• Chang, A. T. C., and L. S. Chiu, 1999: Nonsystematic errors of monthly oceanic rainfall derived from SSM/I. Mon. Wea. Rev.,127, 1630–1638.

  • ——, and ——, 2000: Monthly oceanic rainfall derived from SSM/I and TMI data. IGARSS, Honolulu, HI, Institute of Electrical and Electronics Engineers, 1367–1369.

  • ——, ——, and T. Wilheit, 1993a: Random errors of oceanic monthly rainfall derived from SSM/I using probability distribution functions. Mon. Wea. Rev.,121, 2351–2354.

  • ——, ——, and ——, 1993b: Oceanic monthly rainfall derived from SSM/I. Eos, Trans. Amer. Geophys. Union,74, 505–513.

  • ——, A. Barnes, M. Glass, R. Kakar, and T. T. Wilheit, 1993c: Aircraft observations of the vertical structure of stratiform precipitation relevant to microwave radiative transfer. J. Appl. Meteor.,32, 1083–1091.

  • ——, L. S. Chiu, and G. Yang, 1995: Diurnal cycle of oceanic precipitation from SSM/I data. Mon. Wea. Rev.,123, 3371–3380.

  • ——, ——, J. Meng, C. Kummerow, and T. Wilheit, 1999: First results of the TRMM Microwave Imager (TMI) monthly oceanic rain rate: Comparison with SSM/I. Geophys. Res. Lett.,26, 2379–2382.

  • Chiu, L., and A. Chang, 1994: Oceanic rain rate parameters derived from SSM/I. Preprints, Climate Parameter in Radiowave Propagation Prediction, CLIMPARA 94, Moscow, Russia, URSI Commission F, 11.3.1–11.3.5.

  • ——, D. Short, A. McConnell, and G. North, 1990: Rain estimation from satellites: Effect of finite field of view. J. Geophys. Rev.,95, 2177–2185.

  • ——, A. Chang, and J. Janowiak, 1993: Comparison of monthly rain rate derived from GPI and from SSM/I using distribution functions. J. Appl. Meteor.,32, 323–334.

  • Edelson, B. I., and Coauthors, 1995: Satellite Communications Systems and Technology, Europe–Japan–Russia. Noyes Data Corporation, 511 pp.

  • Jackson, D. L., and G. L. Stephens, 1995: A study of SSM/I derived columnar water vapor over the global oceans. J. Climate,8, 2025–2038.

  • Kalnay, E., R. Balgovind, W. Chao, D. Edelmann, J. Pfaendtner, L. Tackas, and K. Takano, 1983: Documentation of the GLAS fourth order general circulation model. Vol. I, NASA-TM 86064, NASA Goddard Space Flight Center, 381 pp.

  • Kanellopoulos, J. D., and S. N. Livieratos, 1997: A modified analysis for the prediction of multiple-site diversity performance in earth-space communication including rain height effects. J. Electromagn. Waves Appl.,11, 485–513.

  • Kim, J.-H., and Y. C. Sud, 1993: Circulation and rainfall climatology of a 10-year (1979–1988) integration with the Goddard Laboratory for Atmospheres General Circulation Model. NASA-TM 104591, NASA Goddard Space Flight Center, 228 pp.

  • Rao, M. S. V., W. V. Abbott III, and J. S. Theon, 1976: Satellite-Derived Global Oceanic Rainfall Atlas (1973–1974). NASA SP-410, 186 pp.

  • Rodda, M. J., and A. G. Williamson, 1997: Results of a two year radiometeric measurement propagation programme in New Zealand. Electron. Lett.,33, 326–328.

  • Sharma, A., A. Chang, and T. Wilheit, 1991: Estimation of the diurnal cycle of oceanic precipitation from SSM/I data. Mon. Wea. Rev.,119, 2168–2175.

  • Short, D., and G. North, 1990: The beam filling error in the Nimbus-5 Electronically Scanning Microwave Radiometer observations of Global Atlantic Tropical Experiment rainfall. J. Geophys. Res.,95, 2187–2193.

  • Simpson, J., Ed., 1988: Report of the Science Steering Group for a Tropical Rainfall Measuring Mission (TRMM). NASA Goddard Space Flight Center, 94 pp.

  • Wang, S. A., 1995: Modeling the beamfilling correction for microwave retrieval of oceanic rainfall. Ph.D. dissertation, Texas A&M University, College Station, TX, 99 pp. [Available from Dept. of Meteorology, Texas A&M University, College Station, TX 77843.].

  • Watson, P. A., 1994: Climatically related parameters for prediction of attenuation and cross polarization in rainfall. Preprints, Climatic Parameters in Radiowave Propagation Prediction, CLIMPARA 94, Moscow, Russia, URSI Commission F, 2.1.1–2.1.6.

  • Wilheit, T. T., A. T. C. Chang, M. S. V. Rao, E. B. Rodgers, and J. S. Theon, 1977: Satellite technique for quantitatively mapping rainfall rates over oceans. J. Appl. Meteor,16, 551–560.

