• Adler, R. F., , Kidd C. , , Petty G. , , Morissey M. , , and Goodman H. M. , 2001: Intercomparison of global precipitation products: The Third Precipitation Intercomparison Project (PIP-3). Bull. Amer. Meteor. Soc., 82 , 13771396.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Béranger, K., , Barnier B. , , Gulev S. , , and Crepon M. , 2006: Comparing 20 years of precipitation estimates from different sources over the World Ocean. Ocean Dyn., 56 , 104138.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bhandari, S. M., , and Varma A. K. , 1996: Potential of simultaneous dual-frequency radar altimeter measurements from TOPEX/Poseidon for rainfall estimation over oceans. Remote Sens. Environ., 58 , 1320.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, G., , Chapron B. , , Tournadre J. , , Katsaros K. , , and Vandemark D. , 1997: Global oceanic precipitation: A joint view by TOPEX and the TOPEX microwave radiometer. J. Geophys. Res., 102 , 10 45710 471.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, G., , Ma J. , , Fang C. , , and Han Y. , 2003: Global oceanic precipitations derived from TOPEX and TMR: Climatology and variability. J. Climate, 16 , 38883904.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Crane, R. K., 1990: Space–time structure of rain rate fields. J. Geophys. Res., 95 , 20112020.

  • Harris, D., , Foufoula-Georgiou E. , , and Kummerow C. , 2003: Effects of underrepresented hydrometeor variability and partial beam filling on microwave brightness temperatures for rainfall retrieval. J. Geophys. Res., 108 , 8380. doi:10.1029/2001JD001144.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Janssen, M., , Ruf C. , , and Keihm S. , 1995: TOPEX/Poseidon Microwave Radiometer (TMR): II Antenna pattern corrections and brightness temperature algorithm. IEEE Trans. Geosci. Remote Sens., 33 , 138146.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Keihm, S., , Janssen M. , , and Ruf C. C. , 1995: TOPEX/Poseidon Microwave Radiometer (TMR): III Wet troposphere range correction algorithm and prelaunch error budget. IEEE Trans. Geosci. Remote Sens., 33 , 147161.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kummerow, C., , Poyner P. , , Berg W. , , and Thomas-Stahle J. , 2004: The effects of rainfall inhomogeneity on climate variability of rainfall estimated from passive microwave sensors. J. Atmos. Oceanic Technol., 21 , 624638.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lovejoy, S., , and Schertzer D. , 1990: Multifractals, universality classes and satellite and radar measurements of cloud and rain fields. J. Geophys. Res., 95 , 20212034.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., , and Palmer W. M. , 1948: The distribution of raindrops with size. J. Meteor., 5 , 165166.

  • Marth, P., and Coauthors, 1993: Prelaunch performance of the NASA altimeter for the TOPEX/Poseidon project. IEEE Trans. Geosci. Remote Sens., 31 , 315332.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Masunaga, H., , L’Ecuyer T. , , and Kummerow C. , 2005: Variability in the characteristics of precipitation systems in the tropical Pacific. Part I: Spatial structure. J. Climate, 18 , 823840.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McMillan, A. C., , Quartly G. D. , , Srokosz M. A. , , and Tournadre J. , 2002: Validation of the TOPEX rain algorithm: Comparison with ground-based radar. J. Geophys. Res., 107 , 4038. doi:10.1029/2001JD000872.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ménard, Y., , and Fu L. , 2001: Jason-1 mission. Aviso Newsletter, No. 8, American Association of Museums, Washington, DC, 4–9.

  • Montopoli, M., , Marzano F. S. , , Vulpiani G. , , Fornasiero A. , , Alberoni P. P. , , Ferraris L. , , and Rebora N. , 2006: Spatial characterization of raincell horizontal profiles from C-band radar measurements at mid-latitude. Adv. Geosci., 7 , 285292.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Palmer, R., , Cheong B. , , Hoffman M. , , Frasier S. , , and Lopez-Dekker F. , 2005: Observations of the small-scale variability of precipitation using an imaging radar. J. Atmos. Oceanic Technol., 22 , 11221137.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Quartly, G., 2004: Sea state and rain: A second take on dual frequency altimetry. Mar. Geod., 27 , 133152.

  • Quartly, G., , Guymer T. , , and Srokosz M. , 1996: The effects of rain on TOPEX radar altimeter data. J. Atmos. Oceanic Technol., 13 , 12091229.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Quartly, G., , Srokosz M. , , and Guymer T. , 1999: Global precipitation statistics from dual-frequency TOPEX altimetry. J. Geophys. Res., 104 , 31 48931 516.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruf, C. S., , Keihm S. , , Subramanya B. , , and Janssen M. , 1994: TOPEX/POSEIDON microwave radiometer performance and in-flight calibration. J. Geophys. Res., 99 , 24 91524 926.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumacher, C., , and Houze R. A. , 2003a: Stratiform rain in the Tropics as seen by TRMM Preciptation Radar. J. Climate, 16 , 17391755.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumacher, C., , and Houze R. A. , 2003b: The TRMM Precipitation Radar’s view of shallow, isolated rain. J. Appl. Meteor., 42 , 15191524.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tournadre, J., 2004: Validation of Jason and Envisat dual frequency rain flags. Mar. Geod., 27 , 153170.

  • Tournadre, J., 2006: Improved level-3 oceanic rainfall retrieval from dual-frequency spaceborne radar altimeter systems. J. Atmos. Oceanic Technol., 23 , 11311149.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tournadre, J., , and Morland J. C. , 1997: The effects of rain on TOPEX/Poseidon altimeter data. IEEE Trans. Geosci. Remote Sens., 35 , 11171135.

  • Varma, A. K., , and Liu G. , 2006: Small-scale horizontal rain-rate variability observed by satellite. Mon. Wea. Rev., 134 , 27222733.

  • Varma, A. K., , Gairola R. M. , , Pandey P. C. , , and Singh K. P. , 2001: Use of TOPEX altimeter for the study of diurnal and spatial distribution of southwest monsoon rainfall over the Bay of Bengal and the Arabian Sea. Remote Sens. Environ., 77 , 112121.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Varma, A. K., , Liu G. , , and Noh Y-J. , 2004: Subpixel-scale variability of rainfall and its application to mitigate the beam-filling problem. J. Geophys. Res., 109 , D18210. doi:10.1029/2004JD004968.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wheater, H. S., and Coauthors, 2000: Spatial-temporal rainfall fields: Modelling and statistical aspects. Hydrol. Earth Syst. Sci., 4 , 581601.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zanife, O. Z., , Vincent P. , , Amarouche L. , , Dumont J. P. , , Thibaut P. , , and Labroue S. , 2003: Comparison of the Ku-band range noise level and the relative sea-state bias of the Jason-1, TOPEX, and Poseidon-1 radar altimeters. Mar. Geod., 26 , 201238.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zieger, A., , Hancock D. , , Hayne G. , , and Purdy C. , 1991: NASA radar altimeter for the TOPEX/Poseidon project. Proc. IEEE, 79 , 810826.

  • View in gallery

    (a) TOPEX and Jason Ku- and C-band σ0 relations [for a better reading, the difference f (σ0C) − σ0C is plotted] and (b) std for cycle 2–23. The Jason σ0 values have been corrected for the mean biases for a better comparison of the relations.

