††thanks: Corresponding author<EMAIL_ADDRESS>Corresponding
author<EMAIL_ADDRESS>
# Masses of ground and isomeric states of 101In and configuration-dependent
shell evolution in odd-$A$ indium isotopes

X. Xu  Key Laboratory of High Precision Nuclear Spectroscopy and Center for
Nuclear Matter Science, Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Science, Xi′an Jiaotong University,
Xi′an 710049, China  J. H. Liu  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, China  C. X. Yuan  Sino-French Institute of Nuclear Engineering and
Technology, Sun Yat-Sen University, Zhuhai 519082, China  Y. M. Xing  Key
Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear
Matter Science, Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  M. Wang  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, China  Y. H. Zhang  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, China  X. H. Zhou  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, China  Yu. A. Litvinov  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  GSI
Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, Darmstadt, 64291
Germany  K. Blaum  Max-Planck-Institut für Kernphysik, Saupfercheckweg 1,
69117 Heidelberg, Germany  R. J. Chen  Key Laboratory of High Precision
Nuclear Spectroscopy and Center for Nuclear Matter Science, Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  X. C. Chen
Key Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear
Matter Science, Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  C. Y. Fu  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  B. S. Gao  Key
Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear
Matter Science, Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  School of Nuclear Science and Technology, University of
Chinese Academy of Sciences, Beijing 100049, China  J. J. He  Key Laboratory
of Beam Technology of Ministry of Education, College of Nuclear Science and
Technology, Beijing Normal University, Beijing 100875, China  Key Laboratory
of High Precision Nuclear Spectroscopy and Center for Nuclear Matter Science,
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  S. Kubono  Key Laboratory of High Precision Nuclear Spectroscopy and
Center for Nuclear Matter Science, Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  Y. H. Lam  Key Laboratory of High
Precision Nuclear Spectroscopy and Center for Nuclear Matter Science,
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  H. F. Li  Key Laboratory of High Precision Nuclear Spectroscopy and
Center for Nuclear Matter Science, Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  School of Nuclear Science and
Technology, University of Chinese Academy of Sciences, Beijing 100049, China
M. L. Liu  Key Laboratory of High Precision Nuclear Spectroscopy and Center
for Nuclear Matter Science, Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Nuclear Science and Technology,
University of Chinese Academy of Sciences, Beijing 100049, China  X. W. Ma
Key Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear
Matter Science, Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  School of Nuclear Science and Technology, University of
Chinese Academy of Sciences, Beijing 100049, China  P. Shuai  Key Laboratory
of High Precision Nuclear Spectroscopy and Center for Nuclear Matter Science,
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  M. Si  Key Laboratory of High Precision Nuclear Spectroscopy and Center
for Nuclear Matter Science, Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Nuclear Science and Technology,
University of Chinese Academy of Sciences, Beijing 100049, China  M. Z. Sun
Key Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear
Matter Science, Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  School of Nuclear Science and Technology, University of
Chinese Academy of Sciences, Beijing 100049, China  X. L. Tu  Key Laboratory
of High Precision Nuclear Spectroscopy and Center for Nuclear Matter Science,
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  School of Nuclear Science and Technology, University of Chinese Academy
of Sciences, Beijing 100049, China  Q. Wang  Key Laboratory of High Precision
Nuclear Spectroscopy and Center for Nuclear Matter Science, Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of
Nuclear Science and Technology, University of Chinese Academy of Sciences,
Beijing 100049, China  H. S. Xu  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, China  X. L. Yan  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  J. C. Yang  Key
Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear
Matter Science, Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  School of Nuclear Science and Technology, University of
Chinese Academy of Sciences, Beijing 100049, China  Y. J. Yuan  Key Laboratory
of High Precision Nuclear Spectroscopy and Center for Nuclear Matter Science,
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  School of Nuclear Science and Technology, University of Chinese Academy
of Sciences, Beijing 100049, China  Q. Zeng  Key Laboratory of High Precision
Nuclear Spectroscopy and Center for Nuclear Matter Science, Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of
Nuclear Science and Engineering, East China University of Technology,
Nanchang, 330013, China  P. Zhang  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, China  X. Zhou  Key Laboratory of High Precision Nuclear Spectroscopy
and Center for Nuclear Matter Science, Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  School of Nuclear Science and
Technology, University of Chinese Academy of Sciences, Beijing 100049, China
W. L. Zhan  Key Laboratory of High Precision Nuclear Spectroscopy and Center
for Nuclear Matter Science, Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  S. Litvinov  GSI Helmholtzzentrum für
Schwerionenforschung, Planckstraße 1, Darmstadt, 64291 Germany  G. Audi
CSNSM, Univ Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, 91405 Orsay,
France  S. Naimi  RIKEN Nishina Center, RIKEN, Saitama 351-0198, Japan  T.
Uesaka  RIKEN Nishina Center, RIKEN, Saitama 351-0198, Japan  Y. Yamaguchi
RIKEN Nishina Center, RIKEN, Saitama 351-0198, Japan  T. Yamaguchi  Department
of Physics, Saitama University, Saitama 338-8570, Japan  A. Ozawa  Insititute
of Physics, University of Tsukuba, Ibaraki 305-8571, Japan  B. H. Sun  School
of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191,
China  K. Kaneko  Department of Physics, Kyushu Sangyo University, Fukuoka
813-8503, Japan  Y. Sun  School of Physics and Astronomy, Shanghai Jiao Tong
University, Shanghai 200240, China  Key Laboratory of High Precision Nuclear
Spectroscopy and Center for Nuclear Matter Science, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  F. R. Xu  State
Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking
University, Beijing 100871, China

###### Abstract

We report first precision mass measurements of the $1/2^{-}$ isomeric and
$9/2^{+}$ ground states of 101In. The determined isomeric excitation energy
continues a smooth trend of odd-$A$ indium isotopes up to the immediate
vicinity of $N=50$ magic number. This trend can be confirmed by dedicated
shell model calculations only if the neutron configuration mixing is
considered. We find that the single particle energies are different for
different states of the same isotope. The presented configuration-dependent
shell evolution, type II shell evolution, in odd-$A$ nuclei is discussed for
the first time. Our results will facilitate future studies of single-particle
neutron states.

###### pacs:

21.10.Dr, 21.10.Pc, 27.60.+j

Properties of the nuclides around the doubly-magic nucleus 100Sn have
attracted intense research efforts both in experiment and theory 100SnPPNP .
Of particular interest are the isomeric states which provide unique insight
into the nuclear structure. Many isomers were predicted and some of them have
been observed around 100Sn 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9 ; 10 . Various
implications from the obtained results on nuclear structure 2 ; 3 ; 4 ; 5 ; 6
; 7 ; 8 ; 9  and on astrophysics 10  have been extensively discussed.
Currently, all known isomers in this region were discovered by using decay
spectroscopy.

In odd-$A$ indium isotopes ($Z$ = 49), the ground states have _J_ π = 9/2+
with the $\pi(1g_{9/2})^{-1}$ proton-hole character. When promoting a proton
from $\pi 2p_{1/2}$ orbital to $\pi 1g_{9/2}$, the $\pi(2p_{1/2})^{-1}$
proton-hole state is formed. Due to the slow $M$4 transition from the 1/2-
state to the 9/2+ ground state, the former state is always a $\beta$-decaying
isomer. On the one hand, the excitation energies of such isomers are directly
related to the energy gap between the $\pi 2p_{1/2}$ and $\pi 1g_{9/2}$
orbitals, and thus allow the study of the gap evolution as a function of
neutron number. On the other hand, proton occupations inside the same nucleus
in either $\pi 2p_{1/2}$ or $\pi 1g_{9/2}$ single-particle orbital may affect,
via the proton-neutron ($p$-$n$) interactions, the ordering of neutron
orbitals, e. g., $\nu 1g_{7/2}$ and $\nu 2d_{5/2}$. It has been shown Yusu2014
; Kre2016  that the monopole part of the $p$-$n$ interaction plays a crucial
role for the shell evolution within the same nucleus, the so-called type II
shell evolution. Such a newly reported shell evolution can be investigated in
odd-$A$ indium isotopes since indium has just one proton less than the magic
tin ($Z=50$) and has thus relatively pure proton particle-hole excitations.

