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Multi-Source Dynamic Graph Learning for Compound-Flood Forecasting in Managed Coastal Systems
Liangjun You, Min Wu, Orlando Woods, Dongsheng Luo
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Abstract:Compound flooding in managed coastal systems is influenced by hydrological conditions and water-management activity observed across multiple monitoring stations. Current forecasting models can capture temporal dependencies with low average errors, but global error metrics may conceal poor reproduction of prolonged high-water plateaus that are relevant to flood early warning. Because hydrometeorological and operational signals are distributed across heterogeneous gages, single-site records do not fully represent high-water dynamics. Nevertheless, unconstrained fusion of cross-site signals can degrade the stability of local temporal forecasts. This work proposes an anchored forecasting framework that incorporates cross-site information through state- and lead-dependent bounded residual corrections. A multi-source regime representation constructed from hydrometeorological and operational observations adaptively calibrates inter-site relationships and correction scales, enabling targeted cross-site adjustment while preserving the local temporal forecast as a stable anchor. Beyond conventional global error statistics, we evaluate event-scale high-water characteristics through the temporal alignment of forecasted and observed high-water processes. Experiments demonstrate that selectively integrating multi-station dynamic conditions improves the prediction reliability of sustained high-water plateaus while maintaining high accuracy during routine hydrological conditions, supporting flood early warning and water-management decision support.
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- Source: https://arxiv.org/abs/2608.01775v1
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Multi-Source Dynamic Graph Learning for Compound-Flood Forecasting in Managed Coastal Systems Liangjun You 0009-0006-1427-5197 City University of Hong Kong (Dongguan)China 72540091@cityu-dg.edu.cn , Min Wu A*STARSingapore wumin@a-star.edu.sg , Orlando Woods Singapore Management UniversitySingapore orlandowoods@smu.edu.sg and Dongsheng Luo 0000-0003-4192-0826 Singapore Management UniversitySingapore luodongsheng01@gmail.com (2027) Abstract. Compound flooding in managed coastal systems is influenced by hydrological conditions and water-management activity observed across multiple monitoring stations. Current forecasting models can capture temporal dependencies with low average errors, but global error metrics may conceal poor reproduction of prolonged high-water plateaus that are relevant to flood early warning. Because hydrometeorological and operational signals are distributed across heterogeneous gages, single-site records do not fully represent high-water dynamics. Nevertheless, unconstrained fusion of cross-site signals can degrade the stability of local temporal forecasts. This work proposes an anchored forecasting framework that incorporates cross-site information through state- and lead-dependent bounded residual corrections. A multi-source regime representation constructed from hydrometeorological and operational observations adaptively calibrates inter-site relationships and correction scales, enabling targeted cross-site adjustment while preserving the local temporal forecast as a stable anchor. Beyond conventional global error statistics, we evaluate event-scale high-water characteristics through the temporal alignment of forecasted and observed high-water processes. Experiments demonstrate that selectively integrating multi-station dynamic conditions improves the prediction reliability of sustained high-water plateaus while maintaining high accuracy during routine hydrological conditions, supporting flood early warning and water-management decision support. The data and source code used in this study are publicly available at https://github.com/YljyLjylJ125/Compound-Flood-Forecasting. compound flooding, high-water forecasting, dynamic graph learning, spatiotemporal forecasting, managed coastal systems †copyright: none†conference: The 33rd ACM SIGKDD Conference on Knowledge Discovery and Data Mining; August 1–5, 2027; San Jose, CA, USA†booktitle: Proceedings of the 33rd ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’27), AI for Sciences Track, August 1–5, 2027, San Jose, CA, USA†journalyear: 2027†ccs: Applied computing Environmental sciences 1. Introduction Figure 1. Distributed observations across a high-water episode. The schematic follows environmental forcing, neighboring water levels, and control operations from onset through peak and recession. Aligned conceptual time series for rainfall, groundwater, neighboring water levels, pump and gate operations, and the target water level during a sustained high-water episode. Figure 2. Managed coastal monitoring and water-control system in South Florida, where rainfall, groundwater, surface water, pumps, and gates jointly shape water-level dynamics. A South Florida landscape containing rainfall, shallow groundwater, canals, wetlands, a coastal boundary, pumps, gates, and distributed monitoring stations. Flooding poses serious risks to human safety, infrastructure, and regional economies (Hirabayashi et al., 2013). Coastal flood forecasting becomes more difficult when several drivers interact. Compound events may result from simultaneous meteorological, hydrological, and coastal forcing (Wahl et al., 2015). Their combined effects may exceed those of an individual driver (Zscheischler et al., 2020). Heavy precipitation and elevated coastal water levels are also expected to coincide more often under climate change (Bevacqua et al., 2020). Forecasting water levels during events therefore requires accurate temporal prediction and a principled mechanism for deciding when observations elsewhere in the system should modify a local forecast. Water-control infrastructure also shapes flood behavior in managed coastal basins. Rainfall supplies water, antecedent groundwater affects subsurface storage, and high downstream or coastal levels can slow drainage. Pumps and gates regulate flows through canals and storage areas (Obeysekera et al., 2011). These influences occur at different locations and time scales: rainfall may coincide with elevated groundwater, neighboring stages may remain high after rainfall ends, and control operations may alter the rise or recession of local stage. Because their effects need not appear simultaneously in the target record, forecasting becomes a distributed observation problem in which different sites become informative at different event stages. Figure 1 summarizes this event-scale sequence of distributed observations. South Florida combines low relief, porous geology, heavy precipitation, coastal influence, and extensive water management infrastructure (Jane et al., 2020). Figure 2 summarizes this setting. Surface-water stage (WATER) describes the evolving regional state; rainfall (RAIN) records forcing; groundwater stage (WELL) represents antecedent conditions; and pump (PUMP) and gate (GATE) records describe control activity. The network is therefore a distributed observation of interacting environmental and operational processes rather than a set of independent time series. The prediction target throughout this paper is surface-water stage. In managed coastal systems, locally sustained high stage can provide an early indication of flood-relevant conditions. When it occurs alongside elevated coastal water or hydrologic forcing, it is consistent with known compound-flood hazard mechanisms (Ward et al., 2018). We therefore treat high-water episodes as a flood-relevant intermediate hydrologic state that provides a particularly hydrologically meaningful reference for compound-flood monitoring and early situational awareness. The predictive value of these observations varies over time. Target stage is strongly persistent in routine periods, whereas high-water episodes may depend more on rainfall, groundwater, neighboring stages, and control activity. Errors averaged over all station-hours are dominated by routine conditions and can still easily obscure delayed onset, shortened duration, incorrect peak magnitude, or different prediction delays despite similar pointwise errors (Jhin et al., 2024). Evaluation should therefore consider both full-record accuracy and high-water evolution. We formulate cross-station information as a conditional departure from a local temporal reference. A channel-wise PatchTST estimates the target trajectory from its WATER history. An input-dependent heterogeneous graph then