Improved simulation of carbon and water fluxes by assimilating multi-layer soil temperature and moisture into process-based biogeochemical model

Study area

The studied forest flux site is located in the National Natural Conservation Park of Changbai Mountains of Jilin Province, China (42°24′9″N, 128°05′45″E), as shown in Fig. 1. The climate in the Changbai Mountains is temperate and continental, and is influenced by the monsoon. Its annual average precipitation is approximately 713 mm, and precipitation occurs mainly over June to August. The annual average temperature is 3 .6°C. The terrain surrounding the forest flux site is flat, with an average elevation of 738 m. According to the average seasonal patterns shown in Fig. 2, the strong seasonal variability experience at this site provides an opportunity to evaluate the performance of the proposed data assimilation under varying climatic and biophysical conditions. Thus application of this method to other forest ecosystems can be considered. The forest land is covered predominantly with temperate broadleaf Korean pine forest consisting mainly of Pinus koraiensis, Tilia amurensis and Fraxinus mandshurica (Wang et al. 2005).

Data

An EC system was set up on a 62-m high tower, and sensors were fixed on a boom located at a height of 40 m that extended 3 m upwind of the tower to minimize flow distortion (Wang et al. 2005). One sensor was used to gauge the carbon dioxide (CO₂) concentration profile and the other served to record routine meteorological observations (Wu et al. 2005). Meteorological data were measured continuously from 2003 to 2007 using an open path EC system at the forest flux tower. The dataset included air temperature (Temp), relative humidity (RH) (Model HMP45C, Campbell Scientific Inc., Utah, USA), precipitation (Precip) (Model 52,203, Rm Young, Traverse City, Michigan, USA), wind speed, and direction. Photosynthesis active radiation (PAR) was measured with a quantum sensor (Model LI190SB, LI-COR Inc., Lincoln, Nebraska, USA). Other meteorological factors, including vapor pressure deficit (VPD), incoming shortwave radiation (Srad), and day-length (from sunrise to sunset), were calculated using the MTCLIM 4.3 based on measured daily maximum and minimum temperatures and precipitation (Running et al. 1987; Thornton and Running 1999).

The observed soil variables included three-layer temperature and moisture data at depths of 5, 20 and 40 cm, respectively. At the Changbai Mountains forest flux site, the top soil layer (5 cm) is dominated by litter fall, humic substances distribute between 5 and 20 cm depths, and an albic soil layer distributes between 20 and 40 cm depths. Soil water upward and downward movements occur mainly among the three active layers because of the poor penetration of the albic soil layer. The soil layer below 40 cm is dominated by loess, the distribution of vegetation roots over the Changbai Mountains is negligible (Wang and Pei 2002; Zhao et al. 2013). Therefore, three layers of soil moisture were collected using a Micrologger for data acquisition (CR23X-TD, Campbell Scientific Inc., Utah, USA) at a frequency of 30 min at the forest flux site. Then, these 30-min data were averaged on a daily basis.

Water vapor densities and CO₂ were measured using an open path system from 2003 onwards at the forest flux site. The open path EC system contained a three-dimensional sonic anemometer (CAST3, Campbell Scientific Inc., Logan, Utah, USA) and a fast-responding open path infrared gas analyzer (LI-7500, LI-COR Inc., Lincoln, Nebraska, USA). The collection frequencies for raw flux data and climate data were 10 and 0.5 Hz, respectively. The 30-min averaged values of each variable were calculated. A series of preprocessing steps was conducted, including outlier removal, coordinate rotation, time lag analysis, frequency response calibration, and Webb–Pearman–Leuning (WPL) correction (Wang et al. 2005). Half-hourly net CO₂ exchange and energy fluxes including latent and sensible heat fluxes, were calculated using EdiRe software. Specifically, to estimate the night-time net CO₂ exchange, the net CO₂ exchange was regressed with the air or soil temperature using an exponential function. The built model was then used to calculate the ER. Then, the NEE and ER were summed to estimate the ecosystem gross primary productivity (GPP). The daily flux of ET can be expressed in equivalent units of both energy (W∙m^− 2) and water (kg∙m^− 2 or mm∙s^− 1). The conversion from latent energy flux (LE, W∙m^− 2) to ET (mm∙s^− 1) is calculated as ET = LE/λ, where λ is the latent heat of evaporation (Mu et al. 2007, 2009).

