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Journal of Hydrology (2008) 354, 75– 89

available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/jhydrol

Assessing the ecological hydrology of natural ?ow conditions in Taiwan

Fi-John Chang

a

a,*

, Meng-Jung Tsai a, Wen-Ping Tsai a, Edwin E. Herricks

b

Department of Bioenvironmental Systems Engineering, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei 106, Taiwan b Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, USA Received 15 June 2007; received in revised form 19 February 2008; accepted 25 February 2008

KEYWORDS Ecohydrology; Ecohydrologic indicators; Natural ?ow regime; River restoration; Hydrological statistics; Information redundancy

Summary There is a growing use of hydrologic indicators to describe the ?ow needs for organisms in riverine ecosystems. These indicators use hydrologic statistics as a foundation to understand ?ow variability and how this variability is related to the response of riverine ecosystems to natural and altered ?ow regimes. The Taiwan ecohydrology indicator system (TEIS) was developed to identify hydrologic statistics most appropriate to Taiwan ?sheries. We provide a rigorous evaluation of hydrologic statistics used in the TEIS for 52 long-term ?ow records from 23 undisturbed watersheds in Taiwan. We have used the TEIS indicators for general ?ow, ?ow duration, and ?ow frequency to assess the natural ?ow regime conditions in these target watersheds. The correlation coef?cients between TEIS statistics and physiological variables (area and elevation) for the target watersheds were also calculated. The expected high correlations between watershed area and ?ow related statistics were found. Elevation was correlated with frequency statistics. Cluster analysis was used to characterize relationships among TEIS statistics in the target watersheds and then group watersheds with similar characteristics. Both K-mean and SOM clustering methods categorized the watershed statistics into three clusters and supported the assessment of potential redundancy in the hydrologic statistics. Although this analysis identi?ed a high level of information redundancy in hydrological statistics, the actual information redundancy was reduced through the consideration of species life history and ecological requirements because these requirements demand calculation of all statistics that de?ne habitat needs. This analysis supports the use of advanced cluster analysis techniques to supplement the analysis of hydrologic statistics, and uses station grouping and ecological interpretations to evaluate the natural ?ow regimes in Taiwan. ? 2008 Elsevier B.V. All rights reserved.

* Corresponding author. Tel.: +886 2 23639461; fax: +886 2 23635854. E-mail address: changfj@ntu.edu.tw (F.-J. Chang). 0022-1694/$ - see front matter ? 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2008.02.022

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F.-J. Chang et al. The translation of hydrological statistics to ecohydrologic indicators is a continuing challenge to ecohydrology. Limited historical records and the absence of undeveloped comparison watersheds often compromise the natural ?ow regime analyses, and the ecological requirements of native fauna are incompletely understood. Further, methods to relate hydrologic statistics to species or aquatic community condition are still being developed (Herricks and Suen, 2006). There is a continuing need to develop ?ow regime requirements from the needs of organisms. One approach suggested is setting ?ow targets based on an autecological analysis of the existing, or desired, aquatic community and translation of those targets into ecohydrologic indicators (Suen and Herricks, 2006). It is the use of ecohydrologic indicators based on organism requirements coupled with a detailed analysis of hydrological statistics supporting those indicators that is the focus of this paper. The Taiwan ecohydrologic indicator system (TEIS) was developed by Suen (2005) using hydrologic statistics selected to meet species speci?c ?ow requirements. The TEIS used hydrologic statistics identi?ed by Olden and Poff (2003) and the indicators of hydrologic alteration identi?ed by Richter et al. (1996) with the environmental requirements of Taiwan freshwater ?sh species that was Suen and Herricks (2006). At issue is how hydrologic statistics used in the TEIS indicators can provide a useful addition to the existing ecohydrologic analysis. In particular, a demonstration is needed that relates TEIS statistics to a better understanding of ?ow pattern, timing, frequency, and variability that are tied to aquatic community needs. Further, it is known that the actual values of hydrologic statistics can vary over a relatively small land area that is characterized by topographic and climatic differences, which effect discharge and concentration time. Taiwan provides the ideal location to address whether this variability in?uences the interpretation of regional or local ecohydrological conditions. In addition, the calculation of hydrological statistics has brought the recognition that there is a potential for redundancy in the information provided by decision makers. It should be possible to reduce the number of measures and still provide an accurate characterization of ?ow regimes with a reduced set of hydrologic statistics that are more easily understood by watershed managers. The focus of our analysis is Taiwan, an island in the Paci?c Ocean. Taiwan presents an ideal opportunity to evaluate hydrological statistics for the local and regional analysis of ecohydrologic indicators. Taiwan’s land area is approximately 36,000 km2 with mountains reaching 3952 m. In this relatively small area, hydrologic monitoring has been conducted for over 50 years, providing a rich resource of hydrologic data from a dense network of gauging stations. Existing management divides Taiwan into regions and it has been possible to select watersheds that are relatively undisturbed for the natural ?ow regime analysis. The objective of this research is to use advanced analysis procedures, speci?cally modern clustering techniques, to assess the hydrologic statistics proposed in the TEIS, and then to examine the issues of correlation with watershed conditions, regionalization, and information redundancy when ecological issues are included in the assessment of indicator redundancy. To this end, we used TEIS to identify hydrological statistics. Watershed conditions considered

