Comparative analysis of gridded rainfall datasets over the Bagmati river basin, India

In this study, three high-resolution gridded rainfall datasets, viz., Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG), Modern-Era Retrospective Analysis for Research and Applications 2 (MERRA-2), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) have been collected, analyzed, and compared against the ground-based observed rain gauge datasets of Indian Meteorological Department (IMD) of the Bagmati river basin from 2001 to 2014 in the Bihar State of India. Comparison analyses were performed at daily, monthly, seasonal, and annual time scales. Various statistical parameters, contingency tests, trend analysis, and rainfall anomaly index were used for comparison of datasets. Though MERRA-2 had the highest probability of detection (POD) and lowest false alarm ratio (FAR), analysis showed that IMERG data were closely matching with the observed data, whereas MERRA-2 and PERSIANN underestimated the extreme values. For the monthly scale, again IMERG had the most optimal Coefficient of Determination (R²) and Nash-Sutcliffe Efficiency (NSE) values. IMERG also performed well in detecting rainfall trends and identifying wet and dry years. Overall, IMERG was the most suitable dataset at all time scales for future studies in the basin.

HIGHLIGHTS

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Gridded rainfall datasets of IMERG, MERRA-2, and PERSIANN can be used as the substitute for IMD rainfall data in relatively ungauged and data-scarce regions of the Bagmati river basin.
IMERG datasets have the potential to be used for real-time hydrological and climatological studies.
IMERG performed best in cumulative distribution function, trend analysis, statistical evaluation, and box plot analysis.

gridded rainfall datasets, IMERG, MERRA-2, PERSIANN, reanalysis, satellite

INTRODUCTION

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Rainfall datasets are a major influencing factor in most hydrological and climatological studies. The datasets of rainfall are very useful in flood forecasting, climate modeling, water resources management, agriculture, and urban planning (Hamal et al. 2020; Setti et al. 2020; Gautam & Pandey 2022; Ranjan & Singh 2022; Kumar et al. 2023). All these applications require accurate and reliable datasets with easy accessibility. Generally, the source of these datasets is a ground-based rain gauge network. But in most of the developing countries, rain gauge networks are inept and sparse over the region which causes an inadequate supply of data (Hughes 2006; Nanda et al. 2016; Kumar et al. 2017; Rincón-Avalos et al. 2022). These networks are generally expensive to establish and maintain, particularly in remote or difficult-to-access regions. Rain gauges give estimates of rainfall only at point locations (Nanding et al. 2015). They are affected by measurement errors due to wind-induced under-catch or evaporation (Yeditha et al. 2020). So, to solve this issue of authentic data scarcity, gridded rainfall datasets are often used as an alternative (Yeditha et al. 2020; Bhattacharyya et al. 2022; Gautam & Pandey 2022). They have better spatial and temporal resolution, which makes it possible to study rainfall in remote or inaccessible regions (Su et al. 2008; Kidd & Huffman 2011). They provide information in detail, which is important for understanding local variations in rainfall and helps in the continuous monitoring of rainfall (Saikrishna et al. 2021). Most of the gridded datasets are free of cost and easily accessible without restriction in real or near real-time (Sorooshian et al. 2000; Gelaro et al. 2017; Huffman et al. 2020). The gridded datasets have significantly improved the studies involving climate change, flood, landslide, soil erosion, and drought monitoring (Hong et al. 2007; Wang et al. 2016; Xiao et al. 2020; Hinge et al. 2021; Yeditha et al. 2022; Suroso et al. 2023).

The gridded rainfall datasets are broadly categorized into three types, viz., gauge-based datasets (observed), satellite-based datasets, and reanalysis datasets (Wang et al. 2020; Bhattacharyya et al. 2022). The gauge-based datasets are derived from measurements taken at ground-level using rain gauges (Boers et al. 2016). The data are then interpolated onto a regular grid using various methods, such as inverse distance weighting or kriging. (Chua et al. 2022). Examples of gauge-based datasets include the Global Historical Climatology Network (GHCN) (Menne et al. 2012) and the Global Precipitation Climatology Centre (GPCC) (Schneider et al. 2015). The satellite-based datasets are derived from satellite measurements of precipitation using microwave and infrared sensors (Ray et al. 2022). Examples of satellite-based datasets include the Tropical Rainfall Measuring Mission (TRMM), (Huffman et al. 2007), Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG) (Huffman et al. 2020), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) (Sorooshian et al. 2000). The reanalysis datasets are derived from atmospheric models that combine observations from various sources, such as satellites, surface stations, and radiosondes to produce a comprehensive record of the Earth's climate over several decades (Bhattacharyya et al. 2022). Examples of reanalysis datasets include the Modern-Era Retrospective Analysis for Research and Applications 2 (MERRA-2) (Gelaro et al. 2017), European Centre for Medium-Range Weather Forecasts Interim Reanalysis (ERA-Interim) (Dee et al. 2011).

Gridded datasets must undergo evaluation against reliable ground-based observed rainfall to be suitable for hydrological and climatological studies (Xiao et al. 2020). This is necessary because observation methods, instrumentation, and rainfall extraction in gridded products can introduce errors. Additionally, natural variables like climate, rainfall intensity, season, and topography can vary, affecting dataset performance and precision across different areas (AghaKouchak et al. 2012; Sun et al. 2018). Uncertainties in rainfall data can impact hydrologic and climatological modeling predictions, highlighting the importance of initial dataset evaluation.

