MRO-CRISM 2006-2008 MARTIAN CLOUD MAP RETRIEVALS.
D. R. Klassen, (klassen@rowan.edu), B. D. West, Rowan University, New Jersey, USA.

Introduction
There in an inherent difficulty in the visible wavelength
(VIS) and near-infrared (NIR) when one moves from a
technique of tracking cloud positions and getting semiquantitative relative thicknesses to retrieving full optical depth measurements that is much less problematic
in other wavebands such as ultraviolet (UV) and thermal infrared (TIR); namely in the VIS-NIR one needs
to properly characterize the intrinsic surface reflectance
in order to complete the radiative transfer modeling.
Since the spectra are not easily separable into surface
and aerosol components, there are two primary techniques one can use to get an approximate surface spectrum: find your region of interest on another day you
believe to be free of cloud cover and use the retrieved
spectrum as the surface, or find another “nearby” region
in the same image that appears to be similar enough to
your region of interest and appears free of cloud cover
and use that spectrum as the surface proxy. Neither of
these is usable if one is going to scale up the cloud measurements to the entire globe of Mars. Additionally, the
first idea requires that the surface reflectance remain relatively static in time while the second requires surface
reflectance to vary slowly across a scene of interest.
For the past several years we have been working on
devising and improving a technique to retrieve surface
reflectance spectral signatures without any a priori assumptions about the non-variability of the surface itself.
Our only assumption is that all surfaces can be decomposed into a finite set of constant spectral endmembers.
While we have seen limited success on our ground-based
data (due primarily to significant variation in signal-tonoise and various calibration difficulties) we have begun
to see promise on spacecraft-based data.
In this paper we will briefly outline the technique and
present retrieved cloud optical depth maps that will span
an entire martian year and discuss their validity relative
to the current understanding of major cloud cycles.

The Data
We used NIR spectral data taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM)
in its multi-spectral mapping mode. This mode collects data in only 74 wavelengths using subsets of wavelengths from both of its gratings so the spectra nominally
cover the range 0.362–3.920 µm. In this mode the frame
rate of data collection was 15 to 30 Hz along track and
spectra are binned 5:1 or 10:1 cross-track giving a spatial

resolution of about 100 or 200 m (Murchie & CRISM
Team, 2007).
For this work we took spectra from about 20 days in
order to build a (still rather sparse) mapped image cube
(longitude by latitude by wavelength). Spectra were averaged down to a spatial resolution of 1/8◦ × 1/8◦ in order
to reduce the number of points to make computation
feasible. We also reduced the spectral range down to
1.559–3.9235 µm, leaving out the martian atmospheric
CO2 band between 1.875–2.139 µm which tends to confuse the surface recovery technique (Klassen, 2016). So
far we have created 6 such maps that span a martian
year; details on these image cubes are in table 1.
To compute the surface spectral endmembers we created a seventh image cube by zonally averaging each
day of input data then stacking the resulting latitude by
wavelength sets to make a latitude by date by wavelength
image cube. Doing this allows us to run the surface recovery technique across all times but reduces the spatial
information to a more manageable size.

Surface Endmember Recovery
In order to pull out the most spectrally “pure” surface endmembers we used a multi-step process: principal components analysis (PCA) to map the spectra
into a new space based on the internal variation of
the data which also reduces the dimensionality of the
problem (Klassen et al., 1999; Klassen, 2016), target
transformation (TT) to map target mineral spectra in the
PC-space and expand the data cloud (Bandfield et al.,
2000); construct the smallest volume around the resulting cloud using a combination of the Quickhull (Barber et al., 1996) and N-FINDR (Winter, 1999) algorithms; Hyperplane-based Craig Simplex Identification
(HyperCSI) (Lin et al., 2016) to expand that volume until it has only N + 1 vertices around the cloud in the
reduced N -dimensional space.
While PCA is good at finding in-data differences and
“traits”, Klassen & Bell (2001) showed that it was not
enough to pull out purely surface endmembers. The TT
method on top of that is meant to expand the data cloud
by adding spectra that are conceivable surface materials, thereby emphasizing the directions in the PC-space
that correspond to surfaces and minimize the effect of
non-linear and non-surface spectral traits. For this work,
the surface targets are from the MRO CRISM Spectral Library (CRISM Spectral Library Working Group, 2006)
from the Planetary Data System (PDS). The Quickhull
algorithm reduces the number of endmember candidates

MRO-CRISM 2006-2008 Martian Cloud Map Retrievals
Table 1: CRISM Image Cube Information
Name
2006 321
2007 071
2007 170
2007 261
2008 012
2008 167
LS -map

Start Date – End Date

# of Days

Median LS

08 NOV 2006 – 25 NOV 2006
18
136.7◦
01 MAR 2007 – 30 MAR 2007
22
198.8◦
04 JUN 2007 – 03 JUL 2007
30
260.6◦
08 SEP 2007 – 28 SEP 2007
21
316.0◦
28 DEC 2007 – 27 JAN 2008
31
016.4◦
31 MAY 2008 – 25 JUN 2008
21
085.6◦
image of LS by latitude with each day zonally averaged

by finding only those that reside on the data cloud “surface” while N-FINDR then searches those points for
N + 1 vertices that maximize the total volume about
the data cloud. The final step, HyperCSI inflates those
vertices to create the N -dimensional hyper-tetrahedron.
The vertices of this figure are then the “most pure” spectral endmembers in a space defined by the data variation
and all possible surface minerals.

