Abstract

To assess hydrologic regime more comprehensively using the distribution of hydrologic parameters, the probability density function of each parameter is obtained from parameter estimations and goodness-of-fit tests based on the principle of maximum entropy. Then, the Shannon entropy and weights for a multi-attribute decision-making process are used to calculate the degree of hydrologic alteration. This method is applied to the Xiaoqing River in the city of Jinan, China. The results indicate that the diversities of the monthly mean flow and annual extreme flow show decreasing trends that are attributable to human impacts, while the diversities of the timing of annual extreme, high and low flows, and the rate and frequency of flooding show increasing trends. Meanwhile, the overall degree of hydrologic alteration of the Xiaoqing River in Jinan is 0.747, which belongs to a change in the height. Thus, we suggest that the timing and volume of inter-basin water transfer should be reasonably regulated and that the regulation of peak flooding times and peak flow should be strengthened to make them conform to ecological characteristics during the water resource management of the Xiaoqing River.

INTRODUCTION

As the most important factor affecting river ecology, the hydrologic regime is becoming increasingly valued by people. At present, the study of hydrologic regime mainly includes the construction of index systems and research involving the assessment method. In terms of the index system of hydrologic regime, the indicator of hydrologic alteration (IHA) is used to characterize ecological structure information using five aspects that lay the foundation for an analysis of human activities and their impacts on hydrologic regime: flow rates, frequency, duration, timing and alteration rates (Richter et al. 1996). Since its inception, the concept of the index system of hydrologic regime has been continuously expanded to enhance its ability to characterize riverine ecosystems and their statistical significance (Vogel et al. 2007; Bevelhimer et al. 2014; Mackay et al. 2015; Spurgeon et al. 2016). Moreover, some index systems have been developed specifically for the ecological characteristics of certain areas, which makes an index system more consistent with local hydrological and ecological characteristics (Zhang et al. 2012; Wang et al. 2014).

In terms of the assessment method, Richter et al. (1997) proposed the range of variability approach (RVA) to quantify the degree of hydrologic alteration that was widely used at the time through a further analysis of the IHA. Black et al. (2005) proposed the Dundee Hydrologic Regime Alteration Method (DHRAM), which is a more generalized method for analyzing hydrologic regime that employs five levels for the degree of risk of a river. Assessment techniques based on histogram matching methods and hydrologic year types have improved the limitations of RVA (Shiau & Wu 2007; Yang et al. 2014; Yin et al. 2015) so that the assessment factors are more comprehensive. To assess hydrologic regime more objectively and concisely, entropy theory and AHP have been introduced as assessment methods of hydrologic regime (Kim & Singh 2014; Li et al. 2015), which provide new approaches for the assessment of hydrologic regime.

In summary, many studies have been conducted to establish index systems for hydrologic regime that have been especially aimed at the characteristics of different basins. However, although the assessment method has been improved, few studies have been performed to assess hydrologic regime considering the characteristics of hydrologic distribution laws. Thus, the objective of this paper is to outline an assessment method for the alteration degree of hydrologic regime considering the hydrologic distribution law. The principle of maximum entropy and minimum information entropy are used to choose the proper probability density function (PDF) for each hydrologic parameter according to the hydrologic distribution law. In addition, the diversity of each hydrologic parameter with regard to the Shannon entropy and weights for a multi-attribute decision making process are used to obtain the overall degree of hydrologic alteration. This method can provide a more reasonable support system for local departments to practice effective water resource management.

RESEARCH METHODS

Selection of hydrologic parameters and types of PDFs

Selection of hydrologic parameters

An IHA contains 33 hydrologic parameters related to river ecology, and these parameters describe the alteration of the hydrologic regime of a river with respect to the flow, frequency, timing, duration and rise and fall rates based on a long series of daily runoff data (TNC 2009). These parameters comprehensively reflect the hydrologic alteration of a river, and IHAs have been widely used. Thus, 33 IHA parameters are selected in this paper to assess the degree of hydrologic alteration of the river, and each IHA parameter is shown in Table 1.

