Intrinsic Predictability Limits arising from Indian Ocean MJO Heating: Effects on tropical and extratropical teleconnections

Straus, David Martin; Domeisen, Daniela I. V.; Lock, Sarah-Jane; Molteni, Franco; Yadav, Priyanka

doi:https://doi.org/10.5194/egusphere-2023-493

Preprints

https://doi.org/10.5194/egusphere-2023-493

Preprints

27 Mar 2023

| 27 Mar 2023

Intrinsic Predictability Limits arising from Indian Ocean MJO Heating: Effects on tropical and extratropical teleconnections

David Martin Straus, Daniela I. V. Domeisen, Sarah-Jane Lock, Franco Molteni, and Priyanka Yadav

Abstract. Since the Madden-Julian Oscillation (MJO) is a major source for tropical and extratropical variability on weekly to monthly timescales, the intrinsic predictability of its global teleconnections is of great interest. As the tropical diabatic heating associated with the MJO ultimately drives these teleconnections, the effect of the variability of heating among various episodes of the same MJO phase will limit this predictability. In order to assess this limitation, a suite of 60-day ensemble reforecasts has been carried out with the ECMWF forecast model, spanning 13 starting dates from 01 Nov and 01 Jan for different years. The initial dates were chosen so that phases 2 and 3 of the MJO (with anomalous tropical heating in the Indian Ocean sector) were present in the observed initial conditions. The 51 members of an individual ensemble use identical initial conditions for the atmosphere and ocean. Stochastic perturbations to the tendencies produced by the atmospheric physics parameterizations are applied only over the Indian Ocean region. This guarantees that the spread between reforecasts within an ensemble is due to perturbations in heat sources only in the Indian Ocean sector. The point-wise spread in the intra-ensemble (or error) variance of vertically integrated tropical heating Q is larger than the average ensemble mean signal even at early forecast times; however the planetary wave component of Q (zonal waves 1–3) is predictable for 24 days for 01 Nov starts and 28 days for 01 Jan starts. The predictability times, measured by the time at which the error variance reaches 0.5 of its saturation value, decreases to 18–20 days for zonal waves 4–10, and 14 days for waves 11–21. In contrast, the planetary wave component of the 200 hPa Rossby wave source, which is responsible for propagating the influence of tropical heating to the extratropics, is only predictable for 14 to 19 days, very close to the predictability times for the 200 hPa vorticity in the 40° N–50° N latitude belt. In terms of geographical distribution, substantial ensemble spread of heating and 200 hPa vorticity propagates from the tropics to the Northern Hemisphere storm-track regions by days 15–16. Following the growth of upper tropospheric spread in planetary wave heat flux, the stratosphere provides a feedback in enhancing the error via downward propagation towards the end of both Nov. and Jan. reforecasts.

Received: 17 Mar 2023 – Discussion started: 27 Mar 2023

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21 Nov 2023

Intrinsic predictability limits arising from Indian Ocean Madden–Julian oscillation (MJO) heating: effects on tropical and extratropical teleconnections

David Martin Straus, Daniela I. V. Domeisen, Sarah-Jane Lock, Franco Molteni, and Priyanka Yadav

Weather Clim. Dynam., 4, 1001–1018, https://doi.org/10.5194/wcd-4-1001-2023,https://doi.org/10.5194/wcd-4-1001-2023, 2023

Short summary

David Martin Straus et al.

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-493', Anonymous Referee #1, 01 May 2023

Overview:
The paper deals with limits of predictability associated with uncertainties in simulated diabatic heating over the Indian ocean during the MJO. This is investigated by re-running a set of 60-day long ensemble forecasts assuming perfect initial conditions. In other words, the study addresses a component of predictability associated with applied model errors. The error was simulated by stochastic perturbations of the tendencies due to physics geographically limited to the Indian Ocean region 50E-120E and 20N-20S. Their effects on predictability are studied in the ensemble spread of the vertically integrated diabatic heating, of Rossby wave source, of the heat flux and of the vorticity field at 200 hPa. The authors report predictability limits, defined as 0.5 of the saturation value of the ensemble variance, to be between 2 and 3 weeks.

Summary:
The authors address an important problem but the paper in its current shape does not provide significant new insights on the teleconnections associated with the MJO or associated predictability limits. One way to revise the paper would be to compare the results with the operational seasonal forecasts which sample uncertainties in both initial conditions and model errors.

Detailed comments:

1. Assumptions
The authors argue (Lines 55-56) that they apply the "perfect model" assumption in their study of (Lines 46-47) "uncertainties in MJO heating, as witnessed by the variability in the details of heating among different episodes of a given phase." The statement should be re-written in line with what has been done (perfect initial-conditions and simulated model error). Please discuss what is meant by "variability in the details of MJO heating" and provide references.

2. Methodology

a) Lines 59-61: "the stochastic parametrization scheme (SPPT) described in Leutbecher et al. (2017) has been altered so that perturbations which affect (directly or indirectly) diabatic heating tendencies are confined to the tropical Indian Ocean region". Some details would be useful here, such as the amplitude of perturbations compared to the signal. Different wording on what parts of the model physics have been perturbed is provided at different places in the paper, and it should be clarified.

b) The computation of the divergent horizontal wind in Eq. (1) should be explained.

c) What is the sensitivity of the results to the choice of the latitude belt used to compute S?

d) Why is the integrated diabatic heating a good measure of the MJO predictability as compared for example with precipitation?

e) Why is vorticity a good measure of the forecast error growth in the tropics (Figures 8-9)?

f) How is the estimated predictability limit sensitive to different choices of predictability time (Line 211) taken to be 50% of the saturation error?

g) How is the wavenumber analysis performed, is it spherical harmonics space?

h) The ENSO events are introduced in 2.2 and Figures 1-2, but little mentioned after 3.1.

