Urban inland inundation trend early warning method based on combination of Internet of Things and GIS technology

Abstract

The invention relates to the technical field of urban inland inundation early warning, in particular to an urban inland inundation trend early warning method based on the combination of the Internet of Things and the GIS technology, and the method comprises the following steps: collecting urban infrastructure information; constructing an urban rainstorm waterlogging space-time model; constructing an urban waterlogging calculation model; a GIS and Internet of Things combined technology is adopted to collect urban basic information, the urban basic information is vectorized, and powerful data support is provided for an urban rainstorm waterlogging spatio-temporal model; data required by the model is acquired, model parameters are determined, the waterlogging trend is evaluated, and the urban waterlogging depth is inverted; on the basis of traditional waterlogging risk assessment, the waterlogging runoff production, confluence and pipe network drainage model is constructed, regional refined waterlogging trend dynamic simulation is realized, comprehensive and accurate data support is provided for the waterlogging early warning model in combination with application of the Internet of Things technology and the GIS technology, and the waterlogging risk assessment method has the advantages of being high in practicability and easy to popularize. Real-time, dynamic and accurate simulation of the depth and spatial distribution of waterlogging is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of urban waterlogging early warning, and in particular to an urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology. Background Art

[0002] Urban flood models are computer simulation tools used to simulate and predict flood phenomena caused by extreme rainfall events in urban areas. With the acceleration of urbanization, urban flooding problems are becoming increasingly serious, posing a threat to urban infrastructure and residents' lives. Therefore, urban waterlogging trend warning models have become an important technical means for urban planning, management, and flood prevention and disaster reduction.

[0003] In the prior art, the current risk assessment for urban waterlogging is basically based on open source software application algorithm evaluation. Take the SWMM waterlogging warning assessment model as an example: The construction process of the SWMM model is as follows: First, determine the Manning coefficient according to the land use type of the study area. Then divide the sub-catchment area according to the slope and road conditions of the study area, and determine the parameters of each sub-catchment area, including characteristic width, impermeability, slope and other information. Secondly, according to the generalization of the sub-catchment area and the condition of the drainage system, the length, node, burial depth and outlet of the canal are statistically calculated: After the model is generalized, it is necessary to determine the rainfall information, select the precipitation intensity suitable for the study area and synthesize the process rain line as the simulated rain gauge input, and complete the entire model according to the SWMM user manual and drainage network design standards and other information.

[0004] Because the surface runoff process in the calculation process of the SWMM waterlogging warning assessment model is too simple and cannot describe the spatial propagation process of the runoff, it cannot show the actual waterlogging situation in the city. Summary of the invention

[0005] In view of the shortcomings of the existing technology, the present invention provides an urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology, which can establish different disposal processes and mechanism systems according to different waterlogging depths, and achieve the goals of scientific early warning and rapid disposal.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: an urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology, the method comprising the following steps:

[0007] Step 1: Collect information on urban infrastructure;

[0008] Step 2: Construct a spatiotemporal model of urban rainstorm waterlogging;

[0009] Step 3: Construct an urban waterlogging calculation model.

[0010] Preferably, urban infrastructure information is collected, and basic urban information is collected using a combination of GIS and IoT technology, which is vectorized to provide strong data support for the urban storm waterlogging spatiotemporal model.

[0011] Preferably, the basic urban information at least includes: land use type, drainage network information, and rainfall temporal and spatial distribution map.

[0012] Preferably, a spatiotemporal model of urban rainstorm waterlogging is constructed: data required for the model is obtained, model parameters are determined, waterlogging trends are evaluated, and the depth of urban waterlogging waterlogging is inverted;

[0013] The specific steps of implementing the algorithm are as follows:

[0014] S1. Determination of urban rainstorm model:

[0015] For mature rainstorm processes, a rainstorm model suitable for cities is established, and the formula is as follows:

[0016]

[0017] Where: i is rainfall intensity, mm / min or L / (s·hm 2 ); T is the rainstorm return period, t is the rainfall duration, A1 is the design rainfall with a return period of 1 year; C is the rainfall variation parameter; b and c are constants, which together reflect the change of rainfall intensity under the return period;

