# Where Can IMERG Provide a Better Precipitation Estimate than Interpolated Gauge Data?

^{*}

## Abstract

**:**

^{2}) and that IMERG often outperforms interpolated data when the distance to the nearest gauge used during interpolation is greater than 80–100 km. However, there does not appear to be a consistent relationship between this performance ‘break point’ and the geographical variables of elevation, distance to coast, and annual precipitation.

## 1. Introduction

^{2}while the Amazon basin had an average gage density of 0.1/1000 km

^{2}[11].

^{2}) [18]. However, given the uncertainty surrounding interpolated precipitation estimates in regions with such low gauge density, it is unclear if the disagreement between IMERG-F and the interpolated product are a result of IMERG error, error in the interpolated product, or, most likely, a combination of both. The same relationship in which IMERG performance decreased with gauge density was found over a large study area in China [19]. Such results suggest that the suitability of interpolated gauge data to validate SMP estimates decreases with gauge density.

^{2}) within 20% of its true value, respectively over 25, around 25, 15, and 4 gauges are necessary at the 15-min, hourly, 3-hourly, and daily scale”. Similarly, Villarini [20] suggested that, at a minimum, five rain gauges should be used to interpolate and estimate ground reference areal-average precipitation at a 0.25° scale. One shortcoming of this study was the relatively short study period (4 months) and limited study area (two 0.25° TMPA pixels in Rome) [20]. Mandapaka and Lo [21] conducted a similar study based on eight IMERG pixels in Singapore, finding that at least 8–10 gauges per 0.1° pixel are required to limit the areal precipitation estimate error to 25% for daily precipitation estimates. However, the range of gauge densities analyzed in previous studies was much higher than what exists in most parts of the world; the lowest gauge densities evaluated were 1 gauge/0.1° pixel (equivalent to ~80 gages/10,000 km

^{2}), 1 gauge/0.25° pixel (equivalent to ~13 gages/10,000 km

^{2}), and 0.25 gauges/100 km

^{2}(equivalent to 25 gauges/10,000 km

^{2}) by Mandapaka and Lo [21], Villarini [20], and Tian et al. [19], respectively. Given that the Global Precipitation Climatology Center (GPCC) database contains approximately 75,000 stations [5], the average global gauge density over land is approximately 5 gauges/10,000 km

^{2}(assuming that all gauges in the GHCN database lie within the approximate 150 million km

^{2}of Earth’s land surface). Notably, the issue of uncertainty in interpolated gauge estimates is not limited to SMP validation, but also impacts gauge-correction of radar fields, with Peleg et al. [7] finding that “at least three rain stations are needed to adequately represent the rainfall on a typical radar pixel scale”.

^{2}or 10,000 km

^{2}[11,18,22] to stations per 0.25° pixel or 0.1° pixel [19,21,23]. Few studies utilize the distance to the nearest gauge used during interpolation to characterize gauge network density (i.e., Nikolopoulos et al. [16]), even though interpolated accuracy depends heavily on this metric and only 5.9% of the Earth’s land surface lies within 25 km of a rain gauge [5]. Nikolopoulos et al. [16] found that debris flow-triggering rainfall could be underestimated by up to 40% when the nearest available gauge data was 6–7 km away from a debris flow event.

## 2. Data

#### 2.1. Study Area and Period

#### 2.2. Gauge Data

#### 2.3. Satellite Precipitation Data

## 3. Methods

#### 3.1. Pixel Selection

#### 3.2. Inverse Distance Weighting Interpolation Scheme

#### 3.3. Monte Carlo “Data-Limited” Interpolation Scheme

- (a)
- n stations within 1.0° of a pixel are simulated as “available” and are used to generate a “data-limited” precipitation timeseries using IDW interpolation for that pixel (Figure 2a,b).
- (b)
- The resulting data-limited interpolated timeseries is compared against ground-truth precipitation. The following performance metrics are calculated for the data-limited timeseries: root mean square error (RMSE), probability of detection (POD), probability of false alarm (POFA), and Kling Gupta Efficiency (KGE). These performance metrics are further described in Section 3.4.
- (c)
- This scheme is repeated for a range of values of n, from n = 1 to n = nearly all available stations, resulting in a range of POD values and other performance metric values across the range of simulated gauge densities used during data-limited interpolation (Figure 2c). For each simulated value of n, n stations are randomly selected. At least 3000 iterations are performed at each pixel with a range of values for n to simulate a large variety of gauge densities and gauge network configurations.

