A comparative study of rainfall erosivity estimation for ... · A comparative study of rainfall...

Hydrological Sciences—Journal—des Sciences Hydrologiques, 44(1) February 1999 3

A comparative study of rainfall erosivity estimation for southern Italy and southeastern Australia

VITO FERRO, PAOLO PORTO Dipartimento di Ingegneria e Tecnologie Agro-Forestali, Università di Palermo, Viale délie Scienze, I-90128 Palermo, Italy e-mail: [email protected]

BOFU YU Faculty of Environmental Sciences, Griffith University, Nathan, Queensland 4111, Australia

Abstract In this paper, using Sicilian and Australian rainfall intensity data, a comparison between different estimators (modified Fournier index F, FF index) of the rainfall erosivity factor in the USLE was made. The relationship between the modified Fournier index and the mean annual rainfall, P, was theoretically derived. The K constant, linking the FF index and P, and its cumulative distribution function (CDF) were used to establish hydrological similitude among different geographical regions of southern Italy and southeastern Australia. To predict the erosion risk for an event of given average recurrence interval, the probability distribution of the annual value FaJ of the Arnoldus index was studied. In order to establish the theoretical CDF to use as a regional parent distribution, the descriptive ability of LN2 and EV1 distributions was studied by both an at-site analysis and a hierarchical regional procedure. The analysis showed that for each sub-region of southern Italy and southeastern Australia, characterized by a constant coefficient of variation, the erosion risk index is constant.

Etude comparative de l'agressivité des précipitations en Italie méridionale et en Australie du sud-est Résumé Cet article présente une comparaison des résultats obtenus avec différentes méthodes—indice de Fournier modifié F proposé par Arnoldus et indice Fp—pour établir le facteur moyen d'agressivité des précipitations R établi par Wischmeier à partir des données disponibles dans 128 stations en Australie et 629 en Italie. Une relation analytique liant d'une part l'indice d'Arnoldus et la hauteur de précipitation annuelle P et d'autre part l'indice FF et P, est proposée. Le coefficient K qui lie l'indice FF et la hauteur de précipitation P, et la fonction de distribution associée à cette hauteur ont été utilisés pour identifier des similitudes entre les différentes régions des deux entités géographiques étudiées. La distribution de probabilité de la valeur annuelle FaJ de l'indice FF est analysée afin de prédire le risque d'érosion. Dans le but d'obtenir une fonction de distribution synthétique et significative à l'échelle régionale, une analyse a été réalisée pour chaque station à l'aide de deux lois de distribution à deux paramètres (log-normale et Gumbel). Une procédure appliquée à l'échelle régionale démontre que la loi log-normale représente le mieux la distribution des fréquences observées. L'analyse démontre que chaque secteur de l'Italie méridional et du sud-est de l'Australie caractérisé par un coefficient de variation constant possède également un indice de risque d'érosion constant.

INTRODUCTION

Rainfall erosivity is defined as the aggressiveness of the rain to cause erosion (Lai, 1990). The most common rainfall erosivity index is the R factor of USLE

Open for discussion until 1 August 1999

mailto:[email protected]

4 Vito Ferro et al.

(Wischmeier & Smith, 1965, 1978) and RUSLE (Renard et al, 1996). The R factor has been shown to be the index most highly correlated to soil loss at many sites throughout the world (Wischmeier, 1959; Stocking & Elwell, 1973; Wischmeier & Smith, 1978; Lo et al, 1985; Renard & Freimund, 1994).

Regional isoerosivity maps, i.e. maps with contour lines of the same value of the rainfall erosivity factor, R, can be used to identify areas with high potential rainfall erosivity, thus with high risk of severe soil erosion (Bergsma, 1980; Bolinne et al., 1980; Hussein, 1986; Ferro et al, 1991; Yu & Rosewell, 1996a,b; Aronica & Ferro, 1997; Mikhailova et al., 1997) for which soil conservation structures may be necessary.

Since pluviograph data are not readily available in many parts of the world, mean annual (Banasik & Gôrski, 1994; Renard & Freimund, 1994; Yu & Rosewell, 1996c) and monthly rainfall amount (Ferro et al., 1991) have often been used to estimate the R factor for the USLE.

With respect to estimating the R factor using monthly and annual rainfall data, Renard & Freimund (1994) gave a succinct summary of several R factor estimation relationships previously published for various parts of the world. Renard & Freimund (1994), using monthly rainfall data from 132 sites in the continental United States, also developed a new set of relations for estimating R factor in which both mean annual rainfall depth P and the modified Fournier index, F, were used. The F index, proposed by Arnoldus (1980), is defined as:

12 2

F = H^ (1)

in which/),is the mean rainfall amount in mm for month i. Arnoldus (1980) showed that the F index is a good approximation of R to which

it is linearly correlated. Even if F takes into account the seasonal variation in precipitation, Bagarello (1994), analysing data on mean annual rainfall and the modified Fournier index, F, for different European regions (Bergsma, 1980; Bolinne et al., 1980; Gabriels et al., 1986), showed that the F index is strongly linearly correlated to the mean annual rainfall.

