**5.1 Biocomposites using tannins**

Tannins are a group of polyhydroxy phenolic compounds and exhibit good alternatives to synthetic adhesives for green chemistry in developing composites. They are found abundantly in nature. Their functions are to protect the plants against predation and might help in regulating the plant growth. Tannins are heterogeneous in nature and chemically classified into two main groups viz. hydrolysable and condensed tannins. Hydrolysable tannins are small molecular weight (30-3000D) compounds, heterogeneous in nature and hydrolysed by water, acidic or alkaline conditions into smaller water soluble molecules such as gallic acid and ellagic acid (**Figure 2a** and **b**) constituting gallotannins and ellagitannins. The gallotannins and ellagitannins comprise of a central sugar unit esterified with several molecules of

#### **Figure 2.**

*(a) Gallic acid (b) Ellagic acid (c) 5,7,3,4- tetrahydroxyflavan– 3– ol (d) 5,7,3,4- tetrahydroxyflavan– 3,4– diol (e) ABTS (2,2'-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (f) HBT (1-hydroxybenzotriazole).*

#### *Opportunity of Non-Wood Forest Products in Biocomposites DOI: http://dx.doi.org/10.5772/intechopen.97825*

gallic acid and a dimer of gallic acid as the basic phenolic unit known as ellagic acid respectively. Gallotannins, or commonly tannic acid, is the acknowledged source of the hydrolyzable tannins produced by extraction with water or organic solvents from the galls of certain trees, *Quercus infectoria* and *Rhus chinensis*, and pods from *Caesalpinia spinosa*. The European chestnut tree (*Castanea sativa*) and the oak species especially *Quercus montana* also produce hydrolyzable tannins in sufficient amount which are used in leather manufacture. Ellagitannins, a class of hydrolysable tannins produce ellagic acid on hydrolysis under acidic or alkaline conditions. Mostly these are present in angiosperms extractives. Ellagic acid and their derivatives have extensive applications as antioxidants, chelators, technical and biomedical applications. The possible applications viz. antibacterial, antifungal, antiviral, anti-inflammatory, hepato- and cardioprotective, chemopreventive, neuroprotective, anti-diabetic, gastroprotective, antihyperlipidemic, and antidepressant-like activities, among others have gained interest to researchers and reviewed for commercial exploitation [108, 109].

Condensed tannins (nonhydrolyzable tannin or proanthocyanidine) the larger polyphenol groups with high molecular weight upto 30000D compounds, form insoluble precipitates in aqueous solution and are the polymerization products of monomeric flavan–3-ol or flavan-3,4-diol precursors (**Figure 2c** and **d**) [110] which are joined through stable C-C bonds between C-4 and C-8 and between C-4 and C-6. Tannins are dynamically used in tanning of animal hides in the leather processing industry since 1960s, the beginning of the industry due to interaction and precipitation of the proteins [29], adhesive making (especially wood adhesives), fisheries, beverages manufacturing, animal feed, biosourced foams, wood preservatives, corrosion inhibitors, polyurethane surface coatings, epoxy adhesives, binders for Teflon coatings, as mineral absorption and protein, as iron gall ink production, adhesive production in wood-based industry, anti-corrosive chemical production, uranium recovering from seawater, and removal of mercury and methylmercury from solution. In continuum, tannins are also used as bioactive molecules in nutrition science, 3D printing and biomedical devices [109, 111]. Their presence in natural vegetable material has prompted scientific community for their industrial applications in many different ways. Since historical times their traditional use has allowed their further use after diverse chemical modification for various end use functionalized properties. The main inherent feature of the tannins is due to the presence of phenolic structure similar to synthetic phenols. Mostly the condensed tannins are polymers composed of falvan-3-ol monomers and are mainly extracted from bark and wood for commericial purposes. Structural diversity and functions of varied range of tannins are very well described elsewhere in the literature [112–116]. Tannins are extracted from plant material by simple methods. Nevertheless, there are various extraction processes were developed to isolate the tannins for diverse applications. However, the extraction process remains a challenge due to their heterogeneity character and compositions. Recently, various extraction processes, technological applications and their pros and cons were reviewed and appeared in leading scientific reports [117–119]. Due to similar tannin structural properties as that of synthetic phenols, the basis of wood adhesives was started in the middle of 1940s. The world first commercial wood adhesive credit goes to Australia in the 1960s using *Acacia mearnsii* (black wattle) bark tannins. The successes stories of producing tannin wood adhesive are continued till date with the advancements. The other species used in producing commercial taanins are *Pinus radiate* (radiate pine) bark [120].

