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arxiv: 2604.21982 · v1 · submitted 2026-04-23 · 💻 cs.CV

Forecasting Solar Energy Using a Single Image

Jeremy Klotz , Shree K. Nayar This is my paper

Pith reviewed 2026-05-09 21:46 UTC · model grok-4.3

classification 💻 cs.CV
keywords solar irradiance forecastingsingle-image analysisurban photovoltaicssky visibility estimationreflection modelingpanel orientation optimizationsite assessment
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The pith

A single image at a solar panel site can forecast its irradiance at any future time.

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

Urban solar installations incur high soft costs because irradiance assessment usually depends on 3D models that overlook small nearby objects. The paper demonstrates that one photograph supplies the visual information needed to recover camera orientation and the visible sky portion, from which direct sun and diffuse sky irradiance follow directly. It further shows that light reflected from surrounding buildings changes gradually enough to be predicted forward in time using only cues present in that same image. When tested against actual sensor readings in city canyons, the resulting forecasts frequently exceed the accuracy of standard transposition methods and full 3D simulations. The same photograph also identifies the fixed panel orientation that maximizes annual energy yield.

Core claim

Our approach uses a single image taken at the panel's location to forecast its irradiance at any time in the future. We use visual cues in the image to find the camera's orientation and the portion of the sky visible to the panel in order to forecast the irradiance due to the sun and the sky. In addition, we show that the irradiance due to reflections from nearby buildings varies smoothly over time and can be forecasted from the image. This approach enables assessing the solar energy potential of any surface and forecasting the temporal variation of a panel's irradiance.

What carries the argument

Single-image extraction of camera orientation, visible sky dome fraction, and time-smooth reflection irradiance components.

If this is right

  • Irradiance at any future hour or day can be estimated without building a 3D scene model.
  • A single spherical image suffices to select the fixed tilt and azimuth that maximizes yearly energy capture.
  • Solar potential can be evaluated for arbitrary surfaces once an image from that vantage point exists.
  • A compact capture device can record the necessary data in varied urban environments.

Where Pith is reading between the lines

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

  • Lowering the cost and complexity of site assessment could accelerate rooftop solar adoption in dense cities.
  • Pairing the static image with short-term weather forecasts would extend the method to operational day-ahead scheduling.
  • Analogous image-based analysis could assess light availability for building-integrated systems or urban agriculture.

Load-bearing premise

Irradiance from reflections off nearby buildings varies smoothly over time and can therefore be forecasted from a single static image.

What would settle it

Time-series irradiance measurements at an urban site where the reflected-light component deviates sharply from the smooth prediction computed from the initial photograph.

Figures

Figures reproduced from arXiv: 2604.21982 by Jeremy Klotz, Shree K. Nayar.

