Hole-Ice Modelling in IceCube

• Hole-Ice Modelling is the representation of optical properties in the refrozen drill holes around IceCube DOMs, characterized by a clear outer ice and a scattering bubbly central column.
• The modelling employs both explicit geometric representations and effective angular sensitivity approaches to address complexities such as cable shadowing and sensor offset.
• Calibration studies demonstrate that incorporating detailed hole-ice parameters significantly improves photon propagation simulations and the fidelity of local versus bulk-ice models.

Searching arXiv for recent and foundational IceCube hole-ice and ice-modelling papers to ground the article. Hole-ice modelling denotes the representation of the optical properties of the refrozen drill holes surrounding IceCube optical sensors, and of the associated sensor-local geometry that modifies photon emission and detection relative to propagation in undisturbed glacial bulk ice. In IceCube, this problem is distinct from kilometer-scale bulk-ice modelling because every photon emitted by a flasher LED or detected by a Digital Optical Module (DOM) must traverse the local refrozen medium immediately around the sensor. The literature represented here converges on a detector-local picture in which the refrozen hole is not optically homogeneous, and in which sensor orientation, DOM offset, cable shadowing, and effective angular acceptance are tightly coupled to the hole-ice description (Chirkin, 2021, Fiedlschuster, 2019). At the same time, recent bulk-ice work shows that some azimuthal asymmetries in calibration data are better explained by birefringent polycrystalline bulk ice rather than by local hole-ice effects, making the separation between local and bulk systematics a central methodological requirement (Rongen et al., 2021).

1. Physical basis and detector-local optical environment

Hole ice is the refrozen water in the deployment holes made by hot water drill around IceCube DOMs. The optical distinction between hole ice and bulk ice is fundamental: the bulk ice is the deep South Pole glacial medium that governs large-scale propagation, whereas hole ice is the sensor-local refrozen medium that governs the last tens of centimeters before detection and the first tens of centimeters after emission (Fiedlschuster, 2019).

The most explicit physical picture in the cited literature is provided by the calibration study of local ice and sensor properties. There, the refrozen hole is described as a two-component structure inferred from camera images: a highly scattering bubbly central column and a surrounding region of optically very clear refrozen ice (Chirkin, 2021). The qualitative freezing scenario is that dissolved gases, bubbles, and impurities are pushed inward during re-freezing and become concentrated in the center, while the remaining refrozen volume becomes unusually clear. The same study states that the bubbly ice often blocks one or several of the calibration LEDs in every optical sensor and significantly distorts the angular profile of the calibration light pulses, while also affecting the sensors’ response to incoming photons at different locations and directions (Chirkin, 2021).

This detector-local structure matters because hole ice acts on both sides of the optical problem. On the emitter side, flasher LEDs emit from inside or adjacent to the refrozen medium, so a bubbly column can block, scatter, or randomize the calibration light. On the receiver side, photons arriving from the bulk ice can have their local direction distribution modified before reaching the PMT, thereby changing the DOM’s angular response. The literature therefore treats hole ice not as a minor perturbation but as a local transport medium coupled to DOM acceptance, calibration, and reconstruction (Chirkin, 2021, Fiedlschuster, 2019).

2. Geometric models and parameterizations

The preferred explicit local model in the calibration literature is a clear refrozen hole plus a narrow bubbly central column. Camera-motivated scale estimates are given as a refrozen-hole diameter of about $1.5$ times the DOM diameter and a bubbly central column diameter of about $1/2$ of the DOM diameter (Chirkin, 2021). The DOM is not assumed to be centered. Rather, the camera observations suggest that the DOM-sized module was touching the wall of the refrozen hole on one side, while the bubbly central column covered roughly a quarter of the DOM on the opposite side. This geometry motivates a transverse offset between DOM center and column center.

