Rainfall Intensity–Duration–Frequency Curves Dataset for Brazil

Abstract

This is a database containing rainfall intensity–duration–frequency equations (IDF equations) for 6550 pluviographic and pluviometric stations in Brazil. The database was compiled from 370 different publications and contains the following information: station identification, geographic position, size and period of the rainfall series used, parameters of the IDF equations, and literature references. The database is available on Mendeley Data (DOI: 10.17632/378bdcmnc8.1) in the form of spreadsheets and vector files. Since the launch of the Pluvio 2.1 software in 2006, which included 549 IDF equations obtained in the country, this is the largest and most accessible database of IDF equations in Brazil. The data provided may be useful, among other purposes, for designing hydraulic structures, controlling water erosion, planning land use, and water resource planning and management.

Dataset: https://doi.org/10.17632/378bdcmnc8.1

Dataset License: CC-BY

1. Summary

Quantifying heavy rainfall and knowing how it spreads spatially and temporally is extremely important for water resource planning and hydraulic design, such as rainwater drainage structures and erosion control systems.

Since these data are currently dispersed and not available to all potential users, a compilation of an extensive point dataset of Brazilian IDF curves can be used as a reference for scientists and technical staff who deal with urban water systems, dam design, soil erosion control, watershed management, and water resources planning.

The first attempt to compile the information on IDF curves in Brazil was made with the Pluvio 2.1 software, in 2006, and included information from 549 locations, while the present database has information from 6550 locations (around 1000% more).

Regions previously without IDF equations now have them, which can help in the design of hydraulic structures, erosion control, land use planning, and water resource management.

2. Background

Heavy rainfall is associated with high rainfall depths in a short period. Such rainfall can cause considerable negative impacts on the environment and human activities, such as water erosion, flooding, the failure of hydraulic structures, and damage to agricultural production, among others [1].

The correct quantification of this type of rainfall is extremely important for several environmental applications, such as the design of hydraulic structures, land use planning, water resource management, and prediction of environmental disasters. In this context, the importance of knowing the equations for intense rainfalls, also known as intensity–duration–frequency (IDF) equations, stands out, according to the general equation below [2,3].

$${\mathrm{i}}_{\mathrm{m}}={\displaystyle \frac{\mathrm{K}{\mathrm{T}}^{\mathrm{a}}}{{\left(\mathrm{d}+\mathrm{b}\right)}^{\mathrm{c}}}},$$

(1)

in which i_m is the maximum rainfall intensity in mm h⁻¹; T is the rainfall return period (average time interval between exceedances of the maximum intensity value) in years; d is the duration of rainfall in minutes; and K, a, b, and c are statistical adjustment parameters obtained for each location with the availability of pluviographic and/or pluviometric data.

To adjust the IDF equations according to the standard method, a relatively long series of sub-daily rainfall records, measured at a pluviographic station, is required [4]. Such stations are scarce in Brazil. Alternatively, these equations can be adjusted by disaggregating the maximum daily rainfall from rainfall records [5].

Despite its importance, the information on IDF equations in Brazil is scattered in the literature and needs to be systematized in a single database. The first attempt to systematize the IDF equations was made in 2006, using the Pluvio 2.1 Software, which had 549 equations for Brazil. Since then, several studies have established new IDF equations for Brazil, making it necessary to compile the information available in the literature again.

From the above, the dataset described here aimed to systematize, in a single open-access database, the IDF equations established for Brazil.

3. Methods

The study consisted of compiling IDF equations established specifically for Brazil. The equations were compiled through an in-depth literature review including scientific articles, theses, reports, and books that established and/or made available equations for heavy rainfall in Brazil. The search for the papers was carried out with the help of the Web of Science, Science Direct, Scopus, SciELO, and Google Scholar platforms, in addition to technical reports, theses and dissertations not published in journals.

Studies that established equations using the standard method with sub-daily rainfall records and with the alternative pluviometric disaggregation method (rainfall records of maximum daily rainfall) were considered. It should be noted that equations established using disaggregation do not replace those established using pluviographic records. However, they are a viable alternative in the absence of pluviographic information.

4. Data Description

This study gathered IDF equations for 6550 Brazilian stations (Figure 1), for which IDF equations have been established, both through pluviographic records and by the disaggregation of pluviometric data. A total of 711 equations were established with pluviographic records (standard method) and 5839 were established with pluviometric data (disaggregation). The parameters of these equations came from 370 different literature sources.

