## 1. Introduction

[2] The Tropical Rainfall Measuring Mission (TRMM) satellite is now operating in non-Sun synchronous orbit enabling its onboard instruments to capture tropical and part of subtropical rainfall distributions. The advantageous position of the TRMM satellite and its sophisticated instruments, like precipitation radar (PR), enable the mission to successfully monitor rainfall distributions/structures in the tropical regions. The TRMM data satisfied its objectives to capture tropical surface rainfall distribution [*Kummerow et al.*, 2000].

[3] However, in addition to the restrictions on the observations of precipitation or other phenomena due to midlatitude or high-latitude disturbances, the TRMM’s observation is limited by its lifetime. A TRMM follow-on mission is now under discussions in order to give continuity to TRMM’s observation with larger coverage. The objectives of the future mission are not only to extend/expand its observations but also to enhance TRMM’s capability by improving its inherent limitations in the accuracy of the measurements. The future mission is expected, for example, to provide additional microphysical information by discriminating storm into regions of solid, liquid and/or mixed hydrometeors [*Meneghini et al.*, 1998; *Nakamura et al.*, 1998]. For these purposes, a dual-wavelength radar is preferable. The dual-wavelength radar data will allow the use of algorithms that are less sensitive to fluctuations in the drop size distribution (DSD) and independent of the absolute calibration of the radars [*Atlas and Ulbrich*, 1977; *Meneghini et al.*, 1998]. Among those algorithms, a conventional dual-wavelength radar technique (DWRT) is a simple one. The conventional DWRT is expected to improve rainrate retrieval accuracy by providing independent rainrate estimation from rain attenuation and/or to give better rain attenuation correction [*Fujita*, 1983; *Meneghini and Kozu*, 1990].

[4] Nevertheless, satellite-based precipitation products are subjected to biases and stochastic errors [*Barrett et al.*, 1994; *Rudolf et al.*, 1996]. The biases and random errors are due to the sampling frequency, the extension of the sizes of rain cells, the diurnal cycle of rainfall and the uncertainties in the rainrate retrieval algorithms [*Kousky*, 1980; *Bell et al.*, 1990; *Nakamura*, 1991; *Kummerow*, 1998; *Anagnostou et al.*, 1999]. The errors could be either systematic (namely, bias) or nonsystematic (i.e., random error).

[5] Among a variety of uncertainties and error sources, effect of natural variation of DSD is one of the primary, hence a key sources of errors in radar retrievals. The effect of the vertical structure of the storm is another consideration. The variations in the radar measurable are due to, for instance, variations in raindrop temperature, statistical fluctuation in the radar signal and contamination of fluctuating noise also cause variations in the radar retrievals [*Marshall and Hitschfeld*, 1953; *Wexler and Atlas*, 1963; *Srivastava and Carbone*, 1971; *Jameson and Kostinski*, 1996]. In addition to these uncertainties, nonuniformity of rain (NUR) within the field-of-view (FOV) of the sensor introduces biases/errors in the rainrate retrievals [*Short and North*, 1990; *Chiu et al.*, 1990; *Nakamura*, 1991; *Graves*, 1993; *Amayenc et al.*, 1993; *Ha and North*, 1995; *Durden et al.*, 1998; *Chang and Chiu*, 1999; *Kozu and Iguchi*, 1999]. Apparent mismatching in the FOVs of the radars, in the case of multiparameter (namely, dual-wavelength) radar observation, could emanate bias/errors [*Rinehart and Tuttle*, 1982; *Amayenc et al.*, 1993].

[6] Each rainrate retrieval algorithm has its own response to different error sources. The estimation of rainrate from a radar based on a conventional, so-called radar reflectivity (*Z*)-rainrate (*R*) method, often plagued by large uncertainties. The conventional *Z-R* method, for example, has large error due to DSD variation [*Wexler and Atlas*, 1963; *Battan*, 1973]. Unlike this, rainrate retrieval from the microwave attenuation by the dual-wavelength radar [*Fujita*, 1983] assures better accuracy, since rain attenuation has good correlation with rainrate and less sensitive to DSD variation [*Eccles and Mueller*, 1991; *Atlas and Ulbrich*, 1977]. Analyses of the errors in the dual-wavelength radar algorithm (namely, DWRT), however, become complicate since the DWRT utilizes two radar signatures at two different frequencies and at two range gates. The naturally fluctuated DSDs and their scattering and attenuation effects as well as their distributions along and/or across the radar beam play a primary role to infer radar integral parameters within radar beam heights. Any fluctuation in the radar integrals and/or their measurement uncertainties finally couple errors in the radar retrievals.

[7] In this work, we attempt to examine relative sensitivities of DWRT to the variety of error sources, as described previously, based on simulations. Taking into account of the fact that the majority of radar algorithms to estimate rainrate are primarily influenced by the DSD variability, this study primarily focus to gauge relative sensitivities of the DWRT as well as the *Ze* (namely, at 13.6-GHz; hereafter, referred as *Ze*_{14})-*R* algorithm to the DSD variability and try to establish lower bounds of their accuracies. For a definite evaluation of error statistics in the radar retrievals due to natural fluctuations of the DSD combined with the radar beam height, however, a complete data set with measured vertical profiles of raindrop spectra is necessary. At present, we are limited with such data set. We, therefore, attempt to determine roughly the error statistics in the DWRT as well as *Ze*_{14}-*R* estimates based on simple simulation frameworks.

[8] Through the first fold of the simulation scheme, we attempt to generate and determine the significance of the vertical structure of rainstorm (VSR) in the DWRT upon statistically relating a disdrometer-measured DSD at the ground level with vertical profiles of radar reflectivity measured by TRMM PR. Section 2 outlines the TRMM PR measurements of the vertical profiles of radar reflectivity.

[9] Through another fold of the simulation, we made an attempt to evaluate the effect of natural variation of the DSD in the DWRT as well as *Ze*_{14}-*R* estimates based on a simple (namely, slant-path) structure of rain field upon utilizing the disdrometer-measured DSD data. The simulation is tried to make as simple as possible so that we can analyze DSD variability induced errors in the retrievals. The simulation utilizes a large set of disdrometer-measured (for ∼819 days) DSD data. Section 2 outlines the disdrometer measurement and outputs radar integral parameters from the measured DSD. This fold of simulation disregards any effects of the VSR. Also, any evolutions or breakups of the raindrops and/or other plausible error sources are disregarded in the simulation. By interpreting the DSD-derived radar integrals measured in time space into height space, we generate a slanted (which is assumed to be uniform within a specified FOV of the radars), rain field structure, which evolve with time (namely, 1-min averaging) series of the DSD measurement. The simulation also addresses the issues of the effects of the raindrop temperatures as well as statistical fluctuations in the radar signals and noises. Also, an approach to evaluate the effect of the Mie scattering is considered in this simulation study.

[10] Lastly, we addressed the effect of the nonuniformity of rain in DWRT estimates upon simulating horizontally nonuniform rain fields within the radar FOVs by envisioning a running linear average of the measured radar reflectivity factors generated by a slanted uniform rain field structure scheme. The effect of the mismatched FOVs of the two radars in the horizontal plane is also analyzed upon generating mismatched FOVs by shifting one of the radar’s horizontal FOV-structures in time series.

[11] Section 3 explains the simulation methods. Taking into account of the objectives and the allocated frequencies of TRMM follow-on mission’s radar, a dual-wavelength radar observation operating at the frequencies of 13.6 and 35 GHz in a downward looking geometry is considered in the simulations. Results of the simulations are presented and analyzed in section 4. Finally, section 5 summarizes and discusses the results.