When approaching 100Sn, 103In is the most neutron-deficient indium isotope in
which the 1/2- isomeric state, 103mIn, was found 8 . The level structure of
101In was studied via the 50Cr(58Ni, 3p4n)101In fusion-evaporation reaction 8
and the $\beta$-decay of 101Sn 101Snbeta , but 101mIn was not observed in
these experiments. It was estimated in Ref. 8  that the dominant decay mode of
the yet unknown 101mIn is beta decay. There has been a circumstantial evidence
of the existence of the 1/2- isomer in 97In, though its excitation energy and
half-life could not be determined 97In .

The production of the 1/2- state may be less favored in nuclear reactions due
to the low spin. Therefore more sensitive methods should be developed for the
identification of the isomer. To investigate nuclear isomers, the state-of-
the-art mass spectrometry Klaus06  gained importance in recent years thanks to
the improved mass resolution, which is high enough to directly resolve low-
lying isomers from the corresponding nuclear ground states. New isomers have
been discovered with Penning trap 12  as well as storage-ring mass
spectrometry 13a ; 13 ; 13b ; 14 . In such experiments, the excitation energy
is measured directly as the mass difference between the isomer and the ground
state. For already known isomers, mass spectrometry can independently provide
information on the isomer excitation energies 15 ; 16 ; 17 .

In this paper, we report the direct identification of the 1/2- isomer in
101In. Masses of the isomeric and ground states, and thus automatically the
isomer excitation energy, $E_{x}(1/2^{-}){}$, of 101In are determined for the
first time.

The experiment was conducted at the Cooler Storage Ring (CSR) accelerator
complex of the Heavy Ion Research Facility in Lanzhou (HIRFL) located at the
Institute of Modern Physics, P. R. China. It has been done in a similar way as
our previous experiments 16 ; TuPRL ; TuNIMA ; ZhangPRL ; ZhangPRC ; XingPLB .
A 400.88 MeV/u 112Sn35+ primary beam was accelerated and accumulated in the
main storage ring CSRm, operating as a heavy-ion synchrotron. Every 25
seconds, the beam was fast extracted and focused onto a $\sim$10-mm-thick
beryllium target placed at the entrance of the in-flight separator RIBLL2 Xia
jiawen . The projectile fragments were selected and analyzed by RIBLL2. A
cocktail beam of $10-30$ ions per spill was injected into the experimental
storage ring CSRe. The CSRe was tuned into the isochronous ion-optical mode
with the transition energy of ${\gamma}_{t}=1.302$. In this mode the
revolution times of the stored ions depend in first order only on their mass-
to-charge ratios, which is the basis of the Isochronous Mass Spectrometry
(IMS) MHa ; FGM . Both RIBLL2 and CSRe were set to a fixed magnetic rigidity
of _B_ ${\rho}=5.3374$ Tm to optimize the transmission of the _T_ ${}_{z}=3/2$
nuclides centered on 101In49+. Other nuclides within the acceptance of the
RIBLL2-CSRe system of about $\pm 0.2$% were also transmitted and stored in
CSRe. In order to achieve a better mass resolving power, a 50 mm wide slit was
introduced slit2019  in the dispersive straight section of CSRe to reduce the
momentum spread of the secondary beam.

Figure 1: (color online) Part of the revolution time spectrum zoomed in a time
window of 668 ns $\leq$ _t_ $\leq$ 672 ns. The nuclides with well-known masses
(black color) were used as calibrants in the mass calibration. The insert
shows the well-resolved peaks of the ground and isomeric states of 101In.

To measure the revolution times of stored ions, a high-performance time-of-
flight detector (ToF) equipped with a 19 $\mu$g/cm2 carbon foil of 40 mm in
diameter was installed inside CSRe MeiNIMA . The time resolution of the
detector was about 50 ps. Secondary electrons were released from the foil each
time when an ion passed through the carbon foil. The electrons were guided to
a microchannel plate (MCP) by a perpendicularly arranged electric and magnetic
field. The timing signals from the MCP detector were directly sampled with a
digital oscilloscope at a sampling rate of 40 GHz. For each injection of ions
into CSRe the recording time was set to 200 $\mu$s corresponding to $\sim 300$
revolutions of the ions. Those ions which circulated in CSRe for more than
about 75 revolutions (50 $\mu$s) were considered in the data analysis. The
revolution time of each individual ion was extracted from the measured
periodic timing signals TuNIMA . The entire data analyses, including the time
shift correction and particle identification, have been conducted following
the procedures described in Refs. TuNIMA ; ZhangPRC ; XingNIMA . Some details
of the present analysis were reported in Ref. NPR . The final revolution time
spectrum has been obtained by accumulating all events.

Figure 1 presents a part of the revolution time spectrum zoomed in at a time
window of 668 ns $\leq$ _t_ $\leq$ 672 ns. In this time range, the minimum
standard deviation, $\sigma_{T}$, of the peaks was about 0.5 ps corresponding
to a mass resolving power of _m_ /${\Delta}$_m_ ${\sim}$ $3.2\times 10^{5}$
(FWHM). The insert in Fig. 1 illustrates the revolution time spectrum expanded
around 101In. In addition to the main peak corresponding to the ground state
of 101In, seven counts are observed at a mean revolution time of
$\sim$5$\sigma_{T}$ larger than the time of the main peak ($\sim$2.8 ps).
These counts are attributed to the particles other than the ground state of
101In. Given the fact, that all particles in Fig. 1 have been unambiguously
identified as belonging to different series with certain $T_{z}=({Z-N})/{2}$,
and their yields and revolution times for the isotopes of same $T_{z}$ follow
the expected systematics as a function of mass number, the above-mentioned
seven counts can be assigned only to an unknown isomer in 101In.

Table 1:  Mass excess $(ME)$ values of the ground (101In) and isomeric (101mIn) states obtained in the present work. Also given are the numbers of counts, the widths of the revolution time peaks ($\sigma_{T}$), spin parities ($J^{\pi}$), the differences between the experimental and extrapolated values ($\Delta ME$), the measured $(E_{x}^{\rm{CSRe}}$($1/2^{-}$)$)$ and extrapolated $(E_{x}^{\rm{AME16}}$($1/2^{-}$)$)$ excitation energies. The corresponding extrapolated values from AME′16 AME16  are marked with label ’#’.  Atom |  Counts |  $\sigma_{T}$ | $J^{\pi}$ |  $ME_{\rm{CSRe}}$ |  $ME_{\rm{AME16}}$ |  $\Delta ME$ |  $E_{x}^{\rm{CSRe}}(1/2^{-})$ |  $E_{x}^{\rm{AME16}}(1/2^{-})$
---|---|---|---|---|---|---|---|---
|  | (ps) | $(\hbar)$ | (keV) | (keV) | (keV) | (keV) | (keV)
101In | $95$ |  $0.54$ |  $9/2^{+}$# |  $-68550(13)(6)$ |  $-68610(200)$# | $60(200)$ | 0 | 0
101mIn | $7$ |  $0.54$ |  $1/2^{-}$# |  $-67891(48)(6)$ |  $-68060(220)$# | $169(225)$ | $659(50)$ |  $550(100)$#

Most of the nuclides in Fig. 1 have well-known masses. Their mass excess
$(ME)$ values from the latest Atomic Mass Evaluation, AME′16, AME16  were used
to fit their mass-to-charge ratios $m/q$ versus their corresponding revolution
times $T$. A third order polynomial function has been employed. The mass
calibration has been checked by re-determining the $ME$ values of each of the
$N_{c}$ reference nuclides ($N_{c}$ = $17$) by using the other $N_{c}~{}-~{}1$
ones as calibrants. The normalized $\chi_{n}$ defined as:

$\displaystyle\chi_{n}=\sqrt{\frac{1}{N_{c}}\sum\limits_{i=1}^{N_{c}}\frac{[(\frac{m}{q})_{i,\rm{exp}}-(\frac{m}{q})_{i,\rm{AME}}]^{2}}{\sigma^{2}_{{i,\rm{exp}}}+\sigma^{2}_{{i,\rm{AME}}}}}~{},$
(1)

was found to be $\chi_{n}$ = $1.363$. This value is slightly outside the
expected range of $\chi_{n}$ = $1\pm 0.171$ at $1\sigma$ confidence level. A
systematic error of 6 keV has been added to the corresponding statistical
uncertainties. The mass excess values of 101In and its isomer determined in
this work are presented in Table 1.

