Introduction
Thunderstorms constitute a major fraction of tropical rainfall. The distribution of the rain is, however, very patchy. The speed and direction of movement of thunderstorms change with seasons and climatic regions. Many hazardous phenomena also occur with thunderstorms, such as strong gusts, lashing rain, and hail. Meteorologists, as well as society, will gain from a better understanding of thunderstorm behavior. Specifically, meteorologists have to learn the structure and the dynamics of thunderstorms so that they can issue useful forecasts and warnings to the lay community. Therefore, thunderstorms have been observed with airborne instruments, radar, and dense networks of surface instruments. For a review of observations and many numerical simulations of thunderstorm behavior, see Houze (1993).
Weather satellites have added to the knowledge about thunderstorms with visible light (Vis) and infrared (IR) sensors. Bader et al. (1995, chapter 6) reviewed studies in the United States and Europe, correlating the behavior of thunderstorms to their structure seen in satellite images. The advantages of the Vis and IR images are the fine spatial resolution and high temporal frequency of observation. There are disadvantages. First, even with a bispectral view, only the anvil cirrus and the tops of the thunderstorm can be separated. Second, the rain rate from thunderstorms is only roughly correlated with the IR brightness temperature (BT) and reflectivity in the images.
To see through the clouds for a multilevel view, microwaves with wavelengths much larger than ice crystals have to be utilized. Further, because the transparency of moisture and cloud droplets are frequency dependent in the microwave (MW) range, multifrequency MW data appear to be useful for the heightwise sensing of hydrometeor content.
The earliest significant MW observations on thunderstorms came from Adler et al. (1990). They studied a thunderstorm with a microwave sensor and with 4-km spatial resolution from an airplane. The first operational satellite observations useful for looking at thunderstorms came from the Special Sensor Microwave Imager (SSM/I) on the Defense Meteorological Satellite Program satellites. The SSM/I data at 85.5-GHz and with 15-km nadir resolution are certainly usable as images, but at lower frequencies (37, 22.2, and 19.3 GHz) the spatial resolution is coarse and the data are not very useful. At 85.5 GHz, however, SSM/I sees only the rain core within thunderstorms, with the rest of the structure being nearly transparent to the window frequency.
Since 2001, the Advanced Microwave Sounding Unit-B (AMSU-B; Saunders 1993) has been sending data at five frequencies and at 16-km resolution with a 6-hourly global coverage. Viewed as images, these data are seen to contain clouds, moist structures, and (larger) features in different layers. In such images, thunderstorms and their internal structure (down to sensor resolution) can be studied with these images. This advantage of a multilayered view is substantive even against poor temporal and spatial resolution.
The right tool to study structure is one that separates and locates spatial frequencies. Fourier transforms can only separate the spatial frequencies. To locate these frequency components, wavelet transforms (WT) are used (Press et al. 1992). The commonly used wavelet transforms, namely, continuous and discrete decimating, have certain deficiencies. Hence, an interpolating WT called à trous (with holes) WT (Shensa 1992) is used. The Indian subcontinent has a monsoon climate, implying seasonal wind shifts and seasonal thunderstorm behavior. Therefore, the subject of this paper is to show seasonal variety (in six classes) in the structure of thunderstorms over the Indian subcontinent and adjoining seas, as shown by the à trous WT of the AMSU-B data.
This paper is organized as follows. In the next section, the seasonal patterns of pressure and wind over India during the thunderstorm season are discussed. In section 3, a short description of AMSU-B data and their processing is given. In section 4, sizes and BTs of detectable cloud and feature types are discussed. In section 5 the right tool for size-based classification, a multiscale à trous wavelet transform, is discussed. In section 6 examples of the application of this tool for deriving structure of various thunderstorms are given. The last, section 7, is for concluding remarks.
Weather pattern over India during the thunderstorm season
The Indian subcontinent comes under the cold subtropical westerly wind regime in winter (December– March) and in the premonsoon (April–May) seasons. Between these westerly winds and the low-latitude trade wind easterlies, a zone of weak winds occurs, below the subtropical anticyclones. After the monsoon retreat, the westerly winds return to India, but in a weak form.
Figures 1a–1c show the mean sea level pressure, 850- and 300-hPa winds during April 2002, as representative of the premonsoon period. Many deep-amplitude troughs move across the north of India during this period. Thunderstorms occur during the passage of such troughs. As Fig. 1b shows, winds in the 20°–25°N zone are strong and westerly. In the 15°–20°N zone they are weak and westerly. These two cases are considered in sections 6a and 6b, respectively. The subtropical jet (STJ) stream is a part of the cold upper-westerly winds. It has an extra core in the 18°–20°N zone, in March– April.
In April, the peninsula south of 15°–18°N has weak winds throughout the troposphere (Figs. 1b and 1c). This case is considered in section 6c. Light winds are also common in May–early June and immediately after the withdrawal of the monsoon in October. Solar heating is strongest in these periods and many thunderstorms occur. These thunderstorms are similar to those considered in section 6c.
