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  • Stewart, R. E., J. D. Marwitz, and J. C. Pace, 1984: Characteristics through the melting layer of stratiform clouds. J. Atmos. Sci.,41, 3227–3237.

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  • ——, ——, and L. S. Chiu, 1991: Retrieval of monthly rainfall indices from microwave radiometric measurements using probability distribution functions. J. Atmos. Oceanic Technol.,8, 118–136.

  • Willis, P. T., and A. J. Heymsfield, 1989: Structure of the melting layer in mesoscale convective system stratiform precipitation. J. Atmos. Sci.,46, 2008–2025.

  • View in gallery

    The reflectivity data are collected over 10° × 10° lat–long grid boxes and eight regions. The five regions are located in the tropical oceans, and the others are on land: (1) Africa, (2) the Indian Ocean, (3) Australia, (4) the western Pacific Ocean, (5) the central Pacific Ocean, (6) the eastern Pacific Ocean, (7) South America, and (8) the Atlantic Ocean

  • View in gallery

    (a) Vertical cross section along the satellite track and vertical profiles of radar reflectivity at the different scan positions: (b) 6455, (c) 6465, (d) 6500. The scan starts at 9.5°N, 28.8°W, ends at 7.3°N, 25.7°W on 26 Jul 1998

  • View in gallery

    Maps of monthly mean melting-layer altitude from Jan 1998 to Feb 1999. The spatial resolution of the grid is 10° × 10° lat–long. White areas have no melting-layer altitude due to the insufficient occurrence of precipitations or nonexistence of well-defined melting layer

  • View in gallery

    (Continued)

  • View in gallery

    Distributions of the standard deviation of melting-layer altitude from Jan 1998 to Feb 1999

  • View in gallery

    (Continued)

  • View in gallery

    Seasonal variation of monthly mean melting-layer altitude averaged over 10° wide latitude belts: (a) 25°∼35°S and 25°∼35°N, (b) 15°∼25°S and 15°∼25°N, (c) 5°∼15°S and 5°∼15°N, and (d) 5°S∼5°N

  • View in gallery

    The seasonal cycle in monthly melting-layer altitude for eight selected regions. Each bar on the graphs indicates the standard deviation for each month

  • View in gallery

    Mean profiles of reflectivty for eight selected regions and four seasons: (solid) Jan, (dotted) Apr, (dashed) Jul, and (dash–dotted) Oct 1998

  • View in gallery

    The first three eigenfunctions of reflectivity profile for eight selected regions in Jan 1998

  • View in gallery

    Amplitude and phase (peak time) of the diurnal variation of the mean melting-layer altitude for eight selected regions and four seasons: MAM (Mar∼May 1998), JJA (Jun∼Aug 1998), SON (Sep∼Nov 1998) and DJF (Dec 1998∼Feb 1999) from the left to the right in each box. The direction of the arrow indicates the peak time after local midnight in a 24-h clock as shown in lower right corner and the length denotes its amplitude. The diurnal cycle over 90% statistical significance is indicated by thick arrow

  • View in gallery

    Scatterplots of monthly mean autocorrelation functions in 1998 for eight regions. The superimposed line (solid) represents the autocorrelation function of a random variable Y, which is a sum of a spatially red noise X and a spatially white noise ϵ. Here α indicates the lag-1 coefficient of the red noise, represented by the first-order autoregressive process. The e-folding value (e−1) of the autocorrelation is indicated by a horizontally dotted line

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A Summary of Reflectivity Profiles from the First Year of TRMM Radar Data

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  • 1 Department of Atmospheric Sciences, Texas A&M University, College Station, Texas
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Abstract

