Detection and attribution of ﬂ ood responses to precipitation change and urbanization: a case study in Qinhuai River Basin, Southeast China

Both ﬂ ood magnitude and frequency might change under the changing environment. In this study, a procedure combining statistical methods, ﬂ ood frequency analysis and attribution analysis was proposed to investigate the response of ﬂ oods to urbanization and precipitation change in the Qinhuai RiverBasin,anurbanizedbasinlocatedinSoutheastChina,overtheperiodfrom1986to2013.TheMann – Kendalltest wasemployedtodetectthegradualtrendoftheannualmaximumstream ﬂ owandthepeaks over threshold series. The frequency analysis was applied to estimate the changes in the magnitude and frequency of ﬂ oods between the baseline period (1986 – 2001) and urbanization period (2002 – 2013). An attribution analysis was proposed to separate the effects of precipitation change and urbanization on ﬂ ood sizes between the two periods. Results showed that (1) there are signi ﬁ cant increasing trends in medium and small ﬂ ood series according to the Mann – Kendall test; (2) the mean and threshold values of ﬂ ood series in the urbanization period were larger than those in the baseline period, while the standard deviation, coef ﬁ cient of variation and coef ﬁ cient of skewness of ﬂ ood series were both higher during the baseline period than those during the urbanization period; (3) the ﬂ ood magnitude was higher during the urbanizationperiodthanthatduringthebaselineperiodatthesamereturnperiod.Therelativechangesin magnitude were larger for small ﬂ oods than for big ﬂ oods from the baseline period to the urbanization period; (4) the contributions of urbanization on ﬂ oods appeared to amplify with the decreasing return period, while the effects of precipitation diminish. The procedure presented in this study could be useful to detect thechangesof ﬂ oods inthe changingenvironmentandconduct the attributionanalysisof ﬂ ood series. The ﬁ ndings of this study are bene ﬁ cial to further understanding interactions between ﬂ ood behavior and the drivers, thereby improving ﬂ ood management in urbanized basins.

Moreover, several studies have revealed that a decrease in the infiltration of precipitation due to an increase of impervious areas leads to a higher increase in the volume and flood peak of storm runoff for the medium and small floods than that for the really large and rare events (Braud et al. ). Kaspersen et al. () pointed out that an increase in impervious areas had more effects on the hydrological response for more frequent flood events while only a lesser degree effects for less frequent events. They attributed this difference to the fact that the natural surface was able to reach saturation faster during very extreme events and started to behave like the impervious surface rather quickly after the onset of the events. Inversely, the time to saturation is commonly much longer during less extreme events. However, the effect of land-use change on the flood regime cannot always be straightforwardly investigated. Some studies revealed a specific difficulty in detecting flood trends due to several signals overlapping in the analysis process and Hence, an intensive study is essential to be conducted in the specific basins before a generalized conclusion can be drawn. This constitutes the motivation for this study.

METHODS
In this study, the annual maximum streamflow (AMS) series and the peaks over threshold (POT) sampling method were used to obtain the flood series from the daily streamflow data firstly. Secondly, the nonparametric Mann-Kendall test was applied to detect changes in trends of flood series.
Thirdly, the frequency analysis was conducted to assess the frequency variations of flood series. Finally, the attribution analysis proposed in this study was used to quantitatively evaluate the contributions of precipitation change and urbanization to the flood changes. (1) where D denotes the interval time between two flood peaks in days; A is the basin area in km 2 ; Q 1 and Q 2 denote the magnitudes of two flood peaks in m 3 /s, respectively.
It is commonly assumed that a POT series improves an AMS series in the case of a minimum of two or three events per year on average (Mediero et al. ). In order to identify the changes of large, medium and small floods under precipitation change and urbanization, we selected daily flood series with one, two and three events on average per year for the POT time series (referred to as POT1, POT2 and POT3 hereafter, respectively).

Detect trend of the flood series
The temporal trends in AMS and POT time series of flood can be detected by nonparametric trend tests which are more robust to outliers and do not need any assumption about the distribution. In this study, the gradual trend test was performed using the rank-based nonparametric In the study, the computation formula raised by Rosbjerg () was adopted to convert the frequencies of POT and AMS series to the return period for direct comparison. The changes in the return period with same flood size and changes in flood size with the same return period were also analyzed.