summarizes the WATER, RAIN, WELL, PUMP, and GATE network. A multi-source regime representation controls the correction by target and lead, while a lead-dependent bound limits its magnitude. The temporal branch records local support, and the graph branch records the additional departure supported by the observed system state. We compare the framework with temporal, multivariate, and graph forecasters over separated periods, station groups, and forecast horizons using full-record and episode-level measures. The main contributions are as follows: • We formulate high-water forecasting in South Florida as a distributed observation problem that combines natural forcing, antecedent hydrologic state, neighboring water levels, and control activity while preserving a target-site temporal reference. • We develop an anchored dynamic-graph forecaster that introduces network information through state- and lead-specific bounded residuals, making the local forecast and its network-supported correction separately inspectable. • We evaluate whether these distributed observations improve both background water-level dynamics and sustained high-water processes. Training-derived station thresholds define episodes, and detection, onset, peak, and duration metrics complement MSE and MAE to assess flood-relevant process fidelity without using event labels during training. 2. Related Work The forecasting problem connects two strands of prior work: data-driven hydrological forecasting and spatiotemporal learning over distributed monitoring networks. Data-driven hydrological forecasting commonly uses meteorological inputs and basin attributes to predict streamflow or discharge (Shen, 2018; Mosavi et al., 2018). It has advanced rainfall–runoff, extreme-event, and ungauged-basin prediction (Kratzert et al., 2018, 2019; Frame et al., 2022; Nearing et al., 2024), while related work has emphasized uncertainty and scientific knowledge in learned environmental models (Klotz et al., 2022; Karpatne et al., 2017; Read et al., 2019; Willard et al., 2023). In managed coastal networks, surface-water stage, rainfall, groundwater, neighboring stages, and control operations are observed at heterogeneous locations. Their predictive value varies with system state, target location, and lead time, favoring models that use distributed context while retaining a clear local reference. This setting differs from a single catchment with a prescribed drainage hierarchy. A local stage record can be influenced by upstream, neighboring water conditions, antecedent storage, and contemporaneous water-control actions, while the available observations remain incomplete and unevenly distributed. The forecasting task must therefore accommodate heterogeneous evidence without assuming a static physical graph or a universal response rule. Long-horizon forecasters use autoregressive, convolutional, basis-expansion, and attention-based sequence models (Salinas et al., 2020; Lai et al., 2018; Oreshkin et al., 2020; Lim et al., 2021; Zhou et al., 2021). They extract temporal structure well, but a single target sequence cannot represent the distributed context of a managed water system. Early fusion can likewise obscure the distinction between the target trajectory and external information. This distinction is also important for scientific interpretation. A forecast that directly combines all sources may be accurate without clarifying whether a departure from recent local behavior is supported by the wider monitored state. Keeping the local trajectory explicit makes the contribution of distributed observations inspectable and limits the role of cross-station information to revising, rather than replacing, the target-station forecast. Graph forecasters propagate information across observed series using graph signal processing and neural message passing (Shuman et al., 2013; Kipf and Welling, 2017; Veličković et al., 2018). DCRNN, STGCN, ASTGCN, AGCRN, GMAN, and STSGCN model network dependence from evolving observations (Li et al., 2018; Yu et al., 2018; Guo et al., 2019; Bai et al., 2020; Zheng et al., 2020; Song et al., 2020); hydrological studies also use latent graphs and river topology (Seman et al., 2026; Kirschstein and Sun, 2024). These approaches generally do not distinguish the local trajectory from its network-supported revision. This distinction is important for heterogeneous monitoring networks with uneven coverage and time-varying relations. Our formulation treats graph propagation as evidence for a bounded departure from local temporal prediction. 3. Method To resolve this tension, we decompose each forecast into a local WATER trajectory and a bounded departure supported by the contemporaneous network state. This formulation makes the information boundary between the local reference and the network-supported correction explicit. 3.1. Forecasting Objective and Local Reference Let =1,…,NV=\1,…,N\ be a heterogeneous monitoring network and w⊂V_w its NwN_w WATER targets. For node i, ci∈c_i denotes its type, where C contains WATER, RAIN, WELL, PUMP, and GATE, and i∈ℝ2p_i ^2 denotes its coordinates. Each series is standardized with its training-period mean and standard deviation. tX_t and tY_t below denote standardized values. At issue time t, t∈ℝN×LX_t ^N× L contains the L-hour histories of all nodes. Together with its observation mask t∈0,1N×LM_t∈\0,1\^N× L, node types c, and standardized coordinates ¯ P, the model predicts the next H hourly WATER levels ^t∈ℝNw×H Y_t ^N_w× H. Predictions are transformed back to the original station units before error and event evaluation. No observation after t is used in either normalization or forecasting. Directly mapping all observations to the target would still leave local persistence and cross-station information tightly entangled. Instead, we write the forecast as a local trajectory plus a network-supported departure: (1) ^t=t+t. Y_t=A_t+C_t. Here tA_t is computed independently for each target WATER station, whereas tC_t may use all heterogeneous nodes. The first term records what can be predicted from local persistence alone. The second represents a possible departure supported by the wider monitoring system. Both its activation and its admissible magnitude are determined from observations available at issue time, without future event labels. For target WATER node i, the channel-wise PatchTST centers the local history at its latest observed value. It then encodes overlapping patches with parameters shared across target stations and restores the latest value after decoding. Let t,iw∈ℝLx^w_t,i ^L denote the local WATER history ending at t. The anchor forecast is (2) t,i,:=Xi,twH+A(ℰA(Unfoldp,s(t,iw−Xi,twL))).A_t,i,:=X^w_i,t1_H+D_A\! (E_A\! (Unfold_p,s\! (x^w_t,i-X^w_i,t1_L ) ) ). The anchor has no access to other stations, node types, coordinates, or non-WATER variables. Keeping this information boundary explicit makes the graph contribution identifiable: any change relative to tA_t must originate from context unavailable to the local forecaster. The anchor defines the locally supported trajectory that the network branch must preserve or revise. Table 1. Full-record MAE and MSE across forecast horizons of 1, 3, 5, and 7 days. MAE preserves the linear contribution of each absolute stage deviation, whereas MSE squares the deviations and consequently gives greater influence to occasional large forecast errors. MAE (×10−2× 10^-2) MSE (×10−2× 10^-2) Model 1D 3D 5D 7D 1D 3D 5D 7D Ours 5.004± 0.033 9.031± 0.098 11.719± 0.128 14.135± 0.137 1.656± 0.019 4.043± 0.040 5.975± 0.081 7.680± 0.086 NLinear 5.609± 0.053 9.828± 0.090 12.854± 0.146 15.230± 0.173 1.902± 0.017 4.469± 0.045 6.641± 0.077 8.527± 0.097 PatchTST 5.073± 0.038 9.324± 0.126 12.324± 0.160 14.743± 0.142 1.709± 0.019 4.248± 0.049 6.381± 0.087 8.282± 0.107 iTransformer 6.005± 0.051 10.210± 0.077 13.240± 0.137 15.664± 0.132 2.120± 0.029 4.723± 0.074 6.898± 0.096 8.806± 0.113 TimesNet 7.012± 0.093 10.900± 0.166 13.658± 0.175 16.026± 0.205 2.434± 0.032 5.037± 0.066 7.149± 0.113 9.244± 0.164 FourierGNN 6.390± 0.054 10.970± 0.095 14.017± 0.166 16.784± 0.187 1.959± 0.018 4.783± 0.051 7.005± 0.088 9.466± 0.140 MTGNN 8.587± 0.118 13.162± 0.169 17.256± 0.273 19.949± 0.279 6.790± 0.099 14.067± 0.193 18.279± 0.224 21.266± 0.230 AutoTimes 6.037± 0.051 10.087± 0.096 12.990± 0.176 15.324± 0.208 2.046± 0.024 4.599± 0.066 6.710± 0.108 8.579± 0.147 Graph WaveNet 6.181± 0.076 11.492± 0.167 14.611± 0.235 17.756± 0.267 3.072± 0.035 8.728± 0.115 14.280± 0.195 19.864± 0.271 Table 2. Episode F1 and Onset MAE across forecast horizons of 1, 3, 5, and 7 days. Episode F1 summarizes detection across matched, missed, and falsely predicted episodes, while Onset MAE measures start-time error among matched episodes. Station-specific