Impacts identified using Linear Regression Line, Sen’s slope

 

Impacts
of time trends in colombo rainfall pattern on design rain events

 

A.K.D.Y. Abeywickrama

University of Moratuwa, Sri Lanka

Email : [email protected]

Dr. T.M.N. Wijayaratna

University of Moratuwa, Sri Lanka

 

Abstract: Seasonal varying rainfall can have a great socio-economic impact on an
agricultural dependent tropical country like Sri Lanka. More accurate rainfall
prediction can lead for a better performance in water resource management, flood
mitigation, agricultural management etc. Slowly varying components in the
climate system as sea surface temperature. The trends of the precipitation
were identified using Linear Regression Line, Sen’s slope estimator and
Mann-Kendall methods. It was shown that there is an increasing trend in the
average intensities and peak intensities. Furthermore southwest monsoon shows a
decreasing trend both average intensity and peak intensity while 2nd
inter monsoon shows an increasing trend.

Keywords:  time
trends; Colombo rainfall; pattern analysis, non-parametric methods; design
rain           events

1.   
Introduction

Sri Lanka is an island
which is extends between 5°55? to 9°51?N and 79°42? to 81°53?E and rice
cultivation plays a major role in country’s economy as in the case of most
countries in South and Southeast Asia. Irrigated agriculture contributes to 22%
of Sri Lankan exports while 75% of exports are powered from the national grid
electricity which 65% is generated via hydropower. So as country which its economy is heavily depends on the rainfall and the
availability of water resources, studies in rainfall pattern analysis is really
important for Sri Lanka. Also these pattern analysis is far more
important to manage, to plan and to predict the rainfall related adverse
effects such as high floods due to excessive rainfall and more accurate
rainfall forecasting will come in handy in crop cultivation managing. Design of
hydraulic structures such as dams, spillways, culverts, sluice gates etc. also
depend on the time trends of rainfall pattern. Even though the country has a
considerably high average rainfall, due to its seasonal and spatial variability
there is some shortage of water for agricultural, hydropower and domestic use
from time to time. Since this is a tropical country, air temperature doesn’t
varies much throughout a year, except in the upcountry area. Therefore the main
visible climate change is related to annual rainfall and due to Sri Lanka’s
location it is identified that this rainfall is governed by the seasonal
varying monsoon system in Indian Ocean. The mean annual rainfall can be high as
4500-5000mm in high lands and some areas such as southeast and northwest in the
country it can be low as 800-1200mm. The four monsoon seasons were identified
as;

1st Inter
monsoon – from March to April

Southwest monsoon – from
May to September – YALA agricultural season

2nd Inter
monsoon – from October to November

Northeast monsoon –
from December to February – MAHA agricultural season

However over the past
few decades due to the extreme environmental pollution, excessive population
growth, rise of greenhouse gasses, development projects related to irrigation
and agricultural projects the balance of the nature was pushed off a cliff and
the regular rainfall pattern of Sri Lanka was affected in a bad manner. Over
the past few years Sri Lanka was suffered from several severe flood situations
which damaged several hydraulic structures as well as immeasurable damages for
the public properties. Therefore many believed that the annual precipitation
was increased. However those disastrous heavy rainfalls were normally followed
by heavy droughts which lasts for months. So, actually what happened was even
though the number of rainfall events were reduced, the intensity of the
occurred rainfalls were massive and this couldn’t tolerate by the hydraulic
structures which was designed without considering the time trends in rainfall
pattern.

2.   
Time Trends in Rainfall Pattern

As the capital of the
country Colombo has a far more importance than the other cities since it is the
economical centre of the country. Colombo metropolitan area has a population of
5.6 million people in average and over 1 million people come to the city in a
day for various purposes. According to the data from the Department of
Meteorology, Colombo approximately gets an average rainfall of 2400mm per year
and 200mm per month. Furthermore May is the wettest month with an average of
382mm of rain and the driest month is January with a rainfall of 62mm. Also the
hottest and the coldest months are April (29°C) and January (27°C)
respectively. In recent past Colombo was frequently flooded even for a 2-4 hour
rainfall and it caused a lot of property loss and disabled the whole economy in
Sri Lanka. So, a proper knowledge in rainfall pattern in Colombo will far more
helpful in flood mitigation process in the city.

