# Simplified Lake Surface Area Method for the Minimum Ecological Water Level of Lakes and Wetlands

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Lake Surface Area Method and the Simplified Lake Surface Area Method

_{e}) and area (S

_{e}) as the lake storage and area corresponding to the point at which the slope of the S-V reaches a specified value, which is usually the ratio of maximum lake surface area to maximum lake storage (Figure 1a) [9], i.e.,

_{e}, can be determined from the H-S curve (Figure 1a) [9]. When the lake level is below the MELL, the lake surface area decreases rapidly with the decrease of the water level, which is unfavorable for lake ecosystem protection. While it is above the MELL, the lake surface area increases slowly with the increase of water level, which indicates that more water is required for a specified increase of the lake area. At the MELL, a relatively larger lake surface area can be reached at a relatively less water storage.

#### 2.2. Calculation Method

_{0}is the lowest lake level, and H

_{max}is the highest water level in its natural state. The first objective in Equation (6) is a water use objective aiming at maximum water use for humans or minimum water use for the lake ecosystem, which achieves its minimum value of 0 as the lake drying out. The second objective is a habitat protection objective aiming at maximum lake surface area, which achieves its maximum value of 0 at the maximum lake level. Consequently, the ideal point for these two objectives are (0, 0), which cannot be achieved in practice due to the contradictoriness of these two objectives. As a whole, these two objectives aim at providing maximum possible habitat for the lake ecosystem with minimum possible lake water, which expresses the tradeoff between water that is reserved in the lake for ecosystem protection and water that is used by humans.

_{1}and w

_{2}are two non-negative weights with their sum of 1. The function d(H) reaches its minimum when

_{1}= w

_{2}= 1/2) of the two objectives in Equation (6). It is more convenient to determine the MELL numerically from Equation (7). The determination of the MELL that is based on Equations (7) mainly includes the following steps:

_{i}, S

_{i}), i = 1, 2, …, n, sorted in increasing order of H

_{i}in the H-S curve, calculate the corresponding function value d

_{i}, i = 1, 2, …, n, using Equation (7).

_{i}, i = 1, 2, …, n, which is

_{k}= min {d

_{i}, i = 1, 2, …, n}

_{k}

_{−1}, d

_{k}

_{−1}), (H

_{k}, d

_{k}), and (H

_{k}

_{+1}, d

_{k}

_{+1}), the minimum point of which can be taken as an approximation of the minimum point of the evaluation function d(H) in Equation (7) based on the parabola interpolation method for univariate optimization. As a result, the MELL can be estimated numerically from

_{e}is the normalized MELL.

#### 2.3. Case Study

^{5}km

^{2}, and is discharged to the Yangtze River at Chenglingji. The Dongting Lake and the wetlands around the lake provide suitable habitats for aquatic and wetland ecosystems. However, the lake has been shrinking in the past several decades due to natural processes and human activities [3,19], which has resulted in the degradation of ecosystems and a decrease of the fishery resources. To protect the degrading lake ecosystem, it is urgent to study the MELL and the ecological water requirement for the Dongting Lake. Figure 2a shows the Chenglingji water level (H)-lake surface area (S) curve that is based on data from [19].

^{4}km

^{2}. The lake lies in an extremely arid region, with an annual precipitation of approximately 100 mm and a water surface evaporation of over 1500 mm. The lake ecosystem and the surrounding wetland ecosystem, which are fed by the lake water, are important for the local environment. However, lake shrinkage in the last several decades has led to severe ecological and environmental disasters, such as ecosystem degradation, desertification, and sandstorms [20]. The H-S curve of the Ebinur Lake [4] is shown in Figure 2b.

^{2}. It was listed as a national nature reserve in 1996 and in the Ramsar wetlands of international importance in 2002. The wetland provides suitable habitat for aquatic and terrestrial ecosystems, which includes some rare, threatened, and endangered species, such as Oriental Stork (Ciconia boyciana), red-crowned crane (Grus japonensis), white-naped crane (Grus vipio), and whooper swan (Cygnus cygnus). The water level in the wetland has dropped by over 1.0 m in recent decades, which has threatened the habitat for the wetland ecosystem. The H-S curve of the Honghe Wetland [5] is shown in Figure 2c.

