chapter-5 development of modified drought...
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Modeling of rainfall variability and drought assessment in Sabarmati basin, India _____________________________________________________________________________________
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Chapter-5 Development of Modified Drought Index
5.1 Introduction
Drought is generally considered to be occurring when the monsoon fail or are
deficient or scanty. Failure in the monsoon may create crop failure, shortage of
drinking water and affecting the socio-economic life of the rural and urban
community. Generally, the amount of rainfall received by any area/region gives idea
about occurrence of drought in any area/region. The occurrence of drought can be
identified using various drought indices. Drought indices give quantitative
assessment of climatic conditions and can be used as a tool for early warning system,
drought monitoring.
5.2 Relationship between drought indices and micro-climate
Drought is a normal, recurrent feature of climate and it is observed in
all the climate zones, with different characteristics in different regions. Drought is a
climatic anomaly, characterized by deficient supply of moisture resulting either from
sub-normal rainfall, erratic rainfall distribution, higher water need or a combination
of all the three factors. About two thirds of the geographic area of India receives low
rainfall (less than 1000 mm), which is also characterized by uneven and erratic
distributions. While considering drought, it is important to take into account the
onset of rainy season, delay in start of monsoon, breaks in the monsoon, rainfall
intensity, severity, etc. The severity of drought can also be affected by other factors
like temperature, wind velocity, humidity, etc. Assessment of Regional Drought is
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based on drought indices for identifying drought characteristics. Drought Indices
simplify the complex relationships and provide good communication tool. It gives
quantitative assessment of anomalous climatic conditions (intensity, duration, and
spatial extent).Drought Indices provides a basis for drought management.
5.3 Description of Various Drought Indices:
A drought index value is typically a single number, far more useful than raw
data for decision making. There are several indices that measure how much rainfall
for a given period of time has deviated from historically established norms. Although
none of the major indices is inherently superior to the rest in all circumstances, some
indices are better suited than others for certain uses. The drought indices which use
meteorological observations recorded at meteorological stations are called
meteorological drought indices. The drought index which uses rainfall data are
percent of normal (PN), deciles, standardized precipitation index (SPI), effective
drought index (EDI), etc. The indices based on only rainfall data are not only simple
to compute, it has also been shown that these indices perform better compared to
more complex hydrological indices (Oladipio, 1985). In India also there have been
studies related to drought using drought indices based on the rainfall data only.
When the seasonal rainfall received over an area is less than 75% of its long-term
average, it is called meteorological drought (Ray-2000). These studies were mainly
for the monsoon season (June to September) which contributes about 75-90% of the
total annual rainfall over most parts of the country.
5.3.1 Standardized Precipitation Index (SPI):
It is an index based on the probability of rainfall for any time scale. Many
drought planners appreciate the SPI’s versatility. The SPI can be computed for
different time scales, can provide early warning of drought and help to assess
drought severity, and is less complex than the Palmer. It is developed by T.B. McKee,
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N.J. Doesken, and J. Kleist, Colorado State University, 1993. The understanding that a
deficit of rainfall has different impacts on groundwater, reservoir storage, soil
moisture, snow pack, and stream flow led McKee, Doesken, and Kleist to develop the
Standardized Precipitation Index (SPI) in 1993. The SPI was designed to quantify the
rainfall deficit for multiple time scales. These time scales reflect the impact of
drought on the availability of the different water resources. Soil moisture conditions
respond to rainfall anomalies on a relatively short scale. Groundwater, stream flow,
and reservoir storage reflect the longer-term rainfall anomalies. For these reasons,
McKee et al. (1993) originally calculated the SPI for 3,6,12, 24 and 48 month time
scales. The SPI calculation for any location is based on the long-term rainfall record
for a desired period. Standardized precipitation is the difference of precipitation
from the mean for a specified time divided by the standard deviation, where the
mean and standard deviation are determined from the climatological record. The fact
that precipitation is not normally distributed is overcome by applying a
transformation (i.e., gamma function) to the distribution.
