The Diffusion of Constellations of Small SAR Satellites:
A Complex Systems Approach
Ludmila Deute Ribeiro
deute.ludmila@gmail.com
UnB Gama Faculty of Engineering, University of Brasilia, Brazil
Manuel Nascimento Dias Barcelos Junior
manuelbarcelos@gmail.com
UnB Gama Faculty of Engineering, University of Brasilia, Brazil
Abstract:
Marine oil spills may cause major envii l de SAR (Synthetic Aperture
Radar) sensors seem to be one of the most effective instruments for oil spills
monitoring. SAR imagery, provided by large satellites carrying SAR instruments, has
been successfully employed in this task. But the fabrication and deployment issues
associated with placing a large SAR satellite into orbit are not compatible with the
growing demand for spaceborne SAR imagery. Any failures in these satellites can cause
irreparable damage to the user community, because its replacement into orbit is
expensive and time consuming. These constraints might open a “market window” for a
new technology which has recently been developed: the constellations of small SAR
satellites. The present paper proposes an analytical tool for exploring the diffusion of
this innovation in the global market of marine oil spills SAR monitoring: a hybrid model
based on Bass Model and Social Network Analysis.
Keywords: Radar, Synthetic Aperture Radar - SAR, oil spill, diffusion of innovations,
Bass Model, Social Network Analysis - SNA.
1. Introduction
Marine oil spills may cause major environmental damage, especially in coastal waters.
Oil spillages occur frequently in the Gulf of Mexico, due to geological causes.
However, the major sources remain the deliberate discharge of oils by ships carrying it
as cargo, and the accidental oil released in activities associated with the exploration of
seabed. About 75% of oil reserves discovered in Brazil are located in deep water
(between 400 meters and 1,000 meters) and ultra-deep water (above 1,000 meters), and
the drilling and transportation of oil favor the occurrence of accidental spillages.
The most effective instruments for monitoring of marine oil spills seem to be Synthetic
Aperture Radar - SAR sensors carried by airborne or spaceborne observational
platforms. The spaceborne SAR radar sends radio wavelengths to Earth’s surface and
the antenna on the satellite collects the wavelengths hat are reflected back. These
wavelengths are also called “backscatter”. SAR imagery produces a grey-scale image
which represents the radar backscatter from water at the sea surface. The radar
backscatter from the sea surface is reduced in areas where oil is present. The result is
that oil slicks turn out as dark areas on a brighter background of normal sea water
(Souza, 2006).
For marine oil spills monitoring, high-to-coarse spatial resolution SAR images can be
used, but the area of the Earth’s surface imaged by the satellite must be most suitable as
it offers better swath area, so that large areas of water can be better detected for oil
spills. This imagery have been mostly provided by high-performance large SAR
satellites often placed in a Sun-Synchronous Orbit - SSO, generally Medium Earth
Orbit - MEO or Low Earth Orbit - LEO. However, considering the life-cycle costs,
development, and deployment issues related to these traditional satellite systems, we
can conclude that they cannot supply the growing demand for marine oil spills
monitoring by spaceborne SAR sensors.
The main requirements of any satellite missions for monitoring marine oil spills can be
summarized as follows: (a) provide imagery captured over the same spot (on the Earth’s
surface) with high revisit frequency; (b) provide imagery day and night, and in
unfavorable weather conditions (clouds, haze, rain and fog); (c) provide imagery with
large swath areas; (d) provide high-to-coarse resolution imagery; and (e) provide lower
costs of satellite manufacture and launch and minimum deployment time in case of
failure.
The requirement (b) can be attended by any SAR satellite missions. Compliance with
requirements (c) and (d) depends on the image acquisition modes of the satellites.
However, single, large SAR satellites are not compatible with requirements (a) and (e).
First, the detection of contingencies is possible only if a sufficient number of
spaceborne sensors is available, then the constellations appears the only solution in
order to limit the temporal gaps of acquisition caused by utilization of a single
spacecraft. Second, the replacement of these traditional satellites into orbit is expensive
and time consuming, and might be affected by budget constraints of the space agencies
responsible for its development, launch, and operation. Any failures in these satellites
can cause irreparable damage to the user community of images and products.
These constraints might open a “market window” for a new technology which has
recently been developed: the constellation of small SAR satellites.
The present paper proposes an analytical tool to explain the diffusion of this technology
innovation in the global market of marine oil spills monitoring by spaceborne SAR
sensors: a hybrid model based on The Bass Model and Social Network Analysis -SNA.
The structure of the paper is as follows. In Section 2, we analyze the constellations of
small SAR satellites for oil spills monitoring, advantages and disadvantages of this
innovation when compared to the traditional technologies. In Section 3, we briefly
review the main models for innovation diffusion. In Section 4, we present the hybrid
model and, finally, in Section 5, there is a roadmap for its future implementation.
2. Marine Oil Spills Monitoring by Spaceborne SAR Sensors
Remote sensing is the group of techniques that allow us to acquire information of
objects or phenomena, without the necessity of being in contact with them. Nowadays,
when we talk about remote sensing, it generally means the use of imaging sensor
technologies including the use of aircraft and spacecraft boarded instruments
(Mondéjar, 2009).
There are two classes of remote sensing systems. Passive sensors detect natural
radiation that is emitted or reflected by the object or the area being observed. Reflected
sunlight is the most common source of radiation measured by passive sensors. On the
other hand, active sensors emit energy with the intention to scan objects and areas.
Imaging RADAR (RAdio Detection And Ranging) is an example of active remote
sensing and has become an alternative technique for Earth observation, due to several
advantages provided by spaceborne RADAR, the most important of which is the ability
to achieve global coverage (Mondéjar, 2009).
A SAR is a coherent radar system that can generate high- resolution images. Since SAR
is an active sensor, which provides its own source of illumination, it can therefore
operate day and night; able to illuminate with variable look angle and can select wide
area coverage. The use of SAR for remote sensing is particularly suited for tropical
countries, because the microwave sign can penetrate clouds, haze, rain and fog and
precipitation with very little attenuation, thus allowing operation in unfavorable weather
conditions. The potential of SAR in a diverse range of application led to the
development of a number of airborne and spaceborne SAR systems (Chan and Koo,
2008).
