††thanks: This work was supported by the National Key Research and Development
Program (Nos. 2022YFB3503600 and 2021YFA0718500), Strategic Priority Research
Program of the Chinese Academy of Sciences (Nos. XDA15360102), and National
Natural Science Foundation of China (Nos. 12273042 and 12075258).

# The Intrinsic Energy Resolution of LaBr3(Ce) Crystal for GECAM

Pei-Yi Feng  Pei-Yi Feng, Particle and Astrophysics Center, Institute of High
Energy Physics, No. 19 (B), Yuquan Road, Laoshan Street, Shijingshan District,
Beijing, China, 19151915020<EMAIL_ADDRESS>Key Laboratory of Particle
Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China  University of Chinese Academy of Sciences, Chinese
Academy of Sciences, Beijing 100049, China  Xi-Lei Sun  Xi-Lei Sun,
Experimental Physics Center, Institute of High Energy Physics, No. 19 (B),
Yuquan Road, Laoshan Street, Shijingshan District, Beijing, China,
13671137148<EMAIL_ADDRESS>State Key Laboratory of Particle Detection and
Electronics, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China  Cheng-Er Wang  National Engineering Research Center for
Rare Earth, Grirem Advanced Materials Co., Ltd., Beijing 100088, China  Yong
Deng  School of Nuclear Science and Technology, University of South China,
Hengyang Hunan 421001, China  Zheng-Hua An  Zheng-Hua An, Particle and
Astrophysics Center, Institute of High Energy Physics, No. 19 (B), Yuquan
Road, Laoshan Street, Shijingshan District, Beijing, China, 13661351124,
<EMAIL_ADDRESS>Key Laboratory of Particle Astrophysics, Institute of High
Energy Physics, Chinese Academy of Sciences, Beijing 100049, China  Da-Li
Zhang  Key Laboratory of Particle Astrophysics, Institute of High Energy
Physics, Chinese Academy of Sciences, Beijing 100049, China  Chao Zheng  Key
Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese
Academy of Sciences, Beijing 100049, China  University of Chinese Academy of
Sciences, Chinese Academy of Sciences, Beijing 100049, China  Xin-Qiao Li  Key
Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese
Academy of Sciences, Beijing 100049, China  Shao-Lin Xiong  Key Laboratory of
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, Beijing 100049, China  Hong Lu  Key Laboratory of Particle
Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China

###### Abstract

The intrinsic resolution is the primary limitation on the total energy
resolution of LaBr3(Ce) crystal. This intrinsic resolution arises from two
effects: fluctuations occurring in the process of energy transfer to
luminescent centers within the LaBr3(Ce) crystal and the LaBr3(Ce) crystal’s
non-proportional luminescence. Presently, experimental measurements regarding
the intrinsic resolution of LaBr3(Ce) crystal are scarce, and the underlying
physical mechanisms remain incompletely understood. In this paper, we aim to
elucidate the concept of intrinsic resolution. We investigated the entire
physical process of luminescence following energy deposition in the LaBr3(Ce)
crystal, quantifying the various components in the total energy resolution. We
conducted a series of experimental measurements and Geant4 simulations,
determining the intrinsic resolution of LaBr3(Ce) crystal to 100 keV electrons
as 2.12%. The non-proportionality contributes significantly at 1.43%, while
fluctuations in the energy transfer process accounted for 0.27%. It is evident
that non-proportionality in light output constitutes the primary source of
intrinsic resolution. Horizontal and vertical unevenness in light collection
contributed 0.25% and 0.07%, respectively. Statistical fluctuations showed the
largest impact on the total energy resolution, at 2.86%. The contribution from
fluctuations in single-photoelectron events was 0.77%. Furthermore, we
reconstructed the photon response using Geant4, and the consistency between
the simulated relative light yield and the experimentally measured one
confirmed the reliability of the LaBr3(Ce) detector mass model employed in the
simulation.

LaBr3(Ce) detector, Energy Response, Intrinsic Resolution, Non-proportional
Light Yield, Energy Transfer Process

##  I Introduction

LaBr3(Ce) crystals represent a promising advancement in inorganic
scintillators, boasting high light output, exceptional energy and time
resolution, excellent energy linearity, and rapid luminescence decay. These
characteristics of LaBr3(Ce) crystals find wide applications in various
fields, including studies of scintillation mechanisms [1], nuclear
spectroscopy [2, 3, 4], nuclear medicine [5], three-dimensional imaging in
gamma-ray astronomy [6, 7, 8], security and remote sensing [9], gamma-ray
logging [10], and environmental monitoring [11].

The Gravitational wave burst high-energy Electromagnetic Counterpart All-sky
Monitor (GECAM) was developed to monitor various high-energy electromagnetic
events, such as gamma-ray bursts and magnetar flares [12, 13, 14, 15, 16, 17,
18, 19, 20]. Gamma-ray Detectors (GRDs) are the primary detectors on the GECAM
payload, with LaBr3(Ce) crystals as their sensitive materials. GECAM has
achieved a series of research outcomes, some of which have been publicly
reported [21, 22]. On October 9, 2022, GECAM-C detected the brightest gamma-
ray burst to date, free from data saturation, loss, or pulse pile-up effects,
marking the highest-quality observations known internationally [23]. We have
extensively studied the energy response of LaBr3(Ce) crystals [24]. To gain a
comprehensive understanding of the GECAM satellite detector’s performance, we
conducted an in-depth analysis of the energy resolution of LaBr3(Ce) crystals.

Energy resolution stands as a crucial parameter characterizing scintillator
performance [25]. Kelly G.G. et al. initially identified an unexplained
component within the energy resolution of NaI(Tl) crystals irradiated by
137Cs, reaching 6.6% at 662 keV, termed as intrinsic resolution [26]. The
intrinsic resolution constitutes the primary component of the total energy
resolution. Specifically, Iredale P. et al proposed that the non-proportional
luminescence of the crystal is the primary cause for the existence of
intrinsic resolution [27]. This conclusion was further confirmed in
experiments conducted by Moszynski M. et al [28, 29]. Engelkemeir et al.
observed a non-proportionality between the pulse amplitude of gamma rays and
the deposited energy within the scintillator [30]. In the low-energy range,
deficient light output was observed in LYSO(Ce) and BGO crystals, whereas
CsI(Tl) crystals exhibited excessive light output [31, 29].

In fact, the three effects causing non-proportionality in light yield are: (1)
secondary X-rays and Auger electrons generated after photoelectric absorption;
(2) multiple Compton scatterings resulting in the full energy absorption of
gamma rays; (3) the production of $\delta$-rays during secondary electron
scattering. These mechanisms also represent the three diffusion modes of
light. Prescott J.R. and Narayan G.H. confirmed these mechanisms as sources of
intrinsic resolution [32, 33].

Yong D. et al. elucidated that the intrinsic resolution of liquid scintillator
for 976 keV electrons is 1.83%. They indicated that non-proportionality in
liquid scintillator has a minimal contribution to the intrinsic resolution for
electrons, suggesting that fluctuations during energy transfer processes might
largely account for the intrinsic resolution [34]. The intrinsic resolution is
entirely determined by the properties of the material itself. Besides non-
proportional luminescence, the process of energy transfer within the
scintillator to generate photons at luminescent centers is also considered as
an important source of intrinsic resolution, due to the occurrence of
fluctuations in this process.

The current literature shows insufficient depth in understanding the concept
of intrinsic resolution. There is a scarcity of experimental measurements
concerning the intrinsic resolution of crystals, and their underlying physical
mechanisms require further investigation. To better comprehend the limitations
and potential of these scintillators, investigating the entire physical
process influencing the total energy resolution remains of significant
importance. In this paper, building upon existing research on the non-
proportionality of LaBr3(Ce) crystal [24], we quantified the contributions of
six factors—fluctuations in energy transfer, non-proportional luminescence,
uneven light collection, statistical fluctuations in photoelectrons, single-
photoelectron resolution, and electronic noise—towards energy resolution
through a combination of experiments and Geant4 simulation. We aim to clarify
the concept of intrinsic resolution, analyze the relationship between energy
transfer processes, non-proportional luminescence, and intrinsic resolution,
and subsequently explore the sources of intrinsic resolution.

