Degree Days

Understanding Heating and Cooling Degree Days

Degree days are a specialist type of weather data, calculated from readings of outside air temperature. Heating degree days and cooling degree days are used extensively in calculations relating to building energy consumption, but the data is frequently used by those who don’t understand what it really represents… This article aims to set that straight!
Contents

* Heating degree days
* Why are heating degree days useful?
* An example of heating degree days in action
* So how are heating degree days calculated?
* The base temperature of a building
* Turning temperature readings into heating degree days
* Real-world calculation methods
* A note on common base-temperature confusion
* Other types of degree days
* Cooling degree days
* Growing degree days
* Final degree-day advice

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If you want degree-day data for a location near you, I suggest you head over to Degree Days.net. But if you want to understand what degree days really are (and personally I think you really should understand this before using them…), please read on.

There are three main types of degree days: heating degree days, cooling degree days, and growing degree days. If you can understand exactly how one type of degree days work, it’s very easy to understand the others. So I’ve focused most of this article on explaining heating degree days:

Heating degree days
In a nutshell: heating degree days are a measure of how much (in degrees), and for how long (in days), the outside air temperature was below a certain level. They are commonly used in calculations relating to the energy consumption required to heat buildings.

Why are heating degree days useful?
The energy consumption of building heating systems is more complicated than the energy consumption of TVs, kettles, or computers. You can’t just plug a heating system into a Kill-A-Watt meter to find out how much energy it uses each hour, because the energy usage of a heating system varies with the weather…

Essentially, the colder the outside air temperature, the more energy it takes to heat a building.

If you live in the Caribbean, it’s probably warm enough that you won’t need heating at all; if you live in New York, you’ll probably only need heating in the winter; if you live at the North Pole… you’ll probably want your heating on all year round.

But the outside temperature doesn’t just vary from one location to another – it varies all the time, wherever you happen to be. It’s usually colder at night than it is in the day, and any single day/week/month/year is usually at least a little bit warmer or colder than the day/week/month/year before it.

If, like most people, you use your heating system to keep your building at a roughly constant temperature, the amount of energy that your heating system uses will vary from one day/week/month/year to the next, just like the outside air temperature does.

Heating degree days are a simple way to quantify all of this. The idea is that the amount of energy needed to heat a building in any day/week/month/year is directly proportional to the number of heating degree days in that day/week/month/year.

An example of heating degree days in action
(Skip this example if you have no desire to read my somewhat amateur attempt to bring the concept of heating degree days to life…)

Let me introduce you to a man called Dan. Dan is the facilities manager of an office building, and he’s under big pressure to reduce the building’s energy consumption. The company CEO, Jock, has noticed the rising cost of energy, and he’s decided that the business could, and should, save some money by becoming more energy efficient. Jock hasn’t given much thought to how they’re going to become more energy efficient, but he’s certainly putting a lot of pressure on Dan to make it happen…

So, in January 2007, Dan spent a big chunk of his budget on improving the building’s insulation. At the time, he was confident that this would seriously reduce the energy it took to heat the building, and that the savings in the energy bill would very quickly pay for the rather hefty capital cost.

Roll forward to January 2008, a year after Dan’s big insulation spending spree, and Dan has a decidedly stressed look on his face… Jock, who’s a “numbers guy”, wants to see some “solid evidence” that Dan didn’t “squander the company’s hard-earned cash lining the pockets of some fly-by-night jokers”. (No offence intended to the insulation industry – Jock just tends to be a little quick to point the finger…)

Anyway, Dan is sweating, and it’s not because the building’s temperature control is playing up (the well-insulated building is actually helping to keep things at a steady, comfortable temperature). Dan has just added up the heating energy consumption for 2007, and he’s somewhat concerned by what he sees:

* Heating energy consumption in 2006: 452,976 kWh
* Heating energy consumption in 2007: 445,241 kWh

It’s not that there hasn’t been an improvement in the heating energy consumption (there has), it’s just that Dan was rather hoping for more of an improvement… After spending a small fortune on insulation, he was actually rather hoping for significantly more of an improvement…

Now, it just so happens that, in Dan’s neck of the woods, 2007 was quite a lot colder than 2006. Dan is aware of this, and, reluctant to admit that he might have overestimated the energy-saving power of his insulation idea, he is pinning his hopes on being able to prove that 2007’s cold weather was to blame for the disappointing energy savings. Dan tried explaining this theory of his to Jock, but he was met with a rather blunt “Don’t you try fobbing me off with any of your hand-waving nonsense!”

