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arxiv: 2604.18207 · v1 · submitted 2026-04-20 · 📡 eess.SP

A Novel Piecewise Atmospheric Attenuation Model for Free Space Optical Links in Vertical Heterogeneous Networks

Eylem Erdogan , Mohammed Elamassie , Ibrahim Altunbas , Gunes Karabulut Kurt , Murat Uysal , Halim Yanikomeroglu This is my paper

Pith reviewed 2026-05-10 04:05 UTC · model grok-4.3

classification 📡 eess.SP
keywords free-space opticalatmospheric attenuationvertical heterogeneous networkspiecewise attenuation modelcumulative power lossaerosols fog rain cloudszenith anglelink budget
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The pith

A piecewise model provides a unified estimate of atmospheric power loss for vertical free-space optical links by incorporating multiple weather phenomena and the zenith angle.

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

This paper develops a new model to calculate the total attenuation experienced by optical signals traveling vertically through the atmosphere in networks that connect ground stations to aerial and space platforms. It adds together the effects of aerosols, fog, rain, cloud layers, and drizzle while accounting for the angle from the zenith to estimate cumulative power loss. Conventional models often treat these conditions in isolation, which can lead to inaccurate predictions along slant paths. The authors show that their model produces results within 1 dB of detailed layer-by-layer simulations across various weather conditions, offering a practical tool for designing reliable optical links.

Core claim

The paper claims that instead of simplified single-coefficient models, a unified attenuation model can incorporate aerosols, fog, rain, cloud layers, and drizzle, account for the zenith angle, and provide a holistic estimate of the cumulative power loss across atmospheric layers, with the difference between model predictions and layer-resolved MODTRAN simulations remaining within 1 dB.

What carries the argument

The unified piecewise atmospheric attenuation model that sums individual contributions from different phenomena and adjusts for zenith angle to yield total power loss.

If this is right

  • Attenuation shows variations of several decibels across representative weather scenarios.
  • The model offers a practical way to estimate cumulative power loss for link budget studies in vertical heterogeneous networks.
  • Predictions remain accurate within 1 dB compared to detailed simulations.

Where Pith is reading between the lines

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

  • The additive piecewise approach might be extended to include dynamic weather changes over time for real-time link adaptation.
  • Engineers could use this model to compare optical performance against radio frequency alternatives in mixed vertical networks.
  • Further validation in actual field deployments with mixed atmospheric conditions would strengthen confidence in the model's accuracy.

Load-bearing premise

Individual attenuation contributions from different atmospheric phenomena can be combined in a simple additive manner without significant nonlinear interactions or layer-specific coupling effects.

What would settle it

A measurement campaign along a vertical optical path in a mixed weather event that records a total attenuation exceeding the model's prediction by more than 1 dB would disprove the unified model's accuracy.

Figures

Figures reproduced from arXiv: 2604.18207 by Eylem Erdogan, Gunes Karabulut Kurt, Halim Yanikomeroglu, Ibrahim Altunbas, Mohammed Elamassie, Murat Uysal.

Figure 1
Figure 1. Figure 1: Characteristics of atmospheric aerosols with respect to altitude. phenomena attenuation profile, we develop an end-to-end cascade extension of the BL law that partitions the link into altitude slabs, incorporates zenith-angle, and models probabilistic multi-state layer occurrence. This unified formulation goes beyond common treatments that consider these effects separately or rely on a single path-averaged… view at source ↗
Figure 2
Figure 2. Figure 2: Altitude and vertical extent information about aerosol models in the considered scenarios. of ground stations or transmitter/receiver mobility. Above the cloud formations, the weather is clear up to the edge of the troposphere with a vertical extent of ∆L2 = 14.2 km and occurrence probability is set to η2 = 1. In the stratosphere, optical beam can be affected either from sulfuric acid ingredients due to hi… view at source ↗
Figure 3
Figure 3. Figure 3: Transmittance vs wavelength for Scenarios 1, 2, 3, 4 and 5 when the zenith angle is taken as ζ = 10◦ . Zenith angle ζ [deg] 0 10 20 30 40 50 60 70 80 Transmittance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Clear weather Snowy weather Extreme air pollution Foggy weather Rainy weather 0 10 20 30 40 50 0 1 2 3×10-3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Transmittance vs zenith angle for Scenarios 1, 2, 3, 4 and 5 when the wavelength is set to λ = 1550 nm. snow crystals are concentrated in the lowest 2 km of the troposphere. Visibility can drop from 10–15 km under normal cold-cloud conditions to below 0.5 km when the snowfall rate exceeds 2 mm h−1 . Consistent with this classification, Awan et al. [8] report 100–150 m visibilities for 3–5 mm h−1 events ove… view at source ↗
read the original abstract

Free-space optical (FSO) communication is emerging as a key backhaul technology for next-generation vertical heterogeneous networks (VHetNets), whose architecture spans satellites, high-altitude platform stations (HAPS), unmanned aerial vehicles (UAVs), and terrestrial nodes. Along these vertical and slant paths, optical beams traverse successive atmospheric layers that may contain clouds, fog, rain, and aerosols, conditions that conventional single-coefficient Beer-Lambert models typically handle only in isolation. Instead of such simplified formulas, we present a unified attenuation model that incorporates aerosols, fog, rain, cloud layers, and drizzle, accounts for the zenith angle, and provides a holistic estimate of the cumulative power loss across atmospheric layers. Numerical results show several-decibel attenuation variations across representative weather scenarios, while the difference between the proposed model predictions and the layer-resolved MODTRAN simulations remains within 1 dB, thereby validating the accuracy of the proposed model and its practical relevance for VHetNet link-budget studies.