Condensed tannins have been in industrial use for nearly 60 years as replacement for phenolic resins for wood based panels with high resistance against moisture and water as well as for boards with very low subsequent formaldehyde emission. Mimosa tannins, obtained from mimosa bark are usually well appreciated for its functional properties for wood adhesives. A wider industrial usage of tannins suffers from the limited availability of raw materials and high transportation costs. Only South Africa is the only actual producer of mimosa tannins on industrial scale [121]. Tannins react with formaldehyde the main crosslinker, and form hardened and crosslinked structures, similar to synthetic phenolic resins. The methylene bridges are formed between two tannin molecules. These methylene bridges are resistant to environmental factors against hydrolysis due to the strong stability of C-C bonds. Tannin-phenolic resin (tannin wt 40%) and sisal fibres (50 wt%) thermoset adhesives were successfully prepared and met all the required standards viz. Izod impact strength increased significatly. Further, it was also observed that sisal fibres and the tannin–phenolic thermosets have close values of the dispersive component and compatible interaction between the sisal fibres and the tannin–phenolic matrix at the interface [122]. A new source of tannin was also reported as a by product during catechin extraction process from a plant leaves (*Uncaria gambier*) extract and the tannin-phenol-formaldehyde wood adhesive was successfully prepared which met all the international standards [110]. Further, a new source of fibres, obtained from *Pinus roxburghii* needles, was also utilized in preparation of composites using phenolic resin adhesives [101]. Since, the early 1990s there are several scientific reports and reviews pertaining to natural fibres and tannin extracts from a natural sources viz. plants, agriculture wastes are available in the literature [122–131].


*Edited by Bibo Li*

Telomeres, located at the ends of linear chromosomes, are essential for genome stability and integrity. Advances in telomere researches have linked telomere dysfunction with cellular aging and a number of age-related human diseases. Recent studies further expanded our knowledge of telomere functions - telomeres are shown to be important for microbial pathogen virulence and telomere proteins have important non-telomeric cellular functions. This book includes current opinions on selected aspects of telomere research and their implication, in hope to help us focus better on future studies and enhance our research progress.

ISBN 978-953-51-0849-8

Reviews on Selected Topics of Telomere Biology

Photo by ustas7777777 / iStock

## Reviews on Selected Topics of Telomere Biology

**REVIEWS ON SELECTED**

**TOPICS OF TELOMERE**

**BIOLOGY**

## **REVIEWS ON SELECTED TOPICS OF TELOMERE BIOLOGY**

http://dx.doi.org/10.5772/2329 Edited by Bibo Li

#### **Contributors**

Gil Atzmon, Radhika Muzumdar, Bibo Li, Henry Bose Jr., Alla Kalmykova, Sergey Shpiz, Çığır Biray Avcı, Ajlan Tukun, Guvem Gumus-Akay, Konrad Ocalewicz, Didem Turgut Cosan, Ahu Soyocak, Arkasubhra Ghosh, Vinay Tergaonkar, Sena Aydos

#### **© The Editor(s) and the Author(s) 2012**

The moral rights of the and the author(s) have been asserted.

All rights to the book as a whole are reserved by INTECH. The book as a whole (compilation) cannot be reproduced, distributed or used for commercial or non-commercial purposes without INTECH's written permission. Enquiries concerning the use of the book should be directed to INTECH rights and permissions department (permissions@intechopen.com).

Violations are liable to prosecution under the governing Copyright Law.

Individual chapters of this publication are distributed under the terms of the Creative Commons Attribution 3.0 Unported License which permits commercial use, distribution and reproduction of the individual chapters, provided the original author(s) and source publication are appropriately acknowledged. If so indicated, certain images may not be included under the Creative Commons license. In such cases users will need to obtain permission from the license holder to reproduce the material. More details and guidelines concerning content reuse and adaptation can be foundat http://www.intechopen.com/copyright-policy.html.

#### **Notice**

Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book.

First published in Croatia, 2012 by INTECH d.o.o. eBook (PDF) Published by IN TECH d.o.o. Place and year of publication of eBook (PDF): Rijeka, 2019. IntechOpen is the global imprint of IN TECH d.o.o. Printed in Croatia

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*4.6. β-Arrestin Recruitment Assay with Pathhunter®*

This was performed as described previously [54]. In brief, U2OS OPRM1, CHO-K1 OPRD1, or U2OS OPRK1 cells were seeded at a density of 1.0 × 104 cells/well in 96-well clear-bottom white plates and incubated for 48 h. The cells were stimulated for 90 min (in the case of MOR and DOR) or 180 min (in the case of KOR) in a dilution series for each receptor at 37 ◦C under 5% CO2 and the PathHunter® working detection solution was added. The luminescence intensity was measured using FlexStation 3 (BioTek Instruments Inc., Winooski, VT, USA) for 1 h at room temperature. Data are expressed as the maximum signal intensity of each test compound as a percentage of the maximum signal intensity of the positive control.

#### *4.7. Statistical Analysis and Approval for the Study*

Data are presented as means ± SEM for at least three independent experiments. Data from cADDis cAMP assays were analyzed using one-way ANOVA followed by Tukey's multiple comparison tests. A value of *p* < 0.05 was considered statistically significant. All analyses and concentration–response curve fitting were performed using Prism 8 (GraphPad Software, San Diego, CA, USA). All experiments were approved and performed in accordance with the Guide for Genetic Modification Safety Committee, National Cancer Center, Japan.

#### **5. Conclusions**

In the present study, we showed that rubiscolins are G-protein-biased full agonists for DOR, as well as partial agonists for the MOR/DOR heteromers, with limited effects on endogenous ligands or opioid analgesics that activate MOR or KOR. Considering the evidence obtained, we believe that rubiscolins could serve as promising seeds for the development of novel, safer opioids and selective DOR agonists that can be orally used for treating pain.

