Determination of aerosol optical properties with orbital passive remote sensing is a difficult task, as observations often have limited information. Multi-angle instruments, such as the Multi-angle Imaging SpectroRadiometer (MISR) and the POlarization and Directionality of the Earth's Reflectances (POLDER), seek to address this by making information-rich multi-angle observations that can be used to better retrieve aerosol optical properties. The paradigm for such instruments is that each angle view is made from one platform, with, for example, a gimballed sensor or multiple fixed view angle sensors. This restricts the observing geometry to a plane within the scene bidirectional reflectance distribution function (BRDF) observed at the top of the atmosphere (TOA). New technological developments, however, support sensors on small satellites flying in formation, which could be a beneficial alternative. Such sensors may have only one viewing direction each, but the agility of small satellites allows one to control this direction and change it over time. When such agile satellites are flown in formation and their sensors pointed to the same location at approximately the same time, they could sample a distributed set of geometries within the scene BRDF. In other words, observations from multiple satellites can take a variety of view zenith and azimuth angles and are not restricted to one azimuth plane as is the case with a single multi-angle instrument. It is not known, however, whether this is as potentially capable as a multi-angle platform for the purposes of aerosol remote sensing. Using a systems engineering tool coupled with an information content analysis technique, we investigate the feasibility of such an approach for the remote sensing of aerosols. These tools test the mean results of all geometries encountered in an orbit. We find that small satellites in formation are equally capable as multi-angle platforms for aerosol remote sensing, as long as their calibration accuracies and measurement uncertainties are equivalent. As long as the viewing geometries are dispersed throughout the BRDF, it appears the quantity of view angles determines the information content of the observations, not the specific observation geometry. Given the smoothly varying nature of BRDF's observed at the TOA, this is reasonable and supports the viability of aerosol remote sensing with small satellites flying in formation. The incremental improvement in information content that we found with number of view angles also supports the concept of a resilient mission comprised of multiple satellites that are continuously replaced as they age or fail.
Atmospheric aerosols play a potentially significant role in the
global climate, both through direct scattering and absorption of solar
radiation and indirectly by modifying clouds and local meteorology.
Additionally, aerosols contribute the largest overall net radiative forcing
uncertainty
Notable examples of instruments that make use of multi-angle observations
include the Multi-angle Imaging SpectroRadiometer (MISR) and the POlarization
and Directionality of the Earth's Reflectances (POLDER). MISR, launched on
the NASA Terra spacecraft in 1999, observes in four spectral bands and nine
view angles spread in the flight track direction
The instruments described above are what we call “multi-angle” platform
instruments, since all measurements are made from one instrument. New and
rapidly developing technology has created the possibility that several
individual instruments can make a multi-angle observation in an entirely
different manner. We consider formations of single-view angle instruments in
orbit, coordinated to observe the same point simultaneously. This approach
may be advantageous for a variety of engineering, cost or operational
reasons. A formation of small satellites can make multi-spectral measurements
of a ground spot at multiple angles simultaneously as they pass overhead
using instruments with narrow fields of view in controlled formation flight
Illustration of the observation geometry of five single-view-angle
satellites flying in formation
Aerosol optical properties are determined from an orbital measurement,
Simulated viewing geometries in 1 day for nine single-view
satellites in formation flight
The TOA BRDF or BPDF depend upon interactions between incoming solar
radiation and the gases, aerosols, clouds and surfaces that comprise an earth
scene. They therefore can contain information about the optical properties
and quantities of these constituents. A generalized way to retrieve these
values is to compare the measurements,
Figure
The goal of this paper it to examine these differences and determine whether
there are advantages (or disadvantages) of using formations of multiple
satellites with single but adjustable view compared to multi-angle
instruments. Section
The relationship between the systems
engineering model and the science evaluation model from
An architecture is defined as a unique combination of design variables such
as number of satellites, their orbit parameters, the spectrometer or
polarimeter payload's field of view, pixel size, number of spectral bands,
spectral resolution and communication bands for downlink. The methodology
employed to assess the optimal architectures and validate their aerosol
retrieval capabilities couples systems engineering and IC analysis, a method
of science performance evaluation. A trade space of architectures can be
analyzed by varying the design variables in the systems engineering model and
assessing its effect on science products using IC assessment, as shown in
Fig.