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 / 1 minor

Summary. The manuscript proposes a unified piecewise atmospheric attenuation model for free-space optical links in vertical heterogeneous networks (VHetNets). It assembles contributions from aerosols, fog, rain, cloud layers, and drizzle, incorporates zenith-angle dependence for slant paths, and computes cumulative power loss across successive atmospheric layers. Numerical results illustrate several-dB variations across weather scenarios, and the model predictions are reported to agree with layer-resolved MODTRAN simulations to within 1 dB.

Significance. If the piecewise additive construction and validation hold, the model supplies a practical, low-complexity tool for link-budget estimation in satellite-to-ground, HAPS, and UAV FSO links, where conventional Beer-Lambert single-coefficient formulas are inadequate for vertically heterogeneous paths. The reported 1 dB agreement with MODTRAN would constitute a useful engineering approximation for VHetNet system design.

major comments (2)
  1. [Model formulation and validation sections] The central claim of a 'unified' model rests on the piecewise assembly of previously published attenuation formulas and their additive combination across layers. The manuscript must supply the explicit cumulative-loss expression (including how zenith-angle scaling and path lengths are applied per layer) and the precise criteria used to join segments at layer boundaries; without these, the 1 dB MODTRAN agreement cannot be independently verified and the additivity assumption remains untested for co-located phenomena.
  2. [Numerical results and MODTRAN comparison] The validation reports agreement within 1 dB for selected weather scenarios, yet provides no evidence that the same additive construction remains accurate when multiple attenuators (e.g., fog and rain) occupy the same layer or when zenith angles produce long slant paths through overlapping regimes. A direct test of the additivity hypothesis under such conditions is required to support the claim that nonlinear interactions are negligible.
minor comments (1)
  1. [Abstract] The abstract states 'several-decibel attenuation variations' but does not quantify the range or identify the dominant contributor; a table or figure summarizing per-component losses for each scenario would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below with clarifications and indicate the revisions we will make to strengthen the presentation and validation.

read point-by-point responses

  1. Referee: [Model formulation and validation sections] The central claim of a 'unified' model rests on the piecewise assembly of previously published attenuation formulas and their additive combination across layers. The manuscript must supply the explicit cumulative-loss expression (including how zenith-angle scaling and path lengths are applied per layer) and the precise criteria used to join segments at layer boundaries; without these, the 1 dB MODTRAN agreement cannot be independently verified and the additivity assumption remains untested for co-located phenomena.

    Authors: We agree that an explicit cumulative-loss expression and clear joining criteria are required for independent verification. The manuscript describes the piecewise construction and zenith-angle dependence in Section II, but we acknowledge that the full summation formula and layer-boundary rules could be stated more compactly. In the revised manuscript we will insert a dedicated paragraph (new Eq. (3)) giving L_cum = sum_i [ (alpha_aerosol,i + alpha_fog,i + alpha_rain,i + alpha_cloud,i + alpha_drizzle,i) * d_i * sec(theta) ], where d_i is the geometric thickness of layer i and theta is the zenith angle, together with the explicit altitude thresholds used to delineate the layers (0-2 km fog/rain, 2-12 km clouds, etc.). This addition will allow direct reproduction of the reported 1 dB agreement. revision: yes

  2. Referee: [Numerical results and MODTRAN comparison] The validation reports agreement within 1 dB for selected weather scenarios, yet provides no evidence that the same additive construction remains accurate when multiple attenuators (e.g., fog and rain) occupy the same layer or when zenith angles produce long slant paths through overlapping regimes. A direct test of the additivity hypothesis under such conditions is required to support the claim that nonlinear interactions are negligible.

    Authors: The current numerical results focus on representative combined-weather cases, but we accept that they do not explicitly isolate co-located attenuators or extreme slant paths. To address this directly, the revised manuscript will include two new figures and accompanying text that test the additive model against layer-resolved MODTRAN for (i) simultaneous fog and rain within the same 0-2 km layer and (ii) zenith angles of 45° and 60°. These additional comparisons will demonstrate that the discrepancy remains within 1 dB, thereby providing the requested evidence that nonlinear interactions are negligible under the modeled conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: piecewise model combines literature formulas and validates externally against MODTRAN

full rationale

The derivation assembles known per-phenomenon attenuation expressions (aerosols, fog, rain, clouds, drizzle) into a zenith-angle-aware sum and reports agreement with independent layer-resolved MODTRAN simulations to within 1 dB. No equations reduce a claimed prediction to a fitted parameter or prior result by construction, no load-bearing self-citation chain is evident, and the additivity assumption is presented as an engineering approximation rather than a tautology. The result is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that standard single-phenomenon attenuation models remain valid when stitched together; no new free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Attenuation from distinct atmospheric phenomena (aerosols, fog, rain, clouds, drizzle) can be combined additively in piecewise segments without significant cross-effects.
    Invoked when the model is described as incorporating all listed conditions into one holistic estimate.
  • domain assumption Zenith angle dependence can be incorporated via a simple scaling or adjustment factor applied to the base attenuation.
    Stated as part of the unified model that accounts for zenith angle.

pith-pipeline@v0.9.0 · 5496 in / 1419 out tokens · 27361 ms · 2026-05-10T04:05:46.624534+00:00 · methodology

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Reference graph

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