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

  • View in gallery

    Annual average distribution of oceanic rain column height derived from 12 yr (Jul 1987–Jun 1999) of SSM/I data

  • View in gallery

    Mean oceanic rain column height for Jan, Apr, Jul, and Oct (1987–99)

  • View in gallery

    Standard deviation of freezing height for Jan, Apr, Jul, and Oct (1987–99)

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    Seasonal zonal mean of SSM/I oceanic freezing height for the global oceans: Atlantic, Pacific, and the Indian Oceans

  • View in gallery

    (a) Mean rain column height difference between estimates from SSM/I morning (AM) and afternoon (PM) passes. (b) Nonsystematic errors estimated using all 143 months data

  • View in gallery

    Scatterplot of the error vs mean rain column height

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    Distribution of the height of the 0° isotherm computed from GLAS GCM for the period Aug 1987–Dec 1988

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    Mean difference between rain column height derived from SSM/I and height of the 0° isotherm computed from GLAS GCM runs for Aug 1987–Dec 1998

  • View in gallery

    Similar to Fig. 4, except for height of the 0° isotherm computed from GLAS GCM

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Oceanic Rain Column Height Derived from SSM/I

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  • 1 Hydrological Sciences Branch, Laboratory for Hydrospheric Processes, NASA Goddard Space Flight Center, Greenbelt, Maryland, and Center for Earth Observing and Space Research, Institute of Computational Sciences and Informatics, George Mason University, Fairfax, Virginia
  • 2 Hydrological Sciences Branch, Laboratory for Hydrospheric Processes, NASA Goddard Space Flight Center, Greenbelt, Maryland
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Abstract

The climatology of oceanic rain column height derived from 12 years (July 1987–June 1999) of Special Sensor Microwave Imager (SSM/I) data is presented. The estimation procedure is based on a technique developed by Wilheit et al. In the annual mean, the SSM/I-derived oceanic rain height shows a maximum of about 4.7 km in the Tropics and decreases toward the high latitudes to less than 3.5 km at 50°. Interannual variations exhibit seasonal dependency and show maxima of about 200–300 m in the oceanic dry zones and in the midlatitude storm track regions. The rain heights estimated from the morning passes of the SSM/I are lower than those computed from the afternoon passes by about 60 m in the Tropics but are higher north of 40°N. This small difference cannot change the conclusion about the morning maximum in rain rate. The nonsystematic error increases with decreasing rain column height and is estimated to be about 120 m for rain heights of 4–5 km and 200 m at 3.5 km. Comparison with the height of the 0°C isotherm derived from the Goddard Laboratory for Atmospheres general circulation model (GCM) results shows a mean zonal low bias (SSM/I lower than GCM freezing height) of about 200 m in the Tropics. Outside the Tropics, the SSM/I rain column heights are much higher, reaching a difference of 2 km at 50°N. The small bias in the Tropics is consistent with the notion that the melting layer extends over hundreds of meters below the freezing level. Outside the Tropics, the sampling of the SSM/I rain height and the inclusion of nonraining observations in GCM calculations may contribute to the large discrepancy. The freezing height is interpreted as the columnar water content and found to be consistent with columnar water vapor maps retrieved from SSM/I data.

Corresponding author address: Dr. Long S. Chiu, Center for Earth Observing and Space Research, Institute of Computational Sciences and Informatics, George Mason University, Fairfax, VA 22030-4444.

Email: lchiu@gmd.edu

Abstract

The climatology of oceanic rain column height derived from 12 years (July 1987–June 1999) of Special Sensor Microwave Imager (SSM/I) data is presented. The estimation procedure is based on a technique developed by Wilheit et al. In the annual mean, the SSM/I-derived oceanic rain height shows a maximum of about 4.7 km in the Tropics and decreases toward the high latitudes to less than 3.5 km at 50°. Interannual variations exhibit seasonal dependency and show maxima of about 200–300 m in the oceanic dry zones and in the midlatitude storm track regions. The rain heights estimated from the morning passes of the SSM/I are lower than those computed from the afternoon passes by about 60 m in the Tropics but are higher north of 40°N. This small difference cannot change the conclusion about the morning maximum in rain rate. The nonsystematic error increases with decreasing rain column height and is estimated to be about 120 m for rain heights of 4–5 km and 200 m at 3.5 km. Comparison with the height of the 0°C isotherm derived from the Goddard Laboratory for Atmospheres general circulation model (GCM) results shows a mean zonal low bias (SSM/I lower than GCM freezing height) of about 200 m in the Tropics. Outside the Tropics, the SSM/I rain column heights are much higher, reaching a difference of 2 km at 50°N. The small bias in the Tropics is consistent with the notion that the melting layer extends over hundreds of meters below the freezing level. Outside the Tropics, the sampling of the SSM/I rain height and the inclusion of nonraining observations in GCM calculations may contribute to the large discrepancy. The freezing height is interpreted as the columnar water content and found to be consistent with columnar water vapor maps retrieved from SSM/I data.