Attribution analysis
The From Figure 2, we can see that flood size change ΔQ due to precipitation change and urbanization from the baseline period to the change period at the flood frequency i is where Q 1 denotes the flood size of the baseline period at the certain frequency, and Q 2 denotes the flood size of the change period at the same frequency.
The flood size change caused by urbanization ΔQ urban is the difference between Q 2 and Q 3 , which can be written as follows: where Q 3 denotes the flood size of the baseline period with the same causative precipitation of Q 2 .
Then, the precipitation-induced flood size change ΔQ pre can be expressed as  identified and shown in Figure 3. It can be seen from Table 1 that the mean values of flood series in the urbanization period are larger than those in the baseline period, while the standard deviation, coefficient of variation and coefficient of skewness of flood series are both higher during the baseline period than those during the urbanization period. It can also be seen from Figure  year.
The AMS and POT series were fitted to the P-III and GP distributions, respectively, the results are shown in Figure 5.
It can be seen from Figure Table 2. It can be found that the values of PPCC are more than 0.9 for each flood series in the baseline period and urbanization period, but the values of RMSE for POT series are less than those for AMS series, which indicates that the goodness of fit of GP distribution for POT series is better than P-III distribution for AMS series in both baseline and urbanization periods.
The frequencies of POT and AMS series cannot be directly compared, while they must be converted to the return period by the computational formula raised by Rosbjerg () for the purpose of comparison. Table 3 shows the changes in the return period for the same flood size from the baseline to the urbanization period for both AMS and POT series. The return period decreases for the same flood magnitude from the baseline to the urbanization period in both AMS and POT series. The relative decrease in    of the sampling strategy as detailed earlier in Selection of flood series.

Evaluation of causative precipitation and urbanization impacts on changes in flood size
The attribution analysis proposed in this study needs causative precipitation corresponding to each flood event.
The correlation analysis method was used to find best relationship between the flood size and the accumulated precipitation of one-day, two-day, until seven-day at and before the date of the flood event. The six-day accumulated precipitation series was found to have highest correlation   The AMS sampling is useful and effective in flood trend detection and frequency analysis as long as the time period is long enough.
In this study, the frequency curves derived by P-III distribution based on AMS series are not appropriate to analyze Q 1 and Q 2 are the flood sizes of the baseline and urbanization periods with the same frequency, respectively. P 1 and P 2 are the corresponding causative precipitation amount to Q 1 and Q 2 , respectively. Q 3 is the flood size during the baseline period which would be contributed by P 2 .
the flood changes for a number of reasons (more details have already been given in section 4.3): the high flood quantiles are underestimated (Table 4), The changes in the return period and magnitudes are overestimated (Tables 3 and 4), and an incredible increase in estimated flood sizes for the short return period (Table 4). All these issues can be attrib- It should be noted that one frequency distribution was assigned to each of the flood and causative precipitation series in this paper. We believe that applying different distributions might provide different results and is a topic for further study.

CONCLUSIONS
This study presented a procedure combining statistical methods, flood frequency analysis and attribution analysis to examine the response of floods to urbanization and precipitation change in the Qinhuai River Basin, an urbanized basin located in southeast China, over the period from 1986 to 2013. We analyzed AMS, POT1, POT2 and POT3 series, where the three latter series were created by selecting independent peaks over three different thresholds resulting in 1, 2 and 3, flood events per year, respectively. In addition, we considered floods above the POT1 threshold as large floods, floods between the POT2 and POT1 thresholds as medium floods and flood sizes between the POT3 and POT2 thresholds as small floods.
All flood series were constructed from daily streamflow of the baseline period and urbanization period.
The following conclusions can be drawn from this study: (1) The AMS, POT1 and POT2 series showed no significant increasing trends at the significance level of 0.1, and the POT3, medium and small flood series showed significant positive trends at the significance level of 0.1, 0.05 and 0.01, respectively.
(3) The flood magnitude was higher during the urbanization period than that during the baseline period at the same flood frequency (or return period) of exceedance. The changes in magnitudes of small floods were relatively larger than those of large floods from the baseline period to the urbanization period.
(4) The precipitation changes and urbanization are the main driving factors leading floods change in the QRB.
The contributions of urbanization on floods appeared to amplify with decreasing flood size, while the effects of precipitation diminish.
The procedure proposed in this study has been demonstrated to be useful for the trend and attribution analysis of flood series. The findings of this study can advance our understanding of interactions between flood behavior and the drivers, thereby improving flood management in urbanized basins.