Main

Cosmic rays from deep space constantly bombard Earth’s atmosphere, producing copious amounts of gigaelectronvolt-to-teraelectronvolt neutrinos via hadronic interactions. Similar processes yielding higher-energy (teraelectronvolt to petaelectronvolt) neutrinos are expected when cosmic rays are accelerated and interact in violent astrophysical sources, such as in jets of active galactic nuclei (AGN)1. Ultrahigh-energy cosmic rays traversing the Universe and colliding with cosmic background photons are predicted to generate ‘cosmogenic’ neutrinos (ranging from petaelectronvolts to zettaelectronvolts)2. Detecting astrophysical neutrino sources will therefore be the key to deciphering the origin of the ultrahigh-energy cosmic rays.

The weak interactions that make neutrino detection so difficult also allow them to be used as a powerful tool. Neutrinos can escape from extremely dense environments, travelling astronomical distances without being deflected or absorbed. Neutrinos point back directly to their sources, making them a unique messenger to trace the most extreme regions of the Universe. Furthermore, neutrinos oscillate as they propagate through spacetime, transforming among their electron, muon and tau flavours (νe, νμ and ντ, respectively), due to the quantum effect known as flavour-mass mixing3. Measuring neutrino oscillation over astronomical baselines allows us to probe for new physics beyond the standard model4, and also provides new handles for tests on quantum gravity5.

Neutrinos cannot be detected directly. These ‘ghostly’ particles are measured using extremely sensitive technologies, detecting the light produced by the charged particles generated in neutrino–matter interactions. In a general detector set-up, large areas of photon sensors continuously monitor a large body of target mass, for example, pure water6, liquid scintillator7 or liquid argon8, to measure these rare and tiny energy depositions. Neutrino telescopes use massive volumes of natural sea or lake water or glacial ice to observe the low rate of interacting high-energy astrophysical neutrinos.

Theoretical calculations in 1998 suggested that a cubic-kilometre detector would be sufficiently sensitive to the high-energy neutrino flux from AGN jets or gamma-ray bursts9. The IceCube Neutrino Observatory was the first experiment to build a telescope of this scale, instrumenting the deep glacial ice at the South Pole. IceCube made major breakthroughs over its lifetime, discovering a diffuse extraterrestrial neutrino flux in 201310 and presenting compelling evidence for neutrino emission from a flaring blazar11,12 in 2017 and a Seyfert galaxy NGC 1068 in 202213. Dedicated IceCube analyses, along with measurements made by the Astronomy with a Neutrino Telescope and Abyss environmental RESearch (ANTARES) project in the Mediterranean Sea14, have been carried out to resolve the origins of the diffuse cosmic neutrino flux. A wide range of hypotheses have been considered, including all-sky spatial clustering searches15, transient searches16,17,18 and AGN catalogue stacking searches19,20, all yielding inconclusive results so far. This suggests multiple weaker sources21 may contribute to the diffuse flux, such as starburst galaxies or AGNs22, which would require better than 0.1° pointing resolution to resolve23.

Several telescopes, such as Cubic Kilometre Neutrino Telescope (KM3NeT) in the Mediterranean Sea24, Baikal Gigaton Volume Detector (Baikal-GVD) in Lake Baikal25 and the newly proposed Pacific Ocean Neutrino Experiment (P-ONE) in the East Pacific26, are currently under development. Their northern locations will complement IceCube at the South Pole, offering full coverage of the teraelectronvolt-to-petaelectronvolt neutrino sky. Light propagating in the South Pole glacial ice generally experiences long absorption lengths and short scattering lengths. Conversely, deep-sea or lake water has longer scattering lengths but shorter absorption lengths. This reduced light scattering in water allows for substantial pointing resolution improvement in both the track and cascade channels, where the latter channel has been proven to have greatly reduced contamination from atmospheric muons27,28.

