The incidence-angle differences of estimated surface rainfall obtained from the precipitation radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM) satellite were investigated. The bias before the orbit boost in August 2001 relative to the near-nadir statistics was 2.7% over the ocean and −5.8% over land. After the boost, the bias was −3.2% and −9.5%, respectively. These biases were further quantified with respect to error sources, that is, the beam mismatch correction error, detection capability of storms with low-level storm-top height, and residual effects. For shallow storms lower than 3 km, most incidence-angle differences were caused by main lobe contamination. For nonshallow storms, several error factors resulted in 5.3% overestimates over the ocean and 5.1% underestimates over land for the period before the boost. The remaining uncertainty in local low-level profiles was identified as a controversial issue.
The bias-corrected dataset updates the interannual variation in rainfall obtained from the TRMM PR. The increasing rainfall features and recent high-rainfall years were consistent with prior studies based on other microwave sensors. The coherent signals and slight differences in the temporal variation compared with the Global Precipitation Climatology Project (GPCP) data indicate the importance of further internal and cross validations based on long-term observation by multiple sensors.
The precipitation radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM) satellite has been capturing three-dimensional precipitation echoes over the global tropics since late 1997. The long-term data have enabled us to investigate the precipitation climatology and to promote discussions on the accuracy of rainfall estimates obtained from space. In general, previous studies have utilized the entire available dataset captured by the TRMM PR at multiple incidence angles within 17° from its nadir in order to reduce sampling errors (e.g., Hirose et al. 2008). Users must note that the entire dataset includes uncertainties in surface rainfall estimates, associated with the inherent observation properties at different incidence angles (e.g., Iguchi et al. 2009). A significant intrinsic defect is caused by the angle-bin differences of near-surface rainfall at various bottom levels that are free from ground clutter. A critical issue with regard to the observation limit of the main lobe clutter contamination is the difficulty in detecting low-level rainfall structure and shallow storms with low storm-top heights at the swath’s edge. Short and Nakamura (2000) identified the deficiency in the detection of shallow storms over low-rainfall regions, such as the region off the coast of Peru. The observation limit of unobservable shallow storms and snowfall at low levels could pose a serious problem for not only the TRMM PR but also other spaceborne cloud radars (e.g., Marchand et al. 2008) and future satellite observations using the dual-frequency precipitation radar (DPR) on board the Global Precipitation Mission (GPM) core satellite. Hence, it is necessary to evaluate the instrument limitation of low-level storm detection by distinguishing it from retrieval errors.
The missing shallow storms and vertically varied precipitation activities near the surface are problematic uncertainties because of the clutter effect at different angles. A conceptual model of the vertical profile of the near-surface radar reflectivity factor used in the current 2A25 version 6 algorithm directly affects the core product of the estimated surface rainfall rate Rs and the rainfall rate at each height level through attenuation correction. Here Rs is estimated on the basis of radar reflectivity data, just above the ground clutter, with a simple vertical gradient model of evaporation for stratiform and convective types over ocean and land, respectively (the TRMM PR version 6 manual). Such correction methods have been discussed for range-dependent ground radar observations in a number of studies (e.g., Bellon et al. 2007; Tabary 2007; Germann and Joss 2002; Vignal and Krajewski 2001). However, the adequacy of assumptions of the regional profile models has not been verified thus far, for example, for mountainous regions and for severe storms with low-level convective cores. Therefore, further understanding of the low-level variation in rainfall and the difference in the products from current assumptions is necessary; this can be acquired by examining the internal coherence in Rs between incidence angles with regard to the regional profile variability. The path-integrated attenuation estimates of rain profiles in the lower atmosphere will be revised in the next version, and it will require the investigation of the remaining biases on a statistical basis.
