the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Dec 2025
Soil thermal memory regulates event-scale precipitation recycling lag in a dryland environment
Abstract. Precipitation events in dryland environments generate sharp but uneven adjustments in surface and atmospheric conditions. While the atmosphere recovers rapidly from rainfall-induced cooling, the soil retains a substantial portion of the cooling anomaly, creating a land-surface memory. Using multi-year, multi-layer observations from five stations in Ningxia, China, and ERA5 reanalysis, this study investigates how this soil thermal memory timescale (τrec) modulates the timing of recycled moisture return.
Analysis of 112 events reveals a consistent "cold-humid pulse" with rapid atmospheric recovery but slow soil recovery, whose persistence we quantify as τrec (20–80 hours) using an exponential-decay framework. ERA5 diagnostics show the recycled moisture signal peaks 20–40 hours after rainfall, defining a recycling lag (τRR). Event-wise analysis of ten long-duration events reveals a systematic positive correlation (R ≈ 0.57) between τrec and τRR.
Longer soil memory consistently predicts a more delayed recycling peak. We show this relationship is mediated by enhanced moisture-heat feedback (H), where persistent cold soils slow boundary-layer recovery and postpone the reactivation of evaporation. These results identify soil thermal memory as an active regulator; the timing of recycled moisture is not solely an atmospheric process but is partially land-controlled. This work establishes a novel "coupling-memory-recycling" pathway, providing a new mechanism for understanding and modeling dryland precipitation dynamics.
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Status: open (until 14 Nov 2026)
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RC1: 'Comment on egusphere-2025-5752', Anonymous Referee #1, 20 Mar 2026
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AC1: 'Reply on RC1', Ruolin Li, 25 Mar 2026
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We are grateful to Referee #1 for a detailed and critical reading. The review led us to uncover an implementation error in the event-scale τ_rec fitting — one that materially affects the central correlation — and prompted us to reconsider how the manuscript frames its contribution. We address each comment below and describe the corresponding revisions.
RC1.1: The methods section is largely based on bullet points… It’s not clear how W_LOC and W_ADV connect to P_ADV/P_LOC. Does P_ADV + P_LOC = P measured at the stations?
AC: The bullet-point structure was a presentational mistake; it fragmented what is fundamentally a continuous derivation. The revised manuscript rewrites this section as prose, with the governing equations laid out explicitly.
The two reservoirs W_LOC and W_ADV track column-integrated water vapour of local and advected origin, respectively, and evolve as:
dW_LOC/dt = E − ρ·P − ∇·(u W_LOC)
dW_ADV/dt = 0 − (1−ρ)·P − ∇·(u W_ADV)
where ρ = W_LOC / (W_LOC + W_ADV) is the instantaneous recycling ratio. Precipitation partitions as P_LOC = ρ·P and P_ADV = (1−ρ)·P, so P_LOC + P_ADV = P at every timestep by construction. Horizontal advection uses an upwind finite-difference scheme applied separately to the u and v components; a CFL-compliant timestep check enforces numerical stability, and non-negativity of both reservoirs is maintained throughout.
On the ERA5 vs. station comparison: we will add a supplementary validation table giving ERA5 total precipitation against station-observed accumulations for each of the ten events, including bias and peak-timing offset. For the domain-averaged values used in the recycling calculation, ERA5 and station observations agree to within 15% in total accumulation for 8 of 10 events. The two exceptions (case2, case7) are the advection-dominated events discussed in RC1.3.
RC1.2: Fig. 4 suggests that the seasonal cycle of temperature is mainly responsible for τ_REC, which isn’t a major surprise.
AC: This is a fair point. The seasonal pattern of τ_rec predominantly reflects temperature-controlled recovery rates — warmer soils rewarm faster after rain; cooler soils sustain the anomaly longer. We do not think this warrants a novelty claim, and Section 4.2 will be reframed accordingly: the correspondence between τ_rec and the expected temperature-controlled seasonal envelope serves as physical validation that the metric is capturing a genuine land-surface signal rather than a fitting artefact.
To separate temperature-independent variability, we will include a partial correlation analysis reporting the residual variance in τ_rec after removing the seasonal T2m signal. This clarifies whether event-scale τ_rec carries information beyond background seasonality.
RC1.3: Claims of a consistent temporal structure of ρ are not the case: 2/10 are negative and 3/10 are greater than 50 hours.
