the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Inferring flow energy, space and time scales: freely-drifting vs fixed point observations
Abstract. A novel method for the inference of spatiotemporal decomposition of oceanic variability is presented and its performance assessed in a synthetic idealized configuration. The method is designed here to ingest velocity observation. The abilities of networks of reduced number of surface drifters and moorings at inferring spatiotemporal scales of ocean variability are quantified and contrasted. The sensitivities of inference performances for both types of platforms to the number of observation, geometrical configurations, flow regimes are presented. Because they simultaneously sample spatial and temporal variability, drifters are shown to be able to capture both spatial and temporal flow properties even when deployed in isolation. Moorings are particularly adequate for the characterization of the flow temporal variability, and may also capture spatial scales provided they are multiplied and the financial and environmental costs of associated deployments can be assumed. We show in particular that the method correctly identifies whether drifters are sampling preferentially spatial vs temporal variability. This method opens novel avenues for the analysis of existing datasets as well as the design of future experimental campaigns targeting the characterization of small scale (e.g. <100 km) Ocean variability.
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RC1: 'Comment on npg-2024-10', Anonymous Referee #1, 09 May 2024
General:
The manuscript introduces a statistical approach to infer the spatial and temporal scales of ocean currents using drifters and moorings, under the assumption of idealized geostrophic currents. It is well-written and presents some interesting findings that offer valuable insights for optimizing future observational designs in the ocean. I anticipate further advancements and practical applications of this methodology in real-world oceanic contexts.
However, I have a few queries regarding the specifics of the geostrophic field and its applicability to real-world scenarios. While the conclusions drawn are predominantly qualitative, enhancing the experimental design and analysis could yield more quantitative results. Therefore, I have outlined both major and minor comments below for consideration.
Major:
- One basic assumption in the surface current field is geostrophic (a purely rotational flow in line 101). The grid space is set to 2.0 km. Such a horizontal resolution, however, is able to resolve sub-meso scale motions in the ocean, which are not purely rotational. One alternative resolution will be ~10 km under a geostrophic situation. I wonder whether a changed grid space will affect the results and final conclusion. Also, I am interested in the practical application of the method. The AVISO products provide a near-realistic geostrophic surface current field that can be analyzed with this approach. Regional studies based on such data will have better application prospects while avoiding too much computational resources.
- One important goal of this study is to provide guidance on future experimental campaigns. The conclusions are more qualitative than quantitative. Some useful quantitative information could be obtained with an improved experimental design in section 2.5. It would be better to compare the results of SEP[dx] with those in REF or just a baseline of IQW. Larger observation spacing facilitates more observation coverage, but at the same time may lead to large IQW. Once a baseline is set, the selection of an optimal distance [dx] can be discussed. Similarly, more observations are more accurate, but will cost more. A balance can be found with a suitable number of observations.
Minor:
- Line 2: The idealized configuration is geostrophic, of which the latter is more accurate.
- Line 2: ingest surface velocity observation
- Line 11: It’s essential to consider these limitations when assessing the potential applications of any scientific method. As the author mentioned, many ocean processes, such as tides and submesoscale processes, have not been included so far, and it seems that using existing data would encounter computational challenges.
- Line 12: The spatial scale in Figure 1 seems to be meso-scale. Also, the geostrophic assumption requires meso- or large scale.
- Line 123: what are the physical meanings of variables of U, lamda_s, lamda_t? I noticed that some of them occurred in lines 112 to 113.
- Line 142: How was the STD of white noise estimated? Will the results changes if a larger STD value is selected?
- Figures 2 &3: I guess that the comparison between Figure 2 and Figure 3 can be used to confirm the reliability of the MAP results. However, the inconsistency in the axis ranges, especially the horizontal axis, between the two figures makes it difficult to compare them.
- Subsection 2.4: Could you please go into more detail about how these parameters (i.e., U, lamda_s, lamda_t) are evaluated using u and v observations?
- Line 217: I am confused about the title of section 3.2. I thought the Experiment IND[Np] was conducted to investigate the number of observations (drifters or moorings). Why the title is named related to the time series length?
- Figure 5: Why do moorings show better performance than drifters with smaller Np? This is also mentioned in line 236.
- Line 234: what dose “time-only” mean? What is the purpose of this “time-only” drifter?
