Volume 8

Issue 1

##### Environmental Development

JOURNAL OF

POLISH

AGRICULTURAL

UNIVERSITIES

Available Online: http://www.ejpau.media.pl/volume8/issue1/art-04.html

**
ARTIFICIAL NEURAL NETWORKS USE FOR RAINFALL-RUNOFF EROSIVITY FACTOR ESTIMATION
**

Paweł Licznar*
Institute of Building and Landscape Architecture,
Agricultural University of Wroclaw, Poland*

Proposed by Wischmeier and Smith rainfall-runoff erosivity factor (R-factor) is usually recognized as a proper tool for regional climatic condition description in respect to soil erosion by water. It is also a basic input to simple and widespread soil erosion prediction models like USLE and RUSLE. However its calculation on the base of original precipitation records is a very laborious operation and is completely impossible for many locations without a precise precipitation data. The aim of the research was to develop a new simple method of annual R-factor values estimation on the base of very general precipitation data. Examined was the possibility of implementing artificial neural networks for annual R-factor values estimation on the base of the sole summer period and annual precipitation totals. The research was conducted with the use of database containing calculated summer period and annual rainfall-runoff erosivity factor values from 138 stations in Germany. As a result of the study 3 radial basis function networks (RBF) of two to five hidden layer neurons and 2 multilayer perceptrons networks (MLP) with one and two hidden layers were developed. Obtained correlation coefficients of observed versus predicted R-factor values were higher then the coefficients reported previously for the simple linear regression models. The study results suggested the possibility of neural networks technology introduction for R-factor values estimation on the base of precipitation totals instead of simple statistical regional relationships.

**Key words:**
Artificial neural networks, rainfall-runoff erosivity factor, estimation.

**INTRODUCTION**

Rainfall-runoff erosivity factor (R-factor) estimation is the key issue for proper soil erosion by water modeling and land potential and real water erosion hazard estimation. Proposed by Wischmeier and Smith R-factor is generally considered as a useful tool for regional climatic condition description in respect to soil erosion by water [13]. It is a basic input parameter for popular soil-loss equations, like: USLE (Universal Soil Loss Equation) and RUSLE (Revised Universal Soil Loss Equation) [1,2,11,13]. Longtime, at least 22-year rainfall registrations and their detail analysis are necessary for the calculation of R-factor, since it is a total of single storms´ rainfall erosivity, calculated according to the formula [1-4,6,8]:

where:

Rr_{j} - single rainstorm erosivity [1 - EU=1·MJ·ha^{-1}·cm·h^{-1}],

Ek - rainstorm kinetic energy [J·m^{-2}],

I_{30} - maximal 30-min intensity [cm·h^{-1}].

The rainstorm kinetic energy has to be calculated as a total of kinetic energy values for different periods of the storm having different constant intensities. The kinetic energy value for a single period of the storm with a constant intensity is given by the equation [8]:

where:

Ek_{i} - kinetic energy for a single i period of the rainstorm [J·m^{-2}],

I_{i} - storm intensity for i period [cm·h^{-1}],

P_{i} - precipitation total for i period [cm].

The lack of longtime storm intensity registrations and time-consuming procedure of factor calculation do not allow for soil erosion by water proper prediction and soil degradation hazard estimation for many locations. Because of this a number of methods for annual R-factor approximation on the base of some general precipitation data characteristics was proposed. Most popular ones are the simple statistical linear regression models of annual R-factor versus total annual precipitation. More sophisticated Arnoldus and Fournier´s indexes methods are based on the monthly and annual precipitation totals [8]. However the above mentioned methods are of strictly regional nature, based on the set of regional parameters and of very limited accuracy.

Having in mind widespread introduction of modern computation techniques on the field of environmental monitoring and modeling, the new ways of R-factor estimation should be developed to meet a better precision and user-friendly goals. Goovaerts has proposed to use elevation to aid the geostatistical mapping of rainfall erosivity [5]. The artificial neural networks were already successful adopted for a number of different nature meteorological problems solutions [7,9] and for soil erosion and runoff prediction at the plot scale [10].

The aim of the research was to examine the possibility of implementing artificial neural networks for annual R-factor values estimation on the base of general precipitation data. It was a preliminary study conducted to p a methodology useful for future R-factor map development for Poland.

