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Restoration opportunity area and costsMangrove restoration programmes have a greater chance of being successful when implemented in areas where mangroves have previously grown15. These areas have either been subject to deforestation or degradation and may be under government management or private ownership. They are locations that have undergone forest conversion into other land uses, including aquaculture, crops or plantations and urban settlements. Land ownership status is an important factor to consider for determining the availability of land for mangrove restoration7. For example, a higher opportunity and priority would be given to unproductive aquaculture ponds located in the protected and production forest areas which are under government management or leasehold, rather than in areas with other land uses that may be under private ownership (Methods gives detailed forest land tenure classifications in Indonesia). Therefore, managing mangrove rehabilitation should consider factors that include land tenure status and land-cover type as well as biogeomorphology (for example, ensuring that the correct mangrove species are used in hydrologically suitable locations) across landscape scales.We calculated that ~193,367 ha of land may be feasible for implementation of mangrove rehabilitation programmes (Fig. 4). This conservative assessment suggests that the potential for restoration may be only 30% of the current mangrove rehabilitation area target (600,000 ha). Depending on the challenges and opportunities for each of the biogeomorphological categories of land use and the forest land status we considered (see Methods for detailed mapping methodology), we identified that 9% of the potential restorable area was categorized as being within the high opportunity scenario, 33% as medium and 58% as areas falling within the low opportunity scenario. Among these scenarios, ~75% of identified areas have non-protected forest status, implying a greater tenurial challenge to establishing a rehabilitation programme. We identified the five provinces that are among the top ranked of high potential for mangrove restoration in Indonesia, namely East Kalimantan (20% of national restoration potential area), North Kalimantan (20%), South Sumatra (12%), West Kalimantan (5%) and Riau provinces (5%) (Fig. 1c). All of these provinces, except South Sumatra, are among the areas already identified in the current mangrove rehabilitation programme by the BRGM as having high opportunity for rehabilitation4. At the subprovincial scale, we identified the top six regencies with restoration area opportunity >10,000 ha, namely Banyuasin, Bulungan, Tana Tidung, Paser, Berau and Nunukan (Supplementary Table 1). Mangroves across these regions were commonly deforested after 2010 and converted into aquaculture ponds despite being designated as protected forest areas (Supplementary Table 1).Fig. 4: The distribution of mangrove loss area (in hectares) between 2001 and 2020 in Indonesia.Also shown are mangrove loss proportions within different biogeomorphological typology, loss drivers (land-use types), forest land status and identified scenarios of restoration opportunity (low, medium and high).Full size imageConsidering that previous successful (85% survival rates) mangrove rehabilitation around the world has been achieved only at small landscape scales (10–400 ha) with costs varying between US$1,500 ha−1 and US$9,000 ha−1 (refs. 8,16), the large-scale mangrove rehabilitation ambition of Indonesia must be carefully planned. Rehabilitating ~200,000 ha of degraded mangroves will require between US$0.29 billion and US$1.74 billion. The 2021 annual government budget allocation for mangrove rehabilitation under BRGM alone is ~US$0.10 billion17, which is 66–94% lower than the estimated total required budget but with additional international investment18 there is potential for scalable mangrove rehabilitation success.Lessons learned from the past failuresIn Indonesia, unproductive aquaculture ponds have become targets for mangrove rehabilitation programmes (Supplementary Fig. 1). However, metrics of rehabilitation success in these settings reveal low survival rates of planted seedlings, highlighting an urgency to develop new strategies for mangrove rehabilitation and strategies to assess the effectiveness of ecosystem rehabilitation6. For example, a silviculture approach—nursery-based mangrove planting using Rhizophora species—has been adopted for mangrove restoration and management for a long time in Indonesia19. When seedlings are directly