confirm model parameters

[sdtaylor]

basler 2016 has some weird parameter ranges in the supplement, some are restricted to > 0 where I have them ranging neg. and pos. Double check on those. Specifically the alternating model and the uniforc model (they use unified, but the sigmoid function is the same)

[sdtaylor]

Alternating model

I've set a and b to be either positive or neg, and forced c to be positive.

Looking at plots in R. a can +-, b should be > 0, c should be < 0.

Having b < 0 makes the red curve below increase over time

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Cannell and Smith 1983 (original model source) lists only a fitted equation. With a and b positive and c negative.

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Basler 2016 forces a, b, and c to be positive.

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Jeong et al 2012 (precursor to Jeong et al 2013) confines it to < 0, and (presumably) a and b being either positive or negative.

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Botta et al. 2000 sets c < 0. (This influences Jeong et al 2012, 2013). With the resulting a < 0, b > 0, and c < 0. Note the typo in the text of Jeong above saying that c=0.01 instead of c=-0.01

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Basler, D. (2016). Evaluating phenological models for the prediction of leaf-out dates in six temperate tree species across central Europe. Agricultural and Forest Meteorology, 217, 10–21. http://doi.org/10.1016/j.agrformet.2015.11.007 Botta, A., Viovy, N., Ciais, P., Friedlingstein, P., & Monfray, P. (2000). A global prognostic scheme of leaf onset using satellite data. Global Change Biology, 6(7), 709–725. http://doi.org/10.1046/j.1365-2486.2000.00362.x Cannell, M. G. R., & Smith, R. I. (1983). Thermal Time, Chill Days and Prediction of Budburst in Picea sitchensis. The Journal of Applied Ecology, 20(3), 951. http://doi.org/10.2307/2403139 Jeong, S.-J., Medvigy, D., Shevliakova, E., & Malyshev, S. (2013). Predicting changes in temperate forest budburst using continental-scale observations and models. Geophysical Research Letters, 40(2), 359–364. http://doi.org/10.1029/2012Gl054431 Jeong, S.-J., Medvigy, D., Shevliakova, E., & Malyshev, S. (2012). Uncertainties in terrestrial carbon budgets related to spring phenology. Journal of Geophysical Research: Biogeosciences, 117(G1). http://doi.org/10.1029/2011JG001868

[sdtaylor]

Uniforc/Unichill

For uniforc I currently enforce (2 parameter sigmoid function) -20< b < 0 -100 < c < 100. unichill in the chilling function: (3 parameter sigmoid function) 0 > a > 20 -100 < b < 100 -50 < c < 50 unichill in the forcing function: (2 parameter sigmoid function) -20< b < 0 -100 < c < 100

I feel confident in the above ranges after studying potential ranges at this sweet site. The c param in the 2 parameter one, and b in the 3 parameter one, can probably be constrained a bit to match basler 2016.

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Chuine 2000 (Sources for both models) for the 2 param sigmoid function b < 0, c > 0

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Basler 2016 has only the 2 parameter sigmoid function. Enforces both b and c to < 0

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Roberts et al. 2015 uses Uniforc and sets b < 0 and c > 0. They also use Unichill but do not state parameter ranges.

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Xu and Chen 2013 uses Uniforc and sets b < 0 and c > 0. They also use Unichill but do not state parameter ranges.

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Chuine, I. (2000). A Unified Model for Budburst of Trees. Journal of Theoretical Biology, 207(3), 337–347. http://doi.org/10.1006/jtbi.2000.2178 Basler, D. (2016). Evaluating phenological models for the prediction of leaf-out dates in six temperate tree species across central Europe. Agricultural and Forest Meteorology, 217, 10–21. http://doi.org/10.1016/j.agrformet.2015.11.007 Xu, L., & Chen, X. (2013). Regional unified model-based leaf unfolding prediction from 1960 to 2009 across northern China. Global Change Biology, 19(4), 1275–1284. http://doi.org/10.1111/gcb.12095 Roberts, A. M. I., Tansey, C., Smithers, R. J., & Phillimore, A. B. (2015). Predicting a change in the order of spring phenology in temperate forests. Global Change Biology, 21(7), 2603–2611. http://doi.org/10.1111/gcb.12896

[sdtaylor]

I'm pretty confident in these ranges.