3. Model application

acceleration, B = layer thickness, and μ, λ = Lame constants; and Δh

p

Recent Advances in Flood Risk Management

pattern of land subsidence in both time and space.

groundwater pumping model can be formulated as

2.3 Optimal groundwater pumping model

The positive value of Δh

be determined by

Chang et al. [11, 12].

surface.

24

between initial head and preconsolidation head at the end of the t-th time period.

preconsolidation head. The total land subsidence amount at the control point-k can

NL l¼1 ∑ NT t¼1

where NL, NT = the numbers of layer and time period, respectively. More detailed descriptions on the land subsidence model can be found in the studies of

In the process of developing the groundwater subsidence model for the study area, monitored data on pore pressure head and land subsidence during 2007–2009 were used to calibrate the model parameters such as hydraulic conductivity and soil compaction coefficients. Then, monitored data made in 2010–2011 were used for validation. The validated model was used to predict the cumulative land subsidence in the study area over a 10-year period during 2012–2021. Calibration and validation of pore pressure head and land subsidence in the study area were found quite satisfactory for pore water pressure and less satisfactory for land subsidence [13]. The reason might be because groundwater extraction alone is not the only cause for land subsidence. In addition, the 1D consolidation equation used in the land subsidence model cannot account for the body force and viscoelastic effects, which might have influences on land subsidence in thick aquitards. However, the validation results indicate that the simulation model can reasonably reproduce the general

Before developing a viable GWM for optimal pumping in the study area, insights were gained by applying the validated simulation model to examine the subsidence behavior under the existing pumping practice. The simulation results indicated that the levee freeboard and maximum inundation depth have a similar tendency in spatial variation affected by land subsidence. Both tend to become worsened in the near-shore low-lying area due to reduced difference between the sea level and levee crown elevation. Thus, continuing land subsidence would worsen the flood hazard in this area, and the results are consistent with those of Ward et al. [4] and Wang et al. [5]. On the other hand, outside the near-shore low-lying area, it was found that the freeboard and maximum inundation depth do not necessarily get worse. This is because the influence of the downstream boundary condition defined by the sea level is minimal. Instead, the relative variation of land subsidence in space becomes the dominant factor affecting the changes in freeboard and maximum inundation depth because it alters the slopes of drainage channels and the land

By incorporating the above insights about land subsidence—flood hazard interrelationship, an effective GWM model can be developed for reducing the undesirable pumping-induced land subsidence and flood hazard in the study area. For the near-shore low-lying area, one could reduce the land subsidence amount because flood hazard is highly related to the magnitude of land subsidence. For the region outside the near-shore low-lying area, one could reduce the relative variation of land subsidence in space to prevent flood hazard from worsening. The optimal

Δs kð Þ¼ ∑

l,k,t denotes that the initial head is higher than the

p

Δsl,k,t (3)

l,k,t = difference

To demonstrate the positive contribution of GWM to flood hazard reduction in land subsidence prone areas, the optimal groundwater pumping model developed by Chang et al. [13] is applied here to a selected study area in Taiwan.

#### 3.1 Description of the study area

The study area chosen has a catchment area of 267 km<sup>2</sup> located in the northwest part of Yunlin County, Taiwan (see Figure 3). The northern boundary of the study area is defined by the Zhuoshui River, the longest river in Taiwan, and the western boundary is adjacent to the Taiwan Strait. The study area covers nine townships and has four drainage systems consisting of Shihtsoliao, Yutsailiao, Makungtso, and Chiuhuwei. The mean annual rainfall in the study area is about 1200 mm of which about 80% of rainfall occurs between May and September due to monsoons and typhoons (see Table 3). Despite the fact that the mean annual rainfall in the study area is less than half of the average value in Taiwan (i.e., 2500 mm), the study area is still highly susceptible to flood hazard due to its low lying and flat terrain.

