Abstract

Total-sky imager (TSI) and hemispheric-sky imager (HSI) each have a hemispherical field of view, and many TSIs are now deployed. These instruments have been used routinely to provide a time series of the fractional sky cover only. In this study, the possible retrieval of cloud-base height (CBH) from TSI surface observations is examined. This paper presents a validation analysis of a new retrieval using both a model-output inverse problem and independent, ground-based micropulse lidar data. The obtained results suggest that, at least for single-layer cloud fields, moderately accurate (within ∼0.35 km) CBH retrieval is possible.

Introduction

Cloud-base height (CBH) governs the longwave radiative properties of clouds and affects strongly the incident infrared radiation at the surface. The information on CBH can be used to improve significantly the estimates of cloud optical depth from ground-based radiation measurements (e.g., Barker et al. 2004). This important parameter is not obtained accurately from satellite observations, especially for low or thick clouds. To estimate CBH, one can apply both satellite-derived cloud-top and cloud optical depth, and some additional parameterizations that connect cloud optical depth with cloud geometrical thickness (e.g., Smith et al. 1993). Ground-based active instruments have been typically used to verify satellite-derived cloud-height estimates. For example, both cloud radar and lidar measurements provide valuable information about cloud boundaries (e.g., Uttal et al. 1995). However, these measurements are (i) relatively costly and are (ii) zenith pointing, with a very narrow field of view (FOV). Because of their cost and the resulting lack of availability of cloud radars and lidars, these measurements are limited to a few established surface sites. Further, these zenith-pointing measurements suffer from inhomogeneous sampling characteristics. In other words, derived cloud properties (for a given zenith point) may be different from those obtained for an area surrounding these ground-based instruments (e.g., Barker 1996; Berg and Stull 2002; Kassianov et al. 2005). As a result, difficulties can ensue when satellite-derived (for a given footprint) and surface-based (for a given zenith point) products are compared.

For these reasons, it is desirable to have a method for measuring CBH that avoids the above limitations. This method should both (i) be inexpensive and (ii) provide large FOV observations. A few attempts (e.g., Lyons 1971; Rocks 1987; Allmen and Kegelmeyer 1996) have been made to use paired whole-sky cameras to derive CBH. A general feature of these studies is to define corresponding point(s) that are visible to both cameras, and then to retrieve CBH from a known viewing geometry and distance between cameras (triangulation). However, these studies are restricted by human intervention (Lyons 1971), small (close to zenith) viewing angles (Rocks 1987), and computational complexity/instability of the retrieval scheme (Allmen and Kegelmeyer 1996). Recently, Seiz et al. (2002) applied successfully a ground-based sky imager system with two commercial digital cameras (wide-angled lenses) to derive CBH. Combined accurate calibration and sensor orientation can estimate CBH with high precision (Seiz et al. 2002). However, the limited number of such systems restricts their application to CBH monitoring. In contrast, total-sky imagers (TSIs) are widely deployed. These instruments have a hemispherical FOV and routinely provide time series of the fractional sky cover (Long et al. 2001). Also, such imagers can be applied successfully to estimate the nadir-view cloud fraction (Kassianov et al. 2005).

In this paper, we demonstrate how CBH can be derived from paired ground-based hemispherical observations. The suggested method allows for unattended operation, applies a large FOV (100°), and is only modestly complex. The background for the suggested retrieval is presented in section 2. The suggested approach is introduced in section 3. Section 4 describes the numerical experiments and shows the validation results of the model-output inverse problem. Section 5 discusses the application of this retrieval to real TSI/hemispheric-sky imager (HSI) observations during the Atmospheric Radiation Measurement (ARM) Program’s Cloudiness Intercomparison intensive operational period (IOP). In section 6, a discussion of the suggested approach is presented. Section 7 summarizes the obtained results.

Background

In this section, we provide an overview of the background for the suggested retrieval. The basis of this method is formed by the overlapping (common) area of two adjusted images. The overlapping area is specified by statistical analysis of the images. In our analysis, we use images that correspond to FOVs with 100° (the viewing zenith angle is less than 50°) for the following reasons. First, both the three-dimensional (3D) cloud structure and observation (hemispherical) conditions generate occlusion (one cloud can block the view of another cloud behind it) and perspective (cloud size and shape in the image is viewing-angle dependent) effects (Fig. 1). For hemispherical observations, these effects (e.g., mutual shadowing) are very important for large zenith-viewing angles (close to the horizon); however, these effects can be neglected (as a first approximation) for smaller zenith-viewing angles. Second, for the large viewing angles, different cloud sides can be seen by the sky images (Fig. 1). Thus, the effect of cloud thickness on CBH retrieval can be substantial for large viewing angles. To deduce this effect, one should use observations with a limited FOV.

