1) Reservoirs

The reservoir storage capacity varies from time to time and depends on inflow, evaporation, and release through the hydropower plants and via bottom outlets and spillways (Sokolov & Chapman, 1974) . The reservoirs are described by the following water balance equations:

S t + 1 = S t + a t + 1 − r t + 1 − E t + 1

E t + 1 = e t + 1 S ( S t )

r t + 1 = R ( S t , u t , a t + 1 , e t + 1 )

in which:

S_t, S_t+1 (m³): the reservoir storage capacity at time t and t + 1.

a_t+1 (m³): the inflow including precipitation on the reservoir surface.

r_t+1 (m³): the release from the reservoir to downstream through turbines and spillways or bottom outlets; the release volume depends on storage capacity, inflow, release, evaporation of the reservoirs and the requirements of the operation rules.

E_t+1 (m³): the evaporation volume of the reservoirs in the time step t to t + 1; e_t+1: daily evaporation rate; S_(St): the reservoir surface.

2) Hydropower plants

The three parameters, i.e., upstream and downstream water heads, discharge via turbines and energy production are related reflecting in the formula:

p = γ g η H q 10 6

in which:

p (MW): power generation capacity of the turbines.

H (m): difference of upstream and downstream water heads.

q (m³/s): discharge via turbines.

γ water weight and g acceleration of gravity.

The turbine performance η can be presented as a function of (q, H) or (p, H); each type of turbines has its own specific routing hydrograph built to reflect the working scope and performance of the turbines.

The water balance model WEAP—a product of the Stockholm Environment Institute (SEI), is applied to depict the water use system at the upstream multipurpose reservoirs including Son La, Hoa Binh, Thac Ba, and Tuyen Quang (Figure 5).

3) Downstream water uses

The Red-Thai Binh River Delta are one of the complex water transport and use systems. The system includes rivers, intake structures and canals in the hydraulic work systems.

· River flows:

The river water transport can be simulated by describing the system of Saint Vernant equations:

∂ Q ∂ x + ∂ A ∂ t = q

∂ Q ∂ t + ∂ ( α Q 2 A ) ∂ x + g A ∂ h ∂ x + g Q | Q | C 2 A R = 0

in which:

Q: discharge;

A: areas where flows happen;

c: Chezy resistance coefficient;

R: hydrodynamic radius or drag;

Q: momentum distribution coefficient.

MIKE, the mathematical model developed by the Danish Hydraulic Institute (DHI) is used to simulate river flows. The dry season hydraulic model of the Red and Thai Binh river systems is simulated with 34 rivers and cross-sections updated to 2021; 13 upstream boundaries and 37 lateral-flows as flows from upstream and along the rivers; 9 downstream boundaries as the water level at the estuaries. Among the above 13 upstream boundaries are the releases from the 3 large-scale reservoirs including Hoa Binh, Thac Ba and Tuyen Quang (see Figure 6). The most important problem of the Red-Thai Binh River downstream is the fact that the river section is increasingly being incised, causing disequilibrium to the system and lowering the water level in most rivers.

· Water supply schemes:

There are 349 water intake structures that are simulated in the model, including sluices and pumping stations for 28 irrigation districts. The pumping stations are usually located behind the sluices under the dykes except for some submersible pumping stations that intake water directly from the rivers. The water intake flows of the structures depend on the dimension of the structures and the river water level, which is described as follows:

If Z_s > Z_đ then Q = f(Z_s, Z_đ, Q_tk)

On contrary Q = 0

In which:

Q (m³/s): water abstraction discharge of the structure;

Z_s (m): Water level upstream of the structure (river water level);

Z_đ (m): Water level downstream of the structure (on-farm water level);

Q_tk (m³/s): Designed discharge of the structure corresponding to Z_s = Z_tk;

Z_tk (m): Designed water level of the structure;

Function f of each structure is built and described corresponding the to correlation Q = f(Z_s) and incorporated into the model.

1) Hydropower

Electricity of Vietnam (EVN) sets the goal of the industry as to operate and provide safe, stable and reliable electricity to the national power system, in not only ensuring energy security but also minimizing production costs.

Regarding the Red-Thai Binh River system, all relevant studies as well as practice prove that EVN’s goal is to reduce the output of hydropower plants in the first months of the dry season to save water for the end of the dry season. The reason lies in the fact that although the water head is high at the beginning of the dry season, the electricity demand is not as high as at the end of the season. It is proved that at the end of the dry season most of the energy in the national power system is supplied by the thermal power plants, while the cost of hydropower generation is lower according to the data analysis from the electricity production plan of the year 2021 (MIT, 2020) .

EVN’s goal is to increase the economic efficiency of not only one power plant but the entire power system. To be able to analyze the economic efficiency, it is necessary to estimate the economic price of hydroelectricity over time of the year. The value of each KWh of electricity in each month varies due to the different supply-demand relationship of the months. The share of value per KWh generated by hydropower plants can be calculated based on the share of electricity produced each month of the year by all thermal power plants based on alternative cost method (Figure 7).

