Introduction
The Tropical Rainfall Measuring Mission (TRMM) satellite has two microwave sensors for quantitative rainfall measurement: the precipitation radar (PR) and the TRMM Microwave Imager (TMI) (Kummerow et al. 1998). The PR has the advantage of being able to observe the vertical precipitation profile directly, and the same rain-rate retrieval algorithm can be applied over both ocean and land with almost equal accuracy. In contrast, the brightness temperature observed by the TMI does not have vertical resolution. Therefore, without a priori information about the vertical structure of precipitation, the rain rate cannot be retrieved. The microwave imager uses different retrieval algorithms over ocean and land areas because of the difference in background surface emissivity, and its observations are generally less accurate over land than over ocean. The difference in the global mean rain rate calculated using the standard algorithms for PR and TMI has been reduced from 40% to 24% after the revision of both algorithms from version 4 to version 5 (Kummerow et al. 2000), but there are still significant discrepancies in some areas or seasons (Masunaga et al. 2002).
The Global Precipitation Measurement (GPM) project, the successor to the TRMM project, will consist of a primary satellite, with a dual-frequency precipitation radar (DPR) and a microwave imager, and several constellation satellites, with microwave imagers. The DPR is expected to provide higher sensitivity and more accurate estimates than PR. It will operate at a lower sampling frequency than PR, however. Several microwave imagers are needed to increase the sampling frequency to 3-hourly on average, which is a requirement of the GPM project. Therefore, to make the best use of the GPM sensors, it is essential to improve the rainfall retrieval accuracy of the microwave imagers. This need is particularly important over land where the retrieval accuracy is currently unsatisfactory, especially given the widespread demand from various user communities for the application of rainfall observation data for flood warnings and water management systems.
The main reasons for the microwave imager’s use of different retrieval algorithms over land and ocean areas and for the differences in accuracy for these areas relate to differences in the emissivity of the background surfaces. When using a lower frequency (from 6 to 37 GHz), emission from raindrops can easily be identified over ocean areas because the surface emissivity is low. The emission algorithm uses this principle to retrieve rain rates (e.g., Wilheit et al. 1977, 1991). The algorithm is useful for estimating the rain rate below the freezing level because it takes into account the strong physical relationship between brightness temperature at low frequencies and liquid rainfall. Over land, however, the emission algorithm is useless because emission from raindrops is largely hidden by the warm land surface. Hence, a scattering algorithm, using a higher frequency (around 85 GHz), is used for rainfall retrieval over land (e.g., Spencer et al. 1983, 1989). This algorithm is based on the fact that solid precipitation above the freezing level scatters microwave radiation at a higher frequency, with a consequent decrease in the observed brightness temperature (Fig. 1). Because the relationship between the liquid rain intensity at the surface and the observed brightness temperature at higher frequencies is indirect, rain-rate estimates by a scattering algorithm should be carefully examined. Proper assumptions of the drop size distribution of solid precipitation (Bennartz and Petty 2001) and a vertical profile of the precipitation system are needed to improve the accuracy of this algorithm. A quantitative explanation for the above, based on the microwave radiative transfer model (RTM) developed by Liu (1998), is included in the appendix.
Although a scattering algorithm can be applied over both ocean and land areas, its application over land faces another difficulty. Emissions from land surfaces (brightness temperature at the surface) are determined mainly by the physical temperature, vegetation, and soil moisture of the land surface, and emissions vary significantly with time and location. Therefore, variations in the observed brightness temperature caused by land surface conditions must be distinguished from variations caused by precipitation. Land surfaces covered by desert sand or fallen snow produce lower brightness temperatures because sand and snow particles on the ground scatter microwave radiation at a higher frequency. If this phenomenon is not distinguished from scattering by solid precipitation, it leads to false estimates of rainfall over desert and snow-covered areas. Thus, Grody (1991) proposed a method to separate desert sand and fallen snow from precipitation utilizing brightness temperatures observed at a lower frequency by the Special Sensor Microwave Imager (SSM/I) of the Defense Meteorological Satellite Program. This idea was adopted in rain/no-rain classification (RNC) methods to preprocess rainfall retrieval algorithms, such as the Goddard scattering algorithm (GSCAT) (Adler et al. 1994), Ferraro et al. (1994), Ferraro (1997), Kummerow and Giglio (1994), and the Goddard profiling algorithm (GPROF) (Kummerow et al. 1996, 2001), with some modifications.
In this study, we propose new RNC methods that take into account multiscale spatial and temporal variations in land surface brightness temperatures. It is difficult to calculate these brightness temperatures for different types of land surfaces using a radiative transfer model. We therefore summarize TMI data observed under no-rain conditions to produce a statistical database of land surface brightness temperatures. In this paper, we propose new RNC methods based on this database.
Data
TRMM was launched in November of 1997; its orbital altitude was changed from 350 to 402.5 km in August of 2001, and the performance of TRMM has been good up to the present (January of 2005). TRMM has a non-sun-synchronous orbit with an inclination angle of 35° for observation of tropical rainfall with its diurnal variation (Kummerow et al. 1998). The PR is a single-frequency radar of 13.8 GHz, which scans in the cross-track direction. The swath width of the PR is 220 km covered by 49 pixels of approximately 4.3 km × 4.3 km in size (at the nadir, before the change in orbital altitude). The maximum off-nadir angle is 17°. The PR observes echoes from the surface to a height of at least 15 km with a vertical resolution of 250 m.
TMI applies conical scanning with an incident angle of 52.8°. TMI has nine channels for observing brightness temperatures. The frequencies are 10.65, 19.35, 21.3, 37.0, and 85.5 GHz with both horizontal and vertical polarizations except at 21.3 GHz (vertical polarization only). TMI is basically similar to SSM/I; TMI also operates at 10.65 GHz, however, and the frequency of the water vapor channel is slightly different (22.235 GHz for SSM/I). The horizontal resolution [the resolution is defined by means of the effective field of view (EFOV)] is better at a higher frequency than at a lower frequency—63.2 km (cross scan) × 36.8 km (along scan) at 10.65 GHz and 7.2 km (cross scan) × 4.6 km (along scan) at 85.5 GHz (before the change in orbital altitude). The number of samples is 208 per scan at 85.5 GHz; it is 104 per scan at the lower frequencies. The swath width is 760 km. The swath of PR (220 km) is completely covered by that of TMI. Therefore, in this paper, the analyses that need both PR and TMI are done for PR’s swath.
