## 1. Introduction

Satellite remote sensing techniques have shown considerable promise for deriving estimates of rainfall on a global scale. Beginning in 1987 satellite rainfall estimates have been combined with surface observations to provide global monthly rainfall estimates for the Global Precipitation Climatology Project (GPCP) (Arkin and Xie 1994). Both NOAA and NASA Goddard Space Flight Center currently use microwave satellite observations to produce global monthly rainfall estimates that are available to the public through the Internet (Weng et al. 1994; Ferraro and Marks 1995; Adler et al. 1994). These rainfall estimates are being used in many applications such as climate diagnostics studies (e.g., Rasmussen and Arkin 1993), validation of rainfall forecasts from numerical weather prediction (NWP) models (e.g., Janowiak 1992), and as input for surface process models (Shinoda and Lukas 1995).

It is therefore of great interest to know: How accurate are these satellite rainfall estimates? How and why do estimates from different algorithms differ? Can satellite rainfall estimates be improved, and if so, how?

In order to address these issues, several algorithm intercomparison projects have been conducted. The WetNet Precipitation Intercomparison Projects, PIP-1 and PIP-2, examined the abilities of various algorithms that use passive microwave data from the Special Sensor Microwave/Imager (SSM/I) onboard the Defense Meteorological Satellite Program (DMSP) polar orbiting satellites. PIP-1 took the broad view, evaluating satellite estimates of monthly rainfall at coarse grid resolution (2.5°) over the globe (Barrett et al. 1994), while PIP-2 concentrated on pixel-scale estimates of instantaneous rain rates to try to pinpoint reasons for differences between algorithms (Smith et al. 1998).

The GPCP has conducted three algorithm intercomparison projects, AIP-1, AIP-2, and AIP-3 (Arkin and Xie 1994; Ebert et al. 1996). The strategy of the AIPs was to focus on a small region in space and time for which there were both abundant satellite visible/infrared and passive microwave data, and also very high quality surface validation data. AIP-1 evaluated the performance of satellite rainfall algorithms over Japan and surrounding waters during June–August 1989, while AIP-2 evaluated algorithms using data from western Europe during February–April 1991. AIP-3 evaluated satellite estimates of tropical convective rainfall in the equatorial Western Pacific during November 1992–February 1993, using as validation data the shipboard radar rainfall observations collected during the TropicalOcean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE).

This paper presents some of the findings of AIP-3. Section 2 details the data used in the experiment, and section 3 gives an overview of the algorithms that were evaluated. The main results of AIP-3 are presented in section 4. Section 5 examines the performance of four widely available algorithms for two case studies. Finally, some conclusions are given in section 6. A complete compilation of the results of AIP-3 can be found in Ebert (1996).

## 2. Data

### a. Input data

The input dataset for AIP-3, detailed in Table 1, contained satellite, NWP, and ancillary data in a 5° square region in the western Pacific (1°N–4°S, 153°–158°E) during the months of TOGA COARE, November 1992 through February 1993. The satellite input data included hourly Geostationary Meteorological Satellite (GMS)visible/infrared imagery, 5-channel Advanced Very High Resolution Radiometer (AVHRR) visible/infrared imagery, and SSM/I passive microwave data. Daily numerical weather prediction analyses and model output from ECMWF, JMA, and NMC (renamed NCEP) were provided for use in those algorithms that require additional information about the atmospheric state. Monthly GCM rainfall estimates for the TOGA COARE period were provided by the Max Planck Institute. Monthly Pacific atoll rain gauge measurements from 20 years predating the TOGA COARE period (Morrissey and Greene 1991) were also provided.

### b. Validation data

Validation data consisted of maps of calibrated radar rain rates collected from two shipboard Doppler radars (MIT and NOAA/TOGA) located at approximately 2°S, 154.5°E and 2°S, 156°E, as shown in Fig. 1 (Short et al. 1997). The maximum usable range of each radar was 145 km, yielding rainfall measurements in a circularregion approximately 2.5° in diameter. In the regions of overlap of the two radar ranges the maximum of the two rainfall rates was retained for each pixel. With both radars deployed, about one-third of the AIP-3 5° square region contained radar rainfall measurements.

*Z*–

*R*relationship of

*Z*

*R*

^{1.43}

*Z*–

*R*relation was derived by calibrating the radar measurements against disdrometer data from Kapingamarangi Atoll.

