1. Introduction

More than two-thirds of the global precipitation falls in the tropical regions of the earth between 30°N and 30°S [e.g., as inferred from the Legates and Willmott (1990) precipitation climatology]. The latent heat released by tropical precipitation plays a vital role in driving low-latitude circulations and in affecting global circulations through teleconnections in the atmosphere. Furthermore, precipitation provides fresh water, and hence buoyancy, in the ocean and is perhaps the most important component of the hydrological cycle (including precipitation, interception, infiltration, runoff, etc.) over land. Despite its importance, precipitation is still one of the most poorly parameterized physical processes in global climate models. For instance, Gates et al. (1996) showed that different ocean–atmosphere coupled climate models differ significantly even for zonally averaged precipitation climatology. The intermodel standard deviation of precipitation is also comparatively large in the Tropics (e.g., compared with other regions) where precipitation rates are themselves largest (Gates et al. 1996).

Because of its large spatial and temporal variability (including intermittency), precipitation is one of the most difficult atmospheric variables to measure. Rain gauge observations are biased due to the effect of wind and other factors (Sevruk 1982), but this bias in most areas is relatively small in magnitude compared with satellite or model precipitation estimates (Xie and Arkin 1995). However, gauge data are not available over most oceanic regions and unpopulated land regions, and the conversion of point values on a sparse irregular grid into areal means introduces sampling errors. Precipitation over the Tropics can also be estimated using the cloud-top visible/infrared (VIS/IR) data from geosynchronous satellites (Arkin and Meisner 1987; Adler and Negri 1988). This technique provides a good temporal resolution of precipitation; however, it is usually established empirically using observations from a specific region so that the coefficient(s) might be region and season dependent, as suggested by Arkin and Xie (1994). Satellite microwave (MW) observations provide a physically more direct approach to estimate precipitation through the emission-based retrieval of atmospheric liquid water (over ocean) or scattering-based retrieval of precipitation-sized ice above the freezing level (over land or ocean). However, time averages computed from MW observations suffer from inadequate temporal sampling. Several intercomparisons of satellite precipitation algorithms have been conducted in the past few years including the Precipitation Intercomparison Projects 1, 2, and 3, sponsored by the National Aeronautics and Space Administration (NASA) Wet-Net Project, and the Algorithm Intercomparison Projects 1, 2, and 3, sponsored by the Global Precipitation Climatology Project (GPCP). For instance, Xie and Arkin (1995) showed that satellite precipitation estimates based on different techniques (i.e., IR, MW scattering, or MW emission) show significant spatial and temporal differences that are also larger than those between various algorithms based on a given technique. For this reason, various approaches have been developed to merge precipitation products from different sources (Adler et al. 1994; Huffman et al. 1997; Xie and Arkin 1997). However, the quality of the merged data strongly depends upon that of the individual input data sources.

These precipitation data have been useful (but not sufficient) for the evaluation and improvement of weather and climate models, because climate models can be tuned to “realistically” simulate observed precipitation distribution (usually) at a cost of even worse simulation of related moist processes. This is indeed a lesson we have learned from the Earth Radiation Budget Experiment (ERBE): most climate models have been tuned to agree with the ERBE top-of-the-atmosphere radiation data but some of the models might give even worse surface radiation fields (e.g., Kiehl 1998). On the other hand, the value of precipitation data would be significantly enhanced if physical constraints could be found between precipitation and other observable quantities: if a climate model can reasonably simulate precipitation distribution and agrees with this relationship, we would gain a measure of confidence in the underlying causes of the simulated precipitation. The purpose of this paper is to establish a quantitative relationship among tropical precipitation, cloud-top temperature, and precipitable water (i.e, the total column water vapor). This relationship can be used to retrieve precipitation in remote sensing and test the integrity of model precipitation and precipitable water, which are two of the most important (but poorly simulated) model variables.

Modeling and satellite retrieval of precipitation are obviously dependent upon the spatial and temporal scales of precipitation. Considering the difficulty in addressing these issues, as a first step, we focus on monthly averaged precipitation at 2.5° × 2.5° latitude–longitude grids over tropical land, coast, and ocean (between 40°N and 40°S).