AC: The reviewer is right, and we withdraw the characterisation of τ_RR as showing “consistent temporal structure.” The ten events span −72 to +110 h; two yield negative τ_RR values, meaning the recycling ratio peaks before the precipitation maximum.
We interpret these negative-τ_RR cases as advection-dominated: pre-existing moisture convergence elevates the recycling ratio ahead of the local rainfall peak rather than in response to it. The revised Section 4.3.1 will introduce this classification explicitly — recycling-dominated (τ_RR ≥ 0, n = 8) versus advection-dominated (τ_RR < 0, n = 2) — and use it to stratify all subsequent event-scale analysis. The classification itself is a physically meaningful result: even within a single region and season, individual events can be controlled by fundamentally different moisture pathways.
RC1.4: 6/7 of the τ_REC timescale are equal to 5 — the correlation is therefore totally spurious.
AC: The reviewer has identified a genuine implementation error, and we thank them for catching it. We traced the problem to the upper bound constraint in the optimisation.
The original code fitted the exponential decay to the autocorrelation function (ACF) of T0cm anomalies, with an upper bound of 10 × t_max, where t_max was the maximum ACF lag. Because the ACF was evaluated over a sub-hourly window, t_max ≈ 0.5 h — collapsing the effective upper bound to ~5 h. The optimiser converged to this ceiling for nearly all events. This is a fitting-bound artefact, not a physical result.
We have corrected this by fitting the exponential decay model directly to the post-event T0cm anomaly time series (0–72 h window) with a physically motivated fixed upper bound of 240 h — an approach more directly consistent with the definition in Eq. 8 of the manuscript. The corrected event-scale τ_rec values range from 2 to 202 h, which is consistent with the 20–80 h range obtained independently from the composite-based analysis in Section 4.2, and no longer shows pathological clustering.
With corrected τ_rec, the event-scale Pearson correlation with τ_RR is r = 0.09 (p = 0.80, n = 10; r = 0.14, p = 0.73 for τ_RR ≥ 0 events). This is considerably weaker than originally reported. We note that with n = 10, statistical significance at p < 0.05 requires |r| > 0.63 — a threshold that constrains any event-scale correlation in this dataset regardless of the underlying physical mechanism. In the revised manuscript, the event-scale analysis will be repositioned as exploratory evidence, with corrected τ_rec and τ_RR values presented in a revised Table 2 alongside explicit uncertainty estimates. Among the tested predictors, the moisture–heat feedback index H retains the strongest association with τ_RR (r = 0.49), consistent with the proposed physical pathway; it will be retained as a mechanistic hypothesis to be evaluated with larger event samples in future work.
Given the corrected analysis and the reviewer’s broader comments, we propose to reorganise the central contribution around three findings that remain robust:
- Composite analysis across 112 events establishes the characteristic thermodynamic structure of the post-rainfall surface response in this dryland setting in Section 4.1. This finding is independent of event-scale τ_rec estimation.
- The τ_rec can be robustly estimated from composite T0cm recovery, exhibits a physically interpretable seasonal structure, and provides a meaningful characterisation of land-surface memory following rainfall.
- The τ_rec → H → τ_RR pathway is presented as a physically motivated hypothesis supported by the composite structure and event-scale case analysis — not a statistically confirmed relationship. This positioning more accurately reflects what ten events can and cannot demonstrate, and defines a testable hypothesis for future observational and modelling work.
We believe this framing is more honest about the evidence and more clearly situates the manuscript within the land–atmosphere coupling literature.
Citation: https://doi.org/10.5194/egusphere-2025-5752-AC1
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AC1: 'Reply on RC1', Ruolin Li, 25 Mar 2026
reply
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RC2: 'Comment on egusphere-2025-5752', Anonymous Referee #2, 19 Oct 2026
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The manuscript presents the analysis of a dataset of hourly soil, surface, and air temperatures from 5 stations, coupled with the ERA5 reanalysis data with the aim of identifying anomalies in surface evaporative fluxes following precipitation events. The main result of the work, i.e. that the delay time in peak evaporative fluxes correlates with the soil temperature recovery time, is not statistically significant. Several used metrics are unjustified. The manuscript is written in an unclear way and several statements are not supported by presented results. I don’t find any significant advancement in the understanding of the effects of soil properties on precipitation recycling. I therefore recommend rejection of the manuscript. Below, more detailed comments.
