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ICAR-IASRI MSc and PhD Crop Forecasting, Weather-Based Models & Non-linear Growth Models: practice questions

ICAR-IASRI MSc and PhD (Agricultural Statistics, Computer Application, Bioinformatics) · India · ICAR-Indian Agricultural Statistics Research Institute with the IARI Graduate School

Original practice questions written to the published syllabus · not past papers
10worked here, free
40written to this exam in this subject
11syllabus units

What this subject covers

Forecasting harvests before they happen: Fisher's regression integral and weather-indices models, pre-harvest forecasts from biometric characters and farmers' appraisal, agro-meteorological and remote-sensing models, non-linear growth curves (logistic, Gompertz, Richards), and how statistical and crop-simulation models are combined.

In the exams: AICE-JRF Agricultural Meteorology 'statistical models' (present); ICAR MSc/PhD core in modelling; national crop-forecasting programmes (applied); light in national exams

What ICAR-IASRI MSc and PhD asks from it

ICAR-IASRI MSc and PhD programmes

Developing and validating district-level forecast models, fitting logistic, Gompertz and Richards models with iterative methods, composite and remote-sensing models, and calibration and evaluation of crop simulation models.

Where the 40 questions fall

How our questions for ICAR-IASRI MSc and PhD spread across the units of Crop Forecasting, Weather-Based Models & Non-linear Growth Models. Difficulty: 6 easy, 16 medium, 18 hard.

Crop simulation models and their statistical calibration10
Machine-learning and hybrid forecasting models9
Fitting non-linear models: iterative estimation and goodness of fit6
Weather-based models: Fisher's regression integral and weather indices3
Remote-sensing-based yield forecasting with vegetation indices3
Models using plant biometric characters2
Farmers' eye estimates and appraisal-based forecasts2
Non-linear growth models: logistic, Gompertz, Monomolecular and Richards2
Pre-harvest forecasting: purpose and history1
Agro-meteorological and composite models1
Evaluation of forecasts and their use in policy1

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Farmers' eye estimates and appraisal-based forecasts · hard

In double sampling, farmers' appraisals average 24.0 q/ha in a large first-phase sample. In a sub-sample, appraisals average 22.0 q/ha and crop-cutting yields average 25.0 q/ha, with a regression slope of yield on appraisal of 0.9. What is the regression estimate of mean yield?

  1. 27.0 q/ha
  2. 27.3 q/ha
  3. 26.8 q/ha
  4. 25.0 q/ha
Answer and working

C. 26.8 q/ha

y-reg = y-bar(sub) + b(x-bar(large) - x-bar(sub)) = 25.0 + 0.9 x 2.0 = 26.8. 25.0 ignores the first phase; 27.3 is the ratio estimator; 27.0 assumes a slope of 1.

Further reading: ICAR-IASRI crop forecasting reports; Cochran, Sampling Techniques (double sampling)

2 · Agro-meteorological and composite models · hard

When does combining forecasts from weather, remote-sensing and biometric models reduce error most?

  1. When all three models have exactly the same errors
  2. When the sources carry different information and their errors are not highly correlated
  3. When the combination weights are chosen to fit the test years
  4. When one source is far worse than the other two
Answer and working

B. When the sources carry different information and their errors are not highly correlated

Combining averages out independent errors; if errors are highly correlated there is little gain, and choosing weights on the test years is leakage.

Further reading: FAO agro-meteorological crop monitoring methods

3 · Remote-sensing-based yield forecasting with vegetation indices · hard

Which index was designed to reduce the influence of soil background on vegetation indices in sparse canopies?

  1. Simple Ratio of red to blue reflectance
  2. Land Surface Temperature index
  3. Normalised Difference Water Index (NDWI)
  4. Soil-Adjusted Vegetation Index (SAVI)
Answer and working

D. Soil-Adjusted Vegetation Index (SAVI)

SAVI adds a soil-adjustment constant to the NDVI formula to reduce soil brightness effects where the canopy is sparse. NDWI targets water content; LST is thermal.

Further reading: Jones, Plants and Microclimate; remote-sensing crop monitoring literature

4 · Non-linear growth models: logistic, Gompertz, Monomolecular and Richards · medium

In the Richards model Y = K(1 + b exp(-rt))^(-1/m), which special case is obtained with m = 1?