2. Formulation and data

Rain gauge precipitation and GPI data are taken from the GPCP version 1a (Huffman et al. 1997), and precipitable water data from the NASA Water Vapor Project (NVAP), which combines water vapor retrievals from the Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder and Special Sensor Microwave/Imager platforms with radiosonde observations (Randel et al. 1996). Monthly 2.5° × 2.5° data for 5 yr (January 1988–December 1992) are used. Only results between 40°N and 40°S are discussed, because GPI data are not available at higher latitudes.

Figure 1a shows the global distribution of rain gauges for December 1992 in the GPCP version 1a dataset. As expected, gauges are not available over most oceanic regions (e.g., the eastern tropical Pacific) and unpopulated land regions (e.g., Africa). To balance the conflicting requirements of enough rain gauge stations in a grid box (to avoid sampling errors) and of enough grid boxes (to ensure the statistical significance of our evaluation), only grid boxes with no less than three (or two) gauges over land and coast (or oceanic islands) are used in our validation, as shown in Fig. 1b. On average, about 283, 98, and 76 grid boxes are available for each month over land, coast, and ocean, respectively.

Gauge precipitation is taken as the ground truth for the validation of satellite data. Gauge measurement of precipitation is primarily affected by wind-induced turbulence at the gauge orifice and wetting losses on the internal walls of the gauge. These effects typically introduce a bias of less than 10% for rainfall events, but the bias could be as large as 40% for snowfall events (Sevruk 1982; Groisman and Legates 1994). Furthermore, sampling errors would be introduced when a limited number of gauge data are used to obtain the grid box average precipitation (particularly over mountainous terrain) (Rudolf et al. 1994). Xie and Arkin (1995) demonstrated that at least five gauges are necessary to construct an areal-averaged monthly mean for 2.5° × 2.5° grids with an accuracy of root-mean-square (sampling) error within 10%.

3. Validation

To statistically evaluate the performance of (2), the correlation coefficient, mean absolute deviation, bias, and the ratio of derived over gauge precipitation are computed for each month. The coefficients a₁ and a₂ in (2) are optimized with respect to these statistical quantities using the first year’s data and are given in Table 1. Then (2) is evaluated using monthly data for the other four years. Because the year-to-year variations in these statistical quantities are found to be small [e.g., the mean absolute deviation of correlation coefficients (between satellite and gauge monthly precipitation estimates) over land for the 5-yr period is only 0.06 compared to the mean value of 0.75], only the 5-yr averaged results are shown in Table 2. For comparison, Table 2 also shows the above four statistical quantities using GPI and the multisatellite combined precipitation product (denoted as MS) from GPCP (Huffman et al. 1997). While GPI provides a benchmark against which other satellite rainfall estimation techniques must be compared due to its widespread use, MS represents the state-of-the-art technique in satellite precipitation estimation. Between 40°N and 40°S, this multisatellite product is formed from the IR, microwave emission, and microwave scattering estimates: the GPI estimates adjusted by the time- and space-matched microwave estimates (i.e., AGPI; see Adler et al. 1994) where available; the weighted combination of microwave estimates and microwave-adjusted low-orbit IR elsewhere (Huffman et al. 1997).

Table 2 shows that, over land, our algorithm (UA) has a slightly higher correlation coefficient than GPI or MS. GPI has an average positive bias of 0.89 mm day⁻¹ (or 36% overestimate); in contrast, both UA and MS have relatively small mean biases. The mean absolute deviation from UA or MS is also smaller than that from GPI. This demonstrates that the use of precipitable water in our method or the use of other microwave precipitation estimates in Huffman et al. helps reduce the known deficiency of GPI (i.e., precipitation overestimation) over continental regions (e.g., Arkin and Meisner 1987).