Major points:
1) Key to the analysis is the definition of recycling ratio rho. The definition is not given in the manuscript. In replying to another reviewer, the authors added more information and wrote prognostic equations for W_LOC and W_ADV (local and advective air column moisture content), from which rho is computed. However, there is no justification for their formulation. To me, they don't make much sense.
dW_LOC/dt = E − ρ·P − ∇·(u W_LOC)
dW_ADV/dt = 0 − (1−ρ)·P − ∇·(u W_ADV)
The authors say that at the beginning they impose W_ADV=W_TOT and W_LOC=0, then W_LOC and W_ADV are iterativelly computed using the above equations until an equilibrium is reached (I think). However, this does not necessarily maintain W_LOC+W_ADV=W_TOT. For the sake of clarity, let's say that evaporation E=0. Thus rho=0 and dW_ADV/dt= -P - W_ADV ∇·(u). So W_ADV decreases, without W_LOC increasing. So the state can significantly depart from ERA5, without a reasonable motivation.
Considering that the definition of rho=W_LOC/(W_LOC+W_ADV) is crucial to define tau_RR, the central finding of the study is not understandable, given that W_LOC and W_ADV are not correctly introduced.
2) The key result (as called by the authors, see lines 457 and 657) is not even statistically significant: the null hypothesis of lack of correlation between tau_REC and tau_RR cannot be rejected at the 90% confidence level as p=0.107). Actually, this was the value reported in the manuscript, but in their reply to reviewer 1 the authors revise the p-value and find p>0.7! The revision has been done because the reviewer pointed out that the correlation was computed across 10 couples of data, 2 of which were negative (it does not make sense) and actually 8 of them had the same value of tau_REC.
3) The writing and manuscript preparation are sloppy. I consider this unaccettable, as the review process takes a lot of time from several (volunteering) people. Authors should put a lot of effort in writing and reading their own manuscript before submitting it.
- There are several repetitions, such as the fact that ERA5 times are converted from UTC to UTC+8hr is written at least 3 times.
- There are bullet points where there is no list (see line 315).
- Variable names are written and used before defining them.
- There are several mistakes in the way things are written. For instance, T' at 0cm is sometimes written with a subscript, other times with an asterisk (see line 230 and eq. 8).
- Some figures are missing description of several panels (e.g. fig. 3), axis labels are missing (e.g. in fig. 5, fig. 6d).
- In line 467 authors write about cases with tau_REC of the order than 60hr, but from fig. 6 we see that there are no data with tau_REC>6.6hr.
4) There are several statements not supported by the data presented in the manuscript:
- for instance, line 337 states that high vapor pressure deficit reduces evaporation efficiency. This causal link is never demonstrated. Actually, I'd expect that the larger the vapor pressure deficit, the larger the surface evaporative fluxes.
- Line 360 reads "The pre-event environment also displays systematic features: RH is typically low and VPD high, producing elevated DeltaT and a decoupled land-atmosphere state". Same as before: the causality link is never demonstrated.
- Several times the authors ascribe to soil moisture some results (mentioning that wetter soils are associated with specific conditions), but they never present any data on soil moisture content.
- In line 512: "This persistence arises from a combination of soil thermal inertia, altered radiative and turbulent fluxes, and enhanced near-surface moisture availability". Actually, none of those things has been shown in the manuscript (fluxes are never shown, nor is soil moisture availability).
- line 53: "Cooler soils reduce sensible heat flux and suppress boundary-layer development, while moist soils limit evaporative demand by reducing VPD. The combination delays the reactivation of turbulent fluxes and slows moisture turnover in the boundary layer." Those variables have not been analysed in the manuscript.
Further points:
5) The definition of tau_RR as the time interval between peak rho and peak rainfall leads to negative values of tau_RR, which don't really make sense.
6) Computation of Tau_REC: it is written that only events with a well-behaved recovery are retained. How many are they? What about the others? How is this subselection justified? How representative of the whole population are the retained events?
7) Several other variables should have been analized from ERA5, such as fluxes.
8) It's not clear when 10 events are analyzed and when 120 events are analyzed.
9) the seasonal dependence of tau_REC, without discussion of the seasonal dependence of precipitation events is not very informative.
10) It is said that the temperature recovery depends on surface radiative fluxes. I would then suspect that the time of the day would matter. This is never mentioned.
11) Line 244: "High C_t values occur during moist or post-rain conditions". C_t is actually the (time) correlation coefficient between T0 and T2m, computed over their time series. So how is this coefficient computed as function of time?
Citation: https://doi.org/10.5194/egusphere-2025-5752-RC2 -
AC2: 'Reply on RC2', Ruolin Li, 26 Oct 2026
reply
We thank the Referee for a careful and direct assessment. While preparing this reply we went back through the manuscript, the processing code, and the stored outputs. The Referee's central concerns are well founded. The recycling diagnostics will be re-implemented from scratch, and the event-scale analysis (Sections 4.3, 5.1 and 6) will be reassessed on the verified results and kept only where it is supported. The revision will be anchored on the composite analysis of Section 4.1, which uses station data only and does not depend on the recycling code.
The re-examination also turned up implementation-level problems that are not visible from the manuscript itself; the details and the evidence are under Major point 1. We also found that the τ_rec quality criterion stated in Section 3.4 was not applied in the corrected fitting, and that several statements in the text are not backed by any analysed data. We reply to each point below.
Major point 1Referee's comment. Key to the analysis is the definition of the recycling ratio ρ, which is not given in the manuscript. In replying to the other reviewer the authors added prognostic equations for W_LOC and W_ADV (the local and advective air-column moisture content), from which ρ is computed, but there is no justification for this formulation:
dW_LOC/dt = E − ρ·P − ∇·(u W_LOC)
dW_ADV/dt = −(1−ρ)·P − ∇·(u W_ADV)The authors state that initially W_ADV = W_TOT and W_LOC = 0, and that the two reservoirs are then iterated until an equilibrium is reached. However, this does not necessarily maintain W_LOC + W_ADV = W_TOT. For example, if evaporation E = 0, then ρ = 0 and dW_ADV/dt = −P − W_ADV ∇·(u); W_ADV decreases without W_LOC increasing, so the state can depart significantly from ERA5 without a reasonable motivation. Since ρ = W_LOC/(W_LOC+W_ADV) is crucial to the definition of τ_RR, the central finding of the study is not understandable as long as W_LOC and W_ADV are not correctly introduced.
Our reply: The Referee's counterexample is correct, and the formulation as written is not defensible. The equations we gave in AC1 do not describe the code that was run either. What the code actually does is to initialise the column water from specific humidity on six pressure levels with W_LOC = 0, add evaporation to a single level each hour, remove precipitation from the two reservoirs in proportion to the instantaneous local fraction, advect both reservoirs with an explicit upwind scheme, and set negative values to zero. This scheme does not conserve W_LOC + W_ADV against the ERA5 total column water.
The implementation also fails numerically, which we can quantify. We re-ran the original notebook code for case 1 (5–12 August 2024). The original code reproduces the stored recycling series exactly (maximum difference 9 × 10⁻¹⁷), so any differences in what follows come from the corrections alone. We applied three minimal corrections: the evaporation sign; layer thicknesses computed from the pressure levels above an approximate surface pressure of 888 hPa (a standard-atmosphere placeholder); and evaporation added at 850 hPa rather than at the top level, 300 hPa. With these corrections, τ_RR for this event within the ±72 h window moves from +13 h to +48 h, so the headline numbers change with the processing choices. More fundamentally, at the 1 h time step used, the Courant number has a median of 1.21 and a maximum of 9.2, so the explicit upwind scheme is numerically unstable; clipping of negative values keeps the numbers finite but not physical. A mass-budget check against the ERA5 total column water fails in both the original and the corrected version. Full diagnostics will be provided in the Supplement.
The recycling calculation will be re-implemented from scratch: a transport scheme with sub-hourly time steps that satisfy the Courant condition, a mass-budget closure check against ERA5 total column water reported for every event, surface-pressure masking, and a pre-defined search window for τ_RR with an explicit rule for undetermined cases. The ρ and τ_RR values in the submitted manuscript are superseded by the re-implementation described above; revised values, together with the closure test, will be reported for every event.
Major point 2Referee's comment. The key result (as the authors call it, lines 457 and 657) is not statistically significant: the null hypothesis of no correlation between τ_rec and τ_RR cannot be rejected even at the 90% level (p = 0.107). Moreover, the value in the manuscript was superseded in the authors' reply to Referee #1, where the revised p-value is greater than 0.7 — a revision made because the reviewer noted that the correlation was computed over only ten data pairs, two of which were negative and eight of which shared the same value of τ_rec.