The dominant fitted optical parameter in that model is the bubbly-column effective scattering length. The reported best-fit value is approximately $3\ \mathrm{cm}$, with only slight depth dependence, and the authors state that an average of $3\ \mathrm{cm}$ describes the full depth range well (Chirkin, 2021). Because bubbly-column width and effective scattering length are correlated, the cited study fixes the column diameter and fits only the scattering length.

The direct-propagation work adopts a broader cylindrical formalism. Hole ice is represented as one or more cylindrical volumes aligned with the $z$-axis, each with its own center position in $x,y$, optional $z$-range, radius, scattering length, and absorption length (Fiedlschuster, 2019). This permits the representation of the whole drill-hole refreeze column, an inner bubble column, opaque cables modeled as instant-absorbing cylinders, and shifted geometries relative to the DOM. That paper also cites camera observations supporting a relatively clear outer refrozen column and an inner bubble column with much shorter scattering length and diameter about $16\ \mathrm{cm}$ (Fiedlschuster, 2019).

A long-standing alternative to explicit geometry has been an effective DOM angular-acceptance treatment. In that formalism, hole ice is folded into a one-dimensional acceptance curve $a_{\text{DOM,HI}}(\eta)$, where $\eta$ is the photon polar incidence angle measured from below (Fiedlschuster, 2019). The nominal and hole-ice-modified acceptance curves are represented as tenth-order polynomials in $1/2$0: $1/2$1 The key limitation of this effective approach is that it is azimuthally symmetric. Once the DOM is displaced relative to the hole-ice structure, the response becomes azimuthally asymmetric, which no purely polar-angle acceptance can represent (Fiedlschuster, 2019).

3. Sensor geometry, cable shadowing, and effective asymmetry

Hole-ice modelling in IceCube is inseparable from local sensor geometry. Each DOM contains a PMT and a flasher board with 12 LEDs: LEDs $1/2$2–$1/2$3 point $1/2$4 upward, LEDs $1/2$5–$1/2$6 point horizontally, the LEDs are placed in azimuthal pairs at $1/2$7 increments, most emit around $1/2$8, and the nominal beam width is about $1/2$9 RMS (Chirkin, 2021). Because the hole-ice effect is highly localized in azimuth, the exact DOM orientation determines which LEDs or PMT acceptance regions are shadowed by the bubbly column or cable.

Using the single-LED flasher data set, the local-ice calibration study reconstructs the azimuthal orientation of each DOM by simulating each LED with its measured lab angular profile and scanning the DOM azimuth. The 12 likelihood curves per DOM align after $3\ \mathrm{cm}$0 shifts, and the combined likelihood is well fitted by a sinusoidal function. The best azimuth is determined with about $3\ \mathrm{cm}$1 RMS uncertainty (Chirkin, 2021). This also fixes the nominal cable side, since the cable was nominally routed between LEDs 11 and 12.

Cable shadowing is treated as a distinct but coupled detector-local asymmetry. It creates azimuthally localized photon deficits on the covered side and can be approximated as a straight cylinder or with a more realistic curved geometry (Chirkin, 2021). However, the cited studies agree that cable shadow alone is insufficient to explain the strongest calibration asymmetries. The direct-propagation study reports that observed peak suppression is about $3\ \mathrm{cm}$2, whereas cable-only simulations make it implausible that the cable alone can cause the effect (Fiedlschuster, 2019). The local-ice calibration work similarly distinguishes cable-only deficits from bubbly-column behavior, because the latter produces not only shadowing but also pronounced enhancement on the opposite side through direction randomization or reflection (Chirkin, 2021).

This asymmetry led to an effective “DOM tilt” description for fast simulation. When using oversized DOMs, explicit local geometry cannot be represented faithfully, so the asymmetry induced by hole ice is absorbed into an effective angular sensitivity evaluated relative to a tilted DOM axis rather than the nominal vertical (Chirkin, 2021). In that effective treatment, acceptance is lowered for photons arriving from the direction into the PMT and raised for photons arriving from the opposite direction. The cited paper notes that similar tilt distributions appear both when fitting the effective model and when using nominal-size DOMs with explicit bubbly-column simulation, and regards this as puzzling and still under study (Chirkin, 2021).

