Stereoscopic Height and Wind Retrievals for Aerosol Plumes with the MISR INteractive eXplorer (MINX)

2.1. Instrument

The MISR instrument flies aboard Terra, the flagship satellite in NASA’s Earth Observing System (EOS) fleet. Terra is in a near-polar orbit at an altitude of 705 km, descending on the dayside with an equator crossing of 10:30 am local time, and completes an orbit in about 99 min. Each circuit of the Earth falls into one of 233 overlapping “paths” which repeat precisely every 16 days. Since Terra’s launch in December 1999, data have been acquired for nearly 73,000 orbits. Enough fuel remains for operations until at least 2018.

MISR has a unique design for imaging the Earth, using nine push-broom cameras designated Df, Cf, Bf, Af, An, Aa, Ba, Ca, and Da, where An is the nadir-viewing camera and the letters “f” and “a” refer to forward-viewing and aft-viewing, respectively. The camera viewing angles relative to nadir are 70.5° (D), 60.0° (C), 45.6° (B), and 26.1° (A). This design allows the instrument to image every scene at nine viewing zenith angles in line with the ground track of the satellite, in seven minutes. The width of the MISR swath common to all cameras is about 380 km, providing global coverage every nine days at the equator and every two days near the poles [37].

Radiance data are acquired in four spectral bands in each camera. The central wavelengths and effective bandpasses are 446.4 ± 41.9 nm for blue; 557.5 ± 28.6 nm for green; 671.7 ± 21.9 nm for red; and 866.4 ± 39.7 nm for NIR. The radiances are mapped to the Space Oblique Mercator (SOM) projection so that ground sample spacing is 275 m in 12 of MISR’s 36 channels (in the red band of all nine cameras and in all four bands of the nadir camera) and at 1100 m in the remaining 24 channels. More information about the MISR instrument can be found in [12,37].

2.2. Data Products

Raw MISR data are processed and stored at the NASA Langley Atmospheric Science Data Center. Available datasets include Level 1 radiance and geometric products, Level 2 aerosol and cloud products, Level 3 globally gridded statistical summaries, and ancillary datasets generated once and used in routine processing [38]. Level 1 and 2 (swath) datasets are divided into 180 “blocks” per orbit, with each block spanning 140.8 km along-track. Typically about 144 of these blocks are populated with data, their positions in the swath varying with season so they occupy northernmost positions on 21 June and southernmost positions on 21 December. All MISR products are written in HDF format and are freely downloadable [39]. A description of the algorithms for data product generation can be found in [40], and data product specifications for the HDF files can be found in [41]. Because Level 1 radiance products are central to the stereo retrieval process, they are described in greater detail next. A brief description of the operational stereo product is also included to provide a basis for comparison with MINX stereo retrievals.

Two sets of Level 1 radiometrically- and geometrically-calibrated data products are produced for every MISR orbit. Ellipsoid-referenced imagery (GRP_ELLIPSOID) projects the radiances to the surface ellipsoid, which corresponds closely to mean sea level [12,42]. For this data set, features above ellipsoid level, such as clouds and mountains, appear to move when viewed at different camera angles because of parallax. Terrain-referenced imagery (GRP_TERRAIN) is projected to a digital elevation model (DEM) [12,42]. In this projection, mountains and other features on the Earth’s surface appear fixed in position when successive camera images are viewed. However, elevated clouds and aerosol plumes still appear to move between camera images. In the along-track direction (the direction parallel to the ground-track of the satellite), this motion is a combination of apparent motion due to parallax and real motion due to wind [14,15]. In the across-track direction (normal to the along-track direction or right-left across an image), motion relative to the surface is due only to wind. In cameras with more oblique viewing angles, gaps are sometimes visible in terrain-referenced images as a result of line-of-sight occlusions caused by steep terrain.

The stereo retrieval algorithms in the operational MISR L2 cloud products and in MINX utilize the multiple views acquired by MISR to compute the heights and motion-vectors of clouds and other features above the Earth’s surface using a purely geometric, stereoscopic method [16]. The operational stereo product retrieves cloud-top heights and winds automatically for every orbit using ellipsoid-referenced imagery to produce a dataset appropriate for studying global statistics of cloud heights and winds. Consequently, the underlying algorithms must be very fast and use a fixed set of processing parameters that are applied to all scenes equally [17]. Because they are automatic, the operational algorithms lack the advantage of interactivity and human-in-the-loop analysis by which features can be isolated for special study, and the operational algorithms cannot take advantage of visual cues in a scene from which wind direction can be inferred. Instead, both the along-track and across-track components of the wind speed are first derived at relatively coarse spatial resolution in order to mitigate the effects of noise [43]. These results are then applied to initial (zero-wind) retrievals of cloud-top height to produce wind-corrected heights at 1.1 km horizontal resolution. To extract wind direction and the along-track component of wind speed requires well-registered Df/Da (±70°) and Bf/Ba (±46°) camera imagery [43]. Including the most oblique (D) cameras is an essential element of the automatic retrieval strategy, because only these views can take advantage of earth curvature to resolve wind speed [14,15]. These requirements sacrifice some of the redundancy available in MISR’s multi-camera design.