Figure 4 is the topographic map of the study area, which shows its ground elevation ranging from �1.0 to 28 m with reference to the mean sea level. The eastto-west average land surface gradient is less than 1/1000 indicating that the surface runoff produced by heavy rainfall can be easily trapped in the study area. Furthermore, ground elevation in the downstream part of the study area is lower than the average spring high tide of 2.1 m. This implies that flood water in the drainage channels from a rainstorm event may not be effectively drained into the Taiwan Strait due to the backwater effect.

### Figure 3. Geographical location of the study area.


Yunlin County is an important region for agriculture and freshwater fish farming in Taiwan. The two activities require a tremendous amount of fresh water, especially the latter. Due to the lack of sufficient and stable surface water supply in the area, groundwater pumping is widely used to secure fresh water. According to the record, groundwater constitutes 30% of agricultural water usage and almost 100% of domestic use in Yunlin County. Table 1 lists the average groundwater extraction and recharge for the nine townships in the study area which shows that annual average groundwater extraction significantly exceeds the annual natural groundwater recharge. Since groundwater has been excessively pumped for more than 30 years in the general area of Yunlin County, serious land subsidence problem has been created. Figure 5 shows the cumulative land subsidence during 2002–2011 in Yunlin County with negative values representing the ground elevation being

Contour map of cumulative land subsidence in 2002–2011 in the study area.

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management

DOI: http://dx.doi.org/10.5772/intechopen.80665

The study area is highly susceptible to flooding due to low lying and flat terrain. Progressive land subsidence further exacerbates flood hazard. To mitigate flood hazard in the area, the Water Resources Agency (WRA) of Taiwan had spent more than 3 billion \$NT (approx. 0.1 billion \$US) during 2006–2013 to strengthen and heighten the sea wall and levee of drainage channels, construct the polder protection system, and upgrade the pumping stations and tidal gates. Because groundwater extraction in the area was not effectively controlled and managed, the land subsidence continued to erode away the effectiveness of flood protection infra-

After the optimal pumping strategy is obtained, the right-hand branch of the analysis framework (see Figure 1) is implemented to evaluate the effect of GWM. Figure 6 shows the change in the land subsidence amount under the conditions of with and without GWM. A positive-valued change means that the land subsidence is reduced under the optimal pumping scheme. Figure 6 indicates that, while satisfying the groundwater demand of each township, the optimum pumping

3.2 Effect of optimal GWM on land subsidence and flood hazard

lowered.

Figure 5.

structure systems with time.

3.2.1 Land subsidence

27

#### Table 3.

Mean monthly rainfall amount in the study area.

Figure 4. Spatial distribution of ground elevation in the study area.

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management DOI: http://dx.doi.org/10.5772/intechopen.80665

Figure 5. Contour map of cumulative land subsidence in 2002–2011 in the study area.

Yunlin County is an important region for agriculture and freshwater fish farming in Taiwan. The two activities require a tremendous amount of fresh water, especially the latter. Due to the lack of sufficient and stable surface water supply in the area, groundwater pumping is widely used to secure fresh water. According to the record, groundwater constitutes 30% of agricultural water usage and almost 100% of domestic use in Yunlin County. Table 1 lists the average groundwater extraction and recharge for the nine townships in the study area which shows that annual average groundwater extraction significantly exceeds the annual natural groundwater recharge. Since groundwater has been excessively pumped for more than 30 years in the general area of Yunlin County, serious land subsidence problem has been created. Figure 5 shows the cumulative land subsidence during 2002–2011 in Yunlin County with negative values representing the ground elevation being lowered.

The study area is highly susceptible to flooding due to low lying and flat terrain. Progressive land subsidence further exacerbates flood hazard. To mitigate flood hazard in the area, the Water Resources Agency (WRA) of Taiwan had spent more than 3 billion \$NT (approx. 0.1 billion \$US) during 2006–2013 to strengthen and heighten the sea wall and levee of drainage channels, construct the polder protection system, and upgrade the pumping stations and tidal gates. Because groundwater extraction in the area was not effectively controlled and managed, the land subsidence continued to erode away the effectiveness of flood protection infrastructure systems with time.