##  II Experimental Setups

This section introduces the experimental setups utilized in this study. The
single-photoelectron calibration of PMTs is employed to analyze the
contribution of statistical fluctuations in photoelectrons to the energy
resolution. The experimental setup for non-proportional light output is
employed to analyze the contribution of luminescence non-proportionality to
the energy resolution. The setup for horizontal uniformity testing is used to
analyze the contribution of uneven light collection to the energy resolution.

###  II.1 Calibration of the PMT Single Photoelectron

Photomultiplier tubes (PMTs) exhibit high sensitivity and a favorable signal-
to-noise ratio, providing significant advantages in detecting weak light
signals. Accurate Single-photoelectron Calibration (SPEC) of PMTs is crucial,
as it directly impacts subsequent analyses of crystal energy resolution. This
study employed Hamamatsu CR160 PMTs and utilized LED-based calibration for
single-photoelectron spectra [35].

Figure 1: Experimental setup schematic for single-photoelectron calibration.

As shown in Fig. 1, the PMT is placed inside a dark box and supplied with high
voltage by the CAEN N1470. The pulse signal generator RIGOL DG1062Z drives a
LED to emit faint blue-violet light and provides a synchronized signal. This
synchronized signal, after passing through the fan-in and fan-out module CAEN
N625, is polarity-inverted from negative to positive, then connected to the
GG8000 to adjust its gate width. When observing reasonable synchronization
between this signal and the PMT signal on the oscilloscope, the synchronized
signal is utilized as an external trigger for the data acquisition device
DT5751 to eliminate the influence of dark noise. By altering the amplitude of
the pulse signal, the LED’s luminous intensity is adjusted to ensure that the
incident light on the PMT’s photocathode remains at the single-photon level.

###  II.2 Experimental Setup for Non-proportional Light Yield

To measure the non-proportional light output of the LaBr3(Ce) crystal, we
conducted tests and comparative studies on the non-proportionality using
Compton electrons, radioactive sources, and monochromatic X-rays. The Wide
Angle Compton Coincidence (WACC) technique was employed to obtain a broad
energy range of Compton electrons. Figure 2 illustrates the experimental setup
of WACC comprising a radioactive source, high-purity germanium detector
(HPGe), the crystals under examination, and a data acquisition system (Fig.
3). Figure 4 demonstrates the use of the Hard X-ray Calibration Facility
(HXCF) to investigate the crystals’ non-proportionality to X-rays [36, 37,
38]. Figure 5 depicts the data acquisition system used during X-ray response
testing. The experimental introductions, testing procedures, and data
collection for WACC and HXCF have been extensively elaborated in the
publication by our research team [24], hence avoiding excessive repetition in
this paper. The experimental data concerning the crystals’ non-proportionality
utilized in this study has also been experimentally obtained.

Figure 2: Schematic diagram of WACC experimental setup for obtaining Compton
electrons with a wide energy range. Figure 3: Diagram of the data acquisition
system for WACC events. Figure 4: Hard X-ray Calibration Facility. Both the
HPGe and crystal detectors were placed on a displacement platform and
maintained on the same horizontal line. Figure 5: Data acquisition system
diagram for single-energy X-ray detection.

###  II.3 Experimental Setup for Horizontal Uniformity

Different particle incidence positions lead to variations in photon generation
locations within the crystal, resulting in discrepancies in the collection
efficiency at the PMT’s photocathode. The non-uniformity in photon generation
within the crystal is categorized into horizontal and vertical dimensions. The
contribution of non-uniform light collection to the total energy resolution is
determined through ”Spot Scanning” (SS) experiments and Geant4 optical
simulations.

The HXCF (Fig. 4) was also utilized to test the position response of LaBr3(Ce)
crystal to 25 keV X-rays. Setting the coordinate parameters for each point, we
adjusted the displacement platform to align the X-ray with the intended test
positions. As depicted in Fig. 6, with the crystal center as the origin, test
positions were distributed along the X and Y axes, with adjacent points spaced
2 mm apart. There were a total of 25 test positions, each with a statistical
count of no less than 30,000. Background data were collected before and after
the experiment for subtraction purpose.

Figure 6: Crystal’s Be window entrance surface. Distribution and numbering of
test points for assessing the positional non-uniformity of crystals involve 25
designated locations.

##  III Monte Carlo simulation

Geant4, developed by the European Organization for Nuclear Research (CERN)
using C++ object-oriented technology, is a Monte Carlo application package
employed for simulating the transport of particles within matter [39, 40].

###  III.1 Simulation Approach

Geant4 simulations allow for assessing the contributions of light yield non-
proportionality and uneven light collection to the total energy resolution.
Table 1 lists the crystal types and dimensions used in the simulations. Table
2 presents the parameters utilized in the optical simulations. We completed
three simulation tasks using Geant4, outlined as follows:

(1) Simulate the emission of 30,000 energetic gamma photons and track the
energy deposition process within the crystal. Choose the full-energy deposited
events and extract the energies of Compton electrons, photoelectrons, and
Auger electrons from these events. Convolve the energy of these secondary
electrons with the electron response curve obtained from the WACC experiments,
obtaining the light output distribution of events with full photon energy
deposition, subsequently assessing the significance of non-proportionality on
the crystal’s intrinsic resolution.

(2) Simulate the emission of 30,000 energetic electrons, track the energy
deposition process of electrons within the crystal, obtaining the initial
electron energy Einit and deposition energy Edep for each step. Utilizing the
experimentally obtained Compton electron response curve, the difference in
light output between the initial energy Einit and the end energy (Einit–Edep)
for each step represents the light output of that step. Accumulating the light
output values of all steps provides the electron response for a full-energy
deposited event. Following this method, the light output distribution of
electrons with different energies can be obtained, thereby calculating the
non-proportionality component in the crystal’s resolution for different
electron energies.

(3) We configured appropriate optical parameters to simulate a point light
source emitting 20,000 photons from a specified position within the crystal at
a 4$\pi$ solid angle. Tracing the transport of photons within the crystal
revealed the non-uniformity in photon collection efficiency at the PMT’s
photocathode.

Table 1: Types of crystals and their parameters used in Geant4 simulations. Crystal | Diameter | Density | Doping type
---|---|---|---
LaBr3(Ce) | 25.4 mm | 5.06 g/cm3 | 5% Ce3+
Table 2: Optical simulation parameters in Geant4. Material | Refractive index | Absorption length | Reflectivity
---|---|---|---
LaBr3(Ce) | 1.9 | 100 cm | /
Quartz glass | 1.47 | 50 m | /
PMT glass | 1.54 | / | /
Teflon film | / | / | 95%

###  III.2 Evaluating the Contribution of Non-proportionality to Energy
Resolution

Gamma rays deposit energy in the crystal in the form of electrons,
transferring energy to the luminescent center, consequently inducing crystal
luminescence. Upon entry into the LaBr3(Ce) crystal, gamma rays generate
secondary electrons through two mechanisms: (1) Direct occurrence of the
photoelectric effect cascade process generates multiple Auger electrons and
characteristic X-rays; these X-rays, upon secondary absorption within the
crystal, produce secondary photoelectrons. (2) Multiple interactions (e.g.,
Compton scattering) generate one or more electrons; subsequent secondary
photons undergo the photoelectric effect cascade process.

$L_{\gamma}=\int_{0}^{\infty}\Phi(E_{\gamma},E_{e})R_{e}(E_{e})E_{e}dE_{e}.$
(1)

For events with full energy deposition, convolve the experimentally obtained
electron response curve Re(Ee) with the simulated secondary electron energy Ee
to determine its light output Lγ. $\Phi(E_{\gamma},E_{e})$ represents the
electron energy distribution function in Equation 1. When a limited quantity
of gamma photons are incident, determine the light output Lγ,i of the i-th
gamma photon using the discrete convolution as described in Equation 2. Mi
represents the quantity of secondary electrons produced by the i-th gamma
photon in the crystal, while E${}_{(}e,j)$ denotes the energy of the j-th
electron.