Corresponding author address: Dr. Long S. Chiu, Center for Earth Observing and Space Research, Institute of Computational Sciences and Informatics, George Mason University, Fairfax, VA 22030-4444.

Email: lchiu@gmd.edu

1. Introduction

A major objective of the Tropical Rainfall Measuring Mission (TRMM) is the production of at least three years of monthly mean rain rate over 5° latitude by 5° longitude boxes with errors of about 10% for high rain rates and 1 mm h−1 for low rain rates (Simpson 1988). We have developed a technique for estimating oceanic rainfall over the same space and time domain (Wilheit et al. 1991). The technique has been applied to about 12 years of data collected by the Special Sensor Microwave Imager (SSM/I) on board the Defense Meteorological Satellite Program (DMSP) satellites (Chang et al. 1999). The technique has been modified and applied to the TRMM Microwave Imager (TMI) data collected on board the TRMM satellite. A preliminary comparison of the SSM/I- and TMI-estimated rain rates using the TRMM day-one algorithm is given by Chang et al. (1999).

One of the major uncertainties associated with the SSM/I or TMI rain algorithm is the height of the rain column. The rain column height affects the algorithm in two ways. First, the rain column height is a variable that enters directly into the estimation of rain rates. An overestimate of the rain column height will result in an underestimate of the rain rate, and vice versa. Second, the so-called beamfilling correction in the day-one algorithm is tied to the rain column height (Wang 1995). The “beamfilling” error refers to the bias associated with rain estimation from nonuniformly filled field of view associated with spaceborne satellite microwave sensors (Chiu et al. 1990; Short and North 1990). Hence it is crucial to examine the variability and associated errors of the rain column height to interpret the results.

The rain column height (or rain height) is also important in the prediction of radiowave propagation attenuation (Watson et al. 1994; Kanellopoulos and Livieratos 1997). The growth of global satellite communication has raised interest in the use of frequencies higher than the 10–14-GHz band for fixed satellite and mobile applications (Edelson et al. 1995). At these higher frequencies (20–30 and 30–40 GHz), atmospheric gases absorption; scintillation from atmospheric turbulence; and attenuation from rain, ice, and water clouds become important. Climatological rainfall parameters, such as the rain rate for a certain percentage of time exceedance, effective rain path, and rain height are all important parameters in the design of earth–space links.

In this report, 12 years (July 1987–June 1999, with December 1987 missing) of oceanic rain column height derived from the SSM/I are examined. The annual, seasonal, and interannual statistics are presented. These statistics form the baseline for comparison or validation with similar products derived from the ongoing TRMM mission.

In section 2, the procedure for estimating the rain column height is described. The annual, seasonal, and interannual statistics are described in section 3. Nonsystematic error estimates associated with rain column height are presented in section 4. Section 5 contains a preliminary assessment of the rain column height by comparing it with height of the 0° isotherm derived from GCM. Section 6 summarizes and discusses our results.

2. Technique

The technique for estimating monthly oceanic rain rate parameters over 5° latitude by 5° longitude boxes is described by Wilheit et al. (1991). The rain-rate parameters include mean rain rate, conditional rain rate, rain column height, rain fraction, and mean and standard deviation of the rain-rate distribution. The technique has been applied to data collected by the SSM/I on board the DMSP satellites.

The technique for estimating monthly rain-rate parameters is based on an atmospheric model developed by Wilheit et al. (1977). In their model, a Marshall–Palmer distribution of raindrops as a function of rain rate is assumed to exist from the ocean surface to the freezing level (0°C isotherm) in the atmosphere. The freezing level is defined as the height of the rain column. Below this level, all frozen hydrometeors are assumed to change to rain. The terms “freezing level” and “rain column height” or “rain height” will be used interchangeably in the following text. In reality, melting occurs in layers that may be tens to hundreds of meters thick as a mixture of frozen and liquid hydrometeors coexist below the freezing level. To mitigate the effect of cloud liquid water in the rain column, a nonprecipitation cloud containing 0.25 kg m−2 of integrated liquid water is assumed to exist in a 0.5-km layer right below the freezing level. A constant lapse rate of 6.5°C km−1 is assumed. The relative humidity is assumed to increase linearly with height from 80% at the ocean surface to 100% at the freezing level and remains at 100% above the freezing level. The effect of surface wind and surface emissivity variability is not considered. With these model assumptions, only the rain rate and freezing height are needed to completely specify the atmospheric model.

The assumptions of the Wilheit et al. model has been tested with in situ aircraft observations. Chang et al. (1993c) reported aircraft measurements taken in February 1983 in the North Pacific and in March 1983 in the North Atlantic. The observed vertical structure and the moisture content are consistent with the model assumptions of the relative humidity profile and lapse rates. Because of the model assumptions, the freezing height can be interpreted as the columnar water vapor content.

