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Article

Evaluating IMERG Satellite Precipitation-Based Design Storms in the Conterminous U.S. Using NOAA Atlas Datasets

by
Kenneth Okechukwu Ekpetere
1,*,
Xingong Li
1,
Jude Kastens
2,
Joshua K. Roundy
3 and
David B. Mechem
1
1
Department of Geography & Atmospheric Science, University of Kansas, Lawrence, KS 66045, USA
2
Kansas Biological Survey & Center for Ecological Research, University of Kansas, Lawrence, KS 66047, USA
3
Department of Civil, Environmental & Architectural Engineering, University of Kansas, Lawrence, KS 66045, USA
*
Author to whom correspondence should be addressed.
Water 2025, 17(17), 2602; https://doi.org/10.3390/w17172602
Submission received: 28 July 2025 / Revised: 31 August 2025 / Accepted: 1 September 2025 / Published: 3 September 2025
(This article belongs to the Special Issue Advances in Extreme Hydrological Events Modeling)
Browse Figures
Versions Notes

Abstract

Probable Maximum Storms (PMS) are synthetic design storms represented by idealized hyetographs. They play a critical role in assessing extreme rainfall events over extended durations and are widely applied in the hydraulic design of infrastructure such as dams, culverts, and bridges. PMS provide essential input for estimating Probable Maximum Floods (PMF), vital for analyzing worst-case flood scenarios with the potential to cause catastrophic loss of life and property. Despite their importance, the estimation of design storms at ungauged locations, particularly across synoptic scales, remains a major scientific and engineering challenge. This study addresses this gap by utilizing the Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) dataset, which provides near-global estimated precipitation coverage. IMERG’s 24 h design storm hyetographs (expressed as cumulative percentage of precipitation throughout a 24 h period) were modeled and compared with similar reference data from NOAA Atlas 14 across twenty-eight regions and seven larger zones covering most of the conterminous United States (CONUS). Across the regions, the average root mean square error (RMSE) was 3.7%, with a mean relative bias (RB) of 1.4%. The mean normalized storm loading index (NSLI) from NOAA Atlas 14 was −7.7%, indicating that 57.7% of the total precipitation was received during the first 12 h of the storm, whereas IMERG storms exhibited a mean NSLI of −4.1%, suggesting they are also frontloaded but to a lesser extent. Across the broader zones, the mean RMSE was 4.8% and the mean RB was 1.1%. The mean NSLI values were −9.7% for NOAA Atlas 14 and −5.7% for IMERG, again indicating that IMERG storms are less frontloaded. When design storm families were estimated corresponding with different degrees of frontloading (corresponding to the 10, 20, …, 90% deciles of NSLI), the 40th to 60th percentile range exhibited the strongest agreement between IMERG and NOAA Atlas 14 hyetographs.

Graphical Abstract

1. Introduction

To calculate the Probable Maximum Flood (PMF) associated with a Probable Maximum Precipitation (PMP) for a chosen duration (e.g., 24 h), the PMP must first be converted to a synthetic hyetograph known as the Probable Maximum Storm (PMS) [1,2,3,4,5,6,7,8], which represents the cumulative rainfall distribution across the PMP duration. These design storms are critical for modeling probabilistic worst-case flood scenarios [9,10,11]. In essence, design storms represent realistic precipitation patterns intended for use in the design of hydrologic infrastructure such as dams, culverts, and bridges [7,12]. The magnitude and temporal distribution of these storms strongly influence the shape and timing of the resulting runoff hydrograph in rainfall-runoff models [13,14,15], making them essential for accurate PMF modeling.
Within the conterminous United States (CONUS), design storms are typically derived from the Precipitation Frequency Atlas of the United States, which is based on observations from gauge stations [16,17,18,19,20,21]. This Atlas, hereafter referred to as the NOAA Atlas 14 temporal distribution, expresses precipitation probabilities as cumulative percentages at either 30 min or 1 h intervals. These distributions offer several advantages, including the categorization of storm events into a nine-decile family (10, 20, …, 90%) of design storms based on degree of precipitation frontloading.
Previous studies often modeled design storms using Natural Resources Conservation Service (NRCS) curves [1,4,22,23]; however, NRCS curves are increasingly being replaced by NOAA Atlas 14 temporal distribution curves in contemporary engineering practices [18,20]. Despite this shift, no current research evaluates satellite precipitation products (SPPs) against NOAA Atlas 14 temporal distributions which were estimated from gauge records predating the year 2000. To address this gap, the present study compares design storms estimated using Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) data to NOAA Atlas 14 design storms. SPPs such as IMERG, which offers near-global coverage, provide an opportunity to model design storms in both gauged and ungauged regions beyond CONUS [24,25].
IMERG time series can be used to model design storms across a wide range of regions and for both short and long storm durations [26,27,28,29,30,31,32]. IMERG features a spatial resolution of 0.1° (~11 km), a temporal resolution of 30 min, and covers latitudes up to 65° N/S. Studies suggest that IMERG outperforms other SPPs in precipitation estimation when compared to gauge observations [33,34,35]. With data spanning from the early 2000 s to the present and incorporating extensive gauge calibration, IMERG is considered a next-generation SPP capable of capturing recent extreme precipitation events on a near-global scale [36,37,38].
The aim of this work is to assess the degree of correspondence between NOAA Atlas 14 design storms and those estimated from IMERG, which will shed light on the general use of IMERG for this purpose in other locations around the globe. Section 2 introduces the study area, Section 3 and Section 4 present the methodology and results, and Section 5 and Section 6 discuss the findings and conclude the paper.