Introduction

Hydrology is recognized as a critical factor in the geomorphology and ecology of streams and rivers (Karr, 1981; Gordon et al., 2004). Hydrologic events are known to form and maintain channel planform and substrate while interactions among ?ow and channel structures create habitat for aquatic organisms. The understanding of the relationships between the ?ow regime characteristics of a river and its ecological functioning is crucial to the developing science of ecohydrology (Hughes and Hannart, 2003). This recognized connection between ?ow and organisms has resulted in the use of hydrologic statistics to characterize the physical conditions for organisms and to identify the natural ?ow regimes that are expected to enhance native fauna and provide a reasonable target for ?ow management. An emphasis on the ?ow management has encouraged the development of hydrologic indicators for the natural ?ow regimes (Olden and Poff, 2003), and a number of hydrologic statistics have been proposed for use as hydrologic indicators for river restoration and water resources management (Hughes and James, 1989; Poff, 1996; Richter et al., 1996, 1997; Clausen and Biggs, 2000). Olden and Poff (2003) reviewed 171 currently available hydrologic indicators and provided a statistically based framework used in selecting non-redundant hydrologic indices to describe the natural ?ow conditions. Their efforts focused on monitoring locations in the United States and were intended to identify indices that would explain the statistical variation in hydrologic indices and to minimize multicollinearity while adequately representing the ?ow regime. They also had a goal to assess the transferability of hydrologic indices and identify indices that explain the dominant patterns of variance. Although the hydrologic basis for developing indicators is well de?ned by common techniques in stochastic hydrology (Chow et al., 1988), the selection of hydrological statistics for ecohydrological analysis is still the subject of discussion and research. The most common basis for the selection of ecohydrologic indicators is the identi?cation of natural ?ow conditions, assuming that natural ?ows will bene?t native species and more natural communities (Landres et al., 1999; Richter et al., 2003; Allan, 2004). Natural ?ow is a useful target because natural ?ows can be expected to reproduce habitat conditions that lead to sustaining endemic fauna and to support the restoration of ecosystems present before a disturbance if native organisms are still present to colonize a restored river. Critical requirements for the natural ?ow regime determination include a historical record from periods when hydrology was undisturbed by development, or the availability of undeveloped watersheds that can be used as references for the natural ?ow determination. In an ecohydrology analysis a ‘‘natural ?ow regime’’ is a continuing sequence of ?ows that meet ecosystem requirements for (1) the seasonal pattern of ?ows, (2) the Julian date or timing of extreme events, (3) the frequency and the duration of ?oods and droughts, (4) the seasonal and annual ?ow variability, and (5) the expected rate of change in natural ?ows (Poff et al., 1997). Ecohydrologic indicators are thus intended to quantify speci?c values for magnitude, frequency, duration, rate of change, and timing of ?ow conditions, which play important roles in sustaining or restoring the ecological integrity of ?owing water systems.

Assessing the ecological hydrology of natural ?ow conditions in Taiwan differences in geographic location, elevation, and area. Because elevation, coupled with location on East or West slopes, can produce rain shadow effects, and typhoon paths can produce intense, local, rainfall, this analysis considered watershed location as a possible key variable. Watershed area and elevation are commonly used in normalizing the analysis of hydrologic statistics. A critical factor used in station selection was that each watershed was largely undeveloped and that the record was suf?ciently long to develop sound statistics. Our analysis included calculation of hydrological statistics recommended by the TEIS, assessment of the differences among watersheds due to location, area and elevation, cluster grouping of stations based on hydrologic statistics, and the assessment of information redundancy.

77

Physical setting

Taiwan is located in the North Paci?c Ocean sub-tropical jet stream monsoon district. The island is 394 km long, 144 km at its widest point, and shaped like a leaf with a total area of nearly 36,000 km2. A general description ?nds mountains to the East and plains to the West. The most important feature of Taiwan’s topography is the range of mountains running from the northeast corner to the Southern tip of the island. Steep slopes and mountains over 1000 m high constitute about 31% of the island’s land area; hills and terraces between 100 and 1000 m above sea level make up 38% of the land area; and alluvial plains below 100 m in elevation,

where most communities, farming activities, and industries are concentrated, account for the remaining 31%. The longest river in Taiwan is only 176 km long, which drops from near 4000 m to sea level over that distance. The annual average rainfall is 2515 mm, about three times the world annual average. Rainfall is seasonal nearly 78% of the rainfall occurring from the end of spring to the beginning of autumn (May–October). There are known differences in rainfall distribution from the North to the South and with elevation. Fig. 1 shows the topography and the annual average isohyets and ?ve administrative management regions. Isohyets are derived from the monthly rainfall distribution records for the period of 1971–2006. The observed differences in rainfall produce seasonal ?ow periodicity with dry periods from November to April, lasting as long as 6 months. In addition to geographic and seasonal in?uences on hydrology, typhoon passage in?uences rainfall. Typhoons occur with an average frequency of 3.5/year. Typhoon related rainfall has been recorded at over 1000 mm/day. Fig. 2 shows a typical storm hydrograph in Taiwan. The typical typhoon-related ?ow has extremely high ?ow stages in hydrographs lasting for less than a day to a few days. Few or many watersheds may be affected by a typhoon depending on the path and speed of transit. This complex and dynamic hydrologic environment provides a major physical challenge for the 163 freshwater ?sh species known in Taiwan. Further, the hydrologic environment has also promoted an active ?ood defense and engineering management of all rivers ?owing through populated areas leading to the

Figure 1

(a) Topography and (b) annual isohyets and rainfall distributions in Taiwan.

78

3000 2500 Stream flow (cms) 2000 1500 1000 500 0 0 20 40 Hours 60 80 0 10 20 30 40 50 60 70 80 100 Rain (mm)

F.-J. Chang et al. Examples of how these hydrological statistics are expected to relate to organisms and communities are provided by Suen (2005) and Suen and Herricks (2006), but are summarized here for the readers’ convenience. In the TEIS general ?ow statistics de?ne seasonality and can be related to general habitat conditions. Trends in ?ow provide an indication of how habitat needs for spawning, juvenile rearing, or adult maintenance is met. The rate of change statistics provides measures of habitat disruption or the duration stability of habitat needed to complete organism life history. For example, rapid changes in discharge may remove organisms through washout while more gradual change in discharge may provide environmental cues for migration or reproduction (Cushman, 1985; Welcomme, 1985). Using the mean of all positive and negative differences between consecutive values provides a measure of the rate of change in habitat supporting the analysis of the general suitability of those conditions for the maintenance of the target aquatic community. Statistics for high/low ?ow magnitude and duration provide information on ?oods and droughts, which can have signi?cant effects on riverine species. Typhoon events, although large, pass quickly so that 3-day average values re?ect typhoon in?uences in Taiwan’s wet season. Monthly statistics provide a means of tracking within season trends while 1- and 3-day averages allow the de?nition of event characteristics. Examples of ecological connections to ?ow include elevated ?ows that inundate ?oodplains producing the needed habitat for spawning, nursery of fry and juveniles, and foraging habitat. High magnitude, short duration events will inundate ?oodplains, but will also create velocity and turbulence conditions in the channel that lead to injury or death of ?sh (Ward et al., 1999; Harvey, 1987). Correspondingly, the extended duration of high ?ows may exceed the capacity for maintaining location and the duration of low ?ows produces reduced channel habitat and an increased risk of loss of organisms due to changing water quality or predation risk (Magoulick and Kobza, 2003; Herricks, 1996). Frequency statistics are important ecologically because riverine species are adjusted to change but more frequent events present a challenge to organisms. Increasing frequency reduces the recovery time between events leading to an increased effect of any single event. Increasing frequency eventually means that duration and frequency are the same, as in continuous exposure scenarios. Frequency statistics are used to relate events and characterize habitat stability when a single event, or multiple events with lower magnitude, can be expected to produce similar effects. The actual effect of event frequency is complicated because riverine species have evolved the capacity to deal with the change in their environment. In fact, maintenance of a sustainable ecosystem may actually be dependent on periodic disturbances. Increasing or decreasing frequency can lead to ecological damage (Ward and Stanford, 1983). Therefore, the number of high/low ?ow events and the number of hydrograph slope reversals in the dry and wet seasons are important statistics in the TEIS that help identify natural levels of disturbance needed to sustain ecological integrity. Because the life span of most endemic species in Taiwan is in the order of 3 years, the numbers of high/low ?ow events within three consecutive years are the focus of the TEIS.