The computation of SPI requires long term rainfall data. It is found by Thom
(1966) that the gamma distribution function fit to the rainfall time series. The long-
term record is fitted to a probability distribution, which is then transformed into a
normal distribution so that the mean SPI for the location and desired period is zero
(Edwards and McKee, 1997). The rainfall series was fitted to the gamma distribution.
It is defined by its frequency or probability density function. The gamma probability
distribution function (pdf) is given as follows. The alpha and beta parameters of the
gamma probability density function are estimated for each station.
xexxg
11
for x >0
where, x = rainfall amount
= shape parameter =
3411
41 AA
A = n
xx lnln
n = number of rainfall observations
β = scale parameter = ^
x
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Г( ) = gamma function
The gamma distribution function is fitted to the data for estimating the
parameters and β. The gamma cumulative distribution function (cdf) is computed
at each value of x by integrating pdf with respect to x and inserting the estimated
values of and β. The cdf is then transformed into the standard normal distribution
to find SPI. To compute SPI corresponding to a rainfall amount, mark the rainfall
amount on x-axis (Fig.5.1). From this point draw a line parallel to y-axis till it
intersects with the theoretical gamma cdf line. From this point of intersection, extend
a line perpendicular to y-axis till it intersects the standard normal cdf graph. Draw a
line parallel to y-axis from this point upwards to the secondary axis to have the SPI
value.
Figure 5.1 Illustration of computation of SPI for the seasonal rainfall over the country
as a whole obtained through equiprobability transformation from fitted gamma cumulative probability
distribution to standard normal cumulative probability distribution. (Source:NCC Research report
2/2010)
Positive SPI values indicate greater than median precipitation, and negative
values indicate less than median precipitation. Because the SPI is normalized, wetter
and drier climates can be represented in the same way, and wet periods can also be
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monitored using the SPI. McKee et al. (1993) used the classification system shown in
the SPI values table to define drought intensities resulting from the SPI. McKee et al.
(1993) also defined the criteria for a drought event for any of the time scales. A
drought event occurs any time the SPI is continuously negative and reaches an
intensity of -1.0 or less. The event ends when the SPI becomes positive. Each drought
event, therefore, has a duration defined by its beginning and end, and intensity for
each month that the event continues. The positive sum of the SPI for all the months
within a drought event can be termed the drought’s “magnitude”. Table 5.1 Drought Classification as per SPI (Source: http//drought.uni.edu)
SPI Values Drought Criteria As per SPI Drought Class As per SPI
2.0+ Extremely wet G
1.5 to 1.99 very wet F
1.0 to 1.49 moderately wet E
-.99 to .99 near normal D
-1.0 to -1.49 moderately dry C
-1.5 to -1.99 severely dry B
-2 and less Extremely dry A
5.3.2 Percent of Normal: The percent of normal is one of the simplest measurements of rainfall for a
location. It is useful for analyzing a single region or a single season. Percent of
normal is also easily misunderstood and gives different indications of conditions,
depending on the location and season. It is calculated by dividing actual rainfall by
normal rainfall—typically considered to be a 30-year mean—and multiplying by
100%. This can be calculated for a variety of time scales. Usually these time scales
range from a single month to a group of months representing a particular season, to
an annual or water year. Normal rainfall for a specific location is considered to be
100%.
One of the disadvantages of using the percent of normal is that the mean, or
average, rainfall is often not the same as the median rainfall, which is the value
exceeded by 50% of the rainfall occurrences in a long-term climate record. The reason
for this is that rainfall on monthly or seasonal scales does not have a normal
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distribution. Use of the percent of normal implies a normal distribution where the
mean and median are considered being the same. Because of the variety in the
rainfall records over time and location, there is no way to determine the frequency of
the departures from normal or compare different locations. This makes it difficult to
link a value of a departure with a specific impact occurring as a result of the
departure, inhibiting attempts to mitigate the risks of drought based on the
departures from normal and form a plan of response (Willeke et al., 1994).
