Attribution and Causality Analyses of Regional Climate Variability
Round 1
Reviewer 1 Report
It would be good to check in terms of the Language
diagnostics is (diagnostic is/ diagnostics are) 12
the subsequent 19
the Pacific Decadal Oscillation 20
of (in) the statistics of the climate’s 32
of (in) the global 34
a watershed 38
which (that) 39
or, utilizing(or utilize) 47
on a regional or watershed scale. 55, 57
a singular 69
of energy being available 104
It’s written in figure “U=1+(1-W) ln (W)” ?? on the other hand in figure explanation U=1+(1-W) log(W) 164
(the El Niño–Southern Oscillation (ENSO), the Pacific Decadal Oscillation 470
(PDO), the North Atlantic Oscillation (NAO), and the Atlantic Multidecadal Oscillation 471
the El Niño–Southern Oscillation (ENSO) in blue and green, and Sunspot cycle in orange. 487
Author Response
Reviewer 1
It would be good to check in terms of the Language
Response: Thanks for the time spent on reviewing this paper.
diagnostics is (diagnostic is/ diagnostics are) 12
Response: Thanks, changed.
the subsequent 19
Response: Thanks, added.
the Pacific Decadal Oscillation 20
Response: Thanks, added.
of (in) the statistics of the climate’s 32
Response: Thanks, changed.
of (in) the global 34
Response: Thanks, changed.
a watershed 38
Response: Thanks, added.
which (that) 39
Response: Thanks, changed.
or, utilizing(or utilize) 47
Response: Thanks, changed.
on a regional or watershed scale. 55, 57
Response: Thanks, added.
a singular 69
Response: Thanks, deleted.
of energy being available 104
Response: Thanks, changed.
It’s written in figure “U=1+(1-W) ln (W)” ?? on the other hand in figure explanation U=1+(1-W) log(W) 164
Response: Changed the captain to “U=1+(1-W) ln (W)” as in the figure.
(the El Niño–Southern Oscillation (ENSO), the Pacific Decadal Oscillation 470
Response: Thanks, added.
(PDO), the North Atlantic Oscillation (NAO), and the Atlantic Multidecadal Oscillation 471
Response: Thanks, added.
the El Niño–Southern Oscillation (ENSO) in blue and green, and Sunspot cycle in orange. 487
Response: Thanks, added.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments for author File: 
Comments.pdf
Author Response
The reviewed endeavor “Attribution and causality analyses of a changing regional climate” falls within the dome of the Journal. However, there are few points which need to be addressed.
Response: Thanks for the time spent on reviewing this paper.
Why all equations are without any numbers?
Response: Indeed, it should be added, changes are marked in the updated manuscript.
Figure 1. Either authors should use Figure 1a and Figure 1b or merge them in single panel.
Response: Actually, there is only one figure (left side). Right part is the legend for explaining the colors and shapes in the figure. To make it more clear, we label “legend” for the left part (see below).
Figure 2. Caption like “Fig. 2 Flowchart of the two-step attribution and causality analysis on inter-annual scale (left) versus slow feature analysis of causality on monthly scale (right). Input: ecohydrological indices and fluxes of water supply and demand (pink, top). Methods: Attribution analysis (yellow, top left) and causality analysis (blue, bottom) with stepwise results (pink, bottom)” made everything confusing. It would be difficult for the readers to follow the colors and top, left etc. It would be better to name them as panel a, b, c, and d.
Response: Thanks, changed as below.
Fig. 2 Flowchart of the two-step attribution and causality analysis on inter-annual scale (left, a and b) versus slow feature analysis of causality on monthly scale (right, c and d). Input: ecohydrological indices and fluxes of water supply and demand (pink in a and c). Methods: Attribution analysis (yellow in a) and causality analysis (blue in b and d) with stepwise results (pink in b and d).
Figure 3. Authors used a, and b inside the panels while c is outside. It must be consistent. Also what is the reason to show anomaly in separate panels? Would not that be good to show anomaly inside 3a and 3b.
Response: Thanks, changed as below.
Figure 4. I am not sure why authors have used “Table” as part of figure which makes things confusing as in “Line 404”. However, presenting and discussing it as a separate table would be good.