Table 1

IHA parameters (TNC 2009)

IHA parameter groupHydrologic parameters
Magnitude of monthly water conditions (1–12) Mean or median value for each calendar month 
Magnitude and duration of annual extreme water conditions (13–24) Annual minima 1-day, 3-day, 7-day, 30-day, 90-day mean
Annual maxima 1-day, 3-day, 7-day, 30-day, 90-day mean
Number of zero-flow days
Base flow index 
Timing of annual extreme water conditions (25–26) Julian date of each annual 1-day maximum
Julian date of each annual 1-day minimum 
Frequency and duration of high and low pulses (27–30) Number of low pulses within each water year
Mean or median duration of low pulses (days)
Number of high pulses within each water year
Mean or median duration of high pulses (days) 
Rate and frequency of water condition changes (31–33) Rise rates
Fall rates
Number of hydrologic reversals 
IHA parameter groupHydrologic parameters
Magnitude of monthly water conditions (1–12) Mean or median value for each calendar month 
Magnitude and duration of annual extreme water conditions (13–24) Annual minima 1-day, 3-day, 7-day, 30-day, 90-day mean
Annual maxima 1-day, 3-day, 7-day, 30-day, 90-day mean
Number of zero-flow days
Base flow index 
Timing of annual extreme water conditions (25–26) Julian date of each annual 1-day maximum
Julian date of each annual 1-day minimum 
Frequency and duration of high and low pulses (27–30) Number of low pulses within each water year
Mean or median duration of low pulses (days)
Number of high pulses within each water year
Mean or median duration of high pulses (days) 
Rate and frequency of water condition changes (31–33) Rise rates
Fall rates
Number of hydrologic reversals 

Selection of PDFs

Assuming that each IHA parameter can be regarded as a random variable, the least biased PDF of each variable is constructed using the principle of maximum entropy. Combined with the hydrologic distribution curve commonly used throughout China (Luo & Song 2014), a normal distribution, lognormal distribution, gamma distribution and P-III distribution are selected in this paper as the four types of PDFs to fit each parameter. The parameter values for the four types of PDFs can be calculated by MATLAB according to the principle of maximum entropy. Singh (1988) deduced several common PDFs in the fields of hydrology and water resource management, for which the parameter equations are expressed as:  
formula
(1)
where is the nth-order origin moment for x, which is determined by the sample sequence.
By introducing Lagrange multipliers, the least biased p can be deduced by Equation (1) based on the maximum entropy, for which the equation is expressed as:  
formula
(2)
where , , ···, are the Lagrange multipliers.

By deducing the relationship between the PDF parameters and the Lagrange multipliers and that between the Lagrange multipliers and the constraint conditions (Zhao & Song 2017), the relationship between the PDF parameters and the constraint conditions can be finally obtained, which represents the equation set of parameter estimations from which the expressions of the Lagrange multipliers for the four PDF types can be deduced. The minimum information entropy method (Shan et al. 2014) is selected to quantify the goodness-of-fit for the least biased of the four PDF types of the distributions, from which we find that the minimum distribution of the information entropy is the proper type. The expressions for the Lagrange multipliers and the minimum entropy of the four PDF types are shown in Table 2.

Table 2

The expressions for the Lagrange multipliers and the minimum entropy of the four types of PDFs

 NormalLog-normalGammaP-III
     
     
     
Minimum entropy     
 NormalLog-normalGammaP-III
     
     
     
Minimum entropy     

Computation of the alteration degree of the hydrologic parameters

The alteration degree of the hydrologic parameters is expressed as the difference of each IHA parameter within two different periods with the Shannon entropy, the calculation formula which is shown in Equation (3). The Shannon entropy expresses the uncertainty of the variable, which is also known as the diversity of the variables (Singh 1998). If the Shannon entropy is larger, the uncertainty of the variable is larger, and the diversity of the variable is better. The differences in the diversities between the two periods are calculated with Equations (3) and (4), and they reflect the deviation from the natural state of the hydrologic regime of the river.  
formula
(3)
where is the alteration degree of the ith parameter, i = 1, 2, 3…n, and are the changes in the Shannon entropy for a parameter ‘i’ between the two periods, which is expressed as:  
formula
(4)
where is the probability of the ith parameter, which can be determined by the PDF as it is expressed in Equation (2).