A preliminary climatology of reflectivity profiles derived from the first spaceborne precipitation radar (PR), which is on board the Tropical Rainfall Measuring Mission (TRMM) satellite, is described using the data from January 1998 to February 1999. This study focuses on the behavior of the melting-layer (bright band) altitude in stratiform precipitation. This analysis will be useful for improving passive microwave radiometric estimations of rain rates because it provides information about otherwise unknown parameters in the estimation models (the depth of the rain column). The monthly means of the melting-layer altitude estimated over 10° × 10° latitude–longitude grid boxes show that high melting layers (>4.5 km) tend to appear during extreme events such as El Niño and the Asian summer monsoon, and lower melting layers are usually observed in the winter hemisphere, which suggests a close relationship between surface temperature and the melting-layer altitude. Detailed climatologies of the profiles are provided for eight selected regions. For each region the seasonal variation of the meting-layer altitude and the mean and variation of the reflectivity profiles are discussed. The diurnal cycle of the melting-layer altitude and second-moment products, such as the spatial correlation along the satellite track, illustrate the irregular characteristics of the melting-layer altitude.

Corresponding author address: Dr. Kenneth P. Bowman, Department of Meteorology, Texas A&M University, College Station, TX 77843-3150.

Email: k-bowman@tamu.edu

Abstract

A preliminary climatology of reflectivity profiles derived from the first spaceborne precipitation radar (PR), which is on board the Tropical Rainfall Measuring Mission (TRMM) satellite, is described using the data from January 1998 to February 1999. This study focuses on the behavior of the melting-layer (bright band) altitude in stratiform precipitation. This analysis will be useful for improving passive microwave radiometric estimations of rain rates because it provides information about otherwise unknown parameters in the estimation models (the depth of the rain column). The monthly means of the melting-layer altitude estimated over 10° × 10° latitude–longitude grid boxes show that high melting layers (>4.5 km) tend to appear during extreme events such as El Niño and the Asian summer monsoon, and lower melting layers are usually observed in the winter hemisphere, which suggests a close relationship between surface temperature and the melting-layer altitude. Detailed climatologies of the profiles are provided for eight selected regions. For each region the seasonal variation of the meting-layer altitude and the mean and variation of the reflectivity profiles are discussed. The diurnal cycle of the melting-layer altitude and second-moment products, such as the spatial correlation along the satellite track, illustrate the irregular characteristics of the melting-layer altitude.

Corresponding author address: Dr. Kenneth P. Bowman, Department of Meteorology, Texas A&M University, College Station, TX 77843-3150.

Email: k-bowman@tamu.edu

1. Introduction

The Tropical Rainfall Measuring Mission (TRMM) is primarily intended to estimate monthly mean rainfall with a resolution of 5° × 5° latitude–longitude over the tropical oceans during its design lifetime of 3 yr. The data will be used to validate general circulation models and to understand the large-scale atmospheric circulation driven by the latent heat released from tropical precipitation. One of the advantages of TRMM is that sampling errors and related biases, such as beamfilling errors (Chiu et al. 1990; Short and North 1990) are reduced by its low altitude (350 km) and low inclination (35°). In particular, the non-sun-synchronous orbit leads to sampling at all local times over the course of a few weeks and reduces the diurnal bias drastically (Shin and North 2000). The other significant goal of TRMM is to provide three-dimensional radar reflectivity data. The TRMM radar is building a dataset that provides essential information on the vertical distribution of tropical hydrometeors. In addition to its primary scientific purpose, the radar data can be used to tune the algorithms for other instruments such as passive microwave radiometers.

The purpose of this study is to provide a summary of the TRMM radar data. It should prove useful in the estimation of rain rates with the passive microwave instrument. This kind of information is especially valuable because many microwave instruments that are operating (or planned) are without accompanying radars. The common unknown parameter needed in most microwave retrieval algorithms, such as those of Wilheit et al. (1977, 1991), Kummerow and Giglio (1994), and Tesmer and Wilheit (1998), is the thickness of the rain column, which is usually taken to be the melting-layer altitude (freezing-level altitude or in radar meteorology, the bright band). Above this layer most precipitation is in the form of snow or ice and does not attenuate microwaves very much. Most of the algorithms show a significant sensitivity to the altitude of the melting layer, because the rainfall integrated along the path determines the brightness temperature. Many case studies have been conducted to understand the characteristics of the melting layer since the 1950s (Austin and Bemis 1950; Ohtake 1969; Knight 1979; Leary and Houze 1979; Stewart et al. 1984; Fujiyoshi 1986; Klaassen 1988; Willis and Heymsfield 1989; and many others). Due to these field experiments the microphysical features of the melting layer are well established. However, it was impossible to construct a climatology of the melting layer at the global scale before the launch of TRMM. This study will focus on the climatological behavior of the melting-layer altitude as well as the reflectivity profile itself.

