# The Physics and Nuclear Nonproliferation Goals of WATCHMAN: A WAter
CHerenkov Monitor for ANtineutrinos

M. Askins  Physics Department, University of California, Davis CA 95616, USA
M. Bergevin  Physics Department, University of California, Davis CA 95616, USA
A. Bernstein111Corresponding Author, email<EMAIL_ADDRESS>Lawrence
Livermore National Laboratory, Livermore, CA 94550, USA  S. Dazeley  Lawrence
Livermore National Laboratory, Livermore, CA 94550, USA  S. T. Dye  Department
of Natural Sciences, Hawaii Pacific University, Kaneohe, Hawaii 96744, USA  T.
Handler  Department of Physics and Astronomy, University of
Tennessee,Knoxville TN 37996  A. Hatzikoutelis  Department of Physics and
Astronomy, University of Tennessee,Knoxville TN 37996  D. Hellfeld  Department
of Nuclear Engineering, Texas A&M University, College Station, TX, 77843  P.
Jaffke  Department of Physics, Virginia Polytechnic Institute and State
University, Blacksburg, VA 24061, USA  Y. Kamyshkov  Department of Physics and
Astronomy, University of Tennessee,Knoxville TN 37996  B. J. Land  Lawrence
Berkeley National Laboratory, Berkeley, CA 94720, USA  Department of Physics,
University of California, Berkeley, CA 94720, USA  J. G. Learned  Department
of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, HI 96922
USA  P. Marleau  Sandia National Laboratories, Livermore, CA 94550, USA  C.
Mauger  Los Alamos National Laboratory, Los Alamos, NM 87544m, USA  G. D.
Orebi Gann  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Department of Physics, University of California, Berkeley, CA 94720, USA  C.
Roecker  Department of Nuclear Engineering, University of California,
Berkeley, CA 94720, USA  Lawrence Livermore National Laboratory, Livermore, CA
94550, USA  Sandia National Laboratories, Livermore, CA 94550, USA  S. D.
Rountree  Department of Physics, Virginia Polytechnic Institute and State
University, Blacksburg, VA 24061, USA  T. M. Shokair  Department of Nuclear
Engineering, University of California, Berkeley, CA 94720, USA  M. B. Smy
Department of Physics and Astronomy, University of California, Irvine, CA
92697, USA  R. Svoboda  Physics Department, University of California, Davis CA
95616, USA  M. Sweany  Sandia National Laboratories, Livermore, CA 94550, USA
M. R. Vagins  Department of Physics and Astronomy, University of California,
Irvine, CA 92697, USA  K. A. van Bibber  Department of Nuclear Engineering,
University of California, Berkeley, CA 94720, USA  R. B. Vogelaar  Department
of Physics, Virginia Polytechnic Institute and State University, Blacksburg,
VA 24061, USA  M. J. Wetstein  Enrico Fermi Institute, University of Chicago,
Chicago, IL 60637, USA  M. Yeh  Brookhaven National Laboratory, Upton, NY
11973, USA

###### Abstract

This article describes the physics and nonproliferation goals of WATCHMAN, the
WAter Cherenkov Monitor for ANtineutrinos. The baseline WATCHMAN design is a
kiloton scale gadolinium-doped (Gd) light water Cherenkov detector, placed 13
kilometers from a civil nuclear reactor in the United States. In its first
deployment phase, WATCHMAN will be used to remotely detect a change in the
operational status of the reactor, providing a first-ever demonstration of the
potential of large Gd-doped water detectors for remote reactor monitoring for
future international nuclear nonproliferation applications. A demonstration of
remote monitoring of a reactor has been called for in the U.S. National
Nuclear Security Adminstration’s (NNSA) Strategic Plan stratplan .

During its first phase, the detector will also provide a critical large-scale
test of the ability to tag neutrons and thus distinguish electron-flavor
neutrinos and antineutrinos, using gadolinium-doped water. This would make
WATCHMAN the world’s only detector capable of providing both direction and
flavor identification of supernova neutrinos. It would also be the world’s
third largest supernova detector, and the largest in the western hemisphere.

In the first and subsequent phases, the detector will also be a flexible test-
bed for a range of large doped water Cherenkov detector technologies,
including high quantum efficiency photomultipliers, Water-Based Liquid
Scintillator (WbLS), picosecond light sensors, advanced image recognition
methods, and other enhancements. A separate white paper describing Theia, a
WbLS-based Advanced Scintillator Concept Detector (ASDC) has been published,
with a long-term goal of fielding a 50-100 kton WBLS detector situated at the
Long Baseline Neutrino Facility (LBNF). As described in that paper, WATCHMAN
is essential to the demonstration of the advanced technologies that will be
incorporated into the ASDC Alonso:2014fwf . The physics enabled by this
technology development is described in detail in the ASDC paper, including
mass hierarchy measurements, measurement of CP violation in the neutrino
sector, and neutrino-less double beta decay.

Finally, if a compact accelerator is placed nearby, WATCHMAN will enable a
highly sensitive search for sterile neutrinos with few-meter oscillation
wavelengths, and could perform a search for Non-Standard neutrino Interactions
(NSI). The sensitivity in both cases would increase if a WbLS or oil-based
liquid scintillator (LS) target is used. The compact accelerator is now being
developed by the ISoDAR collaboration ISODAR .

This white paper describes the WATCHMAN conceptual design, including the
results of a detailed simulation of the signal and backgrounds, discusses our
current Preferred and Backup Alternative deployment sites, and reviews the
current status of the WATCHMAN nonproliferation and physics programs.

antineutrinos, reactor, water Cherenkov detector, mass hierarchy, supernova,
nonproliferation

###### pacs:

Valid PACS appear here

††preprint: AIP/123-QED

##  I Introduction

Gadolinium-doped water has long been proposed as a medium for large scale
neutrino and antineutrino detectors doi:10.1080/08929880108426496
,Beacom:2003nk . Gadolinium doping is recognized as essential for detection of
low energy antineutrinos with light water Cherenkov detectors. The technique
has been proposed by the LBNE collaboration, because it would permit sensitive
studies of supernovae, cosmological/relic neutrinos and possibly proton decay
2012arXiv1204.2295T . Among its other attractions, WATCHMAN provides a timely
and highly subsidized opportunity to demonstrate the gadolinium option for
LBNE.

The gadolinium dopant ensures efficient detection of the neutron created in
charged-current antineutrino-proton scattering, known as inverse beta decay:

$\bar{\nu}+p\rightarrow e^{+}+n.$ (1)

Here $\bar{\nu}$ is the incident antineutrino, $p$ the target proton, and
$e^{+}$ and $n$ the final state reaction products, a positron and a neutron.

Compared with a pure water Cherenkov detector, gadolinium doping provides the
important advantage of an approximate six-fold increase in the efficiency for
detection of the final state neutron. This benefit derives from two useful
features of the gadolinium nucleus: its high thermal neutron capture cross-
section, and the relatively high energy gamma-ray emissions arising from the
post-capture excited Gd nucleus. Even at $0.1\%$ doping (as measured by the
weight of the Gd element), gadolinium captures about $85\%$ of all neutrons
arising from the inverse beta decay process. The $\sim\\!\\!8\,MeV$ gamma-
cascade following capture generates a strong Cherenkov pulse that is well
above most backgrounds. This time-correlated signal associates the neutron
with the energy deposition arising from the positron which precedes it by a
few tens of microseconds, with the mean time interval determined by the
thermalization and capture time of the neutron in the Gd-doped water.

In the last ten years, significant progress has been made in demonstrating the
potential of gadolinium-doped water as an antineutrino (and neutron) detection
medium. Important milestones include the demonstration of high efficiency
detection of time-correlated neutrons in a ton-scale Gd-doped water Cherenkov
detector Dazeley:2008xk , and detection of gamma-rays arising from a Gd
captures in a small enclosed cell of Gd-doped water placed near the center of
the SuperKamiokande 50,000 ton pure water detector Watanabe2009320 . Very
recently, the EGADS experiment in Japan has demonstrated on a large scale (200
tons) the long-term compatibility of Gd-doped water with typical detector
materials such as stainless steel and Photomultiplier Tubes (PMT’s), and the
ability to recirculate and continuously purify the water via selective
extraction and reintroduction of the gadolinium, using a so-called ’molecular
band-pass’ filtration system EGADS .

While the KamLAND liquid scintillator detector has shown sensitivity to
reactor antineutrinos at 200-400 km standoff distances PhysRevLett.90.021802 ,
direct sensitivity to reactor antineutrinos has not yet been demonstrated with
a gadolinium-doped water detector. The purpose of the WATCHMAN project is to
perform such a demonstration, with important immediate and long-term benefits
for fundamental physics and for international nonproliferation.

To this end, the WATCHMAN collaboration will deploy a gadolinium-doped water
detector a few kilometers from a nuclear reactor. The current preferred
deployment site is the Morton Salt mine in Fairport Ohio, about 13 kilometers
from the single core Perry Nuclear Power Plant. The mine operators have
approved use of this deployment location, the former deployment site for the
Irvine-Michigan-Brookhaven (IMB) detector BeckerSzendy:1992hr .

The demonstration will represent a major step towards a true long range
reactor monitoring capability for nonproliferation purposes. WATCHMAN will
also have a strong fundamental neutrino physics program. It will be the United
States’ only supernova watch detector and will have the unique capability of
flavor identification and neutrino direction in a single detector. It would be
the third largest SN detector in the world. In addition, the same detector may
be used to search for sterile neutrino oscillations and non-standard neutrino
interactions using a nearby compact cyclotron to create an intense neutrino
flux.

The WATCHMAN effort also overlaps closely with plans and technology needs in
the fundamental science community, for very large scale detectors to study
astrophysical neutrinos, neutrino oscillations, and other physical phenomena
such as proton decay and the neutrino mass hierarchy. There is significant
overlap between the membership of the WATCHMAN collaboration and that of the
Advanced Scintillator Detector Concept (ASDC) Alonso:2014fwf . The ASDC
initiative is engaged in planning and design studies for a multi-hundred-ton
WBLS detector to be built in the United States. Because of this overlap,
WATCHMAN can test technologies that are essential to the success of ASDC and
similar future detectors, in whatever country they are ultimately constructed.
Examples include the basic WATCHMAN technology of gadolinium doping and
recirculation of gadolinium-doped water, as well as testing of water-based
liquid scintillator, advanced photomultiplier tubes such as the Large Area
Avalanche Photodetector (LAPPD) LAPPD , wavelength-shifting plates, wireless
readout, and other innovations.

