Author response to referee comments in manuscript wcd-2020-5: “The sensitivity of atmospheric blocking to changes in upstream latent heating – numerical experiments”

1. The introduction section has been restructured: the motivation, scope and objectives are explained more clearly and we included some open questions. 2. A description of the synoptic evolution of the other three cases (in addition to Thor) is included. 3. The figures and corresponding references in the text have been improved. 4. The description of the case-to-case variability has been improved, including a new figure.


Referee comment
The paper investigates the contribution of latent heating during the onset phase of blocking in four case studies spanning the North Hemisphere. The investigation is extended to the maintenance phase for one case study, which is described more thoroughly. The contribution of latent heating is quantified by switching off heating related to cloud processes in a region located upstream of the blocking in sensitivity experiments with the global IFS model. The impact is diagnosed using the potential vorticity anomaly and divergent wind at upper levels mainly. The results show a clear contribution of latent heating, including periods of bursts, to the intensity of blockings and their extent in space and time, with large case-to-case variability that appears to depend on the flow configuration. The paper addresses an important topic in atmospheric dynamics, is based on well-designed numerical experiments, and is well written overall. However, as detailed in the general comments below, it contains majors flaws related to a lack of assessment of the numerical experiments, a lack of balance between one detailed case study and three quicker ones, and a general lack of consistency between text and figures. Although the paper is definitely interesting and valuable, it gives a feeling of subjectivity in the choice of case studies and interpretation. Considering that a systematic analysis of all presented case studies would require much additional work, and as the discussion at the end of Section 4 currently suggests that the impact of latent heating depends on many parameters that cannot be properly covered here, I suggest to remove the additional cases altogether and focus on the Thor case more thoroughly. For instance, with less extra work, the additional sensitivity experiments with alpha=0.5 and 1.5 could be included in Figs. 9-10 to discuss non-linearity, or the respective contribution of microphysics and convection to latent heating could be quantified to contribