Rainfall data classification using Mann-Kendall test statistics associated with Neuro Fuzzy technique: A case study of Chennai district

Abstract

Climate change, rainfall, weather forecasting is of great concern during the past two decades as scientists and researchers are cautious in building standard numerical models to simulate and forecast the weather parameters in efficient and reliable way. In India, the monsoon is largely responsible for rainfall. India experiences three distinct seasons throughout the year as a result of the monsoon, which originates from the reversal of the predominant wind direction from Southwest to Northeast. Between June and October, the Southwest monsoon, sometimes known as the “wet” season, brings significant rainfall across the majority of the nation. The focus of this research work is to analyse the data of rainfall existed in the past 100 years (1901–2000) and implementing artificial intelligent methods to frame certain classification of algorithm which can forecast the level of rainfall in the future. Data from 1901–2000 of Chennai district has been taken into account for this research. Statistical evaluations are done based on the database and the tabulated results shows the significance of rainfall. Wavelet analysis of multi resolution criteria is obtained to extract the information of heavy rainfall. Mann Kendall (MK) test statistics is utilized for classifying the rainfall data in four levels viz., very-low, low, moderate, high and very high. Trend analysis for the 17 years is tested using Neuro Fuzzy optimisation algorithm. The efficient training of Neuro fuzzy algorithm forecasts the possible trend using the classification analysis of MK test.

Keywords

ANFIS Mann Kendall test prediction climate change wavelet analysis

1. Introduction

In India, monsoon rainfall contributes 80% of annual rainfall spreading from June to September [12, 7]. The monsoon hits southern India during May and first week of June and spreads north India during first week of July. Rainfall in India plays major part in economic well-being, earth-atmosphere system, agriculture, farming and disaster management in India. Rainfall patterns of India (1871–1990) were mapped using time series analysis of proximity correlation techniques, fuzzy C-relates to clustering and orthogonal functions [30], and Kulkarni (1992).

Forecasting rainfall is not a simpler task. It requires lot of parameters to be involved in it. Precipitation, temperature, wind speed and wind direction play key role in forecasting rainfall. Forecasting accurate value is very difficult because of these multiple parameters. Thus, using Neuro Fuzzy logic rainfall has been classified into Very Low (VL), Low (L), Medium/Normal (M), High (H), Very High (VH) and their linguistic values are given as an input to this algorithm. The proposed linguistic values arranged in such a way that the values represent the Mann-Kendall Test statistics output values. The input values are coined to have linguistic variables and then fed to ANFIS algorithm to predict rainfall in ranges of value. Thus, in evident, training data was taken from 1900–2014. The testing results proved that the algorithm works well to predict the rainfall in particular range fixed on the Mann-Kendall Test statistics.

1.1 Challenges in rainfall prediction

The history of Indian Seasonal Rainfall (ISMR) prediction is extensive. Sir Henry Blanford started it in 1886 after taking into account the snowfall in the Himalayas. Rao [46], Banerjee [8], Kung and Sharif [31], Bhalme [9], Gowariker [18], Parthasarathy [39, 40, 41], Kumar [27, 28], and Rajeevan [44] are just a several of the researchers who have attempted to create an accurate forecast model. There has been a lot of study done on forecasting ISMR, and some studies have revealed that climate and hydrological cycles are connected [24, 15, 5, 6, 35, 34]. Despite all the efforts made by experts to predict rainfall, the issue still needs to be looked into using artificial intelligence approaches [48, 56]. This study concentrates on the artificial intelligence approach ANFIS in combination with MK statistics to forecast rainfall range for a specific time period. This effort is successful, and the outcomes are solid. The researchers conducted numerous investigations to determine the effects of anthropogenic activities on climate change [21, 16].