planted in unused ponds (Supplementary Fig. 1), dense monoculture plantations often form, which despite providing some ecosystem services (for example, carbon sequestration20) have limited biodiversity value21 and may be less resilient to stressors compared to a diverse assemblages of tree species22.Mangrove restoration projects have often suffered low success rates due to inadequate hydrological site assessments before revegetation23. For example, mangrove planting programmes initiated after the 2004 tsunami were focused on mono-species planting and on reporting the number of seedlings being planted in a given area24. These planting projects most often occurred on undisputed land, such as mudflats, which are inappropriate locations for long-term mangrove growth because of high inundation frequency, high water flow rates and hypersaline conditions that limit seedling establishment and survival24. Planting has also focused in mangrove areas where low canopy cover is observed. While some mangrove areas with low canopy cover may respond to plantings because they are degraded, many sites naturally support low canopy cover, reflecting suboptimal environmental conditions for growth of Rhizophora species, instead favouring growth of highly salt tolerant species such as Avicennia spp.24. Such failures in mangrove rehabilitation efforts, however, have been under-reported with more than 50% of rehabilitation studies not monitored over time (Supplementary Fig. 1).Alternative restoration approaches through repairing hydrology, including excavation and removal of pond walls and tidal gates, have also been introduced15, although this approach has been only practiced in Indonesia at limited scales, mostly in unused aquaculture ponds25. A comprehensive understanding of the opportunity for mangrove rehabilitation in Indonesia is largely unquantified. Additionally, with limited monitoring of mangrove rehabilitation projects, the effectiveness and functionality of mangrove rehabilitation in Indonesia remains largely unknown and therefore it remains challenging to assess rehabilitation effectiveness between approaches and locations in Indonesia. Yet such assessments provide important data to achieve the ambitious mangrove rehabilitation goals of Indonesia.Mangrove governance in IndonesiaMangrove conservation in Indonesia was formally adopted in 1990 (Extended Data Fig. 1 and Supplementary Table 2), when mangroves were designated as protected forests under Law 5/1990 and the Presidential Decree 32/1990. When the Asian tsunami hit Aceh province in 2004, the role of mangroves in wave attenuation and therefore minimizing disaster risks for coastal communities was recognized26. As a result, nearly 30,000 ha of damaged mangroves were rehabilitated to recover coastal resiliency through planting of nearly 24 million seedlings over 60 projects24. However, the success of these programmes was low due to a lack of planning, monitoring and critical supplemental actions24,27. Despite the failure of many mangrove rehabilitation projects post-tsunami, the implementation of the subsequent programmes have not fully adopted best-practice mangrove rehabilitation principles6,7,15,23. In 2007, similar approaches to mangrove rehabilitation and conservation were adopted at a larger, national scale under the Spatial Planning Law (Law 26/2007) and the Coastal Area and Small Islands Management Law (Law 27/2007).In 2012, the National Mangrove Management Strategy (STRANAS Mangrove) was first established and followed by the formalization of the National and Regional Mangrove Working Group whose task was to guide mangrove conservation and rehabilitation. Its main goal was to involve more stakeholders, including civil society organizations and subnational government bodies, in mangrove conservation and rehabilitation28. Until 2017, the technical regulation of strategy and performance indicators for mangrove management was implemented with targets set to rehabilitate 3.49 Mha of mangroves by 204529. In 2020, however, the Mangrove Working Group and its supporting regulations were abolished and the mangrove rehabilitation strategy was subsequently managed by BRGM4. This effectively removed the regional governments (subnational working groups) from decisions related to mangrove management and concentrated development of policy at the level of the national government. The new strategy includes a tenfold increase in the annual rehabilitation target (from 11,250 to ~120,000 ha yr−1) with an overall target of 600,000 ha to be achieved within a shorter timeline (2020–2024). Without clear planning and