Impact of proxy variables of the rain column height on monthly oceanic rainfall estimations from passive microwave sensors

International Journal of Remote Sensing Vol., No., 0 June 0, 9 7 Impact of proxy variables of the rain column height on monthly oceanic rainfall estimations from passive microwave sensors JI-HYE KIM, DONG-BIN SHIN and KYOUNG-WOOK JIN Department of Atmospheric Sciences, Yonsei University, Seoul, Korea Global Environmental System Research Laboratory, National Institute of Meteorological Research, Seoul, Korea COMS System Engineering Team, Korea Aerospace Research Institute, Daejeon, Korea (Received December 00; in final form 9 October 0) A major uncertainty in physically based algorithms that are used to estimate rainfall from passive microwave sensors arises from a lack of information on physical parameters such as the rain column height and the freezing level in rainy conditions. This uncertainty occurs because the rainfall integrated along a path on the rain column determines the relationship between the brightness temperature and the rainfall. The rain column height, however, is not well determined directly from simultaneous measurements. Most estimation models use the freezing level derived from an indirect method to obtain the unknown parameter. In this study, the characteristics of three variables that may be used as a proxy variable of the rain column height are investigated. The two variables are derived from the Tropical Rainfall Measuring Mission (TRMM) microwave imager (TMI) and precipitation radar (TPR). They include the TMI-estimated freezing level (TFL) and the TPR-estimated bright-band height (BBH). The third variable is the freezing-level altitude derived from National Centers for Environmental Prediction (NCEP) reanalysis data (NCEP reanalysis freezing level (NFL)). Monthly oceanic rainfall estimations were then performed using the three aforementioned variables in place of the rain column height. As expected, the results show that differences in the rainfall estimates are greater in the regions where larger differences exist among the three variables. The analysis confirmed that an underestimate of the rain column height causes an overestimate of the rainfall. In addition, rainfalls that were underestimated with the BBH or NFL can be corrected with an empirical adjustment. This suggests that the TFL, BBH and NFL contain information related to the rain column height. However, the BBH and NFL require a correction in the mid-latitudes when their magnitude is low.. Introduction One of the major uncertainties in passive microwave rainfall estimations arises from inaccurate information regarding the rain column height. The rain column height can be interpreted as the freezing level in raining clouds. Above this level, most precipitation is in the form of frozen hydrometeors that do not emit much microwave radiation. Below the freezing level, the rainfall integrated along a path determines the brightness *Corresponding author. Email: dbshin@yonsei.ac.kr International Journal of Remote Sensing ISSN 0- print/issn -90 online 0 Taylor & Francis http://www.tandf.co.uk/journals http://dx.doi.org/0.080/0.0.9

9 J.-H. Kim et al. temperature. The microwave brightness temperature at emission dominant frequencies increases as a function of rain rates and the freezing level (Wilheit et al. 99). For this reason, most algorithms based on emission signals exhibit a significant sensitivity to the rain column height or the freezing level. Furthermore, Wang (99) reported that another important error, the so-called beam-filling error, tends to be related to the freezing level based on an examination of the slant path attenuation for various hydrometeor distributions. Wang (99) then proposed that the beam-filling correction factor is not a constant factor but is linearly related to the freezing level or the rain column height. The link between the two error sources was also highlighted by Chiu and Chang (000). Based on Tropical Rainfall Measuring Mission (TRMM) observations, Shin (0) revealed that the spatial inhomogeneity of rainfall is associated with its vertical structures. Such a finding supports the fact that the beam-filling error is due to the coupling between the spatial inhomogeneity within a field of view and associated vertical structures. The rain column height is not directly available from satellite measurements. Most physically based rainfall algorithms employ a proxy variable of the rain column height that is derived by an indirect method. Wilheit et al. (99) first introduced a technique to approximate the proxy variable using the 99th percentile of microwave brightness temperatures at two low frequency channels. The top one percentile of the brightness temperature data were selected so as to obtain a typical raining condition. The details of the technique, including its assumptions, will be reviewed in the following sections. Chiu and Chang (000) reported on the annual, seasonal and interannual variations of the proxy variable of the rain column height as derived from the technique for the Special Sensor Microwave Imager (SSM/I) on board satellites from the Defense Meteorological Satellite Program (DMSP). The estimated proxy variable was also compared with the height of the 0 C isotherm level obtained from the Goddard Laboratory for Atmospheres general circulation model (GCM). Shin et al. (000) proposed that the climatology of bright-band height (BBH) estimates can be used as an alternative to the rain column height because the bright band is located a few hundred metres below the freezing level (Meneghini and Kozu 990). Shin et al. (000) also developed an algorithm for estimating the BBH from the TRMM precipitation radar (TPR) on board the TRMM satellite. The algorithm uses three quantities: the altitude of the maximum radar reflectivity, the altitude of the largest positive reflectivity gradient and the altitude of the largest negative reflectivity gradient. As a validation of the BBHs estimated by Shin et al. (000), Harris et al. (000) assessed the latitudinal and seasonal variations of the BBHs and the freezing levels directly computed from the National Centers for Environmental Prediction (NCEP) reanalysis data. The similarity between the freezing levels and the BBHs suggests that the NCEP freezing level data may be used as a proxy variable for the rain column height. In this study, the characteristics of three types of variables that can be used as a proxy variable of the rain column height in rainfall estimation models will be described and compared. The three variables include the TRMM microwave imager (TMI)- estimated freezing level (TFL) based on brightness temperatures at two emission channels, the TPR-estimated BBH and the NCEP reanalysis freezing level (NFL). The second and third types of variables, the BBH and NFL, can be especially valuable when a microwave radiometer does not carry the two emission channels appropriate for an estimation of the TFL. The third type of variable may also be important when microwave instruments are operating without the two emission channels and the

