Contributors: Hannes Konrad (DWD), Thomas Sikorski (DWD), Marc Schröder (DWD), Leonardo Bagaglini (CNR), Paolo Sanò (CNR), Giulia Panegrossi (CNR), Elsa Cattani (CNR)

History of modifications

List of datasets covered by this document

Related documents

Acronyms

Scope of the document

This Product Quality Assurance Document provides a description of the product validation methodology for the Copernicus micrOwave-based gloBal pRecipitAtion (COBRA) Climate Data Record, providing daily and monthly gridded precipitation data. COBRA is based on estimations of instantaneous precipitation rate from conically scanning MW imagers, obtained by applying methodologies of the Hamburg Ocean Atmosphere Parameters and Fluxes from Satellite (HOAPS) produced in the scope of the EUMETSAT CM SAF, and from cross-track scanning MW sounders obtained through the newly developed Passive microwave Neural network Precipitation Retrieval for Climate Applications (PNPR-CLIM).

Executive summary

The Copernicus micrOwave-based gloBal pRecipitAtion (COBRA) Climate Data Record is provided as daily and monthly gridded precipitation data at 1° × 1° spatial resolution. The methodology for COBRA validation, as well as quality assurance measures, are provided at regional and global scale and at different temporal resolutions.

Precipitation rate estimates obtained through the newly developed PNPR-CLIM algorithm, based on the use of Fundamental Climate Data Records and specifically designed for later inclusion in COBRA for climate applications, are validated using high-resolution ground-based high quality dataset (MRMS) covering the Contiguous U.S., and compared against global datasets (GPCP and ERA5).
PNPR-CLIM instantaneous as well as hourly gridded precipitation estimates are compared to the corresponding HOAPS precipitation estimates, the other component of COBRA. In the case of instantaneous observations, we aim to compare both PNPR-CLIM and HOAPS observations against independent in situ observations over ocean, too. An intercomparison over land is not necessary as HOAPS observations are only available over ice-free ocean.

The final daily and monthly gridded COBRA products, based on PNPR-CLIM and HOAPS precipitation rate estimates, are validated using ERA5, GPCP and GPCC data products in terms of global annual mean temporal evolution, which also forms the basis for the evaluation of Key Performance Indicators (KPI). COBRA global maps of long-term temporal means and zonal means are compared to the reference products. The mean errors (mean differences between COBRA and the validation datasets) are decomposed in mean hit error, mean false precipitation, and mean missed precipitation, where "mean" again corresponds to temporal averaging. A comparison of spatio-temporally co-located grid cells in COBRA and the validation datasets is carried out. Finally, COBRA is compared to two high-resolution ground-based datasets, MRMS over CONUS and NIMROD covering Western and Central Europe. Most of the analyses are related to the daily gridded COBRA precipitation, except for the comparison with GPCC which can only be carried out in a meaningful sense on a monthly basis. Additionally, the COBRA monthly mean values, which are obtained as averages over instantaneous observations in one month, are compared to the monthly averages of COBRA daily values. KPIs are evaluated for COBRA daily and monthly precipitation.

1 Validated products

1.1 Instantaneous precipitation rates

1.1.1 PNPR-CLIM

PNPR-CLIM is a passive microwave precipitation retrieval algorithm designed for the MHS and AMSU-B cross-track microwave (MW) radiometers observations. The algorithm ingests Level 1 (L1) brightness temperatures (BTs) provided by the FIDUCEO FCDR for MW sounder (AMSU-B/MHS) for the years 2000–2017, and other geographical and model-derived variables to produce Level 2 (L2) instantaneous precipitation rates (mm/h) at the same spatial resolution and generation frequency as the L1 product.

The cross-track scanning radiometers AMSU-B and MHS provide 90 observations per scan, with 1.1° spacing, corresponding to instantaneous field of view (IFOV) elongating as the beam moves from nadir toward the edge of the scan. The PNPR-CLIM resolution corresponds to the size of the IFOV, approximately circular at nadir, about 15.88 km  15.88 km, and elliptic moving to the edge of the scan, up to about 52.83 km  27.10 km (see ATBD [D1] for details). The complete list of PNPR-CLIM output variables is listed in table 1.

