Rainfall erosivity

Introduction

The soil erosive power of rainfall is quantified in the rainfall erosivity factor \(R\). This is a measure for the total erosivity of a number of rainfall events within a defined timeframe (years, months, number of days). The factor is computed by first calculating the erosivity for every rainfall event \(k\) in a timeseries. Secondly, the sum of the erosivity of all events is computed, for every year. Finally, the mean is computed over all the years:

\[R = \frac{1}{n}\sum_{j=1}^{n}[\sum_{k=1}^{m_j}E_k.(I_{30})_k]_j\]
with

  • \(R\): rainfall erosivity factor(\(\frac{\text{J .mm}}{\text{m}^2.\text{h.year}}\)),

  • \(n\), increment \(j\): number of years,

  • \(m_j\), increment \(k\): number of rain events in a year \(j\),

  • \(E\): the total kinetic energy of one single rain event (\(\frac{J}{m^2}\)), and

  • \(I_{30}\) (\(\frac{mm}{h}\)): the maximum rain intensity recorded within 30 consecutive minutes.

In the above equation, the erosivity of one event is defined by the sum of the depth of rainfall (mm) multiplied by the total kinetic energy of the event. The latter is defined as:

\[E = \sum_{r=1}^o e_r \Delta V_r\]
with

  • \(o\): the number of increments for a particular rain event,

  • \(e_r\): the rain energy per unit depth, (\(\frac{\text{J}}{\text{m}^{2}.\text{mm}}\)), and

  • \(\Delta V_r\): the rain depth (mm).

Note these equations assume that events are predefined. Typically, the end of and event is defined by a period of no rainfall. For Flanders, six hours is used as time period, and in addition, only events with a volume of 1.27 mm are retained in the calculations.

Energy per unit depth of rain

There are number of ways to compute the rain energy per unit depth \(e_r\), depending on the area for which the R-factor is computed. For an application for Flanders/Belgium, the rain energy per unit is defined by (Salles et al., 1999, 2002, Verstraeten et al., 2006) (:math:`text{MJ}.text{mm}^{-1}.

text{ha}^{-1}`):

\[e_r = 0.1112i_r^{0.31}\]

with

  • \(i_r\): the rain intensity for every 10-min increment (mm \(\text{h}^{-1}\)).

Prior to the relation estimated for Belgium, an alternative relation was estimated for the USA by Brown and Foster (1987) (see also RUSLE-handbook, Renard et al., 1997):

\[e_r = 0.29(1-0.72e^{-0.05i_r})\]

The use of the type of relation has an important implication on the computation of the R-factor, as the sensitivity of the R-factor for extreme high-intensity events varies significantly depending on the defined relation.

Application on Flanders

In this package, example data are presented for Flanders. For applications of the rainfall erosivity factor in the context of erosion and sediment transport modelling in Flanders a value of 870 \(\frac{\text{MJ.mm}}{\text{ha.h.year}}\) is used since 2006 (Verstraeten et al., 2006). Recently, this value has been updated to 1250 \(\frac{\text{MJ.mm}}{\text{ha.h.year}}\) (Deproost et al., 2018), and has been evaluated in Gobeyn et al. (2021).

References

Brown, L.C., Foster, G.R., 1987. Storm erosivity using idealized intensity distributions. Transactions of the ASAE 30, 0379–0386. https://doi.org/10.13031/2013.31957

Gobeyn, S., Van de Wauw, J., De Vleeschouwer, N., Renders, D., Van Ransbeeck, N., Verstraeten, G., Deproost, P., 2021, Herziening van de neerslagerosiviteitsfactor R voor de Vlaamse erosiemodellering. Departement Omgeving, Brussel, 44 pp.

Renard, K.G., Foster, G.R., Weesies, G.A., McCool, D.K., Yoder, D.C., 1997, Predicting soil erosion by water: a guide to conservation planning with the revised universal soil loss equation (RUSLE), Agriculture Handbook. U.S. Department of Agriculture, Washington. https://www.ars.usda.gov/ARSUserFiles/64080530/RUSLE/AH_703.pdf

Salles, C., Poesen, J., Pissart, A., 1999, Rain erosivity indices and drop size distribution for central Belgium. Presented at the General Assembly of the European Geophysical Society, The Hague, The Netherlands, p. 280.

Salles, C., Poesen, J., Sempere-Torres, D., 2002. Kinetic energy of rain and its functional relationship with intensity. Journal of Hydrology 257, 256–270. https://doi.org/10.1016/S0022-1694(01)00555-8

Verstraeten, G., Poesen, J., Demarée, G., Salles, C., 2006, Long-term (105 years) variability in rain erosivity as derived from 10-min rainfall depth data for Ukkel (Brussels, Belgium): Implications for assessing soil erosion rates. Journal Geophysysical Research, 111, D22109. https://doi.org/10.1029/2006JD007169