EC measurements of carbon and heat fluxes and observations of meteorological and soil data during 2003 to 2007 were thus collected at the Changbai Mountains forest flux site. Additionally, soil texture data were collected from the soil texture map of China with a spatial resolution of 1 km, which was downloaded from the Resource and Environment Data Cloud Platform website. The time series LAI products from 2003 to 2007, with a spatial resolution of 1 km, were provided by the Center for Global Change Data Processing and Analysis of Beijing Normal University. Digital elevation model (DEM) data were obtained from Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM). Latitude and topography were calculated using the DEM at the forest site.

Biome-BGC MuSo model

The Biome-BGC Multi-layer Soil Module version 4.1 (Biome-BGC MuSo v4.1) was developed to improve its ability to simulate carbon and water cycles within terrestrial ecosystems. Biome-BGC MuSo v4.1 improved the multi-layer soil module, and introduced the management and phenological modules. These three modules are independent of each other in the model. In this study, the management module was deactivated during the spinup and normal simulation for the forest. Hence, the logical values of planting, thinning, mowing, grazing, harvesting, ploughing, fertilizing, and irrigation were set to 0 (flag = 0). The thicknesses of the layers from the surface to the bottom were 5, 15, and 20 cm. Thus, the first, second, and third layers were located at depths of 0–5, 5–20 and 20–40 cm, respectively.

This model runs with a daily time step and requires four input files for execution. The first file is the initialization file containing basic site-related information (e. g., elevation, soil texture, CO₂ concentration, and N-decomposition data). The second file is the daily meteorological data file and includes daily air maximum temperature, minimum temperature, precipitation, VPD, solar radiation and day length. The third file is the ecophysiological file and includes the ecophysiological parameters (e.g., ratio of leaf carbon to nitrogen, fine roots and coarse roots, fraction of leaf N in the Rubisco catalytic enzyme, and the maximum stomatal conductance). In this study, the ecophysiological parameter values in Biome-BGC MuSo were determined by the optimized results during the model run. The last input file is a special restart file, which is the output of the spinup and provides inputs for running the model under normal situations. The spinup phase was first performed using the meteorology covering the period 1981 to 2002 obtained from the Data Center of Chinese Meteorological Bureau, and the output endpoint is the input for normal simulation covering the period 2003 to 2007.

In the carbon flux module of the Biome-BGC MuSo model, GPP is calculated using Farquhar’s photosynthesis routine and data on the catalytic enzyme Rubisco in relation to temperature (Farquhar et al. 1980). Photosynthesis is the only process whereby the model can provide carbon into all of the pools. Root maintenance respiration was calculated layer-by-layer using the soil water content (SWC) and soil temperature of each active layer (which differs from the averaged soil water status or soil temperature of the whole soil in the original Biome-BGC model). Growth respiration (GR) in the model was considered as the proportion of all new tissue growth, which was 30% (Larcher 2003).

The net primary productivity (NPP) was calculated using GPP, MR, and GR in the model. The carbon storage of the ecosystem originates from the balance between NPP and heterotrophic respiration (HR), which are regulated by decomposition activities. All litter and soil pools decompose through HR. NEE represents the difference between NPP and HR.

The soil flux module generally describes the decomposition of dead plant material, or litter, in addition to SOM, N mineralization, and N balance (Schwalm et al. 2015). Soil hydrology has significant effects on many soil processes (e.g., SOM, N mineralization, and soil evaporation), and thereby on the carbon and water cycles. Therefore, accurate description of soil hydrology is essential. In the original Biome-BGC model, the soil layer works as a “bucket”, and the soil water flux considers only canopy, interception, snowmelt, outflow, and soil evaporation. Therefore, runoff, percolation, diffusion, pond water formation, and transpiration were added into Biome-BGC MuSo.

Surface runoff occurs when the rate of rainfall exceeds the rate of water infiltrating the soil. Runoff simulation was conducted using the semi-empirical method (Williams 1991). Under the conditions of intensive rainfall, when not all of the precipitation can infiltrate, pond water forms the surface. In Biome-BGC MuSo, evaporation of pond water is assumed to be equal to potential soil evaporation.

The soil temperature of each active layer was calculated using two methods. The first method involved logarithmic downward dampening of temperature fluctuations within the soil (Zheng et al. 1993). In this method, the soil surface temperature is determined by air temperature changes considering the insulating effect of snowcover and the shading effect of vegetation. The temperature of intermediate soil layers is calculated under the conditions of linear temperature change between soil layer depths of 0 cm and 3 m. The soil temperature below 3 m in the model is assumed to be the mean annual air temperature. The other method, uses DSSAT/4 M (Sándor and Fodor 2012) to empirically calculate the soil temperature. Because the former method is preferred (Zheng et al. 1993), we selected the same in this study and compared the results with measurements obtained at the Changbai Mountains forest flux site.

