the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A semi-parametric hourly space-time weather generator
Uwe Haberlandt
Abstract. Long continuous time series of meteorological variables (i.e. rainfall, temperature and radiation) are required for applications such as derived flood frequency analyses. Observed time series are however generally too short, too sparse in space, or incomplete, especially at the sub-daily timestep.
Stochastic weather generators overcome this problem by generating time series of arbitrary length. This study presents a major revision to an existing space-time hourly rainfall model based on a point alternating renewal process, now coupled to a k-NN resampling model for conditioned simulation of non-rainfall climate variables.
The point based rainfall model is extended into space by the resampling of simulated rainfall events using a simulated annealing optimisation approach. Large station networks (N > 50) are now able to be modelled with no significant loss in the spatial dependence structure.
Modelling of non-rainfall climate variables, i.e. temperature, humidity and radiation, is achieved using a non-parametric knearest neighbour (k-NN) resampling approach, coupled to the space-time rainfall model via rainfall state. As input, a gridded daily observational dataset (HYRAS) was used. A final disaggregation step was then performed on all non-rainfall climate variables to achieve an hourly output temporal resolution.
The proposed weather generator was tested on 400 catchments of varying size (50–20,000 km²) across Germany, comprising 699 sub-daily rainfall recording stations. Results indicate no major loss of model performance with increasing catchment size, and a generally good reproduction of observed climate and rainfall statistics.
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Ross Pidoto and Uwe Haberlandt
Status: closed
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RC1: 'Comment on hess-2023-45', Simon Michael Papalexiou, 29 Mar 2023
This is a useful paper and deserves consideration. I will avoid a generic summary and list right away several comments that hopefully the authors might find useful.
As a general comment, the methods described suit more multisite methods, especially for precipitation. At the hourly or finer scales, space-time precipitation has components or advection and anisotropy, and it is not clear if what these methods preserve in this regard (I wil get back to that).
- please see also Papalexiou (2022) which is dedicated only to precipitation.
- Rainfall is described by the single-model as an alternating sequence of independent wet and dry spells. How valid this assumption is?
- I can understand the 1 mm limit but based on what rationale the DSDmin = 4 hr was set?
- if u,v are in [0,1] then where are F_U(u) and F_V(v). Check the notation please.
- What is the justification of this choice? Have you tested e.g., the Gumbel dependence and was not suitable? Did you observe asymmetries? Please justify.
- Similarly, what led you to the Weibull choice for DSD and WSA. Great that you’ve drop the 4-parameter Kappa but why Weibull is a good model for the WSA. If you consider that, e.g., the hourly wet value distribution is a specific distribution then then WSA would be its convolution. Specifically, for the Weibull there were some attempts to justify it theoretically as a rainfall distribution by Wilson & Toumi (2005); it was also used in meta statistical approaches for daily rainfall e.g., (Marani & Ignaccolo, 2015; Marra et al., 2018, 2023) and it seems it does a good job in describing the extremes but if it is suits well for the WSA it will be nice to show some evidence. Also, here you’re using the 3-par version which also can end up with ζ quite larger than the min so you might have inconsistencies in low values. Can you explain please? The same point holds for the distribution choice of the WSD. Is the LN supported by the literature? By your own analysis in this dataset?
Equation 7. So this implies that the tail of intensity is exponential? It could for this region but in general this contradicts many global studies indicating that the tails are not exponential but heavier. Exactly for this reason, in the past I explored the Generalized Gamma to allow heavier right tails and recently some Generalized Exponential distributions having similar tails (see Papalexiou, 2022). I believe the choice of model is crucial as we’re risking underestimating the potential for extremes. Please explain.
Also what is the correlation structure within the event? Clearly at hourly resolution there is strong autocorrelation within wet values (see Papalexiou, 2022).
- lower phi is typically used for the gaussian pdf, here you need capital phi Φ
Section 2.2. Operationally, how fast is this optimization approach? When you mention that the occurrence criterion in the hardest to converge does this imply that in many cases it does not converge at all?
