# On Approaches to Analyze the Sensitivity of Simulated Hydrologic Fluxes to Model Parameters in the Community Land Model

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Site Description

#### 2.2. Model Parameterization

#### 2.3. Response Variables and Metrics

#### 2.4. Effective Sampling and Sensitivity Analysis Methods

#### 2.4.1. Sampling Methods

#### 2.4.2. Sensitivity Analysis Approaches

#### ANOVA Based on GLM

#### GCV Based on the MARS Model

#### SRC Based on the LM

#### ANOVA Based on SVM

## 3. Results and Discussion

#### 3.1. Effects of Choices of Response Variables/Metrics

**Figure 2.**Boxplots for different response variables and metrics as a function of input parameters specific yield (${S}_{y}$).

#### 3.2. Effects of Choices of SA Approach

**Figure 4.**Proportion of sensitivity for residual in 108 months. (

**a**) Residual of total runoff (runoff) ANOVA (GLM 1st order); (

**b**) Residual of subsurface runoff (qdrai) ANOVA (GLM 1st order); (

**c**) Residual of surface runoff (qover) ANOVA (GLM 1st order); (

**d**) Residual of latent heat (LH) ANOVA (GLM 1st order).

**Figure 5.**The four most important input parameters (red blocks) for different response variables (total runoff, ${q}_{drai}$, ${q}_{over}$, and LH), metrics (NSC, LMSE, and residual), and four SA approaches (SRC based on LM, ANOVA based on SVM, GCV based on second-order MARS, and ANOVA based on second-order GLM).