Sea
surface temperature (SST) in Indian Ocean is directly influenced to the precipitation
in Sri Lanka. High sea surface temperatures in western Indian Ocean, Indian
Ocean Dipole will cause large convergence in lower troposphere which will eventually
cause enhanced rainfall in Sri Lanka. Most studies conducted for the long-term
variations of rainfall in country was influenced by monthly tools. So, an analysis
which based on daily rainfall data and observe how seasonal rainfall totals
reflect the frequency of daily totals can be more effective in rainfall pattern
analysis since it allows to determine the number of times totals exceed a given
threshold in a given period of time. Also evaporation is lead to the cool down
of Sea Surface Temperatures, which cause to the reduction of convection of the
following year.

There
are three major characteristics for rainfall as amount, frequency and intensity
which depend on both time and spatial factors. The annual rainfall received for
a particular region may depend on several factors such as depletion of the
ozone layer, global warming, rate of consumption of fossil fuel, deforestation
etc. For the case study which was done by Karunathilaka and Dabare, 2017, to
identify the changes in rainfall pattern in Sri Lanka, they studied monthly
rainfall data up to 1998 which was recorded at 15 gauging stations. In this
study non parametric statistic methods such as Mann-Kendall method followed by
Sen’s slope estimator, regression line method had been used to identify the
time trends in rainfall pattern. To simplify the study the data set had been
divided into two set according to the time period, i.e. as short-range study (from
36 to 50 years) and long-range study (from 98 to 130 years).

a.   
 Mann-Kendall Method

Mann (1945) presented a non-parametric
test for the randomness against time which is widely used to identify the
trends in meteorological and hydrological time series. This is a non-parametric
method which has been widely used in rainfall trend detection and produced
promising results over the years. The methodology of this test is to determine
whether the value of a random variable is generally increasing or decreasing in
statistical terms over a certain period of time. The advantage of this test is
there is no need for the assumption of normality of the random variable and
this test will only determine the direction and not the magnitude of the
trends. However the detectable trends by the Mann-Kendal method may not be
necessarily linear but this test is less affected by the outliers due to it is
based on sign of differences and not on the values of the random variables.

 

b.   
 Sen’s Slope Method

Sen’s
slope method is a non-parametric linear slope estimator. The main advantages of
this method is that it is not affected by gross data error, missing data or
outliers as in linear regression method. This method is mainly used to
determine the magnitude of the trend line and the method of approach is based
on using the slope medians as an estimation of the overall slope to compute the
slopes for all the pairs of ordinal time points.

 

Procedure
for calculating the slope as a change in measurement per change in time.

 

                                 (1)

 

The variance for Sen’s
slope is determined by following equation.
 

 

 

 

 

 

 

The ranks of the lower (M1) and upper (M2)
confidence limits are given by equation (2) and (3).

             …….
(2)

            ……. (3)

c.   
 Student’s t-test

This is the parametric test of non-parametric
linear regression method and it considers the linear regression of the random
variable Y on time X. The regression coefficient ? (the Pearson correlation coefficient) is the
computed regression line slope coefficient computed from the data. This gives
by the following equation.

