J. Meteor. Res.  2017, Vol. 31 Issue (6): 1167-1182 PDF
http://dx.doi.org/10.1007/s13351-017-7050-1
The Chinese Meteorological Society
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#### Article Information

ZHANG, Guo, Guangsheng ZHOU, and Fei CHEN, 2017.
Analysis of Parameter Sensitivity on Surface Heat Exchange in the Noah Land Surface Model at a Temperate Desert Steppe Site in China. 2017.
J. Meteor. Res., 31(6): 1167-1182
http://dx.doi.org/10.1007/s13351-017-7050-1

### Article History

in final form September 15, 2017
Analysis of Parameter Sensitivity on Surface Heat Exchange in the Noah Land Surface Model at a Temperate Desert Steppe Site in China
Guo ZHANG1, Guangsheng ZHOU1, Fei CHEN1,2
1. State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China;
2. National Center for Atmospheric Research, Boulder, CO 80302, USA
ABSTRACT: The dominant parameters in the Noah land surface model (LSM) are identified, and the effects of parameter optimization on the surface heat exchange are investigated at a temperate desert steppe site during growing season in Inner Mongolia, China. The relative impacts of parameters on surface heat flux are examined by the distributed evaluation of local sensitivity analysis (DELSA), and the Noah LSM is calibrated by the global shuffled complex evolution (SCE) against the corresponding observations during May–September of 2008 and 2009. The differences in flux simulations are assessed between the Noah LSM calibrated by the SCE with 27 parameters and 12 dominant parameters. The systematic error, unsystematic error, root mean squared error, and mean squared error decompositions are used to evaluate the model performance. Compared to the control experiment, parameter optimization by the SCE using net radiation, sensible heat flux, latent heat flux, and ground heat flux as the objective criterion, respectively, can obviously reduce the errors of the Noah LSM. The calibrated Noah LSM is further validated against flux observations of growing season in 2010, and it is found that the calibrated Noah LSM can be applied in the longer term at this site. The Noah LSM with 12 dominant parameters calibrated performs similar to that with 27 parameters calibrated.
Key words: parameter optimization     sensitivity analysis     temperate desert steppe
1 Introduction

Arid and semi-arid region covers approximately 40% of global continental area (Verhoef et al., 1996). This region is very vulnerable and sensitive to climate change (Guan et al., 2017). However, over the arid and semi-arid region, it is still a daunting challenge for land surface models (LSMs) to correctly represent surface heat exchange for these water-limited desert steppe ecosystems (Chen et al., 2010; Zeng et al., 2012). LSMs include numerous physical parameterization schemes and employ lots of physical and physiological properties (green vegetation fraction, surface albedo, roughness length, canopy resistance, soil hydraulic properties, etc.). Realistic representation of key hydrological processes within LSMs, at the price of increasing number of parameters specified and accurate parameterization functions used, is important for accurate numerical weather forecast and climate prediction (Yin et al., 2016). Inappropriate parameter values will probably result in significant model errors. Since proper parameters for an LSM are critical, it is necessary to choose reasonable parameter values to represent relevant physical processes (Sen et al., 2001; Yin et al., 2016). In order to improve the behavior of LSMs, many efforts have been made to specify model parameters to represent the system properties as closely as possible (Chen and Zhang, 2009; Yin et al., 2016). The parameters in most LSMs are usually internally calculated by other variables, or prescribed by look-up tables. Therefore, the approach adjusting the prescribed parameters is employed to estimate parameter values, by minimizing observation-output differences of the model as consistently as possible over some chosen periods (Duan et al., 1993). This process is known as “model calibration”, also called “parameter optimiza-tion”. In the past two decades, among many model calibration algorithms developed in hydrological fields, the shuffled complex evolution (SCE) global optimization algorithm developed by Duan et al. (1993) has been successfully applied in hydrological models and could find the global optimum in the defined parameter range (Rode et al., 2007; Marcé et al., 2008; Wang et al., 2009). However, studies have shown that single-criterion parameter estimation can be of limited value when applied to LSMs because good performance in any one variable will not necessarily guarantee good performance in any other (Abramowitz et al., 2008; Gupta et al., 2009). The main objective of this study is not traditional applications of single-criterion optimization methods, but the comparison between model response with a set of all parameters and dominant parameters calibrated and the applicability of model with a set of optimized parameters in a longer term at this site. How a single-criterion optimization affects the objective variable and the other outputs is also in our scope of investigation.

One approach to identify the dominant parameters controlling model behavior is through the use of sensitivity analysis to evaluate the parameter’s influences on the model outputs (Tang et al., 2007). By distinguishing the prescribed parameters as sensitive or insensitive parameters, crucial parameters are identified through the computation of the relative contribution of prescribed parameters (Saltelli, 2002; van Werkhoven et al., 2008). The hybrid local-global sensitivity analysis method, distributed evaluation of local sensitivity analysis (DELSA), is developed recently (Rakovec et al., 2014). In DELSA, the assessment of parameter sensitivity is based on local gradients of the model performance with respect to model parameters at multiple points throughout the defined parameter range. It integrates three existing sensitivity analysis methods: the method of Morris (Morris, 1991; Herman et al., 2013), the Sobol’method (Sobol, 1993), and regional sensitivity analysis (Hornberger and Spear, 1981). The reader refers to the study by Rakovec et al. (2014) for more details.