Improving the confidence in measuring rainfall is vital, and further understanding of the interannual variation is required to determine the type of long-term variations captured by the TRMM PR. Hence, the increasing significance of a study on incidence-angle dependency of rainfall retrieval is enhanced according to expectations for further applications. Although previous studies have provided observational evidence of increased tropical rainfall, particularly over oceans (e.g., Wentz et al. 2007), understanding the observational deficiencies is crucial to assessing the trends and amplitude of the interannual variability in global-scale rainfall among observations and models (e.g., Allan et al. 2010; Soden 2000; Douville et al. 2006). The TRMM PR is a unique sensor with a more than 10-yr rainfall record over ocean and land; it is highly sensitive to global interannual variation (Gu et al. 2007). John et al. (2009) examined the temporal variation over the tropical ocean from observed and simulated precipitation datasets, and they showed that the TRMM radar retrieval has less sensitivity to temperature change, as compared to other satellite data. However, they did not consider the effect of altitude change in August 2001. The orbit boost for enhancing the lifespan of the TRMM satellite has possibly degraded its shallow storm detection ability at the swath’s edge owing to the increase in footprint size and the extended main lobe clutter regions. Several studies have shown that the amount of weak convective rainfall decreased after the boost (e.g., Liao and Meneghini 2009; Nakazawa and Rajendran 2009). To explain the differential factors, Shimizu et al. (2009, hereafter S09) showed that the boost induced a 5.9% decrease in Rs, which was composed of a sensitivity degradation by the altitude boost (0.5%) and angle-bin differences in the rainfall retrieval (5.4%). Further, they revealed that the beam mismatch biases in the second half, that is, the right-hand side, of the scan (2.9%) and the residual factors related to the increase in the footprint size of the TRMM PR (2.5%) account for the incidence-angle differences. Here, the long-term data record enabled us to assume that stable rainfall statistics can be captured as a function of the incidence angle. In addition, the near-nadir (NN) statistics are assumed to be of the highest quality in terms of observation limitation. The bias in the increase in footprint size includes retrieval errors for both shallow and nonshallow storms in addition to the observation limit of missing shallow storms. The regional variations in such multiple error factors and their impact on the spatial variation in rainfall are debatable. Hence, extensive investigation is required in this regard.
The objective of this study is to verify the impact of possible error sources on the global and regional variation in Rs between the incidence angles for two periods before and after the orbit boost. To quantify the observation limit and remaining algorithm issues, the incidence-angle differences in the detection of shallow and nonshallow storms, beam mismatch effect, and other residual retrieval errors were investigated as a continuation of S09. We also investigated the impact of the incidence-angle bias correction on the interannual variation in tropical rainfall.
2. Incidence-angle dependency
a. Rainfall statistics for different incidence angles
To investigate regional differences in the internal statistical consistency before and after the orbit boost, we used rainfall-rate data obtained from the TRMM PR 2A25 version 6 product for six years (1998–2000 and 2002–04). A database was compiled for each incidence angle over each 2.5° latitude–longitude grid. The global value was obtained as an areal average covering 35°N–S, that is, the northern and southern observation limit of the TRMM PR at its nadir. In this study, the databases for ocean and land were compiled according to the dominant surface types for each 2.5° block on the basis of 5-minute gridded elevations/bathymetry for the world (ETOPO5) data.
In general, at nadir, the lowest range bin free from surface clutter is 500 m above the ground, whereas the mode is around 750 m over mountainous areas and around or greater than 1 km along the Himalayas. As shown in Fig. 1, the contamination level rises toward the swath’s edge and the mode becomes 1750 m at the swath’s edge both in the first and second halves of the scan (for the 1st–24th and 26th–49th angle bins). The lowest clutter-free level of 500 m was obtained at near-nadir angles between the 23rd and 27th bin (±1.4°) from 49 angle bins. The off-nadir detectable level for severe storms is relatively low according to the clutter-elimination algorithm. The cause and impact of the reduced number of severe storms at the edge will be discussed later.
To verify the impact on the missing low-level storms, shallow and nonshallow storms were classified on the basis of storm-top height, that is, the top of three consecutive significant echoes for each rain profile. The threshold of the storm-top height for shallow storms was set to 3 km, allowing some sampling at all angle bins, consistent with the natural statistics of shallow storms in conjunction with trade wind inversion (Short and Nakamura 2000).
