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REVIEW 4 major objections 5 minor 35 references

Resampling Methods that Generate Time Series Data to Enable Sensitivity and Model Analysis in Energy Modeling

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Two bootstrap methods can resample a single observed year of hourly solar, wind, and load data into large ensembles of alternative series that are close to the original, making time-series sensitivity analysis feasible for energy planning…

desk verdict A candid, useful paper with a real use case and honest limitations, but the abstract's distributional claim outruns the in-sample validation. read the letter →

arxiv 2502.08102 v1 pith:GRTJWNAI submitted 2025-02-12 stat.CO

Kelly Wang , Steven O. Kimbrough This is my paper · ORCID
classification stat.CO
keywords synthetictimeseriesbootstrapresamplingenergysystemsmodelingsensitivityanalysisrobustnesssolarPVwindpowerPJMdata
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

Energy capacity-planning models demand decades of hourly wind, solar, and load data, but analysts usually have only one observed year to work with. This paper argues that two non-parametric bootstrap methods, Nearest Neighbors Lagged Bootstrap (NNLB) and Symmetric Block Bootstrap (SBB), can resample that single year, treated as a circular sequence, into arbitrarily many alternative series that are visually and statistically close to the original. If this holds, the generated series can be treated as stochastic draws from the same underlying distribution and used for robustness and sensitivity analysis, answering questions the authors care about: how many days per year might renewable supply fall below a threshold, and how much does that count vary. The paper also introduces two procedures, incremental selection and altered-difference distribution, for creating series systematically higher or lower than the observed one, explicitly motivated by climate change and renewable-drought planning. The supporting evidence is a year of PJM hourly solar, wind, and load series, with comparisons of means, medians, quartiles, standard deviations, autocorrelations, and counts of under- and over-production days.

What carries the argument

The paper's central machinery is the symmetric window-and-pool resampling scheme (SBB) and the lagged nearest-neighbor scheme (NNLB). In SBB, each hourly observation $x_i$ is the focal slot of a window $w_i = \langle x_{i-n},\dots,x_i,\dots,x_{i+n}\rangle$ of size $1+2n$ on a circular year; the $p$ windows closest in Euclidean distance to $w_i$ form a pool, and a new series is built by uniformly choosing one window from each pool and taking its focal value. In NNLB, a lag vector of the $l$ preceding hours (again circular) is matched to its $k$ nearest lag vectors, and the successor values are resampled with a $1/j$ kernel. The paper also defines the performance statistics $\theta^-$ and $\theta^+$, which sum, over blocks of length $l$, the amounts by which a generated series falls below or above the original beyond a threshold $e$; these statistics are what turn a batch of synthetic series into a distribution of an energy-relevant performance measure.

What would settle it

Generate ensembles from PJM 2021 and compare the distribution of a summary statistic (e.g., annual mean, lag-24 autocorrelation, or count of days below 95% of the training year) against the same statistic computed on actual PJM 2020, 2022, or a longer holdout year; if the holdout values fall far outside the ensemble distribution, the series are not credible draws from a common distribution.

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Extended reading notes

Core claim

The central claim is that bootstrap resampling from a single observed series yields credible alternative instances of the same time-series distribution, despite the series being visibly non-stationary. SBB, the method the authors prefer, forms for each hour a window of neighboring hours on a circular year, keeps the $p$ most similar windows by Euclidean distance, and resamples the focal value from that pool; NNLB instead matches lagged predecessor vectors and resamples successors. The paper reports that generated series pass the ocular test and match summary statistics, while still showing energy-relevant variability: for solar, an average of about 24 (window 5, pool 20) to 89 (window 9, pool 100) days per year fall at least 5% below the original; for wind, the comparable range is about 0.5 to 15 days. The displacement methods shift the level of a series by adding draws from a chosen distribution or by scaling the difference between two series, and the case study propagates this through a scaled-up renewable system: a configuration meeting 90% of annual load with 50% curtailment produces 64 shortage days for the original data, with the 1000 generated series spreading this count between 61 and 69. The paper's stated conclusion is that such ensembles are apt for robustness, sensitivity, and general post-solution analysis of energy planning models, and plausibly beyond.