The relationship between F and P can be derived using the following definition of variance, var(X), of a random variable X (Haan, 1977):

var(X) = E(x2)~~E2(X) (2)

in which E(X) is the mean of the X variable and E(X2) is the mean of X2. From equation (2) it follows:

Y^X2 =N-E2{X)[\ + CV2{X)] (3)

in which CV(X) is the coefficient of variation of the X variable. Finally if X = pb

i.e. the mean monthly rainfall, equation (3) can be rewritten:

12 f 12

2>2=12Xft ^CV2(Pà — i—'12 ;=i w=i

(4)

A comparative study of rainfall erosivity estimation 5

and from equation (4) one obtains: 12 n2 P r

*--zt=£[i+CT"W]=*. 12 (5)

in which Km = 1 + CV2(p,). Equation (5) shows that the modified Fournier index is clearly proportional to the

mean annual rainfall, P. In addition, equation (5) shows that the F index varies from P/12 when rainfall is uniform throughout the year to P when all rainfall occurs in one month (Yu & Rosewell, 1996c). Table 1 lists, for each region, the number nR of the investigated sites and the corresponding Km value estimated by regression of P/12 against F.

Table 1 Rvalues for the investigated regions.

Region Km

Abruzzo-Molize Apulia Belgium France New South Wales Portugal Sicily South Australia The Netherlands UK

169 2

31 104 24 3

39 90 21 85

1.1006 1.1240 1.0243 1.0269 1.1799 1.4121 1.4309 1.2239 1.0730 1.0417

In Fig. 1 the pairs (P, F) are plotted for some European Countries (Bergsma, 1980; Bolinne et al., 1980; Gabriels et al., 1986) and for some regions having a nonuniform rainfall distribution in the year (Abruzzo-Molize, Apulia, Portugal, Sicily, South Australia) (Bagarello, 1997; Elia, 1991; Coutinho & Tomàs, 1994; Yu & Rosewell, 1996a). Figure 1 shows that for the regions having a quasi-uniform

1 1 X BELGIUM

A FRANCE

a UK

O THENETÏIEÏOANDS

F=P/12

° J R ^

•AP^

>/

a)

1 X ABRtlZZO-MOLISE

A APULIA

A NEW SOUTH WALES

D PORTUGAL

O SICILY

» SOUTH AUSTRALIA

F=P/12

° o,C

o x ~*

X

x ^ - ^

b)

P [mm] P [mm] Fig. 1 Relationships between F index and mean annual rainfall for some Australian and European regions.

6 Vito Ferro et al.

rainfall distribution in the year the pairs (P, F) are very close to the straight line F = Pi'12, while the other regions have Km values greater than 1.1.

In order to take into account the actual monthly rainfall distribution during each year of a period of N years, Ferro et al. (1991) proposed a FF index, which is based on the F index for individual years, FaJ:

12

12 V2- 5> 'j a,]

/=1 J 12

z 1=1

(6)

A-

where pQ is the rainfall depth in month / (mm) of the year j and P, is the rainfall total for the same year. The FF index is simply the mean of FaJ for a period of N years:

y = l

1{W i j

iV-f-'fr' P: y = l ( = l i

(7)

This FF index takes into account, for each year, the link between the monthly rainfall depths and the corresponding annual rainfall, and Ferro et al. (1991) also found that the FF index was well correlated with the rainfall erosivity, i.e. the R factor, calculated for a period of Nyears.

The following relationship is derived using equation (3) with X = pu:

ZA-12 '2> i,j 12

l + CVl{pu (8)

in which CV(pu) is the coefficient of variation of the pu variable. From equation (8) one obtains:

12 L Fa^^V+CV\PiJ)

Rearranging equation (9): N _ F . \ "P-

and then

FF =

N 12 &iN 7 = 1

l + CVl(Pu)

(9)

(10)

12

Ji>. l + CV2(PiJ) M ;

N

y=i

12 (11)

For each raingauge the constant K is an indicator of the monthly rainfall distribution in the year, with greater K values ( > 1) corresponding to more seasonal rainfall distributions. The FF index was used to determine the erosion risk for Sicily (Ferro et al., 1991) and the analysis carried out using 41 recording raingauges,


showed that R is linearly correlated to FF and R is better correlated to FF than P (Aronica & Ferro, 1997). This last result can be justified given that P is a robust estimator of the R factor for regions where high rainfall erosivity corresponds to high annual rainfall. For regions, such as Sicily, where intensity indices (Ferro et al., 1991) are required for soil erosion studies, FF is a better estimator of the R factor because FF takes into account the rainfall seasonal distribution.

USLE and RUSLE models can be used both to predict average long-term soil loss based on average long-term rainfall data and to design conservation practices to limit soil erosion to an acceptable value named soil loss tolerance (Wischmeier & Smith, 1978). However soil losses are frequently due to a few severe storms characterized by high intensity and large total rainfall amount. According to Larson et al. (1997) conservation systems designed to provide protection against average long-term events leave the land vulnerable to soil erosion during severe rainfall storms. For this reason these authors suggested, as an alternative, to design conservation practices to limit soil erosion to an acceptable value corresponding to a severe storm with a specified average recurrence interval, T. If this proposal is adopted, the knowledge of the theoretical cumulative distribution function of R factor would be needed to estimate the rainfall erosivity RT of given average recurrence interval, T.

