Enhancing the Lagrangian approach for moisture source identification through sensitivity testing of assumptions using BTrIMS1.1

Mu, Yinglin; Evans, Jason; Taschetto, Andrea; Holgate, Chiara

doi:https://doi.org/10.5194/egusphere-2025-2833

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https://doi.org/10.5194/egusphere-2025-2833

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22 Jul 2025

| 22 Jul 2025

Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).

Enhancing the Lagrangian approach for moisture source identification through sensitivity testing of assumptions using BTrIMS1.1

Yinglin Mu, Jason Evans, Andrea Taschetto, and Chiara Holgate

Abstract. Moisture is the fundamental basis for precipitation, and understanding the sources of moisture is crucial for comprehending changes in precipitation patterns. Lagrangian models have been employed for moisture tracking in both extreme weather events and climatological studies as a means to gain insight into driving physical processes. Lagrangian moisture tracking models follow independent air parcels based on a set of defined assumptions. Despite the existence of many Lagrangian models and studies applying them for moisture tracking, these assumptions are seldom thoroughly tested.

In this study, we use the Lagrangian model BTrIMS to demonstrate the impact of these assumptions on the results of moisture source identification. In particular, we test the method’s dependence on the number of air parcels released; the height that parcels are released; the vertical movement of air parcels; the vertical well-mixed assumptions that lead to different moisture identification methods along trajectories, the within-grid interpolation method and the back-trajectory time step. We find that releasing approximately 200 air parcels per day from each grid point is necessary to obtain accurate results for a region of 10 grid points or more (an area of ~9,000 km² in this case). Additionally, the vertical movement of air parcels, their release height, and along-trajectory identification method of moisture substantially affect the identified moisture sources, whereas within-grid interpolation and back-trajectory time step within a reasonable range has a relatively minor role on the results. The mechanisms behind these assumptions involve heat exchange, precipitation formation height, vertical mixing of surface evapotranspiration, and numerical noise, all of which must be carefully considered for realistic results.

Based on the results of sensitivity tests and analysis of underlying mechanisms behind the assumptions, we improve the Lagrangian model BTrIMS1.0 to a new version (BTrIMS1.1) for broader applicability. The findings of this study provide critical information for improving Lagrangian moisture source identification methods in general and will benefit future research in this field, including studies examining changes in moisture sources due to climate change.

Received: 14 Jun 2025 – Discussion started: 22 Jul 2025

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Yinglin Mu, Jason Evans, Andrea Taschetto, and Chiara Holgate

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RC1:
'Comment on egusphere-2025-2833', Anonymous Referee #1, 12 Aug 2025 reply
This study investigates the sensitivity of the Lagrangian estimation of moisture sources for precipitation to the choice of different assumptions and configurations, using the model BTrIMS. The authors explore several factors that could guide researchers in selecting appropriate settings for moisture tracking, such as the number of parcels released, the time step in the trajectory method, the initial vertical distribution of parcels, and the influence of different interpolation methods or mixing schemes. Although only one model is used, the results of some of the experiments are easily extrapolated to other models. Overall, the study is well-defined, clearly presented, and well written. The main area of improvement lies in the presentation of results, as in the absence of a general ground truth it is difficult to identify the optimal configuration from certain experiments. Furthermore, presenting the results for the three analyzed cases, together with a more rigorous exposition of the methodology, would help readers follow the conclusions more easily, as elaborated in the general and specific comments below.
General comments
Lack of a reference configuration for comparison. Except for the test involving the number of air parcels released per grid point, there is not a reference configuration against which to compare the results. It would be beneficial to define a standard or “reference configuration” of BrTrIMS, which would be the most complex and realistic one, and then analyze how relaxing specific assumptions or modifying different components of the configuration impacts the results. For instance, the reference configuration could involve releasing 1000 air parcels per grid point, using the wind field for the vertical movement (kinetical scheme), using the ET-mixing method for moisture tracking, applying bicubic interpolation, and employing the smallest time step. Using this approach and clearly stating the reference setup in Sect. 2 would help the reader in following the analysis, as I find it difficult to determine the exact configuration that is being used in each subsection of Sect. 3. For example, what is the time step in Sect. 3.1? How many parcels per grid point are released in Sect. 3.6? Additionally, in cases where it is unclear which configuration is more realistic (such as choosing between the ET-mixing approach and WaterSip for moisture tracking) I would avoid making categorical statements about one setup underestimating results compared to the other, since there is not a “ground truth” for direct comparison in these cases.