$L_{\gamma,i}=\sum_{j=1}^{M_{i}}R_{e}(E_{e,j})E_{e,j}.$ (2)

Select full-energy deposited events from the simulated 30,000 events,
calculate the light output for each event as per Equation 2, obtaining the
light output distribution for gamma photons with a specific energy. Use the
centroid of the light output distribution to represent the incident photon
response Rγ (Equation 3), and utilize the standard deviation $\sigma$ of the
light output distribution to represent the contribution of non-proportional
light yield $\delta_{\gamma,non}$ to the total energy resolution (Equation 5).

$R_{\gamma}=\frac{\overline{L_{\gamma}}}{E_{\gamma}}=\frac{1}{E_{\gamma}}\frac{1}{N}\sum_{i=1}^{N}L_{\gamma,i}.$
(3)

$\sigma^{2}=\frac{1}{N-1}\sum_{i=1}^{N}(L_{\gamma,i}-\overline{L_{\gamma}})^{2}.$
(4)

$\delta_{\gamma,non}=\frac{\sigma}{\overline{L_{\gamma}}}.$ (5)

Equations 3, Equations 4, and Equations 5 are used to quantify the
contribution of non-proportionality to the total energy resolution.
$\overline{L_{\gamma}}$ represents the average light yield of events with full
energy deposition, $E_{\gamma}$ stands for the energy of gamma photons, and N
is the quantity of selected events with full energy deposition. Later in this
paper, we will present the intrinsic resolution $\delta_{\gamma,int}$. By
comparing $\delta_{\gamma,non}$ with $\delta_{\gamma,int}$, we analyze the
relationship among the total energy resolution, intrinsic resolution, and the
contribution of non-proportionality, assessing the impact of non-
proportionality on the crystal’s energy resolution.

When the incident particle is an electron, its energy deposition process
within the crystal differs from that of gamma photons. Electron interactions
with matter are simpler than those of gamma photons, involving scattering,
ionization, and bremsstrahlung. Similarly, we need to select events with full
energy deposition. We tracked the electron transport within the crystal,
associating relative light yields with the energy of each step’s start and end
points. Referring to previously obtained experimental electron response curves
[24], we derived the light yields for the start and end points of one step,
and their difference represents the computed light yield for that step.

$L_{e,u}=\sum_{v=1}^{M_{u}}\\{R_{e}(E_{v,in})E_{v,in}-R_{e}(E_{v,out})E_{v,out}\\}.$
(6)

In Equation 6, $L_{e,u}$ represents the light yield of the crystal for the
u-th electron, $M_{u}$ denotes the steps through which the total energy of the
u-th electron is deposited within the crystal, $R_{e}$ stands for the electron
response curve obtained from the WACC experiment, $E_{v,in}$ and $E_{v,out}$
respectively represent the initial and final energies of the v-th step.
Similar to the case of gamma photons, calculate the contribution of non-
proportionality to the electron energy resolution $\delta_{e,non}$ using
Equation 7, Equation 8, and Equation 9.

$R_{e}=\frac{\overline{L_{e}}}{E_{e}}=\frac{1}{E_{e}}\frac{1}{N}\sum_{i=1}^{N}L_{e,u}.$
(7)

$\sigma^{2}=\frac{1}{N-1}\sum_{i=1}^{N}(L_{e,u}-\overline{L_{e}})^{2}.$ (8)

$\delta_{e,non}=\frac{\sigma}{\overline{L_{e}}}.$ (9)

##  IV Results

Previous publications have only considered the impact of statistical
fluctuations in photoelectrons apart from intrinsic resolution. This
simplistic method resulted in an overestimation of the calculated intrinsic
resolution [41, 42]. To better understand the intrinsic resolution, we
investigated the process of particle detection using the LaBr3(Ce) crystal and
data acquisition, quantifying the contributions of six factors to the total
energy resolution.

$(\sigma/E)^{2}=\delta_{trans}^{2}+\delta_{non}^{2}+\delta_{un}^{2}+\delta_{st}^{2}+\delta_{spe}^{2}+\delta_{noise}^{2}.$
(10)

In Equation 10, $\sigma$/E represents the electron total energy resolution,
$\delta_{trans}$ indicates fluctuations in the energy transfer process,
$\delta_{non}$ denotes the contribution of the non-proportional luminescence,
$\delta_{un}$ accounts for uneven light collection, $\delta_{st}$ represents
statistical fluctuations during photon-to-photoelectron conversion at the
PMT’s photocathode, $\delta_{spe}$ stands for the PMT’s single-photoelectron
resolution, and $\delta_{noise}$ signifies the contribution of dark noise to
the total energy resolution. In this study, we utilized high-performance PMTs,
hence the contribution of dark noise can be negligibly small. As
$\delta_{trans}$ and $\delta_{non}$ are entirely determined by the material’s
intrinsic properties, we collectively term these two components as the
intrinsic resolution of the crystal (Equation 11).

$\delta_{int}^{2}=\delta_{trans}^{2}+\delta_{non}^{2}.$ (11)

Figure 7 displays the energy resolutions of LaBr3(Ce) crystal for 9–100 keV
X-rays measured using the HXCF, represented by the standard deviation
1$\sigma$ of the full-energy peak. At 100 keV, the energy resolution of
LaBr3(Ce) crystal is 3.99% $\pm$ 0.0976%. Near the K-shell electron binding
energy (38.931 keV), the energy resolution deteriorates by no more than 0.5%.

Figure 7: Total energy resolution of LaBr3(Ce) crystal for X-rays measured
using HXCF.

Figure 8 illustrates the energy resolutions of LaBr3(Ce) crystal for 3–400 keV
Compton electrons measured using WACC, also represented by the standard
deviation 1$\sigma$ of the full-energy peak. At 100 keV, the energy resolution
of LaBr3(Ce) crystal is 3.31% $\pm$ 0.2725%. Near the K-shell electron binding
energy, there is no deterioration in the electron’s energy resolution.

Figure 8: Total energy resolution of LaBr3(Ce) crystal for Compton electrons
measured using WACC.

###  IV.1 Single-photoelectron Fluctuations

Figure 9 depicts the photoelectron spectrum of CR160 PMT operating at –1600V.
A double Gaussian fit was performed, yielding the fitting results shown in
Figure 9, and resulting in a calculated single-photoelectron resolution of
28.21% $\pm$ 0.0091% for CR160. Figure 10 illustrates the single-photoelectron
response at different voltages, revealing an exponential increase in the
number of channels with voltage increment. The absolute light yield of the
LaBr3(Ce) crystal $N_{photoelectron}$ was obtained through single-
photoelectron calibration, and using Equation 12, the contribution of single-
photoelectron fluctuations to the total energy resolution was computed.

$\delta_{spe}=\frac{(\sigma/E)_{spe}}{\sqrt{N_{photoelectron}}}.$ (12)

Figure 9: Photomultiplier Tube (PMT) CR160’s single-photoelectron spectrum at
–1600V operating voltage. Figure 10: Single-photoelectron response of the
Hamamatsu CR160 PMT at different operating voltages.

###  IV.2 Statistical Fluctuations

The contribution of statistical fluctuations in the number of photoelectrons
to the total energy resolution, denoted as $\delta_{st}$, is represented by
Equation 13. Here, Nphotoelectron stands for the number of photoelectrons
obtained through single-photoelectron calibration of the PMT. The gain
variance of the PMT represented by $\varepsilon$, commonly taken as 0.1.
Building upon our previous HXCF and WACC experiments, we calculated the
contribution of statistical fluctuations in the number of photoelectrons for
LaBr3(Ce) crystal at each energy, as illustrated in Fig. 11. The contribution
of statistical fluctuations during Compton electron testing was found to be
lower than that during X-ray examination. We observed that statistical
fluctuations in LaBr3(Ce) crystal generally contribute significantly to the
resolution. At 100 keV, they respectively reach 3.01% $\pm$ 0.0602% for X-rays
and 2.86% $\pm$ 0.0572% for Compton electrons. During X-ray testing, there are
jumps of no more than 0.05% near the K-shell binding energy. According to this
chapter’s findings, the contribution of single-photoelectron fluctuations to
the total energy resolution in Chapter IV.1 amounts to 0.77% $\pm$ 0.0027%.