Computation of weights and overall alteration degree

The impact of each IHA parameter on the river ecology and hydrologic regime has a different degree. After the alteration degree of each IHA parameter is obtained, it cannot be assumed that a parameter with a large alteration degree also has a high weight and, thus, we need to reasonably determine the weights for each parameter. The ordered weighted averaging (OWA) operator, which was proposed by Yager (1988), is a multi-attribute decision making method that reorders the data according to the sequence and then applies weights according to the location of the data for their aggregation. Thus, the determination of weights is a key aspect in the calculation of the OWA operator. Two important correlation measures of the weight of an OWA operator, called ‘orness measure’ and ‘dispersion measure’, were proposed by Yager (1988). The ‘orness measure’ is used to measure the degree of the ‘or’ operation or the ‘and’ operation, while the ‘dispersion measure’ is used to measure the alteration degree of each data point utilized in the aggregation value. The calculation of the weight of an OWA operator based on the maximum entropy principle is expressed as:  
formula
(5)
where is the weight of the ith parameter, and is the degree of optimism.
At present, there are various methods for calculating the weight of an OWA operator (Xu 2005; Jin & Qian 2016). The calculation of the weight of an OWA operator based on a normal distribution (shown in Equation (6)) considers not only the information regarding the data location but also the data size while still satisfying the maximum entropy principle, thus providing a reasonable method for the calculation of the weights of the data. Thus, we first used the weight algorithm based on a normal distribution to calculate the weight of each IHA parameter. Then, because the hydrologic distribution of the IHA parameters may be different, the set weights based on the lognormal distribution were proposed to fit the hydrologic distribution law, which is expressed as:  
formula
(6)
 
formula
(7)
where is the value of the ith parameter, and and are the mean and standard deviation of the data, respectively.
After the weight of each parameter is calculated, the alteration degree of each parameter is multiplied with the corresponding weight, after which a summation is carried out to obtain the overall alteration degrees of the 33 parameters, as shown in Equation (8):  
formula
(8)
where is the alteration degree of each parameter, and C is the overall degree of hydrologic alteration considering the hydrologic distribution.

STUDY AREA

The Xiaoqing River in the city of Jinan is an urban river and the most important flood discharge channel in Jinan. The drainage map of the Xiaoqing River Basin is shown in Figure 1. Huangtai Station was built within the trunk channel, which started to monitor the water level and flow beginning in 1953. To study the impacts of hydrologic alteration on the river ecology, the historical data of the Xiaoqing River (Lu 1993; Wang 2015) are investigated in this study. The data from the 1970s indicate that ‘the river is clear with fish and shrimp’, which therefore demonstrated a navigational capacity and little human interference regarding the hydrologic regime. Since the mid-1980s, the ecology of the Xiaoqing River has become badly damaged due to rapid development and urbanization, and the Xiaoqing River has become a ‘black river and smelly river’ as a consequence of serious sedimentation in the river, which resulted in a strong disturbance to the hydrologic regime of the river. Combined with the actual situation, two research periods of 1960–1985 and 1986–2014 are selected in this paper, which represent a good ecological period and an urbanized impact period of the river, respectively.

Figure 1

Schematic diagram of the Xiaoqing River Basin in Jinan.

Figure 1

Schematic diagram of the Xiaoqing River Basin in Jinan.

RESULTS AND DISCUSSION

Determination of PDFs

The daily runoff data from Huangtai Station on the Xiaoqing River during 1960–2014 is selected to calculate the five groups of the 33 hydrologic parameters of the IHA. The parameters for the four types of PDFs during the two periods are calculated by MATLAB, the results of which are shown in Tables 3 and 4.

