the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Effects of complex terrain on the shortwave radiative balance: A sub–grid scale parameterization for the GFDL Land Model version 4.2
Enrico Zorzetto
Sergey Malyshev
Nathaniel Chaney
David Paynter
Raymond Menzel
Elena Shevliakova
Abstract. Parameterizing incident solar radiation over complex topography regions in Earth System Models (ESMs) remains a challenging task. In ESMs, downward solar radiative fluxes at the surface are typically computed using plane parallel radiative transfer schemes, which do not explicitly account for the effects of a three-dimensional topography, such as shading and reflections. To improve the representation of these processes, we introduce and test a parameterization of radiation-topography interactions tailored to the Geophysical Fluid Dynamics Laboratory (GFDL) ESM land model. The approach presented here builds on an existing correction scheme for direct, diffuse and reflected solar irradiance terms over three-dimensional terrain. Here we combine this correction with a novel hierarchical multivariate clustering algorithm which explicitly describes the spatially varying downward irradiance over mountainous terrain. Based on a high-resolution digital elevation model, this combined method first defines a set of sub–grid land units ("tiles") by clustering together sites characterized by similar terrain-radiation interactions (e.g., areas with similar slope orientation, terrain and sky view factors). Then, based on terrain parameters characteristic for each tile, correction terms are computed to account for the effects of local 3-D topography on shortwave radiation over each land unit. We develop and test this procedure based on a set of Monte Carlo ray tracing simulations approximating the true radiative transfer process over three dimensional topography. Domains located in three distinct geographic regions (Alps, Andes, and Himalaya) are included in this study to allow for independent testing of the methodology over surfaces with differing topographic features. We find that accounting for the sub–grid spatial variability of solar irradiance originating from interactions with complex topography is important as these effects lead to significant local differences with respect to the plane-parallel case, as well as with respect to grid–cell scale average topographic corrections. Finally, we quantify the importance of the topographic correction for a varying number of terrain clusters and for different radiation terms (direct, diffuse, and reflected radiative fluxes) in order to inform the application of this methodology in different ESMs with varying sub-grid tile structure.
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Journal article(s) based on this preprint
tiles, and for each tile we evaluate solar radiation received by land based on terrain properties.
Enrico Zorzetto et al.
Interactive discussion
Status: closed
-
CEC1: 'Comment on egusphere-2022-770', Astrid Kerkweg, 07 Oct 2022
Dear authors,
unfortunately I am not able to access the zenodo archives cited in the Code and Data availability section. Please check and correct them.
Best regards, Astrid Kerkweg (Executive Editor)
Citation: https://doi.org/10.5194/egusphere-2022-770-CEC1 -
AC1: 'Reply on CEC1', Enrico Zorzetto, 10 Oct 2022
Thank you for your comment. The data statement in the paper include the DOIs but not the full link to the host website. I will make sure the full link is added in the revised version of the manuscript.
The DOIs and links to Data and Code in the "Assets" section of the submission are correct.
Citation: https://doi.org/10.5194/egusphere-2022-770-AC1
-
AC1: 'Reply on CEC1', Enrico Zorzetto, 10 Oct 2022
-
RC1: 'Comment on egusphere-2022-770', Anonymous Referee #1, 06 Nov 2022
Topography controls many land surface processes. This manuscript combined an existing parameterization for solar radiation over complex terrain with a novel hierarchical multivariate clustering algorithm in GFDL. This work is very interesting and promising for applying in land surface models. However, how the authors considered the land cover types with different albedo values and energy balance is not clear; the performance of the proposed tile-level methods against the original grid-cell level methods for calculating regional average values is unknown; and more details in the physical explanations of some equations needs to be clarified,. Besides, how will the authors combine their tile separating and the existing tile schemes in GFDL? Please see below for my specific comments.
Major comments:
- Line108-109: the authors stated that in GFDL, the diffuse radiation received by the (flat) surface corresponds here to the sum of Fdif and Fcoup. If so, how did the authors calculate Fdif and Fcoup in Eq.1 for GFDL?
