Assessment of PERSIANN Satellite Products over the Tulijá River Basin, Mexico

Abstract

Precipitation is a fundamental component of the Earth’s hydrological cycle. Therefore, monitoring precipitation is paramount, as accurate information is needed to prevent natural hydrological disasters, such as floods and droughts. However, measuring precipitation using rain gauges is complicated due to their sparse spatial distribution. Satellite precipitation products (SPPs) are an alternative source of rainfall data. This study aimed to evaluate the performance of PERSIANN-CCS and PDIR-Now SPPs over the Tulijá River Basin (Chiapas, Mexico) using scatter plots, categorical statistics, descriptive statistics, and decomposing total bias. Additionally, bias correction was performed using the quantile mapping (QM) method. QM is a technique used to improve the fit of SPPs with respect to rainfall observations through a transfer function, aiming to reduce systematic errors in SPPs. The results indicate that the PDIR-Now product tends to overestimate rainfall to a large extent, thus showing better performance in detecting rain events. Meanwhile, PERSIANN-CCS underestimates precipitation to a lesser extent. The findings of this study demonstrate that correcting the bias of SPPs improves estimations of rainfall records, thereby reducing the percentage bias and root mean square error.

1. Introduction

Precipitation is one of the most critical processes for hydrology; it varies in amount, time, and space [1]. Therefore, monitoring it and having accurate and reliable information is essential to prevent natural disasters. Intense rainfall may lead to floods, endangering life and property, while very little rainfall can result in droughts, which impact agriculture and cause famine [2].

Accurate and timely measurements of precipitation are crucial for various applications, such as climate predictions, analysis of hydraulic infrastructure risk, agriculture, and water resource management [3,4].

Currently, there are three instruments for measuring precipitation: rain gauges, radars, and meteorological satellites [4,5]. Rain gauges and radars are ground-based observation methods with good temporal coverage but low spatial coverage and are mainly used in developing regions where observations by this method are very limited or unavailable [6]. On the other hand, satellite-based precipitation products (SPPs) have complete spatial coverage, even over remote regions, high altitudes, and oceans; however, they often have errors in rainfall estimation, with biases that must be corrected [7]. Sensors coupled with meteorological satellites take readings in various bands of the electromagnetic spectrum to estimate rainfall [8,9], using techniques ranging from visible (VIS) and infrared (IR) radiations to methods based on passive and active microwaves (MW) [10].

Each technique has its advantages and disadvantages. For example, MW-based estimates offer more precise rainfall estimation but have poor temporal coverage and low spatial resolution [2]. On the other hand, IR-based sensors have good temporal and spatial resolution, but the accuracy of rainfall estimation is poor [2,11]. Currently, some techniques combine information from IR and MW sensor bands to obtain SPPs with fewer limitations and take advantage of the benefits each sensor offers [10,11,12,13,14].

In recent years, different satellite precipitation products (SPPs) have been developed to estimate precipitation, such as (a) the Famine Early Warning Systems Network Rain Fall Estimation (FEWS-Net RFE) [15]; (b) Tropical Rainfall Measuring Mission (TRMM) sensor package [16]; (c) Climate Prediction Center (CPC) Morphing Technique (CMORPH) [17]; (d) Precipitation Estimates from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) [18]; (e) Multi-Source Weighted-Ensemble Precipitation (MSWEP) [19]; (f) Climate Hazards Group Infrared Precipitation with Station data (CHIRPS) [20]; (g) Global Satellite Mapping of Precipitation (GSMap) [21]; (h) Global Precipitation Climatology Centre (GPCC) [22]; (i) TRMM Multi-satellite Precipitation Analysis (TMPA) 3B42RT [23]; and (j) the Integrated Multi-satellite Retrievals for GPM (GPM IMERG) [24,25], among others.

During the last decade, various research groups have focused on evaluating the estimates of satellite precipitation products (SPPs). Rivera et al. [26] studied the accuracy of CHIRPS estimates in the Central Andes region of Argentina. The research objective was to quantify CHIRPS’ ability to represent spatial patterns of precipitation, seasonal variability, and interannual variability. The study demonstrated that CHIRPS adequately reproduces the abovementioned characteristics; however, the SPP performance is deficient in areas above 1000 m above sea level (m a.s.l). Similarly, Saeidizand et al. [27] analyzed the CHIRPS system’s performance for 2005–2014 in different regions of Iran, comparing it with rain gauge data. The results indicated that CHIRPS performs better in low-lying areas of the southern coast and during months dominated by convective rainfall.

In the Pacific slope region and the coast of Ecuador, Erazo et al. [28] employed a dense network of rain gauges to generate a monthly resolution product on a 5 × 5 km grid. This product was used to evaluate the performance of four SPPs (TRMM, GPCC, CRU, ERA-Interim Reanalysis). The study demonstrated that TRMM could adequately estimate the seasonal characteristics of rainfall, its quantity, and long-term climatological patterns, exhibiting better performance in low-lying areas. Lekula et al. [29] analyzed the Central Kalahari basin, Africa, to evaluate the daily rainfall detection capabilities of four SPPs with different spatial resolutions: (a) FEWS-NET RFE 2.0 (11 × 11 km); (b) TRMM-3B42 v7 (27 × 27 km); (c) CMORPH v1 (8 × 8 km); and (d) CMORPH v1 (27 × 27 km). The study assessed the spatiotemporal variability of rainfall and bias correction of the different SPPs. The results indicated that FEWS-NET RFE 2.0 showed the best performance. However, by decomposing the bias, they demonstrated that all SPPs underestimated precipitation. Finally, bias correction improved the correlation of SPP estimates with rain gauge records but increased the spatial variability of rainfall.

