Three sets of CLIGEN v5.3 input files for international locations are presented, differentiated by having monthly parameters determined from minimums of 30-, 20-, and 10-year records (note that assumptions were made to handle data gaps which are discussed in Sect. 2.2) (Fullhart et al., 2020a). The distribution of locations for the three datasets is in Fig. 1, which shows 7673 parameter sets based on 30-year records (left panel), 2336 parameter sets based on 20-year records (middle panel), and 2694 parameter sets based on 10-year records (right panel). All locations are unique, with no overlap in locations between the three datasets. As may be seen in Fig. 1, there is relatively sparse coverage for South America, Africa, and southern Asia, while North America, Europe, and Australia have relatively dense coverage. The spatial density of all stations is shown in Fig. 2 so that density may be judged in places where overcrowding of points occurs in Fig. 1, and Table 1 enumerates the number of stations on each continent. Furthermore, a .kmz map layer is available on the Ag Data Commons website (link given in Sect. 4) that can be imported into Google Earth as an interactive map and allows the CLIGEN station closest to an area of interest to be found.

As 30 years is traditionally the minimum record length needed to represent climate, the 30-year dataset may be used to characterize climate normals (Bojinski et al., 2014). The 20- and 10-year datasets, reflecting the most recent monthly records available at each location, may be more representative of current climates in some cases considering the non-stationarity of current and projected climate conditions (IPCC, 2013). In soil erosion modeling, a 20-year record has been suggested as the minimum length needed to represent rainfall erosivity (Wischmeier and Smith, 1978), which may be estimated using CLIGEN (Lobo et al., 2015). It should be noted that in non-stationary climates, CLIGEN inputs may be adjusted to represent departures from climate normals (Pruski and Nearing, 2002; Zhang, 2005; Vaghefi and Yu, 2016). For example, Zhang (2013) determined how CLIGEN's precipitation intensity and skewness factors scale with monthly precipitation to correct for future changes in precipitation.

A list of parameters and their definitions that were determined for each input file is given in Table 2. These parameters are used to model statistical distributions that are randomly sampled by CLIGEN to derive daily outputs. Some parameters such as TMAX AV and TMIN AV (refer to Table 2 for definitions) are also typical climate benchmarks. Another climate benchmark, average monthly precipitation, may be determined by the following calculation from input parameters: 1avg. monthly precip.=n⋅Pavg⋅{P(W|D)/[1-P(W|W)+P(W|D)]}, where n is the number of calendar days in the month being considered, and Pavg is the MEAN P CLIGEN parameter.

The various input parameters were derived from an assortment of data sources. In general, there were two main categories of sources: (1) ground-based precipitation networks, and (2) land-surface and meteorological models that assimilate remote sensing data and ground observations and which reproduce historical time series of variables of concern. The sources of data had various temporal resolutions. In most cases, the data were used to make direct calculation of parameters, but for parameters where the available data were insufficient for direct calculation, parameter estimations were done. Each data source and the resulting parameters are discussed in detail in the following sections.

The primary source of precipitation data is the Global Historical Climate Network-Daily (GHCN-Daily) maintained by NOAA (Menne et al., 2012). The locations shown in Fig. 1 correspond to those of selected stations from GHCN-Daily. These ground-based records enabled direct calculation of five parameters related to precipitation accumulation: MEAN P, S DEV P, SKEW P, P(W/W), and P(W/D) (see Table 2 for their definitions). The GHCN-Daily dataset undergoes rigorous quality control, both to check for consistency of formatting and for the integrity of daily values. Values are removed that fail any test in a suite of quality tests which identify a variety of problems. Durre et al. (2010) outlined 19 of the quality tests in detail.

Short record lengths and missing data precluded a wide majority (∼90 %) of GHCN-Daily stations from being used to create CLIGEN input parameters. A substantial number of data gaps necessitated an assumption for the calculation of the five monthly parameters related to accumulation. To handle gaps, records were queried starting with the most recent year available and going backwards in each time series until the number of months needed could be produced by replacing gaps with existing records from earlier in the time series. Therefore, it was assumed that time series do not need to be temporally continuous. This means that records were accepted which did not necessarily come from sequential months, but which had at least 30, 20, and 10 complete individual months for each calendar month, in order to derive the 30-, 20-, and 10-year monthly statistics, respectively. As a result, record lengths were queried that were often longer than the number of years needed. Also, since representing recent data was a priority, 96 % of stations included at least some data after the year 2000, and 81 % included some data after the year 2010. Ranges of years queried for each station are given in an extensive table available on the Ag Data Commons website (link given in Sect. 4). The ranges are defined by the first and last years with at least one monthly record accepted for use. Ranges in excess of the 30-, 20-, and 10-year minimum record lengths are due to data gaps for respective datasets. The longest viable record length (of 30, 20, and 10 years) was used for each station, such that if a 30-year record was possible, 10- and 20-year records were not created. Therefore, no stations have multiple datasets created for them. This treatment of data gaps complicates the validation of the determined climate benchmarks against other datasets with similar temporal ranges, and the effect of non-stationarity and long-term climate cycles should also be considered.

