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    Probability (%) of rain as functions of cloud-top temperatures. Black columns correspond to the combined visible reflectance and spatial temperature gradient screening; white columns correspond to the combined visible reflectance, spatial temperature gradient, and cloud particle size screening. On the lhs are probabilities obtained using NCEP hourly gauge-adjusted radar analysis and instantaneous GOES observations made at 30 min before the ending of NCEP hourly integration. On the rhs are probabilities obtained using nearly coincidental instantaneous GHRC radar and GOES observations

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    Mean rain rate (mm h−1) as function of cloud-top temperatures for different geographical regions in the continental United States: (a) NW (40°–50°N, 100°–120°W); (b) SW (20°–40°N, 100°–120°W); (c) NE (40°–50°N, 60°–100°W); and (d) SE (20°–40°N, 60°–100°W)

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    Flow chart of the algorithm

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    Scatterplots of gauge vs GMSRA-derived daily rainfall totals at different spatial scales for a region located at 25°–45°N and 70°–110°W on (left) 18 Jun 1997, (middle) 24 Jun 1997, and (right) 9 Oct 1999

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    Scatterplots of gauge vs GMSRA-derived daily rainfall totals at different spatial scales for (left) 15 Sep 1999 for a region located at 30°–40°N and 73°–83°W, (middle) 16 Sep 1999 for a region located at 35°–45°N and 73°–83°W, and (right) 28 Sep for a region located at 37°–43°N and 87°–93°W

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    Scatterplots of gauge vs GMSRA-derived daily rainfall totals at different spatial scales for (left) 2 Apr 2000 and (right) 3 Apr 2000 for a region located at 29°–37°N and 86°–94°W

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    Scatterplots of gauge vs (top) GMSRA- and (bottom) GPI-derived monthly rainfall totals at monthly scale for (left) Sep and (right) Oct for the whole CONUS

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    Time series of precipitation of gauge observations and of GMSRA and GPI estimates in (top) Sep for a region located between 35°–40°N and 95°–100°W and (bottom) in Oct for a region located between 30°–35°N and 85°–90°W

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GOES Multispectral Rainfall Algorithm (GMSRA)

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  • a Department of Meteorology, University of Maryland at College Park, College Park, Maryland
  • b NOAA/NESDIS E/RA2, Camp Springs, Maryland
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Abstract

A multispectral approach is used to optimize the identification of raining clouds located at a given altitude estimated from the cloud-top temperature. The approach combines information from five channels on the National Oceanic and Atmospheric Administration Geostationary Operational Environmental Satellite (GOES): visible (0.65 μm), near infrared (3.9 μm), water vapor (6.7 μm), and window channels (11 and 12 μm). The screening of nonraining clouds includes the use of spatial gradient of cloud-top temperature for cirrus clouds (this screening is applied at all times) and the effective radius of cloud-top particles derived from the measurements at 3.9 μm during daytime. During nighttime, only clouds colder than 230 K are considered for the screening; during daytime, all clouds having a visible reflectance greater than 0.40 are considered for the screening, and a threshold of 15 μm in droplet effective radius is used as a low boundary of raining clouds. A GOES rain rate for each indicated raining cloud group referenced by its cloud-top temperature is obtained by the product of probability of rain (Pb) and mean rain rate (RRmean) and is adjusted by a moisture factor that is designed to modulate the evaporation effects on rain below cloud base for different moisture environments. The calibration of the algorithm for constants Pb and RRmean is obtained using collocated instantaneous satellite and radar data and hourly gauge-adjusted radar products collected during 17 days in June and July 1998. A comparison of the combined visible and a temperature threshold of 230 K (e.g., previous infrared/visible algorithms) with the combined visible and a threshold of 15 μm demonstrates that the latter improves the detection of rain from warm clouds without lowering the skill of the algorithm. The quantitative validation shows that the algorithm performs well at daily and monthly scales. At monthly scales, a comparison with GOES Precipitation Index (GPI) shows that GOES Multispectral Rainfall Algorithm's performance against gauges is much better for September and October 1999.

Corresponding author address: Dr. Mamoudou B. Ba, Raytheon-ITSS, 4400 Forbes Blvd., Lanham, MD 20706. mba@atmos.umd.edu

Abstract

A multispectral approach is used to optimize the identification of raining clouds located at a given altitude estimated from the cloud-top temperature. The approach combines information from five channels on the National Oceanic and Atmospheric Administration Geostationary Operational Environmental Satellite (GOES): visible (0.65 μm), near infrared (3.9 μm), water vapor (6.7 μm), and window channels (11 and 12 μm). The screening of nonraining clouds includes the use of spatial gradient of cloud-top temperature for cirrus clouds (this screening is applied at all times) and the effective radius of cloud-top particles derived from the measurements at 3.9 μm during daytime. During nighttime, only clouds colder than 230 K are considered for the screening; during daytime, all clouds having a visible reflectance greater than 0.40 are considered for the screening, and a threshold of 15 μm in droplet effective radius is used as a low boundary of raining clouds. A GOES rain rate for each indicated raining cloud group referenced by its cloud-top temperature is obtained by the product of probability of rain (Pb) and mean rain rate (RRmean) and is adjusted by a moisture factor that is designed to modulate the evaporation effects on rain below cloud base for different moisture environments. The calibration of the algorithm for constants Pb and RRmean is obtained using collocated instantaneous satellite and radar data and hourly gauge-adjusted radar products collected during 17 days in June and July 1998. A comparison of the combined visible and a temperature threshold of 230 K (e.g., previous infrared/visible algorithms) with the combined visible and a threshold of 15 μm demonstrates that the latter improves the detection of rain from warm clouds without lowering the skill of the algorithm. The quantitative validation shows that the algorithm performs well at daily and monthly scales. At monthly scales, a comparison with GOES Precipitation Index (GPI) shows that GOES Multispectral Rainfall Algorithm's performance against gauges is much better for September and October 1999.