3.1. History

MISR’s operational stereo product does not generally retrieve heights and winds with the precision and fine resolution required for detailed study of small aerosol features such as smoke or volcanic plumes. In order to effectively utilize the redundant, multi-angle, stereoscopic capabilities of MISR, the MINX interactive visualization application was developed to complement the operational stereo product by providing users a tool to retrieve height and wind information interactively with both the wind and height reported at high spatial resolution and enhanced precision. MINX is written in the Interactive Data Language (IDL) [44]. It enables a user to explore the structure and dynamics of aerosol features having visible structure in multi-angle images by iterating on stereo retrievals using different combinations of wind direction and other parameters. The MINX program can be downloaded from the Open Channel Foundation website [45] and is available for Mac OS X, MS Windows, and Linux platforms. Since 2006, MINX has been used under the auspices of the MISR Plume Height Climatology Project (MPHCP), aimed at creating an aerosol injection height climatology to support wildfire, climate change, and air quality studies [21]. To date, about 13,000 smoke plumes have been digitized from selected parts of the 13-year MISR data record, and retrieved heights, winds, and other information have been compiled into a publicly accessible, online database [27]. NASA and the US Environmental Protection Agency (EPA) supplied original funding for the project.

3.2. Data Requirements

MINX requires all nine camera files of terrain-referenced imagery (GRP_TERRAIN) to derive accurate heights and winds over land [42]. For aerosols over open ocean, ellipsoid-referenced imagery (GRP_ELLIPSOID) must be used. This is because the DEM and the ellipsoid are identical over the ocean and terrain-referenced imagery is not available for analysis. An additional MISR Level 1 data product is needed for MINX stereo retrievals. The geometric parameters product (GP_GMP) contains zenith and azimuth viewing angles for each camera at 17.6 km resolution, but they are interpolated to 275 m during stereo retrievals. This geometry is essential for modeling ray-paths from the surface to the satellite. The MISR Ancillary Geographic Product (AGP) is one further product MINX requires to perform stereo retrievals. This dataset contains the Digital Elevation Model (DEM) and surface feature IDs that include land/water identifiers. These data are stored at 1.1 km spatial resolution, and a single file is available for each of the 233 different MISR paths.

MINX does not require MISR Level 2 products for retrieving heights. However, three products can optionally be loaded and displayed. Optical depths and other parameters from the aerosol product (AS_AEROSOL) can be displayed as histograms for a digitized region, and smoke, dust, cloud, and land masks from the Support Vector Machine (SVM) datasets [46] in the cloud classifiers product (TC_CLASSIFIERS) can be overlain on radiance imagery to assist in identifying aerosol types. Finally, stereo heights and winds from MISR’s operational stereo products (the older TC_STEREO and newer TC_CLOUD) can be compared with MINX retrieval results on height/wind profile plots.

3.3. The MINX GUI

MINX presents the user with a graphical user interface (GUI) that includes a large viewing window in which the nine camera images from a portion of an orbit can be displayed in an animation loop using play/pause movie controls. This animation capability is one of the most important features of MINX because it enables study of the 3D context of a scene and allows the user to detect scene content that would otherwise be difficult to discern in a single, nadir-view image from a conventional satellite instrument such as MODIS. During initial loading of camera images into the animation window, radiance values are converted into top-of-atmosphere bi-directional reflectance factors (BRFs) given by the usual relation:

The animation window is the workspace in which a user digitizes the boundary of a polygon inside which heights and winds are retrieved on a grid of regularly spaced points. Figure 1 shows the result of digitizing the outline of a plume (dashed aqua line) and a wind direction (yellow arrow along plume axis) and of computing wind-corrected heights. Red dots represent MODIS thermal anomalies from the MOD14 product, often associated with fire hot spots [47,48], which can be processed using a MINX utility function and then displayed on the MISR image. The animation window shows the MISR nadir camera imagery in its original SOM projection. The motion of the satellite relative to the animation window is from the top to the bottom as the Terra satellite descends on the day lit side of the Earth. For most scenes, such as the one shown in Figure 1, this means that the image is oriented approximately north-south, with north toward the top of the image and west to the left. Selecting the Geography toggle on the animation window, overlays a latitude-longitude grid and geographic outlines, to assist in orienting the user.

The wind direction was defined using several non-co-linear points to illustrate that MINX interpolates the line with a cubic spline. Wind directions are computed and stored at uniform spacing along this curve. When stereo retrievals are performed on a pixel inside the digitized polygon, the wind direction from the point on the curve nearest that pixel is used. Figure 2a,b shows the corresponding height and wind profiles generated by MINX for the digitized plume in Figure 1. The height profile in Figure 2a shows zero-wind heights (red points), wind-corrected heights (blue points), and terrain heights (green line), all referenced to sea level. The wind profile in Figure 2b shows the components of the wind in the across-track (green points) and along-track (magenta points) directions. In this figure, positive across-track motion represents features that move from left to right in the MINX animation window, corresponding to winds that blow from nearly west to east. Positive along-track winds are associated with features moving from the bottom to the top of the MINX animation window, corresponding to winds that blow nearly from south to north. The profiles in Figure 2a,b share a distance axis on which the origin is the first point digitized in the animation window (the aqua circle near the source of the plume at the lower left of the digitized polygon in Figure 1).

