A Greedy Algorithm for Optimal Sensor Placement to Estimate Salinity in Polder Networks

Round 1

Reviewer 1 Report

The paper deals with intersting topic of optimal sensor placement of salinity level in Polder networks. It is well written but could be better if some additions are made as follows:

(1) Discuss or give some results on using 2 PCAs or 4 PCA and etc.

(2) Comments on the worst estimation performance case.

Author Response

Reviewer 1

The paper deals with interesting topic of optimal sensor placement of salinity level in Polder networks. It is well written but could be better if some additions are made as follows:

Comment 1: Discuss or give some results on using 2 PCAs or 4 PCA and etc.

Response: We thank the reviewer for pointing this issue. The low-order PCA model can be formulated by any number of PCs. In this study, we restricted ourselves to 3 PCs by considering the threshold we assigned for the total variance explained by the PCs. As we stated on line 189 of the original manuscript, we used 90 % as the threshold for the total variance explained.  As shown in Figure 4 of the manuscript, the first 3 PCs exceeds the threshold of 90 %. Increasing the number of PCs used for low-order PCA model and the sensor placed increases the performance as shown in Table 1 of the manuscript (starting form one PC one sensor to three PC and three sensors). For each new sensor placement, the GA picks a new location by keeping the previous sensor selection fixed. As Table 1 of the original manuscript illustrates, the performance of the placement increases by addition of a new sensor. This increase continues by adding new PCs and sensors as expected (Figure 1 of this response).

Figure 1 Performance of the placement up to 10 sensors placed

As can be seen in Figure 1 of this response, which shows the performance of the placement up to 10 sensors, the performance of the placement increases with the number of PCs used and sensors placed as expected. Although, in this study we did not consider the economic value of installing a sensor in place directly, we think a limitation on the number of sensors is practical considering economic feasibility for a certain estimation efficiency. We included the following parts to the manuscript to explain our choice as follows:

(Line 266 - 268 of the revised manuscript):

We selected the first three PCs for the low-order PCA model since the variance explained by the first three PCs exceeds the threshold of 90 % that we defined for this study.

(Line 365 - 367 of the revised manuscript):

The accuracy of the low-order PCA model increases with the number of PCs used, and this number depends on the user defined threshold for the variance explained by the selected PCs (90 % in this study).

Comment 2: Comments on the worst estimation performance case.

Response: We can discuss the worst estimation performance  (in NRMSE )in two ways depending on the location or the disturbance estimation (boil location, boil flux) that effects the model. The placement can perform worst in a location that is not represented by the low-order PCA model. As we discussed in section 3.2 (Principal Component Analysis) of the original manuscript, the location dependent coefficients and time signals of the first two PCs can be identified by certain types of ditches of the catchment with high salinity variance. Those ditches are captured with a higher accuracy by the low-order PCA model and therefore, the estimation performance of the sensor placement is higher compared to the ditches that are not captured by the low-order PCA model. An example is the node 51 (Figure 9 of the original manuscript) which is close to the inlets and is not represented accurately  by the low-order PCA model and the estimated salinity has mismatches. However, as we also discussed in lines 279-281 of the original manuscript, that location has lower salinity values and the mismatch observed does not exceed 30 mg/l.  We made the following change in section 3.3 of the revised manuscript:

(Line 281 - 285 of the revised manuscript):

This location is close to the inlets of the catchment where the water is fresh and the salinity variance is low compared to the rest of the catchment. Therefore, the principal component values of the first two PCs are low for this location (Figure. 7). The estimation of salinity is better at locations which are identified by the PCs used for the low-order PCA model like locations 170 and 445.

The second factor that will result in a worst estimation performance are large errors in estimation of the disturbances (boil locations, boil fluxes) within our model, and thus resulting a wrong sensor placement. We illustrated the performance drop with respect to different scenarios due to modelling or measurement errors in Section 3.5 (A posteriori Assessment of Robustness of Sensor Placement to Measurement and Modeling Errors) of the original manuscript. As we stated in lines 340-345, the worst estimation performance is observed in case of wrong boil location estimation. We added the following to the conclusion:

(Line 378 - 380 of the revised manuscript):

Wrong estimation of boil locations results in lack of important variance information which is crucial for capturing the dynamics caused by the boils, resulting in worse salinity estimation performance for the sensor placement.

Author Response File: Author Response.docx

Reviewer 2 Report

I enjoyed reading your paper. It is well written with no grammatical or spelling errors. 

The results of your research have obvious practical applications.  You all should be recognized for contributing to potential solutions for salinity management and its importance in agricultural production.

I have only one minor suggestion. In figure 5 you refer to original salinity, which I assume is modeled salinity and not empirically derived data. However, the word original doesn't really capture this distinction.

Author Response

Reviewer 2

I enjoyed reading your paper. It is well written with no grammatical or spelling errors. The results of your research have obvious practical applications.  You all should be recognized for contributing to potential solutions for salinity management and its importance in agricultural production. I have only one minor suggestion.

Comment 1: In figure 5 you refer to original salinity, which I assume is modeled salinity and not empirically derived data. However, the word original doesn't really capture this distinction.

We thank the reviewer for pointing this mistake. The data plotted is simulated (modelled) by the SOBEK model. We labeled the same data as “simulated” in Figures 9-11. Therefore, we replaced Figure 5 with the following version and also corrected the caption of the figure.

Figure 5. Comparison of the reconstructed salinity using 3 PCs and the simulated salinity at node 172