# UXsim: An open source macroscopic and mesoscopic traffic simulator in
Python—a technical overview

Toru Seo111Tokyo Institute of Technology<EMAIL_ADDRESS>The
corresponding author

###### Abstract

This note describes a technical overview of UXsim, an open source
macro/mesoscopic traffic simulator in pure Python programming language. UXsim
is based on Kinematic Wave model (more specifically, mesoscopic version of
Newell’s simplified car-following model) and dynamic user optimum-like route
choice principle, which are well established methodology in the transportation
research field. It can compute dynamical network traffic flow and have basic
visualization and analysis capability. Furthermore, users can implement their
own models and control methods into the simulator by using Python, thanks to
the flexibility of the language. The simulator and its codes are freely
available at https://github.com/toruseo/UXsim under the MIT license.

##  1 Introduction

Vehicular traffic flow plays essential roles in today’s civilization. However,
it faces several critical issues such as congestion, accidents, and
environmental burden. Macroscopic traffic simulation is important to
understand and manage dynamic urban-scale vehicular traffic flow. Mesoscopic
traffic simulation is a type of macroscopic traffic simulation, in which some
microscopic nature of traffic is incorporated in order to enhance simulation
capability while keeping computational efficiency high.

UXsim is a new open source macroscopic and mesoscopic traffic simulator
developed by the author. It is written in pure Python and its common
libraries. Thus, it can be used and modified flexibly by users. Although
Python’s computational efficiency is not so high, UXsim can compute large-
scale traffic phenomena fairly effectively thanks to the use of the
macro/mesoscopic model.

This note describes a technical overview of UXsim, namely, its simulation
logic with simple examples. The details are throughly explained in Seo (2023),
a Japanese book on general macroscopic traffic flow theory and simulation. The
main functions of UXsim are as follows:

  * •

Dynamic network traffic simulation with a given network and time-dependent OD
demand.

  * •

Implementation of traffic management schemes (e.g., traffic signals, inflow
control, route guidance, congestion pricing).

  * •

Basic analysis of simulation results (e.g., trip completion rate, total travel
time, delay), and their export to pandas.DataFrame and CSV files.

  * •

Visualization of simulation results (e.g., time-space diagram, MFD, network
traffic animation).

Just for information, the origin of the name “UXsim” is as follows. “U” stands
for uroboros, a mythical snake that embodies some essence of network traffic
congestion. “X” means the position coordinates, which is the most important
state variable in the employed mesoscopic traffic flow model. “sim” signifies,
of course, simulation. UXsim and its codes are freely available at
https://github.com/toruseo/UXsim under the MIT license.

##  2 Simulation logic

###  2.1 Models

####  2.1.1 Overview

The simulator is based on Kinematic Wave (KW) model (Lighthill and Whitham,
1955; Richards, 1956) and dynamic user optimum-like route choice principle,
which are well established and common methodology in the transportation
research field. More specifically, it is constructed by combining the
following models.

Link/Vehicle model determines traffic dynamics on links. The mesoscopic
version of Newell’s simplified car-following model (Newell, 2002), also known
as X-model (Laval and Leclercq, 2013) is employed for this purpose. This is
equivalent to KW model with a triangular fundamental diagram. In this model,
vehicles travels as fast as possible, while maintaining safe spacing and
headway which are speed-dependent. Thus, it can reproduce traffic congestion
and queuing phenomena fairly accurately.

Node model determines inter-link transfer of traffic. The mesoscopic version
of the incremental node model (Flötteröd and Rohde, 2011; Flötteröd, 2016) is
employed for this purpose. This model can reproduce merging and diverging
traffic in a manner consistent with KW model.

Route choice model determines network-level decision of travelers. Dynamic
user optimum (Kuwahara and Akamatsu, 2001), also known as the reactive
assignment, with stochasticity and delay is employed for this purpose. In this
model, travelers tend to choose the shortest path to the destination that
minimizes instantaneous travel time. However, instantaneous travel time is
highly volatile, so a kind of inertia is added to traveler’s decision making
process by incorporating stochasticity and delay.

####  2.1.2 Details

For reference, important model formula are presented in this section. Users do
not necessarily need to understand these contents to use UXsim, but
understanding on them would be useful for advanced usage and customization of
UXsim. For further details, please refer to Seo (2023) or the original
articles mentioned in Section 2.1.1.

Regarding the Link/Vehicle model, the driving behavior of a platoon consists
of $\Delta n$ vehicles in a link is expressed as

$\displaystyle X(t+\Delta t,n)=\min\left\\{\begin{array}[]{l}X(t,n)+u\Delta
t,\\\ X(t+\Delta t-\tau\Delta n,n-\Delta n)-\delta\Delta
n\end{array}\right\\},$ (3)

where $X(t,n)$ denotes position of platoon $n$ on time $t$, $\Delta t$ denotes
simulation time step width, $u$ denotes free-flow speed of the link, $\delta$
denotes jam spacing of the link.

The Node model is computed by the following algorithm:

  1. 1.

Let $i$ be time step number

  2. 2.

Select incoming link $l$ with probability $\alpha_{l}/\sum_{l}\alpha_{l}$,
where $\alpha_{l}$ is the merging priority parameter of link $l$. If all
incoming link have been selected, go to step 6.

  3. 3.

Select the vehicle that exists at the end of link $l$. Hereafter, the vehicle
is denoted as $n$. If there is no such vehicle, go back to step 2.

  4. 4.

Let $o_{n}^{i}$ be the outgoing link that vehicle $n$ want to go. Check
whether link $o_{n}^{i}$ has a sufficient (larger than $\delta\Delta n$)
vacant space at its starting position, and do the following:

     * •

If yes, transfer vehicle $n$ from link $l$ to link $o_{n}^{i}$.

     * •

If no, vehicle $n$ cannot move, so do nothing.

  5. 5.

Go back to step 2.

  6. 6.

Increment time step ($i:=i+1$) and go back to step 2.

The Route choice model is computed by the following steps. Let $b_{o}^{z,i}$
be a dummy variable that is 1 if link $o$ is a part of the shortest path from
every nodes to destination $z$ on time step $i$, and 0 otherwise. Shortest
path search is performed every $\Delta i_{B}$ time steps. When shortest path
search is performed, we update $B_{o}^{z,i}$, an attractiveness of link $o$
for vehicles with destination $z$ on time step $i$, as

$\displaystyle B_{o}^{z,i}=(1-\lambda)B_{o}^{z,i-\Delta i_{B}}+\lambda
b_{o}^{z,i},$ (4)

where $\lambda$ is a given weight. We assume that the initial $B_{o}^{z,0}$ is
equal to $b_{o}^{z,0}$. Finally, outgoing link $o^{i}_{n}$ of vehicle $n$ is
determined as $o$ with probability $B_{o}^{z,i}/\sum_{o}B_{o}^{z,i}$, where
$z$ is the destination of $n$.

###  2.2 Implementation

The implementation of the models are summarized in the following diagrams.
Fig. 1 shows a static structure of UXsim as a class diagram (based roughly on
Unified Modeling Language). Each three-row rectangle represents a class. The
top row denotes the class name, the second row denotes key variables, and the
third row denotes key functions.

Similarly, Fig. 2a shows a dynamic computational flow of entire simulation of
UXsim as an activity diagram. Fig. 2b shows that of an instance of Vehicle
class in UXsim. For the details, please see the codes.

Figure 1: Class diagram of UXsim (translated and modified from Seo (2023))

(a) Entire simulation

(b) Specific vehicle

Figure 2: Activity diagrams of UXsim (translated and modified from Seo (2023))

###  2.3 Key inputs

Some of the key inputs for simulation are as follows:

  * •

Reaction time of vehicles $\tau$. This value determines the simulation time
step width. This is a global parameter.

  * •

Platoon size for mesoscopic simulation $\Delta n$. This value determines the
simulation time step width. This is a global parameter.

  * •

Route choice model parameters: shortest path update interval $\Delta i_{B}$
and weight value $\lambda$.

  * •

Lists of nodes and links. They define the network structure.

  * •

Parameters of each link. For example, length, free flow speed $u$, jam density
$\kappa$, and merging priority parameter $\alpha$.

  * •

Parameters of each node. For example, position and traffic signal setting.

  * •

Demand. For example, origin, destination, and departure time of each vehicle
are specified.

Roughly estimating, the computational cost of the simulation is proportional
to the total number of vehicles, and inverse proportional to $\tau$ and
$\Delta n^{2}$.

