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Guodong Sun1, Mu Mu2, Fei Peng3

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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 How to choose the optimized parameters?
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) Minimum： Bi et al., 2014 the southeast of Arizona 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)
The Princeton dataset ( , 1o×1o, interpolated to a 30-min temporal resolution; Sheffield et al., 2006) 7 7

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

9 Reason of four regions: different dry and humid conditions
Study regions Northeast China：Semi-humid ( oE； oN) North China ：Arid and semi-arid ( oE； oN) North China ： Semi-humid ( oE； oN) South China ：Humid ( oE； oN) Northeast China 各个研究区域内格点编号 (Ma and Fu, 2005) 图：中国近50年干湿分布图 North China: arid and semi-arid North China: semi-humid South China Reason of four regions: different dry and humid conditions 9

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
(a): Northeastern China with the semi-humid climate type (b): North China with the semi-arid climate type (c): North China with the semi-humid climate type (d): South China with the humid climate type Study area Climate type Season Northeast China Semi-humid Summer North China Semi-arid Autumn All season South China Humid

15 Physical mechanisms Semi-Arid region Semi-humid region Humid 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! (~ 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 Observation strategy for physical parameters
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) Regional sensitivity (Franks et al., 1997) the Multicriteria Method (Bastidas et al., 1999) Monte Carlo Sensitivity Analysis (Demaria et al., 2007) Morris method (Morris, 1991) ……… Parameter combination Limitation： Not detecting the sensitivity of parameter combination!

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 CoLM model? 23

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 Parameter combination
Case (arid and semi-arid, soil moisture, CoLM) Parameter combination：three soil-type parameters one vegetation-type parameter 个例 季节 Location Cost function Parameter combination C_SM 5 春季 0.2460 P01, P05, P07, P14 C_SM 6 0.2967 P01, P05, P06, P07 C_SM 7 0.3022 C_SM 8 0.2779 P01, P04, P05, P07 C_SM 9 0.2556 C_SM 10 0.2719 P01, P05, P06, P14 C_SM 11 秋季 0.4764 C_SM 12 0.4091 P01, P03, P05, P06 C_SM 13 0.4256 C_SM 14 0.4581 C_SM 15 0.4328 C_SM 16 0.4450 C_SM 17 0.3748 P01, P04, P05, P14 C_SM 18 0.5307 C_SM 19 0.3915 C_SM 20 0.4261 C_SM 21 0.4159 C_SM 22 0.4111 C_SM 23 0.4573 C_SM 24 0.4347 C_SM 25 0.4219 C_SM 26 0.4478 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: , DOI: /j.jhydrol 26

27 CNOP-P method : single parameter sensitivity
Step 2 Case Season Location The rank of the parameter sensitivity (Parameter sensitivity increases from left to right) C_SM 5 Spring P01 P05 P07 P14 P03 P08 P02 P06 P19 P18 C_SM 6 P04 C_SM 7 P09 C_SM 8 C_SM 9 C_SM 10 C_SM 11 Autumn P15 C_SM 12 P28 C_SM 13 C_SM 14 C_SM 15 C_SM 16 C_SM 17 C_SM 18 C_SM 19 C_SM 20 C_SM 21 C_SM 22 C_SM 23 C_SM 24 C_SM 25 C_SM 26 27

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) 30

31 Parameter combination
Case (arid and semi-arid, soil moisture, CoLM) Parameter combination：three soil-type parameter one vegetation-type parameter 个例 季节 Location Cost function Parameter combination C_SM 5 春季 0.2460 P01, P05, P07, P14 C_SM 6 0.2967 P01, P05, P06, P07 C_SM 7 0.3022 C_SM 8 0.2779 P01, P04, P05, P07 C_SM 9 0.2556 C_SM 10 0.2719 P01, P05, P06, P14 C_SM 11 秋季 0.4764 C_SM 12 0.4091 P01, P03, P05, P06 C_SM 13 0.4256 C_SM 14 0.4581 C_SM 15 0.4328 C_SM 16 0.4450 C_SM 17 0.3748 P01, P04, P05, P14 C_SM 18 0.5307 C_SM 19 0.3915 C_SM 20 0.4261 C_SM 21 0.4159 C_SM 22 0.4111 C_SM 23 0.4573 C_SM 24 0.4347 C_SM 25 0.4219 C_SM 26 0.4478 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: , DOI: /j.jhydrol 31