2. Study Area and Datasets

2.1. Study Area

The NOAA Atlas 14 temporal distributions have been established for twenty-eight regions comprising seven distinct zones across CONUS (Figure 1). The zones are defined based on unique climatic characteristics that differentiate them [17,18]. The zones include: the semiarid Southwest (Zone 1, consisting of two regions), the Ohio River Basin and surrounding states (Zone 2, one region), California (Zone 6, fourteen regions), the Midwestern states (Zone 8, four regions), the Southeastern states (Zone 9, two regions), the Northeastern states (Zone 10, two regions), and Texas (Zone 11, three regions). The delineations made by NOAA Atlas 14 are based on observed patterns of extreme precipitation, utilizing factors such as 24 h mean annual maximum precipitation, elevation, and latitude [18].

2.2. IMERG Precipitation Datasets

The IMERG dataset, which begins in 2000, features a spatial resolution of 0.1° (~11 km), a temporal resolution of 30 min, and provides near-global coverage between 65° N and 65° S. IMERG is a satellite-based precipitation dataset generated by merging inputs from several sources, including the GPM Profiling Algorithm (GPROF), Precipitation Retrievals and Profiling Scheme (PRPS), PERSIANN-Cloud Classification System (PERSIANN-CCS), Combined Radar-Radiometer Algorithm (CORRA), and the Global Precipitation Climatology Project’s monthly satellite-gauge product (PCP-SG) [36,39]. The IMERG final product is calibrated against more than 80,000 stations from the Global Precipitation Climatology Centre (GPCC) [36,40].
IMERG Version 7 provides three precipitation variables in each product: PrecipitationCal, PrecipitationUncal, and HQprecipitation. PrecipitationUncal represents the original multi-satellite precipitation estimate, while HQprecipitation provides the merged microwave-based precipitation estimate. PrecipitationCal is a calibrated product that combines information from both PrecipitationUncal and HQprecipitation, adjusted using GPCC gauge observations [37,41]. For this study, the PrecipitationCal variable from the final run of IMERG Version 7 (which served as the target dataset) was retrieved from Google Earth Engine Cloud Computing platform, and the python code used for this analysis is provided in the data section.

2.3. NOAA Atlas 14 Temporal Distributions

For this study, NOAA Atlas 14 temporal distributions were obtained for the 24 h duration precipitation events that exceed the precipitation frequency estimates for a 2-year average recurrence interval [17,18]. The temporal distribution type considered is the “All” case, which utilizes the complete storm event catalog to determine the distribution of cumulative precipitation profiles. Values within these cumulative precipitation profiles are expressed as percentages of the total storm precipitation at 30 min intervals, except for Zones 1 and 2, where data are provided at hourly intervals. Temporal distribution curves corresponding to nine percentiles (10, 20, …, 90%) corresponding with increasing frontloading are downloaded for the probabilities of occurrence of cumulative precipitation totals [18] across the various regions within CONUS. It is important to note that while the IMERG percentiles for this study are calculated (details in the method section), the NOAA reference data are downloaded as is for the different regions and zones. Figure 2 illustrates a sample temporal distribution curve for a 24 h duration for the Mississippi Valley region (region 4) which serves as reference data for the IMERG assessment [16].