Figure 2 A typical storm’s hydrograph in Shihmen reservoir, Taiwan (2000/08/22 $ 25 Bills Typhoon).

modi?cation of many watersheds. The undisturbed watersheds selected for this analysis were watersheds not subject to major hydrologic alteration or development that would be expected to alter ?ow characteristics.

Taiwan ecohydrology indicators

The suite of hydrological statistics selected for analysis in this paper is taken from the Taiwan ecohydrology indicator system (TEIS). The development of the TEIS was based on the considerations of Taiwan-speci?c factors. For example, the general ?ow statistics re?ect the 10-day averaging period used by Taiwan’s Water Resources Agency in reservoir management as well as a traditional reference time frame in the Chinese agricultural society. Statistics for dry and wet seasons were identi?ed to address sub-tropical seasonality in Taiwan. Time periods for duration and frequency were set based on the typical storm characteristics and the needs of the ?sh community as identi?ed by an autecology matrix (Suen and Herricks, 2006). Trend statistics were developed based on the ?sh species life history and were de?ned for different locations in the watershed based on ?sh community characteristics. The resulting indicator system provides a means to integrate hydrologic, ecological, and human management in?uences using a new synthesis of hydrologic statistics and provides a useful tool for the ecosystem based water resources management in Taiwan (Chang and Herricks, 2005). The TEIS includes 35 hydrologic statistics for magnitude, frequency, duration, rate of change, and timing. Re?ecting ?ow management in Taiwan means that stream ?ow statistics are summarized for 10-day periods. These 36 items that provide indicators for general ?ow, and the four indicators focused on Julian date, were not used in the analysis. Mean stream ?ows were simply statistics based on management convenience and were only used in general ?ow description. Although timing issues are recognized as important in ecohydrologic analysis, the inherent variability in ?xing a Julian date produced by typhoons limited the use in analysis procedures. Like Poff (1996), timing was shifted to a secondary analysis that would be speci?c for the species targeted, which is not the focus of this paper. Hydrologic statistics follow TEIS grouping for the rate of change, high/low duration, frequency, and duration. Table 1 provides a listing of the 30 of the TEIS hydrologic indicators used in this analysis.

Assessing the ecological hydrology of natural ?ow conditions in Taiwan

Table 1

The mean values of clustered stations for physiographic factors and 30 TEIS indicators Mean SD K-means #1 (5 stations) #2 (15 stations) #3 (32 stations) SOM #1 (13 stations) #2 (15 stations) #3 (24 stations)

All stations (52 stations) Watershed characteristics Area (km2) Elevation (m) TEIS characteristic 1. Mean of all positive differences between consecutive values in dry season (cms) 2. Mean of all positive differences between consecutive values in wet season (cms) 3. Mean of all negative differences between consecutive values in dry season (cms) 4. Mean of all negative differences between consecutive values in wet season (cms) 5. Dry season 1-day minimum (cms) 6. Dry season 10-day minimum (cms) 7. Dry season 30-day minimum (cms) 8. Dry season 90-day minimum (cms) 9. Dry season 1-day maximum (cms) 10. Dry season 10-day maximum (cms) 11. Dry season 30-day maximum (cms) 12. Wet season 1-day minimum (cms) 13. Wet season 10-day minimum (cms) 14. Wet season 30-day minimum (cms) 15. Wet season 1-day maximum (cms) 16. Wet season 3-day maximum (cms) 17. Wet season 10-day maximum (cms) 18. Wet season 30-day maximum (cms) 19. Number of season (times) 20. Number of season (times) 21. Number of season (times) 22. Number of season (times) low ?ow events within each dry low ?ow events within each wet high ?ow events within each dry high ?ow events within each wet 236 393 200 455

639 234

315 459

136 386 2.00 13.02 0.93 5.26

473 342 6.45 48.38 2.27 14.45

194 466 2.60 19.67 0.98 6.57

112 377 1.75 9.57 0.92 4.37

Group 1 – Differences between consecutive values 3.22 2.50 9.11 3.85 22.48 1.29 7.63 Group 2 2.73 3.04 3.51 4.64 58.6 26.7 16.8 3.57 4.34 6.51 411.9 250.2 121.7 64.6 20.85 0.89 6.01 72.64 3.08 21.26 25.93 1.47 8.14

– High/low ?ow event magnitudes 2.64 7.41 4.80 2.88 8.23 5.28 3.21 9.33 6.00 4.09 12.35 7.63 46.4 165.3 77.5 20.1 69.7 38.0 12.5 41.9 25.0 3.50 10.2 5.83 4.11 12.4 6.84 6.17 19.3 9.42 371.5 1244 485.7 226.2 761.3 303.1 190.4 365.5 153.1 56.5 190.1 83.4