Shame on you, Dan, for forgetting that Jock is a numbers guy…

Fortunately all is not lost, as a colleague has tipped Dan off to these things called heating degree days. They’re basically a measure of how cold the temperature was, but they’re specifically for heating – if you’ve got 10% more degree days in any day/week/month/year you should expect 10% more heating energy consumption in that day/week/month/year, all other things being equal.

So, Dan hunted the web until he found Degree Days.net, a site that generates degree days for locations around the world. He found a weather station near the office building, and downloaded a few years’ worth of heating degree days for that location. He quickly assembled the following figures:

* Heating degree days in 2006: 3,320 (I’ll explain what this number really means shortly)
* Heating degree days in 2007: 4,092

Applying some simple arithmetic:

* kWh per degree day in 2006 = 452,976 / 3,320 = 136
* kWh per degree day in 2007 = 445,241 / 4,083 = 109

Comparing these two figures, Dan concluded that the heating energy efficiency in 2007 was around 20% better than that in 2006. Well done Dan: your insulation plan was a good one, and the company should make good savings from it for many years to come. In fact, it was such a good idea, Jock has convinced himself that it was his idea all along… So, Dan, it’s looking unlikely that your insulation success will help your bonus, but at least you can stop sweating – your job security is no longer in immediate danger.

So how are heating degree days calculated?
Well, there’s one correct way to calculate heating degree days (which requires vast quantities of temperature data – infinite quantities to be precise), and numerous different ways to approximate the same result using less temperature data.

Nonetheless, irrespective of the exact calculation method, it always starts with a base temperature:

The base temperature of a building

With regard to heating degree days, the base temperature of a building is the temperature below which that building needs heating.

Let’s consider a regular office building. In fact, seeing how I put all that effort into the Dan story, let’s consider the office building that Dan the facilities manager is in control of.

Dan tries to keep the office building heated to around 20C (about 68F) – after many years on the job he has determined that this is the temperature at which he gets the least number of people complaining that it’s too hot or too cold.

On a summer day, when the outside temperature is 20C or above (about 68F), as you can probably guess, Dan switches the heating off – there’s no point in heating a building when it’s already warmer than the temperature you want it.

In fact, Dan has figured out that he can switch the heating off when the outside temperature reaches 17C (62.6F) – a few degrees below the desired inside temperature. The office has a lot of warm people in it and a lot of warm office equipment too – this essentially provides a few degrees of free heating. In technical terms, this would be described as an average internal heat gain of 3C, or 5.4F.

So, when the outside temperature is below 17C (62.6F), the heating needs to be on, and when the outside temperature is above 17C (62.6F), Dan can switch the heating off without incurring any more complaints than usual about it being too cold. Of course more people might complain that it’s too hot, but that’s a different story.

What this means is that the base temperature of Dan’s building is 17C, or 62.6F.

All buildings have a base temperature – it varies from building to building, but you can think of it as depending on two things:

1. What temperature is the building heated to? (e.g. Dan’s building is heated to 20C or 68F.)
2. How much free heating comes from the people and equipment inside the building? In other words, what’s the average internal heat gain?

The base temperature of your building will determine the base temperature of the heating degree days that you should use to do your calculations.

(Advanced note: In reality it’s more complicated than that – the best base temperature to use can also depend on the thermal properties of the building, the heating schedule, and external influences like solar gains. But considering the two factors above can help you to get a reasonable first estimate. If you’ve got good records of the building’s energy consumption, it’s a good idea to refine your estimated base temperature experimentally, using linear regression analysis.)

Anyway, that explains the base temperature… But what do the heating-degree-day numbers actually mean? To understand this, you need to have a rough idea of how the figures are calculated.

Turning temperature readings into heating degree days
With the appropriate use of big, scary-looking formulae, it’s quite possible to make it look as though degree-day-data calculation is something that’s best left to the experts. But it’s actually very straightforward to turn temperature readings into degree days. I’m going to use a few example calculations to explain how the process works for heating degree days.

