CROSSREFERENCE TO RELATED APPLICATIONS

The present application relates to commonlyowned, copending U.S. patent application Ser. No. ______, filed ______, entitled METHODS, SYSTEMS AND COMPUTER PROGRAM STORAGE DEVICES FOR GENERATING A RESPONSE TO FLOODING (Docket Number YOR920090382US1), the entire contents and disclosure of which is incorporated by reference as if fully set forth herein.
BACKGROUND

The present disclosure relates generally to methods, systems and computer program storage devices for generating a flooding forecast.

In one specific example, the present disclosure relates generally to methods, systems and computer program storage devices for generating a flooding forecast for an urban environment.

In another example, a fully conservative model may be utilized that allows employing an unstructured hybrid grid (1dimesional/2dimensional) to represent an urban area, where the 1dimesional grid is a simplified representation of part of the domain.

Flooding, and especially flash floods, often create conditions that slow traffic and cause major congestion and delays on expressways, highways, and other regional transit systems. Moreover, urbanization, shifts in land use patterns and related changes in surface permeability have reduced the ability for the ground to absorb precipitation, which lowers the peak runoff and causes an increase in the likelihood of a flood.

In the recent past, severe storms have impacted several large cities around the world, producing floods and significant property damage due to the lack of adequate flood warning systems. Such problems have occurred in major cities around the world. For example, the New York City metropolitan area was impacted by a mesoscale convective system (“MCS”) in August 2007, with rainfall exceeding three inches in less than two hours in some areas. The subway system was partially closed due to flooding, streets were impassable, and over two and a half million people and numerous businesses were affected. A similar flooding event happened in July of 2007 in London. The flooding significantly impacted the Underground transportation system during the evening rush hour leading to the closing of many tube stations and forcing riders to utilize overcrowded buses.

In the United States, average annual flood losses have nearly tripled since 1950 from $1.5 billion to more than $4 billion. In the 1990s alone, average annual flood losses have exceeded $7 billion. Between 1995 and 1999 alone, flood damage topped $40 billion. In the United Kingdom, flood damage during the summer of 2007 exceeded 3.2 billion British Pounds.

Due to climate change it is likely that heavy and highly variable precipitation events will increase in frequency in regions already vulnerable to flooding events. Coastal regions will also be at an increased risk for flooding as sea levels rise and the frequency of coastal storms increases. The cost associated with the damage from flooding is likely to rise and the number of people affected by flooding will increase.
DESCRIPTION OF RELATED ART

U.S. Pat. No. 7,136,756 relates to a realtime hydrologic modeling system to determine the hydrologic properties of a selected geographic region. In a preferred embodiment, a drainage network of individual cells is created for the geographic region. The outflow of a selected cell within the drainage network is determined by solving the runoff from cells upstream of the selected cells until the flow of all upstream cells is known. The flow value of a cell is based upon factors such as runon, infiltration, and precipitation. In another embodiment the outflow of a selected cell is determined by setting simulated flow rates to equal measured flow rates at observation points upstream of the selected cell and within the drainage network. The flow rates of cells upstream of the observation points are adjusted proportionally based on hydrologic quantities of runoff, precipitation and drainage area to determine the outflow of the selected cell.

U.S. Pat. No. 7,039,565 relates to a hydraulics software system for a onedimensional hydrodynamic numerical model for modeling unsteady flows in sewer and storm water urban drainage systems. The inventive software uses as a numerical model, an implicit fourpoint, finitedifference solution technique to solve the onedimensional SaintVenant equations. The software is designed to select that numerical model, or equation that best describes, or best exhibits the behavior of each of the various structures and flows encountered in complex hydrodynamic systems such as a sewer and storm water drainage systems. Local partial initial modification for subcritical and supercritical transcritical flows is provided. Relaxation for pipe/channel networks are included for achieving computational performance and robustness for commercial software for practical use in water resource engineering.
SUMMARY

The present disclosure relates generally to methods, systems and computer program storage devices for generating a flooding forecast.

In one specific example, the present disclosure relates generally to methods, systems and computer program storage devices for generating a flooding forecast for an urban environment.

In one embodiment, a method for generating a flooding forecast is provided, the method comprising: maintaining a representation of a geographical region, the representation comprising: (a) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (b) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portion, in such a manner that the first and second portions together form a single mixed mesh; and providing at least one water level prediction responsive to the modeling.

In another embodiment, a program storage device readable by machine, tangibly embodying a program of instructions executable by the machine for generating a flooding forecast is provided, the program of instructions, when executing, performing the following steps: maintaining a representation of a geographical region, the representation comprising: (a) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (b) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portion, in such a manner that the first and second portions together form a single mixed mesh; and providing at least one water level prediction responsive to the modeling.

In another embodiment, a computerimplemented system for generating a flooding forecast is provided, the system comprising: a storage element that stores a representation of a geographical region, the representation comprising: (a) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (b) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; a modeling element in operative communication with the storage element, the modeling element modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portion, in such a manner that the first and second portions together form a single mixed mesh; and an output element in operative communication with the modeling element, the output element outputting at least one water level prediction responsive to the modeling.
BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a block diagram of a system according to one embodiment.

FIG. 2 depicts a block diagram of a system according to one embodiment.

FIG. 3 depicts a diagram showing parameters employed in the ShallowWater Model, where L>>h.

FIG. 4 depicts a diagram showing mesh elements in xy and ξη spaces.

FIG. 5 depicts a diagram showing a hybrid mesh (which comprises 1dimensional grid elements and 2dimensional grid elements) according to one embodiment

FIG. 6 depicts detail of a portion of the diagram of FIG. 5 showing various controlvolumes in the hybrid mesh (this relates to a numerical discretization and integrated approach).

FIG. 7 depicts a block diagram of a workflow process architecture (related to a hydrological aspect) according to one embodiment.

FIG. 8 depicts example water velocity vectors according to one embodiment (showing a continuous velocity field).

FIG. 9 depicts a block diagram of an architecture according to one embodiment.

