The 22 000 ha study area (extending from 2∘5′29′′ S, 104∘3′14′′ E to 1∘57′11′′ S, 104∘14′1′′ E) is part of an ecosystem restoration concession, the Sumatra Merang Peatland Project (SMPP), which is located within the largest peat swamp dome in South Sumatra – the 140 000 ha Merang-Kepayang peat dome. The area is an ecologically significant wetland close to Berbak Sembilang National Park, and as is the case with many other swamp forests in Southeast Asia, it has been degraded by logging of the primary forest and by the construction of drainage canals. After more than a decade of widespread illegal logging, the SMPP rehabilitation project began in 2017 with an initial installation of 87 temporary box dams (wooden frames filled with bags with earth or peat; ), followed by 203 permanent peat compaction dams that were constructed between 2019 and 2021. The SMPP area remains uninhabited, and pioneering native forest species (e.g., ferns such as Blechnum indicum and Nephrolepis biserrata and tree species such as Archidendron clypearia and Macaranga pruinosa) are the main vegetation cover, with only 200 ha of original peat swamp forest habitat remaining.

Our study site, a large subset of the SMPP area, contains 219 km of canals and 168 dams (Fig. ). The locations of the peat compaction dams were based on elevation difference by distance . The typical dam is made out of surrounding peat and covers the canal width entirely up to the local peat surface. The peat depth averages at about 5 m. There are five patrol posts inside our area, each consisting of a weather station and six daily measured dipwells along a 200 m transect perpendicular to the nearest canal. There are 111 additional dipwells measured manually at an approximately monthly frequency. The weather stations were composed of an ombrometer, a thermometer, and a hygrometer. The WTD loggers used were simple perforated PVC pipes. Weather and WTD data were collected for 365 d, starting from 22 January 2020.

We constructed a hydrological model that produces daily WTD maps. The model consists of a canal network module (CNM) and a peat hydrological module (PHM). At each time step, these modules work in an alternate fashion to update the next day’s canal water level (CWL – meters, negative downwards) and WTD across the study area. First, the CNM computes and updates the CWL using the amount of water expected to have flowed in the peatland–canal interface, which was computed by the PHM in the previous time step. Then, the PHM computes and updates the WTD using the newly computed CWL. The PHM allows for bidirectional water flow between the canals and the peatland, but it only updates the state of the WTD not the CWL.

The CWL and the WTD are essentially the same quantity: water height above a common reference datum; therefore, they are described in this text with the same symbol, h. The context is hopefully clear enough for the reader to discriminate between the two. In the following, each module is described in more detail.

We simulated the WTD over 1 year for eight different scenarios. Each simulation started from the same initial WTD (see Sect. ). We ran the model with two different weather data (dry and wet years), two different blocks states (blocked or without any blocks), and two different peat hydraulic transmissivities, T. The eight different scenarios arise from a combination of all of the above factors (23=8).

Apart from those, we also conducted a simple reality check for the model, in which we visually compared the model results with WTD sensor data. The reality check was computed using locally measured weather station data for a single set of values of the peat hydraulic properties. This was only meant as an informal check of the plausibility of our model and was not a part of the main results of this work.

We will use 〈ζ〉 to indicate the spatially averaged WTD and ζ‾ to indicate the temporal average. Additionally, the quantity 9Δζ=ζblocks-ζno-blocks will be used to indicate the WTD difference between two modeled scenarios that only differ by the blocking condition.

CO2 emissions in the study area were modeled as a linearly increasing function of WTD, 10mCO2(ζ)=-aζ+b, where the negative sign implies that the emissions increase with deeper WTD (note that ζ is negative below ground). Equation () was used for below-ground WTD. The CO2 emissions resulting from above-ground WTDs were set to be equal to the emissions at the surface – i.e., mCO2(ζ>0)=b. In this work, we used the values from , a=74.11 Mgha-1m-1yr-1 and b=29.34 Mgha-1yr-1. These values were obtained for an Acacia plantation, which may not give the most accurate estimation of the emissions from a rehabilitating natural peat swamp forest. Therefore the reader is encouraged to treat the CO2 emission results as a rough estimation of their magnitude.

Following the notation introduced in Eq. (), we will denote the difference in CO2 emissions due to the block influence by ΔmCO2.