32 CNOP-P method : single parameter sensitivity
Step 2 Case Season Location The rank of the parameter sensitivity (Parameter sensitivity increases from left to right) C_SM 5 Spring P01 P05 P07 P14 P03 P08 P02 P06 P19 P18 C_SM 6 P04 C_SM 7 P09 C_SM 8 C_SM 9 C_SM 10 C_SM 11 Autumn P15 C_SM 12 P28 C_SM 13 C_SM 14 C_SM 15 C_SM 16 C_SM 17 C_SM 18 C_SM 19 C_SM 20 C_SM 21 C_SM 22 C_SM 23 C_SM 24 C_SM 25 C_SM 26 32

33 OAT method : single parameter sensitivity
Case Season Location The rank of the parameter sensitivity (Parameter sensitivity increases from left to right) C_SM 5 Spring P05 P01 P07 P14 P03 P06 P02 P19 P18 P08 C_SM 6 P04 C_SM 7 C_SM 8 P15 C_SM 9 P09 C_SM 10 C_SM 11 Autumn C_SM 12 C_SM 13 C_SM 14 C_SM 15 C_SM 16 C_SM 17 C_SM 18 C_SM 19 C_SM 20 C_SM 21 C_SM 22 C_SM 23 C_SM 24 C_SM 25 C_SM 26 33

34 Northeast China with semi-humid
Results (Soil moisture) Northeast China with semi-humid All cases (3 cases) CNOP-P 57.8% CNOP_single 54.4% OAT 56.5% North China with semi-humid All cases (7 cases) CNOP-P 63.4% CNOP_single 51.9% OAT 52.8% 34

35 South China with humid All cases (8 cases) CNOP-P 66.4% CNOP_single
50.7% OAT 35

36 North China with arid and semi-arid
Good cases：12 Bad cases：3 CNOP-P CNOP_Single OAT All cases(15) 58.8% 54.6% Good cases(12) 58.7% 52.6% Bad cases(3) 59.5% 62.8% 36

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 enormous computational cost！
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 44

45 Case: arid and semi-arid region
Step 2 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 45

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 North (arid and semi-arid) North (arid and semi-arid)
Sensible heat CNOP CNOP_Single OAT Average 58.3% 45.1% 46.6% Northeast 35.8% 35.5% North (arid and semi-arid) 84.3% 55.5% 57.2% North (semi-humid) 40.5% 43.3% 42.7% South 34.2% 31.7% 34.6% Significant improvement Comparative Latent heat CNOP CNOP_Single OAT Average 62.9% 47.6% 44.8% Northeast 53.8% 53.2% 51.1% North (arid and semi-arid) 78.3% 51.8% 48.5% North (semi-humid) 41.4% 41.5% South 33.5% 31.9% Significant improvement Comparative 47

48 North China with arid and semi-arid
All cases (15 cases) CNOP-P 58.8% CNOP_single 54.6% OAT All cases (33 cases) CNOP-P 61.6% CNOP_single 53.1% OAT 53.4% 48

49 North (arid and semi-arid)
Sensible heat CNOP CNOP_Single OAT Average 58.3% 45.1% 46.6% Northeast 35.8% 35.5% North (arid and semi-arid) 84.3% 55.5% 57.2% North (semi-humid) 40.5% 43.3% 42.7% South 34.2% 31.7% 34.6% 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! 49

50 North (arid and semi-arid)
Latent heat CNOP CNOP_Single OAT Average 62.9% 47.6% 44.8% Northeast 53.8% 53.2% 51.1% North (arid and semi-arid) 78.3% 51.8% 48.5% North (semi-humid) 41.4% 41.5% South 33.5% 31.9% 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! 50

51 Discussion Regional differences about the most sensitive parameters
The number of the most sensitive parameters Future application to reduce the uncertainty of model simulation Optimization algorithm

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