Comment on essd-2020-370

Dear Editor The editorial support team Copernicus Publications Hello I am thankful to you for allowing me to review ESSD manuscript. The present MS targeted the calculation of R factor for China using high resolution data. The work was a good and tedious one and I liked it. However, I am against its acceptance for publication thanks to many deficits and ambiguities found in the context and made it unclear in many aspects. The big issue refers to the rationale of the work. The formulation of the research setup needs more strong rationale particularly in the viewpoint of agreement with real conditions. No proper reviewing of literatures with further focuses on the main goals of the study and recent none-Chinese ones has been made. It has no detailed and documented information on methodology. It has no comprehensive and integrated discussion. According to the comments mentioned above and some comments, revisions or suggestions appended in the context, I therefore suggest resubmitting a new and substantially improved MS. My all comments and suggestions have been annotated in the reviewed file as an attachment.

by distrometers, which are not easy to obtain for long periods. Fortunately, there is a good relationship between kinetic energy KE and the instant intensity I, so KE was estimated based on KE-I relationship using breakpoint data in USLE and RUSLE. One-minute interval data are the finest resolution data measured by automatic tipping bucket rain gauges we can obtain up to now. Therefore, breakpoint data and 1-min data are the best datasets for deriving precipitation intensity and estimating rainfall erosivity given the absence of raindrop sizes observations. We have revised here into "One-minute data are the finest resolution data measured by automatic tipping bucket rain gauges we can obtain up to now, therefore they are one of the best datasets for deriving precipitation intensity and estimating rainfall erosivity.".
1.17 Line 72: "The study of  was chosen". Should be "The study of Yin et al. (2019) was chosen". Response: We have revised the manuscript accordingly.
1.18 Line 73: "New R factor and 1-in-10-year EI30 maps were produced in this study may improve the estimation of the soil loss in mainland China." You have worked on R factor and therefore not allowed concluding soil loss or soil erosion rates!! Response: Quality estimates of the R-factor would allow improved erosion prediction using the RUSLE technology.
1.19 Table 1: How these interpolation techniques have been matched?? Response: We agree that these interpolation techniques were not matched. After further confirmation, we modified the "Contour mapping" into" unknown", the "Kriging" method by Zhang et al. (2003) and Liu et al. (2013) into "Ordinary Kriging".
1.20 Line 89: "Observation was suspended in the snowy season". How did you do it?? Response: As mentioned in Line 111-113, if the observations were suspended in cold season, precipitation occurred during this period of time were not included in this study for the following two reasons: (1) Stations with missing observations in cold season were mostly distributed in the northern part of China, where the climate is usually dry in winter due to the monsoon system; (2) Usually the precipitation in cold season was in the form of snow other than rain.
1.21 Figure 1: How this gap region was managed?? Response: This region was interpolated with Universal Kriging. We agree that a lack of stations in this region would bring about large uncertainty in the estimation of rainfall erosivity in this region. We have added some discussions on this limitation: "(d) Station distribution and density. In western China, the stations were sparse and unevenly distributed, which affect the interpolation accuracy".
1.22 Figure 2: Same issue!! Lack of station!! Response: It is true that station densities in Tibetan Plateau and southern Xinjiang are limited, especially for 1-min resolution data. There are large areas without any observation due to its high elevation in Tibetan Plateau and great desert in southern Xinjiang. The evaluation based on 1-min data does not cover these areas without observations in this study. As mentioned above, we have added some discussions on this limitation: "(d) Station distribution and density. In western China, the stations were sparse and unevenly distributed, which affect the interpolation accuracy".
1.23 Line 119: "period of >= 6 hours of non-precipitation was regarded as the separation of two rainfall storms". This criterion has to be adjusted for the study region!! Response: Minimum inter-event time (MIT) is an index used to delineate independent storms from sub-daily rainfall records. An individual storm is defined as a period of rainfall with preceding and succeeding dry periods less than MIT. To be comparable with Wischmeier and Smith (1978), and (Renard et al., 1997), 6 hrs was adopted as the MIT in this study, since this paper on a data product is all about enabling the application of the RUSLE in a consistent manner.