Load-bearing premise

The load-bearing premise is that one year of hourly data, wrapped end-to-end to form a circle, is a valid empirical stand-in for the unknown distribution that generated the data, enough that resampling it produces credible other years.

Editorial extensions

If this is right

  • Any single observed or forecast hourly series, solar, wind, or load, can be expanded into hundreds of alternative series without fitting a parametric model to the generation process.
  • Because the methods preserve the daily autocorrelation structure, downstream analysis can use duration and ramping statistics (24-hour and 48-hour underage blocks), not just annual totals.
  • The incremental-selection and altered-difference methods give planners a principled way to explore systematically higher loads and renewable droughts, directly addressing climate-change planning needs.
  • Model outputs inherit variability from the synthetic ensembles: in the case study the shortage-day count varies from 61 to 69 across 1000 generated series, bracketing the original year's 64.
  • NNLB's tendency to produce nonzero solar generation at night is a known artifact that the paper identifies; for solar data it recommends SBB.

Reading between the lines

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

  • A direct extension the paper does not perform is a holdout validation: generate ensembles from 2021 and check whether PJM 2020 or 2022 summary statistics fall inside the bootstrap distributions; if they do not, the 'same distribution' conclusion would need qualification.
  • The circular-wrap trick is convenient for annual data but would erase any year-to-year drift in a multi-decade planning horizon; pairing SBB with a second-stage displacement of the annual mean would keep the machinery while reintroducing non-stationarity.
  • The altered-difference method's fixed scalar $\alpha$ keeps all hourly differences proportional; letting $\alpha$ vary by block would model years of differing severity (a mild drought versus an extreme one) and could be compared against the resulting shortage-day distributions.
  • The reported small SBB bias, where series means skew away from extreme values, suggests a bias-correction step on the focal slot could be added if planners need unbiased mean supply estimates.
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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

4 major / 5 minor

Summary. The paper proposes using two non-parametric bootstrap-style resampling methods, the Nearest Neighbors Lagged Bootstrap (NNLB) and the Symmetric Block Bootstrap (SBB), to generate large ensembles of synthetic hourly time series (solar PV, wind, and load) from a single observed year of PJM data, with the stated purpose of supporting sensitivity, robustness, and post-solution analysis in energy systems modeling. It also introduces two techniques for systematically displacing a series, called incremental selection and altered-difference distribution, and illustrates them in a case study that scales up PJM wind and solar generation to examine curtailment and shortfall statistics. The paper's central validation claim, stated in the abstract, is that the generated series are 'both visually and by statistical summary measures close to the original observational data' and in consequence 'credibly taken as stochastic instances from a common distribution, that of the original series of observations.' The paper is clearly written, extensively documents the statistical behavior of the generated ensembles, and honestly reports a small bias in the SBB method.

Significance. If the central claim could be sustained, the paper would address a real gap in energy modeling practice: a simple, assumption-light way to produce hundreds of plausible alternative hourly time series from a single observed or forecast series, for use in robustness and sensitivity analyses. The manuscript is also valuable as an exposition of the two methods, with reproducible code, thorough descriptive statistics, and an honest account of the methods' known biases, including the SBB mean bias and NNLB's production of nighttime solar. However, as it stands the central claim is not established by the evidence presented. All validation is in-sample: the generated series are compared only against the 2021 series from which their resampling pools were built, and the method parameters are chosen by a sweep that explicitly seeks closeness to that same series. The reported summary statistics (means, quartiles, coefficients of variation, lag-24 autocorrelation, counts of days below a threshold) are marginal features that do not constrain the joint temporal distribution, and the circular wrap-around assumption is unverified.