**Supplementary Materials:** The following are available online, Synthesis of rubiscolin-5 and -6.

**Author Contributions:** Conceptualization, Y.U. and K.M.; validation, Yusuke Karasawa and K.M.; investigation, Y.K. (Yusuke Karasawa), T.M., Y.K. (Yui Kuroda), M.N., A.K., K.O., and M.Y.; data curation, Y.U. and K.M.; resources, H.F. and T.M.; writing—original draft preparation, Y.K. (Yusuke Karasawa); writing—review and editing, Y.U. and K.M.; supervision, H.F., K.Y., M.I., and M.H.; project administration, Y.U.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by JSPS KAKENHI Grant Numbers JP18K07404, JP18K08858, JP21K06584, and The National Cancer Center Research and Development Fund 29-A-48.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Guide for Genetic Modification Safety Committee of National Cancer Center, Japan (approval no. B85M1-17, 29 March 2017) and the Recombinant Gene Research Safety Committee of the Jikei University (approval no. D2020-050, 13 January 2021).

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The principal author and one coauthor (M.Y.) are employees of a pharmaceutical company (Viatris Pharmaceuticals Japan Inc. and Pfizer Japan Inc., respectively). However, the present study has no financial or other relationships with these companies, as it was entirely sponsored by and performed at the Jikei University School of Medicine, National Cancer Center Research Institute, and Juntendo University Graduate School of Medicine.

**Sample Availability:** Samples of the compounds are not available from the authors.

#### **References**


*3.2. Biological Evaluation*

All synthesized furan hybrids were analyzed for their in vitro hydrogen peroxidescavenging activity (HPSA), inhibition albumin denaturation (IAD), metal-chelating activity (MChA), and antitryptic activity (ATA). The results observed in vitro were contrasted with those predicted in silico. The results are presented in Table 1.

**Table 1.** Biological evaluation findings from in vitro and in silico. The IC50 values are expressed for the following activities—hydrogen peroxide-scavenging activity (*HPSA*), inhibition of albumin denaturation (*IAD*), metal-chelating activity (*MChA*), and anti-tryptic activity (*ATA*). As reference points, ascorbic acid (AA), quercetin (Qrc), ibuprofen (Ibu), and ketoprofen (Ket) were used. Lipophilicity (*RM*) is a non-dimensional quantity because it is acquired via thin-layer chromatography and is a function of *Rf*. The terms "calculated anti-inflammatory activity (*cAnti-I*)" and "calculated anti-arthritic activity (*cAnti-A*)" are expressed as Pa (probability "to be active"), and assess the likelihood that the investigated molecule is a member of the sub-class of active compounds (resembles the most typical molecular structures in a subset of "actives" in the PASS training set). The molecule with the highest level of activity has a value of 1. **H1–4**—furan derivatives.


*2.1. Materials*

Two types of samples, namely mortar and concrete samples, were mixed, and ordinary Portland cement was used in both types of samples. The fine aggregate used in the two types of samples was river sand, and the relative density of this sand was 2.62. The coarse aggregate used in concrete samples was a dolomitic limestone with a relative density of 2.65. As shown in Table 1, the mortar samples were designed to span three water to cement ratios (w/c = 0.4, 0.45 and 0.5), and the w/c of the concrete sample was fixed to 0.5 to figure out the influence of coarse aggregate on the guided wave technique.

**Table 1.** Mixture designs and setting times of mortar and concrete samples.

–not applicable.


2. Methodology

significant differences in the storage of water resources, determining a method by which to

Recently, Taiwan has been affected by climate change, which is resulting in distinct wet and dry seasons with stronger rainfall intensity in the wet season and a lack of rain in the dry season [7]. Variations in Taiwan's topography and uneven distribution of rainfall, with more in the mountains than in the plains and more in the northern than in the southern areas, are causing uneven distribution of water resources in time and space. Taiwan's annual average rainfall is up to 2500 mm, which is approximately 2.5 times more than the annual global average rainfall. Nevertheless, Taiwan is still facing a surface water shortage problem in the dry season. In southern Taiwan, which is the most serious area, the ratio of wet season rainfall and dry season rainfall is as high as 9:1 [8]. Therefore, in this study, the southern area is set as the study area to discuss what groundwater resource problems this area will be facing in the future. The water balance concept is used to explore the storage-discharge relationship, and a low flow analysis is used to assess the lowest groundwater storage in southern Taiwan. The assessment results can be provided to water resource agencies to assist with water resource management plans.

Low flow analysis, which is a hydrological method widely used to estimate hydraulic parameters, is used to characterize basin characteristics and assess groundwater storage trends. Brutsaert and Nieber [9] analyzed six basins in the Finger Lakes region of upstate New York using the lower envelope fitting method to characterize recession curves in order to estimate specific yield. Szilagyi et al. [10] pointed out that complexity of basin shape, hydraulic conductivity heterogeneity, and gently sloping impermeable layers do not affect the estimation of hydraulic conductivity and mean aquifer depth. Field-based estimates of these hydraulic parameters using a low flow analysis are a beneficial method for evaluating discharge data