$\delta_{st}=\frac{1+\varepsilon}{\sqrt{N_{photoelectron}}}.$ (13)

Figure 11: Statistical fluctuations of photoelectrons contribute to the total
energy resolution when testing LaBr3(Ce) with X-rays and Compton electrons.

###  IV.3 Non-uniformity in Light Collection

Due to varying light emission positions in the LaBr3(Ce) crystal and the
impact of uneven light collection, the measured full-energy peak position and
energy resolution vary with the incident position of X-rays. Figures 12 and 13
present the test results, showing fluctuations of 3.08% for the peak position
and 4.31% for the energy resolution. Experimentally, the LaBr3(Ce) crystal we
used exhibited excellent uniformity. The contribution of uneven light
collection to the total energy resolution is quantified using Equation 14,
resulting in a contribution of 0.25% $\pm$ 0.0099% due to horizontal non-
uniformity in the LaBr3(Ce) crystal.

$\delta_{un}=\frac{\sigma}{mean}.$ (14)

Figure 12: Relative full-energy peak position of LaBr3(Ce) crystal varies with
position in the X and Y directions. Figure 13: Energy resolution of LaBr3(Ce)
crystal varies with position in the X and Y directions..

Geant4 simulations were conducted to analyze the variation in photon
collection efficiency at different radial positions along the LaBr3(Ce)
crystal for depths of 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm. The results, depicted
in Figure 14, are normalized to the 1 mm depth along the central axis. A
decreasing trend in photon collection efficiency is observed from the
LaBr3(Ce) crystal’s center towards its edges, showing an approximate decrease
of 1.4% at the periphery compared to the center. The simulation results
exhibit a slight underestimate compared to the ”spot scanning” experimental
outcomes due to external factors influencing the testing. At a position
emitting light at the central axis and a depth of 1 mm, the photon collection
efficiency of the LaBr3(Ce) crystal is approximately 88%, with a relative
variation of less than 1% within the 5 mm depth range. To eliminate the
influence of horizontal non-uniformity, the average of 14 data points for each
depth was computed. After simplification, Equation 14 yields a contribution of
vertical non-uniformity for the LaBr3(Ce) crystal of 0.07% $\pm$ 0.0065%.

Figure 14: Relative photon collection efficiency of LaBr3(Ce) crystal varies
with position.

###  IV.4 The Contribution of Non-proportionality

To describe the electron response within a continuous energy range, empirical
Equations 15 and 16 were used to fit the Compton electron response curve
obtained from the WACC experiment of the LaBr3(Ce) crystal [43, 44]. Here,
NPR(Ee) represents the electron response and Pn denotes fitting parameter.
Merely fitting the energy range observed in the WACC experiment is
insufficient, as Geant4 simulation results indicate that most secondary
electrons generated by the cascade of photoelectric effects have energies
mostly below a few keV. Therefore, extending the fitting curve to the low-
energy range of 0–3 keV is necessary.

$NPR(E_{e})=P_{0}+P_{1}x+P_{2}x^{2}+P_{3}x^{3}.$ (15)

$x=log(E_{e}).$ (16)

The fitted electron response curve was convolved with the secondary electron
energies obtained from Geant4 simulations. Based on Chapter III.2, the
calculated responses of gamma photons for different energies are depicted in
Figures 15 (a), (b), and (c), corresponding to 25 keV, 60 keV, and 100 keV,
respectively (e.g., the distribution of light yield). These figures also
illustrate the contribution of the non-proportionality component to the total
energy resolution and the calculated response (average response divided by
incident energy). It’s noteworthy that this distribution doesn’t exhibit a
Gaussian shape but rather displays some complex structures due to the diverse
nature of secondary electron energies resulting from photon-matter
interactions.

For 100 keV gamma photons, the reconstructed response Rγ for the LaBr3(Ce)
crystal is 0.8977 (equivalent to 89.77 keV), falling short of 100 keV due to
the deficient luminescence in the LaBr3(Ce) crystal [24]. At 100 keV, the
contribution of luminescence non-proportionality to the total energy
resolution is 2.28% $\pm$ 0.0003%.

Figure 15: The reconstructed energy response distributions for 25 keV (a), 60
keV (b), and 100 keV (c) gamma photons and 25 keV (d), 60 keV (e), and 100 keV
(f) electrons are presented. The figures also display the statistical count of
full-energy deposited events, the contribution of luminescent non-
proportionality to the total energy resolution, and the reconstructed relative
responses.

Based on the methodology outlined in Chapter III.2, the calculated responses
of electrons at different energies are provided. Figures 15 (d), (e), and (f)
represent the light output distributions for incident energies of 25 keV, 60
keV, and 100 keV, respectively. For electrons at 100 keV, the reconstructed
response Re of LaBr3(Ce) crystal is 0.9250 (equivalent to 92.50 keV). Electron
responses at the same energy surpass gamma photon responses due to differing
interaction mechanisms between particles and matter, as elucidated in our
previous energy response research [24]. At 100 keV for electrons, luminescence
non-proportionality contributes 1.43% $\pm$ 0.0036% to the total energy
resolution.

We successfully reconstructed the distributions of gamma photon responses and
electron responses. The statistics of incident particles in the Geant4
simulation amount to 30,000. For gamma photon events, the majority were full-
energy deposited events, whereas for electron events, less than 20,000 involve
full energy deposition. Due to the ”deficient” luminescence of LaBr3(Ce)
crystal, the reconstructed responses do not exceed the energy of the incident
particles, consistent with the findings of the HXCF and WACC experiments. We
compared the convolved photon response with the reported relative light output
of LaBr3(Ce) crystal [24], as depicted in Fig. 16. The great consistency
within the error range signifies the reliability of the Geant4 simulation
results.

Figure 16: Comparison between reconstructed photon response and experimentally
obtained relative light yield.

###  IV.5 Intrinsic Energy Resolution

Both gamma photons and electrons ultimately result in secondary electron
diffusion and energy deposition within the crystal. Hence, computing the
intrinsic resolution of the crystal requires utilizing the outcomes from
electron incidence. For 100 keV electrons, the contribution of energy transfer
fluctuations is calculated as 0.27% $\pm$ 0.0030% using Equation 10, while the
intrinsic resolution of the LaBr3(Ce) crystal is determined as 2.12% $\pm$
0.0022% via Equation 11. Among the potential sources contributing to the
intrinsic resolution, the non-proportionality component appears to have a
substantial impact. We consider luminescence non-proportionality to be the
primary source of intrinsic resolution. However, the fluctuations in energy
transfer should not be disregarded as they are an inherent property of the
material. Table 3 provides a comprehensive breakdown of all factors
contributing to the total energy resolution at 100 keV.

Table 3: Contributions of individual components to the total energy resolution at 100 keV. Component | Method | Result
---|---|---
$\sigma$/E ($\gamma$) | HXCF | 3.99 $\pm$ 0.0976%
$\sigma$/E (e) | WACC | 3.31 $\pm$ 0.2725%
$\delta_{spe}$ | SPEC | 0.77 $\pm$ 0.0027%
$\delta_{st}$ ($\gamma$) | SPEC + HXCF | 3.01 $\pm$ 0.0602%
$\delta_{st}$ (e) | SPEC + WACC | 2.86 $\pm$ 0.0572%
$\delta_{un}$ (horizontal) | SS | 0.25 $\pm$ 0.0099%
$\delta_{un}$ (vertical) | Geant4 | 0.07 $\pm$ 0.0065%
$\delta_{non}$ ($\gamma$) | HXCF + Geant4 | 2.28 $\pm$ 0.0003%
$\delta_{non}$ (e) | WACC + Geant4 | 1.43 $\pm$ 0.0036%
$\delta_{trans}$ | Equation 10 | 0.27 $\pm$ 0.0030%
$\delta_{int}$ | Equation 11 | 2.12 $\pm$ 0.0022%

##  V Conclusion

Building upon the published energy response of LaBr3(Ce) crystal [24], we
conducted an extensive investigation into its energy resolution. We analyzed
six potential factors contributing to the energy resolution and quantified
their respective contributions. The total energy resolutions of LaBr3(Ce)
crystal for gamma rays and Compton electrons were measured through the HXCF
and WACC experiments. Single-photoelectron calibration provided details about
the single photoelectron resolution and statistical fluctuations. Horizontal
and vertical non-uniformities were assessed separately by the SS experiments
and Geant4 optical simulations, elucidating their respective impacts on energy
resolution. Convolution of the electron response non-proportionality curve
with secondary electron energies obtained from Geant4 simulations unveiled the
non-proportionality component within the total energy resolution.

