Is it possible to apply the regional frequency analysis to daily extreme air temperature data?

Martins, Letícia Lopes; Souza, Julia Camila de; Sobierajski, Graciela da Rocha; Blain, Gabriel Constantino

doi:10.1590/1678-4499.20220061

Letícia Lopes Martins

Conceptualization

Investigation

Methodology

Writing – original draft

Writing – review & editing

Instituto Agronômico – Programa de Pós-Graduação em Gestão de Recursos Ambientais – Campinas (SP), Brazil.

http://orcid.org/0000-0002-0299-3005

Julia Camila de Souza

Conceptualization

Investigation

Methodology

Writing – original draft

Writing – review & editing

Instituto Agronômico – Programa de Pós-Graduação em Gestão de Recursos Ambientais – Campinas (SP), Brazil.

http://orcid.org/0000-0002-6471-5406

Graciela da Rocha Sobierajski

Conceptualization

Investigation

Methodology

Formal analysis

Data acquisition

Writing – original draft

Writing – review & editing

Instituto Agronômico – Centro de Fruticultura – Jundiaí (SP), Brazil.

http://orcid.org/0000-0002-7211-9268

Gabriel Constantino Blain ^**Corresponding author: gabriel.blain@sp.gov.br

Conceptualization

Investigation

Methodology

Formal analysis

Data acquisition

Validation

Writing – original draft

Writing – review & editing

Visualization

Supervision

Instituto Agronômico – Centro de Biossistemas Agrícolas e Pós-Colheita – Campinas (SP), Brazil.

http://orcid.org/0000-0001-8832-7734

Section Editor: Patrícia Cia

*Corresponding author: gabriel.blain@sp.gov.br

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Figure 1
Major steps of a Monte Carlo simulation designed to evaluate the performance of the regional frequency analysis based on L-moments applied to homogeneous groups of extreme air temperature series.

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Figure 2
Air temperature series. State of São Paulo, Brazil.

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Figure 3
Root-mean squared errors (RMSE; °C) between Q(F) values (; right side and , left side) and their corresponding simulated air temperature values. The RMSE values presented for each generalized extreme value distributions, sample size and cross-correlation (ρ) is the average values of 10,000 Monte Carlo simulations.

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Figure 4
Rate at which both discordance (RD) and d measures, calculated under the multiplicative (a to c) and additive (d to f) approaches, falsely flagged synthetic air temperature series as discordant. The homogeneous groups were generated from the generalized extreme value (GEV). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Figure 5
Rates at which the H measure, calculated under the multiplicative (a to d) and additive (e to h) approaches, correctly accepted the hypothesis of homogeneity. The homogeneous groups were generated from the generalized extreme value (GEV), considering the parameters shown in : Monte Alegre do Sul (MAS), Ribeirão Preto (RP) and Ubatuba (UBA). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Figure 6
Rate at which both d (a to c) and discordance (RD) (d to f) measures correctly flagged synthetic air temperature series as discordant (multiplicative approach). The heterogeneous groups were generated from the generalized extreme value distribution – and comprised two homogeneous groups (Hom.Group1 and Hom.Group2). Hom.Group1 was generated from the parameters of the location of Monte Alegre do Sul (; minimum air temperature), while Hom.Group2 was generated from the parameters of the location of Ribeirão Preto (; minimum air temperature). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Figure 7
Rate at which both d (a to c) and discordance (RD) (d to f) measures correctly flagged synthetic air temperature series as discordant (additive approach). The heterogeneous groups were generated from the generalized extreme value distribution (and comprised two homogeneous groups – Hom.Group1 and Hom.Group2). Hom.Group1 was generated from the parameters of the location of Monte Alegre do Sul (; minimum air temperature), while Hom.Group2 was generated from the parameters of the location of Ribeirão Preto (; minimum air temperature). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Figure 8
Rates at which the H measure, calculated under the multiplicative (a to c) and additive (d to f) approaches, correctly rejected the hypothesis of homogeneity. The heterogeneous groups were generated from the generalized extreme value and comprised two homogeneous groups (Hom.Group1 and Hom.Group2). Hom.Group1 was generated from the parameters of the location of Monte Alegre do Sul (; minimum air temperature), while Hom.Group2 was generated from the parameters of the location of Ribeirão Preto (; minimum air temperature). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Figure 9
Regional growth curves for daily-extremes values of minimum and maximum air temperature. Both plots were constructed under the regional approach considered in the case study.

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Figure 10
Quantiles of non-exceedance probabilities [Q(F)] for four locations of the state of São Paulo, Brazil. The [Q(F)] values (blue line) were calculated through the index flood approach applied to a generalized logistic distribution (GLO = 1.03, 023, 0.09; minimum air temperature) and to a generalized extreme value distribution (GEV = -0.66, 1.25, 0.05); maximum air temperature). The index flood assumed the sample mean value of each air temperature series and was calculated under the additive approach.