Response: This is because we need colored table to be consistent with the legend of the figure. But unfortunately, as a table it is required to be black and white.
To be less confusing, we changed “table” related descriptions. For example, (see statistics in Fig. 4).
Figure 5. Comments as for “Figure 3”.
Response: Thanks, changed as below.
Figure 6. Using figure numbers as “A” and “a” makes manuscript confusing. Authors should use other options.
Response: Thanks, changed as below.
Fig. 6. Time series of annual means of a) the normalized driving force generated by slow feature signals when m = 13 and b) the power spectrum of the wavelet transform coefficient for the reconstruction of the driving force for I) net radiation, II) precipitation and III) dryness ratio. Significant regions are surrounded by black isolines.
Figure 7. Comments as for “Figure 4”.
Response: Thanks but same as Figure 4, a colored table helps our illustration, so we kept it.
Author Response File: Author Response.docx
Reviewer 3 Report
Thank you for this sound and high-quality manuscript on detecting and separating effects on the changing regional climate. It is well prepared.
I would suggest a shorter and more precise conclusion. 2 pages are too detailed and not concluding but discussing a lot (e.g. line 534 explanations on why not using GLMs etc).
Author Response
Reviewer 3
Thank you for this sound and high-quality manuscript on detecting and separating effects on the changing regional climate. It is well prepared.
Response: Thanks for the time spent on reviewing this paper.
I would suggest a shorter and more precise conclusion. 2 pages are too detailed and not concluding but discussing a lot (e.g. line 534 explanations on why not using GLMs etc).
Response: This is helpful. The original conclusion is separated into two sections (Discussion plus conclusion as below, see also manuscript).
- Discussion
Different from logistic regression, GLM regression, or Granger causality analysis, this approach requires the use of both climate forcing time series (independent variables) and climate component time series (dependent variables). The goal is to diagnose the background climate forcing behind local climate variability without prior knowledge. The variations in oceanic and atmospheric modes at different timescales significantly contribute to global and regional climate variability, resulting in trends, cycles, random walks, or combinations thereof in the dependent time series. Regressing non-stationary time series through logistic regression, GLM regression, or Granger causality analysis can lead to false results, so it is necessary to first transform the non-stationary time series into a stationary time series before applying the chosen regression (further information and causality analyses can be found in Runge et al. 2019 and San Liang 2014).
The wavelet transform is utilized in this study to extract features from time series, as it shows the variation (power) of a time series as a function of time and period. However, it may not be effective for feature extraction when there are strong annual or seasonal cycles in the time series. To resolve this issue, it is advisable to use a decomposition method, such as EOF or SFA analysis, prior to the wavelet transform to remove annual and seasonal cycles.
Therefore, a two-step attribution and causality analysis has been introduced as an up-scaling approach to examine environmental changes. This method is applied to time series of land surface water and energy fluxes, which characterize the eco-hydrology at a regional scale. The first step is an attribution model, which separates external climate influences from internal anthropogenic causes of environmental changes related to land use and land cover. External climate processes indicate water supply and demand at a larger scale, while internal or anthropogenic forcing components describe the partitioning of evaporation and sensible heat or discharge fluxes at a regional scale and smaller.
In the first step of attributing land use and land cover environmental change, a random walk length or equilibrium state from time series is needed. Bye et al. (2011) tested the random walk length from 8 global mean quantities with 100-year and 1000-year scales. For 100-year time series, a random walk length of 24 years on land and 20 years over ocean characterizes the random variability of climate on the scale of civilizations, estimated at 20 years. For 1000-year time series, results suggest a random walk length of 30 years, which should be tested further.
The subsequent causality analysis employs singular spectrum analysis to identify evolving driving forces and slow feature causality analysis (SFA) for non-linear analysis using area mean water supply/demand. The first EOF determines the inter-annual contribution of external climate processes, while the slowest forcing of SFA determines the time derivative.
