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Uncertainties and sensitivities analysis for the soil moisture due to model parameter errors

Uncertainties and sensitivities analysis for the soil moisture due to model parameter errors. Guodong Sun 1 , Mu Mu 2 , Fei Peng 3 1 LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences 2 Institute of Atmospheric Sciences, Fudan University

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Uncertainties and sensitivities analysis for the soil moisture due to model parameter errors

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  1. Uncertainties and sensitivities analysis for the soil moisture due to model parameter errors Guodong Sun1, Mu Mu2, Fei Peng3 1 LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences 2 Institute of Atmospheric Sciences, Fudan University 3 Numerical Weather Prediction Center, China Meteorological Administration

  2. Outline • Introduction • The model and the method • Numerical results and analysis • Discussion

  3. Introduction • One contributing factor is the existence of model errors which leads to uncertainties in the numerical simulations for soil moisture. (Hansen, 2002; Ziehn et al., 2012) • Correct (mathematical) description of mechanisms driving physical processes, and uncertainty in the parameter set (Zaehle et al., 2005), and so on

  4. Luo et al., 2013 • Three-Layer Variable Infiltration Capacity (VIC-3L) land surface model. • the observed data from an AmeriFlux site (Duke Forest Loblolly Pine (USDk3)) located within the Blackwood Division of Duke Forest near Durham, North Carolina, USA (35.98N, 79.09W).

  5. It is an important tool to improve ability of the numerical simulation and numerical forecast to reduce the model error. • Data assimilation system, optimal methods (Bastidas et al., 1999; Wang et al., 2001; Moolenaar and Selten, 2004; Duan et al., 2006; Rosero et al., 2010) • Bi et al., 2014 • the southeast of Arizona • Minimum： How to choose the optimized parameters?

  6. Questions： • How is the maximal uncertainty of the impacts of model parameters errors on the soil moisture on earth? • What parameters are main contribution factor to uncertainty of estimated soil moisture? • How is the role of the above parameters to improve the simulation ability and prediction skill?

  7. Model and Data Model: the Common Land Model; CoLM, Dai et al., 2003) Data: • The Princeton dataset (1948-2010, 1o×1o, interpolated to a 30-min temporal resolution; Sheffield et al., 2006)

  8. Physical parameter： soil: 8 vegetation: 7 Other: 13 Li et al.( 2013) 28 physical parameter in CoLM model

  9. Study regions Northeast China (Ma and Fu, 2005) 各个研究区域内格点编号 • Northeast China：Semi-humid (126.0-127.5oE；46.0-47.5oN) • North China ：Arid and semi-arid( 112.5-114.0oE；37.5-39.0oN) • North China ： Semi-humid (113.5-115.0oE；32.5-34.0oN) • South China ：Humid (116.0-117.5oE；26.0-27.5oN) North China: arid and semi-arid North China: semi-humid South China Reason of four regions: different dry and humid conditions 图：中国近50年干湿分布图

  10. Questions： • How is the maximal uncertainty of the impacts of model parameters errors on the soil moisture on earth? • What parameters are main contribution factor to uncertainty of estimated soil moisture? • How is the role of the above parameters to improve the simulation ability and prediction skill?

  11. Conditional nonlinear optimal perturbation related to parameters(CNOP-P) approach(Mu, et al., 2010) cost function: ：the nonlinear propagator from 0 to T ：CNOP-P • CNOP-P represents a type of parameter perturbation or error, which could cause the maximal uncertainty or error of simulation and prediction.

  12. Monthly latent heat flux Monthly sensible heat flux

  13. Differential Evolution (DE, Storn and Price,1997) • Not use the gradient of the problem being optimized • DE can therefore also be used on optimization problems that are not even continuous, are noisy, change over time, etc Flowchart of DE algorithm

  14. Uncertainty of soil moisture due to parameters errors

  15. Physical mechanisms Semi-Arid region • Soil moisture in autumn • — CNOP-P-type parameter error restrains evapotranspiration Semi-humid region • Soil moisture in all seasons • — CNOP-P-type parameter error restrains evapotranspiration Humid region • Soil moisture in spring and summer • — CNOP-P-type parameter error restrains evapotranspiration and runoff • Soil moisture in autumn and winter • — CNOP-P-type parameter error restrains evapotranspiration

  16. Part 1：Summary 1) The seasonal characters are shown for the uncertainty of estimated soil moisture due to parameters errors. 2) The source of uncertainty of estimated soil moisture seems to evapotranspiration!