The standard products of PR and TMI are published by the National Aeronautics and Space Administration and Japan Aerospace Exploration Agency. Level-1 and level-2 standard products (version 5) are used in this study. The period of analysis is from 1998 to 2000, before the change in orbital altitude. Data given by PR products, including surface-type flags (land/ocean/coast) from the standard product 2A21 (Meneghini et al. 2000); rain flags (rain certain/rain possible/no rain), rain type (convective/stratiform), and storm height from the standard product 2A23 (Awaka et al. 1998); and the near-surface rain rate from the standard product 2A25 (Iguchi et al. 2000), were used in this study. Data given by TMI, including brightness temperature from the standard product 1B11 and surface and rain flags from the standard product 2A12 (Kummerow et al. 2001), were also used.
Rain/no-rain classification method
In general precipitation retrieval algorithms, the RNC is applied after quality checks and land/ocean classification and before the actual retrieval. RNC assigns a deterministic flag for rain or no rain to observations; then, only observations with a rain flag are processed in the retrieval algorithm. This deterministic method is used to reduce the computational burden.
Review of previous RNC methods
A number of methods for RNC over land have been used in previous retrieval algorithms. The RNC developed by Grody (1991) and classifications methods used in subsequent studies (shown in Table 1) basically had a common structure. Here, we briefly introduce their ideas. More extensive review of RNC methods can be found in Ferraro et al. (1998).
First, the existence of scattering was assessed, and then screens to remove desert and snow-covered areas were applied (Fig. 2). In the first step, Grody (1991) focused on the 85.5-GHz channel with vertical polarization (denoted as 85 V). The observed brightness temperature of 85 V [denoted as TB (85 V)] is compared with the estimated TB (85 V) without the scattering effects of precipitation [hereinafter, TBe (85 V)]; the difference is calculated as SI = TBe (85 V) − TB (85 V), where SI is the scattering index. To estimate TBe (85 V), Grody (1991) developed a global equation, such as TBe (85 V) = A + B × TB (19 V) + C × TB (22 V) + D × [TB (22 V)]2, from regression analysis of SSM/I data, where A, B, C, and D are constants independent of time and area (see Table 1). When SI is larger than 10 K, the observation is classified as “scattering.” Otherwise, it is classified as “no scattering.” GSCAT2 (Adler et al., 1994) and Kummerow and Giglio (1994) used 85 H instead of 85 V. GSCAT2 always uses constant value (251K) for TBe (85H) without using regression equations such as Grody (1991). Ferraro (1997) used 37 V as well as 85 V because SSM/I’s 85-V channel was unstable in the early stages. The minimum rain rate detectable by an algorithm using 37 V is much larger than that of an algorithm using 85 V, because scattering at 37 V is weaker than at 85 V. As shown in the appendix, TB (19 V) and TB (22 V) over land are less sensitive to precipitation than TB (85 V) and more accurately reflect the land surface background. Because the estimated TBe (85 V) does not decrease for desert and snow-covered areas, these areas are mostly judged as precipitation at this step.
In the second step, desert and snow-covered regions are removed from the scattering data by the use of lower-frequency observations. To detect desert regions, polarization differences in the brightness temperature at 19 GHz, TB (19 P) = TB (19 V) − TB (19 H), are utilized (P indicates polarization). The principle of the detection is that TB (19 P) for desert is large because there is less volume scattering by vegetation. In Grody’s method, if TB (19 P) is larger than 20 K, the data are judged as “scattering by desert,” which means no rain. The threshold of TB (19 P) is low, when TB (85 H) is high, to detect relatively weak scattering by sand particles in semiarid areas. For example, Ferraro et al. (1994) decreased the threshold to be 7 K when TB (85 V) is larger than 253 K.
In contrast, 22 V is used to detect fallen snow. On the principle that physical temperatures and brightness temperatures are low when the land surface is covered by snow, data with a low TB (22 V) are judged as “scattering by fallen snow,” which means no rain. In Grody (1991), the criterion for detecting fallen snow is that TB (22 V) < 257 K and TB (22 V) < 158 K + 0.49 × TB (85 V). The second inequality is necessary to incorporate the fact that heavy rainfall decreases TB (22 V) as well as TB (85 V). This fact is illustrated in the appendix where a decrease in TB (22 GHz) (e = 0.9) with heavy rainfall (more than 10 mm h−1) and solid precipitation can be seen. This method can detect dry snow but is not good at discriminating between wet snow and precipitation. Therefore, Adler et al. (1994) implemented a spatial nonuniformity check to discriminate between wet snow and precipitation using horizontal information provided by TB (85 H) when TB (22 V) is in the medium range between significantly low (dry snow) and high (precipitation). When the standard deviation of TB (85 H) is large, the data are judged as “scattering by precipitation.”
RNC method of GPROF
RNC method of GPROF is fundamentally the same as the above-mentioned idea. GPROF mainly uses TB (85 V) and assumes that TBe (85 V) is equal to simultaneously observed TB (22 V). Therefore, SI is calculated by TB (22 V) − TB (85 V). When SI is smaller than 8 K, the pixel is judged as no rain.
The pixels with SI larger than 8 K are tested with desert and snow screens. The desert screen includes the semiarid area screen similar to Ferraro et al. (1994); then, the threshold of TB (19 P) is set lower when TB (85 H) is high. The snow screen incorporates the idea of Adler et al. (1994) to remove ambiguity between “snow” and “precipitation.” However, even after the spatial nonuniformity check, some pixels have “ambiguous” flag. To reduce the ambiguity as much as possible, the adjacent pixels with certain RNC flags are referred. The details of the recent GPROF algorithm can be found in McCollum and Ferraro (2003), as well as Kummerow et al. (2001).
