# Use of SMAP Soil Moisture and Fitting Methods in Improving GPM Estimation in Near Real Time

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Sets

#### 2.1. China Merged Perception Analysis (CMPA)

#### 2.2. GPM IMERG

#### 2.3. SMAP Soil Moisture

#### 2.4. Additional Datasets

## 3. Model and Method

#### 3.1. API Model

_{sat}(approximately equal to the soil porosity, taken from the gridded soil characteristics data set of China, as described in Section 2.4)—under no circumstance would this increase cause soil moisture to exceed Θ

_{sat}. h is the depth of the surface soil layer, fixed to 45 mm, which is similar to the sensing depth of SMAP observations.

^{CDF}is the CDF matching corrected SMAP soil moisture to be used in the assimilation procedure, SMSMAP is the original SMAP soil moisture, and SMAPI is the soil moisture modeled by API.

#### 3.2. Assimilation Algorithm

_{SMAP},

_{opt}, which represents the optimal number of the SMAP observations that produces the smallest RMSE, as described later in this section. The blue line in Figure 2a represents the soil moisture simulated by the API model forced with this original precipitation in an assimilation window.

_{threshold}is used to separate the daily precipitation accumulation data into two different categories. Two distributions are used to generate new artificial rainfall based on a multiplicative factor k for these two categories

_{threshold}, the rain value will be altered by an exponential function determined by the generation of uniformly distributed random numbers (rand); otherwise, a gamma distribution, defined by two shape parameters 0.145 and 5.43, is used to generate the random numbers (randg) [64]. In the example shown in Figure 2b, the rain event on 18 June is larger than P

_{threshold}(30 mm) so the second line of Equation (6) is applied, while the first line is used for other rain events as they are lower than 30 mm.

_{SMAP,opt}, decides each assimilated window. Reasonable results are obtained for values ranging between three and seven SMAP observations. Less than three observations can result in degradation, since more SMAP samples are necessary to compensate the possible uncertainties of individual SMAP data. More than seven observations can also lead to degradation because of a long-time assimilated window. The optimal SMAP observations N

_{SMAP,opt}for each grid cell is obtained through a trial process in which the RMSE of simulated soil moisture (relative to the SMAP observations) is calculated and the N

_{SMAP}with the smallest RMSE is chosen as the optimal. (2) The number of the ensemble simulations. Since we get very similar results with the number of 100, 200, and 300, we finally select 100 to limit computation cost; (3) The value of P

_{threshold}, which determine the rainfall category. Considering huge regional difference in precipitation magnitudes over China, we determine the best P

_{threshold}for each grid cell separately as we do for N

_{SMAP}.

#### 3.3. Fitting Correction Methods

#### 3.3.1. Linear Fitting Correction

_{linear}is simply calculated by the satellite estimates multiplied by the correction factor a

_{O}(i, t) is the GPM (or SMP) precipitation at grid cell i and time t, P

_{linear}(i, t) is the corresponding linearly corrected precipitation, and a

_{i}for each grid cell i is derived on the least square fit between precipitation from CMPA and GPM (or SMP) in the calibration period.

#### 3.3.2. Nonlinear Fitting Correction

_{nonlinear}is calculated as

#### 3.3.3. CDF Fitting Correction

_{O}is the calibrated CDF of GPM (or SMP) based on the 2015–2016 data, and F

_{CMPA}

^{−1}represents the inverse process of CDF of CMPA precipitation.

#### 3.3.4. Performance Metrics

## 4. Results

#### 4.1. Parameter Values for Seven Correction Methods

_{SMAP,opt}of assimilation algorithm have a stable range between 4 to 7, whereas P

_{threshold}shows a strong spatial heterogeneity. That may be because N

_{SMAP,opt}is related to the observing frequency of SMAP, which is not very different across space. By contrast, P

_{threshold}is determined by the magnitude of daily precipitation intensity that varies greatly across China, as shown in Figure 1. The median of the parameter a

_{1}in GPM-Linear correction is 0.67, which shows that GPM greatly overestimates precipitation in most areas. The GPM products is improved by the SM correction, as the median of the parameter a

_{2}in SMP-Linear correction becomes 0.91. The parameter c

_{1}in GPM-Nonlinear correction is less than 1 in most areas with the median of 0.57, which indicates a highly nonlinear relationship between CMPA and GPM. The nonlinear relationship still exists after GPM is corrected with SM in SMP-nonlinear, as reflected by the median value (0.74). The parameters in the CDF matching correction method have a larger variability, reflecting stronger spatial heterogeneity.