1.24 Line 120: "amount of >= 12 mm". Do not think it would be too much?? Response: We do not want to be too creative here, just to use ULSE/RUSLE guideline to be consistent. Some storms with total precipitation amount less than 12 mm but with high intensity and short duration may result in soil loss, whereas some storms with total precipitation amount more than 12 mm but with low intensity may not result in soil loss. As Xie et al. (2002) pointed out, in practice, it is impossible to separate erosive and non-erosive rainfalls completely based on only one or two threshold values because of the complexity of rainfall characteristics and temporal variations in the system response in terms of runoff and soil loss. Xie et al. (2002) identified the erosive rainfall threshold that storms actually caused erosion were omitted from the calculations, while certain storms that do not cause erosion were included in the calculations in order to balance those omitted. In the study, rainfall and runoff data measured for three plots and a small watershed from 1961 to 1969 at the Zizhou experimental station of the Yellow River Basin in China were used. The erosive rainfall amount threshold proposed by Xie et al. (2002) was 12 mm, which was very close to the threshold suggested in the USLE (12.7 mm).
1.25 Line 123: "intensity I30 (mm h-1)". How sure you are that it is the best index?? Response: Wischmeier and Smith (1958) analyzed precipitation and soil loss data from fallow plots at three observation stations in Missouri, Iowa, and Wisconsin and identified that the event EI30, the product value of total storm kinetic energy (E) and its maximum 30-min intensity (I30), estimated the single storm soil erosion best. Wischmeier (1959) analyzed approximately 8000 plot-years of basic runoff, soil loss, and associated precipitation and related data in 21 states in the eastern part of the United States gathered by the National Runoff and Soil Loss Data Center from the erosion stations that were operating at that time. They confirmed the R factor's suitability at these locations, not only for fallow plots but also for continuous row crop plots, and not only for storm-to-storm variation but also for seasonal and yearly variations.
1.26 Line 123: "1-hour intensity H60 (mm h-1)". It is strange!! What for it was?? Response: For hourly data, it cannot calculate I30 directly. When there is only hourly precipitation data available, product of the kinetic energy, E, and the maximum 1-hour intensity, H60, in the storm was used to calculate the storm rainfall erosivity, which was then adjusted by multiplying a conversion factor proposed in Yue et al. (2020) to be comparable with EI30 based on breakpoint data or 1-min interval data.
1.27 Line 132 (equation 5): Still I am not convinced!! Response: Yue et al. (2020) showed that the R factor calculated by 1-hour rainfall data had a good linear relationship with that estimated by 1-min data based on observation rainfall data at 1-min intervals from 62 stations over China. The determination coefficient R 2 was 0.994. The slope of the regression model (1.871) can be regarded as a conversion factor to obtain the R factor using hourly data.
1.28 Line 150: "The effective years of hourly data were no less than those of daily data (37% of the stations)". On which basis?? Response: We have revised here as "The calculation of the R-factor considered the following two cases: (1) The effective years of hourly data were no less than those of daily data (871 out of 2,381 stations); (2) The effective years of hourly data were less than those of daily data (1,510 out of 2,381 stations).".
1.29 Line 153: "then adjusted by the mean annual rainfall calculated by daily data". How this equation has been attested?? Response: The exponent value of 1.481 was estimated using the relationship between the mean annual precipitation and the R-factor. The latter was computed using 1-min and daily rainfall data for 35 stations in China with a common period of record of > 10 years (Fig. 2) as follows: = 0.156 · 1.481 , (Eq. 9 in the revision) where Rmin was the R-factor (MJ mm ha -1 h -1 a -1 ), and Pm was the mean annual precipitation (mm) using 1-min data. The coefficient of determination (R 2 ) was 0.776 for Eq. 9.
To adjust the R-factor from hourly data of shorter record length to those from daily data of longer record length with Eq. 8 in the revised manuscript, daily data from 1,510 stations were used. where Pd and Ph are the mean annual precipitation estimated using daily data and hourly data, respectively. The adjustment proceeded as follows: (1) Calculate the mean annual precipitation and the R-factor (denoted as R) from the daily data of 1,510 stations; (2) Let M be the sample size of daily data, and N that of hourly data, and M > N. Randomly select N years of daily data and calculate the mean annual precipitation (Psample) and the Rfactor of the sample data, and call this Rsample; (3) Adjust the R-factor using the mean annual precipitation for the selected N years: where adj is the adjusted R-factor, P is the mean annual precipitation using all the available daily data; (4) Calculate the absolute relative error of the adj and the using the following equation: (5) Repeat the step (2) to (4) 50 times and calculate the 5th-, 25th-, 50th-, 75th-and 95th percentile of ARE and ARE ; (6) Compare the difference between the percentile values of the absolute relative error before (ARE ) and after adjusting (ARE ).
