Forecasting future technological needs for rice crop in India Questionnaire

1
Pests and Diseases Forewarning System
Amrender Kumar
Scientist Indian Agricultural Statistics
Research Institute, Library Avenue, New Delhi,
INDIA akjha_at_iasri.res.in
2
Crop Pests - Weather Relationship
Crop
Weather
Pests
3

• Diseases and pests are major causes of reduction
  in crop yields.
• However, in case information about time and
  severity of outbreak of diseases and pests is
  available in advance, timely control measures can
  be taken up so as to reduce the losses.
• Weather plays an important role in pest and
  disease development.
• Therefore, weather based models can be an
  effective scientific tool for forewarning
  diseases and pests in advance.

4
Why pests and disease forewarning

• Forewarning / assessment of disease important
  for crop production management
• for timely plant protection measures
• information whether the disease status is
  expected to be below or above the threshold level
  is enough, models based on qualitative data can
  be used qualitative models
• loss assessment
• forewarning actual intensity is required -
  quantitative model

5
Variables of interest

• Maximum pest population or disease severity.
• Pests population/diseases severity at most
  damaging stage i.e. egg, larva, pupa, adult.
• Pests population or diseases severity at
  different stages of crop growth or at various
  standard weeks.
• Time of first appearance of pests and diseases.
• Time of maximum population/severity of pests and
  diseases.
• Weekly monitoring of pests and diseases progress.
• Occurrence/non-occurrence of pests diseases.
• Extent of damage.

6
Data Structure
Historical data at periodical intervals for 10-15
years
Year Observation Observation Observation Observation Observation Observation Observation
Year 1 2 3 4 . . .
1 y11 y12 . . . . .
2 y21 y22 . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
10-15 . . . . . . .
7

• Historical data for 10-15 years at one point of
  time
• overall status
• disease intensity
• crop damage.

8

• Data for 5-6 years at periodic intervals
• For week-wise models, data points inadequate
• combined model for the whole data in two steps
• Data at one point of time for 5-6 years
• Model development not possible
• Qualitative data for 10-15 years
• Qualitative forewarning
• Occurrence / non-occurrence of disease
• Mixed data conversion to qualitative
  categories
• Data collected at periodic intervals for one year
• Within year growth model

9

• Choice of explanatory variables
• Relevant weather variables
• appropriate lag periods depending on life cycle
• Crop stage / age
• Natural enemies
• Starting / previous years last population of
  pathogen

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Forecast Models

• Between year models
• These models are developed using previous years
  data.
• The forecast for pests and diseases can be
  obtained by substituting the current year data
  into a model developed upon the previous years.
• Within year models
• Sometimes, past data are not available but the
  pests and diseases status at different points of
  time during the current crop season are
  available.
• In such situations, within years growth model
  can be used, provided there are 10-12 data points
  between time of first appearance of pests and
  diseases and maximum or most damaging stage.
• The methodology consists of fitting appropriate
  growth pattern to the pests and diseases data
  based on partial data.

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• Thumb rules
• Most common
• Extensively used
• Judgment based on past experience with no or
  little mathematical background
• Example
• A day is potato late blight favorable if
• the last 5 - day temperature average is lt 25.50
  C
• the total rainfall for the last 10 days is gt
  3.0 cm
• the minimum temperature on that day is gt 7.20 C
• Trivedi et al. (1999)

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• Regression models
• Relationship between two or more quantitative
  variables
• The model is of the form
• Y ?0 ?1 X1?2 X2 . ?p Xp e ,
• where
• ?is are regression coefficients
• Xis are independent variables
• Y variable to forecast
• e random error
• Variables could be taken as such or some suitable
  transformations

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• Cotton
• of incidence of Bacterial blight (Akola)
  Weekly models (42nd to 44th SMW)
• Data used 1993-1999 on MAXTemp, MINTemp, RH1
  (morn), RH2 (aft) and RF X1 to X5) lagged by
  2 to 4 weeks
• Model for 44th SMW
• Y 133.18 - 3.09 RH2L4 1.68 RFL4 (R20.78)

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• Potato
• Potato aphid is an abundant potato pest and
  vector of potato leaf-roll virus, potato virus Y
  , PVA, etc.
• Potato aphid population Pantnagar (weekly
  models)
• Data used 1974-96 on MAXT, MINT and RH
• X1 to X3) lagged by 2 weeks
• Model for December 3rd week
• Y 80.25 40.25 cos (2.70 X12 - 14.82)
• 35.78 cos (6.81 X22 8.03)