- I guess the branched non-sequential procedure is describe correctly, yet to be honest as a reader I got lost here and mathematically it is really not clear what exactly spatiotemporal correlation structure this grouping of primary and secondary stations produces.
- so this approach will preserve only the lag-1 correlations?
- Just to be sure, the disaggregation you are using is not stochastic? Right? Each daily value in transformed to the hourly ones by using the deterministic functions if I understand well. If this is the case then there aren’t any fluctuations. Please clarify and state that in the text.
- So the process preserves correlations within each catchment and not in the whole network of the 699 stations, right? Up to how many stations can this method applied effectively. For example, in our latest work (Papalexiou et al., 2023) we can go up to 10,000 stations easily preserving marginals and corrections. What are exactly the theoretical components that your approach preserve?
Please see also the works of (Peleg et al., 2017) and (Paschalis et al., 2013).
- This means that monthly variations within this summer and winter period is smoothed out? If you assess the simulation monthly within this period will it match the observed monthly characteristics?
Section 4.3. Can you show a graph of a synthetic time series and an observed, and maybe for a station the probabilities of the length of wet and dry spells vs the observed ones?
Section 5.2.
As I mentioned I feel that this is better described as a multisite model. Does this approach have any control over advection (linear or described by generic velocity fields) or anisotropy that characterize fine scale precipitation (please see Papalexiou et al., 2021). These are important points that need to be clear discussed for precipitation even as limitations of this approach.
How about the lagged correlations of precipitation?
Section 5.3. I wonder again if the grouping in winter and summer, e.g., Fig 14 is too coarse, especially for the variables such as temperature where there typically strong monthly variations.
Overall, this is an interesting and useful paper that improves and extends the authors previous works and has its place in the literature. There are many methodological choices that can be better justified, several points that need clarifications, some algorithmic descriptions were hard to follow, the assessment of the generated time series can be improved, and finally, I felt that it is was not clear what theoretical properties this approach exactly reproduces and what are the limitations. I believe also a discussion section will benefit the paper were the authors should summarize limitations, maybe future extension, and put their work in context with other works. My comments are optional, and the authors can ignore them, yet I deem that this work needs amendments to became clearer and more accessible.
Sincerely,
Simon Michael Papalexiou
Marani, M., & Ignaccolo, M. (2015). A metastatistical approach to rainfall extremes. Advances in Water Resources, 79, 121–126.
Marra, F., Nikolopoulos, E. I., Anagnostou, E. N., & Morin, E. (2018). Metastatistical Extreme Value analysis of hourly rainfall from short records: Estimation of high quantiles and impact of measurement errors. Advances in Water Resources, 117, 27–39.
Marra, F., Amponsah, W., & Papalexiou, S. M. (2023). Non-asymptotic Weibull tails explain the statistics of extreme daily precipitation. Advances in Water Resources, 173, 104388. https://doi.org/10.1016/j.advwatres.2023.104388
Papalexiou, S. M., Serinaldi, F., & Porcu, E. (2021). Advancing Space-Time Simulation of Random Fields: From Storms to Cyclones and Beyond. Water Resources Research, 57(8), e2020WR029466. https://doi.org/10.1029/2020WR029466
Papalexiou, S. M., Serinaldi, F., & Clark, M. P. (2023). Large-domain Multisite Precipitation Generation: Operational Blueprint and Demonstration for 1000 Sites. Water Resources Research, e2022WR034094. https://doi.org/10.1029/2022WR034094
Papalexiou, S.M. (2022). Rainfall Generation Revisited: Introducing CoSMoS-2s and Advancing Copula-Based Intermittent Time Series Modeling. Water Resources Research. https://doi.org/10.1029/2021WR031641
Paschalis, A., Molnar, P., Fatichi, S., & Burlando, P. (2013). A stochastic model for high-resolution space-time precipitation simulation. Water Resources Research, 49(12), 8400–8417. https://doi.org/10.1002/2013WR014437
Peleg, N., Fatichi, S., Paschalis, A., Molnar, P., & Burlando, P. (2017). An advanced stochastic weather generator for simulating 2-D high-resolution climate variables. Journal of Advances in Modeling Earth Systems, 9(3), 1595–1627. https://doi.org/10.1002/2016MS000854
Wilson, P. S., & Toumi, R. (2005). A fundamental probability distribution for heavy rainfall. Geophysical Research Letters, 32(14), L14812. https://doi.org/10.1029/2005GL022465
Citation: https://doi.org/10.5194/hess-2023-45-RC1 -
AC2: 'Reply on RC1', Ross Pidoto, 20 Jun 2023
Dear Simon,
thank you very much for reviewing our manuscript and for the numerous and insightful comments. Please find in the supplement my comments to all points raised. In the attachment, the original reviewer comments appear in black text and my response in red text.