Corresponding author address: Dr. Mamoudou B. Ba, Raytheon-ITSS, 4400 Forbes Blvd., Lanham, MD 20706. mba@atmos.umd.edu

Introduction

High-quality estimates of the amount and spatial distribution of precipitation at various timescales are very important for a wide range of applications, such as the climatic description of rainfall over ocean areas, river forecasting, flood control, and water resource management. Accurate estimation of rainfall areas is also of great interest in numerical weather prediction studies. Geosynchronous imager satellite observations, currently limited to visible (VIS) and infrared (IR) wavelengths, are very important for precipitation estimation and monitoring because they offer near-continuous observations of cloud systems. However, the major problem of estimating rainfall from these measurements is the difficulty of distinguishing between precipitating and nonprecipitating clouds. For example, methods based on IR [e.g., the Geostationary Operational Environmental Satellite (GOES) Precipitation Index (GPI); Arkin and Meisner 1987)] do not distinguish thick cirrus clouds from deep convective ones. The result is that the area and/or frequency of derived rain is generally overestimated. In addition, these IR techniques, which are quite common, are most applicable for deep cold convective clouds and thus work best in the Tropics.

Precipitation processes in clouds with warm tops are very sensitive to the microphysical structure of their tops. Specifically, precipitation processes are more efficient when water droplets or/and ice particles grow to larger sizes. This process cannot be detected by measured cloud-top temperature alone. An optimum way to detect warm raining clouds may be obtained by using microwave radiation, which interacts directly with large precipitating hydrometeors. However, use of microwave techniques, which are based on the emission from cloud water droplets at low frequency (e.g., 19 GHz), are limited to clouds over water surfaces where there is a high contrast between the low emissivity of the water surface and the high emissivity of the cloud liquid water (Ferraro 1997). For glaciated clouds, high frequencies of 85 GHz or higher are used, which takes advantage of the scattering of microwaves by ice particles to detect raining clouds (e.g., Weng et al. 1994; Liu and Curry 1992; Spencer 1986).

Pilewskie and Towmey (1987) have shown that information about cloud-top microphysics can be obtained from the reflected solar radiation at several wavelengths in the near-infrared portion of the solar spectrum. For example, quantitative retrievals of cloud-drop radii were made by Arking and Childs (1985) using the Advanced Very High Resolution Radiometer (AVHRR) 3.75-μm window channel. Platnick and Twomey (1994) also used the 3.75-μm AVHRR window channel to sense the variation of cloud albedo with changes in cloud drop concentration. Rosenfeld and Gutman (1994) and Lensky and Rosenfeld (1997) used the effective radius (reff) of clouds particles derived from the AVHRR 3.75-μm window channel to detect warm raining clouds.

The current technique, referred to as the GOES Multispectral Rainfall Algorithm (GMSRA), combines multispectral measurements of the GOES satellites to estimate rainfall. One of the principal innovations of GMSRA relative to previous infrared/visible algorithms is that it combines several cloud properties used in a variety of techniques in a single and comprehensive rainfall algorithm. To be specific, the technique uses cloud-top temperatures as a basis of rain estimation (e.g., Arkin and Meisner 1987; Ba et al. 1995; Vicente et al. 1998), and it utilizes the effective radii of cloud particles (e.g., Rosenfeld and Gutman 1994) and spatial and temporal temperature gradients (e.g., Adler and Negri 1988; Vicente et al. 1998) to screen out nonraining clouds.

In general, methods based on cloud-top temperature tend to overestimate rainfall in dry environments and underestimate in more moist atmospheres. A review of several studies by Smith (1979) suggests that the precipitation efficiency, which is the ratio of the observed rainfall to calculated cloud condensates, depends upon the environmental humidity. In the current study, an empirical moisture factor correction developed by Scofield (1987) and modified by Vicente et al. (1998) is used to adjust the GOES rainfall estimates.

Data

The data used in this study include satellite data from GOES, radar and rain gauge data, and atmospheric moisture products (integrated precipitable water and relative humidity from 500-mb surface) obtained from the National Oceanic and Atmospheric Administration (NOAA) National Weather Service Eta Model analysis. The ground-based data include 15-min radar reflectivity obtained from the Global Hydrology Resource Center (GHRC) at Marshall Space Flight Center (MSFC), hourly gauge-adjusted radar rain rates, and daily gauge rainfall obtained from the National Centers for Environmental Prediction (NCEP).

GOES data from five channels are used: the visible channel (0.65 μm), used when available to select optically thick clouds; channel 2 (3.9 μm), used to retrieve reff of hydrometeors during daytime; the water vapor channel (6.7 μm); and thermal channels 4 (11 μm) and 5 (12 μm). The 11-μm channel is used to determine cloud-top brightness temperature, and the 12-μm channel is used in conjunction with the 11-μm channel to estimate cloud-top temperature. The estimated cloud-top temperature is utilized to compute the thermal emission at 3.9 μm, which is then subtracted from measurements of that channel to yield the reflected solar radiation in the 3.9-μm spectral band.

