PREHARVEST FORECAST OF CROP YIELD AN OVERVIEW

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1 PREHARVEST FORECAST OF CROP YIELD AN OVERVIEW K.N. Singh Indian Agricultural Statistics Research Institute, New Delhi-02 Reliable and tiely forecasts of crop production are required for various policy decisions relating to storage, distribution, pricing, arketing, iport-export, etc. The official forecasts (advance estiates) of ajor cereal and coercial crops are issued by Directorate of Econoics and Statistics. However, these advance estiates are only guestiates and not the objective estiates. In working out these estiates there is a lot of subjective assessent (of course by the experts) based on several qualitative factors. There is thus a need to develop statistically sound objective forecasts of crop acreage and production. Various organisations in India and abroad are engaged in developing ethodology for pre-harvest forecast of crop yields / production using various approaches. The ain factors affecting crop yield / production are inputs and weather. Use of these factors fors one approach for forecasting crop production. The other approach uses plant vigour easured through plant characters. It can be assued that plant characters are integrated effects of all the factors affecting production. Yet another approach is easureent of crop vigour through reotely sensed data. Since area under the crop is available in advance of harvest through Tiely Reporting Schee (TRS) and reotely sensed data, the proble ainly reduces to forecast of yield rate.. Yield forecast using weather Fisher (924) and Hendricks and Scholl (943) have done pioneering work in crop weather relationship. They have given odels which require sall nuber of paraeters to be estiated while taking care of distribution pattern of weather over the crop season. Fisher assued that the effect of change in weather variable on crop in successive periods would not be an abrupt or erratic change but an orderly one that follows soe atheatical law. He assued that these effects are coposed of the ters of a polynoial function of tie. Further, the value of weather variable in w-th period, X w was also expressed in ters of orthogonal functions of tie. Substituting these in usual regression equation and utilising the properties of orthogonal and noralised functions, he obtained Y = A 0 + a 0 ρ 0 + a ρ + a 2 ρ a k ρ k + e where Y denoted yield, A 0,a 0,a,a 2,...a k are constants to be deterined and ρ i (i=, k) are distribution constants of X w. Fisher has suggested to use k = 5 for ost of the practical situations. In fitting this equation for k = 5, the nuber of constants to be evaluated is 7. This odel was used by Fisher for studying the influence of rainfall on the yield of wheat. Hendricks and Scholl (943) have odified Fisher's technique. They divided the crop season into n weekly intervals and have assued that a second degree polynoial in week nuber would be sufficiently flexible to express the effect of weather on yield in successive 57

2 weeks. Further, they have used values of weather as such. Under this, the odel was obtained as Y = A 0 + a 0 Σ X w + a Σ w X w + a 2 w w Σ w w²x w + e In this odel nuber of constants to be deterined reduces to 4, irrespective of n. This odel was extended for two weather variables to study joint effects. Since the data for such studies extended over a long period of years, an additional variate T representing the year was included to ake allowance for tie trend. Another iportant contribution in this field is by Baier (977). He has classified the crop-weather odels in three basic types.. Crop growth siulation odels 2. Crop-weather Analysis odels 3. Epirical statistical odels The ost coonly used odels in crop forecasting are Epirical Statistical odels. In this approach, one or several variables (representing weather or cliate, soil characteristics or a tie trend) are related to crop responses such as yield. The weighting coefficients in these equations are by necessity obtained in an epirical anner using standard statistical procedures, such as ultivariate regression analysis. Several Epirical Statistical odels were developed all over the world. The independent variables included weather variables, agroeteorological variables, soil characteristics or soe suitably derived indices of these variables. Water Requireent Satisfaction Index (WRSI), Theral Interception Rate Index (TIR), Growing Degree Days (GDD) are soe agrocliatic indices used in odels. Southern Oscillation Index (SOI) has also been used with other weather variables to forecast crop yield (Raakrishna et al. 2003). To account for the technological changes year variable or soe suitable function of tie trend was