Table 3

The parameters for the four types of PDFs in the good ecological period

Normal
Log-normal
Gamma
P-III
μσμσαβαβc
First group 5.167 1.351 1.606 0.283 13.933 0.371 11.636 0.126 19.699 
5.065 1.160 1.595 0.246 18.350 0.276 91.341 0.121 16.150 
4.565 1.059 1.492 0.235 19.268 0.237 31.767 0.188 1.403 
5.054 2.189 1.527 0.448 5.513 0.917 16.105 0.545 3.730 
6.042 2.830 1.686 0.500 4.585 1.318 14.035 0.755 4.559 
7.025 3.824 1.769 0.661 2.921 2.405 160.729 0.302 41.459 
11.826 5.167 2.369 0.483 5.073 2.331 18.743 1.194 10.545 
13.144 5.680 2.476 0.478 5.153 2.551 20.212 1.264 12.395 
10.553 4.346 2.264 0.464 5.545 1.903 20.022 0.971 8.892 
10 7.025 3.389 1.841 0.479 4.763 1.475 4.048 1.684 0.206 
11 6.365 2.989 1.752 0.452 5.238 1.215 2.754 1.801 1.406 
12 5.389 1.619 1.640 0.309 11.335 0.475 61.332 0.207 7.287 
Second group 13 2.592 0.971 0.871 0.436 6.306 0.411 2.821 0.001 1.666 
14 2.786 1.001 0.950 0.416 6.887 0.404 4.931 0.002 1.283 
15 3.040 1.030 1.044 0.400 7.547 0.403 3.549 0.010 4.699 
16 3.689 1.192 1.247 0.367 8.693 0.424 7.887 0.001 4.346 
17 4.320 1.230 1.420 0.308 11.830 0.365 6.541 0.200 0.404 
18 45.232 20.228 3.693 0.533 4.369 10.352 8.826 0.395 66.111 
19 37.131 18.446 3.474 0.571 3.725 9.967 9.819 3.225 37.822 
20 27.631 12.714 3.197 0.532 4.275 6.463 4.113 0.208 7.128 
21 18.025 7.473 2.796 0.472 5.370 3.356 5.438 0.278 13.182 
22 14.124 5.552 2.557 0.464 5.654 2.498 3.403 0.145 3.904 
23 – – – – – – – – – 
24 0.395 0.090 −0.954 0.235 19.644 0.020 7.764 0.264 0.299 
Third group 25 138.960 63.563 4.834 0.475 5.130 27.086 3.278 32.719 13.883 
26 209.560 37.064 5.329 0.183 32.234 6.501 7.726 1.335 40.204 
Fourth group 27 10.200 5.377 2.175 0.575 3.554 2.870 7.995 0.267 4.742 
28 6.040 8.580 1.296 0.914 1.133 5.332 8.397 0.101 14.328 
29 8.760 4.226 2.002 0.681 3.129 2.799 9.647 1.479 2.732 
30 3.040 1.652 0.975 0.542 3.824 0.795 9.341 0.960 2.487 
Fifth group 31 0.433 0.154 −0.903 0.378 7.833 0.055 8.532 0.112 0.359 
32 0.452 0.137 −0.842 0.327 10.455 0.043 3.471 0.218 0.400 
