STABLE ISOTOPES AS TOOLS FOR WATERSHED HYDROLOGY MODEL DEVELOPMENT, TESTING
A. B. MAZURKIEWICZ Oregon State University,
3. RESULTS AND DISCUSSION
where c is breakthrough concentration and t is time. The numerator is the fi rst moment (concentration weighted average) of the tracer distribution and the denominator is the zeroth moment, or total mass. At this point it is worth stating clearly that strictly speaking, the MRT defi ned by equation 6 is equivalent to that defi ned through convolution only when the direct simulation incorporates the same fl owpath distribution as is incorporated by the isotope- based procedure (which is a top-down estimate of the true fl owpath complexity within the catchment). The environmental tracers behind the convolution approach access the full catchment volume and more importantly is maintained within zones of essential immobility. Clearly, as a simplifi cation, the catchment model would not be expected to incorporate that degree of heterogeneity. Our goal is evaluate the degree to which the simplifi cation affects model residence time. If we can establish that the differences are highly signifi cant, we can then successfully reject the model as a simulation of catchment chemistry due to over simplifi cation, and use that as a sound basis to iteratively incorporate additional complexity.
FIG. 1. Simulation results for stream discharge. The Y axis on the upper plate is log transformed to outline more clearly model failures at lower discharge. Calibration strategy focused on peak fl ows. The two simulations plotted as dashed lines represent the outside envelope of the 147 simulations found with Nash-Sutcliffe effi ciencies over 0.75. Measured values are plotted as a solid line
0 25 50 75 100
9/30 10/20 11/9 11/29 12/19 1/8
Date
Runoff (L/s)
Measured Run1426 Run1836
0.1 1 10 100
9/30 10/20 11/9 11/29 12/19 1/8
Date
Runoff (L/s)
Measured Run1426 Run1836
FIG. 2. Simulated tracer breakthroughs represented as an envelope incorporating data from all simulations with effi ciencies over 0.75. All breakthrough curves occur within the plotted envelope. Maximum concentrations are not displayed as 50 mg/L due to the 0.2 day sampling period (with a 0.01 day simulation time step).
0 5 10 15 20
9/2 10/12 11/21 12/31 2/9 3/20 4/29
Time
Breakthrough (mg/L)
also collected and are represented in Figure 2. The initial concentration of tracer reported in the channel is less than the initial concentration of 50 mg/L because of rapid initial breakthroughs occurring prior to the fi rst sampling step.
Nash Sutcliffe effi ciencies of higher fl ows indicate that the model is capable of reproducing discharge in the catchment, even under the relatively restricted list of calibrated parameters. Maximum values of effi ciency were 0.83.
While low fl ow dynamics were clearly not as well represented (Figure 1 and the maximum effi ciency), our use of untransformed discharge in the calculation of effi ciency biased the results away from these values. Additional calibration using log transformed discharge may result in improved low fl ow estimates, but was not included in this analysis. As is common with conceptual models of this type, scatter plots of parameter value against effi ciency indicates a signifi cant degree of parameter uncertainty (Fig. 3). This lack of identifi ability was most notable for the saturated hydraulic conductivity, for which the highest effi ciencies could be established across the entire prior parameter range (Fig. 4). From the standpoint of storm discharges, we view these model simulations as acceptable.
Given the number of parameters, and the tuning of three of them, this is not a surprising result. The next step is to evaluate the model against additional integrative criteria. In this case we utilize the unique MRT of each of the model simulations.
Directly simulated mean ages across the prior parameter range, varied from 30 to 95 days and results indicate a tradeoff between longer mean ages and discharge effi ciency. Maximum effi ciencies for the longer aged simulations dropped to a value of approximately 0.5. Parameter values versus effi ciency are outlined in Figure 4, and indicate the importance of the storage term in this result. Lower porosities (in combination with the structure and other parameters) can successfully reproduce discharge characteristics, but result in short MRTs. An increase in total storage can result in longer residence times,
FIG. 3. Nash Sutcliffe discharge effi ciency versus mean residence time. While modeled stream mean residence are always considerably less than measured values, a tradeoff exists between high discharge effi ciency and longer, more realistic, residence times.
0.1 0.3 0.5 0.7 0.9
30 50 70 90 110
Mean Residence Time (days)
Q Efficiency
but discharge simulations are negatively effected. This result, while not entirely unexpected, leads us to the conclusion that total available storage within the catchment is better approximated by models resulting in the longer MRT, but that this storage must be more variably allocated within the system.
While Figures 1 and 2 focused on stream water MRT, the distributed calculation of stocks and fl ows results in the estimation of MRT results at all discreet locations within the watershed. Stewart and McDonnell [16]
developed a set of MRT values based on convolution of 18O from an array of suction lysimeters in the northwest corner of the basin (Fig. 5). This work led to the hypothesis at Maimai that water ages in the downslope direction. Here we extended these data to the entire basin based on a 2 meter elevation grid from which we calculated the fl owpath distance to the nearest stream channel, based on the single direction D8 algorithm. Flowpath lengths for each of the deeper suction lysimeters were collected and the simple linear relationship between fl owpath length and water age was used to regionalize age estimates to the entire catchment. Results from the 2 m grid were averaged up to a 10 m grid to correspond in scale to model calculations (Fig. 5). We restricted the data to the deeper lysimeters that were representative of transient saturation because the hydrologic model does not explicitly simulate the vadose zone.
Distributed soil MRT were not collected for each of the high effi ciency simulations, but were collected (subsequent to the Monte Carlo simulation) for a set of representative parameters. In this case we selected the set of parameters with the longest MRT for further examination. As suggested by Stewart and McDonnell [16], the direct simulations of MRT display increases in a characteristic fashion downslope, but MRT range is only approximately 4 days. This small directly simulated range is a direct refl ection of the lack of spatial variability of the parameters. The distance from each reservoir (or grid cell) to the stream, along with local slopes, do vary in space. Given the explicit grid based routing scheme, this fact must result in some degree of downslope aging. However, porosities, soil depths, and other tunable model parameters were not varied in space. The choice to maintain spatial homogeneity of these parameters was justifi ed if the results satisfactorily explained evaluative criteria. This was arguably the case if peak fl ows were the only criteria, but is
Figure 4. Monte Carlo results for the 3 tuned parameters.
0.5 0.7 0.9
0.1 0.35 0.6
Total Porosity
Q Efficiency
0.5 0.7 0.9
100 200 300 400
K (m/d)
Q Efficiency
0.5 0.7 0.9
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PLE
Q Efficiency
clearly not the case when looking at MRT. With this unambiguous rejection, along with the model’s inability to capture both stream MRT and discharge dynamics with the same parameter set, the spatial variation of at least some of the model parameters is justifi able.