Many researchers around the globe have evaluated the gridded rainfall datasets against ground-based rainfall measurements. For instance, the results of a study by Miri et al. (2019) showed that Global Precipitation Mission (GPM)-IMERG outperformed other satellite datasets (TRMM_3B42 and PERSIANN-Climate Data Record (CDR) with R² as 0.6 and 0.83 at daily and annual scales, respectively over Iran. According to Tang et al. (2020) study in China, the precision of IMERG precipitation estimations rose from 2001 to 2018 due to improvements in satellite sensors. Ramos Filho et al. (2022) showed that in areas with few rain gauges, Satellite Precipitation Products (SPPs) can be used to establish precipitation thresholds. Bhattacharyya et al. (2022) performed a comparative analysis of different gridded rainfall datasets and India Meteorological Department (IMD) gauge-based gridded datasets over India. Notably, the PERSIANN-CDR dataset exhibited a predominant drying trend, while both the Climate Prediction Centre (CPC) and MERRA-2 showcased a wetting trend across all extreme rainfall indices. Reddy & Saravanan (2022) based on the study of seven SPPs in the Godavari basin, India concluded that finer resolution SPPs can be used for regional-scale hydrological studies after comparison. Sireesha et al. (2020) appraised the performance of precipitation datasets of IMD, TRMM, GPCC, and MERRA-2 in the Sina basin. Based on all the tests, TRMM datasets were ascertained as suitable for climatic or hydrological studies. Using the hydrological model J2000, Kumar et al. (2017) assessed the TMPA-3B42 v7 dataset and rain gauge observations in the Kopili river basin and reached the conclusion that bias-corrected TRMM precipitation has the potential to substitute the observed rainfall dataset in regions with limited data or ungauged basins. This is due to the dataset's superior spatial and temporal resolution.

Bagmati river is an international river flowing between Nepal and India. In India, it flows through the state of Bihar. The region is prone to floods, and the existing rain gauge network in the Bagmati basin is relatively inefficient, leading to a lack of adequate data for hydrological and climatological studies. Despite the importance of the Bagmati river basin in Bihar, no studies have been found that have employed satellite-based datasets like IMERG, PERSIANN, or reanalysis datasets like MERRA-2 to understand the hydrological and climatological conditions of the region. This highlights the need for more research in this area, especially given the challenges posed by floods in this densely populated and developing state.

The main objectives of this paper are (1) to compare three gridded datasets, viz., IMERG and PERSIANN (satellite-based datasets) and MERRA-2 (reanalysis datasets) with respect to observed daily, monthly, seasonal, and annual rain gauge datasets of the Bagmati river basin of Bihar and (2) to investigate the limitations in these gridded rainfall datasets.

STUDY AREA AND DATA COLLECTION

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Study area

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The Bagmati river is a perennial river that flows through two nations: Nepal and India. It originates at the Shivpuri range of hills in Nepal at latitude 27°47′ N and longitude 85°17′ E, at an elevation of 1,500 m above msl. The river enters north Bihar at the village of Shorwatia in Sitamarhi district, which is about 2.5 km north of the Dheng Railway Bridge. The total length and basin area of the Bagmati river in Bihar are 394 and 6,500 km², respectively. The average annual rainfall and temperature are 1,255 mm and 27 °C, respectively (Kumar et al. 2020). The soil in the area is mainly alluvial. The Bagmati river meets the Kamla river at Jagmohra village of Samastipur, and finally outfalls into the Kosi river near Badlaghat, Khagaria. Figure 1 shows the location of the present study area, i.e., the Bagmati river basin in Bihar. This figure also shows the rain gauge stations considered in this study, which are Benibad, Dheng, Kamtaul, and Hayaghat. Figure 2 depicts the digital elevation model of the Bagmati river basin, depicting its ground surface topography. The elevation ranges from 40 to 99 m above mean sea level. Figure 3 shows the river network of the Bagmati river basin, displaying the Bagmati river and its tributaries, Adhwara, Lalbhekya, Lakhandei, Khiroi, and Kamla-Bagmati Sangam.

Figure 1

Study area depicting the Bagmati river basin.

Figure 2

Digital elevation model of the Bagmati river basin.

Figure 3

River network of the Bagmati river basin.

Data used

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The analysis was carried out based on the available daily data from the years 2001 to 2009 and monthly and annual data from 2001 to 2014 of the rain gauge stations of IMD. The different gridded daily rainfall datasets for the same period were downloaded. The source of different gridded datasets is mentioned in their respective sections. The Digital Elevation Model (DEM) tiles of 90 m of Shuttle Radar Topography Mission (SRTM) were downloaded from the website of the United States Geological Survey (USGS) Earth Explorer (https://earthexplorer.usgs.gov/) for preparing the digital elevation model, basin delineation, and river network map.

Daily gridded rainfall data

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In this study, three gridded datasets are used, viz., IMERG, MERRA-2, and PERSIANN. In these datasets, the area of interest is divided into a regular grid of cells, and the amount of rainfall that occurred in each cell is estimated based on observations from various sources, such as satellite sensors, rain gauges, radar, or atmospheric models (Tang et al. 2020; Ray et al. 2022).

IMERG

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IMERG-gridded SPP datasets were developed by the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA) for GPM. It leverages data from satellites in low-earth orbit and geostationary satellites, combining microwave-calibrated infrared satellite estimates to provide accurate estimates of rainfall. The quickest version of IMERG provides rainfall data within 4 h of the observation (Huffman et al. 2020). In this study, ‘Final Run’ datasets of IMERG have been used. These datasets were downloaded from the website of GIOVANNI (https://giovanni.gsfc.nasa.gov/giovanni/).

MERRA-2

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MERRA-2-gridded reanalysis dataset was developed by NASA. It utilizes the Atmospheric General Circulation Model and the Global Statistical Interpolation (GSI) atmospheric analysis system to estimate rainfall. The dataset incorporates rainfall estimates derived from assimilating data from satellites, surface stations, and aircraft into the atmospheric model (Gelaro et al. 2017). The data are updated with a latency period of 14 h. In this study, the MERRA-2 datasets were downloaded from the website of NASA Power Data Access Viewer (https://power.larc.nasa.gov/data-access-viewer/).

