Modeling river water temperature with limiting forcing data: air2stream v1.0.0, machine learning and multiple regression
Abstract. The prediction of river water temperature (WT) is of key importance in the field of environmental science. Water temperature datasets for low order rivers are often in short supply, leaving lake/reservoir water quality modelers with the challenge of extracting as much information as possible from existing datasets, usually without the use of physically based models, due to the significant amount of data required (e.g., river morphology, degree of shading, wind velocity). In this study, five models are used to predict the water temperature of 83 rivers (with 98 % missing data): three machine-learning (ML) algorithms (Random Forest, Artificial Neural Network and Support Vector Regression), the hybrid Air2stream model with all available parameterizations and a Multiple Regression. The machine learning hyperparameters were optimized with a Tree-structured Parzen Estimators algorithm and the results of each model are presented as an ensemble of 12 individual optimized model runs. The meteorological datasets were obtained from the fifth-generation atmospheric reanalysis, ERA5. In general terms, the results of the study demonstrate the vital importance of hyperparameter optimization and suggest that, from a practical modeling perspective, when the number of predictor variables and observed river WT values are limited, the application of all the models considered in this study is relevant (models ensemble mean annual – Root mean square error (RMSE): 2.75 ºC ± 1.00; Nash-Sutcliffe efficiency (NSE): 0.56 ± 0.48). The model that performed best was Random Forest (annual mean - RMSE: 3.18 ºC ± 1.06; NSE: 0.52 ± 0.23). The results also revealed the existence of a logarithmic correlation among the RMSE between the observed and predicted river WT and the watershed time of concentration. The RMSE increases by an average of 0.1 ºC with a one-hour increase in the watershed time of concentration. (watershed area: μ= 106 km2; σ=153).
Manuel C. Almeida and Pedro S. Coelho
Status: final response (author comments only)
RC1: 'Comment on gmd-2022-206', Anonymous Referee #1, 29 Dec 2022
- AC1: 'Reply on RC1', Manuel Almeida, 18 Jan 2023
RC2: 'Comment on gmd-2022-206', Anonymous Referee #2, 13 Jan 2023
- AC2: 'Reply on RC2', Manuel Almeida, 18 Jan 2023
Manuel C. Almeida and Pedro S. Coelho
Manuel C. Almeida and Pedro S. Coelho
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Review of “Modeling river water temperature with limiting forcing data: air2stream v1.0.0, machine learning and multiple regression” by M. Almeida and P. Coelho
Determining inflow temperatures of rivers or streams into receiving water bodies is a critical need. The authors are to be commended for addressing this topic. The overall theme of the paper was not crystal clear – was this about modeling river water temperatures themselves or modeling the inflows into receiving water models? Did the modeling include hydrology models predicting depth and flow? If so, then it was not clear that the models used were compared to flow and depth data which are critical for modeling river temperatures. Also, the overall RMSE error for the models was much higher than accepted river temperature models. This leads to the conclusion that there were underlying issues in the datasets used in the model. If the datasets were improved, would the conclusions of the study have been any different? An important aspect of this paper that was not evaluated was the advantages and disadvantages of using a physical based model rather than correlations and regressions to model water temperature.
Abstract: Line 16: define variables used for ‘Multiple Regression’ – this should be a separate sentence in the Abstract where the variables used for the different approaches are described.
Abstract: After reading the abstract, the reader is not left with a better understanding on how to fill in data gaps, other than just take more measurements!
Line 44-45: ‘common practice to average out sub-daily effects and to consider a daily discretization for modeling purposes’ – the impacts of this should be explored further since this can impact significantly the waterbody being modeled
Line 45: ‘Air temperature approximates the equilibrium temperature of a river and is, therefore, frequently used as the independent variable;’ – these are indeed different even though the air temperature responds to the same atmospheric forcing as the equilibrium temperature of the waterbody. So, the text should read that air and equilibrium temperature correlate – but are not approximations for each other.
Line 65-70: Almost as important as the approach used are the variables used in the regression and other models. Could a listing of the predictor variables be itemized? Or is it just air temperature?
Line 74: Why single out wind velocity? One also needs air temperature, dew point temperature (or relative humidity), cloud cover and short-wave solar radiation also to compute the heat balance.
Line 76-77: It is not clear if the river modeling is using the predictors or if it is just the boundary conditions are being predicted for use in a river model.
Table 1: I assume the error statistics are for the river WT – not the boundary conditions. So, I assumed in reading this that for each of these models, there was no explicit river model other than the correlations/stochastic models. But as a reader I am confused since I thought the intent of the paper was focused on boundary conditions and techniques to determine boundary conditions.
Line 86/87/105: Now the focus moves to lake or reservoir models. I thought the focus was on river models as the receiving water body – see Line 96. I agree that developing the boundary conditions would benefit lake/reservoir models, but the focus in the abstract and throughout the paper needs to be refocused to include any receiving water quality model, not just rivers.
Line 136/Table 2: I have no idea what the total number refers to in Table 2 nor the statistics. Are these ‘predictors’ or are these WT in the rivers? What are the units of mean, etc.? And please itemize clearly what the predictors are for training and validation. Or do they vary? This is critical to understanding if this approach can be used by others.
Line 143: ‘model a significant number of watersheds’ – does this mean just for WT and flow? Or does it include stage also?
Line 148/149: Not having on-site meteorological data is large weakness of this study. We have found that the on-line estimates are often poor and significantly affect the model predictions. In the basin where you did your analysis, there must be some meteorological stations that could have been used for ground-truthing the ERA5 ‘data’. Doing that comparison would also help inform readers of the bias in using estimates when there is no on-site meteorological data.
Line 155: Why was this lapse rate chosen, -6.5oK/km? What are the impacts of assuming a fixed lapse rate over all your model domains?
Line 163: Why is there a larger training dataset than a validation dataset? One would expect then with more training data that the results should be ‘better trained’ or more valid? What happens if the training and validation datasets were 80-20%?
Line 196: ‘The results from the various models were evaluated with six metrics considering the observed and predicted annual, dry and wet season datasets for river WT.’ Does this imply that the predicted annual WT was used as a metric? Of what value is such a metric? Most river WT models are focused on maximum daily temperatures for fish habitat.
Line 243 Eq (1): The equation has an error in the last term.
Eq (1): This river equation assumes that the flow rate is based on steady-state flow with no dispersion. I assume this model runs on a daily time step – assuming a new steady-state distribution each day? This should be clarified. Also, the term H is a critical parameter in this model, how was it determined and what were the meteorological variables necessary for its computation?
Eq (4): What precisely were the regression variables used in this model?
Line 285: Was time of concentration only for the hydrology prediction? What is the hydrology model prediction equation?
Line 317: With the best performing model to have a RMSE of over 3oC is not convincing. For river temperature models, this type of error in the river or in the boundary conditions is too high. There must be other issues with your approach that lends itself to such a poor predictor. In our experience, river models (and lakes and reservoirs) are often well below 1oC RMSE. I would not use any of these approaches if it had such a high RMSE. And if you fixed the underlying issues, the best approach may change.
Table 4 – provide units. By annual datasets – what does that mean? You are comparing annual averages or daily averages to field data?
Table 5 – provide units. Explain dry season datasets – daily data during dry season, or averaged data over an entire season?
Table 7 – provide units.