We identified two main contributors to the intrinsic resolution of the
LaBr3(Ce) crystal: the non-proportionality in luminescence and fluctuations in
energy transmission to the luminescent center. For 100 keV electrons, we
calculated the non-proportionality component as 1.43% $\pm$ 0.0036%, the
contribution of energy transmission fluctuation as 0.27% $\pm$ 0.0030%,
resulting in an intrinsic resolution of the LaBr3(Ce) crystal at 2.12% $\pm$
0.0022%. It’s noteworthy that subtracting all considered factors from the
measured total energy resolution is a conservative approach due to the
unexplored interdependencies among these components. This study not only aids
in comprehending the detector performance of the GECAM satellite series but
also represents a rare in-depth investigation into the intrinsic resolution of
LaBr3(Ce) crystal internationally.

##  VI Acknowledgments

This work was supported by the National Key Research and Development Program
(Nos. 2022YFB3503600 and 2021YFA0718500), Strategic Priority Research Program
of the Chinese Academy of Sciences (Nos. XDA15360102), and National Natural
Science Foundation of China (Nos. 12273042 and 12075258)

## AUTHOR CONTRIBUTIONS

All authors contributed to the study conception and design. Material
preparation, data collection and analysis were performed by Pei-Yi Feng. The
first draft of the manuscript was written by Pei-Yi Feng and all authors
commented on previous versions of the manuscript. All authors read and
approved the final manuscript.

## CONFLICT OF INTEREST

The authors declare that they have no competing interests.

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# The Need for Ethical, Responsible, and Trustworthy Artificial Intelligence
for Environmental Sciences

<EMAIL_ADDRESS>Imme Ebert-Uphoff  David John Gagne II  Ann Bostrom  *
Electrical and Computer Engineering, Colorado State University, Fort Collins,
80523, CO, USA  Cooperative Institute for Research in the Atmosphere, Colorado
State University, Fort Collins, 80523, CO, USA  Computational and Information
Systems Laboratory, National Center for Atmospheric Research, Boulder, 80301,
CO, USA  Evans School of Public Policy & Governance, University of Washington,
Seattle, 98195, WA, USA

(15 December 2021)

###### Abstract

Given the growing use of Artificial Intelligence (AI) and machine learning
(ML) methods across all aspects of environmental sciences, it is imperative
that we initiate a discussion about the ethical and responsible use of AI. In
fact, much can be learned from other domains where AI was introduced, often
with the best of intentions, yet often led to unintended societal
consequences, such as hard coding racial bias in the criminal justice system
or increasing economic inequality through the financial system. A common
misconception is that the environmental sciences are immune to such unintended
consequences when AI is being used, as most data come from observations, and
AI algorithms are based on mathematical formulas, which are often seen as
objective. In this article, we argue the opposite can be the case. Using
specific examples, we demonstrate many ways in which the use of AI can
introduce similar consequences in the environmental sciences. This article
will stimulate discussion and research efforts in this direction. As a
community, we should avoid repeating any foreseeable mistakes made in other
domains through the introduction of AI. In fact, with proper precautions, AI
can be a great tool to help reduce climate and environmental injustice. We
primarily focus on weather and climate examples but the conclusions apply
broadly across the environmental sciences.

###### keywords:

ethics, artificial intelligence, weather, climate

††journal: Environmental Data Science

2020 4 10.1017/eds.2020.xx

[1]Amy McGovern0000-0001-6675-7119 0000-0001-6470-1947 0000-0002-0469-2740
0000-0002-6399-3404

[1]School of Computer Science and School of Meteorology, University of
Oklahoma, Norman, 73019, OK, USA

McGovern et al.

This position paper discusses the need for the environmental sciences
community to ensure that they are developing and using artificial intelligence
(AI) methods in an ethical and responsible manner. This paper is written at a
general level, meant for the broad environmental sciences and earth sciences
community, as the use of AI methods continues to grow rapidly within this
community.

##  1 Motivation

Artificial Intelligence (AI) and Machine Learning (ML) have recently exploded
in popularity for a wide variety of environmental science applications (e.g.
Reichstein et al., 2019; McGovern et al., 2019; Gensini et al., 2021;
Lagerquist et al., 2021; Hill and Schumacher, 2021; Schumacher et al., 2021;
Gagne et al., 2020). Like other fields, environmental scientists are seeking
to use AI/ML to build a linkage from raw data, such as satellite imagery and
climate models, to actionable decisions.

While the increase in applications of AI can bring improved predictions, e.g.,
for a variety of high-impact events, it is also possible for AI to
unintentionally do more harm than good if it is not developed and applied in
an ethical and responsible manner. This has been demonstrated in a number of
high-profile cases in the news outside of weather or climate (e.g., Tan, 2020;
O’Neil, 2016; Benjamin, 2019). We argue that the potential for similar issues
exists in environmental science applications and demonstrate how AI/ML methods
could go wrong for these application areas.

On the other hand, AI can also be helpful for environmental sustainability. AI
is already being applied to enable the automated monitoring of our ecosystems
to support accountability for climate justice. Applications include monitoring
land cover changes to detect deforestation (Karpatne et al., 2016; Mithal et
al., 2018), counting populations of endangered species in very-high resolution
satellite data (Duporge et al., 2021), and tracking bird populations in radar
data (Lin et al., 2019; Chilson et al., 2019). Automated monitoring of
retrospective and real-time datasets can help interested parties to monitor
environmental trends and respond appropriately.

There are both instrumental and consequential as well as principled ethical
perspectives such as duties and virtues for AI environmental scientists to
consider. These are entangled in the biases and pitfalls this paper explores.
Debiasing has the potential to address both.

Note, we assume the reader is generally familiar with the concepts of AI and
ML and do not focus on any specific AI/ML methods but instead on the
applications across environmental sciences. For brevity, we refer to AI/ML as
AI throughout the rest of the paper.

##  2 How AI can go wrong for environmental sciences

Although Arthur C. Clarke’s famous line "Any sufficiently advanced technology
is indistinguishable from magic" was not directed at AI, it may seem that way
to many new users of AI. It seems as if one simply has to give an AI method
data and use a pre-made package and an amazing predictive model results. The
problem with this approach is that AI is not magic and can be led astray in a
number of ways, which we outline here.

Box 1 provides a non-exhaustive list of ways in which AI can go wrong for
environmental sciences, and other issues that can arise. We discuss this list
in more depth below and provide examples from the environmental sciences to
illustrate them.

Ways in which AI can go wrong for environmental sciences Issues related to
training data: 1. Non-representative training data, including lack of geo-
diversity 2. Training labels are biased or faulty 3. Data is affected by
adversaries Issues related to AI models: 1. Model training choices 2.
Algorithm learns faulty strategies 3. AI learns to fake something plausible 4.
AI model used in inappropriate situations 5. Non-trustworthy AI model deployed
6. Lack of robustness in the AI model Other issues related to workforce and
society: 1. Globally applicable AI approaches may stymie burgeoning efforts in
developing countries. 2. Lack of input or consent on data collection and model
training 3. Scientists might feel disenfranchised. 4. Increase of CO2
emissions due to computing Box 1:  A non-exhaustive list of issues that can
arise though the use of AI for environmental science applications.