Spaceborne SAR imagery has provided a strong contribution in a large number of
disasters such as the explosion of the Deepwater Horizon oil platform on April 20,
2010, off the southeast coast of Louisiana, United States. Shortly after the explosion, oil
began leaking from the broken wellhead nearly one mile beneath the surface of the Gulf
of Mexico. During the disaster, the detection and mapping of oil slicks included space-
based SAR imagery such as RADARSAT (Canadian), Cosmo SkyMed (Italian) and
TerraSAR-X (German), the major Earth Observation programs that are operationally in
orbit and which are based on state-of-art SAR instruments.
RADARSAT is a large satellite placed in a low SSO, 798 kilometers above the Earth.
So far, the RADARSAT program succeeded in launching two satellites RADARSAT-1
and RADARSAT-2, of which only the second is still operational.
Launched in November 1995, and equipped with a SAR instrument operating in C-
band, RADARSAT-1 was a Canadian-led project involving the Canadian federal
government, the Canadian provinces, the United States and the private sector. It
provided useful information to both commercial and scientific users in such fields as
disaster management, interferometry, agriculture, cartography, hydrology, forestry,
oceanography, ice studies, and coastal monitoring. In May 2013, the first Canadian
Earth Observation Satellite has been officially declared non-operational after a final
anomaly consigned the satellite to what will be a very slow de-orbit to a final burn-up in
Earth’s atmosphere. Launched in December 2007, RADARSAT-2 offers technical
advancements that enhance many environmental SAR applications. RADARSAT-2
imagery has been successfully used in marine oil spills monitoring.
The evolution of this program is the RADARSAT Constellation. A constellation is
composed of two or more spacecraft in similar orbits with no active control by either to
maintain a relative position (Sandau, 2010).
The mission development has begun in 2005, with satellite launches planned for 2018.
The baseline mission includes three medium-size satellites, but the constellation is
designed to be scalable to six satellites. The RADARSAT Constellation is being
designed for three main uses: (i) maritime surveillance; (ii) disaster management; and
(iii) ecosystem monitoring (CSA, 2014).
COSMO SkyMed (COnstellation of small Satellites for Mediterranean basin
Observation) is a dual-use Earth Observation mission, commissioned and funded by
Italian Space Agency - ASI and Italian Ministry of Defense - MoD. Since the beginning
of 2011, the system is fully operational. It consists of four medium-size satellites, each
one with total mass at launch of 1,700 kg, and equipped with a multi-mode high
resolution SAR instrument operating in X-band (9.6 GHz), providing COSMO SkyMed
adequately supports user needs such as world-wide coverage and high revisit frequency
in the order of few hours. Due to the need of many combinations between swath width
and spatial resolution, the COSMO-SkyMed SAR was chosen as a multimode sensor
operating in: (i) a SpotLight mode, for metric resolutions over small images; (ii) two
StripMap modes, for metric resolutions over tenth of km images; and (iii) two ScanSAR
modes for medium to coarse (100 m) resolution over large swath ~200 km in Huge
Region Mode (Angelucci and Giampaolo, 2012).
The synergic use of X and L band is also possible by cooperation between the Italian
Space Agency (Agenzia Spaziale Italiana -ASI) and the Argentine National Commission
on Space Activities (Comisién Nacional de Actividades Espaciales - CONAE) relevant
to the Italian-Argentine System of Satellites for Emergency Management - SIASGE,
integrated by the four X-band COSMO-SkyMed satellites and the two L-band
SAOCOM satellites.
The German SAR system TerraSAR-X/Tandem-X development is based on a public-
private-partnership agreement - PPP between the German Aerospace Center DLR and
EADS Astrium GmbH. The medium-size satellite TerraSAR-X (total mass at launch =
1,230 kg) also combines the ability to acquire high resolution images for detailed
analysis as well as wide swath images for overview applications.
TerraSAR-X imagery can be acquired in one of these main acquisition modes: (i)
staring SpotLight mode: down to 0.25m resolution, 4 km (swath width); (ii) high
resolution SpotLight mode: up to 1m resolution, 5 to 10km swath width; (iii) SpotLight
mode: up to 2m resolution, 10km swath width; (iv) StripMap mode: up to 3m
resolution, 30 km of swath width; (v) ScanSAR mode: up to 18.5m resolution, 100km
swath width; and (vi) wide Scan SAR mode: up to 40 m resolution, 270 km swath width.
In 2010 TerraSAR-X was joined by his “twin” TanDEM-X. The two satellites now fly
in a unique satellite constellation at a distance of 200 meters. The TerraSAR-X and
TanDEM-X main mission objective is to generate High Resolution 3D SAR imagery via
interferometry.
To better understand the characteristics of the three major SAR satellite systems for oil
spills monitoring see Table 1.
A new concept of spaceborne synthetic aperture radar implementation has recently been
proposed - the constellation of small spaceborne SAR systems. In this implementation,
several flight-formations of small satellites cooperate to perform multiple space
missions (Li, Bao, Wang, and Liao, 2006).
Constellations of small SAR satellites have many advantages over conventional SAR
satellite systems. The coherent combination of several SAR images obtained from
different observing angles can improve the image resolution and provide accurate
geometric information. Furthermore, combining a broad illumination source with
multiple small receiving antennas placed on separate formation-flying small satellites,
we can obtain high-resolution SAR images of wide areas. The implementation of
satellite constellations to increase the time resolution and ground coverage is a unique
feature of small satellites. Another reason for using the constellation of small SAR
satellites is to mitigate the cost, fabrication, and deployment issues associated with
placing a large SAR satellite into orbit. Furthermore, the likelihood of system failure
can be reduced since failure generally occurs only to individual small satellites, instead
of a large satellite carrying an entire system (Li, Bao, Wang, and Liao, 2006).
In short, instead of launching a single, large-to-medium, high-performance satellite, the
capabilities of the system are distributed across several satellites, increasing revisit
frequency, and introducing a more robust (resistant to random failures), flexible system
that can be maintained at lower cost and launched into orbit using smaller, less
expensive launch vehicles. This brings the responsiveness that is needed for
emergencies and for disaster support.
