Atmospheric motion vector retrieval using improved tracer selection ...

Theor Appl Climatol DOI 10.1007/s00704-014-1115-1

ORIGINAL PAPER

Atmospheric motion vector retrieval using improved tracer selection algorithm Inderpreet Kaur & S. K. Deb & C. M. Kishtawal & P. K. Pal & Raj Kumar

Received: 20 June 2013 / Accepted: 28 January 2014 # Springer-Verlag Wien 2014

Abstract Tracer selection is the fundamental step in the retrieval of atmospheric motion vectors (AMVs). In this study, a new technique for tracer selection based on extracting the corner points in an infrared (IR) image of a geostationary satellite for the retrieval of AMVs is developed. Corner points are frequently used in computer vision to identify the important features of an image. These points are usually characterized by high gradient values of the image intensity in all directions and lie at the junctions of different brightness regions in the image. Corner points find application in computer vision for motion tracking, stereo vision, mosaics, etc., but this is the first time that the information from corners is used for tracer selection in AMV retrieval. In the present study, a commonly used Harris corner (HC) detection algorithm is followed to extract corners from the image intensity of an IR image. The tracers selected using the HC method are then passed on to the other steps of the retrieval algorithm, viz., tracking, height assignment, and quality control procedures for the retrieval of AMVs. For the initial development of the HC, Meteosat-7 IR images are used to derive AMVs for July I. Kaur (*) : S. K. Deb : C. M. Kishtawal : P. K. Pal : R. Kumar Atmospheric and Oceanic Sciences Group, Space Applications Centre, Indian Space Research Organization, Ahmedabad, Gujarat 380015, India e-mail: [email protected] I. Kaur e-mail: [email protected] S. K. Deb e-mail: [email protected] C. M. Kishtawal e-mail: [email protected] P. K. Pal e-mail: [email protected] R. Kumar e-mail: [email protected]

and December 2010. The AMVs retrieved using HC are validated against collocated radiosonde observations, and the results are compared with the local anomaly (LA) method as reference. LA is used for tracer selection in operational AMV retrieval algorithm from the Indian geostationary satellite Kalpana-1. AMVs retrieved using HC have shown considerable improvement in the AMV accuracy over the AMVs derived using LA.

1 Introduction Atmospheric motion vectors (AMVs) are derived by tracking cloud or water vapor features in sequential satellite images. AMVs derived from multispectral images form the single biggest source of tropospheric wind observations, particularly over oceans and high latitudes. Studies have highlighted the importance of AMVs in operational numerical weather prediction (NWP), where AMVs are used during assimilation for preparation of the initial state of the atmosphere. They form one of the most important inputs to the NWP models over oceans due to sparse conventional observations and also over low latitudes due to low geostrophic coupling between mass and flow fields (Bormann et al. 2011). Several studies have also emphasized the benefit of using AMV data on tropical cyclone track forecasts (Zapotocny et al. 2008; Langland et al. 2009; Deb et al. 2010, 2011; Berger et al. 2011). Continuous improvements in the sensor technology, model resolution, and assimilation strategies have placed a high demand on AMV quality. This poses greater challenges for the AMV retrieval community to thrive towards improving the AMV data quality. The automated AMV retrieval is a series of structured steps involving the tracking of cloud or water vapor in sequential images. Most operational retrieval schemes employ a series of identical steps, namely tracer selection, tracer tracking, height

I. Kaur et al.

assignment, and quality control (Niemann et al. 1997; Menzel 2001). Potential tracers are identified from the first image in the sequence, and the relative displacement vectors are obtained by locating the tracer over a search region in the subsequent image. Different pattern matching techniques based on cross-correlation and Euclidean distance (Dew and Holmlund 2000) are used to find the best match for each tracer in the subsequent image. The derived displacement vector gives an estimate of the atmospheric motion. Finally, each derived vector is assigned a height and assessed for quality. Various operational agencies utilize different criteria for tracer selection depending on the satellite sensor and resolution specifications. At the National Environmental Satellite Data and Information Service (NESDIS), tracers with maximum gradients are chosen (Niemann et al. 1997) and spatial coherence analysis (Coakley and Bretherton 1982) is used to filter out tracers with small variability. The Japan Meteorological Agency (JMA) identifies tracers over 0.5° latitude/longitude grids. Boxes of 32×32 pixels over each grid are selected as prospective tracers by analyzing the histogram of equivalent blackbody temperature (EBBT) (Oyama and Shimoji 2008). For the Indian geostationary satellite Kalpana-1, the tracers are identified as 20×20 pixel boxes over a fixed grid using local image anomaly method (Deb et al. 2008). Lately, the focus has been on the optimization of the tracer size with respect to the temporal and spatial resolutions of the images (Sohn and Borde 2008; Park et al. 2012). A small tracer size contains less information (features) and tracking it over a larger time interval leads to high AMVerrors (Dew and Ackermann 2010). Similarly, larger tracers might contain multilayer cloud features and hence produce an averaged motion over different layers (Sohn and Borde 2008). Besides optimization of the tracer size, characterization of the tracers into good/bad tracers is also important as all tracers do not give a good estimate of the atmospheric circulation. Most operational AMV producers screen out the undesirable tracers on the basis of the entropy, contrast, and number of cloudy pixels. Removal of undesirable tracers not only improves the overall quality of the wind field but also saves onto the computing resources. In addition to identifying poor tracers a priori to tracking, the use of automatic quality control is also imperative for the current operational wind extraction schemes in order to create near-real-time data sets that have a positive impact on NWP. Motion tracking over a sequence of images is a wellestablished branch of computer vision. Computer vision tasks such as stereo and motion estimates require locating common features across two or more views. Various techniques based on local features of the image are used for motion tracking. In this study, we have tried to extend a motion tracking technique to find the prospective tracers for AMV retrieval, and a new method for tracer selection based on “corner points” is developed. In computer vision terminology, corners are points