1.03 1.18 1.42 2.04 33.14 14.7 9.06 1.46 1.92 3.15 247.2 145.5 69.0 36.2

6.47 7.13 8.05 10.32 122.1 55.3 34.7 8.38 9.96 14.6 852.8 527.1 259.6 137.9 0.25 2.24 2.00 4.15

2.52 2.81 3.25 4.27 47.1 22.7 14.9 3.34 4.05 6.07 386.2 234.3 113 59.8 0.48 2.17 2.33 4.07

0.73 0.87 1.08 1.64 29.7 12.9 7.80 0.96 1.32 2.17 176.2 102.9 49.0 26.0 2.41 5.59 3.91 6.05 (continued on next page)

Group 3 – Frequency of high/low ?ow events and reversals 1.30 2.04 0.36 0.21 1.96 3.76 2.97 5.01 3.27 1.64 1.86 2.84 2.17 4.79 1.81 1.99 3.74 4.81 3.56 5.64

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80

Table 1 (continued) Mean SD K-means #1 (5 stations) 11.74 19.98 38.94 45.88 #2 (15 stations) 3.95 16.11 37.88 43.28 #3 (32 stations) 19.18 26.14 39.80 48.81 SOM #1 (13 stations) 7.01 17.57 37.49 43.79 #2 (15 stations) 7.16 18.12 37.30 43.45 #3 (24 stations) 22.36 28.22 41.07 50.60

All stations (52 stations) 23. Number of low ?ow events within consecutive 3 years (times/3 years) 24. Number of high ?ow events within consecutive 3 years (times/3 years) 25. Number of hydrologic reversals in dry season (times/year) 26. Number of hydrologic reversals in wet season (times/year) 27. Mean duration of low ?ow events in dry season (days/time) 28. Mean duration of high ?ow events in dry season (days/time) 29. Mean duration of low ?ow events in wet season (days/time) 30. Mean duration of high ?ow events in wet season (days/time) 14.07 22.65 39.16 46.93 15.03 9.23 10.46 10.89

Group 4 – High/low ?ow event duration 4.20 6.34 2.37 0.80 4.07 6.62 4.17 1.29 3.06 1.20 3.77 6.80 4.08 3.61 4.84 5.08

6.07 4.33 7.43 3.76

1.45 3.65 5.65 4.71

2.16 4.14 6.19 4.64

7.02 4.28 7.46 3.60

Wet season: from May to October; dry season: from November to next April; low ?ow event: less than 25% of the mean daily ?ow; and high ?ow event: more than 200 % of the mean daily ?ow.

F.-J. Chang et al.

Assessing the ecological hydrology of natural ?ow conditions in Taiwan Ecosystems are highly dependent on the timing of ?ows. For example, in ?sh species that spawn once a year, this spawning may be keyed to ?ow change, temperature, and maintenance of speci?ed conditions to provide critical habitat for successful spawning and fry development. Thus, ?ow timing is critical to species spawning, egg hatching, or migration (Nesler et al., 1988; Naesje et al., 1995), especially in areas where periodic ?oods are expected (Tew et al., 2002). For these reasons, the Julian date of ?ow events is an important data point to relate organism life history and ?ow.

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a 20

16

Number of Sites

12

8

4

Materials and methods

Method of selection of stations

For a small island, Taiwan has a relatively dense network of ?ow monitoring stations. The watershed characteristics of 430 stations were reviewed and stations subject to modi?ed ?ows from reservoirs or major irrigation systems were eliminated. A ?nal set of 52 stations included records from 23 largely unaltered watersheds, which are intended to support the identi?cation of natural ?ow regimes in these watersheds. Using the daily average ?ow from each station, TEIS indicators were calculated, and the results are provided in Table 1. To provide an initial organization, the TEIS statistics were grouped using the management regions established by the Taiwan Water Resources Agency, North, middle, Southern, and Eastern. This initial organization re?ected mainly political divisions although agency regions did re?ect watershed boundaries and physiographic differences with the Eastern region characterized by a narrow coastal plain and steep, mountain slopes, while the North, middle, and Southern regions are the divisions of the West coast where coastal plains are broad with high density population centers. Measurements were made of watershed area for each gauging station and the elevation of the gage was determined. Although other characteristics of watersheds were measured, only the area and elevation were used as independent variables in this analysis. Watershed areas ranged from 100 to 900 km2 with the majority less than 300 km2, and elevation ranged from sea level to 1800 m, Fig. 3.

0 0 100 200 300 400 500 600 700 800 900

Area (km2)

b 25

20

Number of Sites

15

10

5

0

0

200

400

600

800

1000

1200

1400

1600

1800

Elevation (m)

c 28

24 20

Number of Sites

16 12 8 4

Analytical procedures

A general question facing researchers in many areas of inquiry is how to organize the observed data into meaningful structures, that is, to develop groups of similar stations for a more detailed analysis. Cluster analysis is a useful technique to identify groups that both minimize within-group variation for data in a cluster and maximize between-group variation to identify potential differences between clusters. The advantage of cluster analysis is that it is a technique that can be applied without bias to discover structures in data without providing an explanation/interpretation of the cluster groupings. Clustering techniques have been applied to a wide variety of research problems. In this study, we apply two commonly used clustering algorithms, namely K-means clustering and the self-organizing map (SOM) clus0 0 10 20 30 40 50 60

Length of Record (years)

Figure 3 Numbers of gauging sites with (a) basin areas (b) basin elevation, and (c) lengths of record.

tering. The values shown in Table 1 are the result of Kmeans or SOM clustering providing the average values for the hydrological statistics contained in that cluster group. A brief summary of the two clustering algorithms used in this analysis is given as follows. K-means clustering K-means clustering uses an algorithm to classify objects based on a de?ned number (K) of groups, where K is the

82 positive integer number. The grouping is done by minimizing the sum of squares of distances between the data and the corresponding cluster centroid. The algorithm is described brie?y as follows: (1) Begin with a decision on the value of K = number of clusters. (2) Place K points into the space represented by the objects that are being clustered. These points represent the initial group centroids. (3) Assign each object to the group that has the closest centroid. (4) When all objects have been assigned, recalculate the positions of the K centroids. (5) Repeat steps 3 and 4 until the centroids no longer move. This produces a separation of the objects into groups from which the metric to be minimized can be calculated. ??????????????? s?????????????????????????????? sP P P 2 ?n ? 1? P S2 i?1 i i?1 Si RMSSTD ? ? P?n ? 1? P

F.-J. Chang et al.