The August 2002 mean patterns shown in Figs. 2a– 2c are representative of the southwest monsoon season that lasts from June to October. During this period, thunderstorms embedded in the stratiform clouds occur over the Indian subcontinent. By the end of June, the subtropical anticyclone moves to Tibet and trade winds cover the entire region. The main synoptic-scale features in the monsoon season are the monsoon trough (Fig. 2a) and low pressure systems that move westward along the trough. Low-level winds at 850 hPa (Fig. 2b) are easterly to the north of the monsoon trough, and westerly to the south of the monsoon trough. These two cases are considered in sections 6d and 6e, respectively. The monsoon winds are 5–6-km deep. Strong, easterly winds blow above the monsoon winds. These are strongest over the 10°–25°N zone. The strong core of these winds is termed the tropical easterly jet (TEJ). Figure 2c shows the 300-hPa winds. Thunderstorms considered in section 6e are further divided as occurring under weak easterly winds and those occurring under TEJ.
AMSU-B sensor and data
The AMSU-B instrument flies on the National Oceanic and Atmospheric Administration (NOAA) polar- orbiting satellites. It is a scanning radiometer with a cross-track scan. The instantaneous field of view (IFOV) is 1.1°, which for nadir view is 16 km × 16 km (on ground). Each scan line has 90 pixels covering 2120 km (Goodrum et al. 2001). Each of the 90 pixels is sampled at 89, 150, 183.3 ± 1, 183.3 ± 3, and 183.3 ± 7 GHz. The last three channels are symmetrically distributed at ± 1, ± 3, or ± 7 GHz on the wings of the 183.31-GHz water vapor absorption band. Transmission of microwaves in the five channels of the AMSU-B is frequency dependent because of absorption by moisture and oxygen. The radiances measured by the 89-GHz channel are fully affected by the surface and the lowest layer of atmosphere. Their effect on the 150-GHz channel radiance is partial. The higher-frequency channels show only absorption due to higher clouds and moist layers. These characteristics allow the three-dimensional assessment of moisture and clouds.
AMSU-B data from NOAA Satellite Active Archive for 2001 and 2002, from NOAA-15 and NOAA-16 satellites, is used in this study. NOAA-15 data suffer from radio frequency interference. This is corrected with the method prescribed in appendix M of the NOAA KLM user's guide (Goodrum et al. 2001). The images are geometrically distorted. This distortion was removed by resampling a scan line at a 16-km fixed resolution to 136 pixels. Because the main concern is with structure, BTs from the two AMSU-B instruments are presumed to be without any significant bias. The digital counts data are converted to BTs. The BTs are saved in a byte format. These five-channel × 136 (pixels) × 256 (lines) data are viewed as five images. Latitude– longitude values for each pixel are stored in companion files. Using the latitude–longitude data, a grid is applied to the images. The grayscale is condensed using lookup tables suited for warm or cold temperatures. Warm brightness temperatures are dark while cold brightness temperatures are seen as bright. To meet the requirement of having a reasonably uniform background, 64 × 64 pixel or 1024 km × 1024 km subimages of the channel images are extracted. These subimages are resolved into different spatial scales using the à trous wavelet transform. All of the software is developed in-house.
Overall more than 200 storms of all sizes were studied. Data on wind and thermodynamic profiles of radiosonde stations nearest to the location of thunderstorm are also used.
Detectable cloud types and structure in AMSU- B images
The microwave brightness contrast and size signatures for different cloud types are caused by the spatial distribution of water vapor and hydrometeors, such as cloud droplets, raindrops, ice crystals, and hail, resulting in absorption or scattering within the cloud. Weather satellite images show all the types of clouds and cloud features in varied sizes. Therefore, the sizes and microwave brightness of all cloud types are given in Table 1. Clouds (World Meteorological Organization 1975) and cloud feature sizes are given in terms of AMSU-B pixels of 16 km × 16 km size. What emerges from Table 1 is that none of single elements of any of cumuliform clouds [stratocumulus (Sc), cumulus (Cu), cumulonimbus (Cb), altocumulus (Ac), and cirrocumulus (Cc)] are likely to be discernible in the AMSU-B data because of their size. The types that may be identified in these images are stratus (St) sheets/fog in winter, Cu lines and waves, altostratus (As), cirrus (Ci) streaks, cirrostratus (Cs), cumulus clusters, thunderstorms, and clusters of thunderstorms. It is a viable proposition to classify them mainly by size, supported by their brightness.
Different cloud types should have distinct signatures (Muller et al. 1994). In actual images, clouds occur within a background of water vapor and, sometimes, with surrounding thin clouds. This reduces the contrast in the image. At 150 GHz, the response to ice crystals and raindrops, as well as transparency to water vapor, is high and the contrast is best. Therefore, clouds show well in 150-GHz images. The exception to this is high cirrus. It shows best in 183.3 ± 1 GHz images. Only thunderstorms show in all the channels.