Initially a *Z*–*R* relation of *Z* = 139*R*^{1.43} was used for convective rainfall (“version 1”). The version 1 rainmaps were used to produce an initial set of AIP-3 satellite algorithm validation statistics. These statistics revealed that the radar rain rates were significantly lower than all but one of the satellite and NWP estimates, typically by a factor of 0.5–0.7, suggesting a likely systematic bias. Further examination of the range dependence of the radar rain rates led to an increase in the attenuation coefficient. Recent studies using profiling radars in TOGA COARE showed that the vertical fall speed of raindrops decreased by about 10% between 2-km altitude and the surface, which led to a revision of the *Z*–*R* relation. The combined effect of these improvements in calibration (“version 2”) was to increase the radar rain rates by an average of about 30% (Ferrier et al.)

These version 2 radar rain rates were treated as“truth” against which to compare the satellite algorithms. In the strictest sense, AIP-3 was really an intercomparison between remote sensing estimates, with the radar given greater credibility. It is believed that the radar reliably detected the presence or absence of rain, but the residual uncertainty in calibration must lead to uncertainties in satellite algorithm bias and other validation statistics. Thus, we will use the word “intercomparison” in preference to “validation” throughout this paper.

*Z*–

*R*relationship adopted for stratiform rain was

*Z*

*R*

^{1.43}

### c. Gridding and treatment of missing data

A spatial grid scale of 0.5° was used in the intercomparison. This resolution was chosen so that each sample would represent a fairly large area, as in the GPCP product, while also providing enough samples to enable meaningful intercomparison statistics to be computed.

The radar data were mapped onto the validation grid in the following manner. First, an effort was made to replace any missing 2-km resolution pixels with the average of the four nearest neighbors in space. If all of those were also missing, then the pixel was replaced by the rainfall rate from the previous time step (generally 10 min prior, but no more than 30 min). If that was missing as well, then no further action was taken. The 2-km radar pixels were then averaged onto the 0.5° grid, with a grid value being considered valid only if at least 80% of the pixels contained good (original) data. This requirement eliminates most of the rain rates from the periphery of the radar scans (which are those most likely to be influenced by attenuation effects and are therefore less reliable).

Monthly gridded radar rainfall was obtained in a similar manner. TOGA COARE cruise “months” were used to evaluate the algorithms on monthly timescales (Fig. 2). A cruise “month” was defined as a block of consecutive, complete days during which at least one shipboard radar was located completely inside the 5° square AIP-3 region. These were:

- Month 1 ≡ Cruise 1: 11 November–10 December 1992;
- Month 2 ≡ Cruise 2: 15 December 1992–18 January 1993;
- Month 3 ≡ Cruise 3: 23 January–23 February 1993.

^{−1}), then multiplied by 24 h]. The daily values were summed and scaled appropriately for the “month” with the requirement that at least 80% of daily values be present during the “month.” The monthly totals were then averaged in space to produce the 10 × 10 gridded values. As with the instantaneous grids, each monthly grid box was required to contain at least 80% good (original) data in order to be considered valid. After spatial averaging to the 0.5° grid each“month” contained between 10 and 16 pairs of matched estimates and observations.

## 3. Algorithms

The satellite rainfall algorithms evaluated in AIP-3 fell into five categories. Infrared (IR) algorithms relatethe rainfall rate to the cloud brightness temperature *T*_{B}, implicitly assuming that deeper, colder clouds are more likely to produce heavy rainfall (e.g., Richards and Arkin 1981). Some IR algorithms augment the infrared imagery with visible imagery (VIS/IR), using the cloud albedo to indicate optically thick clouds that may be precipitating (e.g., Hogg 1990). AVHRR algorithms use the infrared split window to detect thin cirrus (Inoue 1987) or to sense water droplet size at cloud top (Rosenfeld and Gutman 1994). SSM/I algorithms can sense the emission of microwave radiation from liquid precipitation particles using the lower-frequency channels (19, 22, 37 GHz), as well as scattering of high-frequency (85 GHz) microwave radiation from frozen precipitation particles (e.g., Grody 1991). Finally, a new class of algorithms is emerging that uses the SSM/I algorithms to “calibrate” the IR algorithms on a monthly basis (“mixed” IR–SSM/I), thus taking advantage of both the superior spatial and temporal sampling provided by the geostationary satellites and the more physically based (and presumably more accurate) nature of the SSM/I algorithms.

A total of 57 satellite rainfall algorithms were submitted by 24 research groups. Each algorithm was assigned a three-character code name indicating the investigator and the version number of the algorithm within the set of results submitted by the group (for example, AD5 refers to the fifth algorithm submitted by Adler’s group). Table 2 lists the algorithms that were evaluated in AIP-3, along with an abbreviated summary of their methodologies. Short descriptions of the algorithms may be found in Ebert (1996); for full descriptions of the algorithms the reader should consult the original references cited in column 2 of the table.