Let’s say that we’re dealing with a building with a base temperature of around 17C (I’m going to stick with Celsius for this explanation, otherwise it’ll get really confusing). It’s the start of July – technically it’s the middle of summer, but the inhabitants of the building are still waiting for “the real summer” to arrive. (I’m from the UK, where it’s depressingly common to spend most of the summer months waiting for “the real summer” to arrive…)

Anyway, consider a single day, let’s say July 1st, when the outside air temperature was 16C throughout the entire day. A constant temperature throughout an entire day is rather unlikely, I know, but degree days would be a lot easier to understand if the outside air temperature stayed the same… So, throughout the entire day on July 1st, the outside air temperature (16C) was consistently 1 degree below the base temperature of the building (17C), and we can work out the heating degree days on that day like so:

1 degree * 1 day = 1 heating degree day on July 1st

If, on July 2nd, the outside temperature was 2 degrees below the base temperature, we’d have:

2 degrees * 1 day = 2 heating degree days on July 2nd

Let’s look at July 3rd – this was a hotter day, and the outside air temperature was 17C, the same as the base temperature (i.e. 0 degrees below the base temperature). This gives:

0 degrees * 1 day = 0 heating degree days on July 3nd

On July 4th it was warmer again: 19C. Again, the number of degrees below the base temperature was zero, giving:

0 degrees * 1 day = 0 heating degree days on July 4th

You might have guessed: when the outside air temperature goes over the base temperature, you don’t get any heating degree days. This makes sense, because you wouldn’t need any heating either.

Right, now let’s make it a little more realistic. July 5th had a temperature of 15C from 00:00 to 12:00, and 16C from 12:00 to 24:00. So for that day we have:

(2 degrees * 0.5 days) + (1 degree * 0.5 days) = 1.5 heating degree days on July 5th

(The 2 degrees is because 15C is 2 degrees below the base temperature of 17C, and the 0.5 days are because 00:00 to 12:00 is half a day. We calculate the heating degree days for each period in the day, and then add them together to get the total for that day: 1.5.)

On July 6th, colder weather started moving in: the temperature was 16C from 00:00 to 06:00, 15C from 06:00 to 12:00, 14C from 12:00 to 18:00, and 13C from 18:00 to 24:00. This gives the following:

(1 degree * 0.25 days) + (2 degrees * 0.25 days) + (3 degrees * 0.25 days) + (4 degrees * 0.25 days)
= 2.5 heating degree days on July 6th

Now, on July 7th, the temperature just kept changing… like it might on a real day… Between 00:00 and 00:30 it was 13C, between 00:30 and 01:00 it was 12.9C, between 01:00 and 01:30 it was 12.9C, between 01:30 and 02:00 it was 12.8C… it started getting warmer around 05:00, peaking at 17C between 14:00 and 14:30, and dropping again until it reached about 13.7C between 23:30 and 24:00. Complicated!

A proper calculation would not make for particularly interesting reading, so I’ll leave most of it out. But essentially you just have to add up the figures for each of the half-hour periods in the day (one half-hour period is 1/48 days):

(3 degrees * 1/48 days) + (3.1 degrees * 1/48 days) + ……. etc.
= 1.9 heating degree days on July 7th

Hopefully by now you’re getting the idea!

So, from the examples above we’ve got:

* July 1st: 1 heating degree day
* July 2nd: 2 heating degree days
* July 3rd: 0 heating degree days
* July 4th: 0 heating degree days
* July 5th: 1.5 heating degree days
* July 6th: 2.5 heating degree days
* July 7th: 1.9 heating degree days

We’d expect the heating energy consumption on each of those days to vary with the heating degree days. So, the heating on July 2nd would use twice as much energy as the heating on July 1st, and, on July 3rd and July 4th, the heating wouldn’t use any energy at all (zero degree days on those days would mean it would be warm enough for the heating to be switched off).

One of the best things about degree days is that you can add them together. Adding together the readings above gives a total of 8.9 heating degree days for the week beginning on July 1st and ending on July 7th. So we’d expect that the heating system would have used 8.9 times more energy in that whole week than it used on July 1st alone.

If you’ve got daily heating-degree-day values for each day in a month, you can add them up to get the total heating degree days for that month. And if you’ve got the heating-degree-day values for each month in a year, you can add them up to get the total heating degree days in the whole year.

And therein lies what I consider to be the beauty of degree days: you can add them up to get totals for long periods of time, and they still represent all the relevant variations in temperature over that whole time period. (Contrast that with an annual average temperature, which would tell you nothing about how much the temperature varied within that year.)

Real-world calculation methods
The calculation method that I explained above is essentially the correct one for calculating heating degree days: for each period over which the outside air temperature was constant, you multiply the degrees below the base temperature by the number of days that the temperature was fixed for (usually small fractions of days), and then you sum all the values together to get the total heating degree days for the period in question.

