Extended Data Fig. 2: Illustration and justification for our method of estimating discharge on the Koyukuk River (which is missing gauge data during our study period from 2016 to 2022) based on the discharge time series from nearby rivers.
a–e, Discharge records from USGS stream gauges at Hughes (66.04696° N, 154.26097° W) (a–e), Pilot Station (61.93369° N, 162.88293° W) (a), Nenana (64.56494° N, 149.09400° W) (b), Stevens Village (65.87510° N, 149.72035° W) (c), Eagle (64.78917° N, 141.20009° W) (d), and Fairbanks (64.79234° N, 147.84131° W) (e). Note that 1 ft3/s is equal to approximately 0.028 m3/s. The discharge data for the Koyukuk River at Hughes are shown in brown and the discharge data from all other stations are shown in green. f–j, A zoom-in of the period 1977–1982, when all six stations were recording discharge data. Note the similarity in the hydrographs between the stations. We ask: can we use the historical period of overlap (f–j) to train a model that infers the discharge on the Koyukuk River given the hydrographs recorded at nearby stations? k, Consider the specific case of the streamflow recorded at Hughes, Pilot Station and Stevens Village. The Koyukuk River carries roughly 20% of the streamflow observed on the Yukon River at Stevens Village (c,h). Thus, the difference in discharge observed at Stevens Village versus Pilot Station (that is, before and after the confluence with the Koyukuk River, respectively) should encode information about the discharge from the Koyukuk River, modulated by a characteristic convolutional smoothing of the hydrograph from upstream to downstream. l, We use a simple neural network to infer the hydrograph from the Koyukuk River (which is not directly observed during our study period from 2016–2022) based on the hydrographs of the Yukon River at Stevens Village and Pilot Station (which have continuous observational records from 2016 to 2022). We train the neural network using the period of overlap when all three stations were collecting data from 1977 to 1982 (Extended Data Fig. 3).