Kind regards,
Ross Pidoto on behalf of the authors
-
RC2: 'Comment on hess-2023-45', Anonymous Referee #2, 31 Mar 2023
The idea of the article is original (development of a space-time rainfall model that can accurately reproduce various rainfall statistics including extreme values) and is also very well organized.
L89: Is there any mechanism in your model to consider temporal autocorrelation of WSD, WSA, DSD while generating them? (Large rainfall is quickly followed by large rainfall, and vice versa) This mechanism will enable the model to reproduce long(er)-term rainfall variability (e.g. weekly, monthly) making it more versatile (Kim et al., 2020).
L147: Why Weibull? Generalized Pareto Distribution may be a better pdf for rainfall peak values. You may want to try the L-moment diagram method to figure out the most optimal distribution of WSP.
Section 2.2. Space-time rainfall synthesis via resampling: I have an impression that the model is too much oriented toward reproducing only spatial-correlation. Do you have any algorithm to ensure space-time correlation at all gauges? The algorithm does not seem to have a capacity to simulate continuous movement of storms. In other words, do the consecutive snapshot of rainfall fields resemble with each other?
Figure 11. The systematic underestimation may be related to the first comment of this review.
I suggest authors to add another figure that shows a diagram showing the space-time autocorrelation between Figure 8 and Figure 9.
Kim, D., and Onof, C., (2020) A stochastic rainfall model that can reproduce important rainfall properties across the timescales from several minutes to a decade, Journal of Hydrology, 589(10), https://doi.org/10.1016/j.jhydrol.2020.125150
Citation: https://doi.org/10.5194/hess-2023-45-RC2 -
AC1: 'Reply on RC2', Ross Pidoto, 20 Jun 2023
Dear reviewer,
thank you very much for reviewing our manuscript and for the productive and supportive comments. Please find in the supplement my comments to all points raised. In the attachment, the original reviewer comments appear in black text and my response in red text.
Kind regards,
Ross Pidoto on behalf of the authors
-
AC1: 'Reply on RC2', Ross Pidoto, 20 Jun 2023
Status: closed
-
RC1: 'Comment on hess-2023-45', Simon Michael Papalexiou, 29 Mar 2023
This is a useful paper and deserves consideration. I will avoid a generic summary and list right away several comments that hopefully the authors might find useful.
As a general comment, the methods described suit more multisite methods, especially for precipitation. At the hourly or finer scales, space-time precipitation has components or advection and anisotropy, and it is not clear if what these methods preserve in this regard (I wil get back to that).
- please see also Papalexiou (2022) which is dedicated only to precipitation.
- Rainfall is described by the single-model as an alternating sequence of independent wet and dry spells. How valid this assumption is?
- I can understand the 1 mm limit but based on what rationale the DSDmin = 4 hr was set?
- if u,v are in [0,1] then where are F_U(u) and F_V(v). Check the notation please.
- What is the justification of this choice? Have you tested e.g., the Gumbel dependence and was not suitable? Did you observe asymmetries? Please justify.