3. Relation to previous work
Many studies addressed the response of tropical and extratropical circulation to MJO-like heating perturbations. I disagree with the authors' statement that (Lines 47-49) "the wealth of MJO teleconnection research discussed above has relied almost exclusively on the Wheeler-Hendon multivariate empirical orthogonal function framework (Wheeler and Hendon, 2004)." See for example https://doi.org/10.1175/JAS-D-18-0203.1 and references herein. Similarly, there is a wealth of research in predictability associated with MJO that is missing in the introduction and discussion of the results.

4. Results
This paper, like several earlier studies of predictability, finds a predictability scale of 2-3 weeks and that longer scale have longer predictability. In the present study, the predictability limit is due to perturbations in model physics. Previous studies such as https://doi.org/10.1175/JAS-D-19-0116.1 find similar intrinsic predictability to be due to small perturbation in initial conditions (perfect model assumption). I wish the authors discussion their predictability results in comparison to other studies of predictability in the tropics and globally.
How does the growth of spread in selected variables compare with the scale-dependent circulation response to heating perturbations in https://doi.org/10.1175/JAS-D-18-0203.1 (their figures 7-8)?
Overall it is unclear why the ensemble spread of diabatic heating is a good measure of predictability limits, rather than prognostic variables of circulation and/or precipitation. For example, how is the amplitude of the ensemble spread in diabatic heating related to the predictability of precipitation? Could the results be coupled with the precipitation validation in the ECMWF model forecasts (e.g. https://doi.org/10.1029/2020GL091022)?

Citation: https://doi.org/10.5194/egusphere-2023-493-RC1
- AC1:
  'Reply on RC1', David Straus, 05 May 2023
  RC1 comments repeated here , authors' replies in bold.
  The paper deals with limits of predictability associated with uncertainties in simulated diabatic heating over the Indian ocean during the MJO. This is investigated by re-running a set of 60-day long ensemble forecasts assuming perfect initial conditions. In other words, the study addresses a component of predictability associated with applied model errors. The error was simulated by stochastic perturbations of the tendencies due to physics geographically limited to the Indian Ocean region 50E-120E and 20N-20S. Their effects on predictability are studied in the ensemble spread of the vertically integrated diabatic heating, of Rossby wave source, of the heat flux and of the vorticity field at 200 hPa. The authors report predictability limits, defined as 0.5 of the saturation value of the ensemble variance, to be between 2 and 3 weeks.
  Response: Our interpretation is not that our study addresses the component of predictability due to model errors, but that it addresses that component due to intrinsic variability in the model (“internal error”). The stochastic parameterization scheme which is used (SPPT) is considered an integral part of the IFS, and other research (i.e. Selz, 2019) supports the notion that the use of such schemes gives more realistic estimates of intrinsic predictability. The novelty of our experiments is that we suppress SPPT outside the Indo-Pacific region, and that is the only change we make. The ensemble spread is thus due entirely to processes internal in the model.
  Summary:
  The authors address an important problem but the paper in its current shape does not provide significant new insights on the teleconnections associated with the MJO or associated predictability limits.
  Response: We may not have emphasized the role of the Rossby wave source in the paper enough: the rate of spread of the Rossby wave source gives an indication of how the spread of the tropical heating is translated into the uncertainty in the mid-latitude response. We agree that more diagnostics concerning the rate of growth of the Rossby wave source (and other measures of the mid-latitude error) will be useful and we intend to provide them.
  One way to revise the paper would be to compare the results with the operational seasonal forecasts which sample uncertainties in both initial conditions and model errors.
  Detailed comments:
  Assumptions
  
  The authors argue (Lines 55-56) that they apply the "perfect model" assumption in their study of (Lines 46-47) "uncertainties in MJO heating, as witnessed by the variability in the details of heating among different episodes of a given phase." The statement should be re-written in line with what has been done (perfect initial-conditions and simulated model error). Please discuss what is meant by "variability in the details of MJO heating" and provide references.
  We plan to discuss, both in the revised Introduction and the Results sections, previous work which the reviewer is correct to point out. These include studies of predictability focusing on the roles of: (a) the size of the initial error (Zhang et al., 2019), (b) the role of domain (polar, mid-latitude, tropical) in which the errors are introduced (Judt, 2020), and (c) specific to the MJO, the spatial and temporal variability of Indo-Pacific heating, as seen in low-resolution models (e.g. Lin and Brunet, 2018) and intermediate resolution models (Kosovelj et al. 2019).
  By “variability in the details of the MJO heating” we mean the differences in the evolution of the magnitude and spatial of the heating between ensemble members that are initialized identically. This spread is an indication of the variation of heating in the real atmosphere among episodes that are characterized by one phase of the MJO.
  Methodology
  
  a) Lines 59-61: "the stochastic parametrization scheme (SPPT) described in Leutbecher et al. (2017) has been altered so that perturbations which affect (directly or indirectly) diabatic heating tendencies are confined to the tropical Indian Ocean region". Some details would be useful here, such as the amplitude of perturbations compared to the signal. Different wording on what parts of the model physics have been perturbed is provided at different places in the paper, and it should be clarified.
  
  b) The computation of the divergent horizontal wind in Eq. (1) should be explained.
  
  The horizontal winds (u,v) on the Gaussian grid were used to compute vorticity and divergent in spectral space (i.e. the coefficient of the spherical harmonics) using standard methods. The vorticity and divergence were truncated to T42. Setting the vorticity spectral components to zero, we transformed back to (u,v). This will be amplified in an appendix.
  c) What is the sensitivity of the results to the choice of the latitude belt used to compute S?
  
  This will be included in the revised version of the paper.
  d) Why is the integrated diabatic heating a good measure of the MJO predictability as compared for example with precipitation?
  