appropriate strategies, these ambitious targets may not be feasible. For example, the annual mangrove rehabilitation area reached between 2017 and 2020 was only 5,318 ha (50% of the target) despite 2.6 million seedlings being planted (Supplementary Table 3). Given the lessons from the previous mangrove rehabilitation and the emerging processes of mangrove governance, it is timely to set an achievable restoration framework with improved planning, evaluation and monitoring.Implication for international environmental agendasA successful mangrove rehabilitation programme can directly contribute to reducing poverty (SDG 1) and maintaining food security and livelihoods (SDG 2), thereby increasing the health and well-being of 74 million coastal people in Indonesia (see Supplementary Table 1 for total population of regions with restoration potential area >5 ha). Additionally, mangrove rehabilitation will directly contribute to other relevant SDGs, such as improving water quality (SDG 6), providing healthy coastal habitats for fish and other marine biodiversity (SDG 14), contributing to emissions reductions and improving coastal resilience from sea level rise (SDG 13) and sustainably managing and protecting terrestrial ecosystems (SDG 15). Mangrove rehabilitation contributions to SDG 1 and 2 are particularly relevant as the current rehabilitation programme is delivered as cash-for-works activities under the National Economic Recovery strategy (PEN) as part of the social welfare payments to alleviate economic impacts of the COVID-19 pandemic17. With the current annual mangrove rehabilitation budget of US$0.10 billion17, further implementation of scalable community-based mangrove restoration with technical support from subnational and non-government stakeholders could increase the benefits to local communities, if administered properly. Therefore, the large investments planned for coastal communities via a national mangrove restoration programme will not only contribute to the economy of coastal communities, potentially reducing poverty across 199 regencies but will also help in securing nearly 4% of the national greenhouse gas emissions reduction target from the land sector.Restoring 193,367 ha of mangroves in the next 5 years (2021–2025) may contribute to carbon sequestration of 22 ± 10 MtCO2e by 2030 (see Methods for detailed estimate calculation and assumptions). Moreover, stopping the current annual rates of mangrove loss of 7,436 ha yr−1 between 2021 and 2030 will reduce up to 58 ± 37 MtCO2e or 12% of the national land sector emissions reduction targets. Clearly, climate benefits from mangrove rehabilitation and conservation in Indonesia are substantial if rehabilitation and conservation can be implemented appropriately and large annual rehabilitation targets are achieved. Indonesia has submitted its updated Nationally Determined Contributions (NDCs) to the United Nations Framework Convention on Climate Change, within which integrated management and rehabilitation of mangroves is a component of the actions to enhance the resilience of coastal ecosystems30. Further ecological aquaculture practices such as silvofisheries which are commonly applied in Indonesia31,32 may provide promising potential for climate change mitigation through mangrove biomass enhancement. With the increased potential for international investment to support mangrove rehabilitation in Indonesia, there is an opportunity for Indonesia to take the lead and show the world how mangrove conservation and rehabilitation can contribute to multiple international environmental agendas.In the past three decades, the governance of mangrove conservation and rehabilitation in Indonesia has been highly variable in approach (Extended Data Fig. 1). The current approach is top-down4 which has risks and may be ineffective at achieving landscape-scale increases in mangrove extent, as was demonstrated post-tsunami24,29. This top-down approach set by national-level agencies, which are responsible for achieving rehabilitation targets, has limited involvement (or investment) by subnational governments. While we have identified key factors that determine land available for mangrove rehabilitation, the success of mangrove rehabilitation is not necessarily assured because of the limited involvement of subnational mangrove working groups. A current ‘one size fits all’ strategy of the national government may not be appropriate to achieve successful mangrove rehabilitation and thus more flexible, localized approaches may increase the likelihood of success. More