training-period thresholds use q=0.95q=0.95. Episode F1 Onset MAE (h) Model 1D 3D 5D 7D 1D 3D 5D 7D Ours 0.833± 0.006 0.652± 0.007 0.543± 0.006 0.470± 0.004 0.350± 0.005 1.658± 0.021 2.318± 0.023 4.121± 0.036 NLinear 0.806± 0.009 0.629± 0.007 0.519± 0.007 0.450± 0.005 0.459± 0.006 2.155± 0.030 4.135± 0.057 6.683± 0.095 PatchTST 0.820± 0.011 0.639± 0.009 0.528± 0.007 0.457± 0.005 0.363± 0.004 1.730± 0.016 3.227± 0.031 5.128± 0.050 iTransformer 0.786± 0.007 0.604± 0.005 0.509± 0.005 0.439± 0.004 0.499± 0.006 2.145± 0.023 5.131± 0.051 8.481± 0.113 TimesNet 0.757± 0.010 0.590± 0.006 0.503± 0.007 0.441± 0.006 0.800± 0.013 2.844± 0.042 6.095± 0.095 9.812± 0.184 FourierGNN 0.772± 0.008 0.573± 0.006 0.481± 0.004 0.385± 0.004 0.587± 0.007 1.873± 0.027 2.484± 0.032 4.386± 0.058 MTGNN 0.717± 0.011 0.548± 0.007 0.422± 0.006 0.363± 0.005 1.203± 0.018 2.187± 0.040 4.088± 0.077 5.463± 0.102 AutoTimes 0.795± 0.007 0.619± 0.008 0.517± 0.006 0.440± 0.005 0.949± 0.012 3.000± 0.041 5.902± 0.091 8.326± 0.136 Graph WaveNet 0.765± 0.009 0.584± 0.006 0.477± 0.007 0.411± 0.004 0.641± 0.007 2.420± 0.039 4.872± 0.052 7.536± 0.128 Table 3. Peak Magnitude MAE and Duration MAE across forecast horizons of 1, 3, 5, and 7 days. Peak Magnitude MAE measures peak-stage error, while Duration MAE measures episode-length error. Both are computed for matched episodes using station-specific training-period thresholds at q=0.95q=0.95. Peak Magnitude MAE Duration MAE (h) Model 1D 3D 5D 7D 1D 3D 5D 7D Ours 0.045± 0.000 0.066± 0.001 0.081± 0.001 0.088± 0.001 2.297± 0.028 12.401± 0.142 23.873± 0.237 33.768± 0.349 NLinear 0.053± 0.001 0.080± 0.001 0.094± 0.001 0.101± 0.001 2.561± 0.031 13.988± 0.178 29.037± 0.422 45.871± 0.594 PatchTST 0.046± 0.000 0.070± 0.001 0.084± 0.001 0.093± 0.001 2.354± 0.031 12.750± 0.181 27.292± 0.368 43.101± 0.635 iTransformer 0.059± 0.001 0.086± 0.001 0.099± 0.001 0.110± 0.001 2.561± 0.025 13.856± 0.161 29.729± 0.408 48.431± 0.676 TimesNet 0.074± 0.001 0.104± 0.001 0.117± 0.002 0.129± 0.002 2.796± 0.045 13.790± 0.247 29.913± 0.487 48.410± 0.846 FourierGNN 0.066± 0.001 0.097± 0.001 0.109± 0.001 0.124± 0.001 2.623± 0.031 13.232± 0.142 25.244± 0.247 35.824± 0.343 MTGNN 0.097± 0.002 0.110± 0.002 0.150± 0.002 0.141± 0.002 3.326± 0.054 15.383± 0.273 31.305± 0.538 39.548± 0.618 AutoTimes 0.057± 0.001 0.086± 0.001 0.098± 0.002 0.107± 0.002 2.536± 0.035 13.445± 0.183 28.250± 0.421 44.861± 0.535 Graph WaveNet 0.073± 0.001 0.103± 0.001 0.132± 0.002 0.132± 0.001 2.925± 0.031 14.580± 0.229 30.540± 0.318 47.260± 0.744 Figure 3. Sensitivity of episode-level performance to the station-specific high-water threshold for the S7S_7 split and 3-day forecast horizon. Four line charts compare nine forecasting models at high-water quantiles 0.70, 0.80, 0.90, and 0.95. The proposed model has the highest Episode F1 and the lowest onset, peak-magnitude, and duration errors at all four thresholds. Figure 4. Relative performance degradation under architecture and observation-source ablations for the S7S_7 split, 3-day forecast horizon, and q=0.95q=0.95 high-water threshold. Two heatmaps show relative degradation in MSE, MAE, Episode F1, Onset MAE, Peak Magnitude MAE, and Duration MAE. The left panel removes dynamic graph construction, event context, the correction bound, their combination, or the complete graph-correction path. The right panel removes neighboring WATER, RAIN, WELL, PUMP and GATE, or all non-WATER observations. 3.2. State-Dependent Network Correction The correction branch begins with the context excluded from the anchor. For node i and historical step τ, it concatenates the observation, mask, type embedding, and standardized coordinate embedding: (3) t,i,τ=[Xi,τ,Mi,τ,citype,iloc].u_t,i,τ=[X_i,τ,M_i,τ,e^type_c_i,e^loc_i]. A shared GRU then produces the window-dependent state (4) t,i=GRUϕ(t,i,t−L+1:t)last∈ℝd.h_t,i=GRU_φ(u_t,i,t-L+1:t)_last ^d. This state places observations with different temporal behavior in a common representation while retaining their type and location. Because it is recomputed for every input window, relations inferred from these states need not remain strictly fixed across routine and high-water periods. Useful sources can change with rainfall, groundwater, and control conditions. We therefore score the directed relation from source node j to receiving node i from their current states, while node type and distance restrict the search through structural biases: (5) st,ij=(qt,i)⊤(kt,j)d+Bci,cj−softplus(ρ)‖¯i−¯j‖2.s_t,ij= (W_qh_t,i) (W_kh_t,j) d+B_c_i,c_j-softplus(ρ)\| p_i- p_j\|_2. Let tK(i)N^K_t(i) be the top-K non-self sources under this score. The row-normalized dynamic adjacency is (6) At,ij=[j∈tK(i)]exp(st,ij)∑k∈tK(i)exp(st,ik).A_t,ij= I[j ^K_t(i)] (s_t,ij) _k ^K_t(i) (s_t,ik). Because st,ijs_t,ij depends directly on the current node states, both the retained neighbors and their relative weights can change across forecast windows. The type and coordinate terms act as structural biases when selecting and weighting neighbors. They do not prescribe a fixed connectivity pattern. The graph therefore acts as an input-dependent predictive structure rather than a fixed description of the monitoring network. The selected sources are aggregated with these dynamic weights, giving the network-informed state (7) t,i=t,i+MLPg([t,i,∑jAt,ijvt,j]).z_t,i=h_t,i+MLP_g\! ([h_t,i, _jA_t,ijW_vh_t,j] ). The dynamic adjacency answers where network information is collected, but not whether it should revise a particular target forecast. That decision depends on the current hydrological and operational regime and may differ across targets and forecast leads. We summarize the observed regime using two mask-normalized statistics for each node type c: the mean absolute standardized magnitude over the most recent r=24r=24 hours, μt,c _t,c, and the signed change over the full lookback, δt,c _t,c. Each statistic uses only observed nodes of type c and an ϵ>0ε>0 denominator safeguard. No event labels or future thresholds are used. An MLP maps the concatenated type-specific statistics to the multi-source regime representation t=MLPe([μt,c,δt,c]c∈)e_t=MLP_e([ _t,c, _t,c]_c ). For target i∈wi _w and lead ℓ∈1,…,H ∈\1,…,H\, the regime gate is (8) gt,i,ℓ=σ(MLPgate([t,i,t])ℓ).g_t,i, =σ\! (MLP_gate([h_t,i,e_t])_ ). The adjacency determines which sources contribute information. The gate maps the current regime to the strength of correction for target i at lead ℓ . The graph state can therefore be computed for every window without forcing the same correction policy across routine and high-water conditions. The gate modulates the correction but does not bound its displacement. A decoder maps t,iz_t,i to residual logits t,i=R(t,i)∈ℝHd_t,i=D_R(z_t,i) ^H. We use a lead-dependent trust-region budget βℓ _ that increases linearly from βmin _ at the first lead to βmax _ at the final lead. This reflects increasing uncertainty with forecast distance while retaining a finite departure at every lead. The bounded correction is (9) Ct,i,ℓ=gt,i,ℓβℓtanh(dt,i,ℓ).C_t,i, =g_t,i, _ (d_t,i, ). The three factors have distinct roles: dt,i,ℓd_t,i, supplies the direction and unconstrained strength of the graph proposal, gt,i,ℓg_t,i, determines how much the current regime supports intervention, and βℓ _ limits the largest admissible departure from the local trajectory. Since 0<gt,i,ℓ<10<g_t,i, <1 and |tanh(⋅)|≤1| (·)|≤ 1, the effective regime-conditioned trust region satisfies (10) |Ct,i,ℓ|≤gt,i,ℓβℓ≤βℓ.|C_t,i, |≤ g_t,i, _ ≤ _ . This inequality is the explicit trust-region guarantee: it limits departure from the anchor without assuming that every graph correction is beneficial. All parameters are optimized jointly using mean squared error over observed WATER targets. Unavailable target entries are excluded by their observation mask. Event labels and episode metrics do not enter training, so improved high-water behavior arises from how the model uses the observed network while controlling its departure from the local reference. For batch size B, dense graph aggregation costs O(BN2d)O(BN^2d). 