5.4 Need of modified drought index
Earlier drought indices developed and used by many researchers uses
weather parameters like rainfall, temperature, evapo-transpiration and remote sense
data to compute drought indices. Although none of drought indices is superior to
other in all situation. Suitability of a drought index depends on its use. Rainfall data
are used to calculate drought index as long term rainfall data are available. Rainfall
data alone may not reflect the range of drought related conditions, but they can work
as one of the practical solution in data-poor regions. Therefore, a new definition of
drought index has been proposed based on standardized precipitation index (SPI)
and number of rainy days to compute modified drought index. SPI represents the
probability of rainfall while the proposed modified drought index considers the
rainfall amount and the duration. This modified index will be superior as it considers
rainfall duration also on which crop growth depends. Therefore, for the purpose of
drought planning this modified drought index will offer better insight on drought
definition.
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5.5 Reconstruction and classification of modified drought index
The SPI developed by McKee et al (1993) is based on the probability of rainfall
for a particular time scale. The basic data used in the study is rainfall data of 20
rainfall stations of Sabarmati basin of Gujarat for the period 1976 – 2007 for the
monsoon period May to October. Based on this data, Standardized Precipitation
Index (SPI) was computed for the districts of Sabarmati basin. After calculating the
SPI values for individual stations, a modified drought index is developed by
multiplying the SPI values with average number of rainy days for individual
stations.
Modified Drought Index= SPI * Number of Rainy Days ……….. (5.1)
The drought classes have been defined considering average SPI and average
number of rainy days for a given station over long time period. Although none of the
drought indices are superior, hence the need of new drought index was felt. Based on
the new drought index calculated, drought years are identified and compared with
the past records of available data.
Based on the modified drought index calculated, drought years are identified
and compared with the past records of drought years in Sabarmati basin. Seven MDI
classes has been defined as class A (< -72), B (-54 to -72), C (-36 to -54), D (-36 to 36), E
(36 to 54), F (54 to 72), and G (>72). The quantitative estimates on MDI for 20 stations
have been done for year 1976-2007.
5.6 Analysis and results
Using the daily rainfall data of 20 stations of Sabarmati basin for the period of
1976-2007, two drought indices; Percent of Normal (PN) and Standardized
Precipitation Index (SPI) were calculated. The analysis is carried out to compute SPI
and PN for the period of 1976 – 2007. Fig: 5.2(a) & (b) shows the time series rainfall
expressed in terms of SPI & PN for the period 1976 to 2007. It is clearly seen that the
year to year variation in both plots are nearly same. The percent of Normal (PN) was
calculated by dividing the actual rainfall by average rainfall and multiplying by
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100%. Based on the available rainfall record, the average rainfall for 20 stations in
Sabarmati basin is 770mm. When the rainfall is between 90-110% of normal rainfall, it
is termed as normal. The seasonal rainfall over a district is classified as moderate
drought when the rainfall over an area is 50-74% of average rainfall and a severe
drought when the rainfall is less than 50% of average rainfall. Drought years for the
20 stations in Sabarmati basin were identified based on PN criteria,. It is observed
that during the period of 1976 to 2007, there were 12years with Normal condition (90-
110%of Normal Rainfall). In the year 1986, 1987, 1995, 1999, 2000 and 2002, all the
stations received less then normal rainfall. In the year 1987, all the stations faced
severe drought situations. The year 1976, 1977, 1994, 1997 and 2006 were received
more than average rainfall for almost all stations.
The SPI value has been calculated as per the methodology explained in section
5.3. The classification of the drought intensities based on the SPI value is given in
Table 5.1. Drought classification based on SPI criteria shows that all the stations
considered for analysis suffered moderate to severe drought conditions in the year
1986, 1987 1999 and 2002. The year 1995, 2000, and 2001 shows around 50% stations
were affected by moderate drought. In the year 1979, 1982 and 1985 around 25%
stations were affected by moderate drought. The year 1976, 1977, 1994, 1997 and 2006
were received more than average rainfall for almost all stations. The year 1978, 1980,
1981, 1983, 1984, 1988, 1989, 1991, 1992, 1993, 1996, 1998, 2003, 2004 and 2007 were
received normal rainfall. One peculiar observation was seen from this analysis that
the year which was suffered by severe drought conditions, the previous year and
next year shows extreme situations.