#### 4.2. Performance Assessment

#### 4.2.1. Statistics

#### 4.2.2. Monthly Series Analysis

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Brocca, L.; Pellarin, T.; Crow, W.T.; Ciabatta, L.; Massari, C.; Ryu, D.; Su, C.H.; Rüdiger, C.; Kerr, Y. Rainfall estimation by inverting SMOS soil moisture estimates: A comparison of different methods over Australia. J. Geophys. Res. Atmos.
**2016**, 121, 12,062–12,079. [Google Scholar] [CrossRef] - Hou, A.Y.; Kakar, R.K.; Neeck, S.; Azarbarzin, A.A.; Kummerow, C.D.; Kojima, M.; Oki, R.; Nakamura, K.; Iguchi, T. The Global Precipitation Measurement Mission. Bull. Am. Meteorol. Soc.
**2014**, 95, 701–722. [Google Scholar] [CrossRef] [Green Version] - Dijk, A.I.J.M.V.; Beck, H.E.; Crosbie, R.S.; Jeu, R.A.M.D.; Liu, Y.Y.; Podger, G.M.; Timbal, B.; Viney, N.R. The Millennium Drought in southeast Australia (2001–2009): Natural and human causes and implications for water resources, ecosystems, economy, and society. Water Resour. Res.
**2013**, 49, 1040–1057. [Google Scholar] [CrossRef] - Herold, N.; Alexander, L.V.; Donat, M.G.; Contractor, S.; Becker, A. How much does it rain over land? Geophys. Res. Lett.
**2016**, 43, 341–348. [Google Scholar] [CrossRef] - Sahoo, A.K.; Sheffield, J.; Pan, M.; Wood, E.F. Evaluation of the Tropical Rainfall Measuring Mission Multi-Satellite Precipitation Analysis (TMPA) for assessment of large-scale meteorological drought. Remote Sens. Environ.
**2015**, 159, 181–193. [Google Scholar] [CrossRef] - Rinaldo, A.; Bertuzzo, E.; Mari, L.; Righetto, L.; Blokesch, M.; Gatto, M.; Casagrandi, R.; Murray, M.; Vesenbeckh, S.M.; Rodrigueziturbe, I. Reassessment of the 2010–2011 Haiti cholera outbreak and rainfall-driven multiseason projections. Proc. Natl. Acad. Sci. USA
**2012**, 109, 6602–6607. [Google Scholar] [CrossRef] [PubMed] - Scholthof, K.B.G. The disease triangle: pathogens, the environment and society. Nat. Rev. Microbiol.
**2007**, 5, 152–156. [Google Scholar] [CrossRef] [PubMed] - Casse, C.; Gosset, M.; Peugeot, C.; Pedinotti, V.; Boone, A.; Tanimoun, B.A.; Decharme, B. Potential of satellite rainfall products to predict Niger River flood events in Niamey. Atmos. Res.
**2015**, 163, 162–176. [Google Scholar] [CrossRef] - Jongman, B.; Hochrainerstigler, S.; Feyen, L.; Aerts, J.C.J.H.; Mechler, R.; Botzen, W.J.W.; Bouwer, L.M.; Pflug, G.; Rojas, R.; Ward, P.J. Increasing stress on disaster-risk finance due to large floods. Nat. Clim. Chang.
**2014**, 4, 264–268. [Google Scholar] [CrossRef] - Wake, B. Flooding costs. Nat. Clim. Chang.
**2013**, 3, 778. [Google Scholar] [CrossRef] - Wu, H.; Adler, R.F.; Tian, Y.; Huffman, G.J.; Li, H.; Wang, J.J. Real-time global flood estimation using satellite-based precipitation and a coupled land surface and routing model. Water Resour. Res.
**2014**, 50, 2693–2717. [Google Scholar] [CrossRef] [Green Version] - Lievens, H.; Tomer, S.K.; Bitar, A.A.; Lannoy, G.J.M.D.; Drusch, M.; Dumedah, G.; Franssen, H.J.H.; Kerr, Y.H.; Martens, B.; Pan, M. SMOS soil moisture assimilation for improved hydrologic simulation in the Murray Darling Basin, Australia. Remote Sens. Environ.
**2015**, 168, 146–162. [Google Scholar] [CrossRef] [Green Version] - Pennington, C.; Dijkstra, T.; Lark, M.; Dashwood, C.; Harrison, A.; Freeborough, K. Antecedent Precipitation as a Potential Proxy for Landslide Incidence in South West United Kingdom; Springer: Nottinghamshire, UK, 2014; pp. 253–259. [Google Scholar]
- Lanza, L.G.; Stagi, L. High resolution performance of catching type rain gauges from the laboratory phase of the WMO Field Intercomparison of Rain Intensity Gauges. Atmos. Res.
