How Strong Is the Yearly Cycle in Mauna Loa CO2? A Seasonal Decomposition
Updated October 2026
Split a series into trend, a repeating yearly cycle and a remainder, then read how strong the cycle is.
Take the long upward trend out of atmospheric carbon dioxide at Mauna Loa and a yearly cycle is nearly all that is left. Its strength is 0.985 on a scale of 0 to 1, so the remainder is 1.5% of what is left after the trend is removed. The high is in May and the low is in September to October. The cycle runs about 6 parts per million from top to bottom (our own calculation from the twelve seasonal means), while the trend rose about 30 percent over 51 years. Here is how the cycle is separated, how to read its strength, and what it does not tell you.
The data and the question
The question: how strong is the yearly cycle in carbon dioxide measured at Mauna Loa, which calendar months are the high and the low (the low is in September to October), and by how much, once the long upward trend is separated out?
Data: one site, monthly mean values, 612 months from January 1975 to December 2025, which is 51 full years. We start at 1975 because the earlier values in the file are another group's record, not NOAA's. Two of the 612 months, December 1975 and April 1984, were filled in by NOAA itself, and we used them as published. Values from December 2022 to July 2023 come from a Maunakea site after the Mauna Loa eruption.
Data/Image provided by NOAA Global Monitoring Laboratory, Boulder, Colorado, USA (https://gml.noaa.gov). Mauna Loa monthly mean CO2: Dr. Xin Lan, NOAA/GML (gml.noaa.gov/ccgg/trends/) and Dr. Ralph Keeling, Scripps Institution of Oceanography (scrippsco2.ucsd.edu/). Public domain; NOAA does not endorse this analysis.
Splitting trend, cycle and remainder
A series like this has three parts stacked together. The trend is the slow movement: here it rises from 330.50 ppm in January 1975 to 428.35 ppm in December 2025, up about 30 percent (29.6%), with an average trend level of 373.45 ppm. The cycle is the pattern that repeats every year. The remainder is whatever is left over.
The method is STL, a decomposition that estimates the trend and the cycle separately. We fixed the yearly shape: the cycle has the same shape in every year, and only the trend and the remainder move. A fixed shape means the same cycle every year, which is how the tool defines it. It also has a cost, covered below.
Values from December 2022 to July 2023 are from a Maunakea site after the Mauna Loa eruption. Any chart of the series carries this note.
How strong is the cycle?
Seasonal strength is 1 minus the variance of the remainder divided by the variance of the cycle and remainder together. It runs from 0 to 1: strong at 0.6 or more, moderate at 0.3 or more, otherwise weak. Here it is 0.985, strong. The remainder is 1.5% of the variation left after the trend is taken out.
If a tool shows this as 0.99, that is its rounding of 0.985.
This describes a cycle. It is not a test, and it does not say the cycle is "significant" in any statistical sense.
The high and the low
The cycle's seasonal index gives, for each calendar month, how far above or below the trend that month sits on average, as a percent of the trend level and in parts per million.
| Month | Percent of trend level | ppm |
|---|---|---|
| January | +0.031% | +0.11 |
| February | +0.199% | +0.74 |
| March | +0.390% | +1.46 |
| April | +0.704% | +2.63 |
| May | +0.820% | +3.06 |
| June | +0.632% | +2.36 |
| July | +0.162% | +0.60 |
| August | -0.432% | -1.61 |
| September | -0.871% | -3.25 |
| October | -0.875% | -3.27 |
| November | -0.543% | -2.03 |
| December | -0.216% | -0.81 |
The high is May, at +0.820% of the trend level, +3.06 ppm. The low is in September to October: October is lowest at -0.875% (-3.27 ppm) and September is -0.871% (-3.25 ppm), only 0.004 percentage points apart. That margin is tiny, so we say the low is in September to October.
From the high in May to the low in September to October, the cycle spans about 6 parts per million. That figure, 6.33 ppm, is our own calculation from the twelve seasonal means, not an output of the tool.
What this does not tell you
- It is one site. Mauna Loa is one place, and this is not a causal claim. We do not explain why the cycle has the shape it has.
- It is a description, not a test. The decomposition shows how big the cycle is. It does not test whether a cycle exists.
- A fixed shape cannot show change. Because the yearly shape is held the same in every year, this reading cannot show the cycle itself changing over the decades. Our addition: a decomposition that lets the shape drift would be needed to ask that.
Run it on your own file
You need one date column and one number. The free tool infers the cadence from the dates, and it needs more than two full cycles, which is at least 25 monthly periods. The free tool finds a yearly cycle in monthly or weekly data; in daily data it finds a weekly cycle. Run the free seasonality tool on your own series. For the general method, see our practical guide to seasonal decomposition.
Questions people ask
These questions are inferred from the sources, not taken from observed search queries.
How strong is the yearly cycle here?
Strong. Seasonal strength is 0.985, on a scale where 0.6 or more counts as strong. The remainder is 1.5% of the variation left after the trend is removed.
When are the high and the low?
The high is May. The low is in September to October, because the two months are 0.004 percentage points apart.
How much did the trend change?
It rose from 330.50 ppm to 428.35 ppm between January 1975 and December 2025, about 30 percent.
Does this explain why carbon dioxide has a yearly cycle?
No. It describes the cycle at one site. It does not say what causes it.
Can the free tool find a yearly cycle in daily data?
Not with this tool: in daily data it finds a weekly cycle.
References
- NOAA Global Monitoring Laboratory. Mauna Loa monthly mean carbon dioxide. Dr. Xin Lan, NOAA/GML, and Dr. Ralph Keeling, Scripps Institution of Oceanography. NOAA GML trends · Scripps CO2 program. Public domain; NOAA does not endorse this analysis.
Three checks on this reading
What we checked before we trusted the numbers.
The same method as the free tool
The decomposition uses a fixed yearly shape (STL). The free tool, run on the same 612 months, gives the same strength, trend and monthly effects at its printed precision.
The low is two months
October is lowest by a hair: September is within 0.004 percentage points of it. We say the low is in September to October.
A described cycle, not a test
This describes the cycle in one site's record. It is not a test, and the fixed shape cannot show a cycle that changed over the years.