- Conclusion: Upscaling by Attribution and Subsequent Causality Analyses
The ecohydrological conditions on a watershed scale are defined by the rainfall-runoff chain that results from the interaction of surface energy and water fluxes. Changes in these conditions can be used to analyze
(i) the distinction between external climate changes caused by climate change (manifested by changes in precipitation and net radiation) and internal changes caused by human activities (which affect the partitioning of heat and water into latent and sensible heat fluxes and runoff), and
(ii) the cause of external climate changes in the rainfall-runoff chain variables
(changes in climate and water and energy sources) that are driven by larger scale climate shifts such as oceanic and atmospheric patterns or the solar cycle.
As an example, this two-step attribution and causality analysis and SFA diagnostic have been applied to the drought-prone regions of the arid water limited southwestern United States. The result indicates the quasi-biennial oscillation and the El Niño-Southern Oscillation as the drivers of the climate-induced forcings. However, without the first step of attribution (or SFA only), a twenty to thirty years’ periodicity as suggested by the dry-wet-dry and vice versa changes described above related to the Pacific Decadal Oscillation is missing.
To summarize, the impact of large-scale climate modes on global and regional climate has been well-studied, but the challenge lies in understanding the key driving factors of these modes at a regional level. Simply establishing statistical relationships between climate indices is not enough to fully grasp the intricate physical interactions between the variables. The two-step attribution and causality analysis that focuses on fluxes and state changes provides a deeper understanding of the underlying physical processes and drives, and can be useful in improving our knowledge of regional climate and adapting to it. This approach can be seen as a first step towards a more comprehensive data-driven attribution and causality analysis for environmental change, beyond the traditional hydrological techniques based on sensitivity and elasticity modules emerging from the Budyko framework. Further enhancement of the analysis, such as incorporating more dimensions like vegetation absorption, soil properties and hydraulic conductivity, is desirable.
Author Response File: Author Response.docx
Reviewer 4 Report
The paper uses complex statistical analyses and inversion techniques to explore the non-stationary forcing of climate variations in 100-year period time series of surface fluxes and hydrological variables from ERA-20CM dataset and trajectories of environmental change in a (U,W) state space.
Two methodologies are put into practice:
- An attribution diagnostic based on the directions and lengths of distances from points associated to a first period with others that correspond a second period when represented at two-dimensional state space based on Budyko’s framework.
- A singular spectrum analysis and empirical orthogonal function analysis of interannual climate forcing to identify the major climate modes through similar independent frequencies, i.e., a causality analysis.
The final objectives of the study are:
- to interpret regional environmental change
- to separate external climate from internal human forcing
- to extract various timescales underlying the forcings embedded in time variability using wavelet analysis.
The area selected for the study is the Southern Intermountain region of the N-American (Arizona, Colorado, New Mexico, and Utah).
The paper stands for a good quality research and it is presented in an almost final form, probably due to previous revisions before the present one. The topic covered reveals a modern-day interest for the atmospheric and environmental research community.
Due to the complexity of the techniques used, the paper is sometimes hard to follow. Nevertheless, it must be underlined that the authors have done a good job providing many references and introducing the successive aspects that arise in the study with sufficient clarity.
Even that the paper can be accepted in its present form, some questions arise that authors should be clarified or correct to their satisfaction:
Line 164: If the formula U=1+(1-W) log(W) is to be the equation of state Ro = P exp(- N/P) that is introduced in line 111, then they are not exactly the same. Please, provide a further explanation of both equations in the document in case they are different concepts, so to clarify the role of both of them.
Lines 181-182 - If dE>0 then dU<0 and dW<0 and vice versa, aren´t they? Please correct in case they are erroneous.
Fig 3: Please try to score abscissa axis at round years such as 1900, 1920, 1940, etc..
Line 351: Please, mark the periods you cite with stripes at the top time series in Figure 3. Why are they selected in opposition to other possible periods? Why do they must begin at decadal year 1 and last exactly for 20 years?
Fig 4: Table top captions should express years in a long format like 1931-1950 to 1951-1970, etc. Please, consider making a table by itself, and not included in the figure.
Line 390 - The dark blue and yellow arrows in figure 4 are almost imperceptible, so try to solve this question in the best possible way for the help of any reader.