The radar-only data used in the calibration and screening evaluation are generated by the GHRC and are available in the form of 15-min reflectivity at 2-km resolution. These products are converted to rain rate using an empirical ZR relation proposed by Woodley et al. (1975). Also, hourly NCEP gauge-adjusted radar rainfall data are used in the calibration of the technique. Initially, NCEP converts the radar reflectivity into rain rate by a standard ZR relation, and hourly rainfall accumulation is obtained by the summation of twelve 5-min rain-rate estimates. NCEP further adjusts the radar using gauges by the Single Optimal Estimation (SOE) procedure (Seo 1998). The final NCEP hourly rainfall products are gridded in 4 × 4 km2 and 15 × 15 km2 cells and are available in near real time.

Note that the Woodley ZR relationship was designed for convective rainfall, but it is used here for all rain situations. Application of this ZR relationship to composite radar reflectivity images by Weather Services International (WSI) resulted in large systematic and random errors in radar estimated rainfall with respect to gauges (e.g., Crosson et al. 1996). It was also found in the dataset collected for the calibration and screening evaluation of the current algorithm (17 days in June and July 1998) that the GHRC rain-rate estimates corresponding to cloud tops warmer than 250 K are generally much higher than the NCEP hourly gauge-adjusted radar rainfall.

Clearly radar would be preferred for screening and calibration because of its close match in space and time to satellite observations. However, because of the characteristics described above, radar data were used for screening, which is a rain/no rain detection for all clouds and rain-rate calibration for cloud-top brightness temperature ≤ 250 K. For cloud-top brightness temperature greater than 250 K, NCEP hourly gauge-adjusted radar was used. Since we expect “warm”-top rainfall to last longer than convective rain events, the use of hourly rain for calibration of rain rate should not cause significant errors in comparison with convective-type rainfall.

Atmospheric moisture products [precipitable water (PW) and relative humidity (RH)] from Eta Model analyses are available every 6 h beginning at 0000 UTC (i.e., 0000, 0600, 1200, and 1800 UTC) and have a resolution of about 0.5°. A scaled factor of the product of PW and RH (see Vicente et al. 1998) computed from these data is used in this study. It is used to adjust rain rates downward for dry environments.

Screening method

Description

The major challenge in estimating rainfall using IR measurements is to distinguish nonprecipitating cirrus from active cold convective clouds. To remove cirrus clouds, an empirical procedure developed by Adler and Negri (1988) was adapted for areas smaller than originally applied. A slope (S) and a temperature gradient (Gt) are computed for each local temperature minimum in a window of 25 GOES pixels [note that Adler and Negri (1988) searched an entire cloud area for points colder than their neighbors]. The terms Gt and S are given by Eq. (1) and Eq. (2), respectively:
i1520-0450-40-8-1500-e1
where Tmin is the local minimum in the window of 25 × 25 pixels, and as in Adler and Negri (1988), Tavg is the mean temperature of the 6 pixels surrounding the current pixel (4 pixels along the scan and 2 pixels across the scan because the pixel offset along the scan is approximately one-half as large as across the scan).

A large Gt is clearly associated with convective clouds; a small Gt indicates a weak gradient associated with cirrus clouds within the window. All pixels having Gt less than S are classified as cirrus clouds and therefore are rejected as nonraining clouds. This screening of cirrus clouds is used at all times and for all clouds having cloud-top temperatures lower than 250 K. In addition to this screening, a check of the brightness temperature difference between the 11-μm and water vapor (6.7 μm) channels is made for clouds colder than 220 K. Negative difference are associated with overshooting tops (Tjemkes et al. 1997) and therefore are retained as raining clouds even though they failed in cirrus screening.

During daytime, when the visible channel is available and the radiance at 3.9 μm is dominated by the solar-reflected part, the effective radius of cloud particles at the cloud tops can be computed for overcast pixels. The first step in deriving the effective particle radius consists of selecting only pixels filled with optically thick clouds because measurements obtained from thin clouds include radiances both emitted and reflected by the clouds and the underlying surface. An empirically determined visible reflectance threshold of 0.40, which is the ratio of observed radiances to solar constant (E0) properly weighted integrally over the GOES spectral band (0.52–0.72 μm) and multiplied by the cosine of solar zenith angle, is used to select optically thick clouds (e.g., Rosenfeld and Gutman 1994). All pixels with visible reflectance below 0.40 are considered to be associated with nonraining clouds.