33 168.520 13.032 5.124 0.079 170.818 0.987 6.483 0.155 31.861 
Normal
Log-normal
Gamma
P-III
μσμσαβαβc
First group 5.167 1.351 1.606 0.283 13.933 0.371 11.636 0.126 19.699 
5.065 1.160 1.595 0.246 18.350 0.276 91.341 0.121 16.150 
4.565 1.059 1.492 0.235 19.268 0.237 31.767 0.188 1.403 
5.054 2.189 1.527 0.448 5.513 0.917 16.105 0.545 3.730 
6.042 2.830 1.686 0.500 4.585 1.318 14.035 0.755 4.559 
7.025 3.824 1.769 0.661 2.921 2.405 160.729 0.302 41.459 
11.826 5.167 2.369 0.483 5.073 2.331 18.743 1.194 10.545 
13.144 5.680 2.476 0.478 5.153 2.551 20.212 1.264 12.395 
10.553 4.346 2.264 0.464 5.545 1.903 20.022 0.971 8.892 
10 7.025 3.389 1.841 0.479 4.763 1.475 4.048 1.684 0.206 
11 6.365 2.989 1.752 0.452 5.238 1.215 2.754 1.801 1.406 
12 5.389 1.619 1.640 0.309 11.335 0.475 61.332 0.207 7.287 
Second group 13 2.592 0.971 0.871 0.436 6.306 0.411 2.821 0.001 1.666 
14 2.786 1.001 0.950 0.416 6.887 0.404 4.931 0.002 1.283 
15 3.040 1.030 1.044 0.400 7.547 0.403 3.549 0.010 4.699 
16 3.689 1.192 1.247 0.367 8.693 0.424 7.887 0.001 4.346 
17 4.320 1.230 1.420 0.308 11.830 0.365 6.541 0.200 0.404 
18 45.232 20.228 3.693 0.533 4.369 10.352 8.826 0.395 66.111 
19 37.131 18.446 3.474 0.571 3.725 9.967 9.819 3.225 37.822 
20 27.631 12.714 3.197 0.532 4.275 6.463 4.113 0.208 7.128 
21 18.025 7.473 2.796 0.472 5.370 3.356 5.438 0.278 13.182 
22 14.124 5.552 2.557 0.464 5.654 2.498 3.403 0.145 3.904 
23 – – – – – – – – – 
24 0.395 0.090 −0.954 0.235 19.644 0.020 7.764 0.264 0.299 
Third group 25 138.960 63.563 4.834 0.475 5.130 27.086 3.278 32.719 13.883 
26 209.560 37.064 5.329 0.183 32.234 6.501 7.726 1.335 40.204 
Fourth group 27 10.200 5.377 2.175 0.575 3.554 2.870 7.995 0.267 4.742 
28 6.040 8.580 1.296 0.914 1.133 5.332 8.397 0.101 14.328 
29 8.760 4.226 2.002 0.681 3.129 2.799 9.647 1.479 2.732 
30 3.040 1.652 0.975 0.542 3.824 0.795 9.341 0.960 2.487 
Fifth group 31 0.433 0.154 −0.903 0.378 7.833 0.055 8.532 0.112 0.359 
32 0.452 0.137 −0.842 0.327 10.455 0.043 3.471 0.218 0.400 
33 168.520 13.032 5.124 0.079 170.818 0.987 6.483 0.155 31.861 
Table 4