3. Method

3.1. Modeling 24 h Design Storms with a 2-Year Return Period Using IMERG

To model IMERG-based design storms, we used a procedure designed to be directly comparable with the NOAA Atlas 14 design storms. Due to NOAA data availability limitations at the time of the study, 22 years of IMERG data (2001–2022) were considered. For each IMERG pixel with its centroid in a particular zone or region, at each IMERG 30 min observation, the cumulative total precipitation from the 24 h ending at that time was computed. From this list of 24 h accumulations, the top 11 non-overlapping events (approximating the 2-year return period across the 22-yr dataset) from each pixel were retained for the design storm analysis.
Let R be an arbitrary NOAA zone or region (Figure 1). Define the following:
N = number of IMERG pixel centroids (pseudo stations) in R
X = [xst] = (11·N) × 48 matrix, where each row is the 24 h time series (30 min time step) from a top-11 IMERG 24 h precipitation event (storm) from an IMERG pseudo station in R
P = [pst], where p s t = 100 · ∑ k = 1 t x s k / ∑ k = 1 48 x s k
Here, pst represents the cumulative rainfall at time t as a percentage of the 24 h total for storm s.
q = 1:9, representing deciles 10, 20, …, 90%
D = [dqt] = 9 × 48 matrix, where dqt is the decile-q percentile from column t of X
With these definitions, D contains the percentage distribution of the 2-year design storm curves from the IMERG dataset according to decile-based, increasing degree of frontloading. Figure 3 summarizes the methodology adopted in this study to compute percentage precipitation for 24 h storms at 30 min intervals across the regions.

3.2. Evaluations Metrics

Three statistical metrics were employed to evaluate the percentage precipitation distributions modeled from IMERG data: relative bias (RB), root mean square error (RMSE), and the normalized storm loading index (NSLI) (Table 1). RB indicates whether IMERG hyetographs underestimate (negative values, less frontloaded) or overestimate (positive values, more frontloaded) compared to the NOAA Atlas 14 hyetographs [42,43]. RMSE quantifies the average magnitude of squared differences between the IMERG and NOAA Atlas 14 hyetographs [42,43]. NSLI measures the difference in cumulative percentage precipitation between the first and second halves of the 24 h period, normalized by the total precipitation over the entire duration [14,44,45].
The mathematical expressions and units of the evaluation metrics are provided in Table 1, where “O” represents NOAA (observed) percentile precipitation, and “P” stands for IMERG (predicted) percentile precipitation. Both O and P are in unit of %. P a is total percentage precipitation after the midpoint, and P t is total percentage precipitation for the 24 h analysis period.
NSLI values range from −100% to +100%, where an NSLI value of 0 indicates an equal quantity of precipitation in the front and back halves of a 24 h event. A negative NSLI suggests that a greater proportion of precipitation occurred before the midpoint (frontloaded), while a positive NSLI indicates that more precipitation occurred after the midpoint (backloaded). Figure 4 illustrates the range of NSLI values relative to the 0-reference point, with values increasing toward the negative axis representing frontloaded storms and those increasing toward the positive axis representing backloaded storms.

4. Results

4.1. Assessment of IMERG Cumulative Distribution at Region Scale

To evaluate the concordance between IMERG and NOAA Atlas 14 percentage precipitation across nine percentile increments (ranging from 10% to 90%), the percentage cumulative distributions of NOAA Atlas 14 were first converted into percentage precipitation for each respective region. For visual comparison, Figure 5 illustrates a randomly selected family of curves showing the IMERG percentage cumulative distributions across the investigated percentile spectrum for one of the regions (e.g., region 1). For each percentile, the IMERG estimates were evaluated against NOAA observation, and the statistical result reported for each level of percentile.
The results of the mean statistical analyses across the percentile spectrum are presented in Table 2. Region 1 (Zone 1) exhibited the highest RMSE at 10.75%, while Region 4 (Zone 6) demonstrated the lowest RMSE at 1.30%. Across all regions and percentile ranges, the average RMSE was 3.7%, with a corresponding mean RB of 1.4%. In terms of precipitation loading, NOAA Atlas 14 exhibited a mean NSLI of −7.7%, indicating that, on average, NOAA Atlas 14 storms are frontloaded by approximately 8% of the total percentage precipitation. In comparison, IMERG storms exhibited a mean NSLI of approximately −4.1%, suggesting that IMERG is also frontloaded but to a lesser extent than NOAA Atlas 14, with an average difference of −3.6%. The tendency for IMERG to exhibit lesser frontload capability than NOAA can be attributed to the coarse temporal resolution of IMERG; for instance, IMERG has a 30 min resolution compared to NOAA’s 5 min. This indicates IMERG may miss short storm events, causing lower cumulative totals than NOAA. A backloaded bias in IMERG could alter hydrograph peaks in PMF modeling.
Overall, these statistics indicate reasonable alignment between IMERG and NOAA Atlas 14 distributions. However, the RB analysis indicates that IMERG tends to underestimate precipitation relative to NOAA Atlas 14 in drier regions, while overestimating it in wetter regions, consistent with findings from a previous study [31].