Fig. 1.

Hemispherical images generated for (left) cumulus and (right) stratocumulus clouds; cloud base (gray) and cloud sides (white). Realizations of cumulus and stratocumulus clouds are obtained from stochastic simulations (section 3).

Fig. 1.

Hemispherical images generated for (left) cumulus and (right) stratocumulus clouds; cloud base (gray) and cloud sides (white). Realizations of cumulus and stratocumulus clouds are obtained from stochastic simulations (section 3).

Overlapping area

Let us consider two TSIs separated in the x direction. The distance between them is Δx1,2. We assume that these TSIs have the same FOV (a cone centered on the zenith with angular width 2α). Also, we assume that a single cloud layer with CBH Hb is located above these two instruments, and CBH does not change significantly within a few hundred meters (Δx1,2∼0.5 km). Therefore, projections of the FOVs onto the horizontal surface at height Hb are circles with the same radius R (R1 = R2 = R). The radius R is connected with the cone zenith angle α and Hb as R = Hbtgα. These two circles partially overlap if Δx1,2 < 2R (Fig. 2). We denote the overlapping area as Sovr. From simple geometrical considerations, one can obtain an equation that links Sovr with Δx1,2 and R. This equation can be written as

 
formula

where Δx* = (Δx1,2/2R) is a dimensionless distance and arcsin(Δx*) is the inverse trigonometric function.

Fig. 2.

Schematic diagram illustrates (top) the geometry of simultaneous surface observations of clouds from two instruments with large FOVs, and (bottom) the corresponding images. Black is used for the overlapping area of two images.

Fig. 2.

Schematic diagram illustrates (top) the geometry of simultaneous surface observations of clouds from two instruments with large FOVs, and (bottom) the corresponding images. Black is used for the overlapping area of two images.

For practical applications, it is convenient to consider the normalized overlapping area S*ovr = (Sovr/S), where S = πR2 is the area of the circle with radius R. From (1a), it follows that the normalized overlapping area S*ovr can be defined as

 
formula

For given values of Δx1,2, α, and S*ovr, one can easily derive CBH Hb by using Eq. (1b). First, the dimensionless distance Δx* is obtained from Eq. (1b). Then Hb is founded as

 
formula

where a = (Δx1,2/2tgα); the parameters Δx1,2 and α are known from the knowledge of the location of the TSIs and their FOV. The dimensionless distance Δx* = f (S*ovr) [see Eq. (1b)] is the single and only unknown. In the next section, we describe a simple way to estimate S*ovr from statistical matching of two adjacent TSI images.

Statistical matching

Image matching is a generic task in many disciplines (e.g., satellite images, side-scan sonar pictures, computer vision), and several research efforts have been devoted to solving this task. Available matching algorithms have different (i) computational complexity, (ii) reliability of obtained results, and (iii) criterion for the similarity of image patches. For example, Markov random field theory (Li 1995) is available for solving computer vision problems (e.g., object matching and recognition, stereo, and motion). We have applied the Markov random field theory to introduce a new stochastic approach to radiative transfer (Kassianov 2003). In our preliminary studies, we start with a simple image procedure. The least squares matching is one of the simplest but widely used processes for image (patches) similarity (e.g., Baltsavias 1991). The minimum sum of the squares of the differences between corresponding values (e.g., pixel gray values) is applied as a criterion for a good match. This criterion has its background in statistics and is theoretically well understood. We use this simple criterion for our initial studies.

Because the two images are obtained simultaneously from two closely located TSIs with the same FOV, the two common point patterns (as viewed from two instruments) have mainly translation differences. Therefore, by relating the images by translation and following a least squares procedure, one can determine the translation parameters (distance between images centers) that best match these two images. Recall that the final output of this analysis is the normalized overlapping area of the two images.