- Figure 6: the red colors are not clear enough. Also, I only found red color in fig.6c. Do the orange colors in (b) and (d) refer to the results of the “time-only” drifter?
Citation: https://doi.org/10.5194/npg-2024-10-RC1 -
RC2: 'Comment on npg-2024-10', Anonymous Referee #2, 11 Jun 2024
The authors stochastically generate a spatially non-divergent flow field with prescribed spatial and temporal covariance functions, intended to approximate oceanic surface flow. They then consider combinations of sparse Eulerian and Lagrangian observing platforms and attempt to infer some of the parameters of the stochastic models in some of the flow regimes. The results show that, in particular, drifters capture both the spatial and temporal parameters well in some cases.
The strength of this manuscript is that it focuses on a fairly narrow stochastic model and a specific methodology for inferring parameters. Thus, one can assess how well the inference method is doing extracting ‘true’ model parameters.
Major comments.
A comment on the flow model:
The authors note in the conclusion that this methodology should be extended to more realistic ocean models, and I strongly agree. The model is a sort of two-dimensional stochastic geostrophic model, lacking even quasigeostrophic (QG) dynamics which is a foundational model for our understanding of both Eulerian and Lagrangian flow statistics. To this point, the slope parameters chosen by the authors are a -3 and -5 slope seem awfully steep compared to what we’d expect in any realistic flow; at least that is my first reaction, but I’ll admit I am not certain. So either way it does seem worth justify these values and perhaps even considering QG dynamics to help the readers get a handle on where these parameters fit into known oceanic flow regimes.
Relatedly, the lack of waves in this model is a big deal. As noted in Beron-Vera & Lacasce’s “Statistics of simulated and observed pair separations in the Gulf of Mexico”, near inertial oscillations are a very dominate signal in the ocean for Lagrangian drifters (and Eulerian mooring for that matter) and fairly dramatically change the expected statistics at certain scales.
A comment on the inference method:
The authors have fixed the slope of the stochastic processes a priori (as noted in the previous comment), and also fed those known slopes into their inference model. This would appear to be a fairly significant limitation to the methodology. I note that some papers have succeeded in estimating the Matern slope parameters (at continuous values) of drifter velocities using e.g. Whittle likelihood techniques such as Sykulski et al 2016, where the Matern was applied to (importantly) Lagrangian time series and not a whole spatio-temporal field with separate spatial and temporal length scale parameters. Is it the case here that the statistical inference for a spatio-temporal field (and the corresponding addition of more parameters) is the reason why the slope parameters cannot be estimated at all (with any inference method, due to data sparsity), or is this rather a computational issue of the MCMC as hinted at in the appendix A.2 where only half integer values can be efficiently used, but potentially could with another inference method? Either way the reasoning for this motivation should be discussed in the main paper and not the appendix so it’s clear.
In addition, even if only half-integer values can be used, it is still reasonable to do some form of (possibly Bayesian) model choice over different half-integer values to select the most appropriate - perhaps the authors could investigate and apply such a procedure? At least this sort of “partial" inference allows the user to broadly select the right regime (e.g. QG with higher slopes) for the data set they have, rather than picking arbitrary and possibly wrong slope parameters which could heavily skew the other parameter estimates when misspecified significantly.
Minor comments:
1) Please define k and l on first usage in equations (7)-(9)
2) Line 123 is unclear, which \lambda is intended, \lamba_s or \lamda_t or some combination, in the computation of the amplitude of the streamfunction?
3) The paper is notation heavy, a table of notation would be very helpful, including providing values of parameters that are fixed, and highlighting which ones are left for estimation.
4) Please give more details on the choice of prior for the MCMC and how sensitive output is to the choice of this prior.
Citation: https://doi.org/10.5194/npg-2024-10-RC2 -
EC1: 'Comment on npg-2024-10', Jie Feng, 20 Jun 2024
The two Reviewers have provided insightful comments. Both of them appreciate the potential application of the method in this study to the optimal design of observing networks. However, Reviewer1 showed some concerns about the rationality of the physical assumption in the high resolution model. Reviewer2 comments on possible influence of the deficiencies of the simplified model on the results. I encourage the authors to submit a revised version of the manuscript in which all the comments from Reviewers should be explicitly addressed.
Citation: https://doi.org/10.5194/npg-2024-10-EC1
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