In this example, the wind-corrected height of the plume increases from about 3 km above sea level (ASL) near the initial height retrievals to over 5 km ASL in a turbulent pulse of rising smoke above the active fire. Then it drops to under 4 km before rebounding to 5 km ASL at about 80 km downwind. Retrieved heights above the rising smoke may have reduced accuracy if the plume is not in a buoyant state, because the MINX algorithm assumes only horizontal motion. The wind speeds show more variability near the fire than downwind, where the mean cross-track component of the wind, v_ct, temporarily stabilizes at about 6 m·s⁻¹, with an along-track component, v_at, of 3 m·s⁻¹. The vector sum of these speeds $w_s=\sqrt{v_{at}^2+v_{ct}^2}$ yields a total wind speed, w_s, of about 7 m·s⁻¹.

Because all the points in a plume are projected into the plane of the height/wind profiles, there may be multiple plume height, terrain height, and wind speed values at the same linear distance from the initial point. This can produce a spread in data values that can clutter the display, but can represent real variability. To produce a more focused profile, a narrower polygon can be digitized. Alternatively, MINX allows a single line to be digitized instead of a polygon. In this case the line acts as the set of points to be sampled and also provides the wind direction at each point. Details on using the MINX software are provided in the MINX on-line documentation [49] and additional information for users can be found in [50].

5.1. Height, Wind, Parallax, and Disparities

A feature above the Earth’s surface is seen by each of MISR’s cameras over a seven-minute period from nine different angles as the Terra satellite passes overhead. Parallax shift causes the feature to project onto the terrain at different locations in each camera [53]. The projected location will shift increasingly toward the top of MISR images as they are viewed successively in MINX in forward chronological order (Df, Cf, Bf, Af, An, Aa, Ba, Ca, Da). The displacement in feature location between two cameras is its disparity and consists of an along-track displacement parallel to the ground track of the satellite and an across-track displacement in the orthogonal direction. The measurement of these two components of disparity provides the raw data for computing stereoscopic heights and winds [16].

In the general case of a feature that is not stationary, there are three unknowns to be determined: height, wind speed in the along-track direction, and wind speed in the across-track direction (Both MINX and the MISR operational stereo products assume no vertical motion [14,15], a reasonable assumption in most natural situations. In the presence of a large component of vertical motion, retrieved heights will be less accurate.) The problem is under-determined (two equations and three unknowns) for a single camera pair, but adding a third, non-symmetric, camera provides a solution [14,15]. This is the approach used in the MISR operational stereo products where all three unknowns must be determined automatically.

5.2. Retrieving Height with No Wind

In the special case of a feature that is motionless, its across-track and along-track disparities due to motion are zero, and its across-track disparity due to parallax is zero, while its along-track disparity is non-zero and due entirely to parallax. The single unknown, height, can be approximated using the relation:

5.3. Retrieving Height with across-Track Wind Only

If there is a component of wind across-track but the along-track component is zero, then there are two unknowns that do not depend on one another, height and across-track wind speed. The two measurements, across-track disparity due to motion and along-track disparity due to parallax, are also independent. The determination of height in this case is identical to the “No Wind” case—it is uniquely determined by the along-track disparity, since the only contributing factor is parallax. The determination of across-track wind speed is uniquely determined by the across-track disparity. One can approximate across-track wind speed by converting across-track disparity to map distance then dividing by the time between the two cameras’ observations. In practice the calculation must consider Earth curvature (which is more important near the edges of the image swath), terrain height, and other factors.

5.4. Retrieving Height with across-Track and Along-Track Winds

When both across-track and along-track components of wind are present, the across-track component of motion can still be estimated from the across-track disparity between two cameras using the method described above. However, the along-track disparity includes contributions from parallax due to height and from real displacement due to along-track wind. Consequently a wind-corrected height must be computed that is different from the zero-wind height. There are now two unknowns remaining (height and along-track wind) with only one measurement (along-track disparity) available to untangle them.

An important innovation in the MINX stereo retrieval algorithm is the ability to incorporate a user-defined wind direction, which provides an additional constraint to the problem. This is accomplished by requiring the user to select, or “digitize,” two or more points with the mouse that define a straight or curved line representing the plume’s motion in response to the mean atmospheric wind. For any point on this line, the wind direction can be represented by the slope of the digitized line, which is the ratio of the along-track and across-track transport distances as well as the ratio of the wind speeds. In other words:

5.5. Retrieval Algorithm Overview

The stereo retrieval algorithm used in MINX is applied independently to each sample point inside a digitized polygon or on a digitized line. At each point, the stereo retrieval is performed independently for each of several camera pairs to take advantage of MISR’s multiple-camera redundancy. The An (nadir) camera, which serves as the reference image for all camera pairings, is displayed in the MINX GUI animation window during digitizing. The An camera is used as the reference for two reasons. First, at the center of the swath, the L1B2 processing projects features in the An camera directly downward (Θ = 0°), whereas at the margins of the swath Θ ≈ 18°, so a 5 km high feature is projected only 1.6 km from its actual vertical position. By contrast, C camera zenith angles vary from Θ = 60° to 62°, causing the projected location of a 5 km high feature to deviate from its true location by 9 km. This means that the An projection has the smallest parallax and best represents the actual location of features above the terrain. Second, MINX attempts to perform stereo retrievals using as many camera pairs as possible. Because the An camera is centrally located, it provides the best choice for use with both forward-looking and aft-looking cameras. The disadvantages of using the An camera are that atmospheric path length is smaller than for the other MISR cameras so that optically thin aerosols are less easily discriminated from the background, and the swath width of the An camera is slightly narrower than the other cameras, so features at the edge of the MISR swath might not be captured in the nadir view.

