1. Introduction

A long time series of finescale observation-based global precipitation is needed to support a variety of studies, including global change, surface hydrology, and numerical weather and climate model initialization and validation. However, data record, sampling, and algorithmic considerations limit the range of scales that could be reported with reasonable accuracy. For example, the World Climate Research Programme (WCRP) established the Global Precipitation Climatology Project (GPCP) with the initial goal of producing precipitation estimates on a monthly 2.5° × 2.5° lat/long grid for a number of years (WCRP 1986). The GPCP is succeeding in this goal, with over two decades of data available (1979–99 at present), and routine production continuing a few months after real time.

Because of the lack of finer-scale precipitation data, numerous applications remain stymied. Researchers wish to validate hydrologic streamflow models by forcing them with observed data that resolve individual storms and catch basins. Even monthly scale events are hard to study with calendar-month averages. Extratropical blocking events are a typical example. They initiate and decay within the span of a few days, but can persist for weeks (Blackmon et al. 1984). Calendar-month averages typically mix blocking and nonblocking periods, whereas daily data allow the researcher to composite the data much more cleanly.

The fundamental barrier to finer-scale estimates is the lack of accurate, dense global data, either from in situ or remote sensors. Some regions do have the possibility of detailed precipitation estimates thanks to local networks of sensors, such as the Weather Surveillance Radar 1988 Doppler (WSR-88D) system in the United States (Crum et al. 1998). A few more regions are covered by relatively dense networks of rain gauges, but the coverage is still far short of global, even with respect to land areas. An additional barrier to daily gauge analyses is that there is no uniform standard for the time of report, even within regions. As a result, at most locations around the world it is necessary to depend on satellite-based passive sensors. Microwave radiometers on polar-orbit satellites produce fairly accurate instantaneous estimates, but their sparse temporal sampling constrains the time/space gridding needed to achieve reasonable random errors in the GPCP dataset.

Infrared (IR) radiometers on geosynchronous satellites (geo-IR) provide excellent time and space sampling, but the quantity being sensed (mostly cloud-top temperature) is indirectly connected to precipitation, particularly on the shortest time and space scales, and most acutely in extratropical latitudes. A problem that geo-IR data share with most satellite datasets is that the viewing geometry becomes unfavorable near the limb of each satellite’s view. This problem can be solved in part at tropical and subtropical latitudes by merging all available geo-IR data, but the issue remains, most acutely at higher latitudes and in cases where the closest geosynchronous satellite is not reporting data. An additional barrier is the need to work with several international partners to obtain administrative permissions, maintain routine data deliveries, and dedicate sufficient computing resources before the use of global, full-resolution geo-IR data can be a reality.

Starting in October 1996, the GPCP set the stage for higher resolution estimates by working with the geosynchronous-satellite operators around the world to collect histograms of geo-IR brightness temperature (T_b) on a 1° × 1° grid covering 40°N–40°S at 3-hourly intervals. The availability of this dataset prompted the authors to develop the Threshold-Matched Precipitation Index (TMPI) to estimate precipitation from the 3-hourly geo-IR histograms, described in section 2. To complete the global coverage, a technique for estimating precipitation outside of the geo-IR coverage using sounding data from low-earth polar-orbit satellites was developed, as described in section 3. Together, these form the One-Degree Daily (1DD) dataset, which is a first approach to estimating global daily precipitation at the 1° × 1° scale from observationally based data. The philosophy is to use statistical parameters from trusted estimates to constrain the overall behavior of the 1DD estimates, and then to use the geo-IR and sounder data to determine the day-to-day behavior. In the same vein, the adjustments are computed and applied a month at a time to ensure simplicity and stability. All of the computations in this paper are carried out separately for each grid box (perhaps with some smoothing) unless otherwise stated. Section 4 provides validation results, and section 5 summarizes some examples of 1DD-based analysis.

The reader should keep in mind that the geo-IR and sounder data are responding to clouds, rather than hydrometeors, so there is a substantial algorithmic uncertainty at the finest scales. Our goal is to provide users with unprecedented flexibility in computing time or space averages according to their own requirements.