FIG. 10 depicts a block diagram of a method according to one embodiment.

FIG. 11 depicts a block diagram of a system according to one embodiment.

FIG. 12 depicts a block diagram of a system according to one embodiment.
DETAILED DESCRIPTION

For the purposes of description the term “realtime” is intended to refer to a system having a response to a given input or event that occurs approximately contemporaneously in time (e.g., without significant time lag between input and system response but not necessarily instantaneously)

For the purposes of description the term “fully conservative model” is intended to refer to numerical methods used to discretize continuous equations of transport which mimic the conservation property of the transported entity at a discrete level.

For the purposes of description the term “single mixed mesh” is intended to refer to a combination of two different kinds of elements (linear and triangular) into a unique numerical mesh. FIG. 5 is an example of a single mixed mesh comprising lines and triangles that represent the streets and central park in Manhattan. FIG. 6 also shows an example of a single mixed mesh (which mixes or combines two or more types of shapes, or elements).

In one embodiment, a hydrological model may be utilized that employs unstructured grids of triangles in a conservative approach to model the surface flow in cities. In one example, this model may be coupled to a realtime data feed from both NEXRAD radar and surface stations to simulate precipitation impact on utilities infrastructure and/or meteorological model outputs. The integrated model may be designed to forecast flooding events with sufficient lead time to allow business and/or or cities to make critical operational decisions.

In another embodiment, flood modeling in urban areas may be simplified by employing 1dimensional grid elements (with a reduction of computational effort and essentially without any loss of generality).

In one example, such 1dimensional grid elements may be used to model streets, underground pipes/pipelines and/or electrical circuits.

In another example, a fully conservative model may be utilized that allows employing an unstructured hybrid grid (1dimesional/2dimensional) to represent an urban area, where the 1dimesional grid is a simplified representation of part of the domain.

Referring now to FIG. 1, this Fig. shows a system according to one embodiment. This system includes a user interface 101, a processor 102, and databases 103. This system may be used to provide various functions and features described herein.

Referring now to FIG. 2, this Fig. shows a system (a hydrometerological system) according to one embodiment (see, Novakovskaia E., Mello U., Treinish L., 2009: An Integrated HydroMeteorological System for Flood Forecasting in the New York City Metropolitan Area. Second TriState Conference. Western Connecticut University. April 2009, which is incorporated by reference herein). The hydrometeorological system of FIG. 2 comprises a mesoscale meteorological model 201 based on the Weather Research and Forecasting system (WRF) 202. The hydrometeorological system also comprises the Watson Hydrological Model (WHM) 203. The meteorological model 201 provides quantitative precipitation forecasts (QPF) (see element 204) to the hydrological model 203. In one embodiment, the hydrological model 203 may also use radarderived quantitative precipitation estimates (QPE) (see element 204) as inputs. These precipitation inputs are the main link between the two models in the hydrometerological system. The hydrometeorological system may also include additional coupling mechanisms between the models such as a change in evaporation rate during the diurnal cycle or a change in the surface characteristics of flooded areas. The mesoscale meteorological model 201 and the hydrological model 203 are calibrated separately based on observations 205, 206 and past forecasts 207, 208.

A further description of the WRF model is available in Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, M. Duda, XiangYu Huang, W. Wang, and J. G. Powers, 2008: A description of the Advanced Research WRF Version 3. NCAR Tech Notes475+STR, which is incorporated by reference herein. In the Skamarock study, initial conditions and boundary conditions (IC/BC) were based on North American Mesoscale model (NAM), which is also known as the Eta Model.

One example of a structure of a quantitative precipitation forecast (QPF) can be found in D. Leuenberger, F. Laudanna del Guerra and A. Rossa, Application of an empirical quality function for radar QPE in an NWP model, ERAD 2010—The Sixth European Conference on Radar in Meteorology and Hydrology, Jun. 30, 2010. In one specific example, a map of reflectivity may be used to estimate an amount of rain. In this regard, traditional reflectivitybased QPE algorithms typically relate radar reflectivity factor (Z) to rain rate (R). However, the equation relating Z to R varies according to the drop sizes distribution of the rain in the volume of interest, which can vary widely from one event to another. Zbased algorithms are sensitive to radar calibration. The standard (nontropical) ZR relation used by the WSR88D is Z=300R^{1.4}.

For the simulation of overland flow the governing equations include the equation for conservation of mass and the equations for the conservation of momentum, such as 3D NavierStokes equations (see, e.g., An introduction to fluid dynamics. G. K. Batchelor,. frs,. London (Cambridge University Press), 1967). In the cases where eddy viscosity and/or density variations are important (e.g. spatial variation of salinity and temperature) the full 3D model is employed. However, in most cases of practical importance vertical effects are negligible, so that one can integrate the continuity and the momentum equations over the depth, applying appropriate boundary conditions at the bottom and the free surface, to obtain the twodimensional Shallow Water Equations. In one example, writing the vector equation explicitly (Cartesian coordinates):

$\rho \ue8a0\left(\frac{\partial u}{\partial t}+u\ue89e\frac{\partial u}{\partial x}+v\ue89e\frac{\partial u}{\partial y}+w\ue89e\frac{\partial u}{\partial z}\right)=\frac{\partial p}{\partial x}+\mu \left(\frac{{\partial}^{2}\ue89eu}{\partial {x}^{2}}+\frac{{\partial}^{2}\ue89eu}{\partial {y}^{2}}+\frac{{\partial}^{2}\ue89eu}{\partial {z}^{2}}\right)+\rho \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{g}_{x},\text{}\ue89e\rho \ue8a0\left(\frac{\partial v}{\partial t}+u\ue89e\frac{\partial v}{\partial x}+v\ue89e\frac{\partial v}{\partial y}+w\ue89e\frac{\partial v}{\partial z}\right)=\frac{\partial p}{\partial y}+\mu \left(\frac{{\partial}^{2}\ue89ev}{\partial {x}^{2}}+\frac{{\partial}^{2}\ue89ev}{\partial {y}^{2}}+\frac{{\partial}^{2}\ue89ev}{\partial {z}^{2}}\right)+\rho \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{g}_{y}$
$\rho \ue8a0\left(\frac{\partial w}{\partial t}+u\ue89e\frac{\partial w}{\partial x}+v\ue89e\frac{\partial w}{\partial y}+w\ue89e\frac{\partial w}{\partial z}\right)=\frac{\partial p}{\partial z}+\mu \left(\frac{{\partial}^{2}\ue89ew}{\partial {x}^{2}}+\frac{{\partial}^{2}\ue89ew}{\partial {y}^{2}}+\frac{{\partial}^{2}\ue89ew}{\partial {z}^{2}}\right)+{\mathrm{\rho g}}_{z}.$