###  2.4 Analysis

UXsim has several built-in analysis and visualization functions. Examples are
as follows:

  * •

Overall traffic analysis (e.g., total travel time)

  * •

OD-level traffic analysis (e.g., travel time, delay)

  * •

Link-level traffic analysis (e.g., traffic volume, delay, dynamic traffic
states)

  * •

Output simulation and analysis results to file or pandas dataframe

  * •

Time-space diagram of trajectories of each link

  * •

Time-space diagram of traffic states (i.e., flow, density, and speed) of each
link

  * •

Cumulative counts of each link

  * •

Macroscopic fundamental diagram (MFD) (Geroliminis and Daganzo, 2007)

  * •

Animation of network traffic state dynamics

  * •

Animation of vehicle flow in network

##  3 Examples

###  3.1 Gridlock and its prevention

Simulation of a simple gridlock congestion is shown as an example. The
scenario setting is illustrated in Fig. 3. There is one circular road, and the
demands are arranged in such a way that they interfere with each other. In
this way, the beginning of some traffic jams and the end of others may engage,
resulting in a gridlock condition.

Figure 3: Gridlock scenario (translated and modified from Seo (2023))

Such simulation can be executed by Code LABEL:gridlock_code. The contents of
each CSV file loaded at lines 16 and 17 are shown in Fig. 4. These code and
CSV files are included in the repository as
demos_and_examples/example_05_gridlock_and_prevention.py.

Code 1: Gridlock

⬇

1from uxsim import *

2import pandas as pd

3

4if __name__ == "__main__":

5 # Define simulation

6 W = World(

7 name="",

8 deltan=5,

9 print_mode=1, save_mode=1, show_mode=0,

10 random_seed=0

11 )

12

13 # Define scenario

14 # import CSV files

15 W.load_scenario_from_csv("dat/uroboros_nodes.csv",

16 "dat/uroboros_links.csv", "dat/uroboros_demand.csv")

17

18 W.finzalize_scenario()

19

20 # Execute simulation

21 W.exec_simulation()

22

23 # Result analysis and save

24 W.analyzer.print_simple_stats()

25 W.analyzer.output_data()

26 W.analyzer.time_space_diagram_traj_links([["WN", "NE", "ES", "SW"]])

27 W.analyzer.macroscopic_fundamental_diagram()

28 W.analyzer.network_anim(detailed=1, network_font_size=0, figsize=(12,12))

29 W.analyzer.network_fancy(animation_speed_inverse=15, sample_ratio=0.3,
interval=5, trace_length=5)

30

31 df_vehicles = W.analyzer.log_vehicles_to_pandas()

(a) uroboros_nodes.csv

(b) uroboros_links.csv

(c) uroboros_demand.csv

Figure 4: Contents of CSV files defining scenario

Some of the outputs of this simulation are shown in Fig. 5. According to
vehicle trajectories shown in Fig. 5a, we can see that traffic was free-
flowing until 1200 s when only one direction traffic demand was traveling.
However, after the second demand started traveling, traffic congestion
immediately occurred at the merging nodes W and E. Each queue generated by
traffic congestion extended quickly and reaches the heads of the other queue.
Then, gridlock happened. The MFD in Fig. 5b clearly shows a typical gridlock
phenomenon. Other outputs such as gif animations are also useful to confirm
the dynamics of gridlock phenomena.

(a) Vehicle trajectories in circular road

(b) MFD

Figure 5: Gridlock simulation

Now let us consider how to prevent a gridlock by implementing proper traffic
management. For example, because the merging nodes are the sources of the
queues that triggered the gridlock, we can prevent the gridlock by increasing
the merging priority of links in the circular road. This can be done by
inserting Code LABEL:gridlock_code2 to line 17 of Code LABEL:gridlock_code:
here, the merging priority parameters of links NE and SW are increased from
the default value 0.5 to 2 In the real world, this kind of management can be
executed by doing ramp metering, signal control, and perimeter control.

Code 2: Gridlock prevention management

⬇

1 W.get_link("NE").merge_priority = 2

2 W.get_link("SW").merge_priority = 2

The results are shown in Fig. 6. It is obvious that gridlock is perfectly
prevented. The circular road was almost always free-flowing, and the MFD’s
state was also in free-flowing or critical regime. Although some congestion
occurred at the entry links (this can confirmed by analyzing other outputs),
such congestion quickly diminishes one traffic in the circular road finishes
traveling. Thus, this kind of traffic management is very effective to prevent
traffic congestion and gridlock with little or no loss to anyone.

(a) Vehicle trajectories in circular road

(b) MFD

Figure 6: Simulation that prevented gridlock

###  3.2 Sioux Falls network

Sioux Falls network is a popular network for testing and benchmarking in the
transportation research field (Transportation Networks for Research Core Team,
2021). Fig. 7 shows simulation results by UXsim. A qualitatively reasonable
traffic pattern on the network was obtained by considering traffic dynamics
and route choice. The specification of the simulation scenario is as follows:

  * •

Simulation duration: 7200 s

  * •

Total number of vehicles: 34690 veh

  * •

Number of links: 76

  * •

Total road length: 314000 m

  * •

Time step width $\Delta t$: 5 s

  * •

Platoon size $\Delta n$: 5 veh

  * •

Route choice update interval $\Delta i_{B}\Delta t$: 600 s

The computation time was about 16 s using Windows 10 computer with 3.79 GHz
CPU and 32 GB RAM.

(a) Network traffic state. The width of each link denotes the number of
vehicles on the link, and the color of each link denotes its average speed
(the darker the slower).

(b) Vehicle trajectories in a corridor at the center of network, northbound
direction.

Figure 7: Simulation results in Sioux Falls network

The repository https://github.com/toruseo/UXsim also contains detailed other
examples such as highway bottleneck, traffic signal control, scenario
generation by script, along with detailed documents.

## References

  * Flötteröd (2016) Flötteröd, G., 2016. Queueing representation of kinematic waves. In: The Multi-Agent Transport Simulation MATSim. pp. 347–351.
  * Flötteröd and Rohde (2011) Flötteröd, G., Rohde, J., 2011. Operational macroscopic modeling of complex urban road intersections. Transportation Research Part B: Methodological 45 (6), 903–922.
  * Geroliminis and Daganzo (2007) Geroliminis, N., Daganzo, C. F., 2007. Macroscopic modeling of traffic in cities. In: Transportation Research Board 86th Annual Meeting.
  * Kuwahara and Akamatsu (2001) Kuwahara, M., Akamatsu, T., 2001. Dynamic user optimal assignment with physical queues for a many-to-many OD pattern. Transportation Research Part B: Methodological 35 (5), 461–479.
  * Laval and Leclercq (2013) Laval, J. A., Leclercq, L., 2013. The Hamilton–Jacobi partial differential equation and the three representations of traffic flow. Transportation Research Part B: Methodological 52, 17–30.
  * Lighthill and Whitham (1955) Lighthill, M. J., Whitham, G. B., 1955. On kinematic waves. II. a theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 229 (1178), 317–345.
  * Newell (2002) Newell, G. F., 2002. A simplified car-following theory: a lower order model. Transportation Research Part B: Methodological 36 (3), 195–205.
  * Richards (1956) Richards, P. I., 1956. Shock waves on the highway. Operations Research 4 (1), 42–51.
  * Seo (2023) Seo, T., 2023. Macroscopic Traffic Simulation: Fundamental Mathematical Theory and Python Implementation. Corona Publishing Co., Ltd., (in Japanese).
  * Transportation Networks for Research Core Team (2021) Transportation Networks for Research Core Team, 2021. Transportation networks for research, https://github.com/bstabler/TransportationNetworks, Accessed 2021-10-01.