  The atmosphere is forced by diabatic heating, which includes latent, radiative and turbulent heating, each of which has its own vertical structure. The precipitation is the vertical integral of only one component (latent heating). While we have not discussed the effects of the vertical structure of heating, this is an area we plan to explore in the future.
  e) Why is vorticity a good measure of the forecast error growth in the tropics (Figures 8-9)?
  
  It is not the only measure; we will examine other measures.
  f) How is the estimated predictability limit sensitive to different choices of predictability time (Line 211) taken to be 50% of the saturation error?
  
  We will present results for the predictability limit as a function of spatial scale and threshold.
  g) How is the wavenumber analysis performed, is it spherical harmonics space?
  
  The zonal wavenumber analysis is performed on latitude circles (i.e. as a function of longitude only) after the fields have been transformed back to the Gaussian grid using a T42 truncation in spherical harmonics.
  h) The ENSO events are introduced in 2.2 and Figures 1-2, but little mentioned after 3.1.
  
  Relation to previous work
  
  Many studies addressed the response of tropical and extratropical circulation to MJO-like heating perturbations. I disagree with the authors' statement that (Lines 47-49) "the wealth of MJO teleconnection research discussed above has relied almost exclusively on the Wheeler-Hendon multivariate empirical orthogonal function framework (Wheeler and Hendon, 2004)." See for example https://doi.org/10.1175/JAS-D-18-0203.1 and references herein. Similarly, there is a wealth of research in predictability associated with MJO that is missing in the introduction and discussion of the results.
  We plan to discuss, both in the revised Introduction and the Results sections, recent previous work which the reviewer is correct to point out. These include studies of predictability focusing on the roles of: (a) the size of the initial error (Zhang et al., 2019), (b) the role of domain (polar, mid-latitude, tropical) in which the errors are introduced (Judt, 2020), and (c) specific to the MJO, the roles of spatial and temporal variability of Indo-Pacific heating on MJO predictability, as seen in low-resolution models (e.g. Lin and Brunet, 2018) and intermediate resolution models (Kosovelj et al. 2019).
  
  Results
  
  This paper, like several earlier studies of predictability, finds a predictability scale of 2-3 weeks and that longer scale have longer predictability. In the present study, the predictability limit is due to perturbations in model physics. Previous studies such as https://doi.org/10.1175/JAS-D-19-0116.1 find similar intrinsic predictability to be due to small perturbation in initial conditions (perfect model assumption). I wish the authors discussion their predictability results in comparison to other studies of predictability in the tropics and globally.
  How does the growth of spread in selected variables compare with the scale-dependent circulation response to heating perturbations in https://doi.org/10.1175/JAS-D-18-0203.1 (their figures 7-8)?
  A number of previous papers show the growth of errors as a function of spatial scale (characterized by zonal wavenumber) for different variables and pressure levels. In the revised paper we will compare our results to those in a similar format.
  Overall it is unclear why the ensemble spread of diabatic heating is a good measure of predictability limits, rather than prognostic variables of circulation and/or precipitation. For example, how is the amplitude of the ensemble spread in diabatic heating related to the predictability of precipitation? Could the results be coupled with the precipitation validation in the ECMWF model forecasts (e.g. https://doi.org/10.1029/2020GL091022)?
  In the tropics, the spread of diabatic heating is presented to document just how variable heating is, and to show the forcing for the extra-tropical spread in circulation. Whether the tropical precipitation in this model is realistic is a different question: it is the total heating that is coupled to the atmospheric circulation. Heating in mid-latitudes is a good indicator of activity in the storm tracks, as much of the heating arises from the warm conveyor belts in extra-tropical cyclones. We will clarify this in the revised paper.
  
  Citation: https://doi.org/10.5194/egusphere-2023-493-AC1
RC2:
'Comment on egusphere-2023-493', Anonymous Referee #2, 04 May 2023

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-493/egusphere-2023-493-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2023-493-RC2
- AC2:
  'Reply on RC2', David Straus, 10 May 2023
  Comments from Reviewer 2 are in regular font – responses in bold small font
  R2 Major Comments:
  While it is true that only the model physics over the Indian Ocean are perturbed, the effect of chaos seeding (Ancell et al. 2018) quickly spreads the error over the whole globe in non-physical ways. This likely means that the results are indistinguishable from results that would have been obtained if SPPT perturbations were added to the entire tropical belt or to another location that is convectively active, such as the Amazon. I suggest testing this out.
  
  This is a valid point – any perturbation will rapidly spread due to variety of reasons, some numerical and some intrinsic to the system. We want to point out that the stochastic parameterization scheme which is used (SPPT) is considered an integral part of the IFS, and other research (i.e. Selz, 2019) supports the notion that the use of such schemes gives more realistic estimates of intrinsic predictability. Thus the effects of restricting the SPPT to the tropical Indo-Pacific region may be confined to the early growth of errors. This may be worth testing in a future project. [The simulations done for this paper were quite computer-intensive.] We thank the reviewer for this interesting reference and will include a discussion of this in the revised paper.
  It would be interesting to see how different the result would be when “butterfly seeding”were used, i.e., tiny initial perturbations of the initial conditions everywhere on the globe, as in Judt (2018) or Zhang et al (2019). I recommend running an additional ensemble with this kind of perturbation and comparing the results with the ones obtained so far (this additional experiment would also be more in line with intrinsic predictability, whichusually addresses predictability limits arising due to miniscule initial condition uncertainty).
  