#### 3.3. Convergence, Under-Sampling Issues, and Model Verification

**Figure 6.**Sensitivity scores convergence for different response variables and SA approaches. (

**a**) NSC of runoff (1st order); (

**b**) NSC of qdrai (1st order); (

**c**) NSC of qover (1st order); (

**d**) NSC of LH (1st order).

## 4. Conclusions

## Supplementary Files

Supplementary File 1## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Henderson-Sellers, A.; Pitman, A.J.; Love, P.K.; Irannejad, P.; Chen, T.H. The Project for Intercomparison of Land-Surface Parameterization Schemes (Pilps)—Phase-2 and Phase-3. Bull. Am. Meteorol. Soc.
**1995**, 76, 489–503. [Google Scholar] [CrossRef] - Henderson-Sellers, A.; Chen, T.H.; Nakken, M. Predicting global change at the land-surface: The project for intercomparison of land-surface parameterization schemes (PILPS) (phase 4). In Proceedings of the Seventh American Meteorological Society (AMS) symposium on global change studies, Atlanta, GA, USA, 28 January–2 February 1996; pp. 59–66.
- Bastidas, L.A.; Hogue, T.S.; Sorooshian, S.; Gupta, H.V.; Shuttleworth, W.J. Parameter sensitivity analysis for different complexity land surface models using multicriteria methods. J. Geophys. Res.
**2006**, 111. [Google Scholar] [CrossRef] - Hou, Z.; Huang, M.; Leung, L.R.; Lin, G.; Ricciuto, D.M. Sensitivity of surface flux simulations to hydrologic parameters based on an uncertainty quantification framework applied to the Community Land Model. J. Geophys. Res.
**2012**, 117. [Google Scholar] [CrossRef] - Göhler, M.; Mai, J.; Cuntz, M. Use of eigendecomposition in a parameter sensitivity analysis of the Community Land Model. J. Geophys. Res. Biogeosci.
**2013**, 118, 904–921. [Google Scholar] [CrossRef] - Nasybulin, E.; Xu, W.; Engelhard, M.H.; Nie, Z.; Burton, S.D.; Cosimbescu, L.; Gross, M.E.; Zhang, J.-G. Effects of Electrolyte Salts on the Performance of Li-O-2 Batteries. J. Phys. Chem. C
**2013**, 117, 2635–2645. [Google Scholar] [CrossRef] - Oleson, K.W.; Dai, Y.J.; Bonan, G.B.; Bosilovich, M.; Dickinson, R.; Dirmeyer, P.; Hoffman, F.M.; Houser, P.R.; Levis, S.; Niu, Y.; et al. Technical Description f Version 4.0 of the Community Land Model (CLM); National Center for Atomospheric Research: Boulder, CO, USA, 2010. [Google Scholar]
- Lawrence, D.M.; Oleson, K.W.; Flanner, M.G.; Thornton, P.E.; Swenson, S.C.; Lawrence, P.J.; Zeng, Z.; Yang, Z.L.; Levis, S.; Sakaguchi, K.; et al. Parameterization Improvements and Functional and Structural Advances in Version 4 of the Community Land Model. J. Adv. Model. Earth Syst.
**2011**, 3, 27. [Google Scholar] - Leng, G.; Huang, M.; Tang, Q.; Gao, H.; Leung, L.R. Modeling the effects of groundwater-fed irrigation on terrestrial hydrology over the conterminous United States. J. Hydrometeorol.
**2014**, 15, 957–972. [Google Scholar] [CrossRef] - Lei, H.; Huang, M.; Leung, R.; Yang, D.; Shi, X.; Mao, J.; Hayes, D.J.; Schwalm, C.R.; Wei, Y.; Liu, S. Sensitivity of global terrestrial gross primary production to hydrologic states simulated by the Community Land Model using two runoff parameterizations. J. Adv. Model. Earth Syst.
**2014**, 6. [Google Scholar] [CrossRef] - Stöckli, R.; Lawrence, D.M.; Niu, G.-Y.; Oleson, K.W.; Thornton, P.E.; Yang, Z.-L.; Bonan, G.B.; Denning, A.S.; Running, S.W. Use of FLUXNET in the Community Land Model development. J. Geophys. Res.
**2008**, 113. [Google Scholar] [CrossRef] - Niu, G.-Y.; Yang, Z.-L.; Dickinson, R.; Dickinson, R.; Gulden, L.E.; Gulden, L.E. A simple TOPMODEL-based runoff parameterization (SIMTOP) for use in global climate models. J. Geophys. Res.
**2005**, 110. [Google Scholar] [CrossRef] - Huang, M.; Hou, Z.; Leung, L.R.; Ke, Y.; Liu, Y.; Fang, Z.; Sun, Y. Uncertainty Analysis of Runoff Simulations and Parameter Detectability in the Community Land Model—Evidence from MOPEX Basins and Flux Tower Sites. J. Hydrometeorol.
**2013**, 14, 1754–1772. [Google Scholar] [CrossRef] - Liu, Y.; Gupta, H.V.; Sorooshian, S.; Bastidas, L.A.; Shuttleworth, W.J. Exploring parameter sensitivities of the land surface using a locally coupled land-atmosphere model. J. Geophys. Res. Atmos.