There were more algorithms evaluated in AIP-3 than in AIP-1 and AIP-2 combined. This is mainly a result of the rapid growth in the number of SSM/I rainfall algorithms, as well as a recent effort by many algorithm developers to combine IR and microwave data into mixed algorithms. Rainfall algorithms were permitted to use any combination of satellite, NWP, and ancillary data. In addition, the NWP precipitation forecasts were also validated to assess the relative merits of satellite-observed versus model-forecast rainfall.

AIP-3 participants provided rainfall estimates for every GMS image, AVHRR image, or SSM/I swath (depending on the algorithm) in the AIP-3 dataset. Rainfall estimates using GMS data were produced on a 0.5° latitude–longitude (10 × 10) grid (i.e., the validation grid), AVHRR estimates on a 0.1° (50 × 50) grid, and SSM/I estimates at full pixel resolution (12.5 or 25 km). Area-weighted averaging was used to map the AVHRR and SSM/I estimates onto the validation grid, while bilinear interpolation was used to obtain 0.5° gridded rainfall estimates from the NWP forecasts. In addition, (calendar) monthly estimates on a 0.5° grid were produced by all groups.

Cruise monthly rainfall estimates were produced forall algorithms for each of the three TOGA COARE cruises. Missing pixels in the geostationary analyses were replaced by the average of the nearest estimates in time, then simply summed for the cruise to get monthly estimates. For AVHRR and SSM/I rainfall estimates average rain rates for each grid box were calculated and multiplied by the number of hours in the cruise to obtain monthly estimates. No attempt was made to replace missing data in the AVHRR and SSM/I analyses or to account for possible diurnal bias. Monthly NWP rainfall estimates were obtained by summing the daily values. In addition, a “climatology” estimate was generated from the 20-year set of monthly Pacific atoll rainfall observations by analyzing them onto a grid using a Barnes analysis, then interpolating to obtain values for the appropriate cruise dates.

## 4. Overall results of AIP-3

*d*

*c*

*d*

*b*

*b*

*d*

*a*

*d*

*E*

*a*

*b*

*c*

*d*

*E*

^{−1}was applied to the radar and satellite rainfall estimates to delineate “rain” and“no rain.” The rationale for this threshold is that rain rates below 0.1 mm h

^{−1}are virtually impossible to detect in SSM/I imagery; 0.025 mm h

^{−1}represents one-quarter of this value, since approximately four (25 km) SSM/I pixels cover the same area as a 0.5° grid box.

In the analysis to follow, the term “IR-based algorithms” is used to denote the set of IR, VIS/IR, AVHRR, and mixed IR–SSM/I algorithms. Results from five algorithms were excluded from this report; IR algorithms MA1, MA2, MA3, and MA4 were found to have incorrect dates and times for many of the analyses, and estimates from SSM/I algorithm MZ2 were produced for only a small number of swaths. Mixed algorithm SH1 used International Satellite Cloud Climatology Project (ISCCP) estimates of cloud optical depth as input data, and as a result gave 3-h rain rate estimates instead of hourly. Algorithm HA1 provided estimates from only one DMSP satellite, resulting in only half as many samples as the other SSM/I algorithms. Algorithm IA3 provided estimates for calendar months, but it was not possible to convert these estimates to cruise months.

### a. Monthly rainfall

The algorithms’ performance on a monthly timescale is of particular importance to the GPCP. Table 4 lists the intercomparison statistics for estimated monthly rainfall using all satellite algorithms and NWP models, where all monthly estimates were pooled in space and time. The mean radar and satellite-estimated values refer to the average monthly rainfall across the three cruise“months.”

It is evident from Table 4 that most of the satellite algorithms overestimated monthly rainfall relative to the radar observations. A few algorithms overestimated rain by a factor of 4–6, while a few estimated as little as two-thirds of the radar rainfall. The median value of the ratio was 1.3; that is, the satellite algorithms typically overestimated the monthly rainfall by about 30%.

The ratio of satellite to radar rainfall was not consistent over the entire period. Figure 3a shows a plot of the median monthly rainfall estimated by IR-based algorithms for each grid box versus the radar-estimated values; Fig. 3b shows a similar plot for SSM/I algorithms. In these plots each of the cruise “months” is indicated by a different symbol. Similar behavior is seen for both IR-based and SSM/I algorithms, except for Cruise 1, in which the SSM/I algorithms were more likely than IR-based algorithms to underestimate the rainfall derived from the radar. The greatest overestimates occurred for Cruise 2, which was a period of enhanced convective activity in the TOGA COARE region (McBride et al. 1995). Median values of the ratio statistic for all algorithms were 0.75 for Cruise 1, which was a relatively quiet period, 1.7 for Cruise 2, and 1.4 for the third cruise.