In this paper, at first, rainfall data from recording raingauges located at 39 Sicilian sites, four South Australia sites and 24 New South Wales sites were used to compare different estimators (P, F and FF index) of the rainfall erosivity factor in the USLE. Then, using rainfall depths measured at non-recording raingauges, five regions of southern Italy (Apulia, Basilicata, Calabria, Campania and Sicily), South Australia and New South Wales were compared by examining the cumulative distribution function (CDF) of the K constant.

Since the knowledge of the spatial distribution of the mean annual value FF of the rainfall erosivity index does not by itself allow one to predict the erosion risk for events with a different average recurrence interval, the theoretical probabilistic model of the FaJ index will be established and an erosion risk index (Ferro et al., 1991) will be estimated for the investigated regions.

COMPARING RAINFALL EROSIVITY FOR SOUTHERN ITALY AND SOUTHEASTERN AUSTRALIA

The investigated areas, shown in Fig. 2, are located in southern Italy and in southeastern Australia. The Italian study area, covering 83 800 km2, is subdivided into five regions: Apulia, Basilicata, Calabria, Campania and Sicily (Fig. 2(a) and (b)). Typical Mediterranean climatic conditions, with intense storms at the end of spring and beginning of autumn and dry spells in summer, are prevalent in most of the area. Particular orography and maritime influence affect the annual rainfall distribution of Calabria and Sicily (Ferro & Bagarello, 1996).

The Australian study area includes two large regions: New South Wales (804 000 km2) and South Australia (984 000 km2). Climatic conditions in south-

8 Vito Ferro et al.

Fig. 2 Investigated areas (a), (b) in southern Italy and (c) in southeastern Australia.

eastern Australia are characterized mostly by different seasonal distributions of rainfall. In New South Wales (Fig. 2(c)) five sub-regions are distinguishable: A (arid, subtropical), B (summer rainfall, subtropical), C (arid, temperate), D (uniform rainfall, temperate), E (winter rainfall, temperate) (Bureau of Meteorology, 1989). The sites considered in this research lie in the B, D and E zones only. In South Australia Mediterranean climatic conditions are prevalent. The data used in

A comparative study of rainfall erosivity estimation

Table 2 Characteristic data of the investigated recording and non-recording raingauges.

Region

Apulia Basilicata Calabria Campania Sicily New South Wales South Australia

nR

20 46 79 56 40 24 4

NR

60 58 56 50 44 28 21

nNR

89 48 135 116 40 24 86

NNR

40 56 54 43 44 28 53

•VR

1916-1988 1921-1987 1921-1987 1951-1988 1921-1970 1858-1988 1860-1993

SPm 1916-1988 1921-1987 1921-1987 1921-1988 1921-1970 1858-1988 1951-1993

this research are the monthly and annual rainfalls published by the Italian Hydrograph Service (IHS) and available from the Australian Bureau of Meteorology archives through the computer program MetAccess.

For each region Table 2 lists the number of recording raingauges, nR, and the corresponding mean sample size NR (years), the number of non-recording raingauges, nm, and the mean sample size Nm of the daily rainfalls. Table 2 also lists the sampling period of the recording, SPR, and non-recording, SPNR, raingauges.

The difficulties with using the standard procedure for calculating R factor in the USLE or RUSLE and the need for isoerosivity maps for regions with few meteorological stations to record rainfall intensity data have stimulated the research of simplified methods for estimating the R factor. Regression analysis between R and those climatic variables that are readily available, such as P, F and FF (Ferro et al., 1991; Renard & Freimund, 1994; Yu, 1995), is commonly used. The correlation between R and a given climate variable can also be used to determine if two regions are homogeneous from a climatic point of view.

The statistical analysis developed for 40 Sicilian recording raingauges showed that, among the simple climatic variables P, F and FF for Sicily, FF is the best estimator of the R factor (Fig. 3):

Fig. 3 Relationships between R and FF indices for Sicily.

10 Vito Ferro et al.

R = 0.5249 F, 1.59 (12)

which is characterized by a correlation coefficient r = 0.63 and a mean square error MSE equal to 202 136.

In spite of the scattering of Sicilian pairs (FF, R), Fig. 4 shows that Sicily and South Australia can be considered two hydrologically homogeneous regions characterized by the following R-FF relationship:

R = 0.6120 F}'56 (13)

having r = 0.64 and MSE = 185 498. Since New South Wales is a large region (30 times larger than Sicily), the

relationship R-FF was separately established for the B zone (summer rainfall, subtropical) and D zone (uniform rainfall, temperate). Figure 5 shows the comparison between the following relationships and the Sicilian pairs (FF, R):

R = 3.4318F^6 for B zone

which is characterized by r = 0.96 and MSE = 1137464, and

R = 2.7015 FxF

Al for D zone

(14a)

(14b)

which is characterized by r = 0.97 and MSE = 88050. The scatter plot of the Sicilian pairs (FF, R) in Fig. 5 clearly shows that no

hydrological similitude can be established between Sicily and the two Australian sub-regions of New South Wales. For comparing the relationship between FF and P for southern Italy and southeastern Australia and for recognizing hydrologically homogeneous areas, the cumulative distribution function of the K constant appearing in equation (11) was also studied.