  • View in gallery

    Distribution of (a) attenuation, (b) FL, (c) rain event length, and (d) rain rate for TOPEX (solid lines) and Jason (dashed lines) rainy samples.

  • View in gallery

    Distribution of δxσ0 at Ku and C bands and of δxΔf(σ0) for (a) TOPEX and (b) Jason nonrainy samples.

  • View in gallery

    (a) Distribution of δxΔf(σ0) = δxAm for TOPEX and Jason rainy samples. (b) Variation of the δxΔf(σ0) std for TOPEX and Jason rainy and nonrainy samples as a function of C-band σ0. (c) Distribution of δxR for TOPEX and Jason and (d) variation of the δxR std as a function of C-band σ0.

  • View in gallery

    Std of δxR for TOPEX as a function of (a) rain rate and C-band surface backscatter, (b) rain event length, and (c) FL.

  • View in gallery

    Geographical distribution of TOPEX std (δxR) for (a) light rain (R < 2.5 mm h−1), (b) moderate rain (2.5 < R < 5 mm h−1), and (c) heavy rain (R > 5 mm h−1). Only the grid cells where there are enough data to ensure a 90% confidence level are shown.

  • View in gallery

    Mean measured SST (°C) field for the TM period data from the National Oceanic and Atmospheric Administration Climate Prediction Center (available online at http://www.cpc.noaa.gov/products/).

  • View in gallery

    (a) Distribution of δtσ0 at Ku and C bands and of δtΔf(σ0) for nonrainy samples. (b) Variation of the std of δtσ0 at Ku and C bands and of δtΔf(σ0) as a function of C-band σ0.

  • View in gallery

    (a) Distribution of δtΔf(σ0) for TOPEX or Jason rain samples (solid line) and TOPEX and Jason rainy samples (dashed line). (b) Variation of the std of δtΔf (σ0) as a function of C band σ0. (c) Distribution of δtR and (d) variation of the std of δtR as a function of C-band σ0.

  • View in gallery

    Variation of the δtR std as a function of (a) rain rate and C-band surface backscatter for TOPEX or Jason rainy samples and (b) rain events length and (c) FL.

  • View in gallery

    Geographical distribution of TOPEX std (δtR) for (a) light rain (R < 2.5 mm h−1), (b) moderate rain (2.5 < R < 5 mm h−1), and (c) heavy rain (R > 5 mm h−1).

  • View in gallery

    Conditional probability (a) of |δtR| over |δxR| and (b) of |δtAm| over |δxAm|.

  • View in gallery

    Mean value of the ratio δtR/δxR as a function of (a) rain rate and C-band surface backscatter, (b) rain event length, and (c) FL. The dashed lines indicate the demarcation between the convective and stratiform classes.

  • View in gallery

    Geographical distribution of the ratio between δtR and δxR for (a) stratiform rain and (b) convective rain. (c) Convective rain fraction.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 15 15 5
PDF Downloads 2 2 0

Analysis of Short Space–Time-Scale Variability of Oceanic Rain Using TOPEX/Jason

View More View Less
  • 1 Laboratoire d’Océanographie Physique et Spatiale, IFREMER, Plouzané, France
  • | 2 National Centre for Antarctic and Ocean Research, Goa, India
© Get Permissions
Full access

Abstract

Information on the spatial and temporal variability of rain rate is important not only for meteorology and hydrology but also for the design of remote sensing and in situ measuring or of millimeter wave communication systems. The Ocean Topography Experiment (TOPEX)/Jason Tandem Mission (TM) collocated rain dataset is used in this study to determine the small space-scale (5 km) and time-scale (70 s) rain variability. TOPEX and Jason dual-frequency (Ku and C bands) radar altimeter data have been extensively used during the past decade to detect and study oceanic precipitations. During the TM, designed to intercalibrate and validate the two altimeters, the two satellites were put on the same orbit with a 70-s time separation. With combined use of altimeter and passive microwave radiometers (also available on board altimeter missions), rain intensity, rain attenuation, rain layer height, rain event length, and surface winds can also be estimated and provide valuable coincident geophysical contextual information. The size of the TM collocated rain database (140 000 samples) is large enough to allow a meaningful statistical analysis of the time–space variability of rain over the World Ocean. The analysis of the different terms contributing to the variability of rain attenuation, from which rain rate is inferred, shows that the geophysical and/or instrumental noise is small enough to allow a meaningful estimation of the variability of the measured rain rate. The analysis of the time and space variabilities and their relation reveals two well-defined regimes. The first one, corresponding to convective rain cells (i.e., rain rate greater than 3–4 mm h−1, length smaller than 50 km, and freezing level greater than 3.5 km), is characterized by high temporal and spatial variabilities (greater than 2–3 mm h−1) that increase with increasing rain intensity and decreasing cell length. Horizontal variability is significantly larger than the temporal one and surface wind has a very limited impact. The second regime corresponds to stratiform and/or weak rain cells. The temporal and spatial variabilities are relatively low (on the order of 1–2 mm h−1) and vary little with rain intensity and cell length. The temporal variability increases with surface wind and largely exceeds the spatial variability (ratio of 2 or more); the ratio strongly increases with increasing wind speed.

* Current affiliation: Ahmedabad, Gujarat, India

Corresponding author address: J. Tournadre, IFREMER, Technopôle Brest-Iroise, 29280 Plouzané, France. Email: jean.tournadre@ifremer.fr

Abstract

Information on the spatial and temporal variability of rain rate is important not only for meteorology and hydrology but also for the design of remote sensing and in situ measuring or of millimeter wave communication systems. The Ocean Topography Experiment (TOPEX)/Jason Tandem Mission (TM) collocated rain dataset is used in this study to determine the small space-scale (5 km) and time-scale (70 s) rain variability. TOPEX and Jason dual-frequency (Ku and C bands) radar altimeter data have been extensively used during the past decade to detect and study oceanic precipitations. During the TM, designed to intercalibrate and validate the two altimeters, the two satellites were put on the same orbit with a 70-s time separation. With combined use of altimeter and passive microwave radiometers (also available on board altimeter missions), rain intensity, rain attenuation, rain layer height, rain event length, and surface winds can also be estimated and provide valuable coincident geophysical contextual information. The size of the TM collocated rain database (140 000 samples) is large enough to allow a meaningful statistical analysis of the time–space variability of rain over the World Ocean. The analysis of the different terms contributing to the variability of rain attenuation, from which rain rate is inferred, shows that the geophysical and/or instrumental noise is small enough to allow a meaningful estimation of the variability of the measured rain rate. The analysis of the time and space variabilities and their relation reveals two well-defined regimes. The first one, corresponding to convective rain cells (i.e., rain rate greater than 3–4 mm h−1, length smaller than 50 km, and freezing level greater than 3.5 km), is characterized by high temporal and spatial variabilities (greater than 2–3 mm h−1) that increase with increasing rain intensity and decreasing cell length. Horizontal variability is significantly larger than the temporal one and surface wind has a very limited impact. The second regime corresponds to stratiform and/or weak rain cells. The temporal and spatial variabilities are relatively low (on the order of 1–2 mm h−1) and vary little with rain intensity and cell length. The temporal variability increases with surface wind and largely exceeds the spatial variability (ratio of 2 or more); the ratio strongly increases with increasing wind speed.

