PaperlayerView exact revision on arXiv

Source-linked AI summary

C-STRIDE: An Observation-Driven AI Digital Twin for Predicting Basin-Wide Flood Fields from Sparse Stream-Gauge Histories

Yanjie Tong, Phillip Si, Yuan Qiu, Peng Chen

arXiv:2609.39005v1cs.AI

TL;DR

Flood prediction must extend sparse local gauge measurements into spatially distributed, time-varying basin fields. C-STRIDE combines gauge histories with terrain and precipitation to predict water depth, with improved next-step and longer-horizon errors when these inputs are used together.

  • Problem

    Sparse gauge histories do not by themselves determine a time-varying basin-wide flood field, although such fields are needed to understand where water is accumulating and how inundation may evolve.

    Source: §1.1 · p. 1, §1.2 · p. 3

  • Method

    C-STRIDE encodes gauge and optional precipitation histories, then uses a terrain-conditioned coordinate decoder to predict water depth, with a gauge forecaster for multi-step prediction.

    Source: §6 · p. 23

  • Results

    Joint conditioning reduces four-event mean relative depth error by approximately 41% versus vanilla STRIDE; at 24 h, full C-STRIDE reaches 14.48% mean relative error with reference future rainfall versus 38.14% for vanilla STRIDE.

    Source: §6 · p. 23

  • Takeaways & Limitations

    In the Des Plaines basin, C-STRIDE combines rapid spatial prediction with observation-driven state estimation from sparse gauges.

    Source: §6 · p. 23

    The evaluation is limited to one basin and four held-out test events, and prospective testing with operational precipitation forecasts and real-time gauge streams remains needed.

    Source: §5.3 · p. 22, §5.4 · p. 23

Abstract

from arXiv · show

Emergency managers need to know where floodwater is, how deep it is, and how it will change over the coming hours across an entire river basin. During a flood, however, real-time measurements come from only a handful of stream gauges, and high-resolution hydrodynamic models are too costly to rerun each time new data arrive or to run as large ensembles. We present C-STRIDE, an observation-driven AI digital twin that turns short records from a few stream gauges, together with terrain and rainfall, into basin-wide maps of water depth and extends these predictions up to a day ahead. It is trained on simulations from a calibrated two-dimensional hydrodynamic model and needs no separate data-assimilation step. In the Des Plaines River basin near Chicago, six gauges inform predictions over 4.2 million 30-m grid cells. Terrain improves the predictions most, rainfall keeps errors from growing over longer horizons, and together they reduce errors by about 40% compared with gauge records alone. When future rainfall is known, errors remain near 15% one day ahead, compared with nearly 40% without rainfall. Given real instead of simulated gauge records, the model shifts its predictions toward the observed hydrographs at three of six gauges without retraining, and it runs about 150 times faster than the hydrodynamic model. These results show how sparse gauges, terrain, and rainfall can be combined into fast, continuously updated flood predictions, a step toward operational flood digital twins that still requires testing with real-time data and rainfall forecasts.

1. Introduction

The paper frames basin-wide flood prediction as connecting sparse, local gauge histories to time-varying spatial fields, then introduces C-STRIDE to combine observations, terrain, and precipitation. Its contribution separates the roles of terrain and rainfall and evaluates prediction across fields, gauges, and computational cost.

1.1. Hydrological digital twins for flood decision support

  • Sparse gauges record local conditions, but emergency response needs spatially distributed information on flood location, depth, and evolution across a basin.The paper casts this integration as physics-anchored simulation, fast surrogate prediction, and observation-driven state estimation.Source: §1.1 · pp. 1–2

1.2. Hydrodynamic models, learned surrogates, and observation integration

  • Prior flood models span physics-based assimilation, learned flood surrogates, and sparse-sensor field reconstruction, while the paper targets basin-wide fields inferred directly from gauge histories.These approaches differ in their runtime inputs and outputs; the paper notes that prior sparse-field methods were mostly shown on fluid, climate, or synthetic benchmarks rather than basin-wide flood fields constrained by real gauge networks.Source: §1.2 · pp. 2–3

1.3. From sparse gauge histories to spatial flood fields

  • Gauge histories constrain recent basin behavior, terrain describes persistent spatial controls, and rainfall helps represent delayed downstream effects, motivating C-STRIDE’s combined inputs.The approach adapts STRIDE’s temporal encoder and coordinate decoder, adds terrain features, and uses a second LSTM to forecast gauge readings for multi-step predictions.Source: §1.3 · pp. 3–4

