The P background climatology is based on chpclim climatology of satellite, gauge, and physiographic indicators . We retain the same climatological period (1980–2009) throughout the HydroGFD3 data set. The chpclim data set comes in two versions: one with full coverage for the 50∘ S–50∘ N latitude band and one with global land coverage. We choose to make the global-coverage version the main choice but add information from the tropical full-coverage version to increase coverage along coastlines and islands. The original 0.05∘ resolution is remapped to the 0.25∘ resolution of the HydroGFD3 data set, ensuring conservation of precipitation totals. Some issues with the chpclim data set were identified through visual inspection, with observational artefacts in mid-northern Siberia and underestimation in Scandinavia. Therefore, these two regions were replaced by gpcch climatological data for the 1980–2009 period (see Supplement for details). To avoid introducing sharp borders, a zone of five grid points was used around each area as a linear transition from one data set to another. Since Greenland P is poorly mapped by both satellite and gauge data, we have chosen to let its climatology be defined by e5 rather than any of the data sets.

For T, we use the cpct climatology (1980–2009) with only a remapping to the 0.25∘ resolution and in-filling of missing data points using e5. The third climatology consists of the wet-day frequency (1980–2009), which is taken from the Nwet of the cru data set of gridded station observations of the number of wet days in a month. Both T and P are remapped to the 0.25∘ resolution using a bilinear-interpolation method.

In a final step, the three climatologies are harmonized by only retaining the grid points that are available consistently in all data sets and all months. This leads also to the final land mask of the HydroGFD3 data set, for which adjusted data are produced.

The elevation is defined by the e5 surface geopotential divided by the gravity of Earth (9.80665 m/s2).

HydroGFD3 makes use of several different data sets, which need to be stitched together in different configurations depending on the use. Without some kind of homogenization between the data sets, sharp changes in the data are unavoidable when switching from one data set to another. The homogenization used here is performed by only making use of anomalies from the different data sets.

In the earlier version HydroGFD1 , which is closely based on the WFD (WATCH Forcing Data) method , each month of the reanalysis data set is adjusted with the absolute monthly mean of the observational data set. This main principle is retained; however, in a new homogenization step we create new absolute observations by first calculating the monthly anomaly compared to the 1980–2009 climatological period calculated for each data set, then adding this anomaly to the HydroGFD3 climatology. Anomalies are additive for T, 1Tanom(year, month)=T(year, month)-Tclim(month), and multiplicative for P, 2Panom(year, month)=P(year, month)/Pclim(month).

The reverse operation is applied after replacing the climatology.

A common issue with coarse-resolution models, such as e5, is a tendency to produce excessive drizzle that reduces the number of dry days in a month. To alleviate potential excessive drizzle, the number of wet days is adjusted before correcting the P amount. This is performed by first determining the target number of wet days in the month, then setting the days with weakest precipitation intensity to 0 until the target is reached. No adjustments are made for too few wet days. The wet-day frequencies in a month are not well covered by observational monitoring records, and the uncertainties are large when available. We have chosen to estimate the number of wet days based on the method of . Note that we do not need to define a wet day using a specific threshold value. Instead, the number of wet days in a month is directly defined by the method. The method essentially relates the number of wet days, Nwet, to the monthly P anomaly, Panom, using also the climatological wet-day frequency (calculated from cru wet-day data set), Nwetclim as a predictor, and a tunable constant k. 3Nwet=Panomk⋅Nwetclim

A value of k=0.28 was derived for HydroGFD2.0 by calibration to the cru observations of the number of wet days in a month together with the cpcp P observations. This value is almost half of that found by , which can probably be related to the data sets used but was found to be highly applicable across the world. A verification of this constant was performed with the cru wet days and the gpcch monthly P anomalies; see Fig. . This reveals an overall high accuracy of the method, with deviations from observations of mostly only a few days in a month but which can in rare cases be as much as 10 d. On average over the 1980–2009 period and for each single grid point, the deviations are close to 0. Thus, the method works well across all areas and with sufficient precision for our purposes.

The production of the corrected data consists of the following steps.

Calculate observed anomalies.

For P, the scaling can cause very large values in some cases, e.g. when e5 severely underestimates the number of wet days. Therefore, P is limited to a maximum of 1500 mm/day, which is close to the highest observed record at that timescale.

To have consistent output in all versions of HydroGFD3, there are internal checks to verify that each of the defined grid points of HydroGFD3 is receiving data after each monthly adjustment. It happens that the land–sea masks of the observational data sets change over time, and they often differ between different data sources. If the anomaly data are not defined for a particular grid point, a search algorithm will identify if there are defined anomalies in grid points within a five-grid-box radius. If the search is successful in finding at least one value, the mean of all values in the search radius is used to fill the grid point value. However, if no defined data are found, the anomaly will be set to 0 for T and 1 for P; in other words, the adjustment will be toward the HydroGFD3 climatology.