Table 1. Three major SAR satellite systems that are operationally in orbit
ITEMS Cosmo SkyMed RADARSAT-2 TerraSAR/Tandem-X
Satellites/Payload | 4 satellites/X-Band | | Satellite/C-Band |2 Satellites in close
Band formation/X- Band
Mass at Launch 1,700 kg 2,200 kg 1,230 kg
Orbit Altitude 620 km SSO 798 km SSO 500 km SSO
Funding and|Italian Space|Canadian Space| PPP between German
Operation Agency (ASI) Agency (CSA) Aerospace Centre
(DLR) and EADS
Astrium
Prime Contractor | Thales Alenia|M ac Donal d|EADS Astrium
Space Italy Dettwiler Associates
(MDA)
Satellite Imagery | e-GEOS MDA Geospatial | Astrium Services
Distributor Service
Launch Vehicle Boeing Delta II Soyuz II Dnepr-1
Resolution| 1 meter up to 3 meters down to 0.25 meters
(Ground Sample
Distance - GSD)
Swath Width ~ 200 km,|500 km, ScanSAR|up to 270 Km, Wide
ScanSAR mode wide mode ScanSAR mode
Revisit Time 140 minutes 24 days, depending|11 days in average;
on acquisition| northern Europe has a
mode. revisit time of typically
3-4 days.
Innovations Generation of High} Higher Spatial|Generation of High
Resolution 3D] Resolution, Higher} Resolution 3D SAR
SAR imagery via | Revisity Frequency,}imagery via
interferometry. data can be accessed | interferometry.
more quickly.
Interoperation | SAOCOM L-Band | Next RADARSAT | Upcoming constellation
with other systems Generation with Spanish satellite
PAZ to be launched in
2014.
Suitable features] High Spatial] Satellite imagery | High Spatial Resolution,
for marine oil| Resolution High|can be combined|High Geometric and
spills monitoring |R e v is i t y| with other imagery | Radiometric Accuracy
Frequency, |and data to improve
Interoperation with | Revisity Frequency
other systems.
Source: Elaborated by the authors from Euroconsult (2012), Angelucci and Giampaolo
(2012), and sites of CSA and Astrium Services.
Exploring these advantages, a new generation of low-cost spaceborne SAR mission is
under planning. Among these the Nova-SAR-S, developed by Surrey Satellite
Technology - SSTL Ltd, spin-out from University of Surrey in 1985, now owned by
European Aeronautic Defence and Space Company - EADS. SSTL Ltd has successfully
developed the Disaster Monitoring Constellation - DMC, a constellation of optical
remote sensing small satellites operated for the Algerian, Nigerian, Turkish, British and
Chinese governments by DMC International Imaging (Baker, Davies, and Boland,
2010; Sweeting, 2012).
NovaSAR-S mission, with up to 3 small satellites (total mass at launch = 400 kg) to be
launched in the upcoming years, is a combination of Commercial Off-The-Shelf -
COTS technologies, SSTL’s tested SSTL-300 avionics, and a S-band solid state power
amplifier technology developed by EADS Astrium. NovaSAR-S satellites will have a
flexible range of image acquisition modes: (i) ScanSAR mode: spatial resolution up to
20 meters, and swath width of 100 km; (ii) Maritime surveillance mode: spatial
resolution up to 30 meters, and swath width of 750 km; (iii) Stripmap mode: spatial
resolution up to 6 meters, and swath width of 15-20 km; and (iv) ScanSAR wide mode:
spatial resolution up to 150 meters, swath width of 30 km. ScanSAR modes will detect
oil spills in coastal areas and in open ocean ( SSTL, 2013).
The mission is designed for several polar and equatorial orbits depending on the target
area of interest. A single satellite using the fine resolution stripmap mode can return to
the same place anywhere on the globe twice a week. A constellation of three satellites
can provide oil spills monitoring with up to one and a half days revisit time in ScanSAR
mode.
Existing systems have been deployed into high inclination orbits - optimized for
northern hemisphere coverage but with very poor service to the equatorial and tropical
regions. Whilst this does provide global access the revisit rates at the equator are
typically less than one per day. Injection into low inclination orbits is of paramount
importance in providing maximum access and revisits to the equatorial and tropical
regions. The AstroSAR-Lite satellite provides a spaceborne SAR system focused to
provide high revisit frequency (up to 15 times a day) and coverage with high resolution
for the regional user in the tropics and sub-tropics (Honstvet, Encke, Hall, and Munro,
2007).
AstroSAR-Lite is optimized to maritime, environmental, security and disaster
monitoring applications. The baseline satellite operates in various modes to obtain
images ranging from 10 km x 1,000 km at 3 meters resolution, up to 100 km x 1,000 km
at 20-30 meters resolutions over the ‘footprints’ of each of several regional users.
The needs for SAR have also been increasing in Asia. Advanced Satellite with New
system Architecture for Observation - ASNARO is a research and development project
for internationally competitive advanced small satellite system. It has been executed by
NEC Corporation and Japan Space Systems under the contract of Ministry of Economy,
Trade and Industry - METI.
ASNARO satellite bus employs the small standard satellite bus (300 kg) NEXTAR,
developed by NEC Corporation, and a small spaceborne SAR designed to achieve high
resolution (less than 0.5 m GSD), by utilizing the X-band radio waves of the 9 GHz
band. ASNARO will operate in three image acquisition modes: (i) Stripmap mode, a
conventional mode, 10 km swath width; (ii) Sliding Spotlight mode, for less than | m
resolution, 10 km swath width; and (iii) ScanSAR mode, 30 km swath width, suitable
for oil spills monitoring (Kimura, Fujimura, and Ono, 2011).
The traditional users of spaceborne SAR imagery are space and environmental agencies,
but today there is a growing interest in oil spills spaceborne SAR monitoring: the
potential new users are oil companies and emerging countries. Miranda et al (2004),
Rodrigues (2011), and Lima (2011) showed that RADARSAT images have been
successfully used by oil companies for oil spills monitoring. So we assume that some
oil companies would be interested in constellations of small SAR satellites provided to
meet their specific needs.
Since the advent of modern technologies, such as microelectronics, small satellites have
also been perceived to offer an opportunity for countries with a modest research budget
and little or no experience in space technology, to achieve Earth Observation and
defense capability, without relying on inputs from the major space-faring nations.