Plant species and pollinatorsMedicago sativa L. (Fabaceae), also called alfalfa or lucerne, is a perennial legume with flowers arranged in a cluster or raceme. It is a self-compatible plant with fairly high outcrossing rate (5.3–30%)46, and it requires insect visits for seed production47. No plant material was collected for this study. Honey bees, Apis mellifera, and alfalfa leafcutting bees, Megachile rotundata, are used as managed pollinators in alfalfa seed-production fields in the USA while bumble bees are commonly used in alfalfa breeding47.Experimental design and pollinator observationsFive 11 m × 11 m patches of M. sativa plants were set up in an east–west linear arrangement at the West Madison Agricultural Research Station in Madison, Wisconsin, USA. Within each patch, we transplanted 169 young plants grown from seeds in the greenhouse, each placed 90 cm apart. These plants grew and, at flowering, a plant had an average of 30.65 ± 16.4 stems per plant, with 4.93 ± 3.41 racemes per stem, and 7.53 ± 2.44 open flowers per raceme.A honey bee hive was placed approximately 100 m from the patches and a bumble bee hive was set up at the center of the southern edge of the patches. For leafcutting bees, a 60 × 30 × 7.6 cm bee board was set up in each of two boxes placed 1/3 and 2/3 along the southern edge of the patches and a half gallon of bees was released at periodic intervals throughout the alfalfa flowering season.Over two consecutive summers, observers followed bees foraging in the alfalfa patches, marked each raceme visited in succession within a foraging bout with a numbered clip, and recorded the number of flowers visited per raceme. After a bee had left a patch, observers went back to the marked racemes and measured the distance and direction traveled between consecutive racemes. Directions were recorded as one of the cardinal directions: North (N), South (S), East (E) or West (W), or inter-cardinal directions: Northeast (NE), Southeast (SE), Northwest (NW) and Southwest (SW). The frequency distributions of distances and directions traveled between two successive racemes are presented for each bee species each year in Figs. 1 (distances) and 2 (directions). The low pollinator abundance permitted observers to follow individual bees foraging in a patch. Little interference among bee species was observed in the patches.Figure 1Frequency distributions for distances traveled between consecutive racemes (cm) for each bee species each year.Full size imageFigure 2Frequency distributions of directions traveled between consecutive racemes for each bee species each year.Full size imageModel for the distance traveled between consecutive racemesWe first determined whether a statistical model best described the distance traveled between consecutive racemes (Modeled Distance), and examined whether the model differed among bee species. We used mixed effect linear models (proc Mixed in SAS 9.3)48 to identify the model that best described the distance traveled by pollinators between consecutive racemes. The model included loge distance as a linear function of loge flower number and bee species as fixed effects. The distance traveled between consecutive racemes and the number of flowers visited per raceme were log transformed prior to analyses in order to improve the models’ residuals. In addition, we included patch and foraging bout as random effects in the model. A foraging bout includes the racemes visited in succession from the time a bee is spotted in a patch to the time it leaves that patch. We used foraging bout instead of individual bee as the random effect because bees were not individually marked in this study. Moreover, to take into consideration the potential correlation between successive observations within a foraging bout, we added clip to the model. Clip 1 represents the first and second racemes visited in the foraging bout; clip 2, the second and third, and so on. Clip was added to the model either as a random effect or as a repeated measure with an AR(1) structure. The combination of random clip and random foraging bout creates a model that is sometimes called the “compound symmetry” model. The AR(1) structure represents correlations that decline exponentially as the gap between measurements increases such that measurements closer together in time are more strongly correlated than measurements further apart. Because we expected bees to visit flowers at close proximity when resources are abundant, we chose this correlation structure as a good potential descriptor of the way distances might be correlated within foraging bouts. We started with a full model which included loge flower number, bee species, patch, foraging bout, and clip either as a random effect or as a repeated measure with an AR(1) structure. We then removed variables and compared models by inspecting AIC values and the p values for each term in the model. We considered both low AIC and statistically significant (p  More