characterized by high curvature in all directions and are used to extract important features in an image. Corners frequently find application in motion detection, image registration, video tracking, and object recognition (Chen et al. 2009) to find the best match between different frames of an environment. Several variants of corner detectors are used by researchers. For this study, the commonly used Harris corner (HC) detector is used to determine the corners in an image. HC is an intensity-based detector which estimates the presence of corners directly from the image gray values (Bankman et al. 2002). This method is computationally fast and invariant to image rotation, illumination, and scaling (Schmid et al. 2000). This paper discusses the development of a new tracer selection technique using HC. Section 2 provides a mathematical overview of HC and extension of the scheme to select tracers. A brief description of the validation methodology is also provided in Section 2. Since the present study is focused mainly on tracer selection technique, the other steps of the retrieval algorithm such as tracer tracking, height assignment, and quality control methods are not discussed in this paper (Kishtawal et al. 2009; Deb et al. 2013). Section 3 discusses the accuracy of the AMVs derived using the new technique and Section 4 concludes the study.

2 Data and methodology 2.1 Data used 2.1.1 IR image data For this study, Meteosat-7 IR images are used. Meteosat-7 is a geostationary satellite positioned at 57.5° E. It has a threechannel radiometer, observing earth in IR (10.5–12.5 μm), visible (VIS; 0.4–1.1 μm), and water vapor (WV; 5.7–7.1 μm) channels. It scans earth every half hour with a spatial resolution of 5 km at subsatellite point for IR and WV images and 2.5-km horizontal resolution for VIS images, respectively. The IR images for the months of July and December 2010 are chosen to demonstrate the initial development of the algorithm. These two months are chosen to include circulation features corresponding to both Indian summer and winter monsoons. 2.1.2 AMV data The performance of the HC technique is compared with the current operational retrieval algorithm used for the Indian geostationary satellite Kalpana-1. For a one-to-one comparison, a reference AMV data set is processed using the Kalpana-1 operational algorithm but with the same set of Meteosat-7 image data. These two AMV data sets differ only in the tracer selection techniques, where the reference

AMV retrieval using improved tracer selection algorithm Table 1 A brief description of the four sets of AMVs compared in the present study Input data Set 1 (represented as “HC” in the text)

Number of images Retrieval algorithm

Meteosat-7 IR 9 images

Tracer selection using HC technique, These two AMV data sets differ and subsequent steps as per only in the tracer selection Kishtawal et al. (2009) and technique Deb et al. (2013) Tracer selection using LA technique, and subsequent steps as per Kishtawal et al. (2009) and Deb et al. (2013) As per Schmetz et al. (1993) AMVs without any quality control are used for validation

Set 2 (represented as “LA” in the text)

Set 3 (represented as “EUM_NF” in the text)

3

Set 4 (represented as “EUM_WF” in the text)

AMVs with QI values greater than 0.8 are used for validation

AMV data set utilizes the LA technique for tracer selection. To demonstrate the benefit of the new approach, an intercomparison of these two data sets is carried out. For the sake of completeness, both these AMV data sets are also compared with an independent AMV data set comprising globally accepted Meteosat-7 AMVs generated at the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). A brief description of AMV data sets used in this study is provided in Table 1 along with the suitable references. 2.2 Harris corner method HC considers a local window in the image and determines the average changes in the image intensity when the window is moved by a small amount in various directions. The change in intensity is measured in terms of the local autocorrelation function of the signal (or gray values) (Harris and Stephens 1988). Mathematically, denoting the image intensity as I, and considering a window centered around (x,y), the change produced by shift (Δx,Δy) is given by X  2 E Δx;Δy ¼ w I −I ð1Þ x;y x;y xþΔx;yþΔy x;y where wx,y is a Gaussian window given by wx;y ¼ e−ðx

2

−y2 Þ=2

ð2Þ

Approximating the shifted image in Eq. 1 around (x,y) by a Taylor expansion truncated to first-order terms, E Δx;Δy ¼

Remarks

  ΔI ΔI 2 þ Δy w Δx x;y x;y Δx Δy

X

ð3Þ

 A¼  B¼

ΔI Δx ΔI Δy

 C¼

2 ⊗w

ð5Þ

⊗w

ð6Þ

2

ΔI Δx



 ΔI ⊗w Δy

ð7Þ

where ⊗ shows convolution of the image with Gaussian. Equation 4 can also be written as    A C Δx ð8Þ E Δx;Δy ¼ ½Δx ΔyŠ C B Δy 

