1. Introduction
Soil carbon dioxide efflux results from microbial production and gas diffusion. The gas exchange of sterilized soil at normal temperatures is not significant in comparison with the respiration [
1]. Under field conditions, it is difficult to separately investigate root respiration and rhizomicrobial respiration and determine the effects of roots on the decompositions of soil organic matter. The flux of plant-derived CO
2 masks the contribution of soil–organic matter-derived CO
2 [
2]. At the global scale, the mean soil CO
2 efflux of bare soil was calculated to be 282–476 g C m
−2 y
−1 [
3].
In general, the CO
2 efflux correlates with precipitation and temperature. However, the overall effect of the soil moisture content and temperature differs by climate zone and seasons. For example, in a short laboratory experiment, rewetting dry soil in a tropical forest did not affect the soil respiration rate [
4]. Similarly, at the field scale, the CO
2 flux rate did not change significantly under the simulated rain conditions [
5]. In dry areas, however, the soil’s microbiological activity quickly responds to changes in the soil moisture content, e.g., under laboratory conditions, the microbial biomass carbon level was found to be approximately two-fold higher within 3 h after rewetting soils in a hot, rain-free season [
6]. Similarly, in a semiarid region, after a simulation of 24 mm of rainfall in the summer, the soil CO
2 efflux was 2.5 times higher [
7]. The significance of the effect of the soil moisture content on the CO
2 efflux of bare soil can be assumed to be highly dependent on the climatic conditions.
Generally, increasing the temperature accelerates microbial activity. By screening soils from the Arctic to the Amazon, the microbial response to increasing the air temperature was mostly found to enhance the temperature sensitivity of soil microbial respiration [
8]. The influence of precipitation was proven to be secondary to that of the temperature when viewed at the global scale [
3]. However, in a subarctic region, the response of CO
2 production in bare soil to increases in the soil temperature was found to be more sensitive in wet soils [
9]. In a study, variations in the soil water content were proven to have a stronger effect when the soil temperature was higher. The soil temperature was found to become a limiting factor of CO
2 efflux out of the growing season and in the dry season [
10]. In a semiarid region, the soil temperature and moisture content were found to have greater impacts on soil respiration in the winter [
11]. Based on these examples, it is shown that the contribution of the two differs by regions and seasons. When soil moisture is limited, soil respiration decreases considerably, and soil moisture exerts control over the CO
2 efflux [
12]. A longer period with a relatively high moisture content can ensure more favorable living conditions for microbes. Sudden water input, i.e., natural precipitation and irrigation causing a sudden increase in the soil moisture content, generally does not result in the sudden propagation of soil microbes and, hence, does not increase CO
2 emissions in the short term [
13].
Several studies [
14,
15] aimed to investigate the effect of the soil temperature and moisture content on soil CO
2 efflux as the main controlling factors. An advantage of these parameters is that they can be continuously monitored in high time resolutions, providing adequate datasets for model calculations. The data gained under different environmental and experimental conditions have been described using many different mathematical models with variable results. For example, based on global, monthly climate data, a log-transformed and an untransformed model were suggested in which terrestrial soil CO
2 emissions significantly and linearly correlated with the published estimates of annual fluxes [
3]. In another study, correlations between the CO
2 flux and soil temperature were found, but significant correlations in each year were not shown [
11]. Some researchers concluded that the exponential and linear relationships between the soil temperature and soil respiration rate do not provide unbiased estimates [
16]. In a further study, the soil CO
2 efflux was described using an exponential function of the soil temperature, and the temperature-normalized CO
2 fluxes were found to relate to the soil water content with a positive linear relationship [
17]. When the correlation of soil respiration with the soil temperature and moisture contents was described by a two-variable exponential–power model, the soil respiration’s sensitivity to moisture was reported to increase with the increasing soil temperature [
14]. In the winter period, the temperature sensitivity negatively correlated with the average soil temperature and moisture, described by exponential and power functions, respectively [
11]. Under some circumstances, no significant correlation could be found between the soil CO
2 emissions and the soil temperature (e.g., [
15]). In a further study, it was shown that exponential and Lloyd and Taylor functions relating CO
2 efflux to the soil temperature could be used to predict soil respiration when the soil water content was above 1/3 of the water-holding capacity. When combining the two parameters into one integrated model, four types of regression equations were successfully established for use in estimating the seasonal changes in CO
2 efflux [
12].
Mathematical descriptions of the contribution of bare soil to the overall CO
2 efflux in different climate zones are necessary to draw realistic conclusions. Furthermore, the systematic comparison of the adequacy of different models, as highlighted decades ago [
16], remains of scientific interest. In addition, to the best of our knowledge, seasonal predictions of future CO
2 emissions using historical, long-term, daily weather data have not yet been published.
Based on this, our objectives were (1) to investigate the explanatory force of the soil temperature and soil moisture contents as variants to the CO2 efflux of bare soil using long-term field data gained under natural environmental conditions in a continental region with a four-season climate in Hungary; (2) to assess the adequacy of different mathematical models appearing in the literature, such as linear, exponential, quadratic exponential, and exponential combined with power function; and (3) to provide estimations of CO2 emissions of bare soil using the model found adequate for use in this region.
4. Discussion
Many reports have discussed bare soil CO
2 efflux based on laboratory measurements, as well as field experiments over periods varying from a few months to several years. Specifically, they have been carried out in different climatic zones [
5,
7,
9,
10,
11,
12,
23,
24].
