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Interconnected Channel and Pond Routing Model
ICPR began as a 1D hydrologic and hydraulic (H&H) model more than 35 years ago with a focus on modeling hydraulically interconnected and interdependent pond systems. Hydrodynamic channel and pipe flow were added in the late 1980s. In 2008, a quasi-2D groundwater module was added (PercPack) which was our first foray into integrated surface water – groundwater modeling. Our latest generation of ICPR, released in 2014, includes both 1D H&H and fully integrated 2D surface water and groundwater flow with an emphasis on interactions between surficial aquifer systems and surface water bodies. 

1D Surface Flow

The computational framework for one-dimensional modeling in ICPR4, is the 'Link-Node' concept.

2D Overland Flow

Two-dimensional overland flow is based on a flexible triangular computational mesh. The mesh generation is fully automated and relies on graphical mapping features including surface DEMs, thematic polygon maps, and features.

2D Groundwater

The focus of the groundwater module is the surficial aquifer and its interaction with surface water bodies. It includes seepage between the ground surface and the surficial aquifer as well as vertical leakage through a confining layer. Seepage and leakage are bi-directional. Spatiotemporal boundary conditions can be applied below the confining layer.

1D Surface Flow

There are three primary building blocks in ICPR4: Nodes, Links and Basins. The computational framework is formed from these building blocks for the 1D portion of ICPR4 and the approach is often referred to as a “Link-Node” modeling concept. 
Nodes are placed at strategic locations in the drainage network. Elevations are calculated at nodes based on inflows, outflows and storage characteristics. Water is moved from node to node via links such as pipes, channels, weirs, pumps, and bridges among others. The full St. Venant equations are used for channel and pipe flow. Energy and diffusive wave options are also available. 

Stormwater runoff can be calculated using traditional unit hydrographs if desired, and delivered to any node in the model. Several options are available for infiltration losses and rainfall excess computations including the curve number method, the Green-Ampt method, and a vertically layered kinematic method. 

ICPR4 includes a number of optional tools to help expedite 1D model construction. These tools extract data from map and surface layers. For example, a breakdown of soil and land cover combinations for each catchment area can be automated inside ICPR4. Channel cross sections can be extracted from a ground surface DEM, as well as storage characteristics for lakes, detention ponds, and wetland depressions.
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2D Overland Flow

ICPR4 uses the finite volume method for 2D overland flow computations. This technique is based on a double mesh where momentum equations are lumped along triangle edges and the mass balance equations are lumped into irregular shaped polygons (“the honeycomb”) formed around the triangle vertices. Water surface elevations are calculated at the triangle vertices and water is moved from polygon to polygon along the triangle edges.
Mesh generation is fully automated, including parameterization. For example, the honeycomb mesh is intersected with land use zones and soil zones to form a set of sub-polygons. Direct rainfall is applied to and infiltration losses calculated for each sub-polygon. Rainfall excess is summed by honeycomb and delivered to its respective triangle vertex.
The triangular mesh and corresponding honeycomb are flexible and unstructured, allowing the mesh to grow and shrink as needed to capture critical areas in the drainage system. 
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2D Groundwater

The 2D groundwater module in ICPR4 is based on the finite element method with a 6-point quadratic triangular element.

  • Heads Calculated at Nodes
  • Saturated Horizontal Flow
  • Seepage at Ground Surface
  • Leakage Through Confining Layer

The focus of the groundwater module is the surficial aquifer and its interaction with surface water bodies. It includes seepage between the ground surface and the surficial aquifer as well as vertical leakage through a confining layer. Seepage and leakage are bi-directional. Spatiotemporal boundary conditions can be applied below the confining layer.  Like the surface, a honeycomb is formed around the vertices of the triangular computational mesh. But unlike the surface, the honeycomb is also formed around mid-nodes.

The surface and groundwater honeycombs are intersected with one another and with soil zones, impervious zones and rainfall zones. The result is a set of sub-polygons, each having a surface ID, a groundwater ID and soil, land cover and rainfall station attributes.

Rainfall excess for any sub-polygon is delivered to the corresponding surface node and recharge is delivered to its associated groundwater node.  Surface and groundwater meshes do not have to be aligned. 
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ICPR4 Features

Models from Maps
Although it is possible to work in schematic mode for 1D projects, ICPR4’s full power is realized through its georeferenced graphic system. Models are constructed and parameterized directly from various types of maps. 

Computational meshes are automatically generated from graphical elements that: (1) characterize the terrain; (2) interface with 1D components; and, (3) establish boundary conditions. The mesh is then intersected with surfaces (e.g., terrain) and thematic polygon map layers. 

The thematic polygon maps further refine the mesh into subsets of soil zones, impervious zones, roughness zones, and rainfall zones among others.
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Flexible Mesh
The 2D computational framework for ICPR4 is based on a flexible unstructured triangular mesh. This approach allows the mesh to shrink where detail is needed and to grow in less critical areas. The result can be orders of magnitude fewer computational cells than a square cell mesh without loss of detail in critical areas. And, fewer cells mean less computational effort, faster run times, and smaller output files.
The 1D H&H module of ICPR4 is fully integrated with the 2D overland flow module. Both 1D and 2D equations are solved simultaneously eliminating awkward numerical handoffs between modules. Storm inlets and underground pipe systems are easily incorporated into the model.
  • Detailed 1D/2D Urban Flood Study
Graphical Elements
A variety of graphical elements are included in ICPR4 that allow you to customize and finesse mesh construction. The graphical elements are categorized as follows: 

  • Terrain Characterization
  • Interface with 1D Elements
  • Establish Boundary Conditions

For example, breaklines are used to define local ridges and valleys. A triangle edge is guaranteed along the breakline, and as mentioned, flow occurs along triangle edges. Strategic placement of a breakline can prevent artificial blockage along flow paths or tunneling through a ridge.

There are a total of 18 2D overland flow graphical elements. These can be drawn manually inside ICPR4, or imported from shapefiles.

Various groundwater graphical elements are used to aid in groundwater mesh construction, similar to overland flow.  Irrigation wells and drains (tile drain or roadway underdrain) can be included in your groundwater project. An exclusion graphic element can be used to model a fully penetrating retaining wall. Boundary conditions can be specified at a point, along a line, or over an area (polygon). Both stage and flow boundary conditions are possible
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Water Surface Profiles
Water surface profiles can be animated along any user defined 1D link path. The profile appears as a “dry” condition until you select a particular simulation. Once the simulation is selected, you can animate the profile using the video play options. 
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The typical way to review results for 2D modeling is with animations. ICPR4 includes a wide selection of possible animations for 2D overland flow including flow and velocity vectors, depth of flow, maximum depth of flow and water surface elevations among others.

Animations can be viewed in “play mode” or you can manually step through them. You can also go directly to a specific point in time. Most animations can be paused and then exported by simply right-clicking on the animation view.
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Groundwater Results
Like overland flow, there is a wide variety of reports and animations available for analyzing the groundwater results. 

Here is an example of a proposed commercial site with 2 retention ponds that rely on percolation for storage recovery. There is a river south and east of the site and groundwater flow is toward the river. Fluctuating water levels in the river automatically become known head conditions for the groundwater model.

Groundwater elevations at hour 120 are shown above. Cross section A–A’ depicts ground elevations, the initial water table and the water table at 120 hours, 4 days after the rain stopped.

Aggregate seepage amounts between the river and the adjacent water table are shown to the right. The river rises faster and higher than the adjacent water table. Consequently, a portion of the river flow seeps from and into the water table. Later, as the river subsides, there is seepage from the water table into the river.

Section B–B’, through the two ponds, indicates that they have not fully recovered after 120 hours.
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