The comparison between the modeled and the measured WTD shows similarity in the range and the dynamics of WTD, as shown in Fig. b. The deepest WTD in both measured and modeled scenarios was about -1.5 m. During most of the year, WTD was between -0.4 and 0.1 m in the majority of the measuring locations. There were two groups of outliers in the sensor data. The sensors with an annual WTD average below -0.7 m corresponded to the easternmost patrol post transect. There were three sensors that recorded an annual WTD average above 0.5 m, but we could not find any pattern to those extreme measurements. The magnitudes of the WTD rise after heavy rainfalls and the WTD drop in the recession periods were similar in the modeled and measured datasets. The water rise and recession slopes were similar as well. As a result, the distribution of annually averaged modeled WTD was similar to the measured one, as can be seen in Fig. c.

The model captured the relevant water flow dynamics during the reality check, and thus it is considered to be plausible under the other weather scenarios presented in the study.

Blocks led to a net rise of the WTD in all modeled scenarios. This is shown qualitatively in Fig. , which aggregates Δζ‾ from all modeled scenarios into a single raster. The existence of more areas with a positive Δζ‾ (colored in blue in Fig. ) means that, overall, blocks produced a net WTD rise across all the modeled scenarios. Averaging over all scenarios, the net average WTD rise was 1.51 cm. Despite the overall WTD rise, in some areas, blocks had the effect of lowering WTD compared to the non-blocked scenario (colored in red in Fig. ). It is also remarkable that the modeled WTD in most of the peatland area far enough from canals (e.g., >1 km) was practically unaffected by the presence or absence of blocks.

The spatially averaged block-induced WTD rise, 〈Δζ〉, differed significantly across different hydraulic property values and weather scenarios, as shown in Fig. . However, 〈ζ〉 was always higher with the blocks than without the blocks (positive 〈Δζ〉) for all modeled scenarios. In other words, the overall rewetting impact of the blocks was positive at all times during the simulated period, regardless of weather conditions or peat hydraulic properties.

Figure b and c show that rainfall events reduced the difference between the WTD in the blocked and non-blocked scenarios. It may also be seen that, in the dry periods in-between any two large rainfall events, the effect of the blocks was greater. However, dry conditions did not always benefit the blocks' rewetting ability. The extreme drought starting around day 150 in the dry weather scenario shows how canal blocks became less relevant after a certain threshold of external-water-input scarcity. For the first 50 d after the start of the dry period, the gap between blocked and non-blocked WTD increased in the high-transmissivity scenario and stayed relatively constant in the low-transmissivity one (Fig. b and d). However, at around day 200, the gap began to close, and by the end of the dry period, blocks were at their minimum effectivity. As a result, the cumulative block-induced WTD rise averaged over peat hydraulic properties was similar in the wet and dry scenarios – 1.44 cm in the dry year and 1.57 cm in the wet year.

Peat hydraulic properties also played an important role in the degree to which blocks were able to raise WTD. Specifically, a larger hydraulic conductivity (or transmissivity) led to greater differences between the blocked and unblocked scenarios in both weather conditions (Fig. c and d). Averaged over the two weather conditions, the 〈Δζ‾〉 obtained with the high-transmissivity peat (parameter set 2) was 2.13 times greater than the low-transmissivity one (obtained with parameter set 1) – 2.05 cm versus 0.96 cm.

There was remarkable variation in the spatial extent of block influence among the different modeling scenarios. As an example, we show two snapshots of Δζ for the high-transmissivity simulation (parameter set 2) in wet and dry years in Fig. b and c. These figures qualitatively show that the WTD difference due to the blocks at the end of the wet year was small and concentrated around canals. In contrast, the differences at the end of the dry year were more pronounced and extended further spatially. Note that both the positive and the negative block impacts were larger at the end of the dry year; i.e., Δζ was larger in absolute value. The dependence of Δζ‾ on the distance to the nearest block, shown in Fig. a), provides a more quantitative description of the spatial extent of block impact. The effect of blocks on WTD for all modeled scenarios was relevant until about 600 m from the nearest dam, and it markedly decreased from there. The mean annual impact of the blocks on WTD more than 1 km away was negligible (not shown in Fig. a for clarity). This was true across all weather conditions and peat hydraulic properties, albeit with small variations between modeled scenarios. Higher hydraulic conductivities had the effect of increasing the spatial extent of the blocks' influence.