In the last few years, several small satellite constellations with
atmospheric science sensors have successfully flown (e.g., the Cyclone Global
Navigation Satellite System or CYGNSS;
As described in previous literature
This figure is an illustration of information content assessment
concepts. We consider a state space (blue) representing all possible
geophysical parameter values. Each point within this space is a plausible
geophysical state, expressed as the vector
This paper focuses on only those design variables in the systems engineering
model that pertain to orbital design and payload pointing strategies of a
satellite formation. Specifically, these variables are number of satellites,
altitude and inclination of the chief orbit, the relative differences between
the Keplerian elements of different satellites and strategies for payload
pointing for obtaining multi-angular images simultaneously. Three potential
strategies or imaging modes are
Fixed reference satellite, wherein one satellite always points nadir while
others point at the ground spot below the reference satellite; Variable reference satellite, which is the same as 1 except that the
reference satellite varies; Tracking mode, where all satellites track pre-defined ground points as
they emerge from and disappear over the horizon.
The third imaging mode obviously provides the most angular coverage, at the cost of spatial coverage because only a small set of ground points can be tracked with one formation of satellites.
We have not optimized the design variables in this paper, but instead have used
formation architecture designs that have been shown to be optimum for land
surface (not TOA) BRDF estimation from space, as averaged over 1 day of
simulation
We use an IC assessment method that applies Bayesian statistical techniques
to connect measurements to the expected retrieval success of geophysically
relevant parameters. This technique is described for atmospheric remote
sensing by
Figure
All measurements have uncertainty, so an observation is really an expression
of a volume within observation space, represented by both
This presumes that
A useful reformulation of
Correlation strength (values close to 1 or
The IC assessment tools we have described here, while
powerful, have a number of limitations and caveats that must be mentioned. We
can predict uncertainty for a retrieval, but this assumes we have
perfect knowledge of observation uncertainty (and the assumption that
such uncertainty is Gaussian), perfect forward model simulation of geophysical reality (although
perfect algorithm ability to converge to the best retrieval from the observations, and localized forward model linearity about the points used to calculate the Jacobian matrices.
Of course, we are far from perfect. This IC assessment technique therefore
presents the best case scenario for a given measurement. It is useful because
we have a quantitative means to connect the observation and scene conditions
to retrieval ability with limited computational expense. This means our
assessment is ideal for relative comparisons (minimizing the impact of
assumptions) for specific hypothesis tests. As we will describe in more
detail later, we test 16 different observation configurations, each with more
than 100 orbital geometries, for six different scenes, for a total of
nearly 10 000 individual assessments. We do this to provide a thorough test
of the IC contained in small satellites in formation and multi-angle
observations on one platform.
We should also note that swath width, spatial resolution and other details
associated with the ability of an observing system to properly sample the
global state are not assessed in this analysis. This study can be considered
one step simpler than a full blown Observing System Simulation Experiment
(OSSE), where a global model of aerosol properties is sampled by an observing
system to determine its capability (for example,
Our hypothesis is that the IC content contained in observations by small
satellites in formation flight is comparable to that of multi-angle
observations on one platform, where the primary difference is that such
observations have a variety of view zenith and azimuth angles and are not
restricted to one azimuth plane as is the case with a single multi-angle
instrument. To test this, we simulate a variety of different observation
geometries while keeping all other instrument characteristics (such as
spectral sensitivity and measurement uncertainty) the same. Instruments
systems with sensitivity to linear polarization are tested along with those
that have sensitivity to radiance or reflectance alone (see
Sect.
RAAN and mean anomaly in degrees for each satellite in the selected
formations with respect to the first satellite, and the number of
observations in a day with a solar zenith angle,
We simulate between three and nine small satellites in formation flight to
compare to a multi-angle instrument with nine view angles in the along-track
direction. The small satellites are considered to have a single-viewing angle
each, while the nine view angles of the multi-angle instrument were chosen to
mimic MISR. The MISR instrument observes in the along-track direction at
70.5, 60, 45.6 and 26.1
We use the systems engineering model to simulate angular measurements over
1 day (
Architectures corresponding to the lowest average (rms) surface BRDF error
over time, when compared to CAR data, are used as case studies in this paper.
All the satellites are in a 650 km circular orbit at a 51.6
The orbital elements proposed above are achievable within commercial small
satellite technology. These elements allow for relative separation between
the formation's satellites, such that they can point at the same surface spot
nearly simultaneously.
The inputs (simulated measurements) from the systems engineering model to the
IC analysis model, as seen in Fig.
We use a nested RT model that first computes the single scattering Lorenz–Mie
solution to Maxwell's equations for spheres, then incorporates that with
other computations for a plane parallel, multiple scattering scene using the
“doubling or adding” method
For a given parameter vector,
We considered two types of scenes and simulated each with three different
levels of aerosol loading. For most cases of multi-angle aerosol property
retrieval, the IC contained in a scene depends on instrument
configuration, decisions about which parameters to retrieve, and aerosol
load, and only weakly on aerosol optical properties
Characteristics of the two scene types selected for simulation with
our RT software.