The following figure shows that for most stations, the absolute relative error of the R-factor decreased after the adjustment. The decreasing mainly ranged 0~20%, indicating a corresponding improvement in the R-factor by 0~20%. Figure 1 Decrease in the absolute relative error after following the adjustment 1.30 Line 162 (equation 9): The entire investigation hinges on a set of recessive equations and models developed by formers which certainly leads to an cumulative errors or uncertainties for which no justification has been provided!!! Response: About the validation of Eq. 9, please refer the previous comment and response. In addition, some discussions on the uncertainty were added in the revision: "…… (c) The adjustment of the R-factor from the stations with less effective years (Eq. (8)). This is based on a power function (Eq. (9)) of the mean annual precipitation and rainfall erosivity using 1-min and daily rainfall data of 35 stations" in the discussion part.
1.31 Line 226: "3.1 Accuracy evaluation on erosivity maps" It seems to be precision rather accuracy!! Response: Accuracy is how close a measurement/estimation is to the correct value for that measurement. The precision of a measurement system refers to how close the agreement is between repeated measurements (which are repeated under the same conditions). We think it is accuracy here in this study.
1.32 Line 230: "particularly noticeable for western China". Where limited stations are available!! Response: We agree that limited stations were used in western China to estimate and evaluate the rainfall erosivity. More stations have been used for western China in this study compared with previous studies, which improved the accuracy of rainfall erosivity estimation for this region.
1.33 Figure 3: It seems to me senseless!! Response: The scatterplot shows R factor values estimated in this study and those from the previous study  with those calculated based on 1-min interval data, which was assumed to be the true values of rainfall erosivity. The figure (Fig. 4 in the revision) and Table 2 in the manuscript showed for the R factor, the values in the map of Yin et al. (2019) were underestimated where the R factor was relatively high, and overestimated where the R factor was relatively low. R factor values estimated in this study had smaller error comparing with those in Yin et al. (2019).
1.34 Figure 4(c): What do you imply from?? Response: Figure 4(c) (Figure 5(c) in the revision) shows the distribution of the relative errors of the 1-in-10-year EI30 for this study and Yin et al. (2019) by comparing them with true values based on 1-min precipitation data. It indicated that the relative errors in this study concentrated in the range of -10%~10%, whereas those in Yin et al. (2019) concentrated in the range of -25% ~ -15% and +15% ~ +25%, which were larger than those in this study. We have added these explanations in the revision to make the implication of the figure clearer.
1.35 Figure 5: Any map has to contain important places and localities!! Response: We have added them in the revised version.
1.36 Figure 6: How reliable these differences are?? Response: Figure 6 (Fig. 9 in the revision) shows the differences between R factor and the 1-in-10year EI30 in this study comparing with the previous study ). An independent dataset (62 stations with 1-minute data) was used to evaluate the accuracy of two groups of maps. Figure 3, 4 (Fig. 4, 5 and 6 in the revision) and Table 2 demonstrated the results of comparison. It is true that most of 62 stations distributed in the eastern part of China, where most water erosion occurs. The uncertainty in western areas with limited observations is large and we have discussed it in the revision as "(d) Station distribution and density. In western China, the stations were sparse and unevenly distributed, which affect the interpolation accuracy.".
1.37 Figure 7: Firstly, the former comments and inquires have to be addressed!! Response: We have addressed them in the revision.
1.38 Line 303: "3.3.3 Contribution of the interpolation method" Is it really contribution?? Title it properly!! Response: We revised it into "Effect of the interpolation method".
1.39 Figure 9: To me they are not comparable, since each has been developed for a particular purpose and with a specific resolution!! Response: The erosivity map proposed by Panagos et al. (2017) is for a global scale and it has provided a good basis for the comparison of rainfall erosivity among different regions in the world. Mainly due to the number of observation stations obtained, two studies showed some differences. It is suggested to use the R factor map in this study for China since independent 1-min precipitation dataset has been used to show that maps in this study outperform those from Panagos et al. (2017). We have added these explanations in the revision to make it clearer.