In soil erosion and runoff modeling, precipitation intensity is a critical factor (Pruski and Nearing, 2002; Nearing et al., 2005). The two parameters related to precipitation intensity, MX.5P and TimePk (refer to Table 2 for definitions), require data with high-frequency measurements such that hyetographs for a single precipitation event may be resolved. Since GHCN-Daily did not have adequate temporal resolution, MX.5P was estimated from the daily data using a temporal downscaling model, and TimePk was assumed to follow representative TimePk values for given Köppen–Geiger climate classifications. The development of these procedures is discussed in Fullhart et al. (2020b, 2021). High-resolution data needed for these procedures came from the Automated Surface Observing System (ASOS) maintained by NOAA with stations distributed across the United States and its territories (Doesken et al., 2002).

In CLIGEN, the MX.5P input parameter is used to parameterize statistical distributions of normalized peak intensity. The definition of MX.5P is as follows: 2MX.5P=1k∑i=1n=kmaxI30i,…,maxI30n, where k is the number of times (years) a record for a given month exists in the dataset, and maxI30 is the maximum 30 min intensity (mm h-1) for each monthly record (Yu, 2005). Since maximum 30 min intensity is most accurately determined from data with as high frequency of measurement as possible, deriving values from data with lower resolutions results in underestimation bias, therefore necessitating use of the temporal downscaling model for MX.5P. The downscaling model took GHCN-Daily data to estimate the MX.5P value that would be expected if derived from the 1 min data. The downscaling model is a machine learning regression using gradient boosting trained with 609 ASOS stations (Fullhart et al., 2020b). The model requires 11 predictor variables shown in Table 3, which are statistics that may be determined from daily data and geographic information, some of which are already CLIGEN inputs. While MX.5P from 1 min resolution was estimated by the model, the predictor variable with the single most predictive power was MX.5P derived from daily data, which was calculated based on an assumption that intensity was constant for the duration of daily intervals (and was therefore grossly underestimated). MEAN P and S DEV P were also important predictors. The MX.5P values estimated by the model were found to have an RMSE of 0.148 in. (3.76 mm) (Fullhart et al., 2020b).

The second intensity parameter, TimePk, represents values at 12 equal intervals along the cumulative distribution function (CDF) of normalized time-to-peak intensity for events recorded at a given station (TimePk is the only input parameter that does not represent monthly values, though there are 12 values per station, each representing quantiles of the CDF). For a given TimePk interval, the definition is as follows: 3TimePki=Ntp(i)Ntot, where TimePk(i) is the TimePk value at interval i, tp is time-to-peak intensity normalized to the event duration, Ntp(i) is the number of events where tp <=i, and Ntot is the total number of events. Interval, i, ranges between 1/12 and 12/12 and varies by increments of 1/12 (Yu, 2005). Events were separated by >=6 h of no precipitation.

In Fullhart et al.  (2021), it was shown that using climate-average TimePk values for the Köppen–Geiger climate classification of a given station resulted in <10 % error relative to true TimePk values, suggesting little variation in TimePk within climate classifications. In this previous study, a different weather station network was used – the U.S. Climate Reference Network (USCRN) at 5 min resolution (Diamond et al., 2013). For the new dataset of CLIGEN inputs, the analysis was repeated for the climate classifications represented by the 1 min ASOS network, though in some cases, climate classifications exclusive to the USCRN were used. Table A1 shows the assumed TimePk values for each climate classification. Of the 30 highest-order climate classifications, 19 were represented by ASOS and USCRN. The remaining 11 classifications were assumed to be the averages of the other TimePk values within respective first-order groups (of which there are five, where A is tropical, B is arid, C is temperate, D is cold, and E is polar). As such, the climate classification of each station was used to index the assumed TimePk values used in the CLIGEN input files. The climate classification of each station was determined based on the Köppen–Geiger climate map of Beck et al. (2018) representing the 1980–2016 time period at 0.083∘ resolution.