?1?

P is the number of clusters, n is the sample size, and Si is the standard deviation of ith cluster. The R-squared metric provides a measure of the extent to which clusters are different from each other. The value of RS lies between 0 and 1 with values close to 1 indicating a high difference between clusters PG P 2 i2G kx i ? x k k k?1 2 R ?1? ?2? Pn k 2 i?1 kx i ? x k where G is the number of clusters in hierarchical level. The RS always decreases with the number of clusters. The SPRSQ compares clustering results and provides a measure of the difference between two results. When the SPRSQ is larger, this indicates that the result of the ?rst cluster is preferred

np ?nq nr SPRSQ ? Pn

SOM clustering SOM clustering uses an algorithm introduced by Kohonen (1982). SOM generates lower dimensional topological ordered maps of input data through learning, which is very useful for analyzing high-dimension data. Once SOM is determined, the output of the network to the input vectors can be recalled from the classifying results memorized in the network. The SOM algorithm is an unsupervised classi?cation that uses competitive learning strategy to adjust the connected weights between the input and the hidden layers and to form a topographically ordered map in the hidden layer. Different from other clustering methods for unsupervised data, SOM can be highly non-linear, directly showing the similar input vectors in the source space by points (Chang et al., 2007).The learning algorithm of the training connected weights in SOM is summarized as follows (1) Initialize network weight vectors. (2) Randomly choose an input vector from input space. (3) Determine the winning neuron by calculating the Euclidean distance between the input vector and the weight vectors of all neurons in the hidden layer. (4) Adjust the weight vector of the winner as well as the weight vectors of its neighboring neurons according to the learning rule. (5) Iterate the procedures from 2 until the weight vectors stabilize. After a large number of iterations, each input vector is mapped onto a speci?c neuron in the hidden layer in the way that the weight vector of the neuron is closer to the input vector. Cluster group determination An important issue in cluster analysis is the selection of the number of cluster groups that are used to organize data. Three common test statistics were used to identify a cluster, the root-mean-square standard deviation (RMSSTD), the R-squared (RS), and the semipartial R-squared (SPRSQ). The RMSSTD is a measure of homogeneity within clusters based on Eq. (1). Large values of RMSSTD indicate that the clusters are not homogeneous

kx p ? xq k2 ? xk2

i?1 kx i

?3?

where nr = np + nq, np and nq are the samples of cluster p and cluster q. SPRSQ denotes the difference between the previous R2 and the present R2. The relative change in the values of the RMSSTD, RS, and SPRSQ statistics as the number of clusters increase can be useful in determining the number of clusters. In our analysis, we calculated statistics at each stage in the clustering algorithm, which allowed plotting the values against the number of clusters. A marked decrease or increase for RMSSTD, RS and SPRSQ, respectively, was the criterion used to identify when a satisfactory number of clusters was selected (Sharma, 1996).

Results and discussion

The results of the calculation of TEIS hydrologic statistics for the 52 gauging stations are provided in Table 1. The mean watershed area was 236 km2 and the mean elevation was 393 m indicating that undisturbed watersheds were small and generally located in higher elevations. Table 1 provides the mean and standard deviation for 30 hydrologic statistics of the TEIS. The mean stream?ow for the 36 tenday period of the TIES is replaced with the average fractional ?ow by month as shown in Fig. 4. The remainder of the table provides the average values of watershed hydro-

Figure 4

Average fractional monthly ?ows by month.

Assessing the ecological hydrology of natural ?ow conditions in Taiwan logic statistics for the stations grouped by K-means and SOM clustering. When watershed area is considered, the majority of the watersheds in this analysis (32) had an average area of less than 140 km2, Table 1, with the typical record length of 20– 50 years, Fig. 3c. The 30 TEIS indicators shown in Tables 1 and 2 are grouped in categories considering ?ow variability based on differences in consecutive values, high/low ?ow statistics based on frequency analysis, event frequency, and high and low ?ow event duration. The TEIS statistics are numbered 1–30 to relate to Fig. 7 where the relative normalized value of cluster averages is compared. Fig. 7 also demonstrates the capacity of the clustering algorithm to group similar stations and provides cluster groupings for these data.

83

Characteristics of ?ow in Taiwan rivers

Flow conditions in Taiwan rivers can be characterized based on general watershed conditions identi?ed in this analysis,

Table 2

from the average fractional monthly ?ows determined for all 52 stations, and TEIS statistical summaries. Because of the limited river length ?ow travel times are short. Watershed selection minimized human in?uences supporting the natural ?ow regime analysis so that seasonality of stream ?ow is in?uenced mostly by the seasonal cycle of precipitation. In the wet season (May–October), precipitation is in the form of typhoons and/or high intensity rainfall events producing daily rainfall values of hundreds to over a thousand millimeters. Although snow is present at high elevations, the snowmelt contribution to hydrology is limited to winter months in high elevations. The average seasonal distribution of ?ow ?nds about 80% of the ?ow occurs in the wet season with the highest fraction during August and September, Fig. 4. TEIS statistics show that the rate of ?ow rise is two or three times of the falling rate in both seasons, while the ?ow rise and fall in wet season are about seven times of dry season, respectively. The ?ow rising rate is 3.22 (dry season) and 22.48 (wet season), and the falling rate is 1.29 (dry season) and 7.63 (wet season), Table 1,

Correlation Coef?cients between TEIS parameters and physiographic variables –area and elevation Area (km2) Elevation (m) ?0.094 ?0.196 ?0.219 ?0.311 ?0.068 ?0.083 ?0.093 ?0.103 ?0.163 ?0.090 ?0.061 ?0.003 ?0.022 ?0.056 ?0.227 ?0.210 ?0.182 ?0.169 0.431(#1) 0.758(#2) 0.317(#1) 0.653(#2) 0.582(#1) 0.528(#2) 0.511(#1) 0.253(#1) 0.449(#1) 0.452(#3) 0.468(#3) 0.680(#2)

Group 1 Mean of Mean of Mean of Mean of

– Differences between consecutive values (cms) all positive differences between consecutive values in dry season all positive differences between consecutive values in wet season all negative differences between consecutive values in dry season all negative differences between consecutive values in wet season