RNC methods proposed by this study
Our proposed RNC methods also calculate SI = TBe (85 V) − TB (85 V). Whereas Grody and GRPOF estimate TBe (85 V) using observed brightness temperature at lower frequencies, we use a statistical database to determine TBe (85 V) (Fig. 2). As explained in more detail in the next section, brightness temperatures observed under no-rainfall conditions over land were statistically summarized in a database, which we call the “land surface brightness temperature database.” Spatial and temporal variations in brightness temperature, including the effects of sand and fallen snow, are contained by this database. Our proposed methods do not require screening for desert and snow cover, and thus they require only one step for rain or no-rain classification using SI.
Other RNC methods using land surface brightness temperature database
Conner and Petty (1998) and Bauer et al. (2002) used a statistically estimated brightness temperature database under no-rain conditions in their RNC and rain-rate retrieval algorithm. In their study, the statistical database is responsible for the changes of land surface brightness temperature on a large scale caused by soil type and vegetation cover. The changes on a short time scale caused by soil moisture and snow cover are to be removed in terms of principal component analysis. Conner and Petty (1998) tested their method over the United States and compared the results with other RNC methods (introduced in section 3a). The superiority of their new method over previous methods was not clearly shown. Bauer et al. (2002) improved this method to be successful to show that their method is superior to traditional methods in some regions such as India and Africa.
The large difference between these two studies and our study is the way to estimate land surface brightness temperature. Bauer et al. (2002) follow the RNC method of Grody (1991) to find the observations under no-rain conditions. In this point, their method is not completely independent from previous traditional methods. In our study, the simultaneous observations of PR and TMI are used to prepare the land surface brightness temperature database, as will be shown in the next section.
Land surface brightness temperature database
We focused on quasi-simultaneous observations by PR and TMI to select brightness temperature data under no-precipitation conditions. As shown in Fig. 3, PR observations—the center of which are in a TMI footprint in the case of 85 GHz—are used as references for TMI observations. Here, the TMI footprint is defined by means of EFOV as shown in section 2. We should pay attention to Bauer et al. (2002), which considered parallax effects between TMI and PR and the antenna pattern of TMI in their matchup technique. Because TMI observes with a larger incident angle and PR observes with near-nadir view, corresponding PR pixels with a TMI slant observation are different by the altitude. The TMI footprint may be shifted toward the subsatellite point to consider the signal from higher altitude. The parallax correction is not involved in this study, because it is difficult to calculate accurately the altitude from which the main signal comes. Another issue is that the signal also comes from outside of the EFOV. Bauer et al. (2002) enlarged the footprint by a factor of 2.5 from EFOV. When the footprint size is larger, observations that have a very weak signal by precipitation have to be removed, and the number of available samples for the database is significantly reduced. Therefore, we defined the footprint by means of EFOV.
When all of the PR observations within a TMI footprint have a no-rain or rain-possible flag, the TMI observation is judged to be under a no-rain condition. The PR rain flag labeled as rain possible often results from noise, and the standard product 2A25 does not give any rainfall retrievals to rain-possible pixels. That is why we regard rain possible as being no rain in this paper. TMI brightness temperature data observed under no-rain conditions are summarized in the database with resolutions of 1 month and 1° latitude × 1° longitude. These resolutions were determined by considering the trade-off between sampling number and the scale on which the variations of land surface brightness temperature can be explained.
For example, the distributions of brightness temperature under no-rain (July 1998 and 1999), no-rain (July 2000), and rain (July 2000) conditions for a grid (30°–31°N, 110°–111°E) are shown in Fig. 4. Figure 4a shows the probability density function (PDF), and Fig. 4b shows the cumulative distribution function on a Gaussian scale. If the distribution is a normal distribution, it becomes a linear line in Fig. 4b. The two thin lines in Fig. 4b are Gaussian distributions that have the same averages and standard deviations as those of the actual distributions of brightness temperature under no rain. The distributions under no-rain conditions fit the Gaussian distributions well, although they are slightly distorted. This fact is clearly seen in Fig. 4b: the actual curves deviate from the fitted lines where the deviation is less than −2. Decreases in the brightness temperature that result from high-altitude ice clouds such as anvils, which cannot be detected by PR, may account for the lower temperatures. However, distributions under no rain can basically be represented as Gaussian distributions. From the discussion above, the average and standard deviation of TB (85 V) are calculated to represent the distribution, and they are stored in the database. In addition, the coefficients of the linear regression lines between TB (85 V) and brightness temperatures at lower frequencies are stored in the database.
Evaluation of rain/no-rain classification
Methods
RNC method adopted by GPROF and our proposed methods are compared in this section. The period of this evaluation was the entire year of 2000. The results of RNC by GPROF are available in the standard product 2A12. Below we explain the details of our proposed methods for producing RNC.
We propose two RNC methods (M1 and M2) for real-time use and two RNC methods (M1+ and M2+) for postprocessing. Here, M1 and M1+ refer to the average μ and standard deviation σ from the corresponding grid of the database. The TBe (85 V) is set at μ, and the threshold for SI is set at k0σ, where k0 is a constant in time and space. In an evaluation of 1 month in 2000, a database for the same month in 1998 and 1999 was used in M1, wheras a database for the same month in 2000 was used in M1+. Method M1+ cannot be applied in real-time use and is tried here to provide a comparison with M1. We can see the effect of interannual changes in the database by comparing the accuracy of RNC produced by M1 and M1+. Figure 4a shows the thresholds for TB between no rain and rain for M1 and M1+ (k0 = 2.8). Whereas Adler et al. (1994) uses a constant TB as a threshold, the thresholds for M1 and M1+ change with month and grid.
Evaluation
The evaluation of RNC is based on the assumption that RNC by PR is always perfect. This assumption is acceptable in evaluating RNC by TMI over land, because PR detects precipitation independent of land surface type with high accuracy. In the same way, to separate no-rain TMI observations to produce the database described in section 4, the RNC for the TMI footprint (85 GHz) is determined by PR. Here, the parallax and antenna pattern problems indicated in section 3 arise again. We tried to incorporate parallax effect and antenna pattern in the evaluation of the following analysis (shown in section 5c). Still, the results, especially the order of superiority among RNC methods, are not changed by the different matchup techniques. Therefore, we applied the simple matchup in this study.
