Know your chill models

The challenges of calculating chill. By Anna Mouton.

The amount of winter chill a deciduous fruit tree receives will affect how it wakes up in spring. Insufficient chill results in trees that linger over flowering and foliation — growers will want to kick-start these trees with rest-breaking agents. But how can we tell when a tree is likely to be a slow riser?

This is where chill models come in. They use temperature data to calculate how much winter chill trees received. Growers use the output of chill models to make decisions on rest-breaking treatments. Chill models can also inform cultivar selection when establishing orchards.

To understand the pros and cons of existing chill models, Fresh Quarterly spoke with modelling expert Prof. Eike Luedeling, who leads the Horticultural Sciences Group within the Institute of Crop Sciences and Resource Conservation at the University of Bonn.

Chilling hours model

The chilling hours model was one of the earliest attempts at a temperature-based model. The origin of this model is obscure. The paper usually cited as the source is Weinberger, 1950, but Weinberger refers to it being first mentioned in a conference presentation in 1932, by a plant pathologist. “So he worked on diseases, not on chill,” says Luedeling.

To calculate chill using the chilling hours model, simply add up the number of hours with temperatures between 0°C and 7.2°C. In South Africa, chilling hours are usually added for the period 1 May to 31 August. “It’s easy — everyone can do it with an Excel spreadsheet,” says Luedeling. “The problem is that it’s not really a proper model. It’s more like a rule of thumb.”

Luedeling points out that the seemingly precise value of 7.2°C is just a conversion from 45°F. “Another problem is that there’s a really hard threshold. When you have 7.2°C, you have your chilling hour, but if you have 7.5°C, you get nothing. That’s not how biology works.”

Although the chilling hours model is still popular in the northern hemisphere, it hasn’t been very useful in South Africa. The model doesn’t allow for chill that occurs at temperatures above 7.2°C. It also doesn’t take the negative effects of high temperatures into account, or the positive effects of moderate temperatures following chilling temperatures.

“The good news is, if you’ve been using this model to estimate the effects of climate change, you probably came away with too pessimistic an expectation,” says Luedeling. “A little bit of warming can have a massive effect on the results from this model.”

The Utah model

In 1974, Richardson and co-workers published a new model that tried to address some of the shortcomings of the chilling hours model. They called it the Utah chill-unit model, but many South Africans refer to it as the Richardson model.

The Utah model differs from the chilling hours model in using weighted chill units rather than hours. Every hour at temperatures between 1.4°C and 12.4°C counts toward chill, but the amount contributed depends on the temperature. For example, an hour at 1.5°C–2.4°C contributes 0.5 chill units, whereas an hour at 2.5°C–9.1°C contributes 1.0 chill unit.

Another refinement of the Utah model is the recognition of the negative impact of higher temperatures. The model accounts for this using negative chill units. For example, for an hour at 16.0°C–18.0°C, 0.5 chill units are subtracted from the total.

“I think the Utah model is an improvement, if the temperature ranges are actually correct,” says Luedeling, “which we don’t know. The elephant in the room is always that we’re dealing with different species. Is it really justified to use the same parameter sets and the same models?”

In South Africa, chill units are frequently calculated from daily temperatures starting on 1 May. This is not the correct application of the Utah model, because it leads to the accumulation of a large number of negative chill units at the start of winter. To avoid this, Richardson and co-workers specify that the calculation must be calibrated annually for each weather station.

How is this done? The cumulative total number of chill units is plotted on a chart every day from the start of winter. Initially, the line will slope downward, due to the accumulation of negative chill units, but eventually the trend will reverse as the weather cools. The inflexion point is where chill begins to accumulate — it is taken as zero. Chill units should only be counted from zero onward.

A modified version of the Utah chill-unit model was published by Linsley-Noakes and colleagues in 1994. They called their model the daily-positive Utah chill model. It is also commonly referred to as the Infruitec model.

The daily-positive model is more accurate than the Utah model in regions with mild winters. To calculate chill units using the daily-positive model, first count the chill units for a day. If the total for the day is negative, do not add it to the cumulative total for the season. If the total for the day is positive, add it to the cumulative total — hence the name daily positive. With this model, there can never be a negative total number of chill units.

The dynamic model

“I’m surprised to hear that South Africans are using the Utah model,” comments Luedeling, “because it has long been found not to work well there.” He believes that the dynamic model is currently the best option for calculating chill.