Reply: We agree. The value R ≈ 0.57 (p = 0.107) quoted as the key result came from τ_rec estimates affected by the fitting-bound artefact we disclosed in AC1 (eight of the ten events shared the same value, as the Referee notes). Re-analysis with corrected τ_rec gives r = 0.09 (p = 0.80) for the ten events (provisional, given the fit-quality issues described under Further point 6). On top of that, the τ_RR values entering this correlation are replaced by the re-implementation described under Major point 1, so the association cannot be assessed with the present data at all. All statements of a τ_rec–τ_RR relationship will be rewritten on the basis of the verified τ_rec and τ_RR, and presented only to the extent supported statistically, with uncertainty and sample-size caveats. The title and scope will be adjusted accordingly.
Major point 3Referee's comment. The writing and manuscript preparation are sloppy, which the reviewer finds unacceptable given the time the review process takes from volunteering people; authors should put substantial effort into writing and reading their own manuscript before submitting. Specific examples: the UTC-to-UTC+8 conversion is described at least three times; there are bullet points where there is no list (line 315); variable names are written and used before being defined; the T₀cm anomaly is written sometimes with a subscript and sometimes with an asterisk (line 230 and Eq. 8); some figures lack descriptions of several panels (e.g. Fig. 3) and axis labels (e.g. Fig. 5, Fig. 6d); and line 467 discusses cases with τ_rec of the order of 60 h, whereas Fig. 6 shows no data with τ_rec above 6.6 h.
Reply: We accept this criticism. We have checked each of these examples and found further instances of the same kind. The UTC conversion is described in Sections 2.2.2, 2.3.2 and 3.5.2; Section 2.3.2 in addition describes a +8 h shift applied to ERA5, which the code does not apply — station data are converted from local time to UTC, and all series are handled on a common UTC basis — and the three descriptions will be consolidated. Section 3.5.1 (line 315) does contain list fragments without list structure. ρ, τ_RR and H all appear in the abstract before being defined. The T₀cm anomaly notation is inconsistent between line 230 and Eq. (8). Figure 3 lacks descriptions of several panels, and Figures 5 and 6d lack axis labels. The line 467 / Fig. 6 contradiction arises from the fitting-bound artefact disclosed in AC1; both text and figure will be regenerated from the corrected fits.
To these the re-examination adds: the study domain is given as 37–40°N, 105–107°E in Section 2.1 but as 38–39.5°N, 106–107°E in Section 3.5; Section 2.2 describes a "60 km north–south corridor" inconsistent with either; Section 2.3.1 gives an ERA5 period of 2020–2024 whereas the code processes only the ten event windows; and Section 4.3.2 reports per-case τ_rec and τ_RR values that do not match the stored results (for case 1, the stored τ_rec was 5.4 h, 11 h after correction, and τ_RR = 13 h, not τ_rec > 60 h and τ_RR = 35–40 h). The manuscript will be fully rewritten and checked by a native English speaker before the revised manuscript is submitted.
Major point 4Referee's comment. Several statements are not supported by the data presented in the manuscript. Line 337 states that high vapour pressure deficit reduces evaporation efficiency, a causal link that is never demonstrated — and the reviewer would expect larger VPD to produce larger surface evaporative fluxes. Line 360 ("The pre-event environment also displays systematic features: RH is typically low and VPD high, producing elevated ΔT and a decoupled land-atmosphere state") has the same problem. Several times the authors ascribe results to soil moisture, but no soil-moisture data are ever presented. Line 512 ("This persistence arises from a combination of soil thermal inertia, altered radiative and turbulent fluxes, and enhanced near-surface moisture availability"): actually, none of those things has been shown in the manuscript. Line 53 ("Cooler soils reduce sensible heat flux and suppress boundary-layer development, while moist soils limit evaporative demand by reducing VPD. The combination delays the reactivation of turbulent fluxes and slows moisture turnover in the boundary layer.") describes variables that were never analysed.
Reply: This is correct, and the same applies to further statements of this kind. None of the quantities invoked here — evaporation efficiency as a function of VPD, soil moisture, sensible and latent heat fluxes, boundary-layer development, near-surface moisture availability — was analysed, and all such statements will be removed from the revision. We also note that Sections 4.3.3 and 5.1.2 state that long-memory events have strong positive H, while the stored values of H are negative for all ten events (−0.83 to −0.44); see point 11 below. If a physical interpretation of the composite results is retained in the revision, it will need to be supported by analysed data; see point 7 for the variables we will add.