 A C The 2×2 symmetric matrix M ¼ captures the C B intensity structure of the local neighborhood. Let λ1 and λ2 be the two eigenvalues of M. Both eigenvalues are proportional to the local autocovariance function and form a rotationally invariant description (Harris and Stephens 1988). Small values of both λ1 and λ2 imply the smooth nature of the local autocorrelation function, signifying flat features. If one eigenvalue is high and the other low, the local autocorrelation function is ridge-shaped, indicating an edge. If both eigenvalues are high, the local autocorrelation is sharply peaked, indicating a corner. For corner points, small shifts in any direction results in a sharp change in the intensity. To avoid the explicit computation of the eigenvalues, HC utilizes a corner response function (CRF) to determine the corner points. CRF is defined as R ¼ jM j−k fTrg2

ð9Þ

For small shifts, E can be written as 2

E Δx;Δy ¼ AðΔxÞ þ 2CΔxΔy þ BðΔyÞ

2

ð4Þ

where |M|=AB−C2 and Tr=A+B. k is a constant and is determined empirically with values lying in the range 0.04–0.25.

I. Kaur et al.

Small values of k facilitate the algorithm to detect sharper corners. For the current study, the value of k was fixed at 0.04. The local maxima of the CRF define the corner points. 2.3 Local anomaly method The operational AMV retrieval algorithm from Kalpana-1 images uses local image anomaly (LA) method for tracer selection (Deb et al. 2008). A window of 20×20 pixels in cloudy regions is selected as a prospective tracer by computing the local image anomaly. Local image anomaly is defined as  Xn Xn   ai; j ¼ ð10Þ I ð i; j Þ−I   i¼1 j¼1 where I(i,j) represents the gray value for the (i,j) pixel of the template window, n is the size of the window, and I represents the average of gray values within that window. 2.4 Use of HC for tracer selection and retrieval of AMVs In the present study, Meteosat-7 IR images are used to extract the corners. The flow chart of the steps followed for extracting the corners from the image intensity is given in Fig. 1. The various steps of the technique are briefly described below. 1. Compute CRF: Using Meteosat-7 IR image as the input, for each pixel of the image, the Gaussian derivatives of the image intensity are computed. These image gradients are used to calculate the CRF (Eq. 9) for every pixel. Since CRF is computed for each pixel of the image, the resulting output after application of HC has the same dimension as the input image. The output image is often referred as “cornerness map.” Each pixel of the image will have a “cornerness” value which indicates the suitability of the pixel to be a corner. 2. Thresholding: Local maxima of the CRF in the cornerness map are defined as the corner points. However, before extracting the corners, all values of CRF below a certain threshold are set to zero. This helps in ruling out the identification of corner points with low CRF. The threshold value is set empirically as per the requirement of the application. It should be high enough to remove local Fig. 1 Flow chart showing the various steps for extracting corners using the Harris corner detector

maxima which do not represent true corners, but low enough to retain true corners. For the present study, the threshold value was fixed after manual inspection of few threshold images. Once, the value was fixed, it was not changed for the entire study period. The output image after thresholding is also referred as threshold map. Figure 2a shows the input grayscale image and Fig. 2b shows the threshold map for the same. Pixels associated with land and water features usually have low values of CRF and are removed after thresholding. Well-defined coastal boundaries are also easily captured by the corners, but these points are screened out during thresholding. It is observed that no separate analysis of the corner points representing the coastal features is required. Similarly, for clouds with large horizontal extent, pixels lying in the center are ruled out as corner points. 3. Non-maximal suppression: Non-maximal suppression (NMS) is a technique used to isolate significant features in an image. For each pixel in the threshold map, NMS sets the value of CRF to zero if its value is smaller than all the pixels in a certain distance. For the present case, a 5×5 matrix around each pixel is chosen and CRF for all pixels is compared. CRF for pixels having a value less than the maximum value in that window is set to zero. After NMS is applied, the pixels having nonzero CRF values are classified as the corner points. Figure 2c shows the extracted corner points superimposed on the input image. After all corner points are extracted, these points are used to define the tracers for vector retrieval. 4. Remove any corner associated with land/ocean: Before application of HC, pixels are not classified as a cloudy/ non-cloudy pixel, but thresholding (as in step 2) eliminates most of the corners associated with land, ocean, and coastal features. Any stray corner points which are left after thresholding are screened by analyzing the gray level values of the image. The average value of all the gray values lying in the 15×15 pixel window centered on each corner is estimated, and corners with the average gray values greater than a predetermined threshold are discarded. The threshold for the present study was fixed at 130 for normal 8-bit IR images. After empirical inspection of a large number of IR images, it is observed that pixels with gray values greater than 130 represent the