PERSIANN

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PERSIANN-gridded satellite-based precipitation product (SPP) was developed by the Center for Hydrometeorology and Remote Sensing (CHRS), USA. The product utilizes infrared brightness temperature data from geostationary satellites to estimate precipitation (Sorooshian et al. 2000). The product's fastest variant can provide data within 15–60 min of observation. In this study, the PERSIANN datasets were used which were downloaded from the website of the CHRS Data Portal (https://chrsdata.eng.uci.edu/).

The details of various gridded rainfall datasets used in this study are tabulated in Table 1.

Table 1

Summary of gridded rainfall datasets used for the study area

Sl. No.	Name (data provider)	Spatial coverage	Temporal resolution (min)	Temporal coverage	References
1.	IMERG (NASA and JAXA)		30	2000–present	Huffman et al. (2020)
2.	MERRA-2 (NASA)		60	2000–present	Sorooshian et al. (2000)
3.	PERSIANN (CHRS, USA)	Global	60	1980–present	Gelaro et al. (2017)

Sl. No.	Name (data provider)	Spatial coverage	Temporal resolution (min)	Temporal coverage	References
1.	IMERG (NASA and JAXA)		30	2000–present	Huffman et al. (2020)
2.	MERRA-2 (NASA)		60	2000–present	Sorooshian et al. (2000)
3.	PERSIANN (CHRS, USA)	Global	60	1980–present	Gelaro et al. (2017)

METHODOLOGY

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Flowchart of methodology

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The methodology of the study in terms of flowchart is presented in Figure 4. Firstly, the ground-based observed rain gauge datasets (IMD) and gridded datasets (IMERG, MERRA-2, and PERSIANN) were collected. For gridded datasets, grid points were extracted for the Bagmati river basin. The estimation of rainfall for a given station was performed through the use of bilinear interpolation. This interpolation method takes into account the magnitude of rainfall recorded at various grid points surrounding the station in question and uses this information to estimate the rainfall at the station's precise coordinates (Gadelha et al. 2019). For computing mean basin rainfall, the Thiessen polygon method was adopted.

Figure 4

Flowchart of methodology.

The gridded datasets were evaluated against the benchmark IMD datasets at daily, monthly, seasonal, and annual scales to assess the best-gridded dataset that can capture the rainfall pattern and distribution similar to the observed datasets. For this, monthly, seasonal, and annual datasets were computed from the daily gridded datasets from the years 2001 to 2014. Cumulative Distribution Function (CDF) plot and contingency test have been performed using daily data. For the monthly level, monthly rainfall box plots and statistical metrics were analyzed. For the seasonal level, the seasonal rainfall box plot and Mann–Kendall (M–K) and Sen's Slope (SS) test results were analyzed. For the annual level, the annual rainfall plot, descriptive statistics, and the rainfall anomaly index (RAI) were analyzed. Based on all analysis, a heat map was made to rank the gridded datasets. The details of all these analyses have been described in a further section.

Contingency test

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The contingency test assesses the ability of a satellite to capture rainy and non-rainy days using categorical metrics (Bharti & Singh 2015; Navale et al. 2020).

Four categorical metrics were evaluated in contingency tests: Hit (H), which represents the number of days when rainfall events were recorded at both the rain gauge station and the satellite; Miss (M), which represents the number of days when rainfall events were recorded by the rain gauge station but not by the satellite; False Alarm (F), which represents the number of days when rainfall events were recorded by the satellite but not observed in the rain gauge station; and Correct Negative (Q), which represents the number of days when neither the rain gauge station nor the satellite recorded any rainfall events, indicating non-rainy days.

Based on the above categorical metrics, two contingency indices were calculated. The first is the probability of detection (POD), which represents the number of events correctly detected by the satellite datasets compared to the observed datasets (Bharti & Singh 2015; Navale et al. 2020). It is calculated using the formula:

(1)

where H indicates a hit; M indicates a miss. The value of POD ranges from 0 to 1, with a value closer to 1 indicating a good capability of the satellite to capture rainfall events compared to the observed datasets.

The second contingency index was the false alarm ratio (FAR), which represents the number of events when rainfall events were recorded by the satellite when no event was represented in the observed data (Bharti & Singh 2015; Navale et al. 2020). It was calculated using the formula:

(2)

where F indicates a false Alarm; H indicates a hit. The value of FAR ranges from 0 to 1, with a value closer to 0 indicating accurate datasets compared to the observed datasets. For this study, a rainfall threshold of 0.1 mm/day is considered to cause a rainfall event (Gadelha et al. 2019).

Cumulative distribution function

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To compare the daily distribution of gridded and observed rain gauge datasets, the CDF was plotted. The CDF for daily rainfall datasets gives information about the probability of observing rainfall equal to or below a particular value (Park 2018).

The CDF for rainfall is calculated using the following formula:

(3)

here

is the CDF function of the rainfall dataset; R is the daily rainfall amount; x is the threshold value of the rainfall amount for which probability (P) is to be calculated.

M–K and SS test

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The M–K test was performed to identify significant trends in seasonal rainfall time series. This test works by comparing the observed data to two hypotheses. Under the null hypothesis (H0), it is assumed that the data are unrelated and does not display any trend. Conversely, the alternative hypothesis (Ha) entertains the idea of a monotonic trend. The Q statistic is calculated in the following manner:

(4)

where sgn is the sign function, n denotes the number of data points,

denotes rank for

th observations and

denotes rank for

th observations.

The Q-statistic variance (⁠

⁠) is defined by :

(5)

Using the Q and

⁠, standard test statistic (⁠

⁠) is computed as follows:

(6)

After this p-value is obtained. The p-value less than 0.05 (significance level) indicates that the observed trend is likely to be statistically significant. More details of the method of performing this test can be found in studies of Kumar et al. (2022) and Zhang et al. (2023).

SS was used to identify if the rainfall trend was increasing or decreasing (Sen 1968). The SS is given as :

(7)

where the rainfall data values at time periods i and j are given by

and

⁠.

If the SS value is positive, it indicates an increasing trend, while a negative value suggests a decreasing trend.

