Precipitation trends analysis by Mann-Kendall test: a case study of Paraíba, Brazil

Xavier Júnior, Sílvio Fernando Alves; Jale, Jader da Silva; Stosic, Tatijana; Santos, Carlos Antonio Costa dos; Singh, Vijay P.

doi:10.1590/0102-7786351013

Sílvio Fernando Alves Xavier Júnior

Departamento de Estatística, Universidade Estadual da Paraíba, Campina Grande, PB, Brasil.

http://orcid.org/0000-0002-4832-0711

Jader da Silva Jale

Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Recife, PE, Brasil.

http://orcid.org/0000-0001-7414-1154

Tatijana Stosic

Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Recife, PE, Brasil.

http://orcid.org/0000-0002-5691-945X

Carlos Antonio Costa dos Santos Corresponding author: Carlos Antonio C. dos Santos, carlos.santos@ufcg.edu.br.

Unidade Acadêmica de Ciências Atmosféricas, Universidade Federal de Campina Grande, Campina Grande, PB, Brasil.

http://orcid.org/0000-0003-2414-2911

Vijay P. Singh

Biological and Agriculture Engineering, Texas A&M University, College Station, TX, USA.

Corresponding author: Carlos Antonio C. dos Santos, carlos.santos@ufcg.edu.br.

Month	Model	ME	RMS	MS	RMSS	ASE	SDI	ECI
Jan	Spherical	0.0034	0.9410	0.0038	0.9991	0.950	41.29	0.1624
	Circular	–0.0022	0.9369	–0.0011	0.9990	0.946	42.79	0.005
	R. Quadratic	0.0116	0.9530	0.0069	0.9813	0.980	39.95	0.4986
Feb	Pentasph.	–0.0146	0.9536	–0.0114	1.0250	0.920	34.08	0.6012
	Spherical	–0.0148	0.9573	–0.0093	1.0391	0.912	43.24	0.8033
	Tetraspherical	–0.0184	0.9555	–0.0143	1.0317	0.917	39.07	0.7599
Mar	Gaussian	–0.0013	1.2012	0.0037	0.9998	1.199	53.49	0.1528
	Spherical	–0.0075	1.1362	–0.0003	0.9774	1.165	38.21	0.4617
	Tetraspherical	–0.0076	1.1172	0.0001	0.9786	1.147	33.33	0.4284
Apr	Gaussian	–0.0600	1.2102	–0.0417	0.9903	1.228	48.03	1.0453
	Spherical	–0.0491	1.2082	–0.0344	0.9924	1.223	27.40	0.8578
	Tetrasph.	–0.0327	1.2097	–0.0227	0.9977	1.219	16.80	0.5380
May	K-Bessel	–0.0159	0.9927	–0.0086	1.0011	0.986	0	0.2343
	J-Bessel	–0.0163	0.9995	–0.0124	1.0066	1.005	0	0.4049
	Tetraspherical	–0.0417	1.0229	–0.0308	1.0445	0.979	2.727	1.3732
Jun	Rat. Quadratic	–0.0082	2.0497	–0.0042	1.0248	1.978	26.36	0.3872
	K-Bessel	0.0025	2.0516	0.0014	1.1007	1.831	30.17	0.8972
	Pentaspherical	0.0106	2.0539	0.0054	1.0550	1.921	22.30	0.6894
Jul	Spherical	–0.0261	0.9658	–0.0214	0.9832	0.988	52.34	0.8500
	Circular	–0.0349	0.9628	–0.0298	0.9889	0.978	52.33	1.0150
	Pentasph.	–0.0186	0.9664	–0.0144	0.9686	1.004	53.08	0.8411
Aug	Gaussian	–0.0021	1.3396	–0.0003	1.0479	1.275	60.01	0.6077
	Exponential	0.0112	1.2936	0.0087	1.0437	1.236	31.59	1.2178
	Spherical	0.0062	1.3228	0.0055	1.0558	1.250	50.11	1.1135
Sep	J-Bessel	0.0043	1.1225	0.0037	1.0547	1.065	51.11	1.0730
	Rat. Quadratic	0.0133	1.1327	0.0104	1.0763	1.053	36.05	1.9935
	Tetrasph.	–0.0032	1.1208	–0.0028	1.0407	1.078	39.34	0.8071
Oct	Gaussian	–0.0241	1.4932	–0.0143	1.0717	1.391	46.52	1.4122
	Exponential	–0.0269	1.5077	–0.0141	0.9919	1.524	67.31	0.6617
	Spherical	–0.0283	1.5061	–0.0158	1.0514	1.437	53.15	1.2344
Nov	Exponential	–0.0054	1.0956	–0.0040	1.0416	1.047	51.55	1.1176
	Spherical	0.0004	1.0790	0.0024	1.0323	1.043	62.67	0.8031
	Circular	–0.0049	1.0825	–0.0023	1.0367	1.041	63.86	0.8792
Dec	Circular	0.0311	1.1372	0.0206	1.0749	1.039	36.77	1.4780
	Rat. Quadratic	0.0254	1.1339	0.0184	1.0071	1.110	55.33	0.7735
	Hole Effect	0.0349	1.1146	0.0216	1.1086	0.996	41.18	1.8271

ρ_{k} = \frac{\sum_{k = 1}^{n - k} (x_{t} - {\bar{x}}_{t}) (x_{t + k} - {\bar{x}}_{t + k})}{{\sum_{t = 1}^{n - k} {(x_{t} - {\bar{x}}_{t})}^{2} * \sum_{n - k}^{t = 1} (x_{t + k} - {\bar{x}}_{t + k})}^{2}}

Z_{c} = {\begin{matrix} \frac{S - 1}{\sqrt{V a r (S)}}, i f S > 0 \\ 0, i f S = 0 \\ \frac{S + 1}{\sqrt{V a r (S)}}, i f S < 0 \end{matrix}

A_{i} = {\begin{matrix} \frac{A B S {(M S)}_{i}}{M A X (A B S (M S))}, & w h e n M A X (A B S (M S)) > 0 \\ 1, & w h e n M A X (A B S (M S)) = 0 \end{matrix}

B_{i} = {\begin{matrix} \frac{A B S {(R M S S - 1)}_{i}}{M A X (A B S (M S))}, & w h e n M A X (A B S (R M S S - 1)) > 0 \\ 1, & w h e n M A X (A B S (R M S S - 1)) = 0 \end{matrix}

[1] Corresponding author: Carlos Antonio C. dos Santos, carlos.santos@ufcg.edu.br.

Brasil

Brasil

Precipitation trends analysis by Mann-Kendall test: a case study of Paraíba, Brazil

Análise de tendência da precipitação usando o teste de Mann-Kendall: um estudo de caso na Paraíba, Brasil

Abstract