The differences of Rs among scan angles in terms of the globally averaged cumulative distribution for shallow and nonshallow storms before the boost are displayed in Fig. 2. Over the ocean, rain statistics based on data near nadir (23–27 bins) were consistent. For nonshallow storms, overestimates of strong rainfall rates appeared around the incidence angle of 10°, that is, the 10th and 39th bin, reflecting the known deficiency of the attenuation correction in conjunction with the hybrid surface reference (HSR) method over the ocean (Meneghini et al. 2004). A complete description of the error estimates and correction has been provided by Seto and Iguchi (2007). In the statistics at the swath’s edge, underestimates of rainfall were significant for shallow storms. For nonshallow storms, the contribution from weak (strong) rainfall is greater (less) than that near nadir. The total difference between the near-nadir and the edge data over the ocean was smaller than that for shallow storms. Thus, over the ocean, the difference in total rainfall at nadir and the swath’s edge was mainly attributable to the shallow rain estimates. Over land, the patterns of the nadir ±1 and ±2 bins were almost identical to each other (the standard deviation is around 1%). Nevertheless, the total rainfall at nadir is overestimated by around 8%, as compared to the near-nadir data, resulting from the differences in strong rainfall rates (>20 mm h−1). This issue may be attributable to an uncertainty in the surface backscattering cross section over land (e.g., Iguchi et al. 2009; Meneghini et al. 2004; Seto and Iguchi 2007). On the other hand, intense rainfall off nadir was generally underrepresented. Thus, the total bias over land mainly resulted from estimates of the intense nonshallow storms.
To further evaluate the self-consistency, referential rainfall statistics were generated by compiling the TRMM PR data around its nadir. In this study, the reference data were obtained on the basis of near-nadir data of the 23rd–25th angle bins over ocean and 23rd–24th angle bins over land, considering the reduced main lobe contamination effect, internal consistency of Rs between incidence angles, and exclusive beam mismatch effect after the boost. The beam mismatch effect is regarded as an error resulting from the overcorrection of surface echo contamination in the second half of the scan after the boost (for details, see S09). To distinguish the bias from the beam mismatch effect, the referential near-nadir data used herein is based on the first half of the scan.
On the basis of the near-nadir data, annual rainfall and the fraction of rainfall resulting from shallow storms (<3 km) are depicted for the two periods in Fig. 3. The regional difference in annual rainfall before and after the boost showed natural variation in the ascending and descending branches of the Walker circulation associated with the El Niño and La Niña phases, as described by Nakazawa and Rajendran (2009). Over the ocean, the rain fraction of shallow storms shows a negative correlation with the annual rainfall. More specifically, the area of the maximum rain fraction resulting from shallow storms was not collocated over areas with minimum rainfall. More than 95% of the rainfall was brought by shallow storms 2000 km off the coast of Peru and Angola. This could be attributed to the strong atmospheric subsidence of Hadley and Walker circulation. In contrast, the minimum rainfall over the ocean off of Peru and Angola is in conjunction with the upwelling effect, causing low sea surface temperatures. Similar features also appeared over the eastern Pacific in the Northern Hemisphere. Over a large part of land, the rain fraction of shallow storms was less than 5%. The highest fraction appeared over the Tibetan Plateau, where small-scale precipitation systems dominate (Hirose et al. 2009). Similarly, moderate fractions are distributed over highlands (e.g., the Andes) and dry regions (e.g., the Sahara), where large-scale precipitation systems seldom occur (Hirose et al. 2009).
The storm-top height histograms near nadir and at the swath’s edge are shown in Figs. 4a–d. Here, the swath-edge statistics were compiled on the basis of data from the first and second angle bins. The incidence-angle dependency on the relationship between the range bin (250 m) and the storm-top height has been taken into account in this study. Significant incidence-angle differences in the histograms appeared for the shallow storms and for storms with a top height either around or in the upper part of the melting layer. It clearly shows the effect of the viewing geometry difference in incidence angles and orbit boost on the detection of shallow convective rain over the ocean. Figures 4e–h show the averaged Rs for each storm-top height, angle bin, and rain type . In general, higher storms result in greater , whereas becomes weak for a storm top higher than 12 km. The relationships near nadir and at the swath’s edge are similar for shallow storms. In contrast, the of nonshallow storms observed near nadir were greater than that at the swath’s edge. This may be partly due to the observation limit with the decrease in strong rainfall off nadir and retrieval errors of the slant-path effect on the relationship between the storm-top height and corresponding surface rainfall. Moreover, the angle-bin difference in the rain-type classification may appear because of the lack of spatial data to detect the smeared bright band near the scan edges (Awaka et al. 2009). On the basis of the occurrence frequency of storms and , the contribution to total rainfall near nadir was obtained (Figs. 4i–l). The significant difference between angle bins was shown for shallow storms lower than 3 km, particularly for convective rain over the ocean. The error sources for shallow and nonshallow storms are deemed separable from these features.