Focus on the Australian event. Although this study analyzes three different precipitation events (Australia, Pakistan and Scotland cases), the main manuscript presents results only for the Australian event. I believe that in most subsections it would be feasible and beneficial to include results for all three events, either by presenting them side by side or by averaging. For instance, in Sect. 3.1, the results shown in Fig. 1 could be averaged across the three events, which would provide the same information. In the case of Fig. 2 averaging may provide less valuable information, but it would still be possible to show the curves for all three events using a single value of pattern correlation, and move the analysis for different values of the pattern correlation to the supplement. Similarly, the subsequent maps could be easily displayed for all three events together, as there is minimal overlap between them.

Specific comments
L59-1: COSMO is a meteorological model used for numerical weather prediction and atmospheric research, not an Eulerian method for moisture tracking. In Winschall et al., (2014) they use an Eulerian tagging approach implemented in this model. It would be useful to clarify this information.
L59-2: The water vapor tracers implemented in the WRF model are most commonly abbreviated as WRF-WVTs. Also, the correct article to cite is Insua-Costa et al., (2018), where this tool is presented and validated in detail.
L60-61: Here it is asserted that Eulerian moisture tracking methods “are precise”. While this is true in general, the accuracy of these methods depends on how well the meteorological models in which they are implemented represent reality. It is possible to have a model simulation very deviated from reality, and then the moisture source calculation would be accurate in the model world, but not in reality. In this case, a moisture tracking method using reanalysis would be more accurate. Please, clarify that water vapor tagging methods depend on the accuracy of the underlying meteorological model.
L75: For accuracy and rigor, please use this more-explicit form of the trajectory equation dX/dt=u[X(t)], where the full dependence on time is highlighted. The velocity field u may also depend on time, not only on the 3-dimensional position. Furthermore, although it is useful to interpret dx and dt as the air parcel’s displacement in one time step and the time step, from a mathematical point of view it is not correct to state that, since dX/dt is just the derivative of X with respect to time.
L79-81: This may lead to misunderstanding, as it appears that Dirmeyer and Brubaker, (1999) do not use the wind fields at all. Please rephrase to indicate that wind fields are used in trajectory calculations to drive the horizontal movement of the parcel.
L84: FLEXPART also includes a detailed description of turbulence.
L97: Typo in “These two identification methods also differS in this”.
L100: “Due to limitations in Eulerian methods for moisture tracking”. It would be useful to expand on these limitations. In L61 the need to predefine water source regions is mentioned. What about the computational requirements of these methods?
L113: “there are three schemes based on different theories”. Please, refer to the section/subsection where these schemes are introduced and explained.
L136-137: “The air parcels are advected by wind” suggests a forward tracking of air parcels. Please rephrase for clarity. Also, here and in other parts of the manuscript, there is a reference to a “predefined large domain”, but it is not stated anywhere what this domain is (it may be deduced from Fig. 4). It would be useful to include a visualization of the domains in the appendix.