Both rain rate and columnar water contribute to the microwave emission at the SSM/I channel frequencies. The Wilheit et al. technique uses a combination of the vertically polarized 19.35- and 22.235-GHz channels (2 × 19–22 GHz) to extract the rain signal. This combination channel minimizes the effect of water vapor variability on the rain signal. A functional dependency of the brightness temperature on the rain rate and freezing level [R–T relation; see Eqs. (4) and 5 in Wilheit et al. 1991] is derived based on radiative transfer calculations and the atmospheric model. The microwave brightness temperature increases with rain rate and freezing heights but saturates at a rain rate of about 15 mm h−1 for a freezing level of 4–5 km. Further increase of the rain rate causes a decrease in the brightness temperature, hence creating a double value function at the high brightness temperature values.

To compensate for the effect of undersampling and the double value nature of the R–T relation, histograms of the brightness temperature of the combination channel are fitted to mixed lognormal distributions of rain rate via the R–T relation. The parameters in the rain-rate distribution model are the rain fraction, the mean and standard deviation of the (conditional) rain-rate distribution. A beamfilling correction is applied to the monthly rain rate. The original beamfilling correction was an empirical correction based on rain-rate statistics derived from the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment. It has been modified from the empirical correction (Wilheit et al. 1991) to one that is dependent on the rain column height (Wang 1995) for the day-one TMI algorithm.

The technique for computing the freezing level is described in Wilheit et al. (1991, appendix A). The freezing levels can be computed from the scatter diagram of the 19- and 22-GHz brightness temperatures. In producing rainfall maps from the electrically scanning microwave radiometer data, Rao et al. (1976) argued that a much higher freezing height (>3 km) than climatology is needed to produce realistic rain rates. The implication is that the freezing height under rainy conditions is higher than that in nonraining conditions. Since only the brightness temperature of the rainy pixels is needed to compute the freezing height, the technique uses the upper 99th percentile brightness temperature of the vertically polarized 22.235 and 19.35 GHz to guarantee rain existence. The memory storage of the scatter diagrams of the brightness temperatures at 1-K bins is also simply prohibitive for most PCs or workstations. From these two brightness temperatures, a freezing height is estimated in the brightness temperature space. Meteorological conditions that deviate substantially from the model atmosphere will introduce erroneous rain rate and freezing heights. Over extremely dry regions, where the rain probability is less than 1%, this assumption will also introduce a bias to the estimated freezing height. This dataset, however, represents the first of its kind in estimating freezing height from radiometric measurements that is homogeneous and of sufficiently long duration and hence may be useful for climatological and climate change studies. Chiu and Chang (1994) reported preliminary statistics of the freezing heights based on about 7 years of SSM/I data. The SSM/I rain-rate climatology and error estimates associated with these monthly rain rates are documented by Chang et al. (1993a, 1999). Chiu et al. (1993) and Chang and Chiu (1999) compared the SSM/I rain rate with other operational or semioperational satellite rain-rate algorithms. They demonstrated that climate signals, such as the El Niño–Southern Oscillation, can be extracted from the SSM/I oceanic rain rates (Chang et al. 1993b).

All of the rain-rate parameters are provided by the Polar Satellite Precipitation Data Center (PSPDC) as part of the National Aeronautics and Space Administration’s (NASA) contribution to the Global Precipitation Climatology Project. The rain-rate parameters are available on the World Wide Web (http://ltpwww.gsfc.nasa.gov/PSPDC/SSMI.rain.rate.html).

3. Annual, seasonal, and interannual variations

Twelve years (July 1987–June 1999, with December 1987 missing) of oceanic monthly rain column heights are computed. Preliminary calculation of the standard deviation (SD) shows isolated spikes in the spatial distribution. A quality check was first performed on the FL datasets. Extreme low isolated FL values were found in the Indian Ocean, in the middle Pacific, and in the high northern latitudes off the coast of America for isolated years or months. These grid boxes may be contaminated by land or compromised by the small number of samples. The grid boxes with FL less than 2 km were omitted from our analysis. They represent less than 0.1% of the total dataset.

Figure 1 shows the annual average freezing height derived from 12 years of SSM/I data. The FL structure is basically zonal with a maximum of 4.7 km in the Tropics, decreasing rapidly to less than 3.5 km at 50° latitudes. High FL regions correspond to major rain areas, such as the intertropical convergence zone (ITCZ) and the South Pacific convergence zone (SPCZ) and in the Indian Ocean. Another major feature is the intrusion of an area of low FL in the eastern South Pacific from the subtropics into the Tropics. Distinct zonal asymmetry is found in the Atlantic, with low FL in the oceanic dry zones.

While the structure in the Tropics remains basically zonal year round, zonal asymmetry is more pronounced at the seasonal scale. Figure 2 shows the average FL for January, April, July, and October. The major feature is the seasonal variation of the high FL area in the western Pacific/Indian monsoon region. There is generally a negative zonal (east–west) gradient (west lower than east) in most months. The only exception is the positive gradient in January at 40°–50°N in the Atlantic. The zonal FL follows a season migration, and is highest in the summer hemispheres. The intrusion of the low FL area in the eastern South Pacific is largest in the southern winter to spring (December–October). Another area of low FL appears in the eastern Northern Atlantic and Pacific, which is largest in the northern winter seasons (January and April).