major comments (4)
  1. [§3.2.3, §3.3.3] The central claim that the generated series are 'credibly taken as stochastic instances from a common distribution, that of the original series of observations' is not supported by the validation presented. Both NNLB and SBB construct their resampling pools from the single 2021 PJM series, and the reported fit statistics (means, quartiles, coefficients of variation, lag-24 autocorrelation) are computed on the same series that generated them; this is an in-sample, partly tautological comparison. Moreover, these marginal summaries do not constrain joint temporal structure: they would not detect, for example, destroyed drought persistence, altered ramp sequences, or unrealistic transitions between dissimilar blocks. I recommend adding an out-of-sample or holdout test—e.g., generate ensembles from 2021 and compare the distribution of ensemble statistics to the observed statistics of 2022 and 2023 PJM data—and testing temporal features beyond lag-24 autocorrelation, such as block maxima, run lengths of low production, spectral density, or ramp-rate distributions.
  2. [§3.2.3, §3.3.3] The parameter choices (lag l and neighbor count k for NNLB; sash n and pool size p for SBB) are described as 'arrived at through a parameter sweep in which we took care that the generated series not deviate too much from the original series.' This makes the reported closeness to the original partly a consequence of the tuning criterion rather than a property of the methods. The paper does not report how sensitive the results are to these parameters, and the documented bias in the mean grows substantially with larger windows and pools (for example, solar SBB mean is 671.24 vs. original 673.31 at window 5/pool 20, but 665.64 vs. 673.31 at window 9/pool 100). A principled criterion for selecting these parameters, or at least a systematic sensitivity analysis showing the trade-off between bias and variability, is needed to support the claim that the methods faithfully reproduce the source distribution.
  3. [§3.2.2, §3.3.2] Both algorithms treat the annual series as effectively circular, so that the predecessor of the first observation is the last observation and the successor of the last is the first. The paper asserts in a footnote that '[t]his is appropriate for annual data and concatenations thereof,' but provides no evidence for this assumption. For strongly seasonal energy data, the artificial adjacency between late December and early January could generate artifacts in synthetic series near the year boundary, and the assumption is a modeling choice with real consequences for the empirical distribution being resampled. I recommend testing the sensitivity of the results to this assumption, for example by comparing with a non-circular variant that excludes windows crossing the boundary, and checking that generated series do not show anomalous behavior in the first and last days of the year.
  4. [§3.2.4, §3.3.4] The 'days below 95%' analyses report distributions such as a mean of 24.25 days below 95% for solar SBB at window 5/pool 20, and the text suggests this says something about the chance that 'another year of generation drawn from the same distribution would have 30 or so drought days.' This interpretation presupposes exactly the claim that the ensemble represents independent draws from the generating process, which is the unvalidated in-sample assumption flagged above. To make this inference, the paper would need to compare the synthetic distribution of days-below-threshold against the year-to-year variation actually observed in PJM (e.g., how many days in 2022 or 2023 fell below 95% of the 2021 values). Without such a benchmark, the reported counts are descriptive properties of the resampling scheme, not predictive statements about future years.
minor comments (5)
  1. [§3.2] The section title reads 'Nearest Neighbors Lagged Bootstap'; 'Bootstap' should be 'Bootstrap'.
  2. [§1] In the fourth paragraph of the Introduction, 'series that are are systematically more extreme' contains a duplicated 'are'.
  3. [§3.1] The formulas for θ^+ and θ^- contain the notation 'lX i=1', which appears to be a typographical corruption of a summation sign; also, the text does not clearly state whether the empirical distributions are over chunks of length l within one generated year or over entire generated years. Since the 'days below' statistics are per-chunk counts, this should be clarified.
  4. [§4.3] The case study states that the distribution of the statistic Φ (number of 24-hour periods in which renewable supply is below 90% of demand) was collected for the 1000 synthetic series, and gives a range of 61–69 days, but no histogram, table, or summary statistics for Φ are actually shown. Please present this distribution, or state clearly that it is deferred to the supplemental code and give the key quantiles in the text.
  5. [§5.1] The sentence 'We have found only two practicable methods for generating synthetic time series suitable for post-solution model analysis' could be read as contradicting the broader literature reviewed in §2.2; I suggest rephrasing to make clear that the claim is limited to methods meeting the specific requirements of this use case (large ensembles of annual hourly series without parametric stationarity assumptions).