An advantage of our approach is that it does not depend on any rainfall product derived from the precipitation radar. Only the raw reflectivity data are used.

2. Data

Reflectivity data (so-called 1C21 in TRMM data classification) from the TRMM precipitation radar (PR) from January 1998 to January 1999 are used in this study. The TRMM satellite orbits the earth with an inclination of approximately 35° and an altitude of 350 km. The TRMM PR, one of five instruments on the TRMM satellite, measures the returned power at 13.8 GHz (2.17 cm). The PR scans across the ground track of the satellite every 0.6 s with a 34° scan angle, corresponding to a swath width of 215 km (Kummerow et al. 1998). The central ray among the 49 rays in each scan views the nadir (0° zenith angle). The reflectivity profiles of the nadir rays were binned in 10° × 10° longitude–latitude grid boxes for the latitudinal band between 35°N and 35°S, and also over eight selected regions (Fig. 1). The five regions are selected in the tropical oceans (the Indian, the western Pacific, the central Pacific, the eastern Pacific, the Atlantic) and the others are in land (Africa, Australia, and South America). Data below 1.5 km were excluded to avoid the influence of strong reflections from the surface. The reflectivity is expressed in dBZ where dBZ = 10 log10Z, and Z is the radar reflectivity factor. The 1C21 data are not corrected with any propagation loss due to rain or other atmospheric gases.

Figure 2 shows an example of a reflectivity cross section along a segment of the satellite track in the tropical Atlantic Ocean and three selected vertical profiles from the segment. A distinct bright band is found between 4.5- and ∼5.0-km altitude in the stratiform precipitation (Fig. 2a). The bright band can be interpreted as a transition layer where ice particles are melting. According to Houze (1997), the bright band is a clear feature of stratiform precipitation, although the bright band in all of stratiform precipitation structures may not be observed due to the detection ability of radar. The melting of frozen hydrometeors also occurs in convective precipitation. However, the bright band is not usually observed in convective precipitation due to strong convective air motions. The bright band or melting layer has larger reflectivity relative to its surroundings due to the increased dielectric constant of melting precipitation particles and the growth of droplets by coalescence. The decreasing reflectivity in the lower part of the melting layer is attributed to the breakup of droplets resulting from the increased terminal velocity (Battan 1973). The bright band is usually observed more distinctively with the lower-frequency microwaves because the enhancement of the reflectivity in the melting layer relative to that in the snow or rain is greater at the lower frequencies (Menighini and Kozu 1990).

