1. Introduction

Passive microwave (PMW) measurements are widely used for estimating rain rate from space because of the interaction of microwave radiation with cloud droplets and precipitation-size hydrometeors. The previous literature demonstrates that the spaceborne microwave radiometer-based rain retrieval algorithms are superior to infrared/visible-based algorithms (Wilheit et al. 1994; Ebert and Manton 1998; Smith et al. 1998; Yang 2004). The interaction between microwave radiation and cloud hydrometeors are frequency dependent—absorption and emission primarily take place at lower frequencies while scattering takes place at higher frequencies (Janssen 1993, 295–304). Because of such interactions it is possible to physically invert the measured radiation for the rainfall estimates (e.g., Smith et al. 1992; Mugnai et al. 1993; Kummerow et al. 1996, 2001; Yang and Smith 1999; Olson et al. 2006).

Emissions at low frequencies are more directly related to the precipitation processes, and thus the emission signals provide better physical data for rainfall estimates. However, the use of emission signals is suitable for the ocean because the high surface emissivity (∼0.8–0.9) over the land can obscure emitted radiation from the hydrometeors (Janssen 1993; Ferraro et al. 1998).

On the other hand, scattering signals can be used for rain estimates over both land and ocean because the scattering from clouds is attributed mainly to the upper part of clouds where ice particles are abundant (Grody 1991; Ferraro and Marks 1995). However, the scattering-based algorithm retains difficulties in identifying “warm rain,” which occurs without substantial upper-level ice particles, as often found in the orographic precipitation described by Houze (1993, 502–538). Consistent with the known problems, Todd and Bailey (1995) showed that there are difficulties in detecting topographically induced precipitation, even with microwave measurements, over orographical areas such as the South Wales in the United Kingdom, where the seeder–feeder enhancement mechanism described by Bergeron (1965) has been observed (Browning et al. 1974). Porcú et al. (2002) also showed that underestimates of the rainfall from both infrared and microwave radiation measurements are very common over the terrain areas, suggesting that the topographical effect should be incorporated in the rain retrieval system in order to enhance the retrieval accuracy.

Thus, the inclusion of topographic effects in the retrieval system is much needed to improve the accuracy of microwave-based rainfall estimates over complex terrain areas where radar and rain gauge measurements are limited. Efforts were made to obtain better rain estimates over complex terrain areas using various diagnostic models for evaluating the topographical impact on the detailed horizontal distribution and the rainfall intensity (Collier 1975; Bell 1978; Sinclair 1994; Misumi et al. 2001; Roe 2005). From those efforts, it was shown that the diagnostic models are able to produce precipitation fields down to a few kilometers by combining large-scale wind, temperature, and moisture data with detailed topographical information.

Vicente et al. (2002), in a rare study of this type, developed a topographic correction technique for better IR-based rain retrievals. The technique incorporates interactions between the wind vector and the slope as a multiplier to enhance or diminish the IR-based rainfall estimates. Accordingly, it is important to examine how the PMW-based technique resolves the topographically induced rainfall. Such studies will lead to a better understanding of the PMW retrieval mechanism over terrain areas and thus the obtained results can be applied for improving the capability of the PMW-based algorithms.

In line with the need to include the topographic effect, we examine how the topography over the Korean peninsula influences rain estimates from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) measurements, and develop TMI-based rainfall estimates over the Korean terrain areas. This study was motivated by the fact that more than two-thirds of the Korean peninsula is covered by relatively complex terrain and thus any improvement of satellite estimates of rainfall needs to include the terrain effect.

2. Training data and rain algorithm

We intend to investigate the topographical effect on the microwave rain retrieval from the TMI measurements. The TRMM satellite was launched onto a nonsunsynchronous orbit with a low inclination angle of 35° on 22 November 1997 for measuring the tropical precipitation by the United States and Japan (Kummerow et al. 1998). The TMI measures microwave radiances at 10.65, 19.35, 21.3, 37, and 85.5 GHz. Each frequency has one vertical and one horizontal polarized channel, except for the 21.3 GHz channel, which has the vertical polarization only.