It is interesting to note that the tendency for some satellite algorithms to underestimate the lower rainfall amounts and overestimate the higher rainfall amounts in AIP-3 is counter to the behavior of similar algorithmsestimating monthly rainfall in AIP-1 and AIP-2 (Lee et al. 1991; Allam et al. 1993). This may have to do with the nature of the rainfall in TOGA COARE. Light rain periods were characterized by frequent shallow convection with cells that were too small to be resolved by the SSM/I algorithms and too warm to be detected by the IR-based algorithms. Periods of intense convection, such as occurred during Cruise 2, were accompanied by large cirrus shields that were misdiagnosed as raining by the IR-based algorithms. The reason for the SSM/I algorithms overestimating convective rainfall is unclear.

The rms differences ranged from about 50 to over 700 mm mo^{−1}, with the lowest values corresponding to those algorithms having the lowest bias values, and the largest rms differences corresponding to the highly biased algorithms. The bias-adjusted rms measures the standard deviation of the difference and was less than the magnitude of the mean radar-estimated rainfall for most of the algorithms. One VIS/IR algorithm, HO1 (RAINSAT), had an adjusted rms value of 21% of the radar-estimated monthly rain. The bias and adjusted rms difference of the “climatology” estimate were also lower than those of many of the satellite algorithms.

The correlation coefficient measures the ability of algorithms to detect changes in rainfall over space and time. There is a high degree of correlation between the satellite-estimated and radar-estimated monthly rainfall when all monthly estimates are considered together, with correlation coefficients ranging from 0.69 to 0.90. The NWP models were somewhat less skillful in estimating monthly precipitation, with correlation coefficients of around 0.4.

To determine whether these correlation coefficients were statistically significant and distinguishable from each other, an analysis of the correlation coefficients was carried out following Xie and Arkin (1995). They outline a pair of significance tests that take into account the nonrandom nature of the samples. An effective sample size is proposed that modulates the raw sample size using the spatial autocorrelation function. For the 41 monthly rainfall samples, the effective sample size ranged between 25 and 30, depending on the algorithm. The significance tests showed that all of the correlation coefficients were significantly different from zero, but that two given correlation coefficients must be separated by about 0.15–0.25 (for the range of correlations shown in Table 4) to be considered statistically different at the 95% confidence level. This indicates that it is not possible, from this limited number of samples, to determine with certainty which algorithm estimated monthly rainfall with the greatest skill. It is clear, however, that the satellite rainfall algorithms outperformed all of the NWP models and climatology.

Figure 4 shows a plot of the correlation coefficient between satellite-estimated and radar-estimated monthly rainfall versus the bias-adjusted rms difference normalized by the mean radar rainfall. Successful algorithms, that is, those with high correlations and low rmsdifferences, fall in the upper left portion of the plot. At monthly timescales, the skill of the geostationary (IR, VIS/IR, and mixed IR-SSM/I) algorithms exceeds slightly that of the AVHRR and SSM/I algorithms, with greater correlation coefficients and a tendency toward lower bias-adjusted rms differences. It appears that the advantage of superior temporal and spatial sampling in the geostationary algorithms outweighs the advantage of more physically direct measurements in the SSM/I algorithms, at least on timescales of up to a month.

### b. Instantaneous rainfall

Estimates of instantaneous rainfall rate from all satellite algorithms were intercompared for a “common set” of grid boxes, that is, those for which all algorithms produced rainfall estimates. This process of intercomparing the “lowest common denominator” of instantaneous rain rate estimates ensured that the intercomparison statistics had comparable meaning for all types of algorithms. The “common set” was identical to theset of grid boxes containing SSM/I estimates (since for every SSM/I swath there was a corresponding GMS image measured within half an hour) and contained up to four images each day. Due to the inherent lag in overpass times between the NOAA and DMSP satellites,the intercomparison statistics for AVHRR algorithm IN1 were necessarily computed for a different sampling of data than the common set.

Table 5 and Fig. 5 present the intercomparison statistics for the satellite-estimated instantaneous rain rates.As in the monthly intercomparison, the statistics were computed by pooling all estimates in space and time. The common set contained 1760 samples, with a mean radar-estimated rain rate over all grid boxes of 0.2 mm h^{−1}. Compared to the radar data, almost all of the satellite algorithms overestimated the rain rates, typically by a factor of 1.5, but a few by more than four times. Rms differences varied from 0.6 to 2.7 mm h^{−1}, with the majority of both the IR-based and SSM/I algorithms producing rms differences between three and six times the average radar-estimated rainfall.