used in the odels. Soe workers have also used two tie trends. Moving averages of yield were also used to depict the technological changes. In contrast to epirical regression odels, the Joint Agricultural Weather Inforation Centre eploys the crop weather analysis odels that siulate accuulated crop responses to selected agroeteorological variables as a function of crop phenology. Observed weather data and derived agroeteorological variables are used as input data. USDA and FAO are the two organisations that systeatically forecast world agricultural production and global crop inforation based on weather. Daily onitoring of satellite weather iages and eteorological data provides the fraework for agricultural weather analysis. Daily, weekly and seasonal suaries are processed and erged with historical weather and crop data for evaluation of the crop yield potential. FAO has also carried out nuber of studies using agro eteorological odels. The ethodology consists of developing an index depending on water deficit / water surplus in successive periods of crop growth. These odels have good potential for early crop yield assessent for rainfed crops. (Frere and Popov. 979). 58

3 In India, ajor organisations involved in developing ethodology for forecasting crop yield based on weather are IMD and IASRI. The ethodology adopted by IMD involves identification of significant correlations between yield and weather factors during successive overlapping periods of 7 to 60 days of the crop growing season. By analysing the correlation coefficients for statistical and phenological significance, the critical periods when the weather variables have significant effect on yield are identified. The weather variables in critical periods alongwith trend variables are used through ultiple regression analysis to obtain forecast equations. Using this ethodology odels were developed for principal crops on eteorological subdivisions basis. Data fro various locations are averaged to get the figures for eteorological sub-divisions and these are utilised to develop the forecast odel. Monthly forecasts are issued fro these odels by taking the actual data upto tie of forecast and noral for the reaining period. In soe odels yield Moisture Index, Generalised Monsoon Index, Moisture Stress, aridity anoaly Index are also used (Sarwade, 988; Sarkar, 2002). IASRI Approaches At IASRI, the odel suggested by Hendricks and Scholl has been odified by expressing effects of changes in weather variables on yield in the w-th period as function of respective correlation coefficients between yield and weather variables. This will explain the relationship in a better way as it gives appropriate weightage to different periods. Under this assuption, the odels were developed for studying the effects of weather variables on yield using coplete crop season data whereas forecast odel utilised partial crop season data. These odels were found to be better than the one suggested by Hendricks and Scholl. The forecast odel finally recoended was of the for p p Y = A0 + aijzij + aii' jzii' j+ ct + e i= j= 0 i i' = j= 0 where Z ij = r iw j X iw and Z ii'j = r j ii'w X iw X i'w w= w= Here Y is yield, r iw /r ii'w is correlation coefficient of yield (adjusted for trend effect) with i-th weather variable (X iw ) /product of i-th and i'-th weather (X iw X i w ) variables in w-th period, is week of forecast, p is nuber of weather variables used and e is error ter. In this approach, for each weather variable, two types of indices were developed, one as siple total values of weather variable in different periods [un-weighted index -Z i0 ] and the other one as weighted total [weighted index Z i ] weights being correlation coefficients between yield /de-trended yield (if trend is present) and weather variable in respective periods. On siilar lines, for studying joint effects, un-weighted & weighted indices for interactions were coputed with products of weather variables (taken two at a tie). Stepwise regression technique was used to select iportant indices in the odel. These 59