* Current affiliation: Ahmedabad, Gujarat, India

Corresponding author address: J. Tournadre, IFREMER, Technopôle Brest-Iroise, 29280 Plouzané, France. Email: jean.tournadre@ifremer.fr

1. Introduction

Information on the spatial and temporal variability of rain rate is important not only for meteorology and hydrology but also for the design of remote sensing and in situ measuring systems, for the measurement of areal rainfall accumulation, and for the design of millimeter wave communication systems. For example, knowledge of the short time-scale variability is essential when comparing rain-rate estimates from different data sources for calibration purposes, and the knowledge of the subpixel-scale rain-rate variability is imperative in dealing with beam-filling problems associated with rain retrieval from satellite microwave radiometer data (Kummerow et al. 2004; Harris et al. 2003). Rain gauge and/or radar data have been used to estimate the spatial and temporal structure of the rain process over land (Crane 1990; Palmer et al. 2005; Montopoli et al. 2006) and a large numbers of theoretical studies have been published on rainfall structure and variability modeling (e.g., Lovejoy and Schertzer 1990; Wheater et al. 1986). However, very few studies (Varma and Liu 2006; Varma et al. 2004; Masunaga et al. 2005) have been published on the space and time variabilities of oceanic precipitation and their relation, especially at small scale, and none on the distribution of these variabilities over the global ocean, mainly because of a lack of pertinent data. Indeed, the resolution of microwave sensors is in general too low to allow the analysis of variability at scales smaller than 25–50 km. High-resolution sensors such as the precipitation radar on board the Tropical Rainfall Measuring Mission (TRMM) cover only the tropical region. Furthermore, it is not yet possible to have a temporal resolution from satellite sensors better than 30 min for geostationary satellites and several hours for polar orbiting satellites. Since the launch of the Ocean Topography Experiment (TOPEX)/Poseidon, the first dual-frequency altimeter to be flown in space, the capability of this kind of instrument to measure rain over the ocean has been well established (Bhandari and Varma 1996; Tournadre and Morland 1997; Quartly et al. 1996, 1999; Chen et al. 1997; McMillan et al. 2002) and the highly successful TOPEX mission, running over more than a decade, has provided a unique opportunity to study the space–time distribution of oceanic rain over both the global ocean (Chen et al. 1997; Quartly et al. 1999; Chen et al. 2003) and for specific oceanic regions (Varma et al. 2001). More recently, Tournadre (2006) demonstrated that the combined use of the coincident altimeter and radiometer measurements available on board altimeter missions allows the determination of freezing-level altitude and a more precise estimate of rain rates. To continue the task of providing the important oceanographic data time series originated by TOPEX/Poseidon, the Jason satellite, carrying updated versions of the same instruments, was launched in December 2001. Both missions operated together for several years before the failure of TOPEX in October 2005. During the initial phase of Jason, TOPEX and Jason were put in the same orbit for a period of 7 months (15 January–16 August 2002), TOPEX trailing Jason by 70 s. The objective of the so-called Tandem Mission (noted TM hereafter) was to cross-compare and calibrate the instrument’s performances as well as the derived geophysical products. The detailed results from the analysis of data collected during the TM have been published in three specials issues of Marine Geodesy (volume 26, issues 3–4; volume 27, issues 1–4). During the TM, the TOPEX and Jason measurements were almost perfectly collocated in space (within 2 km) and were separated by 70 s. On the other hand, both altimeters have a ground-track resolution of 5.8 km. Although the sampling of the ocean by altimeters is limited to the subsatellite track, and only one time lag is available, the TM collocated rain dataset provides a very unique opportunity to examine and study the short space-scale and time-scale variabilities of oceanic rainfall and their relationship on a global scale.

The present study thus aims at describing the small time-scale (70 s) and space-scale (5.8 km) variability of rainfall on a global scale using the TM collocated rain measurements. Section 2 describes the two dual-frequency radar altimetric missions and their instruments. The characteristics of the measurements during the tandem phase (TM) are also explained. Section 3 describes in detail the TOPEX/Jason rain event collocated dataset generated using the dual-frequency altimeter measurements from TOPEX and Jason. This dataset includes Ku-band backscatter attenuation, rain rate, rain layer height, rain event length, and surface backscatter. Section 4 analyzes the different terms contributing to the short space and time variability of the measured backscatter coefficient to demonstrate that the geophysical and/or instrumental noise does not hamper the determination of rainfall variability. The rainfall variability in both space and time is then analyzed in terms of rain rate, freezing level (FL), rain event length, sea surface temperature, and surface backscatter (local wind). Section 5 studies the relationship between space and time variability and its dependence on the different rain parameters and local wind. The last section summarizes the important conclusions of the study.

2. Altimeter data

a. TOPEX/Poseidon

The TOPEX/Poseidon satellite, developed by the National Aeronautics and Space Administration (NASA) and the French Space Agency (CNES) and launched on 10 August 1992, was dedicated to ocean altimetry and provided more than 12 yr of data. Its primary instrument was the NASA radar altimeter (NRA), which operated at 13.6 GHz (Ku band) and 5.3 GHz (C band) simultaneously. Depending on sea state, the altimeter footprint varied from 10 to 20 km in diameter. The satellite sampled the ocean surface between 66°S and 66°N at a 1-s interval (corresponding to a 5.8-km ground distance) for each of the 254 passes that make up a 9.9156-day repeat cycle. A detailed description of the NRA instrument and data processing is given in Zieger et al. (1991) and Marth et al. (1993). The satellite also carried the TOPEX/Poseidon microwave radiometer (TMR), whose primary mission was the determination of tropospheric water vapor path delay correction for the altimeter range (Ruf et al. 1994; Janssen et al. 1995; Keihm et al. 1995). TMR was a nadir-viewing microwave radiometer that operated at three frequencies of 18, 21, and 37 GHz with footprint diameters of 43.4, 36.4, and 22.9 km, respectively. TMR was temporally and spatially coaligned with the TOPEX altimeter to accommodate its mission requirements. In addition to water vapor retrieval, TMR also provided useful data of cloud liquid water.

b. Jason

The CNES/NASA Jason mission is designed to ensure the continuity of the observation and monitoring of the ocean provided by TOPEX/Poseidon and it has basically the same characteristics. It was launched on 7 December 2001. Its main instrument is the Poseidon-2 altimeter, which is derived from the experimental Poseidon-1 altimeter. The dual-frequency Poseidon-2 operates at the same frequencies as the NRA, that is, 13.6 GHz (Ku band) and 5.3 GHz (C band). A detailed description of the Poseidon-2 altimeter is given in Ménard and Fu (2001). The Jason microwave radiometer (JMR), a Jet Propulsion Laboratory instrument of TMR heritage, is a passive receiver that collects radiation emitted by the ocean at frequencies of 18.7, 23.8, and 34 GHz (i.e., marginally different from the TMR ones). The footprint diameters are similar to the TMR ones (i.e., 41.6, 36.1, and 22.9 km, respectively).

c. TOPEX/Jason TM collocated dataset

During the TM, Jason-1 was positioned 70 s in front of TOPEX/Poseidon on the same orbit, in order to cross-calibrate their instruments. The mission lasted 7 months (Jason cycles 2–22, TOPEX cycles 345–366). The near-simultaneous measurements from the same altitude of the same sea surface locations by the Jason-1 and TOPEX/Poseidon altimeters enabled a rigorous comparison and correlation of the Jason-1 and TOPEX/Poseidon altimetry measurements and derived oceanic parameters. The TM measurements have been used to assemble a collocated dataset of ocean samples. The following collocation criteria are used: separation distance less than 2.5 km (half the along-track resolution) and separation time less than 76 s. Only valid data (i.e., for which the quality flags are good) for both sensors are considered. The resulting dataset contains several millions points. The distance between the TOPEX and Jason collocated samples varies from 0 to 2.5 km with a mean of 1.2 km. The time separation varies from 67 to 75 s with a mean of 71.5 s.