MINX allows the user to choose which cameras to pair with the nadir camera for image comparison. In practice, the choice depends largely on considerations of plume topology and processing time. Features on topologically complex or rapidly changing cumuliform surfaces become increasingly distorted due to perspective change and temporal evolution as the viewing zenith angle of the comparison camera increases from A to D. Differences in shadows also become accentuated. This challenges the image matcher, described below, and increases the likelihood of spurious matches. Using only A and B cameras is indicated when plume topology is very complex and rapidly changing, as in the eye-wall of a hurricane to give an extreme example. Adding the D cameras generally improves retrieval results only in cases where the plume surface, such as a boundary layer cloud field, is relatively flat. Including cameras with large view angles also results in greater than linear increases in processing time, because more oblique angles produce larger parallax shifts and require larger comparison images in which to perform image matching as discussed in the next section.

5.6. Image Matching

MINX uses a template-based image matcher whose cost metric is the Pearson correlation coefficient given by:

The image-matcher is applied to red-band data in two passes of a pyramid scheme to reduce computation time. In the first pass, a template from the reference image and a target from the comparison image are resampled to 1.1 km in each dimension using simple pixel averaging. In the second pass, the full 275 m resolution of the red band is used. Once a target pixel in the comparison image is found whose patch best corresponds with the reference template, the match is refined to sub-pixel resolution by fitting a cubic-polynomial surface to the correlation matrix, interpolating the coefficients to a 0.2 pixel grid and locating the sub-pixel grid coordinate with the largest correlation coefficient.

It is more accurate to attribute correlation coefficients and matcher results to entire template-sized areas than to single pixels at the center of the matcher templates. Figures 3 and 4 illustrate this on two different cloud scenes by varying the size of the template used in the retrieval. In Figure 3a, a single cloud less than 1 km in diameter and 1 km above the surface is centered in the image. The rest of the scene consists of mottled, dark terrain. The dashed cyan box encloses the comparison region where matching was attempted. Figure 3b–e shows color-coded, zero-wind heights at pixel locations spaced by 550 m (two 275 m pixels) retrieved with successively larger matcher templates, which are user selectable and listed in Table 2. Although the cloud itself is smaller than any of the templates, the area over which MINX retrieves heights extends outside the bounds of the cloud and is approximately the size of the template. This is best understood by inspecting Figure 3a, in which a red square the size of the Medium image matcher is placed over the cloud. The center pixel of the matcher template, where the result of the correlation operation will be placed, is indicated by the red dot in the center of the template’s outline. Although the center pixel does not touch the cloud, pixels on the edge of the template that include the cloud generate a strong response that dominates the correlation.

Figure 4a shows an overcast scene with complex cumulus features whose zero-wind heights vary from 2 to 12 km. Figure 4b–e was made in an identical fashion to the panels in Figure 3. The predominant effect of increasing template size on the cloudy texture in Figure 4 is to spatially smooth the details of the height field, illustrating that the image-matching process operates like a smoothing filter. This is most clearly seen in the comparison of Figure 4b,e.

Image matching is easily the most CPU intensive step in the stereo retrieval process. The CPU time required to compute disparities with different size matchers is highly dependent on hardware. For example, on a 3.4 GHz Quad-Core iMac with OS X 10.8 (Mountain Lion) and 16 gigabytes of memory, the elapsed time to complete the image-matching step on a large smoke plume containing over 6,000 points is 88 s for the Small matcher and 176 s for the Large matcher. The CPU time is approximately linear with matcher area.

The disadvantages of the larger templates can sometimes be offset by their ability to reduce noise yielding more robust correlations that can significantly improve retrieval coverage. Smaller matchers are most appropriate when fine spatial detail is important and a scene has good data quality or has small-scale variations in plume height. Selecting the appropriate template size for a scene is a matter of user experience and, often, trial-and-error.

5.7. Forward Modeling

Stereo retrievals are performed in MINX using a spherical Earth model with locally superimposed terrain heights. Separate algorithms are used for zero-wind retrievals and wind-corrected retrievals. Zero-wind heights are computed analytically, but wind-corrected heights and wind speeds are computed in a forward modeling step that is applied independently to along-track and across-track components of feature motion. Across-track winds must also be modeled, because the geometry is more complicated than the simplifications in the above discussions suggest.