1.4. Contributions and evaluation scope

  • C-STRIDE combines gauge-history encoding, terrain-conditioned continuous decoding, and precipitation-conditioned forecasting, and can be queried at individual locations or across the basin.The study also tests observed gauge inputs, withheld tributary gauges, and altered sensor inputs; next-step depth-field prediction is reported as approximately 150× faster than a SynxFlow simulation on the same GPU, although the computations differ in scope.Source: §1.4 · p. 5
  • Joint terrain and precipitation conditioning reduces four-event mean relative depth error by approximately 41% compared with vanilla STRIDE, while full C-STRIDE reaches 14.48% error at a 24-h horizon with reference future rainfall.Terrain gives the larger individual improvement in next-step field prediction; precipitation limits error growth during multi-step forecasting.Source: §1.4 · p. 5

2. Study area, data, and problem setup

The study uses SynxFlow simulations to define a sparse-observation task: predict water depth at queried locations from gauge histories, terrain, and rainfall. The case study uses 94 simulations and six gauges in the Des Plaines River basin.

2.1. High-fidelity simulator for generating the synthetic dataset

  • SynxFlow generates the reference data by solving the two-dimensional shallow-water equations on a masked rectangular grid and outputs future depth and discharge states from initial conditions, terrain, roughness, and precipitation.Its numerical scheme uses a Godunov-type finite-volume method, with an adaptive time step chosen according to the CFL condition.Source: §2.1 · p. 5

2.2. Sparse-observation prediction problem

  • The task estimates water depth at a queried location and horizon from a window of gauge observations, precipitation, and static terrain features.One-step prediction uses historical observations and rainfall; multi-step prediction additionally requires future precipitation, with the default evaluation supplying reference rainfall.Source: §2.2 · p. 6

2.3. Des Plaines River basin case study

  • The Des Plaines River case uses six USGS gauges, 4,188,840 active 30-m cells, and 94 simulations, with 90 trajectories for training and four held out for testing.The simulations run for 96 hours and use spatially varying precipitation fields; gauge inputs are noisefree simulated depths unless otherwise stated.Source: §2.3 · p. 6

3. The C-STRIDE model

C-STRIDE extends STRIDE’s sparse-observation reconstruction with terrain, optional precipitation, and multi-step forecasting. The section also specifies sampled-cell training and the inference protocol and metrics used to evaluate the model.

3.1. STRIDE recap: delay-embedded continuous decoding

  • STRIDE factorizes sparse-observation reconstruction into a temporal encoder and coordinate-conditional decoder, with its approximation rationale depending on stable delay observability.The condition is that the system state be stably identifiable from K+1 delayed observations.Source: §3.1 · p. 7

3.2. C-STRIDE architecture

  • C-STRIDE adds terrain features to coordinate decoding, optional precipitation to observation histories, and a separate gauge LSTM to extend one-step field predictions through sliding-window feedback.Predicted gauge values and supplied rainfall are appended to the window; rainfall at a forecast step first affects the next field prediction.Source: §3.1 · p. 7, §3.2 · pp. 8–9

3.3. Training strategy and scalability

  • Training minimizes normalized-depth error against SynxFlow fields and separately trains gauge forecasters, using random cell subsets to keep pointwise decoding costs tied to sampled queries.Each window uses 105 sampled points, and each minibatch contains four windows; training and evaluation retain event cells reaching at least 0.1 m depth.Source: §3.2 · p. 9, §3.3 · p. 9

3.4. Digital-twin inference protocol and evaluation metrics

  • At inference, the model updates a fixed-length gauge history, predicts the next field, then advances later forecasts using predicted gauge values; finer-than-30-m queries add no information beyond training resolution.Accuracy is established only on the evaluated reduced grids.Source: §3.4 · p. 10
  • Field evaluation averages snapshot-wise relative L2 error and RMSE over each event’s reduced grid; the L2 measure weights deeper cells more heavily.The metrics are computed per snapshot and then averaged, rather than pooled across space and time.Source: §3.4 · pp. 10–11
  • Evaluation also measures gauge NSE, KGE, and peak-depth error, flood extent at a 0.5 m threshold, computational time, and forecast error at horizons of 1, 4, 6, 12, and 24 steps.Flood-extent measures include critical success index, precision, recall, and frequency bias.Source: §3.4 · p. 11

4. Results

The results section evaluates C-STRIDE’s fast spatial prediction and observation-driven state estimation, alongside multi-step forecasting, observation-interface sensitivity, and computational cost.