  While we agree that this would be an interesting comparison, there is an arbitrariness in perturbing initial conditions. In fact the whole purpose of the cited paper of Zhang et al. is to compare the error growth due to current, operational uncertainty in the initial conditions (taken from multiple reanalyses) to a hypothetical “perfect” scenario that is implemented by arbitrarily reducing the initial condition uncertainties by a factor of 100. Such a study could be implemented in the ECMWF modeling system since there is in place a procedure to perturb the initial conditions (although we did not use this in the simulations). As above, this computer-intensive proposal is a goal for a future project. Again the Discussion section of the paper will be augmented by a discussion of this alternate approach to estimating “intrinsic” predictability.
  Is it necessary to discuss the Nov and Jan initialization experiments separately? In my opinion no, as the differences between Nov and Jan events are not large enough to warrant the extra work for the reader to keep track of two sets of results. I therefore recommend combining all experiments into one “grand experiment”. This shouldn’t affect the conclusions.
  
  This is a valid point for most of the diagnostics. It is only for the figures relating to the role of the stratosphere that we have reasons to discriminate the Jan. and Nov. initial conditions. This is because the polar vortex may not be fully formed in November, so that the “stratospheric pathway” towards uncertainty growth will have a different time scale for the Nov and Jan runs. But we will try to combine the results from all the runs for the other diagnostics.
  It looks like Fig. 3 is not referenced in the text. Furthermore, I am not sure why the “Rossby wave source” is analyzed at all. I suggest removing this analysis or better motivating it.
  
  This is simply a mistakeo on our part – there was discussion of the Rossby Wave Source in our first draft which inadvertently got omitted. The Rossby Wave Source is one dynamical indicator of how the tropical heating affects the extra-tropical circulation, and we will motivate it more fully in the revised version.
  Section 3.4 seems to be lacking a conclusion, or at least I’m left with this impression.
  
  Minor Comments:
  L.45: How does the presence of baroclinic instability limit the predictability of MJ teleconnections? Through error growth associated with baroclinic instability? Yes- this will be mentioned.
  
  Figs. 1-3 and 6-9 imply that the runs are 30 days long, while the other figures show the entire 60 day time period. Why are only the first 30 days shown in the Hovmöller plots? Maybe nothing interesting happens after 30 days, but then it should be indicated somewhere so the reader doesn’t end up confused whether or not the experiments are 30 or 60 days long.The experiments are 60 days long, but for some diagnostics it is only the first 30 days that are interesting. This will be clarified in the text.
  
  L.102: Just curious, why are you not using ERA5 to initialize the ensembles? The model configuration is that used by ECMWF for its monthly forecasts, and the system is set up to use ERA-Interim for initial conditions.
  
  L. 155-177: I don’t think the description of the figures is necessarily wrong, but I do see a
  
  lot of noise in the Hovmöllers and not so much of the described
  We will look at this carefully.
  Fig. 1 (and Fig. 2): The evolution of the standard deviation in panels (d) shows very little propagation with the maximum being anchored between 70 and 100 deg E, unlike the heating amplitude . Is this because of the continuous perturbation in this region? Yes you are correct. This will be mentioned in the text
  
  L. 188: “In the Indian Ocean the two fields are comparable.” I disagree, there seems to be more red in Fig. 1d than in Fig. A1 over the Indian Ocean. Our point was only that the SPPT induced noise in the Indian ocean heating that has a the same order of magnitude as uncertainty that can be estimated from reanalyses, not that the two fields are nearly identical. This will be clarified.
  
  L. 211: Where does the 0.5 threshold come from? It seems arbitrary. In response to another reviewer, we will show the predictability times as a function of threshold.
  
  L. 298: “small scales” is relative, wavenumber 21 is “large scale" from the view of a synoptic/mesoscale meteorologist. Yes that was a bad choice of wording; we will correct.
  
  Citation: https://doi.org/10.5194/egusphere-2023-493-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-493', Anonymous Referee #1, 01 May 2023

Overview:
The paper deals with limits of predictability associated with uncertainties in simulated diabatic heating over the Indian ocean during the MJO. This is investigated by re-running a set of 60-day long ensemble forecasts assuming perfect initial conditions. In other words, the study addresses a component of predictability associated with applied model errors. The error was simulated by stochastic perturbations of the tendencies due to physics geographically limited to the Indian Ocean region 50E-120E and 20N-20S. Their effects on predictability are studied in the ensemble spread of the vertically integrated diabatic heating, of Rossby wave source, of the heat flux and of the vorticity field at 200 hPa. The authors report predictability limits, defined as 0.5 of the saturation value of the ensemble variance, to be between 2 and 3 weeks.

Summary:
The authors address an important problem but the paper in its current shape does not provide significant new insights on the teleconnections associated with the MJO or associated predictability limits. One way to revise the paper would be to compare the results with the operational seasonal forecasts which sample uncertainties in both initial conditions and model errors.

Detailed comments:

1. Assumptions
The authors argue (Lines 55-56) that they apply the "perfect model" assumption in their study of (Lines 46-47) "uncertainties in MJO heating, as witnessed by the variability in the details of heating among different episodes of a given phase." The statement should be re-written in line with what has been done (perfect initial-conditions and simulated model error). Please discuss what is meant by "variability in the details of MJO heating" and provide references.

2. Methodology

a) Lines 59-61: "the stochastic parametrization scheme (SPPT) described in Leutbecher et al. (2017) has been altered so that perturbations which affect (directly or indirectly) diabatic heating tendencies are confined to the tropical Indian Ocean region". Some details would be useful here, such as the amplitude of perturbations compared to the signal. Different wording on what parts of the model physics have been perturbed is provided at different places in the paper, and it should be clarified.

b) The computation of the divergent horizontal wind in Eq. (1) should be explained.

c) What is the sensitivity of the results to the choice of the latitude belt used to compute S?

d) Why is the integrated diabatic heating a good measure of the MJO predictability as compared for example with precipitation?

e) Why is vorticity a good measure of the forecast error growth in the tropics (Figures 8-9)?

f) How is the estimated predictability limit sensitive to different choices of predictability time (Line 211) taken to be 50% of the saturation error?

g) How is the wavenumber analysis performed, is it spherical harmonics space?

h) The ENSO events are introduced in 2.2 and Figures 1-2, but little mentioned after 3.1.

