Reprint of: Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model

Integrated hydrologic models coupled to land surface models require several input parameters to characterize the land surface and to estimate energy fluxes. Uncertainty of input parameter values is inherent in any model and the sensitivity of output to these uncertain parameters becomes an important consideration. To better understand these connections in the context of hydrologic models, we use the ParFlow-Common Land Model (PF-CLM) to estimate energy fluxes given variations in 19 vegetation and land surface parameters over a 144-hour period of time. Latent, sensible and ground heat fluxes from bare soil and grass vegetation were estimated using single column and tilted-v domains. Energy flux outputs, along with the corresponding input parameters, from each of the four scenario simulations were evaluated using active subspaces. The active subspace method considers parameter sensitivity by quantifying a weight for each parameter. The method also evaluates the potential for dimension reduction by identifying the input-output relationship through the active variable - a linear combination of input parameters. The aerodynamic roughness length was the most important parameter for bare soil energy fluxes. Multiple parameters were important for energy fluxes from vegetated surfaces and depended on the type of energy flux. Relationships between land surface inputs and output fluxes varied between latent, sensible and ground heat, but were consistent between domain setup (i.e., with or without lateral flow) and vegetation type. A quadratic polynomial was used to describe the input-output relationship for these energy fluxes. The reduced-dimension model of land surface dynamics can be compared to observations or used to solve the inverse problem. Considering this work as a proof-of-concept, the active subspace method can be applied and extended to a range of domain setups, land cover types and time periods to obtain a reduced-form representation of any output of interest, provided that an active subspace exists. Active subspaces identify important input parameters and how they relate to output.Proof-of-concept domains show potential for dimension reduction of land surface.Important land surface parameters depend on land cover and flux type.Land surface inputs and energy flux outputs can be related by a quadratic polynomial.Lateral flow has negligible effect on the land surface parameter-flux relationship.

[1]  Soroosh Sorooshian,et al.  Exploring parameter sensitivities of the land surface using a locally coupled land-atmosphere model , 2004 .

[2]  Ronaldo I. Borja,et al.  Block-preconditioned Newton–Krylov solvers for fully coupled flow and geomechanics , 2011 .

[3]  Zong-Liang Yang,et al.  Quantifying parameter sensitivity, interaction, and transferability in hydrologically enhanced versions of the Noah land surface model over transition zones during the warm season , 2010 .

[4]  Keith Beven,et al.  Changing ideas in hydrology — The case of physically-based models , 1989 .

[5]  Reed M. Maxwell,et al.  Groundwater-fed irrigation impacts spatially distributed temporal scaling behavior of the natural system: a spatio-temporal framework for understanding water management impacts , 2014 .

[6]  Gregory P. Asner,et al.  Variability in Leaf and Litter Optical Properties: Implications for BRDF Model Inversions Using AVHRR, MODIS, and MISR , 1998 .

[7]  Keith Beven,et al.  On the sensitivity of soil-vegetation-atmosphere transfer (SVAT) schemes: equifinality and the problem of robust calibration , 1997 .

[8]  George Shu Heng Pau,et al.  A reduced-order modeling approach to represent subgrid-scale hydrological dynamics for land-surface simulations: application in a polygonal tundra landscape , 2014 .

[9]  Chang-Hoi Ho,et al.  Roughness Length of Water Vapor over Land Surfaces and Its Influence on Latent Heat Flux , 2009 .

[10]  Marcel G. Schaap,et al.  Improved Prediction of Unsaturated Hydraulic Conductivity with the Mualem‐van Genuchten Model , 2000 .

[11]  Stefan Kollet,et al.  Sensitivity of Latent Heat Fluxes to Initial Values and Parameters of a Land‐Surface Model , 2010 .

[12]  Juliane Mai,et al.  Use of eigendecomposition in a parameter sensitivity analysis of the Community Land Model , 2013 .

[13]  Ann Henderson-Sellers,et al.  A Factorial Assessment of the Sensitivity of the BATS Land-Surface Parameterization Scheme , 1993 .

[14]  Ann Henderson-Sellers,et al.  The Project for Intercomparison of Land Surface Parameterization Schemes (PILPS): Phases 2 and 3 , 1995 .

[15]  Roni Avissar,et al.  An Evaluation with the Fourier Amplitude Sensitivity Test (FAST) of Which Land-Surface Parameters Are of Greatest Importance in Atmospheric Modeling , 1994 .

[16]  Rafael Muñoz-Carpena,et al.  Insights on geologic and vegetative controls over hydrologic behavior of a large complex basin – Global Sensitivity Analysis of an integrated parallel hydrologic model , 2014 .

[17]  R. Mahmood,et al.  Simulating sensitivity of soil moisture and evapotranspiration under heterogeneous soils and land uses , 2003 .

[18]  Mary F. Wheeler,et al.  A parallel, implicit, cell‐centered method for two‐phase flow with a preconditioned Newton–Krylov solver , 1997 .

[19]  Keith Beven,et al.  TOPMODEL : a critique. , 1997 .

[20]  G. N. Geller,et al.  Leaf and environmental parameters influencing transpiration: Theory and field measurements , 1980, Oecologia.

[21]  Reed M. Maxwell,et al.  The impact of subsurface conceptualization on land energy fluxes , 2013 .

