Developing an effective 2-D urban flood inundation model for city emergency management based on cellular automata

Flash floods have occurred frequently in the urban areas of southern China. An effective process-oriented urban flood inundation model is urgently needed for urban storm-water and emergency management. This study develops an efficient and flexible cellular automaton (CA) model to simulate storm-water runoff and the flood inundation process during extreme storm events. The process of infiltration, inlets discharge and flow dynamics can be simulated with little preprocessing on commonly available basic urban geographic data. In this model, a set of gravitational diverging rules are implemented to govern the water flow in a rectangular template of three cells by three cells of a raster layer. The model is calibrated by one storm event and validated by another in a small urban catchment in Guangzhou of southern China. The depth of accumulated water at the catchment outlet is interpreted from street-monitoring closed-circuit television (CCTV) videos and verified by on-site survey. A good level of agreement between the simulated process and the reality is reached for both storm events. The model reproduces the changing extent and depth of flooded areas at the catchment outlet with an accuracy of 4 cm in water depth. Comparisons with a physically based 2-D model (FloodMap) show that the model is capable of effectively simulating flow dynamics. The high computational efficiency of the CA model can meet the needs of city emergency management

Velocity distributions near the upper domain boundary obtained with various open boundary conditions: (a) OBC Eq (3a), (b) OBC Eq (3b), (c) OBC Eq (3c), (d) OBC Eq (3d), (e) OBC Eq (4), (f) OBC Eq (5).

<p>Velocity vectors are plotted on every ninth quadrature points in each direction within each element.</p

Bouncing water drop (drop radius 1mm, initial height <i>H</i>₀ = 3.2mm): temporal sequence of snapshots of the air-water interface at non-dimensional time instants: (a) <i>t</i> = 0.05, (b) <i>t</i> = 0.25, (c) <i>t</i> = 0.4, (d) <i>t</i> = 0.55, (e) <i>t</i> = 0.7, (f) <i>t</i> = 0.85, (g) <i>t</i> = 1.0, (h) <i>t</i> = 1.15.

<p>Bouncing water drop (drop radius 1mm, initial height <i>H</i>₀ = 3.2mm): temporal sequence of snapshots of the air-water interface at non-dimensional time instants: (a) <i>t</i> = 0.05, (b) <i>t</i> = 0.25, (c) <i>t</i> = 0.4, (d) <i>t</i> = 0.55, (e) <i>t</i> = 0.7, (f) <i>t</i> = 0.85, (g) <i>t</i> = 1.0, (h) <i>t</i> = 1.15.</p

Physical and numerical parameter values for the air jet in water problem.

<p>Physical and numerical parameter values for the air jet in water problem.</p

Bouncing water drop (drop radius 1mm, initial height <i>H</i>₀ = 3.2mm): temporal sequence of snapshots of the velocity field at non-dimensional time instants: (a) <i>t</i> = 0.05, (b) <i>t</i> = 0.25, (c) <i>t</i> = 0.4, (d) <i>t</i> = 0.55, (e) <i>t</i> = 0.7, (f) <i>t</i> = 0.85, (g) <i>t</i> = 1.0, (h) <i>t</i> = 1.15.

<p>Velocity vectors are plotted on every fifth quadrature points in each direction within each element.</p

Parameter values for convergence tests.

<p>Parameter values for convergence tests.</p

Another window of time history of the average vertical-velocity magnitude, suggesting a somewhat different flow state.

<p>Result is obtained using the open boundary condition <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154565#pone.0154565.e008" target="_blank">Eq (3b)</a>.</p

Spatial/temporal convergence rates: (a) Mesh and boundary conditions; (b) Numerical errors versus element order showing spatial exponential convergence (with fixed Δ<i>t</i> = 0.001); (c) Numerical errors versus Δ<i>t</i> showing temporal second-order convergence rate (element order fixed at 18).

<p>On the face the open boundary condition <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154565#pone.0154565.e008" target="_blank">Eq (3b)</a> is used.</p

Time histories of average vertical-velocity magnitude from different open boundary conditions: (a) OBC Eq (3a), (b) OBC Eq (3b), (c) OBC Eq (3c), (d) OBC Eq (3d).

<p>Time histories of average vertical-velocity magnitude from different open boundary conditions: (a) OBC <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154565#pone.0154565.e007" target="_blank">Eq (3a)</a>, (b) OBC <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154565#pone.0154565.e008" target="_blank">Eq (3b)</a>, (c) OBC <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154565#pone.0154565.e009" target="_blank">Eq (3c)</a>, (d) OBC <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154565#pone.0154565.e010" target="_blank">Eq (3d)</a>.</p

Air jet in water: Temporal sequence of snapshots of the air-water interface at time: (a) <i>t</i> = 22.9997, (b) <i>t</i> = 23.0372, (c) <i>t</i> = 23.0747, (d) <i>t</i> = 23.1122, (e) <i>t</i> = 23.1497, (f) <i>t</i> = 23.1872, (g) <i>t</i> = 23.2247, (h) <i>t</i> = 23.2622, (i) <i>t</i> = 23,2922, (j) <i>t</i> = 23.3222, (k) <i>t</i> = 23.3522, (l) <i>t</i> = 23.3822, (m) <i>t</i> = 23.4197, (n) <i>t</i> = 23.4572, (o) <i>t</i> = 23.5172.

<p>Results are obtained using the open boundary condition <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154565#pone.0154565.e008" target="_blank">Eq (3b)</a>.</p