# Triage and investment optimisation for peatland restoration (Scottish Woodlands)

## Challenge Participants

- Eric Hall, University of Dundee ([e-mail])
- Luis Espath, University of Nottingham ([e-mail])
- Roxane Andersen, University of the Highlands and Islands ([e-mail])
- Nicole Augustin, University of Edinburgh ([e-mail])
- Radia Rayan Chowdhury, CSX/Teeside University
([e-mail])
- Adnan Khan, James Hutton Institute ([e-mail])
- Ehsan Jorat, Abertay University ([e-mail])
- Chris Fallaize, University of Nottingham ([e-mail])
- Josh Finn, University of Nottingham ([e-mail])

## Summary of challenge

Scottish Woodlands manages a portfolio of peatland restoration projects for large estates (these are Scottish Woodlands' clients). Large estates may have parcels of land that are suitable for peatland restoration. There are public grants available to help with the cost of restoring peatland and restored peatland can be used to attract carbon credits (private finance). In certain circumstances, restoring degraded peatland can be more profitable than managing a woodland on the same site. Scottish Woodlands' peatland manager plays a role in assessing the site suitability, designing the resotration works, preparing funding applications for public finance (e.g., Peatland ACTION), navigating carbon credit pathways under Peatland Code, and exploring alternative restoration techniques where appropriate.

A typical situation is that an estate has a large parcel of land containing regions of degraged peat that may be suitable for restoration. These regions of degraded peat must be triaged and then choices about which restoration projects to proceed with must made that take into account a number of considerations and constraints. Currently, this work is done more or less 'by hand'. Peatland managers would like to improve the initial appraisal and triage of large estates into priority areas for restoration. They are also interested in developing tools that help them make optimal decisions.

### Background

For a large estate ($O(1e3)$ hectares) the smallest unit that can be considered for restoration is a _hyrdological unit_. Hydrological units vary in size but should be taked as 'defined' (one can obtain maps that define hydrological units). The reason for considering hydrological units is due to the complexities of funding for peatland restoration projects. A single hydrological unit may have a number of features (e.g., drains or eroded peat) that may need to be restored in order to restore the hydrological unit. Restoration is viewed as a classification; a feature/hyrdological unit moves between classes and this is how success is evaluated. Peat condition/classification is defined by Peatland Code (IUCN categories): actively eroding, drained, near natural, modified. Moving peat from state 'actively eroding' and restoring it to 'modified' is an act of carbond abatement that can be used to earn carbon units, which have a cash value in market. Examples of actively eroding peat are hags and gullies. (Nb. carbon units are calculated based on the state of the peat (classification) not based on a measure of carbon sequestered etc).

Peatland restoration is funded via public and private mechanisms. Peatland Action is the primary public funding mechanisms. It only pays for capital investment (the intervention itself) and receipients are bound to maintain the investment for around ~10 years. That is, the landowner pays for costs associated with maintenance such as repairs to restored features e.g. dams to block up drains. The main source of private funding is through Peatland CODE by trading carbon units from emission reduction associated with restored peatland. Contracts for carbon units have ~30-100 years terms and the contract length depends on peat depth (100 yrs needs 1m deep of peat). Only certain categories of peatland qualify, but funds can be used for both investment and planning. Carbon units are closely aligned with IPCC reporting from land use sector, prescribed by Peatland CODE based on emission reductions achieved by moving from a degraded category to a less degraded category. Peatland CODE has a simple, linear function that allocates units of carbon annually, which can be sold upfront (unverified) or sold post-verification at specified times: e.g., in year 5 and every 10 yrs after. The amount of units for a given area in a given category is fixed.

### Approach

In the study group, we first considered the problem of optimisation and decision support as we thought this migth inform the modelling that would be required for triage. The challenge holder presented three different 'Client Profiles' that speak to motivaiton and approach to peatland restoration. These profiles are:
1. **Carbon**: This client wants to maximise carbon units, has a higher risk appetite, and higher capital/expenditure.
2. **Biodiversity and hydrology**: This client is interested in peatland restoration for conservation aspects. They are amenable to research projects (including not carbon unit generating interventions) and their public profile is important.
3. **Limited risk**: these are typically smaller clients that undertake projects that need to be cost neutral as they have very limited risk appetite. They are interested in smaller, low risk projects such as drain blocking and have other priorities for adjacent land, suhc as agricutlure or shooting.