Cloud Optical Depth Calculation
With the recovered surface endmember spectra now
known, the measurement of cloud optical depth is simply a matter of creating a test spectrum from a radiative
transfer model, using ice and dust optical depth and coefficients to linearly combine the endmembers and vary
those seven parameters until a least-squares best fit between model and data is found. This is done for each
point, in each map.
The radiative transfer program used was that of Wolff
et al. (2009) which was built upon the DISORT subroutines (Stamnes et al., 1988). The program inputs include the incidence, emission, and phase angles for each
point—reduced to the image set average for simplicity;
a dust cloud particle effective size (reff = 1.5 µm), effective size distribution variance (νeff = 0.4), and radiative
phase function (from Tomasko et al., 1999); an ice cloud
particle effective size (reff = 2.0 µm), effective variance
(νeff = 0.1), and radiative phase function (from Clancy
et al., 2003); and vertical profiles of pressure and temperature. The program uses the 41-layer profiles from
MGS-TES ick 1629–163.
In practice, running the model for each point in each
map through a full error minimization is computationally prohibitive so we adopted the technique of Wolff
et al. (2011) wherein we make a set of models over a
reasonable range of all seven parameters and use this
as a sort of look-up table—that is we simply look for
the best fit between the data and this subset of possible
models and then record the cloud optical depth for that
point and move on.
The resulting cloud optical depth maps are presented
in figure 1.

Results & Discusion
As we start our sequence in northern summer (figure 1a)
the largest optical depths are over the Tharsis peaks and
Alba Patera and the aphelion cloud belt (ACB) is apparent with optical depth about 0.20–0.30. The ACB then
disappears first followed later by the loss of orographic
clouds as perihelion approaches (figures 1b and 1c).
With the recession of the north polar cap we see
clouds in the far north (figure 1d) with optical depths
less than about 0.20 at the edge of Utopia in the east
and Acidalia in the center and by northern spring (figure
1e) those northern clouds have thickened to greater than
0.25 with the increase in available water vapor.
Finally (figure 1f) we are back to early northern
summer and, while significantly sparser in data than the
other maps, we can just make out orographic clouds and
hints of the ACB.
Quantitatively, we can compare optical depths within
the ACB to other studies. At its height in the 2006 321
map we see 0.2 ≤ τ12.1 µm < 0.3; Smith (2004) measured zonally averaged ice TIR optical depth of ≥ 0.15
with MGS-TES and Mateshvili et al. (2009) measure
zonally averaged ice UV optical depth at 0.3–0.4 in the
cloud belt latitudes at similar LS . All of these results
appear to be generally consistent.
While we see great promise here in that we can
create cloud maps with optical depths that are in agreement with previous results, we do note that there is some
aliasing in the maps—the calculation of clouds over particularly dark regions seems to fail.
We have also not presented any dust optical depth
maps as it turns out those are not giving reasonable
values—the best fit matching seems to break down at
trying to distinguish between bright regions with thin
dust clouds and instead returns them as dark areas with
bright dust above them. We believe this is in part because
there is great spectral similarity between bright regions
and dust. We are investigating methods of restricting
results based on dust optical depth to see if that will
work better.
Finally, we have several more CRISM data files we
can process into maps, redo the endmember recovery,
and perhaps find some distinctions that will help in both
of these issues.

MRO-CRISM 2006-2008 Martian Cloud Map Retrievals

Ice Cloud Optical Depth (

12.1 m)

Ice Cloud Optical Depth (

12.1 m)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

(a) 2006 321

(d) 2007 261

Ice Cloud Optical Depth (

12.1 m)

Ice Cloud Optical Depth (

12.1 m)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

(b) 2007 071

(e) 2008 012

Ice Cloud Optical Depth (

12.1 m)

Ice Cloud Optical Depth (

12.1 m)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

(c) 2007 170

(f) 2008 167

Figure 1: Ice cloud optical depth maps for the six spectral
image cubes; all τ -maps are presented on the same color scale
from 0 < τ < 0.4 for clearer comparison.

Figure 1: -continued- Ice cloud optical depth maps for the six
spectral image cubes; all τ -maps are presented on the same
color scale from 0 < τ < 0.4 for clearer comparison.

MRO-CRISM 2006-2008 Martian Cloud Map Retrievals
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