###  2.1 Issues related to training data

AI models follow the well-known computer science adage: Garbage in, garbage
out. If the training data is not representative of what we actually want to
use the AI model for, then it will produce models that do not accomplish our
goals. Because training data are key, issues related to them are particularly
common and hard to avoid. First of all, as we demonstrate in the examples
below, it is extremely difficult to create a data set that does not have some
kind of bias or other shortcoming, even if it was developed with great care
and with the best intentions. Secondly, while the data developers might be
aware of many (but usually not all) of the shortcomings, the scientist using
the data to train AI models might be completely unaware of them, since there
is no standard (yet!) in the community to document these shortcomings and
include them with the data. Furthermore, whether a data set is biased also
depends on the application. It might be perfectly fine to use a data set for
one purpose, but not for another. Lastly, there is no established set of tests
to check for the most common biases in environmental science data sets.

It is important to understand that when AI models are trained on biased data,
they inherit those biases. This phenomenon is known as coded bias (O’Neil,
2016; Tan, 2020) and is easy to understand - if a hail data set shows hail
occurring only in populated areas (see Example 1(a) below), the AI system
trained on this data set is likely to also predict hail only in highly
populated areas, making the AI model just as biased to population density as
the data it was trained on. Since established algorithms are often used in
regions or under circumstances other than the origin of the data, such an
algorithm can even perpetuate the bias beyond the regions and circumstances it
was trained on.

####  2.1.1 Non-representative training data

Statistical distribution of training, testing, and validation data: If the
training data is non-representative statistically, the output is likely to be
biased. This could include geographic or population biases (discussed in more
detail in Section 2.1.2) but it could also include unintentional temporal
biases. For example, if an AI model is trained on data from 1900-1970,
1970-2000 is used as a validation set, and then 2000-2020 is used as a test
set, the model may not be properly accounting for climate change. Sensor
limitations provide other examples. Many sensors require sunlight for high
quality observations, and thus many phenomena are under-observed at night.
Similarly, inferring certain surface conditions from satellites using passive
sensors tends to be easier for clear sky conditions.

Lack of geo-diversity: In order to enable AI algorithms to facilitate
environmental justice we thus need to ensure that different populations are
well represented in their training data. This includes ensuring that the data
is diverse geographically, including addressing population biases and biases
in sensor placements that could affect the ability to obtain a statistically
representative training set. For example, the national radar network has
coverage gaps which can inadvertently under-represent some populations, as
indicated in Figure 3 (Sillin, 2021; Shepherd, 2021). We should explicitly
take population representation into account for the design of future sensor
networks and seek to close gaps in existing sensor networks by placing
additional sensors in strategic locations. Furthermore, we can put AI to good
use by developing AI algorithms to estimate sensor values at the missing
locations based on other sensor types, such as generating synthetic radar
imagery from geostationary satellite imagery (Hilburn et al., 2021).

####  2.1.2 Training labels are biased or faulty

Human generated data sets: Obtaining data for environmental science prediction
tasks is often quite challenging, both in terms of finding the data and in
terms of identifying a complete data set. For example, if one was to predict
hail or tornadoes but only to use human reports, there is a known bias towards
areas with higher population (Allen and Tippett, 2015; Potvin et al., 2019) as
shown in Figure 1). If more people live in an area, there is a higher chance
that someone observes and reports a hail or tornado event. This might bias the
AI model to over-predict urban hail/tornadoes and under-predict rural
hail/tornadoes.

A related issue is that even if a diverse geographical area is represented in
the dataset, the AI model will focus on patterns that are associated with the
most common regimes and areas where the hazard occurs most frequently. It also
may ignore patterns that affect a small portion of the dataset since the
contribution to the overall training error is relatively small. For example,
solar irradiance forecasts from an AI model trained across multiple sites in
Oklahoma had higher errors at the sites in the Panhandle compared with central
Oklahoma due to limited representation of Panhandle weather in the dataset
(Gagne et al., 2017).

(a) Hail reports follow population

(b) Tornado reports follow population

Figure 1: Hail and tornado reports both show a clear population bias with
reports occurring more frequently along roads and cities. This can be seen as
examples of (i) data being missing in low population areas (Section 2.1.1) and
(ii) faulty labels (Section 2.1.2). Panel a is from Allen and Tippett (2015);
Panel b is from Potvin et al. (2019)

(a) Human estimates and observations of wind speed

(b) Human reports of max wind speed versus measured max wind speed from
Edwards et al. (2018).

Figure 2: Human reports of wind speed show biases in both perception of the
speed itself (Panel a) and in the binning of the data (Panel b). Both panels
are from Edwards et al. (2018). This example highlights both non-represenative
training data (Section 2.1.1) and biased and faulty labels (Section 2.1.2)

Figure 2 illustrates the typical biases of humans to estimate wind speed due
to two effects. Figure 2(a) shows that humans tend to overestimate wind speed,
and thus tend to classify it as severe at levels that are not actually
considered severe. Thus, human reported wind speed results in training data
with significant bias toward higher wind speeds. Figure 2(b) illustrates that
humans tend to assign wind speeds in discrete increments, with a strong bias
toward multiples of five, i.e., 60, 65, 70, etc., kt. This example also
demonstrates how non-representative training data and the biases could result
in an AI algorithm that does not predict true wind speed impacts correctly.

Sensor generated data sets: A potential response to this data issue could be
to use only sensor-based data, such as radar-derived hail estimates. We often
assume that sensors are inherently objective yet that is not guaranteed.
First, the data from these sensors must be interpreted to create a full data
set. For radar-derived hail data, there are well known overprediction biases
to the data (e.g., Murillo and Homeyer, 2019). Second, data from sensors may
also be incomplete, either due to sensor errors or missing sensors. With many
sensors, there are areas which are well represented and areas where data is
lacking. Sensor placement often depends on geological features, e.g., there
might be a lack of sensors at remote mountain tops or in empty fields.
Economical reasons can also come into play in the placement of sensors, such
as the placement of crowd-sourced sensors where there are more affluent
people. Consider for example the deployment of air quality sensors. While the
EPA has a network of just over 1,100 air quality sensors that are relatively
evenly distributed throughout the US, this is not the case for the popular new
generation of low-cost air quality sensors, called PurpleAir. There are now
over 5,500 PurpleAir sensors deployed in the US, but they are deployed in
significantly Whiter, higher income areas than the national average (deSouza
and Kinney, 2021). Access to these sensors in less-privileged communities is
needed to democratize air pollution data (deSouza and Kinney, 2021).

Figure 3: Coverage of the national Doppler weather network (green and yellow
circles) overlaid with the black population in the southeast United States,
courtesy of Jack Sillin. This is an example of non-representative data
(Section 2.1.1)

####  2.1.3 Data is affected by adversaries

Adversarial data is a well-known problem in machine learning (e.g., Nelson et
al., 2010; Goodfellow et al., 2018; Diochnos et al., 2018). Adversaries can
cause an AI model to either learn a faulty model or to be used incorrectly
when applied to real-world data. For example, there are well-known examples of
minor changes to speed signs causing a computer vision system to see a 35 mph
speed limit as an 85 mph speed limit, something that could be quite dangerous
in an autonomous car.

AI applied to environmental science data has to contend with two kinds of
adversaries: humans and the environment. One needs to be aware of both types
of adversaries when training and applying the AI models to the real-world.

Human adversaries:  When using human reported data there is always the
possibility of users intentionally adding bad data. Figure 4 provides two
examples. Figure 4(a) provides the screenshot of wind reported by someone who
hacked the crowd-sourced mPing system for the state of Alabama. Note the long
line of wind reported outlining the state border which clearly represents an
intentional input of incorrect information. Such data would be detrimental to
any AI model trained on this data. A second source of human adversarial data
is insurance fraud (Davila et al., 2005). As the number of expensive natural
disasters are increasing (Figure 4(b)), the number of fraudulent weather-
related insurance claims is increasing, with estimates of fraudulent reports
hovering around 10% (Sorge, 2018). Such fraudulent reports can also affect
training data for AI by appearing in the databases of severe weather reports.