This work outlines our plan to construct a next-generation neutrino telescope in the South China Sea. The Tropical Deep-sea Neutrino Telescope (TRIDENT), nicknamed Hai-Ling in Chinese (‘ocean bell’) (https://trident.sjtu.edu.cn/en), aims to rapidly discover multiple high-energy astrophysical neutrino sources and greatly boost the measurement of cosmic neutrino events of all flavours. To achieve this goal, TRIDENT will instrument a massive volume of seawater and employ precise photon timing measurement to optimize its neutrino pointing resolution. Due to Earth’s rotation and TRIDENT’s position near the Equator, the detector’s highest sensitivity band for up-going neutrinos will scan the entire sky, providing substantial visibility to all potential neutrino sources.

Results

A suitable site for constructing a deep-sea neutrino telescope demands multiple conditions. The depth should be large enough, for example, ≳3 km, to effectively shield cosmic-ray backgrounds and minimize the influence of biological activities. Experiences from the pioneering Deep Underwater Muon And Neutrino Detector (DUMAND) project (https://www.phys.hawaii.edu/dumand/dumacomp.html) suggest that a large and flat area such as an abyssal plain is preferred, and it should keep away from high rises or deep trenches to avoid complex current fields. The ocean floor should be flat and possess sufficient bearing strength to support the mounting of the equipment. On the basis of the successful operation of ANTARES for the past decade, a deep-sea neutrino telescope could safely operate under a current strength of less than ~20 cm s−1 (ref. 29). Close proximity to a shore is required to ensure the infrastructure for power supply and data transmission via seafloor cable connections.

On the basis of the above requirements, an area near 114.0° E, 17.4° N was selected as a suitable location to build a large-scale deep-sea detector. The geographic information of the site is described in Methods and Extended Data Fig. 1. Following the location selection, we carried out the TRIDENT pathfinder experiment (TRIDENT Explorer, T-REX for short). With T-REX, we measured the optical properties of the seawater and also quantified the oceanographic conditions at the chosen site, including water current, temperature, salinity and radioactivity (Methods and Extended Data Figs. 2 and 3).

Optical properties of the deep-sea water

Neutrino telescopes observe neutrino interactions by detecting Cherenkov photons generated in the medium. By measuring the number of these photons and their arrival times, information about the neutrino involved in the interaction can be reconstructed. To efficiently detect this light, excellent optical clarity is an important requirement in site selection.

The propagation of Cherenkov photons is predominantly affected by absorption and scattering. Absorption converts the photon energy into atomic heat via photon–molecule interactions30, which reduces the total number of observable photons. Scattering, in contrast, causes photons to change their direction of propagation. This leads to a blurring of arrival times for Cherenkov light arriving at photon detection units, thus degrading the angular resolution of the neutrino telescope.

In seawater, scattering is dominated by two elastic processes, Rayleigh and Mie scattering, which can be quantified by their mean free path, denoted as λRay and λMie, respectively. Mie scattering typically results in a small deflection angle and requires an additional parameter, cosθMie, to represent the mean scattering angle. The overall scattering effect, described by λsca, can thus be expressed as: 1/λsca = 1/λRay + 1/λMie. Meanwhile, the absorption effect can be quantified using λabs. As both absorption and scattering can occur during photon propagation, the concept of an attenuation length, λatt, is introduced to depict the exponential reduction in the intensity of a light beam within the medium, and can be formulated as: 1/λatt = 1/λabs + 1/λsca.

When dealing with a spherical isotropic light source, however, it becomes more convenient to measure an effective attenuation length, λeff,att, which approximately describes the decrease in the total observable photons \(\propto {{\rm{e}}}^{-D/{\lambda }_{{{{\rm{eff,att}}}}}}{D}^{-2}\) over a propagation distance D31. Notably, λeff,att differs from the canonical attenuation length λatt as it also encompasses scattered photons in the observed light.

To decode all these optical parameters, precise in situ measurements were conducted with T-REX, as shown in Extended Data Fig. 4. The core detection unit consists of three modules. At the middle is a light-emitter module equipped with light-emitting diodes (LEDs) of three wavelengths, which can emit photons isotropically with two modes: pulsing mode and steady mode. There are two light receiver modules located at 41.8 m and 21.7 m vertically above and below the light emitter, respectively, performing a near-far measurement. Both modules are equipped with two independent and complementary measurement systems, a photomultiplier tube (PMT) system and a camera system. The former primarily records PMT waveforms to extract the timing information of the detected photons emitted by pulsing LEDs, while the latter records images of the steady light emitter to measure the angular distribution of the radiance (Methods and Extended Data Figs. 5 and 6).