[0018] S2. Determination of urban runoff model:

[0019] Obtain urban runoff data during a rainstorm process. The specific runoff formula is as follows:

[0020]

[0021] I a =λS

[0022]

[0023] In the above formula, Q is the runoff (mm): P is the rainfall (mm): Ia is the initial loss of the catchment area composed of plant interception, initial infiltration and filling before runoff (mm): S is the maximum possible interception after runoff occurs (mm): CN is a comprehensive parameter reflecting the characteristics of the basin before rainfall;

[0024] S3. Determination of urban catchment model: Use GIS technology to divide urban sub-catchment areas;

[0025] S4. Determination of the hydraulic model of the rainwater pipe network: The task of surface runoff calculation is to convert the net rainfall of each sub-basin into the outflow of the basin. The urban surface runoff can be solved through hydrological models and hydraulic models.

[0026] Preferably, the determination of the urban confluence model is specifically divided as follows:

[0027] S31. Determination of land use type: GIS technology is used to extract land use classification and underlying surface information from the urban land type study area, in preparation for statistical watershed parameter information, the underlying surface of the urban area is divided into four categories: buildings, vegetation, roads and rivers, and digitized under ArcGIS software. After digitization, the Statistics tool in GIS is used to perform land type area statistics, and the areas of these four underlying surfaces are obtained and counted;

[0028] S32. Establishment of digital terrain: According to different needs, digital terrain can include different contents, including digital elevation model, water flow direction, water flow accumulation, slope aspect, water flow length, sub-basin elements. The digital elevation model is the basis for establishing the digital watershed. The surface hydrology related contents of the digital elevation model are obtained through the processing and analysis functions of ArcGIS software, and the drainage volume of the catchment area pipe network is calculated:

[0029] The calculation is based on the pipe network data and rainfall duration data. The formula is as follows:

[0030] Q p =q max Δt

[0031] In the above formula, Q p is the drainage volume of the pipe network, in m3 / s, q max It represents the maximum drainage capacity of the pipe in the catchment area, in m3 / s; Δt is the rainfall duration, one of the parameters of rainfall data, in s;

[0032]

[0033] The above formula is the Manning formula calculation: n is the pipe wall roughness, d is the pipe diameter, the unit is m: S is the pipe bottom slope.

[0034] Preferably, an urban waterlogging calculation model is constructed: the steps for estimating the waterlogging depth and waterlogging range using volumetric methods such as GIS are as follows:

[0035] Using DEM data on ArcGIS platform to simulate and calculate the scope of the flooded area and the flood height of each point in the area;

[0036] Equal volume calculation algorithm:

[0037]

[0038] In the above formula: W—total water volume within the flooded area:

[0039] A—Waterlogged Area:

[0040] E w (xy)——Elevation of water surface:

[0041] E g (xy)—ground elevation:

[0042] dσ——the infinitesimal area of ​​the waterlogged area.

[0043] Preferably, considering that the flow rate of urban rainstorm waterlogging is relatively small, the water surface can be approximated and simplified for easy calculation. The water surface is approximated as a plane, and the formula is simplified to:

[0044]

[0045] In the above formula, E w To obtain a unified water surface elevation for the entire area, the entire waterlogged area A is discretized into several grid areas, and spatial interpolation is used to assign values ​​to the ground elevation grids. After discretization, the above formula can be transformed into:

[0046]

[0047] In the above formula, Δσ is the grid area, N is the total number of grids in the waterlogged area, and E g (i) is the elevation of the i-th grid, and the unknown quantities at this time are N and E w , and the N parameter can be obtained through E w and E g The relationship between the water surface elevation E and the water surface elevation E is obtained by dichotomy. w To solve.