Based on the systematics, a low-lying $1/2^{-}$ isomer 101mIn was predicted to
have a half-life comparable to the ground state AME16 . The excitation energy
determined in the present work, $659(50)$ keV, is in a reasonable agreement
with the extrapolation of AME′16 AME16  and the shell model calculations
101Snbeta . Following the systematics of $1/2^{-}$ isomers in odd-$A$ indium
isotopes, see Fig. LABEL:101In, a spin-and-parity of $1/2^{-}$ is assigned
here to the new isomer in 101In.

The available experimental data on the excitation energies of the $1/2^{-}$
states, $E_{x}(1/2^{-})$, in odd-$A$ indium isotopes extend now to the
immediate vicinity of the doubly-magic nucleus 100Sn. These energies provide a
direct information on the relative position of the $\pi 1g_{9/2}$ and $\pi
2p_{1/2}$ single particle orbitals, i. e. the $Z=40$ sub-shell gap. It has
been shown Ag2019  that the size of the $Z=40$ subshell gap is strongly
affected by the spin-isospin part of the proton-neutron interaction. To get
more insight into the structure of the $9/2^{+}$ ground state and the
$1/2^{-}$ isomer in 101In as well as the microscopic origin of the $Z=40$ sub-
shell evolution in this region, dedicated shell-model calculations have been
performed by using the KSHELL code kshell  with the state-of-the-art monopole-
based universal interaction $V_{\rm MU}$ plus a spin-orbit force from
M3Y($V_{\rm MU}+LS$) Tensor2 ; M3Y . The $V_{\rm MU}$ interaction consists of
a Gaussian central force and a tensor force Tensor2  and has been successfully
applied to describe the shell structure of exotic nuclei in various regions
application1 ; application2 ; application3 ; application4 ; application5 . In
our calculations, the model space for protons consisted of the $\pi
1f_{5/2},\pi 2p_{3/2},\pi 2p_{1/2}$, and $\pi 1g_{9/2}$ orbitals. For
neutrons, three model spaces were considered, namely the $\nu 2d_{5/2}$ single
orbital, the $\nu 1g_{7/2}$ single orbital, and the $\nu 2d_{5/2},\nu
1g_{7/2},\nu 3s_{1/2},\nu 1h_{11/2}$, and $\nu 2d_{3/2}$ five orbitals. In all
calculations, 78Ni was taken as an inert core and the single particle energies
were tuned in order to give a consistent $E_{x}(1/2^{-})$ value for 101In. The
calculated results are presented in Fig. LABEL:101In. We see from this figure
that if the neutrons are restricted only to the $\nu 1g_{7/2}$ orbital, the
$E(1/2^{-})-E(9/2^{+})$ energy difference rapidly decreases from 101In to
107In (the blue line in Fig. LABEL:101In). An inverse trend is observed if the
neutrons are added to the $\nu 2d_{5/2}$ orbital (the green line in Fig.
LABEL:101In). This indicates that the calculations with pure neutron
configurations can not reproduce the systematics of the experimental energy
differences between the $9/2^{+}$ and $1/2^{-}$ states.

When the model space containing five neutron orbitals is considered in the
calculations, the experimental trends of energy spacings can be well
reproduced by the theory as shown by the red line in Fig. LABEL:101In. On the
one hand, this result indicates that the new $1/2^{-}$ isomer in 101In is
formed in a similar proton-hole configuration as the other isomers in odd-$A$
indium isotopes. On the other hand, the neutron configuration mixing should be
considered in understanding the microscopic structure of these states.

Based on the properties of the spin-isospin part of the proton-neutron
interaction discussed in Ref. otsuka2001 ; Tensor1 ; Tensor2 , it is known
that the interactions between a $j=l+1/2$ proton with a
$j^{\prime}=l^{\prime}-1/2$ neutron is more attractive than the one for the
$j=l+1/2$ proton with a $j^{\prime}=l^{\prime}+1/2$ neutron and vice versa.
From this scenario, one may expect that the relative position of $\nu
1g_{7/2}$ and $\nu 2d_{5/2}$ orbitals in each indium isotope depends on the
proton configuration. The $1/2^{-}$ isomer and the $9/2^{+}$ ground state
correspond to $\pi(2p_{1/2})^{-1}$ and $\pi(1g_{9/2})^{-1}$ configurations,
respectively. With respect to the $9/2^{+}$ ground state, the accumulated
effects for the $1/2^{-}$ isomer, due to one proton gain in $\pi 1g_{9/2}$ and
one proton loss in $\pi 2p_{1/2}$, can lead to the reduction of energy spacing
or even an inversion of the $\nu 1g_{7/2}$ and $\nu 2d_{5/2}$ orbitals.

Figures LABEL:occupy92 and LABEL:occupy12 show the neutron occupation numbers
extracted from our calculations with the neutron model space of $\nu
2d_{5/2},\nu 1g_{7/2},\nu 3s_{1/2},\nu 1h_{11/2}$, and $\nu 2d_{3/2}$. For the
$9/2^{+}$ ($1/2^{-}$) state throughout the region of interest, the valence
neutrons occupy mainly the $\nu 2d_{5/2}$ ($\nu 1g_{7/2}$) orbital with
considerable contributions from the $\nu 1g_{7/2}$ ($\nu 2d_{5/2}$) neutrons.
The neutron configuration mixing in the $\nu 2d_{5/2}$ and $\nu 1g_{7/2}$
orbitals gives a flat trend of $E_{x}(1/2^{-})$ in 101In through 113In. Otsuka
$et~{}al.$ have shown otsuka2001 ; Tensor1 ; Tensor2  that, by adding protons
to the $\pi 1g_{9/2}$ orbital, the $\nu 2d_{5/2}$ and $\nu 1g_{7/2}$ orbitals
become linearly closer, and that they are almost degenerate when approaching
$Z=50$. The close-lying $\nu 2d_{5/2}$ and $\nu 1g_{7/2}$ orbitals favor
neutron configuration mixing as results from our calculations.

Furthermore, as can be seen in Figs. LABEL:occupy92 and LABEL:occupy12 the
neutron occupation of the $\nu 2d_{5/2}$ orbital is larger than that of the
$\nu 1g_{7/2}$ orbital for the $9/2^{+}$ ground state, while this ordering is
inverted for the $1/2^{-}$ isomers. As discussed before, the different neutron
occupancies for the $9/2^{+}$ and $1/2^{-}$ states in each indium isotope
indicate that the $\nu 2d_{5/2}$ and $\nu 1g_{7/2}$ single particle energies
may be different in the two states of the same nucleus. From 99In to 113In,
Fig. LABEL:espe shows that the $\nu 1g_{7/2}$ neutron effective single
particle energies (ESPE) in the $9/2^{+}$ states are $\sim$1 MeV shifted
downwards in the $1/2^{-}$ states if taking ESPE of $\nu 2d_{5/2}$ as
reference. It is worth emphasizing that the ordering of the $\nu 2d_{5/2}$ and
the $\nu 1g_{7/2}$ orbitals changes for the $1/2^{-}$ states at around 109In,
while for the $9/2^{+}$ ground states the ESPE of $\nu 1g_{7/2}$ is larger
than that of $\nu 2d_{5/2}$ in all considered indium isotopes.

