the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Jul 2026
Slope-Constrained Orography (SCO v1.0) for explicit discrete-slope control in terrain preprocessing: a case study with WRF-ARW (v4.6.1)
Abstract. Kilometre-scale Weather Research and Forecasting (WRF) simulations over terrain with steep slopes often require strong smoothing to prevent numerical instability, but conventional domain-wide filters alter terrain at every grid point, regardless of whether local slopes require reduction. Slope-Constrained Orography (SCO) is an offline terrain preprocessing method that prescribes a target slope angle θ and adjusts only those grid points whose eight-neighbour elevation differences exceed the implied bound, leaving the remaining terrain unchanged while permitting stable numerical integration. By prescribing the slope constraint directly, SCO replaces the trial-and-error of filter-based smoothing with a single, geometrically interpretable control parameter. In a 1 km WRF case over the highly complex terrain of the southeastern Tibetan Plateau, the least-modified stable SCO member modifies 14 % of points with a mean elevation change of 8.2 m, compared with 100 % modification and 108.1 m for the corresponding WRF Preprocessing System (WPS) member. The stable SCO member produces lower near-surface wind and temperature errors in this case, consistent with improved terrain representation.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2076', Anonymous Referee #1, 27 Aug 2026
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RC2: 'Comment on egusphere-2026-2076', Anonymous Referee #2, 29 Aug 2026
The authors describe a simple and practical approach to a long-standing problem in high-resolution WRF simulations over complex terrain. Steep slopes can cause numerical instability, while repeated domain-wide smoothing removes much of the terrain structure that motivates the use of a fine grid in the first place. SCO addresses this problem by prescribing a discrete-slope constraint and adjusting only the parts of the terrain that exceed it. This method should be useful to a broad WRF community. The authors might eventually consider packaging SCO as an optional part of the standard WPS terrain-processing workflow and exploring its contribution to the official WRF/WPS code base in the future.
Overall, this manuscript provides a simple and useful solution to an important practical problem in high-resolution modeling over steep terrain. I am happy to recommend publication subject to minor corrections. My comments mainly concern how the method is described and how it can be easily used by other researchers. I recommend a minor revision.General comments
#1 The manuscript describes θ as the “sole control variable” or as a single parameter. From a user’s perspective, θ is clearly the main attraction of the method, but the solver also contains fixed settings for the boundary treatment, local tightening, and convergence tolerances. It would be more accurate to describe θas the primary user-facing parameter, or as the only parameter varied in this study, with the remaining quantities identified as fixed solver settings.
#2 SCO22 and WPS120 are the least-modified stable members among the discrete candidates tested, rather than exact stability limits or globally optimal solutions. The wording should reflect this. It would also help to state more directly that the comparison is workflow-based: how much terrain modification does each preprocessing pathway require to obtain a tested member that satisfies the same 48 h stability criterion?
#3 The paper already contains most of the elements of a useful practical workflow, but they are spread across several sections. A short summary in the Discussion could describe how a user would diagnose the raw terrain, generate a coarse sequence of θvalues, bracket the passing–failing interval with stability integrations, refine the interval if needed, and select the least-modified stable tested member.
#4 The conclusions should remain tied to the case-study evidence. The results show that θ is a useful construction and search coordinate within SCO, but not that one slope value provides a universal WRF stability threshold across preprocessing methods, domains, or configurations.
#5 Add a concise practical workflow for users. One of the strengths of SCO is that candidate terrain fields can be generated rapidly and organised using a directly interpretable target angle. The discussion would benefit from a short recommended workflow for practical use.Specific comments
Line 141 and 159. “The least-modified stable member” should be qualified as referring to the candidates tested.
Line 170. “Every unstable member terminates” makes the terrain member sound like the integrating system. The WRF integrations using those terrain members are what terminate.
Line 175. “The two marginal stable members” is difficult to interpret. These are the stable members nearest the sampled stability boundaries.
Line 205. “Statistically indistinguishable” seems stronger than warranted because the paired test does not account for spatial correlation among stations. A statement about no detectable difference under the approximate stationwise test would be more consistent with Sect. 3.3.
Figure 5: Correct the line-style description in the caption.
A final check of abbreviations would be useful, some abbreviations are used before they are defined.Citation: https://doi.org/10.5194/egusphere-2026-2076-RC2
Data sets
Reproducibility archive for "Slope-Constrained Orography (SCO v1.0) for explicit discrete-slope control in terrain preprocessing" Yulong Ma, Xingwen Jiang, Lin Mu, and Zhiwei Heng https://doi.org/10.5281/zenodo.20809228
Model code and software
SCO v1.0: Slope-Constrained Orography for WRF terrain preprocessing Yulong Ma https://doi.org/10.5281/zenodo.19501184
Weather Research and Forecasting (WRF) Model and WRF Preprocessing System (WPS) (WRF-ARW v4.6.1) WRF Community and NCAR https://doi.org/10.5281/zenodo.20809210
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- 1
Review of manuscript egusphere-2026-2076, "Slope-Constrained Orography (SCO v1.0) for explicit discrete-slope control in terrain preprocessing: a case study with WRF-ARW (v4.6.1)" by Y. Ma et al.