**2004**, 109. [Google Scholar] [CrossRef] - Van Griensven, A.; Meixnera, T.; Grunwaldb, S.; Bishopb, T.; Diluzioc, M.; Srinivasand, R. A global sensitivity analysis tool for the parameters of multi-variable catchment models. J. Hydrol.
**2006**, 324, 10–23. [Google Scholar] [CrossRef] - Campolongo, F.; Cariboni, J.; Saltelli, A. An effective screening design for sensitivity analysis of large models. Environ. Model. Softw.
**2007**, 22, 1509–1518. [Google Scholar] [CrossRef] - Borgonovo, E.; Castaings, W.; Tarantola, S. Model emulation and moment-independent sensitivity analysis: An application to environmental modelling. Environ. Model. Softw.
**2012**, 34, 105–115. [Google Scholar] [CrossRef] - Pan, W.; Bao, J.; Lo, C.; Lai, K.; Agarwal, K.; Koeppel, B.J.; Khaleel, M. A general approach to develop reduced order models for simulation of solid oxide fuel cell stacks. J. Power Sources
**2013**, 232, 139–151. [Google Scholar] [CrossRef] - Bao, J.; Xu, Z.; Lin, G.; Fang, Y. Uncertainty quantification for evaluating impacts of caprock and reservoir properties on pressure buildup and ground surface displacement during geological CO2 sequestration. Greenh. Gases Sci. Technol.
**2013**, 3, 338–358. [Google Scholar] [CrossRef] - Friedman, J.H. Multivariate Adaptive Regression Splines. Ann. Stat.
**1991**, 19, 1–67. [Google Scholar] [CrossRef] - Aiken, L.S.; West, S.G. Multiple Regression: Testing and Interpreting Interactions; Sage Publications Inc.: Thousand Oaks, CA, USA, 1991. [Google Scholar]
- Morris, M.D. Factorial sampling plans for preliminary computational experiments. Technometrics
**1991**, 33, 161–174. [Google Scholar] [CrossRef] - Sobol, I.M. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. Engl. Transl.
**1967**, 7, 86–112. [Google Scholar] [CrossRef] - Friedman, J.H. Fitting funcctions to noisy data in high dimensions. In Proceedings of the 20th Symposium on the Interface, Reston, VA, USA, 20–23 April 1988.
- Anscombe, F.J. The Validity of Comparative Experiments. J. R. Stat. Soc. Ser. A
**1948**, 111, 181–211. [Google Scholar] [CrossRef] - Box, G.E.P. Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification. Ann. Math. Stat.
**1954**, 25, 290–302. [Google Scholar] [CrossRef] - McCullagh, P.; Nelder, J. Generalized Linear Models, 2nd ed.; CRC press: Boca Raton, FL, USA, 1989. [Google Scholar]
- Chambers, J.M.; Hastie, T.J. Statistical Models in S; Chapman and Hall/CRC: Boca Raton, FL, USA, 1992. [Google Scholar]
- Friedman, J.H.; Silverman, B.W. Flexible Parsimonious Smoothing and Additive Modeling; Stanford Linear Accelerator: Stanford, CA, USA, 1987. [Google Scholar]
- Friedman, J.H. Fast MARS; Tech. Report LCS110; Stanford University: Stanford, CA, USA, 1993. [Google Scholar]
- Drucker, H.; Burges, C.J.C.; Kaufman, L.; Smola, A.J.; Vapnik, V. Advances in Neural Information Processing Systems 9 (NIPS). In Proceedings of Neural Information Processing Systems 1996, Denver, CO, USA, 2–5 December 1996; pp. 155–161.
- Smola, A.J.; Scholkopf, B. A tutorial on support vector regression. Stat. Comput.
**2004**, 14, 199–222. [Google Scholar] [CrossRef] - Tong, C. PSUADE User’s Manual; Lawrence Livermore National Laboratory: Livermore, CA, USA, 2009.
- Williams, C.K.I. Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond. In Learning and Inference in Graphical Models; Kluwer: Dordrecht, The Netherlands, 1998. [Google Scholar]
- Mehrotra, K.; Mohan, C.K.; Ranka, S. Elements of Artificial Neural Networks; Massachusetts Institute of Technology Press: Cambridge, MA, USA, 2000. [Google Scholar]
- Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L.R. Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model. Hydrol. Earth Syst. Sci. Discuss.