4. Results

  • The evaluation examines field prediction and flood extent for fast spatial prediction, and gauge hydrographs and observed USGS inputs for observation-driven state estimation.Physical anchoring is inherited from prior evaluation of SynxFlow against USGS observations and is not re-evaluated here.Source: §4 · p. 11
  • The full configuration uses both terrain and precipitation, and comparisons include terrain-only, precipitation-only, vanilla STRIDE, CLDNet, and CLDNet with LD-EnSF variants.The four STRIDE configurations share architecture and training settings and differ only in their inputs.Source: §4 · p. 11
  • Table 5 reports mean snapshot depth errors for the April 2013 flood and the four-event average, with estimates one step ahead of a 12-step observation history.The relative error normalizes depth error by the reference field, while RMSE reports its magnitude in meters.Source: Table 5 · p. 12

4.1. Aggregate next-step prediction accuracy

Terrain and rainfall reduce next-step depth error, while terrain-only conditioning gives the strongest average gauge fidelity. Full C-STRIDE also responds to observed gauge histories, though gains vary by site and held-out tributary predictions are mixed.

4.1. Aggregate next-step prediction accuracy

  • 10.63% four-event relative error: full C-STRIDE reduces error from 18.14% by approximately 41% and yields the lowest RMSE.On the April 2013 event, relative error falls from 13.69% to 8.38%, and RMSE from 0.0961 to 0.0589 m.Source: §4.1 · p. 12
  • Terrain-only C-STRIDE reaches 14.23% relative error versus 20.88% for CLDNet + LD-EnSF, while adding rainfall lowers error further to 10.63%.Terrain gives the larger individual gain; rainfall adds a further improvement to the terrain-conditioned estimate.Source: §4.1 · p. 12
  • Full C-STRIDE has the lowest mean error over most of the event, but configuration curves cross near its end.Figure 2 shows mean snapshot-wise relative L2 error, with shading for one standard deviation across events.Source: §4.1 · p. 12, Figure 2 · p. 13
  • At location H, vanilla STRIDE underestimates the peak by about 1.31 m and misses recession; full C-STRIDE overshoots the crest by about 0.27 m.Location H is about 25 km from the nearest gauge; terrain-only C-STRIDE overshoots the same crest by 0.61 m.Source: §4.1 · pp. 12–13

4.2. Hydrograph fidelity at USGS gauges

  • Terrain-only C-STRIDE gives the best average gauge fidelity, while full C-STRIDE's mean peak-depth error is 6.33% versus 3.10% for vanilla STRIDE.The larger full-model mean is mainly due to DuPage and Salt Creek; median NSE improves to 0.960 versus 0.937 for vanilla STRIDE.Source: §4.2 · pp. 13–14, Table 6 · p. 13
  • After retrospective mean alignment, USGS-input predictions improve NSE at Des Plaines, Salt Creek, and Riverside, but decrease it at Russell, Gurnee, and DuPage.At DuPage, the observed-input prediction peaks 11 hours early and overshoots the observed crest by approximately 0.31 m.Source: §4.2 · pp. 13–15
  • With tributary gauges withheld from the encoder, USGS mainstem inputs improve Salt Creek NSE from 0.004 to 0.346, but leave DuPage NSE essentially unchanged.Salt Creek's peak remains 7 hours late, while DuPage's peak shifts from 1 hour late to 7 hours early.Source: §4.2 · pp. 15–16

4.3. Flood-extent metrics

At a 0.5 m depth threshold in the April 2013 event, full C-STRIDE gives the strongest flood-extent scores. Terrain accounts for most of the improvement, and pooled scores partly count persistently wet cells as hits.

4.3. Flood-extent metrics

  • Full C-STRIDE has the highest CSI, precision, and recall, with CSI reaching 0.933 at the 0.5 m threshold.The reported metrics aggregate valid snapshots and evaluation cells for the April 2013 event.Source: §4.3 · p. 16, Table 8 · p. 16
  • Terrain conditioning accounts for most of the flood-extent improvement; adding precipitation to terrain conditioning yields the best overall inundation mask.Precipitation alone has only a modest effect in this single event.Source: §4.3 · pp. 16–17
  • Vanilla STRIDE slightly under-predicts flooding with frequency bias 0.987, while full C-STRIDE is nearly unbiased.Persistently wet cells such as river channels count as hits in pooled scores, partly raising absolute CSI values.Source: Table 8 · p. 16, §4.3 · p. 17

4.4. Multi-step forecast skill

Across 24-step forecasts without new gauge observations, rainfall-conditioned C-STRIDE limits error growth, with the full model outperforming sparse-input alternatives at longer reported horizons. Forecasts also depend on recursive gauge predictions, and tested rainfall mismatch changes the 24-hour error only slightly.