(a) Screenshot of hacked data from mPing from Cappucci (2020)

(b) Catastrophe related insured losses from 1970 to 2018 from (RE, 2018;
Scotti, 2019). With at least 10% of weather-based insurance claims estimated
as fraudulent (Sorge, 2018), there is increasing motivation for humans to
report incorrect severe weather data

Figure 4: Humans sometimes create adversarial data, which may be ingested by
an AI model (Section 2.1.3). While in example (a) the user intent is to create
false inputs, in example (b) the motivation for the false reports is more for
personal financial gain (insurance fraud). Nevertheless, both can cause
problems for AI by directly affecting reports databases used by AI models

Weather as an adversary: Weather can act as its own adversary, especially when
collecting observations for extreme events. For example, when seeking to
observe the severity of storms, sensors can fail due to power outages caused
by a strong storm (Fig. 5(a)) or a strong storm can even destroy sensors (Fig.
5(b)).

(a) Power outages following a hurricane

(b) A destroyed Oklahoma Mesonet station following a severe wind gust

Figure 5: Weather also creates its own adversaries (Section 2.1.3) by creating
power outages (a) or destroying sensors (b), especially during major events.
Graphics from Staff (2021); Mesonet (2020)

###  2.2 Issues related to the AI model

In addition to problems caused by bias or other complications in the training
data, AI models can also develop issues on their own. Examples are given in
this section.

####  2.2.1 Model training choices

Model training choices will affect every aspect of the AI model. While AI
methods are based on mathematical equations and thus often seen as
“objective", there are countless choices that a scientist has to make that
greatly affect the results. These choices include: (i) which attributes (e.g.,
which environmental variables) to include in the model; (ii) which data
sources to use; (iii) how to preprocess the data (e.g., normalizing the data,
removing seasonality, applying dimension reduction methods); (iv) which type
of AI model to use (e.g., clustering, random forest, neural networks, etc.),
(v) how to choose hyper parameters (e.g., for random forest - how many trees,
maximal depth, minimal leaf size, etc). Each of these choices has significant
impact and can lead to vastly different results with severe consequences. For
example, the choice of spatial resolution for the output of a model can be
crucial for environmental justice. Training an AI model to predict urban heat
at a low spatial resolution may average out, and thus overlook, extreme values
in small neighborhoods, while using a higher spatial resolution could reveal
those peaks but potentially introduce noise.

####  2.2.2 Algorithm learns faulty strategies

AI models are tasked to learn patterns in the data that help them come up with
good estimates or classifications. Sometimes, even if the data are not faulty
in the traditional sense, they may contain spurious correlations that are not
representative of the real world and that the AI model learns to exploit. This
issue could be discussed in the section on data-related issues (Section 2.1),
but we chose to include it in this section since it is so closely coupled with
AI model development, and often only diagnosed once an AI model has been
developed.

(a) Tornado prediction model from Lagerquist et al. (2020) and Randy Chase
(Chase and McGovern, 2022). When examining the model, we discovered that
adding random noise to the reflectivity did not decrease predictions as
expected.

(b) Example of a partial dependency plot (Molnar, 2018) which shows how an AI
model could produce unphysical results when given unexpected inputs (Section
2.2.4). From (Chase et al., 2021)

Figure 6: Examples of an AI learning to fake something plausible (Section
2.2.3) and of a model generating unexpected output when applied to data
outside of the range of expected data (Section 2.2.4)

One approach to identifying when the AI has learned a faulty strategy is to
either use interpretable or explainable AI (XAI) (e.g., Ras et al., 2018;
Molnar, 2018; Samek et al., 2019; McGovern et al., 2019; Ebert-Uphoff and
Hilburn, 2020). In the case of interpretable AI, the models are intended to be
understandable by human experts (Rudin, 2019) while explainable AI attempts to
peer inside the black box of more complicated models and identify the internal
strategies used by the models. Both approaches allow a human expert to examine
the model and potentially to identify faulty strategies before deploying a
model.

Figure 6(a) is an example of how an AI model can learn a faulty strategy and
how this can be discovered through XAI. In this example, a deep learning model
was trained to predict tornadoes (Lagerquist et al., 2020) and then examined
to identify what the model had learned. Unexpectedly, we discovered that the
model was still predicting a high probability of tornadoes even if the
reflectivity image contained mostly noise (Chase and McGovern, 2022).

####  2.2.3 AI learns to fake something plausible

The emergence of an advanced type of AI algorithm, namely the Generative
Adversarial Network (GAN) introduced by Goodfellow et al. (2014), yields the
ability to generate imagery that looks extremely realistic. The result of a
GAN can be seen as one possible solution (an ensemble member) which might not
be representative of the distribution of possible solutions. An important
question is how forecasters would respond to GAN imagery with intricate small
scale features that look overwhelmingly realistic, but might not be as
accurate as they appear to be. Ravuri et al. (2021) conducted a cognitive
assessment study with expert meteorologists to evaluate how forecasters
respond to GAN imagery of radar for precipitation nowcasting. They concluded
that for their application forecasters made deliberate judgements of the
predictions by relying on their expertise, rather than being swayed by
realistic looking images (Suppl. C.6. of Ravuri et al. (2021)). Nevertheless,
the jury is still out whether that is generally the case. Such methods might
sometimes trick forecasters into greater trust than is warranted. Similar
methods are used to generate deep fake images and videos (Adee, 2020) which
have successfully fooled people into believing misinformation (Vaccari and
Chadwick, 2020). If similar approaches are used in environmental science,
trust in AI models could be lost.

One of the major dangers of generative models used in contexts where they are
parameterizing fine scale data (Gagne et al., 2020) or filling in missing data
(Geiss and Hardin, 2021) is the lack of guarantees about what data they use to
fill in the gaps. If an ML model is trained without any physical constraints,
it is possible for the algorithm to insert spurious weather features. If this
occurs in otherwise data sparse regions, forecasters may not have any
additional data to discredit the false prediction for many hours. More subtle
discrepancies would be the most problematic since they are harder for
forecasters to catch.

####  2.2.4 Models used in inappropriate situations

Another model-based issue that can arise is when an AI model is trained for
one situation, perhaps a specific weather regime or for a specific
geographical area, and then applied to new situations where it is not
physically meaningful. In such situations, the AI may predict incorrectly,
without giving any warning, which could lead to loss of life and environmental
injustice.

For example, Figure 6(b) shows a partial dependence plot (Molnar, 2018) of the
predictions of an AI method predicting total ice water content (i.e., mass of
snow in a cloud) from radar data (Chase et al., 2021). If input given to the
model is uncharacteristic of the training dataset, the output may be not
physically realistic. This issue also comes up frequently when ML is used to
replace Numerical Weather Prediction parameterization schemes. If the ML model
is transferred to a different climate or geographic regime or even to the
hemisphere opposite where it was trained (where the sign of many common
variables are flipped), it often performs quite poorly.

####  2.2.5 Non-trustworthy models deployed

Ensuring that a model is trustworthy is a key part of ethical and responsible
AI. Often AI systems are deployed before they are ready, in particular before
they have been thoroughly tested and validated by domain experts. Fig. 7 shows
the results of a commercial AI system predicting damage caused by a
hypothetical 7.0-magnitude earthquake in the Seattle area. The three panels
show results from three different version of the system delivered to the city
of Seattle to assist them to plan where to establish earthquake shelters. The
widely differing results in the three panels arose from using different data
sources, but also from programming errors (e.g., counting each apartment in a
high-rise building as a separate structure). Deploying the model before it was
ready for operation forced the city to revamp nearly completed plans for
sheltering earthquake-displaced residents that were developed using the
original version Fink (2019). The trust in the AI system was so eroded that
the city considered terminating their contract, and only kept it because the
company found an external funder and could offer it to Seattle for free.