As shown in Fig. LABEL:101In, adding neutrons to the $\nu 1g_{7/2}$ ($\nu
2d_{5/2}$) orbital induces lowering (lifting) of the $\pi 1g_{9/2}$ orbital as
compared to the $\pi 2p_{1/2}$ orbital. Similarly, in each indium isotope the
$\nu 1g_{7/2}$ ESPE becomes lower with respect to the $\nu 2d_{5/2}$ orbital
when a proton is moved from $\pi 2p_{1/2}$ to $\pi 1g_{9/2}$. Recently, type
II shell evolution has experimentally been confirmed in the neutron-rich even-
even nuclide 96Zr Kre2016  and the odd-odd nuclide 70Co 70Co . Here, a new
example of type II shell evolution is suggested to take place in neutron-
deficient odd-$A$ indium isotopes, which is induced by the position of the
single proton hole. The strong many body correlations among two proton
orbitals with $j_{1}=l_{1}+1/2$ and $j_{2}=l_{2}-1/2$ and two neutron orbitals
with $j_{3}=l_{3}+1/2$ and $j_{4}=l_{4}-1/2$ contribute to the present results
of both, type I and II, shell evolution in neutron-deficient indium isotopes.
Further cases may exist in other regions of the nuclear chart.

In summary, by using the storage-ring based isochronous mass spectrometry, we
have measured for the first time the masses of the $1/2^{-}$ isomer and the
$9/2^{+}$ ground state of 101In. This extends the systematics of excitation
energies of the $1/2^{-}$ isomers in indium isotopes approaching $N=50$. The
similar excitation energies of the $1/2^{-}$ isomers indicate a stable $Z=40$
subshell gap from 101In to 113In. Our state-of-the-art shell-model
calculations with $V_{\rm MU}$ plus a spin-orbit force can well describe the
available experimental data, and show that the strong configuration mixing of
valence neutrons play a key role in explaining the smooth trend of
$E_{x}(1/2^{-})$ as a function of neutron number. Furthermore, our
calculations show that the energies of the $\nu 1g_{7/2}$ and $\nu 2d_{5/2}$
orbitals are different in the $1/2^{-}$ and $9/2^{+}$ states of the same
indium isotope. This observation is valid for all considered here indium
isotopes. Such configuration-dependent shell evolution, the so called type II
shell evolution, studied in the present work will prompt further studies of
single-neutron states by means of ${\beta}$-decay and transfer reaction
experiments using radioactive-isotope beams.

We thank the staff of the accelerator division of the IMP for providing the
stable beam. This work was supported in part by the National Key R&D Program
of China (Grant No. 2018YFA0404401 and No. 2016YFA0400504), the Key Research
Program of Frontier Sciences of CAS (Grant No. QYZDJ-SSW-S), the NSFC (Grants
No. 11605249, 11605248, 11605252, 11605267, 11575112, 11835001, 11711540016
and 11775316), the Helmholtz-CAS Joint Research Group HCJRG-108, Deutscher
Akademischer Austauschdienst (DAAD), Programm des Projektbezogenen
Personenaustauschs (PPP) with China (Project ID 57389367), and the CAS
External Cooperation Program (Grant No. GJHZ1305). Y.A.L. is indebted to the
European Research Council (ERC) for support under the European Union’s Horizon
2020 Research and Innovation Programme (Grant Agreement No. 682841 "ASTRUm").
Y.H.Z. acknowledges support by the ExtreMe Matter Institute EMMI at the GSI
Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. X.L.T.
acknowledges support from the Max Planck Society through the Max-Planck
Partner Group.

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# Deep Learning for blind spectral unmixing of LULC classes with MODIS
multispectral time series and ancillary data

José Rodríguez-Ortega
Department of Computer Science and Artificial Intelligence, DaSCI
University of Granada
Granada
<EMAIL_ADDRESS>
LifeWatch-ERIC ICT Core
Seville
<EMAIL_ADDRESS>
&Rohaifa Khaldi
LifeWatch-ERIC ICT Core
Seville
<EMAIL_ADDRESS>
&Domingo Alcaraz-Segura
Department of Botany
Faculty of Science, University of Granada
Granada
<EMAIL_ADDRESS>
&Siham Tabik
Department of Computer Science and Artificial Intelligence, DaSCI
University of Granada
Granada
<EMAIL_ADDRESS>

###### Abstract

Remotely sensed data are dominated by mixed Land Use and Land Cover (LULC)
types. Spectral unmixing is a technique to extract information from mixed
pixels into their constituent LULC types and corresponding abundance
fractions. Traditionally, solving this task has relied on either classical
methods that require prior knowledge of endmembers or machine learning methods
that avoid explicit endmembers calculation, also known as blind spectral
unmixing (BSU). Most BSU studies based on Deep Learning (DL) focus on one
time-step hyperspectral data, yet its acquisition remains quite costly
compared with multispectral data. To our knowledge, here we provide the first
study on BSU of LULC classes using multispectral time series data with DL
models. We further boost the performance of a Long-Short Term Memory
(LSTM)-based model by incorporating geographic plus topographic (geo-
topographic) and climatic ancillary information. Our experiments show that
combining spectral-temporal input data together with geo-topographic and
climatic information substantially improves the abundance estimation of LULC
classes in mixed pixels. To carry out this study, we built a new labeled
dataset of the region of Andalusia (Spain) with monthly multispectral time
series of pixels for the year 2013 from MODIS at 460m resolution, for two
hierarchical levels of LULC classes, named Andalusia MultiSpectral
MultiTemporal Unmixing (Andalusia-MSMTU). This dataset provides, at the pixel
level, a multispectral time series plus ancillary information annotated with
the abundance of each LULC class inside each pixel. The dataset
111https://zenodo.org/record/7752348#.ZBmkkezMLdo and code
222https://github.com/jrodriguezortega/MSMTU are available to the public.

_Keywords_ LULC $\cdot$ Deep Learning $\cdot$ Spectral unmixing $\cdot$
Ancillary data

##  1 Introduction

LULC mapping is normally addressed by classifying each pixel in a satellite
image into a LULC class. Frequently, the spatial resolution of an image and
the thematic resolution of its LULC legend do not match, which leads to the
mixed pixel problem, where pixels are not pure but contain several LULC
classes. Accordingly, many methods have tried to estimate the relative
abundances of each LULC class in a pixel from the combined spectral signature
[1]. Such estimation of the spectrum and the abundance of the LULC classes
present within each pixel is known as spectral unmixing and is one of the most
challenging areas of research in Remote Sensing (RS) [2]. Various unmixing
approaches, including linear and nonlinear methods, have been developed [3,
4]. Many of these approaches require the use of the pure spectral signature
(the endmember) of each LULC class. However, the acquisition of endmembers
might be hard in areas dominated by mixed pixels [5]. To overcome this
limitation, several works have introduced the concept of BSU as an alternative
approach to avoid the need to derive any endmember spectra or making any prior
assumption about their mixing nature.

In the last years, modern DL models have been increasingly employed for
addressing BSU by directly learning the input-output mapping from the spectra
of mixed pixels to their corresponding class abundances. Several studies have
explored the potential of DL methods for BSU in LULC mapping [2, 6, 7].
Nevertheless, the majority of these studies concentrate solely on
hyperspectral data [4]. Indeed, hyperspectral data provides a clear advantage
over multispectral data since the former provides a larger amount of
information. Nevertheless, in practice, the acquisition and analysis of
hyperspectral data is more expensive, more computationally demanding and
spatially constrained than multispectral data [8, 9], especially when
considering time series [4]. For these reasons, the practical way to explore
the potential of spectro-temporal information in the problem of unmixing is by
using multispectral multitemporal data. Some works have started exploring
approaches without the need of endmember extraction with multispectral time
series data [5, 10], however to the best of our knowledge, none have explored
a complete DL solution where recurrent neural networks (RNN), particularly
Long-Short Term Memory (LSTM) networks, are a perfect fit and have been
applied to a number of RS problems [11, 12, 13].

