# Data Patterns In Hydroclimatic Data Biology Essay

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The consequence of not understanding data patterns in hydroclimatic data may lead to misinterpretations and misjudgements by both hydrologists and water resources managers (Grayson et al. 1996; Kundzewicz and A. Robson 2000; Petrow and Merz 2009). Under the current awakening to global climate change patterns, and its resultant effect on local hydrodynamic systems which consequently includes large extreme flood events, a shift in the occurrences of high and low flows, and the change and shift in the timings of these events, the need to fully understand underlying patterns and data becomes imminent. Tangible evidence now suggests that hydroclimatic data can no longer be assumed as being stationary and harmonic (Birsan et al. 2005; Kundzewicz and A. Robson 2000; Petrow and Merz 2009; Sang, Wang, and Liu 2012; Villarini, J. A. Smith, et al. 2011). Thus a thorough understanding of historical data would provide much valuable insights to our past and enable us to prepare for our future.

Though other factors are much more important, the global effect of climate change/variability can readily be measure in the outputs of local streams and water bodies (Hao et al. 2007; Kundzewicz and A. Robson 2000; Magnuson et al. 1997). With this has seen a recent surge in the analysis of trends and patterns in various river networks and water bodies around the world (Brabets and Walvoord 2009; Burn and Cunderlik 2004; Kumar et al. 2009; Partal and Kahya 2006; Petrow and Merz 2009; Tao et al. 2011). However, many of these notable studies primarily include the statistical treatment of the matter only. Though usually underutilized, visual exploratory analysis provides added insights which are often concealed by only statistical treatises of the matter only (Kundzewicz and A. Robson 2000; Radziejewski and Kundzewicz 2004; A. J. Robson 2004). Moreover, detection of trends and patterns in streamflow records are not trivial as streamflows naturally varies year to year. Land-use changes and flow regulations may also conceal underlying patterns. Other artificial influences, such as surface and groundwater abstractions, when present add to the complexity of the matter (Wilby, Wedgbrow, and Fox 2004).

In order to improve upon our understandings of streamflow trends and patterns, this paper relies heavily on both visual and statistical analyses of data. This paper begins with a description of the study area. Methodology provides the relevant literature and assumptions used in this study. Results and Discussions show the outputs of the various research stages and both visual and statistical methods are compared. Conclusion gives the summary of the findings of this research.

## Study Area and Data Availability

The Chengcun basin (Latitude: 29Â°43'0.12"N, Longitude: 117Â°47'60.00"E) is located in the southernmost part of the Anhui Province of China (Figure : Location of Chengcun Basin in China and Figure : Chengcun Basin). It covers an area of 290km2 with the longest stream length being 3.6 km. The elevation ranges from 236m to 1619m above sea level (masl). The basin lies in a humid region with rainfall and temperature averages of 1600mm and 17oC per annum. Daily evaporation values measures around 2mm. There are 10 rain gauge stations in the basin, and one hydro-metrological station at Chengcun which measures evaporation and stream flow in addition to rainfall. Streamflow data used in this study were from 1986 to 1999 and included hourly records for flood events.

Figure : Location of Chengcun Basin in China

Figure : Chengcun Basin

## Methodology

An investigation into possible alternatives in exploring time series data would reveal several varied alternatives and paths for both visual and statistical treatises (Kundzewicz and A. Robson 2000; Petrow and Merz 2009; Radziejewski and Kundzewicz 2004). The selection of particular exploration alternatives and/or paths usually depends on the focus of the research and the underlying pattern hoped to be discovered. In visual data analysis, time series plots, scatter plots, and step plots are examples of what is usually employed to discover the hidden patterns in the data (Kundzewicz and A. Robson 2000). Statistical analyses of hydrological time series data in both time and frequency domain usually employed include auto-correlation functions, Spearman's correlation coefficients, Mann-Kendall tests, Fast Fourier Transform, Wavelet analyses, etc. (Sang, Wang, and Liu 2012; Sang et al. 2009). Since an array of possibilities exists for exploring stream flow time series data, the following methods were selected for this project based on simplicity of application and popularity amongst researchers.