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Aphid popn. in 3rd week of December at
Pantnagar
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GDD approach

• GDD ? (mean temperature base temperature)
• The decision of
• Base temperature
• Initial time
• Not much work on base temperature for various
  diseases
• Normally base temperature is taken as 50 C
• Under Indian conditions, mean temperature is
  seldom below 50 C
• Use of GDD and simple accumulation of mean
  temperature will provide similar results in
  statistical models
• Need for work on base temperature and initial
  time of calculation

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• Under Indian conditions, other variables also
  important
• Model using simple accumulations not found
  appropriate
• Models based on weighted weather indices

where
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Y variable to forecast xiw value of
i?th weather variable in w?th period riw
weight given to i-th weather variable in w?th
period riiw weight given to product of xi and
xi in w?th period p number of weather
variables n1 and n2 are the initial and final
periods for which weather variables are
to be included in the model e error term
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• Experience based weights
• Subjective weights based on experience.
• Weather variable not favourable weight 0
• Weather variable favourable weight ½
• Weather variable very favourable weight 1

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• Example
• Favourable relative humidity ? 92
• Most favourable relative humidity ? 98
• Weather data
• Year Week No.
• 1 2 3 4 5
  6
• 1993 88.7 90.1 94.4 98.3 98.0
  95.0
• 94.0 93.3 94.9 93.3 92.0
  88.1
• 90.3 91.9 90.4 87.9 86.4
  89.7
• --------------------------------------------------
  --------------
• --------------------------------------------------
  --------------

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• Weighted Index
• 0x 88.7 0x90.1 0.5 x 94.4 1 x 98.3
• 1 x 98 0.5 x 95 271.0
• 0.5 x 94 0.5 x 93.3 0.5 x 94.9
• 0.5 x 93.3 0.5 x 92 0 x 88.1
  232.6
• 0 x 90.3 0 x 91.9 0 x 90.4 0x 87.9
• 0 x 86.4 0 x 89.7 0.0
• -------------------------------------------------
  --------------
• --------------------------------------------------
  --------------

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Interaction Both variables not favourable
weight 0 One variable not favourable, one
variable favourable weight 1/8 One variable
not favourable, one variable highly favourable
weight ¼ Both variables favourable weight
½ One variable favourable, one variable
highly favourable weight ¾ Both variables
highly favourable weight 1
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Correlation based weights riw
correlation coefficient between Y and i-th
weather variable in w?th period riiw
correlation coefficient between Y and product
of xi and xi in w?th period
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• Modified model
• Model using both weighted and unweighted indices

where
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• For each weather variable two types of indices
  have been developed
• Simple total of values of weather variable in
  different periods
• Weighted total, weights being correlation
  coefficients between variable to forecast and
  weather variable in respective periods
• The first index represents total amount of
  weather variable received by the crop during the
  period under consideration
• The other one takes care of distribution of
  weather variable with reference to its
  importance in different periods in relation to
  variable to forecast
• On similar lines, composite indices were computed
  with products of weather variables (taken two at
  a time) for joint effects.

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Pigeon pea

• Phytophthora blight (Kanpur)
• Average percent incidence of phytophthora blight
  at one point of time
• Data used 1985-86 to 1999-2000 on MAXT, MINT,
  RH1, RH2 and RF (X1- X5) from 28th to 33rd SMW
• Y 330.77 0.12 Z121 .. (R2 0.77)

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• Sterility Mosaic
• Average percent incidence of sterility mosaic
• Data used 1983-84 to 1999-2000 for MAXT, MINT,
  RH1, RH2 and RF (X1- X5) from 20th to 32nd SMW
• Y -180.41 0.09 Z121 (R2 0.84)

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• Validation for subsequent years

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Groundnut

• Late Leaf Spot Rust Tirupathi
• Disease indices at one point of time
• Data used MAXT, MINT, RH1, RH2, RF and WS from
  (X1- X6)
• - 10th to 14th SMW (Rabi or post rainy)
• - 41st to 46th SMW (Kharif or rainy)

