Spatial mapping of annual rainfall in the São Francisco River Basin

Precipitation is an important object of study and plays an important role in the dynamics of rainfall distribution in a region. This study investigated the spatial and temporal variation of precipitation in the São Francisco River Basin (SFRB). A historical series of data from 1989 to 2018 was analyzed, and a random function was decomposed into trend and residual components for analysis of precipitation. Interpolation techniques were used to analyze precipitation spatial behavior over time, using high-resolution precipitation maps. Our results showed that the exponential model prevailed in four periods. The findings also showed a high precipitation variability in the SFRB and enabled us to monitor precipitation behavior over the years, as well as in the different sub-regions in SFRB. Finally, important information was obtained, enabling, for instance, the identification of vulnerable areas suffering from lack of rainfall.

Keywords:
kriging; R software; variogram

Authorship

Willian dos Santos Oliveira

Faculdade de Engenharia. Universidade Federal da Grande Dourados (UFGD), Rodovia Dourados/Itahum, Km 12, Unidade II, Caixa Postal: 364, Cep: 79804-970, Dourados, MS, Brazil. E-mail: oliveira.wds@outlook.comUniversidade Federal da Grande DouradosBrazilDourados, MS, BrazilFaculdade de Engenharia. Universidade Federal da Grande Dourados (UFGD), Rodovia Dourados/Itahum, Km 12, Unidade II, Caixa Postal: 364, Cep: 79804-970, Dourados, MS, Brazil. E-mail: oliveira.wds@outlook.com

http://orcid.org/0000-0003-0166-0660

Elias Silva de Medeiros ^**Corresponding author: Elias Silva de Medeiros, e-mail: eliasmedeiros@ufgd.edu.br

Faculdade de Ciências Exatas e Tecnologia. Universidade Federal da Grande Dourados (UFGD), Rodovia Dourados/Itahum, Km 12, Unidade II, Caixa Postal: 364, Cep: 79804-970, Dourados, MS, Brazil. E-mail: eliasmedeiros@ufgd.edu.br, alessandrasilva@ufgd.edu.br, lucianoantonio@ufgd.edu.br Universidade Federal da Grande DouradosBrazilDourados, MS, BrazilFaculdade de Ciências Exatas e Tecnologia. Universidade Federal da Grande Dourados (UFGD), Rodovia Dourados/Itahum, Km 12, Unidade II, Caixa Postal: 364, Cep: 79804-970, Dourados, MS, Brazil. E-mail: eliasmedeiros@ufgd.edu.br, alessandrasilva@ufgd.edu.br, lucianoantonio@ufgd.edu.br

http://orcid.org/0000-0002-9694-4019

Alessandra Querino da Silva

http://orcid.org/0000-0002-1702-0169

Luciano Antonio de Oliveira

http://orcid.org/0000-0001-5054-2623

^*Corresponding author: Elias Silva de Medeiros, e-mail: eliasmedeiros@ufgd.edu.br

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (3)
Tables (4)
Formulas (1)

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Figure 1.
Maps of the hydrographic regions of the São Francisco River Basin (SFRB), highlighting its main reservoirs and 333 rain gauge stations (Figure 1a), and the spatial distribution of altitude (Figure 1b).

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Figure 2.
Annual precipitation data for the basin as a function of longitude, latitude and altitude.

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Figure 3.
Map of accumulated annual precipitation (mm) in the São Francisco River Basin.

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Table 1.
Descriptive measures of accumulated annual precipitation in 333 rain-gauge stations in the São Francisco River Basin.

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Table 2.
Multiple linear regression model estimates of accumulated annual precipitation.

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Table 3.
Result of the leave-one-out cross-validation for the interpolation methods IDW, Ordinary Kriging and Universal Kriging.

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Table 4.
Estimates of the fitted variogram models for each of the six periods under study and spatial dependence index (SDI).

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(1)

Figure 1. Maps of the hydrographic regions of the São Francisco River Basin (SFRB), highlighting its main reservoirs and 333 rain gauge stations (Figure 1a), and the spatial distribution of altitude (Figure 1b).

Figure 2. Annual precipitation data for the basin as a function of longitude, latitude and altitude.

Figure 3. Map of accumulated annual precipitation (mm) in the São Francisco River Basin.

Table 1. Descriptive measures of accumulated annual precipitation in 333 rain-gauge stations in the São Francisco River Basin.