3. Relation to previous work
Many studies addressed the response of tropical and extratropical circulation to MJO-like heating perturbations. I disagree with the authors' statement that (Lines 47-49) "the wealth of MJO teleconnection research discussed above has relied almost exclusively on the Wheeler-Hendon multivariate empirical orthogonal function framework (Wheeler and Hendon, 2004)." See for example https://doi.org/10.1175/JAS-D-18-0203.1 and references herein. Similarly, there is a wealth of research in predictability associated with MJO that is missing in the introduction and discussion of the results.

4. Results
This paper, like several earlier studies of predictability, finds a predictability scale of 2-3 weeks and that longer scale have longer predictability. In the present study, the predictability limit is due to perturbations in model physics. Previous studies such as https://doi.org/10.1175/JAS-D-19-0116.1 find similar intrinsic predictability to be due to small perturbation in initial conditions (perfect model assumption). I wish the authors discussion their predictability results in comparison to other studies of predictability in the tropics and globally.
How does the growth of spread in selected variables compare with the scale-dependent circulation response to heating perturbations in https://doi.org/10.1175/JAS-D-18-0203.1 (their figures 7-8)?
Overall it is unclear why the ensemble spread of diabatic heating is a good measure of predictability limits, rather than prognostic variables of circulation and/or precipitation. For example, how is the amplitude of the ensemble spread in diabatic heating related to the predictability of precipitation? Could the results be coupled with the precipitation validation in the ECMWF model forecasts (e.g. https://doi.org/10.1029/2020GL091022)?

Citation: https://doi.org/10.5194/egusphere-2023-493-RC1
- AC1:
  'Reply on RC1', David Straus, 05 May 2023
  RC1 comments repeated here , authors' replies in bold.
  The paper deals with limits of predictability associated with uncertainties in simulated diabatic heating over the Indian ocean during the MJO. This is investigated by re-running a set of 60-day long ensemble forecasts assuming perfect initial conditions. In other words, the study addresses a component of predictability associated with applied model errors. The error was simulated by stochastic perturbations of the tendencies due to physics geographically limited to the Indian Ocean region 50E-120E and 20N-20S. Their effects on predictability are studied in the ensemble spread of the vertically integrated diabatic heating, of Rossby wave source, of the heat flux and of the vorticity field at 200 hPa. The authors report predictability limits, defined as 0.5 of the saturation value of the ensemble variance, to be between 2 and 3 weeks.
  Response: Our interpretation is not that our study addresses the component of predictability due to model errors, but that it addresses that component due to intrinsic variability in the model (“internal error”). The stochastic parameterization scheme which is used (SPPT) is considered an integral part of the IFS, and other research (i.e. Selz, 2019) supports the notion that the use of such schemes gives more realistic estimates of intrinsic predictability. The novelty of our experiments is that we suppress SPPT outside the Indo-Pacific region, and that is the only change we make. The ensemble spread is thus due entirely to processes internal in the model.
  Summary:
  The authors address an important problem but the paper in its current shape does not provide significant new insights on the teleconnections associated with the MJO or associated predictability limits.
  Response: We may not have emphasized the role of the Rossby wave source in the paper enough: the rate of spread of the Rossby wave source gives an indication of how the spread of the tropical heating is translated into the uncertainty in the mid-latitude response. We agree that more diagnostics concerning the rate of growth of the Rossby wave source (and other measures of the mid-latitude error) will be useful and we intend to provide them.
  One way to revise the paper would be to compare the results with the operational seasonal forecasts which sample uncertainties in both initial conditions and model errors.
  Detailed comments:
  Assumptions
  
  The authors argue (Lines 55-56) that they apply the "perfect model" assumption in their study of (Lines 46-47) "uncertainties in MJO heating, as witnessed by the variability in the details of heating among different episodes of a given phase." The statement should be re-written in line with what has been done (perfect initial-conditions and simulated model error). Please discuss what is meant by "variability in the details of MJO heating" and provide references.
  We plan to discuss, both in the revised Introduction and the Results sections, previous work which the reviewer is correct to point out. These include studies of predictability focusing on the roles of: (a) the size of the initial error (Zhang et al., 2019), (b) the role of domain (polar, mid-latitude, tropical) in which the errors are introduced (Judt, 2020), and (c) specific to the MJO, the spatial and temporal variability of Indo-Pacific heating, as seen in low-resolution models (e.g. Lin and Brunet, 2018) and intermediate resolution models (Kosovelj et al. 2019).
  By “variability in the details of the MJO heating” we mean the differences in the evolution of the magnitude and spatial of the heating between ensemble members that are initialized identically. This spread is an indication of the variation of heating in the real atmosphere among episodes that are characterized by one phase of the MJO.
  Methodology
  
  a) Lines 59-61: "the stochastic parametrization scheme (SPPT) described in Leutbecher et al. (2017) has been altered so that perturbations which affect (directly or indirectly) diabatic heating tendencies are confined to the tropical Indian Ocean region". Some details would be useful here, such as the amplitude of perturbations compared to the signal. Different wording on what parts of the model physics have been perturbed is provided at different places in the paper, and it should be clarified.
  
  b) The computation of the divergent horizontal wind in Eq. (1) should be explained.
  
  The horizontal winds (u,v) on the Gaussian grid were used to compute vorticity and divergent in spectral space (i.e. the coefficient of the spherical harmonics) using standard methods. The vorticity and divergence were truncated to T42. Setting the vorticity spectral components to zero, we transformed back to (u,v). This will be amplified in an appendix.
  c) What is the sensitivity of the results to the choice of the latitude belt used to compute S?
  
  This will be included in the revised version of the paper.
  d) Why is the integrated diabatic heating a good measure of the MJO predictability as compared for example with precipitation?
  