The equations obtained based on pluviographic records originated from 133 different studies, whose average length of the pluviographic series used for their establishment is 16 years; however, this length is quite variable (3 to 58 years). The equations originating from disaggregation coefficients applied to the pluviometric series came from 244 different publications. Regarding the length of the series, the minimum period observed is 4 years, and it is not possible to infer the average or maximum since most of the studies indicate that the length of the series is greater than 15 or 25 years. Although compiled in the dataset, the use of IDF equations established with very a short rainfall series should be avoided.

The standard procedure outlined in [6] was employed in all the studies that developed equations from sub-daily (pluviographic) data. This procedure considers an annual series of maximum rainfall intensities corresponding to various durations, for example, 10, 20, 30, 40, 50, 60, 120, 180, 240, 360, 720, and 1440 min. For each rainfall duration (d), the maximum average rainfall intensity (i_m) is estimated for a range of return periods, namely 2, 5, 10, 20, 50, and 100 years. The estimation of i_m utilizes a probability distribution function, which is selected based on the results of a goodness-of-fit test—either the Kolmogorov–Smirnov, Chi-squared, Filliben, or Anderson–Darling test [7]. The probability distribution functions most frequently utilized include Gumbel, two-parameter Log-Normal, three-parameter Log-Normal, three-parameter Pearson, three-parameter Log Pearson, and Generalized Extreme Value. Finally, using the i_m for different durations and return periods, the parameters of Equation (1) (K, a, b, and c) are estimated using nonlinear least squares solving algorithms, such as the Gauss–Newton method [8].

A similar approach was employed in all the studies that established the IDF equations using daily precipitation data (pluviometric data). The only distinction lies in the application of a disaggregation method, which converts the series of daily maximum depths into maximum rainfall intensities corresponding to various durations (10, 20, 30, 40, 50, 60, 120, 180, 240, 360, 720, and 1440 min). The maximum daily depths are transformed into shorter duration rainfall using the method of relations between rainfall of different durations (rrdd). This method utilizes coefficients to adjust the daily rainfall amounts, converting them into sub-daily rainfall depths and, ultimately, into maximum rainfall intensities associated with the specified durations [7].

The data available in Mendeley Data [9] were organized to ease the access to detailed information about the stations. They are presented in the .xlsx format for spreadsheets (tables) and .gpkp, .shp, .json, and point vector files for use in a GIS environment. The spreadsheets are stored in the folder “1—Datasheets (XLSX file)”, while the vectors are in the folders “2—GIS Vector file (geopackage)”, “3—GIS Vector files (shapefile)”, and “4—GIS Vector files (geojson)”, with one for each file type.

In the folder “1—Datasheets (XLSX file)”, there is only one file called “IDF_Curves_Brazil.xlsx”. This file contains three spreadsheets: Standard, Disaggregation, and Reference list. The first two contain the information relevant to the stations and their respective IDF equations. The Reference list spreadsheet contains a list of all the literature references of the studies that gave rise to the compiled equations. The information contained in the columns of the Standard and Disaggregation spreadsheets is presented in

Table 1. Information on each column of the spreadsheets and vector files containing the IDF equations for Brazil.

Column Name	Content
State	State in which the station is located
Agency	Agency responsible for operating the station
Code	Code assigned to the station by the Agency
Name	Name given to the station
Latitude (°)	Latitude in degrees
Longitude (°)	Longitude in degrees
Altitude (m)	Altitude in meters
Start year	The first year of the series (pluviometric or pluviographic) used to establish the equation
End year	The last year of the series (pluviometric or pluviographic) used to establish the equation
Years	Number of years in the series used to establish the equation
K	Value assigned to parameter K (Equation (1))
a	Value assigned to parameter a (Equation (1))
b	Value assigned to parameter b (Equation (1))
c	Value assigned to parameter c (Equation (1))
R2	Coefficient of determination of the established equation
Duration range	Range of rainfall duration for which the equation is valid
Reference	Literature reference of the source work, expressed through code associated with the “Reference list” spreadsheet
Disaggregation coefficients *	Type of disaggregation coefficient used: general (established, in general, for any location), national (established for the entire country), regional (established for the state or region of the station), local (established for the station itself), or no information (not reported in the work)
Disaggregation reference *	Literature reference of the work from which the disaggregation coefficients originated, expressed through exposed code associated with the “Reference list” spreadsheet

* columns present only in the “Disaggregation” spreadsheet.

.

In the folder “2—GIS Vector file (geopackage)”, there is only one file called “IDF_Curves_Brazil.gpkg”. This file, in geopackage format, contains two point vectors and a table. The table contains the “Reference list”, previously mentioned. The two point vectors refer to the stations contained in the Standard and Disaggregation spreadsheets, with the same information listed in Table 1.