The continuity equation reads:

$\frac{\partial \rho}{\partial t}+\frac{\partial \left(\rho \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89eu\right)}{\partial x}+\frac{\partial \left(\rho \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89ev\right)}{\partial y}+\frac{\partial \left(\rho \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89ew\right)}{\partial z}=0.$

A further assumption employed in diffusion models is the neglect of the advective term. This assumption is used in several studies in the literature (see, e.g. Hromadka II, T. V. and Yen, C. C., 1987, A Diffusion Hydrodynamic Model (DHM), U.S.G.S. Water Resources Special Report 874137; Lal, W., 2005. Regional Simulation Model (RSM): Theory Manual, South Florida Water Management District (SFWMD), Office of Modeling (OoM), Web: http://www.sfwmd.gov/site/sub/m_rsm/pdfsksmtheoryman.pdf#RSM_Theory; Kolditz, O., Delfs, J. O., Beinhorn, M., and Bürger, C. M., 2006. A compartment approach for hydrosystem analysis based on objectoriented principles, ZAG, University of Tuebingen, Tuebingen, Germany. GeoSysPreprint [200622], Center for Applied Geosciences, University of Tübingen.; Sudicky, 2006—all three of these articles being incorporated by reference herein).

Ponce et al. (1978) analyzed the applicability of diffusion models compared to complete Shallow Water equations and concluded that the larger the bed slopes and the longer the wave period the more applicable is the diffusion model. Often overland flows occur in larger bed slopes. Jordan (2003) has shown that acceleration (inertia) terms sum to nearly zero for Froude numbers less than 4. Thus, it is a reasonable assumption for the application case studied here, since most of the analyzed domain is not very steep.

Integrating the conservation equations vertically over the depth of the flow (h), as shown in FIG. 3 (where length L>>h), which is delimited by the elevation of the surface of the water, δ, and the bathymetry of the ground, ζ, the mass conservation and momentum conservation equations can result in a single diffusive equation. See, Randall, D. A., 2006, The Shallow Water Equations, Selected Papers, Department of Atmospheric Science, Colorado State University, Fort Collins, Colo., web: http://kiwi.atmos.colostate.edu/group/dave/pdf/ShallowWater.pdf

$\begin{array}{cc}\frac{\partial h}{\partial t}=\frac{\partial}{\partial x}\ue89e\left({\mathrm{hk}}_{x}\ue89e\frac{\partial \left(h+\u03db\right)}{\partial x}\right)+\frac{\partial}{\partial y}\ue89e\left({\mathrm{hk}}_{y}\ue89e\frac{\partial \left(h+\u03db\right)}{\partial y}\right)+Q\ue89e\text{}\ue89e\mathrm{Where}& \left(1\right)\\ {k}_{i}=\frac{{h}^{2/3}}{{n}_{i}\ue89e{\uf603\partial \left(h+\u03db\right)/\partial s\uf604}^{1/2}}& \left(2\right)\end{array}$

and index i refers to x and y coordinates.

The other relevant parameters present in previous equations are the roughness coefficient (n_{i}), and the source/sink terms.

Q=R−I−E±C (3)

comprising rainfall (R), infiltration (I), evaporation (E), and canals (C). The slope of water surface gradient in Eq. (2) is given by

$\begin{array}{cc}\partial \left(h+\u03db\right)/\partial s=\partial H/\partial s=\sqrt{{\left(\frac{\partial \left(h+\u03db\right)}{\partial x}\right)}^{2}+{\left(\frac{\partial \left(h+\u03db\right)}{\partial y}\right)}^{2}}& \left(4\right)\end{array}$

Reference will now be made to an example numerical approximation. In this work the numerical solution of Eq. (1) is obtained using a variation of the Control Volume Finite Element (Patankar, 1980), in which the approximate equations are obtained by integrating the divergent form of the partial differential equation over nonoverlapping control volumes, which are the dual elements of the of the numerical mesh elements. In unstructured meshes, the control volumes are formed by joining lines from the barycenter of a triangle to the median edges (faces) using the information of the node definition (mesh nodes) and the connectivity matrix.

In this method the equations can be solved in the computational domain using a standard element—linear or triangular in local coordinates (ξ) or (ξ, η), respectively. This procedure allows each element to become independent of other elements. In addition, each element is treated equally, no matter how distorted the element may actually be in terms of the global coordinates. FIG. 4 shows examples of linear and triangular elements in xy and ξη spaces. The domain of local coordinate system (ξ, η) is defined as shown in FIG. 4. In the same figure it is shown also the location of the nodes and their numbering sequence. One can note that the nodes are numbered from 1 to NNE in counterclockwise direction where NNE is the number of nodes per element (2 for linear edge segments and 3 for triangles). Using a general procedure the total water level, as well as other variables of interest, can be approximated over the entire domain in terms of shape functions N_{j }and the values of the variable at nodes, that is,

$\begin{array}{cc}h+\u03db=\sum _{j=1}^{\mathrm{NNE}}\ue89e{N}_{j}\ue8a0\left(\xi ,\eta \right)\ue89e{\left(h+\u03db\right)}_{j}& \left(5\right)\end{array}$

where the aforementioned local shape functions are defined for triangles according to

