[1] Uncertainties in hydrologic parameters could have significant impacts on the simulated water and energy fluxes and land surface states, which will in turn affect atmospheric processes and the carbon cycle. Quantifying such uncertainties is an important step toward better understanding and quantification of uncertainty of integrated earth system models. In this paper, we introduce an uncertainty quantification (UQ) framework to analyze sensitivity of simulated surface fluxes to selected hydrologic parameters in the Community Land Model (CLM4) through forward modeling. Thirteen flux tower footprints spanning a wide range of climate and site conditions were selected to perform sensitivity analyses by perturbing the parameters identified. In the UQ framework, prior information about the parameters was used to quantify the input uncertainty using the Minimum-Relative-Entropy approach. The quasi-Monte Carlo approach was applied to generate samples of parameters on the basis of the prior pdfs. Simulations corresponding to sampled parameter sets were used to generate response curves and response surfaces and statistical tests were used to rank the significance of the parameters for output responses including latent (LH) and sensible heat (SH) fluxes. Overall, the CLM4 simulated LH and SH show the largest sensitivity to subsurface runoff generation parameters. However, study sites with deep root vegetation are also affected by surface runoff parameters, while sites with shallow root zones are also sensitive to the vadose zone soil water parameters. Generally, sites with finer soil texture and shallower rooting systems tend to have larger sensitivity of outputs to the parameters. Our results suggest the necessity of and possible ways for parameter inversion/calibration using available measurements of latent/sensible heat fluxes to obtain the optimal parameter set for CLM4. This study also provided guidance on reduction of parameter set dimensionality and parameter calibration framework design for CLM4 and other land surface models under different hydrologic and climatic regimes.Citation: Hou, Z., M. Huang, L. R. Leung, G. Lin, and D. M. Ricciuto (2012), Sensitivity of surface flux simulations to hydrologic parameters based on an uncertainty quantification framework applied to the Community Land Model, J. Geophys.
Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. We present a new approach to data-driven discovery of ordinary differential equations (ODEs) and partial differential equations (PDEs), in explicit or implicit form. We demonstrate our approach on a wide range of problems, including shallow water equations and Navier–Stokes equations. The key idea is to select candidate terms for the underlying equations using dimensional analysis, and to approximate the weights of the terms with error bars using our threshold sparse Bayesian regression. This new algorithm employs Bayesian inference to tune the hyperparameters automatically. Our approach is effective, robust and able to quantify uncertainties by providing an error bar for each discovered candidate equation. The effectiveness of our algorithm is demonstrated through a collection of classical ODEs and PDEs. Numerical experiments demonstrate the robustness of our algorithm with respect to noisy data and its ability to discover various candidate equations with error bars that represent the quantified uncertainties. Detailed comparisons with the sequential threshold least-squares algorithm and the lasso algorithm are studied from noisy time-series measurements and indicate that the proposed method provides more robust and accurate results. In addition, the data-driven prediction of dynamics with error bars using discovered governing physical laws is more accurate and robust than classical polynomial regressions.
Compressive sensing is used to determine the flow characteristics around a cylinder (Reynolds number and pressure/flow field) from a sparse number of pressure measurements on the cylinder. Using a supervised machine learning strategy, library elements encoding the dimensionally reduced dynamics are computed for various Reynolds numbers. Convex L1 optimization is then used with a limited number of pressure measurements on the cylinder to reconstruct, or decode, the full pressure field and the resulting flow field around the cylinder. Aside from the highly turbulent regime (large Reynolds number) where only the Reynolds number can be identified, accurate reconstruction of the pressure field and Reynolds number is achieved. The proposed data-driven strategy thus achieves encoding of the fluid dynamics using the L2 norm, and robust decoding (flow field reconstruction) using the sparsity promoting L1 norm.
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