For optically thick clouds defined as having a visible reflectance greater than 0.40, the transmissivity at 3.9-μm wavelength can be neglected. So with the assumption that the cloud is a Lambertian surface, the emissivity can be expressed by 1 − A, where A is the spectral albedo at 3.9 μm. Thus, the observed radiance L at 3.9 μm is then given by
i1520-0450-40-8-1500-e3
where S0 is the solar irradiance in the GOES 3.9-μm band and PEBB is the equivalent blackbody emitted thermal radiation at 3.9 μm for cloud-top temperature Tc. Thus, the albedo A is obtained from Eq. (4):
i1520-0450-40-8-1500-e4
The estimation of (Tc) is done using a split-window technique based on coefficients derived for ocean surfaces (Wu et al. 1999) with emissivity close to unity:
i1520-0450-40-8-1500-e5
where Tb4 and Tb5 are cloud-top brightness temperatures for the GOES's channel 4 and 5, respectively, and ΔT is Tb4Tb5. The use of this split-window technique may be questioned for very high cloud tops, where little water vapor is available above the cloud, and channel 4 alone may provide the cloud-top blackbody brightness temperature. However, PEBB at 3.9 μm at low temperatures is small (e.g., Tb4 = 200 K, PEBB = 0.002 09 mw m−2 sr cm−1) relative to the solar reflected part at the same wavelength and therefore has little effect in the determination of A. Thus, at such low temperatures where ΔT approaches zero, Eqs. (5) and (6) will still provide acceptable results for Tc and the calculated PEBB. Meanwhile, the radiance at 3.9 μm increases rapidly with increasing temperature, and the thermal emission from atmospheric water vapor becomes significant for high temperatures (e.g., greater than 260 K). This means that for warm tops (when significant amount of water vapor is available above the cloud top), Tb4 may be significantly different from the actual cloud-top temperature. This, in turn, results in uncertainties in the determination of A. Therefore, using Eqs. (5) and (6) is justified to correct the water vapor contamination at these “warm” temperatures (e.g., Rosenfeld and Lensky 1998). Once Tc is obtained, PEBB is calculated from Planck's equation and used in Eq. (4) to solve for A.
The effective radius is defined as
i1520-0450-40-8-1500-e7
where N(r) is the number concentration of particles having radius r. The effective radius, which is dependent on the spectral albedo A at 3.9 μm, is retrieved using the results obtained by Rosenfeld and Gutman (1994), which were tabulated in a lookup table of A versus reff using an inversion of a radiative transfer model (Nakajima and King 1990). That lookup table was originally calculated for AVHRR channel 3. However, the spectral difference of the NOAA/AVHRR's channel 3 (3.350–4.100 μm) and that of the GOES's channel 2 (3.697–4.115 μm) is very small, and the spectral albedo in these two bands for practical purposes is assumed to be identical. Therefore, it is believed that use of the Rosenfeld lookup table obtained for the NOAA/AVHRR's channel 3 is justified. The maximum value of the effective radius that can be obtained in the Rosenfeld lookup table is 30 μm because A at 3.7 μm saturates quickly for clouds with large particles (Rosenfeld and Lensky 1998). It was shown by Rosenfeld and Gutman (1994) that clouds having an effective radius higher than 14 μm at their top contain precipitation-sized hydrometeors that can be detected by weather radars. The effective radius is used here to extend the rainfall algorithm to warmer clouds where the infrared-only algorithm is ineffective.

We compared the values of retrieved effective radius obtained from the two-dimensional lookup table to those of a three-dimensional model (A. Heidinger 2000, personal communication), but the differences were not significant for the purpose of this study. Moreover, the two-dimensional lookup table is computationally more efficient for real-time rainfall estimation from GOES observations.

Evaluation of screening method

To evaluate the performance of the algorithm in rain detection and the usefulness of the effective radius of cloud particles for improving the screening of nonrain, contingency tables of rain versus nonrain, as determined by the ground-based rainfall measurements (GHRC radar and NCEP gauge-adjusted radar) and by the satellite algorithm, are set up. To minimize erroneous data, observations where the NCEP estimate = 0 and GHRC estimate > 0 or where the NCEP estimate > 0 and GHRC estimate = 0 are rejected. A Heidke skill score (Skill), as described by Conner and Petty (1998), is computed from these tables. Also computed is a probability of detection (POD) and a false alarm ratio (FAR). These different statistical measures are defined in the following equations:
i1520-0450-40-8-1500-e8
where q1, q2, q3, and q4 are defined in Table 1, which also shows the results of the evaluation of screening method. The POD and FAR vary from 0 to 1; the Skill varies from 1 (perfect skill) to −1 (perfect negative skill). Zero represents no skill relative to chance. Ideally, one would like to have a Skill of 1, a POD of 1, and FAR of 0. The reality is that one rarely achieves this, and the statistics have to be used in a diagnostic way to assess whether the screening is working. This should be kept in mind when looking at Table 1, which shows the results of rain versus no rain for different screening methods using data collected during 17 days in June and July 1998. The spatial gradient to screen out the cirrus is applied to all cases presented in Table 1.

When considering only clouds colder than 230 K with visible reflectance greater than 0.40, the satellite detects only 52% of radar rain, with a FAR of 19% and a skill score of 0.25. The poor detection of rain indicates that a relatively significant number of rain events may be associated with clouds warmer than 230 K. When considering all cloudy pixels, that is, all clouds having a visible reflectance greater than 0.40, the POD increases to 0.99, but also the false alarm ratio rises significantly to 0.34 and a poor skill score of 0.04 is obtained. This indicates that the visible threshold of 0.40 is ineffective in screening out nonraining warm clouds. When using a visible reflectance greater than 0.40 and an effective radius at least equal to 15 μm, the FAR drops to 0.26 and the algorithm still detects over 80% of raining clouds as determined by radar. A skill score of 0.29 is obtained for this screening. Increasing the threshold of effective radius to 20 μm does not change the skill score and decreases the FAR by only 2% but reduces the POD to 72% of radar rain. Comparing the screening with a visible reflectance greater than 0.40 and a temperature threshold of 230 K (e.g., previous IR–VIS algorithms) with the screening with a visible reflectance greater than 0.40 and an reff threshold of 15 μm demonstrates that the latter improves the detection of rain without significantly increasing the FAR. These results suggest that one can use a threshold of 15 μm as a low boundary to separate rain from nonrain events. These results of the 15-μm threshold of rain/no rain are consistent with earlier findings of Rosenfeld and Gutman (1994).