4. Calibration observables and inference methodology

The decisive calibration observable for local hole-ice studies is the single-LED flasher run, in which each LED on each working DOM flashes one at a time (Chirkin, 2021). This differs from older all-purpose flasher configurations in which several LEDs flashed simultaneously, smearing azimuthal information. Single-LED data are unusually sensitive to hole ice because each LED should produce a narrow, known emission pattern; if an LED is blocked by local bubbly ice, the observed pattern changes strongly. The literature reports that matched tilted and horizontal LED pairs at the same azimuth often show similarly anomalous behavior, consistent with both lying behind the bubbly column (Chirkin, 2021).

The calibration strategy in the most detailed local-ice study is staged. First, DOM azimuthal orientation is fitted. Second, cable-shadow consistency is checked. Third, the bubbly-column scattering length is scanned in a receiver-side study, yielding the best value of $3\ \mathrm{cm}$3. Fourth, the offset of the bubbly column relative to the DOM is scanned on a grid of about 61 roughly uniformly spaced points on a circle. Fifth, an effective DOM tilt direction is fitted on a 642-point icosahedral grid. Finally, per-DOM overall sensitivity normalization factors are fitted, with an RMS spread of about $3\ \mathrm{cm}$4 in relative in-ice sensitivities (Chirkin, 2021).

A distinctive element of that inference scheme is the emitter-side versus receiver-side decomposition. To isolate effects on photon detection by the receiving DOM, the bubbly column is simulated only for photons with age greater than $3\ \mathrm{cm}$5. To isolate effects on emitted calibration light, the column is simulated only for photons with age less than $3\ \mathrm{cm}$6 from emission (Chirkin, 2021). This separation allows the same data to constrain how the column distorts LED emission patterns and how it modifies DOM response to incoming photons.

The likelihood metric is denoted $3\ \mathrm{cm}$7, described as akin to the saturated Poisson likelihood and summed over about 60,000 LEDs, with a built-in assumption that data and best-fit simulation may still disagree at about the $3\ \mathrm{cm}$8 model-error level (Chirkin, 2021). When emitter-side and receiver-side scans of DOM position relative to the bubbly column are combined, the likelihood at each scan point is smoothed using weights

$3\ \mathrm{cm}$9

with fitted regularization parameter

$3\ \mathrm{cm}$0

The smoothed minimum gives the inferred relative DOM–column position (Chirkin, 2021).

The direct-propagation study uses complementary statistical machinery. For angular-acceptance scans it defines

$3\ \mathrm{cm}$1

and compares simulated acceptance curves to reference curves with a binomial likelihood summarized through $3\ \mathrm{cm}$2 (Fiedlschuster, 2019). For flasher calibration it uses a Poisson likelihood and a finite-MC extension from Glüsenkamp (Fiedlschuster, 2019). The methodological commonality across these approaches is that hole-ice modelling is inferred from detector-wide discrepancies in directional light yield and timing rather than from a direct optical measurement of the refrozen medium alone.

5. Direct propagation, effective acceptance, and simulation regimes

The direct-propagation program reframed hole ice as a true local optical medium. In standard IceCube photon propagation, photons are not stepped by tiny $3\ \mathrm{cm}$3; instead, the code samples the number of interaction lengths to the next scattering or absorption event and converts that budget to geometric distance. The cited work generalizes this machinery so that hole-ice cylinders are treated on the same footing as ice layers (Fiedlschuster, 2019). The governing relation is

$3\ \mathrm{cm}$4

where $3\ \mathrm{cm}$5 is the geometric distance, $3\ \mathrm{cm}$6 the sampled number of interaction lengths, and $3\ \mathrm{cm}$7 the interaction length in medium $3\ \mathrm{cm}$8 (Fiedlschuster, 2019).