b. Assessment factors
To investigate the incidence-angle difference, first, the anomaly of Rs (Anom1) for each angle bin (i) was calculated by the rainfall rates averaged for each storm-top height (h) and the precipitation type (k) of convective (c) and stratiform rain (s) in comparison with the near-nadir (nn) data mentioned above,
Here, and N denote averaged Rs and the number of storms for each storm-top height, respectively; at each angle was reconstructed by interpolation of that based on the near-nadir data because the relationship between the level h and the range bin number is different for each incidence angle. The total bias by incidence-angle difference was obtained by the all-angle-bin average of Anom1. In this study, when the range between h1 and h2 is set to be the surface and 3 km (3 km and top ~20 km), the total bias is known as the shallow rain bias (nonshallow rain bias). Next, we break down the bias into three parts owing to the incidence-angle difference in Rs; (i) the asymmetric bias resulting from the beam mismatch correction errors, (ii) the bias resulting from the variable number of detectable storms, and (iii) the residual errors. These biases were obtained for shallow and nonshallow storms over ocean and land, and before and after the boost, respectively. In this study, the other type defined in the 2A23 algorithm was excluded because most of the type consists of clouds and noise-level echoes (Awaka et al. 2009).
To distinguish the angle-bin effects from the asymmetric feature mainly resulting from the algorithm deficiency, the symmetrized data were generated by copying the data in the first half of the scan (from the 1st to the 24th angle bins) to the second half (from the 26th to the 49th angle bins), as in the case of S09. The asymmetric bias (i) was determined by averaging the difference between the original data and the symmetrized data in Anom1. The bias represents the effect of the beam mismatch correction errors. As for (ii), the missing ratio of rainfall from the shallow storms interfered with the surface clutter (i.e., shallow rain deficiency) was calculated on the basis of symmetrized data as the angle-bin average of the rainfall anomaly, and it mainly resulted from the difference in the number of shallow storms. The definition of the anomaly (Anom2) is similar to that of Anom1, with the exception of replacing with ; that is,
where Anom2 is based on the difference in the number of shallow storms and the ratio of convective and stratiform rain, under the assumption that near-nadir statistics on for each storm-top height are accurate. By applying the same method for nonshallow storms with a level greater than 3 km, nonshallow rain deficiency was also obtained. Anom2 for nonshallow storms is an index of not only the observation limit on the detectable number of storms but also the retrieval errors on , as noted in the previous subsection. The residual error (iii) was derived by subtracting Anom2 from Anom1 on the basis of symmetrized data, which is the difference in , that is, the relationship between the storm-top height and Rs. This bias on shallow storms distinguishes the retrieval error from the missing rainfall effect. For nonshallow storms, both the nonshallow rain deficiency and the residual error are used to examine the retrieval errors.
3. Bias on incidence-angle dependency
a. Shallow storms
In this subsection, we assess the observation limit and retrieval issues for detecting shallow storms. Per-angle Anom1 for shallow storms is shown in the upper panel of Fig. 5, and the angle-bin averages are listed as Sums in Table 1. In general, the off-nadir rainfall was less than the near-nadir rainfall, particularly over the ocean. After the boost, the bias was negatively increased. The shallow rain bias before and after the boost was −2.2% and −4.2%, respectively.
Anom1 for each angle bin was almost symmetric before the boost, and the asymmetric bias for shallow storms before the boost was nearly zero (see A in Table 1). However, the difference between the original and symmetrized datasets reached −0.7% after the boost with a decrease in the second half of scans, particularly in oceanic rainfall; 62% of the asymmetric bias resulted from the missing shallow storms, and the rest was due to the retrieval errors resulting from the beam mismatch correction errors (not shown).
The center panel of Fig. 5 shows the impact of the missing shallow storms in terms of Anom2. The incidence-angle pattern of Anom2 for shallow storms is in closer agreement with that of Anom1, which indicates that the main source of the angle-bin dependence of shallow storm rainfall estimates is the detection capability of the shallow storms. Anom2 was almost zero between 15 and 35 angle bins, and it negatively increased toward the swath’s edge. Over the ocean, where shallow storms are dominant, 8.6% (10.9%) of rainfall is missing due to the lower sampling of shallow storms at the swath’s edge before (after) the boost. The shallow rain deficiency, that is, the effect on rainfall resulting from the lesser number of shallow storms, shown as the average of Anom2 for the symmetrized data before and after the boost, was −2.3% and −3.4%, respectively (see B in Table 1). In the number, after the boost, the missing shallow storms over the ocean accounted for 10.6% (not shown).