It is interesting that the skill score hovers between 0.25 and 0.29, except for the case of all clouds with reflectance greater than 40%, where it was essentially 0. Conner and Petty (1998) compared hourly radar estimates to gauges and also found skill scores averaging about 0.30. Only when compositing over 6 h were they able to obtain an average skill score of about 0.6. It is expected that during nighttime, the infrared-only algorithm will miss rain events associated with cloud tops warmer than 230 K because the algorithm restricts itself to temperature colder than 230 K.

The algorithm calibration

To compute GOES rain rate (RR), a lookup table of cloud-top temperature and probability of rain (Pb) and mean rain rate (RRmean) is computed using NCEP gauge-adjusted radar, GHRC radar, and GOES data collected during 17 days in June and July 1998. As discussed in section 2, hourly rainfall from gauge-adjusted radar was used for cloud tops warmer than 250 K because of the lack of confidence in GHRC estimates for these warm clouds, and GHRC rain rates were used for cloud-top temperatures less than 250 K. However, Pb determined from instantaneous radar observations are used for all clouds, since these are closest in time to the satellite data. The Pb and RRmean are computed after the screening was applied and are for a 10-K bin as in Sheu et al. (1996). The Pb and RRmean are given in the following equations:
i1520-0450-40-8-1500-e11
where Tc is the cloud-top temperature, Nc(Tc) is the number of cloudy pixels, RRoi(Tc) is the observed ground rain rate, and Nr(Tc) is the total of raining pixels as indicated by ground observations. The training dataset was broken up into four areas in an attempt to capture some of the regional characteristics of rainfall. These areas are designated northwest (40°–50°N, 100°–120°W), southwest (20°–40°N, 100°–120°W), northeast (40°–50°N, 60°–100°W), and southeast (20°–40°N, 60°–100°W). The probability of rain in 10° brightness class intervals for visible reflectance greater than 40% and for effective radius greater than 15 μm for each area is shown in Fig. 1. On the left-hand side of Fig. 1 is shown probability of rain obtained using NCEP gauge-adjusted radar, and on the right-hand side is shown probabilities of rain obtained from instantaneous GHRC rain rates. The first thing to note is that the lowest brightness temperature classes have the highest probability of rain and that, up to temperatures of about 240 K, there is no significant improvement in adding the effective radius information based on the 3.9-μm data from channel 2 on GOES. At brightness temperatures warmer than 240 K, however, the influence of the addition of the effective radius information can be seen. For example, in the southeast sector, the addition of the effective radius keeps the probability of rain obtained from instantaneous radar observations at the higher brightness temperatures between 85% and 90% rather than 75%.

Also, the probability of rain is much lower for regions located west of 100°W. This may be related to the difference in the moisture environment and cloud-base heights between the two regions. The atmosphere in the western region is generally drier than that of the eastern states, and cloud bases are generally higher. However, rain processes are complex; they depend on many factors, including the structure of the atmosphere, cloud microphysical processes, and cloud dynamics. We do not know which factors cause the variation of the Pb, but we note that the western regions have different moisture structures than the east. The important point for this investigation is that this difference exists and we can factor it into our calibration. It is noted that if one were to use a single calibration, then significant errors in the estimated rainfall would occur, as found by McCollum et al. (2000) in their study of satellite rainfall over equatorial Africa. Also, a drier environment and higher cloud base affect the amount of rain reaching the ground through evaporation between cloud base and the surface. This mechanism is suggested by the probability of rain computed using hourly gauge-adjusted radar rainfall measurements (left-hand side of Fig. 1). There, an even more dramatic decrease in the probability of rain when compared with the instantaneous radar data is evident. The reason for this is that the radar rainfall measurements include rain at different altitudes while the gauges measure only the rain that reaches the ground. Therefore, it is reasonable to expect the algorithm to overestimate rainfall produced by clouds forming under relatively dry atmospheric conditions and to underestimate rainfall in more moist environments. For example, Scofield (1987) reported that cumulonimbus clouds (Cb) with cold tops over Minnesota may produce less rainfall than Cbs with the same top temperatures over the gulf states because of the generally drier atmosphere of Minnesota. Also, in intermountain western regions, moisture fluxes from the Pacific Ocean are blocked by the Sierra Nevada to the west and the Cascade Mountains to the northwest (see, e.g., Urbanski 1982) causing dry atmospheric conditions over these regions.

The RRmean obtained from GHRC and gauge-adjusted radar data from June and July 1998 for the four areas are shown in Figure 2. The calculations show a quadratic relationship of RRmean versus brightness temperature; it is different in each area, although the NE and SE areas show the greatest similarity. The NE and SE areas exhibit higher rain rates for a given brightness temperature, and the NW region shows the lowest. This is generally consistent with the observed long-term mean, which shows a strong east–west gradient of precipitation in the United States and probably reflects the availability of moisture and atmospheric structure in the eastern areas in comparison with the western sectors in the June/July time period.