**MATERIALS AND METHODS**

The database containing calculated summer period (R_{summer}) and annual (R_{annual}) rainfall-runoff erosivity factor values and registered mean summer period, from May to October, (P_{summer}) and annual (P_{annual}) precipitation totals for 138 stations in Germany was used as a study material. It was the data used formerly by Sauerborn for Germany R-factor map plotting [12]. The general tendency of R-factor values raise with the total precipitations values raise was easy to be observed for the most of the data. The lowest annual rainfall-runoff erosivity factor value R_{annual}=21.9EU [1·EU=1·MJ·ha^{-1}·cm·h^{-1}], was calculated for Elsdorf station with the annual average precipitation of 481 mm only. Whereas the highest value of annual factor (R_{annual}=151.6EU) was calculated for Berchtesgaden station with the annual average precipitation of 1539 mm.

All the data was divided into three subsets: training, validation and test. Dividing of the data into three subsets was mandatory, since the "early stopping" method for improving the generalization of networks was implemented at the training stage. All the subset consisted of the precipitation and calculated R-factor data for 46 different stations each. Some basic characteristic of the data subsets with respect to R-factor values can be found at tab. 3. Precipitation totals: P_{summer} and P_{annual} were the networks inputs and the rainfall-runoff erosivity factor values: R_{summer} and R_{annual} were the networks outputs.

All the computations were made with the use of Statistica 6.0 software and its Neural Networks application. The architectures of 50 different neural networks were developed and their performances were evaluated at the frame of the study. It was possible and made at once with the use of automatic developer command of Networks application. Analyzed were different radial basis function networks with up to 10 neurons in the hidden layers and multilayer perceptrons with up to 2 hidden layers having up to 10 neurons each. Networks´ training was performed according to backpropagation and K-means algorithms in case of multilayer perceptrons and radial basis function networks respectively. As the final result of this trail and error process 5 different architecture networks of best performance were selected. The results of their training and performance are presented below.

**RESULTS AND DISCUSSION**

The chosen networks´ group consisted of 3 radial basis function networks (RBF) of two to five hidden layer neurons and 2 multilayer perceptrons networks (MLP) with one and two hidden layers. Their architectures are presented on fig. 1 and described in detail at tab.1. Training process quality had a value of about 0.6 for all networks and data subsets (tab. 2). The highest registered values of networks´ errors were equal to 0.11 for nets 2 and 3 in case of test subsets. However in general error values were lower and at the range of 0.02-0.07 (tab. 2).

Fig.1. Architecture of developed neural networks: a) net 1 - RBF 2:2-5-2:2, b) net 2 - MLP 2:2-4-2:2 c) net 3 - MLP 2:2-10-5-2:2, d) net 4 - RBF 2:2-2-2:2, e) net 5 - RBF 2:2-3-2:2 |

Table 1. Basis characteristic of developed artificial neural networks´ architecture |

No |
Net type |
Number of neurons in the layers |
Post Synaptic Potential (PSP) functions used |
Activation functions used |
|||

Input layer |
The first hidden layer |
The second hidden layer |
Output layer |
||||

1 |
RBF 2:2-5-2:2 |
2 |
5 |
- |
2 |
linear, radial, linear |
linear, exponential, linear |

2 |
MLP 2:2-4-2:2 |
2 |
4 |
- |
2 |
linear, linear, linear |
linear, hyperbolic, logistic |

3 |
MLP 2:2-10-5-2:2 |
2 |
10 |
5 |
2 |
linear, linear, linear, linear |
linear, hyperbolic, hyperbolic, logistic |

4 |
RBF 2:2-2-2:2 |
2 |
2 |
- |
2 |
linear, radial, linear |
linear, exponential, linear |

5 |
RBF 2:2-3-2:2 |
2 |
3 |
- |
2 |
linear, radial, linear |
linear, exponential, linear |

