Extreme values of ET<sub>0</sub> at Piracicaba, Brazil, for designing irrigation systems

Melo, Verônica G. M. L. de; Frizzone, José A.; Melo, Leonardo L. de; Camargo, Antonio P. de

doi:10.1590/1807-1929/agriambi.v25n10p677-683

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Articles • Rev. bras. eng. agríc. ambient. 25 (10) • Oct 2021 • https://doi.org/10.1590/1807-1929/agriambi.v25n10p677-683 copy

Extreme values of ET₀ at Piracicaba, Brazil, for designing irrigation systems¹ 1 Research developed at Escola Superior de Agricultura “Luiz de Queiroz”, Universidade de São Paulo, Piracicaba, SP, Brazil

Valores extremos de ET₀ em Piracicaba, Brasil, para o dimensionamento de sistemas de irrigação

Authorship SCIMAGO INSTITUTIONS RANKINGS

HIGHLIGHTS:

ET₀ for designing the system capacity was selected considering the system lifespan, irrigation interval, and risk of failure.

As higher the anticipated irrigation system lifespan, higher is the return period needed to attain a low risk of failure.

Gumbel distribution showed to be adequate to characterize the frequency distribution of maximum ET₀ values.

ABSTRACT

Irrigation system capacity is typically defined by analyzing probabilities of non-exceedance of evapotranspiration. The use of mean monthly values of ET₀ may lead to underestimation of the required capacity, whereas use of maximum daily values may result in overestimation of required capacity. This study had the following objectives: (1) to analyze a 30-year series of daily ET₀ data from Piracicaba, SP, Brazil, to evaluate the suitability of the Gumbel distribution for estimating the maximum values of ET₀ organized in periods of up to 30 days; (2) to determine probable maximum values and to select ET₀ values considering the irrigation interval and the risk of failure in terms of irrigation system capacity. Daily data from 1990 to 2019 were used to calculate ET₀ using the Penman-Monteith model. The Gumbel distribution fitted to the data and was suitable for characterizing the frequency distribution of the maximum ET₀. The probable ET₀ for designing irrigation systems can then be estimated based on the expected lifespan, irrigation interval, and return period of ET₀ maximum values. The higher the anticipated irrigation system lifespan, the higher the return period needed to attain a low risk of failure. Using the average of maximum ET₀ values alone leads to underestimation of system capacity and a high risk of failure in terms of irrigation system capacity.

Key words:
extreme values type I distribution; confidence interval; irrigation system design; risk of failure; Gumbel distribution

n (days)	x	Me	Mo	CV (%)	x_max	x_min	x_var (%)	A	C
n (days)	(mm)			CV (%)	(mm)		x_var (%)	A	C
2	13.56	13.52	13.07	6.86	15.84	12.05	23.91	0.129	4.568
3	19.73	19.62	19.02	6.43	22.40	19.07	23.68	0.262	4.236
4	25.61	25.55	25.28	6.21	28.13	22.70	19.30	0.121	3.385
5	31.40	31.33	31.04	7.21	34.85	27.59	20.85	0.100	3.096
6	36.96	37.05	36.99	7.48	41.15	31.79	22.74	-0.092	3.236
7	42.37	42.80	42.66	8.00	47.37	36.43	23.10	-0.372	3.249
8	47.83	47.84	47.95	7.94	54.05	40.73	24.64	-0.009	3.543
9	53.22	53.70	53.81	7.90	60.66	44.37	26.86	-0.342	3.965
10	58.41	59.03	59.19	8.14	67.55	47.03	30.38	-0.389	4.565
15	84.18	85.01	84.93	8.44	96.95	67.80	30.07	-0.352	4.406
20	109.00	110.38	110.91	8.80	124.94	85.37	31.67	-0.432	4.770
25	133.41	134.32	136.62	9.26	156.87	104.26	33.54	-0.221	4.562
30	156.72	157.11	157.87	9.39	183.57	122.36	33.34	-0.080	4.805

