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REVIEW 3 major objections 7 minor 42 references

Long-term prediction of El Ni\~no-Southern Oscillation using reservoir computing with data-driven realtime filter

T0 review · 3 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A causal, data-driven band-pass filter combined with reservoir computing extends ENSO prediction to about two years.

desk verdict The causal filter is a genuinely new idea, but the headline 24-month ENSO skill is measured on a filtered proxy whose parameters are tuned on the full record including the test window, so the central claim is not supported as presented. read the letter →

arxiv 2501.17781 v2 pith:BRAM7I6K submitted 2025-01-29 physics.comp-ph cs.LGphysics.ao-ph

Takuya Jinno , Takahito Mitsui , Kengo Nakai , Yoshitaka Saiki , Tsuyoshi Yoneda This is my paper · ORCID
classification physics.comp-phcs.LGphysics.ao-ph
keywords ENSOpredictionreservoircomputingechostatenetworkrealtimeband-passfiltercausalfilteringBayesianoptimizationseasurfacetemperatureanomalymulti-yearclimateforecasting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the two-year-ahead prediction horizon for ENSO, previously reached by deep-learning models, can be obtained with a much simpler reservoir-computing setup once the input is filtered by a new type of band-pass filter that uses only past observations. The filter is a weighted moving average whose weights are tuned by Bayesian optimization, and its decisive property is causality: unlike conventional moving-average or Butterworth filtering, it never mixes future data into the training or prediction signal, so the whole workflow is usable in realtime operational forecasting. On 180 forecasts initialized monthly between January 2001 and December 2015, the average all-season correlation skill stays above 0.5 for 29 months, which the authors count as about 24 months after subtracting the roughly five-month lag the filter introduces. Because the predicted target is the filtered realtime sea-surface-temperature anomaly rather than the standard Niño-3.4 index, the authors are careful to say that a direct numerical comparison with earlier ENSO forecast studies is not possible.

What carries the argument

The load-bearing object is the realtime filter, a causal weighted moving average with kernel $\Psi(t) = (d_1 \cos(t/(\pi r_1)) + d_2 \cos(t/(\pi r_2))) (w-t)^c / w^c$ for $t \in [0,w]$ and $\Psi(t)=0$ for $t \ge 0$; convolving it with the monthly SST anomaly suppresses fluctuations shorter than about three years and longer than about eight years while using no future values. Its parameters are selected to maximize a dictionary objective that counts how often discretized length-$L$ patterns (keys) are followed by a single value among a prescribed set, together with the lag correlation between original and filtered series. The filtered series is then fed, through an $M$-dimensional delay-coordinate vector with delay $\Delta\tau$, into an echo-state network whose recurrent and input matrices are kept fixed and whose output matrix is fitted by ridge regression; prediction proceeds by recursively feeding the output back as input. All filter and reservoir hyperparameters are calibrated by Bayesian optimization, which the paper argues is what lets the same workflow transfer to other phenomena.

What would settle it

Evaluate the trained model directly against the conventional 5-month-running-mean Niño-3.4 index over 2001–2015: if the all-season correlation skill at 24 months falls below 0.5, the claimed two-year horizon does not transfer to the standard ENSO index. Alternatively, retrain the filter only on data before January 2001 and repeat the evaluation; a drop below 0.5 would indicate the test period influenced the reported skill.

Watch

Extended reading notes

Core claim

The central discovery claimed in the paper is that the main obstacle to long data-driven ENSO forecasts is not the predictor but the preprocessing: standard filters leak future information, and unfiltered data carry fast fluctuations that degrade reservoir training. The authors construct a causal realtime filter—a finite-support convolution kernel supported on $t \in [0,w]$, so that the filtered value at time $t$ depends only on observations at $t, t-1, \dots, t-w$—and tune its parameters together with the reservoir hyperparameters using Bayesian optimization. With the optimized filter and an echo-state network driven by delay-coordinate vectors of the filtered realtime SST anomaly, they report an average all-season correlation skill above 0.5 out to 29 months of lead time, and roughly 24 months once the filter-induced five-month lag is discounted. They interpret this as successfully predicting the multi-year dynamics of ENSO for two years using only past data.