Table 2. Training process performance of developed neural networks |

No |
Net type |
Quality for subsets |
Error for subsets |
||||

Training |
Validation |
Test |
Training |
Validation |
Test |
||

1 |
RBF 2:2-5-2:2 |
0.597484 |
0.623160 |
0.562124 |
0.027297 |
0.021540 |
0.031543 |

2 |
MLP 2:2-4-2:2 |
0.603493 |
0.590687 |
0.543725 |
0.103655 |
0.073683 |
0.114123 |

3 |
MLP 2:2-10-5-2:2 |
0.602873 |
0.590753 |
0.542907 |
0.103766 |
0.073588 |
0.114411 |

4 |
RBF 2:2-2-2:2 |
0.639812 |
0.640724 |
0.593025 |
0.029723 |
0.022244 |
0.032739 |

5 |
RBF 2:2-3-2:2 |
0.602563 |
0.600294 |
0.588970 |
0.027782 |
0.020523 |
0.037191 |

Table 3. The regression statistics of observed versus predicted R_{summer} and R_{annual} rainfall-runoff erosivity factor values for different networks and data subsets |

Subset |
Training |
Validation |
Test |
|||

Parameter |
R |
R |
R |
R |
R |
R |

Net 1 |
||||||

Data Mean |
55.30000 |
46.33409 |
50.46591 |
41.32727 |
53.17209 |
40.78837 |

Data S.D. |
20.66784 |
20.68482 |
15.53913 |
12.05011 |
21.63962 |
21.96549 |

Error Mean |
-0.00000 |
-0.00000 |
1.31536 |
2.09126 |
2.86718 |
6.50261 |

Abs. E. Mean |
12.34870 |
11.51749 |
9.68336 |
8.81338 |
12.16414 |
13.50725 |

Error S.D. |
9.52072 |
8.94088 |
7.64821 |
7.35468 |
10.37541 |
12.75136 |

S.D. Ratio |
0.59748 |
0.55681 |
0.62316 |
0.73139 |
0.56212 |
0.61493 |

Correlation |
0.80188 |
0.83064 |
0.81530 |
0.70675 |
0.83380 |
0.78872 |

Net 2 |
||||||

Data Mean. |
55.30000 |
46.33409 |
50.46591 |
41.32727 |
53.17209 |
40.78837 |

Data S.D. |
20.66784 |
20.68482 |
15.53913 |
12.05011 |
21.63962 |
21.96549 |

Error Mean. |
-0.10915 |
-0.15594 |
0.85416 |
1.48642 |
3.11121 |
6.47046 |

Abs. E. Mean. |
12.47290 |
11.82003 |
9.17876 |
7.92180 |
11.76601 |
12.78433 |

Error S.D. |
9.78051 |
9.57715 |
7.18194 |
6.56042 |
10.26979 |
11.91527 |

S.D. Ratio |
0.60349 |
0.57144 |
0.59069 |
0.65740 |
0.54373 |
0.58202 |

Correlation |
0.79783 |
0.82120 |
0.82232 |
0.75375 |
0.83970 |
0.81544 |

Net 3 |
||||||

Data Mean. |
55.30000 |
46.33409 |
50.46591 |
41.32727 |
53.17209 |
40.78837 |

Data S.D. |
20.66784 |
20.68482 |
15.53913 |
12.05011 |
21.63962 |
21.96549 |

Error Mean. |
-0.32845 |
-0.16088 |
0.59472 |
1.07904 |
2.85987 |
6.39285 |

Abs. E. Mean. |
12.46007 |
11.85349 |
9.17978 |
7.98481 |
11.74829 |
12.95528 |

Error S.D. |
9.70157 |
9.55022 |
7.15016 |
6.58762 |
10.21160 |
12.04765 |

S.D. Ratio |
0.60287 |
0.57305 |
0.59075 |
0.66263 |
0.54291 |
0.58980 |

Correlation |
0.79827 |
0.81955 |
0.82418 |
0.74954 |
0.84011 |
0.80792 |

Net 4 |
||||||

Data Mean. |
55.30000 |
46.33409 |
50.46591 |
41.32727 |
53.17209 |
40.78837 |

Data S.D. |
20.66784 |
20.68482 |
15.53913 |
12.05011 |
21.63962 |
21.96549 |

Error Mean. |
-0.00000 |
-0.00000 |
1.05381 |
1.12391 |
3.16638 |
6.61212 |

Abs. E. Mean. |
13.22354 |
12.77667 |
9.95629 |
9.37304 |
12.83283 |
13.85262 |

Error S.D. |
10.42513 |
10.37550 |
8.27708 |
7.76412 |
11.14431 |
12.77618 |

S.D. Ratio |
0.63981 |
0.61768 |
0.64072 |
0.77784 |
0.59302 |
0.63065 |

Correlation |
0.76853 |
0.78643 |
0.79824 |
0.64174 |
0.80806 |
0.78272 |

Net 5 |
||||||

Data Mean. |
55.30000 |
46.33409 |
50.46591 |
41.32727 |
53.17209 |
40.78837 |

Data S.D. |
20.66784 |
20.68482 |
15.53913 |
12.05011 |
21.63962 |
21.96549 |

Error Mean. |
0.00000 |
0.00000 |
1.13573 |
1.61070 |
4.63843 |
9.56131 |

Abs. E. Mean. |
12.45368 |
11.84444 |
9.32804 |
8.38384 |
12.74509 |
15.94581 |

Error S.D. |
9.55610 |
9.17540 |
7.60161 |
6.67443 |
