data.md

Data Usage

Toy example: Environmental spill function

The Environmental Model function describes the concentration of a pollutant released by two spills in a 1D channel as a function of space and time. Let $C(\mathbf{x})$ denote the pollutant concentration at position $s$ and time $t$. Two equal-mass spills occur at space–time locations (0, 0) and ($L$, $\tau$). The model output is a $d_s$ × $d_t$ array containing scaled concentrations $C(s_i, t_j)$ evaluated on a space–time grid.

Mathematical formulation:

$$ f(\mathbf{x}) = \sqrt{4\pi} C(\mathbf{x}) $$ where $$ C(\mathbf{x}) = \frac{M}{\sqrt{4\pi D t}} \exp\left( -\frac{s^{2}}{4 D t} \right) + I(t>\tau) \frac{M}{\sqrt{4\pi D (t-\tau)}} \exp\left( -\frac{(s- L)^{2}}{4 D (t-\tau)} \right) $$

Here, $I(\cdot)$ is the indicator function and $0 \le s \le 3,; t>0$. Inputs are $M$ (mass), $D$ (diffusion rate), $L$ (location of second spill), and $\tau$ (time of second spill).

Input ranges and descriptions:

Parameter	Range	Description
$M$	[7, 13]	mass of pollutant spilled at each location
$D$	[0.02, 0.12]	diffusion rate in the channel
$L$	[0.01, 3]	location of the second spill
$\tau$	[30.01, 30.295]	time of the second spill

Output: $d_s$ × $d_t$ grid of concentrations

Source: Environmental Model function (Virtual Library of Simulation Experiments). See also Bliznyuk et al. (2008).

Case study A: Synthetic dataset

Topography consists of a parabolic slope starting at $x = 0$ at an altitude of $1332\ \mathrm{m}$, and connecting to a flat land at $x = 3000$ at an altitude of $0\ \mathrm{m}$. Extent of the area in x and y directions are $5000\ \mathrm{m}$ and $4000\ \mathrm{m}$, respectively, whereas the resolution is $20\ \mathrm{m}$. Release zone was defined as an elliptic cylinder, of which the centre is located at $(x, y) = (600, 2000)$ with a minor axis of $100\ \mathrm{m}$ and a major axis of $200\ \mathrm{m}$. Height at each point within the ellipse was defined as $20 m$, which generates a total release volume of $1.432 \times 10^6\ \mathrm{m}^3$.

Source: Yildiz, Anil et. al.

Case study B: Acheron Rock Avalanche

The Acheron rock avalanche—located near Canterbury, New Zealand—occurred approximately 1,100 years before present and was likely triggered by a strong earthquake. The deposit area was estimated to be 0.72 × 10⁶ m² and the deposit volume roughly 8.9 × 10⁶ m³.

The input/output dataset are obtained run via r.avaflow 2.3 with 100 simulations as training set and 20 additional simulations as test set. The input variables are dry-coulomb friction coefficient(μ), turbulent friction coefficient(ζ), release volume(ν₀), respectively. The output variables contain impact area, deposit area, deposit volume, maximum flow velocity, and maximum flow height at position (x, y).

Source: Yildiz, Anil et. al.