# Identifying meteorite droppers among the population of bright ’sporadic’
bolides imaged by the Spanish Meteor Network during the spring of 2022

E. Peña-Asensio,1,2 J. M. Trigo-Rodríguez,2,3 A. Rimola,1 M. Corretgé-Gilart,4
and D. Koschny5
1Departament de Química, Universitat Autònoma de Barcelona 08193 Bellaterra,
Catalonia, Spain
2Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB, C/ de Can Magrans
s/n, 08193 Cerdanyola del Vallès, Catalonia, Spain
3Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Catalonia,
Spain
4Universitat Politècnica de Catalunya (UPC), Carrer de Jordi Girona, 31, 08034
Barcelona, Spain
5TU Munich, Boltzmannstrasse 15, 85748 Garching, Germany E-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The extraordinary weather conditions available between February and March 2022
over Spain have allowed us to analyze the brightest fireballs recorded by the
monitoring stations of the Spanish Meteor Network (SPMN). We study the
atmospheric flight of 15 large meteoroids to determine if they are meteorite
dropper events to prepare campaigns to search for freshly fallen
extraterrestrial material. We investigate their origins in the Solar System
and their dynamic association with parent bodies and meteoroid streams.
Employing our Python pipeline 3D-FireTOC, we reconstruct the atmospheric
trajectory utilizing ground-based multi-station observations and compute the
heliocentric orbit. In addition, we apply an ablation model to estimate the
initial and terminal mass of each event. Using a dissimilarity criterion and
propagating backward in time, we check the connection of these meteoroids with
known complexes and near-Earth objects. We also calculate if the orbits are
compatible with recent meteoroid ejections. We find that $\sim$27% of these
fireballs are dynamically associated with minor meteoroid streams and exhibit
physical properties of cometary bodies, as well as one associated with a near-
Earth asteroid. We identify two meteorite-producing events; however, the on-
site search was unsuccessful. By considering that these fireballs are mostly
produced by cm-sized rocks that might be the fragmentation product of much
larger meteoroids, our findings emphasize the idea that the population of
near-Earth objects is a source of near-term impact hazards, existing large
Earth-colliding meteoroids in the known complexes.

###### keywords:

meteorites, meteors, meteoroids – comets: general – minor planets, asteroids:
general

††pubyear: 2022††pagerange: Identifying meteorite droppers among the
population of bright ’sporadic’ bolides imaged by the Spanish Meteor Network
during the spring of 2022–Identifying meteorite droppers among the population
of bright ’sporadic’ bolides imaged by the Spanish Meteor Network during the
spring of 2022

##  1 Introduction

The interplanetary medium is composed of countless millimeter- and centimeter-
sized objects called meteoroids, some of which eventually cross the path of
our planet (Brown et al., 2002; Murad & Williams, 2002; Trigo-Rodríguez,
2022). These small bodies are fragments produced by the catastrophic
disruption or collisions of comets, asteroids, or even impacts on planets
(Chapman, 2010; Tóth et al., 2011; Gritsevich et al., 2012; Trigo-Rodriguez et
al., 2014). Due to tidal forces and sublimation by high temperatures of the
Sun, cometary aggregates and rubble pile asteroids with efficient disruption
processes suffer fragmentations in their passage through the perihelion,
scattering meteoroids throughout their orbit that constitute the so-called
meteoroid streams (also known as meteor showers) (Jenniskens, 1994, 1998,
2006; Vaubaillon et al., 2019). Some of these meteoroid streams have Earth-
intersecting orbits, so they are generally repeated in annual cycles. After
experiencing different physical phenomena such as orbital perturbations,
impacts with other objects, Yarkovsky, YORP, or Poynting-Robertson effect,
other meteoroids suffer time scale decoherence and end up their space travel
impacting on our planet as sporadic events, that is, apparently not associated
with any known complex (Olsson-Steel, 1986; Bottke et al., 2000; Pauls &
Gladman, 2005; Brož, 2006; Koschny et al., 2019).

The impact of these objects at high velocity with the upper part of our
atmosphere produces a luminous phase in the visible range due to the collision
with the atoms of the air and the consequent melting, evaporation, and
progressive ionization of the meteoroid material (Ceplecha et al., 1998;
Silber et al., 2018). This phenomenon is known as a meteor and is called a
fireball or bolide if its magnitude is greater than that of Venus. From the
observation and analysis of fireballs with ground-based multi-stations, more
than 10 major showers have been established (Quadrantids, April Lyrids,
$\eta$-Aquarids, Southern $\delta$-Aquariids, Perseids, Orionids, Taurids,
Leonids, Geminids and Ursids), that is, meteoroid streams that present
activity of more than 10-15 meteors per hour (Bagnall, 2021). However, there
are hundreds of minor showers with lower activities as well as near-Earth
asteroids, many of them poorly studied, that can produce bright fireballs and,
therefore, potentially meteorite dropper events, just as being a source of
impact hazard to the Earth (Voloshchuk & Kashcheev, 1996; Halliday, 1987;
Madiedo & Trigo-Rodríguez, 2008; Borovička et al., 2015; Trigo-Rodríguez et
al., 2017; Trigo-Rodríguez & Blum, 2022; Peña-Asensio et al., 2022).

The months between January and April are especially relevant from the meteor
science point of view as meteorite fall rates display a peak during the
beginning of spring in either hemisphere (Halliday & Griffin, 1982).
Unfortunately, the weather during winter and spring is usually not helpful for
fireball monitoring and clouds generally prevent detailed trajectory
reconstruction and strewn-field estimates. In this sense, the months of
February and March 2022 were especially clement in the Spanish territory so
the Spanish Meteor Network (SPMN) has been able to record and analyze several
spectacular fireballs, many of them associated with minor meteoroid streams
rather than being sporadic.

In section 2, we first outline the SPMN network’s current infrastructure that
has allowed recording these events with multiple stations. We also mention the
methodology applied for fireball analysis. In section 3, we describe the
results of the atmospheric flight reconstruction, terminal mass prediction,
and heliocentric orbit calculation. In section 4, we analyze the dynamic
associations with parent bodies, near-Earth asteroids and comets, and minor
and major meteoroid streams. In addition, we examined the compatibility of
these events being recently ejected meteoroids. Finally, we discuss the
results in section 5 and offer our conclusions in section 6.

##  2 Data collection and methodology

Since its creation in 2005, thanks to the operability of the SPMN network, the
whole sky of continental Spain is monitored full time, the last decade also
including the Balearic and Canary Islands. Currently, a total of 34 stations
with charged-coupled device (CCD) video and all-sky cameras are operational,
some of them equipped with spectrometers. In addition, three forward-scatter
detectors monitor radio meteors (Trigo-Rodríguez et al., 2004). The stations
involved in the events analyzed in this work are shown in Table 1, also
incorporating the recently installed AllSky7 camera at European Space Agency
Cebreros’ station. This camera array allowed us to record 169 bright meteors
up to an apparent magnitude of -6 between February and March of 2022, from
which we selected the 15 largest multi-station bolides for analysis.

Table 1: Location of the fireball observation points involved in this work. Station | Name | Long (∘) | Lat (∘) | Alt (m)
---|---|---|---|---
A | Alpicat | 0.5568 | 41.6676 | 252
B | Barx | -0.3041 | 39.0146 | 336
C | Benicàssim | 0.0386 | 40.0342 | 15
D | Calar Alto | -2.549 | 37.2212 | 2152
E | Cebreros | -4.3693 | 40.4541 | 700
F | Corbera | 1.8906 | 41.4092 | 501
G | Estepa | -4.8766 | 37.2914 | 537
H | GranTeCan | -17.8919 | 28.7567 | 2267
I | La Murta | -1.6756 | 38.0967 | 469
J | Monfragüe | -6.0108 | 39.7736 | 411
K | Morata de Jalón | -1.4821 | 41.474 | 415
L | Olocau | -0.5363 | 39.6744 | 225
M | Playa Blanca | -13.8241 | 28.8747 | 10
N | Puertollano | -4.1129 | 38.7032 | 697
O | Sant Mateu | 0.1758 | 40.465 | 349

New video processing and trajectory calculation techniques allow the
automation of the analysis process of meteors, bolides, and artificial
fireballs produced by atmospheric re-entries of human-made objects. We
developed the 3D-FireTOC Python code that automates this study allowing the
reconstruction of atmospheric trajectories and the calculation of heliocentric
orbits from multiple recordings by using the intersection of planes method
(Peña-Asensio et al., 2021b; Peña-Asensio et al., 2021a). Unlike traditional
analytical methods, which solve the orbit by correcting for zenith attraction
and diurnal aberration (Ceplecha, 1987), we have now implemented the accurate
IAS15 high-order N-body integrator with an adaptive time step included in the
REBOUND package to compute the heliocentric orbit (Rein & Spiegel, 2015). The
integrator is based on the RADAU-15 developed in Everhart (1985) and has a
high performance resolving close encounters. We account for the Earth’s and
Moon’s oblateness by including the J2 and J4 gravitational harmonic
coefficients thanks to the REBOUNDx module (Tamayo et al., 2020).

For most cases, we performed the astrometric calibration by solving the
polynomial modification of Borovička (1992) proposed by Bannister et al.
(2013), which exhibits a better convergence while ensuring a very excellent
level of uncertainty. To achieve the best fit, we use a simplicial homology
global optimization algorithm to find the absolute minimum (Endres et al.,
2018). For recordings with sufficient background stars, we apply the method
proposed in Borovicka et al. (1995), which produces even lower errors down to
0.01∘ for azimuth and elevation. All calibrations are also cross-checked with
the quadratic model described in Peña-Asensio et al. (2021b).