(Sandau and Briess, 2008 ; Sandau, 2010).
Constellations of Small SAR Satellites can be developed and maintained at lower cost -
small SAR satellites can be built using COTS technologies - and launched into orbit
using smaller, less expensive launch vehicles. Considering all the aspects, its technical
performance is almost equivalent to the performance of traditional, large, high-
reliability SAR satellites. So we assume that developing countries would be also
interested in constellations of small SAR satellites provided to meet their specific needs.
In fact, a new generation of low-cost small spaceborne SAR missions is under planning
and some of them (e.g., ASTROSAR-Lite) are designed to meet the needs of regional
users in the tropics and sub-tropics.
There is, however, a crucial difference between these two technologies: Constellations
of Small SAR Satellites (A1) has not been tested to date, all constellations of small SAR
satellites are in development or deployment phases. In contrast, Large SAR Satellites
(A2 ) have been tested in orbit for years. This fact reduces Aj attractiveness, given that
potential users may have questions about its performance. But these questions will be
overcome after the beginning of the commercial operating phase, planned for the next
two years. Assuming that they have similar cost/ performance, Ai can substitute A2 for
some applications, and even become dominant in the global market. Table 2 provides
analysis of technical and economic factors that can influence the growth and diffusion
of A; in the market dominated by Ao.
Any decision about adopting or not space technologies involves considerable risks, not
counting the transition costs from one technology to another and possible
interoperability problems. Thus, the understanding of the space technologies adoption
process can provide some useful insights for government agencies, universities, and
companies.
Table 2 - Factors that can influence the growth and diffusion of Ai in the market
dominated by Az.
FACTORS Constellations of Small SAR | Large SAR satellites (A2)
satellites (A1)
TECHNICAL
Platforms Reliability
Medium Reliability
High Reliability
Spatial Resolution
Medium to High Spatial Resolution
Higher Resolution : less than 0.5 m
GSD(ASNARO)
High Spatial Resolution
Higher Resolution: down to
0.25 m GSD (TerraSAR)
Revisit Frequency
High (<1 day for all constellations)
Medium (< 1 day only for
COSMO SkyMed)
Swath Width
100/150 Km in ScanSAR mode
~ up to 100 km (TerraSAR/
Tandem ScanSAR mode);
500 Km (RADARSAT-2)
Launch Vehicle
Reliability
Medium Reliability (Dnper,
Cosmos, Minotaur, PSLV, Epsilon)
High Reliability (Soyuz II,
Boeing Delta II, and
Dnper-1)
ECONOMIC
Launch Prices
Low cost per launch for groups of
satellites and for piggyback launch
(US$ 9,5 million/500 kg satellite)
High cost per launch:
Falcon-9: US$ 61.2 M;
Falcon Heavy: US$ 85 M for
up to 6,400 kg GTO
Potential Interest by
government agencies
of developed
countries
Growing interest in the
constellation development (United
Kingdom and Japanese companies
and research centers)
Interest in constellation
development (Italy, Canada,
and Germany space
agencies)
Potential Interest by
government agencies
of developing
countries
Growing interest in the
constellation development (e.g,
DMC constellation)
Growing interest in imagery
acquisition
Potential interest by
oil companies
Growing interest in imagery
acquisition
Growing interest in imagery
acquisition
Potential Use of
COTS
High Potential
Low/Moderate Potential
Satellite development
cost
Relatively Low Costs (~20% of
large satellites development costs)
Higher Costs
Number of Prime
Contractors
Small Number of innovative
companies (ex: SSTL Ltd)
Large Number of Traditional
Prime Contractors
Source: Elaborated by the authors
10
3. Models for Innovation Diffusion
This section reviews and presents some models and modeling approaches for innovation
diffusion. This review intends to be introductory. Our goal is to develop a model for
exploring the diffusion of innovations on the market of oil spills monitored by
spaceborne SAR sensors. This market can be classified as a Complex Adaptive System -
CAS: a kind of system that involves many components that adapt or learn as they
interact, and it is at the heart of important contemporary problems (Page and Miller,
2007; Holland, 2006; Rogers, Medina, Rivera, and Wiley, 2005).
In complex systems modeling, one can follow different paths. Cybernetics, general
systems theory, catastrophe theory, and chaos theory all address deterministic dynamical
systems. These systems are represented by a set of equations that models their
dynamical behavior and determine how the systems are modified on their state space
from time t to time t + 1. Another way of modeling complex behavior, it is based on
examining regularity that emerges from interaction of individuals connected together in
CAS (Anderson, 1999).
The analysis of a Bass Model System Dynamic - SD is a typical example of the
deterministic modeling. In contrast, CAS models represent a genuinely new way of
simplifying the complex, by encoding natural systems into formal systems. CAS models
typically show how complex outcomes flow from simple schemes and depend on the
way in which agents are interconnected. Social Network Analysis - SNA and Agent-
Based Modeling - ABM can be applied to generate CAS models for Innovation
Diffusion.
Starting with the Bass Model, also known as Mixed-Influence Diffusion Model, the
diffusion rate dA/dt can be represented as (Vishwanath and Barnett, 2011):
B= (a+ KAYN-A) a)
where:
a is the external influence coefficient;
N is the population;
K is the constant rate of change or coefficient of diffusion;
Atare the (prior) adopters; and
(N - Ay) are the potential adopters.
11
Integration of the Mixed-Influence Model yields the following cumulative adopter
distribution:
_ N=la(N - Ay)/ (a+ KA, expl-(a+ KA, )(t~ty)]
14 [K(N—A,)/ (a+ KA, expl—(a+ KA, )(t— 1, )] (2)
The plot of the cumulative adopter distribution (Equation 2) results in a generalized
logistic curve (sigmoid function), the shape of which is determined by both a and b.
For the analysis of the Bass Model SD, the adoption of innovations can be viewed as
epidemics spreading by positive feedback as those which have adopted the innovation
(prior adopters) “infected” those who have not (potential adopters). Once the population
of potential adopters has been depleted, the adoption rate falls to zero. The Bass Model
includes also an external source of adoption, usually interpreted as the effect of
advertising and other external influences. These two sources of adoption are assumed to
be independent. Thus, the total adoption rate is the sum of adoptions resulting from
advertisement and any other external influence (Sterman, 2000).