#### 3.4. Performance Metrics

#### 3.5. Regression Fitting

^{2}value of less than 0.5 were not included in results due to lack of fit.

#### 3.6. Comparison of Interpolated Gauge Performance to IMERG

#### 3.7. Assessing the Ability of Interpolated Estimates to Evaluate IMERG

## 4. Results

^{2}lower than 0.5 are excluded. As could be expected, the performance of gauge interpolated estimates for all performance metrics is best at high gauge densities and decreases exponentially at low gauge densities, particularly below 10 gauges/10,000 km

^{2}. The ‘break-even’ points for IMERG-Early and IMERG-Late show the gauge density at which IMERG performance metrics intersect with the predicted performance of interpolated estimates at each pixel. In 35% of CONUS pixels, IMERG-Early RMSE does not intersect with the logistic regression, indicating that generally the RMSE estimated by interpolated gauge data even at very low gauge densities outperforms that estimated by IMERG. For almost all pixels in CONUS and Brazil, IMERG POFA does not intersect with the predicted POFA of interpolated estimates, even at very low gauge densities and high distances to the nearest available gauge.

^{2}, and. POD breakpoints as a function of density demonstrate the greatest range, but generally occur at between 1 and 5 gauges/10,000 km

^{2}. The decline in POD as a function of distance to nearest gauge is much more gradual when described using the monotonic smoothing spline (Figure 4d) than when fit to a logistic regression (Figure 3d).

^{2}and 0 km, indicating that IMERG does not meet or exceed interpolated estimate POFA performance even when barely any gauge data (i.e., one or two gauges) is available. Unlike in Figure 5, which analyzed MC scheme results as a function of simulated gauge density, there does appear to be a discernable relationship between elevation and the distance breakpoints for RMSE. At lower elevations, both logistic regression and monotonic spline fits agree on lower breakpoints, meaning that IMERG outperforms interpolated gauge estimates in terms of RMSE when the nearest gauge is closer at low elevations (~50–100 km) than at high elevations (nearest gauge must be >100 km away). RMSE appears to be exception however; there is no apparent relationship between elevation and distance breakpoints for POD, CC, and POFA.

^{2}, which is comparable to the gauge density covering most parts of the world, or when the distance to the nearest gauge is greater than 40 km. No values are shown for the POFA break-even point as a function of density since IMERG-Early and Late POFA consistently failed to outperform interpolated estimates even when interpolated scheme results were extrapolated to extremely low densities using the monotonic smoothing spline and logistic regression (see Figure 3, Figure 4, Figure 5 and Figure 6). The average and standard deviation of IMERG Early and Late break points as a function of density and distance are generally similar in CONUS and Brazil, although the break-even distance for RMSE and KGE is substantially higher in CONUS than in Brazil.

^{2}or higher. The right column of Figure 7 plots the average percent difference at every pixel between the true performance metrics of IMERG-Early and the metrics estimated using data-limited interpolations with a density less than 5 gauges/10,000 km

^{2}(low gauge density). Overestimation of POD by low density interpolations is generally higher in pixels with higher annual precipitation, reaching a 60% overestimation of the true POD in several pixels.

## 5. Discussion

#### 5.1. Accuracy of Interpolated Gauge Estimates as a Function of Gauge Density and Nearest Gauge Distance

^{2}(Figure 3e and Figure 4e), the POD of interpolated estimates drops sharply at low gauge density. The performance variability for all error metrics increases at low gauge densities (Figure 3 and Figure 4).