2. Threshold-Matched Precipitation Index

The Geostationary Operational Environmental Satellite (GOES) Precipitation Index (GPI; Arkin and Meisner 1987) is one popular IR technique that estimates area-averaged rainfall. It assigns the constant conditional rainrate R_c = 3 mm h⁻¹ to all pixels within a given region that have T_b < 235 K, and assigns zero rain rate to all others. These constants were chosen to maximize correlations with hourly (or longer) radar-estimated rainfall on a 2.5° × 2.5° lat/long grid over the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE) ship array in summer 1974. Adler et al. (1993) held the threshold [T_b(rain)] constant and allowed R_c to vary according to calibration between (approximately) time/space-matched GPI and Special Sensor Microwave Imager (SSM/I)–based rain estimates accumulated for a month, creating the Adjusted GPI. In this paper we introduce the TMPI, which allows both T_b(rain) and R_c to vary, following the probability matching concepts in Kummerow and Giglio (1995) and Xue et al. (1999). For simplicity and stability, the (spatially varying) T_b(rain) and R_c are computed on a monthly basis in the TMPI.

The (observational) datasets used for the TMPI (Fig. 1) at present are as follows.

1. GPCP histograms of geo-IR T_b are compiled on a 1° × 1° lat/long grid over 40°N–40°S at 3-h intervals. The histograms have 24 unevenly spaced classes covering 190–270 K.

2. GPCP Advanced Very High Resolution Radiometer (AVHRR) low-earth-orbit IR (leo-IR) GPI estimates are compiled on a 1° × 1° lat/long grid over 40°N–40°S in 3-h averages.

3. The SSM/I occurrence of precipitation according to the Version 6.0 Goddard Profiling algorithm [GPROF 6.0, based on Kummerow et al. (1996)] is computed by the Goddard Space Flight Center Laboratory for Atmospheres on a 0.5° × 0.5° lat/long global grid for each orbit. GPROF is a physically based retrieval that matches observed radiances from all seven SSM/I channels to cloud-model-based radiances, producing pixel-by-pixel precipitation estimates.

4. The GPCP version 2 satellite–gauge [SG; based on Huffman et al. (1997)] combination precipitation estimates (r_SG) are produced on a 2.5° × 2.5° lat/long global grid by month and are box interpolated to 1° × 1° for this study. The SG applies a sequential combination technique to SSM/I, geo-IR, TOVS (introduced below), and rain gauge analyses.

The geo-IR histograms are interpolated to a 1-K interval (Joyce and Arkin 1997) and corrected for zenith angle effects (Joyce et al. 2001), providing an estimate of the true nadir-view IR T_bs. Both steps tend to broaden the geo-IR histograms because both involve estimating sub-bin histogram structure. Such broadening occurs equally in the calibration and estimation steps, so it likely introduces additional random error, but not bias. The revised geo-IR histograms are matched within ±1.5 h to the microwave-based frequency of precipitation and each is accumulated for the month. To further ensure stability, the monthly matched accumulations are smoothed with a 7 × 7 grid-box boxcar filter. In each grid box, the geo-IR histogram is summed starting with the coldest bin until the cumulative fraction of total pixels matches the microwave-based fractional coverage, and T_b(rain) is set to the corresponding T_b. This T_b(rain) is applied to the 7 × 7-box-smoothed sum of all T_b histograms in the box for the month, yielding the fractional occurrence of rain in the full geo-IR dataset for the month, f_IR. The single local conditional rain rate for all raining pixels during that month is computed as

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because we require the TMPI to sum to the (monthly) SG product over the month to maintain consistency between daily and monthly products. We carry out all computations in millimeters per day, although R_c is discussed in millimeters per hour to conform to the usual representation of pixel-level precipitation.

Preliminary work showed that the T_b(rain) and R_c computed in this first round of estimation contain some unrealistic values. Various combinations of parameters were tested for diagnosing this problem, of which the plot of R_c as a function of T_b(rain) seemed the most useful. Note that most points are tightly clustered (Fig. 2), but there is a scatter of high-R_c outliers. Outliers usually occur in coherent patches (outlined with a red line in Fig. 3 for the sample month of January 1998) that tend to be associated with light precipitation totals or strong gradients in precipitation amount, likely due to sampling problems in the SSM/I data. Such values would tend to cause estimation of a few unrealistically heavy precipitation events during the month. Accordingly, an audit procedure was developed that determines new T_b(rain) that are consistent with the SG values, when required. We lack a definitive theoretical basis for identifying outliers, so we have subjectively chosen a linear cutoff that parallels the main cluster and excludes the highest 10% of boxes for the example month (Fig. 2). At this level of approximation we have neglected the hints at nonlinear behavior for low T_b(rain). The outlier R_c values are deleted and the missing values are smoothly filled from the surrounding values. The “audited” R_c values are used to generate audited f and then T_b(rain) estimates. As shown in Fig. 3, the resulting audited fields are physically reasonable. Small errors in setting these parameters are likely not crucial, since the smoothing due to 1° × 1° gridding and daily summation will mask the detailed pixel-level occurrence of rain. The auditing procedure always reduces R_c and increases T_b(rain) and f [except for T_b(rain) = 269 K].