Statistical metrics

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The gridded rainfall datasets are evaluated against rain gauge observed datasets by numerous performance criteria. If = ith rain gauge data, = ith gridded rainfall data, = Mean of the datasets, and N = Number of observations, then the various statistical metrics used for gridded rainfall datasets performance evaluation are as follows:

(i)
Coefficient of determination ⁠: It is used to assess the goodness of fit between the observed rainfall from IMD and gridded rainfall data. It quantifies the proportion of the variance in the observed rainfall that can be explained by the gridded rainfall data. ranges from 0 to 1, where a value of 1 indicates a perfect fit, suggesting that the gridded rainfall data can explain all the variance in the observed rainfall. The correlation coefficient is given as R. The square of R gives the ⁠. R is computed as (Gautam & Pandey 2022):
(8)
(ii)
RMSE: It measures how spread the gridded rainfall dataset values are from the rain gauge value. It ranges from 0 to ∞. The lower RMSE value represents a better estimation. It is computed as (Gautam & Pandey 2022):
(9)
(iii)
NSE: It measures the predictive ability of the gridded data. It ranges from − ∞ to 1. The value 1 represents the correct rainfall representation. It is computed as (Nash & Sutcliffe 1970):
(10)
(iv)
Percent of Bias (Pbias): It is an indication of the average overestimation or underestimation of the gridded values relative to the observed values. It ranges from -∞ to ∞. PBIAS has an optimum value of 0 with negative values suggesting underestimation and positive values suggesting overestimation. It is computed as (Gautam & Pandey 2022):
(11)

The performance categorization for ⁠, NSE, and Pbias (Sithara et al. 2020) are tabulated in Table 2.

Table 2

Performance categorization for statistical index

Parameter	Range	Performance inference
		Acceptable
		Very good
NSE		Unsatisfactory
		Satisfactory
		Good
		Very good
Pbias		Very good
		Good
		Satisfactory
		Unsatisfactory

Parameter	Range	Performance inference
		Acceptable
		Very good
NSE		Unsatisfactory
		Satisfactory
		Good
		Very good
Pbias		Very good
		Good
		Satisfactory
		Unsatisfactory

RAI for wet and dry year validation

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Rainfall anomaly refers to the deviation between the observed rainfall and long-term average rainfall for a particular region or period. Positive anomalies indicate above-average rainfall, while negative anomalies indicate below-average rainfall. The RAI is calculated as (Van Rooy 1965; El-Tantawi et al. 2021).

The RAI is calculated as follows:

(12)

(13)

where Y indicates the yearly rainfall (mm);

indicates the mean of yearly rainfall (mm) of past series;

indicates the mean of 10 highest yearly rainfall (mm) of past series;

indicates the mean of 10 least yearly rainfall (mm) of past series.

The classification of the years according to the RAI is tabulated in Table 3 (Bougara et al. 2021).

Table 3

Classification of the year according to the RAI

RAI	Classification
≥3.00	Extremely wet
2.00–2.99	Very wet
1.00–1.99	Moderately wet
0.50–0.99	Slightly wet
0.49 to −0.49	Near normal
−0.50 to −0.99	Slightly dry
−1.00 to −1.99	Moderately dry
−2.00 to −2.99	Very dry
≤−3.00	Extremely dry

RAI	Classification
≥3.00	Extremely wet
2.00–2.99	Very wet
1.00–1.99	Moderately wet
0.50–0.99	Slightly wet
0.49 to −0.49	Near normal
−0.50 to −0.99	Slightly dry
−1.00 to −1.99	Moderately dry
−2.00 to −2.99	Very dry
≤−3.00	Extremely dry

RESULTS AND DISCUSSION

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High-resolution gridded rainfall datasets, viz., IMERG, MERRA-2, and PERSIANN have been compared with the ground-based observed rainfall data at the rain gauge stations (Benibad, Dheng, Hayaghat, and Kamtaul) from the year 2001 to 2014 of the Bagmati river basin in Bihar State of India. Figure 5 presents the grid point in all the datasets. The Thiessen polygon with Thiessen weights for the rain gauge stations is shown in Figure 5(a). The grid points and corresponding Thiessen polygon of IMERG, MERRA-2, and PERSIANN are shown in Figure 5(b)–5(d) respectively. IMERG has the highest number of grid points falling inside the basin. There were 51 grid points, three grid points, and nin^#e grid points of IMERG, MERRA-2, and PERSIANN respectively falling inside the basin.

Figure 5

Thiessen polygon: (a) Rain gauge stations; (b) IMERG grids; (c) MERRA-2 grids; and (d) PERSIANN grids.

The contingency metrics for all the datasets at Benibad, Dheng, Hayaghat, and Kamtaul rain gauge stations are presented in Table 4. Across all stations, MERRA-2 consistently exhibits the highest number of hits of 950 days, 937 days, 961 days, and 947 days at stations Benibad, Dheng, Hayaghat, and Kamtaul respectively indicating its superior performance in accurately capturing precipitation events compared to IMERG and PERSIANN. However, IMERG and PERSIANN are not far behind in terms of hit counts and demonstrate competitive results, with values that are generally close to MERRA-2. On the other hand, MERRA-2 also exhibits a higher number of false alarms compared to IMERG and PERSIANN. This suggests that MERRA-2 might overestimate the occurrence of precipitation events, leading to more false alarms (Arshad et al. 2021). The larger grid size of MERRA-2 compared to IMERG and PERSIANN may contribute to the higher number of false alarms. With a larger grid size, MERRA-2 may capture a broader area within each grid cell, potentially including regions with no or minimal precipitation (Ramos Filho et al. 2022). This can lead to overestimation and result in more false alarms. In contrast, IMERG and PERSIANN, with potentially finer grid sizes, are able to capture smaller-scale precipitation events more accurately and with fewer false alarms.

