## On day length, growth potential, and fertilizer estimates

##### 19 August 2014

The temperature-based turfgrass growth potential (GP) was developed by Wendy Gelernter and Larry Stowell at PACE Turf. Based on only one variable – the actual temperature – one can use the GP equation (below) to produce a number between 0 and 1.

$GP = e^{-0.5(\frac{t-t_o}{var})^2}$

where,

GP is growth potential, a value from 0 to 1
e is the base of the natural logarithm, approximately 2.71828
t is the actual mean temperature
to is the optimum temperature, usually set at 20°C for C3 grass, 31°C for C4 grass
var is the variance which adjusts the shape of the curve, 5.5 for C3 species and 7 for C4 species when using °C.

If the GP is close to 1, then we can think of the growth potential as being high, because the actual temperature is close to the optimum temperature for growth. If the GP is closer to 0, then we can think of the growth potential as being low, because the actual temperature will be much colder or much hotter than the optimum temperature.

Temperature is not the only thing that influences turfgrass growth, however. The four main factors that influence growth are temperature, photosynthetically available light, plant water status, and leaf nitrogen content. For more about this, especially as it relates to the growth of warm-season (C4) grass, see A New Way of Looking at the Weather.

Turfgrass managers are able to modify the plant water status and the leaf nitrogen content, so the two independent and uncontrollable growth factors are temperature and light. The GP equation only accounts for temperature. Would it be improved if a correction for daylength, or shade, or light were included?

This question was recently posed, in this conversation on Twitter.

I default to a rather extended answer, because there is not a clear answer to this, but it is something I have considered, and my preference at this time is to ignore light and day length when it comes to GP values. Here's why.

1. The GP is not reality. It is only a number that serves as an index of the potential to grow based on temperature. This analysis of clipping yield at various levels of GP shows that there is a general relationship between GP and yield, but not an exact one.

Clipping yield from korai putting greens on a golf course in Japan from mid 2013 to early 2014

2. The GP equation is simple. Providing a numerical value of potential to grow, based only on temperature, can be practically useful in many ways, even though this number is not an exact description of how the grass will actually grow. Because the GP as it is does not predict growth exactly, and is simply an index of potential to grow, I think adding on layers of additional data for day length and/or photosynthetically available light risk complicating this by assigning too much value to the GP number, even though the growth may not exactly match the GP.

3. When I work with GP, my preference is to keep it as simple as possible, as long as the GP values for a particular site match the reality of observed turfgrass growth. GP is only useful when it somewhat approximates reality, so if day length adjustments, or adjustments for photosynthetic radiation, make the GP a more accurate representation of reality at a particular site, then I would look on such adjustments as a good thing.

In response to questions about possible increased fertilizer requirements at high latitudes due to increased day lengths, I have made some comparisons, and I haven't seen that extended day lengths will necessarily correspond with more light energy for growth.

4. If we look, for example, at Malaga and London specifically, along with some other cities from the northern hemisphere, the estimated daily light integral plotted against day length on 15 June looks like this.

That is, even though the day is longer at London in mid-June, because it is at a higher latitude than Malaga, there is still a greater amount of photosynthetic light at Malaga than at London. Why might this be? It is related to the amount of extraterrestrial radiation at any given latitude, combined with the effect of clouds. On an average June day in London, there will be 6.8 hours of bright sunshine (defined as light > 120 W/m2) on a day with 16.3 hours. At Malaga, even though June 15 has a shorter day length than London, with only 14.5 hours, 10.5 of those hours on an average day will be bright sunshine.

With warm-season (C4) grasses we can make the assumption that the grass can use all of the DLI. With cool-season (C3) grasses, that won't be the case when the light is at its greatest intensity.

I have tried to estimate this by taking a maximum value of 1000 micromoles of light per m2 per second, for each second of day length, and expressing the estimated DLI as a fraction of that. This chart shows that at Malaga, the amount of light supplied on an average day on 15 June is equal to the maximum amount we expect C3 grass to use. At London, even though the day is longer, it appears that on an average day there is less light supplied than the grass can use.

Based on these calculations for June, I don't see a reason to adjust the expected nitrogen use of turf at London to be higher based on day length.

I also looked at this for December, in this chart for estimated DLI on 15 December and this chart for the fraction of usable light that is supplied on average.

In this case, there are again differences in DLI and day length. At Malaga, where there had been nearly 100% of the light that C3 grass could potentially use on 15 June, the amount of light supplied on a typical 15 December day is only 50% of that the grass could use.

But for many of these cities, on 15 December, the amount of photosynthetic light is irrelevant, because the temperature is so cold that the grass can't grow. At Milan, for example, the average temperature in mid-December is less than 5°C. When working through these calculations, the temperature will often be the controlling factor.

5. Light does influence the growth, and consequently the nutrient use of grass. In my analyses of this, it seems that temperature plays the controlling role, with light as a secondary factor. I think that this can be accounted for using the GP equation as is, on a site by site basis. For example, at Malaga or Milan or London, one can use the GP to estimate nitrogen requirement as explained in this document.

One only needs to estimate the maximum amount of N that one will use at that location, in the time (day, week, or month) when N use will be at a maximum. The GP can then be used to adjust the N rate over the course of the year. The key is to choose an appropriate maximum N amount for the location, grass species, and soil type. Any light correction can be embedded in the amount of N one chooses as the maximum. My preference is to utilize GP in this way – it is remarkably simple, and provides a good starting template for nutrient requirements.

6. If adjusting by day length or other adjustment to account for light works better at a particular location, then by all means make the adjustment. The objective of the growth potential is to estimate how the grass will actually have the potential to grow at a location. From all the calculations and observations I've made, I'm not convinced that day length or light adjustments improve upon the estimates we can get from temperature alone. Of course, my experience is mostly at latitudes less than 45°, so there may be something I miss at higher latitudes.