ANALYSES OF CALCULATION METHODS FOR DETERMINATION OF RAIN EROSIVITY FOR SLOVAK REPUBLIC

On the basis of provided data from Slovak Hydrometeorlogical Institute were realized the calculation of rain factor for each rain-guage stations. Because provided data were in digital form, we proceeded to digital processing in graphical environment of Microsoft Excel i.e. each minutes of chosen rain were considered for separate rain division. Calculated data were compared with published values of Soil Science and Conservation Research Institute (SSCRI) and also with Methodology for implementation of research results into agricultural practise. From calculated values were created also the lines of exceedance of probability, which give detail information about occurrence of calculated values of rain factor once per 100, 50, 20, 10, 5 and 1 year. Also there were compared the different methodologies of rain factor calculation and kinetic energy of rain and their influence on final values. From calculated values there were found out that on all examined localities are our calculated values several times higher than in listed publications. These differences can be caused by different methods of data processing but also by number of processed years, because values of rain factor in listed publication were calculated for lower number of years. According to calculated values were created the redistribution of rain factor values on particular months of vegetation periods and it was found out that the highest percentage fall on summer months (June, July, August) and on the other hand, the lowest percentage, on the months April and October, therefore it is necessary to attach importance on soil erosion control especially in summer months. Comparison of different methods of data processing (digital vs. graphical) showed up, that differences in final values of rain factor by using of different methods of data processing are minimal, therefore it can be assumed that used methodology is right. Relations for kinetic energy calculation and different methodologies also significantly influenced final values of rain factor. Calculation of rain according different authors showed up that using relation for kinetic energy designed by Marshall, were obtained lower values, which influenced the final value of rain factor i.e. its final values was more closer to puISSN 1644-0765 DOI: http://dx.doi.org/10.15576/ASP.FC/2015.14.4.5 www.acta.media.pl


INTRODUCTION
The simplest definition of soil fertility is the ability of soil to supply plant nutrients.This ability can be significantly disrupted by many factors.One of these factors is soil erosion which is caused by water concretely by rain.
Soil creates the environment for plants, animals and definitely for man and also represents irreplaceable resource for man.World population increased from 2 to 10.000,000 from the beginning of agricultural production 10 to 12.000 years ago, to 6.5 billion in 2006 and may stabilize to 10-12 billion in 2010.This constantly growing numbers lead us to think about the importance of soil protection, which has incalculable value to mankind.
Soil erosion by water is one of the most widespread forms of soil degradation in Europe affecting an estimated 105 million ha, or 16% of Europe's total land area (excluding the Russian federation; EEA, 2003) [The State of Soil in Europe 2012].In condition of Slovak Republic predominates manifestations of water erosion and potentially is endangered 39,65% (957 173 ha) of agricultural soil [Soil as the Component of Environment in Slovak Republic 2010Republic , 2011]].These alarming numbers invoke detailed need of research of soil water erosion.One of the factors which influenced the rainfall erosion is rainfall erosivity factor R. There are lots of different ways how to calculate rainfall erosivity factor and one of the well know is methodology designed by Wischmeier and Smith [1978].

MATERIAL AND METHODS
Slovak Hydrometeorological Institute in Bratislava provided data about one minute precipitation for chosen meteorological stations situated in area of southwestern Slovakia.Totally were processed data from 5 meteorological stations for different time period.We used the methodology of Wischmeier and Smith [1978] which considers the erosive effective rainfall, those rainfalls, which are higher than 12.5 mm and with intensity higher than 24.00 mm • h -1 in one rain division.The main different in this work is that each minute of rain was consider for individual rain division.The following equations were used for calculation of rain factor: where: R -rain factor, MJ where: KE -kinetic energy of rain, J • m -2 • mm -1 , H z -pecipitation height, mm.
The main difference in this work is that, for the data preparation was design new methodology which is modified Wischmeier and Smith methodology i.e. the chosen effective erosive rainfalls were not divided into rain divisions but each minute of selected rains were considered for individual rain division.This designed methodology eliminates the individual mistakes for choosing of rain divisions.
In the past was also used methodology designed by Wischmeier and Smith, but this methodology used data about precipitation in graphical form.But in the present time are data not only about precipitation recorded in digital form i.e. the data are more detailed and therefore it is better to do calculation with using of these data.The Figure 1 shows the preparation of data for consequent calculation of rain factor.For the data preparation was design new methodology i.e. the chosen effective erosive rainfalls were not divided into rain divisions but each minute of selected rains were considered for individual rain division.This designed methodology eliminates the individual mistakes for choosing of rain divisions.
According Hudson [1971] is calculation of EI 30 and KE > 1 the same, but advantage of KE >1 index is that it can be used also for less detailed records about rains.For both these methodologies it is necessary to know rain depth, which fall down and also appropriate intensities.Simple calculation is introduced in Table 1.
Procedure of calculation according this methodology is following: 1.For chosen rain depth is calculated the rain intensity.2. Then is the rain arrange according intensities shown in the Table 1. 3. For each intensities groups is calculated kinetic energy according following equation: where: 4. At the end, the sums of each intensity are sum up and the total kinetic energy of rain is calculated After calculation of kinetic energy of each rain we proceeded according Wischmeier-Smith methodology i.e. maximal 30-minutes intensity was chosen and the values were inducted to the equation for calculation of rain factor.
The results obtained according Wischmeier and Smith methodology was compared with other introduced equations.These equations take into account the lack of data i.e. they calculate with annual precipitation data.Calculation of R-factor according Šabata [1978]: Šabata expressed rain factor for conditions of Slovak Republic depending on average annual precipitation height: where: H sa -average annual precipitation height, mm.
Expression of R-factor according Holý [1978] for whole year, respectively for vegetation period: where: Hs,r -average annual precipitation height, mm.