At this stage, the reasons for wanting to know the structure of thunderstorms are repeated, namely, to obtain a better understanding of strong winds, lashing rain, and lightning. Strong winds are mainly associated with midlevel wind shear (Houze 1993). This shear produces significant tilt. The tilt may cause the location of the intense rain to shift downstream and may be seen as a shift of the intense BT signature at 183.3 ± 7 GHz.
AMSU-B has a good capability of showing hydrometeors in five different layers from the sensed clouds. This five-layer view may allow an assessment of the clouds' rainfall potential. If a cloud is bright in the 183.3 ± 3 GHz and 183.3 ± 1 GHz channels, it is a tall cloud and large ice crystals are present even at high levels. Such a cloud may possess heavy rain. If (say) the 183.3 ± 3 GHz channel pixels are bright but the 183.3 ± 1 GHz channel pixels are gray, or pixels in both the channels have low brightness, the cloud may not produce significant rain. All these issues are addressed in the first case study in section 6. The case of heavy rain from warm cumulus is different and will bear a separate investigation.
In thunderstorms, each core part, namely, the inner cumulonimbus towers (containing updraft and downdrafts), the altostratus, the cirrus in the anvil, and curved cumulus lines ahead of the gust front, has its own distribution of hydrometeors. Considering the size of AMSU-B pixels, the Cb tower (t) may be 1–2 pixels, the altostratus from cumulonimbus (aS) may be 3–4 pixels broad, and the cirrus anvil (c) may be 2–3 pixels broad. In addition, the cumulus–stratocumulus fields in the vicinity of thunderstorms also show in these images. The present study seeks to find if the signatures of these parts are distinctly seen in different wind regimes. Therefore, size analysis of the inner features of thunderstorms is likely to prove useful in classifying the thunderstorms from AMSU-B images.
Multiscale analysis
Size analysis implies analysis into spatial frequencies or scales. If the meteorological signals were stationary, then Fourier analysis would have helped. The meteorological signals are nonstationary and a wavelet analysis is indicated. The multiresolution transform used in the classification is discussed below.
Wavelet transforms
It is common in science to analyze signals using basis functions. Fourier transforms (FT) are a prime example of analysis using sinusoidal bases. In the discrete case, a complex signal of N samples (length 2N) is rearranged in a frequency domain of exactly 2N values. Thus, the frequency-wise distribution of the magnitude of the signal is known. However, the frequency and space distribution of signal magnitude is not revealed. Wavelet analysis (Press et al. 1992) alleviates this problem.
Wavelet transforms come in two types, continuous (CWT) and discrete (DWT). In a CWT, a mother wavelet is convolved with the function to be analyzed. As the scale and position changes, the subparts of the function at different parts of the domain and of different size are revealed. If the function to be analyzed is N dimensional, all WTs are N + 1 dimensional. This increases the data size and slows down the computation.
The DWTs may be decimating (the amount of the data is reduced in every iteration of the transform) or nondecimating. They are not unique, given the large number of possible analyzing wavelets. Further, decimating DWTs implemented using Mallat's algorithm with Daubechies filters (Press et al. 1992) are not translation invariant. The transforms are also difficult to interpret due to decimation at each resolving scale. To meet these deficiencies in decimating WTs, Shensa (1992) introduced the discrete approximation to the CWT called à trous. The implementation of the à trous DWT is explained quite well in Starck et al. (1998).
À trous wavelet transform
The DWTs using Mallat's algorithm, being decimating transforms (remove data in every successive generation), have the undesirable property of not being translation invariant. For two-dimensional image data, transformed subimages in off-diagonal quarters become difficult to interpret. To circumvent these difficulties the à trous algorithm (Shensa 1992) is used. It is a nondecimating, dyadic algorithm. That is, at all stages the image retains its size. At every stage the image scale doubles, or the objects of 2 times the size are successively revealed. Translation invariance is maintained. Because information is not lost in decimation, the equivalence of pixel values at each scale with radiance would be maintained.
A very brief description of the à trous transform is given below. Let C0(k) be the sampled dataset. This dataset is obtained from the continuous function f(x) by taking the scalar products at pixels k of f(x) with a scaling function Φ(x). The function Φ(x) is a low-pass filter.
- A wavelet function Ψ(x) obeys a dilation equationxlglx
- The discrete wavelet coefficients are calculated withWjklglCj−1kj−1l
The wavelet coefficients Wi(k) at scale i are found using successive approximation Wi+l(k) = Ci(k) − Ci+1(k) and, in such a case, Ψ(x/2)/2 = Φ(x) −1/2Φ(x/2).
Cj are given by Cj(k) = Σl h(l)Cj−1(k + 2j−1l) and in turn h(k) are derived from 1/2Φ(x/2) = ΣI h(l)Φ(x − 1).
Summation above is over the n stages of wavelet coefficients. The CRem(k) is the smooth remainder signal array.