The GOES RR for each indicated raining cloud group referenced by its cloud-top temperature is obtained by the product of Pb and RRmean. This is adjusted by a moisture factor, which is designed to modulate the evaporation effects on rain below cloud base for different moisture environments, and is finally multiplied by a binary factor (1 for growing convection and 0 for decaying convection):
TcPbTcmeanTc
where (Tc) is cloud-top temperature, Pb(0 ≤ Pb ≤ 1) is the probability of rain associated with clouds at the Tc isotherm, and RRmean is the mean rain rate of rainy clouds at temperature level Tc. The growth factor is a binary number determined by the difference of cloud-top temperature between two consecutive half-hour images (the difference of current to the previous image). Negative differences are associated with growing convection (growth = 1), and positive differences are associated with decaying convection (growth = 0). This could be a problem in certain stratiform rain situations where cloud-top temperature does not change very much. This will require more case studies to evaluate the growth rate factor in such rain situations.

The growth factor is computed using a window size of 5 × 5 pixels centered by the current pixel. No cloud drifting in or out of the window is assumed in the growth-rate factor determination. Our experience with the algorithm shows that a growth factor based on a single pixel tends to overestimate the amount and area coverage of rain.

The term PWRH is the product of the precipitable water and relative humidity between the surface and 500 mb (Scofield 1987; Vicente et al. 1998). It is an empirical adjustment factor that has been scaled between 0 and 2 and represents very dry conditions, when all rain is expected to evaporate before reaching the ground, and much greater than normal moist conditions, when rain is expected to be heavier than the mean rain rates from the calibration procedure. Effectively scaled between 0 and 1 by setting all values > 1 to 1, the rain rate either decreases (as one expects in dry environments) or remains the same.

It should be stressed that the moist correction was designed to correct for the evaporation effect of the falling rain below the cloud base. Other factors, such as microphysics, dynamics, and moisture environment, govern the rain processes within the clouds, resulting in different rain rates for different environments.

In the next section, RR(Tc) computed from Eq. (13) is applied to GOES data to estimate rainfall amount at different spatial scales. The algorithm uses the polynomial relationship for each region defined in Fig. 2. Figure 3 depicts the algorithm scheme. During nighttime, the algorithm relies on an IR-only method, and rainfall is computed only for clouds having brightness temperatures colder than 230 K. Our experience with the IR-only screening during the night indicates that GMSRA tends to overestimate the area of rain when a threshold warmer than 230 K is used. Consequently, we chose the 230-K threshold rather than the commonly used 235 K of GPI. It should be pointed out that the GPI threshold was based on comparison with radar over the tropical Atlantic and is not necessarily applicable to the continental United States for instantaneous rain applications.

Evaluation of the algorithm

The statistical measures used to compare the satellite estimates with ground truth measurements are the mean gauge rainfall (G), the mean satellite rainfall (S), the bias, the rmsd, and the correlation coefficient. These quantities are defined in the following equations:
i1520-0450-40-8-1500-e14

All results presented in this section are obtained from the version of the algorithm that has been running routinely since the beginning of August 1999. This version is also used to compute rainfall for two days in 1997 presented here. We performed a validation of the algorithm on daily and monthly basis and for different scales at the station point (12 km), 0.5°, 1°, and 2.5° grid boxes, as explained below.

Daily comparison with gauges

At 12-km resolution, 9 satellite pixels encompassing each individual gauge station are averaged to represent the estimate at that station. At 0.50°, 1°, and 2.5° scales, satellite pixels within each box are averaged and compared with the average of available stations within the corresponding box. It has been shown by Xie and Arkin (1995) that the correlation coefficient between monthly satellite estimates and gauges at 2.5° resolution converges toward a maximum when at least five gauges contained in the grid are used. Substantial errors may still exist, depending upon the distribution of gauges within the grid (Xie and Arkin 1995; Morrissey et al. 1995). For the daily totals, only boxes having at least two gauges for 0.5° box and four for 1° and 2.5° grid boxes are considered in the comparison. This may result in the situation in which there are different geographic locations in the analysis for the 0.5°, 1°, and 2.5° grid boxes and the unusual case of more grid boxes in the analysis for the 2.5° grid than for the 1° grid (e.g., Table 2, September 1999).

Table 2 summarizes comparisons for six cases, three covering nearly the entire United States (18 and 24 June 1997 and 9 October 1999) and three limited areas of significant rainfall (15 and 16 September 1999 during Hurricane Floyd and 28 September 1999). For 18 June 1997, the biases at all scales are nearly one-half of the observed mean, and the correlation coefficient increases significantly with the scale of the spatial integration. For the day of 24 June 1997, the biases are almost the same magnitude as the observed mean, but better correlation coefficients than the case on 18 June 1997 were obtained. For the day of 9 October 1999, the observed mean is nearly the same as the satellite mean with correlation coefficients better than the two cases in June 1997. For the day of 28 September 1999, the biases represent approximately 30% of observed mean, and correlation coefficients were higher than the two cases in 1997. The two remaining cases presented here correspond to results obtained for special meteorological situations during Hurricane Floyd (15 and 16 September 1999). The algorithm performed relatively well for different regions hit by Floyd, as shown by good correlation coefficients, but the biases are highly positive.