The topographical effect on the TMI rain retrieval is examined using a training dataset produced by numerical mesoscale model simulations in conjunction with radiative transfer calculations. The results obtained are incorporated into the TMI rain retrieval algorithm to account for the topography effect. The procedures employed in this paper are shown in the schematic diagram (Fig. 1). Numerical model outputs such as temperature (T), water vapor (q), and the hydrometeor profiles over the Korean peninsula are used as inputs into the microwave radiative transfer model to simulate the TMI brightness temperatures (Tb) at the top of the atmosphere (TOA). The scattering-based rainfall algorithm (Ferraro and Marks 1995) is used for the rain-rate (RR_S) estimation from the simulated TMI brightness temperatures. Estimated rain rates are then compared with the model-produced rain rates (RR_M) in order to examine the topographical effect on the rain retrieval. Finally, the obtained topographical correction factors are included in the TMI rain algorithm as a function of terrain slope (S), lower-level wind (V), and moisture parameters (q).

For validation, the TMI rain rates are compared with ground-based Automatic Weather System (AWS) rain gauge measurements over the Korean peninsula. About 520 AWS rain gauges, operated by Korea Meteorological Administration (KMA), measure the accumulated rain every minute (see Fig. 2 for information about the approximately 520 AWS stations in South Korea). The measurement system consists of automatically reporting tipping rain gauges with 0.5-mm resolution and with about 15-km spatial density. For a comparison of the TMI instantaneous rain estimates with gauge measurements, 1-min rainfall data at a given station are averaged by applying a ±10-min time window centered on the TMI observation time.

b. Rain-rate estimation

For the estimation of the rain rate from simulated TMI brightness temperatures, we use the scattering index (SI; Grody 1991) given in the following equation:

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where Tb and here V represent the brightness temperature and vertically polarized component, respectively. The rain estimation algorithm of using SI was first developed for the Special Sensor Microwave Imager measurements by relating the SI to the radar estimates of rain (Ferraro and Marks 1995). Because the difference in brightness temperature over the land between 21 and 22 GHz is about 0.7 K (corresponding to the SI difference of about 0.9) in the presence of rain, and thus is negligible in the rain estimates, as described in Kummerow et al. (2001), the Tb(22V) in Eq. (1) is replaced by the 21-GHz brightness temperature for TMI. The TMI rain rate is then obtained by relating the TMI-based SI to the model-produced rain rate. Applying TMI brightness temperatures simulated at five model times (10, 11, 12, 13, and 14 h of the simulation) for the 29 April 2003 case, the bias-removed TMI rain estimation algorithm based on model-produced rain rates is obtained as follows:

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where RR_S is the retrieved rain rate (mm h⁻¹). Grody (1991) found that a value of SI greater than 10 K is a good global indicator for the rain. We use a 10-K threshold to screen out no-rain pixels.

The retrieved rain rates RR_S from Eq. (2) are shown in Figs. 3d and 4d. Overall retrieved rainfall shows good agreement with the modeled rainfall in both pattern and magnitude. The retrieved rainfall, however, seems to be weak over mountain areas in the middle south and east areas of Korea, where topographically induced upward motions are expected from the wind field and topography.

3. Development of topographical correction method: Simulation study

In examining the topographical effect on the TMI rain retrieval, the differences between the model-produced rain rate and the retrieved rain rate (i.e., RR_M − RR_S) are related to the topographically forced upslope motion in combination with terrain slope (S), lower-level wind (V), and horizontal moisture flux (qV).

a. Topographical impact on rainfall retrieval

The topographical effect is examined by relating the wind vector (V) to the gradient of the local terrain height (∇Z_h) in the wind direction. It is assumed that the atmospheric vertical motion V · S is forced by wind V blowing over a terrain area whose net slope is S. At a given location X, the net slope S is determined by a type of an averaged terrain height within the horizontal length scale of 2n pixels (2n × 3 km in length) centered at X. This approach is the same as that in Vicente et al. (2002), except for the horizontal length scale for the slope calculation.

Let us consider 2n grid points centered at X with one point A located at any point between X − n and X. Then, the terrain slope (S_AB) between the point A (varying from X − n to X) and one downwind point B (varying from A + 1 to A + n for a given A) is defined by

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where (Z_B − Z_A) is the height difference between two points A and B, while x(B) − x(A) is the horizontal distance between A and B. Because the point B moves downwind from point (A + 1) to point (A + n), the corresponding slopes [i.e., S⁽¹⁾_AB, S⁽²⁾_AB, S⁽³⁾_AB, . . . , S⁽ⁿ⁾_AB] can be calculated for a given point A. The slope at point A (i.e., S_A) is then denoted as a maximum slope out of n values of S_AB; that is,

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Because the point A varies from a point X − n to a point X, we take the average of n + 1 maximum values to get a net slope S for a given location X; that is,

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Using this method, we can take the weighted average of the maximum slopes within the 2n pixels centered at X. Once S is determined, the vertical velocity forced by wind of magnitude V at a point X can be calculated using an inner product of two vectors (i.e., V · S).

