Evaluation of Extreme Precipitation Indices in Brazil’s Semiarid Region from Satellite Data

Abstract

Brazil’s semiarid region (SAB) has a heterogeneous precipitation distribution, with the occurrence of periodic droughts and occasional extreme rainfall events. The precipitation monitoring system in this region is insufficient, but remote sensing products can provide information on rainfall in areas with low data coverage. Thus, the main objective of this study was to evaluate 12 extreme precipitation indices calculated using Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG) data in comparison with indices calculated from data measured by rain gauges for different SAB locations. To evaluate the IMERG product, we used rainfall data measured by 56 rain gauges during the period from 1 January 2000 to 31 December 2020. The satellite product was evaluated through juxtaposition between the IMERG and actual rainfall data, by calculating the statistical indices bias, root-mean-squared error, Spearman correlation, and probability density function. The results showed that most of the extreme precipitation indices were well represented by the satellite data, except for the simple precipitation intensity index (SDII), in which case the correlation coefficient was 0.2. This result can be explained as this index is calculated from the exact value of daily precipitation, while the other indices are estimated by rainfall values above some thresholds. On the other hand, total annual precipitation and precipitation above 1 mm presented Spearman correlation reaching 0.97 in some locations. We conclude that the IMERG database is adequate to represent the maximum precipitation in the Brazilian semiarid region, and the extreme precipitation indices had good performance according to the region where the maximum rain occurred.

1. Introduction

A variety of factors such as land degradation, irregularities in rainfall regimes, lack of irrigation, and strong dependence on subsistence farming contribute to the susceptibility of Brazil’s semiarid region (SAB) to extreme climate and meteorological events, which are becoming more intense and frequent due the climate change [1,2]. The SAB region is climatologically characterized by irregular rainfall in space and time [3]. According to Braga et al. [4], the seasonality of this region is basically marked by strong rainfall variation, with annual rainfall ranging between 250 mm and 1200 mm, with a historical average of around 700 mm per year.

Due to the irregular distribution of rainfall, extreme weather events have a negative influence not only on issues associated with demand for water and food, but on public health issues in the region [5]. An excess or deficit of rainfall has a substantial impact on physical, biological, and human systems [6]. Studies of extreme events, such as [7], have indicated significant increases in rainfall frequency and intensity, with inconsistent time variation. As observed by [8], a longer return period is correlated with a greater magnitude of expected extreme precipitation events. Climate change has caused extreme events in many regions, with significant socioeconomic losses [9,10].

A limitation to the study of precipitation in Brazil is the poor access to accurate data with high temporal and spatial resolution. The spatial distribution of rain gauges in the SAB region is irregular, and, in many cases, has an excessive number of failures [11,12]. This is due to the high cost of installing and maintaining the infrastructure [13]. These instruments are insufficient in many underdeveloped countries, such as Brazil. In 1994, the World Meteorological Organization (WMO) indicated that, in regions with irregular topography, a pluviometer should be installed every 250 km² to obtain good diagnosis of precipitation. In this scenario, the SAB and other regions of Brazil do not have the necessary instrumentation to collect data on extreme events, making it important to evaluate satellite data from remote sensing [12,14,15]. According to Asshad et al. [16], understanding the performance of precipitation products generated from remote sensing compared to reference data such as rain gauges is of great importance before using satellite data. Precise precipitation products with high spatial and temporal resolution are a prerequisite for extreme precipitation analysis [17].

There are several remote sensing algorithms and methods available that can estimate precipitation [18]. The advantages and disadvantages of using each product vary depending on the quality and spatiotemporal resolution of the data. One of the most widely used satellite precipitation databases in the world is that from the TRMM satellite, launched in late 1997 [19].

The TRMM satellite is very efficient in estimating precipitation in tropical regions, and its information was used for studies of the distribution and variability of precipitation according to different algorithms and was found to be a good tool for the detection of extreme events [20,21]. The TRMM satellite orbited with an inclination angle of 35° and was able to complete its orbit in about 90 min, completing around 16 orbits per day [22]. Its time in orbit was envisioned to be approximately 3 years, but it remained in activity for approximately 18 years, making 2015 its last year of data collection [23].

Before the end of the TRMM satellite’s activity in 2015, the Global Precipitation Measurement (GPM) satellite was launched by the National Aeronautics and Space Administration (NASA) together with the Japan Aerospace Exploration Agency (JAXA), in 2014. It began generating a product called the Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG) in early 2015 [24]. IMERG combines precipitation estimates from all microwave sensors aboard the GPM and TRMM satellite constellation with infrared-based observations from geosynchronous satellites and monthly precipitation data [25,26]. Several weather and climate studies have examined the estimated precipitation products from TRMM and GPM satellites [27,28,29].

