Forecasting river temperatures in real time using a stochastic dynamics approach

Abstract

[1] We address the growing need for accurate water temperature predictions in regulated rivers to inform decision support systems and protect aquatic habitats. Although many suitable river temperature models exist, few simultaneously model water temperature dynamics while considering uncertainty of predictions and assimilating observations. Here, we employ a stochastic dynamics approach to water temperature modeling that estimates both the water temperature state and its uncertainty by propagating error through a physically based dynamical system. This method involves converting the governing hydrodynamic and heat transport equations into a state space form and assimilating observations via the Kalman Filter. This model, called the River Assessment for Forecasting Temperature (RAFT), closes the heat budget by tracking heat movement using a robust semi-Lagrangian numerical scheme. RAFT considers key thermodynamic processes, including advection, longitudinal dispersion, atmospheric heat fluxes, lateral inflows, streambed heat exchange, and unsteady nonuniform flow. Inputs include gridded meteorological forecasts from a numerical weather prediction model, bathymetric crosssectional geometry, and temperature and flow measurements at the upstream boundary and tributaries. We applied RAFT to an $100 km portion of the Sacramento River in California, downstream of Keswick Dam (a regulatory dam below Shasta Dam), at a spatial resolution of 2 km and a temporal resolution of 15 min. Model prediction error over a 6 month calibration period was on the order of 0.5 C. When temperature and flow gage data were assimilated, the mean prediction error was significantly less (0.25 C). The model accurately predicts the magnitude and timing of diel temperature fluctuations and can provide 72 h water temperature forecasts when linked with meteorological forecasts and real-time flow/ temperature monitoring networks. RAFT is potentially scalable to model and forecast finegrained one-dimensional temperature dynamics covering a broad extent in a variety of regulated rivers provided that adequate input data are available.

Spatio‐temporal temperature variation influences juvenile steelhead (Oncorhynchus mykiss) use of thermal refuges

“…First, the interaction between diel mainstem variation, mainstem temperature, and flow could enable managers to predict which tributaries may create more effective thermal refuges (i.e., higher likelihood of use), given their longitudinal location and the predictive nature of diel mainstem variation on regulated rivers (Pike et al 2013); these inferences could inform targeted flow management and habitat restoration efforts at tributary confluences. Second, the positive relationship between temperature differential and refuge use, which could be attributed to fish gaining greater relative physiological benefit from refuges created by cooler tributaries, emphasizes the importance of maintaining good riparian habitat along stream corridors.…”

“…Juvenile steelhead rear in the river for 1-3 years before out-migrating to the ocean. During summer months the mainstem reaches temperatures that can be thermally inhospitable to salmonids-mean daily mainstem temperatures at the study sites ranged from 148 to 268C between 2010 and 2012-and juveniles seek out thermal refuges, usually at tributary confluences (Sutton et al 2007 (Pike et al 2013). The number of study sites sampled varied across years (sites 1-4 in 2010; sites 1-3 in 2011; site 1 in 2012) due to access issues (landowner permission) and the number of radio tags available.…”

Water Temperature Ensemble Forecasts: Implementation Using the CEQUEAU Model on Two Contrasted River Systems

“…They suggest looking at the capacity of a model to predict a threshold exceedance instead of solely focusing on the traditional best fit. Given the fact that in many systems, thermal forecasts are issued in order to keep water temperature below a target threshold [13,15,39] the evaluation of threshold prediction capacity of the forecasting system is essential to assess its usefulness. Hence, in addition to the MCRPS, the Brier Score (BS; Equation (14)) [40] was calculated as:…”

“…237.3+Ta ) (15) e a = RH · e s /100 (16) where e s is the saturated vapor pressure. The ensemble meteorological forecasts were extracted in grib2 format through The Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE) portal.…”

“…Research on water temperature has provided the water management community with a plethora of modeling tools (see Benyahya et al [14] for a partial review). Many of these models are key elements for dam operators because they help to meet environmental flow requirements and water quality criteria, while at the same time assisting in the optimization of operations [13,15].…”