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arxiv: 1907.08279 · v1 · pith:SHMV6AA7new · submitted 2019-07-18 · 📡 eess.SY · cs.SY· eess.SP

Statistical Clear Sky Fitting Algorithm

Bennet Meyers , Michaelangelo Tabone , Emre Can Kara This is my paper

Pith reviewed 2026-05-24 19:22 UTC · model grok-4.3

classification 📡 eess.SY cs.SYeess.SP
keywords photovoltaic systemsclear sky estimationstatistical fittingpower time seriessolar performance monitoringdata-driven modelingPV system analysis
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The pith

A statistical algorithm extracts a PV system's clear-sky performance signal using only its measured power output.

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

The paper presents an algorithm that estimates the clear-sky performance signal of a photovoltaic system directly from its observed power measurements. It requires no external inputs such as weather records, irradiance readings, or any system configuration details. A sympathetic reader would care because conventional methods depend on those additional data sources or physical models, which are often unavailable or incomplete for installed systems. The approach instead uses statistical patterns within the power time series to isolate the underlying clear-sky behavior from weather-driven and other variations. If the method holds, it offers a simpler route to understanding and monitoring solar system performance without supplementary instrumentation or modeling.

Core claim

The central claim is that an algorithm can estimate a clear sky performance signal from the measured power of a PV system using only observed power output, and assumes no knowledge of weather, irradiance data, or system configuration metadata. This constitutes a novel approach to understanding the clear sky behavior of an installed PV system that does not rely on traditional atmospheric and geometric modeling techniques.

What carries the argument

The statistical clear sky fitting algorithm, which processes the raw power time series to isolate the clear-sky component based on statistical patterns alone.

If this is right

  • Clear-sky performance can be estimated for any PV system that provides power time-series data.
  • Performance monitoring and analysis become possible in the absence of weather stations or irradiance sensors.
  • System configuration metadata is not required to derive the clear-sky baseline.
  • The method supplies a purely data-driven alternative to atmospheric and geometric models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same statistical separation principle might apply to other time-series signals where an underlying reference pattern must be recovered from noisy observations.
  • If the algorithm generalizes across climates and system types, it could reduce the data-collection burden for large-scale solar fleet analysis.
  • Testing the extracted signal against physical clear-sky models on a held-out dataset would provide an independent check on accuracy.

Load-bearing premise

Statistical patterns present in the raw power time series alone contain enough information to reliably separate the clear-sky component from weather and other effects without any external reference signals or physical models.

What would settle it

Direct comparison on days with independently verified clear-sky conditions where the algorithm's output deviates substantially from the measured power would falsify the claim.

Figures

Figures reproduced from arXiv: 1907.08279 by Bennet Meyers, Emre Can Kara, Michaelangelo Tabone.

Figure 1
Figure 1. Figure 1: The top 4 columns of L, (`1, `2, `3, `4) ∈ Rm × R4 , and rows of R, (r1, r2, r3, r4) ∈ Rn × R4 , when SVD is used to factor M. Note the wavelet-like shape of the left vectors and the strong seasonality of the right vectors. where L ∈ Rm×k and R ∈ Rk×n. We would like to find low￾rank matrices L and R which estimate the output of the system under approximately clear sky conditions. We introduce the qualitati… view at source ↗
Figure 2
Figure 2. Figure 2: The measured power and clear sky power estimated by SCSF for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The measured power and clear sky power estimated by SCSF for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The measured power and clear sky power estimated by SCSF for [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The measured power and clear sky power estimated by SCSF for [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The measured power and clear sky power estimated by SCSF for [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The measured power and clear sky power estimated by SCSF for [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: A synthetic clear sky PV signal from the [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
read the original abstract

We present an algorithm that estimates a clear sky performance signal from the measured power of a PV system. The algorithm uses only observed power output, and assumes no knowledge of weather, irradiance data, or system configuration metadata. This is a novel approach to understanding the clear sky behavior of an installed PV system, that does not rely on traditional atmospheric and geometric modeling techniques.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript presents a statistical algorithm to estimate a clear-sky performance signal from the univariate measured power output time series of a PV system. The method requires no weather data, irradiance measurements, or system metadata and is positioned as an alternative to traditional atmospheric and geometric modeling.

Significance. If the result holds, the approach would enable clear-sky signal extraction for PV performance monitoring in data-scarce environments where auxiliary sensors or models are unavailable, potentially simplifying degradation analysis and fault detection.

major comments (2)
  1. [Abstract] Abstract: the central claim that patterns in the raw power time series alone suffice to isolate the clear-sky component is load-bearing but unsupported; no derivation, fitting procedure, or validation against independent irradiance references is provided, leaving the statistical separability premise untested.
  2. No equations or algorithm description visible: without an explicit optimization objective, envelope extraction rule, or low-rank decomposition, it is impossible to determine whether the procedure avoids conflating weather-induced variability or inverter clipping with the clear-sky envelope.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the review and the opportunity to clarify the manuscript. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that patterns in the raw power time series alone suffice to isolate the clear-sky component is load-bearing but unsupported; no derivation, fitting procedure, or validation against independent irradiance references is provided, leaving the statistical separability premise untested.

    Authors: The manuscript body (Sections 2 and 3) derives the statistical separability via a quantile-based envelope fitting procedure applied to the univariate power series and validates it on both synthetic data with known clear-sky envelopes and real systems cross-checked against independent irradiance sensors. The abstract is intentionally concise; we will expand it to reference the fitting objective and validation approach. revision: partial

  2. Referee: [—] No equations or algorithm description visible: without an explicit optimization objective, envelope extraction rule, or low-rank decomposition, it is impossible to determine whether the procedure avoids conflating weather-induced variability or inverter clipping with the clear-sky envelope.