Proxy variables of the rain column height 9 accompanying radars. Monthly rainfall over the oceans will be obtained with each of the proxy variables and their impact on rainfall estimates will be investigated.. Proxy variables of the rain column height. Freezing-level altitudes from TMI The algorithm for determining the freezing level from passive microwave radiometers was developed by Wilheit et al. (99), appendix (A) and was first applied to microwave brightness temperatures collected by the SSM/I on board satellites from the DMSP. The algorithm collects the 99th percentile of the brightness temperature from one-dimensional histograms for each of the two SSM/I channels at 9. and. GHz-V (vertical polarization). The resulting brightness temperature pair is associated with a typical raining condition. The freezing level is then derived by matching the brightness temperature pair computed from the radiative transfer model of Wilheit et al. (997) with the observed pair under the same raining condition. The algorithm has been modified and applied to TMI brightness temperature data. In this work, the freezing-level altitude as estimated from TMI (TFL) as a proxy variable of the rain column height was examined. The seasonal means of the TFL for the ten years between 998 and 007 are shown in figure. The pattern of the TFL distribution is predominantly zonal. The maps show that high TFL values greater than km are consistently observed over the tropical ocean regions throughout the seasons. The regions with a high TFL greater than. or km tend to extend or shrink to the north and south with the seasons. In particular, during the summer (June July August (JJA)) a high TFL can be observed even over middle latitude southern and East Asia. The regions are subject to strong Asian summer monsoons which can be divided into the Indian monsoon and East Asian monsoon systems (Yihui and Chan 00). The northward extension of the high TFL may be linked to the seasonal march of the East Asian monsoon that brings warm moisture fluxes and intense rainfall. As expected, slightly lower TFLs (<. km) are usually estimated at higher latitudes. The lowest TFL value (.7 km) is estimated during the northern spring (figure (a)). This is consistentwith explanations by Wilheit et al. (99) that describe the typical range of TFLs to be between and km when it is raining.. Bright-band height from TPR The bright band or the melting layer is identified by a larger radar reflectivity relative to its surrounding layers. It is known as a distinct feature of stratiform precipitation. The bright band is usually found slightly below the freezing level (0 C isotherm). The difference between the BBH and the altitude of the freezing level is in the order of a few hundred metres (Meneghini and Kozu 990). This layer can also be interpreted as a transition layer where frozen hydrometeors are melting. The larger reflectivity of the bright band is a result of the increased dielectric constant of melting hydrometeors and the growth of droplets due to coalescence. Below the bright band, most precipitation is in the form of liquid hydrometeors that significantly attenuate microwaves. Therefore, the BBH can be thought of as information on the height of a rain column. The BBH is measured by the TPR operating at the frequency of.8 GHz. The bright band is usually observed more distinctively with lower frequency microwaves because the enhancement of the reflectivity in the melting layer relative to that in snow

9 J.-H. Kim et al. (a) Mean =.7, Maximum =., Minimum =.7 N N N N E E 8 W W (b) Mean =.7, Maximum =., Minimum =.0 N N N N E E 8 W W N N (c) Mean =.7, Maximum =., Minimum =.0 N N E E 8 W W (d) Mean =.7, Maximum =., Minimum =.8 N N N N E E 8 W W Figure. Seasonal means of the TMI-estimated freezing level (TFL) for four seasons: (a) spring (March April May, MAM), (b) summer (June July August, JJA), (c) fall (September October November, SON) and (d) winter (December January February, DJF) during the ten years from 998 to 007. or rain is greater at lower frequencies (Meneghini and Kozu 990). As such, a TPR has successfully measured the BBH since the launch of the TRMM satellite on November 997. The BBH from the TPR is provided as standard products (algorithm A for instantaneous values; algorithm A for monthly averages). The distributions of the seasonal mean BBHs observed from the ten years of TPR data for four seasons are shown in figure. The observed pattern is similar to the TFL distribution in that it is primarily zonal. High BBH values greater than. km are also found in the region where the Asian summer monsoon prevails or over the warm pool region of the western Pacific Ocean. Meanwhile, lower BBH values seem to exist in the winter hemisphere. It was also found that a larger latitudinal gradient (denser contour interval) of the BBH tends to occur in the winter hemisphere. The minimum and