4 odels were successfully used for forecasting yields of various crops at district, agrocliatic zone and state level. (Agrawal et al 980; 983, 986, 200, 2005; Jain et al 980; Mehta, et al. 2000, 200). Besides, weather indices based regression odels, use of coplex polynoials through GMDH technique was also explored. (Mehta, 200). The for of the odel is y = a+ b + + i xi cij xi x j i= i= j = i= j= k = d ijk x i x j x k +... At district level, odel based on tie series data on weather variables has also been developed using technique of discriinant function analysis. The long series of years has been classified into three groups congenial, noral and adverse with respect to crop yields. Using weather data of these groups, linear / quadratic discriinant functions were fitted. These functions were used to find weather scores for each year which were used as regressors in forecast odel. (Rai and Chandrahas 2000). Various strategies were proposed to solve the proble of nuber of variables ore than nuber of observations. (Aditya 2008, Chandrahas et al. 200). Principal coponent regression was also attepted but was not found appropriate. In another approach based on water balance technique, odels for rainfed crops using weighted stress indices have been developed. In this approach, water deficit / surplus has been worked out at different phases of crop growth and using suitable weights, accuulated weighted stress index has been developed for each year which was used as regressor in the forecast odel. (Saksena et al. 200). In contrast to regression approach, Artificial Neural Network (ANN) technique has also been explored for forecasting yields of rice, wheat and sugarcane in Uttar Pradesh. (Kuar et al. 200). 2. Yield forecast based on plant characters Effects of weather and inputs are anifested through crop stand, nuber of tillers, leaf area, nuber of earheads etc. which ultiately deterine crop yield. As such, plant characters can be taken as the integrated effects of weather and crop inputs. Thus the other approach to forecast crop yield is to use plant characters. In USDA, the net yield per acre for each saple plot is coputed as (Vogel, 985). y i = (F i x C i x W i ) L i where F i = Nuber of fruits harvested or forecast to be harvested in the i-th saple plot. C i = Conversion factor using the row space easureent to inflate the plot counts to a per acre basis. W i = Average weight of fruit harvested or forecast to be harvested. L i = Harvest loss as easured fro post-harvest gleanings (the historic average is used during the forecast season). y i = ( Σ n ) for the n saple plots. y i 60

5 Separate odels are used to forecast the nuber of fruits (F i ) to be harvested and the final head weight (W i ). This ethod cannot be followed in India/tropical countries as tie period fro head eergence to aturity is hardly one to two onths for ost of the crops whereas in USA this takes two to three onths. Forecast of head weight at aturity therefore cannot be obtained uch in advance in India, as such this will not be useful for obtaining early forecast in such countries. In India, yield is directly regressed on plant counts and yield contributing characters for obtaining forecast odel. Considerable work has been done at IASRI using this approach. The data are collected at different periodic intervals through suitable sapling design for 3 to 4 years fro farers fields. Two types of approaches have been attepted - Between year odel and Within year odel. 2. Between year odels These odels are developed taking previous year(s) data. Objective yield forecasts are obtained by substituting the current year plant data into a odel developed fro the previous year(s). An assuption is ade that the present year is a part of the coposite population of these (previous) years. Most coonly used odels are based on regression approach. Different Between-year Models Linear regression odels Y = ß 0 + ß X + ß 2 X e where Y and X i are yield and plant characters respectively. These ay be used in original scale or soe suitably transfored variables of these can be used. ß 0 and ß i are constants to be estiated and e is rando error. These odels utilise data at one point of tie only during the crop growth. (Sardana et al. 972, Singh et al. 976, Jha et al. 98, Singh et al. 988). These odels were iproved taking regressors as prinicipal coponents of plant charcters (Jain et al. 984) or growth indices based on plant characters observed on two or ore points of tie during the crop growth (Jain et al 985). The growth indices are obtained as weighted accuulations of observations on plant characters in different periods, weights being respective correlation coefficients between yield and plant characters. Probability odel Multiple regression technique has been extensively used in developing odels for crop yield forecasting. Least squares technique is used for estiating the paraeters of the regression odel. The optiality properties of these estiates are described in an ideal setting which is not often realised in practice. It has been observed that regressions based on different subsets of data produce very different results, raising questions of odel stability. To overcoe soe of the drawbacks of regression odel, probability odel for 6