Figure 6 shows the CDF of K for the five regions of southern Italy (Apulia, Basilicata, Calabria, Campania and Sicily), for South Australia and the two zones B and D of New South Wales. Figure 6 clearly shows that CDF is dependent on

^ A

1 1 1 ! 1 i O SICILY

• SOUTH AUSTRALIA

eq. (13)

• )

O

o o o

°°/° lîÇrP^

O

FF [mm]

Fig. 4 Relationships between R and FF indices for Sicily and South Australia.

A comparative study of rainfall erosivity estimation II

100 -

-

F • • / • ' ' • /

—

/a o

1

\J

ug 90s-

•3P

p

ci 1° |

/ 'm

__

_ u i

_ J

y

.4.

I 1 1 — ( _

- j • D zone

O SICILY

eq. (14b)

f i

Ç

• /

M° °

^%So— aiSsSEE

O

FF [mm] FF [mm]

Fig. 5 Relationships between R and FF indices for Sicily and New South Wales.

o APULIA

a CAMPANIA

x BASHJCATA

o CALABRIA

A N.S.W. - B zone

• N.S.W.-Dzone

A SICILY

• SOUTH AUSTRALIA

Fig. 6 Cumulative distribution function of K constant for the different investigated regions.

geographical factors and that the highest K values correspond to areas having nonuniform rainfall distribution in the year (Calabria, Sicily, New South Wales B zone).

For each investigated region the mean value \x(K) of the K constant, the median value m(K), the standard deviation a(K) and the coefficient of variation CV(K) are listed in Table 3.

In Fig. 7 the empirical pairs (n(K), a(K)) for southern Italy and southeastern Australia (Table 3) are plotted. The figure shows that, even if the CDF of K is dependent on geographical factors, the relationship between the two statistical parameters a(K) and \i(K) can be considered unique.


Table 3 Statistical parameters of K empirical values for each region.

Region \m m(K) v(R) CV(K)

New South Wales B zone D zone South Australia Apulia Basilicata Calabria Campania Sicily

1.722 1.840 1.685 1.662 1.690 1.652 1.879 1.619 2.021

1.727 1.811 1.715 1.625 1.666 1.618 1.805 1.620 1.927

0.311 0.199 0.185 0.160 0.149 0.149 0.250 0.085 0.509

0.180 0.108 0.110 0.096 0.088 0.090 0.133 0.053 0.252

10

a(K)

o.i

0.01

— „ — — ,

J

I —jL

f

/ =7 y '

A B zone

• D zone

• SOUTH AUSTRALIA

O SOUTH ITALY

—

Ë

H(K) 10

Fig. 7 Relationship between a(K) and u(iï) for southern Italy and southeastern Australia.

PROBABILITY DISTRIBUTION OF THE Fai INDEX

By using the values of the erosivity index FF calculated for each investigated raingauge (128 non-recording raingauges for Australia and 629 for southern Italy, see Table 2) and a kriging interpolation method, the isoerosivity maps of southern Italy (Fig. 8) and southeastern Australia (Fig. 9) are produced.

For predicting the erosion risk of events having different average recurrence intervals, Ferro et al. (1991) suggested that each site be characterized by an erosion risk index. The erosion risk index is defined as the ratio of the Fo50 quantile corresponding to an average recurrence interval of 50 years to the mean annual value FF. The estimate of the FaJ quantile, corresponding to an average recurrence interval of T years, requires a selection of a theoretical distribution function which agrees with the empirical CDF of the annual rainfall erosivity values FaJ.

At first an at-site procedure was followed and in order to reduce the uncertainty associated with estimated parameter values we choose two theoretical CDF,

A comparative study of rainfall erosivity estimation

Fig. 8 Isoerosivity maps (FF contour lines) of southern Italy.

Vito Ferro et al.

Fig. 9 Isoerosivity maps (FF contour lines) of southeastern Australia.

i.e. 2-parameter log-normal distribution (LN2) and type-1 extreme value (or Gumbel's) distribution (EV1) and only raingauges with a sample size greater than or equal to 80 years were used. Figure 10 shows, for four investigated raingauges, that for cumulative probability greater than or equal to 0.8 both EV1 and LN2 fit adequately the empirical CDF. The quantile Fa 50 estimated using the original data on FaJ and EV1 and LN2 distributions were also compared. For the EV1 distribution, using the method of moments (Haan, 1977) for estimating the two parameters of the theoretical distribution, the erosion risk index is (Aronica & Ferro, 1997):


0.9 •

0.85 •

0.8 .

.. .... . | 1 NAR ACOORTE POST OFFICE 1

A /

A -mpinc.il

A 1

*•/;

A ;' \

• t*

0.9

0.85 .

0.8

JVKETULTAJ

•7 ! • /.'

• tmpincal

FVl

LN2 1

• / • '

• / '

? • / ' >«

' i

•

.••

,

T>

20 40 SO 100 120 20 30 40 50 60 70 80 90 100

.85

OR .