Figure 3 shows the standard deviation of the interannual variation of the FL. The interannual variability in the Tropics and the rain bands, such as the ITCZ and SPCZ, are relatively small. Large interannual variability is found in the oceanic dry zones and in the midlatitude storm track areas. The largest SDs in FL values (over 300 m) are found in the subtropical highs in the eastern South Pacific and Indian Ocean. The SDs also show seasonal dependency. For example, there is more interannual variability in the south Indian Ocean for July and October (maximum >300 m) than for January and April.

Figure 4 shows the zonal average FL for the global ocean and for the Atlantic, Pacific, and Indian Ocean sectors, respectively. In our study, the Atlantic is confined to the area between the America continent, Asia, and 140°E south of Australia. The Pacific is bounded by the east coast of the Atlantic, and 30°E to the south of Africa. The Indian Ocean is confined between the Atlantic and Pacific. In the global mean, the zonal-averaged FL shows a distinct seasonal cycle with maxima in the summer and minima in the winter. The highest FL (>5 km) is observed in the summer monsoon region in the northern Indian Ocean. Zonal maximum (about 4.8 km) for the Pacific and Atlantic occur in the summer. The amplitude of the seasonal cycle is smallest near the equator (about 0.2 km peak to peak) and increases toward the higher latitudes (peak to peak values of >1 km). There is a slight asymmetry between the hemispheres, with higher seasonal amplitude in the Northern Hemisphere. The zonal mean FL is a maximum near the thermal equator and decreases with latitude. There is a small secondary minimum in the dry areas at 15°–20°S in July–August in the Atlantic. This occurrence in the Atlantic may be due to the low FL values in and the small extent of the SPCZ compared to the South Pacific convergence zone.

4. Diurnal variations and error estimates

The equatorial crossing time for the sun-synchronous DMSP satellites is around 0600–1000 UTC (ascending orbit, morning pass) and 1800–2000 UTC (descending orbit, afternoon pass) local time (Chang and Chiu 1999). The different passes allow an assessment of the FL diurnal cycle. Chang et al. (1995) examined the diurnal cycle in rain rate and found that the rainfall rates are larger in the morning than in the afternoon in the global mean. Since the rain rate is coupled to the freezing height, it is important to examine the diurnal variability of FL.

Figure 5a shows the difference between the AM and PM estimates (AM–PM). In the Tropics, the rain heights computed from the AM data are lower than those from the PM data by about tens of meters. The maximum difference of >100 m, or about 2%–3% of FL, appear in the Indonesian ITCZ region. Other maxima are found in the equatorial Indian Ocean and in the South Pacific dry zone. For latitudes higher than 35°–40°N, however, the AM estimates are higher than the PM estimates. Standard deviations of the PM–AM difference show regions of high interannual variations in the Indonesian–Australian region and in the Indian Ocean.

In order to assess the error associated with these estimates, we follow the technique described in Chang and Chiu (1999). Let Ha and Hp be the height of the freezing level estimated from the AM and PM SSM/I datasets, respectively, and ea and ep be the random error associated with the AM and PM estimates, and 〈 〉 represents an ensemble averaging, that is,
i1520-0442-13-23-4125-eq1
Assuming that the error in the AM and PM estimates are uncorrelated, unbiased, and homogeneous, that is,
i1520-0442-13-23-4125-eq2
the nonsystematic error can be estimated as
i1520-0442-13-23-4125-e1

Applying (1) to the monthly AM and PM estimates, nonsystematic errors are calculated. The ensemble averaging is taken over all 143 monthly pairs. Figure 5b shows the error distribution. The errors are in general less than 150 m between 30°N and 30°S and increase toward higher latitudes. Figure 6 shows a scatterplot of the error estimates versus the mean FL. The errors are higher for low FL values and range from 120 to 290 m for mean FL of about 3–3.5 km and 80 to 170 m for mean FL of 4.5–4.8 km.

5. GCM height comparison

The height of the freezing level (0°C isotherm) is not an operational product in daily weather analysis, but can be obtained from weather analysis or data assimilation studies by general circulation models (GCMs). We compared the SSM/I-derived FL with the height of the 0° isotherm (Zf) estimated from GCM results compiled from the Goddard Laboratory Atmospheres (GLA) GCM Atmospheric Model Intercomparison Project (AMIP) runs. The GLA GCM is used because the monthly means are readily available to us.

A detail description of the GLA GCM is given by Kalnay et al. (1983). In support of AMIP sponsored by the Department of Energy, 10 yr (1979–88) of daily runs of the GLA GCM, using observed sea surface temperature have been carried out (Kim and Sud 1993). The monthly mean temperature have been preserved at the standard reporting pressure levels. The temperatures at these pressure levels are interpolated vertically using the hydrostatic relation to determine the height of the 0°C isotherm (Zf). A spatial filter is applied to the GCM data (resolution 4° latitude by 5° longitude) to convert them to the appropriate 5° × 5° resolution of the satellite product. Eighteen months (July 1987–December 1988) of overlapping GLA GCM data are analyzed.