Table 1 summarizes the measured canonical optical parameters using both the PMT and camera systems in the blue waveband, the optimal waveband for observing Cherenkov photons in water. The two systems work independently and obtain consistent results using different measurement mechanisms. All of the data processing and analysis pipelines are presented in Methods in detail. In addition, measurement results at three different wavelengths, at various depths, are listed in Extended Data Tables 1 and 2.

Table 1 Optical parameters measured in the blue waveband
Full size table

Figure 1 summarizes the measurement results of optical property at TRIDENT’s site and other water-based neutrino telescopes’ sites. To compare with other similar measurements, we conducted another set of analyses to obtain λeff,att, as listed in Table 2, as definitions of the attenuation length in other experiments differ slightly. The results from Long Arm Marine Spectrophotometer (LAMS)32, ANTARES31 and STRings for Absorption length in Water (STRAW-a)33 are effective attenuation lengths, which contain different proportions of scattered photons in their selected data acquisition time windows. The results from Baikal-5D34 and AC9 (ref. 35), however, made measurements of canonical attenuation lengths using specialized laser devices.

Fig. 1: Measured (effective) attenuation length at different neutrino telescope sites.
figure 1

Effective attenuation lengths measured by two independent optical systems, the PMT (black circle) and camera (black square) in T-REX for three wavelengths (405 nm, 450/460 nm, 525 nm), as summarized in Table 2. Data points and error bars indicate the best-fit results and 68% confidence-level regions in the χ2 fitting. The results obtained by the camera system use 20 images for each wavelength, while the results from the PMT system are measured using data samples with ~107 detected photons per wavelength. Measurements from KM3NeT32,35, P-ONE33, ANTARES31 and Baikal-GVD34 are shown for comparison. Also shown is the average observable Cherenkov spectrum from simulation, in which the optical properties measured by T-REX are used.

Full size image
Table 2 Effective attenuation lengths measured at various wavelengths
Full size table

The measured optical properties and water current speeds are promising for operating a large-scale neutrino telescope at the selected site. T-REX’s camera system demonstrated its application as a fast, in situ calibration system, which is particularly important for precise angular reconstruction in underwater telescopes with dynamic environments. In addition, T-REX has been a valuable tool for testing some of TRIDENT’s electronic systems, such as time synchronization technologies and optical fibres for data transmission.

Design of TRIDENT

TRIDENT will be optimized to pinpoint astrophysical neutrino sources from the isotropic diffuse flux discovered by IceCube. The long scattering lengths in deep-sea water allow the Cherenkov photons from a neutrino interaction vertex to propagate in long straight paths to the many optical sensors throughout the detector. Precisely measuring the arrival times of these direct photons strongly improves the angular resolution of track-like events due to νμ (and a fraction of ντ) charged-current interactions, which neutrino telescopes rely primarily on for pointing36. TRIDENT aims to achieve this with the help of modern silicon photon multipliers (SiPMs) that can respond to photon hits within tens of picoseconds37, time digital converters that are capable of digitizing the sharp rising edge of a SiPM waveform38 and the White Rabbit system that can provide precise global time stamps39. With these state-of-the-art technologies, TRIDENT will build hybrid digital optical modules with both PMTs and SiPMs, called hDOMs40, yielding excellent light collection and timing resolution that are capable of accurately measuring the arrival time of unscattered photons. The advantages of using multiple small PMTs have been demonstrated by KM3NeT’s multi-PMT Digital Optical Module (mDOM) system41. Compared with IceCube’s single large PMT DOM, multiple small PMTs allow for an increased photocathode coverage, strong sensitivity to the incident photon direction and finer timing resolution, along with the capability of coincidence triggering on a single DOM. In an effort to further improve angular resolution, the TRIDENT hDOM design adds SiPMs with excellent timing resolution, placed in the spaces between PMTs. The first-rate timing response and additional photocathode coverage of the SiPMs in TRIDENT’s hDOM design are expected to provide improvement in angular resolution compared with traditional PMT-only DOMs, boosting the detector’s source searching ability.