^{2}(Figure 3a and Figure 4a) is consistent with findings by Tian et al. [19] that the MAE at the daily scale varied minimally as a function of gauge density, suggesting that low gauge density has less impact on the error of a gauge interpolated product at the daily scale than at the hourly scale. However, Tian et al.’s [19] finding that the MAE at the hourly scale was greater at low gauge densities suggests that the impacts of sampling error are greater at the hourly scale.

^{2}greater than 0.5 (Figure 3). Estimating the breakpoint for POFA (i.e., the gauge density or nearest gauge distance at which IMERG and interpolated gauge estimates have similar POFA) is difficult because the monotonic cubic spline does not generate regressions that characterize POFA behavior at high distances (due to lack of ‘training data’), and, as previously mentioned, logistic regressions do not fit POFA data well.

#### 5.2. Accuracy of Interpolated Gauge Estimates Relative to IMERG Early and Late

^{2}, interpolated gauge estimates consistently outperform IMERG-Early and IMERG-Late in terms of RMSE, KGE, and POFA (POFA; Figure 5, Table 1). IMERG appears to have the greatest relative advantage over low density interpolations when estimating probability of detection (POD), resulting in break points as high as 20–25 gauges/10,000 km

^{2}and as low as 5 km (Figure 3a, Figure 5b and Figure 6b). In several (but not most) pixels, results indicate that IMERG-Early and -Late can be expected to exhibit higher POD than interpolated gauge estimates where gauge densities are less than 20 gauges/10,000 km

^{2}or when the nearest available gauge is farther than 5 km away, i.e., nearly the entire world. However, this result may also reflect IMERG’s tendency to overestimate light precipitation occurrence [29,37]. The break-even densities for KGE and RMSE estimated using logistic regressions and the monotonic cubic spline agree quite well, although such relatively low break points indicate that interpolated estimates will generally outperform IMERG-Early and -Late (Figure 5a). The break-even distance for POD is lower when calculated using the logistic regression than the monotonic spline (Figure 6b), which may be due to the different ways that these methods extrapolate from the lowest simulated distance to nearest gauge.

#### 5.3. Ability of Interpolated Estimates to Evaluate IMERG

#### 5.4. Interpolated Data Performance as a Function of Climate and Geographic Setting

## 6. Conclusions

^{2}and as a function of distance to the nearest available gauge.

^{2}, which includes the gauge density values that are present in most parts of the world. The ability of interpolated gauge estimates to accurately characterize the probability of detection rapidly decreases at low gauge densities, making satellite products an attractive alternative source of precipitation data for applications which prioritize precipitation detection, such as landslide hazard monitoring systems. However, even at low gauge densities, interpolated gauge estimates provide a relatively robust estimate of IMERG RMSE.

