The study was conducted at Yanchi Research Station of Beijing Forestry University, Ningxia, northwest China (37∘42′31′′ N, 107∘13′37′′ E; 1550 m a.s.l.). The station is located at the southern edge of the Mu Us desert in the transition between the arid and semi-arid climatic zones. Based on 51 years of data (1954–2004) from the meteorological station at Yanchi, the mean annual air temperature at the station was 8.1 ∘C and the mean annual total precipitation (PPT, mm) was 292 mm (ranging between 250 and 350 mm), 63 % of which fell in late summer (i.e., July–September; Wang et al., 2014; Jia et al., 2014). Annual potential evaporation was on average 5.5 kg m-2 d-1 (Gong et al., 2016). The soil at the research station was of a sandy type, with a bulk density of 1.6 g cm-3. The total soil porosity within 0–2 and 5–25 cm depths was 50 and 38 %, respectively. Soil organic matter, soil nitrogen, and pH were 0.21–2.14 g kg-1, 0.08–2.10, and 7.76–9.08, respectively (Wang et al., 2014; Jia et al, 2014). The vegetation was regenerated from aerial seeding applied in 1998 and is currently dominated by a semi-shrub species cover of Artemisia ordosica, averaging about 50 cm tall with a canopy size of about 80 cm × 60 cm (for additional site description, consult Jia et al., 2014, and Wang et al., 2014, 2015).

Two permanent polyvinyl chloride soil collars were initially installed on a small fixed sand dune in March 2012. Collar dimensions were 20.3 cm in diameter and 10 cm in height, with 7 cm inserted into the soil. One collar was set on bare land with an opaque chamber (LI-8100-104, Nebraska, USA) and the other over an Artemisia ordosica plant (∼ 10 cm tall) with a transparent chamber (LI-8100-104C). Soil respiration (µmol CO2 m-2 s-1) was directly estimated from CO2-flux measurements obtained with the opaque-chamber system. Photosynthetic rates (µmol CO2 m-2 s-1) of the selected plants were determined as the difference in CO2 fluxes obtained with the transparent and opaque chambers.

Continuous measurements of CO2 fluxes (µmol CO2 m-2 s-1) were made in situ with a Li-8100 CO2 gas analyzer and a LI-8150 multiplexer (LI-COR, Nebraska, USA) connected to each chamber. Instrument maintenance was carried out bi-weekly during the growing season, including removing plant regrowth in the opaque-chamber installation and cleaning to avoid blackout conditions associated with the transparent chamber. Measurement time for each chamber was 3 min and 15 s, including a 30-second pre-purge, 45-second post-purge, and 2 min measurement period.

Hourly soil temperature (Ts, ∘C) and volumetric SWC (m3 m-3) at a 10 cm depth were measured simultaneously about 10 cm from the chambers using a LI-8150-203 temperature and ECH2O soil-moisture sensor (LI-COR, Nebraska, USA; see Wang et al., 2014). Other environmental variables were recorded every half hour using sensors mounted on a 6 m tall eddy-covariance tower approximately 800 m from our soil CO2-flux measurement site. Air temperature (Ta, ∘C) was measured with a thermohygrometer (HMP155A, Vaisala, Finland). Soil-surface temperature (Tsurf, ∘C) was measured with an infrared-emission sensor (model SI-111, Campbell Scientific Inc., USA). Incident photosynthetically active radiation (PAR) was measured with a light-quantum sensor (PAR-LITE, Kipp and Zonen, the Netherlands) and PPT, with three tipping-bucket rain gages (model TE525MM, Campbell Scientific Inc., USA) placed 50 m from the tower (see Jia et al., 2014).

In this study, CO2-flux measurements were screened by means of limit checking; i.e., hourly CO2-flux data < -30 or > 15 µmol CO2 m-2 s-1 were considered to be anomalous as a result of, for instance, gas leakage or plant damage by insects and removed from the dataset (Wang et al., 2014, 2015). After limit checking, hourly CO2 fluxes greater than three times the standard deviation from the calculated mean of 5 days' worth of flux data were likewise removed. Quality control and instrument failure together resulted in 5 % loss of hourly fluxes for all chambers, 4 % for temperatures, and 8 % for SWC (Fig. 1). Differences in mean annual Ts and SWC between the two chambers were 0.01 ∘C and 0.003 m3 m-3, respectively.