Table 4

Contingency metrics for different gridded datasets

Station	Contingency metrics (days)	IMERG	MERRA-2	PERSIANN
Benibad	Hit	869	950	799
	Miss	160	79	230
	False alarm	777	1,030	645
	Correct negative	1,878	1,625	2,010
Dheng	Hit	893	937	822
	Miss	136	92	207
	False alarm	819	1,046	684
	Correct negative	1,869	1,642	2,004
Hayaghat	Hit	910	961	784
	Miss	119	68	245
	False alarm	890	982	674
	Correct negative	1,798	1,706	2,014
Kamtaul	Hit	876	947	812
	Miss	153	82	217
	False alarm	758	1,032	684
	Correct negative	1,930	1,656	2,004

Station	Contingency metrics (days)	IMERG	MERRA-2	PERSIANN
Benibad	Hit	869	950	799
	Miss	160	79	230
	False alarm	777	1,030	645
	Correct negative	1,878	1,625	2,010
Dheng	Hit	893	937	822
	Miss	136	92	207
	False alarm	819	1,046	684
	Correct negative	1,869	1,642	2,004
Hayaghat	Hit	910	961	784
	Miss	119	68	245
	False alarm	890	982	674
	Correct negative	1,798	1,706	2,014
Kamtaul	Hit	876	947	812
	Miss	153	82	217
	False alarm	758	1,032	684
	Correct negative	1,930	1,656	2,004

Figure 6 shows the graph of POD and FAR results for all stations. From Figure 6(a), it is evident that MERRA-2 exhibits the highest values of POD, followed by IMERG and PERSIANN. Specifically, MERRA-2's POD ranges from 91.06 to 93.09%, IMERG's from 84.45 to 88.44%, and PERSIANN's from 76.19 to 79.88% across different stations. These results agree with previous research conducted by Yeditha et al. (2020), Sharma et al. (2020), Saikrishna et al. (2021), Nepal et al. (2021), Gautam & Pandey (2022), Dangol et al. (2022), Yeditha et al. (2022) and Kumar et al. (2023). Their studies spanning across various regions in India as well as Nepal which shares an international border with our study area align closely with our findings. This supports the consistency of these precipitation products to detect precipitation events in regions similar to our study area. Figure 6(b) further reveals that PERSIANN reports a lower FAR at all stations when compared to other datasets. Among the four rainfall stations, Hayaghat has the highest POD of 93.39% for all three rainfall estimates, indicating that it has the highest proportion of actual rainfall events that were correctly predicted. Dheng has the highest FAR of 52.75% for all three rainfall estimates, indicating the highest proportion of predicted rainfall events that did not occur. In summary, all three rainfall estimates demonstrate satisfactory performance in contingency metrics, with some excelling in POD and others in FAR. Notably, MERRA-2 exhibits the most robust performance in contingency metrics, followed by IMERG and PERSIANN.

Figure 6

Contingency indices for all the stations: (a) POD and (b) FAR.

CDF for daily rainfall datasets

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The CDF plot of daily rainfall datasets for Observed, IMERG, MERRA-2, and PERSIANN at each station over the basin is shown in Figure 7. It was found that CDF of IMERG exhibited the closest match to the observed data in terms of the range of daily rainfall for all stations, whereas MERRA-2 and PERSIANN mostly underestimated the magnitude of extreme rainfall days which can be observed in the range of magnitude of rainfall. The superior performance of IMERG can be attributed to its utilization of finer resolution, frequent satellite overpasses, and the advanced capabilities of its precipitation sensors (Sharma et al. 2020; Tang et al. 2020; Yang et al. 2020; Kumar et al. 2023). A study by Yucel et al. (2011), Solakian et al. (2020) and Kumar et al. (2023) reported that precipitation products generally underestimate rainfall values when compared to rain gauge observation, especially in lower elevation zones. From the zoomed plot of Figure 7(a)–7(d), it can be inferred that for rainfall <10 mm, there is a slight underestimation of rainfall in all gridded datasets. For the rainfall range of 10–50 mm at Benibad, Hayaghat, and Kamtaul rain gauge stations, the SPPs datasets had a matching range as observed but for the Dheng station, there is an overestimation in MERRA-2 and PERSIANN datasets. In contrast to these datasets, IMERG datasets demonstrated better distribution at this station. The higher underestimation of rainfall values in MERRA-2, despite having a higher POD, indicates that the rainfall estimates provided by MERRA-2 are not as accurate as expected. This discrepancy can be due to the larger grid size and nature of the atmospheric model-derived output data used in MERRA-2 (Ramos Filho et al. 2022; Kumar et al. 2023). The larger spatial resolution of MERRA-2 may not effectively capture local-scale processes or account for topographical features that influence rainfall patterns (Bharti & Singh 2015; Hamal et al. 2020). Consequently, the dataset may miss or underestimate precipitation events occurring at smaller scales. Further, MERRA-2 assimilates data from various observations, including satellite data, surface observations and weather station data, into its model. Data assimilation aims to improve the accuracy of the representation of precipitation but biases can still occur during the assimilation process, which introduces inaccuracies in the estimation of rainfall, potentially leading to the observed underestimation of rainfall values (Gelaro et al. 2017). Furthermore, a study by Arshad et al. (2021) in Pakistan revealed that while MERRA-2 accurately captured precipitation intensity, it exhibited limitations in detecting extreme precipitation events in certain areas. The underestimation of extreme rainfall values by PERSIANN is possibly due to the utilization of artificial neural networks and reliance on single-sensor infrared data as part of the PERSIANN methodology which might result in inaccurate rainfall estimates (AghaKouchak et al. 2012; Kumar et al. 2023). Infrared sensors on satellites are sensitive to cloud cover and diurnal temperature variations, which can hinder their accuracy in detecting precipitation under thick cloud layers. However, IMERG overcomes these limitations by incorporating both microwave and infrared sensors, as confirmed by the study conducted by Kumar et al. (2023). Prakash et al. (2018) also calculated the CDF based on the entropy approach. Their findings corroborate that IMERG exhibits a substantial enhancement in depicting the distribution of rainfall over the monsoon trough region of India when compared to its earlier version of TMPA. Thus, IMERG performed best followed by PERSIANN and MERRA-2 in the CDF pattern.

