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Soil loss is one of the main causes of pauperization and alteration of agricultural soil properties. Various empirical models (e.g., USLE) are used to predict soil losses from climate variables which in general have to be derived from spatial interpolation of point measurements. Alternatively, Artificial Neural Networks may be used as a powerful option to obtain site-specific climate data from independent factors. This study aimed to develop an artificial neural network to estimate rainfall erosivity in the Ribeira Valley and Coastal region of the State of São Paulo. In the development of the Artificial Neural Networks the input variables were latitude, longitude, and annual rainfall and a mathematical equation of the activation function for use in the study area as the output variable. It was found among other things that the Artificial Neural Networks can be used in the interpolation of rainfall erosivity values for the Ribeira Valley and Coastal region of the State of São Paulo to a satisfactory degree of precision in the estimation of erosion. The equation performance has been demonstrated by comparison with the mathematical equation of the activation function adjusted to the specific conditions of the study area.

Erosion is considered one of the main causes of depauperation and alteration of soil properties and, consequently, of loss of agricultural soil. Mathematical models are used to quantify and/or predict such losses [

The

Water erosion is causing severe problems to the population that live in the State of São Paulo, such as loss of soil from arable farmland, reduction in public investments in infrastructure works, and degradation in urban areas. Seven thousand cases of gullies, estimated currently, exist in the territory of the State of São Paulo. The cost of the corrective actions required for the stabilization of this geological phenomenon that causes severe water erosion corresponds to 20% of the State’s budget, excluding the costs of restoration of degraded urban areas, constructions, and urban street design schemes, among others. Water erosion in agricultural land is even more critical, for it is estimated that 80% of São Paulo’s agricultural soils are affected by erosion.

The procedures used to estimate rainfall erosivity (

One of the main techniques within ML is the Artificial Neural Networks (ANNs). According to Persson et al. [

An ANN is composed of a set of computational elements called artificial neurons, which relate the output and input values through the following equation:

According to Saito et al. [

Based on the proposition of Moreira et al. [

Part of the study area (Vale do Ribeira) is considered by the United Nations Educational, Scientific and Cultural Organization (UNESCO) as Mata Atlântica biosphere reserve. According to Romão [

The study was conducted in the Ribeira Valley and Coastal region of the State of São Paulo, Brazil (Figure

Altitude, latitude, longitude, annual precipitation, and erosivity of 32 municipalities of the Ribeira Valley and Coastal region of the State of São Paulo.

Municipality | Alt. (m) | Lat. | Long. | Annual precipitation (mm) | |
---|---|---|---|---|---|