Figure 5a illustrates the geometry for the general case of a feature whose motion along-track (from P₁ to P₂) is opposite to the direction of satellite motion. The camera pair includes the An (nadir) reference camera (Cam₁) and an aft-looking comparison camera (Cam₂), which produces a positive time difference (Δt = t₂ − t₁ > 0) between observations. Constants for this case include local Earth radius of curvature R_e; terrain heights E₁ and E₂ at ground locations T₁ and T₂ where each camera projects the feature; and along-track components of zenith angle for each camera, Z₁ and Z₂. Figure 5b is a detailed view of the dotted orange box in Figure 5a, generalized for camera “n”, which corresponds to the comparison camera. Important intermediate variables include angles μ₁ and μ₂ subtended by a vertical through earth’s center and with vertices at feature point locations P₁ and P₂, respectively (seen in Figure 5b), and several angles each with vertices through Earth’s center: angles Φ₁ and Φ₂ between feature point locations and verticals through the terrain points; angle Ω between P₁ and P₂; angle β, subtended by the along-track disparity vector; and d_w, the distance the feature travels between observation points P₁ and P₂. The single pertinent measurement is the along-track component of disparity, D_m. Feature height above the Earth’s surface, H, is the independent variable in the forward modeling scheme, and wind speed, W, is the dependent variable.

The procedure for determining wind speed (W) given an arbitrary feature height (H) can be summarized as follows:

• Determine angles Φ_n from Figure 5b

  • From the law of sines: (R_e + H)/sin α_n = (R_e + E)/sin μ_n

  • α_n = π − Z_n

  • μ_n = sin⁻¹(sin α_n × (R_e + E_n)/(R_e + H))

  • Φ_n = Z_n − μ_n

• Determine W from Figure 5a

  • β = D_m/(R_e + (E₁ + E₂)/2)

  • Ω = β – Φ₂ + Φ₁

  • d_W = Ω × (R_e + H)

  • W = d_W/Δt

The relationship between height and wind speed is linear, so the forward modeling procedure must be performed using at least two height values in each of the along-track and across-track directions to define a pair of linear equations: W_across = f_across(H) and W_along = f_along(H). In practice, several values of height are used and a regression is performed to ensure that the relationship is indeed linear. The intersection of these equations with the equation for the user’s input wind direction, defined by the slope of the direction line (S in Equation (3)), provides a unique solution to the retrieval problem. The slope of the W_across = f_across (H) equation is small, allowing the intercept to stand in as an approximation for the wind speed.

The two linear equations can be represented in 3D-space as a single “solution line”. Figure 6 shows a data cube that represents the results from retrieving winds and wind-corrected height at a single sample point for a single camera pair. A triplet of height, wind speed across-track, and wind speed along-track coordinates identifies each point in the cube. The data value at each 3D coordinate is the difference between the fixed disparities measured by the image matcher and the disparities appropriate to each height/wind-across/wind-along coordinate. The red “Height-wind solution line” represents the set of modeled heights and winds whose disparities exactly match the measured disparities; that is, for every point on the line, the disparity difference is zero. This ambiguity is resolved, as indicated above, by insertion of the green plane representing the user-specified wind direction (yellow arrow). The “Height-wind solution point” marks the intersection of the solution line with the wind direction plane and is the unique solution to the height, wind retrieval problem in MINX.

The data cube is useful for explaining several characteristics of height and wind interactions. For example, the zero-wind height can be found by intersecting the solution line with a plane through the zero-wind axis and parallel to the height, wind-speed-across (XZ) plane. In other words, at an along-track wind speed of zero, the height intersected on the solution line is the zero-wind height. The solution line slopes down in the positive, along-track wind direction (+Y), that is, toward the “top” or north of a MISR swath, opposite to the direction of satellite motion. Therefore, as wind speed toward the north increases, the height must decrease below that of the zero-wind height. Conversely, as wind speed toward the south increases, the height must increase above that of the zero-wind height. It is important to note that zero-wind heights are fictitious and can have values that place them below the terrain surface. When this occurs, the user-supplied wind direction must have a component pointing toward the bottom of the image, in which case the wind-corrected heights will be greater than the zero-wind heights and will be corrected to a position above the surface (see Bodele dust case below).

The solution line lies in a plane parallel to the height/wind-speed-along (YZ) plane and can possess values in only one-half the data cube. Consider a feature with a real component of motion toward the right (positive, across-track) side of a MISR image as represented by the data cube in Figure 6. Any user-specified wind direction with a positive, across-track component (+X) will intersect the height-wind solution line and produce a solution. Conversely, an aerosol feature moving in a negative, across-track direction (solution line in the left half-cube) should produce no solution for the user-specified wind direction shown. This provides a useful test during digitizing of ambiguous scenes for determining whether a positive or negative across-track wind direction is more likely correct.

5.8. Determining Consensus Height and Wind

When all camera pairs have been processed for a sample point, the retrieved results for the cameras that produced successful matches are inspected to determine a consensus height and wind. This process finds the mean height and wind speed values of those camera pairs whose results cluster most strongly around median values. Median values are used to mitigate the degrading effects of outliers. Two clustering passes are executed, and in each pass height-wind results are discarded if they fail to fall within a threshold distance of the median values. Threshold distances are dynamically computed from linear equations whose independent variables are the median height and wind speed being tested. In the first clustering pass, the slope of the height equation is set to 0.45, and its intercept is 0.75 km. In the second pass, the slope and intercept are 0.3 and 0.5 km respectively. For the winds, the slope and intercept are 1.5 and 15.0 m·s⁻¹ in the first pass, and in the second pass they are 1.0 and 10.0 m·s⁻¹. Wind speeds are more sensitive to variations than heights, so their thresholds are kept loose.