The previous studies (Rosolem et al., 2012; Li et al., 2013) have shown that the variation of parameter sensitivity across different models and different plant functional types. The most sensitive parameters in a model also depend on the chosen model output variables (Li et al., 2016). Therefore, the parameter sensitivities on each component of energy budget are investigated respectively in this study. With the aim to identify the dominant parameters controlling the objective criterion, the DELSA method is employed in this study to evaluate the impacts of parameters on the model response, using the root mean squared error (RMSE) between observed and simulated flux as the objective function from May to September (growing season) in 2008 and 2009. The SCE algorithm is used in this study to calibrate the Noah LSM by minimizing the RMSE between observed and simulated flux from May to September in 2008 and 2009. Moreover, the observations in the growing season of 2010 are used to validate the calibrated model further.

The Noah LSM has been widely used in the research and operational communities and been coupled to community weather and regional climate models (Ek et al., 2003). In this study, we employ the Noah LSM (version 3.4) to carry out the investigation with regard to growing season net radiation (Rn), sensible heat flux (H), latent heat flux (LE), and ground heat flux (G) over a desert steppe site in China. Section 2 describes the observations, methods, and the design of numerical experiments. Section 3 discusses the model results, followed by a summary in Section 4. This study might provide the case study for LSMs to correctly represent surface heat exchange for these water-limited desert steppe ecosystems.

2 Data and methods 2.1 Site description and measurements

The Desert Steppe Ecosystem Research Station (44°05′N, 113°34′E) is located in Sonid Zuoqi of Inner Mongolia in Northeast China with growing season spanning from late April to October (Yang and Zhou, 2011). Its plant community consists of the dominant grasses Stipa Klemenzii and Allium polyrrhizum with an average height of 0.2–0.35 m at peak growth stage and the root depth of 0.3–0.5 m. Soil type is classified as sandy loam (with 4.44% clay, 31.04% loam, and 62.21% sand taken from 3 soil samples at this site) by the international soil texture classification system defined by the United States Department of Agriculture (USDA).

Observations (meteorological data and flux data) used in this study were collected from 2008 to 2010. Rn was measured at a height of 2.4 m above the ground using a four-component net radiometer (CNR-1, Kipp and Zonen, Delft, the Netherlands). Air temperature and relative humidity were measured at two levels (2.0 and 3.4 m; HMP45C, Vaisala, Helsinki, Finland). Horizontal wind speed at 2.0 m was measured with a horizontal wind speed sensor (014A, Campbell Scientific Inc., Utah, USA), and horizontal wind speed and wind direction at 3.4 m was measured with a wind set sensor (034B, Met One Inc., Oregon, USA). Precipitation was measured with a tipping-bucket rain gauge (Model 52203, RM Young Inc., Michigan, USA) above the canopy. Soil temperature (ST) profiles at depths of 0.05, 0.10, 0.15, 0.20, 0.40, and 0.80 m were measured by thermistors (107L, Campbell Scientific Inc., Utah, USA). All meteorological data were recorded every 2 s, and half-hourly mean data were logged by a data logger (CR23X, Campbell Scientific Inc., Utah, USA). Surface flux (exchange of heat, water vapor, and CO2) data were obtained with the open-path eddy covariance system installed at a height of 2.0 m. The signals were recorded at 10 Hz by a data logger (CR5000, Campbell Scientific Inc., Utah, USA), and the half-hourly flux data were computed by the eddy covariance method. The details about this site and observations are given by Zhang et al. (2014a, b). The corrections to raw flux include double coordinate rotations (Wilczak et al., 2001) and density effects of heat and water vapor transfer (Webb et al., 1980). Details of data processing can be found in Yang and Zhou (2011).

The ground heat storage flux (G) is calculated as

 $G = G 0 + C s Δ T s Δ t z ,$ (1)

where G0 is the measured ground heat flux at depth z (0.08 m at this site), Ts is the average ST (K; at a depth of 0.05 m) above the heat flux plates, △Ts is the change of the ST over one time step, △t is the time step (in this case △t = 30 min), and Cs is the soil heat capacity (Oliphant et al., 2004).

The energy-balance ratio (EBR) is used to assess the performance of the eddy covariance system (Wilson et al., 2002). It is calculated by using the following equation for hourly periods where all the data (Rn, H, LE, and G) were available:

 $EBR = ∑ ​ ( LE + H ) / ∑ ​ ( R n − G ) ,$ (2)

where Rn is the net radiation (W m–2), and H, LE, and G are sensible, latent, and soil heat fluxes (W m–2), respectively.

EBR is 0.89, 0.81, and 0.84 for 2008, 2009, and 2010, respectively, over the desert steppe in Inner Mongolia. These results are consistent with previous studies (Twine et al., 2000; Wilson et al., 2002). With the discrepancy (i.e., 1−EBR) in energy-balance closure larger than 30%, the utility of flux measurements for model validation or calibration is greatly reduced (Wilson et al., 2002). The discrepancy over this site is 11%, 19%, and 16% for 2008, 2009, and 2010, respectively, less than 30%. Therefore, the fluxes have not been adjusted in this study.

The monthly mean values with the standard error (mean ± SE) of observed Rn, H, LE, and G during the growing seasons of 2008–10 are shown in Fig. 1. There is seasonal and interannual variability in LE, peaking in June, similar to that of Rn. However, the maximum of H occurs in August 2010. Precipitation in June of 2008–10 (omitted) constrains the increase of H, but enhances the LE. A lack of precipitation in July and August of 2010, results in the obvious increase of H but the decrease of LE for the corresponding period (Figs. 1b–c). The monthly mean values of G are relative small compared to other three flux components. The variation pattern is similar to that of Rn, but with smaller variability (Fig. 1d).

 Figure 1 Variations of the observed fluxes in 2008, 2009, and 2010. Values are the monthly mean ± standard error (mean ± SE).
2.2 LSM and numerical experiments 2.2.1 Model description

The Noah LSM employs a Penman potential evaporation method to calculate LE and includes a four-layer soil model with the soil thickness of 0.1, 0.3, 0.6, and 1 m for each layer (Chen et al., 1996). It uses a roughness Reynolds number approach for determining the ratio between the roughness length for heat (zot) and that for momentum (zom; Zilitinkevich, 1995; Chen et al., 1997). The Noah LSM has been extended with canopy resistance as a function of soil water availability and atmospheric conditions and a surface runoff scheme by Chen et al. (1996). It employs three look-up tables (41 parameters in total) to prescribe soil, vegetation, and general parameters.

Hourly forcing data driving the Noah LSM (from 1 January 2008 to 31 December 2010) are from in-situ measurements of precipitation, air temperature, mixing ratio, wind speed, atmospheric pressure, downward shortwave radiation, and downward longwave radiation at this desert steppe site located in Inner Mongolia, China. Model spin-up is applied to each of model runs with the first year forcing conditions repeatedly until the reach of equilibrium of soil state (Cai et al., 2014). The tipping-bucket rain gauge at this site only provides rainfall measurements but not snowfall. Daily Climate Precipitation Center (CPC) of the NOAA and a nearby automatic weather station (AWS) precipitation data are used to fill the gap of in-situ precipitation data in the wintertime. When the daily air temperature is below 0 °C, the average daily precipitation of these two datasets is added into the in-situ rainfall measurements to yield a new adjusted daily precipitation dataset. In-situ rainfall measurements with the adjusted precipitation (same as in the study of Zhang et al., 2014a) are used to drive the Noah LSM continuously. Observations of Rn, H, LE, and G in two separated growing seasons (May–September) of 2008 and 2009 are used to examine the sensitivity of parameters and calibrate the Noah LSM with single objective criterion. The flux observations in the growing season of 2010 are used to validate the applicability of the optimized parameters.

2.2.2 Experiment setup

In this study, based on the control experiment (CTL), we design two experiment sets: (1) sensitivity experiments (DEL1–4), and (2) single-criterion calibration experiments (CAL1–4 and SEN1–4). The summary of numerical experiments is listed in Table 1.

Table 1 Summary of numerical experiments
 Experiment name Experiment setup CTL CTL The minimum and maximum values of LAI and roughness length are set as (0.1, 0.5 m2 m–2) and (0.02, 0.05 m), respectively. The number of root-zone layers is taken as 2. Other parameters are set as default values in the look-up tables Sensitivity analysis DEL1 With the number of root-zone layers prescribed as 2, and the minimum values of LAI and roughness length prescribed as 0.1 m2 m–2and 0.02 m, respectively, the influence of other table-parameters (Table 2) in the Noah LSM is examined by the DELSA using Rn as the objective criterion DEL2 Same as DEL1, but use H as the objective criterion DEL3 Same as DEL1, but use LE as the objective criterion DEL4 Same as DEL1, but use G as the objective criterion Calibration CAL1 Based on DEL1, but Noah LSM is calibrated by the SCE using Rn as the objective criterion CAL2 Same as CAL1, but use H as the objective criterion CAL3 Same as CAL1, but use LE as the objective criterion CAL4 Same as CAL1, but use G as the objective criterion SEN1 Based on CAL1, Noah LSM is calibrated by SCE using Rn as the objective criterion with the 12 dominant parameters SEN2 Same as SEN1, but use H as the objective criterion SEN3 Same as SEN1, but use LE as the objective criterion SEN4 Same as SEN1, but use G as the objective criterion

The detailed descriptions about the experiments are as bellow:

In CTL, the minimum and maximum values of leaf area index (LAI) and roughness length are set as (0.1, 0.5 m2 m–2) and (0.02, 0.05 m) respectively based on in-situ observation. The number of root-zone layers is taken as 2 (representing 0.4-m depth), since the root depth is 0.3–0.5 m over this site. The NESDIS/NOAA 0.144 degree monthly 5-yr climatology green vegetation fraction is applied in this study. Other parameters in Table 2 are set as default values for grassland and sandy loam in the Noah LSM.

Table 2 Parameter constraints and descriptions in the Noah LSM
 Parameter Unit Default Feasible range Description General parameter refdk --- 2.0E–6 5.0E–7, 3.0E–5 Used to compute runoff parameter kdt fxexp --- 2.0 0.2, 4.0 Bare soil evaporation exponent refkdt --- 3.0 0.1, 10 Surface runoff parameter, also used to compute kdt Czil --- 0.1 0.05, 3.0 Zilintikevich parameter Csoil J m–3 K–1 2.0E6 1.26E6, 3.50E6 Dry soil heat capacity sbeta --- –2.0 –4.0, 1.0 Used to compute canopy effect on ground heat flux Vegetation parameter rsmin s m–1 40 30, 500 Minimal stomatal resistance rgl --- 100 30, 150 Radiation stress parameter used in F1 term of canopy resistance hs --- 36.35 36.0, 55.0 Coefficient of vapor pressure deficit term in canopy resistance laimax m2 m–2 2.9 0.3, 4.0 Maximum leaf area index albmin --- 0.19 0.1, 0.23 Minimum surface albedo albmax --- 0.23 0.2, 0.46 Maximum surface albedo zomax m 0.12 0.01, 0.99 Maximum roughness length emissmax --- 0.96 0.92, 0.99 Maximum emissivity topt K 298 293, 303 Optimal air temperature for transpiration cmcmax 5.0E–4 1.0E–4, 2.0E–3 Maximum canopy water capacity used in canopy evaporation cfactr --- 0.5 0.1, 2.0 Exponent in canopy water evaporation function rsmax s m–1 5000 2000, 10000 Maximum stomatal resistance Soil parameter b --- 4.74 3.5, 10.8 Clapp-Hornberger b parameter drysmc m3m–3 0.047 0.014, 0.205 Dry soil moisture threshold at which direct evaporation from top soil layer ends maxsmc m3 m–3 0.434 0.43, 0.70 Saturated soil moisture content (i.e., porosity) refsmc m3 m–3 0.383 0.254, 0.42 Reference soil moisture (field capacity) psisat m m–1 0.141 0.04, 0.62 Saturated soil matric potential satdk m s–1 5.23E–6 5.0E–7, 3.0E–5 Saturated soil hydraulic conductivity satdw m s–1 8.05E–6 1.63E–7, 2.87E–5 Saturated soil hydraulic diffusivity wltsmc m3 m–3 0.047 0.014, 0.205 Wilting point soil moisture quartz --- 0.6 0.1, 0.82 Fractional quartz content of the soil

Since both the minimum and maximum values for LAI, roughness length, and emissivity are table-prescribed in the Noah LSM, we only examine the sensitivity of the maximum values in this study. Because we focus on the growing season, the sensitivity of parameters related to snow and ice are not examined either. In final, there are 6 general parameters, 12 vegetation parameters, and 9 soil parameters (27 parameters in total) to be selected (Table 2, all are from three look-up tables in the Noah LSM). The feasible ranges of the parameters in Table 2 are set based on other literatures (Rosero et al., 2010, 2011).

The impacts of 27 parameters are examined by DELSA using Rn, H, LE, and G as the objective criterion respectively during May–September 2008 and 2009 in experiments DEL1–4 (Table 1). Moreover, the dominant parameters are chosen for each objective criterion.

The Noah LSM with 27 parameters or with the chosen dominant parameters is calibrated by the SCE using Rn, H, LE, and G as the objective criterion respectively during May–September 2008 and 2009 (denoted as experiments CAL1–4 and SEN1–4, respectively in Table 1). The reasonability of sensitivity analysis by the DELSA is discussed through the comparison of model performance between the Noah LSM with 27 parameters (CAL1–4) and with chosen dominant parameters (SEN1–4) calibrated by the SCE, respectively.

2.3 Evaluation methods

Along with the development of parameter optimization, the evaluation of model behavior enables us to understand how parameter changes affect the model performance. Since a model should explain the major pattern of observations as closely as possible, it is important to know how “systematic” and “unsystematic” errors are distributed in a model. Meanwhile, mean squared error (MSE) can be decomposed into three terms, connected with different signals of model behavior respectively (Gupta et al., 2009), providing an efficient way to understand model behavior from different aspects, analyze error source, and improve model structure consequently (Rosolem et al., 2012).

The system error can be expressed as (Willmott, 1981):

 $MSE s = 1 n ∑ i =1 n ( P ^ i − O i ) 2 ,$ (3)
 $P ^ i = a + b O i .$ (4)

The unsystematic error could be expressed as:

 $MSE u = 1 n ∑ i = 1 n ( P i − P i ^ ) 2 .$ (5)

The system is conserved:

 $MSE=MSE s +MSE u ,$ (6)

where $P i ^$ is least-square regression fitting value, Oi is observed value, Pi is model simulated value, and a and b are regression coefficients. In theory, for a good model, MSEs should approach zero and MSEu is close to mean squared error (MSE).

Meanwhile, MSE decomposition can be used to assess the properties in mean level, standard deviation, and cross-correlation associated with each flux simulation. Therefore, we can gain deeper insight into the nature of model response through decomposing MSE. MSE can be decomposed as follow (Gupta et al., 2009):

 $MSE= Δ μ 2 + Δ σ 2 + 2 σ s σ o ( 1 − ρ ) ,$ (7)
 $MSE 2 σ s σ o = Δ μ 2 2 σ s σ o + Δ σ 2 2 σ s σ o + ( 1 − ρ ) ,$ (8)
 $Δ μ = μ s − μ o ,$ (9)
 $Δ σ = σ s − σ o ,$ (10)

where μo and σo are the mean and standard deviation of the observed values; μs and σs are the mean and standard deviation of the simulated values; ρ is the linear correlation coefficient between simulated and observed flux time series; $Δ μ 2 2 σ s σ o$ (denoted as term A) and $Δ σ 2 2 σ s σ o$ (denoted as term B) represent the averaged errors in signal mean and signal standard deviation, respectively; and (1–ρ) (denoted as term C) represents the ability of the model to reproduce dynamical properties of the time series (Gupta et al., 2009; Rosolem et al., 2012). Through examining the variation trend of each term in Eq. (8), how the model behavior is affected by modifying parameters can be assessed. This will enable us gain more insight into the error sources.

3 Results and discussions 3.1 Impacts of parameters on flux simulation from DELSA

The relative influence of all 27 parameters on Rn, H, LE, and Ghas been shown in Fig. 2. The total influence of 27 parameters is 100% on each objective variable. The relative influences are sorted in descending order in DEL1–4, respectively, and the top parameters when accumulated influence accounting for more than 90% are chosen as the dominant parameters for the corresponding criteria.

 Figure 2 The relative contribution of parameters to (a) net radiation (Rn), (b) sensible heat flux (H), (c) latent heat flux (LE), and (d) ground heat flux (G) from DELSA.

Rn: Seven parameters are chosen with the influence decreased in the order of Czil > alb max > zomax > fxexp > quartz > csoil > maxsmc. Czil is most responsive to the Rn simulation with a relative contribution of approximately 50%, followed by albmax. The maximum roughness length zomax, combined with the minimum roughness length, is used to calculate the roughness length for the momentum zom. It takes the third place with the influence of approximately 6% on the Rn simulation (Fig. 2a).

H: Five parameters are chosen with the influence decreased in the order of Czil > alb max > zomax > c soil > fxexp. Czil is most responsive to the H simulation as well, with the influence of approximately 70%. The influence of other parameters on H is similar to those on the Rn simulation (Fig. 2b). Only 5 parameters can account for 90% contribution to the H simulation.

LE: The contributions of parameters are not that concentrated as those for Rn and H. Nine parameters accounting for 90% total influence on LE are chosen: Czil > fxexp > drysmc > maxsmc > b> satdk > rsmin > zomax > wltsmc, indicating that the simulation of LE is more complicated and involves more parameters. Czil is still the most responsive parameter, but with approximately 30% contribution. Parameter fxexp is the secondary, indicating that soil direct evaporation is significant over the desert steppe region. Parameters b and drysmc, impacting soil moisture availability, have great impacts on LE through affecting soil moisture and stomatal conductivity. The parameter rsmin, related to the canopy resistance and evapotranspiration consequently, has a great influence as well (Fig. 2c).

G: Seven parameters are chosen with the influence decreased in the order of Czil > alb max > maxsmc > quartz > fxexp > csoil > zomax. The parameters contributing 90% for G are the same with those for Rn but with different contribution orders (Fig. 2d).

In general, Czil has the most contribution to the flux simulations. Many studies have demonstrated the strong sensitivity of H simulation to Czil (Chen and Zhang, 2009; Trier et al., 2011; Zhang et al., 2014a), consequently the LE and G simulations. Theparameter albmax is the secondary important parameters for Rn, H, and G simulations. The reason is that albmax is involved in the computation of albedo, consequently Rn and skin temperature. G is mainly determined by the modeled skin temperature (Chen et al., 2010; Zeng et al., 2012), and H is parameterized by skin temperature as well. Therefore, there is no doubt that albmax plays an important role in the simulations of these three flux components. Many previous studies have examined the impacts of different roughness length schemes (Yang et al., 2008; Chen et al., 2010; Zeng et al., 2012), and demonstrated that the roughness length is an influential parameter for the surface energy fluxes.

It is noted that although the contribution of maxsmc is comparable between Rn and H, maxsmc is not included in the parameters with adding influence larger than 90% for H since other parameters are much more influential to H. A parameter selected once for any fluxes will be optimized in the next step. Therefore, combined the four sets of chosen parameters, 12 dominant parameters including fxexp, Czil, csoil, rsmin, albmax, zomax, b, drysmc, maxsmc, satdk, wltsmc, and quartz, with added influence more than 90% to flux simulations, are selected to re-calibrate the Noah LSM by the SCE for Rn, H, LE, and G, respectively (experiments SEN1–4 in Table 1).

3.2 Model calibration by the SCE 3.2.1 Comparison of flux simulation with all parameters and dominant parameters calibrated: Quantifying model errors

The statistics of each flux simulation from CTL, experiments CAL1–4 (with 27 parameters calibrated by the SCE), and experiments SEN1–4 (with 12 dominant parameters calibrated by the SCE) have been shown in Fig. 3. The calibrated Noah LSM gives the similar results in 2010 (markers with dashed lines) compared to 2008–09 (markers with solid lines). This indicates that the optimized parameter values obtained from the SCE are applicable in a longer term at this site (Fig. 3). When the Noah LSM with 12 dominant parameters calibrated by the SCE using Rn, H, LE, and G observations of growing seasons in 2008 and 2009, respectively (experiments SEN1–4), the model behaviors are similar with those in CAL1–4 (Fig. 3). This demonstrates the reasonability of the selected dominant parameters.

 Figure 3 The statistics of flux simulations in experiments CAL1–4 and SEN1–4 averaged for growing seasons of 2008–09 and 2010, respectively. (a) RMSE, (b) Bias, and (c) index of agreement. When RMSE→0, bias→0, or IOA→1, the flux simulations are closer to observations.

Compared to experiment CTL, the H simulations improve for almost all calibrated experiments. However, only when the Noah LSM is calibrated by usingRnas the target criteria in experiments CAL1 and SEN1, the Rn simulations are better than CTL. Otherwise, the Rn simulations are worse than those in CTL. The SCE calibration does not have much influence on LE simulations. When the Noah LSM is calibrated by using Rn as the objective criterion, fluxes are all simulated better than those in experiment CTL except for G. But when the Noah LSM is calibrated by using G as the objective criteria, Rn is simulated worse as well.

 Figure 4 The statistics of flux simulations in experiments CAL1–4 and SEN1–4 averaged for growing seasons of 2008–09 and 2010, respectively. RMSEs and RMSEu (W m–2): the squared root of system errors and unsystematic errors for (a) Rn, (b) H, (c) LE, and (d) G, respectively.
 Figure 5 As in Fig.4, but for the mean squared error decompositions for (a) Rn, (b) H, (c) LE, and (d) G, respectively. A: $\frac{\Delta {{\mu }^{2}}}{2{{\sigma }_{\rm s}}{{\sigma }_{o}}}$ (averaged error in signal mean); B: $\frac{\Delta {{\sigma }^{2}}}{2{{\sigma }_{\rm s}}{{\sigma }_{o}}}$ (averaged error in signal variability); C: (1–ρ) (error in dynamical properties of the time series).