### 3.2 Effect of optimal GWM on land subsidence and flood hazard

#### 3.2.1 Land subsidence

After the optimal pumping strategy is obtained, the right-hand branch of the analysis framework (see Figure 1) is implemented to evaluate the effect of GWM. Figure 6 shows the change in the land subsidence amount under the conditions of with and without GWM. A positive-valued change means that the land subsidence is reduced under the optimal pumping scheme. Figure 6 indicates that, while satisfying the groundwater demand of each township, the optimum pumping

Figure 3.

Table 3.

Figure 4.

26

Geographical location of the study area.

Recent Advances in Flood Risk Management

Annual Avg (mm) 1176.8

Mean monthly rainfall amount in the study area.

Spatial distribution of ground elevation in the study area.

Month Jan Feb Mar Apr May Jun Rainfall (mm) 19.6 35.2 50.3 78.2 159.3 269.5 Month Jul Aug Sept Oct Nov Dec Rainfall (mm) 209.5 221.6 100.8 16.7 18.1 14.8

3.2.2 Levee freeboard

DOI: http://dx.doi.org/10.5772/intechopen.80665

Figure 8.

Figure 9.

29

under the 100-year design storm.

Under the optimal GWM, Figure 8 shows the change in the freeboard after a 10 year land subsidence where the study is subject to a 100-year design rainstorm. The solid black line in Figure 8 is the contour of cumulative land subsidence over 2012– 2021 with a contour interval of 2 cm. Figure 9 further shows the histogram of the difference in the 2021 freeboard between the conditions of with and without GWM. The change with the positive value represents that the freeboard with GWM is greater than that without GWM when subject to a 100-year design rainfall. An

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management

Change in the levee freeboard after a 10-year land subsidence under the 100-year design rainstorm with GWM.

Histogram of the difference of the levee freeboard in Year 2021 between conditions of with and without GWM

Figure 6. Reduction in cumulative land subsidence due to GWM in the study area.

#### Figure 7.

Histograms of the cumulative land subsidence in 2012–2021 under the conditions of with and without GWM.

strategy could greatly reduce the land subsidence in the study area. The most reduction in land subsidence ranging from 40 to 60 cm occurs in Huwei and Tuku townships where the land subsidence was the most serious without GWM.

Figure 7 shows the histograms of cumulative land subsidence during 2012–2021 under the conditions of with and without GWM. Without GWM, the histogram on the left shows that the magnitude of land subsidence in the study area varies between 10 and 68 cm with the standard deviation of 13.8 cm. On the other hand, under the optimum pumping strategy, the histogram on the right shows that the range of land subsidence variation is greatly narrowed, and the standard deviation is reduced to 4.1 cm. Both Figures 6 and 7 indicate that the magnitude and the spatial variation of land subsidence in the study area can be significantly reduced through optimum management of groundwater pumping.

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management DOI: http://dx.doi.org/10.5772/intechopen.80665

## 3.2.2 Levee freeboard

Under the optimal GWM, Figure 8 shows the change in the freeboard after a 10 year land subsidence where the study is subject to a 100-year design rainstorm. The solid black line in Figure 8 is the contour of cumulative land subsidence over 2012– 2021 with a contour interval of 2 cm. Figure 9 further shows the histogram of the difference in the 2021 freeboard between the conditions of with and without GWM. The change with the positive value represents that the freeboard with GWM is greater than that without GWM when subject to a 100-year design rainfall. An

#### Figure 8.

Change in the levee freeboard after a 10-year land subsidence under the 100-year design rainstorm with GWM.