Watershed properties such as hydrology, geology, and topography affect streamflow regimes [12]. Thus, through knowing the main factors dominating streamflow recession characteristics, it is possible to understand drainage systems. Zecharias and Brutsaert [13] selected 19 basins in the Allegheny Mountains of the Appalachian Plateaus to investigate streamflow recession curve characteristics, and their results showed that recession time is affected by mean basin slope, drainage density, and the ratio of the hydraulic conductivity and the specific yield. Vogel and Kroll [14] evaluated Massachusetts basin characteristics, and their result showed that recession time is highly correlated with basin area and basin slope. Brutsaert [15] suggested that streamflow recession time is highly correlated with basin area, basin elevation, and stream length. Kirchner [16] used a single-equation rainfall-runoff model to select streamflow data in order to estimate recession time from the headwaters of the Severn and Wye rivers at Plynlimon in mid-Wales. Sánchez-Murillo et al. [17] suggested that geology affects the length of recession time. Metamorphic and sedimentary rocks result in longer recession time. Low flow in flat basalt landscapes recesses rapidly. Knowing the dominating factors related to recession characteristics makes it easier to understand their effects on subsurface properties. Recently, several studies analyzed annual groundwater storage trends in order to assess water supply availability in the future. Sugita and Brutsaert [18] researched perennial groundwater storage and low flow trends in the Kanto region. If the water demand remained constant, there

that are not easily obtained, mainly in low population density area [11].

assess groundwater storage is a very important issue [6].

56 Aquifers - Matrix and Fluids

#### 2.1. Water balance concept

In a catchment, a hydrological system can be represented with the mass conservation equation:

$$\frac{dS}{dt} = P - E - Q \tag{1}$$

where S [LT�1 ] is the unit area water stored in the catchment; P [LT�1 ] is the rate of precipitation; E [LT�1 ] is the evapotranspiration rate; and Q [LT�1 ] is the unit area discharge.

Assuming that discharge is only related to storage, f(S) can be expressed as the storagedischarge relationship

$$Q = f(S) \tag{2}$$

Assuming that Q is an increasing single-valued function of S since storage-discharge function is invertible

$$S = f^{-1}(Q) \tag{3}$$

The discharge change rate through time is yielded by combining Eqs. (1) and (2)

$$\frac{dQ}{dt} = \frac{dQ}{dS} \left. \frac{dS}{dt} = \frac{dQ}{dS} \left( \left. P - E - Q \right. \right) \right| \tag{4}$$

Q is assumed to be an increasing single-valued function of S. Additionally, S cannot be directly measured, and thus dQ dS can be defined as a function of Q

$$\frac{d\mathbf{Q}}{dS} = f'(\mathbf{S}) = f'\left(f^{-1}(\mathbf{Q})\right) = \mathbf{g}(\mathbf{Q})\tag{5}$$

g(Q) refers to the streamflow sensitivity function because it expresses the sensitivity of discharge to changes in storage [16]. Because S cannot be directly measured in the catchment, combining Eqs. (4) and (5) to yield Eq. (6) solves the measurement problem of S, where discharge only has to be expressed as changes in storage

$$g(Q) = \frac{dQ}{dS} = \frac{\frac{dQ}{dt}}{\frac{dS}{dt}} = \frac{\frac{dQ}{dt}}{P - E - Q} \tag{6}$$

Precipitation, evapotranspiration, and artificial input events are excluded in the low flow conditions when groundwater storage is only related to the water flow in the river. Furthermore, mass

The Discharge-Storage Relationship and the Long-Term Storage Changes of Southern Taiwan

conservation law of hydrologic system can display as the following integral function:

relationship between groundwater storage and drainage from the catchment

from the trend of discharge in the river as the following function:

where QL7 is the annual lowest 7-day daily mean flows [LT�1

points after major events should be eliminated.

replace daily flow to reduce uncertainty

follows [21]:

eliminated.

be eliminated.

known base flow equation

2.2.2. The Vogel and Kroll (1992) model

S ¼ � ð∞ t

where S and Q are defined as Eq. (1). Substitution of Eq. (9) in Eq. (11) derives following

According to Eq. (12), the temporal trend of catchment groundwater storage can be obtained

Because daily flow varies, in this study, the annual lowest 7-day daily mean flow is used to

dt ¼ K dQL7

The long-term temporal trend of catchment groundwater storage is significant because it

Obtaining the trend in the catchment groundwater storage requires the characteristics of time scale K. In this study, a lower envelope was adopted, which is defined as roughly 5% data points below the logarithmic plot of change of flow rate data against the flow rate. In order to delete the effectiveness of precipitation, the criteria for the selection of streamflow data are as

a. Changes of flow rate are zero and positive, and sudden anomalous data should be

b. Three data points after the changes in the flow rate are zero and positive, and four data

c. Two data points before the changes in the flow rate are zero and positive should be eliminated. d. When there is suddenly a higher value of change in the flow rate in a dry period, it should

Vogel and Kroll [14] assumed discharge to be linearly related to storage. Eq. (15) is a well-

dS dt ¼ K dQ

dS

reveals whether the catchment will face a water shortage problem in the future.

Q dt (11)

http://dx.doi.org/10.5772/intechopen.73163

59

S ¼ KQ (12)

dt (13)

dt (14)

].

In a catchment, when the precipitation and evapotranspiration are much smaller than discharge, the relationship between discharge and groundwater storage can be most accurately expressed

$$\log(Q) = \frac{dQ}{dS} \approx \frac{-\frac{dQ}{dt}}{Q}\Big|\_{P \ll Q, E \ll Q} \tag{7}$$

Finally, the relationship between discharge and storage is derived from Eq. (7)

$$\int dS = \int \frac{dQ}{g(Q)}\tag{8}$$

#### 2.2. Low flow analysis

In the water balance conceptual method, Eq. (8) represents the relationship between discharge and storage. Brutsaert [21], Vogel and Kroll [14], and Kirchner [16] used low flow analysis models to select recession curves and the same method has been used in this study to characterize southern Taiwan's hydrological behaviors in order to quantify the lowest groundwater storage and to assess southern Taiwan whether facing a groundwater shortage problem in the future.