4. Experimental Design Experiments use SF2Bench (Zheng et al., 2026), an hourly observation network from the managed coastal water system of South Florida. The three chronological splits used in this study span 2010–2023 and, before spatial partitioning, contain 585–716 WATER stations together with 870–964 RAIN, WELL, PUMP, and GATE stations. Each station is associated with an hourly record and geographic coordinates, providing both temporal observations and spatial context for the monitored system. WATER stations provide forecast targets and describe the changing state of surface-water. RAIN represents meteorological forcing, WELL reflects groundwater storage and drainage conditions, and PUMP and GATE record human interventions that redistribute water through the canal network. The resulting task is therefore a forecast of a coupled natural–human system rather than an independent collection of time series. Following the SF2Bench protocol, the main experiment combines the chronological S5S_5, S6S_6, and S7S_7 splits, three station partitions within each split, and forecast horizons of 1, 3, 5 and 7 days. The chronological splits cover different historical periods, the station partitions change the monitored locations, and the four horizons show how performance changes with lead time. Forecasts are returned to the original WATER units before evaluation, allowing full-record errors and episode characteristics to be interpreted by magnitude and timing. This design treats chronological period, spatial composition, and forecast distance as complementary dimensions of generalization. The three splits expose different combinations of hydrologic and operating conditions, while station partitions change both the forecast targets and the network of observations available to support them. Increasing lead time reduces the support provided by the recent target history. Together, these settings test whether distributed context remains useful beyond a particular historical period, station arrangement, or short-term persistence regime. At each forecast issue, every model receives the preceding 48 hours and predicts the immediately following 1-, 3-, 5-, or 7-day trajectory. Training-only normalization and explicit masks are used throughout input, loss, and evaluation, so unavailable readings and observations after the issue time are not treated as model inputs. The proposed forecaster uses 64-dimensional hidden states, a top-20 dynamic neighborhood, and dropout of 0.1. It is trained for 10 epochs with AdamW using a batch size of 64, a learning rate of 10−310^-3, and weight decay of 10−510^-5; the checkpoint with the lowest validation MSE is retained. 4.1. Baselines For comparison, we employ eight baseline models representing distinct methodological paradigms: • NLinear (Zeng et al., 2023) tests whether normalized persistence and trend explain future water-level evolution. • PatchTST (Nie et al., 2023) tests long-range local memory through channel-independent temporal patches. • iTransformer (Liu et al., 2024a) learns dependence across observed series by treating each series as a token. • TimesNet (Wu et al., 2023) represents multi-period variation in recurring and nonstationary water-level dynamics. • FourierGNN (Yi et al., 2023) tests whether spectral structure captures cross-series coupling. • MTGNN (Wu et al., 2020) learns inter-series connectivity and temporal propagation without prescribing a physical graph. • AutoTimes (Liu et al., 2024b) provides an autoregressive comparison built on pretrained language-model representations. • Graph WaveNet (Wu et al., 2019) combines an adaptive graph with dilated temporal convolutions to model network transport and temporal memory jointly. Together, these models cover local temporal forecasting, multivariate dependence, spectral coupling, and learned graph propagation. Their comparison tests whether a stable local reference benefits from a bounded network correction when forecasting high-water processes. 4.2. Evaluation Metrics Performance is evaluated at full-record and process scales. MSE emphasizes large water-level deviations (Gupta et al., 2009), whereas MAE describes the typical absolute error in the original WATER units. High-water episodes are defined strictly relative to the local water-level distribution of each target station. Let xi,tx_i,t denote the original-unit water level and Mi,tM_i,t its observation mask. For WATER station i, the threshold is estimated exclusively from its valid training-period observations as (11) τi(q)=Qq(xi,t:t∈train,Mi,t=1). _i^(q)=Q_q\! ( \x_i,t:t _train,\,M_i,t=1 \ ). The main comparison uses each station’s 95th percentile; q=0.95q=0.95 therefore marks the upper 5% of its valid training distribution. A test hour is an exceedance when the observed or predicted level meets or exceeds its fixed training-derived threshold. An episode begins at the first exceedance and contains at least three exceedance hours; runs separated by no more than six hours are merged. Episodes are evaluated at 24-hour forecast-issue intervals and temporally overlapping observed and predicted episodes are matched one-to-one, prioritizing larger overlap. Matching is one-to-one within each target-station forecast window. Episode F1 therefore reflects recovered, missed, and false-alarm processes, whereas the three episode MAEs are calculated only for matched pairs. The distinction between detection and matched-episode reconstruction is essential for interpreting high-water forecasts. A small onset, peak, or duration error alone could arise from a limited subset of episodes that were recovered successfully, whereas Episode F1 also accounts for missed and false episodes. Reporting the four measures together therefore asks whether a model both identifies an elevated-water process and reproduces its subsequent evolution. Episode F1 balances matched, missed, and false predicted episodes. For matched episodes, Onset MAE measures start-time error in hours, Peak-Magnitude MAE the peak-stage error in original units, and Duration MAE the episode-length error in hours. Because episode frequency and persistence depend on the high-water definition, we repeat the evaluation at q∈0.70,0.80,0.90q∈\0.70,0.80,0.90\ in addition to q=0.95q=0.95, using the same construction rules, S7S_7 split, and 3-day horizon. Ablations use the same S7S_7, 3-day, and q=0.95q=0.95 setting. Architecture variants replace the dynamic graph with a fixed graph, remove event context, the correction bound, both controls, or the complete graph correction. Source variants retain the architecture but exclude neighboring WATER, RAIN, WELL, PUMP/GATE, or all non-WATER observations. 5. Results The experiments address four linked scientific questions. First, does the complete model improve full-record forecasts relative to strong local, multivariate, and graph baselines? Second, does it better represent the sustained high-water processes relevant to flood monitoring, including event occurrence, onset, peak severity, and duration? Third, do these episode-level findings persist when high water is defined at different positions in the station-specific distribution? Fourth, which architectural mechanisms and observation sources account for the improvement? We interpret the pointwise and episode-level results together. Full-record error checks whether event gains come at the cost of the background water-level trajectory, while episode metrics describe the evolution of elevated-water conditions that can precede or accompany flood impacts. Threshold sensitivity tests whether the comparison depends on a single statistical definition of high water, and ablation analysis separates the contributions of the correction design and the distributed observation network. 5.1. Overall Water-Level Forecast Accuracy Table 1 shows that the proposed model has the lowest MSE and MAE at every horizon. At short lead times, the strong performance of the local PatchTST baseline confirms that recent stage persistence explains much of the immediate water-level evolution. As the horizon extends, however, the wider separation from local forecasting indicates that rainfall, groundwater, neighboring stage, and control activity provide increasing predictive context when the recent target history becomes less informative. The joint improvement in MAE and MSE is also scientifically relevant. It shows that the model better represents both routine variations and occasional large departures, rather than improving average behavior by smoothing the trajectory. Because full-record errors are dominated by routine station-hours, these results also indicate that network corrections do not destabilize background water-level dynamics. This is consistent with the anchor preserving local temporal support while the bounded graph branch revises only departures supported by the observed system state. 