For instantaneous rainfall, the IR, VIS/IR, AVHRR, and mixed algorithms had satellite–radar correlation coefficients ranging from 0.39 to 0.58. The SSM/I algorithms performed much better than the IR-based algorithms, with correlation coefficients in the range of 0.60–0.78 for instantaneous rain rates. Within the set of SSM/I algorithms, those that were primarily emission-based and did not use information from the 85-GHz channels showed slightly lower correlations with the radar observations than did those algorithms that included the 85-GHz scattering signal. The statistical significance tests indicate that, for this large number of samples, correlation coefficients differing by more than about 0.04 can be considered statistically distinct at the 95% confidence level. This result shows that the microwave algorithms generally estimate instantaneous rain rates with much greater skill than do the more empirical algorithms that depend on infrared and visible data. The mixed algorithms, although adjusted using SSM/I rainfall analyses, showed similar performance to the IR and VIS/IR algorithms.

The 2 × 2 skill score measures an algorithm’s ability to correctly diagnose the presence or absence of rain, with a score of 1.0 indicating perfect rain detection. Of the algorithms using infrared and visible imagery, AR1 (GPI) showed the greatest skill in delineating raining areas from nonraining areas, with a skill score of 0.46. This reaffirms the utility of infrared brightness temperatures in detecting precipitation in the Tropics. Higher 2 × 2 skill scores were achieved by some of the SSM/I algorithms, with values of up to 0.68. In general, the microwave algorithms showed greater skill than the IR-based algorithms in delineating raining from nonraining areas, which contributed to their greater success in estimating instantaneous rain rates.

### c. Interalgorithm correlations

The similarities between the algorithms can be assessed by computing the correlations between their respective estimates. Mean interalgorithm correlation coefficients are given in Table 6 for monthly and instantaneous rainfall. For each pair of algorithms, interalgorithm correlation coefficients were computed using several thousand gridded instantaneous rain rate estimates or 400 calendar monthly rainfall estimates. These were then averaged for each combination of algorithm types. In Table 6b the values to the lower left of the diagonal represent “wet” correlations; that is, correlations were computed using samples in which at least one of the algorithms estimated rain. The correlations in the upper right of the table were computed from all estimates.

Table 6 indicates that the IR-based algorithms are similar as a group and the SSM/I algorithms are also similar as a group, while the correlations between algorithms of different types are lower. The relative similarity of the IR-based algorithms, especially for monthly rainfall, is hardly surprising since they all relate rainfall to cloud *T*_{B}. The SSM/I algorithms correlate extremely highly with each other for instantaneous rain rates, which may be surprising at first, considering the variety of approaches that are used to estimate rainfall from SSM/I brightness temperatures (Table 2; Wilheit et al. 1994). Even pure microwave emission algorithms such as IA1 and WI1 showed remarkable similarity to pure scattering algorithms such as AD1, BA2, and PE2 (not shown). Most of the SSM/I algorithms use polarization or scattering indices to indicate the presence of rain (see Table 2), which accounts for much of the similarity. Except for the ECMWF model, the monthly NWP and GCM rainfall predictions correlated negligibly with the satellite estimates, as did climatology.

## 5. Case studies

In this section we show examples of four algorithms’ estimates of instantaneous rain rates for two case studies. The two cases examined, 24 December 1992 and 15 February 1993, provide good examples of both convective and widespread stratiform rainfall. In doing this we hope to better understand the behavior of the algorithms, as well as gain further insight into the differences between them.

The four algorithms examined here (AR1, CH1, FE4, and AD1) are familiar techniques in the satellite rainfall community and are currently being used to produce global rainfall climatologies for the wider scientific community. The first, AR1, is the well-known GOESPrecipitation Index (GPI) of Arkin and Meisner (1987). Although it was intended to be used on large timescales (monthly) and spatial scales (≥2.5°), it has demonstrated usefulness in providing instantaneous estimates of rain area (e.g., Puri and Davidson 1992). The GPI rain rate is computed simply as the fraction of pixels in a region with infrared *T*_{B} of 235 K or lower, multiplied by a rain rate of 3 mm h^{−1} to obtain the aerial-average rain rate. The GPI is used by the GPCP to provide estimates of rainfall over land and water between 40°N and 40°S latitude (Arkin and Xie 1994).

The second algorithm, CH1, is a modification of the SSM/I emission algorithm described by Wilheit et al. (1991), which is used to provide global oceanic rainfall estimates for the GPCP. The average freezing level, determined from a scattergram of SSM/I brightness temperatures, is used along with measurements from the low-frequency channels to estimate the rain rate using output from radiative transfer calculations and a simple cloud model. If the signal at 85 GHz shows strong scattering, the emission estimates are replaced by scattering estimates.