#### 2.2.1. The Brutsaert (2008) model

Low flow is a period without precipitation. In these periods, the hydrologic water flow system in the river is only related to the groundwater drainage from the aquifer in the catchment. As exponential decay type function is more commonly used to describe low flows

$$
\dot{Q} = \dot{Q}\_0 \, e^{-\frac{\ell}{\hbar}} \tag{9}
$$

where Q\_ is defined as volume of flow rate in the river [L3 T�1 ]; Q\_ 0 is the value of flow rate at arbitrarily chosen time such as t = 0 [L3 T�1 ]; and K, which is defined as the characteristic of time scale in the catchment, is also referred as the storage coefficient [T].

A power law function is used to describe the relation between the change in the flow rate and the discharge characterized hydrologic behavior in this research (e.g., Brutsaert and Nieber [9])

$$\frac{d\dot{\mathcal{Q}}}{dt} = -a\,\dot{\mathcal{Q}}^b\tag{10}$$

in which a and b are constants [�]. These constants can be characterized to display catchment hydrologic behavior [22].

Precipitation, evapotranspiration, and artificial input events are excluded in the low flow conditions when groundwater storage is only related to the water flow in the river. Furthermore, mass conservation law of hydrologic system can display as the following integral function:

$$S = -\int\_{t}^{\infty} Q \, dt \tag{11}$$

where S and Q are defined as Eq. (1). Substitution of Eq. (9) in Eq. (11) derives following relationship between groundwater storage and drainage from the catchment

$$S = KQ \tag{12}$$

According to Eq. (12), the temporal trend of catchment groundwater storage can be obtained from the trend of discharge in the river as the following function:

$$\frac{dS}{dt} = K \frac{dQ}{dt} \tag{13}$$

Because daily flow varies, in this study, the annual lowest 7-day daily mean flow is used to replace daily flow to reduce uncertainty

$$\frac{dS}{dt} = K \frac{dQ\_{L7}}{dt} \tag{14}$$

where QL7 is the annual lowest 7-day daily mean flows [LT�1 ].

The long-term temporal trend of catchment groundwater storage is significant because it reveals whether the catchment will face a water shortage problem in the future.

Obtaining the trend in the catchment groundwater storage requires the characteristics of time scale K. In this study, a lower envelope was adopted, which is defined as roughly 5% data points below the logarithmic plot of change of flow rate data against the flow rate. In order to delete the effectiveness of precipitation, the criteria for the selection of streamflow data are as follows [21]:

#### 2.2.2. The Vogel and Kroll (1992) model

g(Q) refers to the streamflow sensitivity function because it expresses the sensitivity of discharge to changes in storage [16]. Because S cannot be directly measured in the catchment, combining Eqs. (4) and (5) to yield Eq. (6) solves the measurement problem of S, where

> dQ dt dS dt ¼

In a catchment, when the precipitation and evapotranspiration are much smaller than discharge, the relationship between discharge and groundwater storage can be most accurately expressed

> dS ≈ � dQ dt

> > ð dQ

In the water balance conceptual method, Eq. (8) represents the relationship between discharge and storage. Brutsaert [21], Vogel and Kroll [14], and Kirchner [16] used low flow analysis models to select recession curves and the same method has been used in this study to characterize southern Taiwan's hydrological behaviors in order to quantify the lowest groundwater storage and to assess southern Taiwan whether facing a groundwater shortage problem in the future.

Low flow is a period without precipitation. In these periods, the hydrologic water flow system in the river is only related to the groundwater drainage from the aquifer in the catchment. As

Q\_ ¼ Q\_ 0 e

A power law function is used to describe the relation between the change in the flow rate and the discharge characterized hydrologic behavior in this research (e.g., Brutsaert and Nieber [9])

in which a and b are constants [�]. These constants can be characterized to display catchment

dQ\_

�t

exponential decay type function is more commonly used to describe low flows

where Q\_ is defined as volume of flow rate in the river [L3 T�1

time scale in the catchment, is also referred as the storage coefficient [T].

arbitrarily chosen time such as t = 0 [L3 T�1

dQ dt

P � E � Q (6)

Q j P ≪ Q,E ≪ Q (7)

g Qð Þ (8)

K (9)

]; and K, which is defined as the characteristic of

dt ¼ �a Q\_ b (10)

]; Q\_ 0 is the value of flow rate at

discharge only has to be expressed as changes in storage

2.2. Low flow analysis

58 Aquifers - Matrix and Fluids

2.2.1. The Brutsaert (2008) model

hydrologic behavior [22].

g Qð Þ¼ dQ

g Qð Þ¼ dQ

Finally, the relationship between discharge and storage is derived from Eq. (7)