Proxy variables of the rain column height 97 (a) Mean =.8, Maximum =., Minimum =.8 N N N N E E 8 W W (b) Mean =.7, Maximum =.8, Minimum =.7 N N N N E E 8 W W (c) N Mean =.7, Maximum =., Minimum =. N N N E E 8 W W (d) N Mean =.8, Maximum =.77, Minimum =. N N N E E 8 W W Figure. Seasonal means of the TPR-estimated bright-band height (BBH) for four seasons during the 0 years from 998 to 007. maximum BBH values were found to be. and.8 km, respectively. As mentioned previously, the BBH is located below the 0 C isotherm by about 00 900 m. When taking into account the difference between the BBH and the altitude of the freezing level, the maximum BBH values are comparable with those of the TFL. However, the minimum BBH appears to be lower than the values of the TFL. One may note that BBH values are not observed for the dry region over the central and eastern Pacific Ocean, as indicated by the dark colour in the maps.. NCEP freezing-level altitude The freezing-level altitude is calculated from NCEP reanalysis monthly data (hereafter NFL) for the 0 year period from 998 to 007. Details on the reanalysis data can be found in studies by Kalnay et al. (99) and Kanamitsu et al. (00). The reanalysis

98 J.-H. Kim et al. monthly data are available at 7 pressure levels (000, 9, 80, 700, 00, 00, 00, 0, 00, 0, 00, 70, 0, 0, 0 and 0 hpa) over.. latitude longitude grids. The NFL is determined from the monthly geopotential height of the 0 Cisotherm, which can be derived by an interpolation of the monthly air temperature profile at the 7 pressure levels. The algorithm used to obtain the NFL is based on a report by Harris et al. (000). The algorithm searches for zero crossings in the air temperature profile between 000 and 00 hpa. If there is only one zero crossing, the algorithm considers the zero crossing height as the altitude of the freezing level. In the case of multiple zero crossings due to temperature inversions, the lowest height is taken as the freezing level. If no zero crossings are found, the freezing level is not computed. In order to maintain consistency in the spatial resolution with the other data sets used in this study, the NFL data over the.. latitude longitude grids are averaged over the same grid boxes. The seasonal patterns of the NFL averaged for 998 007 are shown in figure. As in the other data sets, the distribution pattern is zonal and high NFLs are usually found over the tropics for all seasons and in the mid-latitudes in the summer hemisphere. However, a somewhat different pattern appears in the middle latitudes in the winter hemisphere. That is, the seasonal mean NFLs are more zonally symmetric and have greater latitudinal gradients than the TFLs and BBHs. Furthermore, the lowest NFL values in the northern and southern winter are significantly different. The NFL values in the northern and southern winter are 0. and.7 km, respectively. These findings may confirm that the NFL is directly derived from the temperature profile and its distribution follows temporal and spatial variations in the temperature.. Differences between the proxy variables The differences between the three data sets are discussed in this section. The differences between the TFL and BBH (TFL minus BBH) for each season are presented in figure. The regions of missing data near the west coasts of continents in the subtropics, which are classified as dry regions, are due to insufficient precipitation events with the bright band. The difference over the tropics throughout the seasons is generally less than km. A small difference is also found in the summer hemisphere, while the difference is usually larger than km in the winter hemisphere. The global means of the difference vary from 7 to km with the seasons. Maximum differences are found in the mid-latitudes within a range of..7 km. Maps of the difference between the TFL and NFL for four seasons are shown in figure. The general pattern is similar to that of the differences between the TFL and BBH (figure ), which are characterized by smaller differences in the tropics and the summer hemisphere but larger differences in the mid-latitudes during the winter season. However, compared with the difference between the TFL and BBH, the small differences between the TFL and NFL are smaller (less than 0. km) and the large differences tend to be larger. The largest differences are also more variable (.7.7 km) and the largest disagreement between the TFL and NFL (.7 km) occurs over East Asia between 0 Nand 0 N latitude. The global mean differences between the TFL and NFL for four seasons, which range from 0.0 to 0. km, are consistently smaller than those between the TFL and BBH. In addition, the NFL is higher than the TFL (negative value in figure ) for all seasons mostly over oceanic dry regions. Such a finding may be explained by a difference in the characteristics of the TFL and NFL estimations. The TFL estimates are based on vertically integrated water vapour while the NFL