- Eq. 1 and line 260: how did the authors consider the land surface with different albedo (e.g., snow and vegetation)? Different land cover types may have different albedo and thus different reflected energy from adjacent terrain.
- Eq. 2: here the irradiance Ek,l is based on horizontal plane or the inclined plane of pixel k,l? Please give more physical explanations for equation 2.
- Line 264-266: please give more details about the energy conservation and albedo modification.
- Line 273-274: will their difference be larger for cloudy condition?
- Figure 5: why can sky view factors be larger to 1?
- Eq. 12: is this method only empirical?
- How about the performance of the proposed tile-level methods against the original grid-cell level methods for calculating regional average values?
- The authors presents the results based on the corrected factors in Eq.1. However, they may be not easy to understand. How about presenting some results about the radiation fluxes directly, which will be more clearer for the readers?
- The authors proposed tile-level topographic correction methods for solar radiation over complex terrain. However, current sub-grid tile schemes in GFDL consider different soil and vegetation, and topographic characteristics for simulating water and carbon cycles. How did the authors merge their clustering methods for radiation and the existing scheme in GFDL for other processes?
Minor comments:
- Line 16-18: It will be better to show some quantitative metrics rather than only descriptive expression.
- Line 42: why did the author call this method ‘WLH’?
- Line 60-85: these summarize the objective and work of this paper. I suggest the authors simplify them for making them clearer.
- Line124-125: Citing the corresponding papers may be better.
- Line 93: how about vegetation with different PFTs?
- Line 207: kp -> k*p?
- Line 413: he -> the
Citation: https://doi.org/10.5194/egusphere-2022-770-RC1 - AC2: 'Reply on RC1', Enrico Zorzetto, 01 Dec 2022
-
RC2: 'Comment on egusphere-2022-770', Anonymous Referee #2, 21 Nov 2022
Summary and general comments
In this study, a parameterisation for the effects of sub-grid topography on surface shortwave radiation is presented. In a first step, the authors apply Monte Carlo ray tracing to simulate surface shortwave radiation for 3 geographic domains with complex terrain. These experiments serve as a reference to develop the (sub-grid) parametrisation. In a next step, terrain properties (μ, sky view factor and terrain configuration) are linked to modulated radiation fluxes with two statistical models – a Multiple Linear and a Random Forest Regression. Finally, sub-grid effects are considered by merging land units within a grid cell with similar terrain properties by means of hierarchical clustering.
The aim of this study is very interesting and relevant – namely improving the representation of surface shortwave radiation fluxes in an Earth System Model. Due to the plane parallel radiative transfer schemes applied in such models, surface radiation is typically simulated rather inaccurately in areas with complex terrain. The implementation of parameterisations, particularly on a sub-grid scale, has the potential to strongly reduce such biases. The approach presented by the authors is very interesting and the manuscript is well written and structured. However, I struggled to understand certain sections in detail – for instance the hierarchical clustering section in the methods and some passages in the Results and Discussion. Furthermore, the Results and Discussion section is sometimes incomplete in my opinion and should be extended (see the following comments for more details).
Major comments
Section about hierarchical clustering (2.4)
Until section 2.4, the methodology is very well described. However, I struggled to follow section 2.4. For instance, why do you want to partition land in hydrologically coherent units? From a “terrain-radiation-perspective” – this is not obvious. Has this approach been chosen due to an already existing tile classification in the GFDL Land Model?
I’m also confused why the clustering is performed twice (first in k hillslopes, then in p sub-units). I think a detailed flow diagram (e.g. with an example of the step-wise classification of sub-units of a geographic domain) would help the reader to understand these steps. Furthermore, it is also not obvious to me why lakes and glaciers represent separate classes. And are glaciers and lake classes further divided into sub-classes according to their terrain properties? Finally, some parts of section 3.4 (e.g. starting from line 354 could also be moved to the method section).
Analysis and results – improve consistency and completeness
- I’m missing the third domain (Nepal) in Fig. 7. I guess you used one domain to train the model and the other two domains for cross-validation – right?
- I think a performance comparison of the sub-grid to a grid-scale parameterisation would be very interesting to show. With this, you could emphasize the additional benefit of the sub-grid scale scheme.