6 forecasting crop yield using Markov Chain theory has been developed. This ethod, being copletely odel free, does not require any assuption about independent and dependent variables. Markov Chain ethod has the advantage of providing non-paraetric interval estiates and is robust against outliers/extree values. In this ethod, growth process of the crop is divided in s phenological stages. A arkov chain odel is constructed by defining a set of states, which describe the condition of an individual plant (or average condition of a group of plants) at specified tie within the phenological stages. Individual states are defined on the basis of available qualitative and quantitative inforation to describe plant condition. Let n i, for i =,2,...,s denote the nuber of states at the coenceent of stage i. Let A i,i+ for i =,2,...,(s-) denote the (n i x n i+ ) transition atrix which gives the transition probabilities of a plant (or group of plants) oving fro any possible state of stage i to any possible state of stage i+. As a property of transition atrices, each row of an A i,i+ atrix sus to. Let F denote the atrix of transition probabilities fro each of the (n-n s ) states of (s-) interediate stages to each of the n s states, the last (harvest) stage. The n s states are defined as quantitative intervals of yield. F atrix can be obtained as s π Ai, i+ i= s F = π Ai, i+ i= 2 As 2, s A As, s s, s F atrix can be used to forecast crop yields. Each row of F represents a crop condition (state) at a certain crop stage. The n s states of the final stage are defined as quantitative intervals of yield. Each colun of F represents a different yield interval. The values of each row of F are the estiated probabilities of the crop producing a final yield within each of the n s intervals. Thus, each row of F is a predicted yield distribution for a given stage and state. Each of the (n-n s ) forecast yield distributions in the F atrix ay be analysed to get ean and standard error of the forecast. In particular, transition probability atrix A s-,s will give ean and standard error of forecast at stage(s-). This ethod was applied to forecast yield of corn and cotton by USDA (Matis et al. 985, 989) and sugarcane (Jain and Agrawal 992(a); Agrawal and Jain 996). Models using higher order arkov chain and using principal coponents and growth indices of plant characters in arkov chain approach were also developed. (Jain and Raasubraanian,998 ; Raasubraanian and Jain 999; Raasubraanian, et al. 2004). 2.2 Within year odels The 'between year odels' while perforing satisfactorily in typical years ay falter in atypical years. A odel which uses data fro the current growing season only ay be beneficial in iproving forecasts during a year with atypical growing conditions. These odels are developed to provide forecasts of pertinent coponents of crop yield relying 62

7 entirely on growth data collected fro plant observations during the current growing season. A logistic odel having soe yield coponents as dependent variable and an independent 'tie' variable generally fits well to the growth process of crop yield coponents like dry atter accuulation etc. The odel uses repeated observations fro the current year to estiate the paraeters needed to forecast the dependent variable at aturity. Partial crop season data are utilised to fit the curve and the value at harvest is predicted through this curve which in turn is used to forecast yield. (Nealon 976, House 977, Larsen 978, Jain et al. 992(b)). Using the odel based on partial crop season data, the value of the dependent variable is predicted at aturity. However, it is likely to be over estiated when partial crop season data based on sall data points that too falling on the lower side of the curve where the growth has steep rise are used to fit the odel to forecast the yield coponent at aturity. This ay need suitable odification in the odel so as to capture the value at aturity fro partial crop season data. The odified logistic odel has been suggested which solves the proble of over-estiation (Jain et al 992(b)). 3. Models using spectral data Since the approach using plant characters requires collection of data fro farers' fields, the data can be used on characters which can be easured easily without involving uch expertise, cost and sophisticated instruents. Soe characters contributing significantly towards yield ay not find place in the odel due to these liitations. This calls for the necessity of including soe other variables in the odel alongwith bioetrical characters which could take care of such variables indirectly. During the last three decades, considerable work has been carried out in India in the spectral response and yield relationships of different crops at Space Applications Centre, Ahedabad, under the reote sensing applications ission called Crop Acreage and Production