N _{1}(ξ,η)=1−ξ−η (6)

N _{2}(ξ,η)=ξ (7)

N _{3}(ξ,η)=1−η (8)

and for edges according to:

N _{1}(ξ)=1−ξ (9)

N _{2}(ξ)=ξ (10)
In (5)

$h+\u03db=\sum _{j=1}^{\mathrm{NNE}}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{N}_{j}\ue8a0\left(\xi ,\eta \right)\ue89e{\left(h+\u03db\right)}_{j}$

j is an index. If NNE is equal to (for example) 3, the equation would expand to

$h+\u03db=\sum _{j=1}^{3}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{N}_{j}\ue8a0\left(\xi ,\eta \right)\ue89e{\left(h+\u03db\right)}_{j}={N}_{1}\ue8a0\left(\xi ,\eta \right)\ue89e{\left(h+\u03db\right)}_{1}+{N}_{2}\ue8a0\left(\xi ,\eta \right)\ue89e{\left(h+\u03db\right)}_{2}+{N}_{3}\ue8a0\left(\xi ,\eta \right)\ue89e{\left(h+\u03db\right)}_{3}$

Since the shape functions are continuous within elements they can be differentiated. Thus, the components of the water depth gradient can be determined as follows:

$\begin{array}{cc}\frac{\partial \left(h+\u03db\right)}{\partial x}\ue89e{}_{\xi ,\eta}=\sum _{j=1}^{\mathrm{NNE}}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e\frac{\partial {N}_{j}}{\partial x}\ue89e{}_{\xi ,\eta}\ue89e{\left(h+\u03db\right)}_{j}& \left(11\right)\\ \frac{\partial \left(h+\u03db\right)}{\partial y}\ue89e{}_{\xi ,\eta}=\sum _{j=1}^{\mathrm{NNE}}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e\frac{\partial {N}_{j}}{\partial y}\ue89e{}_{\xi ,\eta}\ue89e{\left(h+\u03db\right)}_{j}& \left(12\right)\end{array}$

Note that Eqs. (11) and (12) require the x and y derivatives of the shape functions. These derivatives can be related to the ξ and η derivatives using the chain rule

$\begin{array}{cc}\frac{\partial {N}_{j}}{\partial \xi}=\frac{\partial {N}_{j}}{\partial x}\ue89e\frac{\partial x}{\partial \xi}+\frac{\partial {N}_{j}}{\partial y}\ue89e\frac{\partial y}{\partial \xi}& \left(13\right)\\ \frac{\partial {N}_{j}}{\partial \eta}=\frac{\partial {N}_{j}}{\partial x}\ue89e\frac{\partial x}{\partial \eta}+\frac{\partial {N}_{j}}{\partial y}\ue89e\frac{\partial y}{\partial \eta}& \left(14\right)\end{array}$

or in a matrix form:

$\begin{array}{cc}\left[\begin{array}{ccc}\frac{\partial {N}_{1}}{\partial \xi}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial \xi}\\ \frac{\partial {N}_{1}}{\partial \eta}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial \eta}\end{array}\right]=\left[\begin{array}{cc}\frac{\partial x}{\partial \xi}& \frac{\partial y}{\partial \xi}\\ \frac{\partial x}{\partial \eta}& \frac{\partial y}{\partial \eta}\end{array}\right]\ue8a0\left[\begin{array}{ccc}\frac{\partial {N}_{1}}{\partial x}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial x}\\ \frac{\partial {N}_{1}}{\partial y}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial y}\end{array}\right]& \left(15\right)\end{array}$

where the derivatives in relation to η apply only for 2D elements. Manipulating the previous equation, one can show that the global derivatives (∂N_{j}/∂x and ∂N_{j}/∂y) are given by

$\begin{array}{cc}\left[\begin{array}{ccc}\frac{\partial {N}_{1}}{\partial x}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial x}\\ \frac{\partial {N}_{1}}{\partial y}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial y}\end{array}\right]={\left[J\right]}^{1}\ue8a0\left[D\right]& \left(16\right)\end{array}$

where [D] is a matrix containing the local derivatives of shape functions, and [J] is the Jacobian matrix of the transformation, given, respectively, by

$\begin{array}{cc}\left[D\right]=\left[\begin{array}{ccc}\frac{\partial {N}_{1}}{\partial \xi}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial \xi}\\ \frac{\partial {N}_{1}}{\partial \eta}& \dots & \frac{\partial {N}_{\mathrm{NNE}}}{\partial \eta}\end{array}\right]\ue89e\text{}\ue89e\mathrm{and}& \left(17\right)\\ \left[J\right]=\left[\begin{array}{cc}\frac{\partial x}{\partial \xi}& \frac{\partial y}{\partial \xi}\\ \frac{\partial x}{\partial \eta}& \frac{\partial y}{\partial \eta}\end{array}\right]& \left(18\right)\end{array}$

Therefore, substituting Eq. (16) into (11) and (12), the expression that determines the water depth gradient at any point within a finite element becomes

[∇(h+ζ)]=[J] ^{−1} [D]{h+ζ} _{e} (19)

where {h+ζ}_{e }is the vector of nodal water level values (dimension of NNE), and [J] is the Jacobian transformation matrix, already defined in Eq. (18), which can be easily calculated by

$\begin{array}{cc}\left[\nabla \left(h+\u03db\right)\right]=\frac{1}{2\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89eA}\ue8a0\left[B\right]\ue89e{\left\{h+\u03db\right\}}_{e}& \left(20\right)\end{array}$

and for one dimensional edge elements

$\begin{array}{cc}\left[\nabla \left(h+\u03db\right)\right]\xb7\overrightarrow{n}=\frac{1}{\Delta \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{s}_{12}}\ue8a0\left[{\left(h+\u03db\right)}_{2}{\left(h+\u03db\right)}_{1}\right]& \left(21\right)\end{array}$

where A is the total area of the triangular element, ΔS_{12 }is the length of the line joining points 1 and 2, {right arrow over (n)} is the unit vector oriented in the direction of mesh line [1,2], and