The net block-induced WTD rise in all modeled scenarios led to an overall decrease of CO2 emissions (Fig. ). In the worst-performing rewetting scenario, with dry conditions and a peatland with the lowest studied hydraulic conductivity (parameter set 1), the non-blocked setup emitted an annual total of 0.62 Mgha-1 more than the blocked one. In contrast, in the high-transmissivity scenario (parameter set 2), the block-induced WTD rise was translated into a 1.52 Mgha-1yr-1 CO2 emission reduction for both the dry and wet years. Averaging over peat hydraulic properties, the emission of 1.07 and 1.17 Mgha-1 CO2 was prevented in the whole year for dry and wet years, respectively.

A pursuit to estimate the impact of canal blocking in the restoration of tropical peatlands should meet the following four criteria. First, it should capture the complex and interconnected hydrological processes influencing the block performance. Second, the estimation should be done at spatio-temporal scales similar to the specific scale of the restoration project. Third, a method to meaningfully compare blocked and non-blocked scenarios is needed. Finally, in order to make generalizable claims, the sensitivity to weather conditions and peat hydraulic properties should be accounted for.

These criteria are best satisfied with a combination of empirical methods and process-based modeling. If successful, process-based models are able to combine the relevant physical processes governing water flow at sufficiently large scales. Additionally, they offer a direct method to compare different blocking setups and the ability to study the impact of different weather scenarios and peat hydraulic properties. To our knowledge, the present work, which builds upon our previous study , is the first that tries to meet all the aforementioned criteria in tropical peatlands.

A few studies have modeled tropical peatland WTD , but to our knowledge, only three have focused on the effectiveness of canal blocks, namely the studies of , , and . Both and modeled WTD in large areas and reported that the effect of dams on WTD markedly decayed at 1 km distance from the canals. However, neither of the two works analyzed the effect of different peat hydraulic properties or weather scenarios. The only study that is comparable in scope to ours is that of . Nevertheless, their study area was several orders of magnitude smaller (20 ha), and their CWL was not dynamic but manually fixed to field measurements.

The novelty introduced by our discretization of the open-channel flow equations is also worth underlining. Unlike traditional methods in which junction nodes require a special treatment , our approach describes the water flow at all nodes of the computational domain with the same equation, Eq. (). Our method is automatically applicable to canal networks of arbitrary topology, thus simplifying the model domain-building process.

Five main outcomes can be drawn from the present study.

First, dams were, on average and across all the modeled scenarios, beneficial for the rewetting of the study area. This has been observed in many studies in tropical and temperate peatlands . Canal blocks are mechanisms that increase water residence time in the peatland system, and as a result, they can only raise the average WTD. In turn, assuming a strictly positive impact of WTD rise in terms of CO2 emission reduction, this implies that dams must reduce CO2 emissions overall. However, in line with previous studies , dams were not enough to maintain WTD above the -40 cm limit set by the Indonesian Peatland Regulation Agency everywhere in the peatland during the extremely dry year (see Republic of Indonesia Government Regulation No. 57 Year 2016 about Peatland Ecosystem Protection and Management, 2016).

Second, despite raising the WTD on average, blocks did not do so everywhere in the study area. In some areas downstream from the dams, the WTD was systematically lower in the blocked scenario than in its non-blocked counterpart. To our knowledge, such an effect has not been reported in the literature. Our interpretation of this result is straightforward: the function of dams is to block water, and thus they may reduce water supply to areas with a specific combination of local canal network topology and peat topography.

Third, we found that the impact of dams on WTD was confined to areas close to the blocks. The WTD difference between the blocked and non-blocked scenarios was, on average, 3 cm at 400 m from the canals, and it was 1 mm at a 1 km distance (see Fig. ). Several studies support this claim . , using dipwell measurements, claimed that the radius of action of dams in tropical peatlands is around 170 m, and found the modeled WTD rise due to blocks to be about 10 cm at a distance of 400 m. On the one hand, this result confirms that canal blocks are effective in raising the WTD close to the canals, which is where they are most needed. On the other hand, it suggests that naively extrapolating WTD measurements performed in the vicinity of the canals may lead to an incorrect assessment of the ability of blocks to raise WTD throughout the study area.

Fourth, peat hydraulic conductivity had a great impact in terms of the extent to which dams were able to raise the WTD. This effect was also observed in , where blocks had more impact in the higher-conductivity site. Peat hydraulic properties govern the dynamics of groundwater flow, and in particular, the conductivity (or, in our model, the transmissivity) determines the rate of horizontal water flow . It follows that higher conductivities result in greater responses of WTD to modifications in the CWL. This implies that peatlands with higher hydraulic conductivities have greater potential for greenhouse gas emission mitigation using canal-blocking restoration.

