THE SETUP OF EXAMINING MODEL FOR AVAILABLE WATER QUANTITY UPON WATER-RIGHTS INRIVERS OF TAIWAN

Abstract: For the purpose of reasonable distributiion to water resources a sound management system of water-rights has been carried out. A computing model for examining available water quantity in rivers for water-rights is necessary to assist the authority to pre-examine the application of new water-rights as well as existent ones. A technique of “Link-List” is applied in this model to enhance the search algorithm for random allocation of water-rights and link them together in series. Two major rules, i.e. supplying available water quantity at the applied site and avoiding disadvantage to the related downstream existent water-rights, have to be checked appropriately to decide the approval or rejection for water-rights application.

Keywords: water-rights, Link-List, water quantity

1    INTRODUCTION

The present “registration” issue of water-rights always causes excessive and inaccurate release of water to impede a reasonable utilization on water resources. The “permit” institution is proposed by the administration of water resources to control the limited resources more efficient (Chin, 1996). For a sound management system of water-rights the setup of a considerable examining model to check the issue of water-rights has been carried out. It is part of the project on the study of potential water quantity for any section of rivers in Taiwan. (Sinotech, 1998)

The procedure of examining is suitable for new application as well as existent water-rights. The reasonable and sufficient water quantity for water- rights issue is the goal of this model. It is simple and easy by using only arithmetic computing here. A coupled rainfall-runoff model and Kriging interpolation for potential water quantity at any section along rivers has been done to complete the integration of examining model. (Sinotech, 1998)

2    THE PROCEDURE OF EXAMINING

2.1  Examining criteria

By the “registration” of water-rights administration does examin the water quantity at the applied site only through analyses of flow records nearby. However, the variety of water-rights could be affected by upstream water intakes and it can cause disadvantage to the existent water-rights downstream, too. Therefore, two examining criteria have to be satisfied before the “permit” of water right issued (Chen, et. al., 1997 & 1999).

2.1.1    The availability of water quantity at the specified site

The upper limit of potential water supply (Q_p), which is deducted initially by reserved quantity preserved for base-flow, ecological system, fishery, etc. (Chen, et. al. 1998), has to be deducted by the summation of quantity of existent upstream water intakes at j sites (S{Q_wr}_j-u/s) for availability. The asked quantity of new water-rights application at i site ({Q_wr}_i) has to be less than the availability of water ({Q_av}_i) there firstly.

                 RULE-1： {Q_wr}_i < {Q_av}_i = {Q_p}_I－S{Q_wr}_j-u/s               (1)

2.1.2    The affection to downstream water supply

The diversion of new intake could cause insufficiency of water to its downstream water-rights. The priority of those existent water-rights is always higher than the new one. Therefore, checking of the availability at each downstream site k one by one for enough quantity after deducted by new application at i site is necessary.

               RULE-2：  {Q_wr}_i < {Q_av}_k-d/s                     (2)

2.2    Processes

The major frame of coupled examining model is shown as Figure 1. There are four major modules linked as described below.

2.2.1    Water-rights management supporting module

The needed background data of existent water-rights could be obtained for their locations and diverted water quantity by this module. The approval and recording for new water-rights has to be done here after examining processes passed, too.

2.2.2    Search module

A link-list technology is applied to connect the relationship between each stream segments as well as water-rights sites. The related upstream and downstream existent water-rights sites, even randomly allocated, could be traced easily for specified site of new water-rights through link-list strings.

2.2.3    Potential water quantity module

A coupled rainfall-runoff model and Kriging interpolation for potential water quantity at any section along rivers has been done. The limitation of maximum water quantity supplied by nature through statistical analysis can be calculated here.

2.2.4    Examining module

The comparison of water quantity between availability and necessity for those water-rights through two rules has to be satisfied before “permit”  issued. It is the core of this coupled model. The examined results will be passed back to management supporting module for final decision.

3    LINK-LIST

3.1    Methodology

Link-list is an efficient tool for searching in data structure technology. It has been applied in high-performance computation for astrophysics (Monaghan, 1985) as well as particle hydrodynamics (Chen, 1997). The original concept is that a string of sequential data is constructed to replace randomly and spatially allocated data for convenient searching. Those data are chained together through a specified relationship. Each data has to “remember” its connecting one. By “count-off” from those data one by one a sequential data string can be chained. Then, we can easily trace those locations of related data by this one-dimensional string instead of using neighborhood searching in two-dimensional grids system.

Two sets of memory block are needed as the head of chain (HOC) for tracing the head data for tracing at specified area and link-list (LL) for storing those related data one by one. If there are n records of data N_{i (i=1~n)} among string M_j, we can trace the head of M_j by HOC(M_j)=N₁ and get the next data in sequency by LL(N₁)=N₂, LL(N₂)=N₃,LL(N₃)=N₄,…until LL(N_n)=0 to the end of string. The principle of data structure for link-list is “First-In-First-Out”(FIFO). Reversely, those sets of string HOC and LL are constructed by similar procedures.

3.2    Link of stream segments and water-rights sites

A tree type of river structure can be divided into several segments by lots of nodes. Those nodes are always located at connection of two or more tributaries. As shown in Figure 2 a typical tree structure river is divided to six levels of segments. There are three kinds of link-list strings for connecting, i.e. LLD for downstream link, LLU for upstream link and LLS for side link at the same level. Those link-list strings can be constructed through tracing the upstream and downstream nodes for each segment and chaining them together.

In Figure 2, if we want to trace the upstream and downstream segments for 3E, then upstream segments such as 4E,4F,4G,5A,5B,6A,6B are traced by LLU and LLS and downstream segments such as 2B,1A are traced by LLD, too.