The global mean height of Zf derived from the GLA GCM data are shown in Fig. 7. The maximum Zf of 5 km is found in the equatorial region. The zonal nature of the GCM Zf contrasts that of FL. The Zfs are relatively flat in the Tropics and at midlatitudes. The transition between the Tropics and midlatitude regions are demarcated by a sharp Zf gradient between the two zones. The low FL tongue intrusion from the subtropics in the Southern Hemisphere is also not present in the field of Zf.

Figure 8 shows the difference between annual average FL and Zf for the same period. The FLs are lower than the Zfs in the Tropics by about 200 m. The difference is largest in the South Pacific and South Atlantic dry zones. The FLs are much lower in these dry regions. Outside the Tropics, the Zfs decrease drastically, and the FLs are higher. The difference reaches almost 2 km at 50° latitudes.

We examined the seasonal difference between the FL and Zf. Zonal statistics for Zf similar to those presented in Fig. 8 are presented in Fig. 9. The features of the seasonal cycle are similar in general, and some differences are noted below. The seasonal amplitudes are smaller for Zf than FL in the equatorial region between 10°N and 10°S. Both FL and Zf show maximum in the summer monsoon region in the north Indian Ocean. The zonal averages of Zf are characterized by a drastic decrease from the Tropics to the subtropics, which occurs much more rapidly than that of FL. The seasonal cycles in Zf are also less symmetric, with respect to season, than that of FL, showing a drastic increase in Zf in the northern summer at the northern subtropics.

6. Summary and discussion

In this study, the seasonal climatology of the oceanic freezing height (FL) derived from 12 yr of SSM/I using the technique developed by Wilheit et al. is presented. High FLs tend to be associated with the heavy rain regimes, such as the ITCZ, the SPCZ, and the Indian monsoon regions. The pattern of the FL follows a distinct seasonal cycle, which is similar to that of rain rate. In these heavy rain regions, interannual variability is small, the SDs are of the order of 150 m. Large interannual variability (2–300 m) is found in the oceanic dry regions, particularly in the subtropical eastern Atlantic and Pacific, and the southern subtropical Indian Ocean. The zonal averages of the freezing heights show a distinct seasonal cycle. The seasonal amplitude is smallest near the equator and increases toward the higher latitudes.

The FLs estimated from the PM passes are higher than that estimated from the AM passes, except north of 40°N. This has strong implications for rain-rate estimates. Chang et al. (1995) and Sharma et al. (1991) showed that the rain rate computed from the AM passes is higher than that from the PM passes by about 10%. Since the rain rate is dependent on the freezing height, to what extent is the morning maximum in rain rate attributed to a minimum in the freezing height? If we neglect the effect of scattering in the Wilheit et al. (1991) model [Eqs. (4) and (5)], a 10% decrease in FL results in roughly 12% increase in rain rate. The beamfilling correction is linearly related to FL. For a 10% decrease in FL, the beamfilling correction decreased by about 3%. Since these effects are compensating, the net effect of a 10% decrease in FL is an increase of 8% in beamfilling corrected rain rate. Since the maximum diurnal difference in FL is in general less than 100 m, or 2% of the mean, it can account for <2% change in rain rate. The morning minimum in FL, therefore, cannot be totally responsible for the morning maximum in rain rate. Even if we take into account the errors in FL, which are about 150 m, the conclusion about a maximum in morning rain rate cannot be discounted due to the morning minimum and errors associated with FL.

Comparison with the GLA GCM results shows that the GCM-estimated freezing heights are higher than the SSM/I estimates by 200 m in the Tropics. An error analysis shows that the error in the estimate freezing height is about 120 m at 4.5–4.8 km. The estimated errors in temperature in the GCM are about 1.1 K. If a lapse rate of 6.5 K km−1 is assumed, the error in the freezing height in the GCM is estimated to be about 170 m, which is comparable to the SSM/I estimates. In light of the errors in both Zf and FL, the significance of the difference is probably marginal. The notion that the FL is lower than Zf is consistent with the notion that the rain layer starts below the zero degree isotherm, as a mixture of falling frozen and liquid hydrometeors appear in the melting layer below the 0°C isotherm.

The difference between FL and Zf increases outside the Tropics and reaches 2 km at 50° latitude. Rodda and Williamson (1997) examined 2 yr of radiometric data in New Zealand and found that the use of a freezing height of 2.3 km is consistent with their attenuation measurements. This value is in line with the Zf in those regions and their results indicate an overestimation of the FL at these high latitudes.

Why is there a big difference between FL and Zf at the subtropics? First, the estimation of the freezing height in the Wilheit et al. technique hinges on an assumption of rain existence, and for computational efficiency, the estimates are based on the top 99th percentile of the rain pixel elements.