JBARlj

O empirica

EV1

- L N 2

_ 1° / O

/ o / oi L ° / O !

/o j b j

"Ô T T ^ i - ^ j

J

20 40 60 SO 100 120 140 160 30 60 90 120 1:

Fa,j F*J

Fig. 10 Comparison between empirical CDF and EV1 and LN2 distribution.

ra,50 = 1 + 2.59 CV (15)

in which, for each raingauge, CV is the coefficient of variation of the FaJ index. For LN2, the quantile Fa 50 was determined by the following equation (Castorani

&Gioia, 1981; Haan, 1977):'

Fajo =exp[ti' + M50a'] (16)

in which u50 is the dimensionless variable corresponding to T = 50 years and equal to 2.051, and u.' and a' are the two parameters having the following expressions:

u.'=4in F} Fl.+a2(Faj)_

(17a)

a = In Ft

:[ln(l + CF2)]'

Inserting equations (17) into equation (16), one obtains:

FF FF exp -In

\ + CV' exp j 2.051 In \\ + CV'

, 1 /

(17b)

(18)

-mpinc.il


and rearranging:

ra,50 1

l + CVz w-expj 2.051 Infl + CV2

(19)

Equations (15) and (19) show that, for each selected theoretical distribution, the erosion risk index is only dependent on the coefficient of variation CV.

Figure 11, as an example for Sicily, South Australia and New South Wales, compares the erosion risk index Fa50IFF estimated using the EV1 distribution (ordinate) with the same index estimated using LN2 distribution (abscissa). Figure 11 shows that the two selected probabilistic models allow comparable at-site estimate of the quantile Fai50. For Fa50/FF = 2 the EV1 distribution has a CV value calculated by equation (15) equal to 0.3861. In this case the LN2 law has a skewness coefficient given by the following equation (Alexander et al., 1969):

G=CV3 +3CV which is approximately 1.1396.

(20)

a /

A NEW SOUTH WALES

o SOUTH AUSTRALIA

- X SICILY

perfect agreement

Fl50/FF (LN2) Fig. 11 Comparison between the erosion risk index values estimated by EV1 and LN2 distribution.

If Fa5QIFF based on EV1 is greater than Fa50/FF based on LN2, then CV would be greater than 0.3861 and G, calculated by equation (20) greater than 1.1396. In other words, in Fig. 11 the pairs plotted to the left of the abscissa Fa50/FF - 2 represent a lognormal distribution with a larger skewness coefficient than EV1.

Since the at-site frequency analysis is not able to validate the theoretical distribution to use as the parent distribution, regional analysis was developed (Wiltshire, 1986; Cunnane, 1988; Cannarozzo et al,, 1995; Aronica & Ferro, 1997).

Regionalization allows a reduction of the uncertainty of the quantile estimate FT

and a better choice of the theoretical CDF to reproduce the statistical characteristics (skewness, coefficient of variation, mean) of all observed samples in the region. In addition, a regional technique can be used to estimate model parameters.


The regionalization procedure used is hierarchical and occurs at three sequential levels. At the first level the skewness G is assumed constant over the whole investigated area (homogeneous region). At the second level each region is subdivided into smaller areas, called homogeneous sub-regions, in which CV is constant. At the third level each raingauge is characterized by its scale parameter which is assumed equal to FF. For each regionalization level the used hypothesis (for example, G = constant) is tested by comparing the theoretical regional distribution of a given statistical parameter with the observed regional CDF (Cunnane, 1988).

At the first level the empirical pairs (CV, G) of all investigated regions were initially compared (Fig. 12) in natural space with equation (20) for the LN2 distribution and G = 1.1396 for the EV1 distribution. This comparison indicates an increasing trend of the pairs (CV, G) which agrees broadly with equation (20). The discrepancy between empirical and theoretical values in Fig. 12 can be a result of the strong dependence of the estimated skewness coefficient, G, on the sample size. For this reason for each investigated region the empirical CDF of the skewness was compared with the CDF of 1000 samples of the skewness generated by Monte Carlo simulation. Both LN2 and EV1 were simulated with the mean sample size for the region. At this level of the regionalization, Apulia, Basilicata, Calabria, Campania, Sicily and New South Wales were considered homogeneous regions.

Figure 13 shows, as an example for Apulia, Campania and New South Wales, the comparison between the skewness CDF of historical sequences and of samples generated by EV1 and LN2 distributions. Statistical analysis showed that LN2 distribution is always able to reproduce the empirical CDF of the skewness coefficient.

In particular for obtaining the agreement between empirical and generated skewness CDF, South Australia was divided into four homogeneous areas by using cluster analysis taking into account latitude, longitude and skewness of each investigated raingauge. According to the results of the first level analysis, the following regionalization levels were only developed for LN2.

3 -

! 1 ! « SOUTHEASTERN AUSTRALIA

LN2 !

EV1 f" ^ -

/ < , r -5—•

•

• •

A* m •

r -.* P. ' '

• * 9 j

|

CV

I O SOUTH ITALY

EV1 LN2

c 0

c

L^^^^ 0 cw

0 0

WfcÇT'o d'oc 0

0

°o

0

0 0

7 0 Ç

^ 0

O

O 0

°^^

0.4

CV Fig. 12 Comparison among empirical pairs (CV, G) and theoretical relationship for EV1 and LN2 laws.