The Indian Meteorological Department (IMD) recorded day-to-day rainfall data between 1951 and 2007 [45], which is helpful for agriculture, hydrology, ecology, weather forecasting, monitoring, and analysing rainfall fluctuations [54]. Sontakke et al. [55] documented a recent decline in seasonal rainfall, with winter months experiencing rainfall rates of 47%, 17%, 75%, and 38% less than summer months. Several research on rainfall for drought analysis were presented [13, 50, 20, 38], Sinha and Shwale (2001). The Mann-Kendall mode test, which is grounded on Sen’s method [49], was used by Naresh Kumar et al. to analyse spatiotemporal drought analysis because it can be used to analyse time series data without the use of statistical evaluation functions [17, 19, 42]. The Central Water Commission [11] reported that India’s per-capita water consumption decreased from 5176 m ${}^{3}$ in 2010 to 1434 m in 1951 to around 1588 m ${}^{3}$ in 2025. Some of the important considerations about the water resource planning, including the management changes in the climate and regional imbalances in water supply. Therefore, one of the key elements in climatic change concerns is rainfall. To properly comprehend a pattern, modelling and rainfall forecasting are essential. This research will aid in predicting the range of rainfall for the upcoming several years based on the innovative technique shown here.

2. Methodology

It’s indispensable to study the rainfall data analysis and forecasting using efficient tools.

3. Study area

The city Chennai, the Coromandel Coast and the capital of Tamil Nadu, is situated in latitude 13.0827 ${}^{\circ}$ N and longitude 80.2707 ${}^{\circ}$ E (Fig. 1). It is recognised as India’s fourth-largest economy and the ninth-best sophisticated city in the world, with the third-highest GDP per capita in 2015. Chennai, which is located on the thermal equator, has tropically wet and dry climate. The expected annual rainfall in Chennai is roughly 140 cm, and the temperature will range between 35 and 40 ${}^{\circ}$ C. The years 2005 and 2015 saw the city’s highest yearly rainfall totals. The North-East monsoon brings forth the majority of the rainfall in Chennai [47]. Due to the north-east monsoon season, Chennai, which is situated in the southernmost region of peninsular India, encounters the major part of the country’s year-long rainfall. It gets between 40 and 50 percent of its yearly rainfall in the interior and 60 percent of it towards the shore [22]. In November and December 2015, the coastal areas of Chennai, Kancheepuram, and Tiruvallur had repeated heavy rainstorm storms that damaged across 4 million people and caused commercial damages that totalled almost US$3 billion (The National, 2015). 53 departmental observatories and 68 part-time observatories are among the 121 surface observatories that the Regional Meteorological Centre, Chennai, maintains. It also operates 10 Rawin stations, 1 Radiosonde station, and 13 Pilot Balloon Observatories. Up to 80% of surface runoff occurs in Chennai. It results from the annual divergence between the recharge and extraction zones brought on by settlements.

Figure 1.

Location map of study area.

Figure 2.

Flow chart showing the ANFIS classified MK test statistics.

3.1 Wavelet analysis

Wavelet analysis is indispensable for effectively analysing time series data. This transformation simplifies the process of determining the potential for an event to occur. The spatial and temporal data will give an eagle’s eye view of the real-time data approach. The signal of time-frequency multiresolution functions is disintegrated has advantages over standard time-frequency analysis [32]. The following is the requirement for eligibility:

$\psi(t)\epsilon L^{2}(R)$ satisfy the certain adequacy specifications as

$\displaystyle\psi=\int_{R}\frac{|{\hat{\Psi}(\omega)}|^{2}}{|\omega|}d\omega<\infty$ (1)

$\Psi(t)$ is called wavelet; $\hat{\Psi}(\omega)$ is Fourier transform of $\Psi(t)$ . The Continuous Wavelet Transform (CWT) is defined by the addition of the signals multiplied by calibrated, shifted versions of the wavelet function,

$\displaystyle\Psi_{a,b}(t)=|a|^{-\frac{1}{2}}\Psi\left({\frac{t-b}{a}}\right)$ (2) $\displaystyle W_{f}\textit{year}({a,b})=\langle f(t),\Psi_{a,b}(t)\rangle=|a|^% {-\frac{1}{2}}\int_{R}f(t)\Psi\left({\frac{t-b}{a}}\right)dt$ (3)

Depending on the wavelet’s scale parameter, CWT involves discrete data for sampling in order to extract the prime features. Increased processing time and more memory are needed to calculate the coefficients with finer resolution. Orthonormal supported wavelets are the basis of multiresolution analysis (MRA). Since the representation of specific information provides a clearer image compared to other alteration algorithms similar to Fourier and Short-Term Fourier Transform, its applications are expanding quickly in a variety of scientific domains (STFT). Wavelet has been used in numerous scientific fields, such as river flow models and the analysis of flood forecasts [1, 2, 3]. Wavelet coefficients of rainfall data from the years 2001 to 2017 are displayed in Fig. 3. The multiresolution rainfall scalogram is shown in Fig. 4. Heavy rainfall in the years 2005 and 2015 had greater energy spectrogram dispersion, according to multiresolution. In Fig. 3, the red lines are separated to show the variation for each month of the year.