Among the environmental factors, CO
2 efflux is mainly determined by the soil status and weather conditions. CO
2 efflux can be expected to closely correlate with the preserved soil moisture content. In a crop year, before and after the vegetation period, and even at the beginning and end of the period, bare soils experience higher evaporation loss due to the lack of soil surface cover. In such a period, the soil moisture content is often a limiting factor in soil respiration [
13]. A longer period with a relatively high moisture content could ensure more favorable living conditions for microbes. Generally, sudden water input such as precipitation, which causes a sudden increase in the soil moisture content, does not result in the sudden propagation of soil microbes; hence, it does not increase CO
2 emissions in the short term. Soil moisture does not correlate strongly with the rates of soil respiration [
4]. Contrary to this, under optimal circumstances for microbiological activity, when neither the soil temperature nor water content are limiting factors, high soil CO
2 emissions can be observed [
24]. In experiments, weather conditions showed high fluctuations in the temperature and the unequal distribution of rain. At our experimental site, however, the soil moisture content was found to be very low and varied in a relatively narrow range (
Table S1), resulting from both the local weather- and soil-type characteristics. Under these circumstances, soil microbes could be expected to be less responsive to any changes in the moisture content measured in the field [
25].
The contribution of the different environmental variables has been mathematized by several researchers using different sites, with special interest in the soil temperature and the soil moisture content.
In a study covering a wide range of ecosystems, neither the exponential nor the linear model provided an unbiased estimate for the soil CO
2 efflux when the soil temperature was considered alone [
16]. For bare soils, however, exponential models have been widely used for the description of the relationship between soil CO
2 efflux and soil temperature. Some studies did not prove a direct relationship (e.g., [
9,
15]), while others did, e.g., [
11,
12,
14,
17,
23]. For example, in a dataset related to a semiarid area, the soil temperature as a variable explained 46% of the seasonal changes [
11]. The R
2 for bare soil was found to be similar to our findings. In a highland area, the R
2 was found to be 0.44 and increased to 0.63 when drought-affected dates were excluded [
12]. In our study, data representing the whole year included predominantly dry conditions (
Table S1). Interestingly, at a seasonal scale in a similar location, the R
2 was 0.124, 0.000, 0.447, and 0.002 in the spring, summer, autumn, and winter, respectively [
14].
In a study carried out to describe the rate of respiration in the function of both soil temperature and moisture content, the CO
2 efflux was given as the product of two exponential functions [
19]. Some researchers combined the exponential and power functions of soil temperature and the soil water content, respectively. In one study, with the combination of the exponential function of soil temperature and the power function of the moisture content, the R
2 was 0.82 in the case of bare soil [
12]. For bare lands within a 11-year period, the R
2 was 0.62 [
14]. On a seasonal scale, for bare soil, the R
2 was 0.24, 0.608, 0.59, and 0.11 in the spring, summer, autumn, and winter, respectively [
14]. In one study, bare soil’s CO
2 efflux was described by the product of the power functions of the two variables, and the R
2 was found to be 0.79 [
12]. In another study using the same model, the R
2 was calculated as 0.553 [
11]. As suggested, the moisture content can be expected to have significant effects above one-third of the water-holding capacity. This explains our findings in which the soil moisture did not improve the accuracy of the best-fitting model. Using the power function for the soil water content alone, some researchers found an R
2 of 0.15 for bare soil [
11], while others reported an R
2 of 0.71 [
12]. On a seasonal scale, the R
2 was 0.005, 0.566, 0.062, and 0.11 in the spring, summer, autumn, and winter, respectively [
14]. In one study, temperature-normalized CO
2 fluxes were found to relate to the soil water content with a positive linear relationship [
17]. Based on the findings of these case studies, the contribution of the soil moisture content to the overall effect of weather conditions on the CO
2 efflux of bare soil differs widely, supporting the need for further field experiments, especially in situ, long-term studies continuously monitoring weather and soil parameters.
5. Conclusions
The CO2 emissions from bare soil remain of considerable scientific interest. Several physical, chemical, and biological properties; meteorological parameters (e.g., temperature and precipitation); and hydrologic parameters (e.g., soil moisture content) determine the spatial and temporal variability in CO2 emissions from bare soils. Nevertheless, bare soil surfaces with no vegetation provide suitable environments to study the microbiological activity of soil, because root respiration, as another source of CO2 emissions, is excluded. We determined the validity and accuracy of different mathematical models based on daily data regarding the soil carbon dioxide efflux and soil temperature and extended the best-fitting formula with the soil moisture content. The data were recorded within the period of June 2018–March 2022 under natural field conditions, characterizing undisturbed bare chernozem soil in Karcag, Hungary, a semiarid region with four seasons.
We proved that, for the description of the relationship between the CO2 efflux and the soil temperature, the linear model was not adequate, as the homoscedasticity criteria were not met. The exponential model with quadratic function did not provide more accurate results compared to those of the simplified exponential model. The addition of the soil moisture content to the simplified exponential formula did not improve the accuracy, suggesting that the moisture content under the given environmental circumstances within the investigated time period and location was not considerable. We have found further evidence that the best-fitting models are dependent on the local environmental conditions of the fields.
Based on the Akaike Information Criteria, the exponential model, including the soil temperature as a variable, was used to provide seasonal predictions of the CO2 efflux from undisturbed bare soil for the year 2050 by season, with the consideration of historical trends in the daily mean temperature in the last 30 years. Based on our calculations, in the future, an increase in the CO2 efflux of bare soil can be expected in the warm, dry, temperate climate zone.