^{2}). In line with previous, smaller-scale studies, this work demonstrates that it is critical that users of interpolated gauge data consider the gauge density, as well as distance to nearest gauge, used during interpolation before assuming that these estimates are more accurate than (or suitable for validating) satellite precipitation estimates.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Shige, S.; Kida, S.; Ashiwake, H.; Kubota, T.; Aonashi, K. Improvement of TMI rain retrievals in mountainous areas. J. Appl. Meteorol. Climatol.
**2013**, 52, 242–254. [Google Scholar] [CrossRef] [Green Version] - Tan, J.; Petersen, W.A.; Kirchengast, G.; Goodrich, D.C.; Wolff, D.B. Evaluation of global precipitation measurement rainfall estimates against three dense gauge networks. J. Hydrometeorol.
**2018**, 19, 517–532. [Google Scholar] [CrossRef] - Tian, Y.; Peters-Lidard, C.D.; Choudhury, B.J.; Garcia, M. Multitemporal Analysis of TRMM-Based Satellite Precipitation Products for Land Data Assimilation Applications. J. Hydrometeorol.
**2007**, 8, 1165–1183. [Google Scholar] [CrossRef] - Habib, E.H.; Meselhe, E.A.; Aduvala, A.V. Effect of Local Errors of Tipping-Bucket Rain Gauges on Rainfall-Runoff Simulations. J. Hydrol. Eng.
**2008**, 13, 488–496. [Google Scholar] [CrossRef] - Kidd, C.; Becker, A.; Huffman, G.J.; Muller, C.L.; Joe, P.; Skofronick-Jackson, G.; Kirschbaum, D.B. So, how much of the Earth’s surface is covered by rain gauges? Bull. Am. Meteorol. Soc.
**2017**, 98, 69–78. [Google Scholar] [CrossRef] [PubMed] - Michaelides, S.; Levizzani, V.; Anagnostou, E.; Bauer, P.; Kasparis, T.; Lane, J.E. Precipitation: Measurement, remote sensing, climatology and modeling. Atmos. Res.
**2009**, 94, 512–533. [Google Scholar] [CrossRef] - Peleg, N.; Ben-Asher, M.; Morin, E. Radar subpixel-scale rainfall variability and uncertainty: Lessons learned from observations of a dense rain-gauge network. Hydrol. Earth Syst. Sci.
**2013**, 17, 2195–2208. [Google Scholar] [CrossRef] [Green Version] - Sun, Q.; Miao, C.; Duan, Q.; Ashouri, H.; Sorooshian, S.; Hsu, K.L. A Review of Global Precipitation Data Sets: Data Sources, Estimation, and Intercomparisons. Rev. Geophys.
**2018**, 56, 79–107. [Google Scholar] [CrossRef] [Green Version] - Villarini, G.; Mandapaka, P.V.; Krajewski, W.F.; Moore, R.J. Rainfall and sampling uncertainties: A rain gauge perspective. J. Geophys. Res. Atmos.
**2008**, 113, 11102. [Google Scholar] [CrossRef] - Freitas, E.d.S.; Coelho, V.H.R.; Xuan, Y.; Melo, D.d.C.D.; Gadelha, A.N.; Santos, E.A.; Galvão, C.d.O.; Ramos Filho, G.M.; Barbosa, L.R.; Huffman, G.J.; et al. The performance of the IMERG satellite-based product in identifying sub-daily rainfall events and their properties. J. Hydrol.
**2020**, 589, 125128. [Google Scholar] [CrossRef] - Xavier, A.C.; King, C.W.; Scanlon, B.R. Daily gridded meteorological variables in Brazil (1980–2013). Int. J. Climatol.
**2016**, 36, 2644–2659. [Google Scholar] [CrossRef] [Green Version] - Xu, H.; Xu, C.Y.; Chen, H.; Zhang, Z.; Li, L. Assessing the influence of rain gauge density and distribution on hydrological model performance in a humid region of China. J. Hydrol.
**2013**, 505, 1–12. [Google Scholar] [CrossRef] - Mishra, A.K. Effect of Rain Gauge Density over the Accuracy of Rainfall: A Case Study Over Bangalore; SpringerPlus: Delhi, India, 2013; Volume 2, pp. 1–7. [Google Scholar] [CrossRef] [Green Version]
- Otieno, H.; Yang, J.; Liu, W.; Han, D. Influence of Rain Gauge Density on Interpolation Method Selection. J. Hydrol. Eng.
**2014**, 19, 04014024. [Google Scholar] [CrossRef] - Prakash, S.; Mitra, A.K.; Pai, D.S.; AghaKouchak, A. From TRMM to GPM: How well can heavy rainfall be detected from space? Adv. Water Resour.
**2016**, 88, 1–7. [Google Scholar] [CrossRef] - Nikolopoulos, E.I.; Borga, M.; Creutin, J.D.; Marra, F. Estimation of debris flow triggering rainfall: Influence of rain gauge density and interpolation methods. Geomorphology
**2015**, 243, 40–50. [Google Scholar] [CrossRef] - Anjum, M.N.; Ding, Y.; Shangguan, D.; Ahmad, I.; Wajid Ijaz, M.; Farid, H.U.; Yagoub, Y.E.; Zaman, M.; Adnan, M. Performance evaluation of latest integrated multi-satellite retrievals for Global Precipitation Measurement (IMERG) over the northern highlands of Pakistan. Atmos. Res.
**2018**, 205, 134–146. [Google Scholar] [CrossRef] - Gadelha, A.N.; Coelho, V.H.R.; Xavier, A.C.; Barbosa, L.R.; Melo, D.C.D.; Xuan, Y.; Huffman, G.J.; Petersen, W.A.; Almeida, C. das N. Grid box-level evaluation of IMERG over Brazil at various space and time scales. Atmos. Res.