4.2. Assessment of IMERG Cumulative Distribution at Zone Scale

The IMERG data were also evaluated at the zones based on percentage distribution. For each zone, statistical data from the constituent regions across the nine deciles were aggregated to derive mean statistical values. The mean statistics for each zone across the decile spectrum are summarized in Table 3. Zone 1 recorded the highest RMSE value at approximately 10%, while Zone 6 exhibited the lowest RMSE value at 2.4%. Across all zones, the mean RMSE was calculated to be 4.8%, with a corresponding mean RB of 1.066%.
In terms of storm loading, NOAA Atlas 14 produced a mean NSLI of −9.7%, while IMERG presented a mean NSLI of −5.7%. The RB analysis suggests that IMERG tends to overestimate precipitation compared to NOAA Atlas 14 across most zones, with the exception of Zones 1 and 2, where IMERG generally underestimates relative to NOAA Atlas 14. Additionally, the NSLI results indicate that IMERG is relatively more backloaded.

4.3. Assessment of IMERG Cumulative Distribution at the Percentiles

Assessing the entire percentile spectrum is crucial for assisting users in selecting the most appropriate distribution curves for different regions and zones. The evaluations covered the nine deciles across both regions and zones. Table 4 presents the summarized results of the mean statistics at these percentiles for each region. Notably, the 60th percentile exhibited the lowest RB value of −0.1%, indicating a closer agreement between IMERG and NOAA Atlas 14. Although the 60th percentile recorded a low RB, its has a RMSE of 3.7% compared to the 20th percentile which had the least RMSE value of 2.1%.
When assessing the NSLI for NOAA Atlas 14 and IMERG across all regions and percentiles, the results revealed that the NSLI values for NOAA Atlas 14 decreased consistently from the 10th percentile (25.2%) to the 90th percentile (−38.5%). The best agreement occurred between the 40th and 50th percentiles, with NSLI differences (Diff-NSLI) of −0.7% and −8.0%, respectively. Similarly, IMERG NSLI values showed a decline from the 10th percentile (26.8%) to the 90th percentile (−36.2%), with the best agreement occurring between the 40th and 50th percentiles, where the PD values were 4.2% and −4.8%, respectively.
The overall pattern of the NSLI suggests that both IMERG and NOAA Atlas 14 show better agreement in the lower percentiles (from the 10th to the 40th percentiles), where NSLI values are positive and gradually decrease. Conversely, from the 50th to the 90th percentiles, the models exhibit more frontloaded behavior, with negative NSLI values that also decrease. On average, both IMERG and NOAA Atlas 14 exhibit stronger agreement between the 40th and 60th percentiles, where the NSLI values are close to equal loading. These findings underscore the importance of carefully selecting the appropriate curves based on specific locations and infrastructure design needs.
Table 5 summarizes the mean results across the percentile ranges at the zones. Notably, the 30th to 60th percentiles exhibited low RB, ranging from 0.03% to 1.32%, indicating agreement between IMERG and NOAA Atlas 14 within this range. The RMSE showed an increasing trend, from 2.52% at the 10th percentile to 8.1% at the 90th percentile.
When evaluating the NSLI for NOAA Atlas 14 and IMERG across the percentiles, the results for NOAA Atlas 14 showed an overall decrease in NSLI values, from 28.3% at the 10th percentile to −44.9% at the 90th percentile. The best agreement was observed between the 40th and 50th percentiles. Similarly, IMERG NSLI values also decreased from 29.1% at the 10th percentile to −41.2% reaching the 90th percentile, with the best agreement occurring between the 40th and 50th percentiles.
The overall pattern of the NSLI indicates that both IMERG and NOAA Atlas 14 exhibit more backloaded behavior between the 10th and 40th percentiles, with positive NSLI values that decrease gradually. In contrast, both models are more frontloaded between the 50th and 90th percentiles, where negative NSLI values decrease further. On average, the results demonstrate that both IMERG and NOAA Atlas 14 exhibit better agreement between the 40th and 60th percentiles.