The FL is related to the columnar water vapor content that is constrained by the temperature and humidity profile in the atmosphere through the Clausius–Clapeyron relation. The interpretation of FL as the 0°C isotherm may not be appropriate at these higher latitudes. Within the context of the Wilheit et al. model, the freezing height is an index of the columnar water content in rainy conditions. We empirically fitted the water content (w) and freezing height (FL) from the Chang et al. (1993c) results (their Fig. 6) and found that the relation w (g cm−2) = exp[−0.0047 + 0.41FL (km)] is a good approximation that shows a standard error of 0.015 g cm−2 (for a model assumption of surface relative humidity of 80% and a lapse rate of 6.5 K km−1).

Jackson and Stephens (1995) presented seasonal columnar water vapor maps retrieved from 4 yr of SSM/I data. The seasonal patterns between the FL maps and their columnar water vapor maps are very similar, especially with the intrusion of the dry tongue from the subtropics into the Tropics, and maximum in the ITCZ, the SPCZ, and the Indonesia/Indian Ocean regions. The seasonal cycle in the Indian Ocean/Asian monsoon regions is also similar, with maximum column water vapor of about 5.0 g cm−2 in the northern summer. This is consistent with a FL of 4–5 km in the same region via the empirical relation.

In the Tropics, the temperature variability is small, and hence the spread in the histogram of Zf is small. We therefore expect that the representation of average Zf or FL by the top 1% to be acceptable. Outside the Tropics, there is a larger temperature and moisture profile variability, and hence the assumption on the use of the 99th percentile of the brightness temperature data may be inappropriate for estimating the FL. In fact, this exponential dependency of columnar water vapor on FL points to a skewed distribution of the freezing height if the columnar water content is normally distributed. The mode of the distribution may be further away from the top one percentile in the subtropics than in the Tropics, hence causing the high bias.

Second, the difference between the Zf and FL estimates is that the former method computes the freezing height in both raining and nonraining environments, whereas the latter technique only include the freezing height when raining conditions occur. In the Tropics, where the temperature structure is fairly homogeneous, the temperature differences between raining and nonraining conditions are negligible, which contributed to a small difference in FL and Zf. The rapid decrease of Zf outside the Tropics is probably due to the inclusion of nonraining conditions.

Third, another source of difference, as pointed out in Wilheit et al. (1991) is the assumptions in the atmospheric model. If the structure of the atmosphere deviates substantially from the Wilheit et al. (1977) model, large errors occur.

While there are differences between the height of the 0°C isotherm estimated from GCM and the freezing height estimated from SSM/I outside the Tropics, their difference in the Tropics is small. The SSM/I-estimated freezing levels are derived from radiometric measurements, and hence may be applicable to attenuation models of earth–space links in satellite communication in the Tropics. This dataset is also derived from a relatively homogeneous source of sufficient duration, and hence may be suited for seasonal and interannual studies.

A preliminary comparison of the freezing level derived from SSM/I with TMI and PR using the TRMM version 4 data were made and results presented at the Progress in Electromagnetics Symposium 1999. Recently, TRMM data went through a major reprocessing and the latest version data (version 5) are available. A comparison of the SSM/I and TMI freezing height showed that the TMI is higher than the SSM/I estimates by about 200 m (Chang and Chiu 2000). We plan to further analyze this result and submit the results for future publication.

Acknowledgments

We thank Dr. Y. Sud and G. Walker of NASA Goddard Space Flight Center for providing the GLA GCM results, V. Kuan (formerly of SAIC/GSC), J. Meng of SAIC/GSC, and Z. Liu of GMU/CEOSR for programming and graphics support. This work is supported by NASA Office of Earth Sciences.

REFERENCES

  • Chang, A. T. C., and L. S. Chiu, 1999: Nonsystematic errors of monthly oceanic rainfall derived from SSM/I. Mon. Wea. Rev.,127, 1630–1638.

  • ——, and ——, 2000: Monthly oceanic rainfall derived from SSM/I and TMI data. IGARSS, Honolulu, HI, Institute of Electrical and Electronics Engineers, 1367–1369.

  • ——, ——, and T. Wilheit, 1993a: Random errors of oceanic monthly rainfall derived from SSM/I using probability distribution functions. Mon. Wea. Rev.,121, 2351–2354.

  • ——, ——, and ——, 1993b: Oceanic monthly rainfall derived from SSM/I. Eos, Trans. Amer. Geophys. Union,74, 505–513.

  • ——, A. Barnes, M. Glass, R. Kakar, and T. T. Wilheit, 1993c: Aircraft observations of the vertical structure of stratiform precipitation relevant to microwave radiative transfer. J. Appl. Meteor.,32, 1083–1091.

  • ——, L. S. Chiu, and G. Yang, 1995: Diurnal cycle of oceanic precipitation from SSM/I data. Mon. Wea. Rev.,123, 3371–3380.

  • ——, ——, J. Meng, C. Kummerow, and T. Wilheit, 1999: First results of the TRMM Microwave Imager (TMI) monthly oceanic rain rate: Comparison with SSM/I. Geophys. Res. Lett.,26, 2379–2382.