Over coastal or oceanic regions, MS has a slightly higher correlation coefficient and lower mean deviation than either UA or GPI. However, UA has a negligible mean bias, while MS has significant biases of −0.60 mm day⁻¹ (or 19% underestimate) over coast and −1.08 mm day⁻¹ (or 28% underestimate) over ocean, which are even much larger than those of GPI. Though the absolute deviation over ocean is larger than over land or coast, their relative values with respect to the mean gauge precipitation values are quite similar (e.g., 49%, 51%, and 53% over land, coast, and ocean, respectively, using the UA algorithm). The relatively large absolute deviations over land, coast, and ocean in Table 2 are characteristic of satellite estimates of precipitation (e.g., Xie and Arkin 1995; Huffman 1997). They reflect the deficiency of satellite algorithms in estimating precipitation for specific months, but they are also partly caused by sampling errors due to the use of limited number of gauge data [no less than three (or two) gauges over land and coast (or ocean)] for each grid box, as mentioned earlier.

Figure 2 compares UA, GPI, and MS with gauge precipitation binned at precipitable water (w) intervals of 2 mm. Over land, GPI systematically overestimates precipitation. The MS underestimates precipitation when w is high, and all algorithms overestimate precipitation when w is low. Further analysis reveals that most of the grid boxes with low w are located close to 40°N in winter. Even though gauge bias might be as large as 40% for these boxes (Xie and Arkin 1995), it is still much smaller than the difference between gauge precipitation and GPI in Fig. 2a, confirming that“the GPI cannot be used poleward of 20° in the winter hemisphere” (Xie and Arkin 1995). Over coastal or oceanic regions, MS systematically underestimates precipitation. GPI also underestimates precipitation for intermediate w values but overestimates precipitation elsewhere. To test the statistical significance of satellite and gauge precipitation difference in each w interval (33, 30, and 30 intervals over land, coast, and ocean, respectively) in Fig. 2, the test statistic in Eq. (5.8) of Wilks (1995) is used. Over land, 19 of the UA precipitation values (out of 33) fall within the 95% confidence interval (error bars) around gauge data, while the corresponding number is 17 for MS and only 7 for GPI. Over coastal regions, the numbers of satellite precipitation values that fall within the 95% confidence interval around gauge data are 24, 11, and 11 (out of 30) for UA, GPI, and MS, respectively. Over oceanic regions, the number for UA (24 out of 30) is also much larger than those for GPI and MS (11 and 8, respectively).

To further evaluate UA, GPI, and MS, another dataset (i.e., the Comprehensive Pacific Rainfall Data Base; Morrissey et al. 1995) is used. Comparison of the location of these atoll and island rain gauge stations (Fig. 3a) with Fig. 1a shows that many of the stations have already been included in the GPCP rain gauge dataset used in the above validation, hence their use in validating the meridional distribution of satellite-derived precipitation is emphasized here. To evaluate the meridional distribution of precipitation across the Intertropical Convergence Zone (ITCZ) and the South Pacific Convergence Zone (SPCZ), 18 stations (denoted by the plus signs in Fig. 3a) from 20°N to 30°S and between 166°E and 172°W are selected based on two criteria: over atoll or small island, and less than 5 months of missing precipitation data for the 5-yr (1988–92) period. Five-year average precipitation from these stations and UA, GPI, and MS estimates in the corresponding 2.5° × 2.5° boxes are shown in Fig. 3b. The MS systematically underestimates precipitation as shown in Fig. 3b, while GPI significantly underestimates precipitation over the South Pacific. The observed distribution of precipitation, including the two peaks associated with the ITCZ and SPCZ, is better captured by UA than by GPI or MS; for instance, satellite and gauge precipitation differences in Fig. 2b are 0.33, 0.99, and 0.93 mm day⁻¹ on average for the UA, GPI, and MS, respectively. Furthermore, UA reproduces well the seasonal variation of the meridional distribution of precipitation (not shown). Because of the large precipitation gradient across the ITCZ and SPCZ, precipitation averaged over 2.5° × 2.5° grid boxes, as derived from these three algorithms, cannot reach the peak rate of about 10 mm day⁻¹ from gauge (point) measurements.