L173-L189: Although the description of the Australia event is very complete and detailed, I would move it to the appendix, as it may distract the reader from the main focus of the paper. I would only include a small summary with the most essential characteristics of the event, and perhaps also include a small summary of the other two cases.
L200-201: “total-precipitable-water-weighted height”. The total precipitable water is a two-dimensional field, calculated as the integral of all water components in the atmospheric column. Thus, this expression may lead to misunderstanding. If parcels are released randomly vertically following the humidity profile, please replace “total-precipitable-water” with “humidity”, otherwise explain how parcels are released in more detail.
L225-L238: I do not see the point of having this equation and all the involved parameters here. I would consider moving it to the appendix.
L276-278: Option 2 does not impose a threshold on initial relative humidity or require moisture uptake to occur within the PBL, arguing that subgrid processes can allow the lower troposphere to contribute to precipitation. This is true in general, but it also depends on the chosen time step. Since the time steps used in this study are short (less than 1 hour), I believe that the initial relative humidity threshold may have an important effect on the results. It would be useful to include these results in the appendix, even if the impact on the results is less important than expected.
L291-305: The only difference between the first set of equations and the second is in frac_n1’ and frac_n2’, as fac_q may be updated as fac_q(1- frac_n1’). Considering this can help reduce the number of equations here and also to explain the differences between both sets of equations. If left as is, I would move the equations to the appendix and explain them in detail there.
L318: It would be useful to clarify here if parcels are also released from every grid point where precipitation occurs every time step, or if they are released with less frequency (for example, every 1 or 3 hours).
L321-322: I understand that pattern correlations are calculated by computing the Pearson correlation coefficient between two spatial distributions of moisture sources: the “true” one (1000 parcels) and the tested one (50, 100, 200 and 500 parcels). If this is the case, please explain it in more detail. Otherwise, explain how pattern correlation is calculated.
Furthermore, I think it could be better explained how the results in Fig. 1 are obtained. If I understand correctly, the Australian event involves a certain number of points (around 1000) where precipitation is larger than 1 mm, and then, for each given number of grid points, a smaller region of this size is being selected to calculate the pattern correlation. The smaller the number of grid points, the greater the number of regions that can be selected, and therefore the variability in pattern correlation decreases with the number of grid points.
L351: “Since we only selected four air parcels per grid point”. I understand that you are referring to the maximum number of air parcels per grid point (50, 100, 200 and 500). Thus, it would be more accurate to say “four different numbers of air parcels per grid point”.
L487: Shouldn’t it be “(e)” instead of “(f)”?
L540: Due to the absence of a reference for comparison, I would not use words such as “underestimate”. It is true that WaterSip gives more importance to local sources than other methods, but here there is not a reference methodology with which to compare the results, so it cannot be said whether the correct results are those of WaterSip or those of BrTrIMS.
L546: Shouldn’t it be “comes” instead of “coming”?
L548: What is the meaning here of “air column dividing”?