- The discussion of certain findings should be extended. From the results, it seems that a tile number of ~100 captures the sub-grid characteristics already very well. Do you agree? And would such a number be feasible in an online ESM simulation?
Minor comments
Content-related (text)
Line 42: what does the abbreviation “WLH” stand for?
L139: “uniform” albedo -> how realistic is this assumption?
L139: I appreciate such clear definitions, it simplifies the comprehensibility of the subsequent text greatly!
L157: I’m not sure if I understand this sentence correctly. Do you mean that radiation fluxes significantly departure locally from areal-average fluxes?
L 162: “represents the fraction of the sky dome visible from a target site” -> technically, this is incorrect. Compare e.g. with Helbig et al. (2009) (text next to Eq. 8) and Zakšek et al. (2011). The sky view factor definition of Dozier and Frew (1990) yields the fraction of hemispherical radiation received under the assumption of isotropic radiation. The same is valid for the subsequent explanation of the terrain configuration factor Ct.
L171: Could you explain why you use this terrain configuration definition and not simply Ct = 1.0 – Vd (compare e.g. with Chu et al., 2021)?
L174: I would briefly introduce and explain the parameters μi and μ0 here.
L194: I’m a bit confused by these lines. It seems that you perform the clustering only for soil elements (also according to line 207; kpand kp + 2) and not for glaciers and lakes. What is the reason behind this? I guess glaciated areas and lakes can also have very variable topographic parameters (like e.g. sky view factor).
L204: It’s not obvious to me why you apply the clustering a second time. Generally, to increase the comprehensibility of this section, it might be worth to extend the workflow diagram displayed in Fig. 4. One could show the classification of a certain domain (resolved for every single step).
L207: I’m still a bit puzzled – what is the motivation behind categorizing land surface based on hydrological properties? I don’t see the connection to topography-radiation-processes.
L298: “reflected components are quite linear” -> for frdir, the deviations between MLR and RFR are quite substantial…
L 305: “case in which…” -> I don’t understand this part; there is probably something missing.
L316: First of all, I’m confused about which region (East Alps vs. Peru) is the (in-)dependent domain. The caption of Fig. 7 does not agree with the statement here. Furthermore, I’m not convinced that results from RFR are not location dependent. Looking at Fig. 7, the RFR method consistently indicates a worse performance for the cross-validation domain than the MLR method. For me, this is an indication that obtained relations from the RFR simulation are very location-dependent and not easily transferable to other terrain geometries (i.e. the model is overfitted).
L388: It would be interesting to see the results for these tests too. Maybe you could show them in the supplementary material.
Typos, phrasing and stylistic comments
L124: references not correctly rendered
L153: I was a bit confused by this line, it might be better to write something like: “The MC calculations were performed for three independent domains (Nepal, Peru, East Alps)…” (if that is what you mean)
L157: “determines” -> “determine”
L162: “represent” -> “represents”
L166: “in order to compute the sky view factor”
L198: “eq. 6” -> “Eq. 6”
L215: “if these are present in a given grid cell.”
L220: “the is the indicator” -> “is the indicator”
L263: “eqns. (1)” -> “Eq. (1)”
L273: “angles compute based” -> “angles computed based”
L273: “simulation (5)” -> “simulation (Fig. 5)”?
L290: I would rewrite this to e.g.: “…larger than approximately 5 km the effect disappears.”
L302: “case in which” -> “a case in which”
Figures and Tables
Figure 2: The colorbar labelling is erroneous – I guess it should be “Elevation [m a.s.l.]”. The same is true for the upper-left panel in figure 3. Furthermore, the degree symbol is missing for the cardinal directions.
Figure 4: It seems from these panels (x/y-coordinates) that the MC model was run on a map projection. Could you specify the projection somewhere?