In the second step of analysis, an attempt has been made to develop a modified
drought index. For quantitative assessment of anomalous climatic conditions
(Intensity, Duration, and spatial extent), Standardized precipitation Index (SPI) is
calculated for 20 stations in Sabarmati basin. A modified Drought Index is developed
and calculated by multiplying the SPI values with average number of rainy days for
individual stations for identifying the drought years and shown in Figure 5.3. The
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value of modified drought index for each year of all station has been plotted in Arc
GIS map (Figure 5.4). The analysis shows that during the time period of 1976 to 2007,
majority of rain gauge stations considered for analysis in Sabarmati basin faced
drought in the year of 1986, 1987 and 2002. In the year 1987, out of 20 stations, 5
stations faced moderate drought condition, 14 stations faced severe drought and one
station extreme drought condition. For year 1999, out of 20 stations, only seven
stations were under normal condition, and 13 faced moderate drought condition. In
the year 2002, 50 % stations were under moderate drought conditions. Out of 32
years, nine years (1978, 1980, 1984, 1988, 1989, 1991, 1992, 1993, and 1996) were
normal years for all stations and for years 1977, 1981, 1983, 1990, 1998, 2003, 2004 and
2007 the stations were received normal/above normal rainfall. The modified drought
index has been developed to identify and classify the drought at regional level. The
year 1976 has been considered as a year with more then average rainfall, in the S-W
region of basin, majority of stations received excess rainfall then average rainfall
while in N-W region; all the stations received normal rainfall. In the region N-E, two
stations received excess rainfall while other with normal rainfall. The modified
drought index derived has been found to have strong relationship with severe
drought and wet years.
5.7 Discussion
The variability of rainfall at spatial and temporal level is high in Sabarmati
basin as discussed in previous chapter. The number of rainy days has also been
found to be variable at spatial and temporal scale. The temporal variability found to
be more then spatial variability. So, in the first step of analysis, two drought indices
(SPI and PN) were computed for analyzing the drought condition during a period of
1976 to 2007 for 20 stations in Sabarmati basin. The analysis shows that SPI is better
as compared to PN as it shows dry as well as wet conditions of an area. PN is useful
for analyzing a single region or a single season as it considers only rainfall amount
and use of the PN implies a normal distribution, while the rainfall for a season does
not have a normal distribution. The SPI was designed to quantify the rainfall deficit
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for multiple time scales, which reflect the impact of drought on the availability of the
different water resources. The analysis shows that SPI is better as compared to PN as
it shows dry as well as wet conditions of an area.
5.8 Conclusions
An attempt has been made to develop a drought index for identifying the
drought situations based on SPI and number of rainy days in Sabarmati basin. Based
on SPI, a modified drought index has been developed and results were verified with
past data record on drought and has been found good coherence. The analysis shows
that when there is a variability of rainfall and rainy days at spatial and temporal
scale, MDI may be used for identification of drought at station level. MDI
considers rainfall amount and distribution, which may be used at regional level
drought classification. The overall analysis leads to the following conclusions.
SPI is better as compared to PN as it shows dry as well as wet conditions of an
area.
A new drought index (MDI) based on SPI and number of rainy days for
identifying drought has been developed.