Circularity Check

2 steps flagged · score 6.0 of 10

In-sample validation and resampling-from-input make the 'common distribution' claim partly tautological; hyperparameters are tuned for closeness to the original and the conclusion restates the resampling construction.

  1. self definitional [§3.3.4 'Under-Performance Analysis' (conclusion about SBB; cf. §3.2.2 step 4, §3.3.2 step 3)]
    "The results above serve to demonstrate that the SBB method, like the NNLB method, plausibly replicates the distribution of the original series it samples."

    By construction, SBB draws each x'_i by randomly selecting a window from Pi, where Pi is built from the original X's windows (§3.3.2 steps 2-3), and NNLB draws each x'_i from Nj(i), the k nearest index vectors derived from the original X (§3.2.2 steps 2-4). The distribution being 'replicated' is therefore the empirical resampling distribution of the input series itself. Concluding that the method 'plausibly replicates the distribution of the original series it samples' restates the algorithm; it does not provide evidence that the ensemble is drawn from the unknown, non-stationary generating process. Only marginal summaries (means, std, CV, lag-24 ACF) are compared, always against the same 2021 series that supplied the pools.

  2. fitted input called prediction [§3.2.3 'Examining the Generated Series' (parameter choice); cf. Tables 1-6]
    "These parameters do not have any privileged meaning; they were arrived at through a parameter sweep in which we took care that the generated series not deviate too much from the original series, while still having room to show variability."

    The lag/neighbor sizes (and, by extension, the SBB window/pool sizes) are explicitly chosen so that the generated series stay close to the 2021 PJM original. The same section then presents the observed closeness (Tables 1-6, Figure distributions) as a finding that the method 'captures the main features' of the original. The validation target is the same object used in the selection criterion, so the reported fidelity is inherited from the tuning step rather than an independent out-of-sample result. This is a fitted-input-renamed-as-finding pattern: no holdout year or distributional test on temporal structure is used to support the abstract's stronger 'common distribution' claim.

full rationale

The paper's own equations and procedure descriptions show that every generated observation is sampled from the original 2021 PJM series (NNLB §3.2.2 step 4, SBB §3.3.2 step 3). Consequently, the central validation claim that generated series are 'credibly taken as stochastic instances from a common distribution, that of the original series' is at its core a restatement of the resampling construction plus an unverified leap from the empirical distribution to the true generating process. The parameter sweep admission in §3.2.3 makes the in-sample fidelity partly an artifact of tuning: the authors chose lag/neighbor and window/pool sizes 'to take care that the generated series not deviate too much' and then report that they do not deviate. No second year, holdout period, or formal distributional comparison on temporal features (drought sequences, ramps) is provided, so the leap is not independently supported. However, the paper is not wholly circular: NNLB is an external, published method [25], the SBB method is re-implemented and extended with new analyses rather than merely cited, the directional alteration techniques (§4.1, §4.2) are genuine transformations with independent content, and the PJM mini-study (§4.3) is a concrete application. The self-citation to [26] is disclosed and not load-bearing for the empirical demonstrations. The circularity is therefore partial, concentrated in the validation and in the 'common distribution' interpretation, rather than a case where every result is forced by a self-citation chain or by definition.