The relationship between the topography-forced upslope motion (V · S) and the rain-rate difference (RR_M − RR_S) is examined using a varying horizontal scale for the slope calculation (n × 3 km) and the pressure level for wind. We excluded cases only if both RR_M and RR_S are zero. Here, RR_M − RR_S is thought in part to be due to the orography-related warm rain that is not resolved by the microwave scattering signal, as shown in the positive relationship between RR_M − RR_S and upslope motion (Fig. 5).

Figure 5 shows a scatter diagram of the RR_M − RR_S versus V · S for n = 5 (i.e., 15 km) and wind at the 850-hPa level. The positive correlation of 0.41 noted in the diagram suggests that the satellite-based scattering algorithm underestimates rain rate in the presence of topographically forced vertical motion. This underestimate seems to be due to the physically indirect rainfall estimation based on ice-phase particles aloft, effectively ignoring warm-rain processes such as upslope condensation below the freezing level and the “seeder and feeder” mechanism. In other words, the scattering-based algorithm may not fully detect orographically generated precipitating cloud below the freezing level or orographically induced feeder cloud, resulting in an underestimate of rainfall over the mountain area.

Correlation coefficients between V · S and RR_M − RR_S for four horizontal length scales (i.e., 9, 12, 15, and 18 km) and winds at three pressure levels (800, 850, and 900 hPa) and at the surface are summarized in Table 1. In this analysis, the correlation coefficients for both up- and downstream regions are calculated separately. Based on the Pearson correlation analysis, statistics are given in Table 1 with a 99% confidence level. Although some correlation coefficients are very low, those have a high confidence level because of large data samples. In Table 1, the highest correlation coefficient of 0.41 is found for the net slope (S) computed with a 15-km horizontal scale and the wind vector (V) taken at the 850-hPa level. Not surprisingly, the correlation coefficients noted in the downstream region appear less meaningful. Because the highest correlation is found at the 15-km mean slope and with the 850-hPa wind, further analyses were done with those conditions.

b. Topographical correction methods

To include the orographic factors in the TMI rain algorithm, the rain-rate difference (RR_M − RR_S) is now regressed in the following three different ways: 1) topographically forced upslope motion (V · S); 2) V · S, with the water vapor mixing ratio (q) at the 850-hPa pressure level to express the upward moisture transport by topographically induced upslope motion; and 3) V · S, with low-level moisture convergence (Q_con) defined as an integrated moisture flux convergence from the surface to the 800-hPa level. In this approach, V · S is estimated from the 15-km mean slope and 850-hPa wind, and Q_con is given as follows:

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In Eq. (6) ρ_υ is the water vapor density (kg m⁻³).

Now the regressed equations between the rain-rate difference (RR_M − RR_S) and topographical correction factors are added to the rain retrieval algorithm given in Eq. (2). The resultant three correction algorithms are as follows:

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From the regression analyses between RR_M − RR_S and three topographical correction factors, a new offset of 0.8 is noted in all three equations. Results are interpreted in such way that the mean topographic effect is already included in the offset value of 1.7 in Eq. (2) because the simulated Tbs were related to model-produced rain rate in an average sense. Because of that, when either the wind speed or slope is near zero, the rainfall should actually decrease.

In Eqs. (7)–(9), RR₁, RR₂, and RR₃ represent rain rate (mm h⁻¹) predicted by the three correction methods, respectively, but only for the upslope regions. Water vapor mixing ratio q (g kg⁻¹) and the low-level moisture convergence Q_con (10⁻³ kg m⁻² s⁻¹) are given. The number of sample data used for developing the correction methods and associated correlation coefficients between model rain rates and four retrieved rain rates computed using Eq. (2) and Eqs. (7)–(9) are presented in Table 2.

4. Application to model simulations

In examining the performance of the developed correction methods, three algorithms [Eqs. (7)–(9)] were applied to the MM5 simulations for the 27 August 2003 case. Brightness temperatures at TMI frequencies were again obtained using the MM5 simulations as inputs to the microwave radiative transfer model as described in section 2a. The rain rates without correction (RR_s) were obtained from the rain estimation algorithm given in Eq. (2), while the corrected rain rates of RR₁, RR₂, and RR₃ were obtained by applying methods 1, 2, and 3 in Eqs. (7)–(9), respectively.