$\begin{array}{cc}\left[B\right]=\left[\begin{array}{ccc}{b}_{1}& {b}_{2}& {b}_{3}\\ {a}_{1}& {a}_{2}& {a}_{3}\end{array}\right]& \left(22\right)\end{array}$

with

a _{k} =x _{j} −x _{i } i,j,k=1,2,3 (23)

b _{i} =y _{j} −y _{j } i,j,k=1,2,3 (24)

Since linear interpolation of {h+ζ} is assumed for triangular and edge elements, a constant gradient value is obtained in each element. This numerical method is well studied in the literature and discussion on this method is out of the scope here. More details can be obtained, for example, in Raw, M, 1985, A New Control Volume Based Finite Element Procedure for the Numerical Solution of the Fluid Flow and Scalar Transport Equations, Ph.D. Thesis, University of Waterloo, Waterloo, Ontario, Canada; and Cordazzo, J., 2006, Petroleum reservoir simulation using the Elementbased Finite Volume Method and Algebraic Multigrid, Ph.D. Thesis in Portuguese, Federal University of Santa Catarina, Brazil, both of which are incorporated by reference herein.

Reference will now be made to an example of discretized equations and complex geometries representation As seen in FIG. 5 (showing a number of streets and including Central Park in Manhattan Island, N.Y. City) at a metropolitan area scale most of the streets can be sufficiently represented by 1dimensional line elements, since the flow depth variation over their width can be negligible. Even pipelines can be taken into account with this approach. In areas where 1dimensional dimensionality of flow is not expected, for example, in parks, 2dimensional elements can be employed.

Mixing of 1dimensional/2dimensional elements by preprocessing can be done to create a hybrid (that is, mixed) mesh. FIG. 6 (depicting detail of a part of FIG. 5) shows two controlvolumes, i and j built around 1dimensional and 2dimensional mesh elements respectively. Inside the elements there are some points 601, 602 where the flux is evaluated. These points are located at the midpoints of controlvolumes edges and are called integration points. In accordance with a finite volume method, the domain is divided into control volumes, where the governing equations, Eq. (1), are integrated. The Gauss divergence theorem is then applied where the surface integration is performed over all edges of the control volumes. This integral is evaluated using a midpoint approximation in each edge, which results in

$\begin{array}{cc}\frac{\Delta \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{S}_{P}}{\Delta \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89et}\ue89e{\left(h{h}^{o}\right)}_{P}\sum _{\mathrm{ip}}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{\left[\frac{{\left(h\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e\lambda \right)}^{\mathrm{uds}}}{n}\ue89e\frac{\partial \left(h+\u03db\right)}{\partial {x}_{i}}\ue89e\Delta \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{L}^{\mathrm{ip}}\right]}_{\mathrm{ip}}={\left(Q\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e\Delta \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89eS\right)}_{P}& \left(25\right)\end{array}$

where the superscript “o” refers to quantities evaluated at a previous time level, while the subscripts P and ip refers to quantities evaluated at nodes and at integration points respectively. The superficial area surrounding a node is denoted by ΔS. The length of a controlvolume face located over control points is ΔL. It is through these faces that flux is exchanged between controlvolumes. All source/sink terms are gathered into the term Q. The superscript uds refers to terms calculated using the upstream interpolation function to assure numerical stability. See, Ferziger, J. H. and Peric, M., 2001. Computational Methods for Fluid Dynamics, 2nd ed., SpringerVerlag, Berlin, which is incorporated by reference. See, also Flood Insurance Rate Map, 2006, City of New York, Panel 226 of 457, Map Number 3604970226F, Map Revised, Federal Emergency Management Agency, web: http://gis.nyc.gov/dob/fm/index.htm, which is incorporated by reference. The mobility term, λ, is defined in this equation as

$\begin{array}{cc}\lambda =\frac{{h}^{2/3}}{{\uf603\frac{\partial H}{\partial s}\uf604}^{1/2}}& \left(26\right)\end{array}$

This nonlinear equation system is solved implicitly through Newton's Method. See, Kelley, C. T., 2003. Solving Nonlinear Equations with Newton's Method, Society for Industrial Mathematics, Philadelphia, which is incorporated herein by reference. The time step is variable, being adjustable to fit according to the precipitation data input and output times as well as to satisfy stability and convergence requirements. These requirements are based both on the maximum number of nonlinear iterations and maximum variation of primary value in one iteration and during one time step. Once the linear system for h is solved the velocity is determined diagnostically as follows

$\begin{array}{cc}{V}_{i}=\frac{\lambda}{n}\ue89e\frac{\partial \left(h+\u03db\right)}{\partial {x}_{i}}& \left(27\right)\end{array}$

where the index i represents either the direction along the 1dimensional elements or x and y coordinates within triangular elements. Further, the terms like

$h\ue89e\phantom{\rule{0.8em}{0.8ex}}\ue89e{k}_{x}\ue89e\frac{\partial \left(h+\u03db\right)}{\partial x}$

in (1) represent fluxes. In the discrete version the fluxes are estimated by

$\sum _{\mathrm{ip}}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{\left[\frac{{\left(h\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e\lambda \right)}^{\mathrm{uds}}}{n}\ue89e\frac{\partial \left(h+\u03db\right)}{\partial {x}_{i}}\ue89e\Delta \ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{L}^{\mathrm{ip}}\right]}_{\mathrm{ip}}$

in (25).

Reference will now be made to FIG. 7, showing an integrated system workflow according to one embodiment. High resolution data 701 is used to create a shape file 702. The high resolution shapefile data is used to generate a mesh 704. The boundary and topography information 703 are interpolated to the mesh nodes.