  17. High uncertainty occurs due to parameter errors • It is a effective tool to improve the simulation ability and prediction skill to reduce the uncertainty of parameters • Numerous physical parameters should be reduced! (~102-104 in land models) • What parameters errors should be reduced firstly or in advance?

  18. Questions： • How is the maximal uncertainty of the impacts of model parameters errors on the soil carbon on earth? • What parameters are main contribution factor to uncertainty of estimated soil moisture? • How is the role of the above parameters to improve the simulation ability and prediction skill?

  19. A key issue to answer the above problem is to identify sensitivity of model parameters. Monte Carlo-type stratified sampling OAT Pitman (1994) Zaehle et al.(2005) EFAST Global sensitivity analysis Pappas et al. (2013) Wang et al., (2013)

  20. Current methods: One-at-a-time method (Wilson et al., 1987 a, b; Pitman, 1994) Fourier amplitude sensitivity technique (Collions and Avissar, 1994) Observation strategy for physical parameters Factorial Design technique (Henderson-Sellers, 1992) Parameter combination Regional sensitivity (Franks et al., 1997) Limitation： Not detecting the sensitivity of parameter combination! the Multicriteria Method (Bastidas et al., 1999) Monte Carlo Sensitivity Analysis (Demaria et al., 2007) Morris method (Morris, 1991) ………

  21. Step 1 Choose the physical parameters Choose the optimization algorithm Build the optimization system Define the cost function Eliminate some non-sensitive parameters. Multi-parameters are optimized among the remaining parameters. The maximal uncertainty is obtained for every parameter combination. The sensitive parameters are identified according the extent of uncertainty of numerical simulation. Optimize single parameter. The maximal uncertainty is obtained for every parameter. The each parameters are ranked according to extent of uncertainty of numerical simulation. CNOP-P Step 2 Step 3

  22. Conditional nonlinear optimal perturbation related to parameters（CNOP-P）approach(Mu, et al., 2010) cost function: ：the nonlinear propagator from 0 to T ：CNOP-P • CNOP-P represents a type of parameter perturbation or error, which could cause the maximal uncertainty or error of simulation and prediction.

  23. Physical parameter： soil: 8 vegetation: 7 Other: 13 Li et al.( 2013) 28 physical parameter in CoLM model What is the most sensitive parameter combination (four)among 28 physical parameters within the CoLMmodel?

  24. Experimental design （Step 2） Single parameter optimization：

  25. Experimental design（Step 3） Multiple parameters optimization • 8 parameters are chosen according to step 2 (Removing 20 non-sensitive parameters). • 70(C48 =70) groups of parameter combinations are optimized. The cost function values of 70 groups are calculated and compared. • The sensitivity of parameter combination could be identified!

  26. Case (arid and semi-arid, soil moisture, CoLM) Parameter combination：three soil-type parameters one vegetation-type parameter P01, P05, P06, P14 • Only including parameters related to soil (Li et al., 2013) • Not only including parameters related to soil, but also those related to plant Sun, G. D., F. Peng and M. Mu, 2017c: Uncertainty assessment and sensitivity analysis of soil moisture based on model parameters–results for regions of China, Journal of Hydrology, 555: 347-360, DOI: 10.1016/j.jhydrol.2017.09.059

  27. CNOP-Pmethod : single parameter sensitivity Step 2

  28. Part 2：Summary 1) A new approach of determination of sensitive parameter combination based on the CNOP-P is proposed. 2) The sensitivity of parameter combination is different to the top rank of sensitivity of each parameter! 3) The nonlinear effect of parameter combination!