Evaluation of the HydroGFD3 historical data set is presented for the mean climatology of P and T as well as for regional probability distribution functions (PDFs) of daily data and as monthly mean time series. The two latter evaluations are performed for each of the regions defined by (although we use the correct longitude and latitude coordinates provided by ), commonly referred to as Giorgi regions; see Fig. . One exception is that we have left out the EQF region in the plots of PDFs since it is contained in other included regions. The reason is that it overlaps other regions, and having only 25 regions simplifies the presentation layout of the plots substantially. For both the PDFs and the time series, only data points in the defined grid points of HydroGFD3 are used. The PDFs are pooling all data in each domain, whereas the time series plots are based on regional averages for each monthly time step.

The HydroGFD3 data sets are updated at regular intervals. The “extended” period is updated each month as new e5 and other data sets become available. Each tier works independently and can therefore become available at different times.

The “near-real-time” period is updated at earliest 5 d into the new month, when e5t is available. By then, the cpcp and cpct products are generally available, but gpccf normally needs a few days more. Tier 3 needs no additional data sets and is available together with e5t but is produced at the calendar month time step like the other products. The priority order is independent for each variable and goes from Tier 1–3.

Finally, the “trailing” updates are performed along with e5t and cpcp and cpct updates and is normally available at a 5 d time lag.

The climatological period of HydroGFD3 is set to 1980–2009 and is consistently used in this section. Figure  presents the annual mean climatology of HydroGFD3 for both P and T as well as the bias of the e5 reanalysis to this climatology; e5 has in general a wet and cold bias in mountainous regions in most of the world. The Arctic is generally wetter and warmer in e5; note that Greenland P is bias-free per definition since the HydroGFD3 climatology uses e5 there. The tropics are generally drier and colder in e5.

Figures S1–S4 show the seasonal HydroGFD3 climatology and biases of e5. The bias patterns are rather stable across the seasons, although the magnitude changes somewhat. Most striking are the relative changes in western Africa in the December–February period, but this is the dry period there, and the relative changes are therefore comparing low numbers, which tend to exaggerate the absolute term differences.

We also compare the HydroGFD3 climatologies to other data sets, mainly with a focus on data with daily time steps that could be used equally for the historical period but also to gpcch, which is the main background data set for anomalies in the historical period. Figure  shows the annual mean difference in P of gpcch, cpcp, wfde5-gpcc, and wfde5-cru to the HydroGFD3 climatology. Differences to gpcch are generally within ±10 %, except for parts of the Andes mountain range, the Canadian Arctic, the dry north of Africa, the Himalayan plateau, and Greenland. These are all dry and/or snowy regions, with an inherent observational uncertainty, adding the lower gauge network density in the areas. The presented differences between the data sets are considered well inside this expected uncertainty range. We also remark that uncertainties in Greenland are especially large due to few observations and difficult conditions, and data for this region should be used carefully with HydroGFD3 and other data sets alike. The cpcp data set is generally drier, especially in the Arabian Peninsula; wfde5-gpcc and wfde5-cru are both generally wetter than the HydroGFD3 climatology, especially in the cold seasons (see Fig. S5–S8). This is due to the gauge corrections applied in the wfde5 data, which is also the reason for wfde5-gpcc not being identical to gpcch, which it is based on. There are also discrepancies in large dry desert areas such as the Sahara desert, which arise due to differences in the way the number of wet days is calculated in the different data sets. The WFDE5 implementation would produce NaN (not a number) in division by 0 if the number of wet days was 0, which has not happened so far (reviewer comment by Graham Weedon). In HydroGFD3, division by 0 does occur and is solved by setting the ratio to 0 when the calculated number of dry days equals 0. An incompatibility between P and no observed wet days can act to remove P completely for some months, therefore making a drier data set. Seasonal differences (Fig. S5–S8) show similar patterns as the annual mean for most of the regions but can also differ substantially in some regions. One region that stands out is southern Africa in June–August, where both gpcch and cpcp show much wetter conditions (Fig. S7).

For T, we compare to cru only since cpct is used to build the climatology on top of which cru anomalies are added, and wfde5-cru is adjusted to cru and is per definition identical regarding climatology. Figure  shows the absolute difference in cru and the HydroGFD3 climatology for each season of the climatological year. The largest differences are in the Arctic region, where gauge availability is low. In other regions, such as south-central Africa, the Himalayan plateau, and other orographic regions, the differences are very consistent over all seasons, with deviations up to a few degrees Celsius. This makes us suspect that they are due to differences in the elevation used for the different data sets. The cpct data set does not come with any information on the elevations used. The use of anomalies from the cru and cpct in constructing the final data set removes such effects, but the climatological difference remains.

Figure  shows the PDFs for the complete time period 1980–2009 for P and for each of the data sets e5, hgfd3, cpcp, wfde5-cru, and wfde5-gpcc. In these plots, the spread between the coloured lines representing direct observations or e5 adjusted to observations can be interpreted as indicators of the uncertainty in the observed state. Many regions show fairly high agreement between the data sets, including the original e5 data. In some regions, there is a large spread in the observations, and e5 is somewhere in between, e.g. in ALA, GRL, TIB, and SAH. Again, these regions have large observational uncertainty, making it difficult to determine a ground truth. However, in other regions e5 is deviating significantly in part of the distribution, such as in SSA and WAF moderate intensities and AMZ and EAF extreme intensities.