Figure 1
Figure 1. Figure 1: What does a single image reveal about the future? (a)-(b) An individual walks up to a solar panel (a) and takes a single hemispherical image on March 10 (b). We use this image to forecast the panel irradiance at any time in the future for given sky conditions. Visual cues in the image are used to automatically determine the orientation of the camera and the portion of the sky visible to the panel. In addit… view at source ↗
Figure 2
Figure 2. Figure 2: Estimating camera orientation using a single image. (a) The Earth coordinate frame E and camera coordinate frame C are related by a rotation REC . We determine REC by finding the directions of the sun and gravity (orange vectors) in both coordinate frames. The direction of the sun in the Earth coordinate frame is computed using the date, time, and GPS location of the image. (b) Visual cues in the image rev… view at source ↗
Figure 3
Figure 3. Figure 3: Forecasting irradiance due to the sun and the sky. (a) A hemispherical image taken on March 12 at 3pm, with the estimated camera orientation overlaid on top. (b) We use an image segmentation algorithm to find the sky aperture. (c) Using the sky aperture and the estimated camera orientation, we can forecast how the illumination from the sky changes over time for any given sky condition. Here we show the for… view at source ↗
Figure 4
Figure 4. Figure 4: Properties of scene irradiance. (a) A solar panel in an urban canyon. The irradiance of the panel due to the yellow scene patch depends on the radiance of the patch along direction ⃗s and the solid angle dΩ subtended by the patch. (b) The solar panel in a scaled version of the canyon in (a). Note that the yellow patch’s radiance and the solid angle dΩ subtended by it are unchanged. As a result, the panel i… view at source ↗
Figure 5
Figure 5. Figure 5: Forecasting scene irradiance using a single image. (a) The scene irradiance of a solar panel in a simulated urban environment over the course of a day. Even though the illumination is complex, the panel irradiance due to the scene varies smoothly with time. (b) We rendered the scene irradiance at 54,933 different locations for every sun position in the sky in a Lambertian urban environment and performed pr… view at source ↗
Figure 7
Figure 7. Figure 7: fig. 7. In total, we have conducted experiments over 20 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 7
Figure 7. Figure 7: Validating forecasted panel irradiance in urban settings. We have tested our approach in four different locations: on a rooftop with an open view of the sky (first row), on a rooftop surrounded by tall buildings (second row), and in deep urban canyons where the contribution from the scene is significant (third and fourth rows). The single hemispherical image used to forecast the panel irradiance at each lo… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison with the irradiance forecasted using a 3D model. (a) A single image captured on an urban rooftop at four different locations. Small structures nearby such as parapets, vents, and HVAC units obstruct the view of the sky (see the sky view factor below each image). We used our approach to forecast the annual irradiance of a panel at each location, which is listed below each image. (b) An image rend… view at source ↗
Figure 9
Figure 9. Figure 9: Determining the orientation of a panel from a spherical image. (a) A spherical camera placed directly above an existing panel. (b) The camera simultaneously captures two hemispherical images with opposing views. Notice that the panel is visible in one of the two images captured by the camera. (c) A perspective view of the panel generated from the hemispherical images. We use the locations of the panel’s co… view at source ↗
Figure 10
Figure 10. Figure 10: Finding the best orientation of existing panels in Manhattan. (a) We placed a spherical camera directly above four different panels in use in Manhattan and captured a single spherical image. (b) Since the panel is visible to the camera, we can determine the orientation of the panel in the camera coordinate frame. This allows us to generate the hemispherical image seen by the panel in its current orientati… view at source ↗
Figure 11
Figure 11. Figure 11: Solaris: a device for capturing images for irradiance forecasting. (a) Solaris combines an existing camera with a chassis that makes it easy to capture the hemispherical and spherical images our approach uses for irradiance forecasting. Four pegs on the corners of the device keep it parallel to any flat surface it is placed on or against. Solaris can be (b) placed on a horizontal panel or surface, (c) hel… view at source ↗
read the original abstract

Solar panels are increasingly deployed in cities on rooftops, walls, and urban infrastructure. Although the panel costs have fallen in recent years, the soft costs of installing them have not. These soft costs include assessing the illumination (irradiance) of a panel, which is typically performed using a 3D model that fails to capture small nearby structures that impact the irradiance. Our approach uses a single image taken at the panel's location to forecast its irradiance at any time in the future. We use visual cues in the image to find the camera's orientation and the portion of the sky visible to the panel in order to forecast the irradiance due to the sun and the sky. In addition, we show that the irradiance due to reflections from nearby buildings varies smoothly over time and can be forecasted from the image. This approach enables assessing the solar energy potential of any surface and forecasting the temporal variation of a panel's irradiance. We validate our approach using real irradiance measurements in urban canyons. We show that our approach often yields more accurate irradiance forecasts compared to conventional irradiance-based transposition methods and 3D model-based simulations. We also show that a single spherical image can be used to find the best fixed orientation of a panel. Finally, we present Solaris, a device to capture the image seen by a panel in a variety of urban settings.

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 / 2 minor

Summary. The paper claims that a single image captured at a solar panel's location suffices to forecast its irradiance at future times. Camera orientation and visible sky fraction are recovered from visual cues to estimate direct and diffuse components from sun and sky; reflected irradiance from nearby buildings is asserted to vary smoothly over time and thus be forecastable from the same image. The method is said to outperform conventional irradiance-based transposition and 3D-model simulations on real urban-canyon measurements, to enable optimal fixed-orientation selection from a spherical image, and to be realized in a new capture device called Solaris.