The parameters for the four types of PDFs in the urbanized impact period

  Normal
Log-normal
Gamma
P-III
μσμσαβαβc
First group 9.179 4.607 2.128 0.405 5.814 1.579 2.935 2.464 0.110 
8.162 2.755 2.050 0.314 10.296 0.793 2.433 1.279 0.134 
8.089 2.812 2.036 0.330 9.415 0.859 4.542 0.385 0.122 
7.626 2.885 1.971 0.343 8.490 0.898 1.333 4.665 0.103 
8.231 2.925 2.050 0.341 8.829 0.932 1.816 2.623 0.250 
8.363 3.348 2.057 0.359 7.699 1.086 5.340 0.395 0.165 
12.445 5.922 2.426 0.433 5.422 2.295 3.240 3.338 0.293 
15.873 8.316 2.640 0.503 4.181 3.796 3.803 4.772 0.282 
12.884 5.378 2.475 0.409 6.329 2.036 2.432 4.901 0.120 
10 10.287 4.220 2.247 0.424 6.107 1.684 3.837 1.214 0.160 
11 9.469 3.797 2.173 0.395 6.858 1.381 1.351 7.858 0.151 
12 8.708 3.132 2.107 0.345 8.828 0.986 4.384 0.510 0.196 
Second group 13 5.236 1.827 1.597 0.349 8.735 0.599 1.269 2.064 0.110 
14 5.520 1.943 1.652 0.338 8.993 0.614 2.093 0.841 0.501 
15 5.792 1.890 1.708 0.316 10.364 0.559 0.580 9.839 0.124 
16 6.590 2.271 1.832 0.330 9.467 0.696 3.505 0.418 0.165 
17 7.363 2.609 1.941 0.332 9.195 0.801 3.560 0.534 0.128 
18 68.529 29.453 4.124 0.489 4.990 13.734 9.392 9.829 0.342 
19 47.340 22.203 3.743 0.501 4.540 10.427 7.976 7.758 0.130 
20 34.330 16.308 3.425 0.485 4.676 7.341 8.410 3.751 0.437 
21 21.881 10.257 2.982 0.465 4.974 4.399 4.514 5.153 0.127 
22 16.848 7.071 2.740 0.418 6.112 2.757 5.116 1.896 0.171 
23 – – – – – – – – – 
24 0.552 0.114 −0.617 0.226 21.961 0.025 0.131 0.705 0.117 
Third group 25 162.107 75.777 4.842 1.072 2.179 74.397 9.985 9.995 16.522 
26 203.036 32.539 5.299 0.176 35.817 5.669 9.971 9.969 2.728 
Fourth group 27 6.393 6.784 1.244 1.175 0.950 6.731 3.484 3.801 0.189 
28 1.696 0.885 0.417 0.466 4.630 0.366 0.938 0.889 0.141 
29 10.107 4.450 2.210 0.492 5.013 2.016 4.078 1.195 0.115 
30 7.839 19.905 1.080 1.100 0.627 12.507 7.902 6.326 0.619 
Fifth group 31 0.353 0.198 −1.171 0.539 4.015 0.088 0.327 0.341 0.102 
32 0.363 0.150 −1.090 0.406 6.644 0.055 0.207 0.438 0.104 
33 150.321 51.569 4.915 0.515 5.290 28.413 9.992 9.959 0.196 
  Normal
Log-normal
Gamma
P-III
μσμσαβαβc
First group 9.179 4.607 2.128 0.405 5.814 1.579 2.935 2.464 0.110 
8.162 2.755 2.050 0.314 10.296 0.793 2.433 1.279 0.134 
8.089 2.812 2.036 0.330 9.415 0.859 4.542 0.385 0.122 
7.626 2.885 1.971 0.343 8.490 0.898 1.333 4.665 0.103 
8.231 2.925 2.050 0.341 8.829 0.932 1.816 2.623 0.250 
8.363 3.348 2.057 0.359 7.699 1.086 5.340 0.395 0.165 
12.445 5.922 2.426 0.433 5.422 2.295 3.240 3.338 0.293 
15.873 8.316 2.640 0.503 4.181 3.796 3.803 4.772 0.282 
12.884 5.378 2.475 0.409 6.329 2.036 2.432 4.901 0.120 
10 10.287 4.220 2.247 0.424 6.107 1.684 3.837 1.214 0.160 
11 9.469 3.797 2.173 0.395 6.858 1.381 1.351 7.858 0.151 
12 8.708 3.132 2.107 0.345 8.828 0.986 4.384 0.510 0.196 
Second group 13 5.236 1.827 1.597 0.349 8.735 0.599 1.269 2.064 0.110 
14 5.520 1.943 1.652 0.338 8.993 0.614 2.093 0.841 0.501 
15 5.792 1.890 1.708 0.316 10.364 0.559 0.580 9.839 0.124 
16 6.590 2.271 1.832 0.330 9.467 0.696 3.505 0.418 0.165 
17 7.363 2.609 1.941 0.332 9.195 0.801 3.560 0.534 0.128 
18 68.529 29.453 4.124 0.489 4.990 13.734 9.392 9.829 0.342 
19 47.340 22.203 3.743 0.501 4.540 10.427 7.976 7.758 0.130 
20 34.330 16.308 3.425 0.485 4.676 7.341 8.410 3.751 0.437 
21 21.881 10.257 2.982 0.465 4.974 4.399 4.514 5.153 0.127 
22 16.848 7.071 2.740 0.418 6.112 2.757 5.116 1.896 0.171 
23 – – – – – – – – – 
24 0.552 0.114 −0.617 0.226 21.961 0.025 0.131 0.705 0.117 
Third group 25 162.107 75.777 4.842 1.072 2.179 74.397 9.985 9.995 16.522 
26 203.036 32.539 5.299 0.176 35.817 5.669 9.971 9.969 2.728 
Fourth group 27 6.393 6.784 1.244 1.175 0.950 6.731 3.484 3.801 0.189 
28 1.696 0.885 0.417 0.466 4.630 0.366 0.938 0.889 0.141 
29 10.107 4.450 2.210 0.492 5.013 2.016 4.078 1.195 0.115 
30 7.839 19.905 1.080 1.100 0.627 12.507 7.902 6.326 0.619 
Fifth group 31 0.353 0.198 −1.171 0.539 4.015 0.088 0.327 0.341 0.102 
32 0.363 0.150 −1.090 0.406 6.644 0.055 0.207 0.438 0.104 
33 150.321 51.569 4.915 0.515 5.290 28.413 9.992 9.959 0.196 