ð dS ¼

dS ¼

Vogel and Kroll [14] assumed discharge to be linearly related to storage. Eq. (15) is a wellknown base flow equation

$$
\dot{Q} = \dot{Q}\_0 K\_b^t \tag{15}
$$

where {X1, X2, X3,…, Xn} is streamflow data, which are arranged in accordance with time {T1, T2, T3,…, Tn}, n is the number of data. When n is close to infinity, the probability of the S distribution curve will present as a normal distribution with a mean of 0. In addition, when n is more than 10, the variance of S can be substituted into the following approximate solution:

The Discharge-Storage Relationship and the Long-Term Storage Changes of Southern Taiwan

σ2 ¼ n nð Þ � 1 ð Þ 2n þ 5

In this study, long-term streamflow data are likely to be repeated in the data series; thus,

S � 1 σ

S þ 1 σ

When Z is a positive value, this indicates that the series is exhibiting an increasing trend; in contrast, when the value is negative, it indicates that the series has decreased. At this time, the obtained Z value should be tested by a significance test to assess whether the series is significant. Assuming, a significance level of α, if |Z|≧Zα, the null hypothesis is rejected, which represents that the series has a significant trend; whereas, the series has no significant trend. In the study, the significance level is set as α = 0.05. When |Z|≧1.96, the series has a significant

The Theil-Sen slope [25] is used to estimate the magnitude of the trend slope. The Theil-Sen slope estimation method is different from the slope values calculated using a linear regression, because it selects the median value, and therefore, the properties are less affected by extreme

> Xj � Xi j � i

X tðÞ¼ X1 � Xn , t ¼ 1 � n

� �, for all i < j (22)

values. Thus, it is often used with the MK test. Slope β is defined as follows:

X tðÞ¼ β t þ C

β ¼ Median

u¼1

, S > 0

, S < 0

0 , S ¼ 0

" #

18 n nð Þ � 1 ð Þ� 2n þ 5 X

Finally, the normalized statistical test S values become the Z value, as follows:

8 >>>>><

>>>>>:

Z ¼

Kendall modified the approximated solution Eq. (19) to Eq. (20)

σ2 ¼ 1

where u is the duplicate value number of the data series.

trend. When it is below this level, there is no significant trend.

2.4. Slope test

2.4.1. Theil-Sen slope

18 (19)

http://dx.doi.org/10.5772/intechopen.73163

(20)

61

(21)

(23)

u uð Þ � 1 ð Þ 2u þ 5

where Kb is base flow recession constant [�]. Eq. (16) is derived by Eq. (9) by comparing the Brutsaert (2008) model

$$K = -\frac{1}{\ln \mathcal{K}\_b} \tag{16}$$

Vogel and Kroll's model used a linear regression to define the characteristics of time scale K to represent average basin hydrological behavior. The Vogel and Kroll model has criteria for selection of the streamflow data as follows:

Only accept Q\_ t ≥ 0:7Q\_ t�1:

#### 2.2.3. The Kirchner (2009) model

Kirchner [16] suggested that when evapotranspiration, precipitation, aquifer recharge, and leakage are much smaller than discharge, they can be neglected. At this time, discharge is directly related to changes in storage as shown in Eq. (17) below:

$$\frac{d\mathcal{S}}{dt} = -\dot{\mathcal{Q}}\tag{17}$$

The power law equation proposed by Brutsaert and Nieber [9] is used to represent hydrological low flow analysis. Kirchner's model for streamflow criteria is simpler than the other available alternatives. It only requires the streamflow recession segment.

#### 2.3. Trend test

#### 2.3.1. Mann-Kendall test

Mann-Kendall (MK) [23, 24] test is nonparametric method developed from Kendall's tau (τ). It can be used to test the relationship between two sets of data. The advantages of this method are that the extreme values and missing data problems will not seriously affect the certification value. The MK test assesses the trend in a series via comparing the value of the series before and after to determine whether the series exhibits a specific degree of trend. The null hypothesis given that if there is not significant trend in the series, test statistic S is defined as:

$$\text{Sign}\left(\mathbf{X}\_{j} - \mathbf{X}\_{i}\right) = \begin{cases} +1 & \text{ $\mathbf{X}\_{j} - \mathbf{X}\_{i} > 0$ } \\ 0 & \text{ $\mathbf{X}\_{j} - \mathbf{X}\_{i} = 0$ } \\ -1 & \text{ $\mathbf{X}\_{j} - \mathbf{X}\_{i} < 0$ } \end{cases}, \quad \mathbf{S} = \sum\_{i=1}^{n-1} \sum\_{j=i+1}^{n} \text{Sign}(\mathbf{X}\_{j} - \mathbf{X}\_{i}) \tag{18}$$

where {X1, X2, X3,…, Xn} is streamflow data, which are arranged in accordance with time {T1, T2, T3,…, Tn}, n is the number of data. When n is close to infinity, the probability of the S distribution curve will present as a normal distribution with a mean of 0. In addition, when n is more than 10, the variance of S can be substituted into the following approximate solution:

$$
\sigma^2 = \frac{n(n-1)(2n+5)}{18} \tag{19}
$$

In this study, long-term streamflow data are likely to be repeated in the data series; thus, Kendall modified the approximated solution Eq. (19) to Eq. (20)

$$
\sigma^2 = \frac{1}{18} \left[ n(n-1)(2n+5) - \sum\_{u=1}^{} u(u-1)(2u+5) \right] \tag{20}
$$

where u is the duplicate value number of the data series.