Another study in Africa (Ethiopia, Kenya, and Tanzania) was conducted by Dinku et al. [30], where they evaluated CHIRP and CHIRPS products (CHIRP combined with station observations) comparing them with 1200 rain gauges and 2 similar satellite rainfall products (ARC2 and TAMSAT). In this study, it was determined that the CHIRP and CHIRPS estimates are notably better than ARC2 on a monthly scale, while the performance of TAMSAT at a daily level is better; however, the different SPPs exhibit high spatial variability with weak performance in coastal and mountainous regions.

Given that the SPPs present errors, adjustment methods are applied to reduce systematic bias in these products. These biases are due to mistakes in sensors, retrieval algorithms, and variations depending on environmental characteristics, such as climate, seasons, geography, and topography [31]. Some of the methods used to correct biases in the SPPs include the delta method [32], linear scaling [33], power transformation of precipitation [34], quantile mapping [35], empirical quantile mapping [36], gamma quantile mapping [37], distribution mapping [37], and local intensity scaling of precipitation [38], among others.

Numerous studies have focused on bias correction to reduce systematic errors in satellite algorithms; for example, Gudmundsson et al. [39] used a regional climate model (RCM) and 82 rain gauges to evaluate different bias correction approaches through statistical transformations. Their results demonstrated that most statistical techniques are capable of removing biases. Grillakis et al. [40] proposed a new bias correction method of a general circulation model (GCM) and evaluated its performance through a calibration and validation procedure using cumulative distribution functions (CDF). The technique utilizes multiple segments of transfer functions along the observed and simulated precipitation CDFs. During calibration, they divided the raw model CDFs and observed data into N equally spaced segments on the CDF plot. They found that the proposed method performs well in validation and calibration periods.

Kim et al. [3] analyzed an improved bias correction technique during the seasons, considering the temporal distribution between observed and modeled data (HadRM3). Therefore, the correction was made according to the variation in rainfall characteristics (underestimation and overestimation events) between observed and modeled data. The results indicate that the proposed technique outperformed the conventional bias correction method. Worqlul et al. [41] achieved good results by applying a linear bias correction to the MPEG product, using the corrected data as input in a semi-distributed hydrological model to simulate discharge in two watersheds in Ethiopia. They concluded that using the corrected MPEG data resulted in flow simulation comparable to observed streamflows in both watersheds.

The quantile mapping (QM) method has been successfully implemented in correcting various satellite precipitation products (SPP) [42,43,44,45,46]. The QM method adjusts the precipitation distribution of the satellite product (SPP) with a reference distribution of rain gauge data using cumulative distribution functions (CDF) [47]. Some studies have shown that its performance improves when additional techniques are applied. For example, Ringard et al. [47] used the QM method in the Guiana Shield, dividing the area into different hydroclimatic zones based on precipitation time series with similar profiles. The study demonstrated the relevance of effectively applying the QM method. In a recent study, Katiraie-Boroujerdy et al. [31] evaluated and corrected the bias of PERSIANN-CCS in seven regions of Iran. They applied the QM method in each area using daily rain gauge data. The method was calibrated for eight years (2009–2016), and then the corrected PERSIANN-CCS data were validated with a dataset for the years 2017–2018. The results indicated improved PERSIANN-CCS estimates for calibration and validation periods at monthly, seasonal, and annual scales.

Studies reported in the literature highlight the need to assess the performance of SPPs and analyze potential improvements after bias correction. Therefore, the objectives of the present study are as follows: (a) to evaluate the capacity of monthly precipitation estimation and detection over the Tulijá River Basin (CRT) using the PERSIANN-CCS and PDIR-Now SPPs; (b) to perform bias correction of the two SPPs using the quantile mapping (QM) method; (c) to analyze if there is an improvement in the fit of estimated SPP data after applying bias correction using the QM method.

2. Study Area and Data

2.1. Study Area

The research focused on the Tulijá River Basin (TRB) up to the Salto de Agua hydrometric station in Chiapas, Mexico (CONAGUA code: 30042). The TRB drains an area of 3560.91 km² and it is located in the Grijalva–Usumacinta Hydrological Region (RH30) between parallels 16°40′N to 17°40′N and meridians 91°28′W to 92°32′W (Figure 1). The warm, humid climate predominates in most of the TRB, with a rainfall regime throughout the year. In the high mountains of the basin, at 1500 m a.s.l, the climate is semi-warm, and the most abundant rains occur there, with an average annual precipitation of 2500 to 4000 mm. However, in areas where the elevation is greater than 2000 m a.s.l, rainfall reaches more than 4000 mm per year. The rest of the basin usually has an annual rainfall between 1500 to 2000 mm. From May to October, precipitation ranges between 1500 mm and 2600 mm, while from November to April, precipitation ranges from 350 mm to 1400 mm.

The soil types present in the TRB are acrisol, cambisol, feozem, gleysol, litosol, luvisol, regosol, redzina, and vertisol. However, litosol is the most prevalent soil in the basin, occupying more than half of the total surface area. The average altitude in the TRB is 749.74 m a.s.l.

2.2. Data

Monthly precipitation records from rain gauges and two satellite precipitation products (SPP): PERSIANN-CCS and PDIR-Now, were used for the period from January 2004 to December 2014 (11 years).

2.2.1. Rain Gauges

Monthly precipitation data from 17 rain gauges within and near the TRB (

Table 1. Geographic characteristics and percentage of missing data from the rain gauges of the TRB.