Estiation (CAPE). Spectral indices such as ratio of infra red (IR)/Red(R) and Noralised difference (ND) = (IR-R) / (IR+R) are calculated fro reotely sensed data and are used as regressors in the odel (SAC report 990). The schee needed further iproveent. Project has been forulated to integrate Agroeteorology and Land-based observations alongwith reote sensing data. Project title is Forecasting Agricultural outputs using Space, Agroeteorology and Land-based observations (FASAL). The experience in this context is that reote sensing can suppleent the existing data collection syste but never copletely replace it. The two data collection systes ust be integrated through rigorous statistical ethodology. At Space Application Centre, ethodology has been developed which provides ultiple forecasts for rice and wheat using reotely sensed data for acreage forecast whereas forecasts for productivity are obtained using eteorological and agro-eteorological indices. (Patel et al. 2004). 63

8 4. Models using Farers' Appraisal Farer is the best judge of the likely production in the field. Farers' appraisal, therefore, could serve as a good input for forecasting the yield and replace soe of the characters requiring expertise or use of sophisticated instruents for their easureents and thus reducing the cost on data collection. A study has been carried out to study the feasibility of using farers' appraisal in the forecast odel for sugarcane. (Agrawal and Jain, 996). The results revealed that a reliable forecast could be obtained using plant population and farers appraisal. Another ethodology based on farers appraisal data has been developed using Bayesian approach. The study has been carried out for wheat in Muzaffarnagar district. Expert opinion data were collected in a nuber of rounds in a year by interviewing the selected farers regarding their assessent about the likely crop production and chance of occurrences in various yield classes. Fro these responses average prior probabilities were coputed. Actual harvest yield and farers appraisal data on yield for previous year(s) were taken into account to obtain posterior probabilities which were then used for obtaining Bayesian forecast of crop yield for current year. (Chandrahas et al. 200). 5. Integrated approach Models using data on plant characters alongwith agricultural inputs were found to be better than odels based on plant characters alone in jowar and apple (Jain et al. 985; Chandrahas and Narain, 992). Often it is not possible to include all the variables in a single odel. In such situations coposite forecast can be obtained as a suitable cobination of forecasts obtained fro different odels. Various strategies for cobining forecasts have been suggested under different situations. (Mehta et al., 2000). 6. Data Driven techniques for Crop forecasting Data-driven techniques is a ethodology in which data specific patterns is first detected and subsequently utilized the inforation on these patterns for prediction or classification for out of sapled data. Data-driven techniques has been developed with the contributions fro artificial intelligence, data ining, knowledge discovery in databases, coputational intelligence, achine learning, intelligent data analysis, soft coputing, pattern recognition, etc. The few ones are neural networks, neuro-fuzzy, Decision tree, Expert systes and Support vector achines References Aditya Kaustav (2008). Forecasting of crop yield using discriinant function technique, M.Sc. Thesis, IARI, New Delhi. Agrawal, Ranjana; Jain, R.C.; Jha, M.P. and Singh, D. (980). Forecasting of rice yield using cliatic variables. Ind.J.Agri. Sci. 50(9) : Agrawal, Ranjana; Jain, R.C. and Jha, M.P. (983). Joint effects of weather variables on rice yield, Mausa, 34 (2) : Agrawal, Ranjana; Jain, R.C. and Jha, M.P. (986). Models for studying rice crop-weather relationship, Mausa, 37():

9 Agrawal, Ranjana and Jain, R.C. (996). Forecast of sugarcane yield using eye estiate alongwith plant characters. Bioetrical Journal, 38 (5) : Agrawal, Ranjana; Jain, R.C. and Mehta, S.C. (200). Yield forecast based on weather variables and agricultural inputs on agrocliatic zone basis. Indian Journal of Agricultural Science, 7(7). Agrawal, Ranjana; Raakrishna, Y.S.; Kesava Rao, A.V.R.; Kuar, Arender; Bhar, Lal Mohan; Madan Mohan and Saksena, Asha (2005). Modeling for forecasting of crop yield using weather paraeter and agricultural inputs. (AP Cess Fund project report). Baier, W. (977). Crop weather odels and their use in yield assessents. Tech. note no. 5, WMO, Geneva, 48 pp. Chandrahas and Narain, Pre (992). Pre-harvest forecasting of yield of apple. (IASRI Publication). Chandrahas and Rai, T. (200). Pilot study for