An additional advantage of applying DL in BSU is that ancillary information
(e.g., topography, climate and geographical location) can be easily introduced
to enhance the unmixing task. This ancillary data is successfully used by DL
models to improve the performance during image classification [14, 15, 16].
However, the introduction of ancillary information remains unexplored in
spectral unmixing methods.

In this work, a regional-scale dataset is created for BSU of LULC classes,
where information from more than 500000 MODIS pixels at 460m/pixel is
collected. This dataset provides, for each individual pixel, (1) a
multispectral time series, i.e, monthly observations of the seven spectral
bands of the MODIS sensor, (2) ancillary information containing geographic,
topographic and climatic variables, and (3) their corresponding LULC class
abundances at two different levels of the classes hierarchy. Furthermore, a
first DL-based method is proposed for BSU, consisting of a two branch neural
network (NN) where the first branch process the multispectral time series
using a LSTM-based model and the second branch process the ancillary
information.

The primary contributions of this research can be summarized as follows:

  * •

Development of Andalusia-MSMTU dataset: a novel multispectral multitemporal
dataset with mixed pixels for Andalusia, a highly heterogeneous region in
Spain. Such dataset will open the possibility for new explorations.

  * •

Design and analysis of a DL-based approach to estimate the abundance per pixel
of LULC classes from multispectral time series data with and without ancillary
information.

The rest of this article is structured in the following manner: Section 2
presents the related work. Section 3 provides preliminaries and background.
Section 4 introduces the study area and the data construction process. Section
5 describes the used DL methodology. Section 6 assesses the results obtained.
Section 7 provides a comprehensive discussion of the results obtained,
comparing them with previous works. Finally, section 8 concludes the findings
and sheds light into future works.

##  2 Related work

The related works to our multispectral multitemporal unmixing study are those
that address the problem of spectral unmixing using different approaches and
those that build labeled datasets especially designed for the unmixing
problem.

###  2.1 Spectral unmixing

Spectral unmixing methods are commonly classified as linear mixture models
(LMM) and nonlinear mixture models (NLMM) according to the formulation
describing the mixing process of the different endmembers [17].

LMM propose that the spectral signature of a mixed pixel results from a
summation of endmember spectra, where the contribution of each endmember is
determined by its proportionate area abundance within the pixel. LMM-based
methods have been widely developed in last decades including linear,
geometrical, nonnegative matrix factorization, bayesian and fuzzy models among
others [3, 18, 19, 20, 21]. LMM typically consider that the spectrum of each
LULC class is determined by a single endmember. However, pure pixels from the
same LULC class may have different spectra, which is called intra-class
variability [22]. To overcome this limitation, multiple endmember spectral
mixture analysis (MESMA) models have been developed [23, 24].

Given the difficulty in obtaining numerous pure endmembers in regions
primarily composed of mixed pixels, BSU approaches were introduced to address
this challenge. They include independent component analysis [25], non-negative
matrix factorization [26] or sparse component analysis [27] methods.

BSU have also met DL models, which fall under the category of NLMM. One of the
first DL approaches for BSU was proposed by [28], where they introduce three
spectral bands values and the neural network (NN) outputs the abundances of
three LULC classes. [29] compared NN, LMM, and fuzzy c-means for spectral
unmixing of LULC classes, being the NN the best model given sufficient
training samples. Then, [30] proposed a two-stage ANN architecture that first
reduces the dimension of the input vector using an auto-associative NN, and
performs abundance estimation out of the reduced input using a MLP. Recently,
[6] evaluated autoencoders with different hyperparameters. [31] introduced
MSNet, a multi-stage convolutional autoencoder network designed for
hyperspectral linear unmixing, achieving this by capturing contextual
relationships between pixels. Following the success of transformers
architecture [32], [7] and [33] introduced NN architectures with the attention
mechanism for abundance estimation.

Regarding RNN-based works, the only work on BSU using a LSTM-based network was
introduced by [34]. They proposed a nonsymmetric autoencoder network with a
LSTM component to capture spectral correlation together with an attention
mechanism to further enhance the unmixing performance. For a more detailed
review of DL methods in spectral unmixing see [17] and [4].

Despite the relevance of the temporal dimension information, very few works
have exploited it [4], as hyperspectral time series data is difficult to
obtain. For this reason, we mainly see multitemporal spectral unmixing methods
using multispectral data [35, 36, 37]. A detailed overview of these papers is
condensed into Table 1. However, in this domain most used approaches are
classical methods that need endmembers extraction, which could be problematic.
Only the works of [5, 10] propose a learning-based approach to learn input-
output relationship without the need for endmembers extraction using a SVM-
based approach.

In parallel, there exist few works that incorporate ancillary data to improve
the performance of DL models. Most of these studies occur in the field of
computer vision, such as high inter-class similarity classification problems
[14], plankton image classification [15] or crop type mapping [16].

###  2.2 Labeled datasets based on LULC products

Supervised learning requires high amounts of ground truth data to achieve
better generalization. One of the biggest limitations in spectral unmixing is
the limited availability of ground truth LULC maps [4, 38]. Some areas or
regions, especially in western countries, have LULC ground truth based on
visual interpretation for specific fields of study. For example, SIPNA [39]
was intended for territorial planing in Spain. Its annotation was carried out
by experts during several years. This dataset can be used to annotate RS data.

In parallel, there exist very few public annotated datasets prepared for
supervised spectral unmixing. Only Jasper Ridge [40] and Urban Data [26] are
available. Our work is the first in providing good quality multispectral
multitemporal mixed pixel dataset especially suitable for building umimixing
models for LULC-mapping.

Table 1: List of spectral unmixing works using multispectral and multitemporal
data (HRM: Higher Resolution Map).

Ref. & year | Study area | Source | Spatial-temporal res. | Annotations | # classes | Public | Approach
---|---|---|---|---|---|---|---
[35] 2004 | Yaqui Valley (Mexico) | MODIS | 500m - 8 obs. (months) | HRM (Landsat-derived) | 3 | No | PTU
Great Plains (US) | MODIS | 500m - 8 obs. (months) | HRM (Landsat-derived) | 3 | No | PTU
[36] 2011 | The Netherlands | MERIS | 300m - 7 obs. (months) | HRM (LGN5 L1) | 4 | No | FCLSU
The Netherlands | MERIS | 300m - 7 obs. (months) | HRM (LGN5 L2) | 12 | No | FCLSU
[41] 2012 | Japan | MODIS | 250m - 365 obs. (days) | HRM (Landsat-derived) | 2 | No | TMA-based
[42] 2020 | Broome County (US) | Landsat | 30m - (2000 to 2014) | HRM (NLCD) | 2 | No | RF
[43] 2020 | Rondônia (Brazil) | Landsat | 30m - (1990 to 2013) | HRM (Rondônia) | 5 | No | LSU + RF
[5] 2021 | Daxing (China) | MODIS | 480m - 3 obs. (months) | HRM (Landsat-derived) | 2 | No | STSU
Zibo (China) | MODIS | 480m - 3 obs. (months) | HRM (Landsat-derived) | 2 | No | STSU
Amazon (Brazil) | MODIS | 480m - 3 obs. (months) | HRM (Landsat-derived) | 2 | No | STSU
[10] 2021 | Daxing (China) | MODIS | 480m - 2 obs. (months) | HRM (Landsat-derived) | 2 | No | RSTSU
Zibo (China) | MODIS | 480m - 2 obs. (months) | HRM (Landsat-derived) | 2 | No | RSTSU
Lichuan (China) | MODIS | 480m - 2 obs. (months) | HRM (Landsat-derived) | 2 | No | RSTSU
Ours | Andalusia (Spain) | MODIS | 460m - 12 obs. (months) | HRM (SIPNA L1) | 4 | Yes | LSTM-based
Andalusia (Spain) | MODIS | 460m - 12 obs. (months) | HRM (SIPNA L2) | 10 | Yes | LSTM-based

##  3 Preliminaries and background

We define a multivariate time series as a sequence of observations
$X=(\mathbf{x}_{1},\mathbf{x}_{2},...,\mathbf{x}_{T})$, where $T$ is the
number of observations or time steps. Each observation
$\mathbf{x}_{t}\in\mathbb{R}^{C}$ where $t\in\\{1,...,T\\}$ consists of $C$
variables, such that $\mathbf{x}_{t}=\\{x_{t}^{1},x_{t}^{2},...,x_{t}^{C}\\}$.

