Inter-product biases in global precipitation extremes

Figure 1 shows log–log daily precipitation histograms computed from latitudinally-weighted statistics of daily values on a regular 1° × 1° grid for different datasets. The histogram is not normalised, so excesses and deficits do not cancel each other out. Nonetheless, the inter-product bias characteristics are inhomogeneous across magnitudes of precipitation. For instance, GPCP has higher frequency in the intermediate range of precipitation over ocean but quickly drops below all other datasets once daily precipitation exceeds approximately 30 mm d⁻¹. In contrast, HOAPS has a large tail of high precipitation rates at the expense of a relatively low occurrence of intermediate precipitation. This demonstrates that biases in extremes can be fundamentally different from those that constitute the climatology (light and moderate precipitation). The spread among the products is smaller over land than over ocean.

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It is noted that because precipitation estimates have been averaged onto a common 1° × 1° grid in figure 1, products with a higher native resolution would originally have a better capability of capturing extremes (figure S1 and table S1 is available online at stacks.iop.org/ERL/14/125016/mmedia in the supplementary material). Comparing figures 1 with S1 shows that the precipitation histograms at the original resolution are broadly spread across different products, where high-resolution datasets are indeed able to capture higher extremes. The spread is reduced with the signals of heaviest rains averaged out at the 1° × 1° resolution (figure 1). The inter-product spread, however, does not entirely vanishes, implying product-specific biases as described above.

In the figures that follow, extreme precipitation is defined by a 99th percentile threshold (or R99p according to the ETCCDI indices [23],) on a daily, 1° × 1° scale. We have tested the 30 and 20 mm d⁻¹ thresholds for comparison (see the supplemental material). These two fixed-value thresholds correspond to different percentiles in the individual products and hence could potentially yield different extreme statistics from R99p. The zonal-mean extreme precipitation varies in a quantitative sense with threshold definitions, while the overall pattern stays qualitatively consistent among different thresholds.

Figure 2 shows the global distribution of the 2015 annual climatology of precipitation. Each product is presented as the anomaly field from the product ensemble mean (top left). Note that the magnitude of the anomaly field stays much smaller than the ensemble mean and all the products agree well in the general pattern as well as the zonal means (figures 4 and 5 below). Regional precipitation biases nonetheless show some interesting features. Oceanic precipitation from some products (GSMaP, HOAPS, and 3B42) is systematically higher in the ITCZ and lower in mid-latitudes than the ensemble mean, while others (CMORPH and IMERG) show contrasting spatial patterns in the anomaly field. Such a systematic bias pattern might be related to the built-in statistical relation of IR radiance with surface rainfall because dominant convective systems change from one region to the other. Deep organised systems are typical of the tropics while subtropical rainfall mostly comes from shallow cumulus. Mid-latitude storms are typically associated with synoptic-scale frontal systems. Otherwise it is not obvious why some products exhibit certain regional bias patterns given that the basic architecture of the retrieval algorithms is similar. Characteristic regionality in the global distribution of inter-product biases was also shown by [3]. Small-scale structures with alternating signs dominate outside the ITCZ in GPCP and PERSIANN.

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African and South American precipitation is either largely overestimated or underestimated depending on the products, with the consensus being poor even among the two gauge-based products (CPC and GPCC). The disagreement in the Congo is due largely to the known unavailability of data there in 2015 for GPCC and CPC, while origins of the discrepancy in South America are less clear. CMORPH, GPCP, GSMaP and PERSIANN exhibit a feature in the difference to the ensemble mean from 40 °S southward (GPCP and GSMaP also from 40 °N northward). This coincides with the transition from utilisation of GEO + LEO to LEO data.

The global distribution of extreme precipitation is qualitatively different from the climatology (figure 3). Subtropical bands of enhanced precipitation in the ensemble mean of extremes (top left) are in sharp contrast to the ITCZ, which stands out in the climatology. The spatial structure of extreme precipitation bias is more or less homogeneous although the sign and magnitude differs vastly among products. Figures 2 and 3 together show that extremes and climatology bear no apparent similarity in the geographical pattern either of the ensemble mean or the anomaly field.

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To summarise the inter-product differences, zonal mean precipitation climatology and extremes are plotted over the ocean in figure 4. While there is reasonable agreement for the climatology, different datasets have large differences in their extremes. The spread is relatively modest over land (figure 5) as expected from figure 1. Interestingly, most satellite-based products are bound between the two gauge products (CPC and GPCC) for the climatology over tropical land, presumably because the gauge network there is so sparse that two gauge products disagree from each other, depending sensitively on the choice of stations and interpolation schemes. The currently analysed version of GSMaP is heavily adjusted to the CPC product and closely follows the CPC rain in the zonal-mean climatology. Note that latitudes south of 45 °S over land consist almost solely of the southern tip of South America and suffer from larger statistical noise than other domains. Zonal-mean extremes with fixed rain-rate thresholds (20 and 30 mm d⁻¹) exhibit qualitatively consistent spatial patterns in comparison with the R99p extremes although there are differences in absolute values (figures S2 and S3 in the supplementary material).