## Visual Data Analysis

Since most hydrological data are recorded serially, a fundamental plot of recorded data with order of recording can provide valuable insights when patterns and trend changes are of interest (Kundzewicz and A. Robson 2000). Superimposing and isolating averaging lines (of a larger time step than what was recorded) often adds valuable insights. Averaging lines often used include regression lines, moving averages, and central tendency statistics such as means and medians.

## Time Series and Outlier Detection

Time series plot usually provides the most basic visual exploration of data patterns in hidden hydrological records. Time series and outlier detection usually involves plotting the time ordered line or scatter graphs. In particular, outlier detection is effective by the use of scatter plot, which is a plot of corresponding data using in points instead of lines. However, the presence of a pattern or trend may not be apparently visible and this can be achieved by the data aggregation, filtering and transformation and/or transformation of plotting scales (Kundzewicz and A. Robson 2000).

## Trend and Abrupt Changes

Detection of monotonic trends in flow records was done by the exploration of regression linear lines. Higher order polynomial regression lines (2nd and 3rd) were employed to perceive di-tonic and tri-tonic trends in the data. In order to understand the natural varying nature of trends in the records, the Savitzky -Golay smoothening algorithm was employed (Savitzky and Golay 1964). The Savitzky-Golay algorithm is given by:

\* MERGEFORMAT ()

Where nL and nR are the number of points used to the left or right of the current data point fi; cn is the Savitzky-Golay filter coefficients for higher order moments that can be found in textbooks and commercial software applications. It was decided that a minimum of three years would be enough to smooth the change in regime, thus a time window of 45 data points (monthly) was thus chosen.

## Flow Regime Classification

Streamflow regime classification was explored using the Pardé coefficient(Olsson et al. 2010). Pardé coefficient provides the normalized annual flow coefficients which can show the nature of the streamflow regime. Pardé coefficient (P) is estimated by:

\* MERGEFORMAT ()

Where MQM and MQA is the mean monthly runoff and mean annual runoff respectively.

## Seasonal Decomposition and Residual Analyses

In order to understand the seasonal and annual structure of the data, the STL procedure (Cleveland et al. 1990; Kundzewicz and A. Robson 2000) was applied. Streamflow data was decomposed into loess, seasonal and residual flows. The streamflow data is decomposed as:

\* MERGEFORMAT ()

Where: xt is streamflow data, lt is the loess smooth (which is the smooth of the annual trend or regional forcing), st is the seasonal component (giving by a fixed monthly medians of all records) and et is the residual component (determined from the STL equation Error: Reference source not found).

Use of annual means (Kundzewicz and A. Robson 2000) as an alternative to the STL loess smooth algorithm has been recommended for hydrological records (Cleveland et al. 1990). In this research, however, the Savitzky-Golay smooth (Savitzky and Golay 1964) of the hydrological data was chosen as the estimate for the loess data as it provided a better smooth estimate (see Error: Reference source not foundf) than the annual means (see Error: Reference source not foundb). Seasonal values were represented as fixed monthly median values of all records. The reminder (residue) was found using the STL equation Error: Reference source not found (Cleveland et al. 1990; Luo, Ying, and Bai 2005).

Histograms were used to analyse the underlying distribution of the residuals. The residuals were also tested for autocorrelation as an evidence of their independence. Non-parametric tests (turning points, median crossing, and rank difference tests) for randomness were carried out to conclude the independence of data.