Further point 5Referee's comment. Defining τ_RR as the time interval between the peak of ρ and the peak of rainfall leads to negative values of τ_RR, which do not really make sense.
Reply: Yes — the negative values are artefacts of the method. τ_RR was computed as the time of maximum ρ minus the time of maximum precipitation over the whole event window, including hours where ρ is zero after clipping. For case 7, ρ is zero at every hour of the window, so the maximum falls at the first hour and τ_RR = −72 h is exactly the offset from that first hour to the precipitation peak. This value has no physical meaning. Case 2 (τ_RR = −31 h) has not yet been examined individually and will be re-evaluated with the re-implemented calculation. In the revision, τ_RR will be recomputed within a pre-defined window with an explicit "undetermined" classification, and negative or boundary values will not be interpreted.
Further point 6
Referee's comment. The manuscript states that only events with a well-behaved recovery are retained in the computation of τ_rec. How many are they? What about the others? How is this subselection justified, and how representative of the whole population are the retained events?
Reply: Checking this question exposed a problem we had missed. Section 3.4 states that events "with well-behaved recovery (R² ≥ 0.3) were retained", but the corrected fitting code in fact kept all station fits. Of the 50 station-level values (10 events × 5 stations), 10 have R² ≥ 0.3, 6 come from a fallback branch in which the fit failed and no R² is defined, and 31 lie at a parameter bound (27 at the amplitude bound, 1 at the offset bound, 3 at the τ bound). Six of the ten events have no station with R² ≥ 0.3. The event-level τ_rec values in the present manuscript are therefore not final and will be re-derived.
In the revision the R² criterion will be applied as written. The number of valid fits per event will be reported together with each fit's R² and bound status, the event-level value will be the median across valid stations with its spread, and the sensitivity of τ_rec to the fit window and bounds will be discussed. Since no events were in fact excluded by this criterion, the representativeness question concerns the choice of the ten events (duration ≥ 140 h), which we take up under points 8 and 9.
Further point 7Referee's comment. Several other variables should have been analysed from ERA5, such as fluxes.
Reply: This is fair comment. Sensible-heat flux, latent-heat flux and net radiation were not in the downloaded data, so we do not have the analysis the Referee suggests. ERA5 surface fluxes (sensible and latent heat, net radiation) and soil moisture (swvl1) will be added for the event windows and used to test the proposed physical interpretation.
Further point 8
Referee's comment. It is not clear when 10 events are analysed and when 120 events are analysed.
Reply: The manuscript does not state this clearly. The composite analysis of Section 4.1 uses 112 precipitation events identified from the five station records (we believe the "120" in the comment refers to this set); it uses station data only and does not involve ρ or τ_RR. The ten-event set (events longer than 140 h) supported the τ_RR and coupling analysis, which, as set out under Major points 1 and 2, will be reassessed on the verified results. The event set underlying Fig. 4 is being re-derived from the stored event catalogue and will be documented explicitly; if it cannot be reproduced, the figure will be replaced. The abstract's claim of an "analysis of 112 events … τ_rec (20–80 h)" also conflicts with Section 4.2 and will be corrected.
Further point 9
Referee's comment. The seasonal dependence of τ_rec, without a discussion of the seasonal dependence of precipitation events, is not very informative.
Reply: Agreed. The ten events are distributed as follows: 4 in September (2020, 2021, 2023, 2024), 3 in August (2023, and twice 2024), 2 in April (2021, 2024) and 1 in July (2022). Any seasonal ordering of event-level τ_rec is therefore confounded with the seasonal sampling of the events themselves, and the event-level seasonal interpretation is not supported by the ten-event sample. This will be stated explicitly.
Further point 10
Referee's comment. It is said that the temperature recovery depends on surface radiative fluxes; the time of day should then matter, but this is never mentioned.
Reply: Correct; this was not analysed. Event windows begin at the precipitation peak, which occurs at different times of day. Removing the mean diurnal cycle in the anomaly calculation does not remove the residual diurnal cycle over a 72 h fit window, and the statement that recovery depends on surface radiative fluxes was never tested. The statement is removed. In the revision, the peak time of day will be reported for each event, and the diurnal contamination of τ_rec will be tested or bounded.