First, we overlap these two TSI images (two circles) completely (Fig. 3): the centers of circles are the same, and the distance between their centers, Δximages, is zero (Δximages = 0). For these initial locations, we calculate the merit function ɛ defined as

 
formula

where η1 and η2 are the intensity value at pixel m, corresponding to the first and second images, respectively, and M1,2 is the number of common pixels that belong to these two images. For our preliminary and simple analysis, we apply binary values of η1 and η2 (for cloud pixels η1 and η2 equal 1; for clear-sky pixels η1 and η2 equal 0). Note that TSI and HSI masks include “clear sky,” “thin,” or “opaque” clouds (e.g., Pfister et al. 2003; Sabburg and Long 2004). For this study, we concentrated mostly on cases with the opaque clouds. To specify thin clouds as having clear sky or clouds, visual inspection of the original (color) TSI images is used. We denote the common area (search area) of these two images as Sovr,images. Note that for the complete overlap of two images, the common area Sovr,images is equal to the area of a single image Simage (S1,image = S2,image = Simage). Both the common area Sovr,images and the number of common points M1,2 will decrease as Δx increases; in the limiting case (Δximages = 2 Rimage), both Sovr,images and M1,2 are zero. Because the current version uses binary masks, the considered least squares procedure yields the number of pixel pairs with different clear/cloudy designations.

Fig. 3.

Schematic diagram illustrates the statistical matching of two images.

Fig. 3.

Schematic diagram illustrates the statistical matching of two images.

Second, we move the second image in the right direction (along the OX axis) by a small distance δx (δx is the pixel size) (Fig. 3), and calculate ɛ(1). Then, we repeat ɛ(k) calculations K times for other distances Δx*image = (kδx/2Rimage), k = 1, . . . , K, where Kδx < 2Rimage. As a result, we obtain a set of ɛ(k) values as a function of Δx*image. Next, we determine distance Δx* min at which ɛ(k) is minimized. The common area Sovr,images producing this fit is considered the best estimate of the true value of the overlapping area of the two images. In other words, the statistical matching involves the fitting of two sets of pixels—one set is taken from a static image and another is taken from a mobile image. The statistical matching minimizes discrepancies between these two sets in an overlapping (common) region of static and mobile images. Then we calculate the normalized common area S*ovr,images as S*ovr,images = (Sovr,images/Simage). One can estimate CBH Hb by relating S*ovr with S*ovr,images and solving Eq. (1b).

Approach

As a simplest approximation, it can be assumed that S*ovr = S*ovr,images. However, these two normalized overlapping areas are not necessarily the same for Δx* = Δx* min, because the parameter (or normalized distance) Δx* min is obtained by translation only. This simplest geometrical operation would work perfectly if the two images had been obtained by viewing directions that were parallel to the zenith (all viewing zenith angles equal zero). However, because they are hemispherical observations, the same sky areas are observed with different viewing directions by the two instruments. As a result, the two images (obtained simultaneously by two cameras) are related by a complex transformation. This transformation can include translation, rotation, and scaling. Therefore, the relationship between S*ovr,images and S*ovr must be established (e.g., from mathematical modeling), and then this relationship can be used to estimate CBH as Hb = ax*(S*ovr) [see Eq. (2)]. Below we use a numerical simulation to derive another relationship. Namely, we obtain CBH as a function of parameter Δx*min: Hb = f (Δx*min); this parameter Δx*min is the output of the statistical matching (section 2b).

There are two important issues in this approach. First, the solution of image matching Δx*min must exist and be unique. In other words, the position of Δx*min should be clearly identified; the curve ɛ = f (Δx*image) has a sharp and deep trough at Δx*min. Also, the suggested Hb retrieval must be stable with respect to small variations of Δx*min. Section 4 addresses these issues.

To estimate the accuracy of Hb retrieval, we perform model experiments. Two cloud realizations are obtained by using stochastic simulation methods (e.g., Titov and Kassianov 1999). These realizations represent both cumulus (Cu) and stratocumulus (Sc) clouds (Fig. 4). Synthetic cloud fields are generated for a domain ∼10 km × 10 km, with a 0.025-km horizontal resolution (pixel size). Here we use the terms “Cu clouds” and “Sc clouds” as references to these artificial cloud fields. The cloud aspect ratio γ (vertical to horizontal size) is 0.75 and 0.25 for Cu and Sc clouds, respectively. To estimate γ, we use the mean vertical cloud size and the mean cloud chord length. The latter is defined as the mean distance between the trailing and leading edges of a cloud for a given direction (e.g., Malvagi et al. 1993) (here, in both the x and y direction).

Fig. 4.

Computer realizations of the cloud geometrical thickness generated by the stochastic models: view from nadir, with brightness proportional to the vertical extent of (left) cumulus and (right) stratocumulus clouds.