5. Discussion

5.1. IMERG Percentage Precipitation Distribution at the Region

A quick visual comparison between the percentage precipitation distribution estimated from IMERG at a randomly selected region (Region 1 of Zone 6) suggests a fairly good agreement with NOAA Atlas 14 percentage precipitation distribution curves (Figure 6). Figure 6 suggests that the implemented IMERG design storm model was fairly consistent. The consistent agreement between the IMERG and NOAA percentage precipitation distribution curves in Figure 6 shows the capability of IMERG to capture design storms relatively consistent with NOAA Atlas 14. This demonstrates the potential of utilizing IMERG beyond CONUS and at ungauged regions. In addition, the percentile ranges (10% to 90%) shown in Figure 6 for each of the plots allow users to model the uncertainty in design storm characteristics.

5.2. Patterns in IMERG Percentage Precipitation Across Zones

The evaluation of IMERG percentile precipitation curves reveals interesting patterns that can be discussed under three main themes: across regions, zones, and the nine-percentile range (10–90%). In terms of regions, the study revealed that the least RMSE (1.3%) occurred in region 4 of zone 6. Region 4 of Zone 6 is situated in the northeastern part of California and is influenced by rainfall patterns that are intense and short-lived [46,47,48,49]. Not all precipitation in Region 4 of Zone 6 is captured by IMERG radar due to its short lifespan [50]. The minimal RMSE observed in this region suggests that IMERG may be capturing the precipitation storms effectively. Similarly, Region 1 of Zone 1 recorded the highest RMSE value (10.8%). This region borders arid states such as Nevada, Utah, and parts of Arizona, characterized by low average rainfall throughout most of the year. Additionally, the sparse distribution of gauges in Region 1 implies limited station data availability for calibrating IMERG, which could contribute to the observed high RMSE values, as highlighted by Da Silva [34].
We showed that zone 1 exhibited the most RMSE (10%). Zone 1 consistently records the lowest annual average precipitation across the United States due to its arid nature [51,52]. It has been observed that low-precipitation regions tend to exhibit higher RMSE when comparing station records with IMERG, as it perform relatively well in areas with high precipitation but struggle in arid regions [53]. Conversely, zone 6 showcased the least RMSE estimate (2.4%) compared to other zones. Zone 6 is influenced by cyclonic storms, particularly in its northeastern portions, owing to its proximity to the Pacific Ocean, resulting in frequent rainfall throughout the year [53]. Figure 7 provides a concise overview of IMERG performance across different zones.
At the percentile level, IMERG and NOAA Atlas 14 have better agreement between the 40th to 60th percentile indicated by low RB values, low RMSE, and minimal NSLI values between the 40th to 60th percentile range. The variation across percentile ranges offers options for understanding how IMERG curve behaves at specific regions and zones. These percentile ranges provide a balanced window for engineers to select appropriate IMERG storm curves for PMF modeling.