Several studies (Quartly 2004; Tournadre 2004) published on the intercalibration of TOPEX and Jason backscatter measurements and significant wave height estimates showed good overall agreement between the two sensors. Biases between the Jason and TOPEX σ0 at Ku (0.15 dB) and C (0.45 dB) bands exist, but these are quite stable during the TM (Tournadre 2004) and do not interfere with the rain detection process.

3. Collocated TOPEX/Jason rain dataset

a. Determination of the rain parameters from dual-frequency altimeter

The detection of rain by dual-frequency altimeters is based on the frequency dependence of rain attenuation of the electromagnetic signals (Bhandari and Varma 1996; Tournadre and Morland 1997; Quartly et al. 1996). Basically, it detects occurrences where the Ku-band (13.6 GHz) backscatter measurements (σ0K) are significantly attenuated compared to that of the C band (5.3 GHz). In practice, the measured Ku band σ0K is compared to the Ku band σ0K expected from the measured C band σ0C through a rain-free relationship. For each altimeter (TOPEX, Jason) and for each ∼10-day repeat cycle, the rain-free Ku/C relation, f, is determined by binning the Ku-band σ0K data in intervals of 0.1 dB of C band σ0C. The mean f (σ0C) and standard deviation (std), std(σ0C), are then computed in each bin. The TOPEX and Jason mean relations (for the 20 cycles) are presented in Fig. 1. The relations as well as the std are nearly identical, with slight differences for high σ0C (greater than 23 dB).

The samples detected as rainy for Jason or TOPEX are selected within the TM collocated dataset to create a collocated TOPEX/Jason rain dataset. The detection criteria are the classical ones presented by Tournadre and Morland (1997):
i1520-0426-26-1-74-e1
and
i1520-0426-26-1-74-e2
where Am = Δf (σ0) is the measured Ku-band rain attenuation, f is the mean rain-free Ku/C band σ0 relation, and rms is the rms of the f relation. The radiometer-derived liquid water content LZ is expressed as a quadratic polynomial of the three TMR/JMR brightness temperatures (Keihm et al. 1995). This second criterion is used to ensure the presence of sufficient cloud liquid water and thus to minimize the possibility of false alarm. To avoid any problems with sea ice contamination, only data whose latitudes are between 50°S and 55°N are considered. The samples for which the radiometer data are unavailable were also discarded. The dataset contains 142 851 samples detected as rainy for TOPEX or Jason. For the TOPEX or Jason rain samples, the length l of the rain events and the height of the freezing level are estimated by the method developed by Tournadre (2006). The length is determined by the number of consecutive rain samples and the freezing level is inferred by inverting the radiometer (TMR or JMR) brightness temperatures. It should be noted that for low rain rates and/or small rain cells, the method does not converge in about 50% of the cases (Tournadre 2006). For rainy samples, the rain rate R is computed assuming the Marshall–Palmer raindrop size distribution (Marshall and Palmer 1948),
i1520-0426-26-1-74-e3
where a and b are constants depending on the signal frequency and A is the two-way path attenuation. The values proposed by Quartly et al. (1999), a = 0.0238 dB km−1 and b = 1.203, are used in this study. For samples with nonconvergent freezing levels, a mean climatological value computed from the convergent FL estimate on a monthly basis is used.

As we are considering samples that are rainy for TOPEX or Jason, attenuation and rain rate are also computed if a sample is not detected as rainy by one of the two sensors. If the computed attenuation Δf (σ0) = A is negative, a rain rate is estimated using (3) and the computed or climatological FL. If the attenuation is positive, then both rain rate and attenuation are set to zero (i.e., no rain). Only a small percentage of samples have positive attenuation, about 5% (8143 samples) for TOPEX and about 2% (3078 samples) for Jason.

The rain collocated dataset can be partitioned in several ways. The first criterion is the detection of rain for each of the sensors. The second one is the convergence or the divergence of the freezing-level estimate. Table 1 summarizes the number of collocated TOPEX and Jason samples for the two criteria. TOPEX is more rain sensitive and flags about 10% more samples than Jason. For both sensors, approximately 70% of the rainy samples are associated with convergent FL estimates. Approximately 65% of the TOPEX (or Jason) rainy samples are also rainy for the other sensor. The number of samples that pass both criteria for both sensors is only 48 000 (i.e., only one-third of the global dataset).

This simple analysis shows that for rain cells large and rainy enough to allow the inversion of the radiometer brightness temperature in terms of FL, both sensors detect rain. For smaller rain cells and lower rain rates, TOPEX appears to be more sensitive than Jason. This difference results certainly in part from the sensor’s differences and from slight differences in the flagging process but also from the highly variable nature of the rain process in both time and space.

b. Description of the collocated dataset

The analysis of the samples detected as rainy by both altimeters shows that except for rain event length for which TOPEX detects more short (1 sample long) events than Jason, both altimeters have similar distributions of attenuation, freezing level, and rain rate. This can be seen in Figs. 2a–d, which present the distribution of attenuation, FL, rain events length, and rain rate, respectively, for the collocated dataset. Tournadre (2006) presented a detailed comparison of Jason and TOPEX rain rates and freezing levels for both rainy and FL convergent samples and showed the mean rain-rate difference to be 0.14 mm h−1 with an std of 1.4 mm h−1 and the mean FL difference to be 0.064 km with an std of 0.4 km.

4. Short space- and time-scale rain variability

The TM collocated rain event dataset consists of TOPEX and Jason measurements separated in space and time by less than 2 km and 72 s. The along-track distance between consecutive (1 s) TOPEX or Jason measurements is 5.8 km. The short space-scale variability can be estimated by the analysis of the difference between two along-track consecutive samples of either altimeters and the short time-scale one by the analysis of the difference between collocated TOPEX and Jason measurements. However, as the rain rate is estimated as shown using relation (1) from the measured Ku-band attenuation (defined basically as the difference between Ku- and C-band backscatter), the analysis of the rain variability will be pertinent if and only if the variability of the rain attenuation is significantly larger than the geophysical and instrumental variability of the surface backscatter. It is thus necessary as a first step to analyze the different terms contributing to the space and time variability of the Ku-band rain attenuation.

a. Spatial variability of Ku-band rain attenuation

The Ku-band backscatter coefficient σ0Km measured by an altimeter can be expressed, in absence of rain, by
i1520-0426-26-1-74-e4
where σ0K is the true Ku-band ocean surface backscatter and ε is the instrumental noise. The m superscript refers to measured quantities. In the presence of rain the signal is attenuated, thus the measured backscatter becomes
i1520-0426-26-1-74-e5
where A is the rain attenuation at Ku band. At C band, attenuation is one order of magnitude smaller than that at Ku band and can thus be neglected in a first-order approximation. The measured C-band backscatter coefficient σ0Cm can thus be expressed in the presence of rain as
i1520-0426-26-1-74-e6
The attenuation, Am = Δf(σ0), estimated using (1) is thus
i1520-0426-26-1-74-e7
Using (5) and assuming that the relation between the Ku- and C-band true surface backscatter is identical to the rain-free Ku/C-band relation f used for the rain detection [i.e., σ0K = f (σ0C)], Am can be expressed as
i1520-0426-26-1-74-e8

The attenuation measured by the differential attenuation of the Ku- and C-band σ0 is thus the sum of the true rain attenuation and of a geophysical/instrumental noise εA that includes the noises on Ku band and expected Ku σ0.