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The analysis of time series is based on the same data records as in previous sections, i.e. data records from the FROGS archive [22]. The time series are computed either as weighted averages from daily values on a regular 1° × 1° grid per month or as 99th percentiles for a maximum period from January 1979—December 2018. Besides global means within 50 °N/S, means from three zonal bands are analysed: tropics within ±10°, northern hemisphere within 10 °N and 35 °N, and southern hemisphere within 10 °S and 35 °S. TAPEER does not fully cover these regions and is not part of the global analysis. Results related to the zonal bands are shown in the supplementary material. The averaged time series were further processed in two different ways: (1) For each individual data record, region, and metric (here, mean and 99th percentile), the following processing was applied: the climatological mean and annual cycle were computed. Then, the climatological annual cycle was removed. The resulting time series exhibits anomalies around a mean precipitation level of 0 mm d⁻¹. Finally, the mean precipitation was added again. This approach was also applied by [24]. (2) For each region, for each metric and for the period January 2001—December 2013, the ensemble mean was computed. Then, the difference between each data record and the ensemble mean was normalised to the ensemble mean. This relative anomaly (or bias) time series is also used to estimate stability. Here, stability was computed as the change of the relative bias over the period 2001–2013 using a least absolute deviation method (adapted from the routine MEDFIT on page 703 in [25]). Associated uncertainties were computed following [26, 27] (see equation (6) of [27]). The null hypothesis is that the stability is different from 0%/decade and the alternative hypothesis is that the stability is not significantly different from 0%/decade. The null hypothesis is rejected if the coverage probability >95% (or p < 0.05).

We show results from approach (1) first, as this analysis is defined over the full temporal coverage of each data record. Figure 6 shows such time series for the global ocean and land within 50 °N/S. The vertical axis was optimised to allow a maximum zoom into the figure at the expense of a variable y-axis range. In general, the monthly means exhibit fairly good agreement over the ocean and only GSMaP is biased low. For the monthly means over land two clusters are evident corresponding to CPC and GPCC. Clustering around the gauge-based products may be partly explained by the gauge adjustment procedures: GPCP via its monthly adjustment, while 3B42 use a previous version of GPCC, GSMaP and CMORPH adopt CPC, PERSIANN was adjusted to GPCP monthly precipitation and CHIRPS utilises gauge data (see [28] for details on CHIRPS). The difference between the clusters is approximately 0.5 mm d⁻¹ in the 2000s, associated with a bias between CPC and GPCC. This bias is smaller in the 1980s though. Over land PERSIANN exhibits good agreement with GPCP and GPCC, except prior to the late 1980s. Furthermore, it can be seen that monthly means of HOAPS exhibit anomalies that coincide with ENSO variability. For PERSIANN, anomalies in May and June 1984 and June and July 2017 are evident. These anomalies coincide with systematic regional data gaps over Africa, Europe, and the Indian Ocean (May and June 1984) and anomalously low precipitation over the ITCZ in June and July 2017.

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The results for the 99th percentile exhibit less agreement, i.e. a larger spread, and a lower level of clustering than for mean precipitation. In particular, the clustering around GPCC and CPC is no longer evident. Over the ocean, maximum 99th percentiles of precipitation are similar among 3B42, CMORPH, GSMaP and HOAPS while GPCP exhibits minimum 99th percentiles. An apparent jump to lower 99th percentiles for GPCP over the ocean occurs in late 2008/early 2009. It is noteworthy as it is not present in the other data records. Within GPCP the utilisation of SSM/I data ends in December 2008 and transfers to SSMIS in January 2009 [25]. For the GPCP Daily analysis the SSMI/SSMIS data is used to establish a precipitation frequency or precipitation/no precipitation threshold, with mean precipitation intensity determined by the GPCP monthly precipitation. This produces a conservative 99th (and other high percentile) values. The 2009 shift is likely related to a slight shift in that SSMI/SSMIS precipitation threshold that went undetected. This discontinuity may be sensitive to the threshold for extremes and needs further investigation. Over land 99th percentiles are lowest for PERSIANN and CHIRPS and highest for GPCC, with peak values in early 1982. This maximum coincides with the eruption of El Chichon in March 1982. However, values for January and February 1982 are the second and third highest values. Finally, a decrease in the 99th percentile of 3B42 over land between the start of the time series and 2005 is observed which is not evident in the other data records.