Ensemble Kalman filter

Iterations are established when running the algorithm from steps (1) to (5).

Data assimilation scheme

In this study, the assimilations of soil temperature and moisture were implemented using Eq. 10, with H equal to (1 1 1 1)^T. Once the daily soil temperature and moisture data were available, the model run was interrupted, EnKF updated the Biome-BGC MuSo state variables, and the simulation was re-initialized with the updated states and re-run until the next update was available. All the simulations were conducted from 2003 to 2007. An uncertainty of 10% for model parameters was considered and perturbed based on the Gaussian distribution (White et al. 2000). Sequential assimilation of observed data can be used to correct some uncertainty involved in model parameters (Das et al. 2008). The ensemble members were generated by randomly sampling model parameter combinations from the perturbed arrays (Ines et al. 2013). Two hundred ensemble members were selected to optimize the EnKF framework’s performance in terms of accuracy and computational time. Errors of the soil observations were obtained from the literature (Wang and Pei 2002).

Soil moisture was calculated using the volumetric water content (VWC), soil layer thickness, and water density in Biome-BGC MuSo. Assimilation of the daily SWC in the spinup is converted into the VWC array, which in turn provides reliable SWC during the model simulation phase through the restart file.

Once the daily observations were assimilated into the model, the initialization processes were implemented, and the soil variables were corrected on a daily basis throughout model runtime. This study compared normal simulations using calibrated Biome-BGC and Biome-BGC MuSo and simulations that assimilated soil temperature and moisture. All simulations were conducted for the period 2003–2007.

Evaluation and analysis of modeled estimates

In these equations, X_obs is the observation made at the forest flux site; X_mod is the simulated carbon or water flux, and i is the day of the year. t refers to the total number of days or day windows within one year.

We also analyzed the data assimilation performance of by comparing the difference (ΔRMSE) between RMSE_DA and RMSE_MuSo. A moving window of 15 days was used here. A positive ΔRMSE indicates that the accuracy of the model simulation was improved by our proposed data assimilation stratagem and vice versa. We examined the relationships of ΔRMSE with varying climatic forcings including Temp, Precip, and PAR and three biophysical factors such as soil temperature, soil moisture, and LAI. Therefore, this analysis addressed the situations showing the most significant improvements after assimilating soil temperature and moisture, thereby providing insights to the application of the proposed method to other forest ecosystems.

Evaluating modeled ET with EC measurements

Overall, the original Biome-BGC model underestimated forest ET as shown in Fig. 4a, and the annual average value of 313.04 mm·yr.^− 1 is obviously lower than that of ET_EC, at 448.52 mm·yr.^− 1. The forest ecosystem never experienced soil saturation as per Biome-BGC; this condition is incompatible with the actual conditions in winter and early spring, when deep soil usually converts to permafrost in the Changbai Mountains. According to the coefficient analysis and T-test (Fig. 4b, c, d), ET in Biome-BGC MuSo was improvement, particularly in the growing seasons, with R² = 0.72, RMSE = 0.90 mm·d^− 1, and p < 0.01, compared with the Biome-BGC values of R² = 0.68, RMSE = 1.15 mm·d^− 1, and p < 0.01. Stomatal closure occurred as a result of anoxic conditions, which was not considered in the original model; heavy precipitation usually occurs in the Changbai Mountains during summer. The Biome-BGC MuSo model characterized this aspect. After the optimal soil moisture content was attained, the soil stress index decreased owing to saturation soil stress, which is a characteristic of anoxic soil. Furthermore, with the assimilation of observed soil moisture, the simulation of soil transpiration improved, which promoted the enhancement of ET compared with the EC measurements. In this case, the variables were R² = 0.81, RMSE = 0.70 mm·d^− 1, and p < 0.01, and the annual average ET, 450.48 mm·yr.^− 1, was close to ET_EC (Table 1).

ET	Annual average (mm·yr.− 1)	Spring average (mm·yr.− 1)	Summer average (mm·yr.− 1)	Autumn average (mm·yr.− 1)	Winter average (mm·yr.− 1)
EC	448.52	126.13	304.43	111.02	17.58
Cali	313.04	55.78	153.09	91.09	13.08
MuSo	381.41	71.46	212.56	86.72	10.67
DA	450.48	85.05	245.31	106.39	13.74