#### Figure 9.

Histogram of the difference of the levee freeboard in Year 2021 between conditions of with and without GWM under the 100-year design storm.

strategy could greatly reduce the land subsidence in the study area. The most reduction in land subsidence ranging from 40 to 60 cm occurs in Huwei and Tuku

Histograms of the cumulative land subsidence in 2012–2021 under the conditions of with and without GWM.

Figure 7 shows the histograms of cumulative land subsidence during 2012–2021 under the conditions of with and without GWM. Without GWM, the histogram on the left shows that the magnitude of land subsidence in the study area varies between 10 and 68 cm with the standard deviation of 13.8 cm. On the other hand, under the optimum pumping strategy, the histogram on the right shows that the range of land subsidence variation is greatly narrowed, and the standard deviation is reduced to 4.1 cm. Both Figures 6 and 7 indicate that the magnitude and the spatial variation of land subsidence in the study area can be significantly reduced

townships where the land subsidence was the most serious without GWM.

through optimum management of groundwater pumping.

Reduction in cumulative land subsidence due to GWM in the study area.

Recent Advances in Flood Risk Management

Figure 6.

Figure 7.

28

increase in the freeboard indicates overflow potential from drainage channel systems that is reduced through GWM. The most significant difference reaches 8– 10 cm which occurs in the near-shore low-lying area (see Figure 8). The results clearly indicate that GWM can prevent the levee freeboard from decreasing and thereby sustain the effectiveness of the existing flood protection system over the management period. Even if it is required to upgrade the protection level in some areas, GWM can render a smaller scale for upgrading work and lower capital cost. 3.2.4 Flood damage reduction

DOI: http://dx.doi.org/10.5772/intechopen.80665

Figure 11.

Figure 12.

31

Flood damage relationships for different agricultural produces.

Flood damage relationships for different aquacultural products.

To assess land subsidence-induced flood risk cost in the study area, representative relationships between inundation area and flood damage for several economic crops, aquacultural produces, and buildings were established and are shown, respectively, in Figures 11–13 according to past flood events. Then, by applying the flood inundation model on different land surface topographies in the study area under the conditions of with and without GWM and the design

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management

## 3.2.3 Maximum inundation depth

Figure 10 shows the difference in the maximum inundation depth in Year 2021 with and without GWM under the 100-year design rainstorm. The effect of GWM on the inundation depth is observed to be similar to that on the levee freeboard. It was found that the inundation depth in the near-shore low-lying area increases with 2021 land subsidence even with GWM. However, the range of increase is narrowed because the optimum pumping strategy greatly reduces the land subsidence in this area. The most reduction in inundation depth reaches 4–6 cm which occurs in the downstream of Yutsailiao and Chiuhuwei drainage lines (see Figure 10). The inundation depth could further be reduced if the maximum allowable land subsidence in Eq. (5) is set in a more restrictive manner. However, a more restrictive land subsidence control policy would result in a less amount of groundwater pumping which means that the current demand for the near-shore townships may not be satisfied.

Outside the near-shore low-lying area, the optimum pumping strategy can effectively prevent the inundation depth to be changed because of the reduced spatial variation of land subsidence. An exception is found at the farthest upstream from the Chiuhuwei drainage line where the inundated area grows larger with GWM because the land subsidence cone is moved to this area under the optimum pumping strategy. However, the gradient of land subsidence near this area under the condition of GWM is not as large as that of without GWM. Therefore, the increase in the inundated area would not greatly influence the flood hazard and the effectiveness of the existing flood protection system.

#### Figure 10.

Change in maximum inundation depth after a 10-year land subsidence with GWM under the 100-year design rainstorm.

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management DOI: http://dx.doi.org/10.5772/intechopen.80665

## 3.2.4 Flood damage reduction

increase in the freeboard indicates overflow potential from drainage channel systems that is reduced through GWM. The most significant difference reaches 8– 10 cm which occurs in the near-shore low-lying area (see Figure 8). The results clearly indicate that GWM can prevent the levee freeboard from decreasing and thereby sustain the effectiveness of the existing flood protection system over the management period. Even if it is required to upgrade the protection level in some areas, GWM can render a smaller scale for upgrading work and lower capital cost.