Rain Gauge		Long (°W)	Lat (°N)	Elevation (m a.s.l)	Missing Data (%)
ID Rg	Name
C07001	Abosolo Chiapas	−92.22	16.83	1280	8.51
C07006	Altamirano	−92.06	16.74	1240	7.71
C07022	Playas de Catazaja	−92.02	17.73	10	7.59
C07028	Chacamax	−91.71	17.47	60	6.30
C07071	Guaquitepec	−92.29	17.14	1160	0.02
C07085	Palenque	−91.98	17.51	60	10.30
C07105	Las nubes	−92.34	17.51	93	9.50
C07114	Yaquintela	−91.73	16.91	650	2.36
C07126	Palenque (DGE)	−91.98	17.57	60	11.12
C07141	Salto de agua (DGE)	−92.33	17.57	10	0.02
C07169	Tumbala	−92.30	17.27	1063	3.48
C07177	Yajalon	−92.32	17.17	660	4.83
C07195	Sabanilla	−92.55	17.29	300	2.74
C07315	Paso del cayuco	−92.11	17.23	291	1.52
C07389	Sitala	−92.31	17.02	1100	0.75
C27004	Boca del cerro	−91.49	17.45	14	0.00
C27047	Tenosique	−91.43	17.47	22	3.21

) and administered by the National Water Commission (CONAGUA: https://smn.conagua.gob.mx (accessed on 1 December 2023)) were used. For some rain gauges, it was necessary to complete the data using the U.S. National Weather Service’s method [48] with neighboring rain gauges. Gallegos-Cedillo et al. [49] and Toro Trujillo et al. [50] mention that this method is viable because it can be used at any time step, and conclude that it is an efficient alternative for completing missing data information records. The rain gauge records were used as a reference to analyze the performance of the SPPs.

2.2.2. Rainfall Satellite-Based Products

The PERSIANN satellite products are developed by the Center for Hydrometeorology and Remote Sensing (CHRS) at the University of California, Irvine (UCI) and are available through the CHRS data portal (http://chrsdata.eng.uci.edu/ (accessed on 15 December 2023)). The PERSIANN product family consists of PERSIANN [18], PERSIANN-CCS [51], PERSIANN-CDR [7], PDIR-Now [52], and PERSIANN-CCS-CDR [53], each with different temporal and spatial resolutions (

Table 2. Characteristics of PERSIANN satellite precipitation products.

Product	Abbreviation	Spatial Resolution	Temporal Resolution	Data Period	Reference
PERSIANN-Cloud Classification System	PERSIANN-CCS	0.04° × 0.04°	Hourly, three-hourly, six-hourly, daily, monthly, yearly	January 2003–present	Hong et al. [51]
PERSIANN-Dynamic Infrared Rain Rate near-real-time	PDIR-Now	0.04° × 0.04°	Hourly, three-hourly, six-hourly, daily, monthly, yearly	March 2000–present	Nguyen et al. [52]
Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks	PERSIANN	0.25° × 0.25°	Hourly, three-hourly, six-hourly, daily, monthly, yearly	March 2000–present	Sorooshian et al. [18]
PERSIANN-Climate Data Record	PERSIANN-CDR	0.25° × 0.25°	Daily, monthly, yearly	January 1983–present	Ashouri et al. [7]
PERSIANN-Cloud Classification System-Climate Data Record	PERSIANN-CCS-CDR	0.04° × 0.04°	Three-hourly, six-hourly, daily, monthly, yearly	January 1983–present	Sadegui et al. [53]

).

For this research, the SPPs used were PERSIANN-CCS and PDIR-Now because they have the same spatial (0.04° × 0.04°) and temporal resolutions (1 h, 3 h, 6 h, daily, monthly, and annual), providing flexibility to perform analyses at various temporal resolutions according to the needs of the study. For this work, monthly precipitation data were used, aligning with the specific objectives of our research. Furthermore, to the authors’ knowledge, PERSIANN-CCS and PDIR-Now have not been used to evaluate the capacity for monthly precipitation estimation and detection over the TRB.

PERSIANN-Cloud Classification System (PERSIANN-CCS) is a product with a cloud categorization system based on patches using computer image technology and pattern recognition techniques. This system provides precipitation estimates based on satellite infrared images with a resolution of 0.04° × 0.04° in a 30 min time interval [51,54].

The Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks—Dynamic Infrared Rain Rate near-real-time (PDIR-Now) is an algorithm that primarily relies on IR data from GEO satellites. Using IR data, rainfall estimation is indirectly based on the relationship between cloud top temperature and the precipitation rate. PDIR-Now stands out for its ability to reduce estimation errors and biases, mainly through the dynamic curve shifting technique, which adjusts the curve position using monthly climatological rainfall data with a spatial resolution of 0.04° × 0.04° [52].

3. Methodology

For the evaluation of satellite-based precipitation products (SPP), the following data analysis techniques were employed: (a) scatter plots, (b) categorical statistics, (c) descriptive statistics, (d) bias decomposition, and (e) bias correction using the quantile mapping method (Figure 2). Data analysis was conducted by comparing the recorded precipitation from each rain gauge against its respective SPP pixel match (Figure 3). A rain gauge-to-pixel analysis was performed to compare the precipitation data from the rain gauges with the corresponding SPP pixel. Therefore, estimates of 17 pixels of the SPPs that coincide with the location of the rain gauges were selected.

3.1. Scatter Plots

Scatter plots were used to analyze the linear relationship between monthly rainfall data from rain gauges and SPP (PERSIANN-CCS and PDIR-Now). Each point represents the rainfall recorded by the rain gauge (X-axis) and the SPP (Y-axis).