The σ0m difference between two along-track consecutive samples (i.e., the 5.8-km σ0 variability) is, in the absence of rain, the sum of the geophysical variation of backscatter and instrumental noise variation, that is,
i1520-0426-26-1-74-e9
where eσ = δxεσ is a random variable. The standard deviation of δxσ0m is thus an estimate of the geophysical and instrumental σ0 noise.
In the presence of rain, the along-track difference of the measured attenuation is, using (8),
i1520-0426-26-1-74-e10
where eA = δxεA is a random variable. In the absence of rain this expression reduces to
i1520-0426-26-1-74-e11
which is an estimate of the geophysical/instrumental noise of the measured attenuation. Indeed, the rain attenuation and the geophysical/instrumental noises are uncorrelated, thus, the std of the true attenuation can be expressed as
i1520-0426-26-1-74-e12

The TOPEX and Jason σ0 geophysical/instrumental noises std(δxσ0m) are computed using the TM collocated dataset of nonrainy samples as well as the geophysical/instrumental noise of the measured attenuation, eA = δxΔf(σ0). The attenuation variability std(δxAm) is estimated using only the collocated rainy samples dataset. The stds of the different parameters are given in Table 2.

The TOPEX instrument noise, which is about 0.18 dB at both Ku and C bands, is slightly larger than that of Jason (about 0.15 dB). However, the TOPEX std of eA [i.e., δxΔf(σ0)] is about 3 times larger than that of Jason.

The TOPEX and Jason δxσ0 distributions are quite different as shown in Figs. 3a,b. These differences result from the different methods used for the two satellites to estimate the backscatter. The TOPEX Ku-band values are calculated from the sensor automatic gain control values (AGCs), with compensation for spherical spreading loss and instrument calibration constants. At C band, no correction is applied to σ0. As the AGC quantization is only 1/16th of a decibel (0.0625 dB), the C-band δxσ0 distribution presents an artificial peak at 0 due to the low precision. The Ku-band distribution reflects mainly the variability of the instrumental correction applied to the AGC. The Δf(σ0) noise level (0.182 dB) is thus mainly due to the difference of processing between Ku and C band and to the instrumental correction applied to the Ku band. The Jason Ku- and C-band σ0 are estimated from echo waveform retracking using a maximum likelihood estimator. The processing is homogeneous between the two channels and consistent instrumental corrections are applied to both σ0. This processing scheme performs much better, as already shown by Zanife et al. (2003), and reduces the σ0 noise level significantly. Furthermore, as the instrumental Ku- and C-band noises are highly correlated, they cancel when computing Δf(σ0), resulting in a much lower std (0.08 dB), which represents mainly the wind-induced short-scale σ0 variability. Figure 4a presents the analysis of the measured attenuation variability δxAm for the TOPEX and Jason rainy samples. Because of its higher instrumental noise, the TOPEX std, 0.355 dB, is higher than that of Jason, 0.304 dB. However, the attenuation variabilities δxA estimated using relation (12) are very similar at 0.3 dB. For TOPEX, the attenuation std increases nonlinearly with C-band σ0, from 0.30 dB at high winds (σ0 = 12 dB) to 0.42 dB at low winds (σ0 = 18 dB). For Jason, this increase is significantly weaker—from 0.22 dB at high winds to 0.30 dB at low winds (see Fig. 4b).

The analysis of the backscatter and attenuation variability shows that the geophysical/instrument noise is significantly smaller than the variability of the rain attenuation (on the order of 0.3–0.4 dB) and for a first-order approximation can be neglected for the rain-rate analysis.

b. Spatial variability of rain

The distributions of δxR for TOPEX and Jason presented in Fig. 4c have similar shapes but the TOPEX ones have a larger std (1.3 versus 1.14 mm h−1), mainly because of the higher TOPEX instrumental noise. However, they are close enough to confirm the small impact of the geophysical and instrumental noise on the rain variability estimate. The std of δxR varies weakly with the surface backscatter for Jason with slightly higher values for very high and very low winds. For TOPEX it is constant for high and medium winds, then increases by 0.4 mm h−1 for low winds (i.e., above 16 dB). This results, at least partially, from the impact of the higher geophysical/instrument noise observed for TOPEX at low wind speeds in Fig. 4b.

Figure 5 presents the std of δxR as a function of rain rate, surface (C band) backscatter, rain events length, and freezing level for TOPEX. Similar results were found for Jason and are not presented here. The figure clearly shows that the rain variability is mainly rain-rate dependent. For low rain rate (R < 2.5 mm h−1), the std is nearly constant at 1 mm h−1 and it is also independent of surface backscatter and freezing level. It increases slightly with the rain event length. For medium rain rate (2.5 < R < 5 mm h−1), the std rapidly increases from 1 to 2 mm h−1. It also increases slightly with increasing surface backscatter (thus with decreasing winds) and decreases with the rain event length, the decreasing rate increasing with rain rate. For high rain rate (R > 5 mm h−1), the std increases with rain rate, but at a much lower rate for longer rain cells than for shorter ones. The std also increases slightly with surface backscatter and remains quite independent of freezing level.

The above analysis shows that the horizontal variability of rain depends on the nature of rain and that small convective rain cells (i.e., high rain rate and short rain length) have a high horizontal variability, while weak rain cells or stratiform rain (low rain rate and large rain length) have a much weaker horizontal variability. These results are in agreement with conceptual convective rain cell models such as simple conical cells or more complex Gaussian or exponential cells for which it can be easily shown that the along-track rain gradient increases with rain rate and with the inverse of the diameter.

As the rain-rate variability deviates mainly with rainfall intensity, the rain dataset has been divided into the three rain-rate intensities categories: light (R < 2.5 mm h−1), moderate (2.5 < R < 5 mm h−1), and high (R > 5 mm h−1). Figures 6a–c show the global δxR std distribution for the three rain-rate categories for the TOPEX dataset. In this figure, the std is computed for a 5° latitude by 10° longitude grid, and only the areas where there is enough data to ensure a 90% confidence level are shown. The results found for Jason data are very similar and are not presented here. For the three rain intensity categories the major feature of the distribution is the latitudinal variation with a greater variability in the tropical rainband, in particular in the Pacific warm pool. The higher variability is always associated with higher sea surface temperature, which confirms the relation between horizontal variability and convection. This is particularly obvious for medium and high rain rates where the distribution almost perfectly reproduces the mean SST distribution for the corresponding period as presented in Fig. 7. These results are very similar, at least qualitatively, to the ones presented by Varma and Liu (2006) on the small-scale horizontal variability of rain rate from TRMM data at a 25 km × 25 km scale and on the differences between convective and stratiform rains.