[0048] Beneficial effects of the invention: Based on traditional waterlogging risk assessment, the invention constructs a waterlogging runoff, confluence and drainage model of the pipe network, realizes a regional refined dynamic simulation of waterlogging trends, and combines the application of Internet of Things technology and GIS technology to provide comprehensive and accurate data support for the waterlogging early warning model, realizing real-time, dynamic and accurate simulation of the depth and spatial distribution of waterlogging. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0050] Figure 1 It is the overall structure flow chart of the present invention. DETAILED DESCRIPTION

[0051] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0052] See also Figure 1, Urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology,

[0053] Step 1: Collect information on urban infrastructure;

[0054] Step 2: Construct a spatiotemporal model of urban rainstorm waterlogging;

[0055] Step 3: Construct an urban waterlogging calculation model.

[0056] Collect urban infrastructure information, use GIS and Internet of Things technology to collect basic urban information, vectorize it, and provide strong data support for the urban storm waterlogging spatiotemporal model.

[0057] The basic urban information at least includes: land use type, drainage network information, and rainfall temporal and spatial distribution map.

[0058] Constructing a spatiotemporal model of urban rainstorm waterlogging: obtaining the data required for the model, determining the model parameters, evaluating the trend of urban waterlogging, and inverting the depth of urban waterlogging.

[0059] The specific implementation algorithm is as follows:

[0060] 1. Determination of urban rainstorm model:

[0061] The urban rainstorm intensity formula mainly reflects the extreme value of rainstorms, and cannot fully describe the actual occurrence process of a rainstorm. Due to the uneven distribution of rainfall in time and space, the intensity of rainstorms will change with time. The change process of the rainfall intensity of a rainstorm over time is the rain type, which can also be expressed as a rainfall process line, which is a statistical description of the time distribution of rainfall.

[0062] For mature rainstorm processes, a rainstorm model suitable for cities is established, and the formula is as follows:

[0063]

[0064] Where: i is rainfall intensity, mm / min or L / (s·hm 2 ), T is the rainstorm return period, t is the rainfall duration, A1 is the design rainfall with a return period of 1 year, C is the rainfall variation parameter, b and c are constants, which together reflect the change of rainfall intensity under the return period.

[0065] 2. Determination of urban runoff model:

[0066] Accurately obtain urban runoff data during heavy rain. The specific runoff formula is as follows:

[0067]

[0068] I a =λS

[0069]

[0070] In the formula, Q is the runoff (mm): P is the rainfall (mm): Ia is the initial loss of the catchment area composed of plant interception, initial infiltration and filling before runoff (mm): S is the maximum possible interception after runoff occurs (mm): CN is a comprehensive parameter reflecting the characteristics of the basin before rainfall, which is related to the previous soil moisture, soil type and land use conditions. The previous soil moisture represents the sum of the rainfall 5 days before the rainfall day.

[0071] 3. Determination of urban confluence model:

[0072] When establishing an urban runoff model, the catchment area of ​​the study area needs to be divided into several catchment areas, and the differences in their hydrological characteristics need to be simplified. The model then performs hydrological simulation based on the simplified sub-catchment areas. The accuracy of the sub-catchment area division has an important impact on the accuracy of the model simulation results.

[0073] The urban sub-catchment areas are divided using GIS technology, as follows:

[0074] (1) Determination of land use type:

[0075] GIS technology is used to extract land use classification and underlying surface information from the urban land use study area, in preparation for statistical watershed parameter information. The underlying surface of the urban area is divided into four categories: buildings, vegetation, roads and rivers, which are digitized under ArcGIS software. After digitization, the Statistics tool in GIS is used to perform land use area statistics, and the areas of these four underlying surfaces are obtained and counted.

[0076] (2) Establishment of digital terrain:

[0077] According to different needs, digital terrain can include different contents, including digital elevation model, water flow direction, water flow accumulation, slope aspect, water flow length, sub-basin elements. The digital elevation model is the basis for building a digital watershed. The surface hydrology related content of the digital elevation model is obtained through the processing and analysis functions of ArcGIS software.

[0078] For example, the Hydrology module in ArcGIS is used to fill depressions, extract water flow directions in watersheds, calculate runoff accumulation, and divide sub-watersheds, while omitting the introduction and operation of hydrological analysis such as water flow length calculation and river network classification. DEM depression filling can be done using the Fill tool in the Hydrology toolset, and the DEM generated by interpolation is named depression filling (when a depression area is filled, it may form new depressions with other surrounding areas, so depression filling is an iterative process until no new depressions are generated). The flow direction can be done using the Flow Direction tool in the Hydrology toolset, and the input data is selected as the depression filling data, and the output data is named flow direction. (The direction of water flow refers to the direction in which water flows when it leaves the grid cell. It is usually represented by the 8-direction method, that is, it is represented by 8 different integers: east (1), southeast (2), south (4), southwest (8), west (16), northwest (32), north (64) and northeast (128). The direction of water flow requires the calculation of the distance weighted drop between the central grid and the adjacent grids, that is, the ratio of the elevation difference between the central grid and the neighboring grid divided by the distance between the two grids. The distance between the grids is related to the direction of water flow)

[0079] The runoff accumulation is calculated by the Flow Accumulation tool in the Hydrology toolset. The input data is the flow direction data, and the output data is named the runoff accumulation (the runoff accumulation refers to the runoff accumulation of the grid unit that can be determined by the flow direction during the surface runoff model. For each grid unit, the runoff accumulation value indicates how many flow directions there are from the upstream flowing into the grid. The larger the value, the easier it is for the area to form surface runoff. In the hydrological analysis process, if there is a DEM that has not been processed for the flow direction, that is, there are values ​​other than 1, 2, 4, 8, 16, 32, 64, and 128, the flow direction may be circular, and the runoff accumulation will enter an infinite dead loop state).

[0080] Sub-basin division uses the Basin tool in the Hydrology toolset to complete the work of sub-basin division. The input data is the flow direction data, and the output data is named Basin. (Sub-basin refers to the catchment area divided by natural watersheds. By analyzing the flow direction data of the watershed, all grids that are interconnected and in the same flow basin are determined.)

[0081] Generation of natural watershed: The sub-basin basin data is in the form of raster data. In order to facilitate the statistics and analysis of the watershed, it needs to be transformed into vector data and the vector data is merged according to the value of the basin. The processed vector basin result is the natural watershed.

[0082] 4. Determination of the hydraulic model of the rainwater pipe network:

[0083] The task of surface runoff calculation is to convert the net rainfall of each sub-basin into the outflow of the basin. Urban surface runoff can be solved through hydrological models and hydraulic models.

[0084] Calculation of drainage volume of catchment area pipe network:

[0085] Urban drainage is mainly achieved through drainage pipes buried under urban roads. The drainage capacity of the urban catchment area network describes the volume of water discharged by the network per unit time. The shape, diameter, slope, material, etc. of the buried pipes are obtained through the Internet of Things technology: The drainage capacity of the urban catchment area network refers to the maximum drainage capacity of the network in the catchment area of ​​the network inlet under a certain rainfall duration. It is calculated based on the network data and rainfall duration data. The formula is as follows:

[0086] Q p =q max Δt

[0087] In the above formula, Q p is the drainage volume of the pipe network, in m3 / s, q max It represents the maximum drainage capacity of the pipe in the catchment area, in m3 / s; Δt is the rainfall duration, one of the parameters of rainfall data, in s;

[0088]

[0089] The above formula is the Manning formula calculation: n is the roughness of the pipe wall, dimensionless: d is the pipe diameter, unit is m: S is the slope of the pipe bottom.

[0090] 3. Constructing an urban waterlogging calculation model

[0091] The urban surface runoff process is also the loss process of urban rainstorms. There are many factors that affect the rainfall loss process during the rainfall runoff process. The city's drainage capacity, surface infiltration, plant interception, evapotranspiration, and depression filling are all the main losses of rainfall runoff. When the rainfall meets the needs of vegetation interception, pipe network drainage, and depression filling, and the intensity exceeds the infiltration intensity, water begins to accumulate on the ground, forming surface runoff. At the same time, GIS technology is used to estimate the depth and range of water accumulation.

[0092] (1) According to the principle of water balance:

[0093] W 积水 =W 产流 -W 管排 ①

[0094] In the above formula, W 积水 Represents the total amount of accumulated water, W 产流Represents the total amount of water produced by rainfall after deducting various rain losses, W 管排 The total amount of rainfall discharged through the pipe network can be calculated using Q p to obtain.