With the mean uncertainties obtained in the astrometry for the camera
calibration fit, we generate 1,000 clones to perform a Monte Carlo simulation
following a Gaussian distribution applied to each detected point. We propagate
every clone backward starting with its pre-atmospheric velocity from the
beginning of the detected luminous phase until they are outside the Earth’s
influence, specifically, at 10 times the Earth Hill sphere. We then integrate
forward to the date of impact but without taking into account the
gravitational attraction of the Earth-Moon system to obtain the osculating
orbital elements at the time of the detection (referred to the J2000 equinox).

We further perform a backward integration over 10,000 years evaluating the
evolution of an orbital dissimilarity criterion to test the dynamic
association with parent body candidates. This is necessary as the most
favorable candidate at the time of impact is not always the most reliable
because it may be the result of a coincidence at that precise date. The
meteoroid is integrated with its corresponding 1,000 clones generated from the
uncertainties and the meteoroid streams are modeled by 18 equally spaced
distributed particles over the true anomaly. Based on the orbital
dissimilarity criterion, we assume that an association is robust enough if it
remains below the cutoff for 5,000 years, minimizing the probability of being
a random association (Porubčan et al., 2004).

Different techniques have been developed and discussed to establish the
association between meteors and meteor showers or parent bodies, and they are
still a source of debate today. One of the most established and widely used
criteria is $D_{D}$ (Drummond, 1981), which is a semi-quantitative approach to
measure the dissimilarity of two orbits as a function of their orbital
parameters in the five-dimensional phase.

Based on the $D_{SH}$ criterion (Southworth & Hawkins, 1963), the $D_{D}$
criterion was defined as:

$\begin{split}D_{D}^{2}=\left(\frac{e_{B}-e_{A}}{e_{B}+e_{A}}\right)^{2}+\left(\frac{q_{B}-q_{A}}{q_{B}+q_{A}}\right)^{2}+\left(\frac{I_{BA}}{\pi}\right)^{2}+\\\
+\left(\frac{e_{B}+e_{A}}{2}\right)^{2}\left(\frac{\theta_{BA}}{\pi}\right)^{2},\end{split}$
(1)

where $e$ is the eccentricity, $q$ is the perihelion distance, $I_{BA}$ is the
angle between the orbital planes, $\pi_{BA}$ is the difference between
longitudes of perihelia measured from the intersection of both orbits, and
$\theta_{BA}$ is the orbit angle between the lines of apsides.

The thresholds of the dissimilarity functions, far from defining an exact
barrier, offer an approximation with fair statistical significance, which, in
addition, may vary depending on the inclination of the orbits and the
population size. Therefore, they are not a defining indicator, and it is also
necessary to verify that the orbits are not only similar at a given time but
also that this similarity lasts over time. In this sense, we use 0.18 as a
cut-off for $D_{D}$ (Galligan, 2001). Although this threshold value is high,
we use it as a first filter, but not as the only association condition as we
also check its evolution over time.

In addition, we evaluate if the separation of the meteoroid from its possible
parent body could have occurred in relatively short timescales. For this
purpose, during the orbital integration, we monitor the minimum distance
between the objects and the change in the velocity vector that would be needed
to move from one orbit to the other one. In this way, we can observe if the
velocity change is compatible with typical collisional ejection processes
between small bodies.

We also examined Tisserand’s parameter with respect to Jupiter $T_{j}$, which
is helpful to determine the evolution of small bodies since it remains broadly
constant for long periods. It is used to classify planet-crossing objects,
usually, as Jupiter-family comets (JFCs) if $2<T_{j}<3$ and asteroidal when
$T_{j}>3$.

We evaluate the catastrophic disruption for each event by obtaining the ram
pressure at peak brightness, that is, the bulk aerodynamic strength
($s=\rho\cdot v^{2}$) accordingly to the U.S. standard atmosphere 1976
(Bronshten, 1981). This parameter is typically used to mechanically
characterize the meteoroid and to classify the material regarding the bulk
density. For events that do not present an explosion, we evaluate the peak of
maximum brightness, thus obtaining only an estimate of the lower limit for the
composition.

Additionally, assuming an isothermal atmosphere and applying the dynamic
third-order time-dependent system for characterizing meteor deceleration based
on the velocity ($v$) and the height ($h$), we compute the ballistic
coefficient ($\alpha$) and mass loss parameter ($\beta$) (Gritsevich & Stulov,
2006; Gritsevich, 2008, 2009; Gritsevich et al., 2012; Turchak & Gritsevich,
2014):

$F_{i}(h_{i},v_{i},\alpha,\beta)=2\alpha e^{-h_{i}}-\Delta_{i}e^{-\beta},$ (2)

with $\Delta_{i}=\overline{Ei}(\beta)-\overline{Ei}(\beta v_{i}^{2})$,
$i=1,2,...,n$, where

$\overline{Ei}(x)=\int_{-\infty}^{x}\frac{e^{t}dt}{t}dx.$

These adimensional parameters are defined as

$\alpha=\frac{1}{2}c_{d}\frac{\rho_{0}h_{0}S_{0}}{M_{0}\sin{\gamma}},$ (3)

and

$\beta=(1-\mu)\frac{c_{h}v_{0}^{2}}{2c_{d}H^{*}},$ (4)

where $c_{d}$ is the drag coefficient, $\rho_{0}$ is the atmospheric density
at sea level, $h_{0}$ is the scale height for a homogeneous atmosphere and
$\gamma$ is the slope of the fireball to the local horizon, $M_{0}$ is the
meteoroid mass before impacting the top of the atmosphere, $\mu$ is the
dimensionless shape change parameter, $c_{h}$ is the heat transfer
coefficient, $v_{0}$ is the entry velocity, and $H^{*}$ is the sublimation
heat. $\mu$ is a constant value that relates the cross-sectional area $S$ with
the mass as follows: $S/S_{0}=(M/M_{0})^{\mu}$ (Lyytinen & Gritsevich, 2016).
Note that as it is an atmospheric flight dynamics model with an asymptotic
solution, the minimization problem itself yields an initial velocity at
infinity that corresponds to the pre-atmospheric velocity.

These parameters allow properly describing the atmospheric flight and
estimating the meteor fate based on the so-called $\alpha-\beta$ criterion
(Sansom et al., 2019). The boundaries that delimit the fall likelihood (with a
terminal mass threshold of 50 g) are determined by the two extreme values of
the shape change coefficient: $\mu=0$ when the meteoroid is not spinning and
$\mu=2/3$ when the meteoroid surface is equally ablated due to the rotation.

From the aerodynamic strength values, we assign a meteoroid bulk density based
on Chyba et al. (1993): cometary if $s<10^{5}\,Pa$; carbonaceous if
$10^{5}\,Pa<s<10^{6}\,Pa$; rocky if $10^{6}\,Pa<s<10^{7}\,Pa$; and rocky-iron
if its aerodynamic strength is greater than $10^{7}\,Pa$. This allows us to
fit the object size $D$, the pre-atmospheric mass $M_{0}$, and the terminal
mass $M_{t}$ (the final mass at the end of the luminous atmospheric phase),
being

$M_{0}=\left(\frac{1}{2}\frac{c_{d}A_{0}\rho_{0}h_{0}}{\alpha\rho_{m}^{2/3}\sin\gamma}\right)^{3},$
(5)

where $A_{0}$ is the pre-atmospheric shape coefficient.

The terminal mass can be computed using the last observed velocity in the
following instant mass equation

$M(t)=M_{0}e^{-\frac{\beta}{1-\mu}\left(1-\left(\frac{v(t)}{v_{0}}\right)^{2}\right)},$
(6)

where $v(t)$ is the instantaneous velocity.

##  3 Atmospheric flight and heliocentric orbit

Once the most suitable recordings of each event have been selected, and the
lenses of each camera have been calibrated to correct distortions and found
the transformation between pixel and position in the sky, we can apply the
triangulation using the weighted method of the intersection of planes for
multiple stations to obtain the real position of the meteoroid in each frame.
Each station recorded the events in a single shot, except for the grazing
meteoroid SPMN080322, which moved out of the field of view. Therefore, we had
to combine the recordings from two cameras to obtain the complete luminous
trail. Figure 1 shows a composite of overlapping images of some of the events
recorded and analyzed in the following section.