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Models for LSS and Rust Disease Index -
groundnut (Tirupati)
Disease Data used Model R2
LLS Kharif 1990 - 1998 Y 39.40 - 0.00921 Z120 0.00037 Z460 0.0022 Z141 0.84
LLS Rabi 1990 - 1999 Y 15.95 0.12Z151 0.0057 Z350 0.83
Rust Kharif 1990 - 1995 Y 0.4213 0.0167Z231 - 0.147 Z10 0.94
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• Principal component regression
• Independent variables large and correlated
• Independent variables transformed to principal
  components
• First few principal components explaining
  desired variation selected
• Regression model using principal components as
  regressors

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• Discriminant function analysis
• Based on disease status years grouped into
  different categories low, medium, high
• Linear / quadratic discriminant function using
  weather data in above categories
• Discriminant score of weather for each year
• Regression model using disease data as dependent
  variable and discriminant scores of weather as
  independent.
• Data requirement is more.
• Can also be used if disease data are qualitative
• Johnson et al. (1996) used discriminant analysis
  for forecasting potato late blight.

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• Deviation method
• Useful when only 5-6 year data available for
  different periods
• Week-wise data not adequate for modeling
• Combined model considering complete data.
• Not used for disease forewarning but in pest
  forewarning

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• Assumption pest population / disease incidence
  in particular year at a given point of time
  composed of two components.
• Natural growth pattern
• Weather fluctuations
• Natural pattern to be identified using data in
  different periods averaged over years.
• Deviation of individual years in different
  periods from predicted natural pattern to be
  related with deviations of weather.

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• Mango
• Mango fruitfly Lucknow (weekly models)
• Data used 1993-94 to 1998-99 on MAXT, MINT and
  RH X1 to X3
• Model for natural pattern

t Week no. Yt Fruitfly population count
at week t
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Forecast model

• Y ? 125.766 0.665 (Y2) 0.115 (1/X222 )
  10.658 (X212)
• 0.0013 (Y23) 31.788 (1/Y3) ? 21.317
  (X12)
• ? 2.149 (1/X233) ? 1.746 (1/X234)
• Y Deviation of fruitfly population from
  natural cycle
• Yi Fruitfly population in i-th lag week
• Xij Deviation from average of i-th weather
  variable (i
• 1,2,3 corresponds to maximum
  temperature,
• minimum temperature and relative
  humidity) in j-th lag
• week.

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Soft Computing Techniques
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• With the development of computer hardware and
  software and the rapid computerization of
  business, huge amount of data have been collected
  and stored in centralized or distributed
  databases
• Data is heterogeneous (mixture of text, symbolic,
  numeric, texture, image), huge (both in
  dimension and size) and scattered.
• The rate at which such data is stored is growing
  at a phenomenal rate.
• As a result, traditional statistical techniques
  and data management tools are no longer adequate
  for analyzing this vast collection of data.

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• One of the applications of Information Technology
  that has drawn the attention of researchers is
  data mining, where pattern recognition, image
  processing, machine intelligence i.e concerned
  with the development of algorithms and techniques
  that allow system to "learn are directly related
• Data Mining involves
• Statistics Provides the background for the
  algorithms.
• Artificial Intelligence Provides the required
  heuristics for learning the system
• Data Management Provides the platform for
  storage retrieval of raw and summary data.

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• Pattern Recognition and Machine Learning
  principles applied to a very large (both in size
  and dimension) heterogeneous database for
  Knowledge Discovery
• Knowledge Discovery is the process of identifying
  valid, novel, potentially useful and ultimately
  understandable patterns in data. Patterns may
  embrace associations, correlations, trends,
  anomalies, statistically significant structures
  etc.
• Without Soft Computing Machine Intelligence and
  Data Mining may remains Incomplete

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Soft Computing

• Soft Computing is a new multidisciplinary field
  that was proposed by Dr. Lotfi Zadeh, whose goal
  was to construct new generation Artificial
  Intelligence, known as Computational
  Intelligence.
• The concept of Soft Computing has evolved. Dr.
  Zadeh defined Soft Computing in its latest
  incarnation as the fusion of the fields of fuzzy
  logic, neural network, neuro-computing,
  Evolutionary Genetic Computing and
  Probabilistic Computing into one
  multidisciplinary system.
• Soft Computing is the fusion of methodologies
  that were designed to model and enable solutions
  to real world problems, which are not modeled, or
  too difficult to model. These problems are
  typically associated with fuzzy, complex, and
  dynamical systems, with uncertain parameters.
• These systems are the ones that model the real
  world and are of most interest to the modern
  science.

