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
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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.