Table 1: List of PNPR-CLIM L2 output variables. Spatial resolution follows the radiometer specifications. Temporal resolution depends on location and number of satellites available.

1.1.2 HOAPS v4

HOAPS v4 instantaneous precipitation rates have been produced in the scope of EUMETSAT's CMSAF. They are based on the CMSAF FCDR for MW imagers SMMR, SSM/I and SSMIS (Fennig et al., 2017). In the present context, i.e. for the years 2000–2017, we use observations by SSM/I and SSMIS. The precipitation rate estimates are provided only over open, ice-free ocean. The FCDR and derived precipitation rates have been extended to the microwave imagers AMSR-E and TMI in the scope of the German Federal Ministry for Education and Research's project on decadal climate prediction. These observations have been included here, too.

1.2 Gridded precipitation rates

1.2.1 PNPR-CLIM-only gridded precipitation rates

For a direct comparison of the newly developed PNPR-CLIM output to selected gridded datasets (section 3.1), instantaneous PNPR-CLIM L2 estimates are processed to obtain hourly and daily precipitation on a regular 1° × 1° grid. The hourly precipitation rate (mm/h) at each grid box is defined as the average, over all the available observations (including any swath of any available platform), in that grid box in the given hourly window. Then, daily gridded rates are obtained as daily totals (mm/d) of the hourly gridded values. PNPR-CLIM hourly data have been processed independently from the procedures mentioned in sections 1.2.2 and 1.2.3.

1.2.2 Hourly gridded precipitation rates

The instantaneous precipitation rates in the PNPR-CLIM and the extended HOAPS v4 database are transferred to a global hourly 1° × 1° grid by averaging data for which the respective instrument footprints have overlaps with the respective grid cell (see the ATBD [D1] for details). In the averaging procedure the instantaneous precipitation rates are weighted by the overlap area. Data from the various platforms are treated separately and merged only later in the process (see section 1.2.3 and 1.2.4). Consequently, we are able to compare collocated values in this hourly, 1° × 1°, per-platform database. The algorithm outputs are post-processed in the sense of a bias correction via quantile mapping and filtering of unphysical observations, see the ATBD [D1].

1.2.3 COBRA daily gridded precipitation

The hourly gridded precipitation rates (section 1.2.2) from more than one platform in the same hourly interval and grid cell are averaged where applicable. Gaps are filled by nearest-neighbour interpolation in the temporal dimension (hourly intervals). The resulting 24 hourly values in one day are accumulated to daily precipitation, given as mm/d. The definition of one day is with respect to UTC. As for the hourly gridded values, the daily values are available globally on a 1° × 1° grid.

1.2.4 COBRA monthly gridded precipitation

Monthly gridded values are obtained from the instantaneous rates directly in the same way as the hourly gridded values (section 1.2.2), i.e. weighted averages of all observations in one month on a global 1° × 1° grid, separately for each platform. The merged product is obtained by averaging the values from the different platforms, weighted by the platforms' temporal availabilities in the respective month.

2 Description of validating datasets

2.1 Global gridded datasets

2.1.1 ERA5

The ERA5 (reference C3S, 2017) global climate reanalysis assimilates observations of different meteorological quantities across the globe into a numerical model of atmospheric dynamics. It produces a large variety of output quantities including precipitation. ERA5 output is available in the CDS by C3S (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=overview) in hourly intervals and as monthly means at 0.25° spatial resolution, starting in 1979.

The hourly ERA5 precipitation is temporally accumulated to match the daily resolution of the aggregated satellite-based estimates (sections 1.2.1 and 1.2.3). The monthly mean and daily accumulated ERA5 fields are re-gridded to the 1° × 1° geographic grid by averaging the values in the 16 contiguous 0.25° grid cells that fall into the respective 1° grid cells. ERA5 daily precipitation at 1° × 1° is compared to the PNPR-CLIM daily (aggregated) precipitation (section 3.1.2), while the ERA5 daily and monthly precipitation at 1° × 1° is compared to the daily and monthly COBRA datasets (section 3.3).