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

The methods rest on standard bootstrap exchangeability plus several data-specific modeling choices: circular wrap-around, Euclidean-distance similarity, and capacities assumed constant in 2021. The free parameters (lag, window, pool sizes, thresholds, scaling weights) were tuned or chosen by hand on the 2021 PJM data, so the validation is not fully independent of the data it is tested on.

free parameters (5)
  • NNLB lag l and neighbor count k = l=5, k=20; l=9, k=100
    Selected by parameter sweep to balance fidelity and variability; the paper says these parameters 'do not have any privileged meaning' (§3.2.3).
  • SBB sash n and pool size p = n=2, p=20; n=4, p=100
    Selected by parameter sweep, matching NNLB vector sizes, to keep generated series close to the original while retaining variability (§3.3.2-3.3.3).
  • Underage/overage threshold e = 5% of original series (alpha=0.05), l=24h
    Chosen as a representative measure of drought days; other thresholds are possible but not explored here (§3.1, §3.2.4, §3.3.4).
  • Case-study scaling weights = ws=45, ww=22 (10% curtailment); ws=84, ww=64 (50% curtailment)
    Chosen to hit curtailment targets; the paper acknowledges the choice among equivalent weight combinations was arbitrary (§4.3).
  • Altered-difference scale alpha = 0.5 and 0.9
    Chosen by hand to illustrate the displacement method (§4.2.2).
assumptions (4)
  • standard math The empirical distribution of the observed 2021 PJM year approximates the unknown population distribution, so resampling from it yields valid alternative draws.
    Bootstrap estimation assumes the empirical distribution function is a reasonable proxy for the population; invoked throughout §3.1.
  • domain assumption The time series can be treated as circular, with the end of the year wrapping around to the beginning.
    Stated in §3.2.2 step 1 and §3.3.2 step 1; this creates artificial lag and window pools at year boundaries, which can introduce distortions (e.g., NNLB generating nighttime solar).
  • domain assumption Euclidean distance between lagged blocks or windows is a valid similarity measure for capturing the joint distribution of the series.
    Used in NNLB (§3.2.2 step 2) and SBB (§3.3.2 step 2) to select similar patterns; no justification beyond standard k-nearest-neighbor practice.
  • domain assumption Solar PV and wind capacity were constant during 2021.
    Acknowledged as a limitation in §5.2; the paper notes there was net expansion of both wind and PV during 2021, introducing small but correctable error.

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Cite this review

Pith. "Pith review of Resampling Methods that Generate Time Series Data to Enable Sensitivity and Model Analysis in Energy Modeling." pith.science (2026). https://pith.science/paper/GRTJWNAI

@misc{pith2026250208102,
  author       = {Pith},
  title        = {Pith review of: Resampling Methods that Generate Time Series Data to Enable Sensitivity and Model Analysis in Energy Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GRTJWNAI}},
  note         = {Machine review of arXiv:2502.08102}
}
read the original abstract

Energy systems modeling frequently relies on time series data, whether observed or forecast. This is particularly the case, for example, in capacity planning models that use hourly production and load data forecast to occur over the coming several decades. This paper addresses the attendant problem of performing sensitivity, robustness, and other post-solution analyses using time series data. We explore two efficient and relatively simple, non-parametric, bootstrapping methods for generating arbitrary numbers of time series from a single observed or forecast series. The paper presents and assesses each method. We find that the generated series are both visually and by statistical summary measures close to the original observational data. In consequence these series are credibly taken as stochastic instances from a common distribution, that of the original series of observations. With climate change in mind, the paper further proposes and explores two general techniques for systematically altering (increasing or decreasing) time series. Both for the perturbed and unperturbed synthetic series data, we find that the generated series induce variability in properties of the series that are important for energy modeling, in particular periods of under- and over-production, and periods of increased ramping rates. In consequence, series produced in this way are apt for use in robustness, sensitivity, and in general post-solution analysis of energy planning models. These validity factors auger well for applications beyond energy modeling.

Figures

Figures reproduced from arXiv: 2502.08102 by the authors.