## 3. Results and Discussion

#### 3.1. The Dongting Lake

^{2}/10

^{8}m

^{3}) [21], and is 1.4 m higher than the MELL of 25.0 m that was defined as the critical lake level in the H-S curve [22]. In fact, ΔS/ΔV is relatively large for lake level fluctuations under or above the latter MELL, which indicates that larger lake surface increments can be obtained at smaller water storage increments. For example, the values of ΔS/ΔV for the lake level increasing from 25.0 m to 26.0 m, 26.0 m to 27.0 m are both greater than 25% of the maximum. At the lake level of 24.6 m, 17% of the maximum lake storage provides 61% of the maximum lake surface area. While at the lake level of 26.4 m, 31% of the maximum storage provides 86% of the maximum lake surface area. When the lake level increases from 24.6 m to 26.4 m, the increase of the relative surface area (25%) is significantly greater than that of the relative lake storage (14%). When the lake level increases from 27.0 m to 28.0 m, an increase in the relative storage (9.6%) results in a smaller increase in the surface area (7.1%). From the view of marginal benefit, it is more appropriate to define the MELL as higher than the 24.6 m corresponding to the maximum value of ΔS/ΔV and lower than 27.0 m. The present value of 26.4 m lies in the interval of [24.6 m, 27.0 m], and is more appropriate to be taken as the MELL for the Dongting Lake.

#### 3.2. The Ebinur Lake

#### 3.3. The Honghe Wetland

^{0.822}(Figure 4), which is 1.78 × 10

^{8}m

^{3}, and the corresponding MELL is 52.0 m. Similar results can also be obtained from the numerical method for the lake surface area method (Figure 4). Therefore, the MELL that was determined by the simplified lake surface area method is only slightly lower than that estimated by the lake surface area method.

#### 3.4. More Discussion on the Method and Results

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sketch of (

**a**) the lake surface area method [9] and (

**b**) the simplified lake surface area method.

**Figure 3.**Water level (H)-evaluation function (d) curves for (

**a**) the Dongting Lake, (

**b**) the Ebinur Lake, and (

**c**) the Honghe wetland.

**Figure 4.**Calculation of the minimum ecological water level for the Honghe wetland using the lake surface area method: (

**a**) Water level (H)-surface area (S)-storage (V) curves [19], and (

**b**) S-V and evaluation function (d)-V curves.

No. | Lake/ Wetland | Location | Latitude and Longitude | H_{max}(m) | S_{max}(km ^{2}) | V_{max}(10 ^{8} m^{3}) | Lake Geometry Index |
---|---|---|---|---|---|---|---|

1 | Dongting Lake [19] | Northern Hunan Province, Central China | 28°44′–29°35′ N, 111°53′–113°05′ E | 33.0 | 2395.6 | 192.9 | 4.10 |

2 | Ebinur Lake [4] | Northwestern Xinjiang Uygur Autonomous Region, Northwest China | 44°34′–45°08′ N, 82°35′–83°16′ E | 195.0 | 1051.4 | 33.9 | 1.12 |

3 | Honghe Wetland [5] | Eastern Heilongjiang Province, Northeast China | 47°42′–47°52′ N, 133°35′–133°46′ E | 54.0 | 251.6 | 5.2 | 1.71 |

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**MDPI and ACS Style**

Shang, S.; Shang, S.
Simplified Lake Surface Area Method for the Minimum Ecological Water Level of Lakes and Wetlands. *Water* **2018**, *10*, 1056.
https://doi.org/10.3390/w10081056

**AMA Style**

Shang S, Shang S.
Simplified Lake Surface Area Method for the Minimum Ecological Water Level of Lakes and Wetlands. *Water*. 2018; 10(8):1056.
https://doi.org/10.3390/w10081056

**Chicago/Turabian Style**

Shang, Songpu, and Songhao Shang.
2018. "Simplified Lake Surface Area Method for the Minimum Ecological Water Level of Lakes and Wetlands" *Water* 10, no. 8: 1056.
https://doi.org/10.3390/w10081056