In this paper, we introduce the baseline design, site, and detector
performance characteristics. We then describe how the nonproliferation goals
will be met with the baseline design. Next we provide analyses of sensitivity
for each of the physics goals described above. We conclude with an overview of
progress to date, the likely timeline of the experiment, and its relation to
other large scale detectors being contemplated in the U.S. and worldwide.

##  II Site Selection

The following detection criteria have been defined regarding the
nonproliferation goal of demonstrating remote reactor monitoring capability
with Gd-H2O technology. These criteria helped determine the depth and standoff
distance for the site:

  1. 1.

A signal to background ratio sufficient for $99.7\%$ C.L. ($3\sigma$)
sensitivity to the presence of a reactor operating at full power, based on no
more than roughly 30 days each of reactor-off and reactor-on data. This
implies sensitivity to a single reactor on-off transition, which we consider
most attractive from a nonproliferation standpoint.

  2. 2.

A detector standoff distance no closer than 500 meters from the reactor.

  3. 3.

The detector is meant to demonstrate that low event rate detection is a viable
tool for the nonproliferation community. Therefore, we imposed a requirement
that the total event rate be below a subjective threshold for rare event
detection - here defined as no greater than roughly 10 reactor antineutrino
events per day. A higher event rate would mean that either our choice of
baseline was too close, or our detector mass larger than necessary to allow a
convincing demonstration of standoff detection with relatively low statistics
signal.

Other design and cost criteria also influence the choice of site. These are:

  1. 1.

A detector target mass of approximately one thousand tons.

  2. 2.

A detector target composition of H2O + Gd-salt, with about $0.1\%$ wt percent
Gd concentration.

  3. 3.

An initial detector design that includes a water recirculation system capable
of selective capture and reintroduction of gadolinium (EGADS-like system).

Using these criteria, we performed an extensive survey of domestic reactor
facilities and their surroundings, considering detector deployments at both
underground and underwater sites. Excavation costs are a key concern for
underground sites. To keep excavation costs low, we looked for already
excavated sites near a reactor. The Morton Salt mine in Ohio was the sole site
in the US that met this criterion. It was also found to be compatible with the
other detection criteria defined above.

In addition to the Ohio site, we identified a greenfield excavation deployment
at the Advanced Test Reactor ATR , near Idaho Falls in the state of Idaho. We
found the geology to be compatible with a relatively shallow 300 mwe
overburden tunnel, and a reactor standoff distance of approximately 1
kilometer. However, at this shallow depth, the higher and less well understood
backgrounds would make the measurement more challenging and riskier. The ATR
site remains as a backup option in our planning process.

###  II.1 The Morton Salt Mine and the Perry Nuclear Power Plant

The deployment site for WATCHMAN is the Morton Salt Mine in Fairport, Ohio,
about 13 kilometers from the single core Perry Nuclear Power Plant. Figure 1
shows the location of the power plant and mine along the shores of Lake Erie.
Morton Salt has given our collaboration permission to deploy the WATCHMAN
detector at their facility on a cost neutral basis.

Figure 1: The Morton Fairport Harbor Mine is 13 km from the Perry Nuclear
Reactor. The site is convenient to reach—roughly 25 miles east of Cleveland,
Ohio—and has a long history of supporting DOE science experiments.

Due to the depth and the proximity to the Perry reactor, this site is
especially well suited to a reactor monitoring experiment. In addition, the
Morton company has a long history of hosting DOE experiments. From 1980-1991,
the underground laboratory site housed the IMB proton decay experiment. As a
result, the site has an existing cavern that allows the project to avoid an
otherwise costly greenfield excavation. The layout of the cavern and
laboratory are shown in Figure 2. The cavern, and the remaining IMB laboratory
infrastructure permit a quick and inexpensive refurbishment of the site with
little risk of delay. Access is via a personnel lift roughly 100 meters from
the lab’s entrance; a separate, nearby ore lift serves as a secondary egress.
It should be noted that IMB was a 10,000 ton undoped water Cherenkov detector
with a threshold of about 20 MeV. This high threshold and the lack of a
gadolinium dopant made the detector incapable of detecting reactor
antineutrinos. However, the excavated IMB cavern is an excellent space for the
WATCHMAN deployment, significantly reducing the project cost. Further, the
similarity of the technologies gives strong confidence that it is technically
possible to deploy our smaller 1000 ton water Cherenkov detector at this site,
greatly reducing risk compared to other options.

The Perry boiling water nuclear reactor is a single core commercial plant with
a thermal power rating of 3,758 MegaWatts (MWt). It is one of the most
powerful of this reactor type in the country. As one of the newest reactors
built in the U.S., it is licensed to operate until March 18, 2026 and has
applied for a 20 year lifetime extension. Either date is well beyond the
period needed for all phases of WATCHMAN. In addition, the Morton Salt Mine,
which supplies road salt to the Great Lakes area, has an essentially unlimited
operational future since the salt deposit extends for many miles under the
lake.

Figure 2: The existing underground lab layout at the Morton salt mine in Ohio.
The WATCHMAN deployment will reuse much of this space.

The Perry option also provides a demonstration of sensitivity at greater
standoff – about 13 km compared with $\sim 1-2$ km for the research reactors
we examined - albeit with a higher power core.

###  II.2 Reactor duty cycle

The Perry plant has a typical outage cycle of about 40-50 days. Its single
core is an advantage for our nonproliferation goal, since the contrast with
background is increased compared to sites with more than one core.

###  II.3 Site approvals for deployment

In July 2013, members of the WATCHMAN collaboration met with Morton plant
personnel at the mine. An inspection of the existing cavern showed it to be
intact and suitable to accommodate the WATCHMAN detector. Mine management has
indicated a willingness to host the WATCHMAN detector on a cost-neutral basis.

##  III Nonproliferation Demonstration

The main purpose for the initial phase of WATCHMAN is to demonstrate high
efficiency detection of reactor antineutrinos in a kiloton-scale gadolinium-
doped water (Gd-H2O) Cherenkov detector. Gd-H2O is one of a few media, and
possibly the only medium for which construction of a 100-1000 kiloton scale
detector is achievable on grounds of cost and environmental impact. The
WATCHMAN deployment will demonstrate many of the physics and engineering
features of the larger detectors, and will serve as a guide for their design
and deployment. At the kiloton scale, the detector would be capable of
excluding the existence of an operating 10 MWt reactor with high confidence in
a $\sim\\!25$ kilometer radius. This may itself have some limited utility in
specific states, in which the international community might seek to non-
intrusively and cooperatively confirm the non-operation of either known or
unknown reactors within this radius. The potential utility becomes greater if
the radius can be extended to several hundred kilometers, enabling possible
cross-border detection. This requires large-scale detectors such as those now
being contemplated for deployment to pursue fundamental physics goals. The
most well-developed current example is the proposed Hyper-Kamiokande
experiment HyperKLOI .

##  IV Baseline Design

The baseline WATCHMAN design uses a Gd-H2O target surrounded by a connected
Gd-H2O veto region. The design is constrained by the size of the cavern space
available at the preferred location at Fairport salt mine in Ohio. The
detector vessel is a large self-supporting 300 series stainless steel tank
which must fit in an area of 24.4 meters by 18.3 meters by 23.8 meters. The
diameter and height of this cylindrical tank are 15.8 meters, with a total
water volume of 3540 tons, accounting for displaced water volumes. The
detector is divided into two physical regions by a PMT support structure
inside the tank that separates the inner target region from the outer veto
region. The target region is filled with 1810 tons of Gd-doped water, and the
outer region is filled with 1730 tons of Gd-doped water. Inward-facing target
region PMTs line the inside of the support structure, and opposite-facing PMTs
point into the veto region from the same structure. For our baseline design,
the assumed fractional PMT coverage for the surfaces of the target and veto
regions are $40\%$ and $4\%$ respectively. The effects of variations in the
target PMT coverage are being examined by the collaboration.

The face of the target PMTs is at a diameter of 12.8 meters. Within the region
enclosed by the target PMTs, a smaller virtual fiducial volume is defined,
based on the positions of the particle interactions as reconstructed from the
variation of arrival times of Cherenkov light at the PMTs. For a 1000 ton
fiducial volume Gd-water detector, the diameter and height of this fiducial
region is 10.82 meters. The region outside of the fiducial but inside the PMTs
is referred to as the buffer region. The buffer serves to reduce the rate of
gamma-rays and neutrons in the fiducial region arising from the PMTs and
external radiation.

Figure 3 shows a cutaway drawing of the WATCHMAN detector. The PMT s are read
out via fast ($<$1 ns resolution) digitizing electronics. The arrival time and
intensity of the flashes can be reconstructed to give both the antineutrino
interaction vertex and energy.

Figure 3:  A cutaway view of the WATCHMAN detector (right) showing the
gadolinium-doped water target region, the inward-facing (target) and outward
facing (veto) PMTs, and cosmic ray muon veto region.

The most economical and practical method for this deployment is to have the
tank fabricated from panels that are bolted together to form the cylinder.
These bolted tanks reduce the contamination present in welded tanks and are
faster and less labor intensive to construct. Sealing material will used
between the panels to avoid the need for internal tank liners, with the
material experimentally screened to ensure no adverse reactions with the Gd-
doped water or WbLS. The tank design is also flexible enough to allow a range
of options for the location of fluid interconnects and access ports.