The difference between Anom1 and Anom2 for the symmetrized dataset is attributable to the retrieval differences between the incidence angles. The lower panel of Fig. 5 shows that the largest effect was around −2% in the second half of scans after the boost owing to the beam mismatch correction error. In the average for the symmetrized data, the difference resulting from the retrieval errors was almost zero (see C in Table 1). Hence, the globally averaged retrieval errors could be ignored for shallow storms in comparison with the shallow rain deficiency.
The regional variations in these biases are shown in Fig. 6. The data were compiled for each 2.5° grid and smoothed by a spatial filter. Figures 6a,e show that the shallow rain bias had negative values over most oceans, with its maximum over the low-rainfall regions. The low-rainfall regions were distributed differently before and after the boost, as shown in Fig. 3. However, the degree of the overall negative bias was stronger for the period after the boost. On the other hand, some regions, such as Egypt, had positive values. This point is discussed in section 3c. The regional variation in the asymmetric bias is shown in Figs. 6b,f. The anomaly appeared over the low-rainfall region before the boost, which indicates the existence of insufficient sampling between incidence angles. After the boost, most areas exhibited negative values relative to the symmetrized statistics. The beam mismatch correction errors generally induced the decreasing effect by the extended contamination of the surface echo. The maps of the shallow rain deficiency (Figs. 6c,g) were spatially similar to the shallow rain biases, with significant decreases over the low-rainfall ocean. The zonally averaged shallow rain deficiency had its peak around 20°S, including the ocean off Peru and Angola. In those regions, more than 50% of the rainfall was missed owing to the slant main lobe effect after the boost.
The difference between the shallow rain bias and the shallow rain deficiency showed the overestimated features around Egypt and the coastal ocean near Peru and Angola (Fig. 6d,h). In other words, the off-nadir rainfall estimate was greater than the near-nadir rainfall owing to shallow storms in that region. The primary reason may be the mismatch of assumed low-level rain profiles as described in section 3c.
b. Nonshallow storms
Although upper-level profiles of nonshallow storms are detected, the significant incidence-angle differences are addressed in Fig. 2. In the pattern of Anom1 for nonshallow storms shown in the upper panel of Fig. 7, the remarkable features were overestimates of around 10° over the ocean, singular overestimates at nadir over land, a right–left asymmetric pattern after the boost, and underestimates off nadir over land. The nonshallow rain bias was 2.9% (5.3% for ocean and −5.1% for land) and −0.4% (1.8% for ocean and −8.1% for land) before and after the boost, respectively (see Sumns in Table 1). Excluding the asymmetric bias, the nonshallow rain bias over the ocean became 5.8% before the boost (4.3% after the boost). Significantly, the rainfall will increase by 5% over land when all angle-bin data over land are corrected to be consistent with that near nadir. The asymmetric bias accounted for −2.5% after the boost (see D in Table 1), which is 3.3 times greater than that based on the shallow storms.
The bias resulting from the difference in the number of nonshallow storms (Anom2) was around 10% at the swath’s edge. The nonshallow rain deficiency was 3.7% and 4.8% before and after the boost, respectively (see E in Table 1). The reason of the opposite feature compared to shallow storms has not been verified thus far; however, it indicates the slant incident effect on the attenuation correction causing a greater number of storms and weaker rainfall rates off nadir by considering that the high off-nadir rainfall rates were represented as moderate rainfall rates, as seen in the lower panel of Figs. 1 and 2. The residual bias was −0.5% and −2.7% before and after the boost, respectively (see F in Table 1). The oceanic rainfall at angle bins 15–35 was almost consistent with the near-nadir statistics. The average rain profile over the ocean had its peak around 1 km and decreased at 4% km−1 toward the surface (not shown), which is almost the same as the slope for the pressure correction applied by 2A25 in the clutter region. Most data within bins 15–35 can detect the increasing part of the profile; hence, the decreasing features at and near the swath’s edge may imply that an inadequate vertical profile model degrades the oceanic rainfall only at the swath’s edge. It is important to note that significant underestimates were found over land as −7.4% and −9.3% before and after the boost, respectively. Both a part of the nonshallow rain deficiency and the residual bias would involve retrieval errors. Some of them are controversial issues in conjunction with uncertainties of HSR, surface backscattering over land, nonuniform beam filling effects, and the impact of the current assumption of vertical rain profiles within the clutter level, particularly in low-level convective cores.