Fig. 4.

Computer realizations of the cloud geometrical thickness generated by the stochastic models: view from nadir, with brightness proportional to the vertical extent of (left) cumulus and (right) stratocumulus clouds.

Both Cu and Sc clouds are simulated at each of 22 different altitudes (from 0.75 to 6 km, with 0.25-km vertical increments). A total of 44 cases (22 for Cu and 22 for Sc) are used in these tests. Next, we simulate TSI observations for each case (Fig. 5). In our experiments we assume that the distance between the two instruments is 0.54 km (Δ1,2 = 0.54 km). This distance corresponds to the distance between the TSI and the HSI during a real observational experiment (section 5). Cumulus clouds are used to obtain the relationship Hb = f (Δx*min). Then, this relationship is applied to derive Hb for Sc clouds. We discuss the Hb retrievals for a single-cloud layer only; we have not considered two overlapping cloud layers yet.

Fig. 5.

Computer realizations of processed TSI images (2α = 180°) for (left) cumulus and (right) stratocumulus clouds: clouds (white), clear sky (black). These images obtained for simulated clouds (Fig. 1) and cloud-base height Hb = 2 km.

Fig. 5.

Computer realizations of processed TSI images (2α = 180°) for (left) cumulus and (right) stratocumulus clouds: clouds (white), clear sky (black). These images obtained for simulated clouds (Fig. 1) and cloud-base height Hb = 2 km.

Numerical experiments

The results of a numerical simulation could be useful, if this simulation mimics the main features of TSI/HSI observations. From Fig. 6, one can easily see that TSI and HSI images have a black strip on the rotating mirror that is used to block the direct line of sight to the sun. The strip provides a noticeable region in the image (“black bar”) that starts over the center and extends to the edge of the FOV. This black bar represents neither cloudy nor clear-sky pixels and, therefore, it can affect strongly the Hb retrieval (“bar” effect). To reduce this bar effect, we select windows that are conveniently located in four quadrants within 100° FOV (Fig. 6). These windows are referred to as “upper left,” “upper right,” “lower left,” and “lower right” with respect to the center of the image. During observations the bar can overlap considerably one of the selected windows (e.g., lower left window in Fig. 6). We do not use such an “overlapped” window for the statistical analysis of TSI/HSI observations (section 5). To put it differently, we perform the analysis for three “nonoverlapped” windows only (section 5).

Fig. 6.

Example of (left) TSI- and (right) HSI-processed images with the black bar and four square-shaped windows.

Fig. 6.

Example of (left) TSI- and (right) HSI-processed images with the black bar and four square-shaped windows.

In our numerical experiments, we do not simulate the black bar and perform statistical matching for the given four windows. Figure 7 demonstrates the relationship between ɛ and Δx*image; the minimum values of ɛ are clearly defined, and their positions Δx*min depend considerably on CBH. Note that Δx*min values are almost independent of the cloud types that are considered here (Fig. 7). This is an important feature of the considered image-matching process: we do not need to know cloud properties (e.g., distribution of clouds, their shapes) to determine Δx*min. This important result is valid for the averaged matching parameter ɛavr, as well (Fig. 8). The latter (ɛavr) is obtained by averaging the considered four values of ɛ (Fig. 7).

Fig. 7.

The matching parameter ɛ as a function of normalized distance Δx*image obtained for simulated (left) Cu clouds and (right) Sc clouds, three CBHs (2, 3, and 4 km), and four windows: upper left (UL), upper right (UR), lower left (LL), and lower right (LR).

Fig. 7.

The matching parameter ɛ as a function of normalized distance Δx*image obtained for simulated (left) Cu clouds and (right) Sc clouds, three CBHs (2, 3, and 4 km), and four windows: upper left (UL), upper right (UR), lower left (LL), and lower right (LR).

Fig. 8.

The averaged matching parameter ɛavr as a function of normalized distance Δx*image obtained for simulated (a) Cu and (b) Sc clouds and three CBHs.

Fig. 8.

The averaged matching parameter ɛavr as a function of normalized distance Δx*image obtained for simulated (a) Cu and (b) Sc clouds and three CBHs.