Instrumenting the veto and target regions requires large numbers of
submersible PMTs. Among other choices, Hamamatsu $12^{\verb+"+}$ High Quantum
Efficiency (HQE) PMTs are being considered as the light sensor for this
application. Based on preliminary simulations, 4328 such PMTs would be
required to instrument the fiducial volume and approximately 482 for the veto
region. 2880 inward-facing PMTs will cover the cylinder walls and an
additional 724 PMTs will line the top and bottom surfaces of the cylinder. The
remaining 482 PMTs will face the outer walls, top and bottom of the tank
forming a veto region. All the PMT assemblies will be mounted to modular
framing and/or tension cables that provide positioning and support. Based on
previous large volume detector designs, specifically the LBNE project, our
PMTs will be mounted in injection molded plastic housings that allow each PMT
assembly to be secured from support structure in precise locations.

Table I shows the dimensions of the detector.

Region | Mass (tons) | Height (m) | Diam./Thickness (m)
---|---|---|---
Fiducial (Gd-H2O) | 1000 | 10.8 | 10.8 (diameter)
Buffer (Gd-H2O) | 1049 | 12.8 | 1.0 (thickness)
Veto region (H2O) | 1070 | 15.8 | 1.0 (thickness)
Table 1: The dimensions of the WATCHMAN baseline detector.

###  IV.1 WATCHMAN operational phases

The initial deployment of WATCHMAN will employ a Gd-H2O target. The WATCHMAN
program will accommodate a second phase, in which the target medium is changed
to light WbLS, with a relatively low concentration of scintillator, and
possibly a third phase using pure scintillator. The second phase in particular
would allow demonstration of many of the key technologies to be used in the
ASDC/Theia detector, including LAPPDs, high quantum efficiency photomultiplier
tubes, and the light WbLS itself. The second and third phases will also
accommodate a wider range of physics goals, primarily by increasing the
sensitivity to sterile neutrinos in conjunction with the IsoDAR beam.

##  V Simulations of Reactor Signal and Backgrounds

In this section we describe the reactor inverse beta decay signal and expected
backgrounds in the baseline WATCHMAN design, and present estimates of the
signal detection efficiency and background rejection capabilities of the
detector. These estimates are based on a detailed simulation of the detector
using the GEANT-based Reactor Monitoring SIMulation (RMSIM) package,
maintained by UC Davis. The vertex reconstruction of events was made with the
BONSAI package maintained at UC Irvine. Using the same simulation package, we
treat background and signal for other physics processes elsewhere in the
paper.

As described in the introduction, reactor antineutrinos interact with the
quasi-free protons in water to produce a positron and neutron through the
Inverse Beta Decay (IBD) process. The two final state particles generate
Cherenkov light, which is detected by the PMTs surrounding the Gd-H2O target
volume. The Cherenkov flash from the positron is proportional to the energy of
the incident antineutrino. It induces single photoelectron pulses in a few
dozen PMTs. Each pulse has a width of a few tens of $ns$ defined by the
specific PMT properties and optical dispersion and scattering in the water.
This prompt signal is closely followed by a delayed Cherenkov signal with a
similar time width and a comparable number of struck PMTs. The delayed signal
arises from a cascade of multiple $MeV$-scale gamma-rays (summing to $\sim
8~{}MeV$ ) that are produced upon de-excitation of the gadolinium nucleus,
following its excitation by capture of the IBD-generated neutron. The time
interval between the prompt positron light and the delayed neutron light is
about 20-50 $\mu s$ depending on the gadolinium loading. Compared with
backgrounds, the IBD event pairs are separated by a relatively short time
interval. This temporally close event pair is often referred to as a
correlated or coincident signal. The pair of events are also relatively close
spatially, and have relatively high energies compared to most backgrounds. As
our simulations show, this combination of properties can be used to robustly
suppress backgrounds and isolate a sample of antineutrino events with good
efficiency.

In Gd-H2O detectors, backgrounds for the reactor antineutrino signal fall into
four main categories:

  1. 1.

pairs of accidental coincidences;

  2. 2.

pairs of muogenic fast neutrons;

  3. 3.

beta-n decays from long-lived muogenic radionuclide on oxygen in the water;
and,

  4. 4.

Other reactors

The energies of geological beta decay antineutrinos are too low to create a
significant contribution to the background in water Cherenkov detectors.

Accidental coincidence backgrounds arise when exactly two physically
independent interactions appear close in time ’accidentally’, mimicking the
time-correlated antineutrino signal. These are also referred to as
uncorrelated backgrounds. The remaining backgrounds in the above list are
correlated backgrounds, meaning the same physics process produces both the
prompt and delayed events, with a time distribution similar to that of the
antineutrino-induced positron-neutron signal.

The accidentals rate does not depend on depth but does depend on the
composition of the detector and environs, and on factors such as the shielding
distance of the inner volume from the edge of the detector. The accidental
background rate also depends on energy threshold and vertex position in the
detector, the vertex resolution and the degree of fiducialization.
Fiducialization refers to the definition of a good or ’fiducial’ central
region, away from the PMTs and detector walls, based on the reconstructed
location of the event in the water volume. This location is reconstructed by
comparing the arrival times of individual Cherenkov photons at the hit PMTs.
Even after fiducialization, ambient radioactivity from the detector edge (PMTs
and walls) may still contribute to the accidentals rate via gamma straggling
and vertex misreconstruction. The simulations described below provide
estimates of the accidentals rates before and after fiducialization.

Spallation caused by unvetoed or ’punch-through’ muogenic fast neutrons
generates neutron pairs in the target, which subsequently thermalize and
capture with a time interval and energy ranges characteristic of reactor
antineutrinos. The main concern is muons interacting outside of the detector
which do not produce a veto signal. We note that neutron-induced proton recoil
events an important background in liquid scintillator detectors, are not a
problem in water as nearly all recoiling protons are below the Cherenkov
threshold. This does reduce the direct contribution of high energy neutron
recoil backgrounds in the target region, but renders these fast neutron recoil
events invisible in the veto region.

Table 2: Expected rate of neutrons ($n$) at a depth of 1400 m.w.e. emerging from the side-walls.  $E_{n}$ above | XZ Walls | YZ Walls | All Side Walls | Flux
---|---|---|---|---
| (Hz) | (Hz) | (Hz) |  $n\cdot$day-1
$>$1 (MeV) | 5.77e-02 | 4.36-02 | 2.03e-01 | 17,500
$>$10 (MeV) | 4.02e-02 | 3.04e-02 | 1.41e-01 | 12,200
$>$100(MeV) | 8.34e-03 | 6.30e-03 | 2.93e-02 | 2,530

Long-lived muogenic radionuclides, such as 9Li, can in the course of decaying
generate paired signals with time structures and energy depositions that are
similar to the antineutrino signal. The long lifetimes make direct vetoing of
these radionuclide backgrounds difficult, though a veto may be effected for a
portion of the signal. Because this correlated background has not yet been
directly measured in water, we rely on indirect estimates from related
experiments in order to set bounds on the rates. This results in a large
uncertainty in the radionuclide background estimate. Even with this
uncertainty, we show here that the baseline WATCHMAN design can easily attain
the required sensitivity goals for the reactor signal.

The WATCHMAN collaboration is now in the process of making direct measurements
of the rate of correlated event production from muogenic radionuclides, using
a few ton dedicated underground Gd-H2O detector known as WATCHBOY. The
collaboration has also fielded a high energy neutron spectrometer, the
Multiplicity and Recoil Spectrometer (MARS) at multiple depths in an
underground mine, in order to measure the fast neutron background. Upon
completion of the measurement campaigns, the WATCHBOY and MARS data will
together be used to reduce the uncertainty in the background estimates.

Absent direct measurements, we used two approaches to estimate the rate of 9Li
for WATCHMAN. The first approach was to scale the estimated radionuclide rate
from the KamLAND experiment Abe:PRC81 , a scintillator-based experiment in
which the primary radionuclide production target is carbon. The second was to
scale an upper limit on radionuclide production in the Super-Kamiokande
detector Li:PRD73 , a water-based experiment like WATCHMAN, in which the
primary radionuclide production target is oxygen. Differences in detection
efficiencies, overburden, and fiducial mass were accounted for in the scaling
process. For the KamLAND scaling, the production rate of radionuclides on
carbon was assumed to be identical to that for oxygen.

Real antineutrinos from other reactors also form a small part of the
background for WATCHMAN. These are calculated using the IBD efficiency as
derived from the simulation, based on the locations of all known nearby
reactors. This background is not significant for our measurements at the
Morton site.

We modeled the accidental coincidence rate, muogenic fast neutron and
radionuclide rates in WATCHMAN, assuming our baseline design. If no
backgrounds were present, our simulations indicate that WATCHMAN would achieve
a remarkably high intrinsic signal detection efficiency of $65\%$. This is
indicative of the ultimate performance of the detector as it scales to larger
masses, since the accidentals backgrounds will fall off quickly as the
detector mass grows. This rapid falloff with increasing target volume is due
to the fact that the thickness of water necessary to suppress wall and PMT
backgrounds grows much more slowly than the target volume as the detector mass
is increased. However, as shown here, the efficiency of the demonstration
WATCHMAN detector is necessarily lower than $65\%$, since residual backgrounds
must be suppressed in this relatively small detector, at some (still
relatively modest) cost in signal efficiency.

The models used for each class of background in the simulation were as
follows:

  1. 1.

The rate of di-neutrons from cosmogenic fast-neutrons was evaluate from Mei
and Hime predictions Watchman:MeiHime . The neutron flux estimated for the
four walls of a cavern the size of the Davis cavern are shown in Table
LABEL:table:FastNeutronFlux. With our baseline one meter thick veto and
fiducial skin, the vast majority of the fast neutrons that reach the detector
are either caught by the detector veto or reconstruct outside of the fiducial
volume. Our study shows that out of a incident rate of 17,500 neutrons/day,
only $1.3\pm 0.3$ neutron/day will create a prompt and delayed pair within the
fiducial volume.

  2. 2.

the U/Th/K activity from the PMT glass (341 ppb/1.33 ppm/260 ppm); gammas from
the U/Th chains were isotropically generated at the PMT were found to
reconstruct within the Fiducial volume less than 4% of the time.