Figure 3.

Continuous Wavelet transforms coefficients for the rainfall pattern analysis for Chennai district 2001–2017.

Figure 4.

Multiresolution analysis shows the peak rainfall variations in 2005 and 2015 in Chennai district.

3.2 Mann-Kendall test (MK test)

The most widely used form used among researchers is the MK test [14, 58, 10, 51, 52], Kumar and Jain (2011). The MK test is used to calculate the variations in rainfall fluctuation trend are statistically analysed. In this investigation, Sen’s estimator [49] and the Mann-Kendall (MK) test were applied to analyse the amplitude of rainfall fluctuations from the years 2001 to 2017 [33, 26]. The MK test determines whether a trend is there and whether it is increasing or decreasing in direction.

$\displaystyle S=\mathop{\sum}\limits_{i=1}^{N-1}\mathop{\sum}\limits_{j=i+1}^{% N}\textit{sgn}({x_{j}-x_{i}})$ (4)

where the number of data points are denoted by $N$ .

Assuming $({x_{j}-x_{i}})=\theta$ , the value of $\textit{sgn}(\theta)$ computed as follows

$\displaystyle E[S]=0$ $\displaystyle\textit{Var}(S)=\frac{N({N-1})({2N+5})-\mathop{\sum}\nolimits_{k=% 1}^{n}t_{k}({t_{k}-1})({2t_{k}+5})}{18}$ (5) $\displaystyle Z=\left\{{{\begin{array}[]{ll}\frac{S-1}{\sqrt{\textit{Var}(S)}}% &\text{if }S>0\\ 0&\text{if }S=0\\ \frac{S+1}{\sqrt{\textit{Var}(S)}}&\text{if }S<0\\ \end{array}}}\right.$ (6)

3.3 ANFIS methodology

Before using the ANFIS algorithm, subtractive clustering technique was first applied to the data as part of a clustering analysis. The resulting membership functions have been mapped to increase the firing strengths for each membership function and a specific degree of membership grade between the input and output. Each function includes a key component for the framing of rules and related parameters. Stanley [57] applied ANFIS for comparing time series and non-time series states.

The subtractive clustering algorithm is utilized to the imported rainfall data (using the MATLAB programme “genfis2”). A specific membership function has been assigned to the cluster centres (in this case, the MATLAB command “gaussmf” or “Gaussian membership function”) Each rule has a corresponding membership function. Following the formulation of the rules, a hybrid learning methodology using gradient descent and least square evaluation was used to initialise the ANFIS network.

The ANFIS system has five levels, and each layer’s output is represented by the symbols $O_{1,i}$ , where I represents a sequence of nodes and 1 represents a sequence displaying the line. The explanations for each layer [14] are as follows:

Layer 1 serves to increase the degree of membership, and the Gaussian membership function is applied in this case.

$\displaystyle O_{1,i}=\mu_{A}(x),i=1,2\ldots$ (7)

and

$\displaystyle O_{1,i}=\mu_{B}(y),i=1,2\ldots$ (8)

with $x$ is the MK statistical results and $y$ is the classification levels chosen as the input for the $i$ -th node for training,

$\displaystyle f({x,\sigma;c})=e^{\frac{-({x-c})^{2}}{2\sigma^{2}}}$

by { $\sigma$ and $c$ } are either named variables or the parameters of the membership function. $c$ stands for the cluster centre, and $\sigma$ stands for the cluster bandwidth.

Layer 2 serves to multiply each input signal in order to induce firing-strength.

$\displaystyle O_{2,i}=w_{i}=\mu_{A}(x)x\mu_{B}(y),i=1,2\ldots$ (9)

Layer 3 makes the firing strength more common

$\displaystyle O_{3,i}=\overline{w_{i}}=\frac{w_{i}}{w_{1}+w_{2}},i=1,2\ldots$ (10)

Layer 4 calculates the output using the $p_{i}$ , $q_{i}$ , and $r_{i}$ parameters of the rule.