3.2. Categorical Statistics

Categorical statistics [55] are used to evaluate the performance of satellite products in rainfall detection. These statistics are calculated from a contingency table using reference thresholds (

Table 3. Contingency table to compare rain gauge records and satellite precipitation products.

	Rain Gauge ≥ Threshold	Rain Gauge < Threshold
Satellite ≥ Threshold	H	F
Satellite < Threshold	M	C

) involving four possible event combinations [56,57]: hit (H), false alarm (F), miss (M), and correct negative (C). In this study, monthly rainfall thresholds of 1, 50, 100, 150, 200, and 300 mm were used to assess the performance of the SPP.

The probability of detection (POD) measures the frequency where the SPP correctly estimates rainfall events measured by the rain gauge [58,59]. On the other hand, the false alarm rate (FAR) evaluates the number of events where the SPP detects precipitation, but there is no record by the rain gauge [58,59]. The critical success index (CSI) represents the events where the SPP has correctly estimated rainfall, considering false alarms compared to POD [29,56], and the frequency bias index (FBI) indicates systematic differences in rainfall event frequency based on the SPP and shows whether there is a tendency to underestimate (FBI < 1) or overestimate (FBI > 1) rainfall events [26,55] (

Table 4. Information on the categorical and descriptive statistics used for the evaluation of SPPs at the monthly scale.

	Statistic	Equation	Range	Best Value
Categorical statistics	Probability of detection	$\mathrm{P}\mathrm{O}\mathrm{D}=\frac{\mathrm{H}}{\mathrm{H}+\mathrm{M}}$	0 to 1	1
	False alarm ratio	$\mathrm{F}\mathrm{A}\mathrm{R}=\frac{\mathrm{F}}{\mathrm{H}+\mathrm{F}}$	0 to 1	0
	Critical success index	$\mathrm{C}\mathrm{S}\mathrm{I}=\frac{\mathrm{H}}{\mathrm{H}+\mathrm{F}+\mathrm{M}}$	0 to 1	1
	Frequency bias index	$\mathrm{F}\mathrm{B}\mathrm{I}=\frac{\mathrm{H}+\mathrm{F}}{\mathrm{H}+\mathrm{M}}$	0 to ∞	1
Descriptive statistics	Pearson correlation coefficient	$\mathrm{P}\mathrm{C}\mathrm{C}=\frac{\sum \left(\mathrm{G}\mathrm{a}\mathrm{u}-\overline{\mathrm{G}\mathrm{a}\mathrm{u}}\right)\left(\mathrm{S}\mathrm{a}\mathrm{t}-\overline{\mathrm{S}\mathrm{a}\mathrm{t}}\right)}{\sqrt{{\left(\mathrm{G}\mathrm{a}\mathrm{u}-\overline{\mathrm{G}\mathrm{a}\mathrm{u}}\right)}^2}\sqrt{{\left(\mathrm{S}\mathrm{a}\mathrm{t}-\overline{\mathrm{S}\mathrm{a}\mathrm{t}}\right)}^2}}$	−1 to 1	−1 or 1
	Mean absolute error	$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{\mathrm{N}}\sum \left(\left|\mathrm{S}\mathrm{a}\mathrm{t}-\mathrm{G}\mathrm{a}\mathrm{u}\right|\right)$	0 to ∞	0
	Root mean square error	$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{\mathrm{N}}\sum {\left(\mathrm{S}\mathrm{a}\mathrm{t}-\mathrm{G}\mathrm{a}\mathrm{u}\right)}^2}$	0 to ∞	0
	Percent bias	$\mathrm{P}\mathrm{B}=100\frac{\sum \left(\mathrm{S}\mathrm{a}\mathrm{t}-\mathrm{G}\mathrm{a}\mathrm{u}\right)}{\sum \mathrm{G}\mathrm{a}\mathrm{u}}$	−∞ to ∞	0

Note. Gau = Rain gauge observations (mm), $\overline{\mathrm{G}\mathrm{a}\mathrm{u}}=$ average rain gauge observations (mm), $\mathrm{S}\mathrm{a}\mathrm{t}=$ SPP estimates in the analyzed pixel (mm), $\overline{\mathrm{S}\mathrm{a}\mathrm{t}}=$ average SPP estimate (mm) y N = number of data pairs. H, M and F are defined in Table 3.

).

3.3. Descriptive Statistics

Descriptive statistics measure how SPP estimates differ from rain gauge values. The following statistics were used to evaluate the SPP’s performance in rainfall estimation: Pearson correlation coefficient (PCC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Percent Bias (PB) (Table 4).

PCC measures the linear relationship between SPP estimates and rain gauge observations [26]; MAE is the average magnitude of absolute errors between SPP and rain gauges [29,60]; while RMSE is the square root of the mean squared differences (errors) between SPP and rain gauges [29,60]. Percent Bias (PB) determines the average trend of the SPP; positive values indicate overestimation, and negative values indicate underestimation [26].