  29. Questions： • How is the maximal uncertainty of the impacts of model parameters errors on the soil carbon on earth? • What parameters are main contribution factor to uncertainty of estimated soil moisture? • How is the role of the above parameters to improve the simulation ability and prediction skill?

  30. Benefit of simulated soil moisture by decreasing parameter errors Based on the studies of Mu et al. (2009)and Sun and Mu (2017), defining the extent of reduction of parameter errors due to data assimilation or observation the extent of uncertainty reduction in soil moisture is. The larger it is, the more effective the improvement is. • Three types of parameter errors p: • CNOP-P-type parameter errors for the sensitive four parameter combination (CNOP-P) • CNOP-P-type parameter errors for the sensitive four parameter combination for the top four sensitive parameter for each parameter using the CNOP-P approach (CNOP_Single) • CNOP-P-type parameter errors for the sensitive four parameter combination for the top four sensitive parameter for each parameter using the OAT approach (OAT)

  31. Case (arid and semi-arid, soil moisture, CoLM) Parameter combination：three soil-type parameter one vegetation-type parameter P01, P05, P06, P14 • Not only including parameters related to soil, but also those related to plant Sun, G. D., F. Peng and M. Mu, 2017c: Uncertainty assessment and sensitivity analysis of soil moisture based on model parameters–results for regions of China, Journal of Hydrology, 555: 347-360, DOI: 10.1016/j.jhydrol.2017.09.059

  32. CNOP-Pmethod : single parameter sensitivity Step 2

  33. OATmethod : single parameter sensitivity

  34. Results (Soil moisture) Northeast China with semi-humid North China with semi-humid

  35. South China with humid

  36. North China with arid and semi-arid • Good cases：12 • Bad cases：3

  37. Part 3：Summary 1) The ability of simulation or prediction skill will be improved through reducing the sensitive physical parameters. 2) Compared to the errors of CNOP_single and OAT, CNOP-P-type errors of parameter combination could lead to maximal improvement of prediction skill.

  38. Discussions (1) • Regional differences about the most sensitive parameter combinations • The number of the most sensitive parameter combinations (C48 =70, Cmn) • Future application to reduce the uncertainty of model simulation and prediction

  39. Discussions (2) Step 1 Choose the physical parameters Choose the optimization algorithm Build the optimization system Define the cost function Eliminate some non-sensitive parameters. Multi-parameters are optimized among all parameters. The maximal uncertainty is obtained for every parameter combination. The sensitive parameters are identified according the extent of uncertainty of numerical simulation. Supposing to identify the four most sensitive physical parameter among 28 parameters. optimization experiments will be conducted. Step 2 enormous computational cost！

  40. Thanks！

  41. Source of uncertainty in simulation and prediction Forecast model: • Initial condition • Model • Boundary condition Source:

  42. Poulter et al., 2010 GCB

  43. Step 1 Choose the physical parameters Choose the optimization algorithm Build the optimization system Define the cost function Optimize the multi-parameter. The most sensitive parameters are determined according to cost function values Supposing to identify the five most sensitive physical parameter among 24 parameters. optimization experiments will be conducted. Step 2 enormous computational cost！

  44. The most sensitive parameters within a given number ？ Physical parameter： soil: 8 vegetation: 7 Other: 13 The most sensitive four parameters among 28 physical parameters within CoLM model? Li et al.( 2013) 28 physical parameter in CoLM model

  45. Step 2 Case: arid and semi-arid region Sensitivity analysis of each parameters using the CNOP-P approach Sensitivity analysis of each parameters using the OAT approach The sensitivities of eight parameters are similar for two approaches to determine the sensitivity of each parameter

  46. But: The sensitivity of parameter combination is different to the top rank of sensitivity of each parameter! The nonlinear effect of parameter combination!

  47. Significant improvement Comparative Significant improvement Comparative

  48. North China with arid and semi-arid

  49. Significant improvement Comparative Compared to the errors of CNOP_single and OAT，CNOP-P-type errors of parameter combination could lead to maximal improvement for sensible heat!

  50. Significant improvement Comparative Compared to the errors of CNOP_single and OAT，CNOP-P-type errors of parameter combination could lead to maximal improvement for latent heat!

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