Fig 5: Please, it would be helpful if color legend is also provided, containing rage values, not as the one in next figure.
Line 480 – Parameters Tq (purple), Te1 (blue), Te2 (green), and Ts (orange), please define.
Line 600-602 – The sentence starts with a while conditional but does not end correctly.
Author Response
The paper uses complex statistical analyses and inversion techniques to explore the non-stationary forcing of climate variations in 100-year period time series of surface fluxes and hydrological variables from ERA-20CM dataset and trajectories of environmental change in a (U,W) state space.
Two methodologies are put into practice:
- An attribution diagnostic based on the directions and lengths of distances from points associated to a first period with others that correspond a second period when represented at two-dimensional state space based on Budyko’s framework.
- A singular spectrum analysis and empirical orthogonal function analysis of interannual climate forcing to identify the major climate modes through similar independent frequencies, i.e., a causality analysis.
The final objectives of the study are:
- to interpret regional environmental change
- to separate external climate from internal human forcing
- to extract various timescales underlying the forcings embedded in time variability using wavelet analysis.
The area selected for the study is the Southern Intermountain region of the N-American (Arizona, Colorado, New Mexico, and Utah).
The paper stands for a good quality research and it is presented in an almost final form, probably due to previous revisions before the present one. The topic covered reveals a modern-day interest for the atmospheric and environmental research community.
Due to the complexity of the techniques used, the paper is sometimes hard to follow. Nevertheless, it must be underlined that the authors have done a good job providing many references and introducing the successive aspects that arise in the study with sufficient clarity.
Even that the paper can be accepted in its present form, some questions arise that authors should be clarified or correct to their satisfaction:
Response: Thanks for the time spent on reviewing this paper.
Line 164: If the formula U=1+(1-W) log(W) is to be the equation of state Ro = P exp(- N/P) that is introduced in line 111, then they are not exactly the same. Please, provide a further explanation of both equations in the document in case they are different concepts, so to clarify the role of both of them.
Response-1:
Both energy and water excess (or efficiency) describe proportions of available water and energy which, remaining unused, appear to be relevant to identify the causes of climate and basin change. Note that U = H/N = 1 – E/N and W = Ro/P = 1 – E/P determine the dryness ratio, D = N/P = (1 – W)/(1 – U). Thus, the equation of state, W = Ro/P = exp(-N/P) or E/P = 1 – exp(-D) in the (E/P,D)-diagram, can be formulated as U = 1 + (1 – W) ln(W) in the (U,W)-diagram.
Fraedrich, K., F. Sielmann, D. Cai, and X. Zhu 2016: Climate dynamics on watershed scale: along the rainfall-runoff chain. In: The Fluid Dynamics of Climate, International Centre for Mechanical Sciences (CISM), Springer Verlag, 183-209.
Response-2: And we add in the context:
“(iv) Both energy and water excess (or efficiency) describe proportions of available water and energy which, remaining unused, appear to be relevant to identify the causes of climate and basin change. Note that U = H/N = 1 – E/N and W = Ro/P = 1 – E/P determine the dryness ratio, D = N/P = (1 – W)/(1 – U). Thus, the equation of state (1b), W = Ro/P = exp(-N/P) or E/P = 1 – exp(-D) in the (E/P,D)-diagram, can be formulated as U = 1 + (1 – W) ln(W), which enters the ecohydrological state space or (U,W)-diagram (see Fraedrich et al. 2016)”
Lines 181-182 - If dE>0 then dU<0 and dW<0 and vice versa, aren´t they? Please correct in case they are erroneous.
Response: Well, yes. If dE>0 then dU<0 and dW<0 and if dE<0 then dU>0 and dW>0, when the climate N and P did not change (see below).
As we write in the context:
“(i) Human induced change (of land cover) is characterized by fixed climate forcing (P,N) = constant and greater than 0, which changes the excess energy U = (1 – E)/N and the water flux ratio W = (1 – E) / P, to dU = – dE/N and dW = – dE/P. That is, dE > 0 (< 0) gives (dU,dW) > 0 (< 0). That is, the change in (U, W)-diagram is directed to one of the two quadrants aligned along the main diagonal of internal partitioning: (dW,dU) > 0 or first quadrant (pink) and (dW,dU) < 0 or third quadrant (light blue).”