Results
General comparison of methods
Evaluation indices for the total period and area are compared for M1, M2, M1+, M2+, and GPROF in Fig. 5. Both Figs. 5a and 5b show the RFAO along the abscissa, but Fig. 5a shows the RTDO and Fig. 5b shows the RTDA along the ordinate. Note that the direction of the abscissa in Fig. 5 is contrary to convention. The results for our methods for different k0 from 2.0 to 5.0 are shown. The symbols were drawn using a k0 step of 0.5, whereas the calculations were done and the curves were drawn using a k0 step of 0.1. The ideal results are maximum RTDO (RTDA) = 1 and minimum RFAO = 0. In general, these two purposes are not accomplished at once, because the distributions of TB under no-rain conditions and under rain conditions are overlapped (Fig. 4). When RTDO increases, RFAO decreases, and vice versa. In Fig. 5, if a symbol is located on the upper right (lower left) in relation to another symbol, the former is more (less) accurate than the latter. If a symbol is located on the upper left (lower right) in relation to another symbol, the ratio of rain to the total is higher for the former than for the latter, but it does not indicate which method is more accurate. For each of our methods, the symbol for a larger k0 is located on the lower right of the curve because of the lower ratio of rain to the total observations.
The RTDO, RTDA, and RFAO for GPROF are 59%, 80%, and 0.85%, respectively. To realize as small an RFAO as GPROF, k0 must be set to 2.8 and 3.5 for M1 and M2, respectively. The RTDO is 57% and 63% for M1 and M2, and the RTDA is 81% and 86% for M1 and M2, respectively, in this case. GPROF is superior to M1 in terms of the RTDO, but M1 is superior to GPROF in terms of the RTDA. There is little difference in the RTDO (RTDA) for M1 and M1+ for the same k0; however, M1+ produced a smaller RFAO than M1. This is explained in section 5c(3)i. Method M2 performed better than M1 and GPROF. These results are discussed in sections 5c(3)ii and 5c(3)iii.
RTDO for various types of precipitation
The changes in RTDO according to the characteristics of the precipitation—rain rate, convective/stratiform, and rain-top height—are explained here.
Rain rate
Figure 6 shows the relationship between the RTDO and rain rate for three methods: M1, M2, and GPROF. The global parameter k0 is set to 2.8 for M1 and 3.5 for M2, so that the RFAO for all three methods is almost the same. Figure 6a shows the RTDO for both rain types—convective and stratiform. The RTDO is around 40%, even for a light rain rate of 0.1–0.2 mm h−1. With a heavier rain rate, the RTDO is higher, reaching as high as 90% for rain rates of more than 10 mm h−1. This result is true for all three methods. The strong dependence of the RTDO on the rain rate is not directly explained by the RTM, as shown in the appendix; the brightness temperature calculated using the RTM is weakly dependent on the liquid rain rate. However, as shown in 5c(2)iii, it can be statistically explained in terms of rain-top height. There does not appear to be a large difference between the methods in Fig. 6a, but for a weaker rain rate, GPROF has a higher RTDO than M1, and for a stronger rain rate, GPROF has a lower RTDO than M1. The relatively poor performance of GPROF in detecting heavy rainfall is discussed in 5c(3)iii.
Convective/stratiform
Figure 6b shows the relationship between the RTDO and rain rate for stratiform rainfall, and Fig. 6c shows the same for convective rainfall. The convective/stratiform classification of TMI observations is based on PR observations within the TMI footprint. If the TMI footprint does not contain any convective precipitation according to PR, it is judged as stratiform. Otherwise, it is judged as convective. When Fig. 6b is compared with Fig. 6c, it can be seen that stratiform rainfall is easier to detect than convective rainfall for the same category of rain rate. The relatively poor ability to detect convective rainfall may be partly explained by the tilting of the convective system, because Hong et al. (2000) showed that the tilting of the convective system and the slant path observation of the radiometer make the horizontal displacement of the precipitation signal.
Rain-top height
Because the thickness and strength of the solid precipitation layers also affect the observed brightness temperature at higher frequencies (see the appendix), the relationship between storm height and RTDO is analyzed here. Storm height is an index of rain-top height and is given in the TRMM standard product 2A23. It is determined by the top of nonnoise echoes that continue for more than three range bins (approximately 750 m) in the vertical direction, and this index can be used to estimate the thickness of total precipitation layer. For a TMI footprint, the average storm height observed by PR rain pixels in the footprint is calculated. Figure 7 shows the RTDO for M2 along the ordinate and the storm height along the abscissa for different rain rates: 0.5–1.0, 1.0–2.0, 2.0–5.0, 5.0–10.0, and over 10.0 mm h−1. There is a good relationship between RTDO and storm height. When the storm height is less than 5 km, the RTDO is strongly dependent on storm height but is only weakly dependent on rain rate. When the storm height is over 5 km, however, the RTDO is dependent both on storm height and on the rain rate. Figure 7 also shows the PDF of storm height for each category of rain rate. This result indicates that precipitation with a higher storm height yields a heavier rain rate statistically. Therefore, a strong relationship between the rain rate and the RTDO is seen in Fig. 6, although the direct relationship between them is not very strong. Considering that the freezing level is at most 5 km even in tropical regions, there is a solid precipitation layer when the storm height is over 5 km. When there is a strong rain rate, there is possibly strong solid precipitation; then the rain rate affects RTDOs with a storm height of over 5 km, as shown in Fig. 7. In contrast, the solid precipitation layer is thin or nonexistent with a storm height of less than 5 km. The rain rate has little effect on the RTDO in that case. Results similar to those shown in Fig. 7 can be obtained for GPROF and M1 (figures not shown).