**2009**, 94, 555–563. [Google Scholar] [CrossRef] - Kucera, P.A.; Ebert, E.E.; Turk, F.J.; Levizzani, V.; Kirschbaum, D.; Tapiador, F.J.; Loew, A.; Borsche, M. Precipitation from Space: Advancing Earth System Science. Bull. Am. Meteorol. Soc.
**2013**, 94, 365–375. [Google Scholar] [CrossRef] [Green Version] - Schamm, K.; Ziese, M.; Becker, A.; Finger, P.; Meyerchristoffer, A.; Schneider, U.; Schröder, M.; Stender, P. Global gridded precipitation over land: a description of the new GPCC First Guess Daily product. Earth Syst. Sci. Data
**2014**, 6, 49–60. [Google Scholar] [CrossRef] [Green Version] - Ali, A.; Lebel, T. The Sahelian standardized rainfall index revisited. Int. J. Clim.
**2010**, 29, 1705–1714. [Google Scholar] [CrossRef] - Delrieu, G.; Braud, I.; Berne, A.; Borga, M.; Boudevillain, B.; Fabry, F.; Freer, J.; Gaume, E.; Nakakita, E.; Seed, A. Weather radar and hydrology. Adv. Water Res.
**2009**, 32, 969–974. [Google Scholar] [CrossRef] [Green Version] - Krajewski, W.F.; Smith, J.A. Radar hydrology: rainfall estimation. Adv. Water Res.
**2002**, 25, 1387–1394. [Google Scholar] [CrossRef] - Kidd, C.; Levizzani, V. Status of satellite precipitation retrievals. Hydrol. Earth Syst. Sci.
**2011**, 15, 1109–1116. [Google Scholar] [CrossRef] [Green Version] - Zhao, H.; Yang, S.; You, S.; Huang, Y.; Wang, Q.; Zhou, Q. Comprehensive Evaluation of Two Successive V3 and V4 IMERG Final Run Precipitation Products over Mainland China. Remote Sens.
**2018**, 10, 34. [Google Scholar] [CrossRef] - Huffman, G.; Bolvin, D.; Braithwaite, D.; Hsu, K.; Joyce, R.; Kidd, C.; Nelkin, E.; Sorooshian, S.; Wang, J.; Xie, P. First Results from the Integrated Multi-Satellite Retrievals for GPM (IMERG). In Proceeding of EGU General Assembly Conference, Vienna, Austria, 12–17 April 2015. [Google Scholar]
- Cai, Y.; Jin, C.; Wang, A.; Guan, D.; Wu, J.; Yuan, F.; Xu, L. Spatio-Temporal Analysis of the Accuracy of Tropical Multisatellite Precipitation Analysis 3B42 Precipitation Data in Mid-High Latitudes of China. PLoS ONE
**2015**, 10, e0120026. [Google Scholar] [CrossRef] [PubMed] - Pipunic, R.C.; Ryu, D.; Costelloe, J.F.; Su, C.H. An evaluation and regional error modeling methodology for near-real-time satellite rainfall data over Australia. J. Geophys. Res. Atmos.
**2015**, 120, 135–141. [Google Scholar] [CrossRef] - Prasetia, R.; As-syakur, A.R. Validation of TRMM Precipitation Radar satellite data over Indonesian;region. Theoret. Appl. Clim.
**2013**, 112, 575–587. [Google Scholar] [CrossRef] - Tapiador, F.J.; Turk, F.J.; Petersen, W.; Hou, A.Y.; García-Ortega, E.; Machado, L.A.T.; Angelis, C.F.; Salio, P.; Kidd, C.; Huffman, G.J. Global precipitation measurement: Methods, datasets and applications. Atmos. Res.
**2012**, 104–105, 70–97. [Google Scholar] [CrossRef] - Yin, X.; Gruber, A. Validation of the abrupt change in GPCP precipitation in the Congo River Basin. Int. J. Clim.