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Figure 11
Root-mean squared errors (RMSE; °C) between Q(F) values (calculated from ) and quantiles estimates calculated from the at-site approach. Case study, state of São Paulo, Brazil.

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Figure 4
Rate at which both discordance (RD) and d measures, calculated under the multiplicative (a to c) and additive (d to f) approaches, falsely flagged synthetic air temperature series as discordant. The homogeneous groups were generated from the generalized extreme value (GEV). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

Thumbnail

Figure 5
Rates at which the H measure, calculated under the multiplicative (a to d) and additive (e to h) approaches, correctly accepted the hypothesis of homogeneity. The homogeneous groups were generated from the generalized extreme value (GEV), considering the parameters shown in : Monte Alegre do Sul (MAS), Ribeirão Preto (RP) and Ubatuba (UBA). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

Thumbnail

Figure 6
Rate at which both d (a to c) and discordance (RD) (d to f) measures correctly flagged synthetic air temperature series as discordant (multiplicative approach). The heterogeneous groups were generated from the generalized extreme value distribution – and comprised two homogeneous groups (Hom.Group1 and Hom.Group2). Hom.Group1 was generated from the parameters of the location of Monte Alegre do Sul (; minimum air temperature), while Hom.Group2 was generated from the parameters of the location of Ribeirão Preto (; minimum air temperature). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Figure 7
Rate at which both d (a to c) and discordance (RD) (d to f) measures correctly flagged synthetic air temperature series as discordant (additive approach). The heterogeneous groups were generated from the generalized extreme value distribution (and comprised two homogeneous groups – Hom.Group1 and Hom.Group2). Hom.Group1 was generated from the parameters of the location of Monte Alegre do Sul (; minimum air temperature), while Hom.Group2 was generated from the parameters of the location of Ribeirão Preto (; minimum air temperature). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

Thumbnail

Figure 8
Rates at which the H measure, calculated under the multiplicative (a to c) and additive (d to f) approaches, correctly rejected the hypothesis of homogeneity. The heterogeneous groups were generated from the generalized extreme value and comprised two homogeneous groups (Hom.Group1 and Hom.Group2). Hom.Group1 was generated from the parameters of the location of Monte Alegre do Sul (; minimum air temperature), while Hom.Group2 was generated from the parameters of the location of Ribeirão Preto (; minimum air temperature). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Figure 9
Regional growth curves for daily-extremes values of minimum and maximum air temperature. Both plots were constructed under the regional approach considered in the case study.

Thumbnail

Figure 10
Quantiles of non-exceedance probabilities [Q(F)] for four locations of the state of São Paulo, Brazil. The [Q(F)] values (blue line) were calculated through the index flood approach applied to a generalized logistic distribution (GLO = 1.03, 023, 0.09; minimum air temperature) and to a generalized extreme value distribution (GEV = -0.66, 1.25, 0.05); maximum air temperature). The index flood assumed the sample mean value of each air temperature series and was calculated under the additive approach.

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Figure 11
Root-mean squared errors (RMSE; °C) between Q(F) values (calculated from ) and quantiles estimates calculated from the at-site approach. Case study, state of São Paulo, Brazil.

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Table 1
Parameters of the generalized extreme value (GEV) used to simulate extreme maximum (Tmax) and minimum (Tmin) series in the state of São Paulo, Brazil.

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Table 2
Rates at which the original Z measure and its bivariate extension (Z.bivar) correctly accepted a probability function as the parent distribution of air temperature series forming homogeneous groups. The groups were generated from the generalized extreme value (GEV). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

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Table 3
Rates at which the original Z measure and its bivariation extension (Z.bivar) correctly select a probability function as the best fitting distribution of air temperature series forming homogeneous groups. The groups were generated from the generalized extreme value (GEV). The cross-correlation varied from zero (cross = 0) to 0.8 (cross = 0.8). The length of record is 20 years.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Monte Alegre do Sul (-22.67°S, -46.67°W, 785 m)
GEV (2.1, 2, 0.37)	GEV (34, 0.92, 0.05)
Ribeirão Preto (-21.21°S, -47.90°W, 547 m)
GEV (3.3, 2.60, 0.34)	GEV (36.1, 1.30, 0.35)
Ubatuba (-23.50°S, -45.0°W, 3 m)
GEV (6.3, 1.7, 0.25)	GEV (36.4, 1.4, 0.24)