2.1.2 GPCP

The Global Precipitation Climatology Project (GPCP) provides global estimates of precipitation at monthly resolution since 1979 on a 2.5° × 2.5° spatial grid (GPCP monthly v2.3, Adler et al. 2016, 2018) and at daily resolution since 1996 on a 1° × 1° spatial grid (GPCP daily v1.3, Adler et al. 2017, Huffman et al. 2001). The datasets are based on observations by microwave imagers on polar-orbiting satellites and infrared imagers on geostationary satellites. The monthly product is also calibrated against rain-gauge measurements by the Global Precipitation Climatology Centre (GPCC); the daily product is tied to GPCC indirectly via its calibration with the GPCP monthly product. The data are made available via NOAA's National Centers for Environmental Information. They are also available through the C3S CDS.

To evaluate the performance of the PNPR-CLIM, the GPCP daily accumulated precipitation at 1° × 1° is compared with the daily precipitation estimates based on PNPR-CLIM instantaneous rates (section 1.2.1). Both COBRA daily and monthly datasets are compared to GPCP (section 3.3)

2.1.3 GPCC

The Global Precipitation Climatology Centre (GPCC) provides global precipitation analyses as a contribution to the World Climate Research Programme (WCRP) and to the Global Climate Observing System (GCOS). They are based on in situ observations of precipitation from rain gauges. The observations are collected and processed at DWD. We will use the GPCC monitoring dataset v2020 on a global 1° × 1° grid at monthly resolution (Schneider et al., 2020), which is available at the URL below, starting in 1982.
https://opendata.dwd.de/climate_environment/GPCC/html/gpcc_monitoring_v2020_doi_download.html

We choose not to use the respective daily product because of a mismatch in the definition of one day (UTC for satellite observations vs. local time for in situ observations).

2.2 Regional gridded datasets

2.2.1 Multi-Radar and Multi-Sensor System (MRMS)

The Multi-Radar and Multi-Sensor (MRMS) system incorporates observations from polarimetric radars, automated rain-gauge networks, lightning observations and forecast model predictions over the continental USA (CONUS). Data are produced by the National Oceanic and Atmospheric Administration (NOAA)’s National Severe Storms Laboratory (NSSL) jointly with the University of Oklahoma (Zhang et al., 2016)¹. The MRMS products used in this validation study are listed in table 2. They are archived and freely disseminated by the Iowa State University, Department of Geological and Atmospheric Sciences².

Table 2: List of MRMS products,

Two distinct MRMS datasets are considered:

1. Three years (2015–2017) of instantaneous precipitation rates, used for the PNPR-CLIM L2 precipitation rate quality assessment (section 3.1.1).
2. Two years (2016-2017) of gauge-corrected hourly precipitation accumulations, used for the validation of the daily COBRA product (section 3.3.3).

The validation of the PNPR-CLIM L2 instantaneous precipitation rates (section 1.1.1), against MRMS is described in section 3.1.1. Both PrecipRate and RadarQualityIndex³ are modified to match the satellite product resolution. In particular, following the procedure adopted in Kidd et al. (2018), the resolution of the reference products is reduced to 0.15° (approximately the satellite resolution at nadir) by averaging over contiguous MRMS grid cells. The new gridded variables are denoted by PrecipRate_015deg and RadarQualityIndex_015cdeg.

The validation of the COBRA daily product (section 1.2.3), is described in section 3.3.3. For the analysis, the gauge corrected product is integrated over 24 hour and averaged over a 1°×1° regular horizontal grid to generate a daily accumulated precipitation variable, denoted by GaugeCorr_QPE_24H_100cdeg.