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LightGBMBefore explaining LightGBM23, it is necessary to introduce XGBoost24, which is also based on the gradient boosting decision tree (GBDT) algorithm30. XGBoost integrates multiple classification and regression trees (CART) to compensate for the lack of prediction accuracy of a single CART. It is an improved boosting algorithm based on GBDT, which is popular due to its high processing speed, high regression accuracy and ability to process large-scale data31. However, XGBoost uses a presorted algorithm to find data segmentation points, which takes up considerable memory in the calculation and seriously affects cache optimization.LightGBM is improved based on XGBoost. It uses a histogram algorithm to find the best data segmentation point, which occupies less memory and has a lower complexity of data segmentation. The flow of the histogram algorithm to find the optimal segmentation point is shown in Fig. 3.Figure 3Histogram algorithm.Full size imageMoreover, LightGBM abandons the levelwise decision tree growth strategy used by most GBDT tools and uses the leafwise algorithm with depth limitations. This leaf-by-leaf growth strategy can reduce more errors and obtain better accuracy. Decision trees in boosting algorithms may grow too deep while training, leading to model overfitting. Therefore, LightGBM adds a maximum depth limit to the leafwise growth strategy to prevent this from happening and maintains its high computational efficiency. To summarize, LightGBM can be better and faster used in industrial practice and is also very suitable as the base model in our tide level prediction task. The layer-by-layer growth strategy and leaf-by-leaf growth strategy are shown in Fig. 4.Figure 4Two GBDT growth strategies.Full size imageCNN-BiGRUConvolutional neural networkA convolutional neural network (CNN) is a deep feedforward neural network with the characteristics of local connection and weight sharing. It was first used in the field of computer vision and achieved great success32,33. In recent years, CNNs have also been widely used in time series processing. For example, Bai et al.34 proposed a temporal convolutional network (TCN) based on a convolutional neural network and residual connections, which is not worse than recurrent neural networks such as LSTM in some time series analysis tasks. At present, a convolutional neural network is generally composed of convolution layers, pooling layers and a fully connected layer. Its network structure is shown in Fig. 5. The pooling layer is usually added after the convolution layers. The maximum pooling layer can retain the strong features in the data after the convolution operation, eliminate the weak features to reduce the number of parameters in a network and avoid overfitting of the model.Figure 5Schematic diagram of a convolutional neural network.Full size imageBidirectional GRUIn previous attempts at tide level prediction by scholars, bidirectional long short-term memory networks35 have achieved good prediction results. However, in our subsequent experiments, the bidirectional gated recurrent unit achieved higher prediction accuracy than BiLSTM, so we used the BiGRU network for subsequent prediction tasks.The GRU network36 adds a gating mechanism to control information updating in a recurrent neural network. Different from the mechanism in LSTM, GRU consists of only two gates called the update gate ({z}_{t}) and the reset door ({r}_{t}).The recurrent unit structure of the GRU network is shown in Fig. 6.Figure 6Recurrent unit structure of the GRU network.Full size imageEach unit of GRU is calculated as follows:$${z}_{t}= sigma ({W}_{z}{x}_{t}+{U}_{z}{h}_{t-1}+{b}_{z})$$
(7)
$${r}_{t}= sigma ({W}_{r}{x}_{t}+{U}_{r}{h}_{t-1}+{b}_{r})$$
(8)
$${widetilde{h}}_{t}=tanh({W}_{h}{x}_{t}+{U}_{h}left({r}_{t}odot {h}_{t-1}right)+{b}_{h})$$
(9)
$${h}_{t}={z}_{t}odot {h}_{t-1}+left(1-{z}_{t}right)odot {widetilde{h}}_{t}$$
(10)