The economic price of hydroelectricity is calculated as follows:

c i = θ i ⋅ C

in which:

c_i: converted price of electricity of month i^th.

θ_i: the share of electricity generated in each month of all thermal power plants of month i^th.

C: the annual average price of electricity.

Given such approach, the converted monthly price of electricity varies from the lowest of about VND 1000 in February and September to the highest of about VND 1400 in May (Figure 8).

The hydroelectricity index applied in the study is the economic loss of energy produced in the year of 4 reservoirs: (Hoa Binh, Son La, Thac Ba, and Tuyen

Quang), calculated as follows:

T p = ∑ i = 1 12 c i ⋅ ( D i − E i )

In which:

T_p: economic loss of electricity of the system in the year.

c_i: price of electricity at month i^th.

D_i: total electricity demand of the inter-reservoir system at month i^th.

E_i: total electricity output of the inter-reservoir system at month i^th.

2) Water supply for agriculture

Water supply for the winter-spring crop is the most stressful period due to the seasonal lack of rain, especially in January and February when most provinces simultaneously prepare land, and sow and plant rice. Although many structural measures such as rehabilitation of pumping stations and non-structural measures such as the development of an increased annual water release plan have been used, water shortages still occur frequently in recent years and tend to increase.

According to the design of the water abstraction system and the state of the river bed in the past (from 2004 backward), the water level of 2.5 m at Hanoi can ensure normal operation of the entire downstream water supply structures. However, in recent years, with the riverbed topography continuously changed and according to calculations from the hydraulic model, the water level at Hanoi must be 3.5 m to ensure water abstraction for the upstream of Hanoi.

The goal set by the Ministry of Agriculture and Rural Development is to provide irrigation water for the entire cultivated land, which not only ensures food security but also minimizes losses due to reduced agricultural output and irrigation costs. The irrigation industry index applied in the study is the economic loss of agricultural production:

T a = ∑ i = 1 25 f ( F i , R i , D i )

In which:

T_a: losses to agricultural production due to irrigation water shortage downstream.

F_i: Agricultural land affected by water shortage.

R_i: Irrigation requirement of the irrigation district i^th.

D_i: Water volume supplied to the irrigation district i^th.

f: the function of productivity loss of each irrigation district depends on the water deficit in each development stages of crop. The function of productivity loss that simulated the linear relation of productivity, maximum crop yield coefficient and evapotranspiration, specifically as follows (Hanks & Hill, 1980) :

1 − Y a Y m = K y ⋅ ( 1 − E t a E t m )

in which:

Y_a: actual crop yield.

Y_m: maximum crop yield.

K_y: crop yield coefficient during the growing stages.

Et_a: actual evapotranspiration.

Et_m: potential evapotranspiration.

3) Domestic water supply

Domestic water supply structures are designed at the probability of 95% (MARD, 2022a) that is higher than that of agricultural water supply structures (85%). The domestic water supply works have not been significantly affected when the river water level is low. However, since 2021, the water intake structures feeding for the Da River clean water plant (the water plant that supplies 700,000 m³/day for the western parts of Hanoi capital) has faced with difficulty intaking water. At the beginning of the dry season in 2022, the plant could not get water and had to build 2 temporary pumping stations to pump water from the deeper water in the middle of the river to the shore and then from the shore to the storage.

The water supply industry’s objective is to ensure a stable water supply for people’s daily life and especially in the Hanoi capital area, minimize damage caused by lowered river water level. The water supply sector index applied in the study is the economic loss of drinking water supply:

T w = ∑ i = 1 n d ⋅ ( D i − W i )

In which:

T_w: loss due to water shortage to the water plant.

n: number of water plants.

D_i: water demand of the water plant i^th, depending on the river water level.

W_i: Water volume that can be supplied to the water plant i^th.

d: unit price of bulk water.

4) Navigation

For navigation, the minimum water level required at Long Bien station is 1.1 m (MoT, 2009) . The goal of the navigation industry is to ensure safety and limit disruption to navigation.

When the water level at Hanoi falls below the navigable threshold, the Ministry of Communication and Transport conducts dredging of the river bed in the most critical sections. The cost of this type of intervention depends on the water level in the river, so it should be considered, as an indicator:

· Cost of dredging:

T t = ∑ i = 1 34 d ⋅ V i

In which:

T_t: Dredging cost (VND billion) of the 34 downstream navigation routes to ensure accessibility.

i: navigation route i^th.

d: unit cost of dredging (VND billion/m³).

V_i: Volume to be dredged (m³).