Figures 4 and 5 show the scatterplots of all six cases shown in Table 2 for different spatial scales. One notes that the scatterplot and rms differences (Table 2) are much larger at small scale (12 km). Also, it is seen that at gauge points (12 km), GMSRA tends to overestimate low gauge rainfall and underestimates high gauge rainfall. At 12 km, some satellite pixels may correspond well to raining clouds while at the gauge point there is nonrain recorded, resulting in overall overestimation by satellite algorithm. In general, the satellite tends to underestimate high gauge rainfall because of different spatial resolutions. Also note that the curves used to compute the instantaneous rain rate (Fig. 1) allow only about 20 mm (for the western regions of United States) and about 40 mm (for the eastern regions of United States) for the coldest cloud-top temperatures observed for the period used in the calibration. These rain rates may be too low for special cases associated with tropical systems such as hurricanes. For example, it is found in a recent study of Hurricane Mitch, which caused devastating rainfall over Nicaragua and Honduras, that GMSRA underestimates intense rain amounts (Ferraro et al. 1999). This is also the case presented in Fig. 5 for Hurricane Floyd on 15 and 16 September 1999.

Another heavy rain event was presented in Fig. 6, where GMSRA also underestimated rainfall above 100 mm on 2 April 2000. Note also that GMSRA generally overestimates rainfall below 100 mm, especially for 3 April 2000 (Fig. 6). These two particular cases correspond to a poorly organized system but with locally severe thunderstorms over Mississippi and Alabama that were associated with a severe weather ahead of a strong cold front. Table 3 presents the statistics of the comparison between GMSRA estimates and gauges for these two cases for the regions located at 29°–37°N and 86°–94°W on 2 and 3 April 2000. Good correlation coefficients of 0.59 and 0.73 at 12 km for 2 and 3 April 2000, respectively, are obtained, but the overall biases are highly positive, particularly for the case of 3 April 2000.

Comparison with GPI

In this section, the performance of GMSRA is compared with that of the GPI for the months of September and October 1999. The GPI was selected for comparison because it is an infrared algorithm that has experienced widespread use. It should be pointed out that this comparison is primarily for highlighting some of the improvements that we believe accrue from the GMSRA. We will point out why we think those improvements are occurring, but we do not go into great detail. That is best left for another study. Originally, GPI (Arkin and Meisner 1987) is calculated from the product of the mean fractional coverage (Fc) of cloud colder than 235 K in a 2.5° × 2.5° box, the length of the averaging period in hours (t) and a constant of 3 mm h−1; that is,
Fct.

In the current study, GPI is computed every 30 min (i.e., t = 0.5) in a 0.5° × 0.5° box. The comparison with gauges is based on 1° × 1° box, and all boxes having at least 1 gauge datum are considered in order to maximize the number of grid points. All available gauges with daily observations during September and October 1999 within the continental United States (CONUS) are used in the comparison.

Table 4 summarizes the statistics of the comparison between satellite estimates and gauges for both September and October 1999, and Fig. 7 shows the associated scatterplots. The difference between mean satellite estimates and mean gauges taken over the CONUS gives some indication of the bias of satellite estimates. The biases represent 3% and 42% in September and 11% and 3% in October for GMSRA and GPI, respectively. The slope of regression between gauges and satellite estimates is 0.8 and 0.3 for GMSRA and GPI, respectively (GMSRA is closer to the 1-to-1 line), and the correlation between satellite estimates and gauges is considerably higher for GMSRA than for GPI. Interestingly, the rmsd and bias for GPI are slightly superior to GMSRA in October. Based on this statistical comparison, we believe the GMSRA does exhibit superior performance to the GPI, indicating that GMSRA gives useful estimates of precipitation associated with rain systems with various types of precipitating clouds.

Further information about the two models is shown in the scatterplots of Fig. 7. GMSRA estimates are in the top panel, and GPI estimates are in the bottom panel, with the left-hand side corresponding to September 1999 and the right-hand side to October 1999. Figure 7 indicates that there are many grid points at which gauge-observed rainfall exceeds 150 mm in September, and only a few grid points exceed this amount in October. In September, among those grid points with gauges recording above 150 mm, there are only two grid points at which GPI estimates reach this amount; in October, none exceeds 150 mm. This may be an indication of rain from “warm” clouds undetected by GPI. A close examination of the scatter diagram also shows that there are many grid points in October at which GPI indicates rainfall above 50 mm while gauges have rainfall totals less than 10 mm. This feature is not apparent in the GMSRA scatter diagram and may represent areas of nonprecipitating cold clouds. Also, the GPI appears to have a greater number of points at which gauges are reporting rain above 50 mm but the satellites are not. This may be another case of “warm” rain not being detected (GMSRA suffers this problem at night, GPI all the time). For both months, there are a few locations at which GMSRA significantly overestimates the rain gauge amounts. An examination of the data shows that these locations coincide with the southern half of Florida.

We also looked at the time series of areally averaged rainfall corresponding to two locations bounded by 35°–40°N and 95°–100°W (September) and by 30°–35°N and 85°–90°W (October). They are presented in Fig. 8. There were 87 daily rainfall gauges in September and 128 in October. GMSRA has an overall better performance than GPI in a day-to-day comparison. This is supported somewhat by the skill scores, probability of detection, and false alarm rates, which are 0.51, 0.65, and 0 for GMSRA and 0.28, 0.40, and 0 for GPI for September 1999 and 0.71, 0.75, and 0.1 for GMSRA and 0.45, 0.38, and 0 for GPI for October 1999. It is our assessment that the use of multispectral data contributes to the better performance of GMSRA over GPI.