$\displaystyle O_{4,i}=\overline{w_{i}}f_{i}=\overline{w_{i}}(p_{i}x+q_{i}y+r_{% i})$ (11)

Layer 5 combining all incoming signals, the ANFIS output signal is counted.

$\displaystyle\mathop{\sum}\limits_{i}\overline{w_{i}}f_{i}=\frac{\mathop{\sum}% \nolimits_{i}w_{i}f_{i}}{\mathop{\sum}\nolimits_{i}w_{i}}$ (12)

ANFIS makes use of the MATLAB command $\textit{xbound}=\{\min,\max\}$ , which specifies the input function’s scaling parameter and ranges from the least to highest estimate of the data point. Initially, every data point is normalised and scaled for initialization of training.

4. Novelty of the proposed algorithm

Step 1:

The data is imported to MK – neuro fuzzy algorithm assigned as $x_{i}$ .

Step 2:

The training data is allotted by applying the Gaussian membership function

$\displaystyle f({x,\sigma,c})=e^{\frac{-({x-c})^{2}}{2\sigma^{2}}}$ (13)

where $\sigma=\textit{standard deviation}$ , $c=\textit{mean value}$ .

Step 3:

Following the Mann Kandell test statistics

$\displaystyle\textit{Var}(S)=\frac{N({N-1})({2N+5})-\mathop{\sum}\nolimits_{k=% 1}^{n}t_{k}({t_{k}-1})({2t_{k}+5})}{18}$ (14) $\displaystyle Z=\left\{{{\begin{array}[]{ll}\frac{S-1}{\sqrt{\textit{Var}(S)}}% &\text{if }S>0\\ 0&\text{if }S=0\\ \frac{S+1}{\sqrt{\textit{Var}(S)}}&\text{if }S<0\\ \end{array}}}\right.$

Step 4:

Classification of rainfall associated with linguistic variables.

Step 5: Error estimation:

$\displaystyle\textit{Sample mean}:\mu=\frac{\sum x}{n}$ (15) $\displaystyle\textit{Standard Deviation}:\sigma=\sqrt{\frac{\mathop{\sum}% \nolimits({x-\mu})^{2}}{n-1}}$ (16)

The algorithm now determines the relative difference between the real and fake data. This is equivalent to the error percentage (e). It will follow the trend and noise can be reduced if it is nearer to the integer of synthetic data, or the neighbouring data points.

Thus

$\displaystyle S_{i}=\mathop{\sum}\limits_{i=1}^{n}x_{i}^{m}\ast W_{i}^{m}\pm e$ (17)

where $n$ represents the number of iteartions; $m$ is the dimensional vector; $e$ represents the error percent; $W_{i}$ represents the weighted sample data.

Figure 5.

ANFIS predicted MK test statistics classification.

Figure 6.

ANFIS predicted MK test classification for monsoon.

Step 5:

Neuro fuzzy considers the synthetic data and generates membership functions to find multi-layer model at this stage [Stanley (2015)].

Step 6:

The final firing phase of the ANFIS algorithm allows for the acquisition of the regressed layer model.

Table 1

Statistical variation of rainfall for the year 2001–2017 for Chennai district

Month	Standard deviation	Mean	Coefficient of variation	Skewness	Kurtosis	Maximum rainfall		Maximum rainfall received year	Mann-Kandell test statistics
January	18.20	12.47	145.98	1.368	3.261	88	.8	2011	$+$ 0.533
February	21.31	8.01	266.08	3.471	13.71	88	.8	2011	$+$ 0.770
March	39.71	11.54	343.94	3.69	14.80	165		2008	$+$ 0.770
April	27.23	12.48	218.06	2.218	6.17	84		2001	$-$ 0.315
May	76.78	44.36	173.06	1.65	3.81	210	.6	2004	$-$ 0.34
June	42.85	62.55	68.50	0.66	1.72	137		2010	$+$ 0.68
July	73.07	111.77	65.37	0.97	2.75	269	.8	2001	$+$ 0.65
August	86.05	143.31	60.04	0.96	3.60	366	.4	2011	$-$ 0.06
September	69.55	157.61	44.128	0.58	2.05	286		2011	$+$ 0.96
October	243.22	331.4	73.39	1.72	6.35	1078		2005	$-$ 0.149
November	262.183	364.61	71.90	0.73	3.11	1013	.6	2015	$+$ 0.71
December	138.07	172.70	79.94	0.53	2.169	438	.4	2015	$+$ 0.53

Figure 7.