Even this auditing cannot solve all problems when T_b(rain) = 269 K, because the warmest T_b bin in the merged geo-IR dataset contains all values ≥ 270 K. A region with low cloud tops, such as within a subtropical high, likely should have T_b(rain) ≥ 270 K, but T_b(rain) must be limited to the last distinguishable temperature bin of 269 K (the uniform orange areas in Fig. 3), and will be given an artificially high R_c in the first round of estimation. Presently the auditing procedure replaces R_c outliers by (lower) smooth-filled values, even though T_b(rain) is constrained to 269 K. This prevents unreasonable instantaneous values at the cost of failing to sum to the monthly SG value. The penalty for this choice is small because nearly all cases are in low-precipitation regions. Note that the corresponding lower limit of the histogram bins (190 K) is not a problem in practice. This discussion highlights a fundamental limitation of any simple IR threshold technique—all pixels colder than T_b(rain) are labeled “precipitating,” and all those warmer are not. Thus, all precipitation, including that from “shallow” clouds, is represented in the IR approximation by the “deep” clouds, regardless of whether each deep cloud is actually precipitating. The warm limit becomes a problem when there are so few geo-IR pixels colder than 270 K that the precipitation areas sensed by the SSM/I cannot be replicated in the TMPI.

The final audited R_c and T_b(rain) fields (Fig. 3) provide important insights into the systematic regional variations in geo-IR data for the month. Here, R_c and T_b(rain) are near the GPI values in tropical oceanic zones with “heavy” precipitation, but the corresponding land areas show much colder T_b(rain) with higher R_c. This implies that heavy convection in tropical land areas is deeper and more concentrated than over tropical oceans. In the relatively dry subtropical highs T_b(rain) is warm because there is little or no penetrative convection. The relatively low T_b(rain) and R_c over the Sahara Desert help screen out nonprecipitating cirrus that passes over this region during the boreal winter. The gradients along the northern coast of Africa reflect the transition from desert to the pattern of boreal wintertime storms that typifies the Mediterranean.

Holes occur in individual geo-IR images, most routinely in the Indian Ocean sector, where no geo-IR data were available until June 1998. To compensate, leo-IR estimates from the National Oceanic and Atmospheric Administration (NOAA)–series polar-orbiting satellites are processed to fill in holes as necessary. The leo-IR data appear as GPI estimates in the GPCP merged IR dataset and depict rain areas that systematically cover too much area. We address this problem by forcing the month’s fraction of rainy 3-hourly leo-IR grid-box values to match the same fraction for smoothly filled geo-IR. Similar to our TOVS adjustment (section 3), we set to zero the smallest leo-IR rain rates, then linearly rescale the remaining rates to sum to the monthly SG.

The basic output of the TMPI is a sequence of 3-hourly instantaneous estimates, mostly resulting from geo-IR. In the current release, the 3-hourly images in each day (0000 UTC, . . . , 2100 UTC) are summed to produce the daily value. The daily product is considered more reliable than individual 3-hourly images for two reasons. First, GPI-type IR estimates show better correlation with precipitation as the averaging period increases (Arkin and Meisner 1987). Second, the current procedure does not take into account the time of day (i.e., diurnal cycle biases). As a result, the individual 3-hourly estimates are not part of the current release.

One interesting result of the TMPI procedure is insight into the frequency of occurrence of precipitation. If we define “fractional coverage” as the fraction of all satellite pixels contributing to the grid box that have nonzero rain, and “rain days” as the fraction of days on which a grid box has nonzero rain (i.e., at least one pixel with nonzero rain sometime during the day), then we expect the fractional coverage to be less than rain days. In the case of the TMPI, the ratio of fractional coverage to rain days is less than 0.4 almost everywhere (Fig. 4). Furthermore, TMPI and GPI rain day maps are closer to each other than to the rain days apparently implied by summing GPROF over a day. Thus, “low” (instantaneous pixel level) fractional coverage is consistent with “high” (day-average grid-box level) rain days. This demonstrates that the generally low GPROF rain days values are the result of poor time sampling, usually one or two samples in a day, rather than indicating that the GPROF fractional coverage is unrealistically low. The results of comparing Figs. 3 and 4 also verify that TMPI rain days are higher (lower) than GPI rain days for the TMPI threshold above (below) the GPI T_b(rain) of 235 K.