3. Estimation of the altitude of melting layer

Our major concern here is to construct a preliminary climatology of the altitude of the melting layer, rather than other features such as its thickness or the absolute intensity of the reflectivity. The algorithm for estimating the melting-layer altitude uses three quantities:
  • the altitude of the maximum radar reflectivity Ho = H(dBZmax),
  • the altitude of the largest positive reflectivity gradient Hmax = H([(∂/∂H)dBZ]max),
  • the altitude of the largest negative reflectivity gradient Hmin = H([(∂/∂H)dBZ]min).
The altitude Ho is taken to be the altitude of the melting layer (bright band) if the following conditions satisfy
i1520-0442-13-23-4072-e1
where δH+ and δH are the upper part (between the freezing level and Ho) and lower part of the melting layer, respectively. The terms δH+ and δH are chosen in the following way. The thickness of the melting layer is known to be related to the intensity of precipitation;the thickness of the melting layer increases with rain intensity (Klaassen 1988). A thick band of high reflectivity, as in Fig. 2d, can be a distinct feature of convective precipitation. The melting-layer altitude is usually located slightly below the freezing level (0°C isotherm level), and δH+ is on the order of a few hundred meters (Meneghini and Kozu 1990). In an observational study by Austin and Bemis (1950), δH+ ranges up to about 0.73 km. The thickness of the entire melting layer, as measured by Leary and Houze (1979), ranges from 0.9 to ∼1.5 km. Here we take δH+ = δH = 1 km to correspond to the largest observed depth (1.5 km) ±250 m (the vertical distance between samples). Therefore, profiles with a melting layer deeper than 2 km are not included because such profiles are regarded as elements of convective cells. Of course, the algorithm is too simple to detect 100% of the melting layers in stratiform precipitation, but careful investigation reveals that this simple detection algorithm tends not to select broad melting layers that might have originated from convective cells. Again, this study focuses on the mean statistics of the melting layer, not separating convective and stratiform precipitation. Using a narrow-enough melting-layer criterion may allow us to avoid the contamination from the convective type of precipitations in making the climatology of the melting layer. Figures 2b and 2c show well-defined melting layers with layer altitudes of about 4.6 and 4.8 km, respectively. Profiles such as that in Fig. 2d are not included in this study.

Note that the brightband (melting layer) altitude is also provided as a standard TRMM product (algorithm 2A23). The TRMM algorithm uses a more complicated method than used here. For example, the freezing-level altitude derived from a climatological dataset is considered in the algorithm. Differences between monthly means from this study and algorithm 2A23 are on the order of a few hundred meters over 10° × 10° latitude–longitude grid boxes between 35°N and 35°S, and the difference does not appear to depend on seasons and geolocations. The two methods compare well, and our algorithm is not affected by potential changes in the standard TRMM algorithm.

4. Results

a. Mean spatial structure of melting-layer altitude

Figure 3 shows the distributions of monthly mean melting-layer altitudes Ho for all the months of 1998 and January–February of 1999. Here Ho is calculated using all reflectivity profiles collected within each 10° × 10° latitude–longitude grid box for each month. Due to insufficient occurrence of precipitation or nonexistence of distinct bright bands in stratiform clouds Ho is not defined over all of the grid boxes. Typically about 25% of the grid boxes, usually away from the equator, have no data in a given month. In particular, we cannot usually estimate the melting-layer altitude for the southeastern Pacific, which is usually under high sea level pressure throughout the year.

The pattern is predominantly zonal, extending or shrinking to the north and south with the seasons. The values of Ho range between 2.5 and 5.3 km during the period sampled so far. The highest values of Ho are found in the region where the Asian summer monsoon prevails, while the lowest values can be seen around the latitude of 30° in the winter hemisphere.

The maps show that high values of Ho tend to occur in the equatorial Tropics between January and August 1998. Especially high Ho’s are observed in the central and eastern tropical Pacific Ocean during the period between January and May. These regions shrink for the next three months, June–August. The first quarter of 1998 was under the influence of a strong El Niño, characterized by a warm sea surface temperature (SST) anomaly in the central and eastern tropical Pacific Ocean. The El Niño episode of 1998 was weakening and ending during the second quarter of the year. It appears that the high Ho’s over the two tropical oceanic regions, at least 0.5 km higher than the values during the second half of the year, result from the warm SST anomaly associated with the El Niño. Furthermore, this characteristic is evident in comparing January 1998 and January 1999, which was the beginning month of a La Niña episode. Regions with melting-layer altitude greater than 4.5 km are observed over the central and eastern tropical Pacific Ocean in January 1998, but disappear in January 1999. This is probably related to the cold SST anomaly in these regions. High Ho’s also occur in the regions subject to strong summer monsoon flows. The summer monsoon over southern Asia usually initiates in late spring and is present during the summer with intense rainfalls. The maps from May to August clearly indicate that melting layers higher than 4.5 km over southern Asia are associated with the cross-equatorial monsoon circulation that brings warm moisture fluxes from the equatorial region to southern Asia (e.g., Krishnamurti and Bhalme 1976; Rodwell and Hoskins 1995).