## Effect and Contribution of Climate Change/Variability

The relative effect of climate change/variability, seasonal effects and residual effects was investigated using specialized polar plots and ternary plots. Each of the seasonal decomposition components expressed as a fraction of the measured stream flow. The relative contribution of climate change/variability, seasonal and residual components of the streamflow can be expressed as:

\* MERGEFORMAT ()

\* MERGEFORMAT ()

\* MERGEFORMAT ()

\* MERGEFORMAT ()

\* MERGEFORMAT ()

Where Li, Si, and Ri are the relative contribution of climate change/variability, seasonal structure and residual flows on the streamflow in percentages respectively. Variables li, si, and ri are defined by the STL equation (see Section 3.1.4).

## Statistical Data Analysis

## Tests for Trend

## Mann-Kendall (MK) Test

Since many classical trend studies in hydrology employed the use of Mann-Kendall test (Chen et al. 2007; Feng, G. Zhang, and Yin 2010; Kumar et al. 2009; Modarres and de Paulo Rodrigues da Silva 2007; Partal and Kahya 2006; Petrow and Merz 2009; Svensson, Kundzewicz, and Maurer 2006; Tao et al. 2011; Villarini, J. a. Smith, et al. 2011; Xu, Takeuchi, and Ishidaira 2003), the MK test was employed in this study. The MK test statistic is given by:

\* MERGEFORMAT ()

\* MERGEFORMAT ()

For a time series of y1, y2, y3â€¦ yn (where n is the length of the data) the null hypothesis (H0) of the MK test assumes the data to be independent and identically distributed random variables. This implies that there is no trend in the data (Petrow and Merz 2009). Under this assumption of independence and random distribution of variables, the test statistic S is normally distributed (for n â‰¥ 8) and has an expectation and variance given by:

\* MERGEFORMAT ()

\* MERGEFORMAT ()

The standardized test statistics Z is given by:

\* MERGEFORMAT ()

The null hypothesis (H0) is rejected if Z does not lie within the critical region of significance level of Î± for a two-sided test. A positive or negative value of Z shows an increasing or decreasing trend of the time series respectively.

\* MERGEFORMAT ()

The Kendall correlation coefficient (Ï„) indicates the monotonic increase (+1) or decrease (-1) over time (Olsson et al. 2010). The strength of the correlation is also classified(Olsson et al. 2010) Error: Reference source not found.

\* MERGEFORMAT ()

\* MERGEFORMAT ()

## Spearman's Rank Correlation Coefficient (Rho)

This test, with the same power and rank as the MK test (Kundzewicz and A. Robson 2000). Spearman's rho tests for correlation between two time and data series (Birsan et al. 2005; Gautam, Acharya, and Tuladhar 2010; Kundzewicz and A. Robson 2000; Villarini, J. a. Smith, et al. 2011) . The test statistic is given by:

\* MERGEFORMAT ()

\* MERGEFORMAT ()

Where d is the difference between the rankings of observations and its corresponding transformed rank equivalent. The test statistic (tsrc) follows a Student's t-distribution with v = N - 2 degrees of freedom. The null hypothesis for the tsrc shows that there is no trend (H0 = 0) whilst the alternate hypothesis shows that there is trend (H1 < > 0). At significance level of Î± null hypothesis is accepted if when it is contained in the critical is bounded by:

\* MERGEFORMAT ()

## Tests for Abrupt / Step Change

## Distribution- free CUSUM Test

This distribution-free CUSUM (Kundzewicz and A. Robson 2000; Radziejewski and Kundzewicz 2004) test involves comparing each hydrological data point with the median of the whole dataset and is robust to detect unknown change points in a time series. The test statistic involves the cumulative sum of signs (+ve and -ve for greater or less than the median, respectively) and is given by:

\* MERGEFORMAT ()

Where k = 1, 2, 3â€¦ n. Vk follows the Kolmogorov-Smirnov (KS) two sample statistic (Equation 21 Error: Reference source not found); the critical values at Î± significance levels given by(Grayson et al. 1996) (Equation 22 Error: Reference source not found).