We simulate hemispherical observations of Cu clouds to derive the relationship between CBH and distance Δx*min (the distance where the ɛavr curve has a sharp and deep trough). Figure 9 shows this relationship: the exponential decay (second order) fits the simulated results accurately. The shape of this curve (exponential decay) suggests that Hb retrieval can be very sensitive to Δx*min variation when values of Δx*min are small; this situation occurs when Hb ≥ Hbmax. Therefore, one can expect that for fixed Δx1,2 and FOV, the accuracy of the Hb retrieval could be quite low for clouds with Hb ≥ Hbmax. For a given Δx1,2 and 100° FOV, Hbmax ∼4.5 km. Note, by changing Δx1,2 and/or FOV one can alter the values of Hbmax.

Fig. 9.

Cu clouds: CBH as function of Δx*min. This relationship is obtained for given observational conditions (distance Δx, FOV) by using model simulations.

Fig. 9.

Cu clouds: CBH as function of Δx*min. This relationship is obtained for given observational conditions (distance Δx, FOV) by using model simulations.

To estimate the accuracy of Hb retrieval, we perform a simulation of TSI observations of Sc clouds and derive Hb by using the obtained relationship Hb = f (Δx*min). Figure 10 shows the results of this retrieval. There is good agreement between the derived values Hbd, and original values Hbo of CBH. Although the maximum absolute difference is about 0.4 km (for Hbo = 5 km), for the majority of cases the accuracy of the retrieval does not exceed 0.2 km. It means that the suggested Hb retrieval allows one to estimate CBH with reasonable accuracy (for Hb ≤ Hbmax), and the accuracy of Hb retrieval depends only weakly on cloud type.

Fig. 10.

Sc clouds: derived CBH Hbd vs original CBH Hbo. Exponential fit (Fig. 6) is used to obtain Hbd.

Fig. 10.

Sc clouds: derived CBH Hbd vs original CBH Hbo. Exponential fit (Fig. 6) is used to obtain Hbd.

Certainly, the characteristics of the matching curve determine the error in the derived CBH. This curve is obtained for Cu clouds with γ = 0.75 (original cloud field). How sensitive are the characteristics of this curve, and, consequently, the accuracy of Hb retrieval, to the 3D geometry of Cu clouds (or the cloud aspect ratio γ)? To estimate the effect of γ on the accuracy of retrieval, we apply two additional realizations of Cu clouds with different values of γ. The latter are set to 1.5 and 2.25; these values can be considered as typical (γ = 1.5) and close to extreme (γ = 2.25) values for cumulus clouds (e.g., Benner and Curry 1998). The only difference between simulated Cu clouds (original and two additional cloud fields) is the cloud aspect ratio. Then, we repeat the simulation of TSI observations and CBH retrievals (as described above) by using two additional Cu clouds. Analysis of the model results reveals that CBH retrieval is quite sensitive to γ values if the clouds are relatively low (Hb ≤ 1km); large variations of γ (from 0.75 to 2.25, by a factor by 3) can reduce the accuracy of CBH retrieval by 0.25 km (not shown). The main reason is that, for a given geometry (Δx1,2, FOV and Hb ≤ 1 km), the relative contribution of cloud sides to CBH retrieval can be pronounced. Note, such a noticeable reduction of the accuracy is observed when we apply the matching curves (obtained for Cu clouds with large γ) to Sc clouds with small γ (γ = 0.25). To increase the accuracy of the retrieval of low clouds, the following two steps could be performed. First, cloud type (e.g., Cu clouds) is specified from TSI observations. To do this, one can use the standard deviation of the sky cover that is derived for a 15-min moving window and limited FOV (∼100°); large values of this standard deviation correspond to cumulus clouds. Additionally, there is evidence that TSI retrievals with different FOVs can yield information on γ (e.g., Kassianov et al. 2005). Second, appropriate matching curves are applied for Cu (large γ) and Sc (small γ) clouds.

Cloudiness intercomparison IOP

The ARM Program’s southern Great Plains (SGP) site conducted a Cloudiness Intercomparison IOP from mid-February through mid-April 2003. This site currently operates a single TSI. During the Cloudiness Intercomparison IOP, the original prototype on which the commercial TSI version is based—HSI, with a hemispherical FOV—had been deployed at the SGP site to work in tandem with the TSI to produce stereo, three-dimensional information about the clouds overhead. This information is used to validate the suggested approach. To estimate CBH, we need to know the distance Δx1,2 between these two instruments. The latter is defined from their coordinates (obtained from global positioning system data) and equals 0.54 km. The HSI is located in a southeast direction from the TSI; the relative azimuth angle between the TSI and HSI is about 135° (from the north).