The IMERG product has been evaluated in different regions of the world in juxtaposition with rain gauges, such as in China [30], Pakistan [16], different climatic zones of Brazil [28,31], the Ebro River Basin in Spain [32], Chile [33], and Canada [34]. According to the literature, studies have compared the IMERG precipitation estimates with rain gauge data. However, there is no comparison between the extreme climatic indices calculated by the use of IMERG and rain gauges. Since analysis of extreme precipitation events is important to address scientific questions with practical applications in the context of social problems in the semiarid region of Brazil, we evaluated IMERG’s ability to characterize extreme rainfall in the SAB. The specific objective of this study was to evaluate 12 extreme precipitation indices calculated using IMERG in comparison with indices calculated using precipitation data obtained from rain gauges in different SAB locations. The results can be valuable for activities in sectors such as civil defense, agriculture, health, urban planning, and water resource management.

2. Materials and Methods

2.1. Study Region

The SAB is located between 35.26° W, 46.62° S and −2.68° W, 17.99° S (Figure 1). Most of its area is in the northeast region of Brazil, while a small part is located in the southeast region [35]. It is a region with annual rainfall with high variation, with dry and rainy years alternating irregularly. According to the delimitation of the Ministry of National Integration (2017) and the Brazilian Institute of Geography and Statistics (IBGE) (2018) [36], the region’s estimated population is 27.8 million.

The criteria for delimiting the semiarid region were average annual rainfall less than or equal to 800 mm, Thornthwaite aridity index less than or equal to 0.50, and daily percentage of water deficit greater than or equal to 60%, considering every day of the year [37,38]. As a result, data from a total of 1262 municipalities were used, with 1171 municipalities distributed in all states of northeast Brazil and 91 distributed in the state of Minas Gerais, southeast Brazil [39].

2.2. Data

We used two datasets of daily precipitation. The first one was composed of daily information from the 56 rain gauges installed in meteorological stations managed by the National Institute for Meteorology (INMET). The weather stations’ distribution is shown in Figure 1b, and the data cover the period from June 2000 to December 2020. The second is from the IMERG product version 6, which combines information collected by microwave sensors from the TRMM and GPM constellation and infrared-based observations from geosynchronous satellites [28]. The IMERG uses estimates by the TRMM satellite (from 2000 to 2015 period) and precipitation retrieved by the GPM satellite from 2014 to 2020. The final IMERG database comes from measurements in a 0.1° grid with half-hour sampling. The IMERG data were accessed from NASA’s Goddard Space Flight Center website (https://pmm.nasa.gov/data-access/downloads/gpm), accessed on 20 July 2021.

2.3. Extreme Precipitation Indices

The indices of the Expert Team on Climate Change Detection and Indices (ETCCDI) are based on daily temperature and precipitation. In this study, only indices based on precipitation were used, totaling 12 (

Table 1. Indices of climatic extremes calculated in the present study.

Indices	Definitions	Units
PRCPTOT	Annual total precipitation on wet days	mm
SDII	Simple precipitation intensity index	mm/day
RX 1 day	Monthly maximum 1-day precipitation	mm
RX 5 day	Monthly maximum 5-day precipitation	mm
R95pToT	Annual total PRCP when RR > 95p	mm
R90pToT	Annual total PRCP when RR > 99p	mm
CDD	Maximum length of dry spell, maximum number of consecutive days with RR < 1 mm	days
CWD	Maximum length of wet spell, maximum number of consecutive days with RR ≥ 1 mm	days
R1mm	Annual count of days when PRCP ≥ 1 mm	days
R10mm	Annual count of days when PRCP ≥ 10 mm	days
R20mm	Annual count of days when PRCP ≥ 20 mm	days
R50mm	Annual count of days when PRCP ≥ 50 mm	days

). The reason for choosing these 12 indices was the fact that precipitation is a very important climate element in the SAB for the short, medium, and long term, in addition to being typically used to represent the probability of rare events [40,41].

2.4. Statistical Analysis

To evaluate the IMERG product, we compared the rain gauge observations and satellite estimates (grid points), following the method adopted by [12,28], where the grid point closest to the rain gauge was used. Then, statistical analyses were performed between the two datasets (IMERG and rain gauge). Four statistical measures were used, following previous studies [12,42,43,44]:

(a)

BIAS: It is a comparison of the averages of the two databases, IMERG and rain gauges (Equation (1)). Positive values indicate overestimation and negative values indicate underestimation of the IMERG values in relation to the observed data.

$$\mathrm{BIAS}=\frac{{{\displaystyle \sum }}_{i=1}^{n}Xi-Yi}{n}.$$

(1)

(b)

Root-mean-squared error (RMSE): It is one of the most widely used methods to measure absolute error between two databases. It is sensitive to larger errors and is represented by Equation (2).