-2.50
-1.50
-0.50
0.50
1.50
2.50
3.50
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
AHD BDL BRJ BYD BHL SJT CDL CPW DHR HMT
IDR LML MHD MNS RSP RPW TTI VRP VJA VSI
Figure 5.2(a) Standardized precipitation Index (SPI) for 20 stations in Sabarmati basin
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0
50
100
150
200
250
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
% o
f Nor
mal
AHD BDL BRJ BYD SJT CDL CPW DHR HMT LML
MHD RSP VRP RPW TTI VJA BHL MNS VSI IDR
Figure 5.2 (b) % of Normal (PN) for 20 stations in Sabarmati basin
-125
-75
-25
25
75
125
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
MDI
AHD BDL BYD BRJ SJT BHL CDL CPW DHR IDR
HMT LML MHD MNS RSP VRP RPW TTI VJA VSI
Figure 5.3 Modified Drought Index derived for Sabarmati basin
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-3
-2
-1
0
1
2
3
1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
YEAR
SPI
-3
-2
-1
0
1
2
3
MD
I
SPI_AHD SPI_BRJ SPI_CDL SPI_MHD SPI_SJT SPI_RPW SPI_VSI SPI_LMLSPI_MNS SPI_RSP SPI_VRP SPI_VJA SPI_VDL SPI_DHR SPI_BYD SPI_BHLSPI_CPW SPI_IDR SPI_HMT SPI_TTI MDI_CDL MDI_MHD MDI_SJT MDI_RPWMDI_VSI MDI_LML MDI_MNS MDI_RSP MDI_VRP MDI_BDL MDI_DHR MDI_BHLMDI_CPW MDI_IDR MDI_AHD MDI_BRJ MDI_VJA MDI_BYD MDI_HMT MDI_TTI
Figure 5.3-a Comparison of SPI and MDI for twenty stations of Sabarmati basin for a
period of 1976 to 2007
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Table 5.2 Performance of various drought indices for twenty stations
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Figure 5.4 Modified drought index for 20 stations during 1976-2007 plotted in Arc-
GIS
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Chapter-6 Prediction of Monsoon onset
6.1 Introduction
In arid and semi-arid regions like Sabarmati basin, where rainfall is
limited to a few months per year only, is the most critical factors for the ecological
and environmental processes,. The amount of water available strongly depends on
the rainy season’s on-set, length and end in the areas where most of the agricultural
production depends on rainfall (Ati et al 2002). According to Steward (1991), the
onset is the most important variable to which all other seasonal variables are related.
Rainfall data is most important to hydrologists as it forms basis of many hydrological
studies. The critical problem is the uneven distribution of rainfall during rainy
season and the gap between the successive rainfall events. In order to get maximum
yield, it is necessary to supply optimum quantity of water at right time which may
not be possible every time. The total amount of rainfall in a particular area may be
not sufficient or is not in time. The rainfall may be non-uniform over the crop period.
There are sensitive periods of crop where proper amount of water is required. If
sufficient moisture is not available, yield may be reduced. Due to very high spatial
and temporal variability of rainfall and non uniform distribution of rain during rainy
season, farmers have problems to decide when to start with sowing of plants. Some
of the strategies adopted by farmers to cope with the problems are re-sowing, dry
seeding, crop rotation, exchanging information about rainfall with local workers and
steps for sustaining soil fertility.
It is necessary to predict the onset of rainy season which is the most important factor
and which coincide with the growing season of crops. Information of onset of rainy
season, length and end of season imparts significant information in timely
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preparation of farmland, planting, preparation of equipments and manpower and
also help in contingency planning to the government in the situation of drought.
Due to random distribution of local convection events and potential shifts of
onset dates on site scales, this study will concentrate on determination and prediction
of arrival of monsoon on basin scale. It is focused on onset of monsoon for the
different regions of Sabarmati basin.