Because the current version of the CBH retrieval (from hemispherical observations) is developed for a single-cloud field, any additional cloud layers (above a given field) can affect the retrieval’s accuracy. Also, the strong temporal and/or spatial inhomogeneity (e.g., a strong temporal trend) of the CBH of a given cloud field can affect the CBH retrieval. We perform here some preliminary analyses of cloud fields that are observed during the Cloudiness Intercomparison IOP. The aim is to select appropriate days and temporal intervals with no significant contamination by additional cloud layers (e.g., high clouds) and with a relatively invariant CBH of a given cloud field. We select 3 days in April 2003 with different a CBH (Fig. 11). For some temporal intervals, a second cloud layer occurs frequently over a given cloud field. We define a few intervals (∼0.2 h) where single-layer clouds are mostly observed. These intervals are used to specify four cases that represent different CBH: 04–212500 (case 1), 05–142700 (case 2), 05–175930 (case 3), and 27–130101 (case 4). In these notations, the first two numbers correspond to a particular day in April, and last six numbers represent UTC time (hours, minutes, and seconds). We derive CBH for the considered four cases by using TSI/HSI observations (Fig. 12), and then compare these CBH values with those obtained from independent micropulse lidar (MPL) data.

Fig. 11.

Temporal realizations of the CBH values (best estimations) obtained from micropulse lidar data for (a) 4, (b) 5, and (c) 27 Apr.

Fig. 11.

Temporal realizations of the CBH values (best estimations) obtained from micropulse lidar data for (a) 4, (b) 5, and (c) 27 Apr.

Fig. 12.

Examples of processed (left) TSI and (right) HSI images obtained for (top), (middle) 5 and (bottom) 27 Apr.

Fig. 12.

Examples of processed (left) TSI and (right) HSI images obtained for (top), (middle) 5 and (bottom) 27 Apr.

The following two assumptions are used in the suggested CHB retrieval (section 2): (i) images are circles, and (ii) images have the same size (area). However, we find that these assumptions are not valid for the TSI and the HSI image pairs. For example, the radius of the image depends on direction. The horizontal diameter of a TSI image contains 259 pixels, and the vertical diameter is shorter than the horizontal one by 10 pixels. A similar difference is obtained for the HSI image (the horizontal and the vertical diameters have 255 and 245 pixels, respectively). As a result, these images are not perfect circles (“shape” effect). Also, the TSI image is slightly larger than the HSI image (“size” effect). In our CBH retrievals, we do not use any corrections to remove these size and shape effects. Therefore, we expect that these two effects reduce the accuracy of the CBH estimations.

We perform a statistical analysis for three nonoverlapped windows that are located within the 100° FOV (Fig. 6). The result of this analysis is the matching parameter ɛ as a function of the normalized distance Δx*image. Previously, we define this distance as a ratio of the horizontal shifting of a mobile image to its diameter (section 2). Here, we adjust this definition—the horizontal and vertical values of TSI and HSI images (for a given FOV) are used to obtain an effective value of the diameter. For each of the considered cases, values of the matching parameter ɛi, i = 1, . . . , 3 (obtained for three nonoverlapped windows) are averaged, and then the averaged parameter ɛavr (Fig. 13) is used to estimate CBH. We determine the distance Δx*min at which parameter ɛavr is minimized. Both the obtained distance Δx*min (observations) and model curve (Fig. 9) are applied to estimate CBH from hemispherical observations (Table 1). It can easily be shown that CBH retrievals would be more accurate (the bar effect is minimal) if the ground-based instruments were oriented in an east–west or south–north direction (instead of a southeast direction). If this was the case, the images would be shifted in the horizontal or vertical directions (instead of diagonal shifting), and more pixels of the square-shaped windows (larger overlapping areas) could be used to obtain the matching parameter ɛavr.

Fig. 13.

The averaged matching parameter ɛavr as a function of the normalized distance Δx*image. These four plots are obtained for four considered cases: 04–212500 (case 1), 05–142700 (case 2), 05–175930 (case 3), and 27–130101 (case 4).

Fig. 13.

The averaged matching parameter ɛavr as a function of the normalized distance Δx*image. These four plots are obtained for four considered cases: 04–212500 (case 1), 05–142700 (case 2), 05–175930 (case 3), and 27–130101 (case 4).

Table 1.

Statistics of CBH (mean value HbMPL and standard deviation) obtained from MPL data for 12-min temporal window (second and third columns); CBH estimated from TSI/HSI observations Hbhemisph (third column), and difference between HbMPL and Hbhemisph (fourth column).