Regions where Ho ≈ 4∼4.5 km are located sparsely for the period January–August, but after this period high Ho values are dominant over the Tropics. The existence of a 4- to ∼4.5-km melting layer is limited to within 25° of the equator in the winter hemisphere, but in the opposite (summer) hemisphere, the 4- to ∼4.5-km melting layer tends to extend farther poleward. Low Ho’s (<4 km) are usually found at the latitude higher than 20° in the winter hemisphere and around 30° in the summer hemisphere. The northern boundary of low Ho in northern winter seems to be closer to the equator than the southern boundary. This feature may be attributed to the larger amount of landmass in the Northern Hemisphere (smaller thermal inertia).

The standard deviations (within the month) of melting-layer altitude for each month are presented in Fig. 4. Variability is slightly larger over the Indian Ocean, southern Asia, and around South America, while a low variability, less than about 0.5 km, seems to occur elsewhere. Large variability does not seem to correlate with the seasons, however, nor does it coincide with regions of high Ho.

b. Seasonal variation of melting-layer altitude

Figure 5 shows the seasonal variation of the melting-layer altitudes obtained by averaging monthly mean melting-layer altitudes over 10°-wide latitudinal belts. Higher latitudes in both hemispheres exhibit larger seasonal variability. The transition points, indicating the weak difference of baroclinity between the northern and Southern Hemispheres (Ramage and Hori 1981), occur during the periods April∼May and around November. A symmetric pattern of Ho around the equator is generally found in those periods as in Fig. 3. The melting layer in the equatorial zone (Fig. 5d) is higher in the first half of the year than in the last half of the year, reflecting the warm surface condition associated with the El Niño episode early in the year.

The seasonal variations of Ho for eight selected regions are also shown in Fig. 6. Generally the seasonal cycle is more obvious over land than ocean; the strongest one appears in Australia. The amplitude of the cycle in Australia well exceeds the variations within a month, represented by standard deviation bars in Fig. 6, and the cycle is in phase with the seasonal march of the sun. The seasonal variation in South America is much weaker than that of Australia, but clearly peaks in April. The region selected over central Africa does not exhibit a pronounced annual cycle. This may be because the region is centered at the equator, so that the seasonal differences of both sides tend to be averaged over the domain.

The general shape of the annual curves seems to resemble that the annual variation of the SST over the equatorial oceans. The seasonal variation in the western Pacific is the weakest of the eight regions. It may be associated with the weak annual variation of the SST. The Indian and Atlantic Oceanic regions show moderate annual variations with the peaks occurring during northern spring. The seasonal variations in the eastern and central equatorial Pacific Ocean are slightly larger than those of the other oceans. This may be due to the variation of SST that is associated with El Niño and La Niña that occurred during the period. The data available at this time allow a first estimate of the annual cycle. This estimate will improve as more data become available.

c. Mean and variation of reflectivity profiles

The monthly mean profiles of reflectivity from stratiform precipitations for January, April, July, and October 1998 over eight selected regions are illustrated in Fig. 7. In averaging each month, only profiles with a minimum reflectivity exceeding the rainfall threshold of 15 dBZ (Kummerow et al. 1998) are used. All the calculated mean profiles exhibit melting layers, and the shape of the mean profiles seems to be maintained throughout the year with a slight change of intensity or vertical position.

The shape of the mean profiles is similar to that of the monthly mean profile obtained by Steiner et al. (1995). The mean melting layers over oceanic regions are narrower and better defined than over land. It may be suggested that the more consistent types of stratiform precipitation were involved in the construction of the monthly mean profiles for the oceanic areas.

Some investigators working with passive microwave algorithms such as Tesmer and Wilheit (1998) are concerned with the vertical structure of radar profiles. In particular, they have considered the lapse rate of reflectivity above the freezing level because it is usually related to the distribution of ice particles. The mean profiles have been provided for the reason. In addition, the variability around the mean profiles is also presented. It can be conveniently represented by empirical orthogonal functions (EOFs). The spatial (vertical) EOFs can be obtained by diagonalizing the covariance matrix calculated by subtracting out the spatial mean from the data. The EOF analysis provides a set of mode eigenvalues explaining the portion of total variance accounted for by the EOFs (e.g., North et al. 1982).