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• The main goal of Soft Computing is to develop
  intelligent system and to solve nonlinear and
  mathematically unmodelled system problems Zadeh
  1993, 1996, and 1999.
• The applications of Soft Computing have two main
  advantages.
• First, it made solving nonlinear problems, in
  which mathematical models are not available,
  possible.
• Second, it introduced the human knowledge such as
  cognition, recognition, understanding, learning,
  and others into the fields of computing.
• This resulted in the possibility of constructing
  intelligent systems such as autonomous
  self-tuning systems, and automated designed
  systems.

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soft computing tools

• Soft computing tools include
• Fuzzy sets
• Fuzzy sets provide a natural frame work for the
  process in dealing with uncertainty
• Artificial neural networks
• Neural networks are widely used for modelling
  complex functions and provide learning and
  generalization capabilities
• Genetic algorithms
• Genetic algorithms are an efficient search and
  optimization tool
• Rough set theory
• Rough sets help in granular computation and
  knowledge discovery

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• Why Neural Networks are desirable
• Human brain can generalize from abstract
• Recognize patterns in the presence of noise
• Recall memories
• Make decisions for current problems based on
  prior experience
• Why Desirable in Statistics
• Prediction of future events based on past
  experience
• Able to classify patterns in memory
• Predict latent variables that are not easily
  measured
• Non-linear regression problems

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Application of ANNs

• Modelling and Control
• control systems
• system identification
• composing music
• Forecasting
• economic indicators
• energy requirements
• medical outcomes
• crop forecasts
• environmental risks

• Classification
• medical diagnosis
• signature verification
• character recognition
• voice recognition
• image recognition
• face recognition
• loan risk evaluation
• data mining

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• Neural networks are being successfully applied
  across an extraordinary range of problem domains,
  in areas as diverse as finance, medicine,
  engineering, geology, biology, physics and
  agriculture.
• From a statistical perspective neural networks
  are interesting because of their potential use in
  prediction and classification problems.
• A very important feature of these networks is
  their adaptive nature, where Learning by
  Example replaces Programming in solving
  problems.
• Basic capability of neural networks is to learn
  patterns from examples

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• Type of neural network models
• Two types of neural network models
• Multilayer perceptron (MLP) with different hidden
  layers and nodes
• Radial basis function (RBF)

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Neural network based model

• Steps in developing a neural network model
• Forming training, testing and validation sets
• Neural network model
• No. of input nodes
• No. of hidden layers
• No. of hidden nodes
• No. of output nodes
• Activation function
• Model building
• Sensitivity Analysis

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Data sets

• The data available is divided into three data
  sets
• Training set represents the input- output
  mapping, which is used to modify the weights.
• Validation set is required only to decide when to
  stop training the network, and not for weight
  update.
• Test set is the part of collected data that is
  set aside to test how well a trained neural
  network generalizes.

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• No. of input nodes more than one
• No. of hidden layers one / two
• No. of hidden nodes decided by various rules
• No. of output nodes one
• Activation function hyperbolic

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• Activation function
• Activation functions determine the output of a
  processing node. Non linear functions have been
  used as activation functions such as logistic,
  tanh etc.
• Activation functions such as sigmoid are commonly
  used because they are nonlinear and continuously
  differentiable which are desirable for network
  learning
• Logistic activation functions are mainly used for
  classification problems which involve learning
  about average behavior
• Hyperbolic tangent functions are used for the
  problem involves learning about deviations from
  the average such as the forecasting problem.
• Therefore, in the present study, hyperbolic
  tangent (tanh) function has been used as
  activation function for neural networks model
  based on MLP architecture.

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Input
Output
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Learning of ANNs

• The most significant property of a neural network
  is that it can learn from environment, and can
  improve its performance through learning
• Learning is the process of modifying the weights
  in networks
• The network becomes more knowledgeable about
  environment after each iteration of learning
  process.
• There are mainly two types of learning paradigms
• Supervised learning
• Unsupervised learning

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A learning cycle in the MLP (Backpropagation
Learning Algorithm)
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Three-layer back-propagation neural network
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• Mustard
• Alternaria blight (Varuna, Rohini Binoy)
• Bharatpur (Raj)
• Behrampur (WB)
• Dholi (Bihar)
• Powdery mildew (Varuna and GM2)
• S.K.Nagar
• Variable to forewarn
• crop age at first appearance of disease
• crop age at peak severity of disease
• maximum severity of disease
• Cotton
• Bacterial blight ( of disease incidence) - Akola

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Pests / diseases forewarning-Mustard