3.4. Bias Decomposition

An optimal way to learn more about the origin of SPP errors is to decompose the total bias (TBc—Equation (1)) into three components: hit bias (HB—Equation (2)), miss bias (MB—Equation (3)), and false bias (FB—Equation (4)). Total bias is based on the sum of differences in precipitation intensity over the entire study period (2004–2014) [29,61,62]. The three components of bias, as well as total bias, are presented below:

$$\mathrm{T}\mathrm{B}\mathrm{c}=\sum \mathrm{S}\mathrm{a}\mathrm{t}-\mathrm{G}\mathrm{a}\mathrm{u}$$

(1)

$$\mathrm{H}\mathrm{B}=\sum \left(\mathrm{S}\mathrm{a}\mathrm{t}-\mathrm{G}\mathrm{a}\mathrm{u}\right);(\mathrm{G}\mathrm{a}\mathrm{u}>0\&\mathrm{S}\mathrm{a}\mathrm{t}>0)$$

(2)

$$\mathrm{M}\mathrm{B}=-\sum \mathrm{G}\mathrm{a}\mathrm{u};\left(\mathrm{S}\mathrm{a}\mathrm{t}=0\&\mathrm{G}\mathrm{a}\mathrm{u}>0\right)$$

(3)

$$\mathrm{F}\mathrm{B}=\sum \mathrm{S}\mathrm{a}\mathrm{t};\left(\mathrm{S}\mathrm{a}\mathrm{t}>0\&\mathrm{G}\mathrm{a}\mathrm{u}=0\right)$$

(4)

A negative HB value indicates that the SPP underestimates rainfall, while a positive value suggests overestimation. On the other hand, MB is always negative, representing the total rainfall volume that the SPP did not detect but that was recorded by the rain gauge. Conversely, FB is always positive, indicating the total volume of rainfall erroneously detected by the SPP.

3.5. Bias Correction: Quantile Mapping

The quantile mapping (QM) method was used for bias correction of the SPP (PERSIANN-CCS and PDIR-Now) at a monthly level. Quantile mapping involves establishing a functional relationship between the quantiles of the observed dataset and the quantiles of the simulated or, in our case, satellite datasets. This relationship essentially maps or aligns the quantiles of the satellite products’ values to the corresponding quantiles of the observed precipitation at the gauging stations. The QM method adjusts the monthly satellite precipitation distribution (P_s) to the monthly rain gauge precipitation distribution (P_g) using a transfer function (h) [37,39,47]. QM seeks a transformation of a modeled variable P_s so that its new distribution is identical to that of the observed variable P_g.

$${\mathrm{P}}_{\mathrm{g}}=\mathrm{h}\left({\mathrm{P}}_{\mathrm{s}}\right)$$

(5)

If the variable of interest has a known distribution, the transformation is defined as follows:

$${\mathrm{P}}_{\mathrm{g}}={\mathrm{F}}_{\mathrm{g}}^{-1}\left({\mathrm{F}}_{\mathrm{S}}\left({\mathrm{P}}_{\mathrm{s}}\right)\right)$$

(6)

where F_s is the cumulative distribution function (CDF) of P_s and F_g⁻¹ is the inverse CDF of P_g. Various parametric transformations were used to calculate the CDFs.

Given the pronounced seasonality of rainfall in the study area (CRT), a comprehensive frequency analysis was conducted at a monthly level. This resulted in 12 samples, each corresponding to a specific month of the study period (2004–2014). The goodness-of-fit test, based on the Kolmogorov–Smirnov test, was then employed to identify the distribution that most accurately represents the monthly data. Our study found that the gamma function with two parameters is the best fit. Numerous studies have also confirmed the suitability of the gamma function for the probability density distribution of precipitation [63]. Hence, the gamma distribution parameters were calculated using the method of moments.

The method of moments uses the gamma distribution of the modeled variable satellite data distribution (P_s) with the shape parameter “k” and the scale parameter “θ”, to estimate the mean (µ) and variance (σ²) of its new distribution adjusted to the monthly rain gauge precipitation distribution (P_g), as follows:

$$\mathsf{\mu }=\mathrm{k}\times \mathsf{\theta }$$

(7)

$${\sigma }^2=k\times {\theta }^2$$

(8)

4. Results

The detailed assessment of precipitation patterns is paramount in the river basin studied here, as a good understanding of hydrological processes might prove useful for water resource management, flood prediction, and ecosystem conservation. Moreover, precipitation serves as a primary driver of surface water availability, influencing the timing and magnitude of streamflow, groundwater recharge, and overall basin hydrology. In this context, variations in precipitation distribution can have profound implications for both natural and human environments. By conducting meticulous research on precipitation patterns, spatial and temporal distributions can be uncovered by employing a comprehensive statistical framework to analyze and compare measured precipitation data collected from ground-based rain gauges with precipitation estimates derived from satellite products. However, the integration of these disparate sources demands rigorous statistical treatment to ensure the reliability and comparability of the results. In this study, by subjecting these datasets to robust statistical analyses, we aim to discern patterns, trends, and potential discrepancies between the two sources, thereby enhancing our understanding of precipitation dynamics and improving the accuracy of precipitation assessments.

4.1. Graphic Comparison of Rain Gauges and SPPs (Scatter Plots)

In order to assess the accuracy and reliability of precipitation estimates retrieved from satellite products, it is essential to examine the correlation between these derived values and ground-based measurements. In the following scatter plot interpretation, we analyze the relationship between measured precipitation data and corresponding values of the SPPs. This analysis aims to elucidate the degree of agreement or discrepancy between the two datasets, shedding light on the effectiveness of satellite-derived precipitation estimates in capturing real-world conditions. Through visual examination of Figure 4 and Figure 5, it becomes evident that the correlation between satellite precipitation products (SPPs) and measurements obtained from rain gauges exhibits variability across the range of analyzed gauges. Both SPPs show satisfactory results for different rain gauges. However, PDIR-Now exhibits a better linear relationship (Figure 5) than PERSIANN-CCS (Figure 4). In the present investigation, the trend line shows that PERSIANN-CCS underestimates monthly precipitation while PDIR-Now overestimates it.