[0095] (2) Using GIS equal volume method to obtain waterlogging depth and waterlogging range

[0096] Using DEM data on ArcGIS platform to simulate and calculate the scope of the flooded area and the flooded height of each point in the area; equal volume calculation algorithm:

[0097]

[0098] In the above formula, W is the total amount of water in the flooded area:

[0099] A—Waterlogged Area:

[0100] E w (xy)——Elevation of water surface:

[0101] E g (xy)—ground elevation:

[0102] dσ——the infinitesimal area of ​​the waterlogged area.

[0103] In reality, the surface of flood water in urban areas caused by heavy rain is a complex curved surface, and the surface of flood water with a high flow rate is particularly complex. Considering that the flow rate of urban flood water caused by heavy rain is relatively low, the water surface can be approximated and simplified for easy calculation, and the water surface can be approximated as a plane.

[0104] The formula simplifies to:

[0105]

[0106] ②In the formula, E w is the unified water surface elevation of the entire area. The present invention solves this value by discretizing the study area. The entire waterlogged area A is discretized into several grid areas, and the ground elevation grid is assigned using spatial interpolation. After discretization, the above formula can be transformed into

[0107]

[0108] ③In the formula, Δσ is the grid area, N is the total number of grids in the waterlogged area, and E g (i) is the elevation of the i-th grid. When the grid area is small enough, this formula is closer to the result of the above formula. The unknown quantities at this time are N and E. w , and the N parameter can be obtained through E w and E g The present invention obtains the relationship between the water surface elevation E by dichotomy. w To solve.

[0109] First, define the value range of Ew (E min , E max ), ensure that E min The value of is not greater than the minimum ground elevation of the study area, E max Not less than the sum of the maximum ground elevation and the rainfall height during this period. At this time, set E w The initial value E ave =(E min +E max ) / 2, substitute this value into the formula, and sum the grids in the entire study area. w -E g (i)>0, that is, in E w =E ave When the grid has water accumulation, W increases by [Ew-E g (i)]Δσ, and Ew-E g (i)≤0 means that there is no water accumulation in the grid and the W value does not increase. After the calculation is completed for all grids in the study area, E w =E ave The total water volume W within the flooded area under the condition of flooding is compared with the total water volume P obtained by runoff simulation. If PW>0, it means that the set water surface elevation is too low, and then the water surface elevation is reset. The specific implementation method is: min =E ave , E ave =(E min +E max ) / 2, and then recalculate E w =E ave If PW<0, it means that the set water level is too high, and then reset the water level. The specific implementation method is: E max =E ave , E ave =(E min +E max ) / 2. Through the above calculation method, the values ​​of P and W are gradually approached until the difference is less than the allowable error, and finally the water surface elevation E can be obtained. w Finally, the distribution of water accumulation in the study area is calculated. The specific method is as follows: First, the grid is judged. If E w -E g >0, it means that there is water in the grid area, and the water depth is assigned to D=E w -E g If E w -E g≤0, it means that there is no water accumulation in the grid area, and the water depth is assigned to 0. This method is used to calculate all grids in the study area once, and the water depth and spatial distribution data of the study area are obtained.

[0110] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of the present invention is defined by the attached claims and their equivalents.

Claims

1. The urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology is characterized by: The method comprises the following steps: Step 1: Collect information on urban infrastructure; Step 2: Construct a spatiotemporal model of urban rainstorm waterlogging; Step 3: Construct an urban waterlogging calculation model.

2. The urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology according to claim 1 is characterized by: Collect urban infrastructure information, use GIS and Internet of Things technology to collect basic urban information, vectorize it, and provide strong data support for the urban storm waterlogging spatiotemporal model.

3. The urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology according to claim 2 is characterized by: The basic urban information at least includes: land use type, drainage network information, and rainfall temporal and spatial distribution map.

4. The urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology according to claim 1 is characterized by: Construct a spatiotemporal model of urban rainstorm waterlogging: obtain the data required for the model, determine the model parameters, evaluate the trend of urban waterlogging, and invert the depth of urban waterlogging; The specific steps of implementing the algorithm are as follows: S1. Determination of urban rainstorm model: For mature rainstorm processes, a rainstorm model suitable for cities is established, and the formula is as follows: Where: i is rainfall intensity, mm / min or L / (s·hm 2 ); T is the rainstorm return period, t is the rainfall duration, A1 is the design rainfall with a return period of 1 year; C is the rainfall variation parameter; b and c are constants, which together reflect the change of rainfall intensity under the return period; S2. Determination of urban runoff model: Obtain urban runoff data during a rainstorm process. The specific runoff formula is as follows: I a =λS In the above formula, Q is the runoff (mm): P is the rainfall (mm): Ia is the initial loss of the catchment area composed of plant interception, initial infiltration and filling before runoff (mm): S is the maximum possible interception after runoff occurs (mm): CN is a comprehensive parameter reflecting the characteristics of the basin before rainfall; S3. Determination of urban catchment model: Use GIS technology to divide urban sub-catchment areas; S4. Determination of the hydraulic model of the rainwater pipe network: The task of surface runoff calculation is to convert the net rainfall of each sub-basin into the outflow of the basin. The urban surface runoff can be solved through hydrological models and hydraulic models.

5. The urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology according to claim 4 is characterized by: The determination of the urban confluence model is divided into the following specific categories: S31. Determination of land use type: GIS technology is used to extract land use classification and underlying surface information from the urban land type study area, in preparation for statistical watershed parameter information, the underlying surface of the urban area is divided into four categories: buildings, vegetation, roads and rivers, and digitized under ArcGIS software. After digitization, the Statistics tool in GIS is used to perform land type area statistics, and the areas of these four underlying surfaces are obtained and counted; S32. Establishment of digital terrain: According to different needs, digital terrain can include different contents, including digital elevation model, water flow direction, water flow accumulation, slope aspect, water flow length, sub-basin elements. The digital elevation model is the basis for establishing the digital watershed. The surface hydrology related contents of the digital elevation model are obtained through the processing and analysis functions of ArcGIS software, and the drainage volume of the catchment area pipe network is calculated: The calculation is based on the pipe network data and rainfall duration data. The formula is as follows: Q p =q max Δt In the above formula, Q p is the drainage volume of the pipe network, in m3 / s, q max It represents the maximum drainage capacity of the pipe in the catchment area, in m3 / s; Δt is the rainfall duration, one of the parameters of rainfall data, in s; The above formula is the Manning formula calculation: n is the pipe wall roughness, d is the pipe diameter, the unit is m: S is the pipe bottom slope.

6. The urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology according to claim 5 is characterized by: Constructing an urban waterlogging calculation model: The steps for estimating the depth and range of waterlogging using GIS and other volumetric methods are as follows: Using DEM data on ArcGIS platform to simulate and calculate the scope of the flooded area and the flood height of each point in the area; Equal volume calculation algorithm: In the above formula: W—total water volume within the flooded area: A—Waterlogged Area: E w (xy)——Elevation of water surface: E g (xy)—ground elevation: dσ——the infinitesimal area of ​​the waterlogged area.

7. The urban waterlogging trend early warning method based on the combination of Internet of Things and GIS technology according to claim 6 is characterized by: Considering that the flow rate of urban rainstorm waterlogging is relatively low, the water surface can be approximated and simplified for easy calculation. The water surface is approximated as a plane and the formula is simplified to: In the above formula, E w To obtain a unified water surface elevation for the entire area, the entire waterlogged area A is discretized into several grid areas, and spatial interpolation is used to assign values ​​to the ground elevation grids. After discretization, the above formula can be transformed into: In the above formula, Δσ is the grid area, N is the total number of grids in the waterlogged area, and E g (i) is the elevation of the i-th grid, and the unknown quantities are N and E w , and the N parameter can be obtained through E w and E g The relationship between the water surface elevation E and the water surface elevation E is obtained by dichotomy. w To solve.

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