• Data have been taken from Mission Mode Project
  under National Agricultural Technology Project,
  entitled Development of weather based
  forewarning system for crop pests and diseases,
  at CRIDA, Hyderabad.
• Models were developed for forecasting different
  aspects relating to diseases for Alternaria
  Blight (AB) and Powdery Mildew (PM) in Mustard
  crop.
• The field trials were sown on 10 dates at weekly
  intervals (01, 08, 15, 22, 29 October, 05, 12,
  19, 26 November and 03 December) at each of the
  locations viz., Bharatpur, Dholi and Berhampur
  for Alternaria Blight and at S.K.Nagar for
  Powdery Mildew.
• Data for different dates of sowing were taken
  together for model development.
• Weekly data on weather variables starting from
  week of sowing up to six weeks of crop growth
  were considered
• Forewarning models were developed for two
  varieties of mustard crop for
• Alternaria Blight on leaf and pod (Varuna and
  Rohini Bharatpur, Varuna and Binoy Behrampur
  and Varuna and Pusabold Dholi) and
• Powdery Mildew on leaf (Varuna and GM2
  S.K.Nagar)
• Models have been validated using data on
  subsequent years not included in developing the
  models.

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Mean Absolute Percentage Error of various models
at Bharatpur in different varieties in mustard
crop for Alternaria blight (AB) - 2006-07
Character Variety MLP RBF WI
Maximum severity Varuna (on Leaf) 111.0 153.8 150.1
Age at First app Varuna (on Leaf) 14.0 15.1 14.7
Age at Peak Severity Varuna (on Leaf) 14.1 27.3 22.3
Maximum severity Varuna (on Pod) 113.7 143.6 132.6
Age at First app Varuna (on Pod) 15.7 9.2 14.2
Age at Peak Severity Varuna (on Pod) 3.9 6.4 5.4
Maximum severity Rohini (on Leaf) 184.0 200.6 196.3
Age at First app Rohini (on Leaf) 12.0 15.5 8.9
Age at Peak Severity Rohini (on Leaf) 28.3 27.8 26.2
Maximum severity Rohini (on Pod) 174.8 220.4 229.6
Age at First app Rohini (on Pod) 29.3 28.2 24.7
Age at Peak Severity Rohini (on Pod) 17.2 20.7 19.6
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• Neural networks, with their remarkable ability to
  derive meaning from complicated or imprecise
  data, can be used to extract patterns and
  classifications
• Neural networks do not perform miracles. But if
  used sensibly they can produce some amazing
  results

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• Model for qualitative data
• Data in categories
• Occurrence / non-occurrence, low / medium / high,
  etc.
• Classified as 0 / 1 (2 categories) 0,1,2
  (three categories)
• Quantitative data / mixed data can be converted
  to categories

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Logistic Regression model

• where, L ß0 ß1x1 ß2x2 .ßnxn
• x1 , x2 , x3 ,xn are weather variables/weather
  indices
• e random error
• Forecast / Prediction rule
• If P lt 0.5, then the probability of epidemic
  occurrence will be minimal
• If P ? 0.5, then there is more chance of
  occurrence of epidemic.

66

• Rice
• Leaf blast severity () - Palampur at one point
  of time
• Data used 1991-92 to 1998-99 on MAXT, MINT, RH1,
  RH2, BSH RF X1 to X6 from 23th to 31st
  SMW.
• Model
• L 394.8 -0.0520 Z351-1.5414 Z10
• Validation for subsequent years

Year Observed Forewarning Probabilities
1999-00 1 1 0.88
2000-01 1 1 0.63
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Mustard

• Alternaria blight and White rust
• Data used 1987-88 to 1998-99 on MAXT, MINT, RH1,
  RH2 and BSH (X1 to X5) from week of sowing (n1)
  to 50th smw (n2)
• Model for Alternaria blight
• L - 8.8347 0.0163 Z120 - 0.00037 Z130 -
  0.00472 Z450
• Model for White rust
• L 5.8570 - 0.0293Z40 0.00264 Z230
• Forecasts of subsequent years are

Alternaria blight Alternaria blight Alternaria blight Alternaria blight White Rust White Rust White Rust
Year Observed Forewarning Prob. Observed Forewarning Prob.
1999-00 1 1 0.51 1 1 0.96
2000-01 0 0 0.13 0 0 0.49
2001-02 1 1 0.62 0 0 0.37
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• Within year model
• Model using only one years data
• Data availability for several dates of sowing
• If adequate dates of sowing, models similar to
  between-year models could be developed
• Use for forewarning subsequent years (?)
• Model for single date of sowing
• Forewarning of maximum disease severity
• Applicable when 10-12 data observations between
  first disease appearance and maximum disease
  severity
• Non-linear model for disease development pattern
  growth using partial data

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• Mustard
• Alternaria blight cv. Varuna ( disease severity)
  - Kumarganj
• Data used 1999-2000
• Model
• Yt A exp (B/t)
• Yt pds at time t, A and B are
  parameters,
• t week after sowing (1,2,.)