10.83997 |
14.03690 |

S.D. Ratio |
0.60256 |
0.57262 |
0.60029 |
0.69575 |
0.58897 |
0.72595 |

Correlation |
0.79807 |
0.81982 |
0.85053 |
0.71904 |
0.83696 |
0.82803 |

1 Average value of the target output variable. |

Low error values registered at the end of networks training were confirmed by the results of regression analysis of observed versus predicted R_{summer} and R_{annual} rainfall-runoff erosivity factors. The statistic of the regression analysis for all the networks and datasets were presented at tab. 3. Registered correlation coefficients were usually close to or a little bit higher then 0.8. Smaller values of correlation coefficient, at the range of 0.64-0.75, were observed only in case of validation subset and R_{summer} predictions. Obtained correlation coefficients were in general higher then the coefficients reported by Sauerborn for the simple linear regression models. Correlation coefficients of the linear models were equal to 0.79 for R_{annual }and P_{annual} relationship, 0.57 for R_{summer} and P_{summer} relationship and only 0.45 for R_{annual }and P_{summer} relationship [12].

However the correlation coefficient values were high, the precision of networks predictions was limited. It is confirmed by the quite high average absolute error values (tab. 3). The highest value of average absolute error (15.9) was observed in case of net 5 R_{summer }predictions for the test subset. Limited precision of the net 5 predictions can also be recognized on the base of observed versus predicted R-factor values graphs´ analysis (fig. 2-3). Probably the neural networks´ input should be supported with a more detailed precipitation characteristic (for example monthly precipitation totals) for the R-factor prediction precision increase. However even in a case of net 5, predictions were quite reasonable, since the increase in the annual and summer precipitation totals led to the annual and summer R-factor values increase (see fig. 4 and 5 respectively).

Fig.2. Observed versus predicted R_{annual} by net 5 |

Fig.3. Observed versus predicted R_{summer} by net 5 |

Fig.4. Visualization of R_{summer} predictions by net 5 |

Fig.5. Visualization of R_{annual} predictions by net 5 |

**CONCLUSIONS**

Artificial neural networks of different architectures, even simple ones like single-hidden layer perceptrons and radial basis function networks (RBF) can be successfully implemented for annual and summer period rainfall-runoff erosivity factor values estimation on the base of very general precipitation data. The results of this study suggest the possibility for using neural networks to estimate R-factor values on the base of total precipitations instead of simple statistical regional relationships. However for better prediction accuracy results new neural networks with more detailed precipitation characteristics presented on inputs should be developed in the future.

**ACKNOWLEDGEMENT**

This work was partially supported by the Polish State Committee for Scientific Research - KBN grant 5P06302324. Author wish to thank the Foundation for Polish Science (FNP) for financial support of his research and scientific development.

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Paweł Licznar

Institute of Building and Landscape Architecture,

Agricultural University of Wroclaw, Poland

Plac Gruwaldzki 24, 50-363 Wrocław, Poland

Phone (048)-71-3482-850

email: licznarp@ozi.ar.wroc.pl

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.