4.2. Performance of SPPs Based on Categorical Validation Statistics

After exploring the relationship between the measured (rain gauge) and estimated precipitation (derived from SPPs), in order to understand the frequency of occurrence of the rainfall events, categorical statistics were employed. The evaluation of the SPPs performance was performed by means of different thresholds (1, 50, 100, 150, 200, and 300 mm/month), as shown in the Figure 6. In categorical statistics, the hit (H) and miss (M) are the best criteria for evaluating the performance of the SPPs, since hits indicate that the product detects the amount of rainfall recorded by the rain gauge, and misses show the rainfall recorded by the rain gauge but not detected by the SPP. This demonstrates the sensitivity of the SPP in rainfall detection. The POD statistic relates to the events above, as it is inversely dependent on M and moderated by H (since H appears in the numerator and denominator). A higher POD score indicates better SPP performance. Similar POD behavior is observed in other products, like PERSIANN-CCS and PDIR-Now, since they both have a score close to one at the smallest threshold (1 mm/month).

However, PDIR-Now outperforms PERSIANN-CCS in correctly detecting rainfall events across all thresholds, as its score was close to 0.80 for all of them, while PERSIANN-CCS presented scores close to 0.70 across different thresholds. The ideal value for FAR is zero, meaning no events occurred where the SPP detected rainfall, but the rain gauge did not record rainfall. Figure 6 shows a constant increase in the FAR value for both SPPs as the threshold increases. This indicates that as the threshold grows, more events occur where the SPPs detect rainfall. However, either no rainfall occurred, or the SPPs detected more precipitation than recorded by the rain gauges. In this case, PERSIANN-CCS performs better, as it maintained a relatively low score at thresholds below 150 mm/month.

Regarding CSI, in the PDIR-Now product, the score is slightly higher, but overall, both PERSIANN-CCS and PDIR-Now showed better results at thresholds below 100 mm/month, while at thresholds above this, the score deviates from the ideal score (one). Regarding FBI, both products exhibit both underestimation and overestimation events. For PDIR-Now, overestimation is more noticeable, occurring at thresholds above 150 mm/month, while for PERSIANN-CCS, it occurs exclusively at the largest threshold (300 mm/month).

According to categorical statistics, PDIR-Now better detects monthly rainfall than PERSIANN-CCS, as it presents higher scores. PDIR-Now’s good performance is mainly due to reducing errors and biases using monthly climatological data [52].

4.3. Performance of SPPs Based on Descriptive Validation Statistics

Descriptive statistics are summarized in box and whisker plots (Figure 7), which graphically represent the distribution of the scores for the 17 analyzed rain gauges. For PCC, the ideal score is 1; PDIR-Now presents a higher score in most rain gauges, with 75% of them surpassing a score of 0.70. However, one station showed a relatively low score (0.58). The closer the MAE and RMSE values are to zero, the better the SPP performance. The MAE and RMSE values of PDIR-Now from our study are very high, indicating a considerable difference between the SPP estimates and rain gauge records. PERSIANN-CCS shows similar results, albeit to a lesser extent, as 75% of the rain gauges score below 50 for MAE. PERSIANN-CCS underestimates most rain gauges for PB, with 75% scoring below zero. Conversely, PDIR-Now presents positive values (overestimation) in most rain gauges, reinforcing previous statistics. Following the analyses carried out so far, it was found that PDIR-Now performs better in PCC; however, overestimating precipitation causes the MAE and RMSE to have large values.

4.4. SPPs Bias Decomposition

For a quantitative and continuous analysis of the performance of the SPPs for the entire, complete sample (2004–2014), the total bias was decomposed into hit biases (HB), miss biases (MB), and false biases (FB). Figure 8 presents the various biases of the two SPPs (PERSIANN-CCS and PDIR-Now) as the total amount of rainfall over the eleven-year study period. A quick inspection of Figure 8 shows that the PDIR-Now biases are higher.

The TBc shows negative values (underestimation) and positive values (overestimation) of the SPPs. According to the above, PERSIANN-CCS presents biases in a lesser proportion and underestimates rainfall (values below zero, Figure 8) compared to PDIR-Now, which overestimates rainfall in all rain gauges except for rain gauge C7001. Additionally, graphically, it is observed that the difference between what is recorded by the rain gauges and what is estimated by PDIR-Now is larger. This could be a problem when using this data for different purposes, such as flood forecasting, drought monitoring, or agricultural planning. Therefore, it is essential to correct the biases (errors) that occur in the SPP and evaluate them to determine their performance once corrected.

The MB occurs when the SPP does not detect precipitation, but the rain gauge records it. For this case, the accumulated precipitation of PDIR-Now is less than that of PERSIANN-CCS. This reinforces previous statistical results: PERSIANN-CCS has unfavorable performance detecting rain events. This may be related to the fact that when rain is forming, the top of the cloud has yet to reach the temperature threshold for detecting rain. Therefore, the rain will not be recorded or will be recorded later, which will cause an underestimation of rainfall [29].

Regarding false biases (FB), the two SPPs present a smaller amount of erroneous rain detection, that is, occasions when the satellite detects rain, but the rain gauge does not. Decomposing the bias and, in particular, carrying out an analysis of its components individually has specific uses because it quantitatively evaluates the SPP, providing practical information to validate the SPP, particularly analyzing how the MB and the FB affect the total bias (TBc) [29].