2.2.2 NIMROD

The United Kingdom’s Met Office provides precipitation estimates across Europe based on observations at rain radar stations on a 5 km grid (reference Met Office, 2003) in 15-min time steps. The data are available at http://catalogue.ceda.ac.uk/uuid/82adec1f896af6169112d09cc1174499.

The original NIMROD data are converted to mm/d and averaged to represent daily sums⁴ on their native grid. We filter out daily values that are based on less than 32 quarter-hourly observations (one third in a day). The data are then brought to the much coarser 1° grid by arithmetically averaging all daily values from the native NIMROD grid cells that fall into respective 1° grid cells. Respective spatial averages are discarded if they come from less than 190 NIMROD grid cells (about one third of the maximum number of NIMROD grid cells in the respective 1° grid cells). These threshold values are defined ad hoc. They are required because of frequently occurring data gaps in space and time in the NIMROD database.

A detailed description of the regridding, including an assessment of the above thresholds for filtering, can be found in the PQAR document produced in the scope of brokering GPCP in C3S [D2].

2.3 In situ datasets

2.3.1 OceanRAIN

The Ocean Rainfall And Ice-phase precipitation measurement Network (OceanRAIN, Klepp et al., 2017, Klepp, 2015) provides ship-borne, temporally highly resolved observations of precipitation. Observations are available from eight ships between 2010 and 2017. The data can be accessed at https://cera-www.dkrz.de/WDCC/ui/cerasearch/entry?acronym=OceanRAIN-W.

2.3.2 PACRAIN

The Pacific Rainfall Database (PACRAIN, Greene et al., 2008) comprises daily and monthly in situ observations of precipitation from the tropical Pacific basin. For this document, we will use observations between 2000 and 2015. The environment of the various stations (e.g. atoll, land, mountainous) is logged so that specific comparisons, such as for ocean-like conditions only, can be carried out. The data can be accessed at http://pacrain.ou.edu/.

3 Description of product validation methodology

3.1 Stand-alone verification of PNPR-CLIM instantaneous precipitation rates

3.1.1 Regional verification

3.1.1.1 Study period and data filtering

Instantaneous PNPR-CLIM L2 precipitation rates (section 1.1.1) from 2015, 2016 and 2017 are compared with coincident precipitation estimates from MRMS over CONUS (section 2.2.1), where coincident pixels are identified using a nearest neighbour approach. To select the best available observations, only pixels with RadarQualityIndex_015cdeg > 0.9 are considered. Furthermore, a MRMS pixel is classified as precipitating if PrecipRate_015cdeg > 0.1 mm/h and as non-precipitating if PrecipRate > 0.1 mm/h for less than 10% of the original 0.01° cells within the fixed 0.15° grid box. Similarly, a PNPR-CLIM pixel is considered precipitating (non-precipitating) if the estimated precipitation rate is greater than (lower than) 0.1 mm/h. The chosen threshold of 0.1 mm/h is the sensitivity threshold of the algorithm, as explained in the ATBD [D1].

3.1.1.3 Detection statistics

To determine the detection efficiency of the algorithm, statistical scores for the three-year validation period are evaluated. The contingency table of PNPR-CLIM, considered as predictor (x), and MRMS, considered as reference (y)⁵ is defined as:

From the contingency table, we compute the following statistical metrics (Wilks, 2011):

Probability of Detection (POD):

False Alarm Rate (FAR):

Heideke Skill Score (HSS):

POD indicates the probability of detecting precipitating pixels (perfect score POD = 1). FAR indicates the fraction of predicted fictitious precipitating events (perfect score FAR = 0 ).  combines the previous information and indicates the reliability of the model beyond a random agreement with the truth (perfect score HSS = 1).

3.1.1.3 Estimate distribution

The precipitation distributions of PNPR-CLIM (x) and MRMS (y) are compared by considering their joint normalised density (jnd), Pearson’s correlations coefficient (CC), mean error (ME) and root mean squared error (RMSE).