###  3.1 Recurrent Neural Network

RNN [44] is a NN architecture specifically designed for handling sequential
data. RNN consider the sequential relationship of inputs by using a shared
function $f$ to process each input. RNN process the time series using a
recurrence approach at every time step $t$, computing a hidden state
$\mathbf{h}_{t}$ by considering the previous hidden state $\mathbf{h}_{t-1}$
and the current input $\mathbf{x}_{t}$:

$\mathbf{h}_{t}=f(\mathbf{h}_{t-1},\mathbf{x}_{t})$ (1)

where $\mathbf{h}_{0}$ is normally, at the beginning, the zero vector, i.e.,
$\mathbf{h}_{0}=\mathbf{0}$.

There are several choices on how to process sequential information. In this
work, we focus on the LSTM network, which is an improvement of normal RNN
solving some of its biggest limitations [45]

###  3.2 BRITS

In time series data and specifically in RS data, it is common to find missing
values due to sensor errors, cloud cover and more [46]. To handle this
situation, there exists a type of RNN architecture that can learn to solve two
tasks simultaneously: imputing missing values and classifying the input
sequence data. This model is called Recurrent Imputation for time series
(RITS) [47]. The RITS model perform the imputation algorithm to assist the
classification task and obtain the final classification as:

$\mathbf{\hat{y}}=f_{out}(\mathbf{h}_{T})$ (2)

In practice, considering only unidirectional forward dynamic is problematic
due to slow convergence, inefficiency in training and bias exploding problem
[47]. To overcome these issues a bidirectional version named Bidirectional
RITS (BRITS) model is proposed to learn forward and backward patterns by
accessing information from past and future at any given time step. The final
scheme of BRITS can be seen in Figure 1.

Figure 1: BRITS architecture.

##  4 Study area and data construction

This section describes the study area and provides full details on how the
used dataset was built and processed.

###  4.1 Study area

Andalusia is the second-largest, most populous, and southernmost autonomous
community in Peninsular Spain (Figure 2). Andalusia is one of the most
biodiverse and heterogeneous regions of Europe. It contains steep altitudinal
gradients, and it has a wide variety of landscapes and climatic conditions
which results in a vast variety of vegetation types that hold the greatest
diversity of plant and animal species in Europe. The long and dynamic history
of human activities has also led to a complex landscape configuration with
frequent mosaics of small patches of different types of natural, semi-natural
land covers and human land uses. Hence, Andalusia offers an ideal field
laboratory to test the creation of detailed and fine scale LULC maps
containing the abundance of each LULC class per pixel to monitor the
socioeconomic and environmental dynamics in complex landscapes using DL and
multispectral time series of satellite imagery.

Figure 2: Study area: Andalusia, Spain.

###  4.2 Andalusia-MSMTU dataset construction

To construct Andalusia MultiSpectral, MultiTemporal Unmixing dataset, named
Andalusia-MSMTU, two different processes were used to generate both the time
series plus ancillary data and their labels, respectively.

The time series data were extracted from Terra and Aqua satellites using MODIS
sensor at 460m spatial resolution and at monthly temporal resolution.

Spatio-temporal filtering was applied using MODIS ‘Quality Assessment’ (QA)
flags and the "State QA" flags. Moreover, as the process of Terra and Aqua
data filtering generates many missing values, to further reduce the amount of
noise in the data, two solutions were employed: (1) the 8-days time series
data were transformed into monthly composites by computing the monthly mean
from the individual observations, then (2) the monthly data from the Terra and
Aqua satellites were combined to generate a merged Terra+Aqua monthly dataset.
All this process was performed in Google Earth Engine (GEE) [48] and inspired
by [49].

In addition to the MODIS data, for every pixel we included geographic,
topographic, and climatic ancillary information. Pixel longitude and latitude
were directly extracted from MODIS metadata. Pixel altitude was obtained by
averaging a 30m/pixel digital elevation model [50] to 460m/pixel. MODIS pixel
slopes were calculated using GEE slope calculation algorithm on the same 30m
elevation model. Finally, climatic data were downloaded from REDIAM [51],
including potential evapotranspiration, precipitation, mean annual
temperature, mean of the maximum temperatures, and mean of the minimum
temperatures.

To annotate each MODIS pixel with the abundance of each LULC class, the
official LULC map of Andalusia for the year 2013 (SIPNA) [39] was used. Given
the coarse resolution of MODIS pixels we only considered level one (four
classes) and an adapted version of level two (ten classes) of the
classification hierarchy of SIPNA (Figure 3).

Figure 3: Hierarchical structure of the SIPNA-based LULC classes. The blue
boxes represent the Level 1 (L1) classes. The green boxes represents the Level
2 (L2) classes.

Given that SIPNA provides information at sub-pixel level, we incorporated
every MODIS $460m$ pixel with the exact abundances of the mixture of LULC
classes in that pixel, as illustrated in Figure 4, using QGIS software [52].
The SIPNA polygons were first converted to raster format providing a LULC map
at $10m$ resolution The rasterized map was then downsampled to match the
spatial resolution of MODIS, resulting in the class proportions for each pixel
of Andalusia. Finally, the MODIS pixels abundances annotations were coupled
with their corresponding time series and ancillary data to obtain the
Andalusia-MSMTU dataset. In Figure 5 it is showed an example of the
calculation of class abundances for a given pixel. An illustrative example of
the distribution of abundances of LULC classes in level 1 of the
classification hierarchy over the Andalusia territory is displayed in Figure
6, being "agricultural lands" and "terrestrial lands" the classes that
dominate the Andalusian territory. Andalusia-MSMTU dataset [53] is available
in a public data repository hosted by Zenodo at:
https://zenodo.org/record/7752348#.ZBmkkezMLdo

Figure 4: The used scheme for extracting class abundances for every MODIS
pixel of Andalusia. The original polygons were rasterized to $10m$ resolution
and then degraded to $460m$ resolution to obtain every class abundance.

(a) Google satellite image.

(b) SIPNA LULC map.

(c) Rasterized LULC map.

(d) Level 1 LULC class abundances.

Figure 5: Example of how class abundances are obtained for a given pixel. (a)
shows the satellite image of the pixel. (b) shows the annotated SIPNA
polygons. (c) shows the rasterized map at 10m resolution. (d) shows the
obtained abundance of level 1 classes for that pixel.

(a) Artificial

(b) Agricultural lands

(c) Terrestrial lands

(d) Wetlands

Figure 6: Gradient map of abundances from Andalusia 460m pixels for each LULC
class in level 1 of SIPNA: (a) Artificial, (b) Agricultural lands, (c)
Terrestrial lands, and (d) Wetlands. Blue pixels represent low abundance and
red pixels represent high abundance.