**2013**, 10, 5077–5119. [Google Scholar] [CrossRef] - Ray, J.; Hou, Z.; Huang, M.; Sargsyan, K.; Swiler, L. Bayesian Calibration of the Community Land Model using Surrogates. SIAM J. Uncertain. Quantif.
**2015**, 31, 199–233. [Google Scholar] [CrossRef] - Mu, Q.; Zhao, M.; Running, S.W. Improvements to a MODIS global terrestrial evapotranspiration algorithm. Remote Sens. Environ.
**2011**, 115, 1781–1800. [Google Scholar] [CrossRef] - MODIS Global Evapotranspiration Project (MOD16). Available online: http://www.ntsg.umt.edu/project/mod16 (accessed on 1 December 2015).
- Lyne, V.D.; Hollick, M. Stochastic time-variable rainfall-runoff modelling. In Hydrology and Water Resources Symposium; Institution of Engineers Australia: Perth, Australia, 1979; pp. 89–92. [Google Scholar]
- Niu, G.Y.; Yang, Z.-L.; Dickinson, R.E.; Gulden, L.E.; Su, H. Development of a simple groundwater model for use in climate models and evaluation with Gravity Recovery and Climate Experiment data. J. Geophys. Res.
**2007**, 112. [Google Scholar] [CrossRef] - Woodbury, A.D. A FORTRAM program to produce minimum relative entropy distributions. Comput. Geosci.
**2004**, 30, 131–138. [Google Scholar] [CrossRef] - Hou, Z.; Rubin, Y. On minimum relative entropy concepts and prior compatibility issues in vadose zone inverse and forward modeling. Water Resour. Res.
**2005**, 41. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Moriasi, D.N.; Arnold, J.G.; van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Tarantola, A. Inverse Problem Theory and Model Parameter Estimation; Society of Industrial and Applied Mahematics (SIAM): Philadelphia, PA, USA, 2005. [Google Scholar]
- Bratley, P.; Fox, B.L. Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator. ACM Trans. Math. Softw.
**1988**, 14, 88–100. [Google Scholar] [CrossRef] - Tong, C. Toward a More Robust Variance-Based Global Sensitivity Analysis of Model Outputs; Lawrence Livermore National Laboratory: Livermore, CA, USA, 2007.
- Nossent, J.; Elsen, R.; Bauwens, W. Sobol’ sensitivity analysis of a complex environmental model. Environ. Model. Softw.
**2011**, 26, 1515–1525. [Google Scholar] [CrossRef] - Pleming, J.B.; Manteufel, R.D. Replicated Latin Hypercube Sampling. In Proceedings of the 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Austin, TX, USA, 18–21 April 2005.
- Lee, L.A.; Carslaw, K.S.; Pringle, K.J.; Mann, G.W.; Sprackle, D.V. Emulation of a complex global aerosol model to quantify sensitivity to uncertain parameters. Atmos. Chem. Phys. Discuss.
**2011**, 11, 12253–12273. [Google Scholar] [CrossRef] - Lee, L.A.; Carslaw, K.S.; Pringle, K.J.; Mann, G.W. Mapping the uncertainty in global CCN using emulation. Atmos. Chem. Phys. Discuss.
**2012**, 12, 14089–14114. [Google Scholar] [CrossRef] - Björck, Å. Numerical Methods for Least Squares Problems; Society of Industrial and Applied Mahematics (SIAM): Philadelphia, PA, USA, 1996. [Google Scholar]
- Rao, C.R.; Toutenburg, H.; Shalabh; Heumann, C. Linear Models: Least Squares and Alternatives. In Springer Series in Statistics; Springer: New York, NJ, USA, 1999. [Google Scholar]
- Allison, P.D. Tesing for interaction in multiple regression. Am. J. Sociol.
**1977**, 83, 144–153. [Google Scholar] [CrossRef] - Tukey, J.W. Exploratory Data Analysis; Addison-Wesley: Boston, MA, USA, 1977. [Google Scholar]
- Benjamini, Y. Opening the box of a boxplot. Am. Stat.
**1988**, 42, 257–262. [Google Scholar] - Rousseeuw, P.J.; Ruts, I.; Tukey, J.W. The Bagplot: A Bivariate Boxplot. Am. Stat.
**1999**, 53, 382–387. [Google Scholar]

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**MDPI and ACS Style**

Bao, J.; Hou, Z.; Huang, M.; Liu, Y.
On Approaches to Analyze the Sensitivity of Simulated Hydrologic Fluxes to Model Parameters in the Community Land Model. *Water* **2015**, *7*, 6810-6826.
https://doi.org/10.3390/w7126662

**AMA Style**

Bao J, Hou Z, Huang M, Liu Y.
On Approaches to Analyze the Sensitivity of Simulated Hydrologic Fluxes to Model Parameters in the Community Land Model. *Water*. 2015; 7(12):6810-6826.
https://doi.org/10.3390/w7126662

**Chicago/Turabian Style**

Bao, Jie, Zhangshuan Hou, Maoyi Huang, and Ying Liu.
2015. "On Approaches to Analyze the Sensitivity of Simulated Hydrologic Fluxes to Model Parameters in the Community Land Model" *Water* 7, no. 12: 6810-6826.
https://doi.org/10.3390/w7126662