GEV (2.1, 2, 0.37)							GEV (34, 0.92, 0.05)
N	Cross = 0		Cross = 0.4		Cross = 0.8		N	Cross = 0		Cross = 0.4		Cross = 0.8
N	Z	Zbivar	Z	Zbivar	Z	Zbivar	N	Z	Zbivar	Z	Zbivar	Z	Zbivar
7	86.8	65	85.6	62.2	89.6	67.4	7	90	60.4	90.4	61.6	89.2	67
10	87.8	77.4	87.4	75.2	88	73.6	10	89.2	64.4	90.8	64.2	90	72
15	87.2	86.8	85.2	86	88.4	86.6	15	89.4	77.4	91.6	73	90.8	75.6
20	87	92	87.8	92.6	87	92.6	20	89.4	86.8	90	84.2	91	86
25	88.8	95.4	87.4	95.8	87.4	95.2	25	90.4	92.2	91	88.8	92	90.4
30	88	97.4	88.6	97.2	88.4	98.2	30	90	95.2	89.2	91.6	91.4	94
GEV (3.2, 2.6, 0.34)							GEV (36.1, 1.30, 0.35)
7	89	69.8	91	68	85.8	68	7	86.2	65	90	68.2	89.6	68.2
10	90.2	80.4	89.2	79.2	88	75	10	85.8	76.8	89.4	79	92.4	81.4
15	91.4	91.8	87.8	87.4	88	87.6	15	87.4	87.4	90.4	88.6	89.6	88
20	89.6	95.4	87.2	92.2	89.4	93.2	20	88.4	94	88.4	94	89.2	93.2
25	89.6	97	89.4	96.8	87.8	96.2	25	85	95.2	90	96	88.8	95.8
30	89.2	97.6	88	97.2	89.6	98	30	84.8	96.2	88.8	98.2	90	97.8
GEV (6.3, 1.7, 0.25)							GEV (36.4, 1.4, 0.24)
7	89.2	55.6	90.8	54.4	91.2	64.8	7	88	70.2	85.6	65.6	90	70.4
10	86.2	63.8	91.6	62.4	91.2	71.2	10	88	79.8	86.4	74.4	88.2	79.4
15	88.6	77.8	90.2	78	92.8	78.2	15	87.6	87.8	87.6	87.6	89.6	88
20	90.2	86.2	89.2	86.4	92.2	87.2	20	88	93.6	85	92	87.6	93.4
25	88.4	91.4	87.2	90.4	92.2	92	25	87.6	96.8	86.2	94.6	86.8	96.6
30	89.2	93	87.4	93.8	92	94.8	30	87.6	97.2	86.6	96.6	86	97.6

GEV (2.1, 2, 0.37)							GEV (34, 0.92, 0.05)
N	Cross = 0		Cross = 0.4		Cross = 0.8		N	Cross = 0		Cross = 0.4		Cross = 0.8
N	Z	Zbivar	Z	Zbivar	Z	Zbivar	N	Z	Zbivar	Z	Zbivar	Z	Zbivar
7	57.4	58.8	55.6	58.2	48.8	51.8	7	78.4	75	80.4	78.2	79.8	84.2
10	61.4	62.8	61.2	63.4	54.6	56.6	10	77.2	68	81.2	74	81.4	79.4
15	69.2	70	66.8	68.8	60.2	59.8	15	74.2	59.8	78.2	62.2	80.6	73.2
20	71	71	68.6	68	65.2	64.6	20	76.4	52.6	78.2	58.4	79.8	68.4
25	69.2	69.8	72.2	72	62.4	62.6	25	71	48.2	74.2	49.8	78.2	66
30	72.6	72.2	73.4	73.4	66.2	65.8	30	70.2	44.6	72.8	47.4	77.2	62.2
GEV (3.2, 2.6, 0.34)							GEV (36.1, 1.30, 0.35)
7	57.6	59.8	60.2	61	49.4	52.2	7	40.6	39.2	41	39.2	49.8	46
10	60.4	61.8	62	63.2	54	54.6	10	41.8	39	39	37.2	44.6	42.6
15	66.8	66.2	67.6	67.4	59.6	61.8	15	34.4	35.6	34.6	34	37	35.8
20	66.6	67	69.6	69.2	65	63.4	20	34	34.6	32.6	30.4	36.2	34.8
25	67.8	67.2	70.8	70.4	68	68.8	25	32.8	32.6	30	28.4	33.8	33.8
30	66.4	66.4	71.2	71.2	67.4	67.2	30	28.2	28.4	26.8	26.8	32	32
GEV (6.3, 1.7, 0.25)							GEV (36.4, 1.4, 0.24)
7	53	57.4	55.8	60.6	51.8	57.2	7	48.2	46.4	49.8	47.2	58.6	55.8
10	57.6	64.4	57	62.6	54.2	61.2	10	41	40.8	46.2	44.4	54.4	51
15	60.2	65	62	66.8	58.8	61.4	15	38.4	38.2	40.6	40.6	46.6	43.2
20	61.8	64.2	64.8	65.8	60.4	60	20	36	36.2	36.2	37.6	43.4	42.4
25	63.6	67	67.8	69.6	62	61.8	25	32.2	32	33.4	34.4	41.6	41.2
30	65.8	67	68.2	70.2	64.6	65	30	30.4	29.8	35	35	41.4	40.8

[1] Section Editor: Patrícia Cia

Brasil

Brasil

Is it possible to apply the regional frequency analysis to daily extreme air temperature data?

ABSTRACT