5.2. High-Water Episode Detection and Evolution Table 2 connects the forecast gains more directly to high-water monitoring. The proposed model achieves the highest Episode F1 and the lowest Onset MAE throughout the evaluated horizons. These metrics describe different aspects of the process: Episode F1 measures whether elevated conditions are detected without excessive misses or false alarms, whereas Onset MAE measures whether the transition begins at the correct time. Their joint improvement shows that the model does not merely produce more threshold crossings; it better locates the emergence of sustained high water. This behavior is consistent with the distributed-observation hypothesis. Rainfall, groundwater, neighboring WATER, and control activity can describe a changing system state before its effects are fully expressed in the recent history of the target station. The results do not assign causal influence to an individual source, but they show that their combined state contains predictive information about the occurrence and timing of high-water transitions. Peak magnitude and duration complete this assessment. They describe the severity and persistence of each matched episode. Table 3 examines the amplitude and persistence of matched episodes. The proposed model has the lowest Peak Magnitude MAE and Duration MAE across all horizons, showing that improved detection is accompanied by a closer reconstruction of the episode itself. Peak magnitude describes the maximum stage reached, while duration reflects how long storage, drainage, and control conditions sustain elevated water. The duration task becomes more difficult as uncertainty accumulates over longer horizons, yet the consistent ranking indicates that distributed observations remain informative for the plateau and recession of high-water processes. These errors are conditional on matched episodes and should be read with Episode F1. Their joint improvement indicates that the model better represents episode occurrence, transition, amplitude, and persistence rather than optimizing one event property at the expense of another. Together with the full-record results, this supports a process-based view of forecast quality: monitoring requires both accurate point values and a faithful description of how elevated-water conditions evolve. 5.3. Sensitivity to the High-Water Threshold The operational meaning and frequency of a high-water episode depend on the selected station-specific quantile. We therefore compare Episode F1, Onset MAE, Peak Magnitude MAE, and Duration MAE under q∈0.70,0.80,0.90,0.95q∈\0.70,0.80,0.90,0.95\ for the same S7S_7 split and 3D forecast horizon. Lower quantiles describe more frequent elevated-water conditions, whereas q=0.95q=0.95 isolates the upper tail used in the main comparison. Figure 3 shows that the proposed model ranks first on all four episode metrics at every threshold. Its advantage therefore extends from relatively frequent elevated-water conditions to the less frequent upper tail. The simultaneous ranking in detection, onset, peak, and duration further indicates that the result is not produced by exchanging one aspect of process fidelity for another. This threshold stability is important because no single statistical quantile fully represents the range of high-water conditions relevant to monitoring. The results therefore place the main q=0.95q=0.95 comparison within a broader pattern and show that the predictive value of distributed observations is not directly tied to one event definition. Absolute values across thresholds still describe different episode populations and should not be interpreted as repeated measurements of identical events. 5.4. Ablation Study To examine which representations of the monitored system support high-water forecasting, we conduct two groups of ablations using S7S_7, the 3-day horizon, and the main q=0.95q=0.95 threshold. The architecture variants test three related assumptions: cross-station dependence changes with the observed system state, the need for correction depends on the current hydrologic and operational context, and network-supported departures should remain bounded around the local trajectory. Accordingly, w/o Dynamic Graph uses fixed cross-station relations; w/o Event Context removes the regime representation; w/o Correction Bound removes the lead-dependent bound; w/o Event Context and Bound removes both controls; and w/o Graph Correction retains only the local anchor. Figure 4 reports degradation from the complete model, with larger positive values indicating greater performance loss. The full model performs best across all six metrics, while removing the graph correction causes the largest degradation. Local stage persistence alone is therefore insufficient to represent the evolution of high-water processes. The loss under fixed cross-station relations indicates that the useful network structure varies across hydrological and operational states. The remaining variants further show that deciding when to revise the local trajectory and limiting the magnitude of that revision are complementary requirements. We next use leave-one-source-out analysis to examine the predictive information carried by different parts of the observation network. The variants remove neighboring WATER, RAIN, WELL, PUMP/GATE, or all non-WATER observations while leaving the architecture unchanged. Every removal degrades performance. Neighboring WATER describes the distributed surface-water state, RAIN records external forcing, WELL reflects antecedent groundwater conditions, and PUMP/GATE records managed redistribution. The larger loss after removing all non-WATER observations indicates that these environmental and operational measurements jointly add information beyond spatial WATER observations alone. 6. Conclusion This study examined whether distributed observations in a managed coastal system improve high-water forecasts beyond local stage persistence. The anchored dynamic-graph forecaster retains an explicit target trajectory and uses heterogeneous WATER, RAIN, WELL, PUMP, and GATE observations only through state- and lead-dependent bounded corrections. Across horizons, the model achieved lower full-record MSE and MAE, higher Episode F1, and lower onset, peak, and duration errors than the baselines. Ablations link these gains to dynamic cross-station relations, regime-aware activation, bounded correction, and complementary observation sources. The results show that the wider system state contains predictive information about high-water evolution not fully expressed in recent target history, supporting process-resolved monitoring and water-management planning. Future work should test transferability across managed coastal systems and rarer regimes, incorporate rainfall and coastal-boundary forecasts with planned operations, and introduce hydraulic constraints and predictive uncertainty. 7. Limitations and Ethical Considerations The experiments cover one managed coastal system and a finite range of observed environmental and operational conditions. The learned graph captures predictive relations within this network, so its validity under other basins, sensor configurations, and operating policies still requires external evaluation. Station-specific training quantiles provide a reproducible high-water definition, but not a regulatory flood stage, inundation extent, or damage measure; they nevertheless characterize sustained high stage relevant to compound-flood preparedness. 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Appendix A Algorithmic Description Algorithm 1 Training and Forecasting Procedure of the Anchored Dynamic-Graph Forecaster 1:t−L+1:tX_t-L+1:t and t−L+1:tM_t-L+1:t available up to issue time t; node metadata (,¯)(c, P); WATER targets wV_w; forecast horizon H 2:Multi-step WATER-level forecasts ^t Y_t 3:Initialize Θ=fA,fϕ,g,fr,fc =\f_A,f_φ,g,f_r,f_c\ and the optimizer 4:for each training forecast issue do 5: t←fA(t−L+1:tw)A_t← f_A(X^w_t-L+1:t) ⊳ target WATER histories only 6: t,i←fϕ(i,t−L+1:t,i,t−L+1:t,ci,¯i),i∈h_t,i← f_φ(X_i,t-L+1:t,M_i,t-L+1:t,c_i, p_i), i 7: t←g(t,ii∈)G_t← g(\h_t,i\_i ) ⊳ input-dependent heterogeneous graph 8: ~t,i←Agg(t,t,jj∈),i∈w h_t,i (G_t,\h_t,j\_j ), i _w 9: t←fr(t,i,~t,ii∈w)r_t← f_r(\h_t,i, h_t,i\_i _w) ⊳ current system regime 10: (t,i,t,i)←fc(t,i,~t,i,t),i∈w( α_t,i,b_t,i)← f_c(h_t,i, h_t,i,r_t), i _w 11: t,i←clip(t,i,−t,i,t,i)C_t,i (b_t,i,- α_t,i, α_t,i) ⊳ bounded residual 12: ^t←t+t Y_t _t+C_t 13: ℒ←MaskedMSE(^t,t,tw)L ( Y_t,Y_t,M^w_t) ⊳ no event labels or episode metrics 14: Θ←Update(Θ,∇Θℒ) ( , _ L) 15:end for 16:At each test issue t, evaluate the same forward map using only observations with time index τ≤tτ≤ t 17:return ^t Y_t The local anchor receives only the target station’s WATER history. At the issue time, the graph branch encodes all available heterogeneous observations, reconstructs a state-dependent network, and produces a strictly bounded target- and lead-specific residual correction. Event labels and episode metrics are used only after forecasts are issued, for evaluation. Appendix B Dataset Details SF2Bench represents the managed South Florida water system as an hourly, heterogeneous observation network. Each record is associated with a station type, geographic coordinates, an hourly value, and an observation indicator. The