**2010**, 30, 110–119. [Google Scholar] [CrossRef] - Brocca, L.; Moramarco, T.; Melone, F.; Wagner, W. A new method for rainfall estimation through soil moisture observations. Geophys. Res. Lett.
**2013**, 40, 853–858. [Google Scholar] [CrossRef] [Green Version] - Pellarin, T.; Ali, A.; Chopin, F.; Jobard, I.; Bergès, J.C. Using spaceborne surface soil moisture to constrain satellite precipitation estimates over West Africa. Geophys. Res. Lett.
**2008**, 35, 244–255. [Google Scholar] [CrossRef] - Mccoll, K.A.; Alemohammad, S.H.; Akbar, R.; Konings, A.G.; Yueh, S.; Entekhabi, D. The global distribution and dynamics of surface soil moisture. Nat. Geosci.
**2017**, 10, 100–104. [Google Scholar] [CrossRef] - Crow, W.T.; Bolten, J.D. Estimating precipitation errors using spaceborne surface soil moisture retrievals. Geophys. Res. Lett.
**2007**, 34, 402–420. [Google Scholar] [CrossRef] - Crow, W.T.; Huffman, G.J.; Bindlish, R.; Jackson, T.J. Improving satellite-based rainfall accumulation estimates using spaceborne surface soil moisture retrievals. J. Hydrometeorol.
**2007**, 10, 199–212. [Google Scholar] [CrossRef] - Crow, W.T.; Berg, M.J.V.D.; Huffman, G.J.; Pellarin, T. Correcting rainfall using satellite-based surface soil moisture retrievals: The Soil Moisture Analysis Rainfall Tool (SMART). Water Resour. Res.
**2011**, 47, 2924–2930. [Google Scholar] [CrossRef] - Brocca, L.; Massari, C.; Moramarco, T.; Hahn, S.; Hasenauer, S.; Kidd, R.; Dorigo, W. Soil as a natural rain gauge: Estimating global rainfall from satellite soil moisture data. J. Geophys. Res. Atmos.
**2014**, 119, 5128–5141. [Google Scholar] [CrossRef] [Green Version] - Wanders, N.; Pan, M.; Wood, E.F. Correction of real-time satellite precipitation with multi-sensor satellite observations of land surface variables. Remote Sens. Environ.
**2015**, 160, 206–221. [Google Scholar] [CrossRef] - Pellarin, T.; Tran, T.; Cohard, J.M.; Galle, S.; Laurent, J.P.; Rosnay, P.D.; Vischel, T. Soil moisture mapping over West Africa with a 30-min temporal resolution using AMSR-E observations and a satellite-based rainfall product. Hydrol. Earth Syst. Sci.
**2009**, 13, 1887–1893. [Google Scholar] [CrossRef] - Pellarin, T.; Louvet, S.; Gruhier, C.; Quantin, G.; Legout, C. A simple and effective method for correcting soil moisture and precipitation estimates using AMSR-E measurements. Remote Sens. Environ.
**2013**, 136, 28–36. [Google Scholar] [CrossRef] - Román-Cascón, C.; Pellarin, T.; Gibon, F.; Brocca, L.; Cosme, E.; Crow, W.; Fernández-Prieto, D.; Kerr, Y.H.; Massari, C. Correcting satellite-based precipitation products through SMOS soil moisture data assimilation in two land-surface models of different complexity: API and SURFEX. Remote Sens. Environ.
**2017**, 200, 295–310. [Google Scholar] [CrossRef] - Deng, P.; Zhang, M.; Guo, H.; Xu, C.; Bing, J.; Jia, J. Error analysis and correction of the daily GSMaP products over Hanjiang River Basin of China. Atmos. Res.
**2018**, 214, 121–134. [Google Scholar] - Sheffield, J.; Wood, E.F.; Chaney, N.; Guan, K.; Sadri, S.; Yuan, X.; Olang, L.; Amani, A.; Ali, A.; Demuth, S. A Drought Monitoring and Forecasting System for Sub-Sahara African Water Resources and Food Security. Bull. Am. Meteorol. Soc.
