Easy-to-use spatial Random Forest-based downscaling-calibration method for 1 producing high resolution and accurate precipitation data 2

9 High resolution and accurate precipitation data is significantly important for 10 numerous hydrological applications. To enhance the spatial resolution and accuracy of 11 satellite-based precipitation products, an easy-to-use downscaling-calibration method 12 based on spatial Random Forest (SRF) is proposed in this paper, where the spatial 13 autocorrelation between precipitation measurements is taken into account. The 14 proposed method consists of two main stages. Firstly, the satellite-based precipitation 15 was downscaled by SRF with the incorporation of some high-resolution covariates 16 including latitude, longitude, DEM, NDVI, terrain slope, aspect, relief, and land 17 surface temperatures. Then, the downscaled precipitation was calibrated by SRF with 18 rain gauge observations and the aforementioned high-resolution variables. The 19 monthly Integrated MultisatellitE Retrievals for Global Precipitation Measurement 20 (IMERG) located in Sichuan province, China from 2015 to 2019 was processed using 21 our method and its results were compared with those of some classical methods 22 https://doi.org/10.5194/hess-2021-332 Preprint. Discussion started: 1 July 2021 c © Author(s) 2021. CC BY 4.0 License.

(2) the monthly-based SRF estimation 28 is slightly more accurate than the annual-based SRF fraction disaggregation method; 29 (3) SRF-based downscaling and calibration preforms better than bilinear downscaling 30 (Bi-SRF) and GDA-based calibration (SRF-GDA); (4) kriging seems more accurate 31 than GWR and ANN in terms of quantitative accuracy measures, whereas its 32 precipitation map cannot capture the detailed spatial precipitation patterns; and (5) 33 among the predictors for calibration, the precipitation interpolated by kriging on the inevitably contain large systematic biases. 88 To alleviate the inherent biases, many calibration methods have been proposed for 8 less sunshine. Most rain gathers from July to September, accounting for 80% of total 153 annual precipitation. While in the west plateau, the weather is relatively cool or cold.

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The climate is featured by a long cold winter, a very short summer and rich sunshine 155 but less rainfall. Thus, annual precipitation shows significant spatial heterogeneity, 156 varying from about 400 mm in the west to 1800 mm in the east and with the average 157 annual precipitation of about 1000 mm. Overall, the high spatial and temporal 158 variability of precipitation with the complex topography makes the study site ideally 159 suitable for the evaluation of satellite-based precipitation estimates. The study region has 156 rain gauge stations, which shows an unevenly distribution 166 with high density in the east and low density in the west (Fig. 1). On average, the  After that, the monthly precipitation was produced by aggregating the daily 173 precipitation of rain gauges for each month. monthly IMERG V06B Final Run product was adopted in the study. It was 187 downloaded from https://gpm.nasa.gov/data.

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The mean monthly precipitations based on all rain gauges and IMERG during   The detailed information of the datasets used in the study is shown in Table 1 wherep is the estimated precipitation at the location s 0 , e is the fitting residual, and X s 245 and X ns are the spatial and non-spatial covariates, respectively.

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In addition to spatial coordinates, one spatial covariate (X s ) is estimated to account 247 for the spatial autocorrelation between neighboring precipitation measurements, i.e.  limitation, the ordinary kriging-based variogram is adopted to estimate the 256 interpolation weights, which are obtained by solving the following linear system: where  is Lagrange parameter and     is the semivariogram.

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It can be concluded that the variogram-based weights consider the spatial 260 autocorrelation not only between the adjacent known points but also between the estimated from sample data with the following equation (Goovaerts, 2000): where n is the number of data pairs with the attribute z separated by distance h.  (2) The negative NDVI values were excluded from the original data, which mainly 285 belong to snow and water bodies in the study site. The removed ones were 286 estimated by kriging with their neighbors, which can avoid much information loss. was constructed by SRF: where e is the fitting residual.   overfitting problem could be avoided.   in the middle part, since the precipitation is higher in the middle part than in the other 379 parts (Fig. 1). BPNN (Fig. 7d) yields the poorest results, where many stations have the 380 RMSEs greater than 60 mm. It is followed by GWR (Fig. 7f). RF (Fig. 7c) and  389 The estimation errors of all the methods on a seasonal scale (i.e. spring, summer, 390 autumn and winter) are provided in Table 2. Results indicate that regardless of

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The accuracy rank for all the methods in the four seasons is similar. More specifically,

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BPNN yields worse results than IMERG in spring, summer and autumn, and a better 400 result in winter. GWR is slightly more accurate than BPNN in the four seasons.

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Kriging with a similar accuracy to RF obviously outperforms BPNN and GWR. The

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This is because this year has the largest precipitation (Fig. 2). In comparison, BPNN 432 produces the poorest results in all years, which is followed by IMERG and GWR. RF Since the wettest month was July 2018 (Fig. 2), it was taken as an example to show 440 the precipitation estimates of the proposed method and some classical methods.

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Results (Fig. 12) indicate that all the estimated precipitation maps have a similar 442 spatial distribution and pattern to IMERG, yet the former have more detailed 443 information than the latter due to the inclusion of the high-resolution predictors.

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However, there exist some differences between the methods. Specifically, the kriging map (Fig. 12b) loses many details of spatial precipitation patterns. This is expected as 446 it only uses ground measurements for the interpolation. RF (Fig. 12c) shows obvious 447 unnatural discontinuity. GWR (Fig. 12d) suffers from more variations and fractions 448 compared with neighbors. In comparison, the proposed method (Fig. 12a) produces a 449 good precipitation map. demonstrated that on a monthly scale (Fig. 5) respectively. On an annual scale (Fig. 11), compared to IMERG, the performance of 474 GWR is unsatisfactory in terms of CC. Moreover, the precipitation map of GWR 475 shows some larger values compared to their neighbors (Fig. 12d).

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In contrast, the ML methods including RF and SRF are always more accurate than interpolated to produce input predictors for the first and second stages, respectively.

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The results on the three scales demonstrated the higher accuracy of SRF than RF (see 487 Figs. 5-11, Table 1). Note that although kriging interpolation based on only gauge 488 measurements is more accurate than IMERG, BPNN and GWR, its precipitation map 489 is so smooth that many detailed precipitation patterns are lost (Fig. 12b).    566 In the further studies, we will focus on the following directions. Firstly, other land  SRFdis are more accurate than the classical methods on all temporal scales.

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Moreover, the proposed method ranks the first, indicating that SRF-based 601 downscaling and calibration is more promising than bilinear-based downscaling 602 and GDA-based calibration.

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(2) The comparison between the monthly-based and annual-based estimation 604 demonstrates that there is no statistically significant difference between them, 605 indicating that NDVI can be used for monthly precipitation estimation in the study 606 site.

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(3) Kriging outperforms the original IMERG, BPNN and GWR in terms of RMSE, 608 MAE and CC. However, its interpolation map suffers from serious loss of spatial 609 variation of precipitation, since it only uses the gauge measurements.

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Overall, the proposed methodology is general, robust, accurate and easy-to-use, 614 since its promising performance in the study area with an obvious heterogeneity in 615 terrain morphology and precipitation. Thus, it can be easily applied to other regions, 616 where high resolution and accurate precipitation data is urgently required.