The original model, developed by Sterman(2000), has 2(two) state variables: Potential
Adopters and Adopters. However, because P = A + N, only one of these stocks are
independent, and the model is actually first order (Figure 1).
Figure 1 - Analysis of Bass Model SD
5 5 geal Population NI
Adoption from
Word of Mouth(1)
Potential
Adopters (P1)
Adoption Rate (ARI)
Adoption from
Advertising(1)
Adoption Fraction (i1)
Advertising
Effectiveness(al)
Contact Rate (el)
Source : Sterman, 2000.
12
The arrangement of terms resulting from the analysis of the Bass Model SD (Figure 1),
such as described by Sterman (2000), can be expressed more compactly as:
AR = aP +ciPA/N (3)
where:
i is the adoption fraction and correspond to the proportion of contacts that are
sufficiently persuasive to induce the potential adopter to adopt the innovation;
a is the advertising effectiveness that is a fraction of the adoption rate due to advertising
(I/time period) and corresponds to the influence external coefficient in Equation (1);
c is the contact rate between (prior) adopters (A) and potential adopters (P);
ci corresponds to the coefficient of diffusion K in equation (1);
P are the potential adopters; and
Aare the (prior) adopters.
Assuming N is a constant, then:
N=P+A @)
Even though the reinforcing feedback loop “Word of Mouth” dominates after an early
growth phase, the first adopters are induced through advertisement. The “conversion”
from potential adopter into adopter is generated through the number of contacts between
adopters and potential adopters and the probability that a contact is successful in
attracting a new adopter. The number of adopters compared to the Total Population,
where the innovation takes place, dilutes this effect. As the number of adopter increases,
the number of potential adopter decreases and the balancing feedback loop “Market
Saturation” takes control. “Market Saturation” feedback loop reduces gradually the
growth rate until there are no more potential adopters (Kunc, 2011).
Social Network Analysis - SNA is a technique used to understand the pattern of
interpersonal communication in a social system by determining who talks to whom.
Classical diffusion of innovation models such as Bass Model and SNA has
complemented each approach for over 50 years. Diffusion of innovation research has
been greatly enhanced by SNA because it allows for a more precise specification of who
influences whom during the diffusion process. SNA has benefited from diffusion
research by providing a real-world application to compare and clarify network models.
In the adoption of innovations, decisions often entail some risk, or decision making
under uncertainty. The presence of risk and uncertainty during the diffusion of an
innovation means that individuals are more likely to rely on the behavior of immediate
13
others (peers) rather than on some perception as to what the social norm is. That is, risk
and uncertainty force individuals to turn to their peers to gain more information and
reassurance about decisions of potential adoption (Valente, 1999).
This assumption seems to us perfectly adapted to our social system. In fact, in the
market of marine oil spills monitoring by spaceborne SAR sensors, it seems reasonable
to assume that the decisions of companies and government agencies are taken based on
observed behavior and the information provided by their peers. Thus, it is likely that
networks play a larger role in the diffusion on innovations in this specific market.
4. The Hybrid Model
The Hybrid Model is an analytical tool focus on explaining the diffusion of innovation
Az in the global market of marine oil spills SAR monitoring: Bass Model extensions and
Network Diffusion Model.
A previous step to modeling is innovation classification. Innovations are neither
introduced into a vacuum nor do they exist in isolation. Other innovations exist in the
social system and may have an influence, positive or negative, on the diffusion of an
innovation.
Mahajan and Peterson (1985) have identified four categories of innovation
interrelationships that can affect the adoption rate. Innovations may be: (a) independent
- innovations are independent of each other in a functional sense, but adoption of one
may enhance adoption of others (e.g., microelectronics and small satellites); (b)
complementary - increased adoptions of one innovation result in increased adoption of
other innovation (e.g. small satellites and constellations of small satellites); (c)
contingent - adoption of one innovation (e.g. remote sensing small satellites) is
conditional on adoption of other innovations (e.g. high resolution remote sensing small
instruments that can be deployed on small satellite platforms); and (d) substitutes -
increased adoption of one innovation result in decreased adoption of other innovations
(e.g. constellations of small SAR satellites versus large SAR satellites).
Using data on Table 2, it’s possible to say that the constellations of small SAR satellites
should be classified as a substitute innovation of large SAR satellites. Relative
advantages, as global coverage and high revisit rates of target areas, associated with
reduced costs of development and launch, make this a very attractive option in terms of
cost/ performance. However, we must do some caveats as follows.
Hybrid satellite constellations using multiple layers of LEO small and large satellites
can be designed to meet the emerging remote sensing market. In this case, A and Ay
should be better classified as independent innovations. Another possible scenario is that
large SAR satellites will continue to be developed to meet the high expectations of
government agencies of space-faring nations, in parallel with the development of
constellations of small SAR satellites, by space agencies of developing countries, as a
14
way to get autonomous access to space and develop its own remote sensing capacity.
Some oil companies may also be interested in constellations of small SAR satellites
provided to meet their specific needs. In this scenario, there would be no substitution,
but temporal coexistence of two technological innovations, each one in its specific
market.
4.1 Extending the Bass Model
Mathematical models do not support heterogeneous populations such as government
agencies and oil companies. Additionally, the parameters a and K may not be calculated
from historical data or time series, leaving us the subjective evaluation of external and
internal factors that may influence the diffusion of innovation Aj, which in turn,
inevitably leads to a line of "soft modeling", in which models do not work as a
representation of the real world, but rather as a way to generate debates and views on
the real world. Thus, the SD modeling approach seems to be the best choice for
exploring the dynamical behavior of this social system.
Before applying SD modeling tools, let’s try to extend the Bass Model to explain the
diffusion of emerging technology Ai (Constellations of Small SAR satellites) in the
global market of marine oil spills monitoring by spaceborne SAR sensors. The proposed
extensions are described below.
4.1.1. Extending the Bass Model to express the substitution relationship between Ai
and Ao.