  3. 3.

the background arising from PMT dark noise was taken into account in two
steps. First, PMT dark noise was added in the time window of the event to
properly reproduce the triggering conditions. Second, independent toy Monte
Carlo studies were made of triggers arising from statistical fluctuation as a
function of the trigger time window. The rate of PMT dark noise induced
backgrounds was found to be negligible.

  4. 4.

the detector response to 9Li was evaluated by generating a positron from a
beta-decay spectrum and an associated decay neutron at a vertex distributed
throughout the detector volume and with the correct decay lifetime. The
detector is more sensitive to 9Li than IBD in part due to the higher prompt
energy of the positron. The detection efficiency could be as high as 85%
depending on the triggering conditions. However, two methods are available to
reduce the rate of this background. FIrst the time veto after a high-energy
muons may be increased (particularly for showering muons, which are more
likely to produce radio-nuclides). Second, events can be removed that are near
a reconstructed muon track, while allowing valid events elsewhere in the
fiducial region. The results shown in this section do not have these rejection
techniques applied and are therefore conservative.

The estimates for these backgrounds as a function of detector threshold are
shown in Figure 5.

Figure 4: Detector response to reactor anti-neutrino inverse beta decay on the left. On the right is detector response to mono energetic positrons (in kinetic energy). Table 3: Signal and background estimates for the Standard glass PMT option and the PMT installed 1 meter away from the fiducial volume. The best and worst case scenario are evaluated where the signal to background ratio is maximized as is shown in Figure 5, right. | Best Case (low 9Li expectation) | Worst Case (high 9Li expectation)
---|---|---
IBD Rate (day-1) | 4.3 | 4.6
IBD Efficiency (%) | 22 | 24
Background Rate (day-1) | 1.8 | 6.5
Dark noise ($\leq$ 4.5 kHz) (day-1) | $\ll 0.1$ | $\ll 0.1$
Accidentals coincidence (day-1) | 0.2 | 0.3
Fast-neutron (day-1) | 1.3 | 1.3
Radio-nuclide (9Li) (day-1) | 0.3 | 4.9

Figure 5: Signal and background as a function of the detector threshold and
the detection sensitivity ($S/\sqrt{B}$) for both the low and high estimates
of radio-nuclide production. No muon tagging was assumed to reduce this radio-
nuclide rate, however the low-9Li represent a scenario where the radio-nuclide
background rates are small compared to the di-neutron rates from fast-neutron
and therefore reflect the optimal improvements that could be achieved from
muon-tagging of radio-nuclide.

The analysis criteria were that the events reconstruct within the 1-kton
fiducial volume and that the time difference between the prompt-positron and
delayed-neutron be less than 100 $\mu$s. This short capture time between
prompt and delayed events allows both a lowering of the energy threshold and a
significant reduction in backgrounds. The accidentals coincidence rate ($C$)
per day can be estimated from the singles rate ($S$) per second with the power
law $C=8.6\cdot S^{2}$. The probability, evaluated by simulation, that two
events are at most two meters from each other in the fiducial volume is
($2.3\pm$0.5)%. This reduction results in a coincidence rate in the fiducial
volume of $C=(0.20\pm 0.05)\cdot S^{2}$.

In summary, we have shown that even with conservative assumptions about
backgrounds, the baseline WATCHMAN design can easily accomplish its main
nonproliferation goal of high-confidence detection of the reactor IBD signal
using two 30 day periods of reactor on ( $100\%$ power) and reactor off
data.The simulation package developed for the reactor analysis has been
extended in a consistent way to permit analyses of other physics interactions,
which are described in later sections of this white paper.

##  VI Physics and Detector Research and Development Goals

The WATCHMAN physics program begins with goals that are achievable with the
baseline Gd-H2O Water Cherenkov detector. The main physics goals in the first
phase of the program are:

  1. 1.

world-class supernova sensitivity, he first such capability in the U.S. in two
decades, including the ability to separately identify electron neutrino and
antineutrino signals, to recover directional information, and to potentially
provide an early warning to experiments such as LBNE and LIGO that seek to use
a neutrino pre-trigger to arm their detectors for supernova physics;

  2. 2.

competitive sensitivity to sterile neutrinos, using a compact low energy
neutrino beam provided by the ISODAR program

  3. 3.

unique sensitivity to non-standard neutrino interactions, using the ISODAR
neutrino beam.

In a second phase, using water-based scintillator or oil-based scintillator,
the main goals are:

  1. 1.

Enchanced sensitivity to sterile neutrinos and non-standard neutrino
interactions, using the ISODAR beam; and

  2. 2.

increased efficiency and spectral resolution for supernova antineutrinos.

WATCHMAN’s sensitivity to the neutrino mass hierarchy was examined and found
to be limited at this standoff, regardless of the target fill.

In addition to the physics goals, WATCHMAN is an excellent U.S.-based test-bed
for technological advances that are relevant for future large scale water
detectors. The main technological advance, demonstration of low energy
antineutrino sensitivity using Gd-doped water, is already the main goal of the
WATCHMAN nonproliferation program. In addition, new technologies that can be
fielded in WATCHMAN include, Large Area Picosecond Photodetectors, high
quantum efficiency PMTs, U.S.-manufactured PMTs, water-based liquid
scintillator, Winston cones and wavelength shifting plates can all be tested
in WATCHMAN. This will help ensure U.S. involvement and competitiveness as
large-scale water-based antineutrino detectors are planned and built
worldwide.

In the following sections we discuss each of the physics goals for the water
detector and the follow-on detectors.

###  VI.1 Supernova

Supernova neutrinos carry unique information about one of the most dramatic
processes in the stellar life-cycle, a process responsible for the production
and dispersal of all the heavy elements (i.e., just about everything above
helium) in the universe, and therefore a process absolutely essential not only
to the look and feel of the universe as we know it, but also to life itself.
As a gauge of the community’s level of interest in these particular particles,
it is worth noting that, based upon the world sample of twenty or so neutrinos
detected from SN1987A, there has on average been a theoretical paper published
once every ten days – for the last three decades! This makes it all the more
surprising that the US has not had a supernova neutrino detector of its own in
operation since the end of the IMB experiment (which recorded eight neutrinos
from SN1987A) in 1991. WATCHMAN will be the first US detector since IMB to
have world-class sensitivity to supernova neutrino and antineutrinos.

The next time a Milky Way core collapse supernova goes off, an event expected
to occur every 30 years or so 0004-637X-778-2-164 , it would be extremely
desirable to have a sizable gadolinium-doped water Cherenkov detector like
WATCHMAN in operation when the resulting neutrino wave sweeps across the
planet. This is primarily because the most copious supernova neutrino signal
by far ($\sim$88%) comes from inverse beta events. They are only produced by
one of the six species of neutrinos and antineutrinos which are generated by a
stellar collapse, and so if we could tag them individually by their follow-on
neutron captures then we could extract the $\bar{\nu}_{e}$ time structure of
the burst precisely, gaining valuable insight into the inner dynamics of the
explosion. What’s more, we could then subtract them away from the more subtle
non-$\bar{\nu}_{e}$ signals, uncovering additional information that would
otherwise be lost during this once-in-a-lifetime happening.

Due to its unique capability to immediately identify a galactic supernova as
genuine while the neutrino wave is still passing through the Earth, WATCHMAN
will be able to instantly alert both the astronomical community and other
projects that a core collapse is currently underway. Major physics experiments
such as LBNE, LIGO, and IceCube – whose challenging SN analyses will likely
require matching extremely complex, exceedingly noise-like, and/or
exceptionally sub-threshold signals to a precise external start time – would
benefit greatly from a realtime alert from WATCHMAN. The knowledge gained in
the precious few hours between the arrival of the neutrinos (which are
generated first) and the arrival of the supernova’s first light (the so-called
shock breakout) will serve to guide and optimize the subsequent multi-
wavelength observations of the dying star. In particular, the physical
proximity of WATCHMAN to LBNE means that rapid (few ms) signaling of a
supernova to the Long Baseline Neutrino Experiment’s Akiri:2011dv  trigger
system is possible. This may prove to be useful in simplifying or
strengthening LBNE’s supernova watch capability, with potential attendant cost
savings and improved physics reach. Additional work with the LBNE
collaboration - of which several of the present authors are members - will
seek to quantify these improvements or savings.

Table 4 shows the expected signals in WATCHMAN for a galactic type II
supernova. For a stellar collapse 10,000 light years distant from earth
(somewhat less than halfway to the galactic center) there will be a total of
about 4,000 events seen in WATCHMAN. As one can see, the inverse beta events
dominate the expected signals. However, there is valuable information to be
gained from the other signals, information which would be largely inaccessible
without neutron tagging from dissolved Gd2(SO4)3 .

Neutrino | Percentage of | Type of
---|---|---
Reaction | Total Events | Interaction
$\overline{\nu}_{e}+p\rightarrow n+e^{+}$ | 88 | Inverse Beta
$\nu_{e}+e^{-}\rightarrow\nu_{e}+e^{-}$ | 1.5 | Elastic Scattering
$\overline{\nu}_{e}+e^{-}\rightarrow\overline{\nu}_{e}+e^{-}$ |  $<$1 | Elastic Scattering
$\nu_{x}+e^{-}\rightarrow\nu_{x}+e^{-}$ | 1 | Elastic Scattering
$\nu_{e}+^{16}O\rightarrow e^{-}+^{16}F$ | 2.5 | Charged Current
$\overline{\nu}_{e}+^{16}O\rightarrow e^{+}+^{16}N$ | 1.5 | Charged Current
$\nu_{x}+^{16}O\rightarrow\nu_{x}+O^{*}/N^{*}+\gamma$ | 5 | Neutral Current
Table 4: Breakdown of supernova neutrino events expected in WATCHMAN from a
galactic supernova. Oscillations are taken into account. $\nu_{x}$ indicates
the total interactions of $\nu_{\mu}$, $\nu_{\tau}$, and their antineutrinos.