This list is not exhaustive. Thus, we note that there are many different objectives that one may wish to consider optimising. The differences in objective are driven by not only by the condition of the peatland and the difficulty of restoring it, but by the different funding mechanisms available.

Factors that impact the suitability of a hydrological units for restoration include: accessibility, slope angles, condition (actively eroding, drained, near natural, modified), and peat depth. These factors seem related to geospatial information for which historical data might be available. There are many risks that must also be considered; the potential risks associated with peat restoration (such as critical failure of peat accumulated up a slope) may need separate statistical and mathematical models to inform the overall optimisation (system of systems approach).

## An optimisation problem

We first consider the problem of the optimising the "Carbon" profile as a minimal working example. This profile seeks to choose an optimal restoration portfolio across a given number of hydrological units.

We consider a set of hydrological units $h \in H$ and make the following assumptions:
- Each hydrological unit has a fixed cost for initial restoration.
- Each hydrological unit has a fixed carbon unit return which can be translated into a carbon sales value.
- Each hydrological unit restoration project will take the same, fixed time.

Narrative description of uncertainties:
- The initial restoration cost has high uncertainty (there are many covariates).
- The carbon unit return has low uncertainty as it is specified by Peatland CODE, however, the sales value is subject to market variability.
- Each project will have a fixed contract period that will be related to peat depth and the particular features contained within the hydrological unit.

### Variables

- Cost of resotration $r_h > 0$ (units £) per hydrological units
- Carbon units sales value $c_h > 0$ (units £) per hydrological unit
- Risk aversion $\lambda \in (0, 1)$, with $1$ risk averse
- Restoration budget $B_r > 0$ (units £)
- Risk budget $B_s > 0$ (units £)
- Decision variable $y_h \in \{1,0\}$ (either restore it, or ignore it)

### Constraints

- Total restoration cost cannot exceed restoration budget:
$$ \sum_{h\in H} r_h y_h < B_r \,.$$
- Total risk cost cannot exceed risk budget:
$$ \sum_{h \in H} s_h y_h < B_s \,.$$

### Objective function

For each hydrological unit, the profit is the carbon sales unit less the restoration cost, less a cost of future upkeep that is modified by the landowner's level of risk aversion:
$$ c_h - r_h - \lambda s_h \,.$$

The total profit is
$$ f(c, r, s, y) = \sum_h (c_h - r_h -\lambda s_h) y_h \,, $$
i.e., we only consider profit for restored units. The objective is to maximise the total profit:
$$ \max \sum_h f(c_h, r_h, s_h, y_h) \,. $$

### Optimisation

We would like to find the list of hydrological units to restore that maximise the objective,
$$y_h^* = \arg \max_{y_h} \sum_h f(c_h, r_h, s_h, y_h) \,,$$
subject to:
$$c_h > 0\,, \forall h \in H\,, \qquad \sum_{h\in H} r_h y_h < B_r \,, \qquad \sum_{h \in H} s_h y_h < B_s\,.$$

## Triage problem

- [ ] TODO: add here some introduction/description of sections below.

### Statistical model for initial costs

- [ ] TODO: add reasons for why a statistical model for initial costs might be reasonable
- [ ] TODO: add list of covariates and possible data sources.

### Models for restoration risks

- [ ] TODO: discussion of market variability (what models reasonable here?)
- [ ] TODO: summary of \{slope, elevation, peat depth models\} under restoration
- [ ] TODO: summary of peat failure models (profound change of rewetting)
- [ ] TODO: mention role of rainfall and climate (change)

## Board work, useful links, etc

- Initial description of assumptions per hydrological units:
- Table of restoration and construciton costs: 
- Discussion of risks: 
- JHI drainage and erosion data for Scotland: https://openscience.hutton.ac.uk/dataset/peatland-drainage-and-erosion-scotland
- Comparative analysis of peatland restoration methods:
https://www.climatexchange.org.uk/wp-content/uploads/2023/09/peatland-restoration-methods-a-comparative-analysis.pdf
- Note on maintenance costs of restored peatland:
https://caledonianclimate.com/assets/images/files/ccp-maintenance-paper-final.pdf