6.2 Methodology on prediction of onset
The onset of rainy season (monsoon) is defined in different ways at
present. The principal research areas are India, Australia and West Africa i.e. areas
having water scarcity and rainfall is limited to rainy season. In general two types of
definitions can be distinguished. The definition of monsoon onset is generally based
on the parameters measured on the surface which may be used for agro-
climatologically purposes on local scale or on the basis of atmospheric dynamics by
analyzing the appearance of large-scale circulation patterns in combination with start
of rains. Most researchers refer to rainfall itself in order to determine the onset
and/or end of rainy season. The benefit of this approach is that precipitation tools
are readily available and it exhibits the most direct relationship rather than some
other related factors. For rainfall-alone definition, two sub groups can be found in
literature, a definition based on certain threshold value (e.g. Stern et al.,1981) and a
relative definition using a proportion relative to the total amount (Ilesanmi,1972)
The overall objectives of this investigation are:
1) To develop a reasonable onset definition for Sabarmati basin
2) To predict arrival of monsoon in a region based on arrival of monsoon in
neighboring region.
An attempt has been also made to forecast the rainfall using Box-Jenkins approach of
time series using ARIMA model. The description of model, methodology, data and
performance model has been given in annexure-II.
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6.3 Description of Fuzzy Logic model
For the statistical analysis performed, daily rainfall time series of 20
stations were applied. The meteorological data were obtained from State water data
centre. The data were checked for continuity by calculating monthly and annual
totals. Table 6.1 represents the details of rain gauge stations used for analysis.
A Fuzzy logic approach has been developed to facilitate modeling.
Fuzzy Logic (FL) is not a control methodology, but it is a way of processing data by
allowing partial set membership rather than crisp set membership or non-
membership. This approach to set theory was not applied to control systems until the
70's due to insufficient small-computer capability prior to that time. Fuzzy logic is a
problem-solving control system methodology that lends itself to implementation in
systems ranging from simple, small, embedded micro-controllers to large,
networked, multi-channel PC or workstation-based data acquisition and control
systems. It can be implemented in hardware, software, or a combination of both.
Fuzzy logic provides a simple way to arrive at a definite conclusion based upon
vague, ambiguous, imprecise, noisy, or missing input information. The approach of
fuzzy logic to control problems mimics how a person would make decisions, only
much faster. Fuzzy logic incorporates a simple, rule-based “if x and y then z”
approach to a solving control problem rather than attempting to model a system
mathematically. The fuzzy logic model is empirically-based, relying on an operator's
experience rather than their technical understanding of the system. Fuzzy logic
requires some numerical parameters in order to operate such as what is considered
significant error and significant rate-of-change-of-error, but exact values of these
numbers are usually not critical unless very responsive performance is required in
which case empirical tuning would determine them. Fuzzy logic was conceived as a
better method for sorting and handling data but has proven to be an excellent choice
for many control system applications since it mimics human control logic. It can be
built into anything from small, hand-held products to large computerized process
control systems. It uses an imprecise but very descriptive language to deal with input
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data more like a human operator. It is very robust and forgiving of operator and data
input and often works when first implemented with little or no tuning.
Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory to
deal with reasoning that is approximate rather than precise. In contrast with "crisp
logic", where binary sets have binary logic, the fuzzy logic variables may have a
membership value of not only 0 or 1 – that is, the degree of truth of a statement can
range between 0 and 1 and is not constrained to the two truth values of classic
propositional logic. Furthermore, when linguistic variables are used, these degrees
may be managed by specific functions.
The onset of monsoon has been defined considering three constraints
namely, total amount of rainfall, number of rainy days and percentage of stations
receiving rainfall. An artificial intelligence based fuzzy logic approach has been used
to model the onset of rainy season. A fuzzy logic approach is important as it can
incorporate the sternness of constraints which have to be fulfilled simultaneously. In
this approach, each constraint is attached to a fuzzy membership function using
triangular (subscript T) fuzzy numbers. The first two definition constraints are
attached to a fuzzy membership function using triangular fuzzy numbers while the
third constraint considers the threshold limit. For the first constraint dealing with
total amount of rainfall within a 10 days spell, the triangular fuzzy numbers are (18,
25, +∞) т. This means that membership grade of rainfall totals less than 18 mm is
attached to zero and total larger than 25 mm to one. Between 18 and 25 mm the
membership grade is linearly interpolated. For the second constraint dealing with
number of rainy day, the triangular fuzzy numbers are (1, 3, +∞) т. This means that
membership grade of rainy days less than 1 is attached to zero and more than 3 to
one. The membership grades between 1 and 3 are linearly interpolated and
appropriate values are assigned. If 1 , 2 , 3 are membership grades for amount
of rainfall, number of rainy days and percentage of stations receiving rainfall then,
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the onset date is defined as the first day of year where the product
321 ** exceeds a defined threshold value.