In some images, like the one of the SPMN060222 fireball captured in color from
Corbera, an intense reddish tone due to the glowing ionized air can be seen,
although further color calibrations are necessary for a precise determination
of the tone. In the trace drawn during the atmospheric flights, it can be seen
how several of them show multiple brightness peaks, as a result of the rapid
rotation and differentiated ablation, while others only exhibited a large
final flare due to the catastrophic disruption. The beginning and ending
position, distance flight, and direction of the luminous phase for each event
are shown in Table 2. The initial heights range from $\sim$ 120 to 83 km and
terminal heights (before starting the dark flight) range from $\sim$ 80 to 13
km. As expected, the azimuth and slope have a random distribution, with the
average slope being around 45∘. Note that the slope is measured with respect
to the local horizon, 0∘ corresponding to a fully grazing meteor. In this
regard, we see how the event SPMN010322A traveled through the atmosphere a
notably greater distance than the rest ($\sim$198 km), its slope being close
to 10∘. Event SPMN080322A, although also with a shallow slope, underwent a
rapid disruption at 70 km altitude, which did not allow it to cover a long
distance.

Figure 1: Selection of blended frames of some of the events analyzed in this work: a) SPMN090322C from Calar Alto by José M. Serna García, b) SPMN060222 from Corbera, c) SPMN080222B from Barx, d) SPMN220222 from Alpicat, e) SPMN180222 from Estepa, and f) SPMN110222 from Madrid. Table 2: Recorded fireballs with the beginning and ending position, flight distance traveled, and direction of the atmospheric flight. SPMN code | Datetime (UTC) | Stations |  Long0 (∘) |  Lat0 (∘) |  h0 (km) |  Longt (∘) |  Latt (∘) |  ht (km) | Distance (km) |  Azimuth (∘) |  Slope (∘)
---|---|---|---|---|---|---|---|---|---|---|---
060222 | 2022-02-06 23:03:20 | A,F |  4.324$\pm$0.011 |  42.848$\pm$0.004 |  91.3$\pm$0.4 |  4.392$\pm$0.009 |  42.8570$\pm$0.0031 |  69.16$\pm$0.26 |  22.9$\pm$0.5 |  80$\pm$5 |  75$\pm$4
080222A | 2022-02-08 01:09:54 | A,B,K |  -2.5529$\pm$0.0029 |  41.2470$\pm$0.0012 |  101.594$\pm$0.028 |  -2.5542$\pm$0.0029 |  41.6429$\pm$0.0014 |  41.06$\pm$0.08 |  77.54$\pm$0.32 |  359.4$\pm$0.5 |  51.33$\pm$0.11
080222B | 2022-02-08 23:31:00 | A,B |  1.1353$\pm$0.0010 |  38.9446$\pm$0.0008 |  89.16$\pm$0.07 |  1.1055$\pm$0.0009 |  39.1885$\pm$0.0007 |  36.134$\pm$0.024 |  60.68$\pm$0.22 |  353.97$\pm$0.32 |  60.940$\pm$0.032
110222 | 2022-02-11 02:26:30 | B,E,O |  -3.625$\pm$0.009 |  39.702$\pm$0.007 |  89.8$\pm$0.8 |  -3.731$\pm$0.005 |  39.455$\pm$0.006 |  37.50$\pm$0.21 |  65.5$\pm$0.5 |  198.7$\pm$2.8 |  52.9$\pm$1.2
140222B | 2022-02-14 20:59:07 | G,I,N |  -3.5864$\pm$0.0014 |  37.8739$\pm$0.0004 |  94.646$\pm$0.025 |  -3.2628$\pm$0.0009 |  37.78175$\pm$0.00030 |  49.547$\pm$0.018 |  60.51$\pm$0.22 |  109.69$\pm$0.05 |  48.18$\pm$0.06
180222 | 2022-02-18 01:02:45 | I,J,O |  -6.1642$\pm$0.0023 |  39.380$\pm$0.004 |  88.79$\pm$0.06 |  -6.0776$\pm$0.0034 |  39.5080$\pm$0.0034 |  12.87$\pm$0.15 |  82.9$\pm$0.8 |  26.8$\pm$1.3 |  66.43$\pm$0.18
220222 | 2022-02-22 04:34:24 | A,K |  -0.5435$\pm$0.0010 |  42.3780$\pm$0.0005 |  83.77$\pm$0.08 |  0.1736$\pm$0.0004 |  42.2556$\pm$0.0005 |  38.92$\pm$0.04 |  80.57$\pm$0.13 |  102.42$\pm$0.08 |  33.814$\pm$0.015
010322A | 2022-03-01 00:48:01 | A,C,L |  2.6121$\pm$0.0034 |  41.3954$\pm$0.0020 |  95.79$\pm$0.07 |  1.4258$\pm$0.0018 |  39.9335$\pm$0.0015 |  50.499$\pm$0.024 |  197.0$\pm$0.4 |  211.99$\pm$0.07 |  13.293$\pm$0.024
010322B | 2022-03-01 01:43:57 | B,O |  -2.793$\pm$0.008 |  39.9817$\pm$0.0019 |  101.07$\pm$0.30 |  -3.258$\pm$0.010 |  39.5159$\pm$0.0019 |  71.70$\pm$0.24 |  74.2$\pm$0.7 |  217.7$\pm$1.0 |  23.3$\pm$0.5
080322A | 2022-03-08 00:36:59 | A,F |  0.8633$\pm$0.0008 |  40.6421$\pm$0.0005 |  96.82$\pm$0.08 |  1.7423$\pm$0.0006 |  41.00590$\pm$0.00030 |  80.13$\pm$0.05 |  87.00$\pm$0.12 |  60.904$\pm$0.032 |  11.06$\pm$0.06
080322B | 2022-03-08 19:26:22 | A,L |  1.8383$\pm$0.0005 |  40.4211$\pm$0.0005 |  83.58$\pm$0.05 |  1.8210$\pm$0.0005 |  40.4374$\pm$0.0005 |  36.786$\pm$0.021 |  57.70$\pm$0.18 |  320.613$\pm$0.024 |  54.09$\pm$0.10
090322B | 2022-03-09 03:01:46 | A,B,C |  -1.5107$\pm$0.0010 |  39.8088$\pm$0.0004 |  120.65$\pm$0.07 |  -2.0243$\pm$0.0011 |  39.94857$\pm$0.00035 |  77.071$\pm$0.035 |  71.19$\pm$0.13 |  289.42$\pm$0.04 |  37.75$\pm$0.12
090322C | 2022-03-09 04:25:38 | D,I |  -2.0192$\pm$0.0007 |  36.9452$\pm$0.0009 |  92.94$\pm$0.15 |  -2.1597$\pm$0.0006 |  36.4849$\pm$0.0017 |  58.54$\pm$0.10 |  64.80$\pm$0.05 |  193.73$\pm$0.15 |  32.07$\pm$0.23
100322 | 2022-03-10 01:38:19 | H,M |  -15.540$\pm$0.014 |  30.0550$\pm$0.0034 |  85.4$\pm$0.8 |  -15.600$\pm$0.022 |  29.689$\pm$0.005 |  29.2$\pm$0.6 |  82.5$\pm$0.6 |  188$\pm$5 |  42.94$\pm$0.17
120322 | 2022-03-12 22:15:53 | A,L |  1.1473$\pm$0.0004 |  40.7151$\pm$0.0007 |  94.21$\pm$0.09 |  1.09818$\pm$0.00035 |  40.7597$\pm$0.0006 |  67.85$\pm$0.05 |  27.40$\pm$0.16 |  319.4$\pm$0.4 |  74.30$\pm$0.25

Using the height at which the brightest flare occurs, the air density, and the
velocity at that point, we calculate the aerodynamic strength. According to
the value of this dynamic pressure, we estimate the bulk density as explained
in Section 2, which is used to calculate the pre-atmospheric diameter assuming
a perfect sphere. To obtain the ballistic coefficient and the mass loss
parameter, we assume an aerodynamic drag coefficient of 1.3 and a shape change
coefficient of 2/3 (Gritsevich & Koschny, 2011). The geocentric velocities
range from $\sim$ 63 to 11 km/s, and most of the radiants are in the northern
hemisphere, as depicted in Figure 2 in sinusoidal projection. All the computed
parameters are shown in Table 3 and 4.