c. Time variability of Ku-band rain attenuation

The mean time separation between collocated TOPEX and Jason measurements during the TM is 72 s and fluctuates by less than 1 s. Their mean separation distance is 1.2 km. Neglecting the space variability at 1-km scale, the 70-s σ0 variability can be estimated by differencing the collocated TOPEX and Jason measurements. In the absence of rain, the difference between TOPEX and Jason σ0 can be expressed using (4) as
i1520-0426-26-1-74-e13
It is thus an estimate of the geophysical and instrumental noise of the σ0 measurements. In the presence of rain, the difference between the TOPEX and Jason measured attenuation can be expressed as
i1520-0426-26-1-74-e14
It is thus the sum of the true attenuation variability δtA and a noise eA, which can be estimated in the absence of rain by the difference between the TOPEX and Jason Δf(σ0) as
i1520-0426-26-1-74-e15

Figure 8a presents the distributions of δtσ0m for Ku and C bands as well as the distribution of the Δf(σ0) difference. Their stds are given in Table 2. For the Ku and C bands, the σ0 70-s variability is about 0.15 dB in the absence of rain, while the eA one is about 0.18 dB (i.e., very similar to the 5-km spatial variability). The variability increases with C-band surface backscatter, as can be seen in Fig. 8b. The analysis of the influence of the small variations of the separations in time and space (1 s, 1.2 km) between the TOPEX and Jason measurements revealed no significant impact on the variability.

In the presence of rain, the std of the measured attenuation δtAm is about 0.36 dB, thus much larger than the geophysical and instrument noise. The corrected std is about 0.31 dB, again very similar to the 5-km spatial variability.

Figure 9a presents the δtA analysis for both the TOPEX and Jason, and TOPEX or Jason rainy samples. The two distributions are almost identical and similar to the spatial distribution with an std of 0.357 dB. The influence of surface backscatter presented in Fig. 9b shows that the std is larger at high winds (σ0C < 13 dB), then decreases for medium winds, and increases again for low winds (σ0C < 15 dB). It should be noted that 75% of the data have a surface backscatter between 13 and 16 dB.

d. Time variability of rain

The distributions of δtR, presented in Fig. 9c, are quite similar for TOPEX and Jason rain samples and TOPEX or Jason rain samples. It is slightly skewed toward positive values, with a bias of 0.2 mm h−1 and an std of 1.69 mm h−1. This bias and std are consistent with the results of Tournadre (2006) on the comparison of both rainy and both FL convergent TOPEX and Jason samples. The std of δtR is higher for low and high surface backscatter (i.e., low and high winds) (see Fig. 9d). This wind dependence of δtR is larger than that of δxR, especially at high winds, suggesting a stronger impact of surface winds on the time variability of rain.

Figures 10a–c present the std of δtR as a function of rain rate, surface backscatter, rain event length, and freezing level, respectively, for TOPEX. Similar results were found for Jason and are not presented here. As for the space variability, the time variability is mainly dependent on the rain rate. The distributions present very similar patterns to the ones presented in Fig. 5 for the horizontal rain variability but with lower std values.

At low rain rate (R < 2.5 mm h−1), the std is about 1 mm h−1 and is only weakly dependent on the rain event length. The variability increases somewhat at high winds to reach 2 mm h−1 at σ0 of ∼15 dB. For medium and high rain rate, the std rapidly increases with increasing rain rate, especially for small rain cells. For large rain event length (>25 km), the std increases at a much lower rate and remains below 2 mm h−1.

As for the space variability, the time variability dataset has been partitioned into low, moderate, and high rain-rate intensity categories. The std of the time variability is computed for a 5° latitude by 10° longitude grid, and only the areas where there are enough data to ensure a 90% confidence level are shown. Figure 11 shows the global δtR std distribution for the three categories. The temporal variability pattern strongly differs from that of spatial variability, especially for low rain rate. At low rain rates, the tropical ocean is characterized by low variability (∼1 mm h−1), while the Southern, North Pacific, and North Atlantic Oceans are associated with a high variability (∼2 mm h−1). This pattern clearly reflects the impact of surface winds on the temporal variability particularly evident in the roaring forties and fifties and even in the Arabian Sea where a local maximum associated with the monsoon can be seen. At a moderate rain rate, the variability is relatively homogeneous over the globe. However, this homogeneity certainly results from a combination of the impacts of surface wind at mid- and high latitude and from convection at low latitude. At a high rain rate, the rain cells are predominantly convective and the distribution clearly reflects the sea surface temperature patterns.

5. Relation between short time and space variability

The collocalization in both time and space of the TOPEX and Jason rain measurements is a unique opportunity to analyze the interdependency of the time and space variability of rainfall over the global ocean. The conditional probabilities of |δtA| over |δxA| and |δtR| over |δxR|, presented in Figs. 12a and 12b, show that the time and space short-scale gradients are weakly statistically dependent. If low horizontal gradients are associated with low time gradients and high horizontal gradients with high time gradients, the dispersion of the probability is quite high and strongly increases for larger horizontal gradients.

The ratio of |δtR| and |δxR| has been analyzed as a function of rain rate, surface backscatter, rain event length, and freezing level, and the results are presented in Figs. 13a–c, respectively. To avoid any problems related to the uncertainties of the freezing level estimates, the ratio has been estimated, using (3), as
i1520-0426-26-1-74-e16

The analysis of the time–space variability ratio reveals two well-defined regimes. The first one corresponds to small cells (<40–50 km), medium to high rain rates (>3–4 mm h−1), and high freezing levels (>3–4 km), that is, convective rain cells. It is characterized by high space and time variabilities, which increase with rain intensity and decreasing length. The variability ratio, which is about 1, indicating that the space and time variability are of the same order of magnitude, is quite constant with length, intensity, and freezing level. It increases slightly with increasing surface wind for the lower rain intensity.

The second regime is associated with lower freezing level (<3–4 km) or with light rain (<3–4 mm h−1) and/or large rain cells (>40–50 km). This corresponds to either very light rain and/or stratiform rain and/or decaying convective cells. The space and time variabilities are relatively high and vary little with rain intensity and cell length. The time variability largely exceeds the space one (ratio about 2 to 3) and strongly increases with surface wind and with decreasing length. The rain database has been partitioned into two classes, representing the convective and stratiform cells. The following criteria have been used:

  • convective class: rain rate greater than 4 mm h−1 and length smaller than 50 km and freezing level higher than 3.5 km;
  • stratiform class: rain rate smaller than 4 mm h−1, or length larger than 50 km, or freezing level lower than 3.5 km.
The limits were chosen to have a number of samples in the convective class large enough to allow the computation of a global distribution.

The geographical distribution of the ratio for the two classes, also presented in Figs. 14a and 14b, shows that for stratiform rains, the temporal variability largely exceeds the spatial (ratio greater than 2) over the global ocean. The ratio increases with latitude to exceed a value of 3 outside the tropics. The pattern clearly reflects the wind speed distribution, not only at mid- and high latitudes but also for example in the Northern Hemisphere trade wind regions where secondary maxima can be observed or in the Arabian Sea associated with the summer monsoon. This high temporal variability for low rain rates at mid- and high latitudes shows the difficulty of calibration and validation of satellite-based rain-rate estimates and might explain at least partially the large discrepancies observed in the different rain climatologies at these latitudes (Chen et al. 1997; Adler et al. 2001; Béranger et al. 2006). For convective cells, the distribution of the ratio (see Fig. 14b) has values ranging from 1 to 2.2. The impact of wind is reduced compared to low rain rates but is still noticeable at mid- and high latitudes for which the temporal variability dominates. In the tropical band, the two variabilities are of the same order of magnitude and exhibit little variability.