  The atmosphere is forced by diabatic heating, which includes latent, radiative and turbulent heating, each of which has its own vertical structure. The precipitation is the vertical integral of only one component (latent heating). While we have not discussed the effects of the vertical structure of heating, this is an area we plan to explore in the future.
  e) Why is vorticity a good measure of the forecast error growth in the tropics (Figures 8-9)?
  
  It is not the only measure; we will examine other measures.
  f) How is the estimated predictability limit sensitive to different choices of predictability time (Line 211) taken to be 50% of the saturation error?
  
  We will present results for the predictability limit as a function of spatial scale and threshold.
  g) How is the wavenumber analysis performed, is it spherical harmonics space?
  
  The zonal wavenumber analysis is performed on latitude circles (i.e. as a function of longitude only) after the fields have been transformed back to the Gaussian grid using a T42 truncation in spherical harmonics.
  h) The ENSO events are introduced in 2.2 and Figures 1-2, but little mentioned after 3.1.
  
  Relation to previous work
  
  Many studies addressed the response of tropical and extratropical circulation to MJO-like heating perturbations. I disagree with the authors' statement that (Lines 47-49) "the wealth of MJO teleconnection research discussed above has relied almost exclusively on the Wheeler-Hendon multivariate empirical orthogonal function framework (Wheeler and Hendon, 2004)." See for example https://doi.org/10.1175/JAS-D-18-0203.1 and references herein. Similarly, there is a wealth of research in predictability associated with MJO that is missing in the introduction and discussion of the results.
  We plan to discuss, both in the revised Introduction and the Results sections, recent previous work which the reviewer is correct to point out. These include studies of predictability focusing on the roles of: (a) the size of the initial error (Zhang et al., 2019), (b) the role of domain (polar, mid-latitude, tropical) in which the errors are introduced (Judt, 2020), and (c) specific to the MJO, the roles of spatial and temporal variability of Indo-Pacific heating on MJO predictability, as seen in low-resolution models (e.g. Lin and Brunet, 2018) and intermediate resolution models (Kosovelj et al. 2019).
  
  Results
  
  This paper, like several earlier studies of predictability, finds a predictability scale of 2-3 weeks and that longer scale have longer predictability. In the present study, the predictability limit is due to perturbations in model physics. Previous studies such as https://doi.org/10.1175/JAS-D-19-0116.1 find similar intrinsic predictability to be due to small perturbation in initial conditions (perfect model assumption). I wish the authors discussion their predictability results in comparison to other studies of predictability in the tropics and globally.
  How does the growth of spread in selected variables compare with the scale-dependent circulation response to heating perturbations in https://doi.org/10.1175/JAS-D-18-0203.1 (their figures 7-8)?
  A number of previous papers show the growth of errors as a function of spatial scale (characterized by zonal wavenumber) for different variables and pressure levels. In the revised paper we will compare our results to those in a similar format.
  Overall it is unclear why the ensemble spread of diabatic heating is a good measure of predictability limits, rather than prognostic variables of circulation and/or precipitation. For example, how is the amplitude of the ensemble spread in diabatic heating related to the predictability of precipitation? Could the results be coupled with the precipitation validation in the ECMWF model forecasts (e.g. https://doi.org/10.1029/2020GL091022)?
  In the tropics, the spread of diabatic heating is presented to document just how variable heating is, and to show the forcing for the extra-tropical spread in circulation. Whether the tropical precipitation in this model is realistic is a different question: it is the total heating that is coupled to the atmospheric circulation. Heating in mid-latitudes is a good indicator of activity in the storm tracks, as much of the heating arises from the warm conveyor belts in extra-tropical cyclones. We will clarify this in the revised paper.
  
  Citation: https://doi.org/10.5194/egusphere-2023-493-AC1
RC2:
'Comment on egusphere-2023-493', Anonymous Referee #2, 04 May 2023

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-493/egusphere-2023-493-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2023-493-RC2
- AC2:
  'Reply on RC2', David Straus, 10 May 2023
  Comments from Reviewer 2 are in regular font – responses in bold small font
  R2 Major Comments:
  While it is true that only the model physics over the Indian Ocean are perturbed, the effect of chaos seeding (Ancell et al. 2018) quickly spreads the error over the whole globe in non-physical ways. This likely means that the results are indistinguishable from results that would have been obtained if SPPT perturbations were added to the entire tropical belt or to another location that is convectively active, such as the Amazon. I suggest testing this out.
  
  This is a valid point – any perturbation will rapidly spread due to variety of reasons, some numerical and some intrinsic to the system. We want to point out that the stochastic parameterization scheme which is used (SPPT) is considered an integral part of the IFS, and other research (i.e. Selz, 2019) supports the notion that the use of such schemes gives more realistic estimates of intrinsic predictability. Thus the effects of restricting the SPPT to the tropical Indo-Pacific region may be confined to the early growth of errors. This may be worth testing in a future project. [The simulations done for this paper were quite computer-intensive.] We thank the reviewer for this interesting reference and will include a discussion of this in the revised paper.
  It would be interesting to see how different the result would be when “butterfly seeding”were used, i.e., tiny initial perturbations of the initial conditions everywhere on the globe, as in Judt (2018) or Zhang et al (2019). I recommend running an additional ensemble with this kind of perturbation and comparing the results with the ones obtained so far (this additional experiment would also be more in line with intrinsic predictability, whichusually addresses predictability limits arising due to miniscule initial condition uncertainty).
  