For example, being able to tag the $\bar{\nu}_{e}$ events would immediately
double WATCHMAN’s pointing accuracy back to the progenitor star. This is
merely the result of statistics, since our elastic scatter events (about 3% of
the total) would no longer be sitting on a large background in angular phase
space PhysRevD.68.093013 . WATCHMAN would be the only detector in the world
other than Super-Kamiokande – and the only detector in the Western Hemisphere
– with neutrino pointing capability. Reducing the error on this quantity by a
factor of two, roughly from 10 degrees to 5 degrees, via neutron tagging would
reduce the amount of sky to be searched by a factor of four. This could prove
quite important for the wide-field astronomical instruments which would be
frantically attempting to see the first light from the supernova.

At the same time, this event-by-event subtraction could allow identification
of the initial electron neutrino pulse from the neutronization of the
infalling stellar matter, a key and as yet unobserved input in understanding
supernova dynamics.

What’s more, the neutral current events, which may be easily identified by
their mono-energetic gammas between 5 and 10 MeV once the $\bar{\nu}_{e}$
events are subtracted, are very sensitive to the temperature of the burst and
the subsequent neutrino mixing PhysRevLett.76.2629 .

With a neutrino energy production threshold of 15.4 MeV, the weakly backward-
peaked charged current events are even more sensitive to the burst temperature
and the subsequent mixing PhysRevD.36.2283  than the NC events. As there are
no other good $\nu_{e}$ detectors currently in operation, WATCHMAN’s charged
current events, if distinguishable from the $\bar{\nu}_{e}$ background, would
provide one of the only sources of data on supernova $\nu_{e}$’s.

If the exploding star was big and rather close (say, like Betelgeuse at 600
light years) we would get an early warning of its impending collapse
Odrzywolek2004303 . Approximately a week before exploding, the turn-on of
silicon fusion in the core would raise the temperature of the star
sufficiently that electron-positron annihilations within its volume would
begin to produce $\bar{\nu}_{e}$ just above inverse beta threshold. The sub-
Cherenkov positrons would be invisible, but in WATCHMAN the captures of the
resulting neutrons on Gd2(SO4)3 would result in a sudden and continuing
increase of our usual low energy singles rate.

As early as one day before collapse we would see a several sigma excursion in
our low energy singles rate. The continuing increase in singles rate would
clearly indicate a coming explosion, ensuring that we did not intentionally
turn off WATCHMAN for calibration or maintenance and thereby miss the coming
explosion.

In addition, a gadolinium-enriched WATCHMAN would be sensitive to quite late
black hole formation following a supernova explosion within our galaxy, since
the distinctive coincident inverse beta signals from the cooling phase could
be distinguished from the usual singles backgrounds. An abrupt cutoff of these
coincident signals occurring even several minutes after the main burst would
be the conclusive signature of a singularity being born. Direct observation of
such an event would clearly be of great value, especially when correlated with
electromagnetic signals from X-ray or gamma-ray observatories as well as
gravitational wave observations.

Finally, WATCHMAN would allow us to be absolutely certain that a supernova was
occurring the moment the data started to arrive. This is because the
distinctive correlated $\bar{\nu}_{e}$ event pairs, with the positron and the
neutron capture separated in time by only tens of microseconds, would in
general be well separated from other supernova events, which at for an
explosion at 10,000 light years would come in every millisecond or so at the
height of the burst. This would yield a clear “heartbeat”-like time structure
in the time plot of the events – something that could be easily spotted
online. Of course, if the supernova was close enough that these event pairs
were overlapped by subsequent SN signals then we would also know for sure that
something exciting was happening, and in such a near-field case we may very
well have been waiting for the burst anyway, due to the early warning from
silicon burning. Either way, the surer we are that a supernova has just
occurred, the faster we should be able to get word out to the community.

So, from extracting the neutronization signal, to deconvolving the main burst,
to pointing back at the progenitor star, to observing late black hole
formation, to eventually announcing the event to the world, having Gd2(SO4)3
in WATCHMAN would positively impact just about every physics topic connected
to the detection of a galactic supernova. Much of this physics would be buried
in background, degraded in precision, or wholly inaccessible otherwise. In
summary, the key benefits are:

  1. 1.

Neutron tagging of the inverse beta events would allow the de-convolution of a
galactic supernova’s various signals, which in turn would allow much more
detailed interpretation of the physics of the burst. This will result in
significantly improved pointing back to the exploding star.

  2. 2.

Early warning (hours before the arrival of the supernova neutrino wave) of
large, relatively nearby supernovas would be possible via the observation of
silicon-powered fusion in the dying stellar core.

  3. 3.

Gadolinium would allow very late time black hole formation – minutes after the
initial explosion – to be observed. This critically important signal could
otherwise be hidden by background events.

  4. 4.

The “gadolinium heartbeat” of prompt events rapidly followed by delayed events
in about the same locations would make the arrival of a genuine neutrino burst
instantly identifiable, vital for getting word out to the rest of the world in
a timely fashion.

###  VI.2 Sterile Neutrino Search

In recent years improved data and models of reactor antineutrino emission led
to an increase in the predicted antineutrino flux from fission reactors, which
in turn led to an apparent deficit in observed flux over many separate
experiments, relative to the new prediction PhysRevC.83.054615 ,
PhysRevC.84.024617 . This deficit has been referred to as the reactor anomaly.
Short baseline accelerator experiments such as LSND PhysRevLett.77.3082 ,
PhysRevD.64.112007  and MiniBooNE PhysRevLett.110.161801  have also reported
anomalous results that are difficult to reconcile with the standard three-
flavor neutrino model. This is sometimes referred to as the accelerator
anomaly. A popular (though by no means unique PhysRevC.84.024617 )
interpretation of these results is that another oscillation channel exists,
with at least one sterile (undetectable) neutrino and relatively large mass
eigenstate of at least $\sim 1eV$.

The proposed Isotope Decay At Rest (IsoDAR) experiment PhysRevLett.109.141802
will search for evidence of short baseline sterile neutrino oscillation using
an intense flux of $<E>=6.4$ MeV electron antineutrinos resulting from beta
decay-at-rest of 8Li. The electron antineutrino source will need to be located
next to a kiloton-scale antineutrino detector capable of sufficient energy and
position resolution to reveal oscillations in $L/E$, where $L$ is the source-
detector distance and $E$ is the antineutrino energy.

One of the first sites considered for the IsoDaR beam experiment was the
KamLAND detector. KamLAND’s position and energy resolution are more than
adequate to observe oscillations if the missing mass eigenstate is $\sim 1eV$.
Here we examine the sensitivity of the WATCHMAN detector to sterile neutrinos
using the IsoDAR beam. Of course, there are important practical considerations
related to the feasibility of deploying the beam in the experimental hall.
Very preliminary studies of the feasibility of deployment based on the cavern
layout have been encouraging, though significant engineering work would be
necessary to accommodate the IsoDAR beam. In this white paper, we set aside
these considerations, focusing on the sensitivity of WATCHMAN detector to the
physics signal, assuming the beam is successfully deployed.

Figure 6: The antineutrino flux spectrum of interacting antineutrinos in
WATCHMAN. An estimated $6.26\times 10^{3}$ antineutrino interactions can be
generated over a five-year period with IsoDAR at the proposed beam position
(16 meters from the center of the detector). The energy and position
resolutions for Gd-doped water, Gd-doped water based liquid scintillator and
pure scintillator are also given as a function of energy.

The key difference between the KamLAND and WATCHMAN detectors is the detection
medium, which was liquid scintillator in KamLAND, and will be gadolinium-doped
water in WATCHMAN (in its first phase). In this case, both energy and position
resolution will be lower than for KamLAND, due to the significantly lower
photon production from Cherenkov emission compared to scintillation. However,
we anticipate that the resolution in WATCHMAN will be good enough to exclude
the region of oscillation parameter space most favored by the reactor and
accelerator experiments to date (see Figure 7) or indeed discover an
oscillation if it is there.

The IsoDAR beam is expected to produce approximately $1.3\times 10^{23}$
antineutrinos over a five-year period at an average energy of $6.4$ MeV. The
energy spectrum of the resulting antineutrino interactions is shown in Figure
6. It is slightly higher in energy due to the cross section of the inverse
beta decay reaction on protons, $\bar{\nu}+p\rightarrow e^{+}+n$, which
increases with the square of the antineutrino energy. Just as for reactor
antineutrino experiments, the positron energy ($E_{e^{+}}$), is related to the
antineutrino energy ($E_{\mbox{$\bar{\nu}_{e}$}}$), by

$E_{e^{+}}=E_{\mbox{$\bar{\nu}_{e}$}}-1.8MeV$ (2)

The resulting positron energy distribution peaks at approximately $7MeV$. As
we show here, despite the absence of scintillator in WATCHMAN Phase I, the
$\sim 7MeV$ positrons are detectable with sufficient resolution in the Gd-H2O
target to perform a sensitive search for oscillations.

An IsoDAR deployment at a distance of $L=16m$ from WATCHMAN will have maximal
sensitivity to mass squared difference near $\Delta m^{2}\sim 1eV^{2}$, the
region most favored by the reactor and accelerator anomalies. Figure 7 shows
the expected sensitivity of IsoDAR deployment next to WATCHMAN assuming a 3
year run. The sensitivity for WbLS is also shown, where the medium is assumed
to have a light yield of a few hundred scintillator photons generated per MeV.

Figure 7: Left: The sensitivity of the WATCHMAN detector to $L/E$ (baseline
distance $L$ divided by antineutrino energy $E$), for two different detection
media - water (upper plot) and light scintillator (lower plot). Right: The
sterile neutrino oscillation parameter space excluded by WATCHMAN after 3
years of run time, assuming Gd-doped water (red) and Gd-doped water-based
liquid scintillator (black).

The water-based WATCHMAN detector was assumed to have photocathode coverage of
$40\%$, using 12-inch high quantum efficiency PMTs. Approximately 10
photoelectrons per MeV can be expected from positrons in water. The
sensitivity plots in Figure 7 were based on simulations done for large water
based detector proposals such as LBNE, which in turn grew out of well tested
and tuned simulations from the Super-K detector.