F(G)

0.8 -

0.6 •

0.4 .

0.2 .

0 •

1

IAPULIA' J

— -

a .fl.

~ " " • • \ w "'^

i-

_— M/ —

p ^ ë 5 * "

™ " " "1

- — - -

— - _

if , ! ••:::ËvT - - ff i LN2

o empirical

— 1

F(G)

0.8 -

0.6 ,

0.4 .

0.2 -

0 -

iCAMPANIAi 1 J

f h

I / /

\ if j

, Û—ffî^; 1

v / ' !

/ ' 1 / ;

:

j 1

! EV1

i LN2 ! 1

A empirical ;

F(G)

1 -,

o.s -

0.6 -

0.4 -

0.2 -

0 .

" - - ; -NEW SOUTH WALES

]-

\c —Z-

V

T

• */

• / !• / Br

-

j •

^^__iiii ._..,

•EV1

-LN2 j ..

empirical 1

7 " " "

Fig. 13 Comparison between the skewness CDF of historical sequences and of samples generated by an EV1 and a LN2 distribution.

At the second level, Apulia was divided into five sub-regions (Porto, 1994); Basilicata (Filice, 1987), Calabria (Versace et al., 1989) and Sicily (Cannarozzo


et al., 1995) were divided into three sub-regions, while for Campania, South Australia and New South Wales the same homogeneous regions were adopted as were used at the first regionalization level.

In Fig. 14, the empirical pairs (N, CV) are plotted as an example for sub-region A of Basilicata, Campania and sub-region 2 of South Australia. For each sub-region the coefficient of variation can be assumed constant and equal to the mean

0.6

CV

0.4

BASILICATA - SR A

O

— c v S R A = o. 0

° 8

o o °o° *

0

o > o

e o o 0 O

CV

CV

,CAMPANIA o

CV™ = 0.256 •

10 Ti 60

0.4 -

/ 0.2 -

n i .

0 -

85

'SOUTH AUSTRALIA SR 2

• • •

\ * C \ S R 2 - 0 . 2 6 2 ^ • | •

•

,%

no

Fig. 14 Relationship between CV and the sample size N for some investigated sub-regions.


Table 4 Mean values of the CV corresponding to the raingauges belonging to the selected sub-region.

Region

Apulia

Basilicata

Calabria

Sub-region

1 2 3 4 5 A B C J C T

cvSR

0.298 0.266 0.279 0.315 0.326 0.301 0.389 0.273 0.479 0.302 0.241

Region

Campania Sicily

New South Wales

South Australia

Sub-region

Campania A B C B D 1 2 3 4

cvSR

0.256 0.291 0.352 0.477 0.358 0.362 0.282 0.262 0.266 0.284

value (Table 4), CVSR, of the CV values corresponding to the raingauges belonging to the selected sub-region.

For testing the descriptive ability of the LN2 model and the statistical hypothesis that the CVSR is an estimate of the sub-regional coefficient of variation, for each sub-region the empirical CDF of CV was compared with the coefficient of variation CDF of 1000 Monte Carlo generated samples (Fig. 15). Figure 15 shows, as an example for sub-region 5 of Apulia, Campania, sub-region C of Basilicata and sub-region 2 of South Australia, the ability of LN2 distribution, with a sub-regional coefficient of variation CVSR, to reproduce the empirical CDF of CV.

For each sub-region (Fig. 16) the lack of correlation between the residuals (CV - CVSR) and the mean FF as also evident.

Furthermore, Fig. 17 shows, as an example for sub-region B of Basilicata and the B zone of New South Wales, that the residuals e = CV- CVSR are normally distributed.

For each sub-region, equation (19) with CV = CVSR shows that the erosion risk index FaS0/FF is only dependent on CVSR and consequently can be assumed constant for the region. In other words, each investigated region is divided into erosion risk sub-regions which are coincident with the homogeneous sub-regions selected at the second level of the regionalization procedure.

CONCLUSIONS

The Universal Soil Loss Equation (USLE), and its revised version (RUSLE), were developed to predict average long-term soil loss from cultivated fields for use in conservation planning. The USLE and RUSLE, are still the most widely used soil erosion prediction models and the rainfall erosivity index is currently used as a tool for establishing soil erosion risk areas in which conservation practices may be needed. Since soil losses are frequently due to a few severe storms characterized by high intensity and large total rainfall amount, the conservation systems should be designed using rainfall storms having a specified average recurrence interval.

At first the relationship between the F index and the mean annual rainfall, P and that between the mean annual value of the Arnoldus index FF and the mean annual


CAMPANIA

SOUTH AUSTRALIA y , - S R 2 /

7

/* •/

• /

l • / ¥ /

• : J

/ • •

• empirical

— LN2

,

|

i j

cv cv Fig. 15 Comparison, for some investigated sub-regions, between the coefficient of variation CDF of historical sequences and of samples generated by a LN2 distribution.

rainfall were theoretically derived. The K constant which is the coefficient of proportionality between FF and P was used to compare the investigated regions of southern Italy and southeastern Australia. The analysis showed that the cumulative distribution function of the K constant is dependent on geographical factors and that the highest K values correspond to Mediterranean areas while the lowest ones correspond to regions with a quasi uniform rainfall distribution in the year.