As shown in Figs. 4, 5, RMSEu and RMSEs, and terms A, B, and C in SEN1–4 are similar to those in CAL1–4. Meanwhile, the tendency for 2010 is similar to the average of 2008–09. This indicates that the optimized parameter values from the calibration period (2008–09) can give the similar simulations in the validation period (2010). For the Rn simulation, the proportion of systematic error is larger than unsystematic error in all experiments but CAL1 and SEN1, in which the Noah LSM is calibrated by the SCE using Rn as the objective variable. But calibration using H, LE, or G as the objective variables (i.e., experiments CAL2–4 and SEN2–4) deteriorates the Rn simulation, making both the systematic error and term B increased (Figs. 4a, 5a). For H simulation, the systematic error (term B) is larger (largest) in experiment CTL. The systematic error is smallest in CAL2 and SEN2 (Figs. 4b, 5b). Term B (averaged error in signal variability) decreases, but term A (the averaged errors in signal mean) increases in CAL1–4 and SEN1–4, making the sum of A, B, and C decreases though, compared to CTL (Fig. 5b). The decreased systematic error indicates the calibration improves H significantly. However, the increased term A indicates that it is still challenging in its simulation of long term average. Term A for 2010 is smaller than that in 2008–09 demonstrate this again (Fig. 5b). The improvement for LE simulation is limited after calibration. The systematic error is comparable to unsystematic error in all experiments, except that the systematic error is smaller in CAL3 and SEN3 (Fig. 4c). Term C (the error in dynamical properties of the time series) is largest and term A of LE simulation has no much change (Fig. 5c). This indicates that the Noah LSM could produce better averaged LE over long period, but worse variability and dynamical properties. Only when the Noah LSM is calibrated by using H and G as the objective criterion, the systematic error and term C of G are decreased (CAL4 and SEN4 inFigs. 4d, 5d). The term C is the largest of G(Fig. 5d). Combined with the smallest term A for G simulations, it indicates the calibrated Noah LSM can capture the mean tendency of G, but cannot catch the variability of G well.

Compared to CTL, model calibration by the SCE can reduce the systematic error of the objective flux. When the Noah LSM is calibrated by the SCE using Rn, H, or G as the objective criterion, the simulation of the corresponding flux is best among all experiments, and a significant fraction of model errors can be reduced by parameter optimization. The remained model errors can be attributed to both model structure and model input (Li et al., 2016). Model calibration can improve Rn, H, and G more than LE simulation. One reason is probably that LE includes direct soil evaporation (EDIR), evaporation of canopy intercepted water (EC), and transpiration (ET), involving more sub-processes. Therefore, model errors in LE are probably largely contributed by model structure and input rather than model parameter values.

3.2.2 Flux simulation

Since there is no great difference between CAL1 vs. SEN1, CAL2 vs. SEN2, CAL3 vs. SEN3, and CAL4 vs. SEN4, we focus on the flux simulations of SEN1–4. The monthly mean diurnal cycles of flux during the growing seasons of 2008–09 and 2010 are presented in Fig. 6. The maximum of Rn occurs in June, and all the experiments can capture this pattern well (Figs. 6a, b). CTL and SEN1 can both reproduce the diurnal cycle of Rn well compared to other experiments. However, H is overestimated in CTL by approximately 80–130 W m–2 during the noon (Figs. 6a–d). Therefore, there is no doubt that LE is underestimated in CTL (Figs. 6e, f). Experiments SEN2–4 produce less Rn, especially in SEN3 and SEN4. Compared to CTL, the calibrations (SEN1–4) give the better H simulations around noon, and decrease the biases of H dramatically, but SEN3 and SEN4 underestimates H. The diurnal cycles of H in experiment SEN2 agree well with the observations even in the nighttime (Figs. 6c, d). LE is smaller than H at this site. Therefore, the uncertainties in LE among different experiments are relative small compared to those in Rn and H. LE is underestimated in May–July of 2008–09 in all experiments. It is not surprising that LE is best simulated in SEN3 since it is optimized by using LE as the objective criterion, and the underestimation during the noon is mitigated in 2008–09 (Fig. 6e). Although SEN3 can catch the tendency of the maximum LE in June, it overestimates LE from June to September 2010. In general, CTL simulates G well, unless approximately 1 h early for the occurrence of the peak values around the noon. The G simulation in SEN4 is comparable to that in CTL, but corrects the early peak values occurrence. When the Noah LSM is calibrated by the SCE using Rn, H, LE, and G as the objective criterion (SEN1, SEN2, SEN3, and SEN4, respectively), the simulation of the corresponding flux is best among all experiments (Figs. 6a–d). Even when the pattern of observed H in 2010, peaking in August, is different from its averaged pattern in 2008–09, the calibrated model can capture the pattern well. This demonstrates again that the calibrated model can be applied in a longer term.

Since the improvement of LE is limited after the calibration, the variations of three components in SEN1–4 are shown in Fig. 7. The largest part of LE is direct soil evaporation (EDIR) with the maximum of about 110 W m–2. However, the transpiration (ET) and canopy water evaporation (EC) are approximately 20 W m–2 at most. This is probably one reason that more soil parameters are included in the adding contribution larger than 90%. Along with the grass growing, both the LAI and green vegetation fraction increase in June–August and the bared ground area decreases accordingly. Consequently, the ET increases (Figs. 7e, f) but the EDIR decreases (Figs. 7c, d). The calibrations have no large impact on the EC simulation, except that EC decreases in the nighttime (Figs. 7a, b). Compared to CTL, the calibrations (SEN1–4) increase the EDIR at the most time (Figs. 7c, d), but decrease the ET (Figs. 7e, f).