**2019**, 218, 231–244. [Google Scholar] [CrossRef] [Green Version] - Tian, F.; Hou, S.; Yang, L.; Hu, H.; Hou, A. How does the evaluation of the gpm imerg rainfall product depend on gauge density and rainfall intensity? J. Hydrometeorol.
**2018**, 19, 339–349. [Google Scholar] [CrossRef] - Villarini, G. Evaluation of the Research-Version TMPA Rainfall Estimate at Its Finest Spatial and Temporal Scales over the Rome Metropolitan Area. J. Appl. Meteorol. Climatol.
**2010**, 49, 2591–2602. [Google Scholar] [CrossRef] - Mandapaka, P.V.; Lo, E.Y.M. Evaluation of GPM IMERG Rainfall Estimates in Singapore and Assessing Spatial Sampling Errors in Ground Reference. J. Hydrometeorol.
**2020**, 21, 2963–2977. [Google Scholar] [CrossRef] - Girons Lopez, M.; Wennerström, H.; Nordén, L.Å.; Seibert, J. Location and density of rain gauges for the estimation of spatial varying precipitation. Geogr. Ann. Ser. A Phys. Geogr.
**2015**, 97, 167–179. [Google Scholar] [CrossRef] [Green Version] - Villarini, G.; Krajewski, W.F. Evaluation of the research version TMPA three-hourly 0.25° × 0.25° rainfall estimates over Oklahoma. Geophys. Res. Lett.
**2007**, 34, 1–5. [Google Scholar] [CrossRef] - Almeida, C.; Coelho, V.H.R.; Meira, M.A.; Carvalho, F. Boletim Anual de Precipitação no Brasil (ano 2021); Federal University of Paraíba: Paraíba, Brazil, 2022. [Google Scholar]
- Tang, G.; Clark, M.P.; Newman, A.J.; Wood, A.W.; Papalexiou, S.M.; Vionnet, V.; Whitfield, P.H. SCDNA: A serially complete precipitation and temperature dataset for North America from 1979 to 2018. In Earth System Science Data; Copernicus GmbH: Göttingen, Germany, 2020; Volume 12, pp. 2381–2409. [Google Scholar] [CrossRef]
- Huffman, G.; Bolvin, D.T.; Braithwaite, D.; Hsu, K.; Joyce, R.; Kidd, C.; Nelkin, E.J.; Sorooshian, S.; Tan, J.; Xie, P. NASA Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG) Prepared for: Global Precipitation Measurement (GPM) National Aeronautics and Space Administration (NASA). In Algorithm Theoretical Basis Document (ATBD); NASA: Washington, DC, USA, 2019. [Google Scholar]
- Tan, J.; Huffman, G.J.; Bolvin, D.T.; Nelkin, E.J. IMERG V06: Changes to the morphing algorithm. J. Atmos. Ocean. Technol.
**2019**, 36, 2471–2482. [Google Scholar] [CrossRef] - Stanley, T.A.; Kirschbaum, D.B.; Benz, G.; Emberson, R.A.; Amatya, P.M.; Medwedeff, W.; Clark, M.K. Data-Driven Landslide Nowcasting at the Global Scale. Front. Earth Sci.
**2021**, 9, 1–15. [Google Scholar] [CrossRef] - Yin, J.; Guo, S.; Gu, L.; Zeng, Z.; Liu, D.; Chen, J.; Shen, Y.; Xu, C.Y. Blending multi-satellite, atmospheric reanalysis and gauge precipitation products to facilitate hydrological modelling. J. Hydrol.
**2021**, 593, 125878. [Google Scholar] [CrossRef] - Zhou, Y.; Nelson, K.; Mohr, K.I.; Huffman, G.J.; Levy, R.; Grecu, M. A Spatial-Temporal Extreme Precipitation Database from GPM IMERG. J. Geophys. Res. Atmos.
**2019**, 124, 10344–10363. [Google Scholar] [CrossRef] - Ly, S.; Charles, C.; Degré, A. Geostatistical interpolation of daily rainfall at catchment scale: The use of several variogram models in the Ourthe and Ambleve catchments, Belgium. Hydrol. Earth Syst. Sci.
**2011**, 15, 2259–2274. [Google Scholar] [CrossRef] [Green Version] - Tan, J.; Petersen, W.; Tokay, A. A Novel Approach to Identify Sources of Errors in IMERG for GPM Ground Validation. J. Hydrometeorol.
**2016**, 17, 2477–2491. [Google Scholar] [CrossRef] - Linfei, Y.; Leng, G.; Python, A.; Peng, J. A Comprehensive Evaluation of Latest GPM IMERG V06 Early, Late and Final Precipitation Products across China. Remote Sens.
**2021**, 13, 1208. [Google Scholar] [CrossRef] - Utreras, F.I. Smoothing noisy data under monotonicity constraints existence, characterization and convergence rates. Numer. Math.
**1985**, 47, 611–625. [Google Scholar] [CrossRef] - Zhang, J.T. A simple and efficient monotone smoother using smoothing splines. J. Nonparametric Stat.
**2004**, 16, 779–796. [Google Scholar] [CrossRef] - Virtanen, P.; Gommers, R.; Oliphant, T.E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; et al. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nat. Methods
**2020**, 17, 261–272. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wang, S.; Liu, J.; Wang, J.; Qiao, X.; Zhang, J. Evaluation of GPM IMERG V05B and TRMM 3B42V7 Precipitation products over high mountainous tributaries in Lhasa with dense rain gauges. Remote Sens.
**2019**, 11, 2080. [Google Scholar] [CrossRef]