0.854 0.881 0.847 0.901 0.900 0.905 0.903 0.910 0.892 0.923 0.924 0.946 0.955 0.957 0.928 0.926 0.929 0.939 ?0.278 ?0.257 ?0.281 ?0.257 ?0.213 ?0.203 0.038 ?0.067 ?0.207 ?0.129 ?0.125 0.183

Group 2 – High/low ?ow event magnitudes (cms) Dry season 1-day minimum Dry season 10-day minimum Dry season 30-day minimum Dry season 90-day minimum Dry season 1-day maximum Dry season 10-day maximum Dry season 30-day maximum Wet season 1-day minimum Wet season 10-day minimum Wet season 30-day minimum Wet season 1-day maximum Wet season 3-day maximum Wet season 10-day maximum Wet season 30-day maximum Group 3 – Frequency of high/low ?ow events and reversals Number of low ?ow events within each dry season (times) Number of low ?ow events within each wet season (times) Number of high ?ow events within each dry season (times) Number of high ?ow events within each wet season (times) Number of low ?ow events within consecutive 3 years (times/3 years) Number of high ?ow events within consecutive 3 years (times/3 years) Number of hydrologic reversals in dry season (times/year) Number of hydrologic reversals in wet season (times/year) Group 4 – High/low ?ow event duration (days/time) Mean duration of low ?ow events in each dry season Mean duration of high ?ow events in each dry season Mean duration of low ?ow events in each wet season Mean duration of high ?ow events in each wet season

#1: a log transformation; #2: a power transformation; and #3: an exponent transformation.

84 Group 1. The general pattern of short high ?ow events and long duration low ?ows is con?rmed. Cluster groups have stations with high average values in Cluster 1 with decreasing values in Clusters 2 and 3, Table 1. High/low ?ow event magnitudes High and low ?ow statistics in the TEIS focus on the frequency of occurrence for wet and dry season minima and maxima, Table 1, Group 2. During the dry season, the average minimum ?ow for 1–90 days is all less than 5 m3/s, while the average maximum ?ows of 1–30 days are between 25 and 60 m3/s. During the wet season, the average minimum ?ow for 1–30 days is near 5 m3/s; however, the average maximum ?ows of 1–30 days can be larger than several 100 m3/s. Seven stations had maximum ?ow values higher than 1000 m3/s in the wet season, while 18 stations had a 1-day minimum ?ow of less than 1 m3/s in the dry season. In addition to ecological issues, low stream?ow estimates are required for a variety of water resource management purposes, particularly the diversion of water to agricultural use. This analysis suggests that minimum ?ows will be limiting in all watersheds with over 60% of the watersheds in this analysis providing consistent low ?ow conditions. Frequency of high/low ?ow events and reversals TEIS statistics indicate that the number of low ?ow events ranges from 1.30 to 3.76 times per/year, while the number of high ?ow events ranges from 2.97 to 5.01 times per/year, Table 1, Group 3. The numbers of low and high ?ow events for consecutive 3 year periods are 14.07 and 22.67. The numbers of hydrologic reversals in dry and wet seasons are 39.16 and 46.93, both with a standard deviation of around 10. Fig. 5 summarizes ?ow reversals in the dry and wet seasons for all 52 stations. Suen (2005) de?ned a low ?ow event as the ?ow which is lower than 25% of the average discharge, while the high ?ow event is greater than 200% of the average discharge. These results con?rm that both the number of events and the corresponding ?ow variability are greater in the wet season than that in the dry season. Station by station analysis found four stations, all in South Taiwan, that have low, unvarying ?ows. The ?ow reversal statistic is indicative of a frequency

F.-J. Chang et al. of habitat change and a good indicator of the overall habitat stability. Analysis results indicate that ?ow reversals may average more than 85 times per year indicating few weeks pass without ?ow related habitat change in even undisturbed watersheds in Taiwan. Duration The mean duration of low ?ow events in the dry season is in the order of 4 days with a high standard deviation. The mean duration of low ?ow in the wet season is in the order of 6 days with a standard deviation of about 3, which is one half of the dry season standard deviation. High ?ow durations were 4 days for both dry and wet seasons with a standard deviation near one. The stations in Cluster 3 tended to have higher low ?ow event durations while the high ?ow event durations were near station averages. These results are generally consistent with the analysis of ?ow reversals, which suggest changes occurring weekly, but with a short duration. Summary The natural ?ow conditions for 52 watersheds in Taiwan have been effectively characterized by TEIS statistics. This analysis con?rmed the seasonality of ?ow in Taiwan with distinct wet and dry periods. Increasing values for consecutive measurements averaged 3.22 cms in the dry season and 22.48 cms in the wet season indicating an expected higher ?ow variability in the wet season. The analysis of high/ low ?ows indicated that 1, 10, 30, and 90 day low ?ows are all less than 5 m3/s with some low ?ows less than 1 m3/s in the dry season. Wet season minimum ?ows are also near 5 m3/s but maximum ?ow averages are as high as 411 m3/s with event maximum ?ows exceeding 1000 m3/s. These ?ow characteristics describe a natural ?ow regime with low ?ows nearly the same in both the dry and the wet seasons punctuated by high ?ow events that are more than two orders of magnitude greater than low ?ow conditions. Frequency analysis ?nds that the number of low ?ow events ranges from 1 to 3 per/year, while the number of high ?ow events ranges from 3 to 5 per/year. A useful indicator of ecological condition is the ?ow reversal. The numbers of ?ow reversals in dry and wet seasons were 39.16 and 46.93, respectively. These reversals characterize a ?ow environment that can be expected to ?uctuate regularly in both dry and wet environments every few days. Event duration is short with low ?ow events lasting slightly longer in the wet season than the dry season (6 vs. 4 days). The wet season low ?ows are only slightly greater than dry season low ?ows, and the high ?ow events are typically shorter with very high maximum ?ows, re?ecting the rapid passage of typhoon systems over the island. These results provide insight into the natural ?ow variability that supports populations of native ?sh.

80 Number of hydrologic reversals in wet season

60

40

20

Cluster analysis

0 0 20 40 60 80

Number of hydrologic reversals in dry season

Figure 5 The relation of hydrological reversal in dry season and wet season.

