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  • View in gallery

    (top left) Location of Maqu site in the SRYR in China, (top right) the micrometeorological station, and (bottom) the SMST monitoring network in the Maqu area shown on a DEM map.

  • View in gallery

    Daily averaged (a) precipitation and albedo and (b) temperature of air, surface, and 5-cm soil depth for the period from 27 Nov 2009 (DOY 331) to 31 Mar 2010 (DOY 90).

  • View in gallery

    Average diurnal cycles of December–March measured surface (a) radiation and (b) heat flux components.

  • View in gallery

    Soil freezing characteristics determined from the measured and estimated liquid soil water vs measured soil temperature for depths of (a) 5 and (b) 25 cm.

  • View in gallery

    Average diurnal cycles of December–March measured and simulated (a) sensible heat flux, (b) latent heat flux, (c) surface temperature, and soil temperature for the depths (d) 5, (e) 25, and (f) 70 cm produced by four numerical experiments performed in sections 4 and 5a.

  • View in gallery

    Comparison of the measured and simulated liquid soil water produced by four numerical experiments performed in sections 4 and 5a for each soil layer with a 30-min interval for the period from 27 Nov 2009 (DOY 331) to 31 Mar 2010 (DOY 90): (a) 5, (b) 25, and (c) 70 cm.

  • View in gallery

    Average diurnal cycles of December–March measured and simulated (a) surface temperature and soil temperature for the depths (b) 5 and (c) 70 cm produced by numerical experiments performed in section 5b.

  • View in gallery

    Comparison of the measured and simulated liquid soil water produced by numerical experiments performed in section 5b for each soil layer with a 30-min interval for the period from 27 Nov 2009 (DOY 331) to 31 Mar 2010 (DOY 90): (a) 5, (b) 25, and (c) 70 cm.

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Evaluation of Noah Frozen Soil Parameterization for Application to a Tibetan Meadow Ecosystem

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  • 1 Faculty of Geo-Information Science and Earth Observation, University of Twente, Enschede, Netherlands
  • | 2 Key Laboratory of Land Surface Process and Climate Change in Cold and Arid Regions, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, China
  • | 3 Department of Earth System Science, Tsinghua University, Beijing, China
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Abstract

This study evaluates the Noah land surface model (LSM) in its ability to simulate water and heat exchanges over frozen ground in a Tibetan meadow ecosystem. A comprehensive dataset including in situ micrometeorological and soil moisture–temperature profile measurements collected between November and March is utilized, and analyses of the measurements reveal that the measured soil freezing characteristics are better captured by 1) modifying the parameter bl implemented in the current Noah LSM that constrains the shape parameter of soil water retention curve utilized by the water potential freezing point depression equation to produce appropriate liquid water content θliq under subzero temperature conditions and 2) neglecting the ice effect on soil-specific surface and thus matric potential via setting the empirical parameter that accounts for the effect of increase in specific surface of soil particles and ice–liquid water ck to zero. The numerical experiments performed with the Noah model run show that in comparison to the default Noah LSM, adoption of ck = 0 and site-specific bl values reduces the overestimation of θliq across the soil profile. Implementation of augmentations such as the parameterization of diurnally varying thermal roughness length resolves the overestimation of daytime turbulent heat fluxes and underestimation of surface temperature. Further adoption of a new heat conductivity parameterization reduces the overestimation of nighttime surface temperature. An appropriate treatment of phase change efficiency that accounts for changing freezing rate with varying liquid water contents is also needed to reduce the temperature underestimation across soil profiles.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Donghai Zheng, d.zheng@utwente.nl

Abstract

This study evaluates the Noah land surface model (LSM) in its ability to simulate water and heat exchanges over frozen ground in a Tibetan meadow ecosystem. A comprehensive dataset including in situ micrometeorological and soil moisture–temperature profile measurements collected between November and March is utilized, and analyses of the measurements reveal that the measured soil freezing characteristics are better captured by 1) modifying the parameter bl implemented in the current Noah LSM that constrains the shape parameter of soil water retention curve utilized by the water potential freezing point depression equation to produce appropriate liquid water content θliq under subzero temperature conditions and 2) neglecting the ice effect on soil-specific surface and thus matric potential via setting the empirical parameter that accounts for the effect of increase in specific surface of soil particles and ice–liquid water ck to zero. The numerical experiments performed with the Noah model run show that in comparison to the default Noah LSM, adoption of ck = 0 and site-specific bl values reduces the overestimation of θliq across the soil profile. Implementation of augmentations such as the parameterization of diurnally varying thermal roughness length resolves the overestimation of daytime turbulent heat fluxes and underestimation of surface temperature. Further adoption of a new heat conductivity parameterization reduces the overestimation of nighttime surface temperature. An appropriate treatment of phase change efficiency that accounts for changing freezing rate with varying liquid water contents is also needed to reduce the temperature underestimation across soil profiles.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Donghai Zheng, d.zheng@utwente.nl

1. Introduction

Frozen soils, including permafrost and seasonal frost, are widespread in high-latitude and high-altitude regions and cover more than half of the Northern Hemisphere during winters (Zhang et al. 1999, 2003). The coexistence of ice and liquid water in the frozen soil dramatically changes the soil hydraulic and thermal properties (Farouki 1986; Lawrence and Slater 2008; Lundin 1990) that in turn affects the water and heat distributions across the soil column as well as the exchanges with the overlying atmosphere (Hansson et al. 2004; Stevens et al. 2007; Zhao et al. 1997). The phase change of soil water, namely, freeze–thaw transition, also modulates the surface and subsurface energy partitioning that exerts a profound impact on the global and regional hydroclimatology (Lawrence et al. 2008; Poutou et al. 2004; Viterbo et al. 1999). An investigation of frozen soil processes is, therefore, imperative for global and regional climate change studies.