\* MERGEFORMAT ()

\* MERGEFORMAT ()

## Mann-Witney Test

We used the Mann-Witney test (Chen et al. 2007; Kundzewicz and A. Robson 2000; McKerchar and Henderson 2004; Radziejewski and Kundzewicz 2004; A. J. Robson 2004) to confirm the abrupt change in flow regime. The test assumes that the two sides (before and after) of the streamflow data of a known change point are independent and identically distributed. The null hypothesis (H0) assumes that the medians of the two sides are the same at a significance level of (Î±) and thus there is no abrupt/step change in the data. The test statistic is given by:

\* MERGEFORMAT ()

Where r(xt) is the rank of the observation. The null hypothesis (H0) is accepted when the test statistic (Zc) is within the critical region as given in the equation Error: Reference source not found.

\* MERGEFORMAT ()

## Magnitude of Change

The Kendall-Theil method(Cortés, Vargas, and McPhee 2011; Dinpashoh et al. 2011; Déry et al. 2011; Kumar et al. 2009; Yue, Pilon, and Phinney 2003) for determining the magnitude of monotonic trends in this study was adopted in this study. The method, also known as the Sen's slope (Birsan et al. 2005; Kumar et al. 2009), is non-parametric and has been found by researchers to be more robust compared to the slope of the linear regression line (Dinpashoh et al. 2011; Mair and Fares 2010; Yue, Pilon, and Cavadias 2002). The method is given by:

\* MERGEFORMAT ()

Where Î² is the median of all possible combinations of the data set (Qin et al. 2010). A positive value of Î² denotes an upward trend whilst a negative value denotes a downward trend (Qin et al. 2010)

## Data Pre-Whitening and Tests for Data Independence

Since most hydrological data are not usually free from serial correlation, an approach proposed (Yue, Pilon, and Phinney 2003) and applied by many researchers (Abaurrea et al. 2011; Adamowski and Bougadis 2003; Burn and Cunderlik 2004; Dinpashoh et al. 2011; Khaliq et al. 2009; Kumar et al. 2009; Lorenzo-Lacruz et al. 2012; Partal and Kahya 2006; Petrow and Merz 2009; Yue, Pilon, and Phinney 2003; Yongfang Zhang, Guan, et al. 2011; Yongyong Zhang, Shao, et al. 2011) was applied in this project. This approach implies that serial-correlation be removed from the hydrological data before applying tests that assume independence and no serial-correlation such as the Mann-Kendall test. We summarize this approach in Figure : Flow chart for data pre-whitening. In addition, three non-parametric tests (Turning point, Median crossing, and Rank difference tests) for data independence(Grayson et al. 1996; Kundzewicz and A. Robson 2000) were also carried out. The test are rank based and were used to confirm the randomness of the streamflow data.

Figure : Flow chart for data pre-whitening

The removal of serial-correlation begins by estimating the magnitude of change (see Section 3.2.3) using the Kendall-Theil method and removing it from the original dataset. Lag-1 autocorrelation coefficient (r1) which measures the amount of serial-correlation between adjacent data (Kundzewicz and A. Robson 2000) was then estimated and tested under the various levels of significance (Î± = 0.01, 0.05, 0.1). The auto-correlation coefficient can be estimated by:

\* MERGEFORMAT ()

If serial-correlation was evident at the various significance levels, it is removed from the data series, and then the removed trend is re-added to it. The final dataset Y*(t) can now be assumed to be free of serial-correlation. And statistical tests that require independence of data is applied to Y*(t). However, if no auto-correlation is found in the trend-free dataset Y'(t), the original dataset Y(t) is used as inputs to the statistical tests.