Watersheds with similar values for hydrologic statistics were grouped together using K-means and SOM clustering algorithms. The relationships between the number of clusters produced by K-mean clustering were evaluated using RMSSTD, R-squared, and SPRSQ statistics (Fig. 6). These

Assessing the ecological hydrology of natural ?ow conditions in Taiwan results indicate that when the number of clusters is smaller than 3, the SPRSQ value increases, R-squared value drops, and RMSSTD value is high. We inferred from these results that the appropriate number of clusters was 3. The three clusters of stations identi?ed by K-means and SOM methods are shown in Table 1 and Fig. 7. The numbers of stations are 5, 15, 32 in K-means clusters and 13, 15, 24 in SOM clusters. The average values for hydrological statistics from the stations grouped in K-means and SOM clusters are also provided in Table 1, and standardized values represented in Fig. 7. Fig. 7 reveals that both methods produce three clusters for items 1–18 shown in Table 1, and statistics related to the rate of change and ?ow frequency. SOM clustering grouped stations with less variability in each cluster and shows a clear distinction between the three clusters in all the 30 TEIS indicators. Comparing the results obtained

85

by K-means, SOM suggested that the SOM provides a better clustering for TEIS parameters. Table 1 presents the average values of TEIS statistics for the stations grouped in each cluster for both K-means and SOM clustering. For both methods, Cluster 1 has stations with the largest average values for the rate of change and ?ow frequency statistics and smaller values for event frequency and event duration statistics. Cluster 3 generally has stations with the smallest values for the same statistics. The analysis of Table 1 con?rms the similarity between clustering methods. The major difference is found in Cluster 2 where the K-means clustering has grouped stations with the smallest values for event frequency and event duration statistics. Event frequency and event duration statistics have stations with the smallest values in Cluster 1 using SOM clustering.

a

1.2

SPRSQ

b

25

RMSSTD RSQ

1 0.8 0.6

20 15 10

0.4 0.2 0 12 11 10 9 8 7 6 5 4 3 2 1

5 0

12

11

10

9

8

7

6

5

4

3

2

1

Figure 6

The relationships between the number of clusters and SPRSQ, RSQ, RMSSTD.

a

3.00

cluster1

2.50 2.00 1.50 1.00 0.50 0.00 -0.50 -1.00

1 2 3 4 5 6 7 8

cluster2 cluster3

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

b

1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8

1 2 3 4 5

cluster1 cluster2 cluster3

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Figure 7

The standardized cluster centers of 30 TEIS parameters by (a) K-means and (b) SOM methods.

86 Geographic distribution Fig. 8 shows the geographic locations for stations in each cluster as determined by K-means and SOM clustering. The SOM clusters more evenly distribute stations among clusters and offer alternative interpretations for regionalization and possible in?uences of physiography on watershed characteristics. Both methods group Northern and Western stations in Cluster 3. Eastern watersheds are grouped in Clusters 1 and 2 although there is an overlap between methods and clusters within methods. This result suggests that natural ?ows can be expected to be more similar in Northern and Western areas with Eastern watersheds producing different ?ow conditions. This interpretation is consistent with the physiography in that Eastern watersheds are steeper and potentially more subject to direct typhoon effects. The Western water-

F.-J. Chang et al. sheds are in a coastal plain with Northern watersheds somewhat in the rain shadow of the central mountains. The results of this geographic distribution considering TEIS statistics are informative. For the rate of change statistics, in both clustering methods Cluster 1 grouped stations with higher than average values, Cluster 2 grouped with stations near average values, and Cluster 3 grouped with stations with lower than average values. For other characteristics, there was more differences between Kmeans and SOM clustering. For ?ow frequency statistics Cluster 1 had stations with higher values for both methods, Cluster 2 had stations with high values in K-means and near average for the SOM method. Cluster 3 had below average values for both methods. For event frequency Clusters 1 and 2 in both methods grouped stations with lower than

Figure 8

The geographic location of stations in K-means and SOM clusters.

Assessing the ecological hydrology of natural ?ow conditions in Taiwan average values while Cluster 3 had near average values for K-means and higher than average station in SOM clustering. The clustering of stations for event duration was similar with Clusters 1 and 2 containing stations with averages below or near average and Cluster 3 containing stations with stations having higher than average values. The cluster groupings for both methods provide a means to further re?ne geographic differences in hydrologic statistics. These results suggest that independent of the number of stations in clusters produced by the two methods, clustering grouped stations based on TEIS statistics that have a consistent difference from island averages. When considering Oden and Poff’s objective of discovery of multicollinearity, these analyses indicate that hydrologic statistics do differ in groups of watersheds and that the TEIS provides a set of hydrologic statistics that can be used by either K-means or SOM clustering to identify dominant patterns of ?ow that are important in ecohydrology.

87

Correlation analysis

Correlation analysis is regularly used in hydrology to relate similar variables in a dataset. Because a correlation coef?cient indicates the strength of a linear relationship between two random variables, correlation has provided a basis for

3000 Annual mean flow 2500 2000 1500 1000 500 0 0 200

identifying strong relationships between descriptive variables. Correlation procedures were used in this analysis related TEIS statistics and the two physiographic variables measured for each station (area and elevation). The results indicate that the rate of change and ?ow frequency statistics were highly correlated with watershed area (Table 2). For example, the correlation between area and minimum ?ow was as high as 0.957 for the wet season 30-day minimum. Other correlations between watershed area and some groups of TEIS statistics are not strong. Event frequency and event duration have low, negative correlations with watershed area. This high, and then a lack of, correlation with TEIS statistics is a useful ?nding for ecohydrologic analysis. The correlation between ?ow volume statistics and area is expected and provides some utility in estimating natural ?ow characteristics based on watershed area for ungauged watersheds. The lack of correlation among area and event variables is also expected, because frequency statistics are driven by rainfall variability, which is not normalized by watershed area. The opposite results were observed for elevation. Low, negative correlations with elevation for ?ow volume statistics and moderate correlation was present in event statistics. This is also an expected result because elevation is related to smaller watershed area and watershed location and orientation which can be expected to

Mean of all positive differences between consecutive values in wet season 100 80 60 40 20 0 0 200 400 Area Wet season 30-day minimum 35 30 25 20 15 10 5 0 0 200

CC=0.934

400 600 Area (km2) 800 1000

CC=0.881

600 (km2)

800

1000

Dry season 30-day maximum

60 50 40 30 20 10 0 0 200

CC=0.924

400 600 Area (km2) 800 1000

CC=0.957

400 600 Area (km2) 800 1000

Low flow events in each wet season

35 30 25 20 15 10 5 0 500

Mean Duration of high flow events in each wet season

40

3.0 2.8 2.6 2.4 2.2 2.0 0 500

CC=0.758

1000 Elevation (m) 1500 2000

CC=0.680

1000 Elevation (m) 1500 2000

Figure 9

Correlation patterns.