$$\mathrm{RMSE}=\frac{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(Xi-Yi\right)}^2}}{n}.$$

(2)

(c)

Spearman correlation coefficient (r): It measures the strength of the association between two databases.

$$\mathrm{r}=\frac{{{\displaystyle \sum }}_{i=1}^n{\left(Xi-\overline{X}\right)}^{}{\left(Yi-\overline{Y}\right)}^{}}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(Xi-\overline{X}\right)}^{}}\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(Yi-\overline{Y}i\right)}^{}}}.$$

(3)

(d)

Probability density function (PDF): It describes the behavior, in polygon form, of the frequency distribution of a random variable. The probability of the random variable being less than a given value of interest, x, is calculated using the cumulative distribution function (CDF), as in Equation (4).

$${\mathrm{F}}_x=\mathit{Prob}(X\le x)={{\displaystyle \int }}_{-\infty }^{\infty }f(x)dx.$$

(4)

A Taylor diagram was used to facilitate the comparison between the data estimated by the IMERG and the data from the rain gauges [8,16]. This diagram quantifies the degree of correspondence between the IMERG and rain gauge data in terms of three statistics: RMSE, Spearman’s correlation coefficient (r), and standard deviation (SD).

Scheme 1 presents a flowchart with the method and data treatment.

3. Results and Discussion

The values of the extreme indices from the IMERG and rain gauges are shown in Figure 2 and Figure 3. In general, the indices calculated with the IMERG data were similar to those calculated with the rain gauge data. The PRCPTOT (Figure 2b) shows marked variability, with regions (west edge) reaching values above 1600 mm/year, while, in the drier areas of the SAB, the precipitation reached values between 400 and 500 mm/year. IMERG was able to satisfactorily represent the spatial distribution of total precipitation, although slight underestimation was observed in the northern portion and on the eastern coast. For the SDII index, similar values were obtained (IMERG and pluviometer) for most of the SAB. The exception was the eastern SAB region, where the values calculated from the IMERG data were higher than those calculated from the rain gauge data (Figure 2b). The same occurred for the other intensity indices (Figure 2b–f). In most of the SAB, the indices calculated from the IMERG data and rain gauges were similar, with the greatest differences being observed in the eastern part of the study area. Similar results were reported by [28] when evaluating IMERG daily precipitation data in the eastern portion of the São Francisco River Basin. The authors stated that the low performance of the product may be associated with the predominant cloud type in the region.

Among the frequency indices (Figure 3a–f), R10mm, R20mm, and R50mm were those in which the spatial distribution was best represented by the IMERG data. Similar to SDII (Figure 2b), the CDD (Figure 3a) was overestimated especially on the east coast of the SAB. The rain gauges indicated that, on the east coast, the average values of CDD were around 40 days/year and those of SDII were close to 6 mm/day, while the IMERG indicated average CDD values of around 80 days/year and SDII close to 12 mm/day. Similar results were found with the use of the 3B42 product [28,45]. The authors observed overestimation from satellite data during the rainy season in this region. It is important to mention that the greater differences observed on the east coast might be related to problems in estimating precipitation by satellites due to the presence of warm precipitating clouds [8,17].

The BIAS between the values estimated by IMERG and observed by the rain gauges is shown in Figure 4. In the analysis of the SDII, the variation occurred from 2 mm to 6 mm to the east. This result was probably linked to the fact that this index is an estimation of the exact precipitation content. In addition, according to the literature [12,15], remote sensing products do not properly estimate precipitation from warm clouds, which are predominant in the eastern portion of the study area. The other indices continued to demonstrate that IMERG provides a good estimate. Among them, R10mm can be highlighted, where the BIAS varied from −7.9 to 10.25. This index presented a variation between 0 and 10 mm across practically the entire region, mainly in the northwest and south of the SAB, which is consistent with what was perceived in Figure 3d, similar to the results presented by [8,45]. The other indices did not present the same problem as SDII because they were related to precipitation above some thresholds, not the exact value of rainfall.

The RMSE between the two data sources is shown in Figure 5. It is known that a lower value indicates a better ability of the IMERG product to accurately represent the climatic indices observed by rain gauges. The results were still satisfactory; the RMSE values were small, compared to the order of magnitude of the variables. Similar results were observed by [28], who evaluated the IMERG database for the San Francisco River Basin, which is located in the SAB. The SDII index, for example, follows the same pattern as in Figure 2b, where the east is not well represented, thus presenting higher RMSE values. A similar behavior occurred for R1mm, indicating that, in the east of the SAB, the IMERG overestimated the number of days in the year with precipitation above 1 mm, with values of approximately 50 days. However, for the rest of the region, the difference was around 10 to 15 days. For the number of days with higher precipitation accumulation (R10mm, R20mm, and R50mm), the differences between the databases were smaller. The R50mm presented RMSE values between 0.75 and 3.32. This result indicates that IMERG was able to accurately identify the number of days with the highest rainfall accumulation. The results were similar for the other indices. However, some had lower RMSE even on the east coast of the study region, such as CWD, which represents the maximum number of consecutive wet days in which precipitation is greater than or equal to 1 mm, presenting a minimum value of 1.73 in one of the rain gauges. The RMSE for CWD in the eastern portion was less than 6 days.