The Q10 function (e.g., Eq. 1) was used here to describe the response of Rs to temperature. Earlier studies have shown strong correlation between basal rate of Rs and photosynthesis (Irvine et al., 2005; Sampson et al., 2007). Response of Rs to changes in photosynthesis was, in turn, characterized as a linear function (Eq. 2). Interaction between photosynthesis and temperature on Rs was conveyed through Eq. (3). The instantaneous relative importance (RI) of photosynthesis and temperature on Rs over the growing season was calculated with a correlation-based ratio (see Eq. 4). The importance of photosynthesis on Rs increases with a corresponding increase in RI: Rs=R10×Q10(T-10)/10,Rs=a×P+b,Rs=(a×P+b)×c(T-10)/10,RI=ρpρt, where R10 is the respiration at 10 ∘C; Q10 is the temperature sensitivity of respiration; T is temperature; Pis photosynthesis (µmol CO2 m-2 s-1); a, b, and c are regression coefficients; and ρp and ρt are the correlation coefficients between photosynthesis and Rs and temperature and Rs, respectively.

Pearson correlation analysis was used to calculate the correlation coefficient between temperature or photosynthesis and Rs. Cross-correlation analysis was used to estimate hysteresis in the relationship between temperature and Rs and photosynthesis and Rs. We used root-mean-square error (RMSE) and the coefficient of determination (R2) as criteria in evaluating function performance. To evaluate seasonal variation in diel hysteresis, the mean monthly daily cycles of Rs, Ta, Tsurf, Ts, and photosynthesis were generated by averaging their hourly means at a given hour over a particular month (Table 1). Exponential and linear regression was used to evaluate the influence of SWC on the control of photosynthesis on temperature–Rs hysteresis. Likewise, influences of SWC on diel hysteresis was examined during a wet month with high rainfall and adequate SWC (July, PPT = 117.9 mm) and a dry month with low rainfall and inadequate SWC (August, PPT = 10.9 mm; Wang et al., 2014). In order to evaluate the influence of photosynthesis on diel hysteresis in the temperature–Rs relationship, we compared the time lag (in hours) between measured and modeled Rs by means of Eqs. (1) through (3) with a 1-day moving window and a 1-day time step over the growing season (April to October). Modeled Rs was calculated using the fitted parameters of each function and the measured hourly Tsurf and photosynthesis for each day. All statistical analyses were performed in MATLAB, with a significance level of 0.05 (R2010b, Mathworks Inc., Natick, MA, USA).

Incident photosynthetically active radiation, Ta, Tsurf, and Ts exhibited distinctive daily patterns over the year (Fig. 1a–d), peaking at ∼ 12:00 (local time, LT), ∼ 16:00, ∼ 14:00, and ∼ 17:00, respectively (Fig. 1a–d). Unlike the environmental factors, daily patterns in Rs remained constant over the non-growing part of the year, peaking at 11:00–13:00, and highly variable during the growing season of the year (April to October), peaking between 10:00 and 16:00 (Fig. 1f). Similar to Rs during the growing season, diel patterns of photosynthesis were also highly variable, peaking between 10:00 and 16:00 (Fig. 1e).

Diel patterns of monthly mean Rs were similar to those of Tsurf during the wet month and similar to those of photosynthesis during the dry month (Fig. 2g, h). During the wet month (July), monthly mean diel Rs was out of phase with photosynthesis, but in phase with Tsurf (Fig. 2g). Soil respiration peaked at 16:00, exhibiting similar timing to Tsurf (i.e., 15:00), but 4 h later than photosynthesis (peaking at 12:00; Fig. 2g). During the dry month (August), diel Rs was generally in phase with photosynthesis but out of phase with Tsurf (Fig. 2h). Both photosynthesis and Rs plateaued between 10:00 and 16:00, whereas Tsurf peaked at 15:00 (Fig. 2h).

Among temperatures at the three levels, Tsurf correlated the strongest with Rs due to the high R2 with monthly mean diel Rs (Table 1). Over the growing season, monthly mean diel Rs correlated fairly well with photosynthesis (Table 1). The response of Rs to temperature and photosynthesis was shown to be affected by SWC (Table 2, Fig. 3). During the wet month, Tsurf alone explained 97 % of the variation in diel Rs (via Eq. 1), whereas photosynthesis explained 67 % of the variation (Table 2, Fig. 3a). However, during the dry month, photosynthesis explained 88 % of the variation in diel Rs (via Eq. 2), whereas Tsurf explained 76 % of the variation (Fig. 3b, Table 2). Irrespective of dry or wet periods, Tsurf and photosynthesis together explained over 90 % of the diel variation in Rs (via Eq. 3; see Fig. 3 and Table 2). On the whole, RI varied as a function of SWC, decreasing whenever SWC increased (Fig. 4).

