*3.6. Spatiotemporal Distribution of Rainfall Detection Ability*

According to the results discussed earlier, the error indices varied in different parts of Iran. Since the variation of the error indices, such as rBIAS and MAE, can partly be explained by the rainfall detection ability of the satellite sensors. In this section, the rainfall detection ability of the satellite precipitation products are further assessed through spatial maps of POD and FAR. Figure 13 illustrates the spatial pattern of POD and FAR for four different seasons over the country. It is noted that the three IMERG daily products exhibit a similar spatial pattern of criteria relative to the rain gauge measurements with a slightly higher accuracy and lower bias for the IMERG-Final. Hence, we only discuss the criteria indices obtained from the analyses of the IMERG-Final and rain gauge

measurements in this section. These criteria indices were mapped using Kriging method in Arc GIS 10.4.1 environment.

According to the POD spatial map over the country (Figure 13), the satellite performance regarding precipitation detection shows an acceptable performance in most parts of the country in spring, followed by fall and winter (POD > 0.5). On the contrary, in the summer season, the southwestern parts, which show the best POD in winter, spring, and fall, indicate a low performance of the satellite in precipitation detection (POD < 0.4). It should be mentioned that the southern part of the country receives the end of the monsoon during summer time, for which precipitation is characterized by high intensity short-term rainfall [38]. Since the GPM constellation satellites revisit a given spot approximately every three hours, there is a high possibility that some of these short-term events are not observed by the satellite but by the rain gauges. As discussed in [1,39], higher POD is typically observed in dryer areas, i.e., central deserts (Figure S8), and the lower POD are typical for coastal areas, which is consistent with our findings, i.e., Persian Gulf and Caspian Sea coastal regions for summer (Figure 13).

**Figure 13.** Spatial distribution of POD and FAR for different seasons during the 2014–2017 period.

According to the FAR spatial map of the country, the northwestern followed by the western portion of the country shows lower FAR in winter, spring, and fall. Similar to the POD spatial map, higher FAR is obtained in summer for these regions. In all seasons, the central part of the country shows the highest FAR confirmed by a sparse rain gauge network (see Figure 1b) in the central deserts, i.e., Kavir and Lut deserts that cover the dry and extremely dry zones (Figure S8). As mentioned before, the FAR implies the ratio between the number of rain events that are observed by the satellite but not recorded by the rain gauges.

#### **4. Conclusions**

In this study, the performance of IMERG GPM products was evaluated at a daily (Early, Late, and Final) and monthly temporal resolution using a high-quality rain gauge network over Iran during 2014 to 2017. The study is one of the first IMERG GPM product assessments at a country level taking into account temporal and geospatial properties. In this regard, the study used eight criteria indices, including CC, MAE, rBIAS, POD, FAR, Under, Over, and Equal. Additional analyses were carried out based on these indices taking into account temporal and geospatial features.

The general performance of IMERG products relative to the rain gauge measurements indicated a major improvement in the IMERG accuracy from IMERG-Early to -Final products. However, the two indices of precipitation detection ability, POD and FAR, presented no major changes from Early to Final, which means that the correction algorithms do not account for the temporal correction of the satellite estimates. To evaluate the statistical distribution of rain gauge measurements versus satellite products, the Q-Q plots conclude that the IMERG-Final is not the best choice in extreme rainfall studies, but the IMERG-Early or Late can be used instead. Besides, the temporal performance of IMERG products, as displayed in the radar charts, showed a reduction of rBIAS from IMERG-Early to –Final.

Regarding POD, the best and worst performances were found in the spring and summer seasons, respectively. The FAR radar charts indicated an inferior performance of satellite products during the summer season.

The investigation of the relationship between various physical factors and location-specific factors of rainfall (rainfall index) with the eight mentioned criteria indices showed that CC varied for different rainfall indices. It appears that lower CC values were achieved both in the wettest and the driest locations. Further, by the increase of the rainfall index (from dryer to wetter locations), a lower and higher frequency of overestimation and underestimation, respectively, was observed for all IMERG products. Also, higher values of FAR were detected for the majority of the driest category of locations relative to wetter locations. Higher values of POD were found to be more frequent at dryer locations. As the POD investigated the spatial variability of rainfall within a particular grid, the results confirmed the superior detection ability of satellite sensors relative to gauge measurements (point measurement).

In general, the performance of satellite products increased from IMERG-Early to -Final products at the country level; however, these products need to be validated at the local scale and implemented in various hydrological models for verification. Higher values of FAR in the central part of the country, which is subjected to a sparse rain gauge network, require more caution when the IMERG data products are to be implemented in local-scale studies. This study provides an insight regarding the performance of the GPM IMERG products over all of Iran and can be used as a reference for further examination of the IMERG products in various hydrometeorological and hydrological applications.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2072-4292/12/1/48/s1, Figure S1, Figure S2, Figure S3, Figure S4, Figure S5, and Figure S6. Box plots of the criteria indices corresponding to the evaluation of IMERG-Early, IMERG-Late, and IMERG-Final products for the ten categories (bins) of location based on average dry period (in days), average annual rainfall (in mm year<sup>−</sup>1), elevation (in meter), slope, latitude ( ◦N), and longitude (◦E), respectively, Figure S7. Radar charts of criteria indices for IMERG-Monthly, and Figure S8. Iran's climate zones.

**Author Contributions:** Conceptualization, H.H. and S.H.H.; Data curation, F.F.M. and S.H.H.; Formal analysis, F.F.M. and S.H.H.; Funding acquisition, H.H. and R.B.; Investigation, F.F.M., H.H. and S.H.H.; Methodology, F.F.M., H.H. and S.H.H.; Project administration, H.H. and R.B.; Resources, H.H. and R.B.; Software, F.F.M. and S.H.H.; Supervision, H.H.; Validation, F.F.M., H.H. and S.H.H.; Visualization, F.F.M. and S.H.H.; Writing – original draft, F.F.M., H.H. and S.H.H.; Writing – review & editing, H.H., S.H.H. and R.B. All authors have read and agreed to the published version of the manuscript.

**Acknowledgments:** The authors appreciate the I.R. Iran Meteorological Organization (IRIMO) for providing daily rain gauge precipitation datasets for the entire country. The GPM IMERG products were downloaded from the Goddard Space Flight Center, Precipitation Measurement Missions at National Aeronautics and Space Administration (NASA) at https://pmm.nasa.gov/data-access/downloads/gpm. All authors thank the Center of Middle Eastern Studies and the MECW strategic project at Lund University for the partial financial support. The first and the third authors appreciate partial scholarships by the Department of Scholarship and Overseas Student's Affairs, Iran Ministry of Science, Research & Technology.

**Conflicts of Interest:** The authors declare no conflict of interest.