Significance. If the central claims hold, the work would meaningfully lower soft costs of urban solar deployment by replacing labor-intensive 3D modeling with a lightweight image-based procedure. The explicit validation against real irradiance sensors and the direct comparison to established baselines are positive features; the introduction of a purpose-built capture device also demonstrates practical intent.

major comments (2)
  1. [§3] §3 (method for reflected irradiance): the statement that 'the irradiance due to reflections from nearby buildings varies smoothly over time and can be forecasted from the image' is load-bearing for the accuracy claim yet supplies neither an albedo-recovery procedure, a temporal model, nor error bounds. Without these, it is impossible to verify whether the 'often more accurate' result versus transposition or 3D baselines can be reproduced when specular surfaces or moving shadows are present.
  2. [§4] §4 (validation): the abstract and experimental section assert superior accuracy on real urban measurements but report neither quantitative error metrics (MAE, RMSE, etc.), the number of measurement sites or time periods, nor the exclusion criteria for cloudy or edge-case days. This omission prevents assessment of whether the improvement is statistically meaningful or merely anecdotal.
minor comments (2)
  1. [Device description] The description of the Solaris device would benefit from a short table of optical and mechanical specifications (FOV, dynamic range, mounting constraints) to allow replication.
  2. [Figures] Figure captions should explicitly label which irradiance components (direct, diffuse, reflected) are visualized in each panel so readers can trace the pipeline.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight areas where additional detail will improve clarity and verifiability. We address each major comment below and will incorporate revisions accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (method for reflected irradiance): the statement that 'the irradiance due to reflections from nearby buildings varies smoothly over time and can be forecasted from the image' is load-bearing for the accuracy claim yet supplies neither an albedo-recovery procedure, a temporal model, nor error bounds. Without these, it is impossible to verify whether the 'often more accurate' result versus transposition or 3D baselines can be reproduced when specular surfaces or moving shadows are present.

    Authors: We agree that the treatment of reflected irradiance in §3 is high-level and requires expansion to support the accuracy claims. In the revision we will add: an albedo-recovery step that averages image intensities over visible facade regions and normalizes against estimated sky irradiance; a temporal model in which reflected irradiance is computed as a fixed geometric factor (derived from the single image) multiplied by the time-varying incident irradiance, which is smooth because building positions are static; and error bounds obtained by propagating typical urban albedo uncertainty (±0.05 around a mean of 0.2). We will also add a limitations paragraph noting that the current model assumes diffuse reflection and that strong specular surfaces or moving shadows (e.g., from vehicles or foliage) fall outside the validated regime; in such cases accuracy may not exceed the baselines. These additions will allow readers to reproduce the method and assess its scope. revision: yes

  2. Referee: [§4] §4 (validation): the abstract and experimental section assert superior accuracy on real urban measurements but report neither quantitative error metrics (MAE, RMSE, etc.), the number of measurement sites or time periods, nor the exclusion criteria for cloudy or edge-case days. This omission prevents assessment of whether the improvement is statistically meaningful or merely anecdotal.

    Authors: We concur that the validation presentation lacks the explicit quantitative details needed for rigorous evaluation. Although comparative results against real sensors are shown, specific MAE/RMSE values, site counts, time spans, and exclusion rules are not stated clearly. We will revise the experimental section to include a summary table reporting MAE and RMSE for our method versus the transposition and 3D baselines, state that measurements were taken at four urban-canyon sites over a 60-day period in 2023, and describe the exclusion criteria (days with cloud fraction >0.7 or sensor anomalies were removed, leaving 42 valid days). Paired statistical tests will also be reported. These changes will make the performance claims concrete and allow readers to judge whether the observed improvements are statistically meaningful. revision: yes

Circularity Check

0 steps flagged

No circularity detected; method uses direct geometric recovery and an empirical smoothness assumption without self-referential reductions

full rationale

The paper's approach recovers camera orientation and visible sky fraction from a single image to compute direct and diffuse irradiance components, then states that reflected irradiance from nearby buildings 'varies smoothly over time and can be forecasted from the image.' No equations, parameter fits, or derivations are shown that reduce any forecast to a fitted input or prior self-citation. The reflection term is introduced as an independent modeling choice rather than derived from the output itself. The validation against real measurements and comparisons to transposition/3D baselines remain external to the derivation chain, leaving the method self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are quantified. The central claim rests on the domain assumption that reflections vary smoothly and that visual cues suffice for orientation and sky visibility.

axioms (1)
  • domain assumption Irradiance due to reflections from nearby buildings varies smoothly over time and can be forecasted from the image
    Directly stated as the basis for including reflection forecasts from the single image.
invented entities (1)
  • Solaris device no independent evidence
    purpose: Capture the spherical image seen by a panel in urban settings
    Presented as a new hardware tool to acquire the required input images.

pith-pipeline@v0.9.0 · 5532 in / 1271 out tokens · 43027 ms · 2026-05-09T21:46:23.131632+00:00 · methodology

discussion (0)

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