The goodness-of-fit test is used to select the PDF for each IHA parameter during the two periods according to the principle of minimum information entropy. Figure 2 shows that group 1, which represents the monthly mean flow, is in accordance with a P-III distribution in the good ecological period but is in accordance with a lognormal distribution during the urbanized impact period. Group 2, which represents the annual extreme, is in accordance with both a lognormal and a P-III distribution in the good ecological period but is more in accordance with a lognormal distribution during the urbanized impact period. In addition, to simplify the computations, the parameters of the other groups are chosen as lognormal distributions.

Figure 2

The proper PDF for each group of the IHA. (a) The proper PDFs in the good ecological period. (b) The proper PDFs in the urbanized impact period.

Figure 2

The proper PDF for each group of the IHA. (a) The proper PDFs in the good ecological period. (b) The proper PDFs in the urbanized impact period.

Alteration degree of diversity

When the proper PDF for each IHA parameter in consideration of a hydrologic distribution has been selected by goodness-of-fit tests according to the principle of minimum information entropy, the diversity of each parameter and the alteration degree between the two periods are calculated using Equations (3) and (4), respectively. The results of and are shown in Figure 3.

Figure 3

Diversity and alteration degree of 33 hydrologic parameters.

Figure 3

Diversity and alteration degree of 33 hydrologic parameters.

Figure 3 shows that the diversities of the first two groups of parameters are larger in the good ecological period than in the urbanized impact period; however, most of the parameters in the last three groups are smaller in the good ecological period than in the urbanized impact period. This result indicates that the diversities of the monthly mean flow and annual extreme flow of the Xiaoqing River in Jinan are significantly smaller under the impacts of humans, while the diversities of the frequency, the durations of high and low flow, and the rate and frequency of flooding are larger. These alterations disturb the original hydrologic regime of the Xiaoqing River, the reasons for which are as follows: (1) artificial water transfer and water supply during the urbanized impact period significantly increases the monthly mean flow during the dry months of the year; and (2) the impact of urbanization increases the probability of flooding of the Xiaoqing River, following which, the rate and frequency of flooding also increase.

Comparison of multiple weights

Two methods for calculating the weights for a multi-attribute decision making procedure based on a normal distribution and a lognormal distribution are selected in this paper to calculate the weight values for each IHA parameter. A comparison of the two weighting methods is shown in Figure 4, which shows that the high weights computed based on the normal distribution that are concentrated in the middle of the data and that the difference in the weights between each parameter is small. However, the high weights computed based on the lognormal distribution that are relatively more scattered and that their difference is large.

Figure 4

Comparison of the two weighting methods.

Figure 4

Comparison of the two weighting methods.

At the same time, in order to compare whether the weight values calculated using the two weighting methods are in accordance with the characteristics of local hydro-ecologic changes, 33 IHA parameters of the Xiaoqing River Basin in Jinan are analyzed using principal component analysis (PCA) in this paper to obtain four principal groups with six parameters, which are related to the ecology from the perspective of the interaction between the hydrologic regime and the river ecology. The six parameters are the monthly mean flows of March and May, the minimum 7-day flow, the maximum 3-day flow, the timing of minimum flow and the base flow index. These parameters are almost in accordance with the six hydrologic parameters (i.e. the monthly mean flow of May, the minimum 7-day flow, the maximum 3-day flow, the timing of minimum flow, the rise rates and the number of hydrologic reversals) that are closely related to the abundance of fish that were screened using the genetic programming (GP) algorithm by Yang et al. (2008). To comprehensively assess the hydrologic regime according to the ecological law, this paper selects the monthly mean flows of March and May, the minimum 7-day flow, the maximum 3-day flow, the base flow index, the timing of minimum flow, the rise rates and the number of hydrologic reversals (with corresponding numbers of 3, 5, 15, 19, 24, 25, 27 and 33, respectively) as the basis for assessing the applicability of the two weighting methods.