The scaling function chosen for à trous analysis needs to have good interpolating performance because the analysis introduces zeros (holes) in every new i plane, and this needs smoothening. For this reason, spline functions are favored in the à trous DWT. Two such functions are the triangle function and B3 spline. The convolution masks used with them are hTRI(l) = {0.25, 0.5, 0.25} and hB3(l) = {0.0625, 0.25, 0.375, 0.25, 0.0625}. In the case of a two-dimensional image, matrices hTRI(l)T × hTRI(l) or hB3(l)T × hB3(l) are used for the DWT. Alternately, the filter given above may be used first on the columns, and then on the rows of the image. This procedure is followed in the present case.
Clouds and their background in microwave images
Remotely sensed images show some target objects against a background. The image also contains either additive or multiplicative noise. Additive noise is external to the measurement process, such as thermal noise. Multiplicative noise is intrinsic to measurement, such as the gain of a receiver or striping in the images. If the background and the noise can be described analytically or statistically, they can be removed.
The simplest case is that of a stationary (image) variable and Gaussian noise. In this case the noise standard deviation (SD) may be calculated. If a variable value exceeds 3 times SD, then the value may be safely said to be significant (Starck et al. 1998). In case of multiresolution images, an SD for the whole image, SDim, and then one SDi for each resolution plane are calculated. Starck et al. (1998) state that noise SD for the ith plane is SDim × SDi, in the astronomical case. The wavelet coefficients exceeding this value may be deemed to be significant wavelet coefficients. The wavelet components deemed insignificant are merged with the remainder, CRem, and are subjected to analysis at the next scale. If the noise were multiplicative, a log transformation of the image would make the noise additive and could be removed using the method described above.
The above method works well in the astronomical field with either a dark or slowly varying background. In the atmospheric microwave image case, the ground, sea, and clouds together produce a multimodal intensity distribution. The full image has a large SD and the mean may not be close to any one of the modes. To alleviate this difficulty, 64 × 64 pixel subimages (1024 km × 1024 km) containing clouds of interest are chosen. These subimages have a reasonably uniform background and a single-mode intensity distribution. A threshold, n × SDi (n = 1, 2, or 3), is used for separating clouds from the background.
Despite this procedure described above, some significant, but weak, structure may be lost to the remainder array CRem. To recover such structures, the whole process is iterated (Starck et al. 1998). In the present work three iterations were found to be sufficient for recovering all structures.
In microwave cloud images, the background is formed by radiance filtering through moisture. In the monsoon season the moisture is in a deep layer and clouds have little contrast. The level of significance is, therefore, set at 1 SD. All pixels colder than SDi are deemed significant. Pixels warmer than the threshold are added back to the remainder signal. After one series of wavelets is found, the remainder is once again put through the à trous transform until SD stops changing.
If this transform were to be applied to microwave images either from AMSU-B or the Microwave Humidity Sensor (MHS), the subimages generated over a number of scales would show objects of less than 1, 1– 2, 2–4, 4–8, 8–16, 16–32 … pixels or 16, 16–31, 32– 63, 64–127, 128–255 … km in size. In Table 1 the sizes of various clouds and cloud features are classified. It happens that all of the eight image classes can be safely separated mostly on the basis of size alone. Because the focus is presently on thunderstorms, the wavelet scales 2 and 3 are of interest. During the strong monsoon phase cumulonimbus clouds were smaller in size. For such clouds, scales 1 and 2 are important. In section 5 the various cloud types are analyzed. By basing the analysis on size, coherent parts of thunderstorms are separated or segmented.
Case studies
All of the case studies are from the Indian subcontinent. The geographical location of each thunderstorm case is shown in Fig. 3. The structural behavior of these thunderstorms is explained with wind and humidity data from radiosonde ascents from stations close to the respective thunderstorms. These radiosonde stations are also marked on Fig. 3.
Thunderstorm instances are discussed below, each with the help of three images. Surface and the geographic context of a thunderstorm are seen clearly in the 89-GHz image. Therefore, Fig. 3a is the BT image slice at 89 GHz. Warm BTs are dark while cold BTs are bright (negative image). This image shows the extent of the main convective region. The other two images (Figs. 3b and 3c) are the wavelet transforms at either scales 2 and 3 or scales 1 and 2. The wavelet images are printed positive such that large negative components are dark.
Thunderstorms in strong westerly winds
On 2 April 2002 two thunderstorms were seen over north Bihar, India (A), and southeast Bangladesh (B) in the morning (0730 LST) NOAA-15 pictures. The storm locations were close to 26°N, 87°E and 23°N, 92°E, respectively. These are seen in Figs. 4a–e. Both A and B were seen clearly up to 183.31 ± 3 GHz.
For storm A, the coldest BTs were on the eastern and the southeastern sides. For storm B, the coldest BTs occur slightly inside the storm, on the northeastern side. Among (the five channels, the coldest BTs are in the 150-GHz image. The difference between the coldest BT and the rest of the cloud, or dBT, reduces with frequency (or altitude). However, between 150 GHz and 183.3 ± 3 GHz, the dBT is similar, confirming the origin of most of the scattering from a layer close to medium levels/ freezing level. In the upper layers of the storms, both ice crystal sizes and numbers reduce. No significant displacement of features is seen among the images. The dBT for the 183.3 ± 3 and 183.3 ± 1 GHz varies with individual thunderstorms.