In seawater, the absorption length for Cherenkov photons is a key parameter to consider when designing the detector geometry. Figure 2 shows the anticipated layout of the future telescope, guided by the presented optical property measurements. The detector contains 1,211 strings, each containing 20 hDOMs separated vertically by 30 m, ranging from approximately 2,800 m to 3,400 m below sea level. This arrangement will result in a world-leading instrumented geometric volume of ~7.5 km3. The strings’ pattern follows a Penrose tiling distribution with inter-string distances of 70 m and 110 m, adopting the golden ratio42. Preliminary simulation studies indicate that this uneven layout, compared with a regular distribution of strings, allows for an expanded geometry with a broader window of measurable neutrino energies. TRIDENT in this layout is expected to cover from sub-teraelectronvolt (TeV) to exaelectronvolt energies, optimizing the telescope’s potential for neutrino astronomy43. Building multiple, separated clusters of strings helps to ease the difficulties faced in the construction and maintenance of large telescopes on the seafloor. TRIDENT instead leaves several spiral pathways, allowing underwater robots to access the innermost strings for maintenance. This unsegmented geometry aims to reduce the number of clipping edge events, which are more likely to occur in segmented geometries with wide empty regions between string clusters. The spiral shape of the pathways also helps to reduce the number of ‘corridor events’, which describe undetected muons passing straight through parallel arrays of strings. Acoustic detectors will be installed on each string for high-precision position calibration. These detectors can also be placed sparsely in an array extended beyond the main detector volume, to detect cosmogenic neutrinos with energies well above exaelectronvolts44,45.

Fig. 2: Geometrical layout of the TRIDENT array.
figure 2

The geometrical layout pattern follows a Penrose tiling distribution. Each black dot represents a string of length ~0.7 km and the dashed lines mark the paths for underwater maintenance by remotely operated underwater vehicles (ROV).

Full size image

Source sensitivity and discovery potentials

We conducted a performance study of TRIDENT using in-depth simulations, in particular measuring up-going (neutrinos with zenith angle greater than 80° and that travel long distances inside Earth) track events produced in νμ charged-current interactions. At an energy of ~100 TeV, the angular resolution of TRIDENT is expected to reach 0.1° with an effective area of 5 × 102 m2, as shown in Extended Data Figs. 7 and 8. TRIDENT intends to push the limits of neutrino telescope performance, reaching a new frontier of sensitivity in all-sky searches for astrophysical neutrino sources, as shown in Fig. 3.

Fig. 3: Projected point source sensitivities and discovery potentials of TRIDENT.
figure 3

All-sky point source 90% confidence-level median sensitivity (dashed dot lines) and 5σ discovery potential (solid lines) of TRIDENT with 10 years of data taking. The left panel corresponds to a source energy spectrum index of 2 (labelled E−2) and minimum energy of 10 TeV, while the right panel assumes an index of 3 (E−3) and minimum energy of 1 TeV. The x axis represents the sine declination (sinδ) and the y axis is the neutrino flux (ϕ). KM3NeT, IceCube and IceCube-Gen2 sensitivities15,66,67 are also shown for comparison. IceCube, located at the South Pole, has increased sensitivity to the northern sky. For a source located in the southern sky with a spectral index of 3, TRIDENT will have 4 orders of magnitude improvement in sensitivity compared with IceCube. Similarly comparing to the future telescope KM3NeT located in the Northern Hemisphere yields an improvement factor of approximately 5.

Full size image

The most promising neutrino source candidates found by IceCube, NGC 1068 and TXS 0506+05611,12,13 will be visible to TRIDENT in the up-going neutrino mode, for ~50% of its operation time. Assuming an IceCube best-fit flux, TRIDENT is predicted to discover the steady source NGC 1068 within one year of operation, as shown in Fig. 4. For a transient neutrino burst similar to the TXS 0506+056 2014–2015 case, TRIDENT will detect it with a significance level over 10σ.