Statistics of CBH (mean value HbMPL and standard deviation) obtained from MPL data for 12-min temporal window (second and third columns); CBH estimated from TSI/HSI observations Hbhemisph (third column), and difference between HbMPL and Hbhemisph (fourth column).
Statistics of CBH (mean value HbMPL and standard deviation) obtained from MPL data for 12-min temporal window (second and third columns); CBH estimated from TSI/HSI observations Hbhemisph (third column), and difference between HbMPL and Hbhemisph (fourth column).

To assess how well the suggested method (based on TSI and HSI observations) estimates CBH, we compare CBH values obtained from hemispherical observations (Hbhemisph) with those derived from MPL measurements only. For each case, we obtain the mean CBH (HbMPL) and its standard deviation within a 12-min temporal sample (Table 1). Note that for the considered cases, the mean CBH HbMPL is not very sensitive to the sample size because of the weak temporal variability of CBH (Fig. 11).

For the first case (HbMPL∼1.2 km), the TSI-/HSI-derived CBH Hbhemisph overestimates the CBH by about ∼0.35 km. This large difference is likely produced as a result of the additional layer of high clouds (Fig. 8). Recall that the current version of Hb retrievals assumes the single-cloud layer. Also, there is a considerable difference (∼0.35 km) for the fourth case (HbMPL∼4.7 km). In some instances, this difference exceeds 0.5 km (Fig. 14). Such low accuracy can be explained by a specific feature of the suggested retrieval: the accuracy of the Hb retrieval could be quite low for clouds with Hb ≥ Hbmax (section 4). For given values of Δx1,2 and FOV, Hbmax is about 4.5 km, and this value is comparable with the HbMPL that is obtained for the fourth case (Table 1). For the second and the third cases, the TSI-/HSI-derived CBH is in reasonable agreement with HbMPL (Table 1). Overall, the differences between Hbhemisph and HbMPL can be attributed to the distinctions of the CBH retrievals; size, shape, and bar effects, CBH variability; and an additional (upper/lower) cloud layer.

Fig. 14.

Example (27 Apr) of the temporal realizations of the CBH Hb, derived from MPL (solid squares) and TSI/HSI (open circles) data; the corresponding temporal-averaged Hbavg values are obtained for given 0.6-h window.

Fig. 14.

Example (27 Apr) of the temporal realizations of the CBH Hb, derived from MPL (solid squares) and TSI/HSI (open circles) data; the corresponding temporal-averaged Hbavg values are obtained for given 0.6-h window.

Discussion

To estimate CBH, we use sky image sequences from two separated TSIs. Two adjusted images, obtained simultaneously from two closely located instruments, are matched up by statistical analysis. The result of this analysis is the normalized distance Δx*min between the centers of the adjusted images. This distance specifies the overlapping area of two adjusted and partially overlapping images. By the overlapping area, we mean the portion of cloudy sky that is viewed by these two instruments simultaneously. We compute the cloud base from our knowledge of Δx*min, the distance between the cameras, and their FOV. It should be emphasized that we do not need to figure out what kind of a cloud field (e.g., number of clouds, their individual shapes) is in the overlapping area of the images. We only need to know what portion of the two images overlap, regardless of the cloud type. This is the primary distinguishing feature of the suggested methodology that makes it so much simpler than previous attempts, which needed to determine some cloud features in adjacent images.

The accuracy of the suggested retrieval is determined by four main sources. The first source is the bar effect. This effect is associated with the rotating mirror (part of the TSI and HSI instruments) that blocks the direct line of sight to the sun. To reduce this bar effect, we select windows that are conveniently located in four quadrants. Also, the orientation of the ground-based instruments (e.g., the east–west instead of the southeast direction) could additionally reduce the bar effect (section 5). The second source is size and shape effects. These effects are associated with distinctions between two different instruments (here, TSI and HSI) that are applied for CBH retrieval. These two effects could be removed if two similar instruments are used (e.g., two TSIs instead of a TSI and HSI). The third source is strong CBH variability. In this case, two different instruments (a zenith-pointing MPL with a very narrow FOV, and a TSI with alarge FOV) can observe clouds with different CBH. As a result, the instantaneous values of the derived CBH may have large differences precluding a meaningful comparison. However, an appropriate temporal averaging can substantially reduce this difference (e.g., Fig. 14).