The general pattern of EOFs is characterized by N − 1 zero crossings for the Nth mode. An example of the EOFs for January 1998 is shown in Fig. 8. For all the months during the period, the first three or four EOFs account for at least 90% of the variance of the reflectivity profiles. The percentage variances and cummulative values (parentheses) of the first three EOFs for the month are shown on the top of each panel in the figure. The index-one EOFs are all positive at every altitude, the index-two EOFs cross zero only one time, and the index-three EOFs have two zero-crossings. Therefore, the index-one EOFs describe changes in the intensity of reflectivity. That is, the index-one EOFs shift the mean profile in the horizontal (abscissa) direction, so that the reflectivity profiles similar to the mean profile with a slightly different intensity may contribute to the variation of the mean profile. The index-one EOFs account for 64.1%–76.8% of the total variance for the month and the domains.

The zero-crossing altitude of EOF2 roughly coincides with the monthly mean melting-layer altitudes that will be shown in the following section (Fig. 6). EOF2 describes how the variation from the mean profile is affected by the stratiform clouds whose melting-layer altitude is comparable to the monthly mean melting-layer altitude. The index-two EOFs explain 11.4%–16.5% of the total variance. The variations explained by the third-mode EOFs may be associated with more complicated distortions.

d. Diurnal cycle of melting-layer altitude

The values of Ho derived from each reflectivity profile were averaged within each hour of the day to produce mean hourly melting-layer altitudes for the eight selected regions. To estimate the diurnal cycle of the data, we use a simple sinusoidal model:
HotμAπkftθϵtkt
where Ho(t) indicates the monthly mean melting-layer altitude at each hour t, μ is an added constant, A is the amplitude in kilometers, θ is the phase in hours after local midnight, f is the diurnal frequency [(1/24) h−1], and ϵ(t) is the residual. The estimated amplitude and phase of the diurnal cycle are obtained by the least squares method (Bloomfield 1976).

The results are shown in Fig. 9. The length and direction of the arrow indicate the amplitude of the diurnal cycle and the peak time after local midnight, respectively. A statistical test for the estimated diurnal cycles is performed using the F distribution. Details of the test can be referred to in Wei (1990). In the figure, the diurnal cycle over 90% statistical significance is represented by the thick arrows. Moderate diurnal cycles are found over the Indian Ocean, Australia, and South America in some seasons. The amplitudes range from 0.13 to ∼0.23 km, and the peaks are between midnight and morning. The amplitudes of the diurnal cycle generally do not exceed 10% of the corresponding monthly mean values and are usually much smaller than the standard deviation within each hour. The large variation in each hour, which leads to the weak diurnal cycle, may illustrate the transient nature of the bright band (Klaassen 1988). The diurnal cycle estimates will improve as more data are incorporated in the future.

e. Spatial correlation of the melting-layer altitudes

The spatial correlation of the well-defined melting layer is estimated for eight selected regions and each month of 1998 to see whether a dependency on geolocations and seasons exists. In each month approximately more than 50 scan strips along nadir are employed for each region. The melting-layer altitudes are calculated at every scan point on each scan strip, and the value for undefined scan points is set to zero. With this zero-filled scan strip of melting-layer altitude, the sample autocorrelation function is calculated by
i1520-0442-13-23-4072-e5
where ρ(υ) denotes the sample autocorrelation coefficient of lag υ, Ho is melting-layer altitude, and the overbar represents the average value of a strip.

According to Trenberth (1984) and Nakamoto et al. (1992), in estimating an averaged autocorrelation function with many strips of data, the less-biased estimator can be obtained when the statistics of the entire set of strips are computed than when the individual statistics are averaged. However, the biased estimator may be more appropriate because during a relatively long period (like a month) the use of all the data may smooth any local characteristics. Furthermore, the purpose of finding the spatial correlation in this study is just to examine the pattern of its distribution (or the e-folding lag, which is an indicator of spatial scale). Therefore a systematic bias may be of no importance.