**2014**, 95, 861–882. [Google Scholar] [CrossRef] - Xie, P.; Xiong, A.Y. A conceptual model for constructing high-resolution gauge-satellite merged precipitation analyses. J. Geophys. Res. Atmos.
**2011**, 116. [Google Scholar] [CrossRef] [Green Version] - Shen, Y.; Yu, Y.P.A. A high spatiotemporal gauge-satellite merged precipitation analysis over China. J. Geophys. Res. Atmos.
**2014**, 119, 3063–3075. [Google Scholar] [CrossRef] [Green Version] - Zhang, X.; Tang, Q. Combining satellite precipitation and long-term ground observations for hydrological monitoring in China. J. Geophys. Res. Atmos.
**2015**, 120, 6426–6443. [Google Scholar] [CrossRef] [Green Version] - Joyce, R.J.; Janowiak, J.E.; Arkin, P.A.; Xie, P. CMORPH: A Method That Produces Global Precipitation Estimates From Passive Microwave and Infrared Data at High Spatial and Temporal Resolution. J. Hydrometeorol.
**2004**, 5, 287–296. [Google Scholar] [CrossRef] - Jingjing, Y.U.; Yan, S.; Yang, P.; Xiong, A. Comparative assessment between the daily merged precipitation dataset over China and the worlds popular counterparts. Acta Meteorol. Sin.
**2015**, 73, 394–410. [Google Scholar] - Babar, Z.A.; Zhi, X.F.; Fei, G. Precipitation assessment of Indian summer monsoon based on CMIP5 climate simulations. Arab. J. Geosci.
**2015**, 8, 4379–4392. [Google Scholar] [CrossRef] - Chen, H.; Rucong, Y.U.; Yan, S. A New Method to Compare Hourly Rainfall between Station Observations and Satellite Products over Central-Eastern China. J. Meteorol. Res.
**2016**, 30, 737–757. [Google Scholar] [CrossRef] - Wang, D.; Wang, X.; Liu, L.; Huang, H.; Pan, C. Evaluation of CMPA precipitation estimate in the evolution of typhoon-related storm rainfall in Guangdong, China. J. Hydroinf.
**2016**, 18, 1055–1068. [Google Scholar] [CrossRef] [Green Version] - Wang, H.; Luo, J.; Ye, J.; Li, Z. Comparative analysis of area rainfall in Huaihe River Basin estimated by CMORPH-Gauge merged data and observed rain gauge data. J. Hohai Univ.
**2014**, 42, 189–194. [Google Scholar] - Yang, J.; Shi, L.; Miao, Q.; Zhang, D.; Wan, Y. Precision evaluation of three sets of remote sensing precipitation data in Qinling-Daba Mountains. J. Jiangsu Normal Univ.
**2017**, 2, 77–82. [Google Scholar] - Zhu, Y.; Lin, Z.; Zhao, Y.; Li, H.; He, F.; Zhai, J.; Wang, L.; Wang, Q. Flood Simulations and Uncertainty Analysis for the Pearl River Basin Using the Coupled Land Surface and Hydrological Model System. Water
**2017**, 9, 391. [Google Scholar] [CrossRef] - Huffman, G.A.; Adler, R.; Bolvin, D.T.; Gu, G.; Nelkin, E.; Bowman, K.; Hong, Y.; Stocker, T.; Wolff, D. The TRMM multi-satellite precipitation analysis (TMPA): quasi-global, multiyear, combined-sensor precipitation estimates at fine scale. J. Hydrometeorol.
**2007**, 8, 38–55. [Google Scholar] [CrossRef] - Kubota, T.; Shige, S.; Hashizume, H.; Aonashi, K.; Takahashi, N.; Seto, S.; Takayabu, Y.N.; Ushio, T.; Nakagawa, K.; Iwanami, K. Global Precipitation Map Using Satellite-Borne Microwave Radiometers by the GSMaP Project: Production and Validation. IEEE Trans. Geosci. Remote Sens.
**2007**, 45, 2259–2275. [Google Scholar] [CrossRef] - Joyce, R.J.; Xie, P. Kalman Filter-Based CMORPH. J. Hydrometeorol.
