Bloom prediction from chilling and forcing requirements, assumed to be fulfilled strictly in sequence



This is a pretty rudimentary function to predict phenological dates from chilling and forcing requirements and hourly chilling and forcing data. Note that there are enormous uncertainties in these predictions, which are hardly ever acknowledged. So please use this function with caution.


bloom_prediction(HourChillTable, Chill_model, Chill_req, Heat_req,
  Start_JDay = 305)



a data frame resulting from the chilling_hourtable function.


character string describing the chill model to use. Options are "Chilling_Hours", "Chill_Portions" and "Chill_Units".


numeric parameter indicating the chilling requirement of the particular growth stage (in the unit specified by "Chill_model")


numeric parameter indicating the heat requirement of the particular growth stage (in Growing Degree Hours)


numeric parameter indicating the day when chill accumulation is supposed to start


This function is a bit preliminary at the moment. It will hopefully be refined later.

Chill metrics are calculated as given in the references below. Chilling Hours are all hours with temperatures between 0 and 7.2 degrees C. Units of the Utah Model are calculated as suggested by Richardson et al. (1974) (different weights for different temperature ranges, and negation of chilling by warm temperatures). Chill Portions are calculated according to Fishman et al. (1987a,b). More honestly, they are calculated according to an Excel sheet produced by Amnon Erez and colleagues, which converts the complex equations in the Fishman papers into relatively simple Excel functions. These were translated into R. References to papers that include the full functions are given below. Growing Degree Hours are calculated according to Anderson et al. (1986), using the default values they suggest.


data frame containing the predicted dates of chilling requirement fulfillment and timing of the phenological stage. Columns are Creqfull, Creq_year, Crey_month, Creq_day and Creq_JDay (the row number, date and Julian date of chilling requirement fulfillement), Hreqfull, Hreq_year, Hreq_month, Hreq_day and Hreq_JDay (the row number, date and Julian date of heat requirement fulfillment - this corresponds to the timing of the phenological event.


After doing extensive model comparisons, and reviewing a lot of relevant literature, I do not recommend using the Chilling Hours or Utah Models, especially in warm climates! The Dynamic Model (Chill Portions), though far from perfect, seems much more reliable.


Eike Luedeling


Model references:

Chilling Hours:

Weinberger JH (1950) Chilling requirements of peach varieties. Proc Am Soc Hortic Sci 56, 122-128

Bennett JP (1949) Temperature and bud rest period. Calif Agric 3 (11), 9+12

Utah Model:

Richardson EA, Seeley SD, Walker DR (1974) A model for estimating the completion of rest for Redhaven and Elberta peach trees. HortScience 9(4), 331-332

Dynamic Model:

Erez A, Fishman S, Linsley-Noakes GC, Allan P (1990) The dynamic model for rest completion in peach buds. Acta Hortic 276, 165-174

Fishman S, Erez A, Couvillon GA (1987a) The temperature dependence of dormancy breaking in plants - computer simulation of processes studied under controlled temperatures. J Theor Biol 126(3), 309-321

Fishman S, Erez A, Couvillon GA (1987b) The temperature dependence of dormancy breaking in plants - mathematical analysis of a two-step model involving a cooperative transition. J Theor Biol 124(4), 473-483

Growing Degree Hours:

Anderson JL, Richardson EA, Kesner CD (1986) Validation of chill unit and flower bud phenology models for 'Montmorency' sour cherry. Acta Hortic 184, 71-78

Model comparisons and model equations:

Luedeling E, Zhang M, Luedeling V and Girvetz EH, 2009. Sensitivity of winter chill models for fruit and nut trees to climatic changes expected in California's Central Valley. Agriculture, Ecosystems and Environment 133, 23-31

Luedeling E, Zhang M, McGranahan G and Leslie C, 2009. Validation of winter chill models using historic records of walnut phenology. Agricultural and Forest Meteorology 149, 1854-1864

Luedeling E and Brown PH, 2011. A global analysis of the comparability of winter chill models for fruit and nut trees. International Journal of Biometeorology 55, 411-421

Luedeling E, Kunz A and Blanke M, 2011. Mehr Chilling fuer Obstbaeume in waermeren Wintern? (More winter chill for fruit trees in warmer winters?). Erwerbs-Obstbau 53, 145-155

Review on chilling models in a climate change context:

Luedeling E, 2012. Climate change impacts on winter chill for temperate fruit and nut production: a review. Scientia Horticulturae 144, 218-229

The PLS method is described here:

Luedeling E and Gassner A, 2012. Partial Least Squares Regression for analyzing walnut phenology in California. Agricultural and Forest Meteorology 158, 43-52.

Wold S (1995) PLS for multivariate linear modeling. In: van der Waterbeemd H (ed) Chemometric methods in molecular design: methods and principles in medicinal chemistry, vol 2. Chemie, Weinheim, pp 195-218.

Wold S, Sjostrom M, Eriksson L (2001) PLS-regression: a basic tool of chemometrics. Chemometr Intell Lab 58(2), 109-130.

Mevik B-H, Wehrens R, Liland KH (2011) PLS: Partial Least Squares and Principal Component Regression. R package version 2.3-0.

Some applications of the PLS procedure:

Luedeling E, Kunz A and Blanke M, 2013. Identification of chilling and heat requirements of cherry trees - a statistical approach. International Journal of Biometeorology 57,679-689.

Yu H, Luedeling E and Xu J, 2010. Stronger winter than spring warming delays spring phenology on the Tibetan Plateau. Proceedings of the National Academy of Sciences (PNAS) 107 (51), 22151-22156.

Yu H, Xu J, Okuto E and Luedeling E, 2012. Seasonal Response of Grasslands to Climate Change on the Tibetan Plateau. PLoS ONE 7(11), e49230.

The exact procedure was used here:

Luedeling E, Guo L, Dai J, Leslie C, Blanke M, 2013. Differential responses of trees to temperature variation during the chilling and forcing phases. Agricultural and Forest Meteorology 181, 33-42.

The chillR package:

Luedeling E, Kunz A and Blanke M, 2013. Identification of chilling and heat requirements of cherry trees - a statistical approach. International Journal of Biometeorology 57,679-689.





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