Last, an additional cloud layer (e.g., high clouds) located above a given cloud layer (first layer) could affect the accuracy. These two layers can be observed simultaneously by ground-based instruments with large FOV (TSI and HSI). To address this issue, we have to generalize the CBH retrieval (originally suggested for a single-layer cloud field) to multilayer clouds. One possible way to detect the presence of multiple cloud layers is to apply additional intensity values at the pixels (currently, only binary masks are applied). Because low and high clouds can be distinguished visually on TSI images, one can use this difference for the detection of multilayer clouds.

Also, we intend to generalize the statistical matching of TSI images for overcast clouds (where the sky is completely overcast). This involves including not only the current thin and opaque determination standards to the TSI output, but an additional “dark cloud” specification. Image reprocessing with an original prototype code can provide this specification. The aim of the image reprocessing is to increase the contrast between the opaque and dark pixels. Thus, instead of the overcast cloud decision images being all white (standing for all opaque cloud), we can produce a further breakdown of opaque and dark clouds to give us some patterning (texture) to match. Moreover, we plan to perform retrieval experiments by using temporal sequences of images from a single TSI (with a known wind speed). In this case, two adjusted images will be separated by time instead of distance (like the paired TSI scheme). The main purpose of these experiments is to evaluate the potential for measuring CBH from the dynamic sky view of a single TSI. Certainly, the potential applicability of single-TSI retrieval will be limited to sites with available and reasonably accurate information about the wind speed profile. The latter can obtained from additional measurements (e.g., sounding) or model simulation results.

To increase the accuracy of retrieval for low clouds (Hb∼1 km), the cloud specification (e.g., Cu clouds versus Sc clouds) will be very useful. We think that such cloud specification could be possible from the statistical analysis of temporal realizations of the fractional sky cover (TSI measurements) and other retrievable parameters, such as the cloud aspect ratio (e.g., Kassianov et al. 2005). Additional model simulations and analysis of the TSI observations will be performed to address this issue.

Summary

Total-sky imager and hemispheric-sky imager have a hemispherical field of view and provide a time series of the fractional sky cover. Previously, we have demonstrated (Kassianov et al. 2005) that such instruments can be successfully applied for estimating of the nadir-view cloud fraction. Here, we introduce a new method that further extends the capability of such images. In particular, we suggest a new retrieval of the cloud-base height (CBH) by using sky image sequences from two separated instruments. The current version of this retrieval is developed for single-cloud layers only. We have not considered overlapping cloud layers yet.

We verify the suggested retrieval technique with simulated hemispherical surface observations by using artificial cloud fields (stochastic simulation). The results of the model-output inverse problem suggest that, at least for single-layer-cloud fields, moderately accurate (within ∼0.2 km) CBH retrieval is possible. The accuracy decreases as CBH becomes comparable or exceeds a certain altitude. The latter is a function of the distance between the two instruments and their FOV. In addition, we evaluate the performance of this new retrieval with real surface observations made during the Cloudiness Intercomparison IOP (Oklahoma, 2003). Comparison of TSI-/HSI-derived CBHs with those obtained with an independent micropulse lidar (MPL) measurements shows reasonable agreement (within ∼0.2 km); the largest difference is about 0.35 km. The differences between TSI-/HSI-derived and MPL-derived CBHs can be attributed to distinctions of the CBH retrievals, CBH variability, and an additional cloud layer (e.g., high clouds).

To illustrate the potential for estimating CBH from hemispherical surface observations, we used four cases with typical continental broken clouds from this IOP. The preliminary results suggest that the proposed retrieval has promise. Future work will attempt to further test the suggested retrieval with additional cloud fields. For example, the Boundary Layer Cloud IOP will be held at the ARM Program’s North Slope of Alaska in the summer of 2005 and will provide surface observations of CBH. We plan to use these observations to further evaluate this retrieval. Once we have a well-defined understanding of the strengths and weaknesses of the suggested approach, we plan to generalize it for more sophisticated problems (e.g., two-layer cloud fields).

Acknowledgments

This work was supported by the Office of Biological and Environmental Research of the U.S. Department of Energy as part of the Atmospheric Radiation Measurement (ARM) Program. We thank Gabriela Seiz and Jan Schween for providing useful discussions and two anonymous reviewers for their thoughtful comments.

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Footnotes

Corresponding author address: Dr. Evgueni I. Kassianov, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, Richland, WA 99352. evgueni.kassianov@pnl.gov