archive contains 2,452 stations in five functional groups. WATER stations measure surface-water stage and define the forecasting targets; RAIN stations provide precipitation observations; WELL stations describe groundwater level; and PUMP and GATE stations record water-control activity. The original station values remain in their native units and are standardized separately by series. A flood-observation repository distributed with SF2Bench is not used for model fitting or for defining the high-water episodes in this study. For clarity, the station groups and their roles are summarized below rather than in a separate inventory table: • WATER (993 stations): surface-water stage at canals, structures, and managed water bodies; forecast targets and neighboring surface-water context. • RAIN (349 stations): hourly precipitation observations; external hydrologic forcing. • WELL (582 stations): groundwater level; antecedent storage and drainage context. • PUMP (99 stations): pump operating signals; managed water redistribution. • GATE (429 stations): reported gate-control signals; hydraulic connectivity and control activity. The archive is divided into chronological blocks whose station coverage grows as the monitoring network expands. Table 4 reports the pre-partition station inventory. The main experiments use the three most recent blocks, S5S_5–S7S_7, because they provide the broadest joint coverage of the five observation groups. Table 4. Station availability in the eight SF2Bench chronological blocks before applying the three spatial partitions. Split WATER RAIN WELL PUMP GATE Total S0S_0 159 143 40 17 82 441 S1S_1 227 139 36 18 104 524 S2S_2 332 170 44 26 94 666 S3S_3 402 227 178 31 107 945 S4S_4 518 254 296 48 172 1288 S5S_5 585 216 333 65 256 1455 S6S_6 670 186 317 85 300 1558 S7S_7 716 194 352 89 329 1680 Within each chronological block, SF2Bench supplies three geographically distinct station subsets. They alter both the number of targets and the composition of the observed environmental and operational context. The exact inventories used by this paper are shown in Table 5. A zero PUMP count means that no pump station falls inside that particular geographic subset; it does not indicate that pump data were removed during preprocessing. Table 5. Composition of the three official spatial partitions used for S5S_5, S6S_6, and S7S_7. Split Part WATER RAIN WELL PUMP GATE Total S5S_5 0 20 12 71 0 7 110 1 72 31 40 11 28 182 2 10 6 19 0 3 38 S6S_6 0 19 12 64 0 5 100 1 74 29 35 12 24 174 2 12 3 19 1 4 39 S7S_7 0 22 12 71 0 7 112 1 80 30 24 13 24 171 2 30 9 53 3 17 112 The temporal protocol is summarized in Table 6. Windows are generated hourly with a 48-hour lookback and no gap between the input and forecast intervals. The four forecast lengths are 24, 72, 120, and 168 hours; every valid WATER observation in the selected part is a target, whereas RAIN, WELL, PUMP, and GATE observations enter as contextual inputs. Table 6. Chronological phases used in the main experiments. Split Train Validation Test S5S_5 2010–2012 2013 2014 S6S_6 2015–2017 2018 2019 S7S_7 2020–2021 2022 2023 For each station, the mean and standard deviation are fitted from its training phase and then reused for validation and test data. Standardized values are clipped to [−20,20][-20,20] to limit the influence of isolated sensor artifacts. Missing observations are retained through explicit masks; they are excluded from the masked training loss and all reported errors. Predicted WATER values are transformed back to their original station units before full-record and episode evaluation. The station-specific episode threshold is also estimated from valid training observations only. Episode construction and matching. For each target station i, the high-water threshold is the q-quantile of its valid training-period WATER values, θi=Qq(yi,t:t∈train) _i=Q_q(y_i,t:t _train). The same fixed threshold is applied to observed and forecast WATER levels after they are returned to the original station units. Within each forecast window, an exceedance begins when a valid value is at least θi _i. Consecutive exceedance runs separated by no more than six hourly steps are merged, and a merged interval is retained only when it contains at least three valid exceedance hours. Its onset is the first index of the merged interval, its duration is the length of that interval, and its peak is the largest valid WATER level within it. This construction permits a short interruption in an sustained elevated-water process without treating it as two unrelated episodes. Observed and predicted episodes are extracted independently for every target station at forecast issues sampled 24 hours apart. A true and predicted episode are eligible to match only if their time intervals overlap. Candidate pairs are ranked first by decreasing overlap and then by smaller onset separation; pairs are accepted greedily so that each observed or predicted episode contributes to at most one match. Episode F1 is computed from matched, missed, and false-alarm episodes. Onset MAE, Peak Magnitude MAE, and Duration MAE are computed over matched pairs only, respectively using the absolute difference in onset time, peak WATER level, and interval length. Thus F1 reports whether elevated-water processes are recovered, while the remaining measures describe the timing, magnitude, and persistence of processes that are recovered by both series. Masks, continuity, and forecast windows. Episode extraction never fills missing observations. A time step can enter an initial exceedance run only when its observation mask is valid and its WATER level reaches the station threshold. The six-hour merging rule is applied after those initial runs are identified, so it can bridge a short interruption caused by a below-threshold observation or an unavailable reading. The retained episode must nevertheless contain the required three valid exceedance hours. Its reported duration is the full span from the merged start to end, including any short bridged interval; this makes duration error reflect the persistence of the elevated-water process rather than only the count of isolated exceedance samples. The peak is selected from valid observations in that span. Stations with no valid training values have no well-defined threshold and are excluded from episode evaluation rather than assigned a synthetic level. Forecast windows are evaluated from issue times separated by 24 hours. For a given issue, observed and forecast trajectories cover the same future horizon and use the same valid-target mask. Overlapping windows from different issue times are retained because they represent forecasts that would have been made on different days with different available histories. The episode start and end indices are therefore expressed relative to the corresponding forecast window; the reported onset and duration errors are in hours. No observations after the issue time enter the model input, the graph construction, the local anchor, or the threshold estimate. Observations in the future horizon are used only after the forecast is issued to form the evaluation target. Aggregation and threshold sensitivity. For one model, split, station partition, and forecast horizon, all matched, missed, and false-alarm records produced by the sampled issues and target stations are first combined. Episode F1 is then calculated from the resulting corresponding counts of true positives, false positives, and false negatives. The three MAE measures average absolute errors over matched records, so they quantify process reconstruction conditional on episode recovery; they are interpreted alongside F1 rather than as substitutes for it. The reported tabulated values in the main paper and Table 11 average the three official spatial partitions for the stated chronological split and horizon. The main comparison uses q=0.95q=0.95, which emphasizes the upper tail of each station’s own training-period stage distribution. The threshold-sensitivity analysis repeats the same construction at q∈0.70,0.80,0.90,0.95q∈\0.70,0.80,0.90,0.95\ for S7S_7 and the 3-day horizon. Changing q changes the frequency, typical duration, and peak distribution of the evaluated episodes; the analysis is therefore intended to assess whether the model ranking is retained under different definitions of elevated water, rather than to interpret a numerical change across thresholds as a single common error scale. Recorded episode details. Each evaluation record retains the issue time, target-station identifier, training-derived threshold, and match status. Matched records additionally store signed onset, peak, and duration differences, whose absolute means yield the reported MAEs. Forecasts from distinct 24-hour issue