Accordingly, large efforts have been made recently to develop model physics for the effects of soil freeze–thaw process on water and energy budgets in land surface models (LSMs) and hydrological models (Cherkauer and Lettenmaier 1999; Dankers et al. 2011; Flerchinger and Saxton 1989; Gouttevin et al. 2012; Koren et al. 1999; Niu and Yang 2006). Current frozen soil parameterizations differ widely in the representation of model physics with respect to soil freeze–thaw processes; complexity of model structures and numerical schemes; and choice of governing equations, diagnostic variables, and model parameters (Li et al. 2010; Zhang et al. 2008, 2010). Large differences and discrepancies are found in the simulation of surface water and energy budgets generated by various models driven with the same meteorological forcing (Luo et al. 2003; Slater et al. 2007), for instance, the modeled hydrographs are often out of phase across the Arctic rivers. Further examinations of the model physics and validation against in situ measurements thus remain necessary.

The Tibetan Plateau is also in a substantial part underlain with permafrost and/or subject to seasonally frozen soil (Guo and Wang 2013), which makes the soil freeze–thaw process one of the key features for land surface modeling over the plateau. Recently, striking surface warming and frozen ground degradation have been widely reported (Salama et al. 2012; van der Velde et al. 2014; Wu and Zhang 2010; Wu et al. 2013), which altered the seasonal freeze–thaw cycle (Li et al. 2012) and exerted a profound influence on the local and surrounding hydrology and eco-environment (Cheng and Wu 2007; Jin et al. 2009; Wang et al. 2012). Better understanding and modeling of the frozen soil processes on the plateau is thus imperative because important sources of water and heat associated with freeze–thaw transitions are expected to be affected by climatic changes. In recent years, modeling of surface water and energy budgets on the Tibetan Plateau has been greatly advanced (Yang et al. 2009; Zheng et al. 2016, 2017), and current LSMs have been thoroughly investigated for a better simulation of soil water and temperature profiles (Chen et al. 2010; Zeng et al. 2012; Zheng et al. 2014, 2015c). Most of the studies are, however, mainly focused on thawed soil during the warm monsoon season, and fewer report on frozen soil (Cuo et al. 2015). Su et al. (2013) have recently shown that current LSMs have difficulty in capturing the freeze–thaw cycle on the Tibetan Plateau, and both heat and mass exchanges need to be accurately investigated to capture such process.

In this study, we seek to investigate and enhance the state-of-the-art Noah LSM in its ability to represent frozen soil processes in a Tibetan meadow ecosystem. The Noah LSM has been previously examined and modified to achieve a better simulation of water and heat flow in the thawed soil during the warm monsoon season from June to September (Zheng et al. 2015a,b). A comprehensive dataset including in situ micrometeorological and soil moisture–temperature profile measurements has been collected for the model assessment during the cold season between November and March.

This paper is outlined as follows. Section 2 introduces the Noah model physics and in situ measurements. Section 3 describes the diurnal variations of measured surface energy budgets as well as soil freezing characteristics. Section 4 provides a performance assessment of the Noah model physics associated with frozen soil processes. Section 5 presents a discussion on a performance assessment of alternative treatments of thermal heat conductivity as well as latent energy during water phase change. Section 6 concludes with a summary of the findings.

2. Methodology and measurements

a. Noah LSM frozen soil physics

The default Noah model physics as well as the augmentations associated with water and heat transport for unfrozen/thawed soil are described in detail in our previous studies (Zheng et al. 2015a,b). The model physics associated with frozen soil processes is given below.