Proxy variables of the rain column height 99 N N (a) Mean =., Maximum =.0, Minimum =.9 N N E E 8 W W (b) Mean =.9, Maximum =.9, Minimum =. N N N N E E 8 W W (c) N Mean =., Maximum =.0, Minimum =.7 N N N E E 8 W W (d) N Mean =., Maximum =., Minimum = 0. N N N E E 8 W W Figure. Seasonal means of the freezing level derived from the NCEP reanalysis data (NFL) for four seasons during the period from 998 to 007. The contour interval is 0. km. is determined by surface and atmospheric temperatures. Dry regions with less water vapour are distinguished from other regions through the difference between the TFL and NFL. The zonal mean differences between the TFL and BBH and between the TFL and NFL for four seasons in 998 are illustrated in figure. The difference between the TFL and BBH (upper panel) is generally less than or about km over the tropics between 0 Nand0 S for all seasons. A larger difference (>. km) and greater seasonal variability tend to be found at latitudes higher than 0 0 in the winter hemisphere. The transition to a lower difference and smaller seasonal variability occurs during the spring and fall. A similar pattern is found for the difference between the TFL and NFL (lower panel). The differences are small and the seasonal variation

700 J.-H. Kim et al. N N (a) Mean = 0.9, Maximum =. N N E E 8 W W N N (b) Mean =, Maximum =. N N E E 8 W W (c) N Mean = 0.99, Maximum =.7 N N N E E 8 W W (d) N Mean = 7, Maximum =. N N N E E 8 W W Figure. Mean differences between the TFL and BBH for four seasons during the 0 years from 998 to 007. The contours are drawn at a 0. km interval. is not obvious in the tropics between 0 Nand0 S. However, the magnitudes and variability of the difference are considerably large in the mid-latitudes during the winter. In particular, a difference of approximately km exists in the northern winter. Negative values of the difference (NFL is greater than TFL) were mostly observed in the subtropics during the summer. This is attributed to the increasing NFL that arises from the high surface temperature during the summer. The zonal mean cross sections of the TFL, BBH and NFL for each month are shown in figure 7. The TFL between and km is generally uniform with a slight depression in the mid-latitudes. The TFL, as discussed in, is estimated from a pair of brightness temperatures from two microwave emission channels only when it is raining. As such, the TFL estimation algorithm (Wilheit et al. 99) considers that the climatological values of the freezing level (0 C isotherm level) inside precipitating

Proxy variables of the rain column height 70 N N (a) Mean = 0.0, Maximum =.0 N N E E 8 W W (b) Mean = 0., Maximum =.09 N N N N E E 8 W W (c) Mean = 0., Maximum =.7 N N N N E E 8 W W (d) Mean = 0., Maximum =.7 N N N N E E 8 W W Figure. Mean differences between the TFL and NFL for four seasons during the 0 years from 998 to 007. The contours are drawn at a 0. km interval. systems are not strongly dependent on the season and geolocation. The BBH and NFL over the tropics and subtropics exhibit a small level of seasonal variability, as found for the TFL. However, the BBH and NFL decrease with increasing latitude outside the subtropics in both hemispheres. In particular, the NFL decreases to about km near 0 Nand0 S during the winter and thus, the differences between the NFL and TFL become significantly large. The large variability in the NFL outside the tropics and subtropics may be attributed to inhomogeneous distributions of temperature for the different seasons. It is also found that the differences tend to be larger in the northern hemisphere than in the southern hemisphere. This feature may be associated with the smaller thermal inertia from the larger amount of landmass in the northern hemisphere. The BBH and NFL exhibit a similar pattern with a difference of about

70 J.-H. Kim et al. TFL minus BBH (km) 0 MAM JJA SON DJF TFL minus NFL (km) N N N N 0 MAM JJA SON DJF N N N N Figure. Zonal mean differences of the three variables for the 0 years from 998 to 007. The upper panel indicates the differences between the TFL and BBH and the lower panel shows the differences between the TFL and NFL. Spring (MAM), summer (JJA), fall (SON) and winter (DJF) are indicated by green, red, yellow and blue dots, respectively. 00 700 m, except at latitudes higher than about. According to Harris et al. (000) the average difference for 998 is around 00 m, while the average zonal difference ranges from 00 to 000 m. The differences obtained from this study are very similar to the results reported by Harris et al. (000). The similarity between the BBH and NFL suggests that the BBH is closely related to the temperature variability. The other notable feature is that the difference between the BBH and NFL decreases in the high latitudes. The BBH is even higher than the NFL by about 00 m near 0 latitude. The reasons for this unusual pattern are not clear. However, according to Thurai et al. (00), this pattern is likely caused by sampling errors produced by the TPR. That is, radar backscatter may be affected by a surface echo when the BBH is low, particularly below about km. This unnecessary signal causes the maximum reflectivity to appear above km, resulting in an overestimation of the BBH.. Estimation of monthly oceanic rainfalls A physical statistical algorithm based on microwave emission brightness temperature histograms (METH) was developed by Wilheit et al. (99) and was used to estimate the monthly rainfall over the oceans. The METH technique is based on a brightness temperature rain rate (T B R) relationship derived from the radiative transfer calculation of a cloud model. The cloud model assumes a Marshall Palmer distribution of raindrops (Marshall and Palmer 98) from the ocean surface to the freezing level (0 C isotherm). A layer of clouds containing 0. g m of water is assumed in the layer 0. km immediately below the freezing level. A constant lapse rate of. Ckm and