Wavelet analysis for monsoonal variations.

Figure 8.

Pre monsoonal classification using ANFIS-MK test.

Table 2

ANFIS Training and testing performance for different range of data with the constraints after fixing number of epochs and network size

S.No	Training data	Testing data	Performance
1.	10%	90%	2.5%
2.	30%	70%	9.28%
3.	40%	60%	19.33%
4.	50%	50%	29.28%
5.	60%	40%	89%
6.	70%	30%	90%
7.	80%	20%	95%
8.	90%	10%	98.9%

Figure 9.

Wavelet analysis for Premonsoonal Variations.

Figure 10.

Post monsoonal variations using ANFIS-MK test statistics.

Figure 11.

Wavelet analysis for Post monsoonal variations.

Figure 12.

ANFIS-MK test statistics for winter season.

Figure 13.

Wavelet analysis for variations during winter season.

5. Results and discussion

Table 1 displays a statistical analysis of Chennai district rainfall data from 2001 to 2017. As anticipated by the MK test related with neuro fuzzy, November month consistently has excessive rainfall, as shown by least square fitting and polynomial fitting. There is a shifting of rainfall fluctuations from the years 2005 to 2015, according to least square estimations and estimates from polynomial fitting. The findings show that there is a good correlation linking the parameters as shown by the alternation curve that complies with the conditions present in the occurrence of rainfall in the research location. Chennai is experiencing an upsurge in rainfall during the northeast monsoon throughout the post-monsoon seasons (October to December). Although, it reveals that there is a little decline in comparison with the premonsoon and monsoon seasons of Chennai district when compared with the linear regression analysis. According to polynomial fitting, the trend gets stronger throughout the post-monsoon season. ANFIS obtained input values from MK test statistics for the previous 100 years’ worth of data, and the test results were verified using monthly data for the years 2001–2017. (Fig. 5). The monsoon season in Chennai district is connected with the classification outcomes anticipated by ANFIS. The ANFIS projected Monsoonal fluctuations and wavelet analysis are shown in Figs 6 and 7, respectively. According to the studies mentioned above, it is possible to analyse the variability in monthly rainfall using the ANFIS technique in conjunction with MK test statistics and handle the results effectively for classification and interpretation. Predictions from the ANFIS-MK test for the premonsoon, post monsoon, and winter seasons are demonstrated in Figs 8, 10, and 12. The wavelet analysis for the corresponding seasons is shown in Figs 9, 11, and 13. Table 2: ANFIS Training and testing results for various data sets.

6. Conclusion

In this study, the continuous wavelet transform was used to analyse the amount of rainfall that fell in the Chennai area between the years of 2001 and 2017 (CWT). Actual data is split using continuous wavelet transforms into precise coefficients that provide the majority of the statistics, which in turn aids in sensing the issue. By breaking down the time series data into distinct levels, wavelet transformations can extract information from noisy or erratic time series data. The researchers can more easily understand the statistical model thanks to this study, and the outcome will make it easier to interpret the rainfall time series data. The seasonal and annual rainfall patterns of Chennai district show multi-time scale properties. The trend study over the course of 12 years reveals very small-time scale fluctuations, despite the fact that there will always be a periodic trend that exists between January and December of every month of the year. The results of this study make it abundantly evident that the trends in monsoon’s variation and change in phase have not significantly affected the Chennai district’s yearly rainfall. The direct trends in the rainfall in the Chennai district between 1901 and 2002 are identified by MK test statistics. Monthly trend tests display patterns for various months and seasons.

6.1 Future works

This paper presented ANFIS based MK statistics for rainfall forecasting algorithm and the efficiency with training and validation is checked while applying the ANFIS algorithm. This research predicts the range of rainfall in Chennai after training with large number of training datasets. This method integrated statistical and soft computing approach to forecast the output values. Thus, it supports the conventional and modern approach in bringing out the best performance in forecasting. The only constraint of this algorithm is that it depends only on the linguistic values of the membership functions. If the classes of the linguistic variables are further distinct and precise then the accuracy will be more. Moreover, this research can be improved by adding other meteorological parameters (evaporation, mean temperature, humidity, and soil temperature) to forecast the values accurately.

Footnotes

Acknowledgments

The authors wish to thank the anonymous reviewers for their comments and suggestions.

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