In the above formula, ({z}_{t}) represents the update gate, which controls how much information is retained from the previous state ({h}_{t-1}) (without nonlinear transformation) when calculating the current state ({h}_{t}). Meanwhile, it also controls how much information will be accepted by ({h}_{t}) from the candidate states ({widetilde{h}}_{t}). ({r}_{t}) represents the reset gate, which is used to ensure whether the calculation of the candidate state ({widetilde{h}}_{t}) depends on the previous state ({h}_{t-1}). (upsigma ) is the standard sigmoid activation function; (tanh(cdot )) is the hyperbolic tangent activation function; and (odot ) indicates the Hadamard product. The weight matrices of the update gate, reset gate, and ({widetilde{h}}_{t}) calculation layer are expressed as ({W}_{z},{W}_{r},{W}_{h}); the coefficient matrices of the update gate, reset gate, and ({widetilde{h}}_{t}) calculation layer are expressed as ({U}_{z},{U}_{r},{U}_{h}); and the offset vectors of the update gate, reset gate, and ({widetilde{h}}_{t}) calculation layer are expressed as ({b}_{z},{b}_{r},{b}_{h}).A bidirectional gated recurrent unit network37 is a combination of two GRUs whose information propagating directions are reversed, and it has independent parameters in each, which makes it able to fit both forward and backward data at first and then join up the results from two directions. BiGRU can capture sequence patterns that may be ignored by unidirectional GRU. The structure of BiGRU is shown in Fig. 7.Figure 7The structure of BiGRU.Full size imageTaking the BiGRU’s forward hidden state vector at time (t) as ({h}_{t}^{(1)}) and taking the BiGRU’s backward hidden state vector at time (t) as ({h}_{t}^{(2)}), (upsigma ) indicates the standard sigmoid activation function, and (oplus ) indicates a vector splicing operation. We can calculate the output ({y}_{t}) of a BiGRU network as follows:$${h}_{t}={h}_{t}^{(1)}oplus {h}_{t}^{(2)}$$
(11)
$${y}_{t}=sigma ({h}_{t} )$$
(12)
CNN-BiGRU prediction modelBecause CNN has significant advantages in extracting useful features from a picture or a sequence and BiGRU is good at processing time series, we combine CNN and BiGRU to build the CNN-BiGRU model. The model can be mainly divided into an input layer, a convolution layer, a BiGRU network layer, a dropout layer, a fully connected layer and an output layer. The CNN layer and BiGRU layer are the core structures of the model. The function of the dropout layer is to avoid model overfitting. The CNN layer consists of two one-dimensional convolution (Conv1D) layers and a one-dimensional maximum pooling (MaxPooling1D) layer. The input of BiGRU is the output sequence of the CNN layer, and the BiGRU network is set as a one-hidden-layer structure. The structure of the CNN-BiGRU combination model is shown in Fig. 8.Figure 8The structure of CNN-BiGRU.Full size imageVariable weight combination modelWhen we analyze and predict relatively stationary tide level time series, LightGBM can perform well. However, due to environmental factors such as air pressure, wind force and terrain in reality, most tide level observation sequences are sometimes not relatively stationary, which requires that our tide level prediction model be reasonably able to “extrapolate” based on the sample observations, that is, be capable of generating values that are not in the sample. LightGBM is a tree-based model, which leads to our prediction results being between the maximum and minimum values of sequences. Therefore, LightGBM will not be able to accurately predict the situation or tidal change trend that did not appear in previous observations. However, the CNN-BiGRU model, which is a kind of neural network, has no such problem in theory and will be able to find the trend information that may be hidden in the tide level series. Therefore, we consider providing an appropriate weight for a single base model to build a combination model to improve the accuracy of the tide level prediction task.Principle of the residual weight combination model and improved variable weight combination modelTo improve the prediction accuracy of the combination model, a simple and effective idea is to determine the base models’ weights in the combination model according to the error between the prediction value and the real value. This method is also called the residual weight method, and its calculation formulas for determining the weights are:$$gleft({x}_{t}right)= sum_{i=1}^{m}{omega }_{i}left(t-1right){f}_{i}({x}_{t})$$
(13)
$${omega }_{i}left(t-1right)=frac{frac{1}{overline{{varphi }_{i}}left(t-1right)}}{sum_{i=1}^{m}frac{1}{overline{{varphi }_{i}}left(t-1right)}}$$
(14)
$$sum_{i=1}^{m}{omega }_{i}left(t-1right)=1,{omega }_{i}left(t-1right)ge 0$$
(15)