Figure 1
Figure 1. Demonstration of 21 generated time series for solar energy using the NNLB method. Lag=5. [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Demonstration of 21 generated time series for solar energy using the NNLB method. Lag=9. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Distribution of NNLB means for solar. The table first rows list the statistics used on each of the of the 1000 individual statistics we calculated for each generated NNLB series. For example, the number 0.867 in the bottom left corner of [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (25 more)
Figure 4
Figure 4. Figure 4: Demonstration of 21 generated time series for wind energy using the NNLB method. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Distribution of NNLB block means for wind. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Demonstration of 21 generated time series for energy load using the NNLB method. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Distribution of NNLB means for load. motivation for this study. For example, given a history of wind or solar availability, what sorts of risks of production shortage exist even assuming that the underlying causal generation process remains unchanged? We will now be us…
Figure 8
Figure 8. Figure 8: Distribution of the number of days from 1000 solar NNLB series that fall below 95% of the original [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Distribution of the number of days from 1000 wind NNLB series that fall below 95% of the original [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: Distribution of the number of days from 1000 load NNLB series that fall below 95% of the original [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: Demonstration of 21 generated time series for solar energy using the SBB method. Window [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: Demonstration of 21 generated time series for solar energy using the SBB method. Window [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: Distribution of symmetric block means for solar. [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: Demonstration of 21 generated time series for wind energy using the SBB method. [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: Distribution of symmetric block means for wind. [PITH_FULL_IMAGE:figures/full_fig_p020_15.png]
Figure 16
Figure 16. Figure 16: Demonstration of 21 generated time series for load energy using the SBB method. [PITH_FULL_IMAGE:figures/full_fig_p020_16.png]
Figure 17
Figure 17. Figure 17: Distribution of symmetric block means for load. [PITH_FULL_IMAGE:figures/full_fig_p021_17.png]
Figure 18
Figure 18. Figure 18: Distribution of the number of days from 1000 solar symmetric series that fall below 95% of the [PITH_FULL_IMAGE:figures/full_fig_p022_18.png]
Figure 19
Figure 19. Figure 19: Distribution of the number of days from 1000 wind symmetric series that fall below 95% of the [PITH_FULL_IMAGE:figures/full_fig_p023_19.png]
Figure 20
Figure 20. Figure 20: Distribution of the number of contiguous 48 hours from 1000 solar symmetric series that fall [PITH_FULL_IMAGE:figures/full_fig_p023_20.png]
Figure 21
Figure 21. Figure 21: Five alterations of PJM’s 2021 wind generation data over a time period of 6 hours using the [PITH_FULL_IMAGE:figures/full_fig_p025_21.png]
Figure 22
Figure 22. Figure 22: Five alterations of PJM’s 2021 wind generation data over a time period of 6 hours using the [PITH_FULL_IMAGE:figures/full_fig_p025_22.png]
Figure 23
Figure 23. Figure 23: Five alterations of PJM’s 2021 Wind generation data over a time period of 6 hours using the [PITH_FULL_IMAGE:figures/full_fig_p027_23.png]
Figure 24
Figure 24. Figure 24: Four alterations of PJM’s 2021 Wind generation data over a time period of 24 hours using the [PITH_FULL_IMAGE:figures/full_fig_p028_24.png]
Figure 25
Figure 25. Figure 25: Three alterations of PJM’s 2021 Wind generation data over a time period of 6 hours using the [PITH_FULL_IMAGE:figures/full_fig_p029_25.png]
Figure 26
Figure 26. Figure 26: Seasonal 5 day comparisons of the scaled up renewable energy by the weights [PITH_FULL_IMAGE:figures/full_fig_p031_26.png]
Figure 27
Figure 27. Figure 27: Seasonal 1 day comparisons of altered versions of a scaled up renewable energy dataset by the [PITH_FULL_IMAGE:figures/full_fig_p032_27.png]
Figure 28
Figure 28. Figure 28: Seasonal 5 day comparisons of the scaled up renewable energy by the weights [PITH_FULL_IMAGE:figures/full_fig_p032_28.png]

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.