Figure 10 shows the difference in the maximum inundation depth in Year 2021 with and without GWM under the 100-year design rainstorm. The effect of GWM on the inundation depth is observed to be similar to that on the levee freeboard. It was found that the inundation depth in the near-shore low-lying area increases with 2021 land subsidence even with GWM. However, the range of increase is narrowed because the optimum pumping strategy greatly reduces the land subsidence in this area. The most reduction in inundation depth reaches 4–6 cm which occurs in the downstream of Yutsailiao and Chiuhuwei drainage lines (see Figure 10). The inundation depth could further be reduced if the maximum allowable land subsidence in Eq. (5) is set in a more restrictive manner. However, a more restrictive land subsidence control policy would result in a less amount of groundwater pumping which means that the current demand for the near-shore townships may not be satisfied. Outside the near-shore low-lying area, the optimum pumping strategy can effectively prevent the inundation depth to be changed because of the reduced spatial variation of land subsidence. An exception is found at the farthest upstream from the Chiuhuwei drainage line where the inundated area grows larger with GWM because the land subsidence cone is moved to this area under the optimum pumping strategy. However, the gradient of land subsidence near this area under the condition of GWM is not as large as that of without GWM. Therefore, the increase in the inundated area would not greatly influence the flood hazard and the

Change in maximum inundation depth after a 10-year land subsidence with GWM under the 100-year design

3.2.3 Maximum inundation depth

Recent Advances in Flood Risk Management

effectiveness of the existing flood protection system.

Figure 10.

rainstorm.

30

To assess land subsidence-induced flood risk cost in the study area, representative relationships between inundation area and flood damage for several economic crops, aquacultural produces, and buildings were established and are shown, respectively, in Figures 11–13 according to past flood events. Then, by applying the flood inundation model on different land surface topographies in the study area under the conditions of with and without GWM and the design

#### Figure 11.

Flood damage relationships for different agricultural produces.

Figure 12. Flood damage relationships for different aquacultural products.

B Tð Þ¼ j2021 InunDmg Tð ; w=o GWMj 2021Þ � InunDmg Tð Þ ; w=GWMj 2021 (8)

tion) in Year 2021 under a T-year rainstorm; InunDmg Tð Þ ; w=GWMj2021 and InunDmg T, w ð Þ =o GWMj2021 = inundation damage in the study area with and without GWM, respectively, while subject to the T-year rainstorm. Based on Figure 14(b) and (c), one can obtain Figure 14(d) showing the benefit-frequency relationship for implementing GWM in Year 2021. Then, the annual expected

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management

1

B Tð Þ j2021

where E(B|2021) = annual expected benefit of GWM for the year at the end of the 10-year management period 2012–2021. Note that land subsidence is a continuous process that progresses over the GWM period. It is anticipated that, from the initiation of GWM in Year 2012, the task will begin to accrue flood damage reduction (FDR) benefit over each individual management year with an increasing rate. The present worth of cumulative expected FDR benefit over the 10-year manage-

E Bð Þ� jt

To simplify the computation for economic merit assessment, it is assumed that the yearly FDR benefit increases linearly from zero in 2011 to E Bð Þ j2021 over a 10 year management period. That is, annual expected FDR benefit increases at an annual rate of E Bð Þ j2021 =10. With this discrete uniform gradient cash flow pattern, the present value of the total expected FDR benefit accrued over the 10-year

where UGPW nð Þ ; i = uniform gradient present worth factor, which can be com-

UGPW nð Þ¼ ; <sup>i</sup> ð Þ <sup>1</sup> <sup>þ</sup> <sup>i</sup> <sup>n</sup> � ð Þ <sup>1</sup> <sup>þ</sup> ni i 2

in which n = length of management period, that is, n = 10 in this application. According to the total inundation damage-frequency relationships shown in Figure 14(a)–(c) and Eq. (9), the estimated annual expected inundation damages for Year 2011, Year 2021 (w/o GWM), and Year 2021 (w/GWM) are 213.695, 223.527, and 218.406 M\$NT(million New Taiwan dollars), respectively. Therefore, the incremental inundation damage in Year 2021 due to pumping-induced land