In generating the sensitivity plots, we used the backgrounds in WATCHMAN that
were calculated for the reactor monitoring task, as summarized in section V.
Based on those simulations, we expect that WATCHMAN will detect approximately
5 IBD events per day from the nearby Perry reactor. Backgrounds from both
cosmogenic radionuclide production and fast neutrons from the rock are
expected at about 6 per day. Backgrounds from the rock or from the PMT
structures inside the detector tend to be subdominant due to the requirement
that IBD detection depends on the coincidence detection of both the positron
and delayed neutron. Neutron and gamma-ray backgrounds from the IsoDAR beam
itself will be shielded by rock between the beam and the detector. We assign a
total background rate of $\sim 20$ events per day from the reactor and all
other backgrounds.

We conclude that a sensitive sterile neutrino search can be conducted with the
WATCHMAN detector in its first and follow-on phases, using both the Gd-H2O and
Gd-WbLS targets.

###  VI.3 Non-Standard Neutrino Interactions

As described by Conrad:2013sqa , a sensitive search for non-standard neutrino
interactions can be performed by collecting a sufficiently large number of
antineutrino electron scattering events
($\bar{\nu}+e^{-}\rightarrow\bar{\nu}+e^{-}$). In both the pure Gd-H2O and
scintillator mode, the WATCHMAN detector provides a large target region that
can be used for this purpose, with the antineutrinos coming from the ISODAR
beam. Examples of non-standard interactions include effects on the cross-
section arising from heavy partners of the known light neutrinos, or new gauge
bosons that couple only to neutrinos. In this section we discuss the
sensitivity of the WATCHMAN Gd-H2O and scintillator options to non-standard
neutrino interactions. The IsoDAR source characteristics, and the beam and
detector geometry assumed for the calculations here are the same as described
in section VI.2. However, in this section, we examine Gd-H2O and oil-based
scintillator options, rather than water-based scintillator.

Following Conrad:2013sqa , the modified Standard Model cross section
incorporating potential non-standard couplings is written as:

$\frac{d\sigma(E_{\nu},T)}{dT}=\frac{2G^{2}_{F}m_{e}}{\pi}\left(\tilde{g}_{R}^{2}+\tilde{g}_{L}^{2}(1-\frac{T}{E_{\nu}})^{2}+\tilde{g}_{R}\tilde{g}_{L}\right)$
(3)

Here $\tilde{g}_{R}=g_{R}+\epsilon_{ee}^{eR}$and
$\tilde{g}_{L}=g_{L}+\epsilon_{ee}^{eL}$ are the Standard Model couplings
$g_{L(R)}$ , modified by the NSI parameters $\epsilon_{ee}^{eR(L)}$ for right-
handed and left-handed couplings. Flavor-violating couplings to muon and tau
neutrinos are strongly restricted 1126-6708-2003-03-011  and are not included
in Eqn. (4).

We consider two cases: the WATCHMAN Phase 1 pure Gd-H2O target and the
WATCHMAN Phase 3 scintillator target. We begin with the scintillator case,
expected to be similar to KamLAND/IsoDAR. This case has already been studied
extensively Conrad:2013sqa . We then consider the different treatment of
backgrounds that would be required in a Gd-H2O detector.

####  VI.3.1 Sensitivity with a scintillator target

Backgrounds divide into two categories, beam-related IBD events with a missed
final-state neutron, and non-beam backgrounds arising from solar neutrino
interactions, muon spallation, and ambient radiation from the detector and
nearby rock. In scintillator, the non-beam backgrounds can be measured
$in~{}situ$ accurately by simply turning off the beam. We assume here one year
of total beam off time will be devoted to this measurement. The spectral shape
of the IBD backgrounds can be measured by employing the neutron capture as a
tag. The normalization of this background will depend on an accurate knowledge
of the neutron tag inefficiency - obtained from calibrations. Gamma ray
backgrounds from the detector wall components and from radon in the
scintillator are scaled from the KamLAND/IsoDar prediction by relative
fiducial volume. Cosmogenic radionuclides are expected to contribute
significantly more to the background at WATCHMAN, since they are depth
dependent (see Table 6), and WATCHMAN will be shallower (1430 m.w.e. versus
2700 m.w.e.). We assume that the bulk of radionuclide backgrounds are caused
by showering (high energy) muons passing through the detector. Using a GEANT4
simulation of muon flux as a function of depth and energy, and using a
representative sea level muon energy spectrum, the predicted rate of showering
muons at WATCHMAN, relative to KamLAND is 2.6 times higher. At this rate, the
5 second KamLAND veto must be reduced to 2 seconds in order to maintain an
equivalent live time. We extrapolated the 11Be, 8Li and 8B rates from
KamLAND/IsoDAR using the known isotope lifetimes (See Table 5) to find the
rates at WATCHMAN. The WATCHMAN results shown in Table 6 predict approximately
7030 electron scatter events within the WATCHMAN fiducial volume from an
IsoDAR beam situated 16 meters from the center of the detector.

####  VI.3.2 Sensitivity with a pure Gd-H2O target

In water, antineutrino-electron scattering events generate a Cherenkov cone
that arises from the recoiling electron. The low light output compared to
scintillator changes both the signal and background detection efficiencies and
alters the strategy for isolating the signal. The presence of oxygen in the
target, rather than carbon, increases the variety of radionuclide isotopes
that may be produced via muon spallation. The exact isotopes and their yields,
however, have never been measured in water. We rely on the values in Table 5),
from Li:PRD73 , generated from a FLUKA simulation of the Super-Kamiokande
detector. The expected event rates for each of the five most dangerous
radionuclides were presented in Table 6.

Table 5: The most dangerous long lived cosmogenic radionuclide backgrounds for the water-based Super-K target. The predictions were generated from a FLUKA study by Li:PRD73 . The radionuclide isotopes of interest to the organic scintillator experiment include only a subset of these, 11Be, 8Li and 8B Conrad:2013sqa . Isotope | Half-life (s) | Decay Mode |  Yield $\bf{(\times 10^{-7}\mu^{-1}g^{-1}cm^{2})}$ | Primary Process
---|---|---|---|---
${}^{16}N$ | $7.13$ | $\beta^{-}\gamma(66\%),\beta^{-}(28\%)$ | $18$ | (n,p)
${}^{15}C$ | $2.449$ | $\beta^{-}\gamma(63\%),\beta^{-}(37\%)$ | $0.8$ | (n,2p)
${}^{11}Be$ | $13.8$ | $\beta^{-}(55\%),\beta^{-}\gamma(31\%)$ | $0.8$ | (n,$\alpha+$ 2p)
${}^{8}B$ | $0.77$ | $\beta^{+}$ | $5.8$ | ($\pi^{+},\alpha+$ 2p $+$ 2n)
${}^{8}Li$ | $0.84$ | $\beta^{-}$ | $13$ | ($\pi^{-},\alpha+^{2}H$ $+$ p $+$ n)
Table 6: The estimated elastic scattering signal and predicted backgrounds after 5 years running time for IsoDAR at WATCHMAN. Estimates for both the liquid scintillator and $Gd-H_{2}O$ WATCHMAN targets are given. Also given are background values assuming we use the cosine of the electron scattering angle with respect to the IsoDAR beam as a discrimination parameter. Event Type | Liquid Scintillator | $\bf{Gd-H_{2}O}$ | $\bf{Gd-H_{2}O,cosine(phi)>0.5}$
---|---|---|---
IsoDAR Elastic Scattering Signal | 7030 | 9010 | 9010
Misidentified IBD | 1920 | 153500 | 38380
${}^{208}Tl$ gamma rays | 1154 | 1154 | 289
Steel Support Gamma rays | 437 | 437 | 110
Rock Gamma rays | 1025 | 1025 | 256
${}^{8}B$ Solar Neutrinos | 1700 | 2180 | 540
Radionuclide ${}^{8}B$ | 3155 | 4880 | 1220
Radionuclide ${}^{8}Li$ | 5595 | 12720 | 3180
Radionuclide ${}^{11}Be$ | 2840 | 3690 | 920
Radionuclide ${}^{15}C$ |  | 2320 | 580
Radionuclide ${}^{16}N$ |  | 75750 | 18940
Total Backgrounds | 17830 | 257660 | 64415

The signal efficiency depends strongly upon on the visible energy threshold,
$E_{vis}$. This is necessarily higher in water than in scintillator, since the
number of photons produced is small. In the present analysis, the gamma ray
emissions from impurities in the water, the rock walls and detector walls were
estimated by scaling directly from the IsoDAR NSI paper Conrad:2013sqa , with
the same energy threshold of $E_{vis}=3$ MeV applied. The radionuclide, solar
neutrino and misidentified IBD backgrounds (from IsoDAR and from the Perry
reactor) have known and well defined energy spectra. Therefore no low energy
threshold was applied for these backgrounds.

Beam-related backgrounds are expected to be higher in water than scintillator,
since the efficiency for detecting the IBD final state neutron is
significantly lower ($\sim 80\%$) than in scintillator ($99.75\%$,
Conrad:2013sqa  with cuts optimized for IBD rejection). Since the cross
section per atom and incident antineutrino is around ten times higher for IBD
events compared with ES events, This background must be further suppressed to
achieve a viable result in water. For this purpose, we rely on the angular
correlation between the reconstructed angular direction of the recoiling
electron for ES events and the incoming antineutrino.

Figure 8: The predicted water target detector response as a function of
detected photoelectrons, according to the GEANT4 WATCHMAN simulation (left).
The cosine of the angle between the reconstructed electron direction and the
antineutrino direction for the electron scattering signal and background at
WATCHMAN. The predicted number of IsoDAR events and backgrounds correspond to
5 years run time. Events at cosine(angle) = 1 are defined as pointing directly
away from the IsoDAR beam source (as expected for a scattered electron with
zero scattering angle). Background events were sampled from a flat
cosine(angle) distribution.