6. Conclusions

In this study, 24 h design storms were derived from IMERG data based on rainfall storms that meet 2-year return periods for pixels within NOAA Atlas 14 regions. The percentage rainfall distribution was computed from IMERG time-series precipitation data from 2001 to 2022 for regions and zones using the IMERG pixels with their centroids falling in the regions and zones. Nine percentile distributions (ranging from 10% to 90%) were derived from the series of percentage distributions and juxtaposed against observed NOAA Atlas 14 percent distribution curves.
Across the regions, the average RMSE was estimated at 3.7% while the average RB was estimated at 1.42%. NOAA Atlas 14 showed a mean NSLI value of −7.7% indicating that NOAA Atlas 14 is more frontloaded by ~8% of the total depth, while IMERG yielded a mean NSLI value of −4.1%, indicating IMERG is frontloaded but not as frontloaded as NOAA Atlas 14 with a difference of −3.6%. Across the zones, the mean RMSE was computed at 4.8%, mean RB was 10.7%. NOAA Atlas 14 estimated an average NSLI value of −9.7%, while IMERG presented a mean NSLI value of −5.7% indicating that IMERG was less frontloaded than NOAA Atlas 14 across the zones. The study found the 40th to 60th percentile curve harbors the highest agreement between IMERG and NOAA Atlas 14.
Although the IMERG dataset has shown promise for modeling design storms and can be a useful resource for storm design in ungauged locations, uncertainties still exist regarding how IMERG differs from the reference NOAA data in terms of temporal range, spatial resolution, and data retrieval methods. For example, NOAA data is provided as a set of percentile precipitation distribution curves, but the underlying base datasets used to compute these curves are not made available. It is understood that some regions may rely on base data dating back to the 1950s from which these curve families were derived, whereas IMERG data only dates back to the year 2000. In future evaluations, we plan to access station data that aligns with the IMERG temporal window (2001–2022) for a more robust assessment.
Additional uncertainties that are worthy of note are the lack of proper smoothening mechanism on the NOAA temporal distribution curve, which was not integrated in this study due to lack of transparency on the method used. We believe adding a smoothing effect could potentially enhance the comparability of IMERG to the NOAA data. Lastly, the base data that were used to construct the NOAA temporal distribution curves were not provided, as such the evaluations were limited to the provided percentile curves. Providing such reference data would potentially increase our validation.
In conclusion, the IMERG precipitation has shown prospect for modeling design storms in CONUS to further curb impact on hydrologic infrastructure such as dams, culverts, and bridges. However, the agreement with observation may vary across precipitation regions and quantiles. When compared against CONUS-bound NOAA Atlas 14 data, IMERG design storms exhibited moderate consistency with observed values. These modeled design storms provide valuable insights that can assist practitioners in selecting appropriate percentile curves for infrastructure design (e.g., within the 10% to 90% range). Future research will extend the evaluation of IMERG design storms to locations beyond CONUS.

Author Contributions

Conceptualization, K.O.E., X.L., J.K., J.K.R., and D.B.M.; methodology, K.O.E., X.L., J.K., J.K.R., and D.B.M.; software, K.O.E., X.L., and J.K.; validation, K.O.E., X.L., J.K., J.K.R., and D.B.M.; formal analysis, K.O.E., X.L., and J.K.; investigation, K.O.E., X.L., and J.K.; resources, K.O.E., X.L., and J.K.; data curation, K.O.E.; writing—original draft preparation, K.O.E., X.L., and J.K.; writing—review and editing, K.O.E., X.L., J.K., J.K.R., and D.B.M.; visualization, K.O.E., X.L., J.K., J.K.R., and D.B.M.; supervision, X.L., J.K., J.K.R., and D.B.M.; project administration, X.L. and J.K.; funding acquisition, J.K. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the National Science Foundation under the Kansas NSF-EPSCoR (award number OIA-2148878).

Data Availability Statement

The code and data presented in this study are openly available in GitHub repository https://github.com/Kennethekpetere/Design-Storm-Model.

Conflicts of Interest

The authors declare no conflict of interest.