Comparison of methods
Comparison between M1 and M1+: Effects of interannual variation
Methods M1+ and M2+, which refer to a database for the present year, show better RNC accuracy than M1 and M2, which refer to a database for previous years. There is little difference in the RTDO (or RTDA) produced by M1 and M1+ for the same k0, but the RFAO for M1+ is much better than that of M1. If the distribution of no-rain brightness temperature obeys a normal distribution perfectly, the RFAO for M1+ can be theoretically calculated for a given k0. For example, the RFAO is approximately 0.26% for k0 = 2.8. Actual distributions are slightly distorted in comparison with a normal distribution, extending in the direction of lower brightness temperatures, as shown in section 4. Mainly because of this effect, the RFAO for M1+ is approximately 0.50% and is larger than the theoretical one. The RFAO for M1 is much larger than that of M1+ because of interannual variation in the distribution of no-rain brightness temperatures for present and past data. When the threshold of the TB for M1 is higher than that for M1+, the RFAO and RTDO for M1 are larger. In converse, a lower threshold for M1 results in a small RFAO and RTDO for M1 in comparison with M1+. Both cases can happen as a result of interannual variation, but the increase in the RFAO with a larger threshold is much greater than the decrease in the RFAO with a smaller threshold because the no-rain probability density function is an increasing function of the TB around the threshold. Unless the interannual variation has significant bias, the RFAO for the total evaluation is larger for M1 than for M1+. In contrast, the rain probability density function can be an increasing or decreasing function around the threshold. Therefore, the increase in the RTDO with a higher threshold and its decrease with a lower threshold are almost cancelled. As a consequence, the difference in the RTDO between M1 and M1+ is not large. As above, M1 is inferior to M1+ because of the interannual variations of land surface brightness temperatures.
Comparison between M1 and M2: Effects of diurnal variations in physical temperature
Below we explain why M2 is more accurate than M1. The difference is because of diurnal variations in the RTDA and RFAO (Fig. 8). For M2 and GPROF, the diurnal variations are relatively similar—the RTDA is low around midday and the RFAO is high around evening. For M1, both the RTDA and RFAO are much higher at night than in the daytime. In other words, at night, M1 judges a larger number of observations as having rain than M2 and GPROF. No-rain brightness temperatures are lower at night because of diurnal variations in the physical temperature of the land surface; thus, the constant threshold for the TB produces a higher RFAO at night. On the other hand, TB (85 V) observed under rain conditions is less affected by the physical temperature of the land surface according to the RTM simulation (see the appendix). However, if we assume a mosaic of no-rain and rain areas within a footprint, the dependence of TB (85 V) on the physical temperature under “(partially) rain” conditions can be explained. The large increase in the RTDA of M1 at night indicates that the rain brightness temperature falls at night. However, the negative effect of large RFAO is not compensated by the positive effect of large RTDA. These artificial diurnal variations in RTDA and RFAO disappeared in M2 by changing TBe (85 V) within a month. The difference between M1 and M2 can be explained as above.
Method M2 uses TB (22 V) to incorporate the effects of diurnal variations in physical temperature as does GPROF. If we use other low-frequency channels instead of 22 V, does the accuracy change? Similarly to Fig. 5b, Fig. 9 shows the RTDA and RFAO when 10 V, 19 V, and 37 V are used instead of 22 V in addition to the original M2. Using 19 V produces almost the same results as using 22 V, but using 10 V or 37 V is not as accurate as M2. The brightness temperature of every channel reflects changes in the surface physical temperature under no-rain conditions. As shown in the appendix, the sensitivity of TB (22 V) on the surface physical temperature is especially high because this channel locates around an absorption band of water vapor. This fact can be a reason why using 22 V is suitable to incorporate the changes in physical temperature. Using 10 V is less accurate because the largest footprint for 10 GHz receives more noise than the other channels from outside the test area (equal to the footprint for 85 V). Another reason is that land surface emissivities for 10 GHz vary considerably because of changes in soil moisture and vegetation. These effects distort the relationship between TB (10 V) and TB (85 V), resulting in a decrease in accuracy when using 10 V. Under heavy rainfall conditions, TB (37 V) decreases and becomes less sensitive to surface physical temperatures (see the appendix). Therefore, TBe (85 V) derived from TB (37 V) tends to be too small with heavy rainfall.
Comparison between M2 and GPROF: Detection of precipitation over desert and snow-covered areas
Here we explain why M2 is more accurate than GPROF. Whereas M2 determines TBe as a + b × TB (22 V)obs with different a and b for grids and months, GPROF determines TBe as TB (22 V)obs (a = 0, b = 1) globally. Figure 10 shows the distribution of a, b, and the correlation coefficients between TB (85 V) and TB (22 V) for January and July. The correlation coefficients are as high as 0.9 except for tropical rainforests. In tropical rainforests, physical temperatures do not show large diurnal variations, and the effects of noise caused by atmospheric water vapor and vegetation water changes are more apparent. A negative intercept a is seen for deserts such as the Sahara and for mountainous areas in winter, such as the Andes and Tibet, which probably are covered by snow. This suggests that decreases in TB (85 V) are caused by scattering at the ground.
The distribution maps of the RTDA and RFAO for GPROF and GPROF (without desert/snow screening) and M2 are shown in Fig. 11. Without the screening process, the RFAO for GPROF is high for desert and snow-covered regions and the RTDA is satisfactory for all areas. In contrast, the RFAO for M2 is low, even for desert and snow-covered regions. This result is because the database referred to by M2 has information on when and where scattering occurs as a result of desert and snow cover. To decrease the RFAO in desert and snow-covered areas, GPROF has to use a screening process. After screening is applied, the RFAO is almost zero for desert and snow-covered areas, but the screening process also decreases the RTDA severely in these areas. For example, the RTDA for GPROF is low for the Sahara Desert, inland areas of the Australian Continent, the Middle East, and the Tibetan Plateau in comparison with that of M2. The difference between GPROF and M2 in the accuracy of the RNC mainly comes from these regions. Detailed analyses are shown below for two regions: the Sahara (15°–30°N, 0°–20°E), as an example of a desert area, and the Tibetan Plateau (30°–35°N, 85°–90°E), as an example of a snow-covered area.
Figure 12 shows the relationship between the RTDO and rain rate for the Sahara. Method M2 (k0 = 3.5), GPROF (with screening), and GPROF (without screening) are compared in this figure. The RFAO is shown in the grayscale column on the left. Except for heavy stratiform rainfall, the RTDO for GPROF (with screening) is much lower than for M2. When we compare GPROF with and without screening, it is clear that the screening process significantly reduces not only the RFAO but also the RTDO except in the case of heavy stratiform rainfall.