The regional variation in the nonshallow rain bias is shown in Figs. 8a,e. Considerable overestimates over the ocean and underestimates over most land are shown. The significant positive tendency of nonshallow rain bias and the residual bias over the ocean can be mainly attributed to attenuation correction errors by the current HSR. Some regions such as the Indochina Peninsula were underestimated by more than 10% after the boost. On the other hand, rainfall around dry regions, such as Egypt, was overestimated by more than 100%. The positive value over the low-rainfall land could be explained by the regional characteristics of the vertical gradient of rainfall in the same context as shallow storms (see section 3c). The inhomogeneous pattern of the asymmetric bias before the boost implies that the sampling insufficiency is involved in the near-nadir statistics for nonshallow storms. Despite the highly spatial variation, the decreasing features of the asymmetric bias after the boost were extracted as the impact of the beam mismatch correction errors. The spatial variations of the nonshallow deficiency and the residual bias were almost opposite over land. This poses a difficulty in partitioning retrieval errors, thereby limiting direct comparison with shallow storm deficiency with respect to the observation limit of Anom2 for nonshallow storms.
c. Regional variations of low-level rain profiles
In the 2A25 algorithm, the vertical gradient of the radar reflectivity factor is set to be zero or negative in the clutter region. One of the retrieval errors is attributed to the estimated low-level rain profiles that could be validated with the near-nadir data. In this subsection, residual errors in Figs. 6 and 8 are discussed with respect to the low-level vertical gradient of the radar reflectivity factor (VG_Z) and rainfall (VG_R) based on the near-nadir data before the boost.
Figure 9 shows the low-level vertical gradient for shallow storms. This was obtained as the average of the gradient of the regression line between 0.75 and 1.25 km. The positive value represents the downward-decreasing or upward-increasing characteristics, and vice versa for the negative value. Note that unique downward-decreasing VG_R and VG_Z were shown over the driest region, Egypt, where significant evaporation is expected (e.g., Geerts and Dejene 2005). The assumption of the constant radar reflectivity for convective rain near the surface can possibly be corrected for regions that show remarkable downward-decreasing characteristics. On the other hand, the downward-increasing VG_R and VG_Z were shown over most low-rainfall regions, which implies that shallow storms, especially with a very low-level storm-top height, are dominant in those regions. Some land areas, such as the Sichuan basin, also show the moderate downward-increasing characteristics that are attributable to orographic effects. These downward-increasing profiles are inconsistent with the assumption used in 2A25 version 6; that is, there is no enhancement in surface clutter, evaporation effect for stratiform rain over land, and pressure correction of the terminal velocity. This discrepancy could be ignored, as shown in Figs. 6d,h, whereas it partly causes underestimated residual bias for shallow storms (e.g., over the ocean east of Hawaii and the southern Indian Ocean).
Figure 10 shows the low-level VG_R and VG_Z for nonshallow storms. Unlike the shallow storm pattern, positive values (the downward-decreasing profile) dominated most ocean areas, which can be attributed to the vertical air density effects on the terminal velocity assumed in the 2A25 algorithm, as mentioned previously. The regions with significant downward-decreasing VG_Z corresponded to the overestimate bias shown in Fig. 8d. This suggests the possibility of introducing a regional profile regime toward better representation of the unobserved rainfall resulting from surface clutter.
In addition, the gradient maps (Figs. 9 and 10) indicate a potential bias on the near-surface rainfall at the invisible levels under the clutter-free bottom. Our preliminary experiments on simple extrapolation by the near-nadir rainfall-rate gradient around 1 km showed an about 3% and 7% increase in the near-nadir surface rainfall over the entire region (35°N–S) and in the winter midlatitudes (30°–35°N for December–February and 30°–35°S for June–August), respectively (not shown). The increasing characteristics were remarkable over regions around the Himalayas, where the lowest range bin free from surface clutter is relatively high. The estimates reflected steep downward-increasing convective rain, which may be overestimated because the decrease under the cloud base and the occurrence of elevated convective cores have not been considered. Nevertheless, the low-level rainfall variations in the lowest few hundred meters (<500 m) should be addressed as a possible error source.
4. Implications for annual variation
The globally averaged rainfall based on the original data during 2002–04 decreased by 5.2%, as compared to that during 1998–2000. This study showed that the incidence-angle bias was −5.3%, and it was further divided into −2.0% for shallow storms and −3.3% for nonshallow storms. The slight disagreement from S09 is due to the differences of the average methodology on the target region (35°N–S), the stratiform–convective classification effect, and the definition of near-nadir data. The contribution of shallow storms was further grouped into three parts: the asymmetric bias (−0.7%), shallow rain deficiency (−1.1%), and the residual bias (−0.1%). Similarly, the contribution for nonshallow storms was −2.1%, 1.1%, and −2.3%, respectively.
