*3.2. Error Analyses of IMERG Products*

A comparison of corresponding spatiotemporal rainfall data in the two datasets, i.e., satellite and rain gauge from the same location and time, was carried out using the evaluation indices introduced in Section 2.3.2. Table 1 presents these indices, including CC, MAE, rBIAS, POD, FAR, Equal, Over, and Under for the daily (IMERG-Early, -Late, and –Final) and monthly (IMERG-Final) time scale over the country. The indices were calculated based on the overlaid IMERG pixels and rain gauge data coordinates during the 2014–2017 period. For the comparison purposes, the daily products were accumulated for each month and presented in the monthly time scale, so all products can be compared in a monthly time scale supported with different values for the criteria indices monthly time scale presented in Table 1. It is noted that the algorithms used for producing the IMERG-Monthly product are different from those of the IMERG-Final, although both are gauge-corrected products.


**Table 1.** Error analyses for daily and monthly IMERG products vs. rain gauge measurements in both monthly and daily time scales.

Generally, in the monthly time scale, the IMERG-Monthly product showed the best performance in comparison to rain gauge measurements, in relation to the daily IMERG products, especially for IMERG-Early and IMERG-Late. However, the IMERG-Final products indicated, generally, comparable results and even, to some degree, outperformed the IMERG-Monthly product according to the MAE, rBIAS, FAR, Over, and Equal criteria. The CC between monthly rainfall from gauges and satellite products was the highest, 0.68 for the IMERG-Monthly, and the MAE was the lowest, yielding 0.43 mm day−<sup>1</sup> for the IMERG-Final. In the case of relative bias between rain gauges and satellite products, the results were excellent, yielding less than ±5% except for IMERG-Early in the daily time scale. The bias calculation showed that the IMERG-Early products slightly overestimated the rain gauge measurements at the country level, but a substantial improvement regarding rBIAS can be seen from IMERG-Early, 9% to Final, 0% in daily time scale (Table 1).

Generally, in the case of IMERG daily products, in the daily time scale, criteria indices for the three products did not significantly differ from each other, but the performance of the daily IMERG products relative to the rain gauge measurements improved from IMERG-Early to -Final. The IMERG-Final showed the highest correlation with rain gauge measurements, with a CC value of 0.47, followed by the IMERG-Late and -Early both yielding 0.41. The MAE and rBIAS decreased from the IMERG-Early to -Final products, showing a better performance of the IMERG-Final product relative to –Early and –Late in comparison with the rain gauge measurements in the daily time scale (Table 1).

The results were acceptable for the satellite precipitation detection ability in all daily IMERG products: POD = 0.68% in the daily time scale and POD = 98%–100% in the monthly time scale. The POD did not change from the IMERG-Early to -Final daily products, meaning that the satellite-gauge-adjusted algorithm, used in the IMERG-Final product, did not help for the detection improvement of the IMERG-Early and –Late products. As mentioned in Section 2.2.2, the GPM Core Observatory's temporal resolution is three hours, which results in no calibration of the precipitation observed by the constellation satellites within this gap for a given area. However, this problem is resolved by accumulating the daily into monthly precipitation (POD = 1). Similar results were achieved for FAR calculations. The IMERG daily products showed low performance by having a false detection value of 0.6 while the monthly FAR was 0.23, indicating an acceptable rain detection ability at the monthly time scale (Table 1).

At the daily time scale, in principal, no significant improvement in rainfall detection ability regarding POD and FAR indices were observed. Further, no substantial differences between all three daily products were observed, as the monthly product showed a better performance in the estimation of precipitation considering MAE and rBIAS, and precipitation detection, POD, and FAR.

The over index did not change much from IMERG-Early to -Final and the under index decreased slightly from IMERG-Early (42%) to -Final (41%) products. For the daily products, equal was much smaller than both over and under, and over was 2% to 6% higher than under. However, for the monthly product, equal was about 47%, and over was 17% higher than under (Table 1). The more smoothed nature of the monthly data variation, as compared to daily, is a probable reason for the higher equal

obtained for the monthly product. Also, the larger upper values as compared to under for all products is in line with the overall overestimation shown by the positive rBIAS. However, the cause of a larger difference between upper and under for the monthly product, compared to the daily ones, can be explained under some circumstances. For instance, suppose a month with only one (or few) rainy day is overestimated by the satellite. While, at a daily time scale, this will be counted as only one (a few) day of overestimation in the calculation of over, at the monthly time scale, this would be counted as one month as compared to the length of monthly data, which is almost 30 times shorter than the daily ones, therefore, resulting in higher over.