Two outlined areas (1° × 1° boxes) marked “A” and “B” in Fig. 6 were chosen for the comparison of rain rates without correction (hereinafter “TMI only”) with corrected values. It is because those two areas are located in relatively high mountainous areas that the orographically induced rain rates can be expected when the 850-hPa winds are taken into account. Estimated rain rates averaged over each box are used for examining the three correction algorithms.

The TMI-only rain rates (RR_s) obtained from the simulated TMI brightness temperatures at the model time from the 16th to 23rd hour were averaged at boxes A and B, and their time series are shown in Fig. 7. In both areas, rain rates gradually increased from the 18th hour of the model time, and the heaviest rain rates are found at the 21st hour of the model time. After the 21st hour, rain rates decreased rapidly in the following hours.

For a given model time, TMI-only and corrected rain rates were estimated in each 0.1° × 0.1° subgrid, yielding 100 values in each box. Thus, statistics between the model-produced and satellite-estimated rain rates were calculated from a total of 200 values (from box A plus box B) at each model time. Correlation coefficients and root-mean-square errors (RMSEs) of TMI-only rain rates and corrected rain rates from three methods were obtained (see Fig. 8 for their time series). In Fig. 8a, the correlation coefficients for methods 1 and 2 (RR₁ and RR₂) show little difference in comparison to the relationship between uncorrected rain rates (RR_S) and model-produced rain rates (RR_M). Slightly increased correlation coefficients are found for RR₁ and RR₂ at the 21st model hour, which is the model time when the heaviest rainfall was observed over the both terrain areas. On the other hand, correlation coefficients for method 3 (RR₃) are substantially increased from the 19th hour of the model time. In Fig. 8b, the RMSE trends are similar to those expected from trends of correlation coefficients. The RMSEs for RR₁ and RR₂ are not discernible from RR_S, whereas the decreased RMSE is noticeable for RR₃ from the 19th hour of the model time.

From the above results, it is noted that the area mean orographic corrections made by methods 1 and 2 do not appear to be very significant, except for a slight improvement during strong rainfall events. However, remembering that those coefficients are based on two areas in which there are not only upslopes but also downslopes, the low improvement of coefficients does not necessarily mean that orographically induced vertical wind and/or vertical moisture advection are insensitive to the rain formation. In other words, those factors may be locally important over the upslope areas. In spite of the area averages, however, method 3 shows a significant improvement regardless of the rainfall intensity, suggesting that low-level moisture convergence combined with slope effect may be an important factor in the topographical correction in rain retrieval.

5. Application to TMI measurements

The three correction methods were applied to TMI measurements. Meteorological parameters used for the topographical corrections are obtained from the Regional Data Assimilation and Prediction System (RDAPS) data produced by the KMA, which is based on the MM5 nonhydrostatic mesoscale model with a triply nested grid system (30, 10, and 5 km). The RDAPS, consisting of 33 vertical layers with a top of 50 hPa, gives 48-h forecasts for the 30-km mesh and 24-h forecasts for both 10- and 5-km meshes. The 30- and 10-km resolutions of the RDAPS use the mixed-phase microphysical process (Reisner et al. 1998) and the Kain–Fritsch convection scheme (Kain and Fritsch 1993) in precipitation forecast. In this study, RDAPS wind and water vapor data in the 10-km spatial resolution are chosen when the forecast time and TMI observation time are within the 30 min of each other.

The corrected TMI rain rates were compared with TMI-only rain rates, in conjunction with ground-based AWS rain gauge measurements for validation. Results are shown for Typhoon Maemi, which landed over the Korean peninsula on 12 September 2003. From this application we examine how well the TMI-only estimate describes the topographically induced rainfall and what degree of improvement may be made by including numerical outputs in the satellite rain retrieval procedures.

Figures 9a,b show the AWS rain gauge–measured and TMI-estimated rain rates at the TRMM observation time around 1223 UTC 12 September 2003. For the comparison of the AWS rain gauge measurements with TMI estimates, the AWS 1-min data at a given station are converted into hourly mean rain rates by applying a ±10-min time window centered at the satellite observation time. The TMI rain rates are estimated by applying the rain estimation algorithm of Eq. (2) to the TMI brightness temperatures. The RDAPS 850-hPa wind field and rain rates corresponding to the TMI observation are shown in Fig. 9c.