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Citation: https://doi.org/10.5194/egusphere-2025-2833-RC1
RC2: 'Comment on egusphere-2025-2833', Anonymous Referee #2, 19 Sep 2025 reply

This study uses a variety of sensitivity experiments to assess the uncertainty of moisture source calculations based on methodological assumptions. These experiments cover different setups for trajectory calculations, dataset resolutions and moisture source diagnostics for three case studies. For all experiments, the authors provide recommendations for choosing parameters and diagnostics. The study is well-written and logically structured.

While this study investigates important questions regarding the uncertainty of Lagrangian moisture source identification, it focuses mostly on one moisture source diagnostic (ET-mixing) and relies on previous studies for many recommendations. While the authors imply in the introduction that the new aspects of this study are the combination of several Lagrangian moisture source diagnostics with several case studies and precipitation types, the results focus mostly on an Australian case study and the ET-mixing method. The study could be improved by integrating the three case studies better, extending the sensitivity experiment to test more assumptions for other methods than ET-mixing and better justifying the recommendations and choice of setup.
Main comments:
1. Case study introduction and discussion: In section 2.3, three case studies are introduced, highlighting that "an assumption that is physically meaningful in one region or specific type of precipitation events may deviate significantly from reality in another region or under different meteorological conditions." This is an important aspect to investigate, but only the Australian case study is introduced in the paper with some detail, while the other two remain in the supplement. Further, no synoptic charts of the case studies are shown. The comparison of these case studies take little space in the results and discussion sections, even though it is implied in the introduction that the comparison of events from different climatological regions is a new aspect of this study compared to previous studies (see lines 100-104). To understand the differences between the moisture source diagnostic, it'll help to have a better description of the synoptic processes, instead of climate modes, and e.g. vertical wind shear, vertical moisture structure and boundary layer height.
2. Comparison of moisture source diagnostics: Large parts of the sensitivity experiments are based on a moisture source diagnostic based on the ET-mixing assumption. For one sensitivity experiment, the WaterSip method is used in the BTrIMS1.1 setting, but no sensitivity tests are done on the assumptions going into the WaterSip calculations (e.g. RH threshold or deltaq threshold). Further, the parcel release height is based on a different method (vertical humidity profile) than commonly used in WaterSip (a combination of detlaq and an RH threshold). In this current form, I would not call this study a comparison of several Lagrangian moisture source identifications, as it mostly focuses on one method and does not use standard setups for other methods. Therefore, results for WaterSip from this study are not comparable to many other studies.
3. Physical concepts: Physical processes and concepts, and decisions based on them, could be explained better, e.g. why an RH threshold to detect the cloud layer (layer of origin of precipitation) is worse than using a vertical water vapour profile (section 2.4.3), "well-developed cyclonic boundary" (lines 372-373), moisture convergence and its effect on Lagrangian tracking of moisture, WaterSip and the well-mixed method (line 445ff), the effect of combining ET-mixing and WaterSip on the water budget along the trajectory (Option 3 and 4 in section 2.4.4).
4. Recommendations: Except for the recommendation on the number of parcels released per day, the recommendations on the best setup of the diagnostics should be better motivated. Without knowing the true moisture sources (where it is not known if the ET-mixing or WaterSip method is closer to the truth), the recommendations are often based on theoretical concepts or previous studies, while it is not clear how the sensitivity tests inform these recommendations.
Detailed comments:
Title: What do mean with "enhancing" the Lagrangian approach?

Line 22: 200 air parcels per day -> at different heights? or different time steps? Per grid point?

Line 26: "the mechanisms behind these assumption" -> do you mean the mechanism that lead to different moisture sources based on different assumptions in the moisture source diagnostic? Consider rephrasing.

Line 26: "heat exchange" between air parcels? Or between the surface and the atmosphere?

Lines 57-58: "The tracking process is incorporated into the model in parallel with the water accounting process." What do you mean with "water accounting process"?

Lines 59-60: "The former is primarily used for climatological studies, while the latter is more frequently employed for regional research requiring higher resolution." Can you provide more references for this statement? COSMOtag is also used for regional high resolution simulations (e.g. the cited study by Winschall et al. (2014) is a regional case study).

Line 74: Equation 1 is not yet well described and integrated in text.

Line 84: Also FLEXPART considers turbulence.

Line 93: "as moisture sources" -> as surface moisture sources?

Line 94: Sodemann (2008) -> Sodemann at el. (2008). This reference has been wrongly formatted in several places.

Line 119: Can you provide a reference for cubic interpolation in Lagrangian studies?

Line 123: What do you mean with subprocesses?

Lines 155-156: "Temperature (T) is used to calculate potential temperature (θ) and equivalent potential temperature (θe)." -> also water vapour mixing ratio and pressure are needed to calculate the equivalent potential temperature.

Line 168: Can you be more specific what you mean by different types of precipitation events?

Section 2.3.1: Climate modes are important drivers of interannual variability. To understand differences in the moisture sources, a synoptic-scale description of the events would be more helpful.

Section 2.3.2: A description of how they differ with respect to precipitation type and synoptic settings would help to better understand differences between the events.

Lines 215-216: "Within the boundary layer, potential temperature is modified by convective diabatic processes." This sentence seems disconnected from the method description. Can you clarify, why this is important for quasi-isentropic movement?

Line 225: Equation 2: Consider removing these equations as they are commonly known.

Secion 2.4.3: Why is a vertical profile of precipitable water a good approximation of precipitation formation heights? The specific humidity is mostly highest in the boundary layer, close to the surface, but precipitation forms at elevated heights upon lifting. Tracking precipitation based on the vertical humidity profile might over-represent boundary layer moisture that does not contribute to precipitation.