where ({omega }_{i}left(t-1right)) denotes the weight of the (i) th model at the moment (t-1), ({f}_{i}left({x}_{t}right)) denotes the prediction value of the (i) th model at the moment (t), (gleft({x}_{t}right)) denotes the prediction value of the combination model at the moment (t), and (overline{{varphi }_{i}}left(t-1right)) is the square sum of the predictive errors of the (i) th model at the moment (t-1).Our LightGBM-CNN-BiGRU (combination model) is based on the improved residual weight method. We call it the variable weight combination model. We use the weights calculated by formula (9) and formula (11) to calculate a series of new weights. The new weights from formula (11) will take the residual weight changes in (d) time steps into consideration by averaging the old weights in (d) time steps to improve the stability of the residual weight method.$${omega }_{j}left(tright)=frac{1}{d}sum_{k=1}^{d}{omega }_{i}left(t-kright)left(d=4right)$$
(16)
After obtaining a series of weights through formula (9) and formula (11), we take the absolute value of the error between the prediction value and the true value of each combination model at the moment of (t) as ({delta }_{i,t}) and ({delta }_{j,t}), respectively:$${delta }_{i,t}=mid sum_{i=1}^{m}{omega }_{i}left(tright){f}_{i}left({x}_{t}right)-{y}_{t}mid $$
(17)
$${delta }_{j,t}=mid sum_{i=1}^{m}{omega }_{j}left(tright){f}_{i}left({x}_{t}right)-{y}_{t}mid $$
(18)
Comparing ({delta }_{i,t}) and ({delta }_{j,t}), if ({delta }_{i,t} >{delta }_{j,t}), the combination model uses the new weight ({omega }_{j}left(tright)) in place of the original weight ({omega }_{i}left(tright)). Otherwise, the weight of the combination model remains unchanged.Parameter optimization of the combination modelBecause the LightGBM-CNN-BiGRU (combination model) is a variable weight combination of the prediction results from two base models, the performance of the combination model can be directly improved by separately optimizing the super parameters of the two base models. We mainly use the grid search algorithm and K-fold cross validation method to optimize the parameters. The grid search algorithm is a method to improve the performance of a certain model by iterating over a given set of parameters. With the help of the K-fold cross validation method, we can calculate the performance score of the LightGBM model on the training set and easily optimize its superparameters. The final parameters of the LightGBM model are set to num_leaves = 26, learning_rate = 0.05, and n_estimators = 46.For the CNN-BiGRU network, we mainly improve the prediction accuracy of the model by adjusting the size and number of hidden layers in the BiGRU structure and prevent the model from overfitting by changing the dropout ratio and tracking the validation loss of the network while training.The LightGBM and CNN-BiGRU variable weight combination modelThe workflow of our tide level prediction model is shown in Fig. 9. It mainly includes data preprocessing; training, optimization and prediction of the base models; construction of a variable weight combination prediction model; and evaluation and analysis of the combination model’s performance.

(1)

Data preprocessing: The quality of the data directly determines the upper limit of the prediction and generalization ability of a certain machine learning model. Standard, clean and continuous data are conducive to model training. The data used in this study are from the Irish National Tide Gauge Network, and all of them are subject to quality control. We filled in a small number of missing values and normalized the data to speed up the model training.

(2)

Construction and optimization of base models: We divide the dataset into a training set, a validation set and a test set according to the proportion of 7:1:2 and train the LightGBM model and CNN-BiGRU model with data on the training set. We optimize the parameters and monitor whether the model has been overfitted by tracking the validation loss of the network while training. Finally, we put the data into two base models for training and then obtain the prediction results of a single base model.

(3)

Construction of the variable weight combination model. Based on the prediction results of two single base models obtained in step (2), we calculate the weight of each base model according to the principle of the improved variable weight combination method and then obtain the prediction results of the variable weight combination model.

(4)

Model evaluation and analysis: According to the indexes of the model evaluation, the variable weight combination model is compared with other basic models to analyze its prediction performance after being improved.

Figure 9Prediction flow of the LightGBM-CNN-BiGRU variable weight combination model.Full size image More