1 T2

1 1 þ i

� �<sup>t</sup>�<sup>2011</sup>

<sup>10</sup> � � � UGPV nð Þ ; <sup>i</sup> (11)

ð Þ <sup>1</sup> <sup>þ</sup> <sup>i</sup> <sup>n</sup> (12)

� � dT (9)

(10)

benefit by GWM in Year 2021 can be calculated by

DOI: http://dx.doi.org/10.5772/intechopen.80665

ment period can be obtained as

quite extensive.

puted by [19]:

33

E Bð Þ¼ <sup>j</sup><sup>2021</sup> <sup>ð</sup><sup>∞</sup>

PW EB ð Þ¼ ∑

management period, PW EB ð Þ, can be computed as

PW EB ð Þ¼ E Bð Þ <sup>j</sup><sup>2021</sup>

2021 t¼2012

in which PW EB ð Þ = present worth of cumulative expected FDR benefit; E Bð Þ jt = expected FDR benefit by GWM for Year-t; and i = interest rate. The term E Bð Þ jt can be evaluated by Eqs. (8) and (9) for each individual year according to the flood inundation simulation results using the estimated land surface topography under the condition of with and without GWM. This would require hydraulic inundation simulation for each individual year, and the computation effort could be

in which B(T|2021) = benefit of GWM (in terms of inundation damage reduc-

Figure 13. Damage-inundation depth relationship for buildings in the study area.

#### Figure 14.

Flood damage-frequency relationships under different scenarios. (a) In Year 2011. (b) In Year 2021 W/o GWM. (c) In Year 2021 W/ GWM. (d) Difference between w/o and w/ GWM.

rainstorm of different frequencies, areal extent and maximum water depth of inundation can be determined. These hydraulic modeling results, jointly with land use maps and inundation-damage relationships, allow the establishment of damage-frequency relationships as shown in Figure 14(a)–(c). Figure 14(a) is derived according to Year 2011 land topography of the study area which serves as the initial condition for the 10-year GWM period. Figure 14(b) and (c), respectively, is based on Year 2021 land topography as the consequence of with and without implementing GWM. To assess the economic merit of implementing GWM, the benefit due to inundation damage reduction in Year 2021 can be obtained as the difference between inundation damage with and without GWM, that is,

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management DOI: http://dx.doi.org/10.5772/intechopen.80665

B Tð Þ¼ j2021 InunDmg Tð ; w=o GWMj 2021Þ � InunDmg Tð Þ ; w=GWMj 2021 (8)

in which B(T|2021) = benefit of GWM (in terms of inundation damage reduction) in Year 2021 under a T-year rainstorm; InunDmg Tð Þ ; w=GWMj2021 and InunDmg T, w ð Þ =o GWMj2021 = inundation damage in the study area with and without GWM, respectively, while subject to the T-year rainstorm. Based on Figure 14(b) and (c), one can obtain Figure 14(d) showing the benefit-frequency relationship for implementing GWM in Year 2021. Then, the annual expected benefit by GWM in Year 2021 can be calculated by

$$E(B|2021) = \int\_{1}^{\infty} B(T|2021) \left(\frac{1}{T^2}\right) dT \tag{9}$$

where E(B|2021) = annual expected benefit of GWM for the year at the end of the 10-year management period 2012–2021. Note that land subsidence is a continuous process that progresses over the GWM period. It is anticipated that, from the initiation of GWM in Year 2012, the task will begin to accrue flood damage reduction (FDR) benefit over each individual management year with an increasing rate. The present worth of cumulative expected FDR benefit over the 10-year management period can be obtained as

$$PW(EB) = \sum\_{t=2012}^{2021} E(B|t) \times \left(\frac{\mathbf{1}}{\mathbf{1} + i}\right)^{t - 2011} \tag{10}$$

in which PW EB ð Þ = present worth of cumulative expected FDR benefit; E Bð Þ jt = expected FDR benefit by GWM for Year-t; and i = interest rate. The term E Bð Þ jt can be evaluated by Eqs. (8) and (9) for each individual year according to the flood inundation simulation results using the estimated land surface topography under the condition of with and without GWM. This would require hydraulic inundation simulation for each individual year, and the computation effort could be quite extensive.

To simplify the computation for economic merit assessment, it is assumed that the yearly FDR benefit increases linearly from zero in 2011 to E Bð Þ j2021 over a 10 year management period. That is, annual expected FDR benefit increases at an annual rate of E Bð Þ j2021 =10. With this discrete uniform gradient cash flow pattern, the present value of the total expected FDR benefit accrued over the 10-year management period, PW EB ð Þ, can be computed as

$$PW(EB) = \left(\frac{E(B|2021)}{10}\right) \times UGPV(n, i) \tag{11}$$

where UGPW nð Þ ; i = uniform gradient present worth factor, which can be computed by [19]:

$$UGPW(n,i) = \frac{(\mathbf{1} + i)^n - (\mathbf{1} + ni)}{i^2(\mathbf{1} + i)^n} \tag{12}$$

in which n = length of management period, that is, n = 10 in this application.

According to the total inundation damage-frequency relationships shown in Figure 14(a)–(c) and Eq. (9), the estimated annual expected inundation damages for Year 2011, Year 2021 (w/o GWM), and Year 2021 (w/GWM) are 213.695, 223.527, and 218.406 M\$NT(million New Taiwan dollars), respectively. Therefore, the incremental inundation damage in Year 2021 due to pumping-induced land

rainstorm of different frequencies, areal extent and maximum water depth of inundation can be determined. These hydraulic modeling results, jointly with land use maps and inundation-damage relationships, allow the establishment of damage-frequency relationships as shown in Figure 14(a)–(c). Figure 14(a) is derived according to Year 2011 land topography of the study area which serves as the initial condition for the 10-year GWM period. Figure 14(b) and (c), respectively, is based on Year 2021 land topography as the consequence of with and without implementing GWM. To assess the economic merit of implementing GWM, the benefit due to inundation damage reduction in Year 2021 can be obtained as the difference between inundation damage with and without GWM,

Flood damage-frequency relationships under different scenarios. (a) In Year 2011. (b) In Year 2021 W/o

GWM. (c) In Year 2021 W/ GWM. (d) Difference between w/o and w/ GWM.

that is,

32

Figure 14.

Figure 13.

Damage-inundation depth relationship for buildings in the study area.

Recent Advances in Flood Risk Management

subsidence over a 10-year management period of with and without GWM are, respectively, 9.833 and 4.712 M\$NT. The benefit of GWM in Year 2021 associated with the expected FDR in the study area is E Bð Þ¼ j2021 9:833 � 4:712 ¼ 5:121 M\$NT. Assume that the interest rate is 4.5% and the annual expected benefit by GWM follows a linear increasing pattern from 0 (in Year 2011) to 5.121 M\$NT (by Year 2021), the value of the uniform gradient present worth factor in Eq. (12) is UGPW nð Þ ¼ 10; i ¼ 4:5% = 32.74. The corresponding present worth of the total benefit by GWM accrued in the study area over the 10-year GWM, by Eq. (11), is 16.768 M\$NT or equivalent to an annual benefit of 2.119 M\$NT amortized in 10 years. Conflict of interest

Nomenclature

No potential conflict of interest is present in this chapter.

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management

E Bð Þ jt expected FDR benefit by GWM in Year-t

lying area

lying area

NT number of groundwater management period NUC number of control points outside near-shore low-

Q j ð Þ ; t pumping rate at the j-th well during the t-th time

QDð Þt groundwater demand during the t-th time period <sup>Q</sup><sup>L</sup>ð Þ <sup>j</sup>; <sup>t</sup> minimum pumping rates at the j-th well during the t-

α the ratio of elastic to inelastic compaction per unit increase in drawdown Δsl,k,t land subsidence within layer-l at point-k during the t-th time period Δhl,k,t drawdowns of layer-l, point-k at the end of the t-th

l,k,t difference between initial head and preconsolidation

end of the management period

Δs(•) cumulated land subsidence at control points at the

Δs\*(•) maximum allowable land subsidence at control

head at the end of the t-th time period

points at the end of the management period

th time period <sup>Q</sup><sup>U</sup>ð Þ <sup>j</sup>; <sup>t</sup> maximum allowable pumping rates at the j-th well during the t-th time period

lying area

period

UGPWð Þ∙ uniform gradient present worth factor

time period

ρ<sup>w</sup> density of water

μ, λ Lame constants

Δh p

35

area NL number of layers in groundwater aquifer

NP number of pumping wells

InunDmg Tð Þ ; w=GWMjt inundation damage in the study area with GWM

InunDmg T, w ð Þ =o GWMjt inundation damage without GWM while subject to the T-year rainstorm kuc the kuc-th control point outside the near-shore low-

kc the kc-th control point within the near-shore low-

NC number of control points inside near-shore low-lying

while subject to the T-year rainstorm

B layer thickness

DOI: http://dx.doi.org/10.5772/intechopen.80665

i interest rate

g gravitation acceleration

By comparing the total amount of inundation damage amount in the study area (in the order of 200 M\$NT annually), the GWM benefit associated with FDR does not appear to be very impressive. This might be due to a relatively short management period of 10 years. For sustainable GWM, the period of management would generally be longer and it can be easily shown, by a similar analysis described above, that the economic benefit of GWM in terms of flood damage reduction would grow with the management period. Furthermore, Figure 8 clearly shows that implementing GWM in the land subsidence prone area can sustain the design flood protection level of drainage systems by preventing the freeboard from decreasing. This implies that potential huge saving in the capital cost can be realized because the lower levee height in many parts of the study area would be sufficient if an effective GWM policy is in the place. Also, the maintenance cost for levee systems could be reduced as fewer existing levee segments require height upgrading because the mandated freeboard can be upheld or even improved by GWM.

### 4. Conclusions

Groundwater is an important source of water supply, especially in regions where surface water supply is insufficient or not stable. However, the lack of proper management for groundwater extraction and usage in land subsidence prone areas could create a number of undesirable consequences such as damaging building structures, aggravating flood inundation hazards, and diminishing effectiveness of flood control facilities. This chapter presents a methodological framework demonstrating how a subsidence-focused GWM model can be formulated and applied to obtain an optimal pumping strategy that reduces the negative impact of land subsidence in a coastal region in western Taiwan which is experiencing serious land subsidence and associated flood hazards. Numerical results clearly show that, through the use of an optimal GWM model with an explicit consideration given to subsidence control, one is able to ease off uneven land surfaces and reduce seriousness of land subsidence and flood damage as well as sustain the flood protection level of drainage systems by maintaining a suitable freeboard. All these features provide strong evidence that GWM can play an important role, along with other engineering measures, in providing a sustainable solution to flood inundation problem in land subsidence prone areas.

## Acknowledgements

This study was support by the Water Resources Planning Institute, Water Resources Agency, Ministry of Economic Affairs of Taiwan.

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management DOI: http://dx.doi.org/10.5772/intechopen.80665
