Accurate estimation of precipitation from satellites at high spatiotemporal scales over the Tibetan Plateau (TP) remains a challenge. In this study, we proposed a general framework for blending multiple satellite precipitation data using the dynamic Bayesian model averaging (BMA) algorithm. The blended experiment was performed at a daily 0.25° grid scale for 2007–2012 among Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42RT and 3B42V7, Climate Prediction Center MORPHing technique (CMORPH), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks‐Climate Data Record (PERSIANN‐CDR). First, the BMA weights were optimized using the expectation‐maximization (EM) method for each member on each day at 200 calibrated sites and then interpolated to the entire plateau using the ordinary kriging (OK) approach. Thus, the merging data were produced by weighted sums of the individuals over the plateau. The dynamic BMA approach showed better performance with a smaller root‐mean‐square error (RMSE) of 6.77 mm/day, higher correlation coefficient of 0.592, and closer Euclid value of 0.833, compared to the individuals at 15 validated sites. Moreover, BMA has proven to be more robust in terms of seasonality, topography, and other parameters than traditional ensemble methods including simple model averaging (SMA) and one‐outlier removed (OOR). Error analysis between BMA and the state‐of‐the‐art IMERG in the summer of 2014 further proved that the performance of BMA was superior with respect to multisatellite precipitation data merging. This study demonstrates that BMA provides a new solution for blending multiple satellite data in regions with limited gauges.
The multiclass network equilibrium problem is investigated under a tradable credit scheme. The social planner initially distributes a certain number of credits to all eligible travelers, charges a link-specific number of credits from travelers using that link, and allows for free trading of the credits among travelers. Travelers are assumed to be heterogeneous with a continuously distributed value of time (VOT). For a given tradable credit scheme and VOT distribution, the combined user equilibrium and credit market equilibrium problem is formulated into an infinite-dimensional variational inequality system, and the conditions for the uniqueness of the network flow pattern and the credit price at equilibrium are established. Manageable credit schemes that can decentralize a given target network flow pattern (e.g., the system optimum one) into a user equilibrium link flow pattern is proposed. With a numerical example, it is shown that an appropriate credit distribution rule may make every traveler better off. The stability of a desirable tradable credit scheme is also established, based on rigorous sensitivity analysis.
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