The comparison shows that the high weights, which are greater than 0.045 as calculated by the weighting method based on a lognormal distribution, can better cover the screened hydrologic parameters. Thus, when assessing the alteration of the hydrologic regime of the Xiaoqing River in Jinan, the weighting method based on the lognormal distribution is selected.

Comparison with RVA

Degree of hydrologic alteration with RVA

The RVA, which is expressed using Equations (9) and (10), defines the absolute value of the alteration degree as less than 33.3% of the low-alteration region and greater than 66.7% of the high-alteration region, and it defines the other values as those of the medium-alteration region (Liu et al. 2016).  
formula
(9)
 
formula
(10)
where is the alteration degree of each parameter using the RVA, is the overall degree of hydrologic alteration using the RVA, is the observed frequency that falls within the RVA threshold after the impacts of urbanization, and is the expected frequency that falls within the RVA threshold.

Degree of hydrologic alteration considering the hydrologic distribution law

According to the alteration degree and the weights , the alteration degree of each parameter and the overall degree of hydrologic alteration C are calculated by Equation (8). Because the value of the 23rd parameter (zero flow days) in the Xiaoqing River is zero, the alteration degree of this index is excluded.

The absolute values of RVA are compared with the values of the alteration degrees calculated using the diversity index and weights for the multi-attribute decision making procedure, as shown in Figure 5. The trends of the two alteration degrees for each parameter are alike, whereas parameter 24 (the base flow index) and parameter 25 (the timing of minimum flow) show much difference. The annual sequence values of the base flow index and the timing of minimum flow are analyzed as shown in Figure 6, which illustrates that the observation number built up more than expected within the RVA threshold. This result means that the alteration degree using the RVA cannot be well considered for the parameters beyond the target range, as it may result in a false assessment of the hydrologic regime (Shiau & Wu 2007). Therefore, the method for calculating the hydrologic alteration degree using the diversity index and weights for the multi-attribute decision making procedure reflects the change in the hydrologic regime of the Xiaoqing River more objectively and comprehensively. The overall degree of hydrologic alteration obtained using this method is 0.747.

Figure 5

Comparison of two methods used to calculate the degree of hydrologic alteration.

Figure 5

Comparison of two methods used to calculate the degree of hydrologic alteration.

Figure 6

Sequence values of two parameters and their RVA thresholds. (a) Parameter 24 of the base flow index. (b) Parameter 25 of the timing of minimum flow.

Figure 6

Sequence values of two parameters and their RVA thresholds. (a) Parameter 24 of the base flow index. (b) Parameter 25 of the timing of minimum flow.

CONCLUSIONS

  • (1) In this paper, 33 IHA parameters for the Xiaoqing River in the city of Jinan are calculated using 54 years of daily runoff data from Huangtai Station, and the proper PDF for each parameter in the two periods is obtained by calculating the goodness-of-fit of the minimum information entropy. The results show that the same hydrologic parameters may follow different distributions within the different periods. For instance, the parameters for the monthly mean flow are well represented by the P-III PDF in the good ecological period and are well represented by the lognormal PDF in the urbanized impact period.

  • (2) This method, which combines parameter estimation based on the entropy principle with weights for multi-attribute decision making, considers the objective requirements of the data, the distribution law of the hydrologic parameters and the actual situation of the hydrologic alteration of each parameter. The overall alteration degree in consideration of the distribution of the hydrologic parameters is more objective to reflect the hydrologic alteration.

  • (3) Due to the multi-index attribute of the hydrologic regime, subjective selection is unavoidable when using hydrologic parameters for a comprehensive assessment, which can induce a certain impact on the objectivity. At the same time, because of the use of limited data, especially biological data, our understanding of the hydrologic alteration is hindered. Thus, it is necessary to continue to monitor the flow and biology of the Xiaoqing River so that the hydrologic regime can be more reliably assessed in the future.

ACKNOWLEDGEMENTS

This study was funded by the Non-profit Industry Financial Program of MWR: Key Technology Research and Demonstration Project of Water Ecological Civilization Construction (No. 1261410110030).

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