The cyclonic center in the wind field of Fig. 9c suggests that the cyclonic vortex center is situated inland near the south coast. Although rain observations were made 23 min later, in comparison to the time of the RDAPS wind field, both AWS and TMI rain rates show strong rain centers coincident with the location of the cyclonic wind center. However, the TMI-estimated rain rate shows a pattern that is similar to the cyclonic flow feature off the center of the typhoon, which is not consistent with the AWS-measured rain rate in terms of distribution and intensity. The TMI rain distribution pattern similar to the cyclonic features may indicate that the rain distribution pattern reflects the spiral-shaped high clouds surrounding the low pressure center.

In particular, large discrepancies between the AWS and TMI rain rates are found along the east coastal line where the mountain range extends from north to south. TMI rain rates up to 14 mm h⁻¹ over the east coast appear to be much weaker compared to the heavy rainfall up to 25 mm h⁻¹ found in the AWS rain rates, suggesting that rainfall is much enhanced because of the interactions of strong southeasterly and easterly flow with the topographical barrier.

TMI rain estimates from the correction algorithms of methods 1, 2 and 3 are presented in Figs. 9d–f, respectively. It is clear that all three correction algorithms resulted in more rain in upstream regions along the east coastal line where the scattering-based TMI rain retrieval algorithm underestimates the rainfall compared with AWS rain gauge measurements. Enhanced rainfall is also noted in the mountainous areas in the middle of the peninsula, marked by A in Fig. 6. Consequently, three correction methods accounting for the topographic effect appear to be better than the RDAPS model results, which show little rainfall around the low pressure center, despite the topographically enhanced rainfall along the east coast of the peninsula. It is also shown that the correction seems to bring more realistic TMI results over mountainous areas.

It is clear that the largest enhancement is made by method 2, although the theoretical simulation study indicated that method 3 improves the most. Considering that method 3 employs the moisture flux in the surface boundary layer, the smaller increase by method 3 is probably due to the RDAPS data used for the flux calculation, which may not properly represent atmospheric conditions at the time when TMI measurements were made.

6. Summary and conclusions

We examined the topographical influences on the rain retrievals from microwave measurements over the terrain area of the Korean peninsula by relating numerical model outputs to rain retrievals from simulated TMI brightness temperatures. The rainfall deviation of scattering-based rainfall estimates from model-produced rainfall showed a positive relationship with the topographically forced vertical motion in the upstream region, suggesting that scattering-based microwave rain retrieval algorithms have difficulty in identifying topographically enhanced rainfall. In turn, rainfall may be underestimated when topographically forced vertical motion is present. The largest positive correlation between the rainfall deviation and the computed net slope motion is found when a 15-km horizontal scale for the topographical slope and wind vector at 850-hPa height were considered together, but with a relatively small correlation coefficient of about 0.4. Three topographical correction methods were developed by incorporating slope-forced vertical velocity (method 1), slope-forced vertical velocity plus associated upward vapor flux (method 2), and slope-forced vertical velocity plus vapor flux convergence in the surface boundary layer (method 3) into the scattering-based rain retrieval algorithm.

The developed correction methods were applied for the rain retrievals from simulated TMI brightness temperatures and measured TMI brightness temperatures. The rain retrievals from simulated brightness temperatures showed that the topographical corrections employed in this study provide an improved way of estimating rainfall when a strong rain event is present over the upslope region. In particular, method 3, employing the moisture convergence process in the lower layer, showed a significant improvement regardless of rainfall intensity, suggesting that moisture convergence in the boundary layer below 850 hPa can be an important factor for improving the quality of retrieved rainfall from microwave measurements over mountainous areas.

In addition to the simulation study, it is also shown that the orographic influences on rain formation can be included in the TRMM algorithms, which tend to underestimate the rainfall amount over complex terrain. Consistent with the results from simulated brightness temperatures, topography-corrected estimates of rainfall statistically appear to be in better agreement with the AWS rain gauge measurements than those without correction. Although method 3 shows the largest enhancement and the largest correlation in the simulation study, it is not significantly different from other two methods (methods 1 and 2) when measured TMI brightness temperatures were used with moisture and wind data produced by forecasts at KMA. These may be due to the moisture convergence (wind and water vapor combination) in the boundary layer from model forecasts, which may not represent atmospheric conditions in the lower boundary layer when the TMI measurements were made. In conclusion, this study suggests that satellite rainfall estimates over the complex terrain area can be improved when accurate numerical forecast outputs are properly incorporated with satellite brightness temperature measurements to describe the rain enhancement–associated upslope motion forced by the terrain.