For the purpose of this paper, let’s suppose there is a substitution relationship between
A: and A», vying to become market leader, in a market with size N, where N is a
constant. Thus, the first Bass Model extension is designed to represent the first category
of innovation interrelationship - the substitution relationship between emerging
technology A: (Constellations of Small SAR Satellites) and mature technology Az
(Large SAR Satellites) - by the following diffusion rate equations: (Mahajan and
Peterson, 1985).
dA,
PO (4,4 KA =GA(0)=IN, ACO] 6)
AO «(a+ KA) —CA(O)-(Ny- AO] 6)
dt
15
In Equations (5) and ( 6), ¢, and ¢, represented the hypothesized substitution effect of
the technologies on each other (MAHAJAN and PETERSON, 1985). Equation (5) can
be rewritten as:
dA(t) _
(1)
a aM AO+ KAOLN, — 4,01 6A, OLN, - 4,0]
The term in equation (7) that contains the constant ¢1 represents an interaction between
the adopters of A2 and non- adopters of A; which results in a decrease in the rate of
diffusion for emerging technology A. Equation (6) can be also rewritten as:
dA,(t)
——=a,[N, —A,(t)]+k,A,(t)[N, — A,(t)]— cA, (OLN, — A, (0)]
dt (8)
Figure 2 - The Bass Model SD expressing the substitution between Al and A2.
vi) % ‘Total Population NI
= Adoption from =
Advertising(1) PR+
Effectiveness(al)
Contact Rate (el)
Adoption Rate (AR2) Tol Population NZ
we ee
ou
‘Adoption from Adoption from >
‘Advertising(2) Word of Mouth(2) Adoption Fraction (i2)
Advertising _—aee
Effectiveness(a2)
Contact Rate (€2)
Source: Adapted from Sterman, 2000.
16
In Equations (7) and ( 8), ¢ and ¢ represented the hypothesized substitution effect of
the technologies on each other. Similarly, these differential equations can be viewed as
an extended SD Bass Model (Figure 2) with 2 populations and 4 state variables.
Because P1 = Al + N1, and P2 = A2 + N2, only two of these stocks are independent.
If the signs of c; and co are negative, both technologies have negative impact on one
another, and due to the large market level of mature technology, the emerging
technology never gets the chance to diffuse in the market.
However, if the sign of ci is positive and the sign of c2 is negative, the emerging
technology (A1) will benefit from the existence of mature technology (A2). Under these
circunstances, one can state that there’s a predator-prey relation among these
technologies and that the model will reach an equilibrium condition in which both
technologies coexist in the same market. The dynamics of predator and prey populations
have an oscillatory behavior due to the presence of strong counteracting feedback loop
that forces the system to oscillate around a set of conditions. This feedback mechanism
is illustrated in Figure 3 (Ahmadian, 2008).
Figure 3. Counteracting Feedback loop in the Predator-Prey System
> Predator population
Food supply
# Prey population
Source: Ahmadian(2008)
According to Ahmadian (2008) technical artifacts and infrastructures are factors which
affect the market potential of a technology. For example if there is a common artifact
used in production of both mature technologies and emerging technology, emerging
technology can benefit from the presence of those artifacts. In this case, the mature
17
technology has a positive effect on the emerging technology which makes the
interaction predator-prey interaction.
To study the real dynamics between the two technologies Al and A2, it will be
necessary to pin point what factors can influence the growth and diffusion of an
emerging technology in our specific market. Table 2 shows a first evaluation of these
factors.
1 ad. 1
4.1.2. Extending the Bass Model to express that a p i pter population
continuously in flux is to be expected for a single technology (A 1)
As mentioned before, the Bass model assumes that the ceiling on the number of
potential adopters in a social system, (N-A: ), is fixed at the time an technology
innovation is introduced and remains constant over the diffusion process. Obviously
such an assumption is not tenable with regard theory or practice. From a theoretical
perspective, there is no rationale for a static potential adopter population. In practice, we
found that the market size for oil spills monitoring is increasing. New potential
adopters, such as government agencies of developing countries and oil companies, are
becoming more interested in oil spills monitoring by spaceborne SAR sensors.
In response to this kind of situation, Mahajan and Peterson (1985) proposed extending
the Bass Model to express that a potential adopter population continuously in flux is to
be expected. In this extended model, N is permitted to vary over time:
N(t)= f(SM) (9)
Thus, if f(S(t)) is substituted for N in equation (1), a dynamic Bass Model results:
dA(t (10)
BOW (a KAIL(SI)-A)
The solution of equation (11) is:
i
A= 84 —__ 1p) R00) ss
Ga ns | exp{a(x-t,)+ K@(x)} dx
where A(t=to)= Ao and
(12)
O)= J (SE) ax
18
An equivalent SD model, also proposed by Sterman (2000), assumes that the total
population size is a stock increased by a Net Population Increase Rate that aggregates
births, deaths, and net migration. The Net Population Increase Rate is given by the total
population and the Fractional Net Increase Rate, which can be assumed constant (Figure
4).
Figure 4 - The Bass Model SD incorporating growth in the size of total market
2
a Potential
7 Adopters (P)
Potential Adopters fon Rate (ARI)
Population Minus ~ + .
Advertising,
Adopters (A)
ee +
Sut Adoption from
Word of Mouth
Adoption Fraction(i)
Advertising
Contact Rate (¢)
Ly fear
Net Population
Increase Rate
Fractional Net
Increase Rate
Source: Adapted from Sterman, 2000
Assuming that all increases in population size add to the pool of potential adopters, the
potential adopter population can be written as P = N - A. Even though the potential
adopter population is a stock, it is fully determined by the total population and adopter
population.
4.1.3. Estimation of the parameters, a, K, and N, for a single technology (A 1)
Starting from the equations (7) and (8) for Ai and Ag, let’s estimate its parameters.
Because the Bass Model is essentially a 3-parameter model (a, K, and N), parameter
estimation requires time-series data on the number of adoptions in a minimum of three
time periods. Parameters can be also estimated by means of certain innovation-specific
analogues. According to Mahajan and Peterson (1985), estimation begins by rewriting
the Bass Model in terms of its discrete analogue:
A(t+1)— A(t)=aN + (KN -a)A(t)—bA’(t)
(13)
= A, +A,A(t)+ A,A°(t) + e(t)
19
The “A terms” can then be evaluated numerically by means of ordinary least squares
regression analysis and a, K, and N:
Ay=aN (14)
A3=-b (15)
(16)
N=se ‘A? -4A,A,
3
In the absence of historical or time-series data, parameters can be estimated by means of
certain innovation-specific analogues or expert judgments. Using estimated values it’s
possible to simulate the dynamical behavior of our specific market.