**2011**, 12, 1547–1563. [Google Scholar] [CrossRef] - Hong, Y.; Hsu, K.L.; Sorooshian, S.; Gao, X. Precipitation Estimation from Remotely Sensed Imagery Using an Artificial Neural Network Cloud Classification System. J. Appl. Meteorol.
**1997**, 36, 1176–1190. [Google Scholar] [CrossRef] - Sorooshian, S.; Hsu, K.L.; Gao, X.; Gupta, H.V.; Imam, B.; Dan, B. Evaluation of PERSIANN system satellite-based estimates of tropical rainfall. Bull. Am. Meteor. Soc.
**2000**, 81, 2035–2046. [Google Scholar] [CrossRef] - Huffman, G.J.; Bolvin, D.T.; Dan, B.; Hsu, K.; Joyce, R.; Xie, P. NASA Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG). 2014. Available online: https://pmm.nasa.gov/sites/default/files/document_files/IMERG_ATBD_V5.2_0.pdf (accessed on 7 February 2018).
- Bosilovich, M.G.; Lucchesi, R.; Suarez, M. MERRA-2: File Specification. 2015. Available online: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20150019760.pdf (accessed on 25 September 2015).
- Yuan, H.; Dai, Y.; Xiao, Z.; Ji, D.; Shangguan, W. Reprocessing the MODIS Leaf Area Index products for land surface and climate modelling. Remote Sens. Environ.
**2011**, 115, 1171–1187. [Google Scholar] [CrossRef] - Jönsson, P.; Eklundh, L. TIMESAT—a program for analyzing time-series of satellite sensor data. Comput. Geosci.
**2004**, 30, 833–845. [Google Scholar] [CrossRef] [Green Version] - Shangguan, W.; Dai, Y.; Liu, B.; Zhu, A.; Duan, Q.; Wu, L.; Ji, D.; Ye, A.; Yuan, H.; Zhang, Q. A China data set of soil properties for land surface modeling. J. Adv. Model. Earth Syst.
**2013**, 5, 212–224. [Google Scholar] [CrossRef] [Green Version] - Cordery, I. Antecedent wetness for design flood estimation. Civil Eng. Trans.
**1970**, 12, 181–184. [Google Scholar] - Yan, H.; Dechant, C.M.; Moradkhani, H. Improving Soil Moisture Profile Prediction With the Particle Filter-Markov Chain Monte Carlo Method. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 6134–6147. [Google Scholar] [CrossRef] - Marsaglia, G.; Tsang, W.W. A simple method for generating gamma variables. Acm Trans. Math. Softw.
**2000**, 26, 363–372. [Google Scholar] [CrossRef] - Tan, M.L.; Tan, K.C.; Chua, V.P.; Chan, N.W. Evaluation of TRMM Product for Monitoring Drought in the Kelantan River Basin, Malaysia. Water
**2017**, 9, 57. [Google Scholar] [CrossRef] - Koster, R.D.; Brocca, L.; Crow, W.T.; Burgin, M.S.; De Lannoy, G.J.M. Precipitation estimation using L-band and C-band soil moisture retrievals. Water Resour. Res.
**2016**, 52, 7213–7225. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ma, C.; Li, X.; Wei, L.; Wang, W. Multi-Scale Validation of SMAP Soil Moisture Products over Cold and Arid Regions in Northwestern China Using Distributed Ground Observation Data. Remote Sens.
**2017**, 9, 327. [Google Scholar] [CrossRef] - Sun, Y.; Huang, S.; Ma, J.; Li, J.; Li, X.; Wang, H.; Chen, S.; Zang, W. Preliminary Evaluation of the SMAP Radiometer Soil Moisture Product over China Using In Situ Data. Remote Sens.
**2017**, 9, 292. [Google Scholar] [CrossRef] - Tian, Y.D.; Peterslidard, C.D.; Eylander, J.B. Real-time bias reduction for satellite-based precipitation estimates. J. Hydrometeorol.
**2010**, 11, 1275–1285. [Google Scholar] [CrossRef]