FE4, a scattering-based SSM/I algorithm, is a revised version of the algorithm described by Ferraro and Marks (1995). It is used by NOAA to provide global monthly rainfall estimates, which are available on the Internet, and also contributes estimates of rainfall over land to the GPCP (WCRP 1995). The assumption is made that the rain layer extends above the freezing level and thus produces an observed depression in the 85-GHz brightness temperature. A scattering index is computed from a selection of SSM/I channels, then used both to indicate the presence of rain and to estimate the rain rate using an exponential function.

The fourth algorithm shown in the case studies is AD1, which is the modified Goddard Scattering Algorithm (GSCAT-2) (Adler et al. 1993, 1994). Estimates of instantaneous rain rates calculated using the GSCAT-2 algorithm are routinely produced at Marshall Space Flight Center as part of the SSM/I Pathfinder dataset, which is available via the Internet. After delineating raining and nonraining areas using channels at 37 and 85 GHz, the rain rates are estimated as a linear function of the horizontally polarized 85-GHz brightness temperature.

### a. 24 December 1992

Figure 6a shows the radar rain rates at 1031 UTC 24 December 1992. These observations were made during the mature phase of a mesoscale convective system. The image is characterized by widespread stratiform precipitation within which are embedded numerous cumulus convective cells. In this case the stratiform rain flux exceeded the convective rain flux (Carey et al. 1994). The accompanying GMS IR image from 1045 UTC is shown in Fig. 6b.

Intercomparison of the algorithms is shown in Fig. 7 and in Table 7. The leftmost column in Fig. 7 contains plots of satellite-estimated rain rates at full pixel resolution. (Note: the AR1 algorithm, like most IR-based algorithms, can produce rain rates at the GMS 5-km pixel scale; Fig. 7 shows the 0.5° gridded estimates that were produced for use in AIP-3.) Scatterplots show the satellite-estimated versus radar-estimated rain rates as well as the 1:1 line and a rain/no rain contingency table in the lower right corner of each plot. The rightmost column contains histograms of the bias, that is, the pixel-by-pixel difference between the satellite-estimated and radar rain rates, with the frequencies differentiated into three ranges of radar rain rates. Table 7 gives the intercomparison statistics for estimates both at pixel resolution and averaged onto the 0.5° grid.

Compared to the radar estimates of rain rate, all four of the algorithms overestimated the rainfall falling in the area viewed by the radars. The AR1 (GPI) estimated rainfall field for this scene was fairly homogeneous with rain rates at or near the maximum possible for the algorithm (3 mm h^{−1}). This algorithm diagnosed rain from the cold IR *T*_{B} associated with extensive cirrus cloud cover (Fig. 6b), leading to an overestimate of rain area and almost no spatial correlation with the observations. Because the GPI rain rates were fairly conservative, the bias, ratio, and rms differences were lower than those evaluated for the other three algorithms at 0.5° grid resolution.

SSM/I emission algorithm CH1 also overestimated the rain area, although the rain pattern was much better represented. The correlation of 0.65 at pixel resolution (0.70 at 0.5° resolution) was the highest achieved by the four algorithms. Figures 7e and 7f show that bias was greatest for the heaviest observed rain rates, unlike the AR1 analysis. The stratiform rain extent and intensity were overestimated by CH1; this would occur if thealgorithm was sensing rainfall that evaporated before reaching the surface.

The greatest skill in delineating the rain area in this case was shown by scattering algorithm FE4, with a 2 × 2 skill score of 0.76. This algorithm also produced the greatest positive bias, overestimating the mean rain rate (intensity) by a factor of 6. Algorithm AD1 (GSCAT-2), also a scattering-based algorithm, also significantly overestimated the rain intensity. AD1 used a more selective criterion for determining the pixels likely to be raining, which resulted in a smaller rain area than was observed (the probability of detection was 0.49) but also a reduction in the mean bias. When averaged onto the 0.5° grid, the FE4 and AD1 algorithms produced quite similar intercomparison statistics.

In summary, for this case of widespread convective and stratiform rain on 24 December 1992 the rainfall was overestimated by all of the algorithms to varying degrees. The IR algorithm could not detect the spatial variations in rainfall, while the SSM/I algorithms successfully reproduced the spatial pattern of observed rainfall. The scattering algorithms particularly overestimated the magnitudes of the rain rates.

### b. 15 February 1993

This case, from 0711 UTC 15 February 1993, contained clusters of scattered convection throughout the AIP-3 region. The radar rain map (Fig. 8a) shows several storms in various stages of development and maturity, some with local rain rates exceeding 70 mm h^{−1}. The associated GMS IR image from 0745 UTC shows significant spatial variability, with large cirrus anvils associated with some of the storms. The intercomparison statistics for this case are given in Table 8.