Fig 3: Please try to score abscissa axis at round years such as 1900, 1920, 1940, etc..
Response: Changed as below.
Line 351: Please, mark the periods you cite with stripes at the top time series in Figure 3. Why are they selected in opposition to other possible periods? Why do they must begin at decadal year 1 and last exactly for 20 years?
Response: Well, this is indeed a justified question. First of all, the twenty years window is chosen in accordance with the random walk length to ensure somewhat de-correlated periods. Moreover, Sun and Wang (2011) suggested twenty-year time intervals to capture equilibrium state as well as the sensitivity of evapotranspiration to land surface changes and the sensitivity of external climate forcing to evapotranspiration changes.
However, the start at year 1 is somewhat arbitrary, but it seems to maximize the differences by chance, such that external climate and internal anthropogenic forcing of observed quasi-stationary changes are best synchronized with changes (for all grid points in Fig. 4) in the geographical and eco-hydrological state space. Finally that is what we mainly wanted to demonstrate in the paper.
So in the context, we write:
“(i) The past hundred years of the area averaged annual mean values of dryness (and precipitation) reveal droughts before the 1910s, in 1930s, from the 1950 to the 1970, and at the beginning of the twenty-first century (Fig. 3a and b). Three changes between sub-sequent twenty-year periods are noted: 1931-1950 and 1951-1970 (from wet to dry), 1951-1970 and 1971-1990 (from dry to wet), and 1971-1990 and 1991-2010 (from wet to dry). (ii) Sun and Wang (2011) suggested twenty-year time intervals to capture equilibrium state as well as the sensitivity of evapotranspiration to land surface changes and the sensitivity of external climate forcing to evapotranspiration changes.”
Fig 4: Table top captions should express years in a long format like 1931-1950 to 1951-1970, etc. Please, consider making a table by itself, and not included in the figure.
Response: Changed to long format.
And use it as a figure because we need colored table to be consistent with the legend of the figure. But unfortunately, as a table it is required to be black and white.
Line 390 - The dark blue and yellow arrows in figure 4 are almost imperceptible, so try to solve this question in the best possible way for the help of any reader.
Response: This is because the length (change) of the arrows from the 1st to the 2nd period is too limited. Therefore, we used colors for a better understanding.
Now, we added some labels in the plot to help readers to understand.
Fig 5: Please, it would be helpful if color legend is also provided, containing rage values, not as the one in next figure.
Response: Changed as below.
Line 480 – Parameters Tq (purple), Te1 (blue), Te2 (green), and Ts (orange), please define.
Response: Changed in the caption.
Fig. 7. The time-averaged power spectrum from Morlet Wavelet transform of SFA-extracted (m = 13) slow feature signals for a) Net radiation; b) Precipitation and c) Dryness. The significant points (dots) which pass the significance test at the 0.05 significance level are listed and classified, including the biennial annular mode oscillation (BAMO) and/or the quasi-biennial oscillation (QBO) in purple (Tq), the El Niño–Southern Oscillation (ENSO) in blue (Te1) and green (Te2), and Sunspot cycle in orange (Ts).
Line 600-602 – The sentence starts with a while conditional but does not end correctly.
Response: The paragraph is changed as below:
To summarize, the impact of large-scale climate modes on global and regional climate has been well-studied, but the challenge lies in understanding the key driving factors of these modes at a regional level. Simply establishing statistical relationships between climate indices is not enough to fully grasp the intricate physical interactions between the variables. The two-step attribution and causality analysis that focuses on fluxes and state changes provides a deeper understanding of the underlying physical processes and drives, and can be useful in improving our knowledge of regional climate and adapting to it. This approach can be seen as a first step towards a more comprehensive data-driven attribution and causality analysis for environmental change, beyond the traditional hydrological techniques based on sensitivity and elasticity modules emerging from the Budyko framework. Further enhancement of the analysis, such as incorporating more dimensions like vegetation absorption, soil properties and hydraulic conductivity, is desirable.
Author Response File: Author Response.docx