AMV retrieval using improved tracer selection algorithm Fig. 2 An example showing the retrieval of AMV by using HC for tracer selection. a A portion of the input IR image. b The corresponding threshold map generated after setting all corner response function (CRF) values below a certain threshold to zero. c Corner points identified after applying non-maximal suppression (NMS) to the threshold map. d The wind vectors retrieved over corner locations prior to the filtering procedure. The vectors are for representative purposes and not to scale

land/ocean features. A corner related to cloud information would lead to an average gray scale significantly smaller than 130. In the future, this static, empirically derived threshold could be replaced with a physical calibrated threshold EBBT and that could be further improved by prediction from identified cloud-free scenes and/or NWP surface temperatures. 5. Tracer selection and tracking: Meteosat-7 IR image has 6,250,000 pixels, and in a typical case around 15,000 points are classified as corners after the above four steps. The corner points retained after the last step are used for tracking cloud motion in the subsequent image. Instead of matching a single corner point in the subsequent image, a 15×15 pixel window centered on each corner point is considered as a prospective tracer. It should be noted that no corners are extracted for the second image. For matching the selected tracers, a 45×45 pixel search area is chosen in the subsequent image. The size of the search window is fixed at 45×45pixels to estimate wind speeds up to 60 m s−1. The features contained in the tracer window are matched with 15×15 pixel segments of the search area using automatic pattern recognition based on

the Nash-Sutcliffe coefficient (Nash and Sutcliffe 1970). The Nash-Sutcliffe coefficient is defined as n X

E ¼ 1−

i¼1 n X

ðGt −Gs Þ2

−

Gt −Gt

2

ð11Þ

i¼1

where Gt and Gs represent the gray values for the template − and the search window, respectively. Gt represents the average gray values for the template. n defines the size of the template (15 for the present case). Displacement from the center of the tracer window to the center of the matched window gives the displacement vector. The displacement vector is derived only if matching coefficient, E>0.45. Figure 2c shows the final set of corners for a portion of an IR image, and Fig. 2d shows the corresponding displacement vectors derived over each corner. Previous studies by the authors (Deb et al. 2008) have highlighted the advantage of using the Nash-Sutcliffe coefficient over the standard cross-correlation method. The parameter E shows a higher sensitivity to differences

I. Kaur et al.

between two features than the cross-correlation coefficient. This technique also reduces the chances of finding multiple maxima. Due to better efficiency of the NashSutcliffe coefficient to the noise, we have utilized this technique for tracer tracking in the present study. 6. Preliminary neighborhood screening: Manual inspection of the vectors derived at the corner locations shows that the tracers selected using HC captures the circulation effectively, but along with it, few noisy vectors are also derived. To remove these vectors which deviate substantially from the mean flow, a preliminary neighborhood quality control is carried out. Each derived vector is compared with all the available vectors in its 20×20 pixel neighborhood. Figure 3 illustrates how each vector is compared with its neighbors. The line intersections depict the corner locations; the circle represents the vector under consideration while boxes denote the neighbors. NMS suppresses all corners in the 5×5 pixel neighborhood of each corner; hence, the minimum distance between two corner points is 3 pixels, and each vector can be compared with a maximum of 48 vectors. The speed and direction difference between all available pairs is estimated, but not all vectors are present at each time. A vector consistent with its at least seven neighbors in terms of speed and direction is retained. This preliminary check helps in removing the outliers and smoothens out the flow. In a typical case, out of 14,000 vectors retrieved, around 7,000 vectors are screened out. 7. Buffer generation: The present operational algorithm (used for Kalpana-1) utilizes a wind buffer generated using eight pairs of images for the quality control of AMVs during the retrieval (Deb et al. 2013). This method

is also known as multiplet method (Deb et al. 2013) and has shown an increase in total number of derived winds and an improvement in the accuracy over the traditional triplet method for Kalpana-1 AMVs. The same quality control technique is followed in this study to get the final set of vectors from Meteosat-7 image data. In the multiplet-based algorithm, the wind vectors are derived over each sequential pair of the nine images (1-2, 2-3, 3-4, 4-5, 5-6, 6-7, 7-8, 8-9) of 30-min interval to prepare a wind buffer. The LA tracer selection method identifies the location of tracers at the center of the tracer window (which is design choice); hence, the wind buffer stores the gridded wind information from previous 4 h. However, in the present case, the tracers are selected over dynamic locations and are not part of any grid; hence, to extend the HC tracer selection technique to the multiplet method, the wind vectors are gridded into the LA equivalent grids after the preliminary neighborhood check. The average of all vectors lying in each grid is retained as the gridded vector. No significant change in the number of vectors is observed after gridding. The above procedure is repeated for all seven pairs of images (2-3, 3-4, 4-5, 5-6, 6-7, 7-8, and 8-9) to generate the wind buffer. Subsequent quality control and height assignment procedures remain the same as per the operational algorithm used for Kalpana-1 (Deb et al. 2013).