The  is defined as follows. Given an ordered partition  of the interval [0.1, 50] mm/h, the  of x and y with respect to  is defined by

where the symbol # denotes the set size and C is a normalisation coefficient such that \( \text{max}(jnd) = 1 \) . The more the variables x and y agree, the more the jnd concentrates along the bins diagonal, peaking at the most significant (in terms of both frequency and rate value) precipitation bin. The jnd function is shown by means of a two-dimensional density plot.

The CC,  ME and RMSE, are scalar metrics defined as:

3.1.1.4 Single scenes

Specific case studies relative to MHS/AMSU-B overpasses over the CONUS area are selected. For them, both the PNPR-CLIM and the corresponding MRMS instantaneous precipitation rates are displayed on regional maps. All the selected scenes are visually inspected and discussed to assess the coherence between the two products.

3.1.2 Global verification

3.1.2.1 Study period and conventions

The daily gridded PNPR-CLIM observations (section 1.2.1), ERA5 and GPCP data (sections 2.1.1 and 2.1.2) from 2015 to 2017 are selected for the global verification. It is worth noting that since neither ERA5 nor GPCP can be considered reference (truth) datasets, this verification is intended as an inter-comparison for consistency verification at global scale of PNPR-CLIM with other widely used global datasets.

In the following, the aforementioned datasets are represented as time-dependent fields, namely variables depending on both time and space. However, to make the notation cleaner, the explicit space dependence is omitted, as the various employed statistical metrics are computed along the temporal dimension only. Finally, all the computed fields are used to build global maps.

3.1.2.2 Mean error, root mean squared error and correlation coefficient fields

The three datasets are inter-compared by evaluating three standard metrics: the mean error ME, root mean squared error RMSE and linear correlation coefficient CC. Given two different time-dependent fields x and y, the ME, RMSE and CC are the fields pointwise defined by equations (3.1) in each grid cell.

3.1.2.3 Error decomposition

The x and y inter-product mean errors introduced in 3.1.2.2 can be further decomposed to highlight the contribution to their differences. Following Tian et al. (2009),

where MHE, MMP and MFP are the mean hit error, mean missed precipitation and mean false precipitation respectively. Choosing y as reference dataset (i.e. truth-values), these error components are the time averages of three time-dependent fields, namely the hit error HE, missed precipitation MP, and false precipitation FP fields:

where \( \chi_x (\chi_y) \)  denotes the indicator function of \( \{x > \vartheta\} (\{y > \vartheta\}) \) , being \( \vartheta \)  a fixed detection threshold. By definition, the hit error field encodes the estimation differences of the two variables when both are non-zero (within the detection uncertainties). The missed precipitation field is the amount of precipitation of the reference dataset that is missed by the first dataset. Similarly, the false precipitation field is the precipitation estimated by the first dataset that is not observed by the reference.

3.2 Mutual assessment of PNPR-CLIM and HOAPS v4.0

3.2.1 Comparison of instantaneous observations

3.2.1.1 PNPR-CLIM and HOAPS v4.0 intercomparisons

Co-located pairs of precipitation rates by PNPR-CLIM and HOAPS v4 are identified by searching the database of coincident instantaneous estimates in space and time between the two datasets (over ocean only, since HOAPS is provided over ice-free ocean). Results are quantified in terms of hit rates, false alarm rates, correlation coefficients, and quantiles, means, and RMSE of co-located observations (see section 3.1). They are visualised through scatterplots and histograms.

As the results will likely depend on the similarity of the conditions for each pair of co-located observations, values will be filtered with respect to the temporal and spatial distances between the measurements and the scan position. Other filter categories will be the geographical location (mostly latitude) and the occurrence of precipitation (e.g., filtering out observations seeing zero precipitation). Due to the sporadic occurrence of corrupted input data, an additional filter may be applied to the data with respect to certain platforms. Apart from this, we are planning to contrast observations by the two dataset sources (PNPR-CLIM vs. HOAPS v4) rather than single platforms in these two datasets.

The search for every co-located PNPR-CLIM/HOAPS v4 pair of observations is beyond the scope of this quality assessment, as the database of all instantaneous observations is very large. Consequently, we will focus this exercise on certain selected months or years.