The main implementation, termed Algorithm B in the source material, builds an ordered list of medium boundaries along the current ray, including both ice-layer boundaries and cylinder entry and exit points, then spends scattering and absorption budgets segment by segment according to local material properties (Fiedlschuster, 2019). This supports absolute cylinder scattering and absorption lengths, multiple cylinders, nested or overlapping cylinders, cables, and off-center geometries. What it does not yet reimplement are tilted ice layers, absorption anisotropy, and ice anisotropy (Fiedlschuster, 2019).

The physical background of this formulation uses standard IceCube optical transport quantities. The effective scattering length is given by

$3\ \mathrm{cm}$9

with $z$0 assumed for South Pole ice, and the same scattering-angle behavior assumed inside hole ice as in bulk ice (Fiedlschuster, 2019). The cited paper also reproduces the bulk-ice wavelength dependence

$z$1

with $z$2, and the bulk absorption parameterization $z$3, together with $z$4 (Fiedlschuster, 2019). These expressions are bulk-ice ingredients, but they matter because direct hole-ice propagation must be embedded in the broader optical simulation chain.

The direct-propagation work reaches a strong methodological conclusion about the mismatch between explicit local transport and older effective approximations. The standard hole-ice effective acceptance curve historically associated with an H2 model with hole-ice radius $z$5 and geometric scattering length $z$6 is not reproduced by direct propagation with those same physical parameters (Fiedlschuster, 2019). The best direct match to the standard approximation curve is reported instead for hole-ice radius $z$7 and effective hole-ice scattering length $z$8 (Fiedlschuster, 2019). The paper therefore concludes that the hole-ice approximation used in the standard simulation chain should be recalculated with a new direct-simulation run.

This produces two practical simulation regimes. In detailed simulation with nominal-size DOMs, the recommended representation is explicit geometry: clear refrozen hole, central bubbly column, fitted DOM offset, known azimuthal orientation, and cable shadowing (Chirkin, 2021). In fast production with oversized DOMs, the recommended representation is effective angular sensitivity or effective DOM tilt informed by the explicit calibration (Chirkin, 2021). The direct-propagation literature does not reject effective approximations outright, but argues that they should be re-derived from modern direct simulations rather than inherited from older assumptions (Fiedlschuster, 2019).

6. Empirical results, bulk-ice disentangling, and reconstruction significance

The local-ice calibration study quantifies the detector-wide improvement obtained by progressively enriching the model. Starting from the bulk-ice model of Ref. [bfr], the baseline values are

$z$9

Adding the full hole-ice description gives

$x,y$0

Adding fitted in-ice DOM sensitivities gives

$x,y$1

Adding tilt gives

$x,y$2

With nominal-size DOMs the reported values are

$x,y$3

These results indicate that hole ice alone gives a modest but real improvement, and that its strongest practical effect emerges when combined with per-DOM sensitivity and tilt calibration (Chirkin, 2021).

The direct-propagation study reports a complementary phenomenology. Strong local hole-ice shielding is plausible, radius and scattering length control different aspects of the response, off-center geometry creates strong azimuthal asymmetry, and cable shadow alone is too weak to explain the observed calibration asymmetry (Fiedlschuster, 2019). A preliminary 7-string flasher fit in that study gives a best fit at

$x,y$4

but the author explicitly characterizes this as a proof of concept because of large systematics, including outdated DOM positions, outdated bulk-ice model, no ice tilt or anisotropy in the new propagation, the assumption that all DOMs are centered in hole ice, and the exclusion of two asymmetrically suppressed strings (Fiedlschuster, 2019).