2.5 Validation methodology Meteosat-7 IR images for July and December 2010 are used to retrieve AMVs at 0000 UTC and 1200 UTC using HC. To analyze the effect of the new tracer selection technique, the derived AMVs are validated with the collocated radiosonde observations as per the Coordination Group for Meteorological Satellites (CGMS) guidelines (Menzel 1996). Observations from approximately 250 radiosonde stations are used. It should be noted that very few stations are reporting data regularly. The collocated AMV and radiosonde observations within a horizontal distance of 150 km and pressure difference of 20 hPa are considered for the validation. The main statistical parameters used to determine the accuracy of AMVs as per CGMS guidelines are given as follows: Vector difference: h i1=2 VDi ¼ ðui −ur Þ2 þ ðvi −vr Þ2

Fig. 3 A schematic diagram showing 20×20 neighborhoods (highlighted box) of the retrieved vector. The intersection of the grid lines shows the corner locations; the vector under consideration for neighborhood check is represented by a circle and its neighbors by boxes. Each vector can have a total of 48 neighbors, but not all are present at each instant. Vectors consistent in speed and direction with at least its seven neighbors are retained

ð12Þ

Bias:

bias ¼

1  2 1 i 1 XN h  2 2 2 2 2 u þ v − u þ v i i r r i¼1 N

ð13Þ

AMV retrieval using improved tracer selection algorithm

Mean vector difference (MVD): MVD ¼

1 XN VDi i¼1 N

ð14Þ

Standard deviation (SD): rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XN 2 1 SD ¼ ðVDi −MVDÞ2 i¼1 N

ð15Þ

Root-mean-square vector difference (RMSVD):  1=2 RMSVD ¼ SD2 þ MVD2

ð16Þ

Here subscripts i and r denote the AMV and the radiosonde wind, respectively. u, v, and N denote the zonal wind component, meridional wind component, and total number of collocations, respectively. Normalized RMSVD (NRMS) with respect to mean radiosonde wind speed gives a better estimate of the skill of AMV retrieval as RMSVD increases with speed (Velden 1997). For the current study, NRMS, MVD, bias, and SD are analyzed. On validation with collocated radiosonde observations, collocated pairs with speed difference greater than 20 m s−1 and direction difference greater than 60° are rejected. This criterion allows a rejection of about 5 % of the total collocations in the current case but improves the validation statistics substantially. For the comparison, the AMVs are separated out into three broad layers: upper level (100– 400 hPa), mid level (401–700 hPa), and low level (701– 950 hPa).

3 Results and discussion Table 2 shows the statistical summary of AMVs derived using HC and LA for the month of July 2010. AMVs derived using LA have slightly faster wind speeds at low level in

Table 2 Statistical summary of AMVs derived using LA and HC for July 2010 LA

HC

Av speed low (m s−1) Av speed mid (m s−1) Av speed high (m s−1) % low winds % mid winds % high winds

11.9 12.2 14.9 17 31 52

11.2 12.3 15.1 18 30 52

Product density (%)

27

45

Low, mid, and high levels represent 701–950, 401–700, and 100– 400 hPa, respectively. Product density is defined as the ratio of accepted winds to the total number of tracers possible

comparison to the AMVs derived using HC. At mid and upper levels, both techniques give comparable wind speeds. For both techniques, the ratio of AMVs separated into low, mid, and high pressure levels is the same. More than 50 % of the total AMVs derived belong to the upper atmosphere. Since both methods utilize identical grids to derive the AMVs, a comparison of product density is made. Product density is defined as the ratio of the accepted AMVs to the total number of potential tracers. The total number of potential tracers is taken the same as the total number of grids possible. For the present case, the total number of grids is 141×141 for both LA and HC techniques. HC gives a higher product density in comparison to LA. Selecting tracers by HC helps in deriving AMVs over 45 % of the total grids possible. Figure 4 shows the spatial distribution of the derived winds at high, mid, and low pressure levels in July. Easterly jet predominates the upper level circulation in July, and a significant increase in the number of retrievals over this region from HC is evident from Fig. 4d. The tropics abound with clouds associated with easterly flow in the summer monsoon, and the strong winds blow out these clouds into thin plumes. Thin plumes and cirrus clouds are best suited for tracking due to high gradients associated with them. HC effectively identifies the corners associated with them, and hence, an increase in the total number of retrievals is observed. At low level, a relatively lesser number of winds are derived by HC. More mid level winds are derived by HC in the southern hemisphere, but few gaps are seen in the northern hemisphere. This might be due to presence of clouds with large vertical extent in the mid atmosphere which restricts the number of corners and, hence, the number of retrievals. For an intercomparison of the accuracy of AMVs retrieved from HC and LA, the AMVs are validated against each other. These two sets of AMVs differ only in the tracer selection techniques; hence, their comparison brings out the differences arising due to the implementation of the new tracer selection technique. For comparison, all AMV pairs within 150-km radius and pressure difference of 20 hPa are considered. For this comparison, no winds are filtered according to the direction and speed difference criterion as described in Section 2.5. Figure 5 shows the wind speed and direction scatter density plots. AMVs derived using HC and LA show a correlation of 0.89 in wind speed, while a correlation of 0.92 in wind direction is observed. The AMVs retrieved using both methods show similar speed and direction features. Table 3 gives the MVD, RMSVD, and bias values when AMVs derived using LA and HC are compared with each other at high, mid, and low levels for July 2010. The RMSVD between AMVs derived using HC and LA is 3.5, 2.6, and 2.3 m s−1 at high, mid, and low pressure levels, respectively. When collocated against each other, the AMVs derived using LA show a slightly fast bias over HC. Student’s t test shows that the difference in the mean speeds is not significant at the