4.5. Bias Correction: Quantile Mapping

Bias correction was performed using the quantile mapping (QM) method. The QM method was applied monthly to the SPPs (PERSIANN-CCS and PDIR-Now) to reduce systematic error over the Tulijá River Basin. Cumulative distribution functions (CDF) calculation was based on the two-parameter gamma function. Figure 9 and Figure 10 show the CDFs before and after the bias correction of the SPPs (PERSIANN-CCS and PDIR-Now) corresponding to the reference rain gauge for the entire study period. They also display the corrected estimates of satellite products using the QM method. The two-parameter gamma distribution function fits the rainfall records.

Figure 11 and Figure 12 present the scatter plots of PERSIANN-CCS and PDIR-Now, respectively. It is observed that the QM method improved the linear relationship between the SPPs and the rainfall records. For example, at rain gauge C7001, before correction for PERSIANN-CCS, the R² is 0.55, and for PDIR-Now, 0.51; after bias correction, the R² value increased to 0.70 for both SPPs. This improvement was observed for most of the rain gauges.

The categorical statistics of the two SPPs before and after bias correction are presented in Figure 13. The results indicate that in both corrected SPPs, the POD scores are equal across all thresholds. Figure 13 shows that PERSIANN-CCS had a more pronounced improvement than PDIR-Now. Rainfall detection was poorer for both SPPs at the 300 mm/month threshold. The FAR remained at the same score at different thresholds before bias correction, except for the largest threshold (300 mm/month), where a decrease in value could be observed for both SPPs.

The CSI shows a similar trend before bias correction, with a decreasing score as the threshold increases. However, a slight improvement can be seen after applying the bias correction to both SPPs. The FBI for both corrected SPPs remained at a value of 1 (ideal score) for all thresholds, except at the 300 mm/month threshold with a value of 0.90, indicating underestimation by both SPPs.

Descriptive statistics (PCC, MAE, RMSE, and PB) with the values of the SPPs before and after bias correction by the QM method are presented in Figure 14. It is observed that the PCC increased in all rain gauges for both SPPs; this behavior is more noticeable for PERSIANN-CCS. Similarly, after bias correction, the MAE and RMSE scores decreased, meaning that the values of the SPPs are more similar to those recorded by the rain gauges.

Furthermore, the percent bias (PB) decreased significantly for both SPPs after bias correction. Figure 14 shows that for PERSIANN-CCS, the range of PB values is between −6.4 and 0.0, while for PDIR-Now, it is from −3.8 to 1.5. Also, it was found that there are more cases of underestimation even for PDIR-Now, which, before bias correction, overestimated rainfall and had large scores. Finally, the results show that bias correction by the QM method improves the linear relationship between the SPPs and the monthly rain gauges.

When decomposing the bias of the estimates corrected by QM, it is observed how the accumulated precipitation decreased significantly for both SPPs. For PERSIANN-CCS, the TBc values are negative (underestimation) in most rain gauges except for rain gauge C07141. Before bias correction, the range of values was from −11,030 mm to 3158 mm, and after correction, the values ranges between −1405 mm and 395 mm. On the other hand, PDIR-Now tends to underestimate rainfall to a lesser extent after bias correction (Figure 15). Before bias correction, the range of TBc values was between −1646 mm and 12,492 mm; however, once the bias correction was performed, the TBc scores ranged from −881 mm to 555 mm. When applying bias correction to SPPs using the quantile mapping (QM) method, the corrected estimates showed a better linear relationship with rainfall records. Analyzing the bias decomposition, it was found that both products underestimate precipitation in most rain gauges but to a lesser extent for accumulated precipitation. Therefore, the results indicated that the method works best in reducing the difference in precipitation volume between the estimated and recorded values.

5. Discussion

This study evaluated the efficiency of two SPPs for precipitation estimation and detection over the Tulijá River Basin in Mexico. Categorical and descriptive statistics were employed, along with an analysis of bias decomposition.

Previously, the performances of various SPPs have been evaluated in different regions worldwide [64,65,66,67,68]. It is important to assess the performance of various SPPs in different geographic regions, as each region exhibits different behavior. Cánovas-García et al. [69] evaluated the accuracy of PERSIANN-CCS for three extreme precipitation events in the southeastern Iberian Peninsula. They found that the SPP does not perform well for real-time monitoring, presenting the issue of underestimating high precipitation intensities. Conversely, Dehaghani et al. [70] found that PERSIANN-CCS performs well in detecting the occurrence and non-occurrence of precipitation but overestimates precipitation for different elevations in Iran. According to Nguyen et al. [71], PERSIANN-CCS overestimates extreme rainfall depending on the geographic region and underestimates precipitation in Europe.

In the literature, it has been found that PERSIANN-CCS tends to present overestimations or underestimations of precipitation depending on the geographic region [69,70]. In the present investigation, the trend line shows that PERSIANN-CCS underestimates monthly precipitation, while PDIR-Now overestimates it. Huang et al. [72] obtained similar results; they evaluated PERSIANN products and concluded that all the products tend to underestimate rainfall, except for two relatively new products (PDIR-Now and PERSIANN-CCS-CDR), which perform well at different temporal scales. Huang et al. [72] demonstrated that PDIR-Now performs well in quantitatively estimating precipitation at interannual, annual, and seasonal temporal scales in Taiwan.