**Figure 1.**Mean daily precipitation (mm/day) over China for May to September in 2017 from (

**a**) CMPA and (

**b**) GPM-IMERG-EARLY. The four letters in (

**a**) indicate the 0.5° boxes for which the monthly precipitation time series are shown in Figure 5.

**Figure 2.**Graphical representation of assimilation algorithm using SM data. The figures show an example for a grid point at 109.3°E, 22.1°N from June 12 to 24, 2017. (

**a**) Original rainfall (blue bars) from GPM to be corrected and its associated SM data (blue lines) simulated by API model. (

**b**) Including 100 simulations of artificially perturbed rainfall data (grey bars) and their associated SM data (grey lines). (

**c**) As in (

**b**) but including the best 10 simulations in yellow. (

**d**) As in (

**c**) but with the final output rainfall and SM data in red. The reference data of rainfall (from CMPA) and SM (from SMAP) are marked with green pentacles.

**Figure 3.**(

**a**) Root mean square error (RMSE) of daily precipitaiton between GPM and CMPA, and (

**b**–

**h**) ratio of RMSE between correction method-based (SMP, GPM-Linear, GPM-Nonlinear, GPM-CDF, SMP-Linear, SMP-Nonlinear, SMP-CDF) precipitation and GPM precipitation. Warm color denotes a degradation (higer RMSE), whereas cold color denotes an improvement (lower RMSE) in (

**b**–

**h**). The number at the bottom-left corner of each panel denotes the percentage of improved grid cells by the correction method. The analysis period is from May 1 2017 to September 31 2017. Note that the values 0-18 on colorbar are for (

**a**) GPM, and values 0-1.8 in parentheses for the ratio of RMSE in (

**b**–

**h**).

**Figure 4.**BIAS (mean absolute errors) between different products (

**a**) GPM, (

**b**) SMP, (

**c**) GPM-Linear, (

**d**) GPM-Nonlinear, (

**e**) GPM-CDF, (

**f**) SMP-Linear, (

**g**) SMP-Nonlinear, (

**h**) SMP-CDF and CMPA. The number at the bottom-left corner of each panel denotes the percentage of improved grid cells by the correction method. The analysis period is from May 1 2017 to September 31 2017.

**Figure 5.**Time series of monthly rainfall in May to September of 2017 obtained from CMPA, GPM, and the seven corrected products (SMP, GPM-Linear, GPM-Nonlinear, GPM-CDF, SMP-Linear, SMP-Nonlinear, and SMP-CDF) for the four boxes A, B, C and D shown in Figure 1. RMSE: root-mean-square error in mm/month.

**Figure 6.**Box plot of relative difference in RMSE (%) between SMP and GPM (defined as 100%×(SMP-GPM)/GPM) with different ranges of LAI values.

**Table 1.**Summary statistics of the spatial distribution of the calibrated parameters for the seven correction methods.