- Similarly, what led you to the Weibull choice for DSD and WSA. Great that you’ve drop the 4-parameter Kappa but why Weibull is a good model for the WSA. If you consider that, e.g., the hourly wet value distribution is a specific distribution then then WSA would be its convolution. Specifically, for the Weibull there were some attempts to justify it theoretically as a rainfall distribution by Wilson & Toumi (2005); it was also used in meta statistical approaches for daily rainfall e.g., (Marani & Ignaccolo, 2015; Marra et al., 2018, 2023) and it seems it does a good job in describing the extremes but if it is suits well for the WSA it will be nice to show some evidence. Also, here you’re using the 3-par version which also can end up with ζ quite larger than the min so you might have inconsistencies in low values. Can you explain please? The same point holds for the distribution choice of the WSD. Is the LN supported by the literature? By your own analysis in this dataset?
Equation 7. So this implies that the tail of intensity is exponential? It could for this region but in general this contradicts many global studies indicating that the tails are not exponential but heavier. Exactly for this reason, in the past I explored the Generalized Gamma to allow heavier right tails and recently some Generalized Exponential distributions having similar tails (see Papalexiou, 2022). I believe the choice of model is crucial as we’re risking underestimating the potential for extremes. Please explain.
Also what is the correlation structure within the event? Clearly at hourly resolution there is strong autocorrelation within wet values (see Papalexiou, 2022).
- lower phi is typically used for the gaussian pdf, here you need capital phi Φ
Section 2.2. Operationally, how fast is this optimization approach? When you mention that the occurrence criterion in the hardest to converge does this imply that in many cases it does not converge at all?
- I guess the branched non-sequential procedure is describe correctly, yet to be honest as a reader I got lost here and mathematically it is really not clear what exactly spatiotemporal correlation structure this grouping of primary and secondary stations produces.
- so this approach will preserve only the lag-1 correlations?
- Just to be sure, the disaggregation you are using is not stochastic? Right? Each daily value in transformed to the hourly ones by using the deterministic functions if I understand well. If this is the case then there aren’t any fluctuations. Please clarify and state that in the text.
- So the process preserves correlations within each catchment and not in the whole network of the 699 stations, right? Up to how many stations can this method applied effectively. For example, in our latest work (Papalexiou et al., 2023) we can go up to 10,000 stations easily preserving marginals and corrections. What are exactly the theoretical components that your approach preserve?
Please see also the works of (Peleg et al., 2017) and (Paschalis et al., 2013).
- This means that monthly variations within this summer and winter period is smoothed out? If you assess the simulation monthly within this period will it match the observed monthly characteristics?
Section 4.3. Can you show a graph of a synthetic time series and an observed, and maybe for a station the probabilities of the length of wet and dry spells vs the observed ones?
Section 5.2.
As I mentioned I feel that this is better described as a multisite model. Does this approach have any control over advection (linear or described by generic velocity fields) or anisotropy that characterize fine scale precipitation (please see Papalexiou et al., 2021). These are important points that need to be clear discussed for precipitation even as limitations of this approach.
How about the lagged correlations of precipitation?
Section 5.3. I wonder again if the grouping in winter and summer, e.g., Fig 14 is too coarse, especially for the variables such as temperature where there typically strong monthly variations.
Overall, this is an interesting and useful paper that improves and extends the authors previous works and has its place in the literature. There are many methodological choices that can be better justified, several points that need clarifications, some algorithmic descriptions were hard to follow, the assessment of the generated time series can be improved, and finally, I felt that it is was not clear what theoretical properties this approach exactly reproduces and what are the limitations. I believe also a discussion section will benefit the paper were the authors should summarize limitations, maybe future extension, and put their work in context with other works. My comments are optional, and the authors can ignore them, yet I deem that this work needs amendments to became clearer and more accessible.
Sincerely,
Simon Michael Papalexiou
Marani, M., & Ignaccolo, M. (2015). A metastatistical approach to rainfall extremes. Advances in Water Resources, 79, 121–126.
Marra, F., Nikolopoulos, E. I., Anagnostou, E. N., & Morin, E. (2018). Metastatistical Extreme Value analysis of hourly rainfall from short records: Estimation of high quantiles and impact of measurement errors. Advances in Water Resources, 117, 27–39.
