Another way to look at turfgrass growth potential and overseeding

Winter overseeding is defined by Beard in his Turfgrass Encyclopedia as:

the seeding of cool-season turfgrass(es) over a warm-season turfgrass at or near the start of winter dormancy; it is used in mild climates to: (i) provide green, growing turf during the winter period when the warm-season turfgrass species are brown and dormant and (ii) prevent the wearing away of the dormant lateral stems of the warm-season turfgrass when under intense traffic stress.

A temperature-based turfgrass growth potential can be used to explain the role of temperature in the outcome of overseeding programs. I have shown charts related to this approach, first developed by Wendy Gelernter and Larry Stowell of PACE Turf, in relation to the overseeding of bermudagrass football fields in Japan and of bermudagrass tees, fairways, and rough in Dubai.

In a blog post (J.League Division 1, Grass Types, and Overseeding), I showed the chart reproduced below, with growth potential (GP) calculated based on 2013 temperatures in Kashima, Japan.

plot of chunk kashima1

I suggested that the optimum time for overseeding would be:

After a visit to Dubai, and learning about overseeding there, I calculated the GP and made this chart, with red for C\( _4 \) GP and green for C\( _3 \) GP:

plot of chunk dubai1

The overseeding timing gave a great result this year. Just have a look at this photo from Craig Haldane, Director of Golf Course Maintenance for Dubai Golf, on the eve of the Omega Dubai Desert Classic:

@emiratesgc all set for a great 25th Anniversary @OmegaDDC. Big thanks to my team, great effort!! pic.twitter.com/D6SrTGiYos

— Craig Haldane (@haldane_craig) January 25, 2014

After I had analyzed the 2013 temperatures and plotted the C\( _3 \) and C\( _4 \) GP for Kashima and Dubai, Larry Stowell suggested that I look at the data another way. He said that if I would plot time on the x-axis, and the cumulative sum of the difference between C\( _3 \) and C\( _4 \) GP on the y-axis, I would see something very interesting.

There would be an inflection point, he said, at the point where the C\( _3 \) GP starts to exceed the C\( _4 \) GP. One might consider that to be the start of the optimum overseeding window, because from that point forward, the C\( _3 \) GP will increase, and the C\( _4 \) GP will decrease. Taking the same data of Dubai temperatures in 2013, I calculated the cumulative sum of the difference between C\( _3 \) and C\( _4 \) GP.

And just as he had said, there was an inflection point where the curve changes direction, at the point in time where C\( _3 \) GP starts to exceed C\( _4 \) GP.

plot of chunk dubai2

If you look at the plot for Dubai as I showed it with both C\( _3 \) and C\( _4 \) GP plotted, you will see that the smoothed means of those data intersect on about 20 November. That is the same date at which this inflection point is seen in the difference of the cumulative sum. We can think of this difference very simply. If we are plotting the cumulative sum of C\( _3 \) GP minus C\( _4 \) GP, a negative slope means the temperatures are more suitable for C\( _4 \) than for C\( _3 \) grasses. A positive slope on the chart means just the opposite. Temperatures are more suitable for C\( _3 \) than for C\( _4 \) grasses.

Analyzing versus predicting

It is interesting to look at these calculations related to overseeding, but do they have a practical use in prediction of an optimum date for overseeding? It is easy to analyze what has happened, but it would be especially useful if the results of the analysis can be used to develop a predictive model for the future. For an interesting look at this specific problem, see the gap between data-mining and predictive models which discusses Facebook posts in relation to the transition from being single to in a relationship.

What's the optimum time for overseeding?

When the C\( _4 \) growth potential is higher than the C\( _3 \) growth potential, one expects difficulties in overseeding, because of strong competition from the warm-season grass for the light, water, nutrients, and space required by the overseeded cool-season grass. Likewise, when the C\( _4 \) and C\( _3 \) growth potentials are similar, there will be strong competition from the already-established warm-season grass that may prevent or slow the establishment of the overseed. The optimum time for overseeding, at least as far as the grass is concerned, should be when the C\( _3 \) GP is conistently higher than the C\( _4 \) GP.

To make an attempt at assessing the growth potential as a predictor for overseeding time, I looked up temperature data for the city of Kashima, which I had discussed in this blog post regarding overseed timing in 2013.

Specifically, I obtained the temperature data for the years 1999 to 2013, for the months of August, September, October, and November. These data were downloaded from the Japan Meteorological Agency website using the readHTMLTable function in the XML package in R.

Then I calculated the C\( _3 \) and C\( _4 \) GP, and the difference between them, and plotted the cumulative sum of the difference from 1 August through 30 November for each year. I was looking for an inflection point, as Larry Stowell had suggested, and as I had seen in the plot above with data from Dubai in 2013.

When I plotted this for each of the 15 years (1999 to 2013), this is what I saw.

plot of chunk kashima2

For each year, the cumulative difference plotted from 1 August to 30 November looks like a check mark, first descending during the last days of summer, and then increasing as the temperatures in the autumn become more suitable for cool-season grass.