Figure 7

CDF plots for the following stations (a) Benibad; (b) Dheng; (c) Hayaghat; and (d) Kamtaul.

Monthly scale

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Box plot analysis

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Figure 8 presents a box plot illustrating the monthly rainfall distribution from 2001 to 2014. The box represents the interquartile range, with the bottom edge indicating the 25th percentile and the top edge indicating the 75th percentile. The plot also includes lines connecting the mean values indicated by a cross sign. The horizontal line indicates the median value. The median values are almost identical at all stations in the month of January, February, March, April, October, November, and December for all the rainfall datasets. For the other months, there is variation between the observed and gridded rainfall datasets. The interquartile range of the plot shows that the highest amount of rainfall occurs at all stations across all rainfall datasets in the month of July followed by August and September. The line connecting the mean values across all months exhibited that only observed and IMERG showed fairly matching mean at all stations. In contrast, MERRA-2 and PERSIANN consistently underestimate the mean monthly rainfall values. This alignment between IMERG and observed data echoes findings in studies by Sharma et al. (2020), Nepal et al. (2021), and Kumar et al. (2023). A study by Kumar et al. (2023) in the Gandak river basin of Nepal, which is geographically proximate to our research area corroborates the underestimation of mean monthly rainfall values by MERRA-2 and PERSIANN. It can also be inferred from the line connecting mean monthly values that stations in the upper portion (Dheng and Kamtaul) receive higher rainfall when compared to stations in the lower portion (Kamtaul and Hayaghat).

Figure 8

Box plots of monthly rainfall for the following stations: (a) Benibad; (b) Dheng; (c) Hayaghat; and (d) Kamtaul.

Statistical performance of monthly rainfall datasets

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The monthly gridded rainfall datasets were evaluated against the observed rain gauge datasets. The R², NSE, RMSE, and Pbias of the results are tabulated in Table 5. The monthly correlation for all stations is shown in Figure 9. For all the stations, the three datasets showed decent R² and NSE values, indicating good performance in capturing the monthly variability of rainfall. According to the performance categorization by Sithara et al. (2020), IMERG falls within the ‘very good’ range for R² (R² > 0.75), while both MERRA-2 and PERSIANN exhibit R² values ranging from ‘acceptable’ (R² > 0.5) to ‘very good’ (R² > 0.75). In the case of all three datasets, the NSE values span from the ‘good’ range (0.65 < NSE ≤ 0.75) to the ‘very good’ range (NSE > 0.75). IMERG also reported the lowest values of RMSE for all the stations among all rainfall datasets. For station Dheng, the highest R² and NSE values of 0.87 and 0.86 respectively were reported by IMERG datasets. The IMERG recorded the lowest RMSE value of 57.62 mm/month for station Benibad. Further, IMERG showed negative Pbias indicating underestimation of monthly rainfall, whereas MERRA-2 and PERSIANN showed positive Pbias indicating overestimation of monthly rainfall. MERRA-2 reported high values of Pbias when compared to other datasets with Dheng having the highest Pbias of 15.1%. However, the Pbias by IMERG which ranged from −15 to −2.64% was most optimum as it lay in the range ‘very good’ to ‘good’ as per the performance categorization by Sithara et al. (2020). The better performance of IMERG's monthly rainfall estimates is attributed to its utilization of ground-based rain gauge analyses from the GPCC for its bias adjustments (Prakash et al. 2018; Sharma et al. 2020; Kumar et al. 2023). PERSIANN consistently reported higher values of RMSE when compared to other datasets representing its poor performance. Kumar et al. (2023) also reported a similar underperformance of PERSIANN. A similar statistical result for monthly rainfall estimates by datasets used in this research has been also reported by the study of Yeditha et al. (2020), Hamal et al. (2020), Gautam & Pandey (2022) and Kumar et al. (2023). Thus, the IMERG dataset performs best among the three datasets in terms of accuracy and precision in estimating monthly rainfall for all the stations analyzed followed by MERRA-2 and PERSIANN.

Table 5

Statistical performance of monthly rainfall datasets

Station	Statistical parameters	IMERG	MERRA-2	PERSIANN
Benibad	R²	0.83	0.77	0.74
	NSE	0.82	0.76	0.74
	Pbias	− 2.64	10.16	6.12
	RMSE	57.62	67.10	70.54
Dheng	R²	0.87	0.62	0.75
	NSE	0.86	0.61	0.72
	Pbias	− 5.96	15.10	19.28
	RMSE	58.97	100.02	83.96
Hayaghat	R²	0.77	0.77	0.69
	NSE	0.77	0.75	0.69
	Pbias	− 3.06	13.21	7.51
	RMSE	66.59	68.79	77.00
Kamtaul	R²	0.77	0.69	0.68
	NSE	0.72	0.68	0.68
	Pbias	− 15.00	4.33	1.25
	RMSE	69.88	74.66	75.40

Station	Statistical parameters	IMERG	MERRA-2	PERSIANN
Benibad	R²	0.83	0.77	0.74
	NSE	0.82	0.76	0.74
	Pbias	− 2.64	10.16	6.12
	RMSE	57.62	67.10	70.54
Dheng	R²	0.87	0.62	0.75
	NSE	0.86	0.61	0.72
	Pbias	− 5.96	15.10	19.28
	RMSE	58.97	100.02	83.96
Hayaghat	R²	0.77	0.77	0.69
	NSE	0.77	0.75	0.69
	Pbias	− 3.06	13.21	7.51
	RMSE	66.59	68.79	77.00
Kamtaul	R²	0.77	0.69	0.68
	NSE	0.72	0.68	0.68
	Pbias	− 15.00	4.33	1.25
	RMSE	69.88	74.66	75.40

Figure 9

Monthly correlation of rainfall datasets for the following stations: (a) Benibad; (b) Dheng; (c) Hayaghat; and (d) Kamtaul.