A crucial development in the broader ice-modelling program is the identification of bulk birefringent transport as a source of azimuthal asymmetry that had previously resisted simpler explanations. The anisotropy paper does not model hole ice, drill-hole ice, bubble columns, cable shadowing, or DOM angular acceptance distortions from local ice (Rongen et al., 2021). Instead, it attributes a major class of azimuth-dependent attenuation to light deflection resulting from asymmetric diffusion in the birefringent polycrystalline microstructure of the ice. The final bulk model combines anisotropic absorption with light deflection resulting from propagation through the birefringent ice polycrystal and achieves excellent data-MC agreement in flasher timing and intensity (Rongen et al., 2021). For hole-ice modelling, the importance of this result is diagnostic: azimuthal residuals correlated with ice-flow direction should not be prematurely absorbed into local hole-ice nuisance terms.

The same bulk-ice paper outlines how the IceCube Upgrade could improve this separation. It discusses over 700 additional modules on seven strings, a number of stand-alone calibration devices, and especially eleven Pencil Beam devices that allow a laser-like beam to be directed in arbitrary directions (Rongen et al., 2021). The key predicted signature is that the emission direction of maximum received intensity is offset from the geometric direction of the receiver, enabling sweeps over receiver directions to disentangle absorption and birefringence contributions to the anisotropy at high precision (Rongen et al., 2021). This is not a hole-ice model per se, but it directly bears on hole-ice inference by constraining bulk propagation more cleanly.

A recent Upgrade proceedings item titled "Impact of Hole-ice Calibration on High Energy Event Reconstruction with the IceCube Upgrade" (Dutta et al., 9 Jul 2025) indicates that hole ice remains a recognized issue for directional reconstruction and source sensitivity. However, the provided document contains no substantive body text, no model, no equations, no calibration description, and no quantitative results on reconstruction or sensitivity. In the present literature set, it therefore serves only as evidence that hole-ice calibration is an active Upgrade topic, not as a source of extractable technical content (Dutta et al., 9 Jul 2025).

7. Limitations, unresolved issues, and current status

Several limitations recur across the literature. First, the explicit local model is intentionally simple: one bubbly column plus clear ice, rather than a full microphysical freeze model (Chirkin, 2021). Second, column diameter and scattering length are correlated, so one is often fixed while the other is fitted (Chirkin, 2021). Third, effective DOM tilt reproduces local asymmetry well in fast simulation, but the reason its fitted distribution resembles the result of explicit local-ice simulation is not fully understood (Chirkin, 2021).

The direct-propagation framework also has explicit omissions. It does not yet reimplement tilted ice layers, absorption anisotropy, or ice anisotropy (Fiedlschuster, 2019). That limitation is particularly relevant because the bulk-ice literature now shows that anisotropy can arise from birefringent polycrystalline transport rather than from local detector effects (Rongen et al., 2021). A plausible implication is that earlier local fits may have absorbed part of a bulk residual if the propagation model was incomplete, although the cited papers do not quantify such leakage.

Another unresolved issue concerns the relation between physical geometry and effective acceptance. The direct-propagation study shows that the standard IceCube hole-ice approximation disagrees with all existing direct-propagation methods and should be recalculated with a new direct-simulation run (Fiedlschuster, 2019). The calibration study, by contrast, demonstrates that an effective tilted angular acceptance can nonetheless be operationally useful for oversized-DOM simulation when informed by explicit geometry (Chirkin, 2021). These positions are not contradictory: one concerns the need for recalibration of effective models, the other concerns their practical use once recalibrated.

The current status of hole-ice modelling is therefore two-level. At the physical level, the best-supported detector-local description in the cited literature is a clear refrozen hole plus a highly scattering bubbly central column, with non-negligible DOM offset, cable shadowing, and per-DOM geometry calibration (Chirkin, 2021). At the simulation level, two representations coexist: explicit local-medium propagation for maximal physical fidelity and effective angular-sensitivity or tilt models for computationally efficient large-scale production (Fiedlschuster, 2019, Chirkin, 2021). The broader optical-modelling program adds a third requirement: hole-ice inference must be conducted jointly with improved bulk-ice modelling, especially for anisotropy, so that local and non-local optical systematics are not conflated (Rongen et al., 2021).