1.40 Conclusions: Avoid repetition of results and abstract!! 3.2 Again, as the domain is considerable, there is a question mark to using one energy equation for entire Mainland China. Also, please describe more about using the conversion factor, 1.871, as a representative value for entire domain. Response: Calculation of the kinetic energy requires raindrop disdrometer observation data which are very limited at a national scale. Empirical formulations have been developed for KE-I relationships (Eq. 1-3; Wischmeier and Smith, 1978;Renard et al., 1997;USDA-ARS, 2013). Yin et al. (2017) compared the R-factor calculated by different energy equations (Eq. 1-3) using rainfall data at 1-min interval from 18 stations across the central and eastern regions of China. The results showed that the behavior of the Eq. (3) (RUSLE2; USDA-ARS, 2013) which was used in this study was very similar to that of the Eq. (1) (USLE; Wischmeier and Smith, 1978). While the results from Eq. (2) (RUSLE; Renard et al., 1997) was underestimated by about 9.3%. Therefore, Eq. (3) was used for entire Mainland China, although there must be the uncertainty of the energy equation, which had been discussed in the revised version (Line 355-358).
= 0.119 + 0.0873 log( ), ≤ 76 (2) = 0.29[1 − 0.72exp (−0.082 )] (3) where er is the unit rainfall kinetic energy (energy per mm of rainfall, MJ ha -1 mm -1 ), ir is the intensity (mm h -1 ). We agree that applying the same conversion factor for the entire mainland China may result in some uncertainty. The conversion factor, 1.871, for the R-factor was developed using 1-min observation rainfall data from 62 stations over mainland China by Yue et al. (2020). It was reported in Yue et al. (2020) independent dataset for the validation showed that the symmetric mean absolute percentage error (sMAPE) was about 6.7% (ranging from 0.2% to 37.0%) after applying the conversion factor of 1.871. We have described more about the conversion factor, 1.871 in the revision.
3.3 Using a conversion factor to correct the hourly data is good for estimating the 1-in10-year EI30 but it is concerned that whether the factor, 1.489, could be employed uniformly for entire mainland China. I suggest authors provide some more details that can describe the uncertainty and its variability so readers can pre-understand its reliability before employing the newly developed map to their own applications. Response: We are grateful for your constructive suggestions. As explained in the response above, the conversion factor 1.489 for 1-in-10-year EI30 was developed based on 1-min rainfall data from 54 stations over Mainland China by Yue et al. (2020). Independent dataset for the validation showed the symmetric mean absolute percentage error (sMAPE) was about 15.5% (ranging from 0.4% to 48.4%) after applying the conversion factor of 1.489. It is hoped that more data at high temporal resolution (e.g. 1-min, breakpoint) could be available in future studies to develop conversion factors for different regions. We have described more about the conversion factor, 1.489 in the revision. In addition, we have added more details about the uncertainty of this study in the discussion as follows (Line 355-365): "The uncertainty of the results from this study mainly comes from the following aspects: (a) KE-I model for estimating Kinetic Energy (KE) from the instant precipitation Intensity (I). KE-I model used in this study is from RUSLE2 (USDA-ARS, 2013) and raindrop disdrometer observation data need to be collected to calibrate the KE-I model. (b) The estimation of the erosivity factors from hourly data (equation 5 in the manuscript). The conversion factors were developed based on 1-min rainfall data from 62 stations (Fig. 2 in the manuscript). Hourly data brings information loss in the estimation of instant precipitation intensity comparing with breakpoint data. (c) The adjustment of the R factor from the stations with less effective years (equation 8 in the manuscript). This is based on a power function (equation 9 in the manuscript) of the mean annual precipitation and rainfall erosivity using 1-min and daily rainfall data of 35 stations (Fig. 2 in the manuscript); The degree of uncertainty mainly depends on the annual variation of rainfall erosivity. (d) Station distribution and density. In western China, the stations were sparse and unevenly distributed, which affect the interpolation accuracy. (e) Spatial interpolation model (Universal Kriging in this study) and the interpolation procedures (the division of regions before the interpolation and the mergence of regions after the interpolation)." 3.4 In the verification part, suggest authors show the error on the map. This is to present the spatial distributed error and accuracy of the developed map. Also, it would be nice if authors describe errors varying in different density of gauge network. Response: The distribution of relative error was shown on the following figure, which was evaluated using 1-min rainfall data from 62 stations (for R-factor) and 18 stations (for 1-in-10-year EI30). These have been added in the revision (Fig.6 in the revision). And the variation of the errors in different density of gauge network was shown in Fig. 8 (Fig.11 in the revision) and Table 3 (Table  4 in the revision).
(a) R-factor (b) 1-in-10-year EI30 Figure 4 Spatial distribution of the absolute relative errors in the map of R-factor for 62 stations (a) and in the map of 1-in-10-year EI30 for 18 stations (b) with 1-min observation data.