Spring Frost Prediction Models in Cranberry

Transcription

1 University of Massachusetts Amherst Amherst North American Cranberry Researcher and Extension Workers Conference NACREW 2017 Aug 28th, 9:30 AM - 9:45 AM Spring Frost Prediction Models in Cranberry Peter Jeranyama University of Massachusetts Amherst Cranberry Station, peterj@umass.edu Follow this and additional works at: Part of the Agriculture Commons Recommended Citation Jeranyama, Peter, "Spring Frost Prediction Models in Cranberry" (2017). North American Cranberry Researcher and Extension Workers Conference This Event is brought to you for free and open access by the Cranberry Station at ScholarWorks@UMass Amherst. It has been accepted for inclusion in North American Cranberry Researcher and Extension Workers Conference by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact scholarworks@library.umass.edu.

2 Spring Frost Prediction Models in Cranberry Peter Jeranyama August 28, 2017

3 Functional Aspects of Models Describes the distributional properties of 1 response variable; variability into known & unknown. Represents a mechanism from which data with the same statistical properties as observed data can be generated Assumed to be correct on average. Quality is a not necessarily f(x): complexity or size but its utility.

4 Model Development Philosophy Interpretability and parsimony are critical Nothing is gained by building models that are large & complex that are impossible to observe in practice. Adding variables to a regression model can increase R 2 but can render estimation unstable, imprecise & difficult to interpret.

5 Ockham s Razor Medieval Franciscan monk William of Ockham ( ) is credited with the Ockham s Razor. Pluralitas non est ponenda sine neccesitate Simply interpreted: Plurality should not be assumed (posited) without necessity.

6 Ockham s Razor -Explained Nonlinear models, for example have been considered difficult to fit data in the past. Even recently, Black(1993, p.65) refers to the drudgery connected with the actual fitting of nonlinear models. Modernity in statistical tools is making it increasingly easy to use nonlinear models.

7 Ockham s Razor -Explained It is also loosely phrased: among competing explanations, pick the simplest one In statistical models, simple does not imply the smallest possible model. The selected model should be simple to fit, simple to interpret, simple to justify & simple to apply.

8 Frost Damage in Cranberry Grown on low-lying ground where cold air settles on calm nights thereby increasing the danger of damaging low temperatures. On clear nights with low dew points, leaves radiate infrared radiation further lowering bog temps compared to those areas surrounding cranberry bogs (-10 C temp differences)

9 Dr. Henry J. Franklin (1943) Winter record keeping started in to find formulas to predict cranberry bog frost & degree of coldness. Prof J. Warren Smith from Weather Bureau's work did not yield satisfactory formulas. Dr. Franklin started work on this in 1928 culminating in formulas presented in 1943.

10 Model Development Model: Y ijkm = µ+ α i + β j + γ k + δ m + Ψ n +ε ijkmn Where,µ = Grand mean, α i = i effect of Min_EW; β j = the j th effect of low dew point in EW; γ k = k effect of Min_Worc. ; δ m = m effect of low dew point in Worc. Ψ = n effect of cloud cover in EW εi jkm = Residual error

11 Pearson Correlation Coefficients, N = 88 Prob > r under H0: Rho=0 cloud Min_EW LDP_EW BogT Min_Worc LDP_Worc logcloud cloud Min_EW LDP_EW BogT Min_Worc LDP_Worc logcloud

12 Analysis of Variance Source DF Sum of Squares Mean Square Model Error F Value Pr > F Root MSE R-Square Corrected Dependent Mean Adj R-Sq Total Coeff Var Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept Min_EW LDP_EW Min_Worc LDP_Worc

13 Fit Diagnostics for BogT Residual 0-5 RStudent 0-1 RStudent Predicted Value Predicted Value Leverage Residual BogT Cook's D Quantile Predicted Value Observation 25 Fit Mean Residual Percent Residual Proportion Less Observations 88 Parameters 5 Error DF 83 MSE R-Square Adj R-Square

14 Temperature o F Frost Season Days 12

15 BogT measured values Goodness of Fit for New Model BogT = Min_EW LDP_EW Min_Worc LDP_Worc: R 2 = Predicted BogT values 13

16 Bias Estimation between CCCGA and New Model Measured_BogT PredNew_Model CCGA_Model 14

17 CCCGA Model Fitting Bland-Altman Agreement Difference (Y-X) Average (X+Y)/2 15

18 New Model Fitting Bland-Altman Agreement Difference (Y-X) Average (X+Y)/2 16

19 New Model vs. CCCGA Model Passing-Bablok Parameter: Value 95% Confidence Interval A B (B*X) Bland-Altman Interval of Agreement

20 New Model vs. Measured BogT Passing-Bablok Parameter: Value 95% Confidence Interval A B (B*X) Bland-Altman Interval of Agreement

21 What Next? Continue to explore other variables for inclusion in the model Cloud cover did not yield desirable results Further analysis of strongly associated variables (higher polynomials or exponential functions) Sensitivity Analysis; POD, Hit Rate, False Alarm