Figure 9 shows that the AR1 (GPI) algorithm estimated rainfall in all grid boxes seen by the radar but with a great deal more spatial variability than in the previous case. The rain pattern was well represented, resulting in a correlation coefficient of 0.48, although the average rain rates were too great by a factor of ∼2 when compared to the radar estimates. This led to AR1having the largest bias and rms difference of all the algorithms on the 0.5° grid. However, this algorithm provided the most accurate estimates at high rainfall rates.

The three SSM/I algorithms all underestimated the rainfall in this scattred convection. The emission algorithm, CH1, overestimated the rain area by about 20%. However, the rain rates in many of the pixels with heavy rain were underestimated by several millimeters per hour (Figs. 9e,f). Averaging onto the 0.5° grid smooths out these offsetting errors, resulting in a correlation coefficient of 0.76, the highest of the four algorithms.

Scattering algorithms FE4 and AD1 (GSCAT-2) underestimated the rain area by 36% and 83%, respectively. A strong scattering signal did not seem to be present in many of the pixels that had observed heavy rain rates; AD1 detected almost no rain in the westernone-third of the radar imagery. One reason for the difference in estimated rain extent between FE4 and AD1 is that the latter has a rain rate detection cutoff of 1 mm h^{−1}, and thus does not analyze rainfall at the lowest end of the scale. At the high end of the scale AD1 and FE4 were more successful than CH1 in diagnosing heavy rain rates. The rms differences for the SSM/I algorithms were significantly lower than that of the geostationary algorithm when estimates were averaged onto the 0.5° grid, and the correlation coefficients significantly higher.

In summary, when compared to the radar estimates in this case the IR algorithm overestimated the rain while the SSM/I algorithms underestimated the rain. AR1 (GPI) showed significant skill in diagnosing the rain pattern. For the CH1 emission algorithm the rain area was too large while the estimated rain rates were too small. The SSM/I scattering algorithms underestimated the rain area while producing reasonable rainrates. Nevertheless, all three SSM/I algorithms produced 0.5° gridded estimates that correlated well with the observations.

## 6. Summary and conclusions

AIP-3 evaluated over 50 satellite rainfall algorithms for a 5° square region in the western Pacific Ocean during TOGA COARE, November 1992–February 1993. The satellite algorithms used GMS VIS/IR, AVHRR, and SSM/I data to estimate rainfall on both instantaneous and monthly timescales. Validation data came from two calibrated shipboard Doppler radars measuring rainfall every 10 minutes. All radar observations and satellite rainfall estimates were mapped onto a 0.5° grid to compute intercomparison statistics for the algorithms.

The most important findings of the AIP-3 experiment are the following.

- Most of the satellite algorithms estimated rainfall amounts that were greater than those estimated by the radars, with mean ratio values ranging from 0.6 to 5.1 and a median value of 1.3. There were no categorical differences in bias between algorithms of different types.
- The median value of the ratio of satellite-estimated to radar-estimated rainfall differed substantially for the three cruises, with values of 0.75, 1.7, and 1.3, respectively. This is due to the different rainfall regimes encountered on the cruises. The satellite algorithms tended to overestimate rain in heavy rain situations.
- At monthly timescales, algorithms using geostationary data (IR, VIS/IR, and mixed IR-SSM/I algorithms) exhibited slightly higher correlations with the radar estimates (0.86–0.90) than did estimates based on AVHRR or SSM/I data alone (0.69–0.86). This is a result of the superior spatial and temporal sampling possible using geostationary satellites. Due to the small number of monthly samples, differences of less than about 0.15 between correlation coefficients of the various algorithms are not statistically significant.
- Instantaneous correlations between SSM/I estimates and radar were substantially higher than those of any other type of algorithm, with values in the range of 0.60–0.78. In fact, the lowest of the SSM/I correlations was higher than any other. The statistical significance tests indicated that correlations differing by only a few percent can be considered statistically different with a high degree of confidence. The relative success of the SSM/I algorithms compared to the IR-based algorithms appears to be related in largepart to their superiority in distinguishing raining from nonraining areas. Inclusion of the scattering signal at 85 GHz appears to improve the rain rate estimates relative to those of the emission algorithms.
- The mixed IR–SSM/I algorithms evaluated in AIP-3 had biases, rms difference, and correlation coefficients with the radar estimates that were similar to those of the IR-only algorithms. In order for a mixed IR–SSM/I algorithm to perform better than the IR-only algorithm incorporated within, it must be coupled with a SSM/I algorithm having a significantly smaller mean bias.
- The NWP models overestimated the monthly rainfall during AIP-3. Although they had similar biases and rms differences to the satellite algorithms, the models exhibited much poorer correlations with the radar data (∼0.4).