Figure 7: μ0 not correctly rendered in caption
New references
Chu, Q., Yan, G., Qi, J., Mu, X., Li, L., Tong, Y., et al. (2021). Quantitative analysis of terrain reflected solar radiation in snow-covered mountains: A case study in Southeastern Tibetan Plateau. Journal of Geophysical Research: Atmospheres, 126, e2020JD034294. https://doi.org/10.1029/2020JD034294
Helbig, N., Löwe, H., & Lehning, M. (2009). Radiosity Approach for the Shortwave Surface Radiation Balance in Complex Terrain, Journal of the Atmospheric Sciences, 66(9), 2900-2912. https://doi.org/10.1175/2009JAS2940.1
Zakšek, K.; Oštir, K.; Kokalj, Ž. Sky-View Factor as a Relief Visualization Technique. Remote Sens. 2011, 3, 398-415. https://doi.org/10.3390/rs3020398
Citation: https://doi.org/10.5194/egusphere-2022-770-RC2 - AC3: 'Reply on RC2', Enrico Zorzetto, 01 Dec 2022
Interactive discussion
Status: closed
-
CEC1: 'Comment on egusphere-2022-770', Astrid Kerkweg, 07 Oct 2022
Dear authors,
unfortunately I am not able to access the zenodo archives cited in the Code and Data availability section. Please check and correct them.
Best regards, Astrid Kerkweg (Executive Editor)
Citation: https://doi.org/10.5194/egusphere-2022-770-CEC1 -
AC1: 'Reply on CEC1', Enrico Zorzetto, 10 Oct 2022
Thank you for your comment. The data statement in the paper include the DOIs but not the full link to the host website. I will make sure the full link is added in the revised version of the manuscript.
The DOIs and links to Data and Code in the "Assets" section of the submission are correct.
Citation: https://doi.org/10.5194/egusphere-2022-770-AC1
-
AC1: 'Reply on CEC1', Enrico Zorzetto, 10 Oct 2022
-
RC1: 'Comment on egusphere-2022-770', Anonymous Referee #1, 06 Nov 2022
Topography controls many land surface processes. This manuscript combined an existing parameterization for solar radiation over complex terrain with a novel hierarchical multivariate clustering algorithm in GFDL. This work is very interesting and promising for applying in land surface models. However, how the authors considered the land cover types with different albedo values and energy balance is not clear; the performance of the proposed tile-level methods against the original grid-cell level methods for calculating regional average values is unknown; and more details in the physical explanations of some equations needs to be clarified,. Besides, how will the authors combine their tile separating and the existing tile schemes in GFDL? Please see below for my specific comments.
Major comments:
- Line108-109: the authors stated that in GFDL, the diffuse radiation received by the (flat) surface corresponds here to the sum of Fdif and Fcoup. If so, how did the authors calculate Fdif and Fcoup in Eq.1 for GFDL?
- Eq. 1 and line 260: how did the authors consider the land surface with different albedo (e.g., snow and vegetation)? Different land cover types may have different albedo and thus different reflected energy from adjacent terrain.
- Eq. 2: here the irradiance Ek,l is based on horizontal plane or the inclined plane of pixel k,l? Please give more physical explanations for equation 2.
- Line 264-266: please give more details about the energy conservation and albedo modification.
- Line 273-274: will their difference be larger for cloudy condition?
- Figure 5: why can sky view factors be larger to 1?
- Eq. 12: is this method only empirical?
- How about the performance of the proposed tile-level methods against the original grid-cell level methods for calculating regional average values?
- The authors presents the results based on the corrected factors in Eq.1. However, they may be not easy to understand. How about presenting some results about the radiation fluxes directly, which will be more clearer for the readers?
- The authors proposed tile-level topographic correction methods for solar radiation over complex terrain. However, current sub-grid tile schemes in GFDL consider different soil and vegetation, and topographic characteristics for simulating water and carbon cycles. How did the authors merge their clustering methods for radiation and the existing scheme in GFDL for other processes?
Minor comments:
- Line 16-18: It will be better to show some quantitative metrics rather than only descriptive expression.
- Line 42: why did the author call this method ‘WLH’?
- Line 60-85: these summarize the objective and work of this paper. I suggest the authors simplify them for making them clearer.
- Line124-125: Citing the corresponding papers may be better.
- Line 93: how about vegetation with different PFTs?
- Line 207: kp -> k*p?