We find that the instantaneous TMPI fields show good temporal and spatial consistency among images, and with the daily TMPI field (Fig. 5). As we expect, the daily fields are smoother, broader, and have lower maxima than the instantaneous fields. Tests show that the daily TMPI correctly sum to the monthly SG, except in the subtropical North Pacific, where threshold saturation becomes serious for this particular month. We also note that monthly sums of GPROF have significant differences from monthly sums of the TMPI (i.e., the SG field, not shown), demonstrating that the GPROF fractional occurrence can be used to formulate the TMPI without GPROF precipitation rates somehow affecting the computation.

3. Rescaled daily TOVS

Outside the latitude band covered by the merged IR dataset (40°N–40°S) it is necessary to base the 1DD on a different dataset. We selected the precipitation estimates that are computed as part of the Susskind et al. (1997) Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) Pathfinder Path A dataset. The TOVS Path A algorithm uses an atmospheric model to generate a first guess for retrieval of various atmospheric parameters, including cloud-top pressure, fractional cloud cover, and relative humidity profile from NOAA-series satellite data. The precipitation algorithm is a regression between these parameters and surface data stratified by latitude, month, and land/ocean surface type. The result is instantaneous pixel-by-pixel precipitation estimates. TOVS precipitation was chosen for the 1DD based on global coverage, reasonable performance, and the authors’ previous experience with monthly accumulations of this product in developing the GPCP version 2 SG product. The influence of the model-generated first guess on the final rescaled TOVS precipitation values is currently under study by the authors, but it is believed to be small. The TOVS precipitation estimates are provided as daily averages on a 1° × 1° global grid.

We find that the number of rain days in TOVS is systematically high in comparison with the TMPI for all months and locations. As well, we wish to ensure that the daily values outside 40°N–40°S sum to the monthly GPCP SG. As a first solution to these issues, we reduce the number of TOVS rain days in a month at each grid box as follows: We compute the ratio of the zonal average number of TMPI rain days in the month to the same for TOVS separately for 39°–40°N and 39°–40°S. Then the number of TOVS rain days for the month at each point in an entire hemisphere is scaled by the corresponding ratio (i.e., 39°–40°N for the Northern Hemisphere). We achieve this smaller number of rain days (in the month for the grid box) by zeroing the smallest rain accumulations (Fig. 6). The largest daily rain amount to be zeroed is labeled as the “revised zero point.” The remaining rain days are linearly rescaled to sum to the monthly SG.

An additional minor issue in the original TOVS estimates is a scatter of missing grid values at high latitudes due to the forward scheme used to remap data from satellite to geographical coordinates. We choose to smoothly fill these holes from surrounding data because they are an accident of the gridding scheme.

The resulting revised TOVS estimates show good agreement with the TMPI across the 40°N and 40°S data boundaries. However, enough discrepancy remained on daily maps that smoothing is performed at the boundaries. Specifically, on each day the differences between TMPI and revised TOVS estimates are computed for each of the 39–40°N and 39–40°S grid boxes, then the difference fields are linearly tapered to zero at 50°N and 50°S, respectively, and added to the revised TOVS. Some spurious “feathering” occurs near the edge of the TMPI domain, but the general effect is beneficial.

4. Validation

5. Examples

The 1DD has been computed for 1 January 1997–31 December 1999, and new months continue to be appended a few months after real time. The days 1–2 January 1998 (Fig. 12) are typical of the estimates. Activity in the tropical Pacific reflects the significant El Niño in progress at the time. The day-to-day traceability of the storm system across the North Pacific is typical of 1DD’s performance. Continuity across the January–February 1998 month boundary was analyzed by applying the “wrong” month’s coefficients (i.e., January’s in February and vice versa) to generate 1DD estimates for 10 days on either side of the month boundary. The results are quite reasonable; about 40% of the nonzero grid box values generated with wrong coefficients are within ±5% of the “real” estimates, and approximately 65% are within ±25%. It is true that the differences have regional coherence, so more-gradual transitions between sets of coefficients should be considered in a future release of the data.

