4.3 The uncertainty analysis of the C–G model
For calculating evaporation losses, the C–G model can identify relative
and absolute error sources. The absolute error of the experiment
originates from the error of the measuring instrument itself. The stable
isotope composition of water was frequently analyzed in the laboratory,
and the errors associated with
δ18O and
δ2H were found to be ±0.2‰ and ±0.6‰, respectively.
When the difference between the maximum analytic uncertainty in the
corresponding values and the valid values of two adjacent samples was
the greatest (±0.2‰ and ±0.6‰), the uncertainty range caused an increase
of 0.4‰ in the difference between the values of δP and
δL for δ18O and an increase of 1.2‰ in
the difference between those for δ2H. Considering the
maximum expected uncertainty in the measured δ value, the maximum
difference between the final calculation results of this experiment was
1.67% (f(δ18O)) and
1.35% (f(δ2H)).
However, this difference depends on the relative change in the δ value
owing to evaporation and impacts the samples that exhibit greater
evaporation. It would be worth future research to develop a more
accurate method of measuring isotopes.
The relative error of the experiment depended on the uncertainty
associated with the parameters in the model calculation. We analyzed the
sensitivity associated with each parameter of the model using the
control variable method combined with the test data. As shown in Fig. 9,
in terms of the sensitivity of the model calculation to a change in a
single parameter, parameters such as h, δP, and
δL have a greater influence on the calculation. The
changes in T, δrain, and other parameters had almost no
effect on the calculation of the model. (1) As h varies within the
interval (0.5, 1), each 1% change in h results in a change in f of
0.006 to 0.892. As relative humidity increases, f decreases gradually
until it reaches a fixed value. The surface soil is more strongly
influenced by the atmosphere and its variation is more pronounced.
Essentially, relative humidity (h) is the ratio of the actual water
vapor pressure in the air to the saturated water vapor pressure at the
same temperature, and it reflects how close the atmospheric water vapor
pressure is to the saturated water vapor pressure at the current
temperature. As the relative humidity increases, the saturation pressure
of water vapor in the atmosphere increases, which makes water
evaporation more difficult; therefore, evaporation intensity is
negatively correlated with relative humidity. (2) As
δP(O18) varies within
the interval (-10, 0), each 0.5% change in h results in a change in f
of 0.006 to 0.892. For each soil layer, f decreases followed by an
increase and is then stabilized. The trend of
δL(O18) is
counter-intuitive to that of
δP(O18). As
δL(O18) varies within
the interval (-10, 0), each 0.5% change in h results in a change in f
of 0.019 to 0.462. f increases followed by a decrease and is then
stabilized. In essence, the ratio of the difference between the final
and limiting isotope values of soil water isotopes to the difference
between the initial and limiting isotope values reflects the variation
in soil water content. In addition, soil non-stationary evaporation
isotopes’ limiting evaporation capacity depends on soil water content
and soil medium. In soils with a constant limiting isotopic composition,
i.e., when the hydraulic medium of the soil itself is constant, the
change in evaporation intensity is determined by changes in soil water
content (G.R. Walker, 1988; C.J. Barnes, 1989). As soil water isotopic
values become similar to their initial values, it indicates that the
soil has changed from a non-steady state evaporation state to a steady
state evaporation state. At this point, f describes the evaporation
intensity of each soil layer at steady-state. (3) It should be noted
that although the controlled variable method can reflect the sensitivity
of a certain parameter to the model to a certain extent, it does not
consider the synergistic relationship between the parameters.
Unsaturated soil water movement is affected by temperature gradients
primarily due to saturated water vapor density increasing rapidly with
temperature. As the temperature increases with depth, the temperature
gradient enhances evaporation. In addition, as the temperature decreases
with depth, the temperature gradient reduces evaporation. Thus, a single
temperature control does not show evaporation’s response to temperature
changes.
In summary, the temperature and relative humidity are the root causes of
errors resulting in model calculations. The relative error in the
experiment primarily depends on the uncertainty in the temperature and
relative humidity.