Figure 11 shows the year-to-year variations in annual rainfall averaged over the global tropics (35°N–S). It is similar to S09, but it also displays an updated version by the new definition and exhibits rainfall over ocean and land with the result based on the Global Precipitation Climatology Project (GPCP) version 2 monthly analysis based on both satellite and gauge data. Each line shows the statistics based on the all-angle original (Org) data, near-nadir NN data, and all-angle corrected (Cor) data, with the biases derived in this study and the sensitivity degradation of 0.5% simulated by S09. The GPCP data (G87) were also represented for the same region; however, it was multiplied by 0.874 for comparison with the year-to-year variation because the averaged annual mean was 1060 mm, which is much greater than the average of Cor data (926 mm). The virtually consistent variations in the NN data and Cor data before the boost supported the NN data as being sufficient to represent the annual rainfall over the global tropics. Nevertheless, all angle-bin data should be utilized to reduce sampling errors in detecting the monthly and regional variation. The corrected rainfall shows a quasi-linear change in time, which is likely to be related to the regime shift from the La Niña to the El Niño phase (e.g., Nakazawa and Rajendran 2009; Soden 2000). One can see that significant rainy years are frequently obtained recently, as shown by the fact that the addition of data in 2006 and 2007 resulted in a new highest rainfall year. Results are not substantially altered when considering the year-to-year variation based on the GPCP data. However, the highest record in the decade was different among the datasets.
The interannual variation over the ocean dominates the total pattern, somewhat consistent with previous studies using other sensors (e.g., Wentz et al. 2007). The most significant difference between the GPCP data and the Cor data is the amplitude of variations (e.g., Adler et al. 2009). In the temporal variation, the GPCP data were more sensitive to El Niño and La Niña events, as compared to the Cor data, particularly during El Niño in 1998 (e.g., Li and Fu 2005). The overland interannual variation and amplitude were considerably different from that over ocean, showing a seesaw pattern (e.g., Kumar et al. 2004; Nakazawa and Rajendran 2009). The major visible features are the bimodal peaks in 1999 and 2007, where the abrupt increases correspond to La Niña years. The Cor data show that the last La Niña period brought more rainfall over land, in agreement with the GPCP data, while it was not detected in the Org data.
Table 2 lists the 10-yr gradient of the linear regression of monthly rainfall. The original data indicate a misleading decreasing trend with a ratio of −5.5% for the decade. By the bias correction, the trend was changed to positive, that is, 2.8% for the decade, which is coherent with the GPCP result (3.4%). The ratio of the Cor data is almost equivalent to the GPCP data for the ocean and less over land. Note that the 10-yr gradient is almost twice as much as that for the entire period of the GPCP data (Gu et al. 2007). These positive trends by the Cor data, except for that over land, were found to be statistically significant (>95%) on the basis of a one-sided Student’s t test. Here, the effective degrees of freedom were estimated by N(1 − r)(1 + r)−1 − 2, where r is the lag-1 autocorrelation coefficient of the regression residuals and N is the length of the time series in months (e.g., Gu et al. 2007; Santer et al. 2000; Jones et al. 1997).
5. Conclusions and discussion
In this paper, we focused on an internal validation of the TRMM PR data with respect to the impact of biases resulting from asymmetric features, storm detectabilities, and residual retrieval differences before and after the orbit boost. As shown in Table 1, the total bias was 0.7% before the boost and −4.6% after the boost. A crucial impact was in response to the asymmetric bias, which induced a decrease of −3.2% after the boost. We will need this kind of internal validation again, after revision of the PR algorithm.
The shallow rain deficiency was the major factor of the shallow rain bias. Over the low-rainfall ocean, such as that off Peru, more than 20% rainfall was missed owing to clutter interference at off-nadir scan angles. Other precipitation datasets based on microwave radiometer observations also have difficulty in retrieving weak rainfall signals because the precipitation systems over the low-rainfall region are generally small at the horizontal and vertical scales in view of the radiometer sampling area (e.g., Michelson et al. 2005; Kida et al. 2009). The near-nadir observation using the TRMM PR is advantageous for detecting shallow storms higher than 500 m, which was shown to be informative for analyzing the bias estimates, as shown in this study. However, the impact of shallower storms is unclear, even in the long-term near-nadir radar estimates, because of the minimum detectable threshold. Hence, the missing shallow storms estimated here are the lowest bounds on the shallow storm detection error.