The problem with that approach is that, in the real world, outside air temperature doesn’t remain constant – in fact it changes pretty much all the time. Mathematically speaking you’d need an infinite number of temperature readings to calculate degree days properly.

Fortunately, “mathematically speaking” doesn’t really matter too much in this instance, and half-hourly or hourly temperature readings are plenty good enough to calculate degree days accurately using the method described above.

However, reliable half-hourly and hourly temperature readings are rarely readily available, so there are a number of other approximation methods that are used to calculate degree days from more commonly available measurements of outside air temperature. These methods typically use either the daily maximum and minimum temperatures, or the daily average temperatures.

Personally I’m of the opinion that the the details of the approximation method used are not important, so long as it uses the data it’s given to generate degree-day figures that are very close to those that would be generated by the correct method (or, more realistically, by a method that used half-hourly temperature readings or similar).

A note on common base-temperature confusion
Unfortunately, when it comes to degree days, confusion is abundant, even amongst those that really should know better… So a lot of people are unaware of the fact that degree days can come in any base temperature, and that typically you should choose the base temperature to fit the building that’s energy consumption you’re looking at.

Earlier I gave the example of a particular office building with a base temperature of 17C (62.6F). This is probably a fairly common base temperature for an office building, although the actual base temperature of any particular office building will depend on what temperature it’s heated to, and what people and equipment are in it.

If your building happens to be a swimming pool hall, the base temperature might be more like 26C (78.8F), and you’d want to use a very different set of heating degree days for your calculations. Or maybe you have a just-warm-enough-to-prevent-a-lawsuit factory, or a house that you like to keep uncommonly warm – whatever the building, it will have its own base temperature, and you should use heating degree days with that base temperature when you’re looking at its energy consumption.

So it’s a popular misconception that degree days come with a single base temperature. In the US, this is typically quoted as being 65F, whilst in the UK it’s typically quoted as being 15.5C. I suspect this stems from the days when degree days were made available in magazines and the like, and there was no more room in magazines to fit data with a range of base temperatures than there was the computer technology to calculate and store all that data in the first place.

So the next time you hear something along the lines of “heating degree days have a base temperature of 65F”, you will hopefully know better than to believe it!

(All that said, it makes perfect sense to use a consistent base temperature when you’re comparing the climate of one location with that of another. But when you’re looking at the energy consumption of a building, there’s no doubt about it: you should use degree days with the most appropriate base temperature for that building.)

Other types of degree days
Hopefully by now you have a good understanding of what heating degree days are, and how they are calculated. Now it should be very easy to understand the other two types of degree days – cooling degree days and growing degree days:

Cooling degree days
Cooling degree days are a measure of how much (in degrees), and for how long (in days), the outside air temperature was above a certain level. They are commonly used in calculations relating to the energy consumption required to cool buildings.

I think of them as heating degree days in reverse: whilst heating degree days start adding up when the outside air temperature drops below the base temperature, cooling degree days start adding up when the outside air temperature rises above the base temperature. So the base temperature of cooling degree days is just the temperature above which the building needs cooling. Pretty straightforward, right?

Growing degree days
In their simplest form, growing degree days are calculated in the same way as cooling degree days, but the base temperatures used are based upon the temperatures above which certain plant or insect growth occurs.

Different plants have a different base temperature above which they will start to grow, and their growth will typically be roughly proportional to the amount by which that base temperature is exceeded. This is very similar to the way in which building cooling is proportional to the amount by which the building base temperature is exceeded.

Unlike heating and cooling degree days, growing degree days sometimes have cut-off points (e.g. when the temperature gets over 65F we stop counting – that sort of thing). To be perfectly honest, my expertise are in the heating and cooling side of degree days, so I won’t try to elaborate much further on growing degree days!

Final degree-day advice
Although it’s important to understand how degree days are calculated, there is rarely a need to actually calculate them manually. My company runs a website called Degree Days.net that generates heating and cooling degree days for locations worldwide, to any base temperature, and there are a number of other sources of degree-day data too (albeit sources that focus on specific countries or regions).

One final point: however accurate the degree days are themselves, it’s critical to understand that the calculations that use them are usually only very approximate – there are a number of serious problems with the commonly-used applications of degree days that I’ve not discussed here at all. I wrote a detailed article about these issues called Degree Days – Handle with Care! (yes, that exclamation mark is important!) – you might be interested to take a look at it now you have a good understanding of the basics.

Anyway, best of luck with all your degree-day based work, and I hope that it helps you to save energy!
Martin Bromley

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