Load-bearing premise

The claim's load-bearing premise is that the filtered realtime SST anomaly faithfully represents ENSO, a stand-in supported by a 0.837 lag correlation with the raw anomaly, while the filter parameters were tuned on a record that includes the test years.

Editorial extensions

If this is right

  • The full pipeline—filter construction, model training, and forecasting—can in principle be run in realtime because no future information enters the filtered series.
  • On the filtered realtime SST anomaly, skillful forecasts (correlation above 0.5) extend to 29 months of lead time, or about 24 months after accounting for the filter's five-month backward shift.
  • Predictions initialized around 2010–2011 capture major warm and cold phases of the filtered index up to about three years ahead, while the strong 2015–2016 El Niño is reproduced with relatively low accuracy.
  • The same methodology, with its six filter parameters and nine reservoir parameters tuned by Bayesian optimization, is proposed as a general recipe for multi-year prediction of other high-dimensional climate time series.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the skill metric is computed on the filtered index, the paper does not establish the same two-year skill for the conventional Niño-3.4 index; a separate evaluation on the raw running-mean index would be needed before operational use.
  • The filter parameters were optimized over the full 1870–2022 record, which includes the 2001–2015 evaluation window, so part of the reported skill may reflect information from the test period; retraining the filter on data ending in 2000 would quantify this.
  • The causality property is generic, so the same filter-plus-reservoir workflow is a natural candidate for other oscillatory climate modes such as the Madden–Julian Oscillation or monsoon indices, where future-leaking filters have been a known obstacle.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. This paper proposes a causal 'realtime filter', a one-sided weighted moving average whose parameters are tuned by Bayesian optimization, to band-pass the monthly SST anomaly in the Nino-3.4 region; the filtered series is then used as input and output for an echo-state network with delay-coordinate embeddings. The authors report that the all-season correlation skill of the filtered target remains above 0.5 for 29 months over 180 hindcasts initialized monthly between January 2001 and December 2015, and after discounting a claimed ~5-month lag of the filter, they conclude that ENSO can be predicted 24 months ahead using only past data. The paper also provides code and a systematic hyperparameter optimization framework.

Significance. The paper offers a useful methodological contribution: a genuinely causal filter suitable for operational forecasting, combined with Bayesian optimization of filter and reservoir hyperparameters, and publicly available code. If the headline result were established on the standard Nino-3.4 index with a leakage-free calibration, a 24-month skill horizon would be noteworthy. As it stands, however, the evaluation is performed on a filtered proxy and the filter parameters are optimized on the full 1870-2022 record; both issues bear directly on the central claim and must be resolved before the result can be accepted.

major comments (3)
  1. [IV.A, III.B] The central claim of 24-month ENSO prediction is evaluated on the filtered realtime SST anomaly, not on the standard Nino-3.4 index or the raw monthly SST anomaly. Section IV.A concedes that 'a direct comparison of the prediction horizon to those of previous studies is not possible.' Because the filtered series is a smoothed, phase-shifted transformation of the input, correlation skill on this target can be high even when forecasts of the standard index are poor; the 0.837 maximum lag-correlation at five months does not establish that the two series have the same forecast-relevant dynamics. The abstract and conclusions should either report skill for the conventional Nino-3.4 index or substantially soften the claim that ENSO is predicted for two years.
  2. [II.B, II.D, Table I] The filter parameters are selected by maximizing Eq. (3) together with the maximum lag-correlation 'when applied to the realtime SST anomaly', with no temporal split described; since the realtime SST anomaly spans 1870-2022, this optimization includes the 2001-2015 evaluation window. The filter kernel itself is causal, but its shape is nevertheless fit using information from the test period, which can inflate the reported 29-month above-0.5 skill. The authors should refit the filter on data prior to 2001 only and re-evaluate on 2001-2015.
  3. [II.D, III.B] The reservoir hyperparameters and the random seed x are chosen by maximizing C(24) over 120 sequences from January 1986 to December 1995, and the same metric C(mu) is then reported on the separate 2001-2015 period. While this is a legitimate out-of-sample split, the headline 'above 0.5 for 29 months' is a single post-selection realization; reporting only the selected model's curve without uncertainty bands or comparison to a persistence/climatology baseline makes it difficult to assess whether the apparent skill reflects genuine predictability of the filtered signal.
minor comments (7)
  1. [II.B] The section heading 'Realtime fitering method' should be corrected to 'Realtime filtering method'.
  2. [Fig. 5 caption] The word 'ecch' in the caption should be 'each'.
  3. [III.B] The word 'architechture' should be 'architecture'.
  4. [III.A, III.B] The direction of the five-month shift is described inconsistently ('shifts backward' vs. 'shifted about 5 months into the future'); please clarify with an explicit definition of the lag variable and the implied correction to the prediction horizon.
  5. [II.D] Please specify the exact data period used for the filter optimization; if the full record is used, state it explicitly and discuss the implications for the reported skill.
  6. [Eq. (7)] Please define the range of lead months mu and explain how target years are assigned for lead times greater than 12 months.
  7. [Fig. 7 caption] The phrase 'Tempor al characteristics' should be 'Temporal characteristics'.