Ideally, one could use these data to predict a time at which overseeding should be done in the future. Looking closer at the data for 2010 to 2013 in the charts below, one can see that the accumulated difference tends to decrease through August, it fluctuates up and down a bit as cooler weather starts to arrive, and then at some point the accumulated difference begins a steady rise that lasts through autumn.

plot of chunk example

The summer of 2010 was especially hot in Kashima, and that is shown on the chart - the difference between C\( _3 \) and C\( _4 \) growth potential dropped to -20 units in just over a month from 1 August. Then there was a bit of flattening, and then a change in direction, and inflection in the curve, and from 22 September a continuous increase continued for more than 2 months.

In 2011, one can see that there were inconsistent temperatures from about 18 August until 18 September, with the C\( _3 \) GP sometimes higher than the C\( _4 \) GP, and vice versa, until the final hot spell of the season, after which there was a steady trend of accumulating higher C\( _3 \) GP.

But can this type of analysis be used to predict an overseeding time? I looked at the data for 1999 to 2005, identifying the inflection point for each year, when C\( _3 \) GP started increasing continuously.

To identify the inflection point in a consistent manner, for each year, I identified the final day in the year at which there had been 2 or more consecutive days of C\( _4 \) GP higher than C\( _3 \) GP. That is, I identified the final day in which the cumulative sum of C\( _3 \) - C\( _4 \) GP decreased for 2 or more days in a row.

Then I expressed that date in each year as the day of the year. Let's see if the data from 1999 to 2005 can be used to predict the inflection date, and by extension, the probably overseeding date, for 2006 to 2013.

These identified inflection points were:

A summary of the inflection dates identified for those years is shown here:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     247     256     258     257     260     265

Note that the median of 258 days corresponds with 15 September.

At this point, how might we use the data to predict overseeding dates in the future? I first considered making some confidence interval around the mean inflection date, but I realized that such an exercise would not be especially useful. It is not the mean or median inflection date that we really care about. What we may be concerned about is in predicting a date at which the inflection date has passed, but not by much.

We could choose a date of say October 20, and be sure that there will be no more hot weather, but that would waste a number of good growing days for the cool-season grass. We could choose the mean of the observed inflection days, but this would not be very good, because we could expect that in about half the years to follow, there would still be potentially damaging hot weather after the overseeding had been completed.

What if we add 10 days to the mean, and use that day, 267, or 24 September? That seems to work reasonably well as a target overseeding date. Of course, 24 September is later than any of the inflection dates from 1999 to 2005, so we would be safe there. And from 2006 to 2013, the inflection date ranged from 29 August (in 2009) to 1 October (in 2012), with every year except for 2012 having an inflection date earlier than the target date of 24 September.

That's a pretty basic analysis, and a pretty rough one at that, but using data from 7 years I was able to predict a safe overseeding date 87.5% of the time in the next 8 years.

If one were to employ this type of model, it would be useful to collect data from at least the past 5 years, and then one could update the model every year, adding the most recent year's data into the model, which should lead to a more accurate prediction of overseeding time for the next year.

I'm not sure if other locations have temperatures more or less consistent than at Kashima. It may be that in some locations the date of such an inflection point varies by so many days or weeks that such a predictive model as I have attempted here would be of no use.

I'll show just 3 more charts, this time with all the data from 15 years displayed. In the first chart the C\( _3 \) GP is shown, with data from all 15 years pooled together. The blue line is a smoothed mean value for the data at each day.

plot of chunk final_summary

A quick note on day of the year: 1 August is day 213, 1 September is day 244, 1 October is day 274, and 1 November is day 305, and I have marked the start of each month with vertical lines. The C\( _3 \) GP can be relatively low in August, it gradually increased with a peak in early October, and then it declines in the colder weather of late October and November.

plot of chunk final_C4

With warm-season grass, the GP remains relatively high into early September, and then the C\( _4 \) GP begins a decline that continues until the end of November when warm-season grasses will be fully dormant and the C\( _4 \) GP is effectively 0.

Looking at the difference between the cool-season and warm-season GP (C\( _3 \) GP - C\( _4 \) GP) on a daily basis through this season, one can consider when the optimum time to overseed might be.

plot of chunk final_diff

In this chart, I've marked the start of August, September, October, and November with black lines, and I've shown day 267 (24 September) with a vertical green line. Remember, 24 September is the day I proposed as a reasonable overseeding date at Kashima, based on an analysis of the mean inflection date of the accumulated sum of the GP difference, in the years 1999 to 2005.

When the daily difference is > 0, it means the temperatures are relatively more suitable for cool-season grasses than for warm-season. When the daily difference is < 0, or below the red line on the chart, then the temperatures are more suitable for warm-season than for cool-season grasses.

There are a lot of days with a daily difference < 0 leading up to 24 September, and very few days, in fact only 3 days in 15 years, with C\( _4 \) GP > C\( _3 \) GP after this date. Ideally, one might seed at the end of September, taking advantage of almost the entire month of October, when C\( _3 \) GP is much greater than C\( _4 \) GP.

For more information on these topics, see the Asian Turfgrass Center blog.