3.2.1.2 Comparison of PNPR-CLIM and HOAPS v4.0 with in-situ observations

The OceanRAIN and PACRAIN databases offer independent, in situ-based insight into the real conditions of precipitation over or close to the ocean. PNPR-CLIM and HOAPS v4 instantaneous precipitation rates will be assessed against these in situ observations in the same way as they are compared to each other, see section 3.2.1.1. Results will be separated by the source of the validated datasets (PNPR-CLIM or HOAPS v4) and the validating datasets (OceanRAIN or PACRAIN).

We consider this exercise optional. It can only be carried out if the remaining time before the delivery of the PQAR allows. We will, however, strive to include respective results in the assessment.

3.2.2 Comparison of PNPR-CLIM and HOAPS v4.0 hourly gridded observations

Collocated hourly gridded precipitation rates are identified by searching the complete per-platform hourly gridded dataset for grid cells that are populated with more than one platform over the full period (2000–2017). Latitudes poleward of 75° are excluded because they are rarely available in HOAPS v4 and usually flagged as low-quality estimates in PNPR-CLIM. We do not compare single platforms to each other, but only datasets, i.e., PNPR-CLIM vs. HOAPS v4, PNPR-CLIM vs. PNPR-CLIM, and HOAPS v4 vs. HOAPS v4. Hit rates, histograms, and means of differences, as wells as RMSE in the ensemble of collocated values are evaluated (see section 3.1). These statistics are evaluated partly for the entire ensemble, and in specified subsets such as collocated observations falling into certain latitudinal bands, years, months, and/or ranges of precipitation rate.

We caution that collocated pairs of observations cannot be filtered with respect to the proximity of the underlying instantaneous measurements in space and time. Collocated observations are only known to have occurred in the same 1° × 1° grid cells and in the same hourly interval.

3.3 Assessment of merged, gridded COBRA datasets

The evaluation of the gridded COBRA products focuses very much on the evaluation of the daily product. The monthly gridded product is based on the same observations and will consequently mainly feature a smaller temporal variability than the daily product with its sub-monthly resolved processes. A full analysis of the monthly product would produce redundant results, especially where the sub-monthly variability in the daily data is averaged out. The monthly product is evaluated only in the following contexts:

1. The evaluation of the time series of global means (section 3.3.2.1). These means are necessary for the assessment of Key Performance Indicators (KPI) of the daily as well as the monthly product.
2. The comparison with GPCC (section 3.3.2.6). This comparison is carried out only for the monthly COBRA product. The comparison at daily scale is hampered by supposedly different definitions of one day, a feature that will have a small impact on monthly resolved data.
3. The comparison of the monthly COBRA product with the monthly averages of the daily COBRA product (section 3.3.4). This is done because the respective temporal agglomeration procedures are intentionally not the same.

3.3.1 Assessment of spatiotemporal completeness

Gaps in the daily and monthly fields are identified and quantified.

3.3.2 Comparison with global datasets

3.3.2.1 Time series of global averages

Over the full time period (2000–2017), daily and monthly global average precipitation rates are computed from the COBRA CDR. These values are compared with global averages from the ERA5, GPCP, and GPCC datasets by evaluating differences. We produce figures of the respective time series and common statistics in the time series of differences, i.e., extreme differences, quantiles, mean, and standard deviation. As GPCC is only provided over land, the averaging for the GPCC-COBRA comparison is carried out only over land.

The KPI accuracy and stability are also evaluated based on these time series of global averages with respective GPCP data as daily and monthly reference datasets. For the KPI accuracy, we evaluate the instances when the difference between COBRA and GPCP remain below the target value of 0.3 mm/d (for both daily and monthly data). Ideally, this would be true for each instance (time step) in the time series. For the KPI stability, a polynomial of degree 1 is fitted to the time series of differences in a least-squares sense. The slope of the polynomial represents the KPI stability. The target value for KPI stability is 0.034 mm/d/decade.