The folders “3—GIS Vector files (shapefile)” and “4—GIS Vector files (geojson)” contain two files each, which are related to the stations contained in the Standard and Disaggregation spreadsheets, with the same information listed in Table 1. In the folder “3—GIS Vector files (shapefile)”, the shapefile files are compressed in .rar format. In the folder “4—GIS Vector files (geojson)”, they are in .json format.

Some of the stations compiled in the dataset have more than one IDF equation, for two reasons:

(a)

More than one study was conducted for the station, covering different periods. In these cases (123 pluviographic stations and 1491 pluviometric stations), it was decided to show all the equations, so the user can choose which equations to use. It is strongly recommended to use the equations established using the most recent data and the largest number of years possible. In addition, according to water resource planning and hydraulic design, it is recommended that IDF equations with short and lagged time series have a conservative return period to ensure safe use.

Table 2. Information related to Juazeiro station (Code 0940024) illustrating the existence of two distinct equations (K, a, b, and c) covering different periods of rainfall series (Start year, End year, and Years).

Code	Name	Start Year	End Year	Years	K	a	b	c
0940024	Juazeiro	1988	1999	12	5592.554	0.2420	40.039	1.0930
0940024	Juazeiro	1994	2010	17	1519.000	0.1880	9.300	0.8795

shows the example of the Juazeiro station (Code 0940024), for which two equations were established by different studies, taking pluviographic series with 12 and 17 years of extension from 1988 to 1999, and from 1994 to 2010, respectively.

(b)

The study established more than one equation covering different rainfall duration ranges (d), as illustrated in the example in

Table 3. Information related to Gavião station (Code 0466001) illustrating the existence of two distinct equations (K, a, b, and c) covering different rainfall duration ranges (Duration range).

Code	Name	Start Year	End Year	K	a	b	c	Duration Range
0466001	Gavião	2000	2009	1620.5	0.1364	0	0.8232	d > 2 h
0466001	Gavião	2000	2009	682.8	0.1157	16	0.6234	d < 2 h

, for the Gavião station (Code 0466001). This situation occurred with 45 pluviographic stations and 47 pluviometric stations. In all of these cases, a system of equations was considered for the station, accounting for the existence of only one equation. For example, among the 6550 equations, the two lines in Table 3 were accounted for as only one equation of intense rainfall for the Gavião station.

For some stations, there are both pluviographic equations (Standard) and pluviometric equations (Disaggregation). In this situation, it is recommended to opt for pluviographic equations, which were established based on sub-daily rainfall data. This is because the deviations in the im estimates, when using pluviometric equations (Disaggregation), are about ±50% [10], and they can reach up to a 120% overestimation in extreme cases [11].

For some IDF equations, the start and end years of the pluviographic series were not reported (Start year and End year columns), but only the number of years in the series were. As highlighted previously, the period used in the series increasingly deserves to be addressed, especially due to the context of climate change. It is believed that equations established with a greater amount of data and/or in more recent years are more suitable for the present moment. It is also noteworthy that, from the perspective of climate change, it cannot be guaranteed that the IDF equations obtained in the past can be used in the present or future. This is because historical series can also undergo trends, requiring a stationarity analysis to establish more appropriate equations [12], which is still an open field of research. Several authors [11,12] have highlighted the lack of information on sub-daily precipitation in Brazil and developing countries, which is crucial for constantly updating the IDF equations, especially in the context of climate change. It becomes even more relevant in countries with large territorial extensions in Brazil. However, this is the current information available to users.

When the available data are restricted to pluviometric stations (Disaggregation), it is essential to assess at which level the coefficients used for disaggregation (column “Disaggregation coefficients”) were obtained: local, regional, national, or general. Preference should be given to equations that used coefficients obtained at the local level, followed by regional, national, and general, as they better represent the specific characteristics of each area [13].

The compiled dataset can be useful in future studies of the application of the stochastic framework for the construction of IDF equations that take into account the spatial dependence of precipitation [11,14,15]. It is handy and can help design rainfall curves in a country with a large territorial extension like Brazil.

Despite the wide data from pluviometric stations in the Southeast region of Brazil, the Central–West region has significantly fewer data than other regions of the country, with only 8.17% of the total data. This can result in gaps in the representation of certain locations and an incomplete understanding of rainfall patterns and associated risks in less monitored areas. In regions with a higher density of stations, such as the Southeast, one can have a more detailed and accurate view of climate conditions, while in regions with fewer stations, such as the Central–West, analyses and forecasts can be biased with the insufficient coverage, with a less accurate representation due to the low density of stations.

5. Conclusions

The database presented is the largest and most accessible database of IDF equations in Brazil, with information from 6550 Brazilian locations (around 1000% more than Pluvio 2.1).