##  5 Methodology

Formally, we have a set of $n$ multispectral time series pixels
$\\{X_{1},X_{2},...,X_{n}\\}$ with their corresponding class abundances
$\\{y_{1},y_{2},...,y_{n}\\}$ where $y_{i}\in S^{C},i\in[1,n]$. $S^{C}$ is the
sample space of class abundances commonly referred to as the simplex [54]. In
our case $C$ is equal to 4 and 10 for level 1 and 2 of the hierarchy,
respectively.

To enhance class abundance estimation further, in addition to using the
multispectral multitemporal data we also include ancillary information from
two types:

  * •

Geo-topographic data: Geographical coordinates (longitude and latitude),
altitude and slope.

  * •

Climatic data: Precipitation, potential evapotranspiration, mean temperature,
maximum temperature and minimum temperature.

Below, we describe the architecture of the used model and the evaluation
metrics.

###  5.1 Model architecture

Our approach to estimate the class abundances using multispectral
multitemporal data and ancillary information for each mixed pixel is depicted
in Figure 7. The proposed approach includes three components:

  1. 1.

Spectro-temporal feature extraction: We use BRITS model [47] to extract the
spectro-temporal patterns in presence of missing values from our dataset.

  2. 2.

Ancillary data feature extraction: To incorporate ancillary information, we
process the external information using a linear layer with ReLU non-linearity.

  3. 3.

Concatenation and features combination: The output features of part (1) and
(2) are concatenated and processed by a final dense layer that outputs $C$
(the number of classes) scores.

The final dense layer generates an unbounded outputs $\mathbf{o}$ where
$\mathbf{o}\in\mathbb{R}^{C}$ with $C$ being the number of classes. Following
the work of [55], we applied the softmax transformation to obtain the final
abundances predictions $\mathbf{a}\in S^{C}$:

$a_{j}=\frac{e^{o_{j}}}{\sum_{c=1}^{C}e^{o_{c}}}$ (3)

where $a_{j}$ denotes the abundance prediction for the $j$th class, $o_{j}$
denotes the final layer’s output associated with the $j$th class.

Finally, the NN is optimized by minimizing the mean-square error ($MSE$)
between the abundances predictions and the reference abundances:

$MSE=\frac{\sum_{i=1}^{N}\sum_{c=1}^{C}(r_{ic}-a_{ic})^{2}}{N}$ (4)

where $r_{ic}$ and $a_{ic}$ are the reference abundance and the predicted
abundance, respectively, for the $c$th class in the $i$th sample, and $N$ is
the number of training samples.

Figure 7: Our proposed neural network. The green box denotes the input data
for a given pixel, i.e., multispectral time series data + ancillary data. The
yellow box denotes the BRITS model for multispectral time series feature
extraction, the red box denotes the ancillary data feature extraction layer
and the blue boxes denote the final layers for features combination and
softmax transformation of neural network’s output.

###  5.2 Evaluation criteria

To assess the effectiveness of the proposed unmixing model, four regression
metrics are examined:

  * •

Pearson’s Correlation Coefficient (CC):

$CC=\frac{\sum_{i=1}^{N}(r_{i}-\overline{r})(a_{i}-\overline{a})}{\sqrt{\sum_{i=1}^{N}(r_{i}-\overline{r})^{2}\sum_{i=1}^{N}(a_{i}-\overline{a})^{2}}}$
(5)

  * •

Root Mean Squared Error (RMSE):

$RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{N}(r_{i}-a_{i})^{2}}$ (6)

  * •

Relative Root Mean Squared Error (RRMSE):

$RRMSE=\sqrt{\frac{\sum_{i=1}^{N}(r_{i}-a_{i})^{2}}{\sum_{i=1}^{N}(r_{i})^{2}}}$
(7)

  * •

Mean Absolute Error (MAE):

$MAE=\frac{1}{n}\sum_{i=1}^{N}|r_{i}-a_{i}|$ (8)

where $r_{i}$ is the reference abundance, $a_{i}$ the predicted abundance, and
$\overline{r}$ and $\overline{a}$ are the mean of both variables. Finally, we
also considered F1-score (Formula 9) to evaluate how good is the model in
predicting the majoritarian class in each mixed pixel.

$F1=\frac{2*TP}{2*TP+FP+FN}$ (9)

###  5.3 Experimental design

To analyse the effect of introducing ancillary data and using different levels
of the LULC legend on the performance of our DL approach for spectro-temporal
unmixing, we considered different input data combinations, that is: using (1)
only the multispectral time series data, (2) time series plus geo-topographic
ancillary data, (3) time series plus climatic ancillary data, and (4) time
series plus geo-topographic and climatic ancillary data.

In order to avoid spatial autocorrelation of neighbouring pixels we used a
block train test splitting [56, 57]. Firstly, we divided the entire Andalusian
territory in areas of equal size using blocks of 18x15 kilometers, which means
that each block contains 1250 460m pixels approximately. Subsequently, 80% of
the pixel blocks were assigned randomly to the training set, with the
remaining 20% allocated to the test set. Figure 8 illustrates the areas of
pixels designated for the training and testing sets. The source code to run
these experiments will be available after acceptance at
https://github.com/jrodriguezortega/MSMTU

Figure 8: Train (blue) and test (red) areas.

Implementation details: Our models undergo training using the Adam optimizer
[58] for a total of 200 epochs with a batch size of 2048. We initialize the
learning rate at 0.003 and progressively reduce it via the cosine learning
rate decay scheduler. All experiments were conducted utilizing the PyTorch
deep learning framework [59].

TimeSpec4LULC [49] pre-training: TimeSpec4LULC is an open-source dataset
comprising multispectral time series data for 29 LULC classes, designed for
training machine learning models. This dataset is constructed using the seven
spectral bands from MODIS sensors, providing data at a 460m resolution,
spanning the time period from 2000 to 2021. We found that pre-training BRITS
model on TimeSpec4LULC dataset and fine-tuning it on Andalusia-MSMTU provides
better results that training it from scratch, mainly because of the similarity
between both datasets.

##  6 Experimental results

###  6.1 SIPNA level 1

The comparison between using the four different ancillary data combinations in
terms of the average MAE, RMSE, RRMSE, CC, and F1-score, across the four
classes of level 1 is provided in Table 2. As it can be seen, in general,
including ancillary information always improves the spectral unmixing
performance with respect to the baseline model (using multispectral time
series only). The highest performance is achieved when including both, geo-
topographic and climatic data together with the multispectral time series
showing the lowest MAE, RMSE and RRMSE, with 0.55%, 0.63% and 2.07% of
improvement respectively and highest CC and F1-score with 0.0153 and 0.0101 of
improvement respectively, with respect to the baseline model.

Table 2: Performance comparison in terms of average Mean Absolute Error (MAE),
Root Mean Squared Error (RMSE), Relative Root Mean Squared Error (RRMSE),
Correlation Coefficient (CC) and F1-score of the spectral unmixing for SIPNA
level 1 classes. "Ancillary" column indicates the included ancillary
information in each evaluation.

Ancillary data added | MAE (%) | RMSE (%) | RRMSE (%) | CC | F1-score
---|---|---|---|---|---
None | 6.70% | 12.28% | 42.40% | 0.8570 | 0.8140
Geo-topographic | 6.21% | 11.80% | 40.84% | 0.8691 | 0.8195
Climatic | 6.55% | 12.24% | 42.34% | 0.8582 | 0.8107
Geo-topographic + climatic | 6.15% | 11.65% | 40.34% | 0.8723 | 0.8241

A further analysis of the five metrics for each class is depicted in Figure 9.
In general, including the geo-topographic and climatic information improves
the abundance predictions of all the classes of level 1. The "terrestrial
lands" and "agricultural lands" achieve better performance in terms of CC,
F1-score and RRMSE. However, the classes that benefit the most from adding the
ancillary data are "artificial" and "wetlands" since the relative improvement
is greater in these classes.

It is worth noting that the RMSE and MAE metrics are not fair for comparisons
between classes as they do not take into account the range of abundance values
within each class. The most appropriate metric for these comparisons in this
case is the RRMSE.