onset date = 321 ** --------------------------(6.1)
Where = Onset date,
,01 if ∑ Rf =18 and 11 , if ∑ Rf =25
02 if ∑ Rd =1 and 12 if ∑ Rd =3
13 if 60% stations in a region met criteria 1 and 2
Based on the Fuzzy logic algorithm, software for calculating the values of
membership grades 1 and 2 has been developed in FOXPRO. A filter was applied
on onset date to make prediction relevance, in case the onset definition is beyond the
stipulated monsoon duration.
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Figure 6.1 Fuzzy logic algorithm for membership grade 1
EOF: End of File
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Figure 6.2 Fuzzy logic algorithm for membership grade 2
EOF: End of File
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0
0.2
0.4
0.6
0.8
1
10 15 20 25 30
rainfall amount within 10-day spellM
embe
rshi
p gr
ade
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4
number of wet days within 10-day spellM
embe
rshi
p gr
ade
Condition 1 Condition 2 Condition 3
Figure 6.3 Membership functions representating onset conditions 6.4 Analysis of Results
The daily rainfall values of all rainfall stations were used as input in
order to derive past onset dates. The monsoon onset is the time when first spell of
rains are being received. Therefore it is important to predict arrival of monsoon for a
basin. A Fuzzy logic based approach was used to develop a reasonable onset
definition. Three constraints namely, one- amount of rainfall in ten days, two-
successive number of rainy days and three- percentage of stations receiving rainfall
has been considered for defining onset. Fig 6.3shows the three conditions used for
identifying the onset of monsoon using fuzzy logic approach. The arrows represent
the direction for predicting the onset of rainy season of one region using the current
onset date of another region. The entire basin is divided into three regions based on
similar rainfall characteristics. The analysis of rainfall shows that the variability of
rainfall is very high. The average daily rainfall distribution for regions has been
shown in Figure 6.4 It shows that the all the regions received few amount of rainfall
in the beginning of month of May. The region1 received around 10mm rainfall daily
after mid of June which lasts up to first week of September, while region2 and region
3 receives average daily rainfall of around 10mm after third week of June which lasts
up to end of September. The basin has been classified into three regions based on
terrain, amount of rainfall received and
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cluster of stations. The model results showed monsoon onset for
region-1 on 14th June, region-2 on 17th June, and region-3 on 21st June. The model
captures periodic variability in monsoon onset for various years. The model output
was verified with Indian Meteorological Department’s dates for monsoon arrival
which shows good coherence. The performance of model may be improved using
filter(s).
The Linear Regression models have been developed to forecast
monsoon arrival in region 2 based on onset in region 1 and for region 3 based on
onset in region 2 (Figure 6.6). The model parameters for targeted and independent
region have been found to be 0.40 and 0.35 respectively. The application of onset
model will help farmers to decide crop to be sown and cropping pattern. Such type
of simple tools may be used for advisory services.
Region1
0
6
12
18
0 50 100 150 200Days
Avg
.Rai
nfal
l
Region2
0
5
10
15
20
0 50 100 150 200DayAv
g.R
f
Region3
0
5
10
15
20
0 50 100 150 200Day
Avg.