The five temperature-related parameters, TMAX AV, TMIN AV, SD TMAX, SD TMIN, and DEW PT (refer to Table 2 for definitions), have straightforward calculations. However, the required data were only available for a subset of GHCN-Daily stations. To avoid limiting the analysis to this subset of stations, these data were instead derived from the model outputs of the ERA5 global meteorological/climate analysis (“ECMWF ReAnalysis”, with ERA5 being the fifth major global reanalysis). The ERA5 analysis was created by The European Centre for Medium-Range Weather Forecasts and the Copernicus Climate Change Service (Albergel et al., 2018; Hersbach et al., 2020). Google Earth Engine was used to download maximum and minimum temperatures at daily resolution and average dew point temperatures at monthly resolution from a grid with 0.25∘ × 0.25∘ spatial resolution (see Table A3 for more information). Values obtained from the grid were unchanged, without any weighting based on proximity to neighboring cells or other forms of interpolation. The monthly dew point temperature was a convenient aggregation of data equivalent to the DEW PT CLIGEN parameter, while daily resolution was needed for the remaining CLIGEN temperature parameters to determine both the average and standard deviation of daily max–min temperatures. Use of the ERA5 model also allowed continuous time series to be obtained without gaps for the 30-, 20-, and 10-year datasets (from 1990 through 2019, 2000 through 2019, and 2010 through 2019, respectively).

Incoming shortwave radiation is represented in CLIGEN by the SOL.RAD and SD RAD parameters (refer to Table 2 for definitions) that require solar radiation with units of langley/d where 1 langley = 41 840 J/m2. These parameters were calculated with relatively high-frequency (3 h) estimates that captured daily and day-to-day variability of radiation taken from the Global Land Data Assimilation System (GLDAS) model produced by NASA (Fang et al., 2009) at 0.25∘ × 0.25∘ resolution (see Table A3 for more information). The outputs of the reprocessed GLDAS 2.0 and GLDAS 2.1 versions were used and downloaded from Google Earth Engine (again, no weighting of values was done based on proximity to neighboring cells). The most recent data available were used to create continuous time series with temporal ranges being the same as those for the temperature parameters. For an individual day, incoming solar radiation was modeled by fitting a Gaussian curve through the 3 h time-averaged data points. Doing this avoided underestimation caused by time-averaging, which would have occurred by considering the 3 h data points alone. Also, if the 3 h intervals did not coincide with the time of peak intensity, comparison to ground observations from AmeriFlux data (discussed more later) showed that the Gaussian curve tended to better approximate peak radiation than the greatest 3 h data point.

A number of stations that existed on coasts or on small islands, particularly in the Pacific Ocean, did not have solar radiation data coverage for their locations because the GLDAS product covers only locations beyond a certain coastal proximity. In total, 390 stations had this problem. For these stations, data from the nearest station with existing data were used. A total of 300 of the stations with missing data were within 100 km of a station with data. Some proximities, however, were much further, with islands in the South Pacific being examples. Similarly, some locations in the existing US CLIGEN input dataset used for validation created by Srivastava et al. (2019) did not have observed solar radiation, and their parameter values were taken from the nearest station with available data, which in some cases were at considerable distances, potentially leading to poor validation in Sect. 3.

To ensure locations are matched for validation, a separate validation from that of Sect. 3 was done for solar radiation parameters. In this, GLDAS output was compared to 10 ground-based AmeriFlux stations that monitor ecosystem fluxes including solar radiation (Hargrove et al., 2003). The AmeriFlux network has stations distributed across the North and South American continents, and the 10 stations were selected from a range of latitudes and climates as a representation of global variability. From these stations, a single year was selected that had the fewest data gaps. Comparison to corresponding GLDAS outputs showed reasonable agreement with an RMSE of 36.6 langley/d and with GLDAS being overestimated by <1 % for monthly values of SOL.RAD. Error was more evident for SD RAD, suggesting that GLDAS was not optimum for capturing the day-to-day variability of radiation. The RMSE for SD RAD was 38.6 langley/d with GLDAS being underestimated by 24.1 %.

Very few applications of CLIGEN have used wind data in the past, perhaps the only one being the blowing snow component in WEPP (Nicks et al., 1989). CLIGEN inputs require high-frequency measurement of wind speed (m/s) and azimuthal wind direction. This includes mean, standard deviation, and skewness of daily wind speed on a monthly basis, and determinations of the average daily percentage of time with wind directions coming from the four cardinal directions, four intercardinal directions, and the eight sub-divisions of these (e.g., NNE, ENE) on a monthly basis. However, wind data were not obtainable for the locations corresponding to the GHCN-Daily stations with the level of detail needed for creating CLIGEN input files. The solution to this was to use the “International Conversion Programs” tool (availability given in Sect. 4), which takes the known daily precipitation accumulation and temperature parameters from an international station of interest and finds the existing station in the US CLIGEN dataset with the most similar climate, allowing its wind parameters to be used (and other remaining parameters, if needed). Information regarding the locations from where wind parameters were taken from is given at the bottom of each input file.