Fig. 4: Projected exposure time for discovering potential neutrino sources with TRIDENT.
figure 4

The source fluxes used in this figure: NGC 1068 flux from IceCube best-fit result with spectrum index of 3.2 (ref. 13); diffuse neutrino flux from IceCube best-fit result68; Galactic Centre from conversion of High Energy Stereoscopic System (HESS) gamma-ray observation to neutrino flux upper limit with gamma-ray cut-off energy at 100 TeV (refs. 69,70); Large High Altitude Air Shower Observatory (LHAASO) J1825−1326 from conversion of LHAASO gamma-ray observation to neutrino flux upper limit with cut-off energy at 286 TeV (refs. 71,72). The horizontal black dashed line indicates a significance level of 5σ. In the analysis, the diffuse astrophysical muon neutrinos68 and atmospheric muon neutrinos73 are considered as backgrounds. The minimum energies adopted for each source are shown in the legend.

Full size image

Physics with all neutrino flavours

Once astrophysical neutrino sources are identified, oscillation physics and searches for new physics will become feasible by measuring neutrino flavour ratios at fixed astronomical baselines. In particular, we expect to substantially boost measurements of astrophysical tau neutrino events using modern long-waveform readout electronics46,47 and also identify astrophysical electron antineutrinos via the Glashow resonance channel48. It is a particularly exciting time because IceCube has seen evidence for both types of event49,50,51,52. Drastically boosting the statistics of these event types will produce a plethora of new physics opportunities. Another aspect to improve is the discrimination efficiency between electromagnetic and hadronic showers from νe charged-current interactions and neutral-current interactions of all flavours by their distinct particle compositions53. This will open unique windows via the weak sector to probe physics at an energy frontier out of reach by contemporary human-made accelerators54,55.

Ocean engineering and timelines

It is not a trivial task to construct and operate such a giant array of precision detectors in a highly dynamic water body. Each string is mounted to the seafloor and raised by a buoy tied to the other end. Care should be taken to achieve the correct buoyancy and cable strength, accounting for possible extreme conditions such as benthic storms in the abyss. We carried out the first batch of small-scale tests of the array–current response, using 1:25 scale string toy models in a ship towing tank (https://oe.sjtu.edu.cn/EN/) located on the campus of Shanghai Jiao Tong University (Supplementary Video 1). For current speeds of 10 cm s−1, horizontal string displacements were found to be less than 30 cm. More dedicated testing will be employed to guide the mechanical design of the strings. Modules monitoring the sea currents will be installed among the telescope array to track the instantaneous dynamics of the environment, ensuring smooth operation.

Following hDOM prototype development, a dedicated factory will be built for the mass production and testing of the hDOM and string systems in the port city of Sanya. From there, they can be conveniently shipped out to site for deployment. A pilot project with ten strings installed in the selected site for a technology demonstration is scheduled for ~2026. Construction of the full array can begin following a successful demonstration, commencing measurements in its partially built configuration. The full telescope is envisioned to become live in the early 2030s.

Methods

Geographic information

On the basis of the existing geographic and oceanographic data56, we identified a huge abyssal plain in the northern part of the South China Sea that can meet the critical conditions for building a neutrino telescope. A uniform 10 × 10 km area was investigated on this plain, measured at a depth of 3,475 ± 8 m, which can largely avoid biological activities and provides sufficient overburden to shield cosmic-ray muons down to ~10−8 cm−2 s−1 sr−1 (ref. 57). The seabed of this area is mainly covered by clay silt and the mean slope is only 0.01°. Such a flat seabed ensures a uniform current distribution. A long-term, high-resolution simulation using the Regional Ocean Modeling Systems58 indicates that the average bottom current speed is only 6 cm s−1 over the past 30 years and the maximum value is ~26 cm s−1. The selected site is 180 km from Yongxing Island, where power supply and data transmission over this distance is feasible (Extended Data Fig. 1).

Oceanographic conditions and radioactivity

The water current at different depths was measured at the chosen site using a lowered acoustic Doppler current profiler on 6 September 2021, shown in the lower panel of Extended Data Fig. 2. Below ~2,800 m, the water current speed is less than 10 cm s−1. Its direction and gradient as a function of depth has a smooth profile. Furthermore, the current is steady, changing slowly in time. In addition, the temperature and salinity, measured by a CTD (conductivity, temperature and pressure) instrument, are shown in the upper panel of Extended Data Fig. 2. Below 2,500 m, the temperature becomes constant at ~2 °C.