Rf
Figure 6.4 Average daily rainfall plots for regions during monsoon season
Region1
0
20
40
60
80
1977 1982 1987 1992 1997 2002 2007Year
Region2
0
20
40
60
80
1977 1982 1987 1992 1997 2003Year
Ons
et d
ay
Region3
0
20
40
60
80
1977 1982 1987 1992 1997 2002 2007Year
Ons
et d
ay
Figure 6.5 Onset dates computed based on fuzzy logic approach for 1976 -2007
Modeling of rainfall variability and drought assessment in Sabarmati basin, India _____________________________________________________________________________________
75
6.5 Discussion
As the onset of rainy season is of major interest for managing farming strategies, it is
required that before sowing of plants, farmers should be aware of the onset of rainy
season .In this paper, for Sabarmati basin, based on the past data of daily rainfall
(time period: year 1976 to 2007), analysis of past onset dates and mean rainfall
amount is carried out. For this, Fuzzy logic approach is considered. The entire basin
is divided into three regions based on similar rainfall characteristics. Region1
receives the rainfall in the second week of June and region 2 and Region 3 in the third
week of June. This information is useful to the farmers for growing the seeds. The
survival of seeding is key points for agriculturists (Sultan and Janicot, 2003). For
sowing, it is important to know, whether, (1) the rain is continuous and sufficient to
provide soil moisture during planting time, (2) level of soil moisture will be
maintained or is there any change during growing period to avoid crop failure
(Walter, 1967). The data dependent model for defining monsoon onset using FL for
Sabarmati basin has been developed.
Table 6.1 Details of rain gauge stations Serial Number
NAME OF STATION
RAINFALL REGION
1 AHD 780 2 RPW 709 3 CDL 737
S-W
ModelR1
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35Year
Ons
et d
ay
Predicted Y Observed y
ModelR1
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35Year
Ons
et d
ay
Predicted Y Observed y
Figure 6.6 observed and predicted onset days using linear Regression Analysis
Modeling of rainfall variability and drought assessment in Sabarmati basin, India _____________________________________________________________________________________
76
4 VSI 749 5 BRJ 811 6 MHD 761 7 SJT 738
8 LML 726 9 MNS 718 10 RSP 671 11 VJA 800 12 BDL 712 13 VRP 675 14 DHR 758
N-W
15 BHL 876 16 CPW 906 17 HMT 779 18 IDR 875 19 BYD 836 20 TTI 784
N-E
Table 6.2 Mean onset days and standard deviation
Region Mean onset date
Mean Onset day Std. Dev.
Region 1(S-W) 14-Jun 45 17 Region 2(N-W) 17-Jun 48 15 Region 3(N-E) 21-Jun 52 14
Table 6.3 Linear regression models
Model Target Region
Independent Region
γ threshold
target region
Γ threshold
independent region
Regression Equation
M1 Region 2 (N-W) Region1 (S-W) 0.35 0.40 Y = -0.3683x + 53.795
M2 Region3 (N-E) Region 2 (N-W) 0.35 0.40 Y = -0.3438x + 57.597
Modeling of rainfall variability and drought assessment in Sabarmati basin, India _____________________________________________________________________________________
77
6.6 Conclusion
There are methods to predict the rainfall using meteorological and /or
atmospheric data. In this study, Linear Regression Analysis is used to find out onset
dates of regions using the onset dates of one region. Here, region 1 is considered as
the first region to receive onset and based on that linear regression models has been
developed between regions, which can be useful for predicting inter-region monsoon
onset. (Table 6.3) The analysis leads to following points.
A data dependent model for defining monsoon onset using FL for Sabarmati
basin has been developed.
A linear regression models between regions which can be useful for predicting
inter-region monsoon onset has been developed.
ARIMA methodology of time-series has been attempted to predict rainfall
where the select models fails to catch the trend of series.
As the Sabarmati basin is a semi arid area and most of the agriculture depends on
rainfall in the basin, the analysis of past onset dates helps the farmers in planning
their crop season. Knowing the start of rainy season, they can plan for type of the
crop to be sown and date of sowing. The analysis also helps the farmer for drought
contingency planning if the quantity of rain is less for a particular crop. An attempt
has been made to predict rainfall using ARIMA methodology of time-series.