Fifth, the effect of the weather on the block rewetting ability was non-trivial, with an overall slightly greater impact in the wet year than in the dry year. On the one hand, heavy rainfall events led to smaller differences between the blocked and non-blocked scenarios. And it was in the drier days in between these large rainfall events that the blocks were most effective. Our interpretation of these observations is that, with enough water supply from precipitation, WTD rises regardless of whether dams exist or not, making dams less useful. On the other hand, in extremely prolonged dry periods such as the second half of the dry year, the overall rewetting potential of the dams decreased. This behavior agreed with the findings of Putra et al. in their small-scale empirical and modeling studies . Putra et al. reported a decrease in the effectiveness of blocks during dry periods because canals became completely dry, and therefore, blocks were not able to retain any water. However, our simple model of discharge through blocks, Eq. (), completely restricts water flow through blocks even when the water is below the canal bottom, i.e., when the canal is dry. Even if the canals had dried out, our model would not have been able to reproduce the effect described by Putra et al. Thus, another mechanism must explain the observed behavior. Our suspicion is that a combination of the mentioned block impermeability and the low resolution of the data around canals might be responsible. Two consecutive watertight dams in the same canal reach create a segment that is completely disconnected from other parts of the network. The only water source of that canal segment is either precipitation or incoming water from the peatland. Given its low resolution, the digital terrain model (DTM) was not able to describe the usual depressions of the peat surface around canals, which likely reduced the water inflow from the peatland. As a result, some canal segments, embedded in peatland areas with a certain topography, may have received very little water during long dry periods. In our simulations, the negative Δζ arising from those areas decreased faster than the positive Δζ increased in the rest of the areas, hence the overall decrease in the block rewetting ability after a prolonged dry period. In reality, blocks are permeable, although less conductive than an open channel, and canals are excavated in the peat, which attracts more water from the peatland. Therefore, our results in this regard are likely an exaggeration of a subtler effect that takes place in nature. The conclusion that can be drawn from the combination of Putra's and our studies regarding the influence of weather is the following. The WTD difference between the blocked and non-blocked scenarios is generally greater in the absence of rainfall. Blocks are likely to delay the point at which canals become dry; yet, once that point is reached, blocks cease to have any impact on WTD. When water input into the system is scarce, some areas of a blocked peatland might receive considerably less water than an unmanaged one.

Applications of process-based models have two main sources of uncertainty: the simplifying assumptions made in the construction of the model and the uncertainty in the input data.

The PHM and the CNM use well-established partial differential equations to approximate water flow in peat and in canals. Despite being two dimensional, the groundwater flow equation of the PHM has been shown to accurately represent water movement in such domains where the width exceeds the thickness . The two-dimensional approximation has been used extensively in modeling of hydrology in tropical peatlands . When building the CNM, we tested the diffusive wave approximation against the full open-channel flow equations (Preissmann method; ) and concluded that the diffusive wave approximation was accurate enough for this application (testing not shown in this study). This was, in part, because the daily time step was long enough to remove the effect of the inertial terms present in the full open-channel flow equations. As was pointed out previously, the blocks were modeled as watertight barriers that extend from the surface to the impermeable bottom, while in reality they are relatively porous . The coupling between the PHM and CNM approximates water balance, but it does not strictly conserve mass. However, this is an unavoidable drawback of any hydrological model that solves groundwater and surface water flow in different modules . The error introduced in the coupling was not estimated in this work and is left for future studies, which could use techniques analogous to the ones presented in .

The lack of information about the water flow at the area boundaries hindered the choice of appropriate boundary conditions in both the PHM and the CNM. In particular, there were no data on the water discharge at the catchment outlet, and we set the boundary conditions in the CWL at that point to no-flow Neumann. This choice, although striking at first, is overrun in the PHM step by the fixed -0.2 m Dirichlet boundary conditions. The Dirichlet boundary conditions are themselves a source of inaccuracy in the simulated WTD, as would be the case with any choice of boundary conditions. It seems plausible that the distance to which the signal of the Dirichlet boundary conditions can propagate over the timescale of the simulation may be similar to the distance to which a change in the CWL affects WTD. Given our results in the present study, we can estimate that inaccuracies introduced by the Dirichlet boundary conditions would only affect the WTD up to a 1 km buffer zone around the boundaries of the study area. We nevertheless argue that these inaccuracies do not undermine the results presented in this work because they are based on direct comparisons between different scenarios. Indeed, the WTD difference maps displayed in Figs.  and b and c confirm that the difference between scenarios is negligible at the study area boundaries. It is reasonable to think then that most of the error introduced by the boundary conditions does not have a large effect on our results.

