Mass conservation moves into a distributed hydrologic network: PECAN matches outlet streamflow in a Colorado snow basin but releases winter snowpack early
Synopsis
Mass-conservation constraints had been embedded only in lumped LSTMs, which yield basin-averaged time series and cannot test whether internal states are hydrologically meaningful. PECAN recasts the constraint in a distributed convolutional LSTM, with a strict precipitation-only variant, PECANMC, and a relaxed variant, PECANMCR, trained solely on streamflow at two gauges. In the snow-dominated North Platte Headwaters in Colorado, both variants match lumped deep-learning baselines and the distributed process model VIC on outlet streamflow and expose spatially explicit internal states, yet diagnostics show the model removes winter snow water storage prematurely instead of holding it for spring release.
Interpretation
Mass-conservation constraints extend from lumped neural networks to distributed hydrologic modeling, so the model outputs grid-cell storage and runoff while keeping an explicit water balance. Earlier mass-conserving neural networks were almost exclusively lumped, applying conservation to basin-aggregated fluxes and storage and limiting diagnostics to basin-averaged time series. At daily scale in the North Platte Headwaters watershed in Colorado, both PECAN variants reach outlet streamflow accuracy competitive with lumped deep-learning baselines, a standard LSTM plus MC-LSTM and MCR-LSTM, and with the distributed process-based VIC model.
The model reads LSTM cell states as grid-cell fast and slow water storage and hidden states as the corresponding released fluxes, then routes runoff to gauges. The implementation is a convolutional LSTM: the input gate is normalized across channels so precipitation mass is partitioned proportionally, and a channel redistribution matrix is column-normalized so no grid cell gains or loses water internally. Training uses only observed discharge at two USGS gauges, with no supervision from distributed target variables; part of fast-flow storage recharges a slow-flow linear reservoir, and total runoff is converted to gauge streamflow by the RVIC routing model.
Internal states can be checked against independent observations, which exposes where the model misrepresents hydrologic processes. Against reference soil moisture, PECAN cell states resemble meaningful temporal soil moisture dynamics; against snowpack, the model removes winter snow water storage from the system. Reference data include observation-based UA-SWE snow water equivalent and SMAP L4 soil moisture, plus VIC-simulated soil moisture and evapotranspiration; comparing PECANMC with PECANMCR tests how strict versus relaxed conservation assumptions shape learned hydrologic behavior.
Perspective
The conclusions rest on a proof-of-concept case in the roughly 3,688 square kilometer snow-dominated North Platte Headwaters in Colorado, at daily scale, trained and evaluated only with streamflow at two gauges; readers should treat it as a feasibility test of a distributed mass-conserving network, not a general cross-basin result.
The model removes winter snow water storage prematurely rather than retaining it for spring release, showing that a conservation constraint alone does not guarantee correct snow representation; how the strict and relaxed conservation assumptions differ in behavior remains tied to this watershed's comparison.