Among all the climatic indices evaluated, the correlation between the IMERG data and the rain gauges (Figure 6) was greater than 0.7 for PRECPTOT, R1mm, R10mm, and R20mm in almost the entire study region, reaching values of 0.97 in some locations. Similar results were observed by [17,46], who compared IMERGE with rain gauge data for different regions The other indices showed maximum correlations above 0.7, but values below 0.5 were also observed. It is necessary to state that, even with a lower correlation, we cannot directly infer that it is not possible to correctly estimate precipitation from the IMERG data, which are the source for calculation of the evaluated climatic indices. This observation is based on the BIAS and RMSE values presented earlier (Figure 4 and Figure 5) and on the density curves (Figure 7), presented and discussed below.

Figure 7 shows the density curves between the climatic indices calculated with the precipitation data estimated by IMERG and the observational data from the rain gauges for all 56 observation points. The distributions were similar for most indices, whether they were rainfall totals (e.g., PRCPTOT) or counts of days with rainfall above a certain threshold (e.g., CWD). The biggest differences were found in the SDII, as observed in previous analyses. The curve referring to the pluviometers was bimodal, presenting a peak occurrence around 15 mm and another around 8 mm. The values with the lowest precipitation were not accompanied by the IMERG data, which is likely related to the patterns of underestimation of precipitation in the eastern region of the study area, associated with the difficulty of obtaining accurate precipitation data from warm clouds by remote sensing [8,12,15,47]. Another reason for this underestimation is the low humidity in the region, which makes the duration and extent of extreme precipitation shorter in dry regions than in humid regions, hampering estimation by satellite sensors [48,49].

From the Taylor diagram (Figure 8), it is possible to verify, in summary, comparative statistical metrics between the climatic indices obtained by IMERG and rain gauges. The correlation coefficient, standard deviation, and RMSE are presented. Each index is normalized by the corresponding standard deviation, allowing multiple indices (distinguished by colors and symbols) to be displayed. This type of analysis was described in several studies comparing the performance between meteorological variables collected at the surface and remote sensing products [45]. In general, as observed in previous analyses, most indices showed similarities between the two databases, estimated and observed. The best results were for the R10mm, R20mm, and R50mm indices, as they had a correlation of approximately 0.8, standard deviation close to 1.0, and low RMSE of approximately 0.5. In other words, they presented metrics close to those of the rain gauge data. These indices do not reflect the exact amount of precipitation, but the number of days which reached values above some thresholds. This behavior explains why the statistical metrics presented better results for R10mm, R20mm, and R50mm compared to SDII, for example. SDII is related to the exact amount of precipitation (mm/day). The satellite product used, IMERG, was not able to properly estimate this rain rate for the entire domain. This mainly occurred over the east portion of the study area, which is mainly related to the presence of warm clouds, as previously discussed. The overestimation of the IMERG values to the east of the region caused a low correlation of 0.2 and RSME values above 1.0.

4. Conclusions

The purpose of this study was to evaluate the extreme precipitation indices calculated from the IMERG precipitation database in comparison with observational data from 56 conventional rain gauges managed by INMET in the semiarid region of Brazil (21 years of data). Association of the statistical analyses presented in the form of maps together with the density curves and the Taylor diagram confirmed that the indices of climatic extremes calculated with the satellite estimates were in agreement with the observational data. The SDII index (average precipitation on wet days) did not present good statistical metrics, especially over the eastern region of the study area, a result that might be directly associated with precipitation from warm clouds. In this way, the daily rainfall values varied from 2 mm to 6 mm, with a standard deviation lower than 0.5 and correlation coefficient of 0.2.

Statistical evaluations proved that the results were satisfactory. This means that the information is effective for identifying the best indicators of maximum precipitation. The IMERG product agreed well with the observations based on rain gauges and presented adequate performance for extreme precipitation estimates for the Brazilian semiarid region, mainly for daily precipitation greater than 10 mm (R10mm). This result is extremely important because the spatial distribution of the rain gauges is not adequate for a better assessment of possible changes in climate patterns. The possibility of using data from remote sensing, such as IMERG, makes it possible to expand the evaluation of the indices to locations that do not have rain gauges or long series of observational precipitation data. These climate indices, for example, can also be used for a wide range of applications, such as evaluating indicators related to the spread of climate-related diseases.