5.9. Spectral Band

High spatial resolution data are essential for obtaining high vertical resolution stereo heights. MISR was designed to routinely measure radiances at high resolution (275 m) in only 12 of 36 channels because of limited instrument data bandwidth [12]. This default setting is called “global mode”. MISR can also retrieve high-resolution data in all 36 channels for a limited time, amounting to about 300 km along-track, on each orbit. This setting is “local mode”. The red band was chosen as the high-resolution band in global mode to maximize the contrast between atmospheric aerosols and the Earth’s surface over both water and land [12].

Grasslands, deserts and other scenes can be relatively bright in the red band. When terrain features in these scenes are visible through an aerosol layer, the red band is often not the best choice for retrieving stereo heights [23]. The “true-color” RGB images in Figure 7a–d show a small smoke plume over grasslands near Skukuza, South Africa. These four panels are high-resolution (local mode) images from the An, Aa, Ba and Ca cameras respectively. The yellow arrow in Figure 7a represents the wind direction applied for the wind-corrected height retrieval. The opacity of the smoke increases with camera zenith angle as the optical path length through the smoke increases. The An reference camera, which requires a strong aerosol signal for image matching, sees terrain features through the smoke, making matching difficult. Note that the position of the plume also moves toward the top of the image relative to the ground because of greater parallax in the more oblique cameras.

Figure 8a–d shows the same local mode scene from the Aa camera in gray-scale for blue, green, red and NIR bands respectively. As wavelength increases, atmospheric scattering decreases, and the terrain becomes more visible through the smoke. Zero-wind height retrieval results for each local-mode band are shown in Figure 8e–h, and wind-corrected heights are shown in Figure 8i–l. Also note that wind-corrected heights are lower than corresponding zero-wind heights, reflecting the fact that the wind direction has a component directed toward the top of the image in this case. These figures show that stereo retrieval coverage deteriorates dramatically as wavelength increases. Just as significantly, blue-band, wind-corrected heights are a few hundred meters greater than corresponding red-band heights. In certain cases, the greater sensitivity of the blue band to thinner aerosols allows aerosol features to be matched that correspond to a higher altitude for the plume. For scenes like this one, the blue band is a better choice for image matching, so MINX allows the user to select a blue-band retrieval algorithm when performing stereo retrievals.

Because local mode data are not available for most MISR scenes, which are acquired in global mode, MINX routinely produces 275 m “pseudo-high-resolution” images in all channels displayed in the animation window. This sharpening is accomplished by subdividing each 1,100 m pixel into 16–275 m pixels and assigning them BRFs in the same ratio as in the equivalent 275 m red band pixels for the same camera. The mean BRF of the 16 sharpened pixels is maintained at the level of the original 1,100 m pixel. The panels in Figure 9 are identical to those in Figure 8, except that they use sharpened global mode data rather than local mode data. The gray scale BRF images of the blue, green and NIR bands possess a blocky texture caused by the sharpening algorithm, although the smoke is affected less than the terrain. Heights retrieved using blue and green bands still show significant improvement over red band heights, although they are inferior to equivalent local mode retrievals. Heights retrieved using the NIR band (Figure 9h) are mostly blunders derived from matches on the blocky, sharpened terrain.

6.1. Interpreting Wind Direction

Wind direction is arguably the most important user input to MINX. An incorrect wind direction assigned to a fast-moving aerosol feature can result in wind-corrected height errors of several kilometers. Whereas apparent across-track motion is generally a reliable indicator of true across-track motion, in most cases it is impossible to determine whether the apparent motion of an aerosol feature includes a true component of motion in the along-track direction. In the case of plumes, direction-of-motion can usually be inferred from scene context. But for water or other aerosol “clouds”, without an obvious connection to the ground, few clues may be present. Exceptions can sometimes be found when carefully inspecting the MINX animation sequence in forward chronological order. For example, if a feature appears to move from the top toward the bottom of the image, then real motion toward the bottom due to wind is present and exceeds apparent motion toward the top due to parallax. This typically occurs only in cases with high wind speeds and low feature height (see Bodele dust case below). Other useful sources of information for determining wind direction are shadows cast by aerosol features onto the terrain. The motion of a shadow relative to the ground indicates the direction of true motion, both across-track and along-track.

6.2. Sensitivity of Height to Wind Direction

Figure 10a–c shows three, large, excellent quality smoke plumes in Alaska during a two-week period in early July 2004. White arrows indicate the true wind direction representative of each, as determined from scene context. Red patches are regions where the plume tops are relatively flat. These patches were digitized multiple times with different assumed wind directions at multiples of 10° indicated by the yellow arrows. Each patch yielded more than 200 successful and similar-valued zero-wind heights (shown in red) and a variable number of wind-corrected heights (success in this context simply means that the MINX algorithm returned a height value). The results of this analysis are summarized in Figure 11.

