Rainfall Prediction in the State of Paraíba, Northeastern Brazil Using Generalized Additive Models
Abstract
:1. Introduction
2. Data and Methods
2.1. Study Area
2.2. Data
2.3. Methods
2.3.1. Descriptive Analysis
2.3.2. GAMLSS Model
2.3.3. Model Evaluation Criteria
2.3.4. Efficiency for Seasonal Prediction
3. Results
3.1. Series Investigation
3.2. Application of the GAMLSS Model
3.3. Quantile Prediction
3.4. Efficiency Indicators
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Distribution Function | Abbreviation | Probability Density Function |
---|---|---|
Gamma | GA | to |
Generalized Gamma | GG | to |
Zero Adjusted Gamma | ZAGA | to |
Gumbel | GU | to |
Logistic | LO | to |
Log-Normal | LOGNO | to |
Weibull | WEI | |
to |
Quantiles | Rating |
---|---|
p < Q(0.05) | Extremely dry |
Q(0.05) < p < Q(0.15) | Very dry |
Q(0.15) < p < Q(0.35) | Dry |
Q(0.35) < p < Q(0.65) | Normal |
Q(0.65) < p < Q(0.85) | Rainy |
Q(0.85) < p < Q(0.95) | Very rainy |
Q(0.95) < p | Extremely rainy |
Region | Niño 1 + 2 | Niño 3 | Niño 3.4 | Niño 4 | SOI | AMO | PDO | TNA | TSA |
---|---|---|---|---|---|---|---|---|---|
R1 | 0 | 0 | 0 | 7 | 3 | 0 | 0 | 3 | 1 |
R2 | 0 | 0 | 0 | 7 | 3 | 0 | 0 | 3 | 1 |
R3 | 0 | 0 | 0 | 7 | 3 | 0 | 0 | 3 | 1 |
R4 | 2 | 2 | 2 | 6 | 3 | 0 | 0 | 3 | 2 |
R5 | 2 | 2 | 2 | 6 | 3 | 0 | 0 | 3 | 2 |
Location | Region | Distribution | AIC | BIC |
---|---|---|---|---|
Alhandra | R1 | GG | 4268.73 | 4338.68 |
Mataraca | R1 | GG | 4042.68 | 4081.54 |
Santa Rita | R1 | GG | 3978.83 | 4033.24 |
Areia | R1 | GG | 3954.90 | 4013.20 |
Bananeiras | R2 | ZAGA | 3946.78 | 3989.53 |
Mamanguape | R2 | GG | 4000.79 | 4055.20 |
Sapé | R2 | GG | 3838.31 | 3900.49 |
Araruna | R3 | GG | 3638.50 | 3696.79 |
Campina Grande | R3 | GG | 3618.09 | 3656.95 |
Ingá | R3 | ZAGA | 3571.23 | 3617.87 |
Itabaiana | R3 | GG | 3571.47 | 3629.76 |
Umbuzeiro | R3 | ZAGA | 3701.84 | 3752.36 |
Barra de Santa Rosa | R4 | ZAGA | 3313.38 | 3360.02 |
Caraúbas | R4 | ZAGA | 3183.71 | 3242.00 |
Pedra Lavrada | R4 | ZAGA | 3148.88 | 3207.17 |
Picuí | R4 | ZAGA | 3239.29 | 3285.92 |
Pocinhos | R4 | ZAGA | 3189.53 | 3240.05 |
Salgadinho | R4 | ZAGA | 3292.98 | 3335.73 |
Santa Luzia | R4 | ZAGA | 3344.64 | 3406.82 |
São João do Cariri | R4 | ZAGA | 3356.13 | 3410.54 |
São João do Tigre | R4 | ZAGA | 3276.69 | 3334.98 |
Soledade | R4 | ZAGA | 3297.82 | 3332.80 |
