When Months Go Missing: Data Gaps Can Wreck Space Climate Trend Estimates

Long-term records of the ionosphere are among the most valuable tools in space climate research, but a new study warns that the gaps running through them can quietly distort the very trends scientists are trying to measure. The analysis, published in Discover Space, quantifies for the first time how missing monthly observations affect annual mean values and long-term trend estimates of the F2-layer critical frequency, or foF2, one of the key parameters used to track the slow evolution of the upper atmosphere.

The stakes are higher than they might seem. Long-term variations in the upper atmosphere and ionosphere are linked to the rising concentration of anthropogenic greenhouse gases, and they matter in practical terms as well: the ionosphere directly affects radio communication, navigation and positioning systems, while changes in thermospheric density modulate satellite drag and the long-term evolution of space debris. Detecting the small, gradual signals embedded in decades of data requires observational series of exceptional length and quality, and those series are precisely the ones most prone to interruption.

Ionospheric records archived by data centers can span more than 70 years, yet they frequently contain gaps caused by instrumental failures, operational interruptions or environmental conditions that prevent accurate measurement. To capture interannual variability, researchers typically compute annual means from monthly median values, and the common practice is to accept an annual mean only when at least eight months of data are available, allowing no more than four missing months. Until now, that threshold had been a convention rather than a quantitatively tested rule.

The research team, led by Ana G. Elias and colleagues, addressed this methodological gap by deliberately punching holes in complete datasets and measuring the damage. They used the longest and most complete foF2 time series available, from the Juliusruh station in northern Germany at 54.6 degrees north, whose hourly monthly median values date back to 1957. The study analyzed the period 1960 to 2023, covering 64 years, and considered only noontime data at 12 local time, when solar extreme-ultraviolet flux is the main driver of interannual variability. Three additional stations with complete noontime series, Sodankyla in Finland, Rome in Italy and Kokubunji in Japan, were included; Sodankyla had only two missing monthly values across the whole period, less than 1 percent of the 768 values expected, and these were reconstructed by spline interpolation.

To remove the influence of solar activity before estimating long-term trends, the authors employed the F30 index, the solar radio emission at 30 centimeters wavelength, following recent recommendations that it is the most suitable proxy for this type of analysis. The trend estimation itself used the standard two-step linear regression approach: foF2 is first modeled as a function of the solar proxy and its square, and the residuals of that fit, which represent foF2 with the solar effect filtered out, are then regressed against time to yield the trend.

Artificial data gaps were then introduced in three ways. In the first method, gaps of one to eight months per year were created by considering all possible combinations of missing months within a year and applying the same pattern to all 64 years. The second method generated gaps of the same sizes randomly for each year, repeating each case 200 times per missing month. The third method randomly selected the number of missing months between one and eight each year, a scheme repeated 2,500 times. The resulting artificial series were compared against the complete reference series using four statistical metrics: the maximum relative deviation, the probability of deviations exceeding 5 percent and 10 percent, and the mean relative absolute error.

The results show a clear pattern. Deviations of annual means and trends from the reference values increase with the number of missing months and become substantial once six or more monthly values are missing per year. For annual means, the maximum relative deviation can reach roughly 30 percent when more than six months are missing, which corresponds to about 3 megahertz for a typical 8 megahertz mean value, a deviation larger than the roughly 2 megahertz annual standard deviation of the analyzed series. In other words, a single year’s annual mean computed from a badly gapped record can be off by more than the natural year-to-year variability of the ionosphere itself.

The effect on long-term trends is even stronger. With six or more months missing per year, maximum relative deviations of the estimated trend can reach 80 to 100 percent, meaning the computed trend could in principle be null, completely masking the greenhouse-gas signal in the F2 layer. The reference trends themselves are small, between about minus 0.012 and minus 0.022 megahertz per year across the four stations, with relative errors of roughly 30 percent, so even modest distortions from incomplete data can matter. The authors note that the distributions of annual means and trends derived from the artificial series are almost symmetric around the reference values: averaging over all possible gap combinations, or enough random cases, produces compensating errors and nearly null average deviation, but the dispersion of individual outcomes grows steadily with the number of missing months.

This symmetry carries an important lesson. Individual trend analyses based on gapped historical datasets, which is how many published studies were produced, do not enjoy the compensating effect that comes from averaging thousands of artificial realizations. Any single incomplete series can yield a distorted annual mean or a biased trend value, and since climate-scale studies aim to detect small and gradual signals over decades, even modest distortions can bias the value or even the sign of the inferred long-term trend. The authors emphasize that this quantifies the uncertainty introduced by data incompleteness, which should be taken into account when interpreting long-term ionospheric trends.

The study’s practical conclusion is a quantitative endorsement of the community’s long-standing rule: at least eight valid months per year appear to be a safe choice for reliable annual means and the long-term trends derived from them. The authors acknowledge that the analysis is limited to foF2, and that extending the approach to other key parameters such as the peak height hmF2 and total electron content would broaden the picture. Future work will also examine missing daily values within months, trend estimation at seasonal and monthly scales, and alternative trend detection strategies that reference conditions before 1980 to 1985, when anthropogenic effects in the upper atmosphere appear to become more noticeable. The methodology, they note, could extend to other atmospheric regions and even magnetospheric data, wherever long, gapped time series underpin climatological conclusions.

Subject of Research: How missing monthly data affect annual means and long-term trend estimates of the ionospheric F2-layer critical frequency

Article Title: Data gaps and trend bias relevant to space climate studies

Article References: Elias, A. G., Zossi, B. S., Silvero, C. I., Zamora, D. J., Duran, T., & Abaca, F. (2026). Data gaps and trend bias relevant to space climate studies. Discover Space, 130(1), Article 1. https://doi.org/10.1007/s11038-026-09580-8

Image Credits: AI Generated

DOI: 10.1007/s11038-026-09580-8

Keywords: ionosphere, foF2, space climate, data gaps, long-term trends, annual means, greenhouse gases, thermosphere, satellite drag, statistical methods, Data, gaps