Further, the mesh is generated using high resolution topography data 705 in a geographic coordinate system at 706—in terms of latitude and longitude—since it is usual to have the topography and precipitation data referring to such a system. In one example, internally this data is converted to Universal Transverse Mercator (see, UTM Snyder, J. P, 1987. Map Projections: a Working Manual, USGS Professional Paper 1395. Washington, D.C.: United States Government Printing Office 20, which is incorporated by reference herein), where WGS 1984 is employed here as the reference ellipsoid, i.e. mathematicallydefined surface that approximates the geoid (see, e.g., a definition of a geoid at http://en.wikipedia.org/wiki/Geoid and, with regard to WGS 1984, http://en.wikipedia.org/wiki/World_Geodetic_System). Finally, the data coming from the mesoscale meteorological model, radar, and/or surface observations (e.g., at sparsely located sites) is used as source/sink terms at 707 (the data is used as water source (rain) and/or sink (drainage) in the model) in the overland simulation model 708 to produce forecast 709.

The overland simulation model requires a generation of another mesh for the “source/sink term” to take into account the collected area associated with each 1dimensional mesh node. This area, ΔS on the right hand side of Eq. (25), is employed to calculate the source term in the discretized conservation equation. Using that second mesh is a simple solution for an apparent difficulty in using 1dimensional modeling because, in fact, only a small portion of rain is directly collected on street surfaces, since the ratio of a street's surface area/total area is usually too small (e.g., percent wise). For example, referring to FIG. 5, it can be seen that the area occupied by the lines representing the streets occupy collectively a small amount of the total area. With the approach considered here, the precipitated water flowing to the streets from buildings, parking areas, etc. can be computed, as well.

An alternative embodiment can be realized by simulating a complete basin, namely coupling this model to a subsurface groundwater threedimensional porous media simulator employing tetrahedral numerical meshes (see, Mello, U. T., Rodrigues, J. R. P., and Rossa, A., 2009. A ControlVolume Finite Element Method for Multiphase Fluid Flow in Basin Modeling, Marine and Petroleum Geology, vol. 24 (4): 504518, which is incorporated herein by reference). This may account for all interactions between the surface and subsurface flow regimes, simulating the complete hydrologic cycle.

Referring now back to FIG. 5, this Fig. shows a mesh comprising lines and triangles that represent the streets and central park in Manhattan. Meshing can be defined as the process of breaking up a physical domain into smaller subdomains (mesh elements) in order to facilitate the numerical solution of a partial differential equation. While meshing can be used for a wide variety of applications, an application of interest is the finite element method. Surface domains may be subdivided into linear, triangle or quadrilateral shapes, while volumes may be subdivided primarily into tetrahedra or hexahedra shapes. The shape and distribution of the elements may be defined by automatic meshing algorithms. As mentioned, in FIG. 5, one can see a numerical mesh representing an area of Manhattan which includes streets and a park (Central Park) in the center. The line elements (1 dimensional) represent the streets and the triangle elements (2 dimension) represents open areas (park). The rain is transported differently in streets and parks due to physical (e.g., pavement, soil, grass) features in the two environments.

Reference will now be made to an example case study. For the precipitation data associated with this case study two sources of data were used: radar data and simulated rainfall from the WRF model.

Radar observations and the WRF forecast might not have a complete agreement in timing (or geographic distribution) of rainfall events, and in general it is unreasonable to demand such agreement. First, WRF provides more lead time since it can be run in advance while radar observations are real time by definition. Even real time observations may provide lead time to flooding events as there is some lag between rainfall and rising water levels. Second, even radar observations are a partial sampling of actual rainfall. Many different atmospheric phenomena can generate response in radar data and not all of these are due to precipitable water. Therefore, it is common practice to accept a forecast product for its utility rather than solely based on geospatial alignment, which itself does not have a rigorous quantitative measure. In addition to high resolution weather forecasts and integrated flood modeling as presented here, new radar technologies lie on the horizon to further improve the accuracy and effectiveness of forecasters. See, Rude, D. J., Bass, E. J., Philips, B., 2009: Impact of Increased SpatioTemporal Radar Data Resolution on Forecaster Wind Assessments. 2009 IEEE Conference on Systems, Man, and Cybernetics. October 1114, San Antonio, Tex. See, also, Rude, D. J., Bass, E., Philips, B., 2008: Improving Severe Weather Warnings by Modeling Forecaster Decision Making and Radar Data Assessments. HFES research symposium, Virginia Tech, October 25, Blacksburg, Va.

This case study relates to simulated rainfall associated with a localized MCS moving toward the New York City boroughs and causing urban flooding. The MCS originated over the Plains about 30 hours earlier along a WestEast baroclinic zone according to analysis of meteorological observations on the day of this event (Colle et al., 2009). Both observations and our simulations using WRF show that convection intensified as the storm was progressing toward the coast. Simulated location of the storm epicenter is over the Queens/Brooklyn area that was severely impacted by flooding. Modeled rainfall patterns are also in agreement with AWS/WeatherBug observations from the surface rain gauges, as well as with the KOKX NEXRAD data as described next.

For radar data, several reflectivity products can be used to estimate the precipitation input into the hydrological model. In particular, the vertical composite product was used as input in this case because it brings together data from all altitudes scanned. A single grid point is composed of the maximum reflectivity from each vertical column at that point. Through established empirical and statistical relationships the data in dBz units from radar can be converted to mm/h, which is a more convenient precipitation data unit.

In this study the data from KOKX NEXRAD radar, within the WSR88D radar network, located at Long Island, N.Y., were oversampled at 100 m resolution and used to derive rain rates as inputs for the hydrology model. Level II radar data was processed by WDSSII (Warning Decision Support System—Integrated Information) algorithms to create the composite reflectivity grid, see, Lakshmanan, V., Smith, T., Stumpf, G. J. and Hondl, K., 2007. “The warning decision support system—integrated information,” Weather and Forecasting, vol. 22, no. 3, pp. 596612. Computational efficiency within this component of the system is high, providing the foundation for realtime flood forecasting capabilities.

For the hydrological model it was assumed here that certain regions represent the more permeable surface areas and in which the flow of water is treated as twodimensional. For this reason a mesh of triangles is generated over these blocks. On the streets a 1dimensional mesh is generated, since in this scale the water level variations along the width can be neglected for practical considerations. These areas were defined based solely on visual inspection of satellite photos. In another example, use of this kind of information may be based on an objective procedure.