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Water 17 02602 g001
Figure 1. NOAA Atlas 14 regions and zones: Semiarid Southwest (Zone 1, consisting of two regions), Ohio River Basin and surrounding states (Zone 2, one region), California (Zone 6, fourteen regions), Midwestern states (Zone 8, four regions), Southeastern states (Zone 9, two regions), Northeastern states (Zone 10, two regions), and Texas (Zone 11, three regions).
Figure 1. NOAA Atlas 14 regions and zones: Semiarid Southwest (Zone 1, consisting of two regions), Ohio River Basin and surrounding states (Zone 2, one region), California (Zone 6, fourteen regions), Midwestern states (Zone 8, four regions), Southeastern states (Zone 9, two regions), Northeastern states (Zone 10, two regions), and Texas (Zone 11, three regions).
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Figure 2. The 24 h temporal distribution curve for the Mississippi Valley region (region 4) [16,17,18]. The temporal distribution percentile curves (10–90%) denote the range of values at each time step that capture most of the variability in the dataset, allowing for both median and extreme behavior assessment through time.
Figure 2. The 24 h temporal distribution curve for the Mississippi Valley region (region 4) [16,17,18]. The temporal distribution percentile curves (10–90%) denote the range of values at each time step that capture most of the variability in the dataset, allowing for both median and extreme behavior assessment through time.
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Figure 3. Estimating 24 h design storms with 2-year return periods using IMERG data.
Figure 3. Estimating 24 h design storms with 2-year return periods using IMERG data.
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Figure 4. NSLI chart showing the range of values from −1 to +1 (scaled −100% to +100%) with reference to the mid-point (at the 0-mark). Values increasing towards the negative axis are frontloaded while values increasing towards the positive axis are backloaded.
Figure 4. NSLI chart showing the range of values from −1 to +1 (scaled −100% to +100%) with reference to the mid-point (at the 0-mark). Values increasing towards the negative axis are frontloaded while values increasing towards the positive axis are backloaded.
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Figure 5. Family of curves showing 24 h percentage cumulative distribution curve for region 1. The plot compares the percentage precipitation distribution estimated from IMERG against NOAA Atlas 14. The figure shows fair agreement between IMERG and NOAA Atlas 14.
Figure 5. Family of curves showing 24 h percentage cumulative distribution curve for region 1. The plot compares the percentage precipitation distribution estimated from IMERG against NOAA Atlas 14. The figure shows fair agreement between IMERG and NOAA Atlas 14.
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Figure 6. Percentage precipitation distribution curves estimated from IMERG at a randomly selected region (Region 1 of Zone 6). The unsmoothed curves depicts the uncertainties with data-driven estimate against the use of functions as demonstrated in Figure 5.
Figure 6. Percentage precipitation distribution curves estimated from IMERG at a randomly selected region (Region 1 of Zone 6). The unsmoothed curves depicts the uncertainties with data-driven estimate against the use of functions as demonstrated in Figure 5.
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Figure 7. IMERG-derived percentile precipitation distribution compared with NOAA across the zones. The comparison is based on an average over the nine percentiles (10–90%). Within the illustration, “O” denotes NOAA Atlas 14, while “P” represents IMERG.
Figure 7. IMERG-derived percentile precipitation distribution compared with NOAA across the zones. The comparison is based on an average over the nine percentiles (10–90%). Within the illustration, “O” denotes NOAA Atlas 14, while “P” represents IMERG.
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Table 1. Statistical formulas, and their corresponding units.
Table 1. Statistical formulas, and their corresponding units.
MetricFormulaUnit