Finally, the normalized statistical test S values become the Z value, as follows:

$$Z = \begin{cases} \frac{S - 1}{\sigma} & , S > 0 \\ 0 & , S = 0 \\ \frac{S + 1}{\sigma} & , S < 0 \end{cases} \tag{21}$$

When Z is a positive value, this indicates that the series is exhibiting an increasing trend; in contrast, when the value is negative, it indicates that the series has decreased. At this time, the obtained Z value should be tested by a significance test to assess whether the series is significant. Assuming, a significance level of α, if |Z|≧Zα, the null hypothesis is rejected, which represents that the series has a significant trend; whereas, the series has no significant trend. In the study, the significance level is set as α = 0.05. When |Z|≧1.96, the series has a significant trend. When it is below this level, there is no significant trend.

#### 2.4. Slope test

Q\_ ¼ Q\_

Brutsaert (2008) model

60 Aquifers - Matrix and Fluids

Only accept Q\_

2.3. Trend test

2.3.1. Mann-Kendall test

Sign Xj � Xi � � ¼

selection of the streamflow data as follows:

t ≥ 0:7Q\_

2.2.3. The Kirchner (2009) model

moving average beginning to increase. b. Delete 30% of the front total recession length.

t�1:

directly related to changes in storage as shown in Eq. (17) below:

available alternatives. It only requires the streamflow recession segment.

where Kb is base flow recession constant [�]. Eq. (16) is derived by Eq. (9) by comparing the

K ¼ � 1 lnKb

Vogel and Kroll's model used a linear regression to define the characteristics of time scale K to represent average basin hydrological behavior. The Vogel and Kroll model has criteria for

a. A recession range is between a 3-day moving average beginning to decrease and a 3-day

Kirchner [16] suggested that when evapotranspiration, precipitation, aquifer recharge, and leakage are much smaller than discharge, they can be neglected. At this time, discharge is

The power law equation proposed by Brutsaert and Nieber [9] is used to represent hydrological low flow analysis. Kirchner's model for streamflow criteria is simpler than the other

Mann-Kendall (MK) [23, 24] test is nonparametric method developed from Kendall's tau (τ). It can be used to test the relationship between two sets of data. The advantages of this method are that the extreme values and missing data problems will not seriously affect the certification value. The MK test assesses the trend in a series via comparing the value of the series before and after to determine whether the series exhibits a specific degree of trend. The null hypoth-

, S ¼ Xn�1

i¼1

Xn j¼iþ1

Sign Xj � Xi � �

(18)

esis given that if there is not significant trend in the series, test statistic S is defined as:

þ1 , Xj � Xi > 0 0 , Xj � Xi ¼ 0 �1 , Xj � Xi < 0

8 ><

>:

dS

0Kt

b (15)

dt ¼ �Q\_ (17)

(16)

#### 2.4.1. Theil-Sen slope

The Theil-Sen slope [25] is used to estimate the magnitude of the trend slope. The Theil-Sen slope estimation method is different from the slope values calculated using a linear regression, because it selects the median value, and therefore, the properties are less affected by extreme values. Thus, it is often used with the MK test. Slope β is defined as follows:

$$\beta = \text{Median}\left(\frac{\mathbf{X}\_j - \mathbf{X}\_i}{j - \mathbf{i}}\right), \text{ for all } \mathbf{i} < j \tag{22}$$

$$\begin{aligned} X(t) &= \beta \; t + \mathcal{C} \\ X(t) &= X\_1 \sim X\_n \; \; t = 1 \sim n \end{aligned} \tag{23}$$

#### 2.5. Change point test

#### 2.5.1. Mann-Whitney-Pettit test

The Mann-Whitney-Pettit (MWP) test [26] can be used to search for significant change points in a data series. The definition of a change point is when a data series {X1, X2,…, Xn} has a change point Xt, order {X1, X2,…, Xt} is F1(X) and {Xt+1, Xt+2,…, Xn} is F2(X), then F1(X) 6¼ F2(X). The definition of Ut,n is as shown in Eq. (24). If there is not a change point in the data series, j j Ut,n on the function of time, t will continue to rise, and there will be no turning point. On the contrary, if there is a change point, j j Ut,n on the function of time t, there will be a decreasing turning point. In the same data series, the turning point may occur several times on behalf of this data series, and there may be more than one change point

$$\text{Sign}\left(\mathbf{X}\_{i} - \mathbf{X}\_{j}\right) = \begin{cases} +1 & , \quad \mathbf{X}\_{i} - \mathbf{X}\_{j} > \mathbf{0} \\ \mathbf{0} & , \quad \mathbf{X}\_{i} - \mathbf{X}\_{j} = \mathbf{0} \\ -1 & , \quad \mathbf{X}\_{i} - \mathbf{X}\_{j} < \mathbf{0} \end{cases}, \qquad \mathbf{U}\_{t,n} = \sum\_{i=1}^{t} \sum\_{j=t+1}^{n} \text{Sign}\left(\mathbf{X}\_{i} - \mathbf{X}\_{j}\right) \tag{24}$$

$$K\_n = \text{Max} \quad |\mathcal{U}\_{t,n}| \quad , \quad 1 \le t < n \tag{25}$$

standards are used for the selection of the streamflow station. First, a streamflow station must provide long-term continuous measurement data; thus, selected stations have at least 40 years of daily flow data. Second, streamflow stations are unaffected by artificial structures such as dams. After screening, Taiwan's southern basin was determined to have six stations complying with the above two criteria. These stations are listed in Table 1 and are located in Figure 1.