[22]  R. Dickinson,et al.  The Common Land Model , 2003 .

[23]  J. Michaelsen,et al.  Estimating grassland biomass and leaf area index using ground and satellite data , 1994 .

[24]  Wei Gong,et al.  Multi-objective parameter optimization of common land model using adaptive surrogate modeling , 2014 .

[25]  Wei Gong,et al.  Assessing parameter importance of the Common Land Model based on qualitative and quantitative sensitivity analysis , 2013 .

[26]  Olaf Kolditz,et al.  Surface‐subsurface model intercomparison: A first set of benchmark results to diagnose integrated hydrology and feedbacks , 2014 .

[27]  D. Lettenmaier,et al.  A simple hydrologically based model of land surface water and energy fluxes for general circulation models , 1994 .

[28]  John E. McCray,et al.  Mountain pine beetle infestation impacts: modeling water and energy budgets at the hill‐slope scale , 2013 .

[29]  Stefan Kollet,et al.  Influence of soil heterogeneity on evapotranspiration under shallow water table conditions: transient, stochastic simulations , 2009 .

[30]  Stacy E. Howington,et al.  Newton-Krylov-Schwarz methods for Richards' equation , 1999 .

[31]  G. Campbell,et al.  An Introduction to Environmental Biophysics , 1977 .

[32]  Christine A. Shoemaker,et al.  CH 4 parameter estimation in CLM4.5bgc using surrogate global optimization , 2015 .

[33]  J. Dudhia,et al.  Coupling an Advanced Land Surface–Hydrology Model with the Penn State–NCAR MM5 Modeling System. Part I: Model Implementation and Sensitivity , 2001 .

[34]  R. Maxwell,et al.  A comparison of two physics-based numerical models for simulating surface water–groundwater interactions , 2010 .

[35]  K. Trenberth,et al.  Earth's Global Energy Budget , 2009 .

[36]  Soroosh Sorooshian,et al.  Sensitivity analysis of a land surface scheme using multicriteria methods , 1999 .

[37]  Xu Liang,et al.  Intercomparison of land-surface parameterization schemes: sensitivity of surface energy and water fluxes to model parameters , 2003 .

[38]  Reed M. Maxwell,et al.  Hydrologic and land–energy feedbacks of agricultural water management practices , 2011 .

[39]  Andrew J. Pitman,et al.  Assessing the Sensitivity of a Land-Surface Scheme to the Parameter Values Using a Single Column Model , 1994 .

[40]  Jason Beringer,et al.  The use of a reduced form model to assess the sensitivity of a land surface model to biotic surface parameters , 2002 .

[41]  Johan Larsson,et al.  Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet , 2014, J. Comput. Phys..

[42]  J. Noilhan,et al.  Sensitivity study and validation of a land surface parameterization using the HAPEX-MOBILHY data set , 1990 .

[43]  Reed M. Maxwell,et al.  Feedbacks between managed irrigation and water availability: Diagnosing temporal and spatial patterns using an integrated hydrologic model , 2014 .

[44]  R. Maxwell,et al.  Interdependence of groundwater dynamics and land-energy feedbacks under climate change , 2008 .

[45]  Fotini Katopodes Chow,et al.  Coupling groundwater and land surface processes: Idealized simulations to identify effects of terrain and subsurface heterogeneity on land surface energy fluxes , 2010 .

[46]  Guang Lin,et al.  Sensitivity of surface flux simulations to hydrologic parameters based on an uncertainty quantification framework applied to the Community Land Model , 2012 .

[47]  Soroosh Sorooshian,et al.  Sensitivity analysis of the biosphere‐atmosphere transfer scheme , 1996 .

[48]  R. Maxwell.  A terrain-following grid transform and preconditioner for parallel, large-scale, integrated hydrologic modeling , 2013 .

[49]  Maosheng Zhao,et al.  Development of a global evapotranspiration algorithm based on MODIS and global meteorology data , 2007 .

[50]  A. Pitman,et al.  Evaluating the Performance of Land Surface Models , 2008 .

[51]  Jozsef Szilagyi,et al.  Net Recharge vs. Depth to Groundwater Relationship in the Platte River Valley of Nebraska, United States , 2013, Ground water.

[52]  Juan J. Alonso,et al.  Active Subspaces for Shape Optimization , 2014 .

[53]  Carol S. Woodward,et al.  Improved numerical solvers for implicit coupling of subsurface and overland flow , 2014 .

[54]  Laura E. Condon,et al.  Implementation of a linear optimization water allocation algorithm into a fully integrated physical hydrology model , 2013 .

[55]  Khachik Sargsyan,et al.  Bayesian Calibration of the Community Land Model Using Surrogates , 2012, SIAM/ASA J. Uncertain. Quantification.

[56]  Jim E. Jones,et al.  Newton–Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems , 2001 .

[57]  P. Huyakorn,et al.  A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow , 2004 .

[58]  Albert Olioso,et al.  An overview of the workshop on thermal remote sensing held at La Londe les Maures, France, September 20–24, 1993 , 1995 .

[59]  R. Maxwell,et al.  Integrated surface-groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model , 2006 .

[60]  Jon Wiernga.  Representative roughness parameters for homogeneous terrain , 1993 .