In the same way those water-rights at each segment can be linked and traced by link-list technology, too. Another set of string LLWR is needed for water-rights connection. If we can trace the related segments for the specified position of water-rights first, the water-rights sites at each segment are linked thereafter. Now, we can trace all the related water-rights sites upstream and downstream for the new proposed water-rights site.

4    APPLICATIONS

Due to fast development of hydraulic technology the interference by artificial structures can cause the flow conditions much different to natural one. Those situations have to be considered and modified for examining model. They would be discussed below.

4.1    Example 1 (ordinary condition)

For a condition much similar to natural condition no artificial facility divert the natural flow condition. Monthly potential water flow (Q_p) can be calculated by the “Potential water quantity module” for those sites of existent water-rights. As shown in Figure 3 there are 11 existent intake sites are located along a stream with the same water-rights Q_wr=0.01cms. If we need to set a new intake #20 between #2 and #3 sites with water-rights Q_wr=0.15cms. Comparing the new discharge with existent intakes as shown in Table 1a we can find that the insufficiency of water in July only. By single month analysis in July we can find that the availability of downstream sites of #10 and #3 can not be satisfied in Table 1b. However, if we adjust the intake discharge in July down to Q_wr=0.05cms, then permit can be issued with satisfied examining.

4.2    Example 2 (pump station)

For hydraulic electricity a pump station can be constructed for this purpose. The tailwater released to downstream site or not could affect the water-rights issuing as example shown in Figure 4. The background conditions are similar to those in example 1 and a new #20 water-rights for pumping with Q_wr=0.06cms is proposed between #9 and #8 sites. If the tailwater is diverted out, the single month analysis as shown in Table 2a indicates the problems in July at existent sites #2 and #8. However, if tailwater released just downstream with minor loss to 0.04cms, then the problem can be fixed and permit can be issued as shown in Table 2b.

For a special condition by adding flow (Q_re) at specified site from other catchment the availability for downstream sites can be recharged, Q_av = Q_p - S{Q_wr}_u/s+Q_re , which is similar to the result in Table 2b. The credit could be increased for new applications of water-rights.

4.3    Example 3 (reservior)

A reservoir can totally vary the natural condition to artificial controls. The dam blocks the river to store natural flow for electricity, flood mitigation, drought control, etc. purposes. The river can be divided into two parts as ordinary condition upstream of reservoir and total flow adjustment downstream. The latter condition is concerned at this section. The availability for those existent water-rights sites are change to Q_av = Q_p‘+Q_R-S{Q_wr}_u/s-R , in which Q_R=outflow by reservoir release, Q_p’ =potential sideflow from catchment downstream the reservoir and {Q_wr}_u/s-R=existent upstream intakes between specified site and reservoir. The outflow by reservoir release Q_R is controlled by reservoir operation and upstream inflow hydrograph. The “Potential water quantity module” has to be modified to couple with the special condition for reservoir.

For the conditions in Example 1, if we need to set a new intake #20 between #2 and #3 sites with Q_wr=0.25cms, we cannot go through between March and august as shown in Table 4a. For the similar background conditions as shown in Example 1 cited, however, the upstream of #8 water-rights site is replaced by a reservoir with Q_R=0.26cms as shown in Figure 5. The availability of downstream existent intake site is increased and the problem in Table 4a is fixed as shown in Table 4b. The term SUM[Qwr-u/s] in Table 4b is negative due to recharge including released reservoir outflow. The artificial control can properly modify the unbalanced monthly natural flow distribution for human utilization more efficient.

5    CONCLUSIONS

Due to the loose control for releasing water-rights without considerate examining the total sum of water-rights quantity may exceed much more than the supply of potential water quantity in rivers. A rigorous model is necessary for inquiring and checking a reasonable and realizable application of water-rights. The administration of water resources should restore the existent water-rights for efficient and accurate management.

References

[1]  Managhan, J.J. (1985), “Particle Methods for Hydrodynamics”, Computer Physics Report, Vol.3, pp.71-124.

[2]  Chin, J.C. (1996). “The Institution of Water-rights in Taiwan”, Proceeding of Water-rights Management Conference, Taipei, Taiwan, pp.1-13. (in Chinese).

[3]  Chen, Y.C., Kung, C.S. & Shu, S.K. (1997). “The Model of Examining Available Water Quantity for Water-rights in Rivers”, Journal of Taiwan Water Conservancy, Vol.45, No.1, pp24-32. (in Chinese).

[4]  Chen, Y.C. (1997). “The Application of Random-Walk Particle Method in Numerical Simulations”, Proceeding of Computer Application in Civil and Hydraulic Engineering Conference, Shinchu, Taiwan, pp.1031-1041. (in Chinese).

[5]  Sinotech Engineering Consulting Ltd. (1998). “The Study of Potential Water Quantity for Any Section of River in Taiwan” ,The 3^rd Annual Report prepared for Water Resources Bureau. (in Chinese).

[6]  Chen, Y.C., Kung, C.S. & Shu, S.K. (1998). “The Reserved Water Quantity and Water-rights in Rivers”, Journal of Engineering Environment, Vol.17, pp.79-85. (in Chinese).

[7]  Chen, Y.C., Kung, C.S. & Shu, S.K. (1999). “The Setup of Examining Model for Available Water Quantity upon Water-rights in Rivers”, The 10^th Conference for water resources, July 1999, Taichung, Taiwan. (in Chinese).

Table 1  The examining results for example 1

Table 2  The examining results for example 2

Table 3  The examining results for example 3

Fig. 2  The link-list of segmernts in tree type river structure

Fig. 3  River segments and water- rights in Example 1 (ordinary condition)

Fig. 4  River segments and water-rights in Example 2 (pump station)