4.4. Multi-step forecast skill

  • The 24 hourly fields are forecast without new gauge observations, so predicted gauge values replace unavailable observations as the window advances.The evaluation uses 40 forecasts from 10 origins per event, with the same origins for all configurations.Source: §4.4 · p. 17
  • Rainfall conditioning limits forecast error growth: forcing-only C-STRIDE reaches 18.28% at horizon 24, while terrain's advantage over vanilla STRIDE disappears by then.Full C-STRIDE has the lowest mean error among the four unperturbed configurations at each horizon.Source: §4.4 · p. 17, Table 9 · p. 18
  • 14.48% versus 36.37% relative depth error at horizon 24: full C-STRIDE outperforms persistence, and is better at reported horizons from 4 onward.Persistence uses the complete preceding reference field, unlike the sparse-input learned models.Source: §4.4 · p. 17, Table 9 · p. 18
  • Gauge-only forecaster error rises from 1.27% at the first step to 42.63% at 24 h, versus 9.30% and 16.48% for the rainfall-conditioned forecaster.Rainfall helps long-horizon gauge forecasting but not the first step; the reported one-step errors use different evaluation snapshots.Source: §4.4 · pp. 17–18
  • Rainfall mismatch raises full-model horizon-24 error from 14.48% to 14.72%, while horizon-one error is unchanged.The tested perturbation matters far less than omitting rainfall altogether; future rainfall enters after the first prediction.Source: §4.4 · p. 19

4.5. Sensitivity to the observation interface

Longer observation histories improve next-step accuracy, while fewer available gauges yield nearly unchanged field-level error in one tested configuration. Accuracy degrades gradually as input noise increases.

4.5.1. Window length

  • 24-step history reaches 8.61% mean relative error versus 11.44% for the 12-step default, with comparisons made at common prediction times.A longer record is needed before the first prediction; the study retains 12 steps as the default for consistency with the main experiments.Source: §4.5.1 · p. 19, Figure 10 · p. 20

4.5.2. Sensor robustness

  • Four mainstem gauges give 10.67% error versus 10.63% for the six-gauge model, while tributary dropout raises error to 11.15%.In the four-gauge configuration, tributary gauges are omitted entirely; in 50% dropout, tributary records are jointly removed at selected times and filled from the nearest available observation.Source: §4.5.2 · p. 20
  • Input noise level 0.20 raises error to 12.43%, approximately 17% above the default.The tested noise is zero-mean Gaussian noise scaled by the across-gauge or across-rainfall-value standard deviation at each time step.Source: §4.5.2 · p. 20

4.6. Computational cost

C-STRIDE’s inference is substantially faster than the hydrodynamic reference in the reported next-step comparison, while the measurements also show low per-field and gauge-query costs and faster repeated forecasting.

4.6. Computational cost

  • 0.262 s per field was the reported next-step prediction time after a one-time full encoder–decoder training cost of approximately 26.2 h.The timing was measured on one NVIDIA L40S GPU.Source: §4.6 · p. 20
  • Restricting queries to six gauge locations reduced runtime to 3.55 ms per snapshot; 40 forecasts of 24 steps took 247.37 s total, including forecast preparation and scoring.Source: §4.6 · p. 21
  • 21.99 s for April 2013 next-step prediction of all fields is approximately 150 times faster than SynxFlow’s 96-h simulation, though the computational scopes differ.SynxFlow advances depth and momentum over the full grid; C-STRIDE predicts depth at selected locations, and its forecast timing covers overlapping target times.Source: §4.6 · p. 21

5. Discussion

Terrain provides the largest single error reduction, while rainfall contributes more at longer forecast horizons and observed gauge histories shift some predictions. The discussion also identifies remaining operational and evaluation boundaries.