The desert mask for GPROF judges a higher TB (19 P) as no rain. As shown in the appendix, however, the difference in brightness temperatures caused by different surface emissivities remains at a rain rate of up to 10 mm h−1. Therefore, GPROF has difficulty separating “desert” and “rainfall over desert.” However, TB (85 V) is reduced, even over a low-emissivity surface, by precipitation, and M2 can separate desert and rainfall over desert to some degree.
Figure 13 is the same figure as Fig. 12 but is for the Tibetan Plateau region. The RTDO for GPROF is almost zero at any strength for both convective and stratiform rainfall. Method M2 produces a relatively high RTDO for heavy rainfall of around 50% for a rain rate of 10 mm h−1. This RTDO is less than the global average, but it is much better than that of GPROF.
With a snow mask, GPROF judges lower TB (22 V) as no rain (snow covered). Because the emissivity of 22 V is high even over snow-covered areas, the rainfall over snow-covered areas decreases TB (22V) (see the appendix). Therefore, separating snow cover from rainfall over snow cover is almost impossible for GPROF, and it is more difficult to detect heavier rainfall than light rainfall. Method M2 should also work well over snow-covered regions. The RTDO is not as good as that of the global average, however. This result may be because the surface height is as high as 4 km and the rain layer is thin.
The important point is that M2 can detect rainfall over desert and snow-covered regions to some degree, whereas such rainfall is almost ignored by GPROF. This conservative approach leads to a relatively lower RTDO for GPROF for heavy rainfall, as shown in section 5c(2)i.
Summary
Previous RNC methods over land after Grody (1991) first check the existence of scattering by comparing the observed TB at high frequencies with the background brightness temperature TBe estimated from observed brightness temperatures at lower frequencies to classify the data into “scattering” and “no scattering.” They then screen out desert and snow-covered regions from the scattering data. In contrast, our proposed methods utilize a database of brightness temperatures under no-rain conditions to estimate TBe and do not require any screening.
Method M1 uses the average of TB (85 V) for the corresponding grid and month as TBe (85 V). This simple method shows RNC accuracy comparable to GPROF, but it has the disadvantage that the RFAO is high at night. Method M2 improves on M1 by considering diurnal variations in land surface physical temperatures. Method M2 estimates TBe (85 V) by substituting observed TB (22 V) into the prepared regression lines between TB (85 V) and TB (22 V) under no-rain conditions. Our results indicate that M2 is more robust than GPROF because M2 can detect rain over desert and snow regions that is almost totally screened out in GPROF.
To produce a consistent database under no-rain conditions, spaceborne precipitation radar is essential. Without TRMM-like satellites, such a database cannot be produced globally. Data from a 2-yr period were used to produce the database in this study, but this period is not long enough to remove sampling bias. If we used data from a longer period for the construction of the database, the accuracy of the database could be further improved. An expanded database would also partly compensate for differences between M1 and M1+ (M2 and M2+). For GPM observations, a database could be produced using TRMM observations over 6 yr.
Some problems remain to be resolved. The GPM target area would be up to 70°N/S. A database built on TRMM observations could not be applied to areas outside the TRMM coverage area (within 35°N/S). The GPM microwave imagers would have a slightly different frequency than TMI [e.g., 85.5 GHz for TMI, but 89.0 GHz for Advanced Microwave Scanning Radiometer (AMSR)-E], and the database would need to be adjusted for each sensor. To overcome these problems, we need to develop a radiative transfer model of land surfaces.
It is not discussed in this paper how the global parameter k0 should be set. To find the optimum k0, it is necessary to evaluate missed rain amount and false rain amount quantitatively. The false rain amount is dependent on retrieval algorithm, which is not specified in this study. Therefore, quantitative discussion on the optimum k0 cannot be done in this study. Instead, the following can be said at the stage of this paper. The setting of k0 is dependent on user requirements to a certain degree. If k0 is set smaller, missed rain amount is smaller and false rain amount is larger. If the produced rain map is used for flood warning, k0 should be set smaller for safety reasons. On the other hand, k0 should be set larger if the rain-rate product is used for drought warning. In this sense, indetermination of k0 can be an advantage in our proposed method.
The study shows the potential of using statistical information on brightness temperature to realize more accurate RNC methods. If we can overcome the problems noted above, the proposed methods can be recommended for use in algorithms for the GPM.
Acknowledgments
This study is part of a larger study, “Production of a high-precision, high-resolution global precipitation map using satellite data (GSMaP),” led by Prof. Ken’ichi Okamoto (Osaka Prefecture University, Japan) under the program Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Agency (JST). We appreciate JST’s subsidy of this study. The authors are grateful for the many helpful comments and assistance provided by members of GSMaP. The source code for GPROF was made available by Dr. Christian Kummerow (Colorado State University), and the microwave radiative transfer code was provided by Dr. Guosheng Liu (The Florida State University) through Dr. Kazumasa Aonashi (Meteorological Research Institute, Japan). Their kindness is greatly appreciated.
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APPENDIX
Calculation Using a Microwave Radiative Transfer Model
To support the main discussion, here we discuss the sensitivity of brightness temperature to precipitation and surface parameters in relation to a microwave radiative transfer model developed by Liu (1998) (Liu-RTM).
Settings
Liu-RTM applies a discrete ordinate method (DOM) to solve microwave radiation transfer for the plane-parallel atmosphere. All of the precipitation and cloud particles are assumed to be spherical. Hence, differences in scattering and emission with polarization are not expressed. The details are published elsewhere (Liu 1998).
For the following calculations, the DOM stream number is set at 4. The atmosphere has 24 layers, each 500 m thick. The lapse rate of air temperature is 6.5 K km−1, and the surface temperature is equivalent to the air temperature at the bottom of the atmosphere. The type of precipitation is rainfall below the freezing level and snowfall (particle density, 0.04 g cm−3) above the freezing level. For the drop size distribution, Marshall–Palmer for rain and Sekhon–Srivastava for snow is assumed. For simplification, clouds are not considered. The incident angle is 52.8°, assuming the use of TMI.