The fraction of zero-wind retrievals that produced successful wind-corrected heights (Figure 11a) and the median (Figure 11b) and standard deviation (Figure 11c) of wind-corrected heights were computed and are shown color-coded for each of the plumes in Figure 10. The true wind directions are indicated with vertical arrows. The x-axis of each graph represents assumed wind direction measured in degrees, with zero corresponding to the positive along-track direction (toward the top of the MISR swath) and +90° and −90° corresponding to across-track directions. Zero-wind heights correspond to retrievals that assume all motion is in the across-track direction (±90° in Figure 11b). Because the MINX algorithm cannot retrieve heights corresponding to directly along-track wind, the values on all panels near 0° and 180° in Figure 11 are equal to zero. A glance at the data cube in Figure 6 reveals why the MINX algorithm fails when attempting retrievals in the purely along-track direction. When the across-track component of the wind is zero, the solution line lies in the height/along-track wind (YZ) plane through the Zero-wind axis, and cannot uniquely intersect any user-provided wind direction. However, data quality begins to deteriorate before across-track motion reaches exactly zero, because the plane containing the wind direction intersects the solution line at a small angle, leading to increased sensitivity of height and wind speed to noise and small errors in the assigned wind direction.

As shown in Figure 11a, successful retrievals of wind-corrected heights are present when the assumed wind direction is either left or right of the along-track direction. In other words, retrievals are possible only when the assumed wind direction is in the same half-plane occupied by the true wind direction. The fraction of successful retrievals varies from case to case, but is generally high within 60° of the across-track directions (±90° on the x-axis). Interestingly, coverage remains nearly 100% for the purely across-track plume corresponding to Figure 10b, shown in blue, over a range of 120°.

The relationship between wind direction and wind-corrected heights is shown in Figure 11b. For all three plumes, regardless of true wind direction, retrieved wind-corrected heights monotonically decline as the digitized wind direction approaches the positive along-track direction. Consider the simplified situation where the across-track disparity gives a fixed value for the across-track wind speed, v_ct. Equation (3) provides a method to calculate v_at directly by simply multiplying by the user-defined slope. The slope is related to the assumed wind direction plotted in Figure 11. If the assumed wind direction is 0°, all the wind is in the purely along-track direction. If the assumed wind direction is 90°, all the wind is in the purely across-track direction. At 45° the wind is divided equally between the along-track and across-track direction. Therefore, as the assumed wind direction tends toward 0°, the fraction of the wind in the (positive) along-track direction increases, leading to a decrease in the wind-corrected heights, for the reasons described earlier.

Finally, Figure 11c demonstrates that the standard deviation of retrieved heights tends to be a minimum near the true wind direction. This is because selection of the correct wind direction yields the best match among the retrieved disparities leading to results that are spatially consistent.

6.3. Negative Heights

Figure 12a shows a large dust storm in the Bodélé Depression in northern Chad, for which MINX retrieves wind speeds in excess of 20 m·s⁻¹ (Figure 12c), with an along-track component of wind directed toward the bottom of the image. This region has been identified as one of the largest dust sources on the planet due to the interaction of the nearby terrain and downward momentum mixing from a nocturnal low-level jet that lifts diatomite deposited from paleolake Mega-Chad [54]. The red, zero-wind heights in the profile of Figure 12b lie 1 km below the blue, wind-corrected points and even below both the terrain level (the green line at 0.3 km elevation) and sea level. Although this is a mathematically valid result, it is not physical. Correcting the heights using the appropriate wind speed (blue points) produces reasonable heights at about 0.5 to 1.0 km above the terrain. Figure 12b shows that the dust plume heights increase from near the surface to about 700 m a distance 100 km downwind from the source and rise slowly but steadily thereafter. Although other researchers have reported a technique for deriving wind speeds from the Bodélé using the two MODIS instruments on the Terra and Aqua satellites separated in time by nearly three hours [55], MINX using MISR provides a nearly instantaneous retrieval of both heights and winds at high spatial resolution.

6.4. Small-Scale Wind Variations

Figure 13a shows the An (nadir) camera image of an ash plume above the Augustine Volcano in Alaska, captured by MISR on 30 January 2006. The volcano itself is visible in the lower left of the image, with the plume extending to the upper right. The clear pattern of ribs diverging bilaterally from the central spine of the plume is suggestive of plume bifurcation, a phenomenon in which wind shear creates rotating vortices that can separate to produce distinct lobes. Bifurcation similar to the type suggested for Augustine has been observed in other volcanic eruptions and has been modeled and discussed in the literature [56].

MINX was used to determine the height of the Augustine plume using a single wind direction. The map of wind-corrected heights and the digitized wind direction are shown in Figure 13b along with the corresponding height profile in Figure 13d. The unusual dichotomy in the heights—approximately 5,500 m on the northwest side and 4,600 m on the southeast—suggests that variation in wind direction may be involved. On the assumption that the ribbing represents the direction of ash transport within vortices, the two lobes of the plume were digitized independently using wind directions parallel to the ribbing. Figure 13c,e shows the resulting wind-corrected height map and profile respectively. On the northwest side, wind-corrected heights have dropped by ∼200 m; on the southeast side, they have increased by 300–400 m. The range in heights has also been reduced substantially, which suggests that the plume is relatively flat. The height changes are consistent with the observation noted above that wind-corrected heights increase as wind direction is increasingly oriented toward the bottom of the image, and heights decrease as wind direction tends toward the top.

7.1. Puyehue-Cordón Caulle Eruption

On 5 June 2011, the Chilean volcano Puyehue-Cordón Caulle began erupting in a series of spectacular events that sent ash plumes more than 16 km into the stratosphere. Thick ash disrupted air traffic as far away as New Zealand and shut down many air carriers in South America. In southern Argentina, thick layers of ash covered towns and farms, endangering people and livestock, and forcing thousands of people to evacuate their homes. The ash plumes from Puyehue-Cordón Caulle were captured in more than 10 MISR overpasses, and those orbits were analyzed using MINX to determine the height and speed of transport of the ash.