Results shown in figure 6 are discussed further because several minima and maxima of globally (within 50 °N/S) averaged values coincide with ENSO: Maxima and minima in mean precipitation and in 99th percentiles over the ocean are observed in 1998, 2010 and 2016 as well as in 1999, 2008 and 2011, corresponding to El Niño and La Niña events, respectively. Mean precipitation minima over land coincide with El Niño events in 1983, 1992, 1997, and 2016. Maxima are present in 1999/2000 and 2010/2011, coinciding with La Niña events. It is noticeable that the 99th percentiles over land do not exhibit minima/maxima in coherence with ENSO. The imprint of ENSO on precipitation was discussed, e.g. in [29, 30] and the contrasting behaviour in mean precipitation between land and ocean was also described, e.g. by [30] [31]. identified the impact of El Chichon and Pinatubo as minima in 1983 and 1991 in precipitation from GPCP [29]. observed coherent variability between precipitation extremes and ENSO over the tropical ocean and increased amplitudes of this variability with increasing percentiles [32]. emphasised that the response of precipitation to ENSO has a strong regional imprint which can locally exceed the expectation from Clausius–Clapeyron due to amplifications of ENSO dynamics by atmospheric feedbacks. They further concluded that the response of precipitation in the warm, moist ENSO regions is similar to the extreme response discussed in [29] while the tropic-wide response to ENSO is small due to compensating moistening and drying effects. Results from analysis of scaling or regression between precipitation and sea surface temperature data can be found in papers mentioned above and in particular in [33] who also utilised data records from FROGS. Note that the minimum in mean precipitation over land in 2005 does not correlate with ENSO or volcanoes. At present, this anomaly cannot be explained. Finally, it is noted that results presented in sections 3.1 and 3.2 are affected by the El Niño in 2015/2016. The observed response of HOAPS to ENSO partly explains the observed behaviour presented in these previous sections.

Time series of anomalies relative to the ensemble mean for the global ocean and land within 50 °N/S are shown in figure 7. Overall features are fairly similar to results shown in figure 6. This is in particular valid for the overall agreement in mean precipitation over the ocean, the clustering in mean precipitation over land and the larger spread in biases for 99th percentiles than for mean precipitation. To some extent the small bias among the mean precipitation over ocean can be explained with the adjustment of PERSIANN and CMORPH to GPCP (the latter over ocean only, see [34]). Maximum temporal variability in mean precipitation over ocean is observed for HOAPS and 3B42, with opposing minima and maxima between both data records reflecting maximum difference in the response to ENSO. The 99th percentile anomaly of CHIRPS over land exhibits a pronounced annual cycle. This indicates that CHIRPS exhibits the largest amplitude of the annual cycle. While hardly evident in figure 6, it can be seen in figure 7 that CHIRPS and CMOPRH are not closely following the 99th percentile anomaly of CPC over land.

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Stability estimates were computed for all time series shown in figure 7 with results provided in table 1. The spread in stability estimates over the ocean is fairly small, with generally non-significant differences among the products. An exception is the stability of 3B42. Prior to 2008 3B42 anomalies are smaller compared to the period after 2010 (see figure 7). In June 2009 elements of the precipitation hardware of TRMM were switched from nominal to back-up (https://pmm.nasa.gov/sites/default/files/document_files/TRMMSenRevProp_v1.2.pdf). However, a clear temporal coincidence between a jump in anomalies and this event is not evident. Stability estimates for 99th percentiles over ocean exhibit a larger spread with values ranging from −6.7%/decade (GPCP) to 7.4%/decade (3B42). Here, stability estimates are generally significantly different. GPCP exhibits the largest difference in stability between mean precipitation and the 99th percentile: while the mean precipitation of GPCP exhibits the highest level of stability, the low stability of the 99th percentile time series is explained by the jump in that time series occurring in late 2008/early 2009 (see second panel of figures 6 and 7). As mentioned earlier, this jump coincides with the change in the utilisation of SSM/I and SSMIS data.

The stability estimates for mean precipitation over land exhibit a fairly small spread, though with quite a few significant differences. CHIRPS, CMORPH and GPCC exhibit non-significant and low stability estimates while the stability estimate of GSMaP (5.3% ± 0.52%/decade) is the largest observed estimate over land. GPCP and GSMaP show maximum absolute stability estimates for 99th percentiles over land. The spread in 99th percentiles is smaller for land-based results than the equivalent ocean-based values. A possible explanation could be the direct or indirect use of rain gauges in the various products. While differences still exist because of the way the rain gauges are incorporated into products, an overall reduction in the land-based variability is not surprising.

It is emphasised that the ensemble mean contains contributions from all data records, including artificial trends and anomalies. Thus, the above stability discussion cannot address the true stability of the data records. However, the presented stability results allow the identification of stability issues in a relative sense and support the identification of spurious changes in the mean relative bias.