4,2. Network Models of the Diffusion of Innovations
Studies on the diffusion of innovations on networks usually start from the
questionnaires, through which respondents must provide details of their interaction with
others. Using these data, it is possible to reconstruct the network in which vertices
represent individuals and links represent interactions. Usually, questionnaires address
issues of centrality (which individuals are more connected to others and which have
most influence) and connectivity (whether and how individuals are connected to others
through the network).
Network centrality is the degree that the links in a graph are concentrated in one or a
group of individuals. A centralized network contains a few members who are the locus
of contacts, whereas a decentralized network has the connections spread among many
members in the network. Centralized networks have faster diffusion because once the
innovations are adopted by a central member of members, it is more rapidly spread to
the rest of the system. In a decentralized network, it takes longer for the innovation to
reach everyone in the network. However, in situations of greater risk/uncertainty, with
slower diffusion, when the perceived advantageousness of the innovation is in question,
centrality impedes diffusion (Valente, 1995).
Centrality refers to an individual vertex and is defined by the in-degree of a vertex
divided by (N-1). /n-degree measures how many edges are incident on a vertex.
Centralization characterizes the entire networks and captures the inequality on the
distribution of centrality (Valente, 1995).To calculate the centralization, we can use the
Freeman’s general formula:
XIC,*)-C, HI a7
“(= 1-2)
=
20
where:
C,(n*) = maximum value of centralization in the network;
C,(i) = centrality of a particular node, and
N = number of vertices or nodes.
Betweenness Centrality measures the degree an individual lies between other
individuals on their paths to one another. A high Betweenness Centrality indicates that
individuals acts an intermediary between many others in the network. To calculate the
Betweenness Centrality we use:
C= > 8a O/ 8p (18)
where:
gjx = the number of the shortest paths connecting j and k;
gix (i) = the number that actor i is on.
Usually normalized by:
Coli) = Cy) /[r— In 2)/2] a9)
Finally, Closeness Centrality is the extent an individual is near other individuals in the
network. Thus, closeness centrality individuals act as rapid conduits for an innovation
because they are able to rapidly spread information and influence concerning the
innovation to numerous others. (Valente, 1995).
Closeness Centrality is based on the length of the average shortest path between a
vertex (or node) and all vertices in the graph:
RM oye: aarti
CTY AGI
(20)
where:
21
d(i,j) = is the number of ties in the geodesic between i and j. Usually normalized by:
C= (C.@)/(N -D Q1)
There are countless software tools for SNA. GEPHI platform allows visualization and
basic network metrics calculation. NETLOGO may be useful in understanding the basic
properties of dynamic processes on networks, including diffusion. iGraph is for
programming. There is a SNA package for “R”, a statistical programming language.
PAJEK is a free software that allows network analysis and visualization. There are
many other platforms not mentioned here.
5. Conclusions
The previous Section presented an hybrid model - a combination of Bass Model
extensions and SNA Model — for exploring the diffusion of the constellations of small
SAR satellites, in the specific market of marine oil spills monitoring by spaceborne
SAR. In order to meet this goal, we have selected, in Section 4, three Bass Model
extensions and some essential network metrics. The hybrid model has not been
implemented yet, because parameters calculation depends on field research. The future
hybrid model implementation should follow these steps:
(a) Bass Model Implementation:
¢ 4.1.1 and 4.1.2 Bass Model extensions;
* Parameters (a, K, and N) estimation in 4.1.2. using time-series data on the number
of the adoptions in a minimum of three times periods as described in 4.1.3. In the
absence of time-series data, parameters can be estimated by means of certain
innovation-specific analogues or expert judgments. (This is a more realistic option,
given that the emergent technology Ai is being developed); and
¢ Use of computational tools to simulate different scenarios on innovation diffusion.
(b) Network Diffusion Model Implementation:
¢ Application of questionnaires, through which respondents must provide some
details of their interaction with others, in order to calculate network metrics;
¢ Visualization of the network and network metrics calculation using software tools
(e.g. GEPHI); and
¢ Inferences about the diffusion process on network, using software models(e.g.
NETLOGO models).
22
Acknowledgements:
We would like to thank Professors Ricardo Matos Chaim and Rita de Cassia Silva for
their comments and suggestions, and the other members of UnB Gama Faculty of
Engineering for the support and friendship provided throughout this work.
References
Ahmadian A. 2008. System dynamics and technological innovation system: Models of
multi-technology substitution processes. Master of Science Thesis. ESA Report n° 2008:
15, Chalmers University of Technology. Goteborg, Sweden Retrieved July 20, 2014,
from http://publications.lib.chalmers.se/records/fulltext/74728.pdf/
Astrium Services. 2014. TerraSAR-X Radar Satellite Imagery. Retrieved July 20, 2014,
from http://www.astrium-geo.com/terrasar-x/
Anderson P. 1999. Complexity Theory and Organization Science. Organization Science
10(3): 216-232 Special Issue: Application of Complexity Theory to Organization
Science. Retrieved July 20, 2014, from http://www.jstor.org/stable/2640328/
Angelucci M. and Giampaolo D. 2012. COSMO SKYMed e-GEOS Supports
Development of Innovative Services. 13th IICWG (International Ice. Charting Working
Group), Tromso, Norway, October 15-19, 2012. Retrieved July 20, 2014 from https://
nsidc.org/noaa/iicwg/presentations/IICWG-2012/Angelucci_ COSMO_SkyMed_e-
GEOS.pdf/
Baker AM, Davies P, and Boland L. 2010. Moving Towards Commercial Earth
Observations Services with Small Satellite Constellations. In Sandau, R; Roeser, HP;
Valenzuela, Arnoldo (Eds). Small Satellites for Earth Observation: Selected
Contributions. XXII, 406 p, Springer.