Period	Minimum	Maximum	Mean	Median	Standard deviation	CV (%)
1989-1993	367.8	2540.1	1143.7	1225.3	391.3	34.2%
1994-1998	390.8	2935.44	1124.3	1140.2	374.5	33.3%
1999-2003	86.4	1705.2	999.1	1026.3	332.9	33.3%
2004-2008	12.00	2087.4	1083.2	1092.5	374.2	34.5%
2009-2013	209.3	2031.8	1039.3	1086.7	387.5	37.3%
2014-2018	183.7	1457.3	797.3	805.3	294.4	36.9%

Table 2. Multiple linear regression model estimates of accumulated annual precipitation.

Variable	1989-1993	1994-1998	1999-2003	2004-2008	2009-2013	2014-2018
(Intercept)	6641**	6334**	5571**	6632**	6244**	3903**
Latitude	-0.5575**	-0.5742**	-0.4776**	-0.5771**	-0.5313**	-0.2874**
Longitude	-2.7376**	-1.8111**	-1.9654**	-2.0110**	-2.0965**	-1.9545**
Longitude²	0.0014**	0.0010**	0.0011**	0.0011**	0.0011**	0.0010**
Altitude	0.2358**	0.3185**	0.2544**	0.0884**	0.1235**	0.1776**
R²	80.12%	73.69%	79.89%	78.56%	75.91%	75.14%

**Significant at 1% significance level by the t-test.

Table 3. Result of the leave-one-out cross-validation for the interpolation methods IDW, Ordinary Kriging and Universal Kriging.

Year	Variogram	Universal Kriging			Ordinary Kriging			IDW
Year	Variogram	MAE	RMSE	R²	MAE	RMSE	R²	MAE	RMSE	R²
1989-1993	Spherical	100.47	167.58	81.6%	102.87	172	80.7%	121.21	177.62	79.3%
1989-1993	Exponential	99.92	166.82	81.8%	103.31	172.53	80.5%
1989-1993	Gaussian	102.59	168.37	81.4%	126.5	197.28	75.4%
1994-1998	Spherical	96.42	169.50	79.5%	97.06	172.47	78.8%	133.76	194.97	72.8%
1994-1998	Exponential	95.93	168.21	79.8%	97.09	172.53	78.8%
1994-1998	Gaussian	96.13	165.41	80.4%	101.8	177.65	77.5%
1999-2003	Spherical	78.50	115.87	87.8%	86.29	126.2	85.6%	112.48	152.38	79.0%
1999-2003	Exponential	78.97	116.19	87.8%	86.63	127.25	85.3%
1999-2003	Gaussian	80.03	117.35	87.5%	110.31	152.35	80.3%
2004-2008	Spherical	104.12	146.86	84.6%	102.04	141.14	85.7%	127.79	176.11	77.8%
2004-2008	Exponential	103.62	145.71	84.8%	101.61	140.86	85.8%
2004-2008	Gaussian	105.30	147.05	84.5%	107.76	148.76	84.5%
2009-2013	Spherical	104.58	157.65	83.4%	139.15	189.34	78.0%	135.14	193.66	75.0%
2009-2013	Exponential	102.05	155.71	83.8%	100.17	155.23	83.9%
2009-2013	Gaussian	108.38	160.29	82.9%	158.55	207.56	73.6%
2014-2018	Spherical	77.19	104.30	87.4%	77.43	104.5	87.4%	115.54	149.06	74.3%
2014-2018	Exponential	76.73	104.10	87.5%	77.46	104.5	87.4%
2014-2018	Gaussian	78.39	106.01	87.5%	81.18	108.62	86.4%

Table 4. Estimates of the fitted variogram models for each of the six periods under study and spatial dependence index (SDI).

Year	Kriging	Model	Nugget	Sill	Range	SDI
1989-1993	Universal	Exponential	13865.66	49675.08	270.22 km	27.91%
1994-1998	Universal	Gaussian	13086.72	51637.18	180.32 km	25.34%
1999-2003	Universal	Spherical	10579.20	23285.90	368.81 km	45.43%
2004-2008	Ordinary	Exponential	13898.82	57729.62	176.46 km	26.36%
2009-2013	Ordinary	Exponential	24043.98	74007.37	471.89 km	32.49%
2014-2018	Universal	Exponential	8646.65	23335.71	155.36 km	37.05%

(1)

Z (s) = Y (s) + ε (s)

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Instituto de Pesquisas Ambientais em Bacias Hidrográficas Instituto de Pesquisas Ambientais em Bacias Hidrográficas (IPABHi), Estrada Mun. Dr. José Luis Cembranelli, 5000, Taubaté, SP, Brasil, CEP 12081-010 - Taubaté - SP - Brazil
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Spatial mapping of annual rainfall in the São Francisco River Basin

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[1] ^*Corresponding author: Elias Silva de Medeiros, e-mail: eliasmedeiros@ufgd.edu.br