Seasonal scale

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Box plot analysis

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India has four major seasons, i.e., summer season (March–May), south-west (SW) monsoon (June–September), post-monsoon (October–November), and winter season (December–February) (Subramanya 2013). The interquartile range for the SW monsoon season was highest in every rainfall dataset, which indicates that this season brings maximum rainfall in the region. Zakwan & Ara (2019) also reported that the monsoon brings 85% of total rainfall in Bihar. The presence of intense multiple low-pressure areas over the Bay of Bengal and moisture-laden air from the Arabian Sea during monsoon contributes to the heavy rainfall in Bihar (Subramanya 2013). Box plots of seasonal rainfall for the year 2001–2014 with lines connecting the mean values for all station is shown in Figure 10. IMERG has slightly overestimated while MERRA-2 and PERSIANN have highly underestimated the mean rainfall values. Our results are consistent with the study by Hamal et al. (2020), Tang et al. (2020) and Saikrishna et al. (2021) who assessed seasonal rainfall using these datasets in their respective study area. The median values of different gridded data are mostly identical to the observed for summer, post-monsoon and winter seasons. However, for the monsoon season, there is variation in median values between observed and different gridded data. It can also be observed that station Dheng has the highest interquartile range which indicates that it receives maximum rainfall out of all the stations in all the seasons. It is possibly because this station is located at a higher elevation when compared to the other stations. It is also on the immediate leeward side or rain shadow area of the Himalayan Mountain range. The moisture-laden winds from the Bay of Bengal when encountering the barrier of these mountain causes orographic lifting of wind which contributes to the significant amount of rainfall at this station. For Dheng station, the extreme value of rainfall in SW monsoon is successfully captured only by IMERG as indicated by its similar whiskers compared to the observed. Consequently, IMERG's seasonal statistics resembled more closely to those derived from the observed data when compared to other datasets. Meanwhile, MERRA-2 and PERSIANN demonstrated relatively similar performance to each other.

Figure 10

Box plot of seasonal rainfall for the following stations: (a) Benibad; (b) Dheng; (c) Hayaghat; and (d) Kamtaul.

Trend validation by mann kendall and sen slope test

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The results of the M–K and SS tests for summer and monsoon seasons are tabulated in Table 6 and for post-monsoon and winter seasons are tabulated in Table 7. It was observed that for all the types of rainfall datasets except MERRA-2 across all the stations and seasons, p values generally exceed 0.05 indicating an overall insignificant trend of rainfall in the basin. The Sen's slope also suggested an overall decreasing trend at all stations across all seasons except the winter season. For instance, in the summer season, there is an insignificant decreasing trend in all the datasets except MERRA-2, where it an insignificant increasing trend for all stations. For the SW monsoon season, the test result indicates that there is a decreasing trend in all the datasets except the MERRA-2 dataset, in which there is an increasing trend for all stations. However, PERSIANN datasets show a significantly decreasing trend at all the stations except Dheng. For the post-monsoon season, the observed rainfall indicates that there is an insignificant increasing trend in rainfall for all the stations except for Dheng, where there is an insignificant decreasing trend. For the winter season, the results indicate that there is an insignificant increasing trend in rainfall for all stations except for Dheng, where there is no trend. Zakwan & Ara (2019) as well as Kumar et al. (2022) have both documented a similar pattern of overall decreasing rainfall trends. In their study, Zakwan & Ara (2019) examined IMD datasets for the entirety of Bihar and reported a decline in rainfall during the monsoon season, post-monsoon season, and winter season. Their analysis, which included parametric and non-parametric trend assessments, indicated declining trends for nearly all months except May. Notably, May showed an increasing trend in rainfall, a phenomenon possibly linked to climate change, as suggested by Zakwan & Ara (2019). Overall results showed that IMERG recorded the most similar trend in all seasons like observed datasets followed by PERSIANN. MERRA-2 showed the opposite trend to that of observed rainfall which is possibly due to inaccurate estimates of rainfall magnitude as discussed earlier.

Table 6

Result of M–K and SS test for summer season and SW monsoon

Table 7

Result of M–K and SS test for post monsoon and winter season

Annual scale

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Descriptive statistics of annual rainfall datasets

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The annual average rainfall over the Bagmati basin has been computed using the Thiessen polygon method for all the datasets and presented in Figure 11. The year 2007 has the highest annual rainfall for all the datasets except MERRA-2, which has the highest peak in the year 2008. North Bihar experienced one of the worst floods in its living memory in the year 2007 (Tripathi et al. 2022). In 2007, the month of July experienced rainfall levels that were five times greater than the monthly average calculated over a thirty-year period. The basin received less rainfall than usual in the years 2005, 2009, and 2010. The trendlines in Figure 11 suggest that annual rainfall is decreasing in the case of observed, IMERG, and PERSIANN data, while MERRA-2 shows an increasing trend. These observations are in line with the research conducted by Zakwan & Ara (2019), who similarly reported a decreasing trend in annual rainfall. The minimum, maximum, mean, and standard deviation of annual rainfall datasets have been computed and tabulated in Table 8. A similar inference of statistics of observed annual rainfall can be derived from box plot analysis of annual rainfall reported by the study of Kumar et al. (2022) in the Bagmati river basin. IMERG has minimum, maximum, mean, and standard deviation very close to observed. The analysis of mean annual precipitation data reveals that MERRA-2 and PERSIANN tend to exhibit a systematic underestimation of annual rainfall, while IMERG demonstrates a tendency to overestimate annual precipitation levels. This observation aligns with the findings of the study conducted by Kumar et al. (2023). They reported analogous statistics regarding annual rainfall, highlighting that the majority of gridded rainfall datasets exhibit a tendency to underestimate the magnitude of annual rainfall. Furthermore, research by Gautam & Pandey (2022) has corroborated these observations, specifically with regard to IMERG, indicating that it consistently overestimates annual rainfall magnitudes across different regions in India. These consistent findings warrant careful consideration when utilizing gridded rainfall datasets in hydrological and climatological studies.