To investigate the tilt of the thunderstorm, the à trous transform of the subimages at 89 and 183.3 ± 3 GHz, at scale 1, is shown in Figs. 5a and 5b, respectively. For storm A, the edges do not show any significant shift. Given the 16-km resolution of the AMSU-B sensor, this is as expected. Given the loose structure of storm B, sharp edges are not seen at all. Therefore, until the resolution of MW sensors improves to 5–8 km, this part of the thunderstorm structure cannot be described.
In Figs. 6a–e, the à trous transform of all the subimages is shown at scale 2. In these images, objects of scale 2, or 16–32 km, are highlighted. This size includes the main core of the thunderstorm and some trailing features associated with the thunderstorm environment. The extended features to the northeast of storm B are of this type. Because these are mainly seen in the lower frequencies, these are low-level Sc–Cu-type clouds. This was also seen in Fig. 4.
From the image analysis carried out so far, it may be concluded that as far as a minimal and robust description of thunderstorm structure is concerned, one subimage (at 89 GHz) and two à trous transformed images (at scale 2 and 3, or scale 1 and 2 from either 150 or 183.3 ± 3 GHz) suffice. This is followed in the following case studies.
In Fig. 7a both A and B are elliptical with the major axis along the south-southwest–north-northeast direction facing the westerly wind. The cloud A in Fig. 7a is intense toward the east with two distinct BT minima (not visible with the brightness lookup table used). Cloud B is more intense toward the southwest. In Figs. 7b and 7c wavelet transforms at scales 2 and 3 are shown. At scale 1 (Fig. 5a), no intense structures are seen. One small bright structure each in both clouds A and B is clearly seen at scale 2. In Fig. 7c, both the clouds are intense over the entire extent of the cloud; A is more rounded, while B is elongated. Cloud B also has a tail trailing toward the north-northeast. This confirms the expectation expressed in Table 1 that significant structure associated with this type of thunderstorm is at scales 2 and 3 and not 1. Hence, except in the strong monsoon case, scale-1 wavelet images are not shown.
The upper winds of Patna (25.60°N, 85.10°E) at 0000 UTC [0530 Indian Standard Time (IST)], about 80 km west of cloud A, are used for the discussion. The wind is mostly westerly. It varies from 90° at 10 kt at the surface, to 80° at 20 kt at 300 m, to 230° at 4 kt at 925 hPa, to 315° at 13 kt at 850 hPa. With this shear, the main cloud moves steadily toward the southeast. Maximum wind speed change of 16 kt occurs between 600 and 523 hPa (4.36 and 5.43 km altitude). The wind remains steady at 290° at 50–60 kt above 500 hPa. With this profile, the cloud would be leaning forward (toward the southeast), more so between 600 and 520 hPa. With this wind profile the t part (that is, the tower) of A is in the leeward part of the storm and the aS part is windward. These are marked in Fig. 7b. Cloud A does not show any cirrus canopy because there is no detrainment with the wind at the cloud-top level.
The relative humidity for Patna was 80% at 925 hPa, 50% at 850 hPa, and dropped to 20% at 660 hPa (3600 m). The entire supply of moisture is, therefore, through the low level. Through the 600–525-hPa layer dry entrainment would have been there.
The upper winds over Agartala (23.88°N, 91.25°E) are used to explain the behavior of B. Wind at 925 hPa is 020°/17 kt. This explains the southern position of the t part. At 850 hPa wind is 340°/19 kt, and by 750 hPa (2.6 km) wind is 260°/30 kt. Above 750 hPa wind direction varies little—the speed increases to 52 kt by 300 hPa. The main layer for vertical shear is between 585 and 525 hPa (4.6–5.4 km). In this layer shear is 260°/ 12 kt and temperature changes from −4.5° to −10.5°C. This wind profile explains the northeastward shift of aS and its intensity. Because vertical shear is not large at higher levels, a separate cirrus anvil is not seen.
Thunderstorm in strong upper westerly winds
On 4 April 2002 a well-developed thunderstorm with two cells was seen in the evening (1930 LST) NOAA- 15 picture, just off the Andhra Pradesh coast, close to 16°N, 82°E (Figs. 8a–8d). The brightest part of the storm was facing west-southwest. Winds were mainly westerly with high speeds in upper levels. In Fig. 8a, the cloud top appears to stream away to the east. The scale-2 image for 183.3 ± 1 GHz (cirrus level) is seen in Fig. 8d.
In Fig. 8b, two distinct Cb cells are visible with the southeastern cell more intense. Grayish plumes appear to stream from the two cells toward the east-northeast. These are about 6–8 pixels in length and 2–3 pixels wide. One longer plume extends another 8–10 pixels. The main Cb cells appear to be rich in hydrometeors while the gray plumes have fewer hydrometeors or have smaller hydrometeors. In Fig. 8d, the plume of the southeastern cell streams northeastward. Cirruslike plumes are extending toward the east from the two neighboring thunderclouds in Fig. 8d. In Fig. 8c the individual cells have merged and a large oval shape with dark (very large negative) values is visible. The size of the oval is similar to the individual plumes at scale 2. The other longer puff is also visible. Its shape strongly resembles a Gaussian plume.