To account for water phase change in frozen soil, a source–sink term is added to the thermal diffusion equation describing soil heat flow (Koren et al. 1999):
e1a
e1b
where Ts is the soil temperature (K), t is the time (s), z is the soil depth (m), ρice is the density of ice (kg m−3), Lf is the latent heat of fusion (J kg−1), θ is the total soil water content (m3 m−3), θice is the soil ice content (m3 m−3), κh is the thermal heat conductivity (W m−1 K−1), Cs is the thermal heat capacity (J m−3 K−1), and Ilat represents the latent heat released or consumed during the phase change of soil water. Both κh and Cs depend on the constituents of the soil matrix (e.g., θ and θice), and their parameterizations in Noah can be found in Peters-Lidard et al. (1998), whereby Zheng et al. (2015b) reported recently on the inclusion of the organic matter effect for the Tibetan soil.
The solution to Eq. (1) is achieved using the fully implicit Crank–Nicholson scheme. The temperature at the bottom boundary (at a depth of 8 m) is generally taken as the annual mean near-surface air temperature, whereas the top boundary is confined by the ground surface temperature Tsfc estimated by
e2
where Ta is the air temperature (K); S and S are the downward and upward shortwave radiation (W m−2), respectively; L is the downward longwave radiation (W m−2); ε is the surface emissivity (unitless); σ is the Stefan–Boltzmann constant taken as 5.67 × 10−8 W m−2 K−4; H is the sensible heat flux (W m−2); LE is the latent heat flux (W m−2); and G0 is the ground surface heat flux (W m−2). Zheng et al. (2015b) reported recently several augmentations such as implementing the scheme of diurnally varying thermal roughness length for heat transfer z0h to improve the surface heat flux and soil temperature simulations for thawed soil over Tibetan Plateau during warm season.
With the assumption that liquid water flow in the frozen soil is analogous to that in unfrozen/thawed soil, the diffusivity form of Richards’ equation can be utilized to estimate unfrozen or liquid soil water movement (Koren et al. 1999):
e3
where θliq is the unfrozen/liquid soil water content (m3 m−3), D is the soil water diffusivity (m2 s−1), K is the hydraulic conductivity (m s−1), and S represents sources and sinks (i.e., infiltration and evapotranspiration; m s−1). Detailed descriptions of the default D, K, and S parameterizations are given in Chen et al. (1996), whereby Zheng et al. (2015a) included in Noah an asymptotic function for root water uptake and vertical heterogeneous soil hydraulic properties to enhance the description of water flow in thawed soil over Tibetan Plateau during warm season.
The heat source–sink term in Eq. (1) is determined by the soil water phase equilibrium estimated using the water potential freezing point depression equation as well as the available heat (Koren et al. 1999). The potential/equilibrium ice content is estimated as a function of both soil temperature and soil moisture content:
e4
where g is the acceleration of gravity (m s−2), ck is an empirical parameter that accounts for the effect of increase in specific surface of soil particles and ice–liquid water (taken as 8.0), Tf is the freezing point temperature taken as 273.15 K, ψs is the soil water potential at air entry (m), θs is the porosity (m3 m−3), and b is an empirical parameter (unitless) related to the pore-size distribution of the soil matrix. The soil type–specific hydraulic parameters (i.e., θs, ψs, and b) are obtained from the class pedotransfer function (PTF) given in Cosby et al. (1984) augmented by Zheng et al. (2015a) to include the effect of organic matter as is typical for the Tibetan soil. Specifically, the effect of organic matter on the soil water retention curve (i.e., θs, ψs, and b) is considered via the additivity hypothesis, which estimates the hydraulic parameters as a weighted combination of mineral and organic fractions (Lawrence and Slater 2008; Zeiliguer et al. 2000) as
e5a
e5b
e5c
where the ft,soc is the volumetric soil organic fraction (unitless) and the hydraulic parameters of mineral soil (i.e., θs,min, ψs,min, and bmin) are obtained from the class PTF given in Cosby et al. (1984), while the hydraulic properties of pure organic matter (i.e., θs,soc, ψs,soc, and bsoc) are derived from Letts et al. (2000). According to Zheng et al. (2015a), the estimated b values are 7.35, 6.40, and 5.20 for depths of 5, 25, and 70 cm, respectively.
The Newton-type iteration is adopted for the solution of Eq. (4) with nonzero ck values (i.e., ck > 0):
e6a
e6b
e6c
where n represents the iterative step. The usage of natural logarithm in Eq. (6b) is to speed up the convergence of iteration.
Niu and Yang (2006) suggested to set the ck value to zero, and the iteration is thus not needed for the solution of Eq. (4) with a zero ck value (i.e., ck = 0):
e7a
e7b
where θliq,p is the potential/equilibrium unfrozen/liquid soil moisture content (m3 m−3). Niu and Yang (2006) showed that Eq. (7) produces more soil ice content than does Eq. (6), and Bao et al. (2016) showed recently the validity of Eq. (7) for a Tibetan frozen soil site.
To avoid the simulation of unrealistically high values for the unfrozen/liquid soil water content at very low temperatures, a limit is set on parameter b in Eq. (4) and Eq. (6) [or Eq. (7)] when estimating ice content:
e8
where bl is an empirical parameter taken as 5.5.

b. Field site and measurements

The Maqu station is located in the source region of the Yellow River (SRYR) over the northeastern part of the Tibetan Plateau (Fig. 1), with elevations varying from 3100 to 4300 m above mean sea level. The weather is characterized by cold dry winters and rainy summers with soils that are generally frozen during cold season between November and April. Land cover in this region is dominated by alpine meadows with heights varying from 5 to 15 cm throughout the growing season. The prevailing soil types are silt loam, sandy loam, and organic soil (Dente et al. 2012; Zheng et al. 2015a).

Fig. 1.
Fig. 1.

(top left) Location of Maqu site in the SRYR in China, (top right) the micrometeorological station, and (bottom) the SMST monitoring network in the Maqu area shown on a DEM map.