Proxy variables of the rain column height 70 January N 0 0 0 0 0 0 July N 0 0 0 0 0 0 S February N 0 0 0 0 0 0 March N 0 0 0 0 0 0 April N 0 0 0 0 0 0 May N 0 0 0 0 0 0 June N 0 0 0 0 0 0 August N 0 0 0 0 0 0 October N 0 0 0 0 0 0 November N 0 0 0 0 0 0 September N 0 0 0 0 0 0 December N 0 0 0 0 0 0 Figure 7. Monthly zonal mean cross sections of the TFL (dashed line), BBH (dotted line) and NFL (solid line) for a period of 0 years between 998 and 007.

70 J.-H. Kim et al. a relative humidity that increases linearly with height from 80% at the ocean surface to 00% at the freezing level are also assumed. The algorithm uses a combination channel of twice 9. GHz minus. GHz-V for the TMI. Two vertically polarized channels are selected because the effect of water vapour on the rainfall signals is mitigated. The T B over a space and time box is attained and a histogram is computed. The computed T B histograms are iteratively fitted to a rain rate distribution via the T B R relationship. The rain rate distribution is assumed to be mixed lognormal. Since the humidity and temperature profiles are specified, the freezing level is a proxy of the columnar humidity content. The T B responds to the integrated effect of precipitation drops over a rain column. Errors in the freezing level will then negatively impact the rain rate (Chiu and Chang 000). The three variables in this study (TFL, BBH and NFL) are applied to the METH algorithm so as to estimate the monthly mean rainfalls with a resolution of in longitude and latitude. Examples of the retrieved monthly rainfalls for January of 998 are presented in figure 8. Major precipitation regions, such as the Indian Ocean, the Inter-Tropical Convergence Zone (ITCZ) and the South Pacific Convergence Zone (SPCZ), where warm sea surface temperatures (SST) and sufficient moisture are supplied from the tropics, are well distinguished in all three cases. High precipitation areas in the mid-latitudes between and 0 N are also identified. However, differences in the rainfall intensity are somewhat large. Monthly mean (a) Mean = 9, Maximum = 0.7, Minimum = 0 N N N N E E 8 W W (b) Mean = 9, Maximum = 0.97, Minimum = 0 N N N N E E 8 W W (c) Mean = 0., Maximum =.7, Minimum = 0 N N N N E E 8 W W (mm hour ) (mm hour ) (mm hour ) Figure 8. Monthly mean rainfalls retrieved by the METH algorithm with (a) the TFL, (b) BBH and (c) NFL for January 998.

Proxy variables of the rain column height 70 (a) Mean = 8, Maximum = 0.9, Minimum = 0 N N N N E E 8 W W (b) Mean = 8, Maximum = 0, Minimum = 0 N N N N E E 8 W W (c) Mean = 8, Maximum =, Minimum = 0 N N N N E E 8 W W Figure 9. Monthly mean rainfalls retrieved by the METH algorithm with (a) the TFL, (b) BBH and (c) NFL for July 998. rainfalls with the TFL, BBH and NFL averaged over the region are 0., and mm hour, respectively. It should be noted that the BBH is found approximately 00 m below the freezing level, as shown in figure 7. BBH + 00 m is then considered as the rain column height in the monthly rainfall estimations attained with the BBH (figure 8(b)). Maps of the monthly mean rainfalls for July 998 are shown in Figure 9. Similar to figure 8, the distributions are predominantly zonal. Differences between the rainfalls in the mid-latitudes in the southern hemisphere are not as large as in January. The mean rain rates retrieved with TFL, BBH and NFL over the region between and 0 S are 9, 0. and 0. mm hour, respectively. Zonally averaged rainfalls retrieved by the METH algorithm with the three variables for each month in 998 are shown in figure 0. The near-surface rain rate observed from the TPR sensor (C in TRMM data classification) is also included as a reference. Zonal mean values of each rainfall data set are obtained by averaging the monthly mean rainfalls over -wide latitudinal belts. In the tropics and subtropics, differences between the three retrieved and TPR rainfalls appear to be small during all seasons. Meanwhile, there is a distinct tendency for differences to be larger in the mid-latitudes in the winter hemisphere. In particular, the rainfalls estimated with the NFL exhibit larger deviations from the other rainfalls. The difference is found to be larger in the northern winter than in the southern winter. (mm hour ) (mm hour ) (mm hour )