Using rainfall intensity data from some Sicilian and Australian meteorological stations, a comparison among different estimators of the rainfall erosivity factor was also carried out. The statistical analysis showed that Sicily and South Australia can be considered two hydrological homogeneous regions and are characterized by the same relationship between R and FF, while no hydrological similitude was established between Sicily and the two zones of New South Wales where rainfall is either uniform throughout the year or summer rainfall predominates.

In order to predict the erosion risk for an event of any average recurrence interval, an attempt was made to determine the most appropriate probability distribution for the Faj index. The statistical analysis, carried out by at-site and regional


> >

j APULIA { -- -J \

a

X

| o S R l

; DSR2

ASR3

XSR4 |

0 S R 5

x°

A X O

> u > o

r-jo

[BASILICATA

" W »o:<* '

S i p

o S R A

DSRB

A S R C

b)

200 50 100 150 200 250 300

CAMPAN1AI SOUTH A

X

°*

1 ~" ' USTRALIA

!

X X

X4

X

o

! »SR 1

o S R 2

: x S R i

I i S R 4

x

* d)

100 200

FP 50

Fig. 16 Relationship between CV~CVSR and FF.

& 0.5

BASILICATA -SR B

/

o '

iv 7f —

0 / o /

o y

empirical

Gauss

a )

NEW SOUTH WALES -SRB

0.2 -0.2

empirical

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Fig. 17 CDF of the residuals for two investigated sub-regions.


procedures, showed that the LN2 distribution, in contrast to EV1 distribution, is able to better reproduce the empirical CDF of both skewness and coefficient of variation of the FaJ index for regions considered.

Furthermore, at the second level of the regional procedure, each investigated region was divided into homogeneous sub-regions in which the coefficient of variation could be assumed constant. For each sub-region the erosion risk index, which is equal to the ratio of the quantile Fa50 corresponding to an average recurrence interval of 50 years to the mean value FF, depends on the coefficient of variation only. The latter can be assumed to be constant for each sub-region. In conclusion, each investigated region is divided into erosion risk sub-regions which are coincident with the homogeneous sub-regions characterized by a constant coefficient of variation.

REFERENCES

Alexander, G. N,, Karoly, A. & Susts, A. B. (1969) Equivalent distributions with application to rainfall as an upper bound to flood distribution. /. Hydrol. 9, 322-344.

Arnoldus, H. M. J. (1980) An approximation of the rainfall factor in the Universal Soil Loss Equation. In: Assessment of Erosion (ed. by M. De Boodt & D. Gabriels), 127-132. Wiley, Chichester, UK.

Aronica, G. & Ferro, V. (1997) Rainfall erosivity over Calabrian region. Hydrol. Sci. J. 42(1), 35-48. Bagarello, V. (1994) Procedure semplificate per la stima del fattore climatico délia USLE nelPambiente molisano

(Simplified procedures for estimating the climatic factor of the USLE in Molise, in Italian). Atti delta Giornata di Studio Sviluppi Recenti delle Ricerche sull'Ewsione e sul suo Controllo (Bari, 17-18 February 1994).

Banasik, K. & Gôrski, D. (1994) Rainfall erosivity for South-East Poland. In: Conserving Soil Resources. European Perspectives (ed. by R. J. Rickson), 201-207. Lectures in Soil Erosion Control, Silsoe College, Cranfield University, UK.

Bergsma, E. (1980) Provisional rain-erosivity map of The Netherlands. In: Assessment of Erosion (ed. by M. De Boodt & D. Gabriels). Wiley, Chichester, UK.

Bolinne, A., Laurant, A. & Rosseau, P. (1980) Provisional rain-erosivity map of Belgium. In: Assessment of Erosion (ed. by M. De Boodt & D. Gabriels), 111-120. Wiley, Chichester, UK.

Bureau of Meteorology (1989) Climate of Australia. AGPS Press, Canberra. Cannarozzo, M., D'Asaro, F. & Ferro, V. (1995) Regional rainfall and flood frequency analysis for Sicily using the two

component extreme value distribution. Hydrol. Sci. J. 40(1), 19-42. Castorani, A. & Gioia, G. (1981) Le piogge annue massime orarie in Puglia—legge di distribuzione degli eventi (The

annual maximum rainfall in Puglia—distribution law at event scale, in Italian). Idrotecnica, 4. Coutinho, M. A. & Tomàs, P. P. Comparison of Fournier with Wischmeier rainfall erosivity indices. In: Conserving

Soil Resources. European Perspectives (ed. by R. J. Rickson), 192-200. Lectures in Soil Erosion Control, Silsoe College, Cranfield University, UK.

Cunnane, C. (1988) Methods and merits of regional flood frequency analysis. J. Hydrol. 100, 269-290. Elia, I. (1991) Determinazione del fattore colturale nella USLE e MUSLE ai fini délia loro applicazione a bacini

montani e collinari (Evaluating the crop factor of USLE and RUSLE for mountainous basins, in Italian). PhD Dissertation, University of Bari, Italy.