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

The micrometeorological observing system at the Maqu station consisted of a 20-m planetary boundary layer (PBL) tower providing wind speed and direction, air temperature and humidity measurements at five heights above ground, and an eddy covariance (EC) system installed for measuring the turbulent heat fluxes. Instrumentations for measuring four radiation components (i.e., upward and downward shortwave and longwave radiation), air pressure, and precipitation are also deployed. A network of 20 soil moisture and soil temperature (SMST) monitoring sites is operational since 2008, of which two sites (CST01 and NST01) situated in the vicinity of the micrometeorological station are used for the analyses. The SMST profiles are automatically measured for depths of 5, 10, 20, 40, and 80 cm below the soil surface using EC-TM ECH2O probes (Decagon Devices, Inc., United States), and the root-mean-square error (RMSE) of soil moisture measurement is about 0.02 m3 m−3 via a soil type–specific calibration according to Dente et al. (2012). In addition, soil samples were collected around the two SMST sites (CST01 and NST01) to quantify the soil properties via laboratory analyses, such as soil texture (sand, clay, and silt) and organic matter content. More details on the measurements and data processing can be found in Dente et al. (2012) and Zheng et al. (2015a).

The presented investigation spans the period from 27 November 2009 [day of year (DOY) 331] to 31 March 2010 (DOY 90), and all the data collected by the micrometeorological observing system and the two SMST sites during this period are reprocessed to values with a 30-min interval. Figure 2a shows the time series of daily averaged measured precipitation and albedo, whereby the albedo is calculated as the ratio of daily averaged measured upward and downward shortwave radiation. Figure 2b presents further the daily averaged measured temperatures of air (i.e., Ta), surface (i.e., Tsfc), and 5-cm soil depth Ts5. It can be noted that the daily averaged measured temperatures are generally below 0°C before DOY 71, and the presence of precipitation (snowfall) leads to the sharp increase of albedo indicating the presence of snowpack, which is generally short lived (less than 3 days for each duration).

Fig. 2.
Fig. 2.

Daily averaged (a) precipitation and albedo and (b) temperature of air, surface, and 5-cm soil depth for the period from 27 Nov 2009 (DOY 331) to 31 Mar 2010 (DOY 90).

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

3. Measured surface energy budgets and soil freezing at the Maqu site

a. Surface radiation and energy budgets

Figure 3a shows the mean diurnal variability for the period December–March of the measured surface radiation. Each component of the surface radiation increases from December to March, and the downward shortwave radiation (i.e., S) dominates the surface radiation budgets, with peak value varying from 600 W m−2 in December to 800 W m−2 in March. The peak values of the upward shortwave radiation (i.e., S) are around 140–190 W m−2, and the surface albedo is on average about 0.23–0.24. The amplitude of the diurnal cycle of the downward longwave radiation (i.e., L) is much smaller compared to other radiation components, with an average value of 200 W m−2. The values of the upward longwave radiation L generally increase from 250 W m−2 at night to 440 W m−2 at noon.

Fig. 3.
Fig. 3.

Average diurnal cycles of December–March measured surface (a) radiation and (b) heat flux components.

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

Figure 3b presents further the average diurnal cycle of the measured surface heat fluxes, within which the net radiation Rn is calculated as the sum of incoming and outgoing shortwave and longwave radiation, that is, Rn = S + LSL, and the ground heat flux (i.e., G0) is estimated as the residual of surface energy balance, that is, G0 = RnH − LE. All surface heat fluxes also increase from December to March as a result of the Rn increase, and H is the main component of the surface energy budgets, with the peak value increasing from 135 W m−2 in December to 200 W m−2 in March. Negative values are generally found for G0 at night, implying the heat loss from the soil column. Following with the sunrise and the warming due to the increase of solar radiation, the G0 increases and reaches its maximum at noon, indicating the transport of heat into the soil column. The contribution of LE is much smaller because the freezing of liquid water constrains the evapotranspiration.

b. Soil freezing characteristics

Figures 4a and 4b show the soil freezing characteristics via plotting the measured soil temperatures with 30-min interval against corresponding measured or estimated liquid water contents for all subzero temperatures during the study period for soil depths of 5 and 25 cm, respectively. The estimated liquid soil water contents are derived via Eq. (7) with different settings of bl values [see Eq. (8)], that is, 5.5, 4.5, 4.0, and 3.5. The usage of Eq. (7) with ck = 0 instead of Eq. (6) is due to its numerical efficiency (Niu and Yang 2006), as has been previously applied to Tibetan frozen soils (Bao et al. 2016). The needed total soil water contents are estimated through linear interpolation between the liquid water contents measured before and after the freeze–thaw cycle as in Flerchinger et al. (2006).

Fig. 4.
Fig. 4.

Soil freezing characteristics determined from the measured and estimated liquid soil water vs measured soil temperature for depths of (a) 5 and (b) 25 cm.