Sumé | R4 | ZAGA | 3376.54 | 3419.28 |
Taperoá | R4 | ZAGA | 3501.20 | 3551.72 |
Água Branca | R5 | ZAGA | 3675.94 | 3730.34 |
Aguiar | R5 | ZAGA | 3670.64 | 3721.16 |
Belém do Brejo do Cruz | R5 | ZAGA | 3553.75 | 3592.61 |
Bonito de Santa Fé | R5 | ZAGA | 3751.72 | 3802.24 |
Brejo do Cruz | R5 | ZAGA | 3674.20 | 3724.72 |
Cajazeiras | R5 | ZAGA | 3853.81 | 3896.55 |
Catingueira | R5 | ZAGA | 3587.68 | 3630.43 |
Catolé do Rocha | R5 | ZAGA | 3678.56 | 3740.74 |
Conceição | R5 | ZAGA | 3641.92 | 3711.87 |
Imaculada | R5 | ZAGA | 3554.64 | 3628.47 |
Mãe D’Água | R5 | ZAGA | 3463.90 | 3518.31 |
Malta | R5 | ZAGA | 3612.42 | 3666.82 |
Manaíra | R5 | ZAGA | 3631.18 | 3689.47 |
Nova Olinda | R5 | ZAGA | 3714.25 | 3780.31 |
Patos | R5 | ZAGA | 3656.41 | 3718.59 |
Pombal | R5 | ZAGA | 3646.57 | 3708.77 |
Princesa Isabel | R5 | ZAGA | 3694.23 | 3748.63 |
São João do Rio do Peixe | R5 | ZAGA | 3710.70 | 3776.77 |
São José de Piranhas | R5 | ZAGA | 3746.43 | 3816.37 |
Sousa | R5 | ZAGA | 3685.23 | 3739.64 |
Triunfo | R5 | ZAGA | 3666.80 | 3728.98 |
Period | Scenario | MAE (mm) | PBIAS (%) | RMSE (mm) | R2 (%) |
---|---|---|---|---|---|
DJF | S1 | 59.56 | 55.1 | 60.87 | 0.65 |
S2 | 71.14 | 65.9 | 75.23 | 0.62 | |
JFM | S1 | 34.21 | 25.3 | 37.54 | 0.8 |
S2 | 45.11 | 33.3 | 45.54 | 0.75 | |
FMA | S1 | 12.95 | −4.2 | 15.02 | 0.96 |
S2 | 1.31 | 0.5 | 1.64 | 0.99 | |
MAM | S1 | 85.25 | −34 | 86 | 0.66 |
S2 | 79.65 | −31.8 | 79.65 | 0.68 | |
AMJ | S1 | 69.62 | −28.2 | 70.19 | 0.72 |
S2 | 62.41 | −25.3 | 64.45 | 0.75 | |
MJJ | S1 | 49.27 | −22 | 69.05 | 0.74 |
S2 | 48.91 | −18.5 | 64.17 | 0.77 |
Period | Scenario | MAE (mm) | PBIAS (%) | RMSE (mm) | R2 (%) |
---|---|---|---|---|---|
DJF | S1 | 35.31 | 31.5 | 44.53 | 0.81 |
S2 | 29.19 | 26.2 | 36.89 | 0.84 | |
JFM | S1 | 25.27 | 17.6 | 30.53 | 0.32 |
S2 | 19.77 | 12.7 | 23.31 | 0.25 | |
FMA | S1 | 15.12 | −7.1 | 17.79 | 0.92 |
S2 | 12.51 | −9.5 | 13.44 | 0.9 | |
MAM | S1 | 64.68 | −34.6 | 71.69 | 0.64 |
S2 | 62.57 | −33.5 | 64.78 | 0.66 | |
AMJ | S1 | 47 | −25.8 | 53.4 | 0.73 |
S2 | 44.15 | −24.3 | 45.72 | 0.75 | |
MJJ | S1 | 30.4 | −18.4 | 39.19 | 0.79 |
S2 | 38.2 | −16.7 | 47.1 | 0.79 |
Period | Scenario | MAE (mm) | PBIAS (%) | RMSE (mm) | R2 (%) |
---|---|---|---|---|---|
DJF | S1 | 44.86 | 15.1 | 45.96 | 0.83 |
S2 | 37.06 | 1.8 | 37.08 | 0.78 | |
JFM | S1 | 21.97 | 17.1 | 24.71 | 0.96 |
S2 | 20.34 | 8.6 | 21.11 | 0.97 | |