Rainfall effects
The first simulation is done only with the rainfall layer. The freezing level is set at 4 km. The rain rate in the rainfall layer is assumed to be vertically constant. The relative humidity of the rainfall layer is set at 100%. The relationship between the rain rate and calculated brightness temperatures for the above conditions is presented in Figs. A1a–c. The frequencies are 19.3, 21.3, and 85.5 GHz for Figs. A1a, A1b and A1c, respectively. The surface emissivity is 0.3, 0.5, 0.7, 0.9, and 0.99 for each line. In Figs. A1a and A1b (the lower-frequency case), the brightness temperature increases with an increase in the rainfall rate up to 10 mm h−1 if the surface emissivity is 0.5, as a typical case for over ocean. The brightness temperature is less sensitive to an increase in rainfall if the surface emissivity is 0.9, as a typical case for over land. In this case, the brightness temperature starts to decrease when the rainfall rate exceeds 5 mm h−1. With a rainfall rate of over 10 mm h−1, differences in surface emissivity do not affect brightness temperatures, and the temperatures decrease with further increases in the rainfall rate. In Fig. A1c (the higher-frequency case), the brightness temperature is not affected by the surface emissivity of over 1 mm h−1 for the rain rate, and the brightness temperature decreases with an increase in the rain rate.
Snowfall effects
The second simulation considers both rainfall and snowfall layers. The rainfall layer is 4 km deep, the rain rate is 10 mm h−1, and the relative humidity is 100%. The surface emissivity is 0.9. The bottom of the snowfall layer is 4 km above the surface. The rain-top height (two layers deep) is 6, 8, 10, and 12 km. The relationship between the snowfall rate and brightness temperatures under the above conditions is presented in Figs. A1d–f. The frequencies are 19.3, 21.3, and 85.5 GHz for Figs. A1d, A1e and A1f, respectively. The lines and symbols indicate different rain-top heights. The brightness temperature decreases with an increase in the snowfall rate and with an increase in the rain-top height at each frequency. There is high sensitivity at 85.5 GHz, because higher-frequency observation is sensitive to smaller-sized ice. When combined with the results of the previous section, it can be seen that rainfall has a stronger effect at low frequencies and over ocean areas but snowfall has a stronger effect at high frequencies and over land areas.
Effects of surface physical temperatures
The purpose of the final simulation is to assess the effects of surface physical temperatures on observed brightness temperatures for both clear and rain conditions. The freezing level varies from 0 to 5 km. The surface physical temperature is set to be equivalent to the air temperature at the surface and varies from 273.15 to 305.65 K. Surface emissivity is set at 0.9 for all frequencies. Figure A2 shows the relationship between surface physical temperatures and observed brightness temperatures. Figure A2a assumes a no-rain case, but the relative humidity is set at 100% both below and above the freezing level. Of the frequencies used by TMI, the sensitivity to surface physical temperature is highest for 85.5 GHz; 21.3 GHz shows higher sensitivity than 19.3 and 37.0 GHz, and 10.7 GHz shows the lowest sensitivity. The thick solid line indicates the brightness temperature without any atmospheric effects (=0.9 times the surface physical temperature). The difference between each simulated line and the solid line indicates the effects of water vapor. Because 21.3 GHz is located on one of the water vapor absorption lines, the observed brightness temperature at this frequency is high in comparison with that for lower frequencies. Figure A2b assumes a rain case with a rainfall layer (5 mm h−1 below the freezing level). At 85.5 and 37.0 GHz, the brightness temperature reflects the surface physical temperature only slightly. At frequencies below 21.3 GHz, the brightness temperature reflects the physical temperature almost as strongly as for the no-rain case.
Schematic for microwave radiative transfer at 85.5 GHz over land.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Schematic for microwave radiative transfer at 85.5 GHz over land.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Schematic for microwave radiative transfer at 85.5 GHz over land.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Schematic of RNC methods in GPROF and methods proposed in this study.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Schematic of RNC methods in GPROF and methods proposed in this study.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Schematic of RNC methods in GPROF and methods proposed in this study.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Collocation between PR and TMI. An ellipse shown by thick solid curve indicates EFOV at 85 GHz, which is regarded as a TMI footprint. Dark gray pixels provide references for TMI observations. Considering the parallax effects between TMI and PR, light gray pixels may produce references. Considering the antenna pattern, surrounding PR pixels may produce references.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Collocation between PR and TMI. An ellipse shown by thick solid curve indicates EFOV at 85 GHz, which is regarded as a TMI footprint. Dark gray pixels provide references for TMI observations. Considering the parallax effects between TMI and PR, light gray pixels may produce references. Considering the antenna pattern, surrounding PR pixels may produce references.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Collocation between PR and TMI. An ellipse shown by thick solid curve indicates EFOV at 85 GHz, which is regarded as a TMI footprint. Dark gray pixels provide references for TMI observations. Considering the parallax effects between TMI and PR, light gray pixels may produce references. Considering the antenna pattern, surrounding PR pixels may produce references.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Distributions of TB (85 V) under no-rain conditions (Jul 2000), under no-rain conditions (Jul 1998 and 1999) and under rain conditions (Jul 2000) for a grid (30°–31°N, 110°–111°E) as an example. (a) Ordinate indicates probabilistic density function. Thresholds of TB between rain and no rain for M1 and M1+ are shown. (b) Ordinate indicates cumulative distribution function, but expressed as Gaussian distribution scale.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Distributions of TB (85 V) under no-rain conditions (Jul 2000), under no-rain conditions (Jul 1998 and 1999) and under rain conditions (Jul 2000) for a grid (30°–31°N, 110°–111°E) as an example. (a) Ordinate indicates probabilistic density function. Thresholds of TB between rain and no rain for M1 and M1+ are shown. (b) Ordinate indicates cumulative distribution function, but expressed as Gaussian distribution scale.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Distributions of TB (85 V) under no-rain conditions (Jul 2000), under no-rain conditions (Jul 1998 and 1999) and under rain conditions (Jul 2000) for a grid (30°–31°N, 110°–111°E) as an example. (a) Ordinate indicates probabilistic density function. Thresholds of TB between rain and no rain for M1 and M1+ are shown. (b) Ordinate indicates cumulative distribution function, but expressed as Gaussian distribution scale.