.18 3.94

Av. abs. dev 7.09 8.08 2.54 9.07 3.71

Districts/ Years

Rohtak Bhiwani Sirsa

Est.Yield(q/ha)

RD(%) Est.Yield(q/ha)

RD(%) Est.Yield(q/ha)

RD(%)

2004-05 11.99 -4.42 11.59 7.14 13.84 16.64

2005-06 8.17 -7.00 10.02 -10.45 14.04 13.52

2006-07 13.81 2.38 12.17 -5.40 14.23 7.39

Av. abs. dev 4.60 7.66 12.51