times remain separate decisions, so overlapping future windows are not collapsed into one reconstructed series. Thresholds, masks, and one-to-one matching are fixed within each reported setting. Appendix C Baseline and Training Configurations All models use the same training schedule, while model-specific settings retain the conventions of their respective forecasting architectures. The common optimization and episode-evaluation settings are listed in Table 7; the instantiated architecture settings are described below. Table 7. Common training and evaluation configuration. Setting Value Lookback 48 hourly steps Forecast horizons 24, 72, 120, and 168 hourly steps Optimizer AdamW Learning rate 10−310^-3 Weight decay 10−510^-5 Epochs 10 Batch size 64 Gradient-norm clip 1.0 Random seeds 3 Normalized clip [−20,20][-20,20] Main episode quantile q=0.95q=0.95 Episode issue stride 24 h Minimum episode duration 3 h Episode merge gap 6 h • NLinear: last-value-centered linear map from 48 inputs to H outputs. • PatchTST: channel-independent PatchTST with 3 encoder layers, hidden size 128, 16 heads, patch length 16, stride 8, RevIN, and dropout 0.2. • iTransformer: hidden size 512, 8 heads, 2 encoder layers, feed-forward size 2048, and dropout 0.1. • TimesNet: two TimesBlocks, five dominant periods, model/feed-forward size 32, six inception kernels, and dropout 0.1. • FourierGNN: spectral embedding 256, hidden size 512, three complex graph-convolution stages, and sparsity threshold 0.01. • MTGNN: three layers, learned graph, node embedding 40, residual channels 32, skip channels 64, end channels 128, and dropout 0.3. • AutoTimes: frozen GPT-2 base backbone; token length 24; two-layer encoder/decoder MLPs of width 256; and dropout 0.1. • Graph WaveNet: adaptive adjacency with four blocks and four dilation layers; residual channels 32, skip channels 256, end channels 512, and dropout 0.3. The eight baselines are exactly those used in the main comparison. Their settings retain the defining temporal, spectral, or graph representation of each architecture, while the common input window, forecast targets, optimization schedule, and checkpoint rule remain fixed. NLinear and PatchTST use direct temporal mappings and patch-based temporal representations, respectively. iTransformer, TimesNet, FourierGNN, and AutoTimes provide alternative multivariate or frequency-aware representations; MTGNN and Graph WaveNet construct learned dependencies across the observed network. Appendix D Detailed Results Tables 8–10 report the split-specific results underlying the aggregate comparisons in the main text. Entries are means ± standard deviations over the three official spatial partitions, so the three tables expose performance across chronological blocks, network compositions, and forecast horizons. Within a table, each metric is reported at the four lead times used in the main study. MAE and MSE are calculated from the inverse-transformed WATER forecasts, whereas the episode measures use the station-specific training quantile q=0.95q=0.95 and the matching procedure described in Appendix A. The tables therefore distinguish changes in ordinary stage error from changes in episode occurrence, timing, peak level, and persistence. The three chronological blocks provide complementary views of the same forecasting task. Their station partitions change the monitored locations and the mixture of auxiliary observations, while the lead times progressively reduce the direct support available from the recent target history. For a fixed split and lead time, the model columns can be compared directly within each metric block. The standard deviations summarize the variation over the three official station partitions, not variation from random model initialization. They consequently describe how a reported result changes with the spatial composition of the monitored system, including the number and type of contextual stations available to the forecast. The tables retain all six metrics so that routine stage accuracy and high-water process reconstruction can be inspected together for every chronological block. Table 8. Detailed S5S_5 results averaged over the three spatial parts for the earliest evaluated historical block. Entries are means ± standard deviations over Parts 0, 1, and 2. MAE and MSE use the ×10−2× 10^-2 scale of the main text, and episode metrics use station-specific training thresholds at q=0.95q=0.95. Metric Lead Ours NLinear PatchTST iTrans- former TimesNet Fourier GNN MTGNN AutoTimes Graph WaveNet MAE ×10−2× 10^-2 1D 5.174± 0.032 5.738± 0.049 5.194± 0.041 6.023± 0.046 7.017± 0.096 6.369± 0.049 6.237± 0.088 6.214± 0.051 5.683± 0.068 3D 9.234± 0.103 10.048± 0.082 9.504± 0.121 10.290± 0.072 10.943± 0.154 11.315± 0.089 11.403± 0.118 10.311± 0.093 10.805± 0.145 5D 11.895± 0.118 13.021± 0.139 12.498± 0.162 13.414± 0.129 13.728± 0.167 14.281± 0.149 14.593± 0.205 13.270± 0.163 14.321± 0.229 7D 14.280± 0.129 15.302± 0.153 14.772± 0.142 15.636± 0.130 15.899± 0.208 17.130± 0.183 17.068± 0.228 15.462± 0.198 17.014± 0.249 MSE ×10−2× 10^-2 1D 1.904± 0.023 2.199± 0.018 1.958± 0.020 2.400± 0.033 2.661± 0.035 2.104± 0.020 1.994± 0.028 2.308± 0.027 1.975± 0.022 3D 4.568± 0.044 5.072± 0.049 4.817± 0.052 5.380± 0.083 5.581± 0.067 5.062± 0.047 4.862± 0.057 5.229± 0.074 4.865± 0.064 5D 6.694± 0.084 7.409± 0.076 7.164± 0.088 7.689± 0.101 7.919± 0.115 7.293± 0.080 7.516± 0.079 7.595± 0.117 7.163± 0.090 7D 8.482± 0.089 9.384± 0.101 9.242± 0.117 9.690± 0.121 9.962± 0.166 9.316± 0.125 8.911± 0.095 9.514± 0.154 9.294± 0.125 Episode F1 1D 0.867± 0.007 0.835± 0.009 0.858± 0.011 0.825± 0.007 0.827± 0.011 0.815± 0.007 0.780± 0.012 0.827± 0.007 0.801± 0.009 3D 0.729± 0.008 0.701± 0.008 0.711± 0.009 0.686± 0.006 0.667± 0.006 0.656± 0.007 0.612± 0.007 0.698± 0.008 0.628± 0.005 5D 0.630± 0.006 0.602± 0.007 0.621± 0.008 0.603± 0.006 0.606± 0.008 0.556± 0.004 0.508± 0.007 0.609± 0.007 0.560± 0.008 7D 0.565± 0.005 0.536± 0.005 0.546± 0.006 0.537± 0.005 0.531± 0.007 0.459± 0.004 0.403± 0.005 0.534± 0.006 0.493± 0.004 Onset MAE 1D 0.367± 0.005 0.433± 0.005 0.432± 0.005 0.493± 0.006 0.705± 0.012 0.419± 0.005 0.397± 0.005 0.874± 0.011 0.598± 0.006 3D 1.491± 0.019 1.842± 0.026 1.523± 0.013 1.830± 0.019 2.343± 0.030 1.633± 0.025 2.359± 0.040 2.881± 0.036 0.962± 0.013 5D 2.150± 0.018 3.820± 0.051 3.322± 0.029 4.015± 0.037 4.850± 0.075 2.340± 0.028 4.262± 0.073 4.827± 0.072 4.480± 0.044 7D 3.431± 0.030 6.035± 0.084 5.459± 0.050 5.486± 0.066 6.852± 0.119 3.093± 0.038 7.903± 0.134 6.416± 0.097 6.025± 0.097 Peak MAE 1D 0.058± 0.000 0.071± 0.001 0.060± 0.000 0.074± 0.001 0.096± 0.001 0.079± 0.001 0.087± 0.001 0.072± 0.001 0.092± 0.001 3D 0.087± 0.001 0.104± 0.001 0.090± 0.001 0.109± 0.001 0.119± 0.002 0.121± 0.002 0.150± 0.002 0.110± 0.001 0.134± 0.001 5D 0.110± 0.001 0.120± 0.001 0.110± 0.001 0.126± 0.001 0.133± 0.002 0.143± 0.002 0.188± 0.003 0.123± 0.002 0.169± 0.002 7D 0.116± 0.002 0.130± 0.001 0.122± 0.001 0.131± 0.001 0.142± 0.002 0.173± 0.002 0.178± 0.003 0.136± 0.002 0.169± 0.001 Duration MAE 1D 1.743± 0.021 1.973± 0.023 1.935± 0.024 1.818± 0.015 2.160± 0.030 1.942± 0.021 2.392± 0.036 2.022± 0.025 2.240± 0.021 3D 9.328± 0.097 10.001± 0.135 8.667± 0.114 9.027± 0.108 9.960± 0.186 11.129± 0.109 10.259± 0.176 9.581± 0.123 11.312± 0.167 5D 17.526± 0.181 20.454± 0.284 18.253± 0.230 18.988± 0.276 20.538± 0.336 21.697± 0.209 29.376± 0.488 19.178± 0.301 21.390± 0.193 7D 25.159± 0.277 32.558± 0.379 30.599± 0.458 30.487± 0.436 33.886± 0.623 36.493± 0.311 39.814± 0.574 29.570± 0.315 33.492± 0.471 Table 9. Detailed S6S_6 results for the intermediate evaluated historical block. Entries are means ± standard deviations over the three spatial parts. Metric Lead Ours NLinear PatchTST iTrans- former TimesNet Fourier GNN MTGNN AutoTimes Graph WaveNet MAE ×10−2× 10^-2 1D 5.001± 0.033 5.388± 0.052 4.907± 0.036 6.200± 0.054 6.722± 0.079 6.210± 0.053 8.927± 0.113 5.810± 0.050 5.778± 0.065 3D 8.854± 0.085 9.610± 0.090 9.116± 0.118 10.241± 0.085 10.855± 0.158 10.589± 0.097 13.293± 0.178 9.846± 0.102 12.358± 0.178 5D 11.786± 0.141 12.534± 0.148 12.205± 0.141 13.190± 0.147 13.547± 0.166 13.925± 0.183 18.212± 0.284 12.768± 0.177 14.163± 0.229 7D 14.258± 0.134 14.949± 0.176 14.625± 0.140 15.665± 0.124 16.046± 0.210 16.645± 0.183 20.062± 0.297 15.192± 0.223 17.282± 0.260 MSE ×10−2× 10^-2 1D 1.489± 0.016 1.637± 0.016 1.508± 0.017 2.003± 0.029 2.134± 0.029 1.764± 0.016 2.383± 0.040 1.824± 0.022 1.601± 0.017 3D 3.641± 0.035 3.975± 0.040 3.832± 0.042 4.352± 0.063 4.679± 0.064 4.074± 0.045 4.867± 0.060 4.140± 0.057 4.779± 0.064 5D 5.437± 0.078 5.973± 0.071 5.817± 0.082 6.410± 0.084 6.485± 0.112 6.125± 0.073 8.009± 0.093 6.058± 0.104 6.578± 0.089 7D 7.053± 0.085 7.735± 0.097 7.540± 0.094 8.206± 0.100 8.667± 0.170 7.782± 0.109 9.699± 