  1. The logistic model
  2. The Gompertz model
  3. The monomolecular model
  4. The exponential model
Answer and working

A. The logistic model

With m = 1 the formula is K/(1 + b exp(-rt)), the logistic. The Gompertz is the limit as m tends to 0; the monomolecular corresponds to m = -1 with b negative.

Further reading: Ratkowsky, Nonlinear Regression Modeling; Seber and Wild, Nonlinear Regression

5 · Non-linear growth models: logistic, Gompertz, Monomolecular and Richards · hard

Why is a fitted asymptote K unreliable when growth data cover only the early, nearly exponential phase?

  1. Few data lie near the plateau
  2. Early growth data always contain negative values
  3. The rate parameter becomes exactly zero in early data
  4. The asymptote can only be estimated by linear regression
Answer and working

A. Few data lie near the plateau

In the early phase several combinations of K and r fit almost equally well, so K has a huge standard error and is highly correlated with r. Extrapolating to final size is unreliable.

Further reading: Ratkowsky, Nonlinear Regression Modeling; Seber and Wild, Nonlinear Regression

6 · Fitting non-linear models: iterative estimation and goodness of fit · medium

Why is R-squared a weak criterion for comparing non-linear growth models?

  1. It decreases whenever a parameter is added
  2. It is always exactly 1 for non-linear models
  3. It lacks the usual sum-of-squares decomposition
  4. It can only be computed for linear models with two parameters
Answer and working

C. It lacks the usual sum-of-squares decomposition

For non-linear models the total sum of squares does not split into regression and residual parts as in linear regression; RMSE, residual plots and information criteria are preferred.

Further reading: Bates and Watts, Nonlinear Regression Analysis; Seber and Wild, Nonlinear Regression

7 · Crop simulation models and their statistical calibration · easy

What do crop simulation models such as the CERES models in DSSAT compute?

  1. A single regression of yield on total rainfall
  2. Daily crop growth from weather, soil, management and cultivar data
  3. Only the market price of the crop at harvest
  4. Area under the crop from satellite images alone
Answer and working

B. Daily crop growth from weather, soil, management and cultivar data

Process-based simulation models step through the season day by day, simulating phenology, biomass, partitioning, and soil water and nitrogen balances.

Further reading: Wallach, Makowski, Jones and Brun, Working with Dynamic Crop Models

8 · Crop simulation models and their statistical calibration · easy

Which crop simulation model was developed by FAO with a focus on yield response to water?

  1. AquaCrop
  2. WOFOST
  3. InfoCrop
  4. CROPGRO
Answer and working

A. AquaCrop

AquaCrop is FAO's water-driven crop model. CROPGRO is the DSSAT legume model, WOFOST is used in the EU's crop monitoring, and InfoCrop was developed in India.

Further reading: Wallach, Makowski, Jones and Brun, Working with Dynamic Crop Models

9 · Machine-learning and hybrid forecasting models · medium

A random forest forecasts district yields with very high accuracy under random 10-fold cross-validation, but performs poorly in the next season. What is the most likely reason?

  1. The next season had no weather data at all
  2. Random forests cannot use weather variables
  3. Cross-validation always underestimates accuracy
  4. Folds leaked correlated years and districts
Answer and working

D. Folds leaked correlated years and districts

Yields are correlated in time and space; random folds put the same year or nearby districts in both training and test sets, inflating accuracy. Leave-one-year-out or forward validation is honest.

Further reading: Zhang (2003); Wallach et al., Working with Dynamic Crop Models

10 · Evaluation of forecasts and their use in policy · hard

A government is deciding whether to permit wheat exports using a forecast. Why should the forecast be issued with an uncertainty range?

  1. A range is required only when the point forecast is negative
  2. Uncertainty is irrelevant once a model is validated
  3. Ranges always make forecasts more accurate
  4. The costs of over- and under-estimating differ, and decision-makers must weigh the risk of each
Answer and working

D. The costs of over- and under-estimating differ, and decision-makers must weigh the risk of each

Overestimating may lead to exports followed by costly imports; underestimating may trigger unnecessary imports that depress farm prices. Decisions under asymmetric costs need the distribution, not just a point.

Further reading: Hyndman and Athanasopoulos, Forecasting: Principles and Practice; ICAR-IASRI reports

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Crop Forecasting, Weather-Based Models & Non-linear Growth ModelsThe full study manual, free ICAR-IASRI MSc and PhDFormat, sections and how it has changed

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