Vishakhapatinam (17.70°N, 83.30°E) is quite close to the thunderstorm. Its thermodynamic profile at 1200 UTC is used to understand the behavior of the storm. The environment is moist up to 700 hPa and dry above 500 hPa. The winds vary between 240° and 310° and become strong and westerly at high levels. The wind shear in the 600–500-hPa layer is northerly at 10 kt. In this layer the air is becoming dry. The northerly 10-kt wind change would then cause entrainment of dry air in the storm. In the 380–315-hPa layer, shear is roughly westerly at 15 kt. This layer is producing the plumes emanating from the storm. The layer is between 7.9 and 9.2 km and at a temperature between −25.5° and −32.5°C. The plume clouds are likely to be mostly water droplets with few ice crystals. This probably explains the gray appearance of the plumes. Above 9.2 km the shear is southwesterly at 5 kt. Thus, clouds above 9.2 km stream toward the northeast, as seen in Fig. 8d. Thus, it is possible to separate the t and c parts of the cloud.
Thunderstorms in light winds
On 16 April 2001, thunderstorms are seen in the evening (1930 LST) NOAA-15 picture (Fig. 9a). Two thunderstorms are marked A and B in Fig. 9a. Cloud A is close to 15°N, 78.5°E and B is close to 12°N, 77°E. The interesting feature of both A and B is that the appearance is rounded. It does not change in Figs. 9b and 9c. If anything, the clouds become more symmetrical.
The nearest radiosonde station to both A and B is Bangalore (12.96°N, 77.58°E). However, the 1200 UTC 16 April data are not available. Because in April winds are light over the southern peninsula, Chennai (formerly Madras 13.0°N, 80.18°E) data are used. Winds are light, not exceeding 15 kt up to 200 hPa. Below 700 hPa, wind direction is also changing. With the wind profile showing no change, the cloud is nearly vertical and very slow moving. The humidity profile is highly humid up to 200 hPa. Thus, midlevel dry and cold entrainment is not available. In this cloud it is not possible to see any displacement between the t, aS, and c parts.
Thunderstorms to the north of the monsoon trough
On 7 July 2002 seven thunderstorms in an arc were seen in the afternoon (1430 LST) NOAA-16 picture over Uttar Pradesh, between 25°–30°N and 75°–82°E (Figs. 10a–c). The location of the central thunderstorm is over 28.5°N, 79°E. The thunderstorms were very close to the Himalayas. The wavelet scales 2 and 3 show much clutter at 150 GHz. Hence, scale-2 and -3 wavelet transforms of the 183.31 ± 3 GHz image are used for recognizing the thunderstorm structures. The scale-2 image shows the thunderstorms have a 2–3 pixel size and to be reasonably intense. Scale-3 clouds are larger, up to 4 pixels, and have a noticeably weaker intensity as compared to other scale-3 images. At both of the scales, the cloud appearance is rounded with no significant streaming parts c.
The southwest monsoon was strong. The upper winds of Delhi (28.58°N, 77.20°E) and Lucknow (26.75°N, 80.88°E) at 1200 UTC (1730 IST) are used because the thunderstorms were spread over a large geographic region. The axis of the monsoon trough was to the south of the region of these thunderstorms. The wind speed over Delhi and Lucknow is between 5 and 10 kt, right up to 200 hPa. Wind direction over Delhi is roughly from 20° and over Lucknow it is from 50°. These profiles imply that there is no significant wind vertical shear in Figs. 10a–c. Therefore, the shape of clouds at scales 2 and 3 is symmetrical, as may be expected.
The air over Delhi was saturated between 4.8 and 7.8 km, where the temperature was +1.2° to −14°C. In this layer only water droplets may be expected. Further, the largest wind speed of 17 kt occurred at 400 hPa, at the top of this layer. Thus, very few water droplets were blowing out of the clouds. This probably is the explanation of the weak intensity at the scale 3 (Fig. 10c).
Thunderstorms to the south of the monsoon trough
To the south of the monsoon trough, the wind direction below 500 hPa varies between west-southwest and west-northwest. The upper-level winds are easterly and increase in speed above 300 hPa. During the weak monsoon phase, low-level winds become weak, less than 10 kt, while in the strong monsoon phase the wind speed increases to 25 kt. The upper easterly winds also change between 15 and 60 kt during the two phases. Both cases are illustrated below.
Weak monsoon phase
A thunderstorm is seen close to 20°N, 83°E in the early morning (0230 LST) NOAA-16 picture of 2 August 2002. It is shown in Figs. 11a–c. The coldest brightness temperature in the 150-GHz image was −99°C. This corresponds to the spot marked t in Fig. 11b. In Figs. 11b and 11c the storm spreads toward the northeast of point t, but is mainly in the east–west direction. The aS part in Fig. 11c is larger and more intense than the region around t in Fig. 11b.