Circularity Check

2 steps flagged · score 6.0 of 10

Claimed 24-month ENSO skill is evaluated on a filtered target whose parameters were tuned on the full record, including the 2001-2015 evaluation window, and whose link to the standard Niño-3.4 index is an assumed 0.837 lag correlation.

  1. fitted input called prediction [Section II.D (Bayesian optimization) and Section III.B (Prediction skill); data period in Section II.A]
    "The hyperparameters of the realtime filter are chosen to maximize the product of the objective function in Eq. (3) when applied to the realtime SST anomaly, and the maximum lag-correlation between the original and filtered monthly SST anomaly. ... To evaluate the prediction skill of the current method, the sequence of training and prediction is conducted 180 times with different t0 every month between January 2001 and December 2015."

    No training/evaluation split is stated for the filter: Section II.A defines the data as 1870-2022, and Fig. 4b reports the lag correlation over the entire data period. The 2001-2015 evaluation window is therefore inside the record used to fit the six filter parameters in Table I. The filtered series y* used as the forecast target is produced by these fitted weights, so the all-season correlation skill in Eq. (7) is computed against a target whose construction already used information from the evaluation period. Moreover, Eq. (3) explicitly selects filter parameters by maximizing how often a pattern in y* is followed by one of its discrete values, i.e., it optimizes the predictability of the target series.

  2. self definitional [Section III.A (filtered index assumption) and Section IV.A (discussion)]
    "The maximum correlation is 0.837 with a lag of five months, and we assume that the filtered realtime SST anomaly can be used as an alternative index for the state of ENSO. ... the target time series is the filtered realtime SST anomaly, which is not identical to the conventional Ni˜no 3.4 index. Therefore, a direct comparison of the prediction horizon to those of previous studies is not possible."

    The headline claim that the model predicts ENSO dynamics for 24 months is evaluated on this assumed alternative index. The paper redefines the quantity to be predicted as the filtered realtime SST anomaly, justified only by a lag correlation of 0.837, and then subtracts the filter's 5-month phase shift to convert 29 months of skill on the filtered series into 24 months of 'ENSO' prediction. Since the paper concedes that the target is not the conventional Niño-3.4 index and that direct comparison with previous studies is impossible, the ENSO-specific claim reduces to skill on a self-defined filtered target; the link to actual ENSO dynamics is an assumption rather than part of the evaluated prediction.

full rationale

The paper's reservoir-computing component has some independent content: reservoir hyperparameters and random matrices are selected on a 1986-1995 validation period and then evaluated on 2001-2015, so the ESN training itself is not trivially circular. However, the central ENSO skill claim is compromised in two linked ways. First, the realtime filter parameters are optimized on the full 1870-2022 record, which includes the 2001-2015 evaluation window, and the reported skill is computed on the filtered series produced by those parameters; this is information leakage from the test period into the construction of the target. Second, the paper explicitly assumes the filtered realtime SST anomaly is an alternative index for ENSO based on a lag correlation of 0.837, and the 24-month result is obtained by subtracting the filter's 5-month shift from skill on that proxy. The paper itself acknowledges that direct comparison with previous ENSO prediction studies is not possible because the target is not the conventional Niño-3.4 index. The self-citations to Nakai and Saiki (2021) are used only as post-hoc hyperparameter guidance and are not load-bearing for the claimed skill. Overall, the result is partially circular: the target is a fitted, smoothed transformation selected for predictability, and the filter fit includes the evaluation period. A refit of the filter on data before 2001 and scoring the standard Niño-3.4 index would be required to support the 24-month ENSO claim.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's central claim rests on many fitted parameters: six filter kernel parameters, eight reservoir hyperparameters, a selected random seed for reservoir matrices, and unstated discretization parameters (K, gamma, Lmin, Lmax). The filter kernel and the dictionary objective are ad hoc modeling choices rather than derived requirements. No new physical entities are introduced.