In addition to the incurred dredging costs, the number of days when the water level is low also causes difficulties for the operation of water transport means:

· X_t1.1: Number of days in the year when the water level at Long Bien, Hanoi station is lower than the navigable threshold [day]

X t 1.1 = { 1     h t H N < 1.1   m 0       otherwise

When the water level at Hanoi falls below the discontinuity threshold of 0.4 m, transport on the Red River becomes complete standstill, so the following sub-indices should also be considered when analyzing the scenarios:

· X_t0.4 Number of days in the year when the water level at Long Bien, Hanoi station is lower than the discontinuity threshold [day]

X t 0.4 = { 1     h t H N < 0.4   m 0       otherwise

5) Environment

In order to protect the ecological environment of rivers and wetlands, all hydraulic works must release, or discharge downstream a minimum volume of water corresponding to a probability of 90% (Q_90%) in dry season (MARD, 2022a) .

Calculated results of salinity concentration at the estuaries according to different discharge levels from the reservoir and the water level at Hanoi (Nguyen et al., 2021) show that it is necessary to maintain a flow at Son Tay of 2500 m³/s in order to ensure salinity repulsion for intaking water during land preparation period.

During the rest of the dry season, only 1100 m³/s is enough to push saline water for water intaking, so the prevention thresholds are set at 2500 m³/s and 1100 m³/s and the following indices are determined to monitor compliance with these thresholds (IWRP, 2012) :

· Index of environmental requirement during the increased water release period: number of days when inflows to Son Tay is below 2500 m³/s

X e 2500 = { 1     Q t S T < 2500 0       otherwise

· Index of environmental requirement during the normal period:

X e 1000 = { 1     Q t S T < 1100 0       otherwise

Given the status quo of deeply incised riverbed, the water level at Hanoi maintained during the release periods cannot be met as required by the Operation Rules 740 (see Table 1 and Figure 9). Although the required release volume increases according to the scenarios but the release duration is limited in just 3 times, the total amount of water intaken into the systems is still of 17% deficit

(KB6). This is because the stressful period of water use lasts from January to March, but the increased reservoirs release only happens in 15 - 20 days and the capacity of hydraulic works cannot intake enough water in such a short duration to feed for the remaining 2 months. Thus, it is necessary to increase the release duration as well in order to reduce the amount of water shortage downstream.

1) Hydropower

Power output is the lowest at 30.97 million MWh in KB1—base flow release and the highest at 32.99 million MWh in KB4—actual release in 2021. However, in terms of economics with electricity prices varying by month, the power output in KB2—release according to electricity demand—is the highest and higher than that of KB1 and KB6 about VND 2600 billion/year and VND 1600 billion/year, respectively.

2) Water supply for the downstream

In terms of water supply for agriculture, the proportion of downstream cultivated areas affected by water shortage gradually decrease from 28% in KB1 to 17% in KB6. Productivity loss due to water shortage is estimated at about VND 5.6 to 9.4 trillion and the difference of agricultural loss between KB2 and KB6 is about VND 3750 billion (see Figure 10).

For navigation, the volume to be dredged increases from 160,000 m³ in KB6 to 256,000 m³ in KB1. Damage caused by lowered water level that leads to compulsory dredging is about VND 38 to 61 billion depending on the scenarios. The dredging volume is the smallest in KB4 with release according to reality in 2021, and bigger in KB5 and KB6 because the release in KB5 and KB6 is concentrated in the increased release period and is less than that in KB2 and KB4 in normal release period.

3) Economic analysis

Calculations of benefits and losses of the relevant sectors shows that there is an imbalance between the benefits of electricity generation and the reduction of

downstream water supply losses. Economic benefits from electricity generation is much larger than those of downstream agricultural production. This is why the economic optimization method should not be used to analyze and select the operation rules. Thereby, the study applied the scenario analysis method to choose reasonable release alternatives.

In the scenarios, the mean water level at Hanoi varies in the range of 0.45 to 3.29 m during the increased release periods. Economic analysis reveals that although KB2 gives the best energy economic efficiency, the overall economic efficiency of all downstream industries increases gradually from KB2 to KB6 though the increase is not much. Considering the efficiency of power generation along with the goal of ensuring energy security (saving water for the end of the dry season, beginning of the flood season), KB2 is selected. However, for downstream economic sectors, especially agricultural production, KB6 should be chosen to ensure water supply during the increased release period.

The use of a large amount of water in January and February (as in KB5 and KB6) will affect water security for the rest of the dry season as well as energy security in the hot weather at the beginning of the rainy season as besides the release through maximum power generation in those scenarios, bottom outlet release is sometime required that should rarely happen. The scenario that could harmonize the stakeholders’ benefits would range from KB2 (no increased release) to KB4 (release via maximum power generation).

Given the present channel incision, the irrigation industry cannot afford to invest in rehabilitating and upgrading hydraulic works to meet the new conditions, then the KB4 is said to be the scenario that brings benefits harmony among the sectors. KB4 is the actual operation scenario in 2021 that has been agreed between representatives of the two largest water users, the Ministry of Industry and Trade (EVN) and the Ministry of Agriculture and Rural Development (Directorate of Water Resources).