During the wet month, hysteresis was not observed to occur in the monthly mean Tsurf–Rs relationship, whereas 2-hour lags were found to occur in the photosynthesis–Rs relationship (Table 1; Fig. 3a). During the dry month, the opposite was observed, where 1-hour lags were found to occur in the Tsurf–Rs relationship (Table 1, Fig. 3b). Over the growing season, Tsurf lagged behind Rs by about 0–4 h (Fig. 5b), and Rs lagged behind photosynthesis by about the same amount (Fig. 5c). This led to time lags between measured and modeled Rs regardless of the variable, Tsurf, or photosynthesis, resulting in about 26 % of the days of the growing season (accounting for 184 days, in total) having no time lag (Fig. 5e, f). However, taking into account both Tsurf and photosynthesis as input variables in the definition of Rs (via Eq. 3), time lags between measured and modeled Rs were mostly eliminated (Fig. 5a, d), with 84 % of the days of the growing season displaying no time lag.

Diel hysteresis in both relationships (i.e., Tsurf–Rs and photosynthesis–Rs) was shown to be affected by SWC (Fig. 6). Over the growing season, diel hysteresis between Rs and Tsurf was linearly related to SWC in a downward manner, when SWC < 0.08 m3 m-3 (ratio of SWC to soil porosity of 0.26; Fig. 6a). Hysteresis was not evident when SWC > 0.08 m3 m-3 (Fig. 6a). In contrast, diel hysteresis between Rs and photosynthesis was linearly related to SWC in an upward manner when SWC < 0.08 m3 m-3 (Fig. 6b), but ceased to be related when SWC > 0.08 m3 m-3 (Fig. 6b).

In our study, we found that the diurnal pattern in temperature (Ta, Tsurf, and Ts) lagged behind Rs by 0–4 h, which resulted in a counterclockwise loop in the relationship between Rs and temperature. Although the magnitude of hysteresis between Rs and temperature differed among the three temperature measurements, their seasonal variation was generally uniform. Among the temperature measurements, Tsurf was more closely related to diel Rs, resulting in weaker hysteresis. Magnitude of hysteresis between Rs and temperature was comparable to those in other plant systems, e.g., 3.5–5 h in a boreal aspen stand (Gaumont-Guay et al., 2006) and 0–5 h in a Chinese pine plantation (Jia et al., 2013). However, the direction of hysteresis was unlike that reported by Phillips et al. (2011), who had reported Rs lagging behind soil temperature.

In general, transfer of heat (downward) and gases (upward) through the soil complex by simple diffusion would take time to occur. Increased SWC would serve to impede this transfer (Millington and Quirk, 1961). If physical processes alone controlled hysteresis, you would expect Rs to lag behind Tsurf and hysteresis to increase with increasing SWC. However, such rationalization is not supported by our observations, which show Tsurf to lag behind Rs and hysteresis to decrease with increasing SWC. As a result, physical processes alone cannot account for the observed patterns in hysteresis between Rs and temperature. Combining photosynthesis and Tsurf as explanatory variables of Rs (via Eq. 3), we found 84 % of the days over the growing season had no observable lag between measured and modeled Rs, relative to 27 % of the days when Tsurf alone was used (associated with to Eq. 2), suggesting that photosynthesis has an important role in governing hysteresis in desert shrubland. Along with other studies, including those of Tang et al. (2005), Vargas and Allen (2008), Carbone et al. (2008), Kuzyakov and Gavrichkova (2010), and Wang et al. (2014), our findings provide increasing evidence of the role of photosynthesis in regulating diel hysteresis between Rs and temperature.

The 0–4 h lag between Rs and photosynthesis observed is consistent with those observed in earlier studies, e.g., 0–4 h lag between ecosystem-level photosynthesis and Rs in a coastal wetland ecosystem (Han et al., 2014) and 0–3 h lag between plant photosynthesis and Rs in a steppe ecosystem (Yan et al., 2011). Short time lags suggest rapid response between recent photosynthesis and Rs (Kuzyakov and Gavrichova, 2010). This response is significantly faster than suggested in earlier studies, when approached from an isotopic or canopy/soil flux-based methodology (Howarth et al., 1994; Mikan et al., 2000; Jonson et al., 2002; Högberg et al., 2008; Kuzyakov and Gavrichova, 2010; Mencuccini and Hölttä, 2010; Kayler et al., 2010; Han et al., 2014).