  • Chiu, L., and A. Chang, 1994: Oceanic rain rate parameters derived from SSM/I. Preprints, Climate Parameter in Radiowave Propagation Prediction, CLIMPARA 94, Moscow, Russia, URSI Commission F, 11.3.1–11.3.5.

  • ——, D. Short, A. McConnell, and G. North, 1990: Rain estimation from satellites: Effect of finite field of view. J. Geophys. Rev.,95, 2177–2185.

  • ——, A. Chang, and J. Janowiak, 1993: Comparison of monthly rain rate derived from GPI and from SSM/I using distribution functions. J. Appl. Meteor.,32, 323–334.

  • Edelson, B. I., and Coauthors, 1995: Satellite Communications Systems and Technology, Europe–Japan–Russia. Noyes Data Corporation, 511 pp.

  • Jackson, D. L., and G. L. Stephens, 1995: A study of SSM/I derived columnar water vapor over the global oceans. J. Climate,8, 2025–2038.

  • Kalnay, E., R. Balgovind, W. Chao, D. Edelmann, J. Pfaendtner, L. Tackas, and K. Takano, 1983: Documentation of the GLAS fourth order general circulation model. Vol. I, NASA-TM 86064, NASA Goddard Space Flight Center, 381 pp.

  • Kanellopoulos, J. D., and S. N. Livieratos, 1997: A modified analysis for the prediction of multiple-site diversity performance in earth-space communication including rain height effects. J. Electromagn. Waves Appl.,11, 485–513.

  • Kim, J.-H., and Y. C. Sud, 1993: Circulation and rainfall climatology of a 10-year (1979–1988) integration with the Goddard Laboratory for Atmospheres General Circulation Model. NASA-TM 104591, NASA Goddard Space Flight Center, 228 pp.

  • Rao, M. S. V., W. V. Abbott III, and J. S. Theon, 1976: Satellite-Derived Global Oceanic Rainfall Atlas (1973–1974). NASA SP-410, 186 pp.

  • Rodda, M. J., and A. G. Williamson, 1997: Results of a two year radiometeric measurement propagation programme in New Zealand. Electron. Lett.,33, 326–328.

  • Sharma, A., A. Chang, and T. Wilheit, 1991: Estimation of the diurnal cycle of oceanic precipitation from SSM/I data. Mon. Wea. Rev.,119, 2168–2175.

  • Short, D., and G. North, 1990: The beam filling error in the Nimbus-5 Electronically Scanning Microwave Radiometer observations of Global Atlantic Tropical Experiment rainfall. J. Geophys. Res.,95, 2187–2193.

  • Simpson, J., Ed., 1988: Report of the Science Steering Group for a Tropical Rainfall Measuring Mission (TRMM). NASA Goddard Space Flight Center, 94 pp.

  • Wang, S. A., 1995: Modeling the beamfilling correction for microwave retrieval of oceanic rainfall. Ph.D. dissertation, Texas A&M University, College Station, TX, 99 pp. [Available from Dept. of Meteorology, Texas A&M University, College Station, TX 77843.].

  • Watson, P. A., 1994: Climatically related parameters for prediction of attenuation and cross polarization in rainfall. Preprints, Climatic Parameters in Radiowave Propagation Prediction, CLIMPARA 94, Moscow, Russia, URSI Commission F, 2.1.1–2.1.6.

  • Wilheit, T. T., A. T. C. Chang, M. S. V. Rao, E. B. Rodgers, and J. S. Theon, 1977: Satellite technique for quantitatively mapping rainfall rates over oceans. J. Appl. Meteor,16, 551–560.

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

Fig. 1.
Fig. 1.

Annual average distribution of oceanic rain column height derived from 12 yr (Jul 1987–Jun 1999) of SSM/I data

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 2.
Fig. 2.

Mean oceanic rain column height for Jan, Apr, Jul, and Oct (1987–99)

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 3.
Fig. 3.

Standard deviation of freezing height for Jan, Apr, Jul, and Oct (1987–99)

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 4.
Fig. 4.

Seasonal zonal mean of SSM/I oceanic freezing height for the global oceans: Atlantic, Pacific, and the Indian Oceans

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 5.
Fig. 5.

(a) Mean rain column height difference between estimates from SSM/I morning (AM) and afternoon (PM) passes. (b) Nonsystematic errors estimated using all 143 months data

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 6.
Fig. 6.

Scatterplot of the error vs mean rain column height

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 7.
Fig. 7.

Distribution of the height of the 0° isotherm computed from GLAS GCM for the period Aug 1987–Dec 1988

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 8.
Fig. 8.

Mean difference between rain column height derived from SSM/I and height of the 0° isotherm computed from GLAS GCM runs for Aug 1987–Dec 1998

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

Fig. 9.
Fig. 9.

Similar to Fig. 4, except for height of the 0° isotherm computed from GLAS GCM

Citation: Journal of Climate 13, 23; 10.1175/1520-0442(2000)013<4125:ORCHDF>2.0.CO;2

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