n (days)	Parameter µ	CI for µ		Parameter β	CI for β		D_sup K-S
n (days)	Parameter µ	LL	UL	Parameter β	LL	UL	D_sup K-S
2	13.118	12.801	13.436	0.807	0.572	1.042	0.078
3	19.104	18.629	19.578	1.207	0.928	1.569	0.096
4	24.824	24.236	25.412	1.496	1.143	1.957	0.104
5	30.270	29.436	31.105	2.122	1.616	2.785	0.109
6	35.588	34.572	36.604	2.585	1.832	3.337	0.109
7	40.679	39.419	41.939	3.205	2.272	4.138	0.116
8	45.941	44.528	47.354	3.594	2.548	4.641	0.099
9	51.106	49.472	52.739	4.155	2.945	5.365	0.107
10	56.023	54.133	57.914	4.808	3.729	6.202	0.107
15	80.614	77.822	83.406	7.101	5.494	9.178	0.097
20	104.153	100.271	108.036	9.876	7.000	12.751	0.114
25	127.259	122.433	132.084	12.273	8.700	15.846	0.129
30	149.368	143.562	155.173	14.766	11.445	19.049	0.127

n (days)	Probability of obtaining a maximum ET₀ > x, F’ (x)
	0.50 (T_R = 2 years)	0.25 (T_R = 4 years)	0.20 (T_R = 5 years)	0.10 (T_R = 10 years)	0.05 (T_R = 20 years)
	ET₀ (mm period^-1)
2	13.42 [13.07;13.42]	14.12 [13.65;14.60]	14.33 [13.81;14.85]	14.94 [14.27;15.60]	15.52 [14.71;16.33]
3	19.55 [19.04;20.06]	20.61 [19.91;21.1]	20.91 [20.15;21.68]	21.82 [20.85;22.79]	22.69 [21.51;23.87]
4	25.37 [24.74;26.00]	26.69 [25.52;27.56]	27.07 [26.11;28.02]	28.19 [26.97;29.41]	29.27 [27.78;30.75]
5	31.05 [30.15;31.95]	32.91 [31.67;34.16]	33.45 [32.09;34. 82]	35.04 [33.30;36.79]	36.57 [34.45;38.70]
6	36.49 [35.50;37.48]	38.82 [37.83;39.81]	39.51 [38.41;40.60]	41.43 [40.44;42.42]	43.47 [42.48;44.46]
7	41.82 [40.61;43.03]	44.65 [43.44;45.86]	45.53 [44.36;46.70]	47.95 [46.74;49.16]	50.27 [49.06;51.48]
8	47.23 [45.87;48.59]	50.38 [49.02;51.74]	51.49 [50.11;52.85]	54.08 [52.72;55.44]	56.76 [55.40;58.12]
9	52.59 [51.09;54.09]	56.23 [54.73;57.73]	57.31 [55.75;58.87]	60.52 [59.12;62.12]	63.56 [62.6;65.06]
10	57.79 [55.76;59.81]	62.01 [59.27;64.76]	63.24 [60.24;66.23]	66.84 [63.06;70.63]	70.30 [65.72;74.89]
15	83.22 [80.23;86.21]	89.46 [85.39;93.53]	91.27 [86.83;95.71]	96.59 [90.98;102.21]	101.71 [94.89;108.52]
20	107.74 [104.31;111.17]	116.05 [112.62;119.48]	118.61 [115.39;121.83]	126.55 [123.118;129.98]	134.12 [130.69;137.55]
25	131.59 [127.17;136.01]	142.21 [137.79;146.63]	145.49 [141.21;149.77]	154.99 [150.57;159.41]	163.52 [159.41;167.94]
30	154.78 [148.57;160.99]	167.77 [159.33;176.20]	171.52 [162.32;180.72]	182.60 [170.97;194.22]	193.23 [179.14;207.31]

Unidade Acadêmica de Engenharia Agrícola Unidade Acadêmica de Engenharia Agrícola, UFCG, Av. Aprígio Veloso 882, Bodocongó, Bloco CM, 1º andar, CEP 58429-140, Campina Grande, PB, Brasil, Tel. +55 83 2101 1056 - Campina Grande - PB - Brazil
E-mail: revistagriambi@gmail.com

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[1] * Corresponding author - E-mail: vegaspar.vg@gmail.com

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Extreme values of ET0 at Piracicaba, Brazil, for designing irrigation systems1 1 Research developed at Escola Superior de Agricultura “Luiz de Queiroz”, Universidade de São Paulo, Piracicaba, SP, Brazil

Valores extremos de ET0 em Piracicaba, Brasil, para o dimensionamento de sistemas de irrigação

HIGHLIGHTS:

ABSTRACT

Extreme values of ET₀ at Piracicaba, Brazil, for designing irrigation systems¹ 1 Research developed at Escola Superior de Agricultura “Luiz de Queiroz”, Universidade de São Paulo, Piracicaba, SP, Brazil

Valores extremos de ET₀ em Piracicaba, Brasil, para o dimensionamento de sistemas de irrigação