In kvantas/hyetor: Analyze fixed interval precipitation time series

knitr::opts_chunk$set(
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Introduction

The R coefficient (MJ.mm/ha/h/yr) is defined as the long-term average of the product of the kinetic energy of a storm and the maximum 30 min intensity [@renard1991rusle]:

$$R = \frac{1}{n} \sum_{j=1}^{n} \sum_{k=1}^{m_j} (EI_{30})_{k}$$

where

• $n$ is the number of years with rainfall records,
• $m_j$ is the number of storms during year $j$ and
• $EI_{30}$ is the erosivity of storm $k$.

The erosivity $EI_{30}$ (MJ.mm/ha/h) is equal to:

$$EI_{30} = \left( \sum_{r=1}^{m} e_r \cdot v_{r} \right) \cdot I_{30}$$

where:

• $e_r$ is the energy of rainfall (MJ/ha/mm),
• $v_r$ is the rainfall depth (mm) for the time interval $r$ of the hyetograph, which has been divided into $r = 1, 2, ..., m$ sub-intervals, such that each one of these is characterized by constant rainfall intensity and
• $I_{30}$ is the maximum rainfall intensity for a 30 minutes duration.

The quantity $e_r$ can be calculated for each $r$ using one of the kinetic energy equations:

1. Wischmeier and Smith equation, used in USLE: $e_r = 0.119 + 0.0873log_{10}(i)$ with the upper limit of 0.283 MJ/ha/mm if ${i} > 76$ mm/h. [@wischmeier1958rainfall].
2. Brown and Foster equation, used in RUSLE $e_r = 0.29(1 - 0.72 e^{-0.05i})$ [@brown1987storm].
3. McGregor et al. equation used in RUSLE2 $e_r = 0.29(1 - 0.72 e^{-0.082i})$ [@McGregor1995].

In the above equations $i_r$ is the rainfall intensity (mm/hr) and $e_r$ is the kinetic energy per unit of rainfall (MJ/ha/mm) for the interval $r$.

The rules that apply in order to single out the storms causing erosion and to divide rainfalls of large duration are:

1. A rainfall event is divided into two parts, if its cumulative depth for duration of 6 hours at a certain location is less than 1.27 mm.
2. A rainfall is considered erosive:
3. if it has a cumulative value greater than 12.7 mm or
4. during a time period of 15 mins a cumulative value of precipitation of at least 6.4 mm is recorded.

Example

This is an example that uses the internal data set in order to compute the corresponding rainfall erosivity values.

library(hyetor)
library(tibble)
library(dplyr)
library(lubridate)

# view data
prec5min

The following code can be used to:

a) Fill the time-series. b) Compute the rainfall erosivity values per storm. c) Filter the above values using cumulative precipitation height and maximum 15 minutes intensity rules.

ei_values <- prec5min %>%
  hyet_fill(time_step = 5, ts_unit = "mins") %>%
  hyet_erosivity(time_step = 5) %>%
  filter(cum_prec > 12.7 | max_i15 > 4 * 6.4)

ei_values

After the calculation of $EI30$ values the $R$ coefficient can be computed with:

# add years and months variables
ei_values <- ei_values %>%
  mutate( year = year(begin))

# compute R
R_coeff <- ei_values %>%
  group_by(year) %>%
  summarise(R = sum(erosivity)) %>%
  ungroup() %>%
  summarise(R = mean(R)) %>%
  unlist()

R_coeff

References

kvantas/hyetor documentation built on Sept. 2, 2019, 12:57 a.m.