I. Kaur et al. Fig. 4 Spatial distribution of derived AMVs for July, 15×15 pixel tracer size for a–c LA at high, mid, and low pressure levels and d–f HC at high, mid, and low pressure levels

high level, but the differences at mid and low levels are significant in 95 % confidence interval. Since the tracer tracking step is similar for both, the averaging of the vectors over the grid smoothens out the circulation. This might be the reason for lower wind speeds among AMVs derived by HC. To further investigate the accuracy of the AMVs derived using HC and LA, the AMVs derived from both the techniques are validated against the collocated radiosonde observations for July and December 2010. The Meteosat-7 AMVs provided by EUMETSAT are used by various NWP centers; hence, to demonstrate the benefit of this new approach, a comparison with EUMETSAT AMVs is also provided. It should be noted that in the present study, though Meteosat-7 images are used to derive AMVs in all data sets, the algorithm employed by EUMETSAT is significantly different from the current retrieval algorithm, especially the utilization of multiple images and the quality control procedure. For the current HC methodology, no final quality indicator of each derived final wind vector is computed; hence, comparisons against both with and without quality-filtered EUMETSAT AMVs are considered. It should be noted that this quality filtering (Holmlund 1998) is imperative for a successful use of the EUMETSAT winds and that it significantly improves the statistics for the EUMETSAT winds, but the comparison against non-filtered AMVs gives an indication of the utility

of the new approach providing good-quality vectors. In addition, the comparison against filtered EUMETSAT AMVs with all observations having quality indicator (QI) values greater than 0.8 is also considered. For all four sets of AMVs (Table 1), wind bias, MVD, NRMS, and SD with respect to radiosonde observations are compared. RMSVD values increase with the increasing wind speed; hence, NRMS is used for a better estimation of AMV accuracy. The validation results for upper, mid, and low levels are listed in Table 4. From Table 4 it is observed that, at high level, the number of collocations for HC against radiosonde observations is more than that for LA. The number of collocations increases by almost 30–40 % for high level winds owing to the increase in the number of retrievals in HC at high level. At mid and low levels, the number of collocations for both LA and HC are comparable. At high and mid levels, the total number of collocations for EUM_NF AMVs is almost 50 % less than that for the AMVs derived using the LA technique. Lesser number of collocations can be attributed to the difference in the tracer size box. EUMETSAT utilizes a 32×32 pixel tracer box, while in this study, a 15×15 pixel tracer box has been used. Quality filtering further reduces the total number of collocations for EUM_WF. In comparison to EUM_NF, only half of the collocations pass the quality check at high levels, while at mid and low levels, a drastic decrease is observed. At

AMV retrieval using improved tracer selection algorithm

Fig. 5 a Wind speed scatter density for AMVs derived using LA and HC. b Same as a but for wind direction

low levels, for the month of December, the total number of collocations for EUM_NF, LA, and HC is comparable, but for July, HC and LA lack in identifying the low level tracers effectively. At high level, the NRMS for HC improves by almost 7 % (0.43 to 0.40) for July in comparison to that for LA. Similar results are seen in December, when high level NRMS improves by almost 10 %. The MVD for EUM_NF AMVs and HC AMVs is comparable at high levels, though the NRMS for the former is higher, indicating the faster mean wind speed for the AMVs derived using HC. At high level, the MVD of EUM_WF AMVs is lower than those of all the three sets of AMVs for both the months, but NRMS values for HC and EUM_WF are grossly comparable. The bias values for AMVs derived using HC and EUM_WF are observed to be comparable for both the months. The AMVs derived using HC also show an increased slow bias at high levels in comparison to those derived using LA. The upper troposphere is associated with moderate easterly flow in the summer monsoon and strong subtropical westerly jet in the winter monsoon. AMVs are bound by spatial and temporal resolutions and cannot effectively resolve the circulation associated with the

jets. This shortcoming of the AMVs to resolve the jet speed might be the reason for increased slow bias at high level. Tracking of multilayer clouds is also attributed to the reason behind pronounced slow bias at upper levels (Bresky et al. 2012). In the present study, the vectors derived at the corner locations are averaged to a grid. Though the vectors with similar gray values are averaged, multilayer averaging can affect the accuracy of the final product. In mid level, the percentage of improvement in NRMS for AMVs derived using HC over LA is observed to be 13 % for both the months. In July, the MVD is grossly comparable for all four sets of AMVs. The AMVs derived by HC show the least bias values in comparison to all the other three AMV sources. In terms of NRMS, HC gives a better accuracy over LA and EUM_NF, but the NRMS values for EUM_WF are observed to be lower. NRMS is observed to be 0.35 for EUM_WF AMVs for both the months, and the corresponding values for HC AMVs are 0.50 and 0.39 for July and December, respectively. Maximum improvement is seen at low level, where NRMS for AMVs derived using HC shows an improvement of more than 20 % over LA AMVs. AMVs derived using HC also

