Soil respiration is strongly related to the soil temperature, thus the simplest model to predict soil respiration uses soil temperature as the single variable. In this case, an exponential or Arrhenius equation is used, as mentioned before. Since soil moisture is anther important factor influence soil respiration, the power of prediction is greatly enhanced by incorporating the influence of soil moisture. Other factors, such as LAI (Norman et al., 1992), air temperature and precipitation (Raich and Potter, 1995), are also added as model variables in some studies. Here we introduce two soil respiration models, one of which only considers the effect of soil temperature and the other takes soil moisture into consideration.
Model with the effect of only soil temperature
Frank, el al. (2002) modeled the effect of soil temperature to predict soil respiration in northern semiarid grasslands.
Soilflux = ((A1A2A3)z) maximumflux
z: shape parameter(1.5 in this case)
maximumflux: maximum measured soil respiration flux
Figure 3 shows the fit of the model for the grassland data. The percentage of difference between the observed and predicted soil fluxes averaged for all observations is 1.5% for this model.
GRESP models and its variation
In 1974, Bunnell and Tait modeled the influence of soil temperature and soil moisture on soil respiration using a model named as GRESP.
where GRESP: the respiration rate (g CO2 m-2h-1)
T: soil temperature (degrees Celsius)
M: soil moisture (grams of water per gram of dry weight times 100 percent)
a1: the % moisture content at half field capacity
a2: the % moisture content at half “maximum retentive capacity”
a3: the theoretically maximum respiration rate at 10 ºC when moisture is non-limiting
a4: the Q10 coefficient (sensitivity to temperature)
Although GRESP has been applied successfully to tundra, boreal forests and temperate bogs ecosystems (Heal, 1979), it has some limitations: (i) respiration equals to zero only when temperature is zero; (ii) the relationship between soil respiration and temperature is expressed as simple exponential equation without upper limit; (iii) Q10 is assumed constant.
Some variations of GRESP model have been proposed by other researchers, e.g. the BRESP model fit by Schlentner and Van cleve (1985), the FRESP model fit by Carlyle and Ba Than (1988). The BRESP model differs from GRESP by adding an upper and lower limit of the response of soil respiration to temperature.
where BRESP: the respiration rate (g CO2 m-2h-1)
a1, a2: the same as GRESP model
a3: a scaling factor, no biological meaning
a4: the Q10 related parameter
a5: the lower limit of soil respiration
Carlyle and Ba Than modified the model by allowing Q10 dependent on substrate moisture so that it can be applied to very dry conditions.
FRESP= ; A4=
where FRESP is the respiration rate (g CO2 m-2h-1)
a4: a parameter linking Q10 to substrate moisture content
a5: the lower limit for the Q10 quotient
Figure 4 shows the fit of a respiration in an eighteen-year-old pinus radiata stand with three models. For this particular data, FRESP model fit best (r2=0.85), while the other two models give poor fit (GRESP: r2=0.09; BRESP: r2=0.15). Schlentner and Cleve (1985) obtained an r2 value of 0.58 for both GRESP and BRESP for mature forests, indicating the fitness of this type of models is site-specific.
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