Evaluating modeled carbon fluxes with EC flux

The daily EC measurements obtained during 2003–2007 were used to evaluate the simulated fluxes of the Changbai Mountains forest flux site. Compared with the daily EC measurements, the calibrated Biome-BGC (ER_Cali) significantly overestimated the ER (Fig. 5); the annual average ER was 1868.55 gC·m^− 2·yr.^− 1, which is significantly higher than ER_EC, at 1035.55 gC·m^− 2·yr.^− 1 (Table 2). Furthermore, the overestimation was particularly prominent in summer, and the average value of ER_Cali, at 1004.88 gC·m^− 2·yr.^− 1, was nearly twice that of ER_EC, at 578.43 gC·m^− 2·yr.^− 1. In the original model, SOM decomposition was affected by soil temperature, moisture, soil carbon and N content, whereas root maintenance respiration was influenced by soil temperature as well as the carbon and N content. In Biome-BGC MuSo, the soil temperature and moisture affect HR and are calculated layer-by-layer using soil temperature and the SWC of each active layer. Accordingly, the estimate for ecosystem respiration (ER_MuSo), at R² = 0.81, RMSE = 2.50 gC·m^− 2·d^− 1, and p < 0.01, showed improvement over ER_Cali, at R² = 0.78, RMSE = 3.24 gC·m^− 2·d^− 1, and p < 0.01. Along with the inputs of observed daily soil temperature and moisture, the variations in ER_DA were constrained at both seasonal and annual scales. In particular, the value in the summers was at 850.30 gC·m^− 2·yr.^− 1, and the annual value was 1467.05 gC·m^− 2·yr.^− 1. This led to improvements in the respiration estimates, at R² = 0.85, RMSE = 1.97 gC·m^− 2·d^− 1, and p < 0.01 over the ER_MuSo.

ER	Annual average (gC·m−2·yr.−1)	Spring average (gC·m− 2·yr.− 1)	Summer average (gC·m− 2·yr.− 1)	Autumn average (gC·m− 2·yr.− 1)	Winter average (gC·m− 2·yr.− 1)
EC	1035.55	148.48	578.43	255.73	52.92
Cali	1868.55	346.94	1004.88	426.59	90.14
MuSo	1613.73	222.39	925.59	362.09	103.66
DA	1467.05	200.71	850.30	332.64	83.41

According to the EC measurement, the forest site served as a carbon sink in 2003 and 2004, with average total NEE values in winter of 9.76 gC·m^− 2·yr.^− 1 and 2.13 gC·m^− 2·yr.^− 1, respectively. This result indicates that photosynthesis exceeded the vegetation respiration under low-temperature conditions. The three modes captured the daily patterns in NEE, as indicated by the EC measurements. The simulated carbon exchange with the atmosphere derived from the calibrated Biome-BGC (NEE_Cali), Biome-BGC MuSo (NEE_MuSo), and assimilated Biome-BGC MuSo (NEE_DA) models were evaluated against EC measurements (Fig. 6). In general, NEE_Cali, NEE_MuSo and NEE_DA captured the same seasonal pattern for the carbon sink and source at this forest site (Fig. 6a). According to the R² and T-test results shown in Fig. 6b–d, NEE_DA agreed the best with EC flux measurements, with R² = 0.70, RMSE = 1.16 gC·m^− 2·d^− 1, and p < 0.05, followed by NEE_MuSo and NEE_Cali, at R² = 0.67 and 0.64, RMSE = 1.23 gC·m^− 2·d^− 1 and 3.34 gC·m^− 2·d^− 1, and p < 0.05 and < 0.01, respectively.

The improved estimates in NEE_MuSo are attributed to the advancements in multi-layer simulation, and those in NEE_DA resulted in an improvement in soil respiration optimized by the soil temperature and water content for each given soil layer. The assimilation of daily multi-layer soil temperature and moisture data into Biome-BGC MuSo facilitated the daily running of the model by correcting it in real time.

Analysis of climatic and biophysical factors

Figures 7 and 8 provide three-dimensional graphs for ΔRMSE, and the averaged climatic and biophysical factors with a window length (WL) of 15-d. Most of the ΔRMSE_ET and ΔRMSE_ER values were positive, which illustrated that the assimilation promoted the performances of ER and ET, even under extreme climate conditions of low air temperature and PAR and little precipitation. However, even under suitable climatic conditions, negative values of ΔRMSE_NEE occurred frequently, which demonstrates that the performances of NEE were synthetically affected by aboveground and underground ecological processes.

As shown in Fig. 8, the high values of ΔRMSE are related to suitable soil temperature and sufficient water conditions. This finding also proves a direct relationship between soil temperature and ER and between soil moisture and ET. LAI is an important biophysical parameter; its high value contributed to improvement of the assimilation scheme. This assimilation strategy appeared to be more suitable for a densely forest area. However, the effects of soil temperature, soil moisture, and LAI on ΔRMSE_NEE were not significant.