Table
The ocean surface reflectance was parameterized to represent a moderate
Chl
Sample radiative transfer (RT) software output, for the
maritime-ocean scene described in Table
The RT model was used to compute the simulated measurement vector
Figure
After completing the steps described above, IC assessment is
performed by calculating the retrieval error covariance matrix,
As stated above,
Our IC assessment involves the calculation of many (more than 100 for
each scene and instrument configuration) retrieval error covariance matrices,
Because of the scale of our IC assessment results, we present a subset that
illustrate the overall outcome in light of our goal to compare observations
by formations of single-view instruments to a multi-angle instrument. We
start by comparing the DFS (Sect.
The degrees of freedom for signal (DFS, described in
Sect.
As described in Sect.
Aerosol optical thickness (AOT) relative uncertainty at 555 nm is
plotted for continental aerosols over land
Regardless of scene type, all plots show a gentle increase in DFS as the number of satellites in each configuration are increased. DFS for the nine-satellite configuration and the multi-angle satellite with nine viewing angles are nearly indistinguishable, with differences in the mean values well within the variability range due to geometric differences in the orbit. This indicates that the capability of a measurement system, at least as expressed by the DFS, is primarily governed by the number of viewing angles, but not how those views are distributed within the BRDF or BPDF (although views from both the multi-angle satellite and the small satellites flying in formation are widely distributed throughout the BRDF or BPDF). Furthermore, this figure shows that the number of view angles gradually increases the DFS, such that a seven- or eight-satellite configuration is nearly as capable as the nine-satellite configuration or the nine-view multi-angle satellite configuration. For reflectance-only scenes over the ocean, in fact, the DFS tends to level off after five or six satellites, indicating diminishing returns with more angles. Polarimetric ocean and both reflectance-only and polarimetric land scenes benefit from additional viewing angles, although the DFS increase becomes more gradual.
A subtle difference between the single-view satellite configurations and the multi-angle instrument is present for the ocean case utilizing reflectance and polarization. In this case, the range of DFS values is slightly larger for the former compared to the latter. This means that, over the course of an orbit, there is a greater variability in the DFS for observations, although the mean uncertainty remains the same. In terms of ability to create global aerosol statistics, this difference may be irrelevant, but a study with a full OSSE may help identify whether there is a systematic geographical difference of relevance to the global aerosol distribution.
As expected, instrument configurations that utilize polarization have greater
DFS, since they have access to more information. In fact, polarimetric
observations over the ocean have a DFS of nearly 5, almost the theoretical
limit (6) for that type of retrieval. We also do not see a large influence
of the simulated AOT on the DFS. Since ability to retrieve aerosol optical
properties depends on the aerosol load itself
The AOT, as a measure of aerosol load, is one of the primary parameters
retrieved from an instrument system. Our analysis expects the retrieval
algorithm to independently determine the fine- and coarse-size-mode
properties, including the individual mode optical thickness. The total AOT is
a simple summation, so the uncertainty in its retrieval can be easily
computed via Eq. (
Unlike, Fig.
These results support our hypothesis that single-view satellites in formation flight are equally capable as multi-angle observations on an individual satellite, provided that the number of viewing angles are the same. Furthermore, loss of one or more single-view satellites does not contribute much to an increase in uncertainty.
Uncertainty in the effective radius for the fine aerosol size mode
is plotted for continental aerosols over land
The uncertainty of determining the effective radius (one of two parameters
defining size distribution) of the fine (small) aerosol size mode is plotted
in Fig.
We chose to display the fine-mode effective radius because it is a parameter that was shared between both types of scenes, although the fine size mode contributed different amounts to the total AOT in each scene. For ocean scenes, the fine mode contributed 36 % to the total AOT, while over land the contribution was 90 %. This means the fine size mode had a stronger role modifying the observed BRDF and BPDF over land than over ocean, contributing to the lower uncertainties for the former compared to the latter. Otherwise, the uncertainty for the fine-mode effective radius follows many of the same patterns as the AOT. For the lowest simulation AOT (0.05), uncertainty was close to the a priori value for the reflectance only instruments, but slightly better for instruments that used polarization. Additional angles do help a bit more than was the case for AOT, although the improvement is gradual. Furthermore, we found no significant differences between the nine satellites in formation flight compared to a multi-angle satellite with nine views.
Diagonal values for the mean averaging kernel matrices,
The averaging kernel matrix (
The most obvious inference from Fig.
These results represent the mean value of
Finally, what is clear from Fig.