The authors describe a new "Slope controlled Orography" (SCO) methodology for intelligent smoothing of terrain in order to reduce terrain slopes sufficiently to permit the WRF model to run stably, while retaining far more terrain variation than traditional smoothing methods that apply a simple smoothing kernel uniformly over the model domain. The method is very successful in this aim, and promises much greater fidelity to small scale meteorological variation in high resolution WRF simulations in steep terrain compared to previously, although there remain interesting questions such as a difference in slope stability threshold between the existing WPS method and the new SCO method. I felt that the paper's prose was rushed in places, with the authors pacing themselves insufficiently to maintain clarity, and some parts were confusing. Still, I'm happy to recommend publication subject to minor corrections in line with my comments below.
General comments:
The authors briefly investigate the spectral response of their filter compared to the WPS filter, but they only depict two SCO examples in their plot (Figure 8). Global spectral filters remove a well-defined portion of the spectrum of variation, local filters such as diffusion operators or gaussian filters have a spectral response that concentrates at the scale of the kernel size but increases with the number of filter applications. Do the authors have a feel for whether the SCO method has a relatively stable spectral response, or is it likely to vary significantly from one terrain dataset to another? How do they see it sitting between the extremes of spectral filters (well-defined response function) and local filters (response function depends on how aggressively the filter is applied).
The authors, in evaluating the quality of the simulations, only test bias and RMS errors vs. observations in this study. But these are not necessarily the most informative metrics for testing performance of convection-permitting resolution simulations, and it is the reproduction of qualitatively realistic detail evidencing the better reproduction of hitherto unresolved processes (such as convection, small scale gravity waves, complex terrain boundary layer behaviour) that is often desirable on increasing resolution. Are they able to comment on the variability that occurs in meteorological fields within the simulations? For instance, Sheridan et al. (2023) were able to demonstrate increased variability (resolved turbulence, essentially) in wind fields with an improved smoothing method (one similar in effect to SCO).
Specific comments:
41-42. The workflow aspects seem to have little to do with the constraint "theta", and it's confusing that these aspects are conflated in a single sentence.
42. Some introduction of what "geogrid" and "metgrid" represent (perhaps within an overview of the WRF LAM workflow) would be useful to non-WRF users.
43-44. The demonstration would be best at the end of 2.2, not here.
46. "the local bound" should be "a local bound" - you haven't explained the local bound yet.
49. Instead of redirecting the reader to the Appendix here, say "explanation to follow". The overview should be simple and gentle.
49-50. Mention of curvature constraints is distracting here when the reader is trying to understand the existing algorithm - by all means mention it somewhere more appropriate such as the conclusions.
60. Equation (1) appears to indicate the maximum of the slope over the eight neighbour pairs. What's the significance of this maximum? It's not discussed in the text.
63. Smax,int was already introduced at line 58, why is it mentioned again here? Why are you referring to section 2.3?
65-66. If the cardinal elevation difference constraint is Delta-x*tan(theta) then the diagonal constraint is sqrt(2)*Delta-x*tan(theta). This constraint is exactly in keeping with the slope theta, so why do you say the diagonls are under-constrained? The octagonal correction is described as removing the directional anisotropy, but all it does is multiply the constraint by cos(Pi/8) - for both the cardinal and diagonal pairs. The authors cite this as the reason Smax,int settles near theta_eff instead of theta. So it merely tightens the constraint uniformly, across both cardinal and diagonal directions, making no alteration to any directional / anisotropy aspect.
76. Presumably the authors mean columns as well as rows.
84. Lpq is not defined, or linked to the explanation of the bounds in section 2.2.
98-99. "Stopping rule" , "criterion": mixing terminology like this is confusing, pick a term and stick with it. If the convergence criterion references theta, and not theta_eff, why do the results in Table 1 cluster at theta_eff?
Section 2.4 - explain the purpose of this important subsection at its outset.
106. This is not "spatial clustering", but clustering in the slope parameter space?
109-110. The MAE and modified area fraction should be explained in separate sentences.
112. "short-wave". "small scale" would make more sense.
124-125. The suggestion here is that the timestep must be reduced when more smoothing is applied in D01, which is the opposite of what I'd expect (smoothing makes the model more stable and may permit use of a longer timestep). I think what you mean is that this tactic improves stability in *D02*. But doesn't this undermine the comparison of different treatments of D02 terrain, since the experiments' stability in D02 now depends on both the terrain in D02, and the differences in the driving model D01 for different experiments?
177-178. Are the authors able to speculate why this is?
Figure 5 caption - it is the solid line that denotes theta_eff in the plot.
179. I struggle to make sense of this sentence - "surrounding these members"?
242-245. It strikes me that the retention of terrain complexity with SCO, in addition to slope - in other words small scale spectral content - is what differs from the smoothly varying terrain of many-pass WPS. Have the authors considered looking at the second derivative of the terrain instead of just the slope?