Drained peatlands are one of the main sources of carbon dioxide (

Peatlands occupy around 3 % of global land area but hold up to one-third (630

Water table depth (WTD) has been found to be the key variable controlling

Studies of canal and ditch blocking in temperate peatlands describe how WTD rises for peatland restoration have been commonly carried out using drain or canal blocks constructed from surrounding peat material, mineral soil or artificial materials

To the best of our knowledge there is no systematic approach to support finding optimal block positions

Our objective in this work was to build a computational scheme based on a simple hydrological model coupled with an optimization algorithm that maximizes the amount of rewetted peat with a given number of canal blocks. The hydrological model uses the Boussinesq equation to compute WTD as a two-dimensional surface. Using the WTD – a proxy for the

The study area was located in Siak, Riau, Indonesia (Fig.

For our computations we used the

The computation consists of the following modules: the canal water level subroutine, the hydrological model and an optimization algorithm. Figure

Schematic representation of a single iteration of the computation showing the most relevant input and output and the interaction between the modules. The numbers in parentheses refer to the corresponding section in the main text. DEM stands for digital elevation model. The optimization algorithm proposes a particular position for the canal blocks,

Terms and symbols used in the study.

This subroutine calculates the CWL (

In order to compute how

the water level of

When a block is built in a given pixel of the canal raster, its water level and the water level of upstream pixels rise up to match the height of the block with no delay. In what follows, instead of using the block height as a variable, we use the block head level (

Side view of a canal. The solid blue and the brown horizontal lines represent the initial CWL,

A detailed description of the algorithm used to implement these rules and compute

The peat hydrological model simulates the two-dimensional WTD surface for a given configuration of the blocks. From there it computes the target variable of the optimization algorithm,

In this setup, the transmissivity is given by

The degree of decomposition (hemic, sapric) affects the hydraulic conductivity. Hydraulic conductivity values for different decomposition stages were adopted from

Hydraulic conductivity decreases exponentially with depth

Woody peat is the dominant material in tropical peat deposits. The van Genuchten function was used to compute the volumetric water content of peat at depth

Derived

Cross section of the simulated WTD for 3 consecutive dry days after a big rainfall event and peat hydraulic properties.

Ponding water in fully saturated profiles was neglected, and all surface water was removed from the computation, therefore assuming that the typical runoff velocity of water is greater than the infiltration velocity.

All simulations started from a fully saturated landscape, i.e.,

The spatially averaged WTD (

In order to estimate the annual

The exact values of

The management question of finding the position of a given number of blocks in such a way that the amount of emitted

Let

The objective function

Even global optimization algorithms are not guaranteed to find the optimal solution in a search space in which all options cannot be tested. Given that there exists no guarantee that the process will converge towards the true global minimum of

Block locating methods and their parameters. The values of the parameters were decided empirically.

The parameters used for both algorithms were fixed by trial and error, and they are shown in Table

This optimization setup is computationally expensive regardless of the optimization algorithm used. The main bottleneck of the computation is the numerical solution of the Boussinesq equation, Eq. (

To evaluate the performance of the optimization algorithms, we compared the resulting

In order to enable a meaningful comparison between different setups, the average WTD resulting from these simulations was normalized with the average WTD in the absence of blocks, i.e.,

In a similar vein, we define the improvement of any block locating method to be

Yet some more insight can be gained by looking at the results in terms of marginal benefits. We define the marginal benefit of building

The quantities from Eqs. (

In order to demonstrate that the peat hydrological model and the canal water level subroutine reproduce the expected qualitative behavior of the WTD, two figures are shown. Figure

The behavior of the canal water level subroutine is demonstrated by comparing the CWL change in a small drained area with and without canal blocks (Fig.

WTD after 3 dry days with and without blocks.

The average WTD was computed using different scenarios with an increasing number of canal blocks (

Peat rewetting performance comparison of random block locations, the rule-based approach and the optimization algorithms (SA: simulated annealing; GA: genetic algorithm; SO: simple algorithm) for different numbers of blocks.

The most straightforward observation is that the more blocks there are, the larger the fraction of peat they will rewet, even if they are placed randomly. The second observation is that the optimization algorithms were able to find systematically better block positions than the random or the rule-based approaches. An informative way to gauge this difference is to realize that they were able to obtain with only 10 blocks the same amount of rewetted peat that the random configurations did with 60 blocks (Fig.