Table 6 shows the beam and non-beam background predicted for a water Cherenkov
WATCHMAN. Note that the misidentified IBD rate is 80 times higher than for
scintillator, since the neutron tagging efficiency drops from $99.75\%$ to
$80\%$. Figure 8 (left) shows the detector background response in WATCHMAN.
Figure 8 (right) shows the results of a GEANT4 simulation of electron
scattering events in WATCHMAN, assuming a run time of 5 years. The Cherenkov
cone reveals the direction of the scattered electron, the scattered electrons
point back to the IsoDAR source. Here we plot the signal and background events
as a function of the cosine of the scattering angle, which is approximately
flat for background, and assumed to be flat here. We anticipate that the water
Cherenkov WATCHMAN experiment will employ a statistical subtraction, based on
scattering angle, to extract the spectral shape and integral number of
electron scattering events.

Figure 9 shows the predicted visible spectrum from the electron scattering
IsoDAR signal events together with all the backgrounds considered here. A
statistical subtraction of the background was performed to extract the visible
energy (in photoelectrons) of the elastic scattering signal using the
scattering angle distribution.

Figure 9: The WATCHMAN detector response as a function of detected
photoelectrons. Shown here are the total background spectrum, the true
scattered electron spectrum from the IsoDAR beam, the sum of the two (the
detected WATCHMAN spectrum), and finally the background subtracted spectrum -
the statistical subtraction of the backgrounds from the detected spectrum,
based on the reconstructed electron-antineutrino scattering angle.

####  VI.3.3 Conclusions

The IsoDAR NSI experiment will be a significant challenge at either KamLAND or
WATCHMAN. For a liquid scintillator target, the WATCHMAN signal to background
will be approximately $\sim 1:2.4$. At KamLAND it will be $\sim 1:1.4$. The
difference is primarily due to WATCHMAN’s shallower depth, but is mitigated by
the larger number of detected events. If high quantum efficiency PMTs are used
at WATCHMAN the energy resolution will be better, potentially allowing for
some further reduction in background and/or an enhanced energy spectrum. As it
stands, we ignore the potential but uncertain gains from energy resolution and
potential problems associated with not having a non scintillating buffer
region between the target and the PMTs. To compare the statistical uncertainty
of both the KamLAND and WATCHMAN scintillator options we must assume some beam
off time is devoted to measuring the background. We assume that one year of
beam off time can be obtained in both experiments. The radionuclide background
component however, can be measured while the beam is on, by analyzing the
event rates immediately following muons. We assume that both KamLAND and
WATCHMAN will be able to measure the rate of mis-ID IBD events to a
vanishingly small uncertainty using calibration sources. With these
assumptions the statistical significances predicted for KamLAND and WATCHMAN
are $19.5\sigma$ and $31.7\sigma$ respectively after 5 years beam on and one
year beam off. These results correspond to uncertainties of $5.1\%$ and
$3.2\%$ respectively.

For the $Gd-H_{2}0$ target, to determine the statistical significance of the
elastic scattering signal we fit a function consisting of the sum of a
constant and exponential to the cosine scattering angle distribution.

$y=A+Be^{5.37x}$ (4)

The slope of the exponential component was fixed at the value determined
earlier (5.37) from a simulation of a large number of signal events - we
assume that in WATCHMAN a directional calibration source will be available to
help determine the exact shape of the signal component for the IsoDAR NSI
experiment. The uncertainty of the integral number of directional elastic
scattered electrons from IsoDAR therefore is given by the fractional
uncertainty of the normalizing intercept of the exponential at
$cosine(\theta)=+1$, which is $\pm 3\%$. The final predicted number of NSI
elastic scattering events from IsoDAR over five years for the $Gd-H_{2}O$
target is therefore $9010\pm 270$, an uncertainty of $\pm 3.0\%$. The reason
the statistical uncertainty of the $Gd-H_{2}O$ result is so small, even though
the signal to background is small (relative to the scintillator option), is
because scattering angle sensitivity allows for a more precise measurement of
the background even while the beam is on.

##  VII Conclusions

WATCHMAN offers a compelling, cost-effective approach to exploiting the unique
synergy between strategic research goals of the U.S. nonproliferation and
physics communities. The detector will provide immediate physics benefit
through its tagging ability for supernova antineutrinos, and consequent
sensitivity to the highly directional supernova neutrino signal. In a follow-
on phase, it will provide a target for the ISODAR neutrino beam, enabling both
a stringent sterile neutrino search and a search for non-standard neutrino
interactions. Perhaps most importantly for the long-term future of U.S.
neutrino physics, WATCHMAN provides a suitably large platform that is uniquely
suited to testing of essential elements of very large neutrino detectors. The
combination of Water Based Liquid Scintillator with Large Area Picosecond
Photodetectors in WATCHMAN will ensure the viability of these technologies for
all follow-on detectors. In recognition of this overlap with the future U.S.
physics program, the WATCHMAN collaboration has grown to include many of the
country’s most knowledgeable experts in water-based neutrino detection, as
well as members of the Advanced Scintillator Detector Concept, an initiative
that is planning for the construction of a multi-hundred-ton WBLS detector in
the United States. The benefit of WATCHMAN to the nonproliferation community
is similarly important. WATCHMAN is a stepping-stone to true long range
discovery or exclusion of small reactors. It provides a path to international,
collaborative efforts at guaranteeing the absence of operating reactors in
wide geographical regions, with important, positive implications for the
nonproliferation regime.

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# Disentangled Non-Local Network for Hyperspectral and
LiDAR Data Classification

###### Abstract

As the ground objects become increasingly complex, the classification results
obtained by single source remote sensing data can hardly meet the application
requirements. In order to tackle this limitation, we propose a simple yet
effective attention fusion model based on Disentangled Non-local (DNL) network
for hyperspectral and LiDAR data joint classification task. In this model,
according to the spectral and spatial characteristics of HSI and LiDAR, a
multiscale module and a convolutional neural network (CNN) are used to capture
the spectral and spatial characteristics respectively. In addition, the
extracted HSI and LiDAR features are fused through some operations to obtain
the feature information more in line with the real situation. Finally, the
above three data are fed into different branches of the DNL module,
respectively. Extensive experiments on Houston dataset show that the proposed
network is superior and more effective compared to several of the most
advanced baselines in HSI and LiDAR joint classification missions.

Index Terms—  Disentangled Non-local, self-attention, hyperspectral, LiDAR,
joint classification

##  1 Introduction

With the advancement of spectral imaging technology, hyperspectral images
(HSIs) have received increasing attention, and have been employed in many
applications, such as marine organism monitoring [1] and land cover
classification [2]. On the other hand, LiDAR data is also widely used in the
classification of high-value crops [3], urban land use analysis. Hyperspectral
and LiDAR data grow rapidly in recent years, inducing many researchers to work
on the joint land cover classification from both data.

HSI has the characteristics of high spectral space dimension and strong data
correlation. Meanwhile, LiDAR images have high spatial resolution, but the
spectral information of it is not as rich as that of HSI. Therefore, when
performing classification tasks, if one single mode of data is used, the
classification performance may subject to certain limitations. For example,
due to the lack of elevation information or the influence of various spectral
changes, a single HSI can hardly distinguish the difference between grasses in
different areas [4]. Therefore, using multimodal data for joint classification
allows people to more accurately identify the interested ground objects.

Until now, many works have successfully demonstrated the advantages of using
multimodal data for classification. For example, the fusion of HSI and
multispectral imagery can greatly improve the spatial resolution [5]. Chen et
al. [6] proposed a new feature fusion framework based on deep neural network
(DNN), which can effectively extract features from HSI and LiDAR data, and
both features are fused through fully connected DNNs.

In particular, with the recent advancement of convolutional neural networks
(CNNs), the fusion strategy based on CNN begins to prevail. In [7], an end-to-
end layered fusion module for CNN is proposed, enabling HSI and LiDAR data to
achieve good collaborative classification performance. Although the module
shows its excellent performance on the corresponding datasets, the larger
receiving field in the convolutional layer and the existence of pooling layer
lead to the lower spatial resolution in the deeper CNN layer, and the
multiscale information of HSI are not fully applied [8]. Therefore, it is
difficult to describe the significant boundary of fine objects in
classification, and correspondingly, the prediction category tends to be
spatially dispersed.

To solve the above problem, inspired by Yin’s work [9], we developed a simple
yet effective HSI and LiDAR joint classification method based on distangled
non-local (DNL) network. The traditional dot-product based attention is split
into a whitened pairwise term and a unary term. The pairwise term fuses the
hyperspectral and LiDAR features. The unary term captures the influence of one
pixel generally over all the pixels in hyperspectral data. The experimental
results on the Houston dataset demonstrate the effectiveness of the proposed
method.

Fig. 1: Schematic illustration of the Disentangled Non-Local (DNL) module. $F$
represents the mixed feature obtained by adding HSI feature and LiDAR feature
according to a certain strategy, while H and L represent the HSI features and
LiDAR features, respectively.

##  2 Methodology

###  2.1 Feature Extraction

Extraction of features from HSI using residual network. To extract multiscale
features, $1\times 1$, $3\times 3$, $5\times 5$ and $7\times 7$ filters are
mixed for depth convolution operation. Meanwhile, the number of these four
types of filters is equal, which is one fourth of the number of channels for
input features. Specifically, one quarter of the channels are convolved with
the $1\times 1$ filter, a quarter of the channels are convolved with the
$3\times 3$ filter, and so on. As such, space correction can be learned at
different scales. Each residual block can be expressed as

$P(X)=s(f(X)+g(X)),$ (1)

where $X$ denotes the input of the residual block, and $P(X)$ denotes the
output of the residual block. $s(\cdot)$ represents the ReLU activation
function. In addition, $f(X)$ represents the residual learning function, which
performs a series of nonlinear transformation operations, and obtains the
output of batching operations. $g(X)$ is a single mapping function, which can
alleviate the problem of gradient disappearance in the network.

At the same time, LiDAR data extracted its elevation information and other
features through CNN. After that, the processed HSI and LiDAR features were
converted to the same scale for addition operation, and then several pooling
and convolution operations were performed to obtain the mixed feature $F$.