Concluding remarks

In this study, a multispectral rainfall algorithm using all five channels on the GOES satellites is presented. The use of visible and near infrared during the day allowed extension of traditional infrared brightness temperature methods, which are mostly used for cold convective clouds, to warm clouds.

One of the objectives of this study was to assess the performance of the algorithm in detecting raining clouds during daytime. Comparing the combined visible and a temperature threshold of 230 K (e.g., previous IR–VIS algorithms) with the combined visible and a threshold of 15 μm demonstrates that the latter allows detection of rain from warm clouds without compromising the skill of the algorithm.

At small scales, the algorithm generally underestimates high rainfall amounts. However, most satellite algorithms cannot estimate high gauge rainfall, especially for short time periods, because of different spatial resolutions. The calibration of GMSRA based on mean rain rates versus cloud-top temperatures does not allow, for example, the computation of heavy rain amounts associated with extreme cases such as hurricanes. However, the agreement of GMSRA estimates with gauge observations increases significantly with areal averaging for daily. It is shown in this study that GMSRA performed much better than GPI, which is based on a single infrared channel.

The algorithm is now running routinely in an experimental mode and is independently evaluated by the National Environmental Satellite and Data Information Service (NESDIS). Experience with this algorithm suggests that although there is reasonably good agreement between GMSRA and gauges when large areal averaging is considered, there are several enhancements that can be made to improve its accuracy, especially for heavy rain estimation. This includes regional calibration for different seasons, including the use of satellite active/passive microwave data, to refresh the calibration of the technique.

Acknowledgments

We thank Dr. John Janowiak of Climate Prediction Center/NCEP/NWS for providing the GPI data. We acknowledge Drs. J. McCollum and R. Kuligowski for their critical reading of the manuscript, Dr. D. Rosenfeld of the Hebrew University of Jerusalem (Israel), and Dr. G. Gutman of NASA/GSFC for helpful discussions regarding the use of GOES channel 2 in deriving effective radii of cloud droplets. Fifteen-minute radar data were obtained from GHRC/MSFC, Huntsville, Alabama.

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Fig. 1.
Fig. 1.

Probability (%) of rain as functions of cloud-top temperatures. Black columns correspond to the combined visible reflectance and spatial temperature gradient screening; white columns correspond to the combined visible reflectance, spatial temperature gradient, and cloud particle size screening. On the lhs are probabilities obtained using NCEP hourly gauge-adjusted radar analysis and instantaneous GOES observations made at 30 min before the ending of NCEP hourly integration. On the rhs are probabilities obtained using nearly coincidental instantaneous GHRC radar and GOES observations

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Fig. 2.
Fig. 2.

Mean rain rate (mm h−1) as function of cloud-top temperatures for different geographical regions in the continental United States: (a) NW (40°–50°N, 100°–120°W); (b) SW (20°–40°N, 100°–120°W); (c) NE (40°–50°N, 60°–100°W); and (d) SE (20°–40°N, 60°–100°W)

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Fig. 3.
Fig. 3.

Flow chart of the algorithm

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Fig. 4.
Fig. 4.

Scatterplots of gauge vs GMSRA-derived daily rainfall totals at different spatial scales for a region located at 25°–45°N and 70°–110°W on (left) 18 Jun 1997, (middle) 24 Jun 1997, and (right) 9 Oct 1999

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Fig. 5.
Fig. 5.

Scatterplots of gauge vs GMSRA-derived daily rainfall totals at different spatial scales for (left) 15 Sep 1999 for a region located at 30°–40°N and 73°–83°W, (middle) 16 Sep 1999 for a region located at 35°–45°N and 73°–83°W, and (right) 28 Sep for a region located at 37°–43°N and 87°–93°W

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Fig. 6.
Fig. 6.

Scatterplots of gauge vs GMSRA-derived daily rainfall totals at different spatial scales for (left) 2 Apr 2000 and (right) 3 Apr 2000 for a region located at 29°–37°N and 86°–94°W

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Fig. 7.
Fig. 7.

Scatterplots of gauge vs (top) GMSRA- and (bottom) GPI-derived monthly rainfall totals at monthly scale for (left) Sep and (right) Oct for the whole CONUS

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Fig. 8.
Fig. 8.

Time series of precipitation of gauge observations and of GMSRA and GPI estimates in (top) Sep for a region located between 35°–40°N and 95°–100°W and (bottom) in Oct for a region located between 30°–35°N and 85°–90°W

Citation: Journal of Applied Meteorology 40, 8; 10.1175/1520-0450(2001)040<1500:GMRAG>2.0.CO;2

Table 1.

Contingency table for different screening methods and also showing the definition of q1, q2, q3, and q4. The term qx is the frequency of occurrence in percent of rain/no rain for the indicated cells. Also the POD, the FAR, and the Heidke skill score are presented

Table 1.
Table 2.

Comparison statistics between daily rainfall amounts of gauges and GMSRA estimates at various spatial resolutions for 18 and 24 Jun 1997; 15, 16, and 28 Sep 1999; and 9 Oct 1999

Table 2.
Table 3.

Comparison statistics between daily rainfall amounts of gauges and GMSRA estimates at various spatial resolutions for 2 and 3 Apr 2000

Table 3.
Table 4.

Comparison statistics of the regression between monthly rainfall amounts of gauges and satellite estimates at 1° × 1° box for Sep and Oct 1999

Table 4.
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