Another thing to note is that the rate at which

As Fig.

Correlation between

The sensitivity of

Sensitivity of the average WTD to a difference in the block head level,

In order to draw further conclusions about the beneficial environmental impact of building canal blocks, we simulated the WTD for a full year under two different regimes: without any blocks and with the best available positions for the maximum number of blocks (80). Rainfall intensity was taken from Pekanbaru airport's weather station data, located in the same province as the target area. The heavy rainfall events registered during December 2012 were used as the starting point for the simulation, which was set up with completely saturated initial conditions. Evapotranspiration was set to 3

Simulated daily WTD for two sites (drained and natural, see Fig.

Nearby blocks were able to raise the water table by approximately 20

We obtained the following annual average values for the entire area:

To the best of our knowledge, this work introduces the first freely available systematic tool that can quantify the rewetting performance of different block configurations. It operates on all the easily available data (data derived from weather and geographic information system, GIS) and combines them in a scientifically coherent way. It is also designed to be computationally feasible for large areas. Therefore, this tool can potentially be very useful for decision makers in greenhouse gas emission mitigation and drained peatland restoration contexts.

The qualitative behavior of the WTD and of the CWL in Figs.

In this study, we did not validate the hydrological model against actual field data because there is no extensive, publicly available dataset. The aim of the paper was not to test a new hydrological model per se but rather to solve a management question by applying a preexisting one with parameter values derived from the literature. We assume that a more precise parameterization would not have changed the outcome of the optimization procedure, and thus the qualitative assessment of the parameters’ fitness was enough to fulfill our principal objective. It might be argued that in the absence of a quantitative validation, there is a high uncertainty in the simulated annual WTD of Fig.

Some remarks about the assumptions made in the canal water level subroutine are in order. As explained in Sect.

Two basic observations can be drawn from Fig.

The second observation is that the optimization algorithms performed systematically better than the random and rule-based approaches. Going into further details, GA and SO were more successful in minimizing

However interesting, comparing the performance of different algorithms was not the objective of this work. Instead, the main conclusion can be drawn by contrasting the outcome of the optimization algorithms with the best humanly available guesses. With the same number of blocks, the reduction in average WTD by the optimized block configuration is systematically greater than the one achieved simply by logical reasoning

It is not expected that a different choice of parameters would affect these general observations of the optimization results. While different parameterizations will result in a different WTD in absolute terms (see, e.g., the case of varying

It is also worth mentioning that solving the steady-state version of the Boussinesq equation, Eq. (

The simulated annual

On the other hand, looking at the

It is clear that canal blocking raises WTD and therefore decreases

When considering the applicability of our method to real-life scenarios, some of its underlying assumptions should be stated clearly. Our method assumes that it is possible to build a block at any given point in the canal raster and that the cost of doing so is constant and independent of site properties.

It remains true that choosing the location of a set of blocks for best performance is a daunting task due to the complexity of the response of the water table and even more so when different types of blocks are considered. Therefore, the specifics of Figs.

We constructed an optimization scheme that looks for the maximum water table rise for a drained peatland area given a fixed amount of canal blocks. Our results show that, with the same amount of resources (i.e., number of blocks), the present computational setup enables a more effective canal blocking restoration of drained peatlands than human guesses do. The computational approach also enables a cost-benefit analysis to solve several management questions.

The information about the topology of the canal network was stored in a (sparse) matrix,

Contiguous upstream pixels were defined in rules 1 and 2 of Sect.

Say we wish to build a block in pixel

Line 1 sets the new value of the CWL in the pixel where the block is built to be

For the sake of readability, Algorithm 1 shows a single step in the process of computing

The source code and the data used are available under the MIT license at

IU and AL contextualized the problem and developed the model code. IU performed the simulations. AB, IB and MN produced and validated the datasets. KH helped formulate the research goals and methods. MP, HH and AL contributed by reviewing and editing the paper. IU prepared the paper with contributions from all coauthors.

The authors declare that they have no conflict of interest.

The authors wish to thank the referees' thorough comments on the paper and Harri Koivusalo for useful discussions about the hydrological modeling. Furthermore, the authors wish to acknowledge CSC – IT Center for Science, Finland, for computational resources.

This paper was edited by Alexandra Konings and reviewed by Alex Cobb and one anonymous referee.