Figure 2: Sinusoidal projection of the geocentric (diamond) and apparent (gray cross) radiants. Radiant pairs are connected with a light blue line. Geocentric radiants are color-coded according to their geocentric velocity. Table 3: Recorded fireballs with aerodynamic strength, ballistic coefficient, mass loss parameter, pre-atmospheric diameter, pre-atmospheric mass, and terminal mass. SPMN code | s (kPa) | $\alpha$ | $\beta$ | D (cm) |  M0 (g) |  Mt (g) |
---|---|---|---|---|---|---|---
060222 |  18.9$\pm$0.4 |  (8.6$\pm$0.7)$\cdot$102 |  10.6$\pm$1.0 |  1.17$\pm$0.08 |  0.83$\pm$0.16 | <1 |
080222A |  724$\pm$7 |  195.1$\pm$3.4 |  1.023$\pm$0.031 |  6.35$\pm$0.10 |  134$\pm$7 |  11.3$\pm$0.5 |
080222B |  501.06$\pm$0.25 |  79.72$\pm$0.27 |  2.244$\pm$0.004 |  13.90$\pm$0.04 |  1405$\pm$13 |  5.363$\pm$0.025 |
110222 |  361.6$\pm$3.5 |  16.1$\pm$1.9 |  11.3$\pm$1.7 |  76$\pm$8 |  (2.3$\pm$0.7)$\cdot$105 | <1 |
140222B |  78.16$\pm$0.15 |  253.7$\pm$1.5 |  2.917$\pm$0.017 |  5.121$\pm$0.027 |  70.3$\pm$1.1 | <1 |
180222 |  1107$\pm$21 |  11.94$\pm$0.23 |  4.70$\pm$0.07 |  25.3$\pm$0.5 |  (2.96$\pm$0.16)$\cdot$104 |  432$\pm$34 |
220222 |  283.6$\pm$1.8 |  102.2$\pm$0.6 |  1.690$\pm$0.022 |  17.02$\pm$0.10 |  (2.58$\pm$0.05)$\cdot$103 |  33.9$\pm$1.2 |
010322A |  209.4$\pm$1.1 |  387$\pm$6 |  2.13$\pm$0.04 |  10.87$\pm$0.16 |  673$\pm$29 |  2.93$\pm$0.17 |
010322B |  17.17$\pm$0.33 |  (1.38$\pm$0.28)$\cdot$103 |  18$\pm$4 |  1.8$\pm$0.4 |  3.1$\pm$1.8 | <1 |
080322A |  2.935$\pm$0.019 |  6898$\pm$28 |  3.60$\pm$0.07 |  0.732$\pm$0.006 |  0.205$\pm$0.005 | <1 |
080322B |  364.7$\pm$2.2 |  82.9$\pm$0.8 |  1.709$\pm$0.026 |  14.42$\pm$0.16 |  (1.57$\pm$0.05)$\cdot$103 |  25.3$\pm$0.8 |
090322B |  25.45$\pm$0.10 |  4831$\pm$29 |  5.974$\pm$0.015 |  0.3274$\pm$0.0013 |  0.01838$\pm$0.00022 | <1 |
090322C |  (4.185$\pm$0.017)$\cdot$105 |  255$\pm$4 |  9.11$\pm$0.17 |  7.16$\pm$0.08 |  192$\pm$7 |  106$\pm$20 |
100322 |  (1.30$\pm$0.14)$\cdot$103 |  40.3$\pm$3.4 |  1.03$\pm$0.33 |  10.1$\pm$0.8 |  (1.9$\pm$0.5)$\cdot$103 |  (1.4$\pm$0.8)$\cdot$102 |
120322 |  19.55$\pm$0.26 |  82$\pm$22 |  140$\pm$34 |  12$\pm$4 |  (1.0$\pm$1.1)$\cdot$103 | <1 |
Table 4: Recorded fireballs with right ascension and declination of the radiant, apparent, geocentric, and heliocentric velocities. SPMN code |  RAa (∘) |  Deca (∘) |  RAg (∘) |  Decg (∘) |  RAh (∘) |  Dech (∘) |  Va,0 (km/s) |  Va,t (km/s) |  Vg (km/s) |  Vh (km/s)
---|---|---|---|---|---|---|---|---|---|---
060222 |  108$\pm$4 |  38.4$\pm$2.2 |  106$\pm$4 |  37.4$\pm$2.5 |  65.6$\pm$0.9 |  5.8$\pm$1.0 |  19.61$\pm$0.09 |  11.229$\pm$0.033 |  16.32$\pm$0.09 |  41.5$\pm$0.5
080222A |  153.14$\pm$0.33 |  2.69$\pm$0.11 |  152.86$\pm$0.34 |  1.70$\pm$0.12 |  106.92$\pm$0.06 |  -7.911$\pm$0.031 |  37.17$\pm$0.24 |  16.329$\pm$0.029 |  35.46$\pm$0.25 |  39.91$\pm$0.33
080222B |  135.60$\pm$0.15 |  10.09$\pm$0.04 |  135.18$\pm$0.16 |  8.23$\pm$0.05 |  82.10$\pm$0.05 |  -4.635$\pm$0.004 |  23.475$\pm$0.005 |  9.7592$\pm$0.0022 |  20.666$\pm$0.006 |  37.79$\pm$0.04
110222 |  211.58$\pm$0.34 |  71.8$\pm$2.0 |  217.9$\pm$1.1 |  74.3$\pm$2.3 |  60.9$\pm$0.8 |  27.0$\pm$1.7 |  20.1$\pm$0.4 |  15.89$\pm$0.20 |  16.8$\pm$0.4 |  35.24$\pm$0.31
140222B |  41.35$\pm$0.08 |  39.312$\pm$0.028 |  30.63$\pm$0.09 |  35.822$\pm$0.023 |  51.850$\pm$0.018 |  5.641$\pm$0.017 |  15.068$\pm$0.013 |  8.905$\pm$0.004 |  10.536$\pm$0.020 |  39.904$\pm$0.019
180222 |  146.3$\pm$0.5 |  17.90$\pm$0.28 |  145.2$\pm$0.5 |  16.39$\pm$0.29 |  91.44$\pm$0.10 |  1.29$\pm$0.07 |  23.95$\pm$0.08 |  20.045$\pm$0.013 |  21.32$\pm$0.09 |  38.79$\pm$0.23
220222 |  149.508$\pm$0.030 |  30.58$\pm$0.06 |  140.248$\pm$0.028 |  23.63$\pm$0.11 |  80.31$\pm$0.07 |  2.559$\pm$0.022 |  15.60$\pm$0.04 |  5.9502$\pm$0.0031 |  11.41$\pm$0.06 |  35.225$\pm$0.034
010322A |  299.19$\pm$0.11 |  50.410$\pm$0.029 |  304.55$\pm$0.12 |  47.034$\pm$0.012 |  49.777$\pm$0.031 |  34.32$\pm$0.04 |  25.56$\pm$0.05 |  9.799$\pm$0.015 |  22.97$\pm$0.05 |  36.477$\pm$0.009
010322B |  288.24$\pm$0.33 |  54.1$\pm$1.1 |  295.0$\pm$0.4 |  51.9$\pm$1.1 |  56.2$\pm$0.5 |  35$\pm$4 |  23.83$\pm$0.06 |  19.43$\pm$0.13 |  21.01$\pm$0.07 |  34.99$\pm$0.34
080322A |  113.58$\pm$0.07 |  -13.672$\pm$0.026 |  104.83$\pm$0.12 |  -21.95$\pm$0.07 |  83.91$\pm$0.06 |  -13.79$\pm$0.07 |  17.157$\pm$0.030 |  13.560$\pm$0.006 |  13.40$\pm$0.04 |  39.542$\pm$0.029
080322B |  121.84$\pm$0.05 |  10.43$\pm$0.09 |  123.60$\pm$0.04 |  6.96$\pm$0.07 |  91.87$\pm$0.07 |  -4.541$\pm$0.026 |  18.72$\pm$0.06 |  8.266$\pm$0.013 |  14.90$\pm$0.08 |  41.49$\pm$0.06
090322B |  259.88$\pm$0.09 |  10.98$\pm$0.09 |  260.24$\pm$0.09 |  10.72$\pm$0.09 |  259.93$\pm$0.27 |  57.545$\pm$0.015 |  63.937$\pm$0.007 |  40.138$\pm$0.033 |  62.749$\pm$0.008 |  41.32$\pm$0.04
090322C |  340.5$\pm$1.2 |  77.58$\pm$0.05 |  6.2$\pm$0.9 |  73.90$\pm$0.14 |  73.418$\pm$0.026 |  18.82$\pm$0.17 |  18.159$\pm$0.018 |  17.96$\pm$0.07 |  14.397$\pm$0.024 |  38.81$\pm$0.05
100322 |  200$\pm$12 |  75.3$\pm$1.7 |  205$\pm$17 |  79.1$\pm$1.8 |  84.42$\pm$0.31 |  24.54$\pm$0.33 |  20.2$\pm$0.7 |  8.358$\pm$0.030 |  17.0$\pm$0.9 |  38.3$\pm$1.4
120322 |  156.87$\pm$0.09 |  28.29$\pm$0.26 |  157.00$\pm$0.10 |  27.05$\pm$0.26 |  104.92$\pm$0.23 |  7$\pm$34 |  21.39$\pm$0.15 |  14.27$\pm$0.06 |  18.27$\pm$0.18 |  40.48$\pm$0.09

Two meteoroids penetrate up to $\sim$ 30 and 13 km altitude starting the dark
flight at a velocity of $\sim$ 8 and 20 km/s, respectively. As can be seen in
Figure 3, from the application of the $\alpha-\beta$ criterion and assuming 50
g as the minimum terminal mass to produce a recoverable fall, event SPMN100322
had some possibility of generating a meteorite with a mass of $\sim$140 g, and
event SPMN180222 was likely to be a $\sim$430 g meteorite dropper.
Unfortunately, a field search campaign was prepared but no fragments were
recovered.