  While we agree that this would be an interesting comparison, there is an arbitrariness in perturbing initial conditions. In fact the whole purpose of the cited paper of Zhang et al. is to compare the error growth due to current, operational uncertainty in the initial conditions (taken from multiple reanalyses) to a hypothetical “perfect” scenario that is implemented by arbitrarily reducing the initial condition uncertainties by a factor of 100. Such a study could be implemented in the ECMWF modeling system since there is in place a procedure to perturb the initial conditions (although we did not use this in the simulations). As above, this computer-intensive proposal is a goal for a future project. Again the Discussion section of the paper will be augmented by a discussion of this alternate approach to estimating “intrinsic” predictability.
  Is it necessary to discuss the Nov and Jan initialization experiments separately? In my opinion no, as the differences between Nov and Jan events are not large enough to warrant the extra work for the reader to keep track of two sets of results. I therefore recommend combining all experiments into one “grand experiment”. This shouldn’t affect the conclusions.
  
  This is a valid point for most of the diagnostics. It is only for the figures relating to the role of the stratosphere that we have reasons to discriminate the Jan. and Nov. initial conditions. This is because the polar vortex may not be fully formed in November, so that the “stratospheric pathway” towards uncertainty growth will have a different time scale for the Nov and Jan runs. But we will try to combine the results from all the runs for the other diagnostics.
  It looks like Fig. 3 is not referenced in the text. Furthermore, I am not sure why the “Rossby wave source” is analyzed at all. I suggest removing this analysis or better motivating it.
  
  This is simply a mistakeo on our part – there was discussion of the Rossby Wave Source in our first draft which inadvertently got omitted. The Rossby Wave Source is one dynamical indicator of how the tropical heating affects the extra-tropical circulation, and we will motivate it more fully in the revised version.
  Section 3.4 seems to be lacking a conclusion, or at least I’m left with this impression.
  
  Minor Comments:
  L.45: How does the presence of baroclinic instability limit the predictability of MJ teleconnections? Through error growth associated with baroclinic instability? Yes- this will be mentioned.
  
  Figs. 1-3 and 6-9 imply that the runs are 30 days long, while the other figures show the entire 60 day time period. Why are only the first 30 days shown in the Hovmöller plots? Maybe nothing interesting happens after 30 days, but then it should be indicated somewhere so the reader doesn’t end up confused whether or not the experiments are 30 or 60 days long.The experiments are 60 days long, but for some diagnostics it is only the first 30 days that are interesting. This will be clarified in the text.
  
  L.102: Just curious, why are you not using ERA5 to initialize the ensembles? The model configuration is that used by ECMWF for its monthly forecasts, and the system is set up to use ERA-Interim for initial conditions.
  
  L. 155-177: I don’t think the description of the figures is necessarily wrong, but I do see a
  
  lot of noise in the Hovmöllers and not so much of the described
  We will look at this carefully.
  Fig. 1 (and Fig. 2): The evolution of the standard deviation in panels (d) shows very little propagation with the maximum being anchored between 70 and 100 deg E, unlike the heating amplitude . Is this because of the continuous perturbation in this region? Yes you are correct. This will be mentioned in the text
  
  L. 188: “In the Indian Ocean the two fields are comparable.” I disagree, there seems to be more red in Fig. 1d than in Fig. A1 over the Indian Ocean. Our point was only that the SPPT induced noise in the Indian ocean heating that has a the same order of magnitude as uncertainty that can be estimated from reanalyses, not that the two fields are nearly identical. This will be clarified.
  
  L. 211: Where does the 0.5 threshold come from? It seems arbitrary. In response to another reviewer, we will show the predictability times as a function of threshold.
  
  L. 298: “small scales” is relative, wavenumber 21 is “large scale" from the view of a synoptic/mesoscale meteorologist. Yes that was a bad choice of wording; we will correct.
  
  Citation: https://doi.org/10.5194/egusphere-2023-493-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by David Straus on behalf of the Authors (13 Jun 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (14 Jun 2023) by Michael Riemer

RR by Anonymous Referee #2 (03 Jul 2023)

RR by Anonymous Referee #3 (04 Jul 2023)

For final publication, the manuscript should be

accepted as is

accepted subject to technical corrections

accepted subject to minor revisions

reconsidered after major revisions

rejected

Were a revised manuscript to be sent for another round of reviews:

I would be willing to review the revised manuscript.

I would not be willing to review the revised manuscript.

Suggestions for revision or reasons for rejection

Review of "Intrinsic Predictability Limits airising from Indian Ocean MJO Heating: Effects on tropical and extratropical teleconnections" by David M. Straus, Daniela I. V. Domeisen, Sarah-Jane Lock, Franco Molteni, and Priyanka Yadav

Synopsis:
The study by Straus et al. aims at identifying predictability limits arising from tropical diabatic heating over the Indian Ocean during MJO phases 2/3. For this purpose, a set of ECMWF-IFS hindcasts is performed with the stochastic parametrization scheme (SPPT) being only applied in a limited range of longitudes over the tropics. The authors find that planetary wave components of the tropical heating and divergence is predictable out to 40 days. However, the Rossby wave source which allows the influence of the tropical heating to propagate to the extratropics is only predictable for 20-30 days. Except for numerous minor technical inaccuracies the paper is well written. In my view, the most important deficit is that the discussion lacks the role that systems other than the MJO could play. For example, the MJO modulates the storm track activity (Moore et al. 2010; Lee and Lim 2012) over the western North Pacific which effects the magnitude of the RWS and presumably its intrinsic predictability. After these minor comments have been addressed, I recommend the paper for publication in WCD.

Minor:
l. 28: Do you mean the stratosphere with "upper atmosphere"?

l. 56: "high resolution" is a relative term. Please try to be more specific.

l. 69: It would be helpful to the reader if the motivation for such initial condition perturbation experiments was provided. Wouldn't such experiments also help to understand the effect of observational uncertainties in those regions?

l. 101: You may want to add that the configuration is close to what was used at that time at ECMWF.

l. 112: Wang et al. (2023) report a pronounced seasonality of MJO teleconnections, e.g., with a stronger positive geopotential height anomaly over the central North Pacific in January to March compared to October to December. Thus, what is the motivation for choosing one initialization date in November and the other in January?