Figure 14a shows a 300 km wide MISR An (nadir) camera image of the ash ejected from Puyehue-Cordón Caulle on 11 June 2011. The main plume with retrieved heights around 6 to 7 km, colored red in Figure 14b, is optically dense and narrow and travels eastward. A secondary plume with lower optical thickness and at a much lower elevation than the main plume is colored blue to blue-green in Figure 14b, and is carried toward the northeast. A third, intermediate ash layer is wider than and below the main plume, has retrieved altitudes between 4 and 5 km, and is identified by the yellow color. The gray terrain around the plumes is covered with ash from previous eruptive events. This illustrates some of the structural complexity that can be extracted from MISR data using MINX.

7.2. Wallow Fire

The image in Figure 15a shows the Wallow Fire in eastern Arizona that burned over 1,200 km² and was one of the largest fires in Arizona history. The data shown were acquired mid-morning on 7 June 2011. The green pine forests of the White Mountains stand out against the lighter desert background. At least 10 bluish-colored smoke plumes from individual hot spots can be seen rising from the forests and being blown toward the upper right (northeast). The fires occur at the margins of dark areas that represent burn scars. In this image, the windblown smoke extends into New Mexico.

Figure 15b shows a map of the smoke heights retrieved using the MISR blue-band and the Extra-large matcher template. Terrain heights average about 2,500 m in this part of Arizona, so the smoke reaches a maximum height of 3 km above the terrain. Individual plumes can be distinguished in the height map, but their detail is smeared because of the large template used for matching. Equivalent analysis of this scene using the MISR red band produced much poorer results, mainly due to the brightness of the underlying terrain at this wavelength. The combination of plume heights from MISR and radiative energy flux from coincident MODIS-Terra 4 micron channel “hot spot” observations (e.g., Figure 1) [47,48] can be used to study the thermodynamics of smoke plume injection height [13,26].

7.3. Red Sea Dust

On 24 July 2010, 20 m·s⁻¹ onshore winds lofted large plumes of dust from dry riverbeds along the Red Sea coast of Sudan to elevations of almost 1.5 km. The MISR image in Figure 16a shows the largest plume, extending for 270 km and approaching within 70 km of the Arabian Peninsula. Figure 16b,c shows MINX wind-corrected heights for the core of the plume in map view and in profile for this plume, respectively. In order to improve retrieval coverage and provide smoother results for this example, the smallest sample size and the largest matcher template were used during digitizing. Because the plume lies over both land and water, a MINX feature that allows automatic selection of blue-band retrievals over land and red-band retrievals over water could have been employed. However, in this case, the red-band produces better results over land due to the color and optical density of the dust.

The wind-corrected height profile in Figure 16c shows the dust rising very rapidly from the source area and reaching its maximum height within 5–10 km downwind. It lingers at this height until reaching the seacoast 40 km from the origin of the profile. Then the plume begins to settle until it sits within a few hundred meters above the water surface at the 170 km mark. The rapid rise over land and persistence of the plume at height may be due to thermal upwelling of air heated by sand. The decline in heights offshore could reflect the boundary layer height, which is generally much higher over desert than adjacent water during the daytime.

Figure 16d shows that total wind speed, which is the vector sum of the along-track and across-track wind speeds, increases with distance from the source, reaching its maximum of about 30 m·s⁻¹ 100 km downwind. Note that the ratio of across-track wind to along-track wind is determined by the wind direction selected in the digitization process. Since this direction varies along the plume, the ratio of wind speeds varies to match it, and the wind-correction applied to retrieved heights varies as well.

7.4. A Pyrocumulonimbus Cloud over the Silver Fire

The spring of 2013 saw severe to extreme drought conditions in the Western United States. This led to a number of destructive wildfires in the Colorado and New Mexico, including the Silver Fire that was ignited by a lighting strike on 7 June 2013. Figure 17a shows the Silver Fire as it appeared in the MISR An (nadir) camera on 12 June 2013 at 18:09 UTC (12:09 pm local time). The bright white feature located in the lower right of the image is a pyrocumulonimbus (pyroCb) cloud, which is caused by intense heating of the air by the fire itself leading to rapid upward motion of the air until the point where condensation occurs. The subsequent release of latent heat from condensation leads to intense vertical development that can even penetrate into the stratosphere [58]. The dramatic difference in height between the pyroCb cloud and the associated smoke plume is clearly evident in Figure 17b,c. The plume was digitized with a wind direction parallel to the long axis of the smoke plume, extending from the fire source in the lower right to the upper left of the image. It is important to note that this wind direction may not be appropriate for the top of the pyroCb due to the possible presence of atmospheric wind shear. Even so, Figure 12c shows that the pyroCb reaches an altitude of almost 12 km above sea level (ASL), compared to the surrounding smoke that reaches only about 7 km in the vicinity of the pyroCb. An important advantage of MINX compared with common radiance-based passive remote sensing techniques is that the stereo retrievals are insensitive to the presence of temperature inversions that occur both at the top of the troposphere/bottom of the stratosphere, as well as near the poles and in the stratocumulus cloud regions of the world [36].