On average, the residual bias for shallow storms was negligible. However, for the regional scale, overestimated features were extracted over dry regions, such as Egypt, where the annual rainfall was estimated as only about 10 mm. Current Rs is around 3% smaller than near-surface rainfall (not shown). By regional modeling of the low-level vertical gradient assumption involving local evaporation, such a local bias will be improved. Our preliminary investigation of the regional characteristics of the vertical gradient in the lower atmosphere and its impact indicated that the local downward-decreasing or downward-increasing patterns could affect Rs significantly. In a more sophisticated step to develop low-level profile models, more complex studies will be necessary by using external environmental variables to estimate evaporation effects under cloud base and orographic effects (e.g., Comstock et al. 2004; Kitchen et al. 1994) for not only the detectable levels by the near-nadir data, but also the undetectable layers lower than the lowest range bin free from surface clutter. Over mountainous regions, the observational limit has not been clearly evaluated because regional sampling for various observation properties, such as the clutter levels, is complex and varied. In the future, regional campaign experiments and model studies on orographic rainfall detection, undetectable brightband structure near the surface, and evaporation under the cloud base would contribute to further improvement of rain estimates and would also be applicable to landslide and flood-monitoring studies.
Observation properties of the detectability and the retrieval bias were not clearly divided for nonshallow storms; however, this study showed some notable features. The main cause for the erroneous estimates is considered to be the HSR correction errors over the ocean. Nevertheless, the majority of the positive bias was due to the difference in the number of detected nonshallow storms between incidence angles. One remaining uncertainty for nonshallow storm retrieval is that the rainfall rate was substantially smaller at the swath’s edge than that near nadir. Further evaluation is needed to separate technical properties of the slant observation, such as brightband detectability. The negative bias over the land was caused by the retrieval errors, possibly related to the insufficient detection of low-level convective cores and attenuation correction problems in severe off-nadir storms, because the number of strong rainfall rates was considerably smaller compared to the near-nadir statistics. With the updated attenuation correction in the next algorithm, the regional variation in strong rainfall rates will be refined and the incidence-angle dependency on the detection of the strong rainfall will be further clarified. Again, the internal consistency verification must be performed to give more credence to the product based on ongoing and revised algorithms, and future observations such as GPM DPR based on the best-available statistics.
With regard to the effect of the bias on temporal variations, this study indicated that contributions from the boost effects have a crucial impact on estimating the 10-yr trend during 1997–2007, as has been pointed out by S09. Our corrected datasets derived a significant increasing trend for the decade over 35°N–S. The temporal variation and its trend were comparable to the GPCP dataset, but differences were detected year by year. For example, in 2006, the tropical rainfall based on our corrected data was the highest for the decade, whereas the rainiest year was 2005, based on GPCP. The limited observation period restricts the interpretation of increasing rainfall over the ocean as the long-term trend; nevertheless, it revealed the following. 1) The averaged rainfall is relatively high in recent years, and 2) the changing ratio is as high as that in prior analyses based on passive microwave observations, compared to model results. For the former conclusion, this study supports the view that rainfall in the last few years is relatively high, both from the TRMM PR and GPCP. Here, it should be acknowledged that well-calibrated satellite observations should be carried out continuously to monitor and update the state of the environment. The latter result indicates GCM deficiencies, even from TRMM PR data, as investigated by John et al. (2009), based on passive microwave sensors. Here, remarkable differences between datasets in the total amount of rainfall should not be ignored for the assessment of the robustness in precision. Further comprehensive cross validation between several data sources is required to clarify the differences associated with rainfall regimes and sensor deficiencies for detecting signals of global warming in the planetary water circulation.
The data used in this paper were provided by the Japan Aerospace Exploration Agency. The authors would like to extend their gratitude to the members of the TRMM project. They wish to thank Mr. Noboru Matsuzuki and Dr. Yasushi Suzuki of the Japan Weather Association for insightful discussions. Thanks are also extended to anonymous reviewers for valuable comments. This study was partly supported by the Ministry of Ed, Culture, Sports, Science and Technology (MEXT), Japan, via a Grant-in-Aid for Scientific Research (Category B, 21710016).