A mesh was used to calculate the collecting areas associated with each 1dimensional element representing the urban streets in the model. As mentioned herein, the flow simulation is not performed in this example over this collecting area mesh.

The simulation is actually accomplished over simulation meshes which are composed in this example by triangles and edges. The boundary condition of a prescribed water depth is applied over the contour adjacent to the river, which takes into account the water level of the river.

Due to different data sources for topography and shapefiles defining the geometry, it is necessary to calibrate the model in order to check the initial equilibrium. This can be done by running the model with a null precipitation term and providing minor corrections in the topography data so that no water from the river enters the domain. The topography data used here is from USGS (2009) with resolution of 1/3 Arc Second (on the order of 10 m).

By using both the meteorological model and the radar data the surface water velocities are validated for physical consistency, as shown in FIG. 8. The smooth transition between the velocities in the 1dimensional and 2dimensional regions is clear (see details 803 and 805 of broader view 801).

Validation of the test case was made where the special flood hazard areas subject to inundation by the 1% annual chance flood (Flood Insurance Rate Map, 2006) were used as a reference solution. This data source is used for comparisons due to the lack of more representative data of the 2007 flood event. The 1% annual flood (100year flood), also known as the base flood, is the flood that has a 1% chance of being equaled or exceeded in any given year.

A comparison between the water depth results employing WRF model and radar data provides that, as expected, the greater precipitation rates correspond to the case when radar data is used, with the higher peaks of accumulation water in the domain (maximum of 3.6 m). Some of the radarderived precipitation does not actually reach the ground due to advection and convective effects among others. Therefore, the amount of rainfall observed in reality is less. Employing the meteorological model the maximum of 1.9 m was reached, which is a more reasonable value. This value may still be an overestimate due to the fact that an infiltration model (including sewage system removal of storm water from the streets) has not been calibrated due to lack of data.

Referring now to FIG. 9, an architecture for performing a flooding forecast according to an embodiment is shown. As seen in this FIG. 9, domain definition (see element 901) is provided to topography input (see element 903) and geographic information (see element 905). Further, the topography input and geographic information is provided to a meshing function (see element 907). Output of the meshing function is provided to a modeling function (see element 909). The modeling function also receives boundary condition specification(s) (see element 911) and forcing terms (see element 913). The forcing terms may be generated by, e.g., radar and/or by any other desired mechanism. Finally, it is seen that a forecast (see element 915) is output from the modeling function.

In one example an output forecast from a model may indicate rainfall precipitation (e.g., accumulated precipitation) over the period of the forecast (e.g., in the form of one or more maps (e.g., color “heattype” maps) and/or animations and or graphs. In other examples, variables of interest may be density of water in clouds, temperature and atmospheric pressure, speed and wind direction, air humidity and accumulated rainfall.

Referring now to FIG. 10, a method (e.g., implemented in a computer system) for generating a flooding forecast according to an embodiment is shown. As seen in this FIG. 10, the method of this embodiment comprises: Step 1001—maintaining a representation of a geographical region, the representation comprising: (a) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (b) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; Step 1003—modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portions, in such a manner that the first and second portion together form a single mixed mesh; and Step 1005—providing at least one water level prediction responsive to the modeling.

Referring now to FIG. 11, a system for generating a flooding forecast according to an embodiment is shown. As seen in this FIG. 11, the system includes: (a) storage element 1103 that stores a representation of a geographical region, the representation comprising: (i) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (ii) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; (b) modeling element 1105 in operative communication with the storage element 1103, the modeling element 1105 modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portion, in such a manner that the first and second portions together form a single mixed mesh; and (c) output element 1107 in operative communication with the modeling element 1105, the output element 1107 outputting at least one water level prediction responsive to the modeling.

Still referring to FIG. 11, it is seen that in one embodiment, storage element 1103 may be in operative communication with receiving element 1101, wherein the receiving element 1101 receives the representation of the geographical region and the representation of the geographical region is stored in the storage element 1103 after receipt by the receiving element 1101.

Referring now to FIG. 12, this Fig. shows a hardware configuration of computing system 1200 according to an embodiment. As seen, this hardware configuration has at least one processor or central processing unit (CPU) 1211. The CPUs 1211 are interconnected via a system bus 1212 to a random access memory (RAM) 1214, readonly memory (ROM) 1216, input/output (I/O) adapter 1218 (for connecting peripheral devices such as disk units 1221 and tape drives 1240 to the bus 1212), user interface adapter 1222 (for connecting a keyboard 1224, mouse 1226, speaker 1228, microphone 1232, and/or other user interface device to the bus 1212), a communications adapter 1234 for connecting the system 1200 to a data processing network, the Internet, an Intranet, a local area network (LAN), etc., and a display adapter 1236 for connecting the bus 1212 to a display device 1238 and/or printer 1239 (e.g., a digital printer or the like).

Reference will now be made to an example output of at least one water level prediction responsive to modeling. In this example, the output of the flooding prediction may be a map of the area of interest which indicates the area(s) subject to flooding. The level of water at the flooding location(s) may be indicated by the water depth, h. Various visualizations may be used (e.g., one or more “heattype” maps and/or graphs (e.g., water level in meters vs. time in minutes)).

As described herein, various embodiments may provide a complete and accurate description of an associated geometry.

As described herein, various embodiments may provide for flood prediction in the context of urban (e.g., city) management.

As described herein, various embodiments may provide for urban flood forecasting and a catchment modeling system.

As described herein, various embodiments may provide for surface and/or subsurface hydrologic modeling (e.g., for flooding forecasting).

As described herein, various embodiments may aid in decisions that may have to be made on a regional and/or national scale if storms become more frequent and/or more severe

As described herein, various embodiments may aid in providing a good forecast model to improve emergency response in managing future storm events.