## Results, Analyses and Discussions

## Exploratory Data Analyses

## Time Series Plot and Analyses

Figure : Time series plot and smoothing of Chengcun streamflow shows the time series plot of monthly streamflow records of the Chengcun Basin. Figure : Time series plot and smoothing of Chengcun streamflowa also shows an overlay of the annual means for each year. This is expanded in Figure : Time series plot and smoothing of Chengcun streamflowb which clearly shows a bi-annual cycle of highs and lows till the year 1993 where this cycle changes. Second and third order polynomial regression fit lines (Figure : Time series plot and smoothing of Chengcun streamflow a and b) show the point of changes for di-tonic and tri-tonic changes in trend. The fit lines (Figure : Time series plot and smoothing of Chengcun streamflow b, c and d) and the Savitzky-Golay smooth line (Figure : Time series plot and smoothing of Chengcun streamflowf) all show an increasing trend; with a showing of an exponential rise in trend from the year 1993. Figure : Time series plot and smoothing of Chengcun streamflowg show a summary of the linear trend, step plot of the annual means and the Savitzky-Golay smooth line. The step plots of the annual means also show relatively higher values after 1993. Therefore, 1993 was chosen as the change point year for these analyses.

Figure : Time series plot and smoothing of Chengcun streamflow

Figure : Annual streamflow time series and trend: (a) time series with linear regression line; (b) stream flow statistics showing minimum, maximum, median and average flow per each year shows the annual stream flow time series. It is evident that there is a change in flow regime and there is also an increasing linear trend. Figure : Monthly streamflow patterns of Chengcun basin shows interesting patterns relative to the months and seasonal structure. It can be seen that in the interim, November, December and January (which can be considered as the winter months) show an increase in linear trend. The Spring months (February, March and April) show a monotonic decrease in trend; whilst the summer months (May, June, July and August) show a rapid increase in linear trend. The autumn periods (September and October) show a dramatic decrease in trend. The gradual monthly increase and decrease in trend over the period suggests a strong change in flow regime. It was expected that a consistent regime would have had a near horizontal monthly linear trend for which Figure : Monthly streamflow patterns of Chengcun basin shows otherwise.

Figure : Annual streamflow time series and trend: (a) time series with linear regression line; (b) stream flow statistics showing minimum, maximum, median and average flow per each year

Figure : Monthly streamflow patterns of Chengcun basin

## Flow Regime Classification

The Pardé coefficient (P) (see Section 3.1.3) estimated for each month of the year shows that there has been a change in flow regime of the Chengcun basin (Figure : Flow regime classificationa). The medians of all P for each month were chosen as the representative regime coefficient. Plotting the medians show that there was a gradual rise in streamflow from the beginning of the year in January till its fall in August in the periods of 1986 -1992. This near broad bell-shaped flow regime is not seen after 1992 (1993 -1999), but rather a lower rise during the first half of the year, followed by very high peak during the month of June and July. Figure : Flow regime classification (b & c) also shows P for the later years (1993-1999) have narrower upper and lower quartile in the distribution of their medians as compared to the earlier years (1986-1992), thus indicating a more consistent regime for the latter period.

Investigation of the relationship between the changes in stream flow regime with the absolute days of flooding indicates a correlation between flow regime and flooding. In Table : Absolute cumulative hours of flooding and Table : Absolute cumulative days of flooding (medians) it is evident that the higher the value of P, the higher the absolute days of flooding. Noticeably, the month of June had an increase of about 94.1% in absolute days of flooding (from 7.6 to 14.3). Also, the floods have been narrowed to the months of April to August after 1993.

Figure : Flow regime classification and box plots; (a) annual flow regime change; (b) 1986-1992 flow regime; (c) 1993-1999 flow regime; (d) 1986-1999 flow regime

Table : Absolute cumulative hours of flooding

Table : Absolute cumulative days of flooding (medians)

## Seasonal Structure and Decomposition

Figure : Seasonal decomposition; (a) observed monthly streamflow; (b) loess effect; (c) seasonal effect; (d) residual effect shows the decomposition of streamflow data series into the annual or loess flow, seasonal cycles and residues. From the graph (Figure : Seasonal decomposition; (a) observed monthly streamflow; (b) loess effect; (c) seasonal effect; (d) residual effecta), it can be seen that the loess component follows a gradual rise and fall and then an exponential rise from 1993. The loess flow component can be thought of as the regional climate/variability driving force effect on the streamflow. This rise can therefore be seen as an increasing effect of the regional climate change/variability forcing on the basin. The regional forcing or loess effect was estimated using the Savitzky-Golay algorithm (see Section 3.1.4).