Table 8

Descriptive statistics of annual rainfall datasets

Rainfall datasets	Minimum (mm)	Maximum (mm)	Mean (mm)	Standard deviation (mm)
Observed	782.28	2,077.80	1,225.16	335.15
IMERG	871.34	1,981.36	1,320.16	307.10
MERRA − 2	783.73	1,578.23	1,098.19	213.58
PERSIANN	821.01	1,533.12	1,091.61	238.62

Rainfall datasets	Minimum (mm)	Maximum (mm)	Mean (mm)	Standard deviation (mm)
Observed	782.28	2,077.80	1,225.16	335.15
IMERG	871.34	1,981.36	1,320.16	307.10
MERRA − 2	783.73	1,578.23	1,098.19	213.58
PERSIANN	821.01	1,533.12	1,091.61	238.62

Figure 11

Annual rainfall time series for the Bagmati basin.

Wet and dry year detection by gridded rainfall datasets

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The rainfall anomalies for all the rainfall datasets of the Bagmati river basin have been computed and shown in Figure 12. For the observed dataset, the years 2001, 2004, 2007, and 2011 were extremely wet, while the years 2002, 2005, 2006, 2009, and 2010 were extremely dry. The RAI values ranged from −6.50 to 21.49, with the highest value recorded in 2007. It can be seen that there is no consistent pattern of rainfall anomalies in the basin. It is possibly due to varying monsoon patterns and El Niño/La Niña events in Bihar (Jha & Ram 2010; Subramanya 2013). Similarly, for the IMERG dataset, the years 2001, 2002, 2003, 2004, 2007, 2008, 2011, and 2014 were extremely wet, while the years 2005, 2009, and 2010 were extremely dry. The RAI values ranged from −6.99 to 16.59, with the highest value recorded in 2007. For the MERRA-2 dataset, the years 2007 and 2008 were extremely wet, while the years 2001, 2002, 2003, 2004, 2005, 2009, 2010, and 2012 were extremely dry. The RAI values ranged from −12.96 to 12.28, with the highest value recorded in 2008. For the PERSIANN dataset, the years 2002, 2004, and 2007 were extremely wet, while the years 2005, 2008, 2009, 2010, 2011, 2012, 2013, and 2014 were extremely dry. The RAI values ranged from −9.59 to 10.15, with the highest value recorded in 2007. The year 2007 was the wettest year with the highest positive anomaly by all the datasets except MERRA-2. Thus, IMERG was better able to detect the years with positive and negative anomalies followed by PERSIANN and MERRA-2.

Figure 12

RAI for the Bagmati basin: (a) observed; (b) IMERG; (c) MERRA-2; and (d) PERSIANN.

Ranking of gridded datasets

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A heat map was prepared based on the results of ranking by different analyses which is shown in Figure 13. The color scheme used in this heat map highlights the differences in performance among the three products, with blue indicating the best performance (rank 1), red indicating the worst performance (rank 3), and white indicating intermediate performance (rank 2). Based on ranking, it can be inferred that IMERG consistently outperforms PERSIANN and MERRA-2 with having a major blue color concentration. The PERSIANN has a majorly white color concentration while MERRA-2 has a majorly red color concentration indicating medium and worst-ranked gridded datasets respectively.

Figure 13

Systematic and random error components in satellite precipitation data sets

Heat map for ranking of different gridded rainfall datasets.

CONCLUSIONS

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In this study, three gridded datasets, viz., IMERG, MERRA-2, and PERSIANN were analyzed and compared with the observed rain gauge datasets. The analysis was performed at station and basin level data for the temporal scale of daily, monthly, seasonal, and annual. Based on the CDF plot analysis of daily rainfall data, it was found that IMERG had the most similar daily rainfall distribution as per the observed data, while MERRA-2 and PERSIANN highly underestimated the extreme rainfall event. This indicates that MERRA-2 has the ability to capture a significant portion of rainfall events but fails to accurately represent the intensity or magnitude of extreme rainfall events. Based on the monthly gridded rainfall datasets, it was found that all gridded datasets perform well in capturing the variability of rainfall, as indicated by very good R² and NSE values. M–K and SS tests showed that there is a decreasing trend of rainfall in summer and monsoon seasons whereas in post-monsoon and winter seasons, there is an increasing trend at most of the stations. A mostly insignificant trend was observed at all stations. IMERG recorded the most similar trend in all seasons like observed datasets followed by PERSIANN and MERRA-2. On the annual scale, wet and dry year detection by different rainfall datasets showed that IMERG had the most similar pattern of rainfall anomalies as compared to the observed dataset. Based on all the analysis, the IMERG, PERSIANN, and MERRA-2 were ranked as rank 1, rank 2, and rank 3, respectively. However, this study also highlighted critical limitations in these gridded rainfall datasets due to sensor technology, data acquisition methods, processing algorithms, and data dissipation. Enhancing these aspects holds the key to future data quality improvements.

So, overall, IMERG datasets can be considered a reliable source of rainfall data at all temporal scales for the Bagmati river basin if there is data scarcity from IMD. While, MERRA-2 and PERSIANN are more suited for use at monthly, seasonal, and annual timescale. The variability observed in rainfall estimation between IMERG and observed rainfall data are attributed to the fundamental differences in their measurement methods. Despite this variability, IMERG datasets have demonstrated remarkable results in various hydrological and climatological studies worldwide. Thus, IMERG datasets may be used for further studies like real-time monitoring of flood, drought, soil erosion, and others in the Bagmati basin and checked for their performance.

DATA AVAILABILITY STATEMENT

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All relevant data are included in the paper or its Supplementary Information.

CONFLICT OF INTEREST

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The authors declare there is no conflict.

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