As described herein, various embodiments may provide for solving of equations for hybrid meshes (where elements have different dimensionality).

As described herein, various embodiments may utilize the diffusion model.

As described herein, various embodiments may solve for 1dimensional and 2dimensional domains.

As described herein, various embodiments may utilize unstructured grids (e.g., where a 1dimensional and a 2dimensional grid are the same entity).

As described herein, various embodiments may utilize a 1dimensional solution which is a simplified representation of part of the domain.

As described herein, various embodiments may provide for implementing a computational model for predicting flooding, wherein: (a) computational simplification is provided without loss of accuracy by using a simplified representation of the part of the domain; (b) areas associated with each grid node are determined for estimating the surface dependent source/sink terms; and/or (c) predetermined numerical equations are solved for each grid node in a conservative framework.

As described herein, various embodiments may provide for a 2dimensional/1dimensional method. In this regard, most of a metropolitan area can be represented by using 1dimensional elements employing the high resolution data available. Even pipelines can be taken into account with this approach. In areas where the one dimensionality of flow is not expected, like in parks, 2dimensional elements can be employed without loss of generality.

Reference will now be made to some example forecast applications that are applied primarily for urban areas where the impact is more severe, aiming to assist the authorities in: (a) defining efficient workarounds when some elements of the system experience difficulties; (b) communicating the severity of the upcoming flood conditions to the population; and/or (c) preemptively planning the urban area layout with the aim of reducing the effects of a future flood.

In other examples, various embodiments may operate offline, online or a combination of both.

In one embodiment, a method for generating a flooding forecast is provided, the method comprising: maintaining a representation of a geographical region, the representation comprising: (a) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (b) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portion, in such a manner that the first and second portions together form a single mixed mesh; and providing at least one water level prediction responsive to the modeling.

In one example, the first portion comprises at least one edge of the second portion.

In another example, the second portion is triangular.

In another example, the modeling takes into account conservation of momentum and energy.

In another example, the modeling combines: (a) a hydrological model, which includes the single mixed mesh; and (b) a mesoscale meteorological model.

In another example, the meteorological model combines: (a) radar; and (b) surface data.

In another example, the providing at least one water level prediction comprises outputting the water level prediction to at least one of: (a) a display monitor; (b) a digital file; and (c) a printer.

In another example, the steps are carried out in the order recited.

In another embodiment, a program storage device readable by machine, tangibly embodying a program of instructions executable by the machine for generating a flooding forecast is provided, the program of instructions, when executing, performing the following steps: maintaining a representation of a geographical region, the representation comprising: (a) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (b) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portion, in such a manner that the first and second portions together form a single mixed mesh; and providing at least one water level prediction responsive to the modeling.

In one example, the first portion comprises at least one edge of the second portion.

In another example, the second portion is triangular.

In another example, the modeling takes into account conservation of momentum and energy.

In another example, the modeling combines: (a) a hydrological model, which includes the single mixed mesh; and (b) a mesoscale meteorological model.

In another example, the meteorological model combines: (a) radar; and (b) surface data.

In another example, the providing at least one water level prediction comprises outputting the water level prediction to at least one of: (a) a display monitor; (b) a digital file; and (c) a printer.

In another example, the steps are carried out in the order recited.

In another embodiment, a computerimplemented system for generating a flooding forecast is provided, the system comprising: a storage element that stores a representation of a geographical region, the representation comprising: (a) at least a first portion having a first dimensionality, the first portion corresponding to a first subregion of the geographical region and the first dimensionality being a 1dimensional dimensionality; and (b) at least a second portion having a second dimensionality, the second portion corresponding to a second subregion of the geographical region and the second dimensionality being a 2dimensional dimensionality; a modeling element in operative communication with the storage element, the modeling element modeling at least one flooding related event within each of the first and second portions in accordance with a respective model that comprises at least a first water level calculation in accordance with the first dimensionality for the first portion and a second water level calculation in accordance with the second dimensionality for the second portion, in such a manner that the first and second portions together form a single mixed mesh; and an output element in operative communication with the modeling element, the output element outputting at least one water level prediction responsive to the modeling.

In one example, the first portion comprises at least one edge of the second portion.

In another example, the second portion is triangular.

In another example, the modeling takes into account conservation of momentum and energy.

In another example, the modeling combines: (a) a hydrological model, which includes the single mixed mesh; and (b) a mesoscale meteorological model.

In another example, the meteorological model combines: (a) radar; and (b) surface data.

In another example, the steps are carried out in the order recited.

In another example, the system further comprises a receiving element, wherein the receiving element receives the representation of the geographical region and the representation of the geographical region is stored in the storage element after receipt by the receiving element.

In another example, the output element outputs the water level prediction to at least one of: (a) a display monitor; (b) a digital file; and (c) a printer.

In other examples, any steps described herein may be carried out in any appropriate desired order.

As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, microcode, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a nonexhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a readonly memory (ROM), an erasable programmable readonly memory (EPROM or Flash memory), an optical fiber, a portable compact disc readonly memory (CDROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The containment (or storage) of the program may be nontransitory.

A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electromagnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

Computer program code for carrying out operations for aspects of the present invention may be written in any programming language or any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like or a procedural programming language, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a standalone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

Aspects of the present invention may be described herein with reference to flowchart illustrations and/or block diagrams of methods, systems and/or computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus or other devices provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowcharts or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by special purpose hardwarebased systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

It is noted that the foregoing has outlined some of the objects and embodiments of the present invention. This invention may be used for many applications. Thus, although the description is made for particular arrangements and methods, the intent and concept of the invention is suitable and applicable to other arrangements and applications. It will be clear to those skilled in the art that modifications to the disclosed embodiments can be effected without departing from the spirit and scope of the invention. The described embodiments ought to be construed to be merely illustrative of some of the features and applications of the invention. Other beneficial results can be realized by applying the disclosed invention in a different manner or modifying the invention in ways known to those familiar with the art. In addition, all of the examples disclosed herein are intended to be illustrative, and not restrictive.