Using the medians of all monthly flows, a consistent seasonal structure is seen in the Chengcun streamflow (Figure : Seasonal decomposition; (a) observed monthly streamflow; (b) loess effect; (c) seasonal effect; (d) residual effectb). It clearly shows peaking in April and June (highest) and low flows in the winter months (November - January). Figure : Seasonal decomposition; (a) observed monthly streamflow; (b) loess effect; (c) seasonal effect; (d) residual effectc shows the nature of the residues. It can be seen that after 1993, the residues then to have higher peaks and dips than earlier. This also indicates a probable change in the underlying regime of flow.

Figure : Seasonal decomposition; (a) observed monthly streamflow; (b) loess effect; (c) seasonal effect; (d) residual effect

## Residual Analysis

Analysing the residual data from the seasonal decomposition showed that the data distribution follows a slight shift from the normal distribution curve (Figure : Distribution of residues; (a) Box plot showing the distribution of residuals; (b) histogram of residuals showing the normal distribution curveb). As can be seen in Figure : Distribution of residues; (a) Box plot showing the distribution of residuals; (b) histogram of residuals showing the normal distribution curvea, the mean (-380.16) and median (-429.23) fell below the zero line (suggesting that the estimated seasonal cycle and loess might be lower than estimated or a change to a higher flow regime in the years). Testing the residues for serial-correlation and data independence showed that there was strong serial-correlation at 99% significance level (Table : Residual data testing for independence (Median Crossing, Turning Point, and Rank Difference) and serial-correlation (Auto-Correlation)). Thus, there was the need to pre-white the original data series to remove the serial correlation before applying the tests that assume presence serial-correlations is absent.

Figure : Distribution of residues; (a) Box plot showing the distribution of residuals; (b) histogram of residuals showing the normal distribution curve

Table : Residual data testing for independence (Median Crossing, Turning Point, and Rank Difference) and serial-correlation (Auto-Correlation)

## Statistical Tests

## Data Pre-Whitening

Data was pre-whitened as the residual analysis showed strong serial-correlation and lack of independence. The pre-whitened data and the original data series were used for all the statistical tests and their results compared correspondingly. Results of auto-correlation (Table 5: Auto-correlation coefficient test results Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)Table : Auto-correlation coefficient test results (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)) showed that even after the pre-whitening of the streamflow data, the months of January, May and June still showed serial-correlation at the same or a higher significant level, suggesting a probable presence of Type-I or Type-II errors (and have not been investigated in this work). Results (Table : Turning point test for data randomness (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively), Table : Median crossing test for data independence (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively) and Table : Rank difference test for data independence (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)) of the non-parametric tests for randomness of data did not show any evidence of data dependence on a monthly scale except for the month of May and June. Annual data however showed data dependence also at significance levels of 95% and 99%.

## Tests for Trend

Table : Mann-Kendall test results for trend (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively), Table : Kendall correlation coefficient ('+', '++', '+++' indicates weak, moderate and strong positive trends, and '-', '--', '---' indicate weak, moderate and strong negative trends) compared with the slope of the linear regression line, and Table : Spearman's correlation coefficient test results for trend (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively) show the results of trend test using the Mann-Kendall, Mann-Kendall correlation coefficient and Spearman's rank correlation tests. Mann-Kendall test and the Spearman's correlation test show that a general trend exists at 95% and 99% significance levels. Also, the trends appear during periods of high and low flows. The direction and strength of the trend is seen in Table : Kendall correlation coefficient ('+', '++', '+++' indicates weak, moderate and strong positive trends, and '-', '--', '---' indicate weak, moderate and strong negative trends) compared with the slope of the linear regression line and it shows an overall moderate increase in annual trend. In can also be seen that pre-whitening the data improved the ability of the tests to detect trends correctly. The level of significance for the detection of trends can therefore be taken at 95% for annual data series and 99% for monthly data series as they were prominent and corresponded with both the Mann-Kendall and Spearman's correlation tests.