Line 258: Can you elaborate on limitations of the well-mixed assumption?

Line 291: Many variables in these equations are not introduced.

Figure 1: The term "kinetic" has not been introduced in the methods section

Section 3.1: Can you introduce better how the number of parcels relate to the number of grid points?

Lines 332-333: "However, a minimum threshold for pattern correlation of each individual grid point must also be considered." Why "must"?

Lines 349-351: " Note that the curves in Fig. 2, Fig. S2, and Fig. S4 are intended as qualitative illustrations only, aimed at showing the relative differences among the various vertical movement schemes of air parcels, since we only tested four air parcels per grid point." What do you mean by qualitative illustrations? Are these not quantitative results from the sensitivity experiments?

Section 3.2, 3.5: What is the setup of the diagnostic (apart from the vertical movement)?

Line 394: "This could be due to the initial θ underestimating the real θ during the air parcel’s movement." What is the real θ? From observations and not from reanalysis?

Lines 425-428: ERA5 runs at a smaller time step than 1-hourly output and parameterises convective processes. Thus, it's true that it does not fully resolve convective processes. But in the hourly output, the instantaneous cloud properties are provided, which represent the cloud location in the model world. As all calculations are based on the reanalysis data, relying on model output for the vertical extent of the cloud, seems reasonable. Therefore, I don't understand why Option 1 (including also water vapour) better represents the location of precipitation formation than Option 3.

Lines 447-450: " Consequently, the WaterSip method will capture the convergence-related atmospheric river, but may not necessarily identify the original, surface evaporative sources of the atmospheric moisture. In contrast, the ET-mixing method records the percentage of moisture from below the current grid point relative to all moisture in the air parcel, and is thus more directly related to surface ET. " Can you explain what you mean by convergence? Large-scale convergence is represented by air parcels and, thus, when tracking moisture along the trajectories, the moisture source along different branches of trajectories are identified by WaterSip and ET-mixing. If there is substantial (turbulent) mixing of air that leads to changes in the moisture content, such a moisture uptake is identified by WaterSip, thereby losing information on the original surface moisture source. But if the convergence of air is not correctly represented by the trajectories (e.g. because strong turbulence/mixing is involved), also ET-mixing will be misrepresenting the moisture sources. Further, if an air parcel takes up moisture due to subscale processes, also ET-mixing might not identify the original source of this moisture as the trajectory flow does not follow the flow of the moisture in the subgrid processes (e.g. during turbulent mixing). Can you be more specific here to which processes you are referring, and if these processes affect the trajectory calculations or the moisture source identification.

Line 481: The recommendation for Option 4 is only based on theoretical assumption. There is no evidence from the studies results that the combination of ET-mixing and WaterSip correctly represent the theoretical framework and the processes in reality. I would not make any recommendation based on these results.

Line 540: "underestimate" -> without knowing the true state, I would not used the terms under- or overestimation

Lines 542-543: "In comparison, the ET-mixing method more directly identifies regions where moisture originates via evapotranspiration from land or ocean surfaces..." This direct connection to the surface is by construction. The moisture source regions could still be missrepresented (see comment on Lines 447-450).

Lines 548-550: " Finally, for the moisture identification, air column dividing and convection are both considered." Does this refer to the recommendation for Option 4? I would not include a recommendation without have a true state for comparison.

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Citation: https://doi.org/10.5194/egusphere-2025-2833-RC2

Yinglin Mu, Jason Evans, Andrea Taschetto, and Chiara Holgate

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https://doi.org/10.5194/egusphere-2025-2833-supplement

Yinglin Mu, Jason Evans, Andrea Taschetto, and Chiara Holgate

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Short summary

Lagrangian approaches have been increasingly employed due to their suitability for extreme events and climatological studies in finding moisture sources of precipitation. However, as these approaches track independent air parcels carrying moisture—rather than simulate processes based on governing physical equations—they rely on several underlying assumptions. This study tests these assumptions and refines the approaches to enhance their broader applicability.


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