Table 3 Comparison of AMVs derived from LA and HC

High Mid Low

Speed bias (LA-HC)

MVD

RMSVD

Mean speed (LA)

Mean speed (HC)

NC

Significance of difference

0.5 0.4 0.6

3.3 2.4 2.1

3.5 2.6 2.3

15.9 12.8 11.1

15.3 12.3 10.4

424,277 176,900 102,967

N Y Y

The last column indicates the significance of differences as given by the t test assuming a 95 % confidence interval. Speed bias, RMSVD, and mean speed are in meters per second Y significant difference, N not a significant difference

I. Kaur et al. Table 4 Validation statistics for the four sets of AMVs as described in Table 1 against collocated radiosonde observations at high, mid, and low levels N Jul 2010, high level LA 13,586 HC 23,071 EUM_NF 5,956 EUM_WF 1,732 Dec 2010, high level LA 10,196 HC 23,264 EUM_NF 4,837 EUM_WF 2,156 Jul 2010, mid level LA 2,262 HC 2,594 EUM_NF 1,169 EUM_WF 125 Dec 2010, mid level LA 3,019 HC 4,511 EUM_NF 1,522 EUM_WF 271 Jul 2010, low level LA 400 HC 487 EUM_NF 850 EUM_WF 75 Dec 2010, low level LA 850 HC EUM_NF EUM_WF

869 815 66

MVD

NRMS

SD

Bias

6.8 6.7 6.8 5.4

0.43 0.40 0.50 0.37

1.8 1.3 4.4 3.3

−1.6 −1.9 −3.7 −1.8

8.1 7.5 7.1

0.39 0.35 0.43

1.9 1.1 4.6

−3.0 −3.4 −3.7

5.8

0.32

3.7

−2.1

5.8 5.7 5.4 5.2

0.58 0.50 0.64 0.35

2.3 1.9 3.4 0.9

1.5 0.2 −2.6 −2.3

7.5 6.7 7.9 6.1

0.45 0.39 0.62 0.35

2.7 1.8 4.8 2

0.1 0.6 −4.5 −0.7

5.7 4.7 4.7 4.4

0.62 0.44 0.77 0.41

1.7 1.0 2.5 0.3

2.1 0.2 −2.3 0.6

7.1

0.68

2.3

0.9

6.3 5.3 3.1

0.53 0.84 0.38

1.4 3.3 0.2

0.2 −2.3 −0.6

Mean vector difference (MVD), standard deviation (SD), and bias are in meters per second NRMS normalized root-mean-square vector difference, N number of collocations

show lower values of standard deviation for both the months. The MVD of AMVs derived using HC is observed to be comparable to that of the EUM_WF AMVs for July, but in December, the MVD is slightly higher. In terms of NRMS, the accuracy of HC is better than that of EUM_NF, but slightly worse in comparison to that of EUM_WF. The validation statistics with collocated radiosonde observations are also analyzed according to the pressure bins. Figure 6a, b gives the bias and RMSVD for HC, LA, and EUM_NF AMVs with respect to pressure (100-hPa bins). Solid, dashed, and dotted lines denote LA, HC, and EUM_NF AMVs, respectively. AMVs derived using HC

show lower values of RMSVD than AMVs derived using LA over the entire troposphere with an exception at 200, 300, and 600 hPa where a slight degradation is seen. But overall AMV quality improves in the high level as already seen in Table 4. The RMSVD values for EUM_NF AMVs are observed to be comparable to those for HC AMVs at low levels, but show a slightly better accuracy at mid levels. At high levels, due to large slow bias, the accuracy of EUM_NF AMVs is lesser than that of HC AMVs. It should be noted that a larger slow bias is observed between 100–200 hPa for all three sets of AMVs. Upper tropospheric jet streams are confined to this pressure range, and this further strengthens the observation that the inability of the AMVs to resolve the jet speeds contributes towards a larger slow bias at high levels. Figure 7a, b gives the mean direction difference and mean speed difference for the three sets of AMVs. Both HC and LA techniques show comparable values of mean direction difference centered around 20° for the entire pressure range, but the EUM_NF AMVs show slightly higher direction differences and the differences are more pronounced at mid levels. At 900 hPa, though HC seems to be performing better, the number of collocations (Fig. 8a) is too few to have a significant comparison. HC and EUM_NF AMVs consistently give a lower value of mean speed difference for low and mid atmospheres, but at high levels, the mean speed differences for all three sets of AMVs are almost comparable. Figure 8a, b gives the total number of collocations and SD at each pressure bin. SD for AMVs derived using HC is lower than those for LA and EUM_NF AMVs consistently at all pressure levels. The plot for the number of collocations shows that HC increases the total number of retrievals at the upper levels, but at the lower level, the EUM_NF AMVs have a higher number of collocations. Accuracies in the AMV are also related to the vector wind speed, and this information is quite important in the data assimilation studies (Velden et al. 1996). Accuracy as a measure of wind speed is also analyzed. The AMVs derived from LA and HC techniques are compared with collocated radiosonde observations with respect to the AMV wind speed. For this comparison, 3 m s−1 AMV wind speed bins are considered. It should be noted that for this comparison only collocated pairs with speed difference less than 20 m s−1 and direction difference less than 60° are considered. Figure 9a, b gives the mean vector difference plotted against average wind speed for LA and HC, respectively. The dotted line gives the total number of wind observations while the solid line gives the MVD. An increase in the wind speed leads to an increase in the MVD values, but for higher values of wind speed, the AMVs derived using HC give a lower MVD in comparison to winds derived using LA. For