It is useful to compare the results of AIP-3 with the results of other satellite rainfall intercomparison studies. The above conclusions, except for (6), reinforce the conclusions of AIP-1. Ebert et al. (1996) found that although the algorithms in AIP-3 showed a higher mean bias, their normalized monthly rms differences were similar to those produced in AIP-1 (summertime rain in Japan) and AIP-2 (springtime precipitation in western Europe). The monthly correlation coefficients of satellite estimates with radar estimates were substantially greater in AIP-3 than in the other two experiments. This is in spite of the fact that the grid boxes in AIP-3 were less than one-quarter the size of those used in AIP-1 and AIP-2, increasing the effects of random errors. The performance of the SSM/I algorithms in AIP-3 is similar to that shown in the western Pacific in PIP-1 (Barrett et al. 1994).

For instantaneous rain rates the IR-based algorithms in AIP-3 had normalized rms differences that were comparable to those found in AIP-1 and much better than those found in AIP-2 (Ebert et al. 1996). The correlation coefficients for the IR-based algorithms in AIP-3 were twice as great as the AIP-1 and AIP-2 values, largely because IR-based algorithms are much better suited to estimate rainfall in tropical convection than in other regimes. The SSM/I algorithms in AIP-3 had greater rms differences and slightly lower correlation coefficients than were found in AIP-1, but these differences can be explained partly by the difference in scale. When the instantaneous rain rate estimates are validated on a 1° grid (comparable to the 1.25° grid used in AIP-1), the rms differences decrease by 18% and the correlation coefficients improve by 15%, making the AIP-3 correlations as high as those in AIP-1.

At SSM/I pixel scale, the algorithms in PIP-2 hadnormalized rms differences of about 1.5 mm h^{−1} and correlation coefficients with the observations of about 0.5 for convective systems over the ocean (Smith et al. 1996). The SSM/I algorithms examined in the two case studies presented here had greater normalized rms differences (particularly for the 24 December 1992 case) but similar correlation coefficients (0.42–0.65).

The differences in algorithm performance between the intercomparison experiments are due to several factors. The most obvious factor is the rainfall regime. This is clearly illustrated by the contrast in performance of the IR-based algorithms in the tropical western Pacific as compared to western Europe in spring. The spatial scale of the analysis influences the validation statistics as spatial averaging smooths out much of the random error. The quality of the validation data is an important factor. This led to an enormous quality control effort in AIP-2 (Allam et al. 1993) and a reanalysis of the radar observations in AIP-3 (Short et al. 1997). Finally, it is expected that the relative success of satellite rainfall algorithms in AIP-3 is partly due to improvements in the algorithms themselves with time, as the results of previous intercomparison experiments have been used to refine existing algorithms and develop new ones.

There remain several areas of improvement for satellite rainfall estimation. These include improved delineation of raining and nonraining areas, possible classification of rain into convective and stratiform types, improvements to the rain physics used by the cloud models in some SSM/I algorithms, and further efforts to combine observations from different spectral regions and observing platforms.

## Acknowledgments

Thanks are due to JMA and the University of Hawaii for supplying GMS imagery to augment the Bureau of Meteorology’s archives during TOGA COARE, J. Wilkerson for supplying the SSM/I data, and G. Wick for providing AVHRR data. Thanks also to M. Saiki (Japan Meteorological Agency), J. Janowiak (National Meteorological Center), and the late Bill Heckley (European Centre for Medium-Range Weather Forecasts) for supplying the model analyses and precipitation forecasts used in this project, M. Morrissey and M. Shafer for providing the Pacific atoll rain gauge dataset, and K. Arpe for contributing GCM monthly precipitation estimates. We are very grateful to D. Short, P. Kucera, and B. Ferrier, who painstakingly prepared the radar rainmaps required to validate the satellite estimates. This project was made much easier by the previous work done by T. Lee and J. Janowiak for AIP-1, and R. Allam and G. Holpin for AIP-2. Superb technical assistance was given by D. Howard, M. Perkins, and P. Meighen. Thanks are also due to the anonymous reviewers whose comments improved the quality of this paper.

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Input and validation data used in AIP-3.

Summary of algorithms submitted to AIP-3.

(*Continued*).

(*Continued*).

Rain/no rain contingency table.

Intercomparison statistics for monthly rainfall for the three cruises combined.

Intercomparison statistics for instantaneous rain rates for the “common set.”

Mean interalgorithm correlation coefficients for (a) monthly rainfall estimates and (b) instantaneous rain-rate estimates. The number of algorithms in each group is given in parentheses. See text for detail of Table 6b.

Intercomparison statistics for instantaneous rain rates for the case study of 24 December 1992, for (a) pixel resolution and (b) 0.5° resolution.

Intercomparison statistics for instantaneous rain rates for the case study of 15 February 1993, for (a) pixel resolution and (b) 0.5° resolution.