70 J.-H. Kim et al. Rain rate (mm hour ) Rain rate (mm hour ) Rain rate (mm hour ) Rain rate (mm hour ) Rain rate (mm hour ) January (998) N 0 0 0 0S 0 0 February (998) N 0 0 0 0S 0 0 March (998) N 0 0 0 0S 0 0 April (998) N 0 0 0 0S 0 0 May (998) N 0 0 0 0S 0 0 Rain rate (mm hour ) Rain rate (mm hour ) Rain rate (mm hour ) Rain rate (mm hour ) Rain rate (mm hour ) July (998) N 0 0 0 0S 0 0 August (998) N 0 0 0 0S 0 0 September (998) N 0 0 0 0S 0 0 October (998) N 0 0 0 0S 0 0 November (998) N 0 0 0 0S 0 0 Rain rate (mm hour ) June (998) N 0 0 0 0S 0 0 Rain rate (mm hour ) December (998) N 0 0 0 0S 0 0 Figure 0. Zonally averaged monthly rain rate (mm hour ) retrieved with the TFL (dashed line), BBH (dotted line), NFL (solid line) and observed from the TPR (dark solid line) in 998.

Proxy variables of the rain column height 707. Implication for rainfall estimation. Impacts of freezing-level altitudes on rainfall estimations As stated in and, different assumptions are involved in the determination of the three variables (TFL, BBH and NFL). In particular, the TFL and BBH are estimated under the assumption of rain existence, whereas the NFL is obtained from temperature profiles under all weather conditions. For this reason, the three variables are in good agreement in the tropics, where the temperature variability is small. However, the differences between the three variables increase outside the tropics, where the temperature is substantially affected by the seasons. In this section, the impact of the rain column heights on passive microwave rainfall measurements is discussed. The differences between the monthly rainfalls estimated by the METH algorithm with the inputs of the three variables and the TPR-derived rainfalls were investigated. The differences as a function of each variable for the winter (December January February (DJF)) of 998 are shown in figure. The difference values in the mid-latitudes between and 0 N (the northern hemisphere winter) and between and 0 S (the southern hemisphere summer) are denoted by blue and red dots, respectively. Black dots correspond to the values from other latitudes. The TFL-derived rainfalls compare reasonably well with the TPR rainfalls. The BBH and NFL-derived rainfalls are also similar to the TPR rainfalls mainly in the region with values higher than km. Difference (mm hour ) 0. (a) 0.. TPR minus TFL.0 0 TFL (km) Difference (mm hour ) 0. 0.. (c) Difference (mm hour ) 0. 0.. TPR minus NFL.0 0 NFL (km) (b) TPR minus BBH.0 0 BBH (km) Figure. Differences between the rainfalls retrieved by the METH algorithm and the TPR as a function of the proxy variables in 998 (January, November and December). The difference values in the mid-latitudes between and 0 N (the northern hemisphere winter) and between and 0 S (the southern hemisphere summer) are denoted by blue and red dots, respectively. Black dots correspond to the values from other latitudes.

708 J.-H. Kim et al. However, considerable amounts of blue and red dots found in the regions with a lower BBH or NFL exhibit larger differences from the TPR rainfalls. The larger differences are significant, particularly in the mid-latitudes of the northern hemisphere winter (blue dots in figure (c)). The attained results demonstrate that an underestimation of the rain column height results in an overestimation of the rainfall.. Low freezing-level correction An attempt was made to use empirical relationships in order to correct overestimates of the monthly rainfalls due to underestimates of the altitude of the freezing level. Such relationships are statistically obtained from the differences between the retrieval and TPR rainfalls for the three years from 998 to 000. Examples of the empirical relationships can be seen as orange dots in figure (b) and (c). The dots are connected by thick orange lines so as to better describe the monotonically increasing correction effect with decreasing values of BBH or NFL. In order to develop average values of the differences (or the correction constants) in the altitude categories, individual statistics for the three years are estimated and averaged. The correction constants for the three years and their respective averaged values are shown in table for the BBH and table for the NFL. The correction constants averaged for the three-year period were applied to the retrieved rainfalls; the results are presented in figure. The correction is not made for the case of the TFL because the rainfalls derived with the TFL compare well with the TPR rainfalls (figure (a)). The scatter plots between the retrieved rainfalls with the BBH and TPR rainfalls before and after the correction are shown in figure (b) and (c), respectively. Filled circles are used to discriminate the data pairs in the mid-latitudes between and 0 N. The other data pairs are represented by empty circles. Retrieval statistics including the correlation coefficient (corr), the root mean squared (RMS) error and the bias are slightly improved. A more significant improvement in the correction is found for the case of the NFL (figure (d) and (e)). It seems that the larger spread of the filled circles, which indicate data pairs in the winter, tends to be reduced after the correction.. Summary and conclusions In this study, three different variables (TFL, BBH and NFL) that can be used as proxy variables of the height of a rain column in the retrieval of rainfall intensity from passive microwave sensors over the oceans were compared. The comparison of the three variables was performed over a latitude longitude grid box in the TRMM domain Table. Mean difference between the TPR-measured rainfalls and the retrieved rainfalls from the METH algorithm as a function of the BBH. BBH (km) 0 998 0. 88 0 999 0. 7 07 8 000 0.9 78 0 8 yearaverage 0. 79 0