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

As shown in Fig. 4, the estimated liquid water contents with the default bl value (i.e., bl = 5.5) adopted by current Noah LSM largely overestimate the measurements for all subzero temperatures, indicating that the default bl value is not suitable for applications to Tibetan frozen soils, and site or soil type–specific values are preferable. It can be also found from Fig. 4 that smaller bl values are more suitable, for instance, the estimated liquid water contents with bl = 3.5 and bl = 4.0 best capture the measurements for soil depths of 5 and 25 cm, respectively.

4. Assessment of Noah frozen soil parameterization

a. Experimental design

Three experiments are designed to assess the performance of Noah frozen soil parameterization with default settings and augmentations (section 2a) as well as site-specific values (section 3b). A control experiment (Ctrl) is performed first by running the Noah LSM with its default model physics. The second experiment (EXP1) contains a Noah model run with the implementation of the augmentations, including a diurnally varying roughness length for heat transfer (i.e., z0h), an asymptotic function for root water uptake, and vertical heterogeneous soil thermal and hydraulic properties all modified to better represent the Tibetan environment (Zheng et al. 2015a,b). For the third experiment (EXP2), Eq. (6) is further replaced with Eq. (7) with ck = 0 because of its numerical efficiency and suitability for Tibetan frozen soil (Bao et al. 2016; Niu and Yang 2006), and the site-specific bl values given in section 3b are also implemented, while other settings are identical to EXP1. Specifically, the value of bl is specified as 3.5 for the first soil layer, and a value of 4.0 is assigned for other soil layers.

All the numerical experiments are forced by the micrometeorological measurements collected from 27 November 2009 to 31 March 2010 at the Maqu site (section 2b), which includes downward and upward shortwave radiation, downward longwave radiation, wind speed, air temperature, relative humidity, air pressure, and precipitation. The prescribed vegetation and soil types are grassland and silt loam, respectively, and the adopted vegetation and soil parameters are identical to simulations reported in Zheng et al. (2015a). Soil moisture and temperature measurements are used to initialize each model run as well as to validate Noah simulations. For both, the measurements collected at sites CST01 and NST01 are averaged for each soil depth (e.g., 0.05, 0.10, 0.20, 0.40, and 0.80 m), and interpolated to the midpoints of the upper three model layers (i.e., 0.05, 0.25, and 0.70 m). Then, the soil moisture and temperature of the fourth layer is taken for initialization equal to the states of the third layer. The Noah simulations are validated further through comparisons of the simulated turbulent heat fluxes with measurements collected by an EC system.

b. Turbulent heat flux and soil state simulations

Figure 5 shows the mean diurnal cycle for December–March of the measured and simulated turbulent heat fluxes (H and LE) and soil temperature profiles, and Table 1 provides the corresponding RMSE computed between all the measurements and simulations with a 30-min interval for the period between 27 November 2009 (DOY 331) and 31 March 2010 (DOY 90). Figure 6 further presents the time series of the measured and simulated liquid soil water profiles with a 30-min interval, and the corresponding RMSEs are listed in Table 2. Analysis of the measured liquid soil water profiles (Fig. 6) reveals that soil water in the first layer (i.e., 5 cm) starts freezing at the beginning of study period (27 November 2009, DOY 331), and the freezing front reaches its maximum around mid-February 2010 (DOY 41). The soil ice in the first layer starts thawing at the end of February (DOY 51) and is almost totally thawed out at the end of study period (31 March 2010, DOY 90). The dates of freezing and thawing are reached at a later time for greater soil depths, for instance, the soil water in the second layer (i.e., 25 cm) starts freezing at about one week later than that of first layer.

Fig. 5.
Fig. 5.

Average diurnal cycles of December–March measured and simulated (a) sensible heat flux, (b) latent heat flux, (c) surface temperature, and soil temperature for the depths (d) 5, (e) 25, and (f) 70 cm produced by four numerical experiments performed in sections 4 and 5a.

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

Table 1.

RMSE computed between the measured and simulated sensible and latent heat fluxes and surface and soil temperature at depths of 5, 25, and 70 cm produced by all the numerical experiments with a 30-min interval for the period from 27 Nov 2009 to 31 Mar 2010.

Table 1.
Fig. 6.
Fig. 6.

Comparison of the measured and simulated liquid soil water produced by four numerical experiments performed in sections 4 and 5a for each soil layer with a 30-min interval for the period from 27 Nov 2009 (DOY 331) to 31 Mar 2010 (DOY 90): (a) 5, (b) 25, and (c) 70 cm.

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

Table 2.

RMSE computed between the measured and simulated liquid soil water at depths of 5 cm θliq5, 25 cm θliq25, and 70 cm (i.e., θliq70) produced by all the numerical experiments with a 30-min interval for the period from 27 Nov 2009 to 31 Mar 2010.

Table 2.

In its default model configuration, Noah (Ctrl) largely overestimates the daytime turbulent heat fluxes (Figs. 5a,b) and underestimates the surface temperature (Fig. 5c), which is greatly ameliorated by the EXP1 with the implementation of the augmentations such as the scheme of diurnally varying thermal roughness length for heat transfer (i.e., z0h). Identical results and explanations have been reported for the thawed soil in the Maqu site during the warm monsoon season as in Zheng et al. (2015b). In comparison to the Ctrl, the EXP1 reduces the RMSE computed between the measured and simulated H, LE, and Tsfc by about 36%, 17%, and 46%, respectively. Similar to the findings reported in section 3b, both Ctrl and EXP1 with the default bl value largely overestimate the liquid water contents (i.e., θliq) in the soil profile (Fig. 6). Consequently, less latent heat [i.e., Ilat; Eq. (1)] is released or consumed during the phase change of soil water, which explains the underestimations found for the temperature in the soil profile as seen in Figs. 5d–f.

Notably, the θliq overestimations by both Ctrl and EXP1 are significantly reduced within the EXP2 (Fig. 6) via the implementation of ck = 0 as well as site-specific bl values, because the measured θliq for depths of 5 and 25 cm during the study period are used to derive the site-specific bl values (section 3b). The EXP2 is able to capture much better the measured θliq dynamics in the soil profile, which reduces the RMSE in comparison to the Ctrl computed between the measured and simulated θliq for depths of 5, 25, and 70 cm by about 69%, 76%, and 53%, respectively. Also, improvements are noted for the simulation of soil temperature (Figs. 5d–f) because of better simulation of soil freeze–thaw transition (i.e., θliq dynamics), and thus Ilat, with RMSE reduced by about 46%, 40%, and 42% for depths of 5, 25, and 70 cm, respectively. In comparison to EXP1, EXP2 produces less liquid water (Fig. 6a) and more ice content for the surface layer that increases the surface heat conductivity. This leads to the increase in the amplitude of the diurnal ground heat flux variation and thus the decrease in the amplitude of the diurnal surface temperature [see Eq. (2), Fig. 5c] and turbulent heat flux (Figs. 5a,b) variations. It can be found that the EXP2 overestimates the nighttime surface temperature and underestimates the temperature across the soil profile (Figs. 5d–f), which will be further investigated in the following section.

5. Discussion

a. Thermal heat conductivity

1) Parameterization

The overestimation of nighttime surface temperature as noted in section 4 by the EXP2 may be caused by the overestimation of thermal heat conductivity in the soil. The κh parameterization currently adopted by the Noah LSM (see section 2a) has recently been modified to represent the Tibetan frozen soil conditions by Bao et al. (2016):
e9a
e9b
e9c
e9d
where κdry, κwet, and κsat are the heat conductivity of dry, wet, and saturated soil (W m−1 K−1), respectively; κice is the heat conductivity of ice (taken as 2.2 W m−1 K−1); κw is the heat conductivity of water (taken as 0.57 W m−1 K−1); κqtz is the heat conductivity of quartz (taken as 7.7 W m−1 K−1); κo is the heat conductivity of other soil particles (taken as 2.0 W m−1 K−1); qtz is the volumetric quartz fraction (unitless); and ρb is the bulk density of dry soil (kg m−3).

2) Surface heat flux and soil state simulations

An additional numerical experiment (EXPS1) is carried out to assess the sensitivity of model results when the default κh parameterization is replaced with the one by Bao et al. (2016) [Eqs. (9a)(9d)], whereby other settings are taken as in EXP2. The average diurnal turbulent heat flux and soil temperature cycle as well as the time series of liquid soil water dynamics produced by EXPS1 are added to Figs. 5 and 6, respectively. The corresponding error statistics are added to Tables 1 and 2 as well.

Notably, the overestimation of nighttime surface temperature is resolved with the implementation of new κh parameterization (Fig. 5c) that reduces the heat conductivity and thus ground heat flux, and the underestimation of the temperature in the deeper soil layers (e.g., soil temperature at 70-cm depth Ts70; Fig. 5f) is largely reduced because less heat is released from the soil column. In comparison to EXP2, this reduces the RMSE computed between the measured and simulated surface temperature, soil temperature at 25-cm depth Ts25, and soil temperature at 70-cm depth by about 21%, 13%, and 30%, respectively (Table 1). The EXPS1-simulated liquid soil water dynamics are comparable to those produced by the EXP2 (Fig. 6, Table 2), while more liquid water is generated for deeper layers (e.g., liquid soil water at 70-cm depth θliq70; Fig. 5f) as the temperature is higher [see Eq. (7b)]. It should be noted that the EXPS1 does not resolve the deficiency in simulating Ts5 (Fig. 5d), which will be addressed in the following section.