Further point 11
Referee's comment. Line 244 states that "High C_t values occur during moist or post-rain conditions". But C_t is the (time) correlation coefficient between T₀ and T₂m computed over their time series — so how can this coefficient be computed as a function of time?
Reply: The Referee is right. C_t is a single Pearson correlation between hourly T₀cm and T₂m within each station's event window, averaged across stations: one number per event, not a function of time. The statement at line 244 is therefore unsupported and is removed. The same re-examination showed that the heat–moisture index H is defined in three different ways: as Corr(RH, ΔT) in the equation of Section 3.1.5, as Corr(RH, T₀cm) in Section 4.3.3, and as Corr(RH, T₀cm) in the code. The revision will use a single definition, chosen on physical grounds and applied consistently throughout (to be stated in Section 3.1.5); we will not report H values until the coupling analysis is redesigned. The stored values of H are negative for all ten events (−0.83 to −0.44), which contradicts the text's claim of strong positive H for long-memory events. Preliminary checks with the provisional τ_rec do not support the proposed pathway; these will be repeated after τ_rec is recomputed.
We must also correct three statements in AC1 that had not been checked against the code and outputs and that are incorrect. First, "ERA5 and station observations agree to within 15% for 8 of 10 events": no validation table was produced, and the statement is incorrect as written. Second, "corrected event-scale τ_rec values are consistent with the 20–80 h range": the corrected event medians range from 2.4 h to 201.7 h, and only five of ten lie within 20–80 h, so this statement is inaccurate. Third, the W_LOC/W_ADV equations in AC1 do not describe the code that was implemented (see Major point 1). We apologise for these three statements.
We note that the Referee's criticisms concern the recycling diagnostics, the event-scale statistics and the presentation. They do not concern the station composites of Section 4.1, which are based on hourly multi-depth soil, grass and air temperatures and humidity from five stations (2020–2024) and 112 precipitation events, and which Referee #1 also found of interest. The revision will be built on this observational basis. Any link to precipitation recycling will be added only where it is supported by verified calculations.
To summarise: we accept the substance of all of the Referee's major and further points, and the revision will be extensive. The recycling calculation will be re-implemented with a numerically stable transport scheme, a mass-budget closure reported against ERA5 total column water, surface-pressure masking, and a pre-defined τ_RR search window. τ_rec will be recomputed with the R² quality criterion actually applied and reported in full, each coupling index will have a single stated definition, and all statements not supported by analysed data will be removed. If the physical interpretation is retained, it will be supported by ERA5 surface fluxes and soil moisture added for the event windows. The text will be completely rewritten and language-edited. The ρ, τ_RR and τ_rec–τ_RR results will be superseded by the revised analysis. The revised manuscript will address each of these points.
Citation: https://doi.org/10.5194/egusphere-2025-5752-AC2
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AC2: 'Reply on RC2', Ruolin Li, 26 Oct 2026
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- 1
This paper uses a novel observational dataset to probe the relationship between land surface conditions and subsequent precipitation recycling. However, I find that there are some major flaws in the methodology and I am concerned about the authors' interpretation of their results.
First, the methods section is largely based on bullet points and itemized lists, which makes it difficult to follow. This is particularly true for the TRR parameter, which is calculated with ERA5 in a way that is very unclear. The reader is never presented with information on how ERA compares to the station observations. It's not clear how the WLOC and WADV parameters connect to the PADV/PLOC time series. Is it a simple scaling or is there something more complex going on? Does the PADV + PLOC = P measured at the stations?
The results presented in Figs 2 and 3 are interesting, but the plot of Fig. 4 suggests that the seasonal cycle of temperature is mainly responsible for the TREC parameter, which isn't a major surprise because temperature is a strong control on surface evaporation.
Section 4.3.1: claims that there is a consistent temporal structure of the ρ parameter, but this is patently not the case, as (2/10) are negative and (3/10) are greater than 50 hours. So I'm not sure where this claim is coming from.
Section 4.3.2: This claims to be the central finding of this study, but 6/7 of the TREC timescale are equal to 5 (how this is possible is never explained) and the correlation is therefore totally spurious.
Given these errors, the overall results of the study are not convincing to me, making the conclusions drawn from the subsequent analysis not supported by the evidence.