Despite being crucial for the understanding of water dynamics, there exist few published measurements of the physical parameters which govern water flow in tropical peat and in canals. Whereas the variability of the peat hydraulic properties was taken into account through the different modeling scenarios, the physical parameters governing open-channel flow were fixed in all the scenarios. In reality, all these – the width, depth, and cross-section shape of the canals; the block discharge coefficient; and the Manning friction coefficient – vary spatially and/or temporally . Since the value of these coefficients has a direct influence on water dynamics, more experimental work is needed to correctly quantify the open-channel flow coefficients for tropical peatlands. One positive point of this study, however, is that the large study area naturally included some variability in terms of the location of canals and blocks. The western part of the catchment, for instance, had more blocks per unit area than the southeastern part. This helped to capture some of the spectrum of canal and block densities typically present in tropical restoration projects without having to explicitly include it in the study design. Indeed, this heterogeneity is represented in the variance of the block impact in Fig. .

Not only the CNM parameters but also the physical parameters of the PHM are expected to have some spatial variability too. Peat hydraulic properties are known to vary with vegetation and land use , and even precipitation and evapotranspiration may change over the study area . Our model could accommodate all this spatial variability, but in the absence of data, we were forced to assume constant values throughout the study area.

The model validation against the dipwell-measured WTD was limited by the coarse resolution of the PHM computational domain. The original resolution of our digital elevation model was 100 m × 100 m, a scale at which tropical peat surface typically presents variations on the order of tens of centimeters . In the absence of further information about the precise elevation of the dipwells, we assumed an uncertainty of comparable magnitude in the dipwell WTD measurements. And since WTD variation at any location was also on the order of tens of centimeters (see Fig. ), this uncertainty prevented any direct quantitative comparison between the modeled and measured WTD. As a result, we resorted to doing a qualitative estimation of the model plausibility (see “Reality check”, Sects.  and ). Two main features of the reality check of Fig.  support the validity of the model. First, the model was unbiased, and the range of modeled and measured WTD was comparable. Second, the modeled WTD presented similar ranges and slopes in the daily dynamics driven by precipitation and evapotranspiration. The origin of the dipwell measurements showing WTD up to 1 m above the surface in Fig.  is unknown to us. They could be due to a wrong datum or due to local depressions that are unnoticeable in the DTM, which canalize the water to certain spots.

The coarse resolution also prevented precise modeling of the canal–peatland interface (see Fig. b and c). This may have led to an underestimation of the water gradient between the canals and the peatland and therefore also to low CWL in very dry conditions (see fifth point in the previous section).

Despite the presented limitations, we claim that the modeling setup presented here has a greater potential to study the rewetting ability of blocks than purely experimental studies have. On the one hand, the effect of some of the aforementioned uncertainties might be partially compensated for by the fact that we have only presented relative comparisons between blocked and non-blocked scenarios. On the other hand, our model gives theoretically coherent estimates of the dam impact throughout the area, which is not possible to do with experimental studies alone.

The present work was limited to the analysis of a single study area, with one block location configuration, for a relatively short period of time. Future studies might consider how varying the number of dams and their positions affects WTD, since, as we know, the dam position is critical . Furthermore, the impact of blocks on WTD would probably change on timescales of decades, which is closer to the typical lifespan of canal blocks . When analyzing long-term scenarios, the effect of climate change on precipitation and evapotranspiration , as well as on peat subsidence , will need to be addressed.

In order to have a more precise estimate of greenhouse gas emissions, future studies should take into account emissions of other compounds, such as methane and nitrous oxides. In fact, having shallower WTD as the only optimization goal may not be desirable due to increased methane emissions – although we are not aware of any studies where methane emissions have been shown to surpass CO2 emissions .

It might be interesting to connect process-based models such as the one presented in this work not only with more extensive empirical studies but also with state-of-the-art remote sensing techniques for WTD measurement, such as in .