Relative Bias (RB) 100 × ∑ i = 1 48 P i − O i ∑ i = 1 48 O i %
Root Mean Square Error (RMSE) ∑ i = 1 48 P i − O i 2 48 %
Normalized Storm Loading Index (NSLI) 2 P a P t − 1 × 100 −100% to 100%
Table 2. Results of mean statistics at the 28 NOAA Atlas 14 regions summarized across the percentile range (10–90%). R is region, Z is zone, Diff-NSLI is the NSLI difference between NOAA and IMERG.
Table 2. Results of mean statistics at the 28 NOAA Atlas 14 regions summarized across the percentile range (10–90%). R is region, Z is zone, Diff-NSLI is the NSLI difference between NOAA and IMERG.
S/NRegionsCentroidsRMSE (%)RB (%)NOAA-NSLI (%)IMERG-NSLI (%)Diff-NSLI (%)
1R1 (Z1)390710.71.7−6.1−1.7−4.4
2R2 (Z1)75729.2−8.5−15.4−12.0−3.4
3R1 (Z2)11,6445.8−1.3−7.8−5.4−2.4
4R1 (Z6)1622.42.9−0.31.6−1.9
5R2 (Z6)2362.45.40.22.0−1.8
6R3 (Z6)2662.51.8−4.6−1.6−3.0
7R4 (Z6)2401.31.5−5.4−3.8−1.6
8R5 (Z6)2852.4−1.60.11.9−1.8
9R6 (Z6)2752.4−7.42.33.6−1.3
10R7 (Z6)1702.32.5−0.81.3−2.0
11R8 (Z6)3002.41.6−6.5−3.0−3.5
12R9 (Z6)2992.70.8−6.1−2.7−3.4
13R10 (Z6)2112.51.8−4.2−1.3−2.9
14R11 (Z6)3072.52.5−3.5−0.8−2.7
15R12 (Z6)1322.4−1.2−4.1−1.3−2.9
16R13 (Z6)2192.7−3.1−7.9−4.1−3.8
17R14 (Z6)11752.8−0.4−7.9−4.1−3.8
18R1 (Z8)12,0545.07.0−19.4−12.7−6.7
19R2 (Z8)14834.25.6−13.8−8.5−5.3
20R3 (Z8)85845.04.0−18.1−11.7−6.4
21R4 (Z8)78513.010.0−8.7−4.7−4.0
22R1 (Z9)78513.010.0−8.7−4.7−4.0
23R2 (Z9)13933.4−10.0−7.0−3.4−3.6
24R1 (Z10)23612.97.4−8.6−4.6−3.4
25R2 (Z10)10112.5−6.1−4.5−1.5−3.0
26R1 (Z11)17286.5−0.5−22.4−14.9−7.4
27R2 (Z11)39774.710.4−16.8−10.7−6.1
28R3 (Z11)10943.43.2−10.3−5.9−4.4
Average3.701.43.7−4.1−3.6
Standard Deviation2.15.32.14.81.9
Table 3. Results of mean statistics at the 7 NOAA Atlas 14 zones summarized across the percentile range.
Table 3. Results of mean statistics at the 7 NOAA Atlas 14 zones summarized across the percentile range.
ZONESZONESRMSE (%)RB (%)NOAA-NSLI (%)IMERG-NSLI (%)Diff-NSLI (%)
111,47910.0−3.4−10.8−6.9−3.9
211,6445.8−1.3−7.8−5.4−2.4
642772.40.5−3.5−0.9−2.6
829,9724.36.6−15.0−9.4−5.6
992443.20.02−7.9−4.1−3.8
1033722.70.7−6.5−3.1−3.5
1167994.84.4−16.5−10.5−6.0
Average4.81.1−9.7−5.7−4.0
St. Dev.2.63.44.73.51.4
Table 4. Results of mean statistics at the percentiles summarized across the regions.
Table 4. Results of mean statistics at the percentiles summarized across the regions.
S/NPercentile (%)RMSE (%)RB (%)NOAA-NSLI (%)IMERG-NSLI (%)Diff-NSLI (%)
1102.20.225.226.8−1.6
2202.12.114.918.0−3.0
3303.30.36.811.0−4.4
4403.43.5−0.74.2−4.9
5503.96.7−8.0−4.8−3.2
6603.7−0.1−15.4−10.7−4.7
7704.1−0.5−23.0−18.6−4.4
8804.71.3−31.0−26.7−4.3
9905.7−0.7−38.5−36.2−2.3
Average3.71.4−7.7−4.1−3.6
St. Dev.1.12.421.321.01.2
Table 5. Results of mean statistics at the percentiles summarized across the zones.
Table 5. Results of mean statistics at the percentiles summarized across the zones.
S/NPercentile (%)RMSE (%)RB (%)NOAA-NSLI (%)IMERG-NSLI (%)Diff-NSLI (%)
1102.52.228.329.1−0.9
2202.43.516.819.3−2.5
3303.90.037.411.5−4.1
4404.16.2−1.33.6−4.8
5504.95.6−9.9−6.4−3.6
6604.91.3−18.8−13.5−5.3
7705.5−8.5−27.8−22.4−5.4
8806.62.1−37.2−31.7−5.5
9908.1−2.9−44.9−41.2−3.7
Average4.81.1−9.7−5.7−4.0
St. Dev.1.84.524.823.71.5
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Ekpetere, K.O.; Li, X.; Kastens, J.; Roundy, J.K.; Mechem, D.B. Evaluating IMERG Satellite Precipitation-Based Design Storms in the Conterminous U.S. Using NOAA Atlas Datasets. Water 2025, 17, 2602. https://doi.org/10.3390/w17172602

AMA Style

Ekpetere KO, Li X, Kastens J, Roundy JK, Mechem DB. Evaluating IMERG Satellite Precipitation-Based Design Storms in the Conterminous U.S. Using NOAA Atlas Datasets. Water. 2025; 17(17):2602. https://doi.org/10.3390/w17172602

Chicago/Turabian Style

Ekpetere, Kenneth Okechukwu, Xingong Li, Jude Kastens, Joshua K. Roundy, and David B. Mechem. 2025. "Evaluating IMERG Satellite Precipitation-Based Design Storms in the Conterminous U.S. Using NOAA Atlas Datasets" Water 17, no. 17: 2602. https://doi.org/10.3390/w17172602

APA Style

Ekpetere, K. O., Li, X., Kastens, J., Roundy, J. K., & Mechem, D. B. (2025). Evaluating IMERG Satellite Precipitation-Based Design Storms in the Conterminous U.S. Using NOAA Atlas Datasets. Water, 17(17), 2602. https://doi.org/10.3390/w17172602

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