HydroGFD3 tends to have higher extremes than other data sets. This is partly a resolution effect due to the 0.25∘ resolution of HydroGFD3 and 0.5∘ of the other data sets used here. A coarser resolution will move all higher intensities toward the lower intensities (to the left in the PDF plots). That the effect differs between regions is because the extremes are also modulated by the magnitude of the applied correction, i.e. the applied scaling. A scaling factor above 1 will increase the extremes and below 1 will decrease them. The baseline climatology therefore has an impact on the extremes. Also the wet-day calculation of HydroGFD3 can affect the results, and we find that the dry regions, e.g. SAH and MED, have more dry days in HydroGFD3 than in the other data sets. When e5 only gives few P days, while the observational anomaly is high, the scaling factor can become very large, and the only process to limit this is the upper limit of 1500 mm/d, which is seldom reached. The wfde5-gpcc, which has a similar methodology as HydroGFD3, still has lower extremes. Besides the above-mentioned undercatch corrections, the lower extremes may be due to the upper threshold applied to each hour, as can be seen in the original wfde5 code in the CDS (Climate Data Store) catalogue ().

For T, the general shapes of the PDFs agree across all data sets and regions (Fig. ). However, there are sometimes substantial differences between e5 and the observational data sets. Typically, e5 displays issues around 0 ∘C, which is common in global models and related to melting conditions. There are also seasonal offsets outside the range of the observations. HydroGFD3 remains fairly close to cpct and wfde5-cru in most cases. Orographic effects on T were not accounted for in this comparison, which can explain some of the differences in regions with varying orography such as TIB.

To get an impression of the temporal trends and to identify potential issues in the time series, we also investigate the time series as an average over the Giorgi regions. To emphasize differences between the data sets, we discuss mainly differences relative to a common reference, here chosen to be e5. In other words, we present the inverse bias of e5 compared to each observational source.

Figure  shows the results for P for the period 1980–2019, and the absolute values are shown in Fig. S9. Note that wfde5-gpcc ends in 2016, wfde5-cru ends in 2018, and gpccm and gpccfg are only available for the last years. The most striking feature is the strong deviations in cpcp for many of the regions. It also varies significantly with time by changing variance, e.g. in SEA, changing mean value, e.g. in CAS, SAS, and AMZ. In some years, there are significant offsets compared to surrounding years, e.g. in 2014 in NEU, NEE, CAS, and MED. Likely, these issues are due to variations in the underlying station network, but we have not verified this. All data sets show signs of an annual cycle in their anomalies to e5 in colder regions, which is indicative of differences between warm- and cold-season precipitation. The wfde5-gpcc and wfde5-cru data sets display stronger anomalies over the annual cycle in the colder regions compared to other data sets. This is likely due to the undercatch corrections, which are larger for snowy conditions. As expected, HydroGFD3 follows the general trends of wfde5-gpcc, and the other data sets have similar trends besides the cpcp deviations just discussed. The gpccm and gpccf have similar mean and variance as gpcch in the overlapping period and show generally consistent behaviour for the later years. However, some larger anomalies occur in, for example, CAN, CAM, SQF, and SAH.

For T, the anomalies to e5 (see Fig.  and Fig. S10) retain a clear annual cycle in many regions. Sometimes, the annual cycle is mainly for wfde5-cru (e.g, NEU, TIB, SAS) but often for all data sets. HydroGFD3 and cpct are in general close to each other because of the HydroGFD3 climatology reducing the offset to 0. However, cpct has some clear “break points” in its time series in some regions. For example, in NEU, there is a marked change in the magnitude of the anomalies from about 0 to 0.5 ∘C to -0.5 to 0.5 ∘C in about 2006. A similar change about that time is visible also for EAS, GRL, MED, SAS, and NAU. Because the climatologies are calculated for the period 1980–2009, part of these changes are included with the earlier weaker variability. HydroGFD3 is based on cru anomalies pre-2016, but from 2016 on, also its variability is subjected to the changes in cpct.

Some regions display a significant offset between the data sets, such as SEA, CSA, MED, TIB, and SAS, with cru having generally lower T values. Interestingly, changes in cpct after 2006 often act to reduce the offset to e5.

The near-real-time products, in Fig.  called “trailing”, use the daily updates of the cpcp and cpct observations. They are therefore subject to the quality of the cpcp and cpct products and the changes in time as discussed in the previous section. This product follows HydroGFD3 fairly closely to that shown in Figs.  and as the main-version Tier 2 is also based on cpcp and cpct but with corrections at calendar months.

In addition, also the “none” products are created with the trailing time window. These only replace the e5 climatology with that of HydroGFD3 and are the simplest form of corrections of the mean. They act as the last failsafe option in the production chain before defaulting to uncorrected e5 data. We do not present this product in the time series plots since it would only constitute a constant annual cycle offset in comparison to e5.