Inversion method of river course depth based on mathematical model and remote sensing of water depth-water surface area

An inversion method of river course depth based on a mathematical model and remote sensing of water depth-water surface area, comprising:

• step (0):
• measuring a water surface area of the river course via the remote sensing and measuring water level of the river course at hydrological stations at the river course;
• step (1):
• constructing a first mathematical model of water depth-water surface area of the river course;
• step (2):
• calculating a relation function between water flowing cross-section area and water depth as well as flow path of the river course and a relation function between area of a triangle at two sides and water depth as well as flow path of the river course based on a type of the river course, and substituting the relation functions into the first mathematical model of water depth-water surface area to obtain a second mathematical model of water depth-water surface area;
• step (3):
• transforming the second mathematical model of water depth-water surface area into a mathematical model of water level-water surface area based on a relationship between water level and water depth;
• solving unknowns in the mathematical model of water level-water surface area combined with a relationship between the water level and the water surface area obtained by the remote sensing, and substituting the unknowns into the second mathematical model of water depth-water surface area to obtain a third mathematical model of water depth-water surface area;
• and
• step (4):
• substituting water surface area extracted by the remote sensing into the third mathematical model of water depth-water surface area to obtain the water depth of the river course, and outputting the water depth of the river course;
• wherein in the step (1), the first mathematical model of water depth-water surface area is as follows:
• H
• =
• (
• ∫
• 0
• L
• A
• 1
• (
• H
• ,
• x
• )
• ⁢
• d
• ⁢
• x
• +
• ∫
• 0
• L
• (
• A
• 2
• (
• H
• ,
• x
• )
• +
• A
• 3
• (
• H
• ,
• x
• )
• )
• ⁢
• dx
• )
• /
• A
• ;
• wherein, H is the water depth, L is a length of the river course, A1(H, x) is the water flowing cross-section area;
• x is the flow path;
• A2(H, x) and A3(H, x) are the area of the triangle at two sides;
• and A is the water surface area;
• in the step (2), the type of the river course comprises a trapezoidal cross-section river course and a triangular river course;
• the relation function between the water flowing cross-section area and the water depth as well as the flow path of the trapezoidal cross-section river course is as follows:
• A
• 1
• (
• H
• ,
• x
• )
• =
• (
• w
• +
• m
• ⁢
• H
• )
• *
• H
• ;
• wherein, A1(H, x) is the water flowing cross-section area;
• w is a bottom width of the river course;
• m is a slope coefficient of the river course;
• and H is the water depth;
• the relation function between the area of the triangle at two sides and the water depth as well as the flow path of the trapezoidal cross-section river course is as follows:
• A
• 2
• (
• H
• ,
• x
• )
• =
• A
• 3
• (
• H
• ,
• x
• )
• =
• 1
• 2
• *
• H
• *
• mH
• ;
• wherein, A2(H, x) and A3(H, x) are the area of the triangle at two sides;
• the second mathematical model of water depth-water surface area of the trapezoidal cross-section river course is as follows:
• H
• =
• A
• -
• wL
• 2
• ⁢
• mL
• ;
• wherein, H is the water depth;
• A is the water surface area;
• w is the bottom width of the river course;
• L is the length of the river course;
• and m is the slope coefficient of the river course;
• the second mathematical model of water depth-water surface area of the triangular river course is as follows:
• H
• =
• A
• 2
• ⁢
• mL
• ;
• wherein, H is the water depth;
• A is the water surface area;
• m is the slope coefficient of the river course;
• and L is the length of the river course;
• based on the remote sensing, the relationship between water level-water surface area is obtained:
• based on remote sensing images, extracting the water surface area of a research area, and combining the water surface area of the research area with the measured water level at the hydrological stations during a same period as the remote sensing images to establish the relationship between water level and water surface area;
• the unknowns in the mathematical model of water level-water surface area are:
• the unknowns in the mathematical model of water level-water surface area of the trapezoidal cross-section river course are the slope coefficient of the river course m, the bottom width of the river course w, and the length of the river course L;
• the unknowns in the mathematical model of water level-water surface area of the triangular river course are the slope coefficient of the river course m and the length of the river course L.