After its validation as shown in Table 2 and Figs. 2–3, (2) is used to obtain monthly precipitation over tropical land, coast, and ocean. Figure 4 shows the distribution of the 5-yr average precipitation using our algorithm, GPI, and the NVAP precipitable water (Randel et al. 1996). The UA and GPI precipitation have similar spatial patterns but differ in details due to the adjustment of GPI by the precipitable water in Fig. 4c. The overall precipitation pattern in Fig. 4a resembles those from satellite–gauge merged estimates of Xie and Arkin (1997) and Huffman et al. (1997), as well as those of the Jaeger (1983) and Legates and Willmott (1990) climatology. Large-scale features include the maxima of precipitation along the ITCZ in the Atlantic, Pacific, and Indian Oceans; along the SPCZ; and over tropical Africa and South America. Dry zones are also well defined in the eastern part of the Atlantic, Pacific, and Indian Oceans, and over North Africa and Australia.

The differences between UA and GPI estimates and between UA and MS are shown in Fig. 5. Over land, UA precipitation is always lower than GPI (Fig. 5a), as implied by (2) with coefficients in Table 1. In particular, it is lower by more than 1 mm day⁻¹ over equatorial Africa, the Amazon basin, and the Tibetan plateau. Over ocean, it is usually higher than GPI (particularly over the southern Pacific). Figure 5b shows that UA precipitation is higher than MS over most of the regions, particularly along the ITCZ in the Indian and western Pacific Oceans, while the reverse is true along the eastern Pacific and Atlantic ITCZ.

The 5-yr average seasonal precipitation fields based on our algorithm are shown in Fig. 6. The ITCZ over the Pacific and Atlantic Oceans is weakest with a break in the eastern Pacific during December–February (DJF) (Fig. 6a), gets elongated during March–May (MAM) (Fig. 6b), and becomes strongest during June–August (JJA) (Fig. 6c) and September–November (SON) (Fig. 6d) with the maximum precipitation in the eastern Pacific in JJA. The SPCZ exists throughout the year but is strongest in DJF and weakest in JJA with a break between the tropical and extratropical portions. The southeast Asian monsoon is strongest in JJA with the maximum rainfall in the Bay of Bengal (Fig. 6c) that moves to the east-central Indian Ocean in SON and reaches northern Australia in DJF. Tropical continental precipitation follows the insolation into the summer hemisphere. The dry zones identified in Fig. 5 exist for all seasons in Fig. 6 and are most extensive and strongest over the ocean in JJA (Fig. 6c), in North Africa in DJF (Fig. 6a), and in Australia in boreal summer (Fig. 6c).

4. Conclusions

An approximate relationship between monthly precipitation, precipitable water, and cloud-top temperature as represented by the GOES Precipitation Index (GPI) is derived based on precipitation thermodynamics. Coefficients in this algorithm are determined using one year of GPCP monthly rain gauge data and then independently tested using four other years of gauge data. Over land, our algorithm (UA) is more accurate than GPI, while over coastal and oceanic regions it has a smaller bias in precipitation estimation than GPI, but has the same correlation coefficient as GPI. Compared with the state-of-the-art multisatellite algorithm (MS) from GPCP (Huffman et al. 1997), our algorithm has a similar accuracy over land, while it has a much smaller bias, but larger mean absolute deviation, over coastal and oceanic regions. Comparison with the Pacific atoll–island gauge data also shows that our algorithm can reproduce well the observed meridional distribution of precipitation across the ITCZ and SPCZ near the dateline.

This algorithm is then used to produce a 5-yr (January 1988–December 1992) 2.5° × 2.5° integrated dataset of precipitation and precipitable water between 40°N and 40°S. The spatial distribution of the 5-yr annual- and seasonal-mean precipitation reproduces the well-known large-scale precipitation patterns and their seasonal variation.

The small bias of our algorithm (particularly over the ocean) suggests that it would be a good data source in precipitation merging algorithms (e.g., Huffman et al. 1997; Xie and Arkin 1997). The relationship among precipitation, precipitable water, and cloud-top temperature can also be used to test the integrity of precipitation and precipitable water in climate model evaluation. Models that can reproduce the observed spatial and temporal distribution of precipitation and agree with this relationship would increase our confidence in their ability to simulate and predict global precipitation. While algorithm development and validation are emphasized in this paper, its application to model evaluation will be reported later. Potential applications of this algorithm to derive precipitation at higher temporal and spatial resolutions (e.g., 5 day, 0.5°) will also be explored in the future.