 Figure 6 Monthly mean diurnal cycle of flux simulations. (a, b) Rn, (c, d) H, (e, f) LE, and (g, h) G. X-axis: UTC time in 1-h step; (a, c, e) monthly mean diurnal cycle averaged for 2008–09; and (b, d, f) averaged for 2010.
 Figure 7 As in Fig. 6, but for (a, b) canopy water evaporation, (c, d) soil direct evaporation, and (e, f) transpiration.
3.2.3 Comparison of optimized parameter values

For different objective criterion, parameters are probably converged to totally different optimal values (Table 3). A comparison calibrated values to default values (Table 3) can provide more insight into understanding the nature of the desert steppe.

fxexp: This is soil evaporation exponent used in the computation of EDIR. Its optimized value for each objective variable is smaller than the default value. The decrease of fxexp indicates more effect of soil moisture availability on direct evaporation over the desert steppe site than the common grassland. This can result in the increase of EDIR (Figs. 7c, d). This is expected since the vegetation is sparse and green vegetation fraction is small at this site.

Table 3 Values of optimized parameters*
 Parameter SEN1 SEN2 SEN3 SEN4 General parameter fxexp 1.65 0.89 0.47 0.67 Czil 1.31 2.12 1.08 1.14 csoil 1.98E6 1.01E6 1.07E6 3.498E6 Vegetation parameter rsmin 983.87 991.66 997.77 952 albmax 0.21 0.31 0.46 0.46 zomax 0.013 0.012 0.72 0.60 Soil parameter b 10.79 7.66 8.13 9.89 drysmc 0.014 0.093 0.014 0.037 maxsmc 0.43 0.521 0.55 0.414 satdk 2.8E−6 0.9E−6 0.7E−6 2.7E−5 wltsmc 0.089 0.062 0.085 0.067 quartz 0.82 0.82 0.82 0.39 *Note that the values in bold are for parameters selected for the corresponding flux.

Czil: The Noah LSM employs Zilitinkevich’s formulation to represent the relationship between roughness length for heat (zot) and momentum (zom), expressed as $z ot = z om exp ( − k C zil Re )$ , where Czil is a constant empirical coefficient, k is the von Karman constant, and Re is the roughness Reynolds number (Zilitinkevich, 1995). Czil is suggested to be 0.1 in the Noah LSM, and could be adjusted between 0.01 and 1.0 (Chen et al., 1997). Recent studies indicate that Czil should be set as a larger value for grassland in order to obtain accurate surface heat exchange coefficient (Chen and Zhang, 2009; Trier et al., 2011). The optimized values over this site are close to other studies (Trier et al., 2011; Zeng et al., 2012). Four optimized values of Czil are all greater than default value. This is consistent with the previous studies that Czil should be increased to reduce surface coupling strength at the short-height vegetative region. For a given surface net radiation flux over this semi-arid site, reducing the surface exchange coefficient implies a reduction of total heat fluxes transferred to the atmosphere (H and LE) but an increase of heat transferred between the surface and soil (G). This is demonstrated well in SEN1 (Fig. 6). This provides a basis for the further modification of surface heat exchange coefficient parameterization.

csoil: This parameter is the dry soil heat capacity, used to calculate the heat capacity of soil layers. The soil layers usually consist of water, soil, air, and ice. If csoil is reduced, the heat capacity of whole layers decreases consequently. All the optimized values in SEN1–3 are smaller than the default values (2.0 × 106 J m–3 K–1). This is consistent with the study from Zhang et al. (2002) and Hu et al. (1990), who found that the heat capacity of dry soils is 1.17 × 106 and 1.28 × 106 J m–3 K–1 at Gobi deserts.

rsmin: This is the minimum of stomatal resistance. All the optimized values of rsmin in SEN1–4 are converged to approximately 1000 s m–1 for the upper bound. The reasons might be the feasible range for rsmin is not wide enough or the physical mechanism of the parameter is unreasonable. However, we could not extend the range infinitely since 1000 s m–1 is large enough for rsmin. It indicates that rsmin is relative large over the desert steppe region in Inner Mongolia, China. This is consistent with the study of Alfieri et al. (2008), who found that the Noah LSM with an rsmin value of 96 s m–1 (larger than the default rsmin value of 40 s m–1) for the grasslands could improve the latent heat flux simulations. As we known, LE consists of EDIR, ET, and EC in the Noah LSM. The LAI and green vegetation fraction are smaller at this site, so ET takes smaller part. It is reasonable that the larger optimized rsmin value is to reduce ET. Combined with the smaller fxexp, resulting in more EDIR, the effect of these two parameters is offset on the LE simulation. Therefore, the absolute values of LE have not many changes (Figs. 6e, f).

zomax: In the Noah LSM, the varying roughness length for momentum zom is calculated by weighting between zomin and zomax. The parameter zot relates zom with Czil. This parameter affects the computation of surface exchange coefficient directly. The optimized values are both smaller than the default value in SEN1 and SEN2. This is expected since the vegetation is shorter over this site and the height of canopy makes great contribution to the aerodynamic roughness length over homogeneous land surface (Ma et al., 2002). CTL overestimates H, the calibration tries to reduce H through the deduction of surface exchange coefficient (Fig. 6). Larger optimized values in SEN3 and SEN4 are in the opposite way for LE and G simulations, trying to enlarge LE and G.

albmax: The optimized albmax values are all greater than the default value in SEN2–SEN4. In the Noah LSM, the albedo (alb) is calculated as follow:

 $alb=alb max + fveg × ( alb min − alb max ) ,$ (11)

where fveg is green vegetation fraction. Since fveg is relative small in the desert steppe site, the increase of albmax would lead to the increase of alb. This is expected, since the sparse vegetation in the desert region makes alb larger than the default value for grassland in the Noah LSM. The increased alb can result in the reduction of Rn in the Noah LSM (Figs. 6a, b).

band satdk: In the Noah LSM, the soil hydraulic conductivity and the soil water potential are computed by $K ( Θ ) = satdk ( Θ maxsmc ) 2 b + 3$ and $Ψ = psisat / ( Θ maxsmc ) b$ respectively, where Θ is the soil water content, and b is a curve-fitting parameter. Therefore, b is an exponent in the function that relates soil water potential (or soil hydraulic conductivity) and soil water content. For each objective criterion, all the optimized values of b in SEN1–4 are greater than the default value. The increase of bleads to the increase of K and ψ, resulting in the increase of soil moisture availability and EDIR consequently. However, all the optimized values of satdk are smaller than the default value in SEN1–3. This can lead to the decrease of K, and offset the effects of increased b to some degree.

drysmc and wltsmc: In the Noah LSM, these two parameters are set as the same value, 0.047 m3 m–3. For Rn, LE, and G simulations, the optimized drysmc (dry soil moisture threshold at which EDIR from top soil layer ends) decreases, compared to the default value. For the H simulation, this threshold increases. But all the optimized values of wilting point (wltsmc) are larger than the default values. This indicates that ET ends earlier than EDIR when there is no enough water supplied in the soil at this site. Even in extremely dry conditions, the water from deeper soil layers could be evaporated directly.

maxsmc: All the calibrated maxsmc values in SEN1–3 are larger than the default value. This is consistent with the report of Shangguan et al. (2013). From the soil database of China for LSM developed by Shangguan et al. (2013)), maxsmc around this desert steppe site is approximately 0.436–0.549 m3 m–3. The larger maxsmc leads to the increase of relative soil moisture saturation and soil hydraulic conductivity. Moreover, it affects the thermal diffusivity and conductivity, consequently the soil heat exchange.

quartz: This quartz fraction is used to compute the thermal conductivity for quartz and other soil components. The increased quartz content leads to the increase of thermal conductivity for the combine solids, since the thermal conductivity for quartz is larger than that for other soil components. All the optimized values are larger than the default value in SEN1–3. That is one reason that the variability of G is large in SEN1 and SEN2.

Since the number of parameters contributing 90% to LE are larger and the influence of one parameter is limited. Moreover, the same parameter may have the opposite effect on different flux components, and their effects may be offset by each other too. Therefore, the direct effect of one parameter might be masked on the model response. For example, the variability of G in SEN3 is small with larger quartz content but that in SEN4 is large with smaller quartz content (Figs. 6g, h).

3.3 Discussion

It should be recognized that the sensitivity of one parameter is closely related to the setup of adjustable ranges that we defined in Table 2. The improper definition of parameter range can make a sensitive parameter appear to be insensitive (Li et al., 2016), and make parameters converged to unreasonable values. The single-objective SCE optimization probably provides the direction how the parameters in the desert region should be changed in, but not the absolute optimal values. As we known, the vegetation is sparse in the desert region and the arid condition makes the vegetation height shorter. The lower green vegetation fraction constrains the ET and benefits EDIR at the desert steppe site compared to other grasslands. Therefore, the parameters related ET are optimized to reduce ET (for instance, the increased rsmin and wltsmc in Table 3), and the parameters related EDIR are optimized to increase EDIR (for instance, the decrease of fxexp and increase of b). Moreover, the surface albedo is larger because of more bared ground at this site, consistent with the above analysis for the increase of albmax. There are studies that the coupling strength for the tall canopy is stronger than that for shorter vegetation (Chen and Zhang, 2009). The increased Czil values (Table 3) are to reduce the surface exchange coefficient in the Noah LSM. This study is not meant to obtain optimal values of parameters applied in the Noah LSM at the desert steppe site but how the parameter changes affect the flux simulation. This study highlights the importance of parameter estimation in improving and developing LSMs. The optimized values in Table 3 help us to understand the parameters qualitatively at the desert steppe site. In the future, more observations should be considered to configure the parameter values in the Noah LSM. Moreover, it should be noticed that the absolute magnitude of reduced model uncertainties by parameter modification is closely related to the observation uncertainty of objective outputs (Fig. 1). The contributions of uncertainties in meteorological inputs are also quite significant. Therefore, in future, more factors should be considered to reduce the uncertainties in flux observations and meteorological forcing.

4 Conclusions

This study focuses on the identification of dominant parameters and the differences in the model response on the objective criterion and other fluxes when the Noah LSM is calibrated by the SCE using the single-objective criterion. The relative impacts of 27 parameters in the Noah LSM is examined by employing the DELSA with single criterion against the flux observations during the growing seasons of 2008–09. For all the flux simulations, Czil is the most dominant parameter. There are 5–7 parameters accounting for the 90% contribution for Rn, H, and G in the Noah LSM. But for the LE simulation, the contributions of parameters are more even and the number of dominant parameters is larger. The variations of parameter sensitivities are different across the different objective criterions. When the Noah LSM is calibrated by the SCE using Rn, H, LE, and G as the objective criterion, the simulation of the corresponding flux is best among all experiments, and a significant fraction of systematic errors and term B can be reduced. When the Noah LSM is calibrated against observations in 2008–09, its behavior in 2010 is comparable, indicating the applicability of the calibrated model. The performance of the Noah LSM with 12 chosen dominant parameters calibrated is comparable to that with all 27 parameters calibrated.

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