developing Bayesian probability forecast odel based on farers appraisal data on wheat crop. (IASRI publication). Chandrahas; Agrawal, Ranjana and Walia, S.S. (200). Use of discriinant function and principal coponent techniques for weather based crop yield forecasts. (IASRI, New Delhi). Fisher, R.A. (924). The influence of rainfall on the yield of wheat at Rothasted. Roy. Soc. (London), Phil. Trans. Ser.B.,23 : Frere, M. and Popov, G.F. (979). Agroeteorological crop onitoring and forecasting. FAO plant production and protection paper, plant production and protection division, FAO, Roe. Hendrick, W.A. and Scholl, J.C. (943). Technique in easuring joint relationship. The joint effects of teperature and precipitation on crop yield. N. Carolina Agric. Exp. Stat. Tech. Bull. 74. House, C.C. (977). A within year growth odel approach to forecasting corn yields. Econoics, Statistics and Co-operative Service U.S. Departent of Agriculture, Washington, D.C Jain,R.C.; Agrawal, Ranjana and Jha, M.P. (980). Effects of cliatic variables on rice yield and its forecast, Mausa 3(4) : Jain,R.C. and Agrawal, R. (992 (a)). Probability odel for crop yield forecasting. Bioetrical Journal, 34(4) : 50-. Jain, R.C.; Agrawal, Ranjana and Singh, K.N. (992 (b)). A within year growth odel for crop yield forecasting. Bioetrical Journal, 34(7) : Jain, R.C.; Sridharan, H. and Agrawal, R. (984). Principal coponent technique for forecasting of sorghu yield, Indian J. Agric. Sci. 54(6) : Jain, R.C.; Jha, M.P. and Agrawal, R. (985). Use of growth indices in yield forecast. Bioetrical Journal, 27(4) : Jain, R.C. and Raasubraanian, V. (998), Forecasting of crop yields using second order Markov Chains. Journal of the Ind. Soc. of Agril. Stats. Vol. LI() : Jha, M.P.; Jain, R.C. and Singh, D. (98). Pre-harvest forecasting of sugarcane yield. Indian. J. Agric. Sci. 5(0) : Kuar, Arender; Raasubraanian, V. and Agrawal, Ranjana (200). Neural network based forecast odeling crops. (IASRI Publication). Larsen, Grog. A. (978). Forecasting (977). Kansas wheat growth. Econoics, Statistics and Cooperative Service, U.S. Departent of Agriculture. Washington D.C Matis, J.H.; Gaito, T.; Grant, W.E.; Iwing, W.C. and Ritchie, J.T. (985). A Markov chain approach to crop yield forecasting. Agricultural Systes, 8 : Matis, J.H.; Birkett, T. and Boudreaux, D. (989). An application of Markov chain approach to forecasting cotton yield fro surveys. Agricultural Systes, 29 :

10 Mehta, S.C.; Agrawal, Ranjana; Singh V.P.N. (2000): Strategies for coposite forecast. JISAS, 53(3). Mehta, S.C.; Satya Pal; Kuar, Vinod (200). Weather based odels for forecasting potato yield in Uttar Pradesh. (IASRI Publication). Nealon, Jack, (976). The developent of within-year forecasting odels for winter wheat. Research and developent branch, Research Division, Statistical Reporting Service, U.S. Departent of Agriculture. Patel, N.K., Chakraborty, M., Dutta, S., Patnaik, S., Parihar, J.S., Moharana, S.C., Das, A., Sarangi, B.K. and Behera, G. (2004). Multiple forecasts of kharif rice in Orissa state - Four year experience of Fasal pilot study. Journal of the Indian Society of Reote Sensing, 32(2) : Rai, T. and Chandrahas (2000). Use of discriinant function of weather paraeters for developing forecast odel for rice crop. (IASRI Publication). Raakrishna, Y.S.; Singh, H.P. and Rao, G. Nageswara (2003). Weather based indices for forecasting foodgrain production in India. Jounral of Agroeteorology 5() :. Raasubraanian, V. and Jain, R.C. (999). Use of growth indices in Markov Chain odels for crop yield forecasting. Bioetrical Journal, 4() : Raasubraanian, V.; Agrawal, Ranjana and Bhar, L.M. (2004). Forecasting sugarcane yield using ultiple Markov chains.(iasri publication) Sardana, M.G.; Khosla, R.K.; Ohri, N.K. and Mitra, P.C. (972). Pre-harvest forecasting of yield rate of jute. Jute Bull. 35 (7 and 8). Sarkar, J. (2002). Forecasting rice and wheat yield over different eteorological sub divisions of India using statistical odels. 56 th Annual Conference of ISAS. Sarwade, G.S. (988). Meteorological yield odels. IRS-UP/SAC/CYM/TN/7/58, SAC, Ahedabad. Saksena, Asha; Jain, R.C.; Yadav, R.L. (200). Developent of early warning and yield assessent odel for rainfed crops based on agroeteorological indices. (IASRI publication). Singh, B.H.; Bapat, S.R. (988). Pre-harvest forecast odels for prediction of sugarcane yield. Indian J. Agric. Sci. 58(6) : Singh, D.; Singh, H.P.; Singh, Singh, P. (976). Pre-harvest forecasting of wheat yield. Indian J. Agric. Sci. 46(0) : Vogel, Fred. A. (985). Crop forecasting ethodology current and future procedures in the U.S. Proceedings of the 45 th session of the International Statistical Institute, held at Asterda : 2.- to