FMA | S1 | 10.49 | 14.8 | 10.59 | 0.87 |
S2 | 3.58 | 5.1 | 3.62 | 0.95 | |
MAM | S1 | 15.91 | −16.7 | 17.83 | 0.83 |
S2 | 22.7 | −23.8 | 23.55 | 0.95 | |
AMJ | S1 | 12.86 | −12.8 | 13.73 | 0.88 |
S2 | 21.13 | −21 | 21.3 | 0.79 | |
MJJ | S1 | 22.67 | −7.6 | 23.79 | 0.86 |
S2 | 23.02 | −16.5 | 27.82 | 0.78 |
Period | Scenario | MAE (mm) | PBIAS (%) | RMSE (mm) | R2 (%) |
---|---|---|---|---|---|
DJF | S1 | 26.26 | 12.3 | 26.61 | 0.77 |
S2 | 27.28 | 11.8 | 27.6 | 0.76 | |
JFM | S1 | 14.86 | −0.2 | 14.86 | 0.88 |
S2 | 17.6 | −3.7 | 17.69 | 0.83 | |
FMA | S1 | 8.55 | 15.8 | 10.66 | 0.86 |
S2 | 5.66 | 10.6 | 7.11 | 0.9 | |
MAM | S1 | 4.36 | −2 | 4.43 | 0.98 |
S2 | 3.09 | −3.2 | 3.31 | 0.97 | |
AMJ | S1 | 10.03 | 26.8 | 12.35 | 0.86 |
S2 | 9.44 | 25.9 | 11.74 | 0.86 | |
MJJ | S1 | 13.13 | 68.5 | 16.68 | 0.76 |
S2 | 13.11 | 68.4 | 17.11 | 0.77 |
Period | Scenario | MAE (mm) | PBIAS (%) | RMSE (mm) | R2 (%) |
---|---|---|---|---|---|
DJF | S1 | 15.33 | −16.8 | 20.28 | 0.82 |
S2 | 20.58 | −17.1 | 24.64 | 0.81 | |
JFM | S1 | 52.9 | −40.3 | 54.47 | 0.59 |
S2 | 55.35 | −42.3 | 59.26 | 0.56 | |
FMA | S1 | 47.08 | −37.6 | 52.52 | 0.61 |
S2 | 49.75 | −39.8 | 52.34 | 0.59 | |
MAM | S1 | 44.77 | −42.3 | 46.1 | 0.57 |
S2 | 43.65 | −41.2 | 44.29 | 0.59 | |
AMJ | S1 | 24.41 | −9.2 | 24.94 | 0.79 |
S2 | 22.77 | −3.8 | 22.87 | 0.84 | |
MJJ | S1 | 16.64 | 48.5 | 21.79 | 0.89 |
S2 | 18.84 | 64.9 | 24.98 | 0.8 |
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Dantas, L.G.; Santos, C.A.C.d.; Olinda, R.A.d.; Brito, J.I.B.d.; Santos, C.A.G.; Martins, E.S.P.R.; de Oliveira, G.; Brunsell, N.A. Rainfall Prediction in the State of Paraíba, Northeastern Brazil Using Generalized Additive Models. Water 2020, 12, 2478. https://doi.org/10.3390/w12092478
Dantas LG, Santos CACd, Olinda RAd, Brito JIBd, Santos CAG, Martins ESPR, de Oliveira G, Brunsell NA. Rainfall Prediction in the State of Paraíba, Northeastern Brazil Using Generalized Additive Models. Water. 2020; 12(9):2478. https://doi.org/10.3390/w12092478
Chicago/Turabian StyleDantas, Leydson G., Carlos A. C. dos Santos, Ricardo A. de Olinda, José I. B. de Brito, Celso A. G. Santos, Eduardo S. P. R. Martins, Gabriel de Oliveira, and Nathaniel A. Brunsell. 2020. "Rainfall Prediction in the State of Paraíba, Northeastern Brazil Using Generalized Additive Models" Water 12, no. 9: 2478. https://doi.org/10.3390/w12092478