## InVEST Urban Flood Risk Mitigation Model

The InVEST model calculates the runoff reduction, i.e. the amount of runoff retained per pixel compared to the storm volume. It also calculates, for each watershed, the potential economic damage, by overlaying information on flood extent potential and built infrastructure.

Flood hazardrisk mitigationeconomic
331

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Application-focused categoriesNatural-perspectiveLand regions

#### Model Description

English {{currentDetailLanguage}} English

Flood hazard comes from different sources, including: riverine (or fluvial) flooding, coastal flooding, and stormwater (or urban) flooding - the focus of this InVEST model. Natural infrastructure can play a role for each of these flood hazards. Related to stormwater flooding, natural infrastructure operates mainly by reducing runoff production, slowing surface flows, and creating space for water (in floodplains or basins).

The InVEST model calculates the runoff reduction, i.e. the amount of runoff retained per pixel compared to the storm volume. For each watershed, it also calculates the potential economic damage by overlaying information on flood extent potential and built infrastructure.

### How it works

#### Runoff production and runoff attenuation index

For each pixel $$i$$, defined by a land use type and soil characteristics, we estimate runoff $$Q$$ (mm) with the Curve Number method:

(1)$\begin{split}Q_{p,i} = \begin{Bmatrix} \frac{(P - \lambda S_{max_i})^2}{P + (1-\lambda) S_{max,i}} & if & P > \lambda \cdot S_{max,i} \\ 0 & & otherwise \end{Bmatrix}\end{split}$

Where $$P$$ is the design storm depth in mm, $$S_{max,i}$$ is the potential retention in mm, and $$\lambda \cdot S_{max}$$ is the rainfall depth needed to initiate runoff, also called the initial abstraction ($$\lambda=0.2$$ for simplification).

$$S_{max}$$ (calculated in mm) is a function of the curve number, $$CN$$, an empirical parameter that depends on land use and soil characteristics (NRCS 2004):

(2)$S_{max,i}=\frac{25400}{CN_i}-254$

The model then calculates runoff retention per pixel $$R_i$$ as:

(3)$R_i=1-\frac{Q_{p,i}}{P}$

And runoff retention volume per pixel $$R\_m3_i$$ as:

(4)$R\_m3_i=R_i\cdot P\cdot pixel.area\cdot 10^{-3}$

With $$pixel.area$$ in $$m^2$$.

Runoff volume (also referred to as “flood volume”) per pixel $$Q\_m3_i$$ is also calculated as:

(5)$Q\_m3_i=Q_{p,i}\cdot P\cdot pixel.area\cdot 10^{-3}$

#### Calculate potential service (optional)

The service is the monetary valuation of avoided damage to built infrastructure and number of people at risk. As of this version of InVEST, the population metrics described here are not yet implemented.

For each watershed (or sewershed) with flood-prone areas, compute:

• Affected.Pop : total potential number of people affected by flooding (could focus on vulnerable groups only, e.g. related to age, language, etc. See Arkema et al., 2017, for a review of social vulnerability metrics). This metric is calculated by summing the population in the intersection of the two shapefiles (watershed and flood-prone area).

• $$Affected.Build$$ : sum of potential damage to built infrastructure in \$, This metric is calculated by multiplying building footprint area within the watershed and potential damage values in $$m^2$$.

##### Aggregation of runoff retention and potential service values at the watershed scale

For each watershed, compute the following indicator of the runoff retention service:

(6)$Service.built=Affected.Build\sum_{watershed}0.001(P-Q_{p,i})\cdot pixel.area$

where $$pixel.area$$ is the pixel area ($$m^2$$), $$Service.built$$ is expressed in $$m^3$$.

### Limitations and simplifications

Runoff production: the model uses a simple approach (SCS-Curve Number), which introduces high uncertainties. However, the ranking between different land uses is generally well captured by such an approach, i.e. that the effect of natural infrastructure will be qualitatively represented in the model outputs. Future work will aim to include a routing over the landscape: ideas include TOPMODEL (there is an R package), UFORE (used in iTree), CADDIES, etc

Valuation approaches: Currently, a simple approach to value flood risk retention is implemented, valuing flood risk as the avoided damage for built infrastructure. Alternative approaches (e.g. related to mortality, morbidity, or economic disruption) could be implemented.

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#### How to Cite

Natural Capital Project (2019). InVEST Urban Flood Risk Mitigation Model, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/26b51b36-62d7-4d4d-b774-877f2c65718a

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