Table 2: Would it be possible for completeness to provide all Nino 3.4 indices in the table?

l. 174-178: Have you considered to provide the definitions of internal error variance, ensemble error variance, and external error variance as equations? This may make it easier to the reader to understand the three parameters.

l. 192: After having read the full manuscript I somehow wonder about the influence of ENSO. From my point of view, this discussion distracts from the main results of the study and I wonder if this aspect should be part of the paper also due to the limited sample size?

l. 201: It is interesting to note that the RWS maximizes roughly 10 days after forecast initialization and that the magnitude of the RWS is larger for the more northern latitudinal band. Is it possible that the high magnitude in RWS between 20 to 35°N is related to synoptic activity which typically increases after MJO phases 2 and 3 over the western North Pacific? For example, Lee and Lim (2012) show negative Rossby wave source over the western North Pacific after MJO Phase 3 (their Fig. 3) which may be related to the outflow of rapidly ascending air streams in midlatitudes that typically reach their peak activity in the same region after MJO phases 2/3 (Quinting et al. 2023; their Fig. 1).

l. 202: The comparison of Figs. 1 and 2 is difficult due to the different longitude ranges. Accordingly, I would like to kindly ask the authors to show the same longitude range in Fig. 1 as in Fig. 2.

l. 239: This is related to my earlier comment: Does this indicate that the RWS is related to divergent flow of midlatitude disturbances rather than to divergent flow directly associated with the convection of the MJO itself? Further, the RWS includes divergence as well as the gradient of vorticity? Did you investigate separately for divergence and vorticity when the forecast error variance reaches a fraction of 0.5, 0.7, and 0.9?

l. 275: Though it is probably difficult to quantify, could the authors include some discussion on the seasonality of the MJO teleconnections. E.g., Wang et al. (2023) report a stronger positive geopotential height anomaly over the central North Pacific in January than in November which likely favours wave flux into the stratosphere.

l. 297: Though I agree with this conclusion, it would be good to emphasize that by day 10 the perturbations in the midlatitudes cover already all longitudes.

l. 310: This statement is related to my previous remark: Have you investigated for the gradient of vorticity when the forecast error variance reaches a fraction of 0.5, 0.7, and 0.9? Such information or at least some discussion would be highly interesting.

l. 313: This sentence can be removed as it is the same as in line 310.

l. 323: I assume that "J" is referring to Judt (2020)? Please clarify.

l. 352: Do you mean with "more globally" simply "globally"? If yes, one could use the operational extended-range predictions of ECMWf as comparison.

Technical:
l. 72: Please remove "the" before "this".

l. 75: SPPT instead of SPTT

l. 112 and elsewhere: Please use the date format as provided in the WCD guidelines: https://www.weather-climate-dynamics.net/submission.html

l. 124: To be consistent throughout the manuscript, please use the "°" symbol when providing coordinate information.

l. 161: "a" instead of "at"

l. 166 and elsewhere: Please make sure to provide units following the guidelines of WCD.

l. 286 and elsewhere: when indicating ranges between two numbers please use en-dash.

l. 338: Insert blank between "Figure" and "7".

Fig. 4: Is it on purpose that the averaging was performed between 15°-32°N?

References:
Lee, Y.-Y., and Lim, G.-H. (2012), Dependency of the North Pacific winter storm tracks on the zonal distribution of MJO convection, J. Geophys. Res., 117, D14101, doi:10.1029/2011JD016417.

Moore, R. W., O. Martius, and T. Spengler, 2010: The Modulation of the Subtropical and Extratropical Atmosphere in the Pacific Basin in Response to the Madden–Julian Oscillation. Mon. Wea. Rev., 138, 2761–2779, https://doi.org/10.1175/2010MWR3194.1.

Quinting, J., Grams, C. M., Chang, E. K.-M., Pfahl, S., and Wernli, H.: Warm conveyor belt activity over the Pacific: Modulation by the Madden-Julian Oscillation and impact on tropical-extratropical teleconnections, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-783, 2023.

Wang, J., M. J. DeFlorio, B. Guan, and C. M. Castellano, 2023: Seasonality of MJO Impacts on Precipitation Extremes over the Western United States. J. Hydrometeor., 24, 151–166, https://doi.org/10.1175/JHM-D-22-0089.1.

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ED: Publish subject to revisions (further review by editor and referees) (17 Jul 2023) by Michael Riemer

AR by David Straus on behalf of the Authors (25 Aug 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (10 Sep 2023) by Michael Riemer

RR by Anonymous Referee #2 (11 Sep 2023)

RR by Anonymous Referee #3 (28 Sep 2023)

ED: Publish subject to technical corrections (11 Oct 2023) by Michael Riemer

AR by David Straus on behalf of the Authors (11 Oct 2023) Author's response Manuscript

Journal article(s) based on this preprint

21 Nov 2023

Intrinsic predictability limits arising from Indian Ocean Madden–Julian oscillation (MJO) heating: effects on tropical and extratropical teleconnections

David Martin Straus, Daniela I. V. Domeisen, Sarah-Jane Lock, Franco Molteni, and Priyanka Yadav

Weather Clim. Dynam., 4, 1001–1018, https://doi.org/10.5194/wcd-4-1001-2023,https://doi.org/10.5194/wcd-4-1001-2023, 2023

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David Martin Straus et al.

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The global response to the Madden Julian Oscillation is potentially predictable. Yet variability in diabatic heating is present even within fixed phases of the MJO. Experiments with a global model probe the limitations imposed by this uncertainty. The large-scale tropical heating is predictable for 24 to 28 days, yet the associated Rossby Wave source that links the heating to the mid-latitude circulation is predictable for 14 to 19 days. This limitation has not been recognized in prior work.


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