Focusing on a particular event, Fig. 13 shows the progression of Hurricane Mitch in late 1998. (Note that the color bar scale covers twice the range of that in Fig. 12.) This storm moved northwest in the western Caribbean, then stalled just offshore of northern Honduras. Mitch lost strength as it meandered across western Honduras, but a remnant circulation wandered west-northwest and emerged in the Bay of Campeche. It rejuvenated to tropical storm status, moved quickly northeast across Florida, and became extratropical. This dataset allows the events reported on land to be seen in the context of the storm’s complete rain production. Individual daily totals were consistent with values for other tropical storms, but the slow forward speed, looping path, and orographic focussing promoted severe flooding across Honduras and Nicaragua.

The 1DD is particularly useful for forming regional/temporal averages of the user’s choosing. For example, the Indian monsoon is summarized in Fig. 14, which displays time–latitude diagrams for 1997–98 of daily precipitation averaged over 85°–95°E (roughly the span of the Bay of Bengal) displayed for the band 30°N–30°S. For 1DD (Fig. 14, left panel), the main envelope of precipitation broadens from the equatorial Indian Ocean (just west of Indonesia) to include the Bay of Bengal in late boreal spring and then retreats six months later, following the annual march of the sun. The figure shows spectacular, short-lived precipitation events due to averaging over a relatively small area. Careful inspection of Fig. 14 shows that the contours tend to be tilted toward the lower right, indicating that many events move south to north, occasionally from well south of the equator (e.g., see May in both 1997 and 1998). For comparison with the observed data (Fig. 14, left panel), similarly processed National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis estimates (Kalnay et al. 1996) are shown in the right panel of Fig. 14. There is fair agreement, even at the daily scale. The NCEP–NCAR reanalysis tends to have more widespread light precipitation than the 1DD and somewhat lower peak values. As a result, the 1DD distinguishes more clearly between active and break periods in the summer. Such differences are qualitatively consistent with the performance that the authors have seen in the reanalysis, but the quantitative implication depends on further research.

6. Concluding remarks

The One-Degree Daily (1DD) precipitation estimation technique is a complete first-generation procedure for estimating global daily precipitation on a 1° × 1° grid. The algorithm contains two parts; the Threshold-Matched Precipitation Index over the latitude band of 40°N–40°S based on a merged geo-IR dataset with leo-IR fill-in, and a rescaled TOVS at higher latitudes based on the Susskind et al. (1997) TOVS precipitation estimates. Both are designed to sum to the GPCP version 2 monthly satellite–gauge combination. The TMPI reflects the frequency of precipitation occurrence computed from SSM/I, and precipitation occurrence in the rescaled TOVS is adjusted to the TMPI at 40°N and 40°S separately. The 1DD has been computed for 1 January 1997–31 December 1999, and additional months are being computed a few months after real time. The time series of global images show strong continuity from day to day and across the 40°N and 40°S data boundaries. Initial validation studies show that mean absolute errors are relatively large, as one would expect from cloud-based methods at fine time- and space scales. On the other hand, users should see better results if they average the 1DD fields in space or time. The key advantage of the 1DD is its flexibility in allowing users to compute these averages according to their own requirements while maintaining consistency with a standard larger-scale product (the GPCP SG).

The GPCP accepted the 1DD as an official GPCP product in August of 2000. The 1DD is now available from World Data Center A (located at National Climatic Data Center, Asheville, North Carolina).¹

Further development of the 1DD is expected to take a number of directions. First, following standard GPCP practices, fields of error estimates are being prepared to accompany the fields of precipitation estimates, similar to those already available for the GPCP version 2. Second, we expect to work toward releasing individual 3-hourly estimates, although there will be gaps in individual fields at higher latitudes. The major issue in this effort is the importance of the time lag between precipitation and cloud-based estimators. Third, estimates based on low-orbit microwave data will be combined directly with calibrated IR estimates. This might include Special Sensor Microwave Imager, TRMM Microwave Imager, and Advanced Microwave Sounding Radiometer data. Fourth, other sensor systems will be examined for inclusion, including daily gauge data. The last suffers significant difficulties in coverage and time-of-report diversity. Last, we expect to evaluate more-sophisticated IR and TOVS algorithms for possible improvements in accuracy.