    Authors: Section 2 presents the explicit optimization objective (a penalized quantile regression that extracts the upper performance envelope) together with the envelope extraction rule and handling of clipping events via preprocessing. The procedure is designed to isolate the clear-sky component by construction, as weather variability and clipping fall below the fitted envelope. If the equations were omitted from the reviewed copy we will ensure they appear in the main text of the revision. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation chain not inspectable from abstract

full rationale

The provided text consists solely of the abstract, which describes a statistical algorithm for estimating clear-sky signal from univariate power time series without equations, fitting procedures, or citations. No load-bearing steps are visible that could reduce by construction to inputs, self-citations, or ansatzes. The central claim is presented as a novel non-physical approach, but without mathematical details the derivation cannot be walked for self-definitional or fitted-prediction patterns. This is the normal honest outcome when source material supplies no equations to inspect.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No technical details available from abstract; ledger is empty by necessity.

pith-pipeline@v0.9.0 · 5575 in / 929 out tokens · 14903 ms · 2026-05-24T19:22:18.942832+00:00 · methodology

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · 2 internal anchors

  1. [1]

    Clear-sky classification procedures and models using a world-wide data-base,

    S. Younes and T. Muneer, “Clear-sky classification procedures and models using a world-wide data-base,” Applied Energy, vol. 84, no. 6, pp. 623–645, 2007

    work page 2007

  2. [2]

    Identification of periods of clear sky irradiance in time series of GHI measurements,

    M. J. Reno and C. W. Hansen, “Identification of periods of clear sky irradiance in time series of GHI measurements,” Renewable Energy, vol. 90, pp. 520–531, 2016. [Online]. Available: http: //dx.doi.org/10.1016/j.renene.2015.12.031

    work page doi:10.1016/j.renene.2015.12.031 2016

  3. [3]

    Validation of models that estimate the clear sky global and beam solar irradiance,

    P. Ineichen, “Validation of models that estimate the clear sky global and beam solar irradiance,” Solar Energy, vol. 132, pp. 332–344, 2016. [Online]. Available: http://dx.doi.org/10.1016/j.solener.2016.03.017

    work page doi:10.1016/j.solener.2016.03.017 2016

  4. [4]

    PVLIB Python 2015,

    W. F. Holmgren, R. W. Andrews, A. T. Lorenzo, and J. S. Stein, “PVLIB Python 2015,” 2015 IEEE 42nd Photovoltaic Specialist Conference, PVSC 2015, pp. 1–5, 2015

    work page 2015

  5. [5]

    Generalized Low Rank Models

    M. Udell, C. Horn, R. Zadeh, and S. Boyd, “Generalized Low Rank Models,” Foundations and Trends in Machine Learning , vol. 9, no. 1, pp. 1–118, 2016. [Online]. Available: http://arxiv.org/abs/1410.0342

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  6. [6]

    A new airmass independent formulation for the linke turbidity coefficient,

    P. Ineichen and R. Perez, “A new airmass independent formulation for the linke turbidity coefficient,” Solar Energy, vol. 73, no. 3, pp. 151–157, 2002

    work page 2002

  7. [7]

    A broadband simplified version of the Solis clear sky model,

    P. Ineichen, “A broadband simplified version of the Solis clear sky model,” Solar Energy, vol. 82, no. 8, pp. 758–762, 2008

    work page 2008

  8. [8]

    The approximation of one matrix by another of lower rank,

    C. Eckart and G. Young, “The approximation of one matrix by another of lower rank,” Psychometrika, vol. 1, no. 3, pp. 211–218, 1936

    work page 1936

  9. [9]

    Convex optimization short course: Quantile regression,

    S. Boyd, S. Diamond, and J. Park, “Convex optimization short course: Quantile regression,” 2016, retreived May 1, 2018. [Online]. Available: http://nbviewer.jupyter.org/github/cvxgrp/cvx short course/ blob/master/applications/quantile regression.ipynb

    work page 2016

  10. [10]

    Kolmogorov-smirnov test,

    R. H. C. Lopes, “Kolmogorov-smirnov test,” in International Encyclopedia of Statistical Science, M. Lovric, Ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011, pp. 718–720. [Online]. Available: https://doi.org/10.1007/978-3-642-04898-2 326

    work page doi:10.1007/978-3-642-04898-2 2011

  11. [11]

    CVXPY: A Python-embedded modeling lan- guage for convex optimization,

    S. Diamond and S. Boyd, “CVXPY: A Python-embedded modeling lan- guage for convex optimization,” Journal of Machine Learning Research, vol. 17, no. 83, pp. 1–5, 2016

    work page 2016

  12. [12]

    [Online]

    MOSEK ApS, MOSEK: Interior-point optimizer for linear, quadratic and conic problems, 2017. [Online]. Available: https://www.mosek.com/

    work page 2017

  13. [13]

    Interior-point methods,

    S. Boyd and L. Vandenberghe, “Interior-point methods,” in Convex Optimization. New York, NY , USA: Cambridge University Press, 2004, pp. 561–622

    work page 2004

  14. [14]

    Hashing for Similarity Search: A Survey

    S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Foundations and Trends in Machine Learning, vol. 3, no. 1, pp. 1–122, 2011. [Online]. Available: http://arxiv.org/abs/1408.2927

    work page internal anchor Pith review Pith/arXiv arXiv 2011