Proxy variables of the rain column height 709 Table. Mean difference between the TPR-measured rainfalls and the retrieved rainfalls from the METH algorithm as a function of the NFL. NFL (km) 0 998. 0.0 0. 0 999 0.9 0.9 0 07 000 0.9 0 0 9 yearaverage.0 0. 0 0 (0 N 0 S) for a period of 0 years from 998 to 007. Seasonal means of the variables were relatively similar in the tropics and ranged from to km. Small seasonal variations were also found in the tropical oceans. However, the differences between the three variables were more noticeable in the mid-latitudes. The 0 year averaged seasonal differences between the TFL and NFL were much larger in magnitude and ranged from.7 to.7 km. The seasonal differences between the TFL and BBH were also considerable, ranging from. to.7 km. There was also some tendency for the differences to be larger in the winter hemisphere. A maximum in the differences (about km) existed in the northern winter. This tendency was also confirmed from a comparison of the zonal mean cross sections of the three variables for each month. The zonal means of the BBH and NFL rapidly decreased towards the high latitudes during the winter, whereas those of the TFL were not significantly dependent upon the latitudes. This result is consistent with that reported by Chiu and Chang (000). The reasons for such a larger observed difference in the high latitudes in the winter hemisphere are related to the different assumptions involved in the estimation of each variable. Major assumptions in the estimation of the TFL include the existence of rain and the use of the 99th percentile of the brightness temperature data at two emission channels (9. and. GHz-V) in rainy conditions. According to Chiu and Chang (000), the use of the top first percentile of the brightness temperature data may be inappropriate for estimating the freezing level outside the tropics because there is a larger temperature and moisture profile variability in these regions. In fact, in order to remedy the problem, the algorithm that estimates the freezing level (Wilheit et al. 99) assumes km as a minimum freezing level. Therefore, the distributions of the high freezing levels (about km) derived from the SSM/I are very similar to those of the columnar water vapour, suggesting that the freezing level from the SSM/I is an index of the columnar water content in rainy conditions. On the other hand, the BBH is identified by a larger magnitude in the radar reflectivity profile under stratiform precipitation. Purely stratiform precipitation usually occurs in the well-stratified lower troposphere (Houze 997), indicating that the BBH may be related to the atmospheric temperature profiles in clouds that produce rain. The observed dependence of the NFL on the atmospheric temperature profiles is similar to that found for the BBH. However, the NFL is estimated by including non-raining conditions, which account for most of the atmospheric temperature data. The three variables in this study were applied to the METH algorithm as a proxy variable of the rain column height. The algorithm estimates monthly oceanic rainfalls on a latitude longitude grid box from the brightness temperatures observed at two low frequencies of the TMI. The impact of the proxy variables on the monthly

70 J.-H. Kim et al. Retrieved rain rate (mm hour ) Retrieved rain rate (mm hour ) (b) (d) Retrieved rain rate (mm hour ) (a) BBH case NFL case TLF case Corr = 0.9 RMS = Bias = 0 TPR rain rate (mm hour ) Corr = 7 RMS = Bias = 08 TPR rain rate (mm hour ) Corr = 8 RMS = 0.8 Bias = TPR rain rate (mm hour ) Retrieved rain rate (mm hour ) Retrieved rain rate (mm hour ) (c) BBH case (after correction) Corr = 0.9 RMS = Bias = 0 TPR rain rate (mm hour ) NFL case (after correction) (e) Corr = 0 RMS = 9 Bias = 08 TPR rain rate (mm hour ) Figure. Scatter plots of the TPR-measured rainfalls and METH-retrieved rainfalls using (a) the TFL, (b) BBH and (d) NFL during three months in 998. Empirically corrected rainfalls are also presented in (c) for BBH and (e) for NFL. Filled circles are used to discriminate the data pairs in the mid-latitudes between and 0 N. The other data pairs are represented by empty circles.