0.091 7.846± 0.142 8.117± 0.122 Episode F1 1D 0.840± 0.006 0.815± 0.008 0.824± 0.012 0.789± 0.007 0.755± 0.009 0.778± 0.008 0.743± 0.012 0.810± 0.006 0.771± 0.009 3D 0.641± 0.006 0.614± 0.007 0.628± 0.010 0.577± 0.005 0.582± 0.006 0.544± 0.006 0.562± 0.006 0.598± 0.008 0.572± 0.006 5D 0.519± 0.006 0.493± 0.007 0.499± 0.006 0.470± 0.005 0.482± 0.007 0.469± 0.005 0.390± 0.005 0.495± 0.005 0.453± 0.006 7D 0.433± 0.004 0.418± 0.005 0.424± 0.005 0.393± 0.004 0.414± 0.005 0.379± 0.004 0.404± 0.005 0.416± 0.004 0.384± 0.004 Onset MAE 1D 0.288± 0.004 0.386± 0.005 0.267± 0.003 0.261± 0.003 0.700± 0.011 0.583± 0.007 2.098± 0.030 0.693± 0.008 0.534± 0.005 3D 1.754± 0.022 2.110± 0.028 1.759± 0.015 1.667± 0.018 2.113± 0.030 0.807± 0.012 2.093± 0.041 2.582± 0.036 2.119± 0.035 5D 1.893± 0.020 3.800± 0.052 2.450± 0.021 4.872± 0.054 6.158± 0.092 2.124± 0.028 2.238± 0.045 6.083± 0.088 4.293± 0.041 7D 4.252± 0.037 5.861± 0.079 3.813± 0.034 9.405± 0.136 11.746± 0.218 3.707± 0.048 5.490± 0.113 8.703± 0.147 7.654± 0.139 Peak MAE 1D 0.031± 0.000 0.035± 0.000 0.032± 0.000 0.037± 0.000 0.041± 0.001 0.041± 0.000 0.062± 0.001 0.037± 0.000 0.047± 0.001 3D 0.052± 0.001 0.060± 0.001 0.057± 0.001 0.068± 0.001 0.069± 0.001 0.077± 0.001 0.078± 0.001 0.063± 0.001 0.080± 0.001 5D 0.065± 0.001 0.074± 0.001 0.070± 0.001 0.074± 0.001 0.081± 0.001 0.086± 0.001 0.117± 0.002 0.079± 0.001 0.104± 0.001 7D 0.073± 0.001 0.082± 0.001 0.076± 0.001 0.086± 0.001 0.094± 0.002 0.092± 0.001 0.114± 0.002 0.083± 0.002 0.105± 0.001 Duration MAE 1D 2.016± 0.023 2.282± 0.026 2.166± 0.027 2.409± 0.023 2.543± 0.042 2.289± 0.028 3.511± 0.053 2.231± 0.033 2.637± 0.027 3D 11.685± 0.134 14.085± 0.186 11.583± 0.183 14.181± 0.167 12.248± 0.230 11.535± 0.120 17.397± 0.300 12.721± 0.177 14.071± 0.225 5D 24.313± 0.250 30.465± 0.475 26.393± 0.333 29.595± 0.384 30.607± 0.499 25.486± 0.263 31.648± 0.533 28.776± 0.400 31.207± 0.312 7D 36.882± 0.388 47.525± 0.602 42.989± 0.607 50.129± 0.659 51.145± 0.937 29.880± 0.300 42.651± 0.632 47.901± 0.603 49.365± 0.739 Table 10. Detailed S7S_7 results for the most recent evaluated historical block. Entries are means ± standard deviations over the three spatial parts. The table includes all four forecast horizons; the 3-day setting is used for the threshold-sensitivity and ablation analyses in the main text. Metric Lead Ours NLinear PatchTST iTrans- former TimesNet Fourier GNN MTGNN AutoTimes Graph WaveNet MAE ×10−2× 10^-2 1D 4.836± 0.034 5.700± 0.059 5.118± 0.037 5.792± 0.052 7.298± 0.105 6.590± 0.059 10.599± 0.153 6.088± 0.052 7.082± 0.095 3D 9.004± 0.105 9.826± 0.097 9.351± 0.138 10.099± 0.075 10.903± 0.185 11.007± 0.100 14.789± 0.211 10.106± 0.092 11.314± 0.177 5D 11.476± 0.125 13.007± 0.150 12.269± 0.177 13.117± 0.134 13.698± 0.193 13.847± 0.166 18.965± 0.329 12.934± 0.187 15.348± 0.245 7D 13.867± 0.148 15.439± 0.190 14.830± 0.144 15.691± 0.143 16.131± 0.198 16.575± 0.194 22.717± 0.312 15.319± 0.202 18.973± 0.290 MSE ×10−2× 10^-2 1D 1.576± 0.019 1.869± 0.017 1.661± 0.020 1.955± 0.025 2.507± 0.032 2.009± 0.019 15.993± 0.229 2.005± 0.023 5.641± 0.066 3D 3.919± 0.041 4.361± 0.047 4.093± 0.054 4.438± 0.076 4.850± 0.069 5.213± 0.061 32.473± 0.462 4.429± 0.067 16.539± 0.217 5D 5.793± 0.082 6.540± 0.083 6.162± 0.090 6.596± 0.103 7.042± 0.112 7.598± 0.112 39.312± 0.499 6.476± 0.103 29.099± 0.405 7D 7.504± 0.084 8.460± 0.094 8.063± 0.111 8.522± 0.119 9.102± 0.157 11.300± 0.185 45.188± 0.503 8.376± 0.146 42.180± 0.567 Episode F1 1D 0.794± 0.007 0.766± 0.009 0.778± 0.011 0.745± 0.006 0.690± 0.010 0.721± 0.007 0.629± 0.010 0.747± 0.007 0.722± 0.009 3D 0.587± 0.006 0.572± 0.006 0.578± 0.009 0.550± 0.004 0.520± 0.007 0.517± 0.006 0.471± 0.007 0.559± 0.007 0.551± 0.006 5D 0.479± 0.006 0.461± 0.006 0.464± 0.006 0.454± 0.005 0.422± 0.006 0.418± 0.004 0.369± 0.005 0.447± 0.005 0.417± 0.006 7D 0.412± 0.004 0.395± 0.005 0.399± 0.005 0.388± 0.004 0.376± 0.006 0.317± 0.003 0.283± 0.004 0.371± 0.004 0.355± 0.004 Onset MAE 1D 0.394± 0.006 0.559± 0.007 0.389± 0.004 0.742± 0.008 0.996± 0.017 0.760± 0.009 1.114± 0.019 1.280± 0.017 0.790± 0.009 3D 1.730± 0.022 2.514± 0.036 1.908± 0.020 2.938± 0.033 4.077± 0.066 3.179± 0.045 2.108± 0.039 3.536± 0.050 4.180± 0.069 5D 2.911± 0.031 4.786± 0.069 3.909± 0.043 6.506± 0.063 7.278± 0.118 2.989± 0.041 5.763± 0.113 6.797± 0.113 5.843± 0.071 7D 4.680± 0.041 8.152± 0.122 6.113± 0.065 10.552± 0.137 10.838± 0.215 6.358± 0.088 2.996± 0.059 9.860± 0.164 8.930± 0.148 Peak MAE 1D 0.044± 0.000 0.053± 0.001 0.045± 0.000 0.066± 0.001 0.085± 0.001 0.078± 0.001 0.142± 0.002 0.063± 0.001 0.080± 0.001 3D 0.059± 0.001 0.076± 0.001 0.062± 0.001 0.080± 0.001 0.123± 0.002 0.093± 0.001 0.103± 0.002 0.084± 0.001 0.097± 0.001 5D 0.070± 0.001 0.087± 0.001 0.073± 0.001 0.096± 0.001 0.136± 0.002 0.099± 0.001 0.143± 0.003 0.093± 0.002 0.124± 0.002 7D 0.076± 0.001 0.092± 0.001 0.082± 0.001 0.112± 0.001 0.150± 0.003 0.108± 0.001 0.133± 0.002 0.100± 0.002 0.121± 0.001 Duration MAE 1D 3.131± 0.040 3.429± 0.043 2.961± 0.042 3.456± 0.036 3.686± 0.062 3.637± 0.044 4.076± 0.073 3.355± 0.048 3.899± 0.045 3D 16.189± 0.195 17.878± 0.213 18.000± 0.246 18.359± 0.208 19.161± 0.325 17.031± 0.197 18.493± 0.342 18.033± 0.249 18.357± 0.295 5D 29.779± 0.280 36.192± 0.507 37.230± 0.541 40.605± 0.564 38.595± 0.626 28.548± 0.269 32.892± 0.593 36.795± 0.562 39.023± 0.449 7D 39.263± 0.383 57.530± 0.802 55.714± 0.840 64.676± 0.933 60.199± 0.978 41.099± 0.417 36.179± 0.648 57.111± 0.688 58.923± 1.022 Appendix E Threshold-Sensitivity Results Table 11. Mean ± standard deviation episode metrics for all models at four high-water thresholds. Episode F1 is higher when episode occurrence is recovered more accurately; the remaining measures are lower when matched-episode timing, peak level, and persistence are reproduced more closely. Best means within each metric and threshold column are boldfaced. Metric Model q=0.70q=0.70 q=0.80q=0.80 q=0.90q=0.90 q=0.95q=0.95 Episode F1 ↑ Ours 0.786± 0.008 0.748± 0.007 0.693± 0.008 0.652± 0.007 NLinear 0.773± 0.009 0.732± 0.009 0.667± 0.008 0.626± 0.007 PatchTST 0.781± 0.010 0.740± 0.011 0.680± 0.011 0.639± 0.009 iTransformer 0.757± 0.006 0.717± 0.006 0.652± 0.005 0.601± 0.005 TimesNet 0.742± 0.007 0.699± 0.008 0.640± 0.007 0.593± 0.006 FourierGNN 0.731± 0.008 0.684± 0.008 0.622± 0.007 0.569± 0.006 MTGNN 0.721± 0.009 0.673± 0.008 0.609± 0.008 0.552± 0.007 AutoTimes 0.766± 0.010 0.726± 0.009 0.661± 0.009 0.622± 0.008 Graph WaveNet 0.748± 0.007 0.705± 0.007 0.635± 0.007 0.581± 0.006 Onset MAE (h) ↓ Ours 1.180± 0.014 1.245± 0.014 1.492± 0.021 1.653± 0.021 NLinear 1.421± 0.018 1.405± 0.021 1.918± 0.030 2.193± 0.030 PatchTST 1.254± 0.011 1.332± 0.011 1.548± 0.016 1.729± 0.016 iTransformer 1.506± 0.017 1.831± 0.021 2.326± 0.023 2.181± 0.023 TimesNet 1.772± 0.025 2.052± 0.029 2.574± 0.045 2.792± 0.042 FourierGNN 1.381± 0.019 1.362± 0.022 1.742± 0.025 1.907± 0.027 MTGNN 1.310± 0.024 1.292± 0.023 1.582± 0.034 2.154± 0.040 AutoTimes 1.620± 0.020 1.596± 0.024 2.407± 0.037 2.942± 0.041 Graph WaveNet 1.268± 0.021 1.570± 0.025 1.558± 0.025 2.460± 0.039 Peak Magnitude MAE ↓ Ours 0.082± 0.001 0.078± 0.001 0.070± 0.001 0.067± 0.001 NLinear 0.093± 0.001 0.090± 0.001 0.085± 0.001 0.079± 0.001 PatchTST 0.084± 0.001 0.080± 0.001 0.072± 0.001 0.070± 0.001 iTransformer 0.100± 0.001 0.100± 0.001 0.088± 0.001 0.085± 0.001 TimesNet 0.114± 0.001 0.112± 0.002 0.109± 0.002 0.105± 0.001 FourierGNN 0.104± 0.001 0.101± 0.001 0.095± 0.001 0.095± 0.001 MTGNN 0.109± 0.002 0.111± 0.002 0.106± 0.002 0.112± 0.002 AutoTimes 0.098± 0.001 0.099± 0.001 0.088± 0.001 0.087± 0.001 Graph WaveNet 0.107± 0.001 0.109± 0.001 0.105± 0.001 0.103± 0.001 Duration MAE (h) ↓ Ours 6.220± 0.073 7.760± 0.086 10.080± 0.125 12.330± 0.142 NLinear 7.080± 0.078 8.790± 0.117 11.580± 0.162 14.180± 0.178 PatchTST 6.480± 0.090 8.030± 0.118 10.470± 0.148 12.840± 0.181 iTransformer 6.850± 0.083 8.480± 0.088 11.140± 0.146 14.060± 0.161 TimesNet 6.980± 0.121 8.660± 0.163 11.430± 0.240 13.580± 0.247 FourierGNN 7.150± 0.065 8.360± 0.086 10.860± 0.125 13.390± 0.142 MTGNN 7.430± 0.128 9.350± 0.160 12.620± 0.212 15.140± 0.273 AutoTimes 6.770± 0.096 8.310± 0.107 10.950± 0.170 13.250± 0.183 Graph WaveNet 6.550± 0.100 8.180± 0.140 11.310± 0.180 14.720± 0.229 Table 11 gives the S7S_7, 3-day comparison underlying Figure 3. The evaluation changes only the station-specific training quantile q, while retaining the same forecast issues, target-observation masks, three spatial partitions, and one-to-one episode-matching procedure. The reported values are means ± standard deviations across the three partitions. For target station i, the threshold is estimated from valid training-period WATER observations only. A value of q=0.70q=0.70 characterizes frequent elevated-water conditions, whereas q=0.95q=0.95 focuses on the station’s upper tail.