870 | 24.42 | 48.65 | 1613.53 | 8612 | |

770 | 24.47 | 49.02 | 1506.12 | 8029 | |

660 | 24.97 | 48.33 | 1986.20 | 10320 | |

3 | 23.8 | 46 | 2295.70 | 11455 | |

80 | 24.78 | 48.18 | 1492.18 | 8848 | |

7 | 24.93 | 47.95 | 2410.09 | 12410 | |

5 | 23.87 | 46.38 | 2774.83 | 13075 | |

20 | 24.52 | 48.1 | 1602.26 | 9273 | |

2 | 23.95 | 46.3 | 2005.74 | 10469 | |

6 | 24.7 | 47.53 | 1567.58 | 8401 | |

2 | 24.9 | 47.8 | 2299.16 | 11469 | |

750 | 23.95 | 46.8 | 1950.91 | 9746 | |

180 | 24.65 | 48.83 | 1327.62 | 7467 | |

(14) Itapirapuã | 580 | 24.57 | 49.17 | 1549.34 | 8323 |

(15) Itariri | 50 | 24.28 | 47.18 | 2249.43 | 11887 |

(16) Jacupiranga | 90 | 24.72 | 48.02 | 1506.09 | 8673 |

(17) Juquiá | 20 | 24.1 | 47.68 | 1794.72 | 9768 |

(18) Juquitiba | 730 | 23.97 | 46.9 | 1897.24 | 10496 |

(19) Miracatu | 30 | 24.25 | 47.37 | 1582.48 | 9765 |

(20) Mongaguá | 20 | 24.08 | 46.62 | 2612.11 | 12685 |

(21) Pariquera Açu | 30 | 24.72 | 47.88 | 1535.12 | 8697 |

(22) Pedro de Toledo | 60 | 24.28 | 47.23 | 1521.21 | 8594 |

(23) Peruíbe | 3 | 24.32 | 47.02 | 2121.70 | 12029 |

(24) Praia Grande | 10 | 24.03 | 46.55 | 2655.47 | 13188 |

(25) Registro | 60 | 24.4 | 47.75 | 1760.53 | 9702 |

(26) Ribeira | 160 | 24.65 | 49.02 | 1343.88 | 7470 |

(27) Santos | 200 | 23.88 | 46.22 | 3615.38 | 15919 |

(28) São Lourenço | 890 | 23.78 | 46.93 | 1567.33 | 9409 |

(29) São Sebastião | 20 | 23.77 | 45.42 | 1305.28 | 7988 |

(30) São Vicente | 10 | 23.97 | 46.37 | 2432.45 | 12015 |

(31) Sete Barras | 20 | 24.38 | 47.93 | 1582.53 | 8921 |

(32) Tapiraí | 870 | 23.97 | 47.5 | 1819.58 | 9764 |

Maximum value | 890.000 | 24.970 | 49.170 | 3615.380 | 15919.000 |

Minimum value | 2.000 | 23.770 | 45.420 | 1305.280 | 7467.000 |

Average value | 225.250 | 24.313 | 47.457 | 1915.118 | 10152.094 |

Standard deviation | 324.730 | 0.371 | 0.957 | 518.301 | 1973.046 |

Location of the study area: Ribeira Valley and Coastal region of the State of São Paulo, Brazil.

The

The

The analysis was performed by means of ML study. The results were obtained using 10-

The correlation coefficient (

The efficiency coefficient (

The spatial distribution of erosivity (

The input variables composed by the latitude, longitude, altitude, and the average annual precipitation values for each station made it possible to adjust (

Table

Summary of the descriptive statistical analysis of erosivity values estimated by Silva et al. [

Indexes | Result |
---|---|

Correlation coefficient ( | 0.97 |

Agreement index ( | 0.99 |

Confidence interval ( | 0.96 |

Efficiency coefficient ( | 0.95 |

Mean absolute error (MAE) | 294.91 |

Mean square error (MSE) | 168711.78 |

Root mean squared error (RMSE) | 410.75 |

Mean percent error (MPE) (%) | 2.95 |

The values found for the correlation coefficient and the agreement index were, respectively, 0.97 and 0.99. As it is known, the more precise and accurate results for

The lower the percentage error, the higher the efficiency of the method used. According to literature, values close to 10% are too low for accurate estimation of rainfall erosivity [

The variability in altitude values shown in the dispersion in data in relation to the mean (Table

The average annual value of rainfall erosivity estimated for the Ribeira Valley and Coastal region of the State of São Paulo, based on the equation of Silva et al. [

Results of the estimation of rainfall erosivity (

Municipality | RPE | ||
---|---|---|---|

Apiaí | 8612 | 8593 | 1,00 |

Barra do Chapéu | 8029 | 8225 | 0,98 |

Barra do Turvo | 10320 | 10198 | 1,01 |

Bertioga | 11455 | 11544 | 0,99 |

Cajati | 8848 | 8613 | 1,03 |

Cananéia | 12410 | 12055 | 1,03 |

Cubatão | 13075 | 13281 | 0,98 |

Eldorado | 9273 | 8990 | 1,03 |

Guarujá | 10469 | 10493 | 1,00 |

Iguape | 8401 | 8957 | 0,94 |

Ilha Comprida | 11469 | 11657 | 0,98 |

Itanhaém | 9746 | 9925 | 0,98 |

Itaoca | 7467 | 7885 | 0,95 |

Itapirapuã | 8323 | 8476 | 0,98 |

Itariri | 11887 | 11366 | 1,05 |

Jacupiranga | 8673 | 8659 | 1,00 |

Juquiá | 9768 | 9634 | 1,01 |

Juquitiba | 10496 | 9734 | 1,08 |

Miracatu | 9765 | 8913 | 1,10 |

Mongaguá | 12685 | 12706 | 1,00 |

Pariquera Açu | 8697 | 8803 | 0,99 |

Pedro de Toledo | 8594 | 8694 | 0,99 |

Peruíbe | 12029 | 10941 | 1,10 |

Praia Grande | 13188 | 12864 | 1,03 |

Registro | 9702 | 9553 | 1,02 |

Ribeira | 7470 | 7938 | 0,94 |

Santos | 15919 | 16285 | 0,98 |

São Lourenço | 9409 | 8412 | 1,12 |

São Sebastião | 7988 | 7955 | 1,00 |

São Vicente | 12015 | 12049 | 1,00 |

Sete Barras | 8921 | 8900 | 1,00 |

Tapiraí | 9764 | 9340 | 1,05 |

Maximum value | 15919,00 | 16285,00 | 0,94 |

Minimum value | 7467,00 | 7885,00 | 1,12 |

Average value | 10152,09 | 10051,19 | 1,02 |

Standard deviation | 1973,05 | 1945,88 | 0,09 |

The equation obtained through the ANN showed higher rainfall erosivity values in 15 of the 32 municipalities of the study area when compared to the values estimated by Silva et al. [

Erosivity values estimated by Silva et al. [

The spatial distribution of rainfall erosivity obtained by Silva et al. [

Spatial distribution of rainfall erosivity (MJ mm

The use of artificial neural networks was found to be viable for the interpolation of rainfall erosivity values for the Ribeira Valley and Coastal region of the State of São Paulo and can be used to a satisfactory degree of precision in the estimation of erosion

The best-fit equation generated by the ANN was a multivariate linear function, with its performance proven when compared to the equation of the activation function adjusted to the conditions of the study area.

The authors thank FUNDUNESP to have contributed part of the rate of publication of this manuscript.