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Evaluations of RNC methods (M1, M1+, M2, M2+, and GPROF) for the total test. The abscissa is RFAO. The ordinate is (a) RTDO and (b) RTDA.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Evaluations of RNC methods (M1, M1+, M2, M2+, and GPROF) for the total test. The abscissa is RFAO. The ordinate is (a) RTDO and (b) RTDA.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Evaluations of RNC methods (M1, M1+, M2, M2+, and GPROF) for the total test. The abscissa is RFAO. The ordinate is (a) RTDO and (b) RTDA.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between near-surface rain rate and RTDO for M1, M2, and GPROF for (a) both convective and stratiform, (b) stratiform, and (c) convective.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between near-surface rain rate and RTDO for M1, M2, and GPROF for (a) both convective and stratiform, (b) stratiform, and (c) convective.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between near-surface rain rate and RTDO for M1, M2, and GPROF for (a) both convective and stratiform, (b) stratiform, and (c) convective.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between storm height and (solid lines) RTDO for M2 and (dotted lines) histogram of storm height for different categories of near-surface rain rate.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between storm height and (solid lines) RTDO for M2 and (dotted lines) histogram of storm height for different categories of near-surface rain rate.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between storm height and (solid lines) RTDO for M2 and (dotted lines) histogram of storm height for different categories of near-surface rain rate.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between local time and (solid lines) RTDA and (dotted lines) RFAO for M1, M2, and GPROF.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between local time and (solid lines) RTDA and (dotted lines) RFAO for M1, M2, and GPROF.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between local time and (solid lines) RTDA and (dotted lines) RFAO for M1, M2, and GPROF.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Comparison of RTDA and RFAO between original M2 (using 22 V) and M2 using 10 V, 19 V, and 37 V instead of 22 V.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Comparison of RTDA and RFAO between original M2 (using 22 V) and M2 using 10 V, 19 V, and 37 V instead of 22 V.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Comparison of RTDA and RFAO between original M2 (using 22 V) and M2 using 10 V, 19 V, and 37 V instead of 22 V.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Regression lines for M2 [TB (85 V) = a + b × TB (22 V)]: (a), (b) intercept, (c), (d) slope, and (e), (f) correlation coefficient between TB (85 V) and TB (22 V) for (left) Jan and (right) Jul.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Regression lines for M2 [TB (85 V) = a + b × TB (22 V)]: (a), (b) intercept, (c), (d) slope, and (e), (f) correlation coefficient between TB (85 V) and TB (22 V) for (left) Jan and (right) Jul.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Regression lines for M2 [TB (85 V) = a + b × TB (22 V)]: (a), (b) intercept, (c), (d) slope, and (e), (f) correlation coefficient between TB (85 V) and TB (22 V) for (left) Jan and (right) Jul.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Spatial distribution of (left) RTDA and (right) RFAO for (a), (b) M2, (c), (d) GPROF without desert and snow mask, and (e), (f) GPROF.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Spatial distribution of (left) RTDA and (right) RFAO for (a), (b) M2, (c), (d) GPROF without desert and snow mask, and (e), (f) GPROF.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Spatial distribution of (left) RTDA and (right) RFAO for (a), (b) M2, (c), (d) GPROF without desert and snow mask, and (e), (f) GPROF.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between near-surface rain rate and RTDO for region (15°–30°N, 0°–20°E) located in Sahara Desert for M2 and GPROF (with/without screening) for (a) both convective and stratiform, (b) stratiform, and (c) convective.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between near-surface rain rate and RTDO for region (15°–30°N, 0°–20°E) located in Sahara Desert for M2 and GPROF (with/without screening) for (a) both convective and stratiform, (b) stratiform, and (c) convective.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Relationship between near-surface rain rate and RTDO for region (15°–30°N, 0°–20°E) located in Sahara Desert for M2 and GPROF (with/without screening) for (a) both convective and stratiform, (b) stratiform, and (c) convective.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Same as in Fig. 12, except region (30°–35°N, 85°–90°E) is located in Tibetan Plateau.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Same as in Fig. 12, except region (30°–35°N, 85°–90°E) is located in Tibetan Plateau.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Same as in Fig. 12, except region (30°–35°N, 85°–90°E) is located in Tibetan Plateau.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Fig. A1. Relationship between (left) rainfall rate or (right) snowfall rate and brightness temperature calculated by microwave radiative transfer model developed by Liu (1998). Frequencies are (a), (d) 19.3, (b), (e) 21.3, and (c), (f) 85.5 GHz.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Fig. A1. Relationship between (left) rainfall rate or (right) snowfall rate and brightness temperature calculated by microwave radiative transfer model developed by Liu (1998). Frequencies are (a), (d) 19.3, (b), (e) 21.3, and (c), (f) 85.5 GHz.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Fig. A1. Relationship between (left) rainfall rate or (right) snowfall rate and brightness temperature calculated by microwave radiative transfer model developed by Liu (1998). Frequencies are (a), (d) 19.3, (b), (e) 21.3, and (c), (f) 85.5 GHz.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Fig. A2. Relationship between surface physical temperature and calculated brightness temperature for (a) the no-rain case and (b) the rain case with 5 mm h−1 rainfall. Relative humidity is set to 100% both below and above the freezing level.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Fig. A2. Relationship between surface physical temperature and calculated brightness temperature for (a) the no-rain case and (b) the rain case with 5 mm h−1 rainfall. Relative humidity is set to 100% both below and above the freezing level.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Fig. A2. Relationship between surface physical temperature and calculated brightness temperature for (a) the no-rain case and (b) the rain case with 5 mm h−1 rainfall. Relative humidity is set to 100% both below and above the freezing level.
Citation: Journal of Applied Meteorology 44, 8; 10.1175/JAM2263.1
Comparison of RNC methods used in previous studies and those proposed in this paper.
Notation for RNC results provided by PR and TMI.