- Line 413: he -> the
Citation: https://doi.org/10.5194/egusphere-2022-770-RC1 - AC2: 'Reply on RC1', Enrico Zorzetto, 01 Dec 2022
-
RC2: 'Comment on egusphere-2022-770', Anonymous Referee #2, 21 Nov 2022
Summary and general comments
In this study, a parameterisation for the effects of sub-grid topography on surface shortwave radiation is presented. In a first step, the authors apply Monte Carlo ray tracing to simulate surface shortwave radiation for 3 geographic domains with complex terrain. These experiments serve as a reference to develop the (sub-grid) parametrisation. In a next step, terrain properties (μ, sky view factor and terrain configuration) are linked to modulated radiation fluxes with two statistical models – a Multiple Linear and a Random Forest Regression. Finally, sub-grid effects are considered by merging land units within a grid cell with similar terrain properties by means of hierarchical clustering.
The aim of this study is very interesting and relevant – namely improving the representation of surface shortwave radiation fluxes in an Earth System Model. Due to the plane parallel radiative transfer schemes applied in such models, surface radiation is typically simulated rather inaccurately in areas with complex terrain. The implementation of parameterisations, particularly on a sub-grid scale, has the potential to strongly reduce such biases. The approach presented by the authors is very interesting and the manuscript is well written and structured. However, I struggled to understand certain sections in detail – for instance the hierarchical clustering section in the methods and some passages in the Results and Discussion. Furthermore, the Results and Discussion section is sometimes incomplete in my opinion and should be extended (see the following comments for more details).
Major comments
Section about hierarchical clustering (2.4)
Until section 2.4, the methodology is very well described. However, I struggled to follow section 2.4. For instance, why do you want to partition land in hydrologically coherent units? From a “terrain-radiation-perspective” – this is not obvious. Has this approach been chosen due to an already existing tile classification in the GFDL Land Model?
I’m also confused why the clustering is performed twice (first in k hillslopes, then in p sub-units). I think a detailed flow diagram (e.g. with an example of the step-wise classification of sub-units of a geographic domain) would help the reader to understand these steps. Furthermore, it is also not obvious to me why lakes and glaciers represent separate classes. And are glaciers and lake classes further divided into sub-classes according to their terrain properties? Finally, some parts of section 3.4 (e.g. starting from line 354 could also be moved to the method section).
Analysis and results – improve consistency and completeness
- I’m missing the third domain (Nepal) in Fig. 7. I guess you used one domain to train the model and the other two domains for cross-validation – right?
- I think a performance comparison of the sub-grid to a grid-scale parameterisation would be very interesting to show. With this, you could emphasize the additional benefit of the sub-grid scale scheme.
- The discussion of certain findings should be extended. From the results, it seems that a tile number of ~100 captures the sub-grid characteristics already very well. Do you agree? And would such a number be feasible in an online ESM simulation?
Minor comments
Content-related (text)
Line 42: what does the abbreviation “WLH” stand for?
L139: “uniform” albedo -> how realistic is this assumption?
L139: I appreciate such clear definitions, it simplifies the comprehensibility of the subsequent text greatly!
L157: I’m not sure if I understand this sentence correctly. Do you mean that radiation fluxes significantly departure locally from areal-average fluxes?
L 162: “represents the fraction of the sky dome visible from a target site” -> technically, this is incorrect. Compare e.g. with Helbig et al. (2009) (text next to Eq. 8) and Zakšek et al. (2011). The sky view factor definition of Dozier and Frew (1990) yields the fraction of hemispherical radiation received under the assumption of isotropic radiation. The same is valid for the subsequent explanation of the terrain configuration factor Ct.
L171: Could you explain why you use this terrain configuration definition and not simply Ct = 1.0 – Vd (compare e.g. with Chu et al., 2021)?
L174: I would briefly introduce and explain the parameters μi and μ0 here.
L194: I’m a bit confused by these lines. It seems that you perform the clustering only for soil elements (also according to line 207; kpand kp + 2) and not for glaciers and lakes. What is the reason behind this? I guess glaciated areas and lakes can also have very variable topographic parameters (like e.g. sky view factor).