5.1. What gauges, terrain, and precipitation each contribute

  • 18.14% →14.23% with terrain, compared with 18.14% →10.63% for the full model, shows terrain’s largest single gain while precipitation adds further error reduction.Terrain also accounts for most of the improvement in inundation extent for the 2013 event.Source: §5.1 · p. 21
  • Without precipitation, errors accumulate more over 24 h; with it, peak errors at gauges can be larger than in the terrain-only model, particularly at tributaries.At the next-step horizon, full C-STRIDE reduces four-event error from 14.23% to 10.63% relative to terrain alone; precipitation’s contribution is more pronounced at longer horizons.Source: §5.1 · p. 21
  • Longer gauge histories help distinguish evolving flood states, while removing tributary gauges changes basin-wide error only slightly and can obscure local hydrograph effects.The discussion recommends evaluating local objectives, such as tributary hydrograph fidelity, separately from aggregate metrics.Source: §5.1 · p. 21

5.2. From simulated to observed gauge inputs

  • USGS gauge inputs shift predictions toward observed timing and magnitude at several gauges without retraining, but can create artifacts and yield mixed results at withheld tributaries.At Salt Creek, NSE rises from 0.004 to 0.346, although the peak remains 7 h late; DuPage is essentially unchanged, and the experiment also reports a spurious early rise at Russell and crest overshoot at DuPage.Source: §5.2 · p. 22

5.3. Toward an operational flood digital twin

  • C-STRIDE supplies fast spatial prediction and observation-driven state estimation, but operational use still requires calibrated uncertainty, operational-forcing tests, changing-network support, and broader predicted outputs.The discussion also identifies a decision interface and feedback to the physical system as requirements for a complete operational twin.Source: §5.3 · pp. 22–23
  • SynxFlow’s single-event speed makes the surrogate’s main computational advantage repeated evaluations such as ensembles, assimilation cycles, and scenario analysis.A break-even estimate requires matched computational scopes and accounting for training-data generation and model training.Source: §5.3 · p. 22

5.4. Limitations

  • The evaluation covers one basin, four held-out events, and six gauges; event-specific masks limit field-accuracy claims to cells reaching 0.1 m.The masks are not known in advance during deployment, so accuracy outside them is not established; the missing-observation experiment also does not establish robustness to causal real-time outages.Source: §5.4 · p. 23
  • Depth predictions inherit simulator limitations, and the evaluation does not establish absolute elevation accuracy, prospective deployment performance, mass conservation, or hydraulic consistency.The simulator uses 30-m terrain and channel geometry, two-class Manning roughness, and event-specific initial and boundary conditions; the model does not predict velocity or discharge.Source: §5.4 · p. 23

6. Conclusions

C-STRIDE combines terrain and precipitation with sparse gauge histories to improve flood-depth prediction and extend forecasts. Its response to observed gauge histories varies by site, and the reported results remain bounded by the tested basin and evaluation setting.

6. Conclusions

  • 18.14% to 10.63%: full conditioning reduced four-event mean relative depth error versus vanilla STRIDE; April 2013 CSI was 0.933 at the 0.5 m depth threshold.For the first prediction step, terrain and precipitation provide complementary information, with terrain giving the larger individual gain.Source: §6 · p. 23
  • 14.48% mean relative error at 24 h with reference future rainfall, versus 38.14% for vanilla STRIDE; tested rainfall mismatch raised full-model error to 14.72%.Full-field persistence is more accurate at the first step, whereas C-STRIDE is more accurate at reported horizons from four steps onward.Source: §6 · p. 23
  • Full conditioning gives the lowest aggregate field error, but terrain-only conditioning yields the best average hydrograph agreement at six gauges, so similar four- and six-gauge field errors can hide local differences.Source: §6 · p. 24
  • Replacing simulated histories with USGS observations improves NSE at three of six gauges, including Riverside’s increase from 0.118 to 0.840, but response is mixed at two withheld tributary gauges.These comparisons use gauge-specific, event-wide mean offsets and assess retrospective responses to observed inputs.Source: §6 · p. 24
  • 21.99 s: full C-STRIDE predicts the April 2013 depth fields about 150 times faster than SynxFlow on the same hardware.Results are limited to one basin, event-specific reference-derived evaluation grids, and deterministic predictions; future work includes prospective operational-forecast tests, independent inundation observations, calibrated uncertainty, and evaluation across basins and sensor networks.Source: §6 · p. 24

Data and code availability

Code, input data, and trained C-STRIDE models are available in the project repository; simulated flow fields can be regenerated from the released inputs.

Data and code availability

  • Code, input data, and trained models are available through the C-STRIDE repository, organized like the CLDNet repository for the same Des Plaines River basin dataset.Source: Data and code availability · p. 24
  • Simulated flow fields are not hosted but can be regenerated with the open-source SynxFlow solver, and USGS gauge records come from the National Water Information System.Source: Data and code availability · p. 24
Loading 2609.39005v1…