RESULTS AND DISCUSSION
The first created chart shows the comparison of frequency of precipitation in each years of examined period on the locality Sereď.The both methodology have different criteria for choosing of erosive effective rainfalls.Wischmeier andSmith andHudson, Sereď [1962-1966] As we can see from created chart, in the years 1963, 1965 and 1966 there occurred the differences in precipitation frequency.In others examined years were number of erosive effective rainfall same for both methodology.According Hudson methodology is number of erosive effective rainfall lower than number of erosive effective rainfalls according Wischmeier and Smith methodology.

Fig. 2. Comparison of precipitation frequency according
The Table 2 shows comparison of R-factor values, which was calculated with using both mentioned methodology i.e.Hudson and Wischmeier and Smith methodology for each year of examined period on Sereď locality.On the base of calculation method was created following Figure 3, which illustrates comparison of average values of rain factor.[1962][1963][1964][1965][1966] As we can see from listed chart, the value, which was calculated according Wischmeier and Smith methodology for meteorological station Sereď for period 1962-1966 is more than 2-times higher than value calculated according Hudson methodology.
Consequently were created charts from obtained values about redistribution of rain factor for each months of vegetation period.This step was necessary because we want to know how different methods of rain factor calculation influenced its redistribution during the vegetation period.
Despite the fact, that values of redistribution of rain factor are different, the highest percentage fall on the same months of vegetation period i.e. on months June, July and August and the lowest on April (when no erosive effective rainfall was observed according both methodologies) and then on September and October.
On the base of listed equation were calculated rain factor and subsequently were created line of exceedance for 50 years, from which were deducted values of rain factor that occur once per 100, 50, 20, 10, 5 and 1 year.These calculated values were compared with values calculated according Wischmeier-Smith formulas.Following tables show calculated values according different methodologies for meteorological stations Myjava and Hurbanovo.Sereď [1962Sereď [ -1966] ] Fig. 5. Redistribution of rain factor according Hudson on the particular months of vegetation period, Sereď [1962][1963][1964][1965][1966] As we can see from Table 3, the values which were calculated according Wischmeier and Smith methodology and subtracted from line of exceedance of probability for locality Myjava are approaching to values which were calculated according equations which take into account the lack of data, despite the fact that rain factor calculation according Wischmeier and Smith was calculated only for 10 years period.For locality Hurbanovo was also created table (Table 4) with calculated values.On this locality is situation quite different as on the locality Myjava.Values which were subtracted from line of exceedance of probability for repetition time 100, 50, 20, 10, 5 and 1 year are very different.For example precipitation occurrence once per 100 years is value calculated according Wischmeier-Smith up to 67 times lower than values calculated according Zachar [1981], Holý [1978] and Šabata [1978].But the situation is different when we look at average values of rain factor.The most is average value calculated according Wischmeier-Smith methodology (48,16 MJ • ha -1 • cm • h -1 ) approximate to average value of rain factor calculated according Zachar (50,60 MJ • ha -1 • cm • h -1 ).

CONCLUSION
Comparing the methodology of Hudson [1973] (KE > 1) and methodology of Wischemeier and Smith [1965], it was found out that the Hudson methodology used for the calculation and the calculated values of R-factor are almost 2-times lower than with using the methodology of Wischmeier and Smith.Also it was found out that aside from used methodology the redistribution of rain factor for individual months of vegetation period is the same.The mentioned fact has very important influence on prevention measures against erosion caused by rain, because especially in this period is soil endangered by erosion, so it is very important to design right anti-erosion measures.This fact point at re-evaluation of used methodology for calculation of rain factor in our conditions.
Comparison of equation which calculate only with annual precipitation with modified Wischmeier and Smith methodology brought conclusion that using of formulas which take into account only annual precipitation are proper only in rare cases because the values calculated according Zachar [1981], Holý [1978] and Šabata [1978] for localities Hurbanovo and Myjava were only in rare cases approaching to values calculated according Wischmeier and Smith modified methodology.We recommend using these formulas only in the case of lack of data because the final values are several times higher and therefore anti-erosion measurements designed according these results (formulas by Zachar, Holý and Šabata) are excessive and expensive.On the other hand in the case of lack of data could be these formulas useful.

Fig. 1 .
Fig. 1.Provided data in digital form in one -minute step in program MS Excel

Table 1 .
Example of calculation according Hudson methodology

Table 2 .
Comparison of annual and average

Table 3 .
Comparison of rain factor values calculated according different formulas, Myjava

Table 4 .
Comparison of rain factor values calculated according different formulas, Hurbanovo