Winds of Bhuwaneshwar (20.25°N, 85.83°E), which is close to the storm location, are considered at 0000 UTC. Winds were 220°/17 kt at 925 hPa, 230°/20 kt at 850 hPa, and 230°/10 kt at 700 hPa. By 500 hPa, the wind became 130°/13 kt. At 400 and 300 hPa, the wind was 100°/23 kt and 90°/33 kt, respectively. The position of the most intense part of the storm in the southwestern part of the thunderstorm is explained by the low-level wind. The shear was 120°/10 kt between the 600- and 500-hPa layer and was 80°/15 kt in the 500–400-hPa layer. This explains the east–west-elongated wavelet components at scales 2 and 3. The shear is not excessive and this is responsible for the spreading of the aS part at scale 3. Even above 300 hPa, wind is not very strong, increasing from 33 to 43 kt. This is related to a rather small cirrus anvil c.
The freezing level was at 5.2 km and the temperature was barely −25°C at 300 hPa (9.7 km). Therefore, ice crystals in the cloud occur probably only in the upper, spread out part. This may explain the higher intensity of the wavelet components at scale 3. This argument does not change even if the wavelet components at 183.31 ± 3 GHz are compared.
Strong monsoon phase
In the 5 August 2002 morning (0730 LST) NOAA- 15 data, a small band of thunderstorms can be seen in Fig. 12a at 89 GHz. The thunderstorms are in a band, seen over and off coastal Andhra Pradesh (marked A). The thunderstorm over the coast is very close to Machilipatinam (16.20°N, 81.15°E). Because the clouds are small in breadth, the wavelet scales 1 and 2 are shown in Figs. 12b and 12c. In Fig. 12b, the cloud is most intense at the eastern end and likely contains the t part of the storm. This figure also shows gray clouds trailing to west for 4–6 pixels. These appear to be the aS part. In Fig. 12c the tails (c) are a little broader, but trail for a long distance, 16–20 pixels, to west.
At 0000 UTC 5 August 2002, the winds over Machilipatinam were strong and westerly in the lower levels. The surface wind at 270°/10 kt became 270°/24 kt at 925 hPa (probable cloud base). Winds weakened to 9 kt at 600 hPa and became 133°/9 kt at 435 hPa. The shear was 112°/16 kt between 4.3 and 7.1 km (and −1° and −18°C). This identifies the layer seen in Fig. 12b as aS. The top-level shear is 100°/14 kt in the 243–200- hPa layer (10.9 and 12.3 km, −47° and −57°C). This explains the cirrus layer trailing far to the west with a strengthening wind (Fig. 12c).
Concluding remarks
A large number of thunderstorms were considered. These fell into the six types of spatial behavior as summarized in Table 2.
The discussion above has been on two themes. The first is about a multiscale analysis of satellite images. By using the à trous wavelet transform, a discrete approximation to the continuous wavelet transforms is introduced into meteorological data analysis. To the best of the authors' knowledge, this analysis has not been documented in the meteorological literature. Being a dyadic (steps increasing by a factor of 2) transform, it is computationally inexpensive and also has the virtue of being translation invariant. The sum of all the wavelet components at a point is the image intensity. This means that contribution of within-cloud processes at each spatial scale can be separated into corresponding images. Though the à trous transform is used extensively in astrophysics, the prescription given by Starck et al. (1998) had to be modified to accommodate image intensities observed in AMSU-B images.
The second theme has been the analysis of thunderstorms over the Indian subcontinent and adjoining seas, as seen in the AMSU-B images. Data from 2001 and 2002 were considered. Over 200 images had thunderstorms. Their wavelet analysis revealed six patterns of the structure of thunderstorms. Three regions, namely, towers t (core up- and downdrafts within cumulonimbus clouds), spreading altostratus aS, and the cirrus anvils c, were identifiable. Figures 13a–e(2) show the schematic representation of the six thunderstorm types. A few additional observations are made here.
When winds throughout the storm are weak (as in Fig. 9) the thunderstorms are slow moving and likely to produce large rain collections along a shorter path. When the monsoon is weak, strong west/southwest winds occur in the 20°–25°N latitudinal belt as in Fig. 11. Weak easterly wind prevails above 500 hPa. The t part in the example of Fig. 13e(1) shown was in the southern end of an east–west-oriented As cloud mass. Cirrus were seen in a limited region. The storm movement is (most probably) to the northeast, given the strong southwest (15–20 kt) winds to 3 km. The anvil- like cloud is broadside to this movement. The scale-2 image is less intense than that of scale 3. This is probably due to fewer ice crystals in the monsoon clouds, because of the high upper-air temperatures in the June– September period.