To precisely measure the radioactivity of the site, in situ water was collected with the CTD instrument and transported back to Shanghai through cold-chain logistics. The radioactivity (predominantly 40K) of the water was then measured by the PandaX team using a high-purity germanium detector59 in the China Jinping Underground Laboratory. The measured abundance of 40K is 10.78 ± 0.21 Bq kg−1, consistent with public data of ordinary seawater. A background analysis with Geant4 (ref. 60) simulation indicates that this level of radioactivity corresponds to a trigger rate of ~2 kHz per single 3-inch PMT assumed with 29% quantum efficiency at 450 nm, as shown in Extended Data Fig. 3, acceptable for operating both T-REX and TRIDENT. During the apparatus deployment and data-taking periods, marine life occasionally showed up and was recorded by our live cameras only above a depth of 1,500 m. No activity was spotted during the 0.5 h camera data-taking period at depths below 3,000 m.

Deployment of T-REX and data taking

To safely deploy the long and delicate apparatus, T-REX, shown in Extended Data Fig. 4, was first packed on the deck like a wire roller, then hoisted into the water. It then unfolded naturally under the action of its buoyancy and gravity. The ballast at the bottom weighs about 700 kg, and the connection cables between the detection modules are made of high-rigidity steel wires to ensure that the low-frequency disturbance of the research vessel will not excite the resonance of the system.

During the deployment process, planned tests were conducted by the camera system at the fixed depths of 1,221 m and 2,042 m. Each test took 8 min to record data. After reaching the target depth of 3,420 m, the whole apparatus was suspended for ~2 h to conduct in situ measurements. The data taking was then divided into two stages. The light emitter was first operated in the pulsing mode to trigger the PMT system, which lasted ~1.5 h. For the wavelength of 450 nm, it took about 50 min to collect more than 107 photons. The data collection for the other two wavelengths, namely, 405 nm and 525 nm, lasted about 10 min for quick measurements. In the second stage, the camera system recorded more than 3,000 images in ~0.5 h when the light emitter was switched to steady mode with wavelengths of 460 nm, 525 nm and 405 nm in sequence. After completing the measurements at the depth of 3,420 m, the whole apparatus was retrieved for recycle.

PMT data analysis

Three-inch PMTs and pulsing LEDs are synchronically triggered by the White Rabbit system at a rate of 10 kHz. The spread of the LED pulses is 3 ns (refs. 61,62). For non-scattered light, the PMT will observe the narrow pulses; for scattered light, the photons will arrive later at the PMT, forming a scattering tail in the photon arrival time distribution. A 1,000 ns data acquisition (DAQ)63 window is set for the PMTs to observe the light from each LED pulse.

PMT data analysis is done in two steps. First, the photon arrival time distribution for each PMT is obtained. Second, the distribution is fitted with light propagation models simulated by Geant4 for various optical parameters64. The ratio of the number of photons detected by the top and bottom PMTs, after correcting the square of distance, shows the effect of absorption. The tail of photon arrival time distribution contains the information of scattering.

The photon arrival time distribution is obtained by getting the times of PMT signals and the number of photo-electrons (Npe) in each signal and then filling the signal times in a histogram with Npe as the weight. PMT signals are found in the waveform if the voltage is higher than one-third of the single photoelectron amplitude. The waveform peak time is determined as the signal time. The waveform is integrated to get the charge, and dividing the charge by the PMT gain yields Npe for each signal. Uncertainties in the signal time, charge integral and PMT gain are considered in the analysis. See Extended Data Fig. 5 for an example of the derived photon arrival time distributions.

