Anomalies and trends of high river ﬂ ow under temperate climatic conditions in north-eastern Romania

Regional water resource management plans include various scenarios related to the anomalies and trends of hydro-climatic parameters. Two methods are used for the identi ﬁ cation of the anomalies and trends associated with high ﬂ ow (annual and seasonal) of the rivers in Eastern Romania, namely the quantile perturbation method (QPM) and the partial trend method (PMT). These methods were selected due to the fact that they are suitable for data sets which do not rely on restrictive statistical assumption as common parametric and nonparametric trend tests do. For six of the nine stations analyzed, the decreasing trend in high extremes for annual high ﬂ ow based on the PTM is the same as the annual trend obtained with the QPM. Using the PI index (associated with PTM) for the estimation of trend intensity, values between (cid:1) 2.280 and (cid:1) 9.015 m 3 /s were calculated for the decreasing trend of the annual high ﬂ ow and between þ 1,633 m 3 /s (in autumn) and (cid:1) 9.940 m 3 /s (in summer) for the seasonal high ﬂ ow. The results obtained on the anomalies and trends of high river ﬂ ow may represent a starting point in the analysis of the evolution of water resources and their effective management.


INTRODUCTION
The identification of the anomalies and trends in the temporal variations of water elements becomes increasingly relevant, given the growing global effects of climate change. Modifications occurring at the hydro-climatic level can trigger significant changes in hydrological parameters, which later reflect in the evolution of water resources and social development at a regional level (Chen et (Willems ) and graphs (Kisi & Ay ) for the identification of anomalies in relation to past events (mean and extreme), such as the quantile perturbation method (QPM) and trend-based ones, such as the partial trend method (PMT).
The QPM was used to identify the anomalies of hydrometeorological extremes (Nyeko-Ogiramoi et al. ), while the PTM, developed by Ș en (), suggests the graphic and statistical identification of trends and has also been widely used (Sonali & Nagesh-Kumar ). To continue and complete this research direction, in the present study, the two aforementioned graphical methods were selected (QPM and PTM) due to their suitability for data sets that do not rely on the restrictive statistical assumption, as in the case of common parametric and nonparametric trend tests. The main objective of the study is, therefore, the application of the methods in question so as to identify the anomalies and trends of high river flow under temperate-continental climatic conditions, which, in turn, is a starting point in the analysis of the evolution of water resources and their effective management.

Study area
The identification of anomalies in groundwater level variation was based on data from nine hydrometric stations in Eastern Romania (Figure 1). The region analyzed, covering and area of over 20,000 km 2 , is characterized by a temperate-continental climate, with maximum temperature and precipitation values in summer (June and July, respectively), and minimum values recorded during the winter season (in February).
The mean annual temperature increases from 7-8 C, in the north, to 9-10 C, in the south. The annual amount of precipitation decreases from 620 mm in the north to 480 mm in the south. In winter, precipitation is mainly solid and most of it is preserved as snow cover until spring because of frequent negative temperatures, which vary from À4 to À6 C, in the north, to À2 to À3 C, in the south (Sandu et al. ). The statistical analyses carried out on data sets regarding seasonal and annual mean temperatures have indicated positive trends for temperature and precipitation in spring and autumn, and decreasing precipitation levels during winter (Croitoru & Minea ).

Data
The statistical analyses were conducted on five data sets

Quantile perturbation method
This method highlights changes in quantiles at the level of temporal subseries compared to the entire time span analyzed. The QPM was applied to monthly high river flows and the three largest high flow values for each season and year were considered the threshold in the present study (Onyutha & Willems ). The first important step in the analysis of anomalies through the QPM lies in the selection of an appropriate subseries. Given the length of the data string (56 years) and the analyses performed on the same type of hydrological parameters, 10 years for the moving window were chosen (Tabari et al. ). This moving window was glided 1 year further starting with the first value from the data string.
A confidence threshold of 95% was established using the nonparametric bootstrap method based on the full series of data (Ntegeka & Willems ).
Given that the analyses are based on temporal data subseries, the following work hypotheses must be taken into account (Willems ): (i) If the interval between two consecutive oscillations identified (either minimum or maximum) is greater than the length of the subseries analyzed, the previous one is considered independent; (ii) If anomalies above or below a certain threshold occurred; and (iii) If maximum and minimum oscillations of anomalies are recorded within the same time span at several neighboring hydrometric stations, the previous one is regarded as significant. The results were illustrated on the same graph so as to allow the identification of intervals with significant anomalies.

Partial trend method
This method can be applied to various extreme values of hydro-climatic parameters, given that the former display significant serial correlations at least in the case of shortmemory basins (Ș en ). Its application is facilitated by the fact that the comparative analysis of data series (high or low extremes) can be carried out without statistical assumptions (Dabanli et al. ).
The first stage of the PTM involves the separation of the data string into two equal subseries in ascending order.
Within the second stage, the series are plotted into a twodimensional Cartesian coordinate system as scatter points and compared against the 1:1 line (median line). The points that are located above the median line on this graphic representation constitute increasing trends, while those located below represent decreasing trends. If the points are concentrated along the median line, they do not indicate any trend. Ș en () suggests the following formula for calculating the slope of a trend: where s is the slope of the trend, y 1 , y 2 are the averages of the first and second series, and n is the total number of data.
To apply this method, the confidence limit (CLσ s ) of the trend slope must be taken into account. This can be expressed with the formula: where Xσ s is mean of σ s series, α is the value for confidence level, σ σs is the standard deviation of the slope standard deviation values, and n σs is the number of standard deviation slopes values obtained. For this study, the statistical significance level for α was selected at 5% ( Figure 2). When slope values fall outside the lower and upper confidence limit, the alternative hypothesis is adopted. On this assumption, we can consider that it is a trend in analyzed data (Yes in Table 2). The type of trend is given by the slope sign, if it is negative, the type of trend is decreasing; if it is positive, the type of trend is increasing and if the slope is equal with 0, there is no trend.
On a similar note, Wu & Qian () suggest an index (PI) for the estimation of overall trend magnitude: where PI refers to overall trend magnitude, x i is the ith value of the first-ordered subseries, y i is the ith value of the secondordered subseries, and x is the average of x i .
In the present study, trend analysis for the  interval was based on the extraction of two subseries with data spanning 28 years each, namely 1955-1982 and 1983-2010. Dividing the data into two subseries allows us to evaluate the changes for the entire data series not only focus on the extreme quantiles.

RESULTS AND DISCUSSION
Trend dynamics at the level of annual series (   The magnitude of the decreasing trend at these stations

CONCLUSIONS
The main conclusions derived from the analysis of high flow anomalies exhibited by rivers in Eastern Romania are the following: 1. The QPM has indicated that six out of nine stations analyzed exhibit a general decreasing trend of river flow     Furthermore, these results can be used for developing current and future management plans for local and regional water resources.

ACKNOWLEDGEMENT
This work was financially supported by the Department of Geography and Research Department from the 'Alexandru Ioan Cuza' University of Iasi.