**Figure 1.**Map of study areas (orange) and gauge datasets used in this work (blue). Pixels that met gauge density requirements as described in Section 3.1 are overlayed (red). Subsets of the study areas near Denver, Colorado and Rio de Janeiro at closer scale are also shown to illustrate gauge network configurations in these regions. The elevation and average annual precipitation of pixels in CONUS and Brazil is also shown. The spread in elevation and annual precipitation is greater in CONUS than Brazil.

**Figure 2.**Monte Carlo “data-limited” interpolation scheme implemented for a 0.1° pixel in Rio de Janeiro (red). (

**a**) All available gauges (black) used to calculate ground truth precipitation for a pixel at (−43.05, −22.85) and randomly selected subset of gauges (light blue) used in one iteration of the Monte Carlo Scheme. (

**b**) Timeseries of ground truth precipitation and data-limited interpolation using subset of gauges shown in (

**a**). Performance metrics for the data-limited interpolation are displayed in light blue. (

**c**) Probability of Detection (POD) calculated for all iterations of the Monte Carlo Scheme plotted as a function of simulated gauge density and logistic regression (orange) and monotonic spline (olive) fit to POD data. The POD of IMERG-Early and IMERG-Late are shown in comparison (dashed black and red lines). (

**d**) POD from Monte Carlo Scheme results as in (b) but plotted and fit with regressions as a function of simulated distance to nearest gauge.

**Figure 3.**Logistic regression results fit to the performance metrics (RMSE, POD, POFA, and KGE) of data-limited gauge interpolations for pixels in CONUS (blue) and Brazil (pink) as a function of (

**a**,

**c**,

**e**,

**g**) simulated gauge density and (

**b**,

**d**,

**f**,

**h**) simulated distance to nearest gauge. The “break-even” gauge densities for each pixel are plotted for IMERG-Early (black) and IMERG-Late (orange). Logistic regressions with r2 < 0.5 are excluded from this plot.