The model used to fit the photon arrival time distribution is composed of (1) emission from the pulsing LEDs, (2) light propagation in the water and (3) detection by the PMTs. It can be written as:

$$[{N}_{{{{\rm{emi}}}}}\times f(t)]\otimes \left[\frac{A}{4\uppi {D}^{2}}\times P \big(t\,| \,{\lambda }_{{{{\rm{abs}}}}},{\lambda }_{{{{\rm{Ray}}}}},{\lambda }_{{{{\rm{Mie}}}}},\left\langle \cos {\theta }_{{{{\rm{Mie}}}}}\right\rangle ,n,D \big)\right]\otimes [\eta \times g(t)],$$
(1)

where Nemi is the number of emitted photons, f(t) is the LED pulse timing profile, A is the effective detection area of the PMT, D is the distance, \(P(t\,| \,{\lambda }_{{{{\rm{abs}}}}},{\lambda }_{{{{\rm{Ray}}}}},{\lambda }_{{{{\rm{Mie}}}}},\left\langle \cos {\theta }_{{{{\rm{Mie}}}}}\right\rangle ,n,D)\) is the photon propagation function, and η and g(t) are the PMT detection efficiency and time response, respectively. The convolution of the LED pulse profile and PMT time response f(t) ⊗ g(t) is measured in the lab. The final model is computed by convolving the simulated photon propagation function and calibrated LED and PMT time response. The blocking effect of cable is less than 0.1% and is neglected in the analysis.

A χ2 fitting method is adopted to fit the photon arrival time distribution with the above model for a pair of PMTs from the top and bottom receiver modules:

$${\chi }^{2}=\mathop{\sum }\limits_{i=1}^{N}\frac{{\left({D}_{i}-{M}_{i}-\mathop{\sum }\nolimits_{k = 1}^{K}{c}_{k} {\beta }_{ki}\right)}^{\!2}}{{{\sigma }_{i}}^{2}}+\mathop{\sum }\limits_{k=1}^{K}{{c}_{k}}^{2},$$
(2)

where Di is the number of photons in the ith bin of the photon arrival time distribution and Mi is the expected value by the model. The uncorrelated uncertainty σi includes statistical fluctuation, electronic noise and uncertainty of LED pulse profile and PMT time response. Correlated uncertainties (βki), with its fluctuating variable ck, include fluctuations of LED brightness, distances, PMT gain, PMT detection efficiencies and the binning effect caused by the 4 ns analog-to-digital converter resolution. Minimization of the χ2 will return the best-fit model and yield the measurement results and uncertainties for the physics parameters: λabs, λRay, λMie, \(\left\langle \cos {\theta }_{{{{\rm{Mie}}}}}\right\rangle\), and refraction index n.

For cross-validation, a Markov chain Monte Carlo (MCMC) technique is also used to obtain the best model using the emcee sampler65. The goal of MCMC is to approximate the posterior distribution of model parameters by random sampling in a probabilistic space. A multi-dimension linear interpolation is performed before the sampling since the model in our case is discrete.

Both the χ2 fitting and MCMC methods follow the same analysis procedure described above but have minor differences in the detailed treatment of convolution. Despite this, the two methods yield consistent results. Three pairs of PMTs from the top and bottom light receivers are used to fit the optical parameters independently, yielding consistent results as well.

The effective attenuation length is derived by comparing the number of photons Nhit received by top and bottom PMTs. Here, Nhit is the integral of photon arrival time distribution over the DAQ window. Simulation studies show that ~25% and ~45% of the Nhit photons are scattered at least once, for the near and far PMT, respectively, making the effective attenuation length deviate from the canonical attenuation length, as discussed before64.

Camera data analysis

It has been discussed extensively among the neutrino telescope community, including IceCube-Gen2, KM3NeT and P-ONE, that cameras can be an excellent tool for optical calibration and in situ environmental monitoring. TRIDENT plans to use a dedicated camera system for fast optical calibration when it becomes operational. The prototype for this camera system, including both hardware design and data-processing pipeline, has been fully tested during the T-REX explorer mission. The camera system of T-REX mainly consists of a 5-million-pixel monochromatic camera with a fixed-focus lens. It is controlled by a Raspberry-4Pi module, which can transfer its real-time data back to the research vessel63. Both top and bottom cameras (denoted as CamA and CamB) are calibrated to have a proper viewing angle of about 16° in the seawater. During the data-taking process, the same series of exposure times of 0.02 s, 0.05 s, 0.07 s, 0.11 s and 0.2 s were configured for all three wavelengths, allowing an adequately broad range to accommodate for the blind conditions in the deep water. The relatively short exposure times can reduce the potential motion blur caused by sea current perturbations affecting the whole apparatus, but are long enough to provide sufficient photon statistics as the camera system operates under the steady mode of the light emitter61,62. The key observable for the camera system is the angular distribution of the radiance, which is converted into grey values of pixels.