## Tests for Step Change

On an annual scale, the Distribution - free CUSUM test (Table : Distribution-free CUSUM test results for step change (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 4.565, 5.089, and 6.099 respectively)) and the Mann-Whitney test (Table : Mann-Whitney test results for step-change (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)) did not show and evidence of step-change. This evidence, seemingly, contradicts Figure : Time series plot and smoothing of Chengcun streamflow. However, on a monthly temporal scale there exists evidence of step-changes during high flow months (June - August) and the low flow months (January - February) at 95% and 99% significance levels. One way which this complexity could be explained is that evidence of trend and change in flow regime would tend to cause an apparent step- change in the flow data series at a later point in time.

Table : Auto-correlation coefficient test results (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)

Table : Mann-Kendall test results for trend (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)

Table : Kendall correlation coefficient ('+', '++', '+++' indicates weak, moderate and strong positive trends, and '-', '--', '---' indicate weak, moderate and strong negative trends) compared with the slope of the linear regression line

Table : Spearman's correlation coefficient test results for trend (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)

Table : Distribution-free CUSUM test results for step change (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 4.565, 5.089, and 6.099 respectively)

Table : Mann-Whitney test results for step-change (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)

Table : Turning point test for data randomness (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)

Table : Median crossing test for data independence (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)

Table : Rank difference test for data independence (Critical values for Î± are Î± = 0.1, 0.05, and 0.01 are 1.069, 1.274, and 1.674 respectively)

## Magnitude of Change

The magnitude of change estimated using the Theil-slope estimator (see Section 3.2.3) was done in a two way, one-way (forward: 1986 â†’ 1999) and one-way (backward: 1986 â† 1999) manner. The Theil-slope takes the median of all possible changes within the data series. Figure 10: Magnitude of change in Chengcun streamflow regime (2T - two tail/way test; 1F - one tail/way forward test; 1B - one-tail/way backward test; A - 1986-1999; B - 1986-1992; C - 1993-1999Figure : Magnitude of change in Chengcun streamflow regime (2T - two tail/way test; 1F - one tail/way forward test; 1B - one-tail/way backward test; A - 1986-1999; B - 1986-1992; C - 1993-1999) indicates the overall change and changes in magnitude before and after 1993. Here, it is evident that though there is general decrease in the magnitude of change. Magnitudes of changes are higher before 1993 than after. It is expected that an increase in the one-way forward direction magnitude of change will give a corresponding fall in the one-way magnitude of change. This correspondence is seen in the magnitudes of the one-way forward and one-way backward annual values (240.20 and -336.64) and provides evidence of trend. Clearer evidences of the monthly magnitudes of trend changes are given in Figure : Two-tail (forward and backward) monthly magnitude of change, Figure : One-way monthly magnitude of change (forward direction: 1986 â†’1999), and Figure : One-way monthly magnitude of change (backward direction: 1986 â† 1999).

