Climate anomalies, that is, deviations from normal, serve as the primary material for studying El Niño and other interannual variability. According to World Meteorological Organization rules, normals are calculated as the average over the last 30 years, but with global warming this approach introduces bias: the normal temperature lags behind reality. A research direction has already emerged around this work, seeking optimal normals: some propose giving more weight to recent observations, others fit linear trends, and still others compare forecast accuracy. This article joins that line of work but shifts the focus from window selection to filter construction, simultaneously accounting for trend and seasonality.
The authors construct a linear causal filter with finite impulse response to estimate monthly climate normals. The foundation is local trigonometric regression: in the neighborhood of each time point, the normal is represented as the sum of a constant, a linear trend, and six seasonal harmonics. The filter is obtained as the solution to a least squares problem and then regularized: they introduce a shrinkage parameter λ that blends the no-trend filter with the trend filter. Additionally, seasonal kernels, such as the Epanechnikov kernel, are used to give more weight to central observations. The parameters λ and window width m are chosen by minimizing the mean squared error of the normal estimate, which accounts for the autocorrelation of anomalies.
For 120 sea surface temperature series in the Niño 3.4 region, the optimal parameters turned out to be close to standard: mean λ = 0.10, mean m = 29.38 years. The difference between anomalies from the new method and NOAA Climate Prediction Center estimates does not exceed 0.3 °C. For 228 wind series, the picture is different: mean λ = 0.49, mean m = 23.86 years, and the standard 30-year filter is selected in only 3 out of 228 cases. The old filter systematically underestimates wind normals, causing anomalies to be overestimated by up to 2 m/s. A stationarity test on anomalies shows a dramatic improvement: the failure rate drops from 55.3% to 3.5% when using the new filter.
This work follows the general quest for optimal climate normals, but differs from neighboring approaches by combining trend, seasonality, and regularization in a single filter with an explicit parameter selection criterion. Neighboring works either fix the window and tune weights, or fit the trend separately without touching the seasonal structure. Here, the filter is derived from a local trigonometric model, and parameters are tuned to minimize estimation error, providing a systematic way to adapt to non-stationarity. For sea surface temperature, the adequacy of standard normals is confirmed, while for wind it is shown for the first time that neglecting the trend leads to noticeable distortion of anomalies.
The method naturally extends to daily data, where the seasonal cycle has 365 harmonics, and the computational cost remains low. One could also consider nonparametric ways to choose the kernel and compare the proposed criterion with cross-validation that accounts for interannual correlation. An open question is the joint estimation of normals for multivariate series, such as temperature and wind, so that anomalies are consistent within a unified model.
The results are important for El Niño monitoring, climate forecasting, and any application where anomalies are used as inputs to statistical models. Improved wind anomalies could enhance the quality of ocean-atmosphere interaction models.
It is worth testing the filter on other climate variables, such as precipitation and pressure, where trends and seasonal shifts may be even stronger. It would also be useful to compare the new method with spline-based and local linear regression approaches within a unified forecasting experiment.
In statistical climatology, the question of how to separate the long-term trend from low-frequency variability, such as the Pacific Decadal Oscillation, remains unresolved. This work shows that the choice of filter for normals directly affects the statistical properties of anomalies, and hence conclusions about relationships between variables. Further progress requires joint modeling of trend, seasonality, and interannual autocorrelation without rigid stationarity assumptions.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This paper introduces a regularized filter based on local trigonometric regression for real-time estimation of climate normals that accounts for trend and seasonality. Using sea surface temperature data from the Niño 3.4 region and wind data from the tropical Pacific, we show that for temperature, the standard 30-year normals perform well, while for wind, the new filter substantially reduces spurious non-stationarity in anomalies (from 55% to 3.5% of stationarity test rejections).
Where its strength is
Combining trend, seasonality, and regularization in a single filter with an explicit criterion for parameter selection provides a systematic way to adapt to non-stationarity, enabling accurate anomaly estimation even when climate variables exhibit a trend.
Where it could go next
Worth trying
Why this may matter
Accurate anomaly estimation is critical for monitoring and forecasting climate phenomena such as El Niño, and the proposed method could become the standard for variables with pronounced trends.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.52, against a usual 0.64. It looks like few have drilled nearby.
The 30-year rule for climate normals arose not from statistics but from practice: when the recommendation was adopted, meteorologists had only 30 years of reliable data at their disposal. Since then, that number has become the standard, even though the climate can change noticeably over such a period.