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Observed, predicted and forecasts of max. percent
disease severity (PDS)

• Reliable forecast of max. pds could be obtained
  for 2 weeks in advance

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Models developed at IASRI

• Sugarcane
• Pyrilla
• Early shoot borer
• Top borer
• Pigeon pea
• Pod fly
• Pod borer
• Sterility Mosaic
• Phytophthora Blight
• Rice
• BPH
• Gall midge
• Mango
• Powdery Mildew
• hoppers
• fruit-fly

• Mustard
• Alternaria Blight
• White Rust
• Powdery Mildew
• Aphid
• Cotton
• American boll worm
• Pink boll worm
• Spotted boll worm
• Whitefly
• Groundnut
• Spodoptera litura
• Late leaf blast
• Rust
• Onion
• Thrips

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References

• Agrawal, Ranjana, Jain, R.C. and Jha, M.P.
  (1983). Joint effects of weather variables on
  rice yields. Mausam, 34(2), 177-81.
• Agrawal, Ranjana, Jain, R.C., Jha, M.P., (1986).
  Models for studying rice crop weather
  relationship, Mausam, 37(1), 67-70.
• Agrawal Ranjana, Mehta, S.C., Kumar, Amrender and
  Bhar, L.M. (2004). Development of weather based
  forewarning system for crop pests and diseases-
  Report from IASRI, Mission mode project under
  NATP, PI, Dr. Y.S. Ramakrishna, CRIDA,
  Hyderabad.
• Denton, J.W., 1995. How good are neural networks
  for causal forecasting? Journal of Business
  Forecasting, 14 (2), 1720.
• Desai, A.G., Chattopadhyay, C., Agrawal, Ranjana,
  Kumar, A., Meena, R.L., Meena, P.D., Sharma,
  K.C., Rao, M. Srinivasa, Prasad,, Y.G. and
  Ramakrishna, Y.S. (2004). Brassica juncea
  powdery mildew epidemiology and weather-based
  forecasting models for India - a case study ,
  Journal of Plant Diseases and Protection, 111(5),
  429-438.
• Gaudart, J., Giusiano, B. and Huiart, L. (2004).
  Comparison of the performance of multi-layer
  perceptron and linear regression for
  epidemiological data. Comput. Statist. Data
  Anal., 44, 547-70.

73

• Hebb, D.O. (1949) The organization of behaviour
  A Neuropsychological Theory, Wiley, New York.
• Hopfield, J.J. (1982). Neural network and
  physical system with emergent collective
  computational capabilities. In proceeding of the
  National Academy of Science (USA) ,79, 2554-2558.
• Kaastra, I. and Boyd, M.(1996) Designing a
  neural network for forecasting financial and
  economic time series. Neurocomputing, 10(3),
  215-236.
• Masters, T. (1993). Practical Neural Network
  Recipes in C, San Diego, Academic Press.
• Rosenblatt, F. (1958). The perceptron A
  probabilistic model for information storage and
  organization in the brain. Psychological review,
  65, 386-408.
• Rumelhart, D.E., Hinton, G.E., and Williams, R.J.
  (1986). Learning internal representations by
  error propagation, Nature, 323, 533-536

74

• Saanzogni, Louis and Kerr, Don (2001) Milk
  production estimate using feed forward artificial
  neural networks. Computer and Electronics in
  Agriculture, 32, 21-30.
• Warner, B. and Misra, M. (1996). Understanding
  neural networks as statistical tools. American
  Statistician, 50, 284-93.
• Widrow, B. and Hoff, M.E. (1960). Adaptive
  switching circuit. IREWESCON convention record,
  4, 96-104
• Zhang, G., Patuwo, B. E. and Hu, M. Y. (1998).
  Forecasting with artificial neural networks The
  state of the art. International Journal of
  Forecasting, 14, 35-62.

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