The first method for the camera system, called the Icentre method, is used to quickly measure the attenuation length of the medium by comparing the grey values in the central region of light-emitter images:

$${\lambda }_{{{{\rm{att}}}}}=-({D}_{{\rm{A}}}-{D}_{{\rm{B}}})/\ln \left(-\frac{{I}_{{{{\rm{A}}}}}}{{I}_{{{{\rm{B}}}}}}\times \frac{{I}_{0}^{{\prime} }}{{I}_{0}}\right).$$
(3)

Here, DA − DB is the relative distance between the two cameras. IA and IB are the mean grey values in the centre region of images from CamA and CamB, corresponding to the directly arriving light from the emitter. \({I}_{0}^{{\prime} }/{I}_{0}\) is the initial intensity ratio of both sides of the light emitter, which is well calibrated. The canonical attenuation length can be derived from such a set-up due to the far distances between the cameras and light emitter, which makes the directly arriving light highly collimated. The open angle of the light emitter is <1.1° for CamA and <0.6° for CamB; thus both absorption and scattering will dissipate the radiance. A Geant4 simulation study shows that there is a small contamination of scattered photons in the centroid pixel, but this contamination ratio is approximately equal in both the near and far cameras, causing an uncertainty of less than 4% on the Icentre method64.

For the image processing, we select images with suitable exposure time and gain, to ensure that all the pixels are within the range of linear response. We then find the centroid of each image and crop it to a unified size of 300 × 300 pixels, shown in Extended Data Fig. 6, to include all the directly arriving light. Then we calculate the mean grey value with 100 central pixels around the centroid from both CamA and CamB images as IA and IB in equation (3) and obtain the final attenuation length.

The uncertainty estimation for the Icentre method includes conventional systematic and statistical errors from the camera response, pre-calibration results of \({I}_{0}^{{\prime} }/{I}_{0}\), the relative distances and the grey value processing. Systematic uncertainties such as luminosity loss at the air–glass–water interface are cancelled out in this set-up.

To decode the absorption and scattering length from the attenuation process, we apply the χ2 fitting method that compares the angular distribution of radiance between experimental data and the simulated data.

Images are selected and cropped using the same procedure introduced in the Icentre method. Then both experimental data and simulated data of CamA and CamB are normalized with the same factor to keep the ratio of grey values of the centre area unchanged. Considering the central symmetry, two-dimensional images are converted into a one-dimensional grey value array by calculating the mean grey value of those pixels, which have the same pixel distance from the centroid. Finally, we choose the first 40 and 20 points in the grey value arrays of CamA and CamB to calculate the sum of χ2 pixel by pixel with the model:

$${\chi }^{2}=\mathop{\sum }\limits_{i=1}^{N}\frac{{\left[{M}_{i}-{T}_{i}\big(1+\mathop{\sum }\nolimits_{k = 1}^{K}{\epsilon }_{k}\big)\right]}^{\!2}}{{\sigma }_{Mi}^{2}+{\sigma }_{Ti}^{2}}+\mathop{\sum }\limits_{k=1}^{K}\frac{{\epsilon }_{k}^{2}}{{\sigma }_{k}^{2}}.$$
(4)

Here, Mi is the measured data in ith pixel bin while Ti is the model prediction. σMi and σTi are both uncorrelated uncertainties coming from statistical fluctuation. ϵ is added to include correlated systematic uncertainties such as the uncertainties in distances and the calibration result of \({I}_{0}^{{\prime} }/{I}_{0}\). Other uncertainties such as the slight de-focusing of the imaging process and the non-uniformity of the light emitter were all included in simulation and added as nuisance parameters when calculating χ2.

Due to the cameras’ limited viewing angle, a numerical factor is required to account for the undetected scattered photons. This factor can be used to convert the canonical attenuation length to an effective attenuation length. This factor is calculated in the simulation assuming the best-fit optical parameters and uncertainties as input. The analysis results are summarized in Fig. 1.