###  2.2 Joint classification based on DNL

Non-local blocks can enhance the context modeling capability of conventional
CNNs. However, according to Yin’s work [10], the attention computation of non-
local can be divided into two terms, namely, paired terms and unary terms,
which are tightly coupled and thus affect each other’s learning. Disentangled
non-local (DNL) attention can eliminate this dilemma. As shown in Fig. 1, HSI
and LiDAR features together with $F$ are used as the input of DNL to fuse
multimodal information. On the basis of not affecting the contextual
relationship, the pixel-wise relationship can be learnt within the same
category of regions, and the influence from boundary pixels to all image
pixels can also be learnt effectively.

The DNL module counts pairs between the features of two locations to catch
long-distance dependencies. Let $X_{m}$ denotes the input features at position
$m$, the output features $Y_{m}$ of the DNL module can be computed as

$Y_{m}=\sum_{n\in\Omega}M(X_{m},X_{n})g(X_{n}),$ (2)

where $M$ represents the set of all pixels on the feature map of $H\times W$,
and $g(\cdot)$ is the value transformation function with parameter $W_{v}$.
($X_{m}$, $X_{n}$) is the embedding similarity function from pixel $n$ (called
key pixel) to pixel $m$ (called query pixel), which can be expressed as

$M(X_{m},Y_{n})=\sigma(q_{m}^{T}k_{n}),$ (3)
$\sigma(q_{m}^{T}k_{n})=\sigma(\underbrace{u_{q}^{T}k_{n}}_{unary}+\underbrace{(q_{m}-u_{q})^{T}(k_{n}-u_{k})}_{pairwise}),$
(4)

where $q_{m}$ represents the query embedding of pixel $m$, and $k_{n}$
represents the key embedding of pixel $n$. $\sigma(\cdot)$ represents the
softmax function. The first term represents the unary relation in which the
key pixel $n$ has the same influence on all query pixel $m$. The second term
represents the pure pairwise relation between the query pixel $m$ and key
pixel $n$.

Table 1: Classification results corresponding to different inputs. L, H and $F$ represent LiDAR features, HSI features and fused features, respectively. NO. | $W_{v}$ | $W_{k}$ | $W_{q}$ | $W_{m}$ | OA
---|---|---|---|---|---
1 | $F$ | H | H | H | 93.48$\pm$0.21
2 | $F$ | H | L | L | 93.14$\pm$0.45
3 | $F$ | L | L | L | 92.85$\pm$0.52
4 | H | H | L | H | 93.12$\pm$0.63
5 | L | H | L | H | 92.71$\pm$0.46
6 | $F$ | H | L | H | 87.10$\pm$0.64
7 | $F$ | H | L | H | 69.11$\pm$0.72
8 | L | L | L | L | 46.96$\pm$0.25
9 | H | H | H | H | 88.52$\pm$0.34
10 | $F$ | H | L | H | 93.74$\pm$0.76
Table 2: Comparison of the classification accuracy (%) using the Houston data NO. | Class | SVM | CNN-PPF | CRNN | CNN-MRF | HRWN | DNL
---|---|---|---|---|---|---|---
1 |  Health grass $\left(198/1053\right)$ |  82.43$\pm$6.95 |  83.57$\pm$0.42 |  83.00$\pm$0.23 |  85.77$\pm$0.31 |  85.61$\pm$0.09 |  82.71$\pm$0.22
2 |  Stressed grass $\left(190/1064\right)$ |  82.05$\pm$1.31 |  98.21$\pm$0.15 |  79.41$\pm$0.98 |  86.28$\pm$0.45 |  85.17$\pm$1.25 |  99.62$\pm$1.12
3 |  Synthetic grass $\left(192/505\right)$ |  99.80$\pm$0.04 |  98.42$\pm$0.44 |  99.8$\pm$0.12 |  99.00$\pm$0.02 |  99.57$\pm$0.18 |  99.60$\pm$0.12
4 |  Tress $\left(188/1056\right)$ |  92.80$\pm$3.84 |  97.73$\pm$0.27 |  90.15$\pm$0.78 |  92.85$\pm$0.87 |  92.20$\pm$0.62 |  95.45$\pm$0.23
5 |  Soil $\left(186/1056\right)$ |  98.48$\pm$0.97 |  96.50$\pm$1.03 |  99.71$\pm$0.12 |  100.0$\pm$0.00 |  100.0$\pm$0.00 |  99.90$\pm$0.43
6 |  Water $\left(182/143\right)$ |  95.10$\pm$2.06 |  97.20$\pm$2.29 |  83.21$\pm$5.44 |  98\. 15$\pm$0.25 |  98.15$\pm$0.86 |  94.40$\pm$0.53
7 |  Residential $\left(196/1072\right)$ |  75.47$\pm$0.75 |  85.82$\pm$0.59 |  88.06$\pm$1.76 |  91.64$\pm$0.38 |  95.98$\pm$0.89 |  88.71$\pm$1.23
8 |  Commercial $\left(191/1036\right)$ |  46.91$\pm$8.43 |  56.51$\pm$0.58 |  88.61$\pm$2.37 |  80.79$\pm$0.56 |  97.59$\pm$0.52 |  94.77$\pm$1.45
9 |  Road $\left(193/1059\right)$ |  77\. 53$\pm$2.76 |  71.20$\pm$1.04 |  66.01$\pm$9.32 |  91.37$\pm$2.08 |  88.66$\pm$0.63 |  97.35$\pm$0.54
10 |  Highway $\left(191/1036\right)$ |  60.04$\pm$1.05 |  57.12$\pm$1.82 |  52.22$\pm$7.84 |  73.35$\pm$0.84 |  86.23$\pm$0.34 |  81.99$\pm$0.42
11 |  Railway $\left(181/1054\right)$ |  81.02$\pm$2.26 |  80.55$\pm$0.36 |  81.97$\pm$3.02 |  98.87$\pm$1.33 |  97.98$\pm$3.06 |  96.77$\pm$0.26
12 |  Parking lot 1 $\left(192/1041\right)$ |  85.49$\pm$2.99 |  62.82$\pm$2.64 |  69.83$\pm$7.64 |  89.38$\pm$2.71 |  97.40$\pm$0.44 |  99.71$\pm$0.53
13 |  Parking lot 2 $\left(184/285\right)$ |  75.09$\pm$0.97 |  63.86$\pm$0.77 |  79.64$\pm$5.13 |  92.75$\pm$1.30 |  91.47$\pm$1.25 |  90.52$\pm$1.84
14 |  Tennis court $\left(181/247\right)$ |  100.0$\pm$0.00 |  100.0$\pm$0.00 |  100.0$\pm$0.00 |  100.0$\pm$0.00 |  100.0$\pm$0.00 |  100.0$\pm$0.00
15 |  Running track $\left(187/473\right)$ |  98.31$\pm$0.14 |  98.10$\pm$0.39 |  100.0$\pm$0.00 |  100.0$\pm$0.00 |  100.0$\pm$0.00 |  100.0$\pm$0.00
| OA |  80.49$\pm$0.38 |  83.33$\pm$0.70 |  88.55$\pm$0.71 |  90.61$\pm$0.54 |  93.61$\pm$0.75 |  93.74$\pm$0.76
| AA |  83.37$\pm$1.10 |  83.21$\pm$0.33 |  90.30$\pm$0.64 |  92.01$\pm$0.48 |  94.40$\pm$0.63 |  94.78$\pm$0.62
| Kappa |  78.98$\pm$0.45 |  81.88$\pm$0.77 |  87.56$\pm$0.77 |  89.87$\pm$0.58 |  93.09$\pm$0.81 |  93.41$\pm$0.79

##  3 Experimental Results and Analysis

###  3.1 Experimental Setup

To verify the effectiveness of the proposed disentangled non-local network for
HSI and LiDAR joint classification, we used Houston dataset acquired by the
NSF-funded Center in June 2012 over the University of Houston campus and
neighboring areas. There are 144 spectral bands that range from 0.38 to 1.05
$\mu$m in it. Beyond that, it presents an area with the size of $349\times
1905$ pixels and the spatial resolution of 2.5 m. The specific number of
training and testing samples can is illustrated in Table 2.

###  3.2 Results and Analysis

We test different feature combinations for the proposed DNL. As illustrated in
Table 1, classification using LiDAR image alone is unsatisfactory. Similarly,
classification using HSI alone is less effective. The best results are
achieved when we use the HSI feature as the key, the LiDAR feature as the
query, and the fused feature as the value. Thereby, we use such configurations
in our following experiments.

To verify the validity of the proposed network, the classification performance
of the proposed DNL was compared with five closely related methods, including
SVM, CNN-PPF[11], CRNN[12], CNN-MRF[13], HRWN[14]. Three evaluation metrics
are used, including overall accuracy (OA), average accuracy (AA) and kappa
coefficient (Kappa), as shown in Table 2. It can be seen that the proposed DNL
shows superiority over other methods, which implies that the disentangled non-
local mechanism indeed performs well in exploiting the multimodal feature
correlations.

Table 3: The comparison between Non-Local (NL) and DNL networks. Method | OA | AA | Kappa
---|---|---|---
NL | 93.22$\pm$0.68 | 93.99$\pm$0.64 | 93.01$\pm$0.72
DNL | 93.74$\pm$0.76 | 94.78$\pm$0.62 | 93.41$\pm$0.79

Beyond that, we also present the results of using traditional non-local (NL)
and DNL in HSI and LiDAR classification, as shown in Table 3. The results show
that DNL performs better than that of traditional NL, which exactly confirms
the analysis in Section 2. Fig. 2 illustrates the classification results of
the proposed method, from which we can clearly see that the boundary of the
network using DNL is clearer, and more clear regional cues can be learnt.

Fig. 2: Classification maps for the Houston data obtained with different
methods.

##  4 Conclusion

In this paper, we propose a novel DNL network for HSI and LiDAR joint
classification. In the network, we first extract the corresponding features
from HSI and LiDAR images according to their own characteristics,
respectively. Afterwards, in order to obtain the feature information more
appropriate to the actual environment, the extracted HSI and LiDAR feature
information is obtained through some operations to obtain the anisotropic
information, so as to prepare for the fusion of the latter two types of
feature information. Finally, the above three types of feature information are
fed into the DNL model to obtain more accurate contextual dependence.
Experiments show that the performance of the proposed model is superior to
several closely related methods.

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