The proportion of convective rain samples, presented in Fig. 14c, shows that convection is primarily associated with the tropical rain region and that the stratiform rain fraction exceeds 90% at mid- and high latitudes. The pattern of the distribution is in agreement, at least qualitatively, with the results of Schumacher and Houze (2003a, b) for the tropical regions using TRMM data.

6. Summary and conclusions

The TOPEX/Jason Tandem Mission, during which the two satellites carrying dual-frequency radar altimeters were put in the same orbit with a 70-s time delay, gives a unique opportunity to study and to analyze the short time-scale and space-scale variabilities of oceanic precipitation and their relationship over the global ocean. During the mission more than 140 000 collocated samples, rainy for TOPEX or Jason, were detected and assembled into a TM rain dataset. This dataset includes measured Ku-band rain attenuation and rain rates as well as the contextual geophysical parameters. The analysis of the different terms contributing to the time and space variability of the rain attenuation shows that the geophysical and/or instrumental noise is small enough to allow a meaningful estimation of the variability of the measured rain attenuation and rain rate at short time (∼1 min) and space (∼5 km) scales. The analysis of the rain-rate variability shows that convective rain, medium and high rain rates (R > 4 mm h−1), and short rain cell lengths (L < 50 km) are characterized by large values of horizontal rain-rate gradients, the variability increasing with increasing rain rates and decreasing cell length. Stratiform rains characterized by low rain rates and/or large cell lengths present much weaker and homogeneous variability around 1 mm h−1. The relation between convection and short-scale horizontal variability is confirmed by the geographical distribution that reproduces the distribution of the mean sea surface temperature. The tropical regions are thus associated with large variabilities for all rain intensities while the rain fields are more homogeneous at mid- and high latitudes. The temporal variability also has a strong relation to convection with high values for small, medium, and high intensity rain cells and lower ones for stratiform rains. However, the analysis shows that surface wind also plays an important role, especially at low rain rates. This is clearly obvious from the geographical distribution at low rain rates that delineates the wind climatology. At medium and high rain rate, convection plays the major role but its importance is smaller than in the case of horizontal variability.

The analysis of the relation between time and space variability reveals two well-defined regimes. The first one corresponds to convective cells (i.e., rain rate greater than 4 mm h−1, rain length smaller than 50 km, and freezing level greater than 3.5 km). The temporal and spatial variabilities are high and the horizontal one is larger than the temporal. Surface wind has a limited impact on both variabilities, except for high winds that are associated with larger temporal variability. The second regime corresponds to stratiform and/or weak rain cells, that is, rain rate smaller than 4 mm h−1 or rain length greater than 50 km, or freezing level lower than 3 km. The temporal and spatial variabilities are relatively low and the temporal variability largely exceeds the spatial one (ratio of 2 or more). Surface wind is a major contributor: the stronger the wind, the larger the ratio.

In conclusion, we have gainfully exploited the one-time unique opportunity of the TOPEX/Jason Tandem Mission altimetric measurements with time separation of ∼70 s to study the short time-scale and space-scale variability of oceanic rain. Extensions of such studies toward a more comprehensive analysis of rainfall variability at different time and space scales may be realizable with fortuitous coincidence resulting from concurrent availability of Jason-1 and Envisat dual-frequency radar altimeters operating in different orbits, in combination with information from passive microwave radiometer systems [Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) on board Aqua and Microwave Imager on board TRMM (TMI), etc.]. Formation flying with satellites and different time/space separations is gaining popularity with earth scientists and may open up exciting possibilities in the time to come for examining the fine structure of different geophysical/meteorological fields.

Acknowledgments

The authors wish to thank the reviewers for their very helpful comments that greatly helped us clarify the manuscript.

REFERENCES

  • Adler, R. F., , Kidd C. , , Petty G. , , Morissey M. , , and Goodman H. M. , 2001: Intercomparison of global precipitation products: The Third Precipitation Intercomparison Project (PIP-3). Bull. Amer. Meteor. Soc., 82 , 13771396.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Béranger, K., , Barnier B. , , Gulev S. , , and Crepon M. , 2006: Comparing 20 years of precipitation estimates from different sources over the World Ocean. Ocean Dyn., 56 , 104138.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bhandari, S. M., , and Varma A. K. , 1996: Potential of simultaneous dual-frequency radar altimeter measurements from TOPEX/Poseidon for rainfall estimation over oceans. Remote Sens. Environ., 58 , 1320.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, G., , Chapron B. , , Tournadre J. , , Katsaros K. , , and Vandemark D. , 1997: Global oceanic precipitation: A joint view by TOPEX and the TOPEX microwave radiometer. J. Geophys. Res., 102 , 10 45710 471.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, G., , Ma J. , , Fang C. , , and Han Y. , 2003: Global oceanic precipitations derived from TOPEX and TMR: Climatology and variability. J. Climate, 16 , 38883904.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Crane, R. K., 1990: Space–time structure of rain rate fields. J. Geophys. Res., 95 , 20112020.

  • Harris, D., , Foufoula-Georgiou E. , , and Kummerow C. , 2003: Effects of underrepresented hydrometeor variability and partial beam filling on microwave brightness temperatures for rainfall retrieval. J. Geophys. Res., 108 , 8380. doi:10.1029/2001JD001144.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Janssen, M., , Ruf C. , , and Keihm S. , 1995: TOPEX/Poseidon Microwave Radiometer (TMR): II Antenna pattern corrections and brightness temperature algorithm. IEEE Trans. Geosci. Remote Sens., 33 , 138146.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Keihm, S., , Janssen M. , , and Ruf C. C. , 1995: TOPEX/Poseidon Microwave Radiometer (TMR): III Wet troposphere range correction algorithm and prelaunch error budget. IEEE Trans. Geosci. Remote Sens., 33 , 147161.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kummerow, C., , Poyner P. , , Berg W. , , and Thomas-Stahle J. , 2004: The effects of rainfall inhomogeneity on climate variability of rainfall estimated from passive microwave sensors. J. Atmos. Oceanic Technol., 21 , 624638.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lovejoy, S., , and Schertzer D. , 1990: Multifractals, universality classes and satellite and radar measurements of cloud and rain fields. J. Geophys. Res., 95 , 20212034.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., , and Palmer W. M. , 1948: The distribution of raindrops with size. J. Meteor., 5 , 165166.

  • Marth, P., and Coauthors, 1993: Prelaunch performance of the NASA altimeter for the TOPEX/Poseidon project. IEEE Trans. Geosci. Remote Sens., 31 , 315332.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Masunaga, H., , L’Ecuyer T. , , and Kummerow C. , 2005: Variability in the characteristics of precipitation systems in the tropical Pacific. Part I: Spatial structure. J. Climate, 18 , 823840.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McMillan, A. C., , Quartly G. D. , , Srokosz M. A. , , and Tournadre J. , 2002: Validation of the TOPEX rain algorithm: Comparison with ground-based radar. J. Geophys. Res., 107 , 4038. doi:10.1029/2001JD000872.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ménard, Y., , and Fu L. , 2001: Jason-1 mission. Aviso Newsletter, No. 8, American Association of Museums, Washington, DC, 4–9.