According to the “goodness of fit” of Eq. (3) to the field data, the time lag between diel photosynthesis and Rs was likely caused by variations in temperature, regardless of SWC. Photosynthesis provide substrates to roots and rhizosphere microbes (Tang et al., 2005; Kuzyakov and Gavrichkova, 2010; Vargas et al., 2011; Han et al., 2014). Temperature directly drives enzymatic kinetics of respiratory metabolism in organisms (Van't Hoff, 1898; Lloyd and Taylor, 1994). Photosynthesis is directly driven by radiation (specifically, photosynthetically active radiation). Temperature is also driven by radiation, but through heating of the surface and subsequent air and soil layers. Thus, diel patterns in temperature continuously lagged behind those of photosynthesis by a few hours (as indicated in Fig. 2). The interactions between photosynthesis and temperature led Rs to lag behind photosynthesis, but temperature lagged behind Rs (Fig. 2). This sequence of events may explain the difference in the direction of hysteresis observed here, in contrast to that reported in Phillips et al. (2011). Such explanation is different from the explanations for forest ecosystems, where the transport of photosynthates and influence of turgor and osmotic pressure may be responsible for the specific coupling observed between current photosynthesis and Rs (Steinmann et al., 2004; Högberg et al., 2008; Hölttä et al., 2006, 2009; Mencuccini and Hölttä, 2010). Variations in coupling dynamics may occur because of differences in vegetation height among ecosystems (Kuzyakov and Gavrichova, 2010; Mencuccini and Hölttä, 2010). Unlike forest ecosystems, low-statured vegetation in shrub systems (∼ 0.5 m) may elicit a few minutes of delay in the transportation of photosynthates and influence of turgor and osmotic pressure (Kuzyakov and Gavrichkova, 2010). Such small time lags cannot be easily identified in hourly measurements, resulting in an apparent temperature-dominated control of photosynthesis and Rs.

Diel Rs varied consistently with Tsurf, with no observable signs of hysteresis, when SWC > 0.08 m3 m-3. However, as SWC decreased from this value, diel Rs varied more closely with photosynthesis, leading to increased diel hysteresis between Rs and Tsurf. These results suggest that SWC played a more important role in regulating the relative control of photosynthesis and temperature on diel Rs over the growing season, supporting our second hypothesis.

A possible explanation for SWC regulating hysteresis might be associated with changes in substrate supply. During the wet period with SWC > 0.08 m3 m-3, increases in SWC ameliorate diffusion of soil C substrates and its access to soil microbes (Curiel Yuste et al., 2003; Jarvis et al., 2007). Amount of substrate to roots and rhizosphere microbes is also expected to be high as a result of high current photosynthesis (Baldocchi et al., 2006). As a result, diel Rs is not limited by C substrates provided by current photosynthesis and soil organic matter. Consequences of diel Rs may vary repeatedly in synchrony with diel temperature, with no indication of hysteresis when SWC > 0.08 m3 m-3 (Fig. 6a). By contrast, during dry and hot phases, with SWC < 0.08 m3 m-3, inadequate soil water limits diffusion of soil C substrates and its access to soil microbes (Jassal et al., 2008) and also suppresses photosynthesis (supported by Fig. 2g, h). As a result, Rs may be limited by C substrates under dry conditions. It has been reported that current photosynthesis can account for about 65–70 % of total Rs over the growing season (Ekblad and Högberg et al., 2001; Högberg et al., 2001). Thus, diel Rs may vary more closely to photosynthesis during dry and hot phases over the growing season (Fig. 2h), resulting in increased hysteresis with decreasing SWC below 0.08 m3 m-3 (Fig. 6b).

The 0.08 m3 m-3 SWC threshold of this study was consistent with an earlier study by Wang et al. (2014) that reported that seasonal Rs decoupled from soil temperature as SWC fell below 0.08 m3 m-3. Earlier studies have reported similar responses of Rs to temperature (Palmroth et al., 2005; Jassal et al., 2008). For example, Rs in an 18-year-old temperate Douglas fir stand decoupled from Ts when SWC fell below 0.11 m3 m-3. Our results suggest that the decoupling of Rs from temperature for low SWC was due to a shift in control from temperature to photosynthesis. Our work provides urgently needed new knowledge concerning causes/mechanisms involved in defining variation in diel hysteresis in desert shrubland. Based on our work, we suggest that photosynthesis should be considered in simulations of diel Rs in drylands, especially when SWC falls below 0.08 m3 m-3.