b. Latent heat of fusion

1) Parameterizations

The underestimation of soil temperature profiles as noted in sections 4 and 5a may be related to the poor simulation of latent heat (i.e., Ilat) released or consumed during the phase change of soil water. In the Noah LSM, Ilat is represented as a source–sink term in the thermal diffusion equation [see Eq. (1)], whereby the whole equation is solved using the fully implicit Crank–Nicholson scheme. In other LSMs, there is an alternative numerical algorithm within which the Ilat is ignored at first while solving the thermal diffusion equation, then the phase change is evaluated, and the soil temperature as well as the ratio of liquid water and ice contents is readjusted by energy conservation during the phase change. Such treatment of Ilat is commonly employed in LSMs, such as Noah-MP (Niu et al. 2011); Community Land Model (CLM; Oleson et al. 2013); Interactions between Soil, Biosphere, and Atmosphere (ISBA) model (Decharme et al. 2011; Masson et al. 2013); and a modified Simple Biosphere Model (Bao et al. 2016) because of its numerical efficiency. For instance, the treatment of Ilat in Noah-MP (Niu et al. 2011) is as follows:
e10a
e10b
e10c
e10d
e10e
where n represents the time step, Tf is the freezing point temperature specified as 273.15 K, θliq,p is the potential/maximum liquid soil water content estimated using Eq. (7b), and Hm represents the excess or deficit of energy during phase change of soil water.
In reality, the freezing point temperature should not be a constant, which can be alternatively estimated using the Gibbs free-energy concept as (Masson et al. 2013; Zhang et al. 2007)
e11
In addition, a parameter ε that represents the phase change efficiency can be introduced into Eq. (10d), which is similar to the method used in the ISBA model (Masson et al. 2013):
e12a
e12b

The above equations assume that the freezing rate (release of latent energy) increases when less liquid water content is present in the soil. It should be also noted that the parameterization of ε is derived empirically via the trial and error method through comparison of the simulations with corresponding measurements.

2) Impact on surface heat flux and soil state simulations

To investigate the performance of these aforementioned alternative treatments of Ilat for their abilities to simulate the soil temperature profiles, three additional numerical experiments are carried out. For the first experiment (EXPS2), the default parameterization of Ilat in the Noah LSM [Eq. (1)] is replaced by the alternative algorithm as described by Eqs. (10a)(10e), while other settings are taken from EXPS1. In the second experiment (EXPS3), Noah is run with the same options as EXPS2 but the freezing point temperature is calculated by Eq. (11) instead of using the constant value 273.15 K. The parameter ε representing the phase change efficiency as described in Eqs. (12a) and (12b) is included in the third experiment (EXPS4), and other settings are identical to EXPS3.

The RMSE statistics computed between the measured and simulated turbulent heat fluxes and soil temperature produced by the three additional numerical experiments are listed in Table 1. It shows that all the three additional experiments produce comparable results for turbulent heat fluxes and surface temperature as the EXP2 and EXPS1, indicating that the implementation of these alternative treatments of Ilat has minor impact on the simulated land–atmosphere exchanges of heat and mass that are mostly controlled by the parameterization of the diurnally varying roughness length for heat transfer (section 4). In support of further analyses, Fig. 7 presents the mean diurnal variability of the measured and simulated surface temperature and soil temperature for depths of 5 and 70 cm produced with the three additional experiments. The results produced by the EXP2 are also shown for comparison purposes. Figure 8 shows further the time series of the measured and simulated liquid soil water profiles, and the corresponding RMSE statistics are added to Table 2. Again, it can be noted that the differences between the mean diurnal cycle of surface temperature simulated with these experiments are small (Fig. 7a).

Fig. 7.
Fig. 7.

Average diurnal cycles of December–March measured and simulated (a) surface temperature and soil temperature for the depths (b) 5 and (c) 70 cm produced by numerical experiments performed in section 5b.

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

Fig. 8.
Fig. 8.

Comparison of the measured and simulated liquid soil water produced by numerical experiments performed in section 5b for each soil layer with a 30-min interval for the period from 27 Nov 2009 (DOY 331) to 31 Mar 2010 (DOY 90): (a) 5, (b) 25, and (c) 70 cm.

Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0199.1

In comparison to the EXP2 and EXPS1, the EXPS2 produces less latent energy during water phase change that leads to the increase in the amplitude of diurnal temperature variation at first soil layer (Fig. 7b) as well as the increase of temperature at deeper layer (Fig. 7c). The underestimation of nighttime temperature in the first soil layer noted for the EXP2 during soil freezing (December–February) is further degraded by the EXPS2, while the soil temperature in deeper layers is improved because of heat conduction from the surface to the deeper layers. Liquid soil water simulations are degraded by the EXPS2 (Fig. 8), and an RMSE increase is noted in Table 2 for the θliq simulations. After replacing the constant Tf with the one estimated by Eq. (11) as in EXPS3, the θliq simulations are improved (Fig. 8), and the corresponding RMSE statistics are reduced in comparison to the EXPS2 by about 33%, 46%, and 17% for depths of 5, 25, and 70 cm, respectively. Improvement is also noted in the simulation of the soil temperature at first layer (Table 1, Fig. 7b), although the overall temperatures across the soil profile are still underestimated.