Product | Parameters | Median | σ | 25th | 75th |
---|---|---|---|---|---|

SMP | N_{SMAP,opt} | 5 | 1.47 | 4 | 7 |

P_{threshold} (mm/day) | 25 | 13.57 | 15 | 35 | |

GPM-Linear | a_{1} | 0.67 | 1.08 | 0.48 | 1.07 |

GPM-Nonlinear | b_{1} | 2.3 | 1.66 | 1.43 | 3.40 |

c_{1} | 0.57 | 0.94 | 0.46 | 0.71 | |

GPM-CDF | k_{1,o} (k_{1,m}) | 0.127(0.104) | 0.097(0.054) | 0.073(0.075) | 0.200(0.141) |

θ_{1,o} (θ_{1,m}) | 12.69(13.65) | 12.18(18.44) | 8.18(3.56) | 21.11(29.65) | |

SMP-Linear | a_{2} | 0.91 | 0.38 | 0.63 | 1.12 |

SMP-Nonlinear | b_{2} | 1.46 | 1.21 | 0.83 | 2.30 |

c_{2} | 0.74 | 0.89 | 0.56 | 0.97 | |

SMP-CDF | K_{2,o} (k_{2,m}) | 0.127(0.163) | 0.097(0.091) | 0.073(0.101) | 0.200(0.223) |

Θ_{2,o} (θ_{2,m}) | 12.69(8.99) | 12.18(7.91) | 8.18(5.47) | 21.11(14.19) |

**θ**with the subscript o denote those are based on CMPA, while the parameters k and

**θ**with the subscript m denote those are based on GPM or SMP.

**Table 2.**Summary statistics of the spatial distribution of performance scores for the seven correction methods against CMPA.

Product | R | RMSE (mm/day) | BIAS (mm/day) | ||||||
---|---|---|---|---|---|---|---|---|---|

10th | 50th | 90th | 10th | 50th | 90th | 10th | 50th | 90th | |

GPM | 0.24 | 0.49 | 0.69 | 1.37 | 5.25 | 13.43 | 0.37 | 2.03 | 5.46 |

SMP | 0.28^{b} | 0.49^{b} | 0.67 | 1.4 | 4.32^{b} | 10.15^{b} | 0.41 | 1.76^{b} | 4.63^{b} |

GPM-Linear | 0.24^{b} | 0.49^{bc} | 0.69^{bc} | 0.86^{bc} | 5.04^{b} | 12.39^{b} | 0.23^{bc} | 1.85^{b} | 5.14^{b} |

GPM-Nonlinear | 0.32^{bc} | 0.51^{bc} | 0.66 | 0.86^{bc} | 4.64^{b} | 11.15^{b} | 0.31^{bc} | 2.19 | 5.61 |

GPM-CDF | 0.27^{b} | 0.50^{bc} | 0.69^{bc} | 2.14 | 6.92 | 18.55 | 0.58 | 2.73 | 7.57 |

SMP-Linear | 0.28^{bc} | 0.49^{bc} | 0.67^{c} | 0.67^{bc} | 4.00^{bc} | 10.40^{b} | 0.18^{bc} | 1.69^{bc} | 4.83^{bc} |

SMP-Nonlinear | 0.31^{bc} | 0.49^{bc} | 0.65 | 0.70^{bc} | 4.07^{bc} | 10.52^{b} | 0.23^{bc} | 1.81^{b} | 5.23^{b} |

SMP-CDF | 0.28^{bc} | 0.49^{bc} | 0.67^{c} | 1.54 | 5.32 | 12.46^{b} | 0.38^{c} | 2.14 | 5.77 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, Z.; Wang, D.; Wang, G.; Qiu, J.; Liao, W.
Use of SMAP Soil Moisture and Fitting Methods in Improving GPM Estimation in Near Real Time. *Remote Sens.* **2019**, *11*, 368.
https://doi.org/10.3390/rs11030368

**AMA Style**

Zhang Z, Wang D, Wang G, Qiu J, Liao W.
Use of SMAP Soil Moisture and Fitting Methods in Improving GPM Estimation in Near Real Time. *Remote Sensing*. 2019; 11(3):368.
https://doi.org/10.3390/rs11030368

**Chicago/Turabian Style**

Zhang, Zhi, Dagang Wang, Guiling Wang, Jianxiu Qiu, and Weilin Liao.
2019. "Use of SMAP Soil Moisture and Fitting Methods in Improving GPM Estimation in Near Real Time" *Remote Sensing* 11, no. 3: 368.
https://doi.org/10.3390/rs11030368