Figure 3: Distribution of the 15 fireballs analyzed over the Spanish territory
during February and March 2022 according to the $\alpha-\beta$ criterion. The
color bar shows the terminal height, the gray solid curve the boundary for a
50 g meteorite assuming no spin of the meteoroid, and the black solid curve
the boundary for a 50 g meteorite assuming equal ablation over the entire
meteoroid surface. We assume $\mu=2/3$ for all meteoroids.

The computed osculating orbital elements at the time of impact of the analyzed
fireballs are compiled in Table 5. As an example of the Monte Carlo
simulation, Figure 4 shows a heat map of the semi-major axis and inclination
distribution for the 1,000 clones of event SPMN010322A at the time of impact
(t=0 year without Earth-Moon gravitational focusing correction) and at the end
of the backward orbital integration (t=-10,000 year).

Figure 4: Typical heatmap of the inclination and semi-major axis distribution
of the 1,000 clones for the SPMN010322A in the Monte Carlo simulation. The top
figure corresponds to the time of impact (t=0 year) without Earth-Moon
gravitational focusing correction. The bottom figure corresponds to the end of
the backward orbital integration (t=-10,000 years).

Four orbits present very high eccentricity values with large semi-major axes,
five can be classified as Jupiter-family comets, while four are asteroid-like
orbits. As expected, the orbits tend to be of low inclination, with the
exception of SPMN090322B which has an inclination of 122∘. None of the
meteoroids had close encounters with the Moon prior to the impact.

Table 5: Recorded fireballs with semi-major axis, eccentricity, inclination, perihelion distance, argument of the perihelion, ascending node, and Tisserand parameter (referred to the J2000 equinox). Uncertainty for the ascending node is 0.0001∘.  SPMN code | a (au) | e |  i (∘) | q (au) |  $\omega$ (∘) |  $\Omega$ (∘) |  Tj
---|---|---|---|---|---|---|---
060222 |  11$\pm$5 |  0.92$\pm$0.04 |  6.1$\pm$1.4 |  0.892$\pm$0.011 |  216.823$\pm$0.011 | 317.8516 |  1.60$\pm$0.21
080222A |  4.3$\pm$0.6 |  0.938$\pm$0.007 |  14.69$\pm$0.10 |  0.2658$\pm$0.0030 |  120.6728$\pm$0.0030 | 138.9337 |  1.77$\pm$0.14
080222B |  2.395$\pm$0.018 |  0.7285$\pm$0.0015 |  5.47$\pm$0.05 |  0.6504$\pm$0.0015 |  78.9636$\pm$0.0015 | 139.8736 |  3.015$\pm$0.014
110222 |  1.60$\pm$0.06 |  0.403$\pm$0.020 |  27.2$\pm$1.0 |  0.954$\pm$0.006 |  208.156$\pm$0.006 | 322.0380 |  4.02$\pm$0.11
140222B |  4.344$\pm$0.033 |  0.7739$\pm$0.0017 |  5.655$\pm$0.010 |  0.98217$\pm$0.00005 |  170.87497$\pm$0.00005 | 325.8715 |  2.320$\pm$0.008
180222 |  3.05$\pm$0.18 |  0.783$\pm$0.011 |  1.53$\pm$0.13 |  0.662$\pm$0.005 |  255.517$\pm$0.005 | 329.0900 |  2.60$\pm$0.09
220222 |  1.605$\pm$0.007 |  0.4698$\pm$0.0026 |  2.68$\pm$0.05 |  0.8510$\pm$0.0005 |  235.6854$\pm$0.0005 | 333.2960 |  4.089$\pm$0.013
010322A |  1.9276$\pm$0.0027 |  0.5469$\pm$0.0006 |  36.06$\pm$0.10 |  0.87346$\pm$0.00008 |  131.68867$\pm$0.00008 | 340.1080 |  3.413$\pm$0.004
010322B |  1.57$\pm$0.06 |  0.411$\pm$0.020 |  35.36$\pm$0.14 |  0.922$\pm$0.007 |  139.445$\pm$0.007 | 340.1481 |  4.00$\pm$0.12
080322A |  3.96$\pm$0.04 |  0.7532$\pm$0.0026 |  13.885$\pm$0.012 |  0.97727$\pm$0.00023 |  15.37103$\pm$0.00023 | 167.1195 |  2.392$\pm$0.012
080322B |  13.5$\pm$1.0 |  0.931$\pm$0.005 |  4.68$\pm$0.04 |  0.9330$\pm$0.0004 |  28.9213$\pm$0.0004 | 167.8948 |  1.570$\pm$0.025
090322B |  11.2$\pm$0.5 |  0.911$\pm$0.004 |  122.44$\pm$0.13 |  0.99250$\pm$0.00009 |  178.06764$\pm$0.00009 | 348.2148 |  1.108$\pm$0.020
090322C |  3.16$\pm$0.04 |  0.688$\pm$0.004 |  18.90$\pm$0.07 |  0.98494$\pm$0.00007 |  168.69848$\pm$0.00007 | 348.2915 |  2.665$\pm$0.019
100322 |  2.8$\pm$0.9 |  0.65$\pm$0.12 |  24.60$\pm$0.17 |  0.98426$\pm$0.00012 |  192.22661$\pm$0.00012 | 349.1653 |  2.8$\pm$0.6
120322 |  6.05$\pm$0.30 |  0.862$\pm$0.008 |  7.92$\pm$0.04 |  0.8339$\pm$0.0023 |  229.2663$\pm$0.0023 | 352.0240 |  1.93$\pm$0.04

##  4 Dynamic association with meteoroid streams and parent bodies

The study of the associations of meteoroids that impact our planet with parent
bodies or meteoroid streams is not a trivial task. There are numerous
mechanisms that prevent the correct linking of meteors with their origins,
from the intrinsically chaotic behavior of planetary systems to non-
gravitational effects and sporadic collisions and interactions (Trigo-
Rodríguez et al., 2005). Because of the high probability that two orbits are
randomly associated (Wiegert & Brown, 2004), we have not only analyzed the
similarity of the orbits at the time of impact but also studied their
robustness over time. From the time evolution of the parent body dissimilarity
criterion, we found some dynamic associations. Figure 5 shows the evolution of
the dissimilarity criterion during the orbital integration of the 15 events
analyzed in this work, along with their most favorable parent body candidates
or meteor shower. Table 6 shows each event with its most likely association,
along with the years of time it lasts under the $D_{D}$ threshold, the minimum
encounter distance, the required ejection velocity at the time of minimum
distance, and the minimum required ejection velocity.

5 out of 15 events, that is, about 30% of the bright fireballs, are below the
cut-off for at least 5,000 years. 4 events would be associated with minor
showers ($\sim$27%) and 1 fireball associated with a near-Earth asteroid
($\sim$7%). In all the associated cases, the required ejection velocity needed
to transform the parent orbit into the meteoroid orbit is in good agreement
with the estimated range for collisions between objects, which can produce a
kick of a few kilometers per second (Melosh, 1984).