Typical mistakes to be avoided, illustrated by this example, are developing a
system without engaging domain experts or local end-users, deploying a system
before it has been rigorously validated, and over-promising the system’s
accuracy to the end user without any scientific evidence. For the latter,
there are many new methods for uncertainty quantification in machine learning
models that we as a community should start utilizing routinely for this
purpose (e.g., Orescanin et al., 2021; Barnes et al., 2021).

Figure 7: Three vastly different damage predictions for the same hypothetical
7.0-magnitude Seattle-area earthquake delivered by different versions of the
same AI system. Figure from Fink (2019)

####  2.2.6 Lack of robustness

While a lack of robustness could also be categorized under models being
inappropriately applied, adversarial data, or even a lack of trust, we
separate it into its own category to highlight the need for robustness in
ethical and responsible AI. Robust AI for environmental sciences will fail
gracefull when outputs are out of range (e.g. Section 2.2.4) and will also
constrain the outputs by the laws of physics. For instance, when preparing a
workshop tutorial, one of the authors was demonstrating a simple ML method
that could predict a local temperature. When presented with an input that was
two standard deviations outside of its training data, the method suddenly
predicted a temperature hotter than the surface of the sun. Such predictions
may contribute to a lack of trust and create environmental injustices.

###  2.3 Other issues related to workforce and society

We have discussed ways that both the training data and the AI model could go
wrong. Here we focus on the broader picture of how AI is applied and developed
and how that relates to environmental justice. This aspect also needs to be
addressed in developing ethical and responsible AI for environmental sciences.

####  2.3.1 Globally applicable AI approaches may stymie burgeoning efforts in
developing countries

Large organizations developing and deploying AI systems, including government
agencies and private companies, generally want their AI systems to be globally
applicable. People in countries outside that of the provider organization can
benefit from technological advances that may not otherwise be available to
them. Provider organizations can benefit from a broader set of customers and
stakeholders. These kinds of global activities work best when researchers and
companies directly engage with different local populations and incorporate
their needs and concerns into the design process. For example, Google’s crisis
team has been working with multiple local and government partners in India and
Bangladesh to create a hyper-local flood forecasting product (Matias, 2021).

However, the relative ease of deploying AI on global datasets can also
increase the temptation for organizations to automate deployment without fully
monitoring its impact. Without direct engagement with various populations,
organizations may not be aware of the unintended consequences of their
algorithms. They also may not have access to observations in these areas to
validate their performance. They may also undercut local providers who are
more aligned with the community but do not have the same resources and
economies of scale to compete on price, especially if the service is offered
for free or is supported by advertising revenue. Government meteorological
centers in both developed and developing countries have dealt with budget cuts
and cost-recovery requirements even before the growth of AI and the private
weather industry, so further adoption of AI could exacerbate these trends.

For example, mobile weather apps have become the primary source of weather
information for younger people (Phan et al., 2018). However, the apps’ uniform
presentation of weather information may result in users not being aware of
more localized and rare weather hazards. A local government or television
meteorologist on the other hand can tailor their communication to highlight
these issues.

####  2.3.2 Lack of input or consent on data collection and model training

As illustrated in the discussion of Figure 7, when collecting local data for
training an AI model or when creating an AI model to inform decisions in or
about a specific place, it is critical that the people affected and those with
local expertise are involved from the beginning (Renn et al., 1995; Stern and
Fineberg., 1996; Chilvers, 2009; Voinov et al., 2016; Pidgeon, 2021). This is
more typically known in the social sciences but not nearly as common in AI.

The types of data that are collected affect the AI models that can be applied
and trained. Understanding that data provides a source of power and that what
is not collected cannot be used (D’Ignazio and Klein, 2020), it is possible to
see that AI could too easily be used to perpetuate environmental and climate
injustices if data are not collected carefully.

In environmental research it has long been noted that engaging those whose
concerns the science is purportedly informing or addressing can improve models
and outcomes, is a moral obligation, and is the virtuous course of action
(e.g., Lemos and Morehouse, 2005). A core duty in all science is honesty, to
respect the dignity and rights of persons (Keohane et al., 2014, e.g.,). In AI
for environmental sciences this requires grappling with how to be transparent
(i.e., show your work – (D’Ignazio and Klein, 2020)) about methodological
biases and uncertainties that are often complex and poorly understood. When
scientific conditions such as sensitivity to training conditions or data
provenance are not reported, that lack of transparency both disempowers and
disrespects those the model may be intended to help, and can make a study
irreplicable and even irreproducible (National Academies of Sciences,
Engineering, and Medicine et al., 2019).

It is thus critical to keep in mind that many types of data and knowledge
already exist outside of the colonial framework in which most AI data has been
collected. For example, scientists must work directly with local leaders to
incorporate Indigenous knowledge (Cartier, 2019; Hiwasaki et al., 2014) in an
ethical and responsible manner.

####  2.3.3 Scientists feeling disenfranchised

There are two primary reasons why scientists might feel disenfranchised.

Scientists not fluent in AI might feel disenfranchised: Environmental
scientists are absolutely essential for the development of meaningful AI tools
for the their domains. Currently, with a lack of education in AI for
environmental sciences, leading scientists may feel excluded from advancing
state-of-the-art tools. They must either learn about AI themselves or
collaborate with AI scientists to be part of major future development in their
field. As a consequence they may feel less independent and less appreciated.
Clearly, we need more educational resources to help environmental scientists
learn the basics of AI in order to empower them to play a leading role in
future developments.

Required computational resources might limit research opportunities to
privileged groups: While AI methods for many environmental science
applications require only modest computational resources, some research now
requires access to extensive high performance computing facilities, which
limits this kind of research to those research groups privileged enough to
have such access. To level the playing field we as a community need to find
ways to develop an open science model that provides access to computational
resources also for other groups who need them (e.g., Gentemann et al., 2021).

####  2.3.4 Increase of CO2 emissions due to computing

It is well known that the increasing computational demands of AI training are
responsible for a surprisingly large carbon footprint worldwide (Xu et al.,
2021; Schwartz et al., 2020). Thus we need to consider, and limit, the carbon
footprint from the computational needs of environmental science. Green deep
learning (aka Green AI) is a new research field that appeals to researchers to
pay attention to the carbon footprint of their research, and to focus on using
lightweight and efficient methods (Xu et al., 2021). We should fully explore
these new developments, including focusing on how to make ML models simpler
for environmental science applications, which would have many advantages,
including increased transparency and robustness (Rudin, 2019), but also lower
computational needs and lower carbon footprints.

##  3 Discussion and Future work

The scientific community is still grappling with the many ethical questions
raised by the introduction of AI in general (Schmidt et al., 2021; Floridi,
2019; O’Neil, 2016) and for earth science applications in particular
(Coeckelbergh, 2021; Doorn, 2021). The effort presented here represents the
beginning of our work on developing a full understanding of the need for
ethical, responsible, and trustworthy AI for the environmental sciences and of
the interactions between ethical and responsible AI and trustworthy AI within
the NSF AI Institute for Research on Trustworthy AI in Weather, Climate, and
Coastal Oceanography (AI2ES, ai2es.org). In an upcoming paper, we plan to
present guiding principles for ethical, responsible, and trustworthy AI for
the environmental sciences.

##### Acknowledgments

We are grateful for the graphic on radar coverage in the southeast US
contributed by Jack Sillin (Cornell), the graphics contributed by Randy Chase
(OU), and references contributed by Amy Burzynski (CSU).

##### Funding Statement

This material is based upon work supported by the National Science Foundation
under Grant No. ICER-2019758 and by the National Center for Atmospheric
Research, which is a major facility sponsored by the National Science
Foundation under Cooperative Agreement No. 1852977.

##### Competing Interests

None.

##### Data Availability Statement

This manuscript does not develop any new data or code.

##### Ethical Standards

The research meets all ethical guidelines, including adherence to the legal
requirements of the study country.

##### Author Contributions

Conceptualization: All authors. Methodology: All authors. Data visualization:
A.M and I.E. Writing original draft: A.M and I.E equally shared the majority
of the writing of this paper. All authors contributed to the writing and
approved the final submitted draft.

##### Supplementary Material

None.

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