  • Montopoli, M., , Marzano F. S. , , Vulpiani G. , , Fornasiero A. , , Alberoni P. P. , , Ferraris L. , , and Rebora N. , 2006: Spatial characterization of raincell horizontal profiles from C-band radar measurements at mid-latitude. Adv. Geosci., 7 , 285292.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Palmer, R., , Cheong B. , , Hoffman M. , , Frasier S. , , and Lopez-Dekker F. , 2005: Observations of the small-scale variability of precipitation using an imaging radar. J. Atmos. Oceanic Technol., 22 , 11221137.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Quartly, G., 2004: Sea state and rain: A second take on dual frequency altimetry. Mar. Geod., 27 , 133152.

  • Quartly, G., , Guymer T. , , and Srokosz M. , 1996: The effects of rain on TOPEX radar altimeter data. J. Atmos. Oceanic Technol., 13 , 12091229.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Quartly, G., , Srokosz M. , , and Guymer T. , 1999: Global precipitation statistics from dual-frequency TOPEX altimetry. J. Geophys. Res., 104 , 31 48931 516.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruf, C. S., , Keihm S. , , Subramanya B. , , and Janssen M. , 1994: TOPEX/POSEIDON microwave radiometer performance and in-flight calibration. J. Geophys. Res., 99 , 24 91524 926.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumacher, C., , and Houze R. A. , 2003a: Stratiform rain in the Tropics as seen by TRMM Preciptation Radar. J. Climate, 16 , 17391755.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumacher, C., , and Houze R. A. , 2003b: The TRMM Precipitation Radar’s view of shallow, isolated rain. J. Appl. Meteor., 42 , 15191524.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tournadre, J., 2004: Validation of Jason and Envisat dual frequency rain flags. Mar. Geod., 27 , 153170.

  • Tournadre, J., 2006: Improved level-3 oceanic rainfall retrieval from dual-frequency spaceborne radar altimeter systems. J. Atmos. Oceanic Technol., 23 , 11311149.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tournadre, J., , and Morland J. C. , 1997: The effects of rain on TOPEX/Poseidon altimeter data. IEEE Trans. Geosci. Remote Sens., 35 , 11171135.

  • Varma, A. K., , and Liu G. , 2006: Small-scale horizontal rain-rate variability observed by satellite. Mon. Wea. Rev., 134 , 27222733.

  • Varma, A. K., , Gairola R. M. , , Pandey P. C. , , and Singh K. P. , 2001: Use of TOPEX altimeter for the study of diurnal and spatial distribution of southwest monsoon rainfall over the Bay of Bengal and the Arabian Sea. Remote Sens. Environ., 77 , 112121.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Varma, A. K., , Liu G. , , and Noh Y-J. , 2004: Subpixel-scale variability of rainfall and its application to mitigate the beam-filling problem. J. Geophys. Res., 109 , D18210. doi:10.1029/2004JD004968.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wheater, H. S., and Coauthors, 2000: Spatial-temporal rainfall fields: Modelling and statistical aspects. Hydrol. Earth Syst. Sci., 4 , 581601.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zanife, O. Z., , Vincent P. , , Amarouche L. , , Dumont J. P. , , Thibaut P. , , and Labroue S. , 2003: Comparison of the Ku-band range noise level and the relative sea-state bias of the Jason-1, TOPEX, and Poseidon-1 radar altimeters. Mar. Geod., 26 , 201238.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zieger, A., , Hancock D. , , Hayne G. , , and Purdy C. , 1991: NASA radar altimeter for the TOPEX/Poseidon project. Proc. IEEE, 79 , 810826.

Fig. 1.
Fig. 1.

(a) TOPEX and Jason Ku- and C-band σ0 relations [for a better reading, the difference f (σ0C) − σ0C is plotted] and (b) std for cycle 2–23. The Jason σ0 values have been corrected for the mean biases for a better comparison of the relations.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 2.
Fig. 2.

Distribution of (a) attenuation, (b) FL, (c) rain event length, and (d) rain rate for TOPEX (solid lines) and Jason (dashed lines) rainy samples.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 3.
Fig. 3.

Distribution of δxσ0 at Ku and C bands and of δxΔf(σ0) for (a) TOPEX and (b) Jason nonrainy samples.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 4.
Fig. 4.

(a) Distribution of δxΔf(σ0) = δxAm for TOPEX and Jason rainy samples. (b) Variation of the δxΔf(σ0) std for TOPEX and Jason rainy and nonrainy samples as a function of C-band σ0. (c) Distribution of δxR for TOPEX and Jason and (d) variation of the δxR std as a function of C-band σ0.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 5.
Fig. 5.

Std of δxR for TOPEX as a function of (a) rain rate and C-band surface backscatter, (b) rain event length, and (c) FL.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 6.
Fig. 6.

Geographical distribution of TOPEX std (δxR) for (a) light rain (R < 2.5 mm h−1), (b) moderate rain (2.5 < R < 5 mm h−1), and (c) heavy rain (R > 5 mm h−1). Only the grid cells where there are enough data to ensure a 90% confidence level are shown.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 7.
Fig. 7.

Mean measured SST (°C) field for the TM period data from the National Oceanic and Atmospheric Administration Climate Prediction Center (available online at http://www.cpc.noaa.gov/products/).

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 8.
Fig. 8.

(a) Distribution of δtσ0 at Ku and C bands and of δtΔf(σ0) for nonrainy samples. (b) Variation of the std of δtσ0 at Ku and C bands and of δtΔf(σ0) as a function of C-band σ0.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 9.
Fig. 9.

(a) Distribution of δtΔf(σ0) for TOPEX or Jason rain samples (solid line) and TOPEX and Jason rainy samples (dashed line). (b) Variation of the std of δtΔf (σ0) as a function of C band σ0. (c) Distribution of δtR and (d) variation of the std of δtR as a function of C-band σ0.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 10.
Fig. 10.

Variation of the δtR std as a function of (a) rain rate and C-band surface backscatter for TOPEX or Jason rainy samples and (b) rain events length and (c) FL.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 11.
Fig. 11.

Geographical distribution of TOPEX std (δtR) for (a) light rain (R < 2.5 mm h−1), (b) moderate rain (2.5 < R < 5 mm h−1), and (c) heavy rain (R > 5 mm h−1).

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 12.
Fig. 12.

Conditional probability (a) of |δtR| over |δxR| and (b) of |δtAm| over |δxAm|.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 13.
Fig. 13.

Mean value of the ratio δtR/δxR as a function of (a) rain rate and C-band surface backscatter, (b) rain event length, and (c) FL. The dashed lines indicate the demarcation between the convective and stratiform classes.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Fig. 14.
Fig. 14.

Geographical distribution of the ratio between δtR and δxR for (a) stratiform rain and (b) convective rain. (c) Convective rain fraction.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHO605.1

Table 1.

Number of collocated TOPEX/Jason samples for the following criteria: TOPEX or Jason rain/no rain (R/no R), TOPEX or Jason convergent FL/divergent FL (FL/no FL).

Table 1.
Table 2.

Std of the spatial and temporal variability of surface backscatter, attenuation, and rain rate.

Table 2.
Save