3.3.2.2 Climatological means

Over the full time period (2000–2017, of T= 6575 days) we analyse the three global datasets available at daily temporal and 1° spatial resolution: COBRA, ERA5 and GPCP (described in section 1.2.3, 2.1.1, 2.1.2). Over three separate sub-periods of six years each, namely 2000–2005, 2005–2011 and 2011–2017, and the entire time period, the climatological means of the three datasets are computed. The differences of these averages among the datasets are also discussed.

3.3.2.3 Error components

The average differences are mean error fields (see section 3.1.2.2) and they are decomposed into the three components, i.e. mean hit errors, missed precipitations and false precipitations for a given reference dataset (see equations (3.2) in 3.1.2.3). The error components between COBRA and GPCP, between COBRA and ERA5, and between ERA5 and GPCP are discussed.

3.3.2.4 Zonal means

The zonal means may highlight meridional fluxes and are crucial for assessing the hydrology balance on a global scale. For each product x, its zonal mean \( \overline{x}^\Lambda \)  is computed as the average of the climatological mean over the latitude \( \lambda \)  (weighting by the 1° resolution in latitude):

The zonal means of the three datasets are intercompared. Furthermore, we analyse the ocean and land zonal means of each dataset. These are given by \( \overline{\chi_{o} \cdot x}^\Lambda \)  and \( \overline{\chi_{l} \cdot x}^\Lambda \) , where \( \chi_o \)  and \( \chi_l \)  are the indicator functions of the ocean and land respectively.

3.3.2.5 Analysis of spatiotemporally collocated grid cells

The distributions of the three datasets available at daily temporal and 1° spatial resolution, COBRA, ERA5, and GPCP are analysed over the entire time period (2000–2017) and sub-periods (2000–2005, 2005–2011 and 2011–2017). Each dataset consists in a three dimensional variable with 6575 × 359 × 719  (time, latitude and longitude) dimension. These N = 1,697,145,575  values define the dataset distribution.

The density functions (Df) of the dataset distributions and respective statistics, as well as overall ME, RMSE and CC are considered in this analysis. The ME,  RMSE and CC are computed accordingly with equations (3.1), and Df is defined by⁶:

All the evaluations are performed near-globally (75°S–75°N) and on single categories identified by land, ocean and 3 latitude bands (75°S–25°S, 25°S–25°N and 25°N–75°N).

3.3.2.6 Comparison with GPCC

The comparison of COBRA with the rain-gauge based GPCC dataset is carried out on the basis of monthly mean values. The respective daily resolved datasets are incompatible because of the definitions of one day in these two datasets. We compare the climatological means based on monthly fields (comparable to section 3.3.2.2).

3.3.3 Comparison with high-resolution regional datasets

For the comparison of COBRA with the high-resolution regional ground-based datasets MRMS and NIMROD, we analyse collocated daily gridded values on 1° × 1° grid (see sections 2.2.1 and 2.2.2). Due to the high spatiotemporal sampling of the original data, we can assume that the MRMS and NIMROD data are representative of daily precipitation. We evaluate common statistics, such as quantiles, means, ME, RMSE, CC (see section 3.1) and illustrate the underlying distributions via scatterplots or histograms. We also produce maps of ME, RMSE and CC.

3.3.4 Internal validation of monthly mean precipitation

COBRA monthly means are not simply computed from the daily gridded values, but from instantaneous observations in each month (see section 1.2.4). This choice was made for three reasons:

• It provides users with a perspective on the data that would otherwise not be accessible.
• The respective standard deviation gives an impression of real spatial and temporal variability in the month.
• As no additional assumptions go into the averaging, in contrast to the hourly gap filling in the case of the daily data, it is as straightforward as possible in terms of processing.

An additional analysis will be included here that will summarize the deviations between the official COBRA monthly mean observations and respective monthly averages of the COBRA daily observations. This analysis will assess differences in the 2000–2017 average spatial fields, comparable to section 3.3.2.2, and in the time series of global averages, comparable to section 3.3.2.1.

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