Canadian Space Agency (CSA). 2014. The RADARSAT Constellation. Retrieved July
20, 2014, from http://www.asc-csa.gc.ca/eng/satellites/radarsat/
Chan YK, and Koo VC. 2008. An Introduction to Synthetic Aperture RADAR (SAR).
Progress In Electromagnetics Research B 2: 27-60. Retrieved July 20, 2014, from
http://www. jpier.org/PIERB/pierb02/03.07110101.pdf/
Euroconsult. 2012. Opportunities in Earth Observation Satellite Services: Lessons of the
Past for the Future. Industry Symposium. 49th Scientific&Technical Subcommittee
23
COPUOS. OSSA, Vienna, February 13. Retrieved July 20, 2014, from http://
Wwww.oosa.unvienna.org/pdf/pres/stsc2012/2012ind-02E.pdf/
Holland JH. 2006. Studying Complex Adaptive Systems. Jr! Syst Sci & Complexity 19:
1-8. Retrieved July 20, 2014, from http://deepblue.lib.umich.edu/bitstream/handle/
2027.42/41486/11424 2006 _article_1.pdf?sequence=1
Honstvet I, Encke I, Hall D, and Munro Y. 2007. ASTROSAR-Lite. Anais XIII Simpoésio
Brasileiro de Sensoriamento Remoto, Florianépolis, Brasil (21-26 abril ), INPE, p.
4907-4913. Retrieved July 20, 2014, from http://www. jpier.org/PIERB/
pierb02/03.07110101.pdf/
Kimura T, Fujimura T, and Ono K. 2011. Small SAR Satellite Technology Promotes
Dissemination of a Comprehensive Space Utilization System. NEC Technical Journal,
6(1). Retrieved July 20, 2014, from http://www.nec.com/en/global/techrep/journal/g11/
n01/pdf/110115.pdf/
Kune M. 2011. Systems Dynamics and Innovation: A complex problem with multiple
levels of analysis. Warwick Business School. Coventry, UK. Retrieved July 20, 2014,
from https://www.theorsociety.com/Media/Documents/Users/CaraQuinton01011978/
OriginalDocument/13_09_2011-09_57_13.pdf/
Li Z, Bao Z, Wang H, and Liao G. 2006. Performance Improvement for Constellation
SAR using Signal Processing Techniques. JEEE Transactions on Aerospace and
Electronic Systems 42(2). Retrieved July 20, 2014, from http://www.geo.uzh.ch/
microsite/rs]-documents/research/SARlab/GMTILiterature/PDF/LBWL06.pdf/
Lima SC, Landau L, and Miranda FP. 2011. Utilizagdo de imagens SAR orbitais para a
detecgao de exsudagdes de dleo na porgao offshore da Bacia de Camamu- Almada.
Anais XV Simposio Brasileiro de Sensoriamento Remoto-SBSR, Curitiba, PR, Brasil,
(30 de abril a 05 de maio), INPE, p. 3618. Retrieved July 20, 2014, from _ http://
www.dsr.inpe.br/sbsr2011/files/p0579.pdf/
Miranda FP, Marmol AMQ, Pedroso EC, Beis! CH, Welgan P, e Morales, LM. 2004.
Analysis of RADARSAT-1 data for offshore monitoring activities in the Cantarell
Complex, Gulf of Mexico, using the unsupervised semivariogram textural classifier
(USTC). Canadian Journal of Remote Sensing, 30(3): 424-436. Retrieved July 20,
2014, from http://pubs.casi.ca/doi/abs/10.5589/m04-019/
Mahajan V, and Peterson RA. 1995. Models for Innovation Diffusion. Series:
Quantitative Applications in the Social Sciences. Sage Publications.
Mondéjar AG. 2009. Feasibility Study on SAR Systems on Small Satellites, Barcelona,
(January). Retrieved July 20, 2014, from https://upcommons.upc.edu/pfe/bitstream/
2099. 1/663 1/1/Final.pdf/
24
Page SE, and Miller JH. 2007. Complex Adaptive Systems: an Introduction to
Computacional Models of Social Life. Princeton University Press.
Rodrigues DF. 2011. Obtengdo de Campos de Vento na Superficie do Mar no Golfo do
México a partir de imagens de Radar de Abertura Sintética (SAR). Dissertagaéo de
Mestrado apresentada a COPPE, Universidade Federal do Rio de Janeiro.
Rogers EM, Medina UE, Rivera MA, Wiley CJ. 2005. Complex Adaptive Systems and
The Diffusion of Innovations. The Innovation Journal: The Public Sector Innovation
Journal, 10(3).
Surrey Satellite Tecnology - SSTL Ltd. 2013. NovaSAR-S Brochure: The Small
Satellite Approach to Synthetic Aperture Radar. Retrieved July 20, 2014, from http://
www.sstl.co.uk/Downloads/SSTL-Brochure-pdfs/SSTL-NovaSAR-Brochure-2013/
Sandau R. 2010. Status and trends of small satellite missions for Earth Observation.
Acta Astronautica 66: 1-12.
Sandau R. and Briess K. 2008. Potential for Advancements in Remote Sensing Using
Small Satellites. The International Archives of the Photogrammetry, Remote Sensing
and Spatial Information Sciences, vol XXXVI, Part B1, Beijing.
Souza DL. 2006. Sistema Inteligente para Detecg’o de Manchas de Oleo na Superficie
Marinha através de Imagens SAR. Dissertagéo de Mestrado. Programa de Pos-
Graduagao em Engenharia Elétrica, Centro de Tecnologia, Universidade Federal do Rio
Grande do Norte.
Sterman JD. 2000. Business Dynamics: Systems Thinking and Modeling for a Complex
World. Irwin/McGraw-Hill, Boston.
Sweeting M. 2012. Small Satellites quo vadis? AIAA Space 2012, Pasadena, California.
Retrieved July 20, 2014, from https://www.aiaa.org/uploadedFiles/About-AIA A/Press-
Room/Key_Speeches-Reports-and-Presentations/2012/Sweeting_Thurs%20_PM.pdf/
Valente TW. 1999. Network Models of the Diffusion of Innovations. The Hampton
Press Communication Series.
Vishwanath, A, and Barnett GA. 2011. The Diffusion of Innovations: A Communication
Science Perspective. Peter Lang Publishing Inc, New York.