Correlation matrixes for scenes with the medium simulated optical
depth (AOT (555 nm)
Figure
Most importantly, these matrices are nearly identical for the nine satellites flying in formation flight and the nine-view multi-angle instrument. This is further support for the hypothesis that satellites in formation flight are equally capable of retrieving aerosol parameters as multi-angle instruments.
Our central hypothesis is that aerosol
remote sensing is performed equally well by the geometric distribution of
observations by small satellites flying in formation and multi-angle views on
a single satellite. The main difference between the two types of observations
is that multi-angle views on a single satellite are restricted to a single
azimuth plane, while small satellites flying in formation observe at a
variety of azimuth angles. Such systems therefore sample the BRDF or BPDF in
different ways. To test this hypothesis, we have generated a variety of
observation formations using a systems engineering orbital model constrained
to feasible satellite bus configurations. The geometries of these formations
where then used as inputs to an IC analysis, which
determines geophysical parameter retrieval capability. This capability was
tested for the aggregate of the observation formations for a variety of
realistic atmospheric aerosol scenes over land and ocean. These tests were
performed for formations of between three and nine satellites to compare to a
multi-angle satellite with nine views. All instruments were simulated with
identical spectral and measurement uncertainty characteristics. Details about
the limitations of our IC technique are discussed in
Sect.
The IC analysis reveals that there is no difference between
the capability of multi-angle satellite instruments on a single platform
compared to an equal number of views from satellites flying in formation.
This equivalence is maintained for a variety of aerosol classes, quantities
and scene types (over land or over ocean). The primary factor affecting
capability (other than spectral characteristics and measurement uncertainty,
which we did not vary) is the number of viewing angles in a observation, and
not their distribution throughout the BRDF and BPDF. This can be explained by
the smooth nature of TOA BRDF and BPDF (see Fig.
We also found that the IC improves only incrementally as the
number of viewing angles increases. For some situations and parameters,
additional viewing angles provide no improvement after a half dozen or so,
while others (typically those for which the observation system has marginal
overall IC) do show improvements that eventually level off
with many view angles. This is slightly lower than the conclusions of
Further investigation into the value of aerosol remote sensing with small satellites in formation would need to address topics we could not consider in this IC study. We assumed that the measurement uncertainties are identical for different designs, and this may not be the case. Small satellites flying in formation may have differences in how they are calibrated compared to single platform spacecraft, and the relative differences between satellites may be more difficult to characterize than the differences between view angles in a single spacecraft. These differences would pertain to specific designs and not be generally applicable as in this paper. Successful co-registration of multi-angle views between designs may vary, but again this is a design-specific metric. Another topic we could not consider was the impact of instrument swath and coverage. Obviously, greater coverage is desirable, but the impact of this in determining climate-relevant information requires the use of a full OSSE. Coupling orbit geometries from the systems engineering model to simulated observations from the nature run of an OSSE would provide the means to more directly assess the ability to observe parameters of relevance to climate.
In addition to our central hypothesis, this analysis reveals useful general
details about the IC of multi-angle and multi-angle
polarimetric observations. As illustrated in Fig.
To date, multi-angle remote sensing of aerosols have only been performed with instruments that make all of their observations on a single spacecraft. Ongoing technological development means that coordinated observations by formations of satellites are becoming a reality. We have demonstrated that the information contained in such observations would be equivalent to a single multi-angle instrument for aerosol remote sensing. While many technical and scientific matters must still be resolved, this provides an opportunity, as these formations may have engineering, cost or other advantages. They may, for example, be more resilient. Our results indicate that the loss of one or more individual satellites does not dramatically impact the IC in the observation, providing for an opportunity to replace lost satellites, ultimately improving observation continuity. Where there remains many aspects of such observations to explore, they hold promise for the future of aerosol remote sensing.
Raw data will be provided by the corresponding author upon request.
KK performed the information content analysis with input from the systems engineering tool developed by author SN. Concept, experiment design and manuscript preparation were joint efforts of both authors.
The authors declare that they have no conflict of interest.
The first author was supported in this research by an award from the NASA New (Early Career) Investigator Program in Earth Science, NNH13ZDA001N-NIP, managed by Ming-Ying Wei and Lin Chambers. The research was conducted at both the NASA Ames Research Center in Moffett Field, California, and the NASA Goddard Space Flight Center in Greenbelt, Maryland. The doubling and adding radiative transfer code used in this work was developed at the NASA Goddard Institute for Space Studies, with recent updates by Brian Cairns and Jacek Chowdhary at that institution. Edited by: Sebastian Schmidt Reviewed by: Feng Xu and Odele Coddington