Figure 5: Evolution of the dissimilarity function $D_{D}$ of the 15 meteoroids with their most favorable candidates during the orbital backward integration over 10,000. The 1,000 clones of each event are also shown.  Table 6: Most likely parent body and meteoroid stream candidates for each event with the minimum $D_{D}$ value, the years that fulfill the $D_{D}$ criterion threshold, the minimum encounter distance, the required ejection velocity at the time of minimum distance, and the minimum required ejection velocity during the orbital integration. SPMN code | Association | Dmin | tD (y) | Smin (au) | VS,min (km/s) | Vmin (km/s)
---|---|---|---|---|---|---
060222 |  $\rho$ Geminids | 0.176 | 180 | 0.186 | 4.7 | 4.7
080222A | o Leonids | 0.174 | 90 | 0.231 | 4.6 | 0.9
080222B | Southern $\delta$ Leonids | 0.018 | 8720 | 0.129 | 0.8 | 0.4
110222 |  $\omega$ Cassiopeiids | 0.101 | 10000 | 0.087 | 9.6 | 1.4
140222B | March Cassiopeiids | 0.121 | 1610 | 0.145 | 10.2 | 0.5
180222 | Southern $\delta$ Leonids | 0.07 | 240 | 0.278 | 13.2 | 2.0
220222 | Northern $\alpha$ Leonids | 0.09 | 10000 | 0.05 | 5.8 | 1.4
010322A | 2019 CV2 | 0.099 | 2640 | 0.264 | 6.0 | 1.7
010322B | 2017 FM91 | 0.092 | 9990 | 0.104 | 6.6 | 2.3
080322A | 2007 DZ40 | 0.073 | 800 | 0.144 | 3.1 | 1.1
080322B | February Hydrids | 0.168 | 600 | 0.37 | 15.9 | 3.0
090322B | 72 Ophiuchids | 0.136 | 9990 | 0.811 | 14.3 | 0.4
090322C | March Cassiopeiids | 0.084 | 110 | 0.34 | 10.9 | 0.8
100322 |  $\psi$ Draconids | 0.106 | 2080 | 0.37 | 5.1 | 2.0
120322 |  $\lambda$ Leonids | 0.125 | 1300 | 0.083 | 7.4 | 2.4

##  5 Discussion

In relation to the various ablation behaviors observed, it is important to
note that this could be the result of the differences between chondritic
meteoroid and cometary aggregate bulk properties. The low density and high
porosity of the latter are directly related to their aerodynamic strengths
(Blum et al., 2006). Cometary streams typically produce centimeter-sized
projectiles causing fireballs with disruptive flares, and multiple sudden
brightness increases or a catastrophic final flare. Due to the heterogeneity
of the meteoroid components, the evaporation temperature of each one is
reached at different altitudes, giving rise to the so-called differential
ablation (Gómez Martín et al., 2017). The aerodynamic overpressure experienced
by meteoroids when they fragment allows for estimating their aerodynamic
strength. This, in turn, allows for deducing the bulk properties of their
meteoroid stream (Kresak, 1982; Trigo-Rodríguez & Llorca, 2006). These types
of large fireballs associated with cometary vestiges are the result of rapid
disruption in micrometric grains and the sudden ablation of volatile mineral
phases driven by the thermal wave in the meteoroid head (Trigo-Rodríguez et
al., 2019).

Even in such circumstances, it is remarkable that the sporadic contribution is
not dominant at all. We found a very significant percentage of bright
fireballs dynamically associated with minor showers. Although during the
orbital integration there are no very close encounters despite the reasonable
ejection velocities, we must point out that we have propagated 18 particles
distributed in true anomaly throughout the orbit of the meteoroid streams, but
at their nominal values for the rest of the orbital elements. Due to the
orbital perturbations accumulated over time and their violent origin, either
by tidal forces disruption or catastrophic collisions, the meteoroid streams
spread toroidally along their orbit and gradually disperse. Some regions even
undergo more pronounced decoherence than others due to the gravitational
influence of the Earth-Moon system or nearby planets.

The minimum ejection velocities calculated to produce the meteoroid orbit from
the parent body have a standard deviation range between 0.16 and 1.4 km/s
(with an average standard deviation of 0.4 km/s) for the studied events.
Although the ejection velocities found are compatible with collisions of small
objects in the inner Solar System, this does not necessarily mean that these
meteoroids have separated from their meteoroid stream or parent body recently;
we just note it as a feasible possibility due to the usual disruption behavior
of crumbling asteroids and comets.

Although remarkable, the high number of minor showers producing fireballs
should not come as a surprise as such a percentage of meteors associated with
meteoroid streams is not unusual. For example, percentages up to 80% between
November and January were already reported belonging to meteor showers (Rao &
Murthy, 1974). On the other hand, among the 2,401 records studied by Lindblad
(1971), apparently, 37% were associated with meteoroid streams. A similar
percentage (41%) was found by Southworth & Hawkins (1963). Of the orbits
analyzed by Jacchia & Whipple (1961), 65% were linked to a meteor shower.
Regarding the Meteorite Observation and Recovery Project (MORP) database, 37%
of the fireballs could be associated with meteoroid stream (Halliday et al.,
1996). Terentjeva (1990) performed a grouping according to event candidates to
produce meteorites, finding that 68% of 554 fireballs studied could be part of
a shower. And also in good agreement with the results of this work, Babadjanov
(1963) reported that of the 185 meteors studied, 73% appeared to be of
cometary origin. Recent studies also show large percentages of meteors
associated with meteor showers, for example, 45% in Colas et al. (2020) and
35% in Drolshagen et al. (2021). Regarding superbolides detected from space,
23% could be associated with meteoroid streams or near-Earth objects (Peña-
Asensio et al., 2022).

Therefore, as previously studied, it is reasonable to expect that a large
percentage of the meteors belong to minor meteoroid streams, but also, as we
show in this work, some meteor showers can be a significant source of large
projectiles for the Earth and the Moon.

##  6 Conclusion

The extraordinary meteorological conditions in Spain during the spring of 2022
have made it possible to obtain high-quality data related to the fireball
activity produced, to a large extent, by minor meteoroid streams. Ground-based
multi-station recordings were possible thanks to the ever-increasing
atmospheric volume monitored by the SPMN network throughout Spain. We reported
15 bright bolides in February and March, two of them being potential meteorite
dropper events. By applying novel computer vision techniques and improved
methods of trajectory reconstruction and heliocentric orbit calculation
implemented in our software 3D-FireTOC, we have been able to study in detail
the atmospheric flight and dynamic association of large cometary and
asteroidal projectiles impacting our planet. Based on the trajectory data, we
computed the initial and terminal mass, the aerodynamic strength, and the bulk
density by means of an ablation model. In consequence, we claim that:

  * •

Among the 169 bright meteors recorded during the spring of 2022 in Spain, 2 of
them were potentially meteorite dropper events.

  * •

We identify the minor showers o Leonids, Southern $\delta$ Leonids, $\omega$
Cassiopeiids, Northern $\alpha$ Leonids, and 72 Ophiuchids, and the asteroid
2017 FM91 as sources of large projectiles during February and March.

  * •

Nearby meteoroid streams can be efficient producers of large projectiles as
they account for the $\sim$27% of the fireballs.

  * •

Near-Earth objects may be a greater source of impact risk than previously
thought.

  * •

It is needed to extend the study and cataloguing of minor showers, since,
although they are not very active in terms of the number of meteors, our work
indicates that they also produce large bolides annually.

  * •

These findings support the idea that certain meteoroid streams associated with
comets or asteroids may represent a short-term impact hazard.

Finally, we think that understanding the origin and mechanisms by which large
meteoroids reach the Earth is of great scientific interest due to the
possibility of associating complexes and parent bodies with fireballs and,
ultimately, meteorites found on Earth and the Moon. The relevance of
associations also reverts in outreach, as we can quickly inform the public
about the origin of the fireballs reported by eyewitnesses.

## acknowledgements

This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No. 865657) for the project “Quantum Chemistry on
Interstellar Grains” (QUANTUMGRAIN). JMT-R and E.P-A. acknowledge financial
support from project PID2021-128062NB-I00 funded by
MCIN/AEI/10.13039/501100011033. AR acknowledge financial support from the
FEDER/Ministerio de Ciencia e Innovación – Agencia Estatal de Investigación
(PID2021-126427NB-I00, PI: AR). AR is indebted to DIUE (project 2017SGR1323).
Cebreros #AMS81 ESA Ground station belongs to the AllSky7 fireball monitoring
project and is operated by Rainer Kresken and Pablo Ramirez Moreta. We also
thank all SPMN station operators whose continuous dedication have allowed to
record these bolides from multiple stations: Jordi Donet Donet, Vicent Ibáñez,
Jose M. Serna, Carlos Alcaraz, Antonio J. Robles, Ramón López, Agustín Núñez,
José A. de los Reyes, Sensi Pastor, Antonio Fernández Sánchez, Antonio Lasala,
Álex Gómez, Juan Gómez, Ramón López, Francisco José García Rodríguez and Cesar
Guasch Besalduch.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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