The Discharge-Storage Relationship and the Long-Term Storage Changes of Southern Taiwan

http://dx.doi.org/10.5772/intechopen.73163

63

Figure 1. The location of streamflow gaging station.

order

Table 1. The characteristics of the study basins of streamflow gaging station [8].

Average elevation (m)

Bazhang River Changpan Bridge 4 309 22,547 0.31 0.05 98.34 Yanshui River Xinshi 4 49 29,402 0.14 0.06 143.4 Erren River Chungde Bridge 4 89 38,553 0.36 0.25 138.3 Gaoping River Laonong 5 1833 99,211 0.70 0.08 803.0

Linbian River Xinbei 5 692 36,815 0.49 0.10 311.4

Length of main stream (m)

Chaozhou 5 233 28,848 0.25 0.06 178.5

Average slope (m/m) Slope of main stream (m/m)

Area (km2 )

Basin Station Stream

Donggang River

To confirm that change points exist, Eq. (25) is used to calculate the extreme value of j j Ut,n that is turning point as Kn. Eq. (26) is used to calculate the probability of a change point. In this study, P = 0.95 is set as the confidence level, where P > 0.95 judges that the time is a significant changing point

$$P = 1 - \exp\left(\frac{-6K\_n}{n^2 + n^3}\right) \tag{26}$$

However, in some data series, a change point may not exist by itself; thus, Eq. (27) is used to calculate each year's P(t) value. The P(t) value is identified when it is greater than the confidence level

$$P(t) = 1 - \exp\left(\frac{-6|U\_{t,n}|^2}{n^2 + n^3}\right) \tag{27}$$

#### 3. Study area

The study area is set in southern Taiwan, including Chiayi, Tainan, Kaohsiung, and Pingtung area. The main basin includes the Bazhang River, the Jishuei River, the Cengwen River, the Yanshui River, the Erren River, the Gaoping River, the Donggang River, and the Linbian River (see Figure 1). The annual average temperature is between 22 and 26�C, and the annual average precipitation is about 2000 mm, with distinct wet and dry seasons. The precipitation is concentrated in the May to October high flow periods, and on the contrary, November to April is the low flow period, which causes the rivers to dry up in southern Taiwan [8]. Two standards are used for the selection of the streamflow station. First, a streamflow station must provide long-term continuous measurement data; thus, selected stations have at least 40 years of daily flow data. Second, streamflow stations are unaffected by artificial structures such as dams. After screening, Taiwan's southern basin was determined to have six stations complying with the above two criteria. These stations are listed in Table 1 and are located in Figure 1.

Figure 1. The location of streamflow gaging station.

2.5. Change point test

62 Aquifers - Matrix and Fluids

Sign Xi � Xj � � ¼

changing point

dence level

3. Study area

2.5.1. Mann-Whitney-Pettit test

The Mann-Whitney-Pettit (MWP) test [26] can be used to search for significant change points in a data series. The definition of a change point is when a data series {X1, X2,…, Xn} has a change point Xt, order {X1, X2,…, Xt} is F1(X) and {Xt+1, Xt+2,…, Xn} is F2(X), then F1(X) 6¼ F2(X). The definition of Ut,n is as shown in Eq. (24). If there is not a change point in the data series, j j Ut,n on the function of time, t will continue to rise, and there will be no turning point. On the contrary, if there is a change point, j j Ut,n on the function of time t, there will be a decreasing turning point. In the same data series, the turning point may occur several times on

To confirm that change points exist, Eq. (25) is used to calculate the extreme value of j j Ut,n that is turning point as Kn. Eq. (26) is used to calculate the probability of a change point. In this study, P = 0.95 is set as the confidence level, where P > 0.95 judges that the time is a significant

P ¼ 1 � exp �6Kn

However, in some data series, a change point may not exist by itself; thus, Eq. (27) is used to calculate each year's P(t) value. The P(t) value is identified when it is greater than the confi-

P tðÞ¼ 1 � exp �6j j Ut,n 2

The study area is set in southern Taiwan, including Chiayi, Tainan, Kaohsiung, and Pingtung area. The main basin includes the Bazhang River, the Jishuei River, the Cengwen River, the Yanshui River, the Erren River, the Gaoping River, the Donggang River, and the Linbian River (see Figure 1). The annual average temperature is between 22 and 26�C, and the annual average precipitation is about 2000 mm, with distinct wet and dry seasons. The precipitation is concentrated in the May to October high flow periods, and on the contrary, November to April is the low flow period, which causes the rivers to dry up in southern Taiwan [8]. Two

, Ut,n ¼ Xt

2

n2 þ n3 � �

n2 þ n3 !

i¼1

Kn ¼ Max Uj j t,n , 1 ≤ t < n (25)

Xn j¼tþ1

Sign Xi � Xj � �

(24)

(26)

(27)

behalf of this data series, and there may be more than one change point

þ1 , Xi � Xj > 0 0 , Xi � Xj ¼ 0 �1 , Xi � Xj < 0

8 ><

>:

Table 1. The characteristics of the study basins of streamflow gaging station [8].