**Figure 4.**Monotonic smoothing results fit to RMSE, POD, POFA, and KGE data from MC interpolation scheme for pixels in CONUS (blue) and Brazil (pink) as a function of (

**a**,

**c**,

**e**,

**g**) simulated gage density and (

**b**,

**d**,

**f**,

**h**) simulated distance to nearest gage. The “break-even” gauge densities for each pixel are plotted for IMERG-Early (black) and IMERG-Late (orange).

**Figure 5.**Break points for gauge densities at which IMERG-Early and Late can be expected to perform similarly to interpolated gauge data in terms of (

**a**) RMSE, (

**b**) POD, (

**c**) KGE, and (

**d**) POFA.

**Figure 6.**Break points for the distance to nearest gauge at which IMERG-Early and Late can be expected to perform similarly to interpolated gauge data in terms of (

**a**) RMSE, (

**b**) POD, (

**c**) KGE, and (

**d**) POFA. Note that the highest distance to nearest gauge assessed was 200 km and that the high number of pixels estimated to have a RMSE break point at 200 km is reflective of the logistic regression’s tendency to “flatten out” at high distances beyond those used during regression fitting.

**Figure 7.**(

**Left column**) Example of IMERG-Early RMSE, POD, KGE, and POFA assessed using data-limited simulations at a pixel in Rio de Janeiro. (

**Right column**) Average percent difference between metrics estimated using data-limited interpolations with gauge density less than 5 gauges/10,000 km

^{2}and the true IMERG metric. Positive percent difference values in right column indicate that data-limited interpolations are overestimating an error metric for IMERG.

**Figure 8.**(

**Left column**) Example of IMERG-Early RMSE, POD, KGE, and POFA assessed using data-limited simulations at a pixel in Rio de Janeiro. (

**Right column**) Average percent difference between metrics estimated using data-limited interpolations with distance to nearest gauge greater than 50 km and the true IMERG metric. Positive percent difference values in right column indicate that data-limited interpolations are overestimating an error metric for IMERG.

**Table 1.**The average and ± standard deviation of break-even points in CONUS and Brazil study areas in terms of both gauge density and distance to nearest available gauge. IMERG-Early breakpoints are shown out of parentheses and IMERG-Late breakpoints are in parentheses.

CONUS Average | Brazil Average | |||
---|---|---|---|---|

Break-Even Density
[Gauges/10,000 km^{2}]
| Break-Even Distance [km] |
Break-Even Density
[Gauges/10,000 km^{2}]
| Break-Even Distance [km] | |

RMSE [mm/day] | 0.1 ± 0.1 (0.1 ± 0.1) | 178 ± 38 (175 ± 35) | 0.4 ± 0.3 (0.4 ± 0.2) | 100 ± 45 (105 ± 40) |

KGE [-] | 0.3 ± 0.3 (0.2 ± 0.2) | 172 ± 59 (179 ± 61) | 0.6 ± 0.4 (0.5 ± 0.4) | 94 ± 53 (113 ± 58) |

POD [-] | 4.7 ± 6.1 (5.9 ± 7.0) | 42 ± 31 (38 ± 27) | 2.4 ± 3.8 (1.6 ± 0.8) | 47 ± 48 (46 ± 45) |

POFA [-] | -- | 246 ± 42 (246 ± 41) | -- | 196 ± 58 (182 ± 65) |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hartke, S.H.; Wright, D.B.
Where Can IMERG Provide a Better Precipitation Estimate than Interpolated Gauge Data? *Remote Sens.* **2022**, *14*, 5563.
https://doi.org/10.3390/rs14215563

**AMA Style**

Hartke SH, Wright DB.
Where Can IMERG Provide a Better Precipitation Estimate than Interpolated Gauge Data? *Remote Sensing*. 2022; 14(21):5563.
https://doi.org/10.3390/rs14215563

**Chicago/Turabian Style**

Hartke, Samantha H., and Daniel B. Wright.
2022. "Where Can IMERG Provide a Better Precipitation Estimate than Interpolated Gauge Data?" *Remote Sensing* 14, no. 21: 5563.
https://doi.org/10.3390/rs14215563