The monthly mean autocorrelation function is obtained by averaging the spatial autocorrelation functions of each strip. Figure 10 shows the scatterplots of the autocorrelation functions for each month in 1998. All the autocorrelation functions show a similar pattern, decreasing exponentially after the lag 1. The most consistent patterns through the year are found in the Indian and the western Pacific Oceans. The e-folding lags from the mean autocorrelation are mostly lags 2 and 3 (8.8 and 13.2 km in length scale) and lags 1, 4, and 5, sparsely. It is hard to find a systematically varying pattern depending on regions and seasons.

An attempt is made to model the autocorrelation functions using a random variable Y, which is a mixture of a red noise X and a white noise ϵ in space. The random variable X may be represented by the first-order autoregressive process (AR1). The autocovariance function of X is then given by Rx(υ) = σ2xαυ, and for the white noise Rϵ(υ) = σ2ϵδυ, where σ2x is the variance of X, σ2ϵ is the white noise variance, α is the lag 1 coefficient of the AR1, and δυ is the Kronecker delta function, which is δυ = 1 if υ = 0, but otherwise δυ = 0. Therefore, the autocorrelation function of YX + ϵ, ρy(υ) may be expressed by
i1520-0442-13-23-4072-e6
and finally,
i1520-0442-13-23-4072-e7
where C = σ2x/(σ2x + σ2ϵ).

The autocorrelation functions of Y are estimated by minimizing total mean-square error between the simulated and observed monthly mean autocorrelations with the assumption of C = 0.5, which implies the same amounts of the random fluctuation σ2ϵ and the red noise fluctuation σ2x exist in the mixed spatial series Y. The simulated autocorrelation functions are superimposed in Fig. 10 (solid line). Generally, the autocorrelation functions of Y seem to well represent the monthly mean autocorrrelations, and the values of the lag-1 coefficient of the red noise for each region are similar, ranging from 0.84 to 0.89. This property may show the spatially homogeneous characteristic of the melting layer. At the same time, the large portion attributable to random fluctuation (as much as the red noise) may be another indicator representing the irregular behavior (in space) of the melting layer.

5. Summary and conclusions

A 14-month climatological study of the altitude of the melting layer in stratiform precipitation (radar bright band) is conducted using reflectivity data from the precipitation radar on the TRMM satellite. The altitude of the melting-layer Ho is estimated by a simple gradient-checking algorithm. Monthly mean fields of the melting-layer altitude Ho are computed over the entire domain covered by the TRMM satellite (35°S to ∼35°N) with spatial resolution of 10°. To further demonstrate the detailed climatologies, eight regions are considered.

The distinct feature of the monthly mean melting-layer altitude Ho is that high melting layers greater than 4.5 km seem to exist in response to extreme phenomena such as El Niño and the Asian summer monsoon. The monthly mean melting layers between 4- and ∼4.5-km altitude are observed widely around the equator with a mild seasonal change during the second half of the year when the unusual phenomena disappear, and lower melting layers are usually found in the winter hemisphere. We have also found that larger seasonal variability tends to occur in higher latitudes and over land. Harris et al. (2000) investigated the difference between the monthly mean melting-layer altitude and the altitute of freezing level (0°C isotherm) in the National Centers for Environmental Prediction (NCEP) reanalysis data. As we mentioned in the earlier section, two quantities, altitude of freezing level and melting-layer altitude, are slightly different, and the difference depends on season and geolocation, usually ranging from a few hundred meters to less than 1 km. The comparison study of Harris et al. (2000) shows that the difference of two monthly mean altitudes ranges from about 300 m over the ocean to about 900 m over land, and concluded that our estimated melting-layer altitudes compare well to the climatology of the NCEP freezing-level data.