Figure 9: Test results for the four SIPNA level 1 classes obtained by
including all ancillary information (green) and without ancillary information
(blue): CC values (top left), F1-score values (top right), RMSE values (middle
left), RRMSE values (middle right), and MAE values (bottom).

To better illustrate the reasons behind these differences in performance
between observed and predicted abundances in each of the four LULC classes,
Figure 10 shows a density scatter plot for each class. The scatter plots of
"artificial" and "wetlands" pixels showed a less aligned distribution along
the 1:1 straight line than terrestrial and agricultural lands. In artificial
and wetlands plots, most points are concentrated in the lowest abundances,
while in terrestrial and agricultural lands points tend to concentrate in both
the extremes of the abundance gradient but also along the 1:1 line. This
proofs that the model works reasonably good for both abundant (terrestrial and
agricultural lands) and scarce (artificial and wetlands) classes.

(a) Artificial

(b) Agricultural lands

(c) Terrestrial lands

(d) Wetlands

Figure 10: Density scatter plots of every level 1 class abundances (predicted
vs reference) for the best model (including all ancillary data). (a)
Artificial, (b) Agricultural lands, (c) Terrestrial lands, and (d) Wetlands.

###  6.2 SIPNA level 2

Again, including ancillary information improves the spectral unmixing task
even in a much more difficult spectral unmixing setting (Table 3). Compared to
the baseline, the best performing model (including all the ancillary data)
decreases the MAE, RMSE and RRMSE by 0.31%, 0.28% and 1.68%, respectively and
increases CC and F1-score by 0.0160 and 0.0188, respectively.

Table 3: Performance comparison in terms of average MAE, RMSE, RRMSE, CC and
F1-score of the spectral unmixing for SIPNA level 2 classes. "Ancillary"
column indicates the included ancillary information in each evaluation.

Ancillary data added | MAE (%) | RMSE (%) | RRMSE (%) | CC | F1-score
---|---|---|---|---|---
None | 5.88% | 11.54% | 59.11% | 0.7504 | 0.6216
Geo-topographic | 5.60% | 11.31% | 57.92% | 0.7635 | 0.6396
Climatic | 5.73% | 11.47% | 58.57% | 0.7566 | 0.6317
Geo-topographic + climatic | 5.57% | 11.26% | 57.43% | 0.7664 | 0.6404

In the same way as in level 1, Figure 11 shows a comparison between the
baseline model and the model including geo-topographic and climatic data for
every class in each of the five metrics used for evaluation. In general,
adding ancillary information improves the abundances predictions of all the
classes. The best performance is achieved in "woody crops" and "annual crops"
classes in terms of CC, F1-score and RRMSE. Besides, adding the ancillary
information to the model achieves a greater improvement for the classes with
the worst results like "combinations of croplands and vegetation", "barelands"
and "artificial".

Figure 11: Test results for the ten SIPNA level 2 classes obtained by
including all ancillary information (green) and without ancillary information
(blue): CC values (top left), F1-score values (top right), RMSE values (middle
left), RRMSE values (middle right), and MAE values (bottom).

Looking at the density scatter plot for each level 2 class in Figure 12, we
see that the correlation between the reference and the predicted abundances is
generally good, except for "combinations of croplands and vegetation" and
"barelands" classes that show a large dispersion. It is worth emphasizing the
strong performance of the model for the class "greenhouses". Despite of having
so few representation of middle range values of abundance in the pixels of
Andalusia, the correlation in this class between the reference and predicted
abundances is similar to the better classes. We argue that the reason for that
could be to their very high albedo, i.e., high reflectance in all bands.
Finally, the worst performance metrics were obtained for "combinations of
croplands and vegetation" class, which may be due to the mixed-nature of this
class definition itself. By combining crop and vegetation this class is a
mixture of some of the other classes and it is complicated for the model to
find the relationships to predict the abundances of this mixed class.

(a) Artificial

(b) Annual crops

(c) Greenhouses

(d) Woody crops

(e) Crops & vegetation

(f) Grasslands

(g) Shrublands

(h) Forests

(i) Barelands

(j) Wetlands

Figure 12: Density scatter plots of every level 2 class abundance (predicted
vs reference) for the best model (including all ancillary data). (a)
Artificial, (b) Annual croplands, (c) Greenhouses, (d) Woody croplands, (e)
Combinations of croplands and vegetation , (f) Grasslands and grasslands with
trees, (g) Shrublands and shrublands with trees, (h) Forests, (i) Barelands,
and (j) Wetlands.

##  7 Discussion

Spectral unmixing of LULC classes is a challenging problem commonly addressed
by physical models with the need for endmember extraction [3, 4]. DL methods
are a great solution as BSU approaches to eliminate the need for endmember
extraction, but previous works only focus on hyperspectral data to estimate
the abundance of mixed pixels. Obtaining time series at regional scales of
such data may be prohibitive due to the cost and time required to acquire them
[8, 9]. Moreover, previous works barely made public the dataset used, impeding
other researchers to try new approaches on the data and make advances in the
field. Finally, no previous work has explored the possibility of adding
ancillary data to enhance the spectral unmixing results, which are used
successfully in other computer vision tasks [14, 15, 16].

In this work, we tried to solve the mentioned constraints of previous works
by: (1) developing Andalusia-MSMTU, a multispectral time series dataset of
mixed pixels labeled with LULC class abundances at two classification levels.
and making our dataset publicly available so other researchers can develop new
approaches in the field of spectral unmixing, and (2) proposing and analysing
DL-based approaches for BSU.

Our results showed that our DL-based method achieved competitive results for
spectral unmixing of LULC classes by using multispectral data. Besides, by
adding ancillary information the model improved in every metric used for
evaluation, showing that adding external data is an interesting avenue to
explore in spectral unmixing problems.

Finally, one significant limitation still exists in our work. Although DL
models have shown great performance in mapping complex input-output
relationships and have demonstrated promising results for BSU of LULC classes,
they lack physical interpretability. This means that it is difficult to
understand how the model arrived at its decision, and it may not be clear why
certain input features were given more weight than others [60]. In the context
of spectral unmixing, physical interpretation may be desirable [61] because it
allows us to understand the underlying physical processes that govern the
interaction of electromagnetic radiation with land surface materials.

##  8 Conclusions

In this work, we introduced and made publicly available Andalusia-MSMTU
dataset, a new DL-ready dataset to explore BSU approaches on multispectral
time series data. Furthermore, we introduced ancillary information to improve
the spectral unmixing performance consisting on two geographic, two
topographic and five climatic variables. Our experiments show that the use of
multispectral time series data for LULC abundance estimation achieves good
results, which can be further improved by including ancillary information.

For future work, we would like to explore taking advantage of spatial
autocorrelation between neighbouring pixels, which provides useful information
for the spectral unmixing task [62], by arranging the MODIS pixels in images
and using a Convolutional-LTSM network with a BRITS-like approach to deal with
missing values. Moreover, given the recent availability of higher spatial
resolution sensors like Sentinel-2, data fusion between MODIS long-term data
and Sentinel-2 higher resolution data is another avenue to explore to improve
spectral unmixing performance. Finally, since common DL-based models lack
physical interpretation and it is sometimes important in the context of
spectral unmixing, an effort to make DL-based methods physically aware is
worthwhile.

## Acknowledgment

This research was partially supported by the project “Thematic Center on
Mountain Ecosystem & Remote sensing, Deep learning-AI e-Services University of
Granada-Sierra Nevada” (LifeWatch-2019-10-UGR-01), which has been co-funded by
the Ministry of Science and Innovation through the FEDER funds from the
Spanish Pluriregional Operational Program 2014-2020 (POPE), LifeWatch-ERIC
action line and by the TED project with reference TED2021-129690B-I00 funded
by the Ministry of Science and Innovation.

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