L204: It’s not obvious to me why you apply the clustering a second time. Generally, to increase the comprehensibility of this section, it might be worth to extend the workflow diagram displayed in Fig. 4. One could show the classification of a certain domain (resolved for every single step).
L207: I’m still a bit puzzled – what is the motivation behind categorizing land surface based on hydrological properties? I don’t see the connection to topography-radiation-processes.
L298: “reflected components are quite linear” -> for frdir, the deviations between MLR and RFR are quite substantial…
L 305: “case in which…” -> I don’t understand this part; there is probably something missing.
L316: First of all, I’m confused about which region (East Alps vs. Peru) is the (in-)dependent domain. The caption of Fig. 7 does not agree with the statement here. Furthermore, I’m not convinced that results from RFR are not location dependent. Looking at Fig. 7, the RFR method consistently indicates a worse performance for the cross-validation domain than the MLR method. For me, this is an indication that obtained relations from the RFR simulation are very location-dependent and not easily transferable to other terrain geometries (i.e. the model is overfitted).
L388: It would be interesting to see the results for these tests too. Maybe you could show them in the supplementary material.
Typos, phrasing and stylistic comments
L124: references not correctly rendered
L153: I was a bit confused by this line, it might be better to write something like: “The MC calculations were performed for three independent domains (Nepal, Peru, East Alps)…” (if that is what you mean)
L157: “determines” -> “determine”
L162: “represent” -> “represents”
L166: “in order to compute the sky view factor”
L198: “eq. 6” -> “Eq. 6”
L215: “if these are present in a given grid cell.”
L220: “the is the indicator” -> “is the indicator”
L263: “eqns. (1)” -> “Eq. (1)”
L273: “angles compute based” -> “angles computed based”
L273: “simulation (5)” -> “simulation (Fig. 5)”?
L290: I would rewrite this to e.g.: “…larger than approximately 5 km the effect disappears.”
L302: “case in which” -> “a case in which”
Figures and Tables
Figure 2: The colorbar labelling is erroneous – I guess it should be “Elevation [m a.s.l.]”. The same is true for the upper-left panel in figure 3. Furthermore, the degree symbol is missing for the cardinal directions.
Figure 4: It seems from these panels (x/y-coordinates) that the MC model was run on a map projection. Could you specify the projection somewhere?
Figure 7: μ0 not correctly rendered in caption
New references
Chu, Q., Yan, G., Qi, J., Mu, X., Li, L., Tong, Y., et al. (2021). Quantitative analysis of terrain reflected solar radiation in snow-covered mountains: A case study in Southeastern Tibetan Plateau. Journal of Geophysical Research: Atmospheres, 126, e2020JD034294. https://doi.org/10.1029/2020JD034294
Helbig, N., Löwe, H., & Lehning, M. (2009). Radiosity Approach for the Shortwave Surface Radiation Balance in Complex Terrain, Journal of the Atmospheric Sciences, 66(9), 2900-2912. https://doi.org/10.1175/2009JAS2940.1
Zakšek, K.; Oštir, K.; Kokalj, Ž. Sky-View Factor as a Relief Visualization Technique. Remote Sens. 2011, 3, 398-415. https://doi.org/10.3390/rs3020398
Citation: https://doi.org/10.5194/egusphere-2022-770-RC2 - AC3: 'Reply on RC2', Enrico Zorzetto, 01 Dec 2022
Peer review completion
Post-review adjustments
Journal article(s) based on this preprint
tiles, and for each tile we evaluate solar radiation received by land based on terrain properties.
Enrico Zorzetto et al.
Data sets
Data used for developing a parameterization for spatial distribution of solar irradiance over rugged terrain Enrico Zorzetto https://doi.org/10.5281/zenodo.6975857
Model code and software
Code for analyzing the sub–grid distribution of shortwave radiation over mountainous terrain. Enrico Zorzetto https://doi.org/10.5281/zenodo.7110618
Enrico Zorzetto et al.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(16262 KB) - Metadata XML
-
Supplement
(11449 KB) - BibTeX
- EndNote
- Final revised paper