free parameters (4)
  • Filter kernel parameters (r1, r2, d1, d2, c, w) = r1=39.333, r2=2.789, d1=0.152, d2=0.448, c=1.086, w=65
    Optimized by Bayesian optimization on the full SST anomaly record (1870-2022) to maximize Eq. (3) and the lag correlation between original and filtered series. These values determine the passband and the causal kernel shape.
  • ESN hyperparameters (Delta_tau, M, N, beta, p, sigma_in, rho, alpha) = Delta_tau=4, M=9, N=244, beta=0.759, p=0.290, sigma_in=0.477, rho=0.712, alpha=0.975
    Optimized to maximize C(24) on the validation period 1986-1995. These control the delay embedding, reservoir size, leakage, sparsity, spectral radius, and input scaling.
  • Random seed x for matrices A and Win = not reported (best selected)
    The Bayesian optimization selects the best random seed for generating the reservoir matrices, effectively choosing the best of up to 1000 trials. This selection on the validation period may overstate skill.
  • Discretization parameters K, gamma, Lmin, Lmax = not reported
    These define the dictionary discretization and pattern matching in Eq. (3). They are prescribed but values are not given in the paper, making reproduction harder and indicating additional tuned quantities.
assumptions (5)
  • ad hoc to paper The parametrized filter kernel (cosine pair times (w-t)^c / w^c) is an appropriate family for extracting 3-8 year variability.
    No first-principles derivation; the functional form is chosen ad hoc and the parameters fitted to the data (Section II.B, Eq. 2).
  • ad hoc to paper The dictionary/key-value objective in Eq. (3) measures the predictability of the discretized filtered series and is a suitable proxy for filter quality.
    The objective is not derived from a prediction-error criterion and its link to forecast skill is not established (Section II.B).
  • domain assumption The filtered realtime SST anomaly is an acceptable alternative ENSO index.
    Based on a lag correlation of 0.837 and a 5-month shift (Section III.A). The paper acknowledges the filtered series is not identical to the conventional Nino-3.4 index.
  • standard math Echo state property and reservoir computing training via ridge regression (Eq. 6) yield a valid data-driven model.
    Standard theory (refs 21-24); the paper imposes rho<1 as a simplification.
  • domain assumption Delay-coordinate embedding reconstructs the ENSO attractor.
    The input uses M=9 delays of the filtered index following Takens embedding and prior guidelines (refs 26, 38).

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Cite this review

Pith. "Pith review of Long-term prediction of El Ni\~no-Southern Oscillation using reservoir computing with data-driven realtime filter." pith.science (2026). https://pith.science/paper/BRAM7I6K

@misc{pith2026250117781,
  author       = {Pith},
  title        = {Pith review of: Long-term prediction of El Ni\~no-Southern Oscillation using reservoir computing with data-driven realtime filter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BRAM7I6K}},
  note         = {Machine review of arXiv:2501.17781}
}
read the original abstract

In recent years, the application of machine learning approaches to time-series forecasting of climate dynamical phenomena has become increasingly active. It is known that applying a band-pass filter to a time-series data is a key to obtaining a high-quality data-driven model. Here, to obtain longer-term predictability of machine learning models, we introduce a new type of band-pass filter. It can be applied to realtime operational prediction workflows since it relies solely on past time series. We combine the filter with reservoir computing, which is a machine-learning technique that employs a data-driven dynamical system. As an application, we predict the multi-year dynamics of the El Ni\~{n}o-Southern Oscillation with the prediction horizon of 24 months using only past time series.

Figures

Figures reproduced from arXiv: 2501.17781 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

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Reference graph

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Reviewed August 10, 2026 · model on record in the stance chip above.