# Urban Flood Risk Mitigation

## Introduction

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 takes a simple curve number approach to calculating rainfall runoff reduction due to land use/land cover and soil characteristics. Runoff reduction can also be thought of as the amount of runoff retained per pixel compared to the storm volume. For each watershed, it also estimates the potential economic damage, and ecosystem service provided, to built infrastructure.

## The Model

### 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:

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

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):

(128)\[S_{max,i}=\frac{25400}{CN_i}-254\]

The model then calculates the fraction of runoff retention per pixel \(R_i\) as:

(129)\[R_i=1-\frac{Q_{p,i}}{P}\]

And runoff retention volume per pixel \(R\_m3_i\) as:

(130)\[R\_m3_i=R_i\cdot P\cdot pixel.area\cdot 10^{-3}\]

With \(pixel.area\) in \(m^2\).

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

(131)\[Q\_m3_i=Q_{p,i}\cdot pixel.area\cdot 10^{-3}\]

#### Calculate potential service (optional)

First, \(\text{Affected.build}\), the sum of potential damage in currency units to built infrastructure, is calculated for each watershed or sewershed \(W\):

(132)\[\text{Affected.build}_W = \sum_{b ∈ B}a(b,W)·d(b)\]

where

- \(b\) is a building footprint in the set of all built infrastructure \(B\)

- \(a(b,W)\) is the area in \(m^2\) of the building footprint \(b\) that intersects watershed \(W\)

- \(d(b)\) is the damage value in \(currency/m^2\) (from the user-input Damage Loss Table) for building \(b\)’s type

We then calculate \(\text{Service.built}\), an indicator of avoided damage to built infrastructure, for each watershed \(W\):

(133)\[\text{Service.built}_W=\text{Affected.build}_W·\sum_{i ∈ W}R\_m3_i\]

where

- \(i\) is a pixel in watershed \(W\)

- \(R\_m3_i\) is the runoff retention volume on pixel \(i\)

\(\text{Service.built}\) is expressed in \(currency·m^3\), and can be used to indicate the ecosystem service of flood retention provided to buildings. Given the simplicity of the model, it should be considered only an indicator, not an actual measure of savings.

## 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 potential avoided damage for built infrastructure. This value may prove useful in comparing risk across nearby watersheds, capturing the different amounts of exposed infrastructure for each watershed. However, since the model does not produce inundation maps, there is no way to confirm that the infrastructure is actually exposed. The output therefore remains a potential benefit. Alternative approaches (e.g. related to mortality, morbidity, or economic disruption) could be implemented. Another service metric is the affected population, i.e. the number of people at risk from flooding. This 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 can be calculated by summing the population in the intersection of the watershed and the flood-prone area.

## Data Needs

Note

Spatial layers for Urban Flood Mitigation may have different coordinate systems, but they must all be projected coordinate systems, not geographic.

Note

Raster inputs may have different cell sizes, and they will be resampled to match the cell size of the land use/land cover raster. Therefore, raster model results will have the same cell size as the land use/land cover raster.

- workspace (directory, required): The folder where all the model’s output files will be written. If this folder does not exist, it will be created. If data already exists in the folder, it will be overwritten.

- file suffix (text, optional): Suffix that will be appended to all output file names. Useful to differentiate between model runs.

- area of interest (vector, polygon/multipolygon, required): A map of areas over which to aggregate and summarize the final results.

  These may be watershed or sewershed boundaries.

- rainfall depth (number, units: mm, required): Depth of rainfall for the design storm of interest.

  This is \(P\) in equation (127).

- land use/land cover (raster, required): Map of LULC. All values in this raster must have corresponding entries in the Biophysical Table.

  All outputs will be produced at the resolution of this raster.

- soil hydrologic group (raster, required): Map of soil hydrologic groups. Pixels may have values 1, 2, 3, or 4, corresponding to soil hydrologic groups A, B, C, or D, respectively.

- biophysical table (CSV, required): Table of curve number data for each LULC class. All LULC codes in the LULC raster must have corresponding entries in this table for each soil group.

  table containing model information corresponding to each of the land use classes in the Land Cover Map. All LULC classes in the Land Cover raster MUST have corresponding values in this table. Each row is a land use/land cover class and columns must be named and defined as follows:

  Columns:

  - lucode (integer, required): LULC codes from the LULC raster. Each code must be a unique integer.

  - cn_a (number, units: unitless, required): The curve number value for this LULC type in the soil group code A. Curve numbers must be greater than 0 and less than or equal to 100.

  - cn_b (number, units: unitless, required): The curve number value for this LULC type in the soil group code B. Curve numbers must be greater than 0 and less than or equal to 100.