88 in?uence rainfall characteristics and corresponding event frequency and duration statistics. The lower correlation re?ects not only elevation differences, but also unknown effects of elevation related to factors such as typhoon path, rain shadowing, or landscape features such as vegetation type and geological controls of geomorphology. Several correlation value plots are provided in Fig. 9.

F.-J. Chang et al. ?ow frequency issues. The analysis identi?ed that the dry season was characterized by consistent low ?ows with relatively small, but regular, changes in ?ow and expected habitat. In the wet season, low ?ows were similar to dry season values, but more frequent events, and events producing ?ows over 100 times low ?ow volumes could be expected. Flow in both dry and wet seasons had high numbers of ?ow reversals, approximately once every 4 days. This natural ?ow regime characterization for Taiwan is generally consistent with the qualitative assessments but TEIS statistics provide a detailed picture of natural ?ows that can be associated directly with the autecology of Taiwan’s ?sheries. Further analysis applied clustering techniques to assess the existing regionalization procedures and to provide a sense of associations among watersheds. Three clusters of stations were identi?ed with clusters de?ning groups of largely Western and Northern stations in the largest cluster, and central and Eastern stations in other clusters. The cluster analysis was useful in analyzing the structure of data resulting from calculating TEIS statistics. The cluster groupings did not have a strong connection to existing regional divisions that were based on purely management considerations. The K-means and SOM clustering methods did produce different cluster groupings with SOM clustering more evenly distributing stations among clusters. Comparing the results obtained by K-means and SOM, the SOM clustering can group stations with less variability in each cluster and can clearly distinguish the difference between clusters. It appears that the SOM provides a better clustering for TEIS statistics. Correlation analysis found a high correlation between watershed area and ?ow variables. Poor correlations were found between watershed area and frequency variables. The identi?ed correlations suggest that it is possible to identify relationships between TEIS statistics and watershed area to help extrapolate the selected results to ungauged watersheds. For example, generally high correlations with ?ow volume statistics suggest that general assessments of ?ow related habitat conditions can be based on watershed area providing a means to develop ?ow management strategies from autecological relationships in ungauged watersheds in Taiwan. Low correlations of watershed area with event statistics suggest that when the analysis of life history or event related effects are needed, watershed area provides a poor means of addressing ecohydrology issues and secondary analysis is required. An assessment of information redundancy found that if the objective was simply historic natural ?ow characterization, there was a high level of information redundancy in the TEIS indicators. If the objective was ecohydrologic characterization of natural ?ows, the TEIS provided the needed statistics to better relate autecological needs of both target species and aquatic communities. The TEIS statistics provide insight into the natural ?ow variability that supports populations of native ?sh. The contrasting conditions between wet and dry seasons drive a life history of native species and provide the opportunity for the management of ?ows to produce habitat conditions which are not advantageous to exotic species by duplicating a natural ?ow regime that has a high frequency of ?ow reversals in both wet and dry seasons.

Redundancy

The presentation of TEIS hydrologic statistics in Table 1 suggests a high level of information redundancy in these statistics as was found by Olden and Poff (2003). In an effort to identify a minimum set of statistics needed to describe the main aspects of ?ow regime, Olden and Poff (2003) used principal components analysis, while this analysis used clustering algorithms. Fig. 7 illustrates the redundancy in hydrologic statistics as determined by K-mean and SOM clustering where clusters contain TEIS statistics for ?ow, magnitude, frequency, and duration. It would be possible based only on these hydrologic statistics to select a small set of statistics for natural ?ow characterization. Although it is possible to identify the information redundancy for purely hydrologic statistics, the actual information redundancy in ecohydrology statistics is not the same. For example, redundancy in hydrologic statistics may be identi?ed for 1-day, 3-day, and 10-day maxima, but these statistics from an ecohydrology perspective each provide information critical for certain species. For example, a species life history, behavior, or physiology determines the effect of ?ow regime change and 1-, 3-, or 10-day minimum or maximum ?ow conditions may result in suitable or unsuitable habitat for a target species. Our analysis shown Table 1 ?nds that the TEIS statistics provide a useful characterization of ?ow conditions that assist in determining how ?ow meets the needs of both target species and groups of species in communities of organisms. The TEIS provided a range of hydrologic statistics with high information redundancy for hydrologic description but non-redundant information that is useful for both the target species and the overall aquatic community management.

Conclusions

The objective of this research was to use selected hydrologic statistics in a comprehensive analysis of ?ow characteristics, information redundancy, and the use of hydrologic statistics in ecohydrology. The ?ow monitoring network in Taiwan provided a dense network of gauging stations where topography and climate are expected to play a major role in watershed hydrology. The Taiwan ecohydrologic indicator system (TEIS) (Suen, 2005) was used to select a group of hydrologic statistics and these statistics were calculated for 52 gauging stations located in relatively undisturbed watersheds. Because watersheds were relatively undisturbed, the hydrologic statistics are expected to identify the natural ?ow characteristics for Taiwan and to reveal how the TEIS statistics could be useful in ecohydrologic interpretations. The TEIS statistics revealed seasonal differences in ?ow and helped characterize changes in consecutive values and

Assessing the ecological hydrology of natural ?ow conditions in Taiwan

89

Acknowledgements

This study is funded by the Water Resources Planning Institute, Water Resource Agency, MOEA, Taiwan, ROC. The Water Resources Agency also provided gauging data used in these analyses. In addition, the authors are indebted to the reviewers for their valuable comments and suggestions.

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