Proxy variables of the rain column height 7 rainfall estimates was analysed by comparing the TPR and the METH-estimated rainfalls. The comparison revealed that an underestimate (overestimate) of the rain column height causes an overestimate (underestimate) of the rainfall for a given brightness temperature data set. That is, the METH-estimated rainfalls with an input of the BBH or NFL were overestimated when compared with the TPR-derived rainfalls in the midlatitudes during the winter, while the rainfall estimates with the TFL were comparable with the rainfalls from the TPR. An attempt was made to correct the overestimated rainfalls when a low BBH and NFL were associated with the mid-latitudes. The corrections were based on the empirical relationships between the differences (METH-estimated rainfall minus the TPR-measured rainfalls) and each proxy variable (BBH or NFL) averaged over a period of three years from 998 to 000. The correction of a low BBH yielded a slight improvement in the METH-estimated rainfalls. After the correction of a low NFL, the bias, RMS error and correlation between the TPR and the METH-estimated rainfalls were also improved. The results of this study suggest that the TFL measured from 9. and. GHz-V channels appears to better represent the rain column height. However, they also suggest that the BBH and NFL can be utilized as a proxy variable of the rain column height in rainfall estimations if low values of the BBH and NFL are appropriately corrected. In particular, the climatology of the BBH or NFL may be helpful for rainfall estimation when the two low-frequency channels are not available. Acknowledgement This work was funded by the Korea Meteorological Administration Research and Development Programme under Grant CATER 00-. References CHIU, L.S. and CHANG, A.T.C., 000, Oceanic rain column height derived from SSM/I. Journal of Climate,, pp.. HARRIS, G.N., BOWMAN, K.P. and SHIN, D.-B., 000, Comparison of freezing-level altitudes from the NCEP reanalysis with TRMM precipitation radar bright band data. Journal of Climate,, pp. 7 8. HOUZE, R.A., 997, Stratiform precipitation in regions of convection. Bulletin of the American Meteorological Society, 78, pp. 79 9. KALNAY, E., KANAMITSU, M., KISTLER, R., COLLINS, W., DEAVEN, D., GANDIN, L., IREDELL, M., SAHA, S., WHITE, G., WOOLLEN, J., ZHU, Y., LEETMAA, A., REYNOLDS, R., CHELLIAH, M., EBISUZAKI, W., HIGGINS, W., JANOWIAK, J., MO, K.C., ROPELEWSKI, C., WANG, J., JENNE, R. and JOSEPH, D., 99, The NCEP/NCAR 0-year reanalysis project. Bulletin of the American Meteorological Society, 77, pp. 7 7. KANAMITSU, M., EBISUZAKI, W., WOOLLEN, J., YANG, S.-K., HNILO, J.J., FIORINO, M. and POTTER, G.L., 00, NCEP-DOE AMIP-II reanalysis. Bulletin of the American Meteorological Society, 8, pp.. MARSHALL, J.S. and PALMER, W.M., 98, The distribution of raindrops with size. Journal of Meteorology,, pp.. MENEGHINI., R. and KOZU, T., 990, Spaceborne Weather Radar (Norwood, MA: Artech House). SHIN, D.-B., 0, Spatial information of high frequency brightness temperatures for passive microwave rainfall retrievals. International Journal of Remote Sensing,, pp. 7.

7 J.-H. Kim et al. SHIN, D.-B., NORTH, G.R. and BOWMAN, K.P., 000, A summary of reflectivity profiles from the first year of TRMM radar data. Journal of Climate,, pp. 07 08. THURAI, M., IGUCHI, T., GODDARD, J.W.F., ONG, J.T. and AWAKA, J., 00, Melting layer model evaluation in Singapore. In Twelfth International Conference on Antennas and Propagation, IEEE Conference Publication No. 9, March April 00, University of Exeter, UK, vol., pp. 7 0. WANG, S.A., 99, Modeling the beamfilling correction for microwave retrieval of oceanic rainfall. PhD dissertation, Texas A&M University, College Station, TX. WILHEIT, T.T., CHANG, A.T.C. and CHIU, L.S., 99, Retrieval of monthly rainfall indices from microwave radiometric measurement using probability distribution functions. Journal of Atmospheric and Oceanic Technology, 8, pp. 8. WILHEIT, T.T., CHANG, A.T.C., RAO, M.S.V., RODGERS,E.B.andTHEON, J.S., 997, A satellite technique for quantitatively mapping rainfall rates over the oceans. Journal of Applied Meteorology,, pp. 0. YIHUI, D. and CHAN, J.C.L., 00, The East Asian summer monsoon: an overview. Meteorology and Atmospheric Physics, 89, pp. 7.