The MHS, a European sensor very similar to the AMSU-B, will be on the new-generation Meteorological Operational Weather Satellite (MetOp) polar-orbiting satellites. The MHS frequencies would be 89, 157, 183.31 ± 1, 183.31 ± 3, and 190.31 GHz. The nadir resolution would be 15 km × 15 km, and each scan would again contain 90 pixels. Thus, it may be expected that the algorithms devised to work with AMSU-B would work also with the MHS and that the conclusions reached above would also be valid for the MHS data users. In the future, polar-orbiting weather satellite data from either AMSU-B or MHS would be broadcast on the Low-Resolution Picture Transmission (LRPT), the future digital equivalent of Automatic Picture Transmission (APT) of today. Because the LRPT is meant for small forecast offices, a better understanding of thunderstorm structure, gained here from AMSU-B, may lead to improved weather forecasts.
Acknowledgments
The work reported here was supported by Grant GOI/348 from the Indian Space Research Organization. The AMSU-B level-1b data were obtained from the NOAA Satellite Active Archive on the Internet. The radiosonde data were obtained from the University of Wyoming's soundings archive. The mean charts for April and August 2002 were obtained from NCEP.
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Premonsoon weather pattern as in Apr 2002. (a) The mean sea level pressure. (b) and (c) The 850- and 300-hPa mean wind patterns (respectively)
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Monsoon weather pattern as in Aug 2002. (a) The mean sea level pressure. (b) and (c) The 850- and 300-hPa wind patterns (respectively)
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Indian subcontinent. The locations of the six thunderstorm cases and the closest radiosonde stations are marked. Shaded ellipses represent the thunderstorms
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Multifrequency view of winter thunderstorms in strong westerly winds on 2 Apr 2001: (a)–(e) 89, 150, 183.3 ± 7 (labeled 176), 183.3 ± 3 (labeled 180), and 183.3 ± 1 (labeled 182) GHz. Latitude lines shown are 20° and 25°N. Longitudes shown are 85° and 90°E. All AMSU-B images shown are of 1024 km × 1024 km size
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Multifrequency view of the edges of the thunderstorm on 2 Apr 2001. Shift of the edges with frequency implies tilt in the thunderstorm. (a) and (b) The edges from à trous analysis at scale 1 for 89 and 183.3 ± 3 (labeled 180) GHz. There is no measurable tilt in the thunderstorm marked A. Edges of the storm B are not clear.
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Multiscale view of the winter thunderstorm on 2 Apr 2001. (a)–(e) À trous analysis at scale 2 for 89, 150, 183.3 ± 1 (labeled 176), 183.3 ± 3 (labeled 180), and 183.3 ± 7 (labeled 182) GHz showing the position of towers in the five frequencies. The 150-GHz image shows the best contrast
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Winter thunderstorms in strong westerly winds on 2 Apr 2001: (a) 89-GHz subimage, and (b) and (c) scales 2 and 3 of the à trous analysis of the 150-GHz subimage, marked 2 and 3, respectively. Here, (a)–(c) refer to the panels from top to bottom
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Winter thunderstorms in strong upper westerly winds on 4 Apr 2002: (a) 89-GHz subimage, and (b) and (c) scales 2 and 3 of the à trous analysis of the 150-GHz subimage, marked 2 and 3, respectively. (d) The 183.3 ± 1 GHz scale 2 subimage showing the cirrus plume, marked 2/182.3. Here, (a)–(d) refer to the top-left, top-right, bottom-left, and bottom-right panels, respectively
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Thunderstorms in light winds on 16 Apr 2001: (a) 89-GHz subimage, and (b) and (c) scales 2 and 3 of the à trous analysis of the 150-GHz subimage, marked 2 and 3, respectively. Here, (a)–(c) refer to the panels from top to bottom
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Thunderstorms to the north of the monsoon trough in weak vertical shear on 7 Jul 2001: (a) 89-GHz subimage, (b) and (c) 183.3 ± 3 GHz (marked 180.3). Higher frequency is chosen to avoid ground clutter related to the Himalayas. Here, (a)–(c) refer to the panels from top to bottom
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Thunderstorms to the south of the monsoon trough in weak vertical shear on 2 Aug 2002: (a) 89 GHz subimage, and (b) and (c) scales 2 and 3 of the à trous analysis of the 150-GHz subimage, marked 2 and 3, respectively. Here, (a)–(c) refer to the panels from top to bottom
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Thunderstorms to the south of the monsoon trough in strong vertical shear on 5 Aug 2002: (a) 89-GHz subimage. In this case the thunderstorm size is smaller and, therefore, (b) and (c) scales 1 and 2 of the à trous analysis of the 150-GHz subimage are shown (respectively). Here, (a)–(c) refer to the panels from top to bottom
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Schematics of the six types of thunderstorms considered. The panels reflect the order of cases studied in sections 6a–6e(2). Arrows show the qualitative direction and speed of the movement of the storm
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0595:COTOIU>2.0.CO;2
Physical sizes of different cloud types (in AMSU-B pixels)a and their brightness properties. The last column shows the wavelet scale(s) at which the cloud may be seen; t, aS, and c are the names used for parts of the thunderstorms
Signatures of different classes of thunderstorms