 ……….. (4)

 

2.4 Trend Analysis

According to
the results from the case study in Sri Lanka, to monitor rainfall trends to predict
the adverse impacts. In that mountainous region in Sri Lanka was used. The main
reason for selecting this area is that most of the hydro power generated this
region and rainfall is the main factor for these. Also, most of the tea estate
located at there and changes in rainfall is directly affected to their
cultivation. For the analysis, 30 years daily rainfall data in 62 rain gauges
were used. In here, universal multifactoral analysis was used & trend
analysis was done using fitting a linear regression line for each station.  The results showed that decreasing trend in
rainfall. Apart from this, highest decrease in rainfall showed in 1st
inter monsoon. 2nd inter monsoon also showed the decrease in
rainfall and both south west monsoon & north east monsoon showed mixing of
increasing & a decreasing trend in rainfall. Similar to the rainfall, rainy
days also decreased. So, this reducing cause to increase the rainfall intensity
in that area. Also, according to the analysis, they found that duration of
rainfall become shorter. Due to this, recharge of ground water was decreased
& surface water flow was increased. This lead to drying up the small
streams and canals in that area. So, they were suggested that further
investigation should be carried out for analysis this situation in that area. To
identify the time series changing points, a preliminary graphical inspection is
highly helpful and meaningful. The annual rainfall time series, averaged over
the whole dataset and also the corresponding interpolated regression line is needed.

Department of
Meteorology predicts rainfall conditions for a period in the daily weather
forecast highlighting the possibility of isolated heavy rainfalls. However it
is not easy to predict quantitative weather forecast by using only the conventional
methods. Because of the importance of the Quantitative Precipitation Estimation
(QPE), to estimate the possible rainfall amount.

The main
factor of using 11 indices are can get more accurate and reliable results in a
given area by using more indices. So, according to the test results, increasing
trends are identified & significant in the all indices. Also, slopes
occurred through the test results were shown statistically insignificant in
most of the cases. Further results show that there is an irregular pattern in
the distribution of both positive and negative slopes.

According to
the (I.C. Mercy, 2015) was done the Trend analysis of rainfall in Enugu state,
Nigeria. For that, monthly rainfall data were used from 2000 to 2013. Also
monthly mean precipitation and mean rainy days were used. This Enugu state
area, the livelihood of the most people are agricultural works. So, most of the
people are farmers. So, identification of changes in rainfall is very important
for their occupations.

During the
rainy seasons they have got very heavy rainfall and other time periods, this
area is mostly very hot and dusty. Rainfall patterns were shown so much
irregularity in this area. This was really affected the livelihood of the
farmers. So, finding these irregularity patterns were done under this study.

Under the
study, rainfall trend was calculated using the sequential plot using time
series analysis. This can be presented as follows (where Y is the value of the
variable under consideration at time t).

                        Y=f(t)

Yt
= a + bt

Yt
= ?o + ?1t + ?t

?t
= ?0 + ?0t

2.5
Average Intensity and Peak Intensity

Average intensity and
peak intensity were calculated for each rain event and graph were plotted for
the relevant time period. However rather than compare the rainfall events in time series it is
better to compare the rainfall events according to the seasons. Because some
seasons affect much higher than the others. In that case comparison of all
events in one time series does not represent accurate behavior of the
precipitation. Although
convectional type rainfall and tropical depression (especially in second inter
monsoon) initiating at the Bay of Bengal and heavy rainfall spells occur within
short time periods are more frequent in this season (B.A. Malmgren et al.,
2003).
Also, second inter-monsoon and south-west monsoon was affected much higher than
other monsoon for the Colombo. (Department of Meteorology).

3.   
Conclusion

It was shown that
there is an increase in the high intensity rain events, especially after 2010,
all the storm events were identified as high intense rain events. The results
were shown that there was an increasing trend in both average intensity as well
as in peak intensity. However peak intensity was shown higher increasing trend
than average intensity. According to the monsoon seasons, south-west monsoon
was shown to increase in the high intensity rain events while 2nd
inter monsoon was shown irregularity in the occurrence of high intensity or low
intense rain events. North-east monsoon was starting to affect after 2010 &
both storm events were identified as high intense rain events.

Acknowledgement

It was a great opportunity
for me to appreciate the guidance of the Dr T.M.N. Wijarathna, the supervisor
for my undergraduate research project.

References

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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