Figure : Magnitude of change in Chengcun streamflow regime (2T - two tail/way test; 1F - one tail/way forward test; 1B - one-tail/way backward test; A - 1986-1999; B - 1986-1992; C - 1993-1999)

Figure : Two-tail (forward and backward) monthly magnitude of change

Figure : One-way monthly magnitude of change (forward direction: 1986 â†’1999)

Figure : One-way monthly magnitude of change (backward direction: 1986 â† 1999)

## Effect of Climate Change/Variability, Seasons and Residues

## Relative contributions to streamflow

The relative contributions climate change/variability or regional forcing (annual), seasonal effect (seasonal) and residual (residue) components were explored using the equations developed in Section 3.1.5. Further explorations of the contributions were done using Ternary. Analysing all monthly and yearly data, ternary plots yielded Figure . A closer look shows that the annual (regional forcing) component (which may be attributed to climate change/variability) is no more than an approximate of 45% (43.59% exact). Seasonal and residual components make up the rest maybe up to 85.95% for seasonal effect and 93.31% for residual effect. This climate change sealing and the respective contributions due to the seasons and residues provides and interesting phenomenon which can be used in effective water resources management.

Figure : Ternary plot showing the relative contributions of the annual (regional forcing or climate change/variability), seasonal and residual effects on Chengcun streamflow

## Distribution of Climate Change/Variability and Season Structure Effects

Further analyses were made to see the monthly distribution of the components of streamflow. This was to further explore and explain the ternary graph (Figure ); and was done by the use of specialized polar plots. A monthly polar plot (Figure : Polar plot showing the relative monthly contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow) shows that regional forcing has its maximum effect during the high flow months (April - July) and is minimum during the low flow periods (October - February). Residual components had their maximum effect during the low flow periods (October - February) and were minimal during the high flow months. Seasonal effect had varied effect during all flows of the period.

A relative stack polar plot of the relative contributions (Figure : Polar rings showing the relative range of contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow) showed that there was a minimum amount of regional forcing present in all streamflow records. Also, though varied, seasonal effect also had a very great role to play, and was present in all flows. The minimum effect of regional forcing was seen maximize during the high flow periods, and very low during the low flow periods. The maximum was during the month of June. Minimum seasonal effects were also maximum during the month of June and also low during the low flow periods. However, the range of effect was generally high and very low during the month of September. Also, it can be seen that the range of residual effect was relatively high during the month of October, though its minimum effect was generally high during the low flow periods. Based on this, rings of effects were constructed (Figure : Polar rings showing the relative contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow) that showed the boundaries and average effect lines for each annual cycle. This was complemented by the Figure : Polar regions showing the monthly contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow which shows the region of effect each annual cycle. Using these charts, it is possible to notice the effects of regional forcing / climate change/variability, seasons and residues on the stream flow. The effect of the residues can be attributed to other factors such as land-use/land-cover changes, and other anthropogenic activities. This clearer pattern makes it very useful in planning for the management of water resources in the Chengcun basin.

Figure : Polar plot showing the relative monthly contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow

Figure : Polar rings showing the relative range of contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow

Figure : Polar rings showing the relative contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow

Figure : Polar regions showing the monthly contributions of climate change/variability, seasonal and residual effects on Chengcun streamflow

## Conclusions

The Chengcun basin lies in a humid region. Analyses of streamflow data by the use of exploratory data analyses and statistical tools suggest that there has been an increasing trend in the streamflow sing 1986. This increase in trend is also accompanied by a change in streamflow regime and this causes and apparent step-change in the streamflow records. However, at significance levels of 90%, 95% and 99%, it is only evident that a positive trend exists whilst not enough evidence is available to guarantee the presence of step-changes. Changes in flow regime suggest a peaking of streamflow for the high flow months and an attenuation of it during the low flow periods for the later years. This peaking has a corresponding increase in the days of flooding, although, there is no apparent increase in days of flooding during the whole year.

Analysing the relative contributions of regional forcing, seasonal and residual effects showed that regional forcing has up to about 43.59% effect on the streamflow and it is highest during the high flow months. Regional forcing can be attributed to climate change/variability or other regional trends. Seasonal effect is varied across the entire year but has a minimum peak during the high flow months. Residual effects, which may be attributed to anthropogenic activities is highest during the low flow periods and can account up to 93.31% of the flows during that time.