  - cn_c (number, units: unitless, required): The curve number value for this LULC type in the soil group code C. Curve numbers must be greater than 0 and less than or equal to 100.

  - cn_d (number, units: unitless, required): The curve number value for this LULC type in the soil group code D. Curve numbers must be greater than 0 and less than or equal to 100.

- built infrastructure (vector, polygon/multipolygon, optional): Map of building footprints.

  Field:

  - type (integer, required): Code indicating the building type. These codes must match those in the Damage Loss Table.

- damage loss table (CSV, conditionally required): Table of potential damage loss data for each building type. All values in the Built Infrastructure vector ‘type’ field must have corresponding entries in this table. Required if the Built Infrastructure vector is provided.

  Columns:

  - type (integer, required): Building type code.

  - damage (number, units: currency units/m², required): Potential damage loss for this building type.

    Any currency may be used.

## Interpreting Results

> - Parameter log: Each time the model is run, a text (.txt) file will be created in the Workspace. The file will list the parameter values and output messages for that run and will be named according to the service, the date and time. When contacting NatCap about errors in a model run, please include the parameter log.

> - Runoff_retention_index.tif: raster with runoff retention index values (no unit, values of 0-1, relative to precipitation volume). Calculated from equation (129).

> - Runoff_retention_m3.tif: raster with runoff retention volume values (in \(m^3\)). Calculated from equation (130).

> - Q_mm.tif: raster with runoff values (mm). Calculated from equation (127).

> - flood_risk_service.shp: Shapefile with results in the attribute table:

>   > - rnf_rt_idx: average of runoff retention index values (\(R_i\)) per watershed

>   > - rnf_rt_m3: sum of runoff retention volumes (\(R\_m3_i\)), in \(m^3\), per watershed.

>   > - flood_vol: The flood volume (`Q_m3`, equation (131)) per watershed.

>   > - aff_bld: potential damage to built infrastructure in currency units, per watershed. Only calculated when the Built Infrastructure Vector input is provided. Note that this does not take into account actual flood depth or extent, so should be used as an indicator only.

>   > - serv_blt: \(Service.built\) values for this watershed (see equation (133)), in units of \(currency·m^3\). An indicator of the ecosystem service of runoff retention for the watershed. Only calculated when the Built Infrastructure Vector input is provided. Note that this does not take into account actual flood depth or extent, so should be used as an indicator only.

## Appendix: Data sources and Guidance for Parameter Selection

### LULC

### Watersheds

### Depth of Rainfall for Design Storm

A design storm is a hypothetical rainstorm used for modeling purposes. The design storm precipitation value should be chosen according to the area and goals. For instance, it could be the average precipitation per rain event, the precipitation at a certain percentile, or the maximum precipitation expected to occur once in 100 years.

To calculate the design storm, users can look up intensity-frequency-duration (IFD) tables available for their city. The storm duration is equal to the average time of concentration of the studied watersheds. Time of concentration can be derived from existing studies or from web tools: eg. https://www.lmnoeng.com/Hydrology/TimeConc.php. See Balbi et al. (2017) for a detailed description of these methods.

### Soil Groups

### Curve Number

### Built Infrastructure

### Potential damage loss for each building type

In the US, HAZUS provides damage data. Globally, a recent report from the European Commission provides useful data: https://publications.jrc.ec.europa.eu/repository/bitstream/JRC105688/global_flood_depth-damage_functions__10042017.pdf

## References

Arkema, K. K., Griffin, R., Maldonado, S., Silver, J., Suckale, J., & Guerry, A. D. (2017). Linking social , ecological , and physical science to advance natural and nature-based protection for coastal communities. https://doi.org/10.1111/nyas.13322

Balbi, M., Lallemant, D., & Hamel, P. (2017). A flood risk framework for ecosystem services valuation: a proof-of-concept.

NRCS-USDA. (2004). Chapter 10. Estimation of Direct Runoff from Storm Rainfall. In United States Department of Agriculture (Ed.), Part 630 Hydrology. National Engineering Handbook. Retrieved from http://www.nrcs.usda.gov/wps/portal/nrcs/detailfull/national/water/?cid=stelprdb1043063

NRCS-USDA Part 630 Hydrology National Engineering Handbook, Chapter 7 Hydrologic Soil Groups. 2007.

NRCS-USDA Part 630 Hydrology National Engineering Handbook, Chapter 9 Hydrologic Soil-Cover Complexes. 2004.

Sahl, J. (2015). Economic Valuation Approaches for Ecosystem Services: a literature review to support the development of a modeling framework for valuing urban stormwater management services.