Regarding the metrics of categorical statistics (POD, FAR, CSI, and FBI), both SPPs showed a good rainfall detection performance (POD). However, the performance of PDIR-Now is relatively better at all thresholds (intense or weak rains). In the case of PERSIANN-CCS, it performs better at thresholds greater than 200 mm/month. On the other hand, with the FBI (frequency bias), it was observed that PDIR-Now overestimates thresholds greater than 150 mm/month and underestimates lower thresholds. Likewise, PERSIANN-CCS underestimates small and large thresholds, only presenting underestimation at very large thresholds (300 mm/month). Similarly, Eini et al. [73] evaluated all PERSIANN family SPPs in Poland and, according to the POD, FAR, and CSI statistics, they concluded that different products could accurately detect precipitation events. They also mentioned that PERSIANN-CDR and PDIR-Now correlate better than other PERSIANN SPPs. This can be related to PDIR-Now reducing errors and biases by using monthly climatological data [52]. The results of Eini et al. [73] agree with another study conducted in Luzon (Philippines), which observed that PERSIANN-CDR has a better ability to qualitatively and quantitatively estimate spatiotemporal variations of monthly precipitation [74].

Gunathilake et al. [75] analyzed the estimates of three satellite products (PERSIANN, PERSIANN-CCS, and PDIR-Now) for use in the HEC-HMS hydrological model. They found that PERSIANN performed better and indicated the need to refine the rainfall retrieval algorithms by PERSIANN products in tropical areas.

When applying bias correction to SPPs using the quantile mapping (QM) method, the corrected estimates showed a better linear relationship with rainfall records. However, the results indicated that the method performs better at reducing the precipitation volume difference between the estimated and recorded values. It is essential to mention that the amount of rain gauge data used in the corrections can significantly influence further reducing the often present biases. Furthermore, bias correction is more accurate when applied to the pixel corresponding to the specific rain gauge. The absence of a dense network of rain gauges limits the ability to validate and verify the accuracy of the corrections. In conclusion, the accuracy of the SPP bias correction decreases with increasing distance from the reference rain gauges. Serrat-Capdevila et al. [45] found that the QM method succeeds in reducing and eliminating mean square error and variance but does not correct correlation error. According to Katiraie-Boroujerdy et al. [31], the QM technique is effective in correcting biases in the PERSIANN-CCS product at aggregated scales, such as monthly, seasonal, and yearly, depending on the availability of rain gauge observations. Therefore, Ringard et al. [47] defined hydroclimatic homogeneous areas with low precipitation variability to estimate parameters for correcting SPP biases. They concluded that the quality of the bias correction is likely to be high because it is applied to similarities in data sharing under hydroclimatic conditions. Therefore, it has been demonstrated that satellite precipitation products (SPPs) are highly useful for complementing or providing rainfall information, particularly in less developed countries due to the need for rain gauge data. However, evaluating, comparing, and validating SPPs is essential, as they present biases.

6. Conclusions

In Southeast Mexico, extreme events related to floods occur, resulting in damage to agriculture, livestock, and infrastructure, economic losses, and thousands of affected inhabitants. Hence, monitoring and accurate precipitation information are essential to make forecasts for preventing natural disasters.

The main objective of this research was to evaluate the performance of PERSIANN-CCS and PDIR-Now SPPs against the records of 17 rain gauges over the Tulijá River Basin (TRB) in the southeast of Mexico. The ability of the two SPPs to detect precipitation was tested at a monthly level for the period 2004–2014 (11 years). Scatter plots and various statistical metrics (categorical statistics, descriptive statistics, and bias decomposition) were employed. The quantile mapping (QM) technique was applied to correct the bias of the two SPPs, calculating the cumulative distribution functions (CDF) with the two-parameter gamma function. Through scatter plots and statistical metrics, it is shown that the method performs well in improving the linear relationship between the corrected SPP data and the rain gauge observations.

PERSIANN-CCS and PDIR-Now are products that estimate rainfall with IR sensors from GEO satellites in near-real-time, providing information every 30 min. Their main advantage is their high temporal resolution. However, their performance is limited because they do not measure rainfall but estimate it indirectly.

The main findings of this study are as follows:

• The SPPs show a good relationship with rain gauge records at the monthly level. Graphically, through scatter plots and with the help of a 1:1 line, the linear relationship between the data were evaluated, finding both overestimations and underestimations by the two SPPs, although PDIR-Now presents higher overestimation. Regarding the metrics of the categorical statistics (POD, FAR, CSI, and FBI), the performance of PDIR-Now is relatively better at all thresholds (intense or weak rains).
• The error of each SPP can be better understood by decomposing the total bias (difference in accumulated precipitation) of the SPPs and the rain gauges. It was indeed found that PDIR-Now tends to overestimate rainfall in large quantities. In contrast, PERSIANN-CCS underestimates it to a lesser extent. Therefore, it is demonstrated that both SPPs perform poorly in capturing the total volume of monthly rainfall over the TRB.

By applying the QM method, it can be observed that the linear relationship between the precipitation recorded by the rain gauge and that estimated by the SPPs increased. However, the decomposition of the bias shows that the difference in the volume of rain between the SPPs and that recorded by the rain gauges is considerably reduced. Finally, it is concluded that both products underestimate rainfall in most rain gauges, but to a lesser extent in accumulated precipitation at the monthly level. The products’ performance was evaluated at a monthly level because other authors have found that when comparing SPP estimates with rain gauge data on smaller time scales, the bias is greater [29,71]. However, these decrease when analyzed at monthly time scales because temporal data accumulates. Therefore, evaluating the satellite product on a monthly level provides us with a good view of its behavior.

The results can help understand the uncertainty of satellite precipitation estimates for studying monthly rainfall variations in Southeast Mexico. However, it would be interesting to carry out further analyses to observe the behavior of SPPs in Southeast Mexico. For example, we could evaluate other variables, such as elevations, seasons, or climatic regions, apply other bias correction methods, or combine these with the quantile mapping method.