The dynamic model was developed in Israel by Erez and co-workers in 1987. They believed that chill accumulates in two steps. Cold temperatures first lead to the formation of an intermediate product which can be destroyed by heat. Once enough of this intermediate product has collected, it changes into a stable dormancy-breaking factor that can no longer be destroyed by heat. This second step happens at milder temperatures than the formation of the intermediate product.

The dynamic model tracks the formation of the intermediate product, calculating when it is transformed into the dormancy-breaking factor, and reporting this as chill portions. As such, the dynamic model more realistically accounts for the impact of high temperatures.

“There are a lot of assumptions going into the dynamic model,” says Luedeling, “but biologically this model is much more convincing. It was based on lots of controlled temperature trials. And when I — and other people — have compared models, the dynamic model has always performed the best.”

Luedeling stresses that the dynamic model was originally based on data from peaches, as were the other models discussed above. The developers of the dynamic model were explicit about the need to calibrate the model for other species, and even for different cultivars. But, says Luedeling, these recommendations have been largely ignored, because of the difficulties involved.

“It’s a complicated model, and I certainly see why it wasn’t picked up right after it was published,” says Luedeling. “But we’re not doing the maths with a pen and paper — we’re not limited to simple models anymore.”

Luedeling has developed a statistical tool called chillR to help with the analysis of temperature data and the calculation of chilling hours, Utah chill units, and chill portions. The tool is available as a free download, but using it does require knowledge of the statistical package R, and some coding skills.

Heat models

Winter chill has a strong effect on bud-break behaviour — but so does heat. Certain growth processes, such as flowering, only occur above a specific minimum temperature. As temperatures rise beyond the minimum, the rate of these processes increases. In theory, it should be possible to estimate the dates of phenological events such as flowering with the aid of a heat model.

Heat accumulation is usually quantified by adding up heat units — as so-called thermal time or degree-days — after dormancy ends. Older heat models assume that trees have a linear response to temperature, so that the number of days from rest-break to flowering is a simple inverse relationship to temperature. Newer models assume that buds become more responsive to heat when they receive more chill. After a cold winter, buds will start growing at lower temperatures, and grow faster, than after a mild winter. This is why a hot spring can galvanise trees into action in spite of a warm winter.

“There’s very little comparison of heat models,” says Luedeling, “or questions about them.” He thinks that the temperature response of trees in active growth is likely to differ significantly from the response of dormant trees, and that existing models tend to gloss over these differences.

Current chill models don’t include heat. While Luedeling is working on a new modelling framework that takes heat into account, he also cautions against losing sight of the goal. “Growers don’t need totally precise knowledge on everything. We shouldn’t get lost in all the little details — we need tools that work. We need to deliver a solution that allows people to adapt to the changes that are coming.”

Modelling the future

“What you have to consider is that making chill models is really hard,” says Luedeling, “because you have a tree bud that looks the same throughout the entire winter. There’s a lot going on in the bud, we know that, but you can’t see it.” He thinks that the processes inside dormant buds probably respond to different temperature cues, and that having a single chill model for all of winter may not be correct.

There are different ways of validating a model, Luedeling explains. “You can look at whether it predicts actual events — that’s what everybody does. A better validation would be to look at whether the processes that we know are happening are implemented in the model.” This requires an understanding of the biology of fruit trees beyond what exists currently.

Another potential source of error is temperature. Chill models are based on hourly temperature data, but these are often inferred from daily minimum and maximum readings.

Nonetheless, Luedeling is confident that models can be both usable by and useful to everyone. He is in the process of publishing a paper on the application of the dynamic model to different cultivars, and has followed the example set by Erez, the horticulturist involved in developing the original dynamic model.

“Erez worked with a physicist — Fishman — and I think she’s the brain behind the equations,” says Luedeling. He too has roped in a physicist-friend to do the mathematical heavy-lifting.

When the dynamic model was developed, scientists used carefully controlled experiments to generate data, but these days it’s hard to find funding for those studies. Luedeling relies on records generated by long-term observations from around the world, including from South Africa. He is collaborating with Dr Esmé Louw of the Department of Horticultural Science at the University of Stellenbosch on a new project to develop a local phenophase-temperature database. Read more about that project in Predicting Bud-break in this issue.

Luedeling also works on climate change, and he highlights the role of models in preparing for the future. “We need planning tools. Where you do rest-breaking, there’s the year-to-year management, which is important, but there’s also the time when you have to plant new trees. And what do you plant when they’ll be there for thirty years? There could be a lot of warming in that period.

“There’s a creeping increase in the risk of major problems — every year the odds get a little worse. At some point growers will have to make some hard choices. You don’t want to discover that something doesn’t work anymore after you’ve already invested ten years in raising the trees.”