The underestimation of the temperature in the soil profile is greatly improved by EXPS4 (Figs. 7b,c), which further implements the parameter ε representing the phase change efficiency. EXPS4 is able to capture the mean diurnal cycle of measured soil temperature in the first layer much better than other numerical experiments, and significant improvement is also achieved for the temperature simulation of deeper soil layers. Notably, the RMSE computed between the measured and simulated soil temperature for depths of 5, 25, and 70 cm is reduced by EXPS4 in comparison to EXPS3 about 48%, 55%, and 31%, respectively (Table 1). It can be thus inferred that the deficiency of the Noah LSM in simulating soil temperature may be related to the inappropriate treatment of phase change efficiency during soil freezing when less liquid water is present in the soil. EXPS4-simulated θliq dynamics are comparable to those produced by EXP2 and EXPS3 for the top two layers (Figs. 8a,b, Table 2), while the overestimation of θliq in a deeper layer (e.g., θliq70) noted for EXPS1 (Fig. 6c) is further amplified in EXPS4 (Fig. 8c) because the temperature is higher. It should be noted that both θliq and Ts measurements are collected at specific depths and then linearly interpolated to the midpoints of model soil layers, while the Noah simulations physically represent the layer-averaged values. Specifically, the measured θliq70 and Ts70 are interpolated from measurements collected at 40- and 80-cm depths, and thus, the difference in freeze–thaw state of each depth may induce interpolation error since the maximum freezing depth is around 80 cm (see Fig. 7c). On the other hand, the simulated θliq70 and Ts70 represent the averaged values of the third model layer between 40 and 100 cm. The mismatch of the depths at which the measurements were taken and for the simulations are representative, and the interpolation may explain why the Ts70 is better simulated by both EXPS1 and EXPS4, while the θliq70 simulation is degraded in comparison to EXP2. Similar findings have also been reported in Xia et al. (2013).

6. Conclusions

In this paper, we investigate and improve the performance of the Noah LSM for simulating coupled water and heat flow in frozen soil over a Tibetan meadow ecosystem. A comprehensive dataset including in situ micrometeorological and soil moisture–temperature profile measurements has been collected for the period between 27 November 2009 and 31 March 2010, and analyses of the measurements reveal that the sensible heat flux H dominates the surface energy budget. It is also shown that the measured soil freezing characteristics are better captured by 1) modifying the parameter bl that constrains the shape parameter of soil water retention curve to avoid the simulation of unrealistically high values for the liquid soil water content at very low temperature and 2) setting the parameter ck that accounts for the effect of increase in specific surface of soil particles and ice–liquid water to zero.

Three numerical experiments are carried out to investigate the performance of Noah frozen soil parameterization with 1) its default model physics (Ctrl) and 2) implementation of augmentations (EXP1), including a diurnally varying roughness length for heat transfer z0h, an asymptotic function for root water uptake, and vertical heterogeneous soil thermal and hydraulic properties. The third experiment (EXP2) further adopts the ck = 0 and site-specific bl values. The default Noah LSM (Ctrl) largely overestimates the daytime turbulent sensible and latent (LE) heat fluxes and underestimates the surface temperature Tsfc, which is greatly resolved by EXP1 with the implementation of the augmentations such as the scheme of diurnal thermal roughness length for heat transfer z0h as also reported in Zheng et al. (2015b) for the warm monsoon season. In comparison to the Ctrl, the EXP1 reduces the RMSE computed between the measured and simulated H, LE, and Tsfc by about 36%, 17%, and 46%, respectively. Both Ctrl and EXP1 largely overestimate the liquid water contents θliq across the soil profile, which is significantly improved by EXP2 via further implementing ck = 0 and site-specific bl values. The EXP2 reduces the RMSE in comparison to the Ctrl computed between the measured and simulated θliq for depths of 5, 25, and 70 cm by about 69%, 76%, and 53%, respectively. Further, it is found that all three experiments underestimate the temperature across the soil profile during soil freezing (December–February) because of the poor simulation of latent heat Ilat released or consumed during the phase change of soil water.

Four additional numerical experiments are conducted to investigate the sensitivity of model results to alternative treatments of thermal heat conductivity κh and Ilat. The results indicate that the overestimation of nighttime Tsfc by the Noah LSM is associated with the overestimation of κh values, and the underestimation of soil temperature profiles may be related to the inappropriate treatment of phase change efficiency that accounts for changing freezing rate with varying liquid water contents in the soil. The mismatching of represented depth between measurements and simulations as well as the interpolation error of measurements may explain why better soil temperature simulation at a deep layer followed with inappropriate θliq simulation. Additional work is, however, still needed to investigate other physical processes such as the vapor movement and its phase change as well as convective heat transport induced with water flow. A better understanding of the frozen soil processes over the Tibetan Plateau will inevitably enhance our ability to predict the impact of climatic change on the high-altitude ecosystems and regional hydrology.

Acknowledgments

This study was supported by funding from the Netherlands Organization for Scientific Research (Project ALW-GO/14-29), the National Natural Science Foundation of China (Grants 41405079 and 41530529), and the Key Research Program of the Chinese Academy of Sciences (Grant KZZD-EW-13). The measurements used in this study were provided by Zoige Plateau Wetland Ecosystem Research Station of CAREERI/CAS. For data access, please contact Jun Wen (jwen@lzb.ac.cn).

REFERENCES

  • Bao, H., T. Koike, K. Yang, L. Wang, M. Shrestha, and P. Lawford, 2016: Development of an enthalpy-based frozen soil model and its validation in a cold region in China. J. Geophys. Res. Atmos., 121, 52595280, doi:10.1002/2015JD024451.

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