Marra, F., Amponsah, W., & Papalexiou, S. M. (2023). Non-asymptotic Weibull tails explain the statistics of extreme daily precipitation. Advances in Water Resources, 173, 104388. https://doi.org/10.1016/j.advwatres.2023.104388
Papalexiou, S. M., Serinaldi, F., & Porcu, E. (2021). Advancing Space-Time Simulation of Random Fields: From Storms to Cyclones and Beyond. Water Resources Research, 57(8), e2020WR029466. https://doi.org/10.1029/2020WR029466
Papalexiou, S. M., Serinaldi, F., & Clark, M. P. (2023). Large-domain Multisite Precipitation Generation: Operational Blueprint and Demonstration for 1000 Sites. Water Resources Research, e2022WR034094. https://doi.org/10.1029/2022WR034094
Papalexiou, S.M. (2022). Rainfall Generation Revisited: Introducing CoSMoS-2s and Advancing Copula-Based Intermittent Time Series Modeling. Water Resources Research. https://doi.org/10.1029/2021WR031641
Paschalis, A., Molnar, P., Fatichi, S., & Burlando, P. (2013). A stochastic model for high-resolution space-time precipitation simulation. Water Resources Research, 49(12), 8400–8417. https://doi.org/10.1002/2013WR014437
Peleg, N., Fatichi, S., Paschalis, A., Molnar, P., & Burlando, P. (2017). An advanced stochastic weather generator for simulating 2-D high-resolution climate variables. Journal of Advances in Modeling Earth Systems, 9(3), 1595–1627. https://doi.org/10.1002/2016MS000854
Wilson, P. S., & Toumi, R. (2005). A fundamental probability distribution for heavy rainfall. Geophysical Research Letters, 32(14), L14812. https://doi.org/10.1029/2005GL022465
Citation: https://doi.org/10.5194/hess-2023-45-RC1 -
AC2: 'Reply on RC1', Ross Pidoto, 20 Jun 2023
Dear Simon,
thank you very much for reviewing our manuscript and for the numerous and insightful comments. Please find in the supplement my comments to all points raised. In the attachment, the original reviewer comments appear in black text and my response in red text.
Kind regards,
Ross Pidoto on behalf of the authors
-
RC2: 'Comment on hess-2023-45', Anonymous Referee #2, 31 Mar 2023
The idea of the article is original (development of a space-time rainfall model that can accurately reproduce various rainfall statistics including extreme values) and is also very well organized.
L89: Is there any mechanism in your model to consider temporal autocorrelation of WSD, WSA, DSD while generating them? (Large rainfall is quickly followed by large rainfall, and vice versa) This mechanism will enable the model to reproduce long(er)-term rainfall variability (e.g. weekly, monthly) making it more versatile (Kim et al., 2020).
L147: Why Weibull? Generalized Pareto Distribution may be a better pdf for rainfall peak values. You may want to try the L-moment diagram method to figure out the most optimal distribution of WSP.
Section 2.2. Space-time rainfall synthesis via resampling: I have an impression that the model is too much oriented toward reproducing only spatial-correlation. Do you have any algorithm to ensure space-time correlation at all gauges? The algorithm does not seem to have a capacity to simulate continuous movement of storms. In other words, do the consecutive snapshot of rainfall fields resemble with each other?
Figure 11. The systematic underestimation may be related to the first comment of this review.
I suggest authors to add another figure that shows a diagram showing the space-time autocorrelation between Figure 8 and Figure 9.
Kim, D., and Onof, C., (2020) A stochastic rainfall model that can reproduce important rainfall properties across the timescales from several minutes to a decade, Journal of Hydrology, 589(10), https://doi.org/10.1016/j.jhydrol.2020.125150
Citation: https://doi.org/10.5194/hess-2023-45-RC2 -
AC1: 'Reply on RC2', Ross Pidoto, 20 Jun 2023
Dear reviewer,
thank you very much for reviewing our manuscript and for the productive and supportive comments. Please find in the supplement my comments to all points raised. In the attachment, the original reviewer comments appear in black text and my response in red text.
Kind regards,
Ross Pidoto on behalf of the authors
-
AC1: 'Reply on RC2', Ross Pidoto, 20 Jun 2023
Ross Pidoto and Uwe Haberlandt
Ross Pidoto and Uwe Haberlandt
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