AMV retrieval using improved tracer selection algorithm Fig. 6 a Bias and b RMSVD for collocated RAOB and AMV pairs at different pressure levels (100hPa bins). Solid, dashed, and dotted lines indicate LA, HC, and EUM_NF, respectively

example, if the MVD at beyond 25 m s−1 is considered as a percentage of the wind speed, the normalized MVD for AMVs derived using HC and LA is 0.25 and 0.28, respectively. This corroborates the earlier results that HC AMVs have a better accuracy in comparison to LA AMVs. Fig. 7 a Mean direction difference and b mean speed difference for collocated RAOB and AMV pairs at different pressure levels (100-hPa bins). Solid, dashed, and dotted lines indicate LA, HC, and EUM_NF, respectively

4 Conclusions Tracer selection in AMV retrieval aims at finding characteristic features in an image that are representative of motion. Widely used operational tracer selection techniques seek tracers with high gradient values and filter out highly coherent

I. Kaur et al. Fig. 8 a No. of collocations and b standard deviation for collocated RAOB and AMV pairs at different pressure levels (100hPa bins). Solid, dashed, and dotted lines indicate LA, HC, and EUM_NF, respectively

tracers. This study presents a new technique for tracer selection based on selecting corners from the image gray values. A widely used corner detection algorithm known as Harris corner (HC) detection is used for extracting the corners in an IR image. The AMVs derived using HC are compared with AMVs derived using local anomaly (LA) technique as reference. Qualitative comparison of both techniques shows a larger number of retrievals in HC at the upper level. Semitransparent cirrus clouds often cover a large part of the upper atmosphere particularly in the summer monsoon, and these clouds often make good tracers due to high gradients associated with them. HC effectively identifies the corners Fig. 9 a MVD for collocations between AMVs derived using LA and RAOB (solid curve) and total number of observations (dotted curve) plotted against average speed (3 m s−1 bins). b Same as a but for AMVs derived using HC

a

b

linked with the cirrus clouds, and this might be the reason for increased number of retrievals at high level. Validation of AMVs retrieved using HC shows a clear improvement in AMV accuracy over LA. Maximum improvement is seen at the low levels, where the NRMS reduces from 0.62 to 0.44 for LA and HC, respectively. High and mid levels also show an improvement of about 7–10 %. But HC leads to a larger slow bias in the upper levels. AMVs derived by EUMETSAT from Meteosat-7 are used operationally by several numerical weather prediction centers and hence provide a quasibenchmark. Comparison of the accuracy of the AMVs derived by HC against unfiltered EUMETSAT AMVs shows

AMV retrieval using improved tracer selection algorithm

comparable accuracy in terms of MVD and RMSVD, but the NRMS values are smaller for the former. But when quality filtering as used operationally for the EUMETSAT winds by the NWP centers is applied, HC AMVs show slightly higher errors. It should be noted that the algorithm used for retrieving AMVs at EUMETSAT differs in many aspects from the present technique and these differences can lead to significant changes in the accuracy. Improved quality of HC AMVs against unfiltered EUMETSAT AMVs gives an indication of the utility of the new approach for providing good-quality vectors. As the current HC methodology did not provide any quality indicator value, generation of the HC AMVs with quality indicator values would be taken up on a high priority. In HC, the AMVs are initially derived over the corner locations. Corners are dynamic and not part of any static grid, but the subsequent multiplet-based retrieval procedure requires the AMVs over a grid. Though gridding of the vectors does not affect the number of retrievals, each wind vector loses out on the significance of the actual pixels contributing towards the tracking and height assignment. In the future, the use of information from the actual vector locations would be investigated. The possibility of incorporating salient features from HC into the operational tracer selection technique will also be explored in the future. With the recent launch of INSAT-3D, this technique can also be explored further using improved imager data from INSAT-3D, when it becomes fully operational. Acknowledgments The authors would like to thank the anonymous reviewer for carefully reviewing the manuscript and providing valuable comments which have helped in improving the manuscript considerably. The authors would also like to thank EUMETSAT (http://archive. eumetsat.int/; http://eportal.eumetsat.int) for providing the Meteosat-7 data. The authors are thankful to Sh. Nikunj Darji, Scientist, Space Applications Centre, for his useful insights into the initial development of the Harris corner technique. The authors are also thankful to the Director, Space Applications Centre, Indian Space Research Organisation, and the Deputy Director, EPSA, for their encouragement.

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