Ferrari, E. (1991) Leggi regionali di crescita degli estremi idrologici in Italia (Growth curves for extreme hydrological data in Italy, in Italian). Rapporto 1990-91, Gruppo Nazionale per la Difesa dalle Catastrofi Idrogeologiche, UU.OO. 1.4-1.36 .

Ferro, V. & Bagarello, V. (1996) Rainfall depth-duration relationship for South Italy. Proc. ASCE 1(HE4), 178-180. Ferro, v., Giordano, G. & lovino, M. (1991) Isoerosivity and erosion risk map for Sicily. Hydrol. Sci. J. 36(6),

549-564. Filice, E. (1987) Analisi idrologica dei massimi annuali delle piogge giomaliere. Una applicazione del modello TCEV

régionale al caso délia Basilicata (Hydrological analysis of the annual maximum daily rainfall, in Italian). Unpublished Thesis, Université délia Calabria, Cosenza, Italy.

Gabriels, D., Cadron, W. & De Mey, P. (1986) Provisional rain erosivity maps of some EC countries. Proc. Workshop on Erosion Assessment and Modelling (Brussels, Belgium).

Haan, C. T. (1977) Statistical Methods in Hydrology. The Iowa State University Press, Ames, Iowa, USA. Hussein, M. H. (1986) Rainfall erosivity in Iraq. J. Soil Wat. Conserv., 336-338. Lai, R. (1990) Soil Erosion in the Tropics: Principles and Management. McGraw-Hill, New York. Larson, W. E., Lindstrom, M. J. & Schumacher, T. E. (1997) The role of severe storms in soil erosion: a problem


needing consideration. J. Soil Wat. Conserv., 90-95. Lo, A., El-Swaify, S. A., Dangler, E. W. & Shinshiro, L. (1985) Effectiveness of EI30 as an erosivity index in Hawaii.

In: So/7 Erosion and Conservation (ed. by S. A. El-Swaify, W. C. Moldenhauer & A. Lo), 384-392. Soil Conservation Society of America, Ankeny.

Mikhailova, E. A., Bryant, R. B., Schwager, S. J. & Smith, S. D. (1997) Predicting rainfall erosivity in Honduras. Soil Sci. Soc. Am. J. 61, 273-279.

Porto, P. (1994) Stima dell'aggressività délia pioggia mediante l'indice di Fournier. Un caso di studio (Estimating the rainfall erosivity index by Fournier procedure. A case study, in Italian). Annali dell'Accademia Italiana di Scienze Forestall, 34.

Renard, K. G., Foster, G. R., Weesies, G. A. & McCool, D. K. (1996) Predicting soil erosion by water. A guide to conservation planning with the revised universal soil loss equation (RUSLE). Agric. Handbook 703. US Govt Print Office, Washington, DC.

Renard, K. G. & Freimund, J. R. (1994) Using monthly precipitation data to estimate the R factor in the revised USLE. J. Hydrol. 157, 287-306.

Stocking, M. A. & Elwell, H. A. (1973) Prediction of sub-tropical storm soil losses from field plot studies. Agric. Meteorol. 12, 193-201.

Versace, P., Ferrari, E., Gabriele, S. & Rossi, F. (1989) Valutazione delle piene in Calabria (Evaluating floods in Calabria, in Italian). Geodata 30, CNR-IRPI, Cosenza, Italy.

Wiltshire, S. E. (1986) Regional flood frequency analysis. Hydrol. Sci. J. 31(3), 321-333. Wischmeier, W. H. (1959) A rainfall erosion index for a universal soil-loss equation. Soil Sc. Soc. Am. Proc. 23, 246-

249. Wischmeier, W. H. & Smith, D. D. (1965) Predicting rainfall-erosion losses from cropland east of the Rocky

Mountains. Guide for selection of practices for soil and water conservation. Agric. Handbook, 282, US Gov. Print. Office, Washington, DC.

Wischmeier, W. H. & Smith, D. D. (1978) Predicting rainfall erosion losses. A guide to conservation planning. US Dept. Agric. Agricultural Handbook, 537.

Yu, B. (1995) Contribution of heavy rainfall to rainfall erosivity, runoff and sediment transport in the wet tropics of Australia. In: Natural and Anthropogenic Influences in Fluvial Geomorphology (ed. by J. E. Costa et al.) Geophysical Monograph 69, 113-123. AGU, Washington, DC.

Yu, B. & Rosewell, C. J. (1996a) An assessment of a daily rainfall erosivity model for New South Wales. Austral. J. Soil Res. 34, 139-152.

Yu, B. & Rosewell, C. J. (1996b) Rainfall erosivity estimation using daily rainfall amounts for South Australia. Austral. J. Soil Res. 34,721-733.

Yu, B. & Rosewell, C. J. (1996c) A robust estimator of the R factor for the Universal Soil Loss Equation. Trans. Am. Soc. Agric. Engrs 39(2), 559-561. Received 16 September 1997; accepted 9 June 1998

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