Mejora de chirimoya en Patate y Guayllabamba

The results of the temperature simulations at various locations and vertical depths, using different parameter settings, were compared with the measured values. Dotty plots were used for identification of the parameter responses to the objective function (SSE). The plots are useful for understanding parameter sensitivity to changes within the defined ranges and the boundary condition adjustments (Wagener et al., 2004). They also provide insight into the identifiability of these parameters and the associated effects of varying model spatial resolution.

In the Monte Carlo analysis, the best parameter settings were chosen based on the minimum sum of squared error between measured data and model results (Figures3.4a and 3.4b). For WSC and SHADE a distinct minimum in the parameter space illustrates that the optimum parameters are quite well identified, but for EXT and TIN this is not the case, i.e., optimal

performance can be achieved with any feasible value of these parameters. Further work is needed to investigate potential parameter interdependencies that could explain part of this effect, but for model optimization the implication is that specified values could be used for these two parameters. The ranges found in the calibration of both model resolutions (187 and 126 segments) for both years (2011 and 2012) show very similar values.

Figure 3.4: Sensitivity analysis results. a: Sensitivity results for Monte-Carlo simulations for the model with 187 & 126 segments. WSC and SHADE are wind sheltering and shading coefficients. EXT and TIN are light extinction coefficient and inflow temperature multipliers

Figure 3.4: Sensitivity analysis results. b: Sensitivity results for Monte-Carlo simulations for the model with 187 & 126 segments. WSC and SHADE are wind sheltering and shading coefficients. EXT and TIN are light extinction coefficient and inflow temperature multipliers

Figure 3.4: Sensitivity analysis results. c: Comparison of model’s results for two sensitive parameters (WSC & SHADE) with the 187 and 126 segments in 2011 & 2012. Each sheet is for the depth which is located and the next 15 meters below it. Since the number of samples were not the same at each depth, the sse/n (n is number of samples) was used instead for consistency

Figure 3.4: Sensitivity analysis results. d: Comparison of model results for two sensitive parameters (WSC & SHADE) for the model with 187 segments at different depths. Each sheet is for the depth which is located and the next 15 meters below it. Since the number of samples were not the same at each depth, the sse/n (n is number of samples) was used instead for consistency

Comparing the results from the 187 and 126 segment models (Figures 3.4a and 3.4b), no significant difference in performance was observed. The model with 187 segments used finer grids and the calculations were continuous from 2011 to 2012. In the model with 126 segments, the calculations for 2011 and 2012 were independent, since in early spring the lake had homothermal conditions of 4 ◦_{C. Although the results from these two grid}

resolutions were not distinguishable, the computational times were significantly less for the coarser grid.

As noted above, the models are sensitive to both WSC and SHADE parameters. In the models with 126 and 187 segments, a fairly similar proportion of the parameter space yielded good performance (Figure 3.4c), implying that the coarser grid model can be used for quicker simulation times without having to compromise accuracy and parameter sensitivity. Lindenschmidt (2006) provides a discussion on the effects of model complexity on parameter sensitivity and modelling accuracy. In the interest of computational efficiency, future studies will be based on the model with 126 segments.

In order to study the model performance at different depths, the reservoir was divided into four vertical layers, each 15 meters thick (Figure 3.4d). Measurements and simulation results at depths 0, 15, 30 and 45 m correspond to the values at depth ranges 0 – 15 m, 15 – 30, 30 – 45 and 45 – 60 meters, respectively. All the measurements within each range were sorted in one column and compared to the simulated values at the corresponding location and depth. Since the number of samples were not the same in each depth range, RMSE values were used instead of SSE to normalize the SSE values. For the top layer, SHADE is more sensitive due to the effects of solar radiation and overflow discharges. Conversely, WSC is more influential on the second layer indicating the effect of wind on mixing in the lower layers. WSC still has an impact on the lower lake layers, whereas SHADE’s influence is diminished at the lake bottom.

The PSO+LM optimization method performed exceptionally well. The code found the best parameter settings after only 41 runs. In order to assure that these results were not by chance, the runs were repeated several times until a total of 1000 runs had been completed. Therefore, the results were used for both sensitivity analysis and accuracy control of the codes and the methodology (Figure III.1a). On average, after 24 PSO runs, the results

Figure 3.5: Simulated (lines) vs measured (dots) temperature for observation station 10 (near Elbow)

were passed to LM to find the best parameter settings after 20 to 30 iterations (Figure

III.1b). The blue circles are parameter values generated by PSO and the red circles are values fine-tuned by LM. There were only two cases where the results from LM were not convincing and LM returned the parameter values to PSO for further exploration of new areas in the parameter space.

As an example, the measured temperature values (dots) were compared with the simulated values (lines) for the stratification and destratification periods near Elbow (Station # 10) (Figure 3.5). The water is thermally stratified in summer and early fall. Early in November the water temperature begins to decrease, leading to the breaking down of the thermal stratification. The discrepancy between measured and simulated temperatures increases when the thermocline location is not calculated correctly, where there are steep temperature gradients (Peeters et al., 2002). A strong wind event can move the thermocline several meters vertically, so using daily meteorological data can produce errors when the reservoir is stratified at windy days. The inclusion of hourly meteorological data, daily hydrometric data and accurate calculations of the water level during the simulations reduced this problem significantly.

In order to extend the description of the thermal regimes over the entire year, water temperatures in winter also required calibration. Temperature data were not available for the winters of 2011 and 2012, but ice data from the 2012 – 2013 winter were available. With α = 0.63 and β = 50 (Tables 3.2 and 3.3), values calibrated by the Blackstrap Lake model, the simulated ice thickening and melting fit the observations reasonably well (Figure

3.6). With the correct ice thicknesses and ice-on durations, solar radiation and wind effects on the ice cover and water column can be estimated. This allows the temperature to be generated for the whole year.

Novel in this work is the quantification and illustration of the effect of different contributing heat sources and sinks to the lake heat budget (Figure 3.7). The values are calculated as the total amount of thermal energy divided by the lake volume. They show the monthly average amount of heat added to or removed from the lake each day. The “surface heat exchange” is the sum of all the shortwave and longwave solar radiation terms and conductive and evaporative fluxes. “Bed” is the heat exchange between sediment and water at the bottom of the lake. The “inflow” and “tributary” show the amount of heat added to the lake by the SSR and Swift Current Creek, respectively. The “outflow” and “evaporation” are the equivalent amounts of heat removed from the lake due, respectively, to water discharged via the outflow and evaporation. “Ice” represents the heat lost at the ice –water interface. The “net” component is the sum of all the components.

The parameters on the right (bed, tributary, evaporation and ice) have a scale one tenth of those on the left (surface heat exchange, inflow, outflow and net). Therefore, their effects are much smaller on the overall lake heat budget. It is interesting to note the large amount of heat input by the inflowing SSR. For example, the inflow water increases the whole lake water temperature by about 0.25 degrees every day in June 2011 and the outflow decreases it by 0.22 degrees. Summing all the components, the lake temperature increases by about 0.14 degrees for each day in June 2011. The three main parameters that influence the heat budget are the surface heat exchanges, inflow and outflow. Since this is a reservoir and outflows are regulated, reservoir management practices can significantly influence the thermal and, consequently, water quality conditions of the lake.

Figure 3.6: Comparison of model original ice model with the modified ice code in both Blackstrap Lake and Lake Diefenbaker in winter 2012/2013

Figure 3.7: Quantitative contribution of different sources to the lake’s heat budget. The parameter on the right (bed, tributary, evaporation and ice) has a scale of one tenth of those on the left (surface heat exchange, inflow, outflow and net). The “surface heat exchange” is the sum of all the shortwave and longwave solar radiation terms and conductive and evaporative fluxes. “Bed” is the heat exchange between sediment and water at the bottom of the lake. The “inflow” and “tributary” show the amount of heat added to the lake by the SSR and Swift Current Creek, respectively. The “outflow” and “evaporation” are the equivalent amounts of heat removed from the lake due, respectively, to water discharged via the outflow and evaporation. “Ice” represents the heat lost at the ice–water interface. The “net” component is the sum of all the components