The analyses of second-moment statistics show the irregular or homogeneous properties of the melting-layer altitude—for example, the uneven distribution of standard deviations (within the month), the inconsistent weak diurnal cycle, and no systematically varying pattern in space. These features from the second-moment statistics may illustrate that the melting layer is rather erratic in occurrence and existence, but the larger-scale mean statistics suggest that the altitude of the melting layer is mainly determined by surface temperature, as we might expect.

Due to the appearance of the El Niño during the period sampled, this climatology of the melting-layer altitude may not be representative of other years. The data and their climatologies in this period are especially valuable, however, because the extreme events such as El Niño and La Niña may not occur again during the mission lifetime of TRMM. Also, the altitude of the melting layer seems to respond to the atmospheric variables and phenomena so that the data may be used for many purposes. For example, the 30–60-day oscillations (Madden and Julian 1971), which are an important factor in modeling climate change at the month to seasonal timescale, may be investigated.

Acknowledgments

We are grateful to the Tropical Rainfall Measuring Mission project office of the National Aeronautics and Space Administration for its support through Grant NAG5-4753. TRMM data were provided by the EOS Distributed Active Archive Center (DAAC) at Goddard Space Flight Center.

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Fig. 1.
Fig. 1.

The reflectivity data are collected over 10° × 10° lat–long grid boxes and eight regions. The five regions are located in the tropical oceans, and the others are on land: (1) Africa, (2) the Indian Ocean, (3) Australia, (4) the western Pacific Ocean, (5) the central Pacific Ocean, (6) the eastern Pacific Ocean, (7) South America, and (8) the Atlantic Ocean

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 2.
Fig. 2.

(a) Vertical cross section along the satellite track and vertical profiles of radar reflectivity at the different scan positions: (b) 6455, (c) 6465, (d) 6500. The scan starts at 9.5°N, 28.8°W, ends at 7.3°N, 25.7°W on 26 Jul 1998

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 3.
Fig. 3.

Maps of monthly mean melting-layer altitude from Jan 1998 to Feb 1999. The spatial resolution of the grid is 10° × 10° lat–long. White areas have no melting-layer altitude due to the insufficient occurrence of precipitations or nonexistence of well-defined melting layer

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 4.
Fig. 4.

Distributions of the standard deviation of melting-layer altitude from Jan 1998 to Feb 1999

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 5.
Fig. 5.

Seasonal variation of monthly mean melting-layer altitude averaged over 10° wide latitude belts: (a) 25°∼35°S and 25°∼35°N, (b) 15°∼25°S and 15°∼25°N, (c) 5°∼15°S and 5°∼15°N, and (d) 5°S∼5°N

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 6.
Fig. 6.

The seasonal cycle in monthly melting-layer altitude for eight selected regions. Each bar on the graphs indicates the standard deviation for each month

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 7.
Fig. 7.

Mean profiles of reflectivty for eight selected regions and four seasons: (solid) Jan, (dotted) Apr, (dashed) Jul, and (dash–dotted) Oct 1998

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 8.
Fig. 8.

The first three eigenfunctions of reflectivity profile for eight selected regions in Jan 1998

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 9.
Fig. 9.

Amplitude and phase (peak time) of the diurnal variation of the mean melting-layer altitude for eight selected regions and four seasons: MAM (Mar∼May 1998), JJA (Jun∼Aug 1998), SON (Sep∼Nov 1998) and DJF (Dec 1998∼Feb 1999) from the left to the right in each box. The direction of the arrow indicates the peak time after local midnight in a 24-h clock as shown in lower right corner and the length denotes its amplitude. The diurnal cycle over 90% statistical significance is indicated by thick arrow

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

Fig. 10.
Fig. 10.

Scatterplots of monthly mean autocorrelation functions in 1998 for eight regions. The superimposed line (solid) represents the autocorrelation function of a random variable Y, which is a sum of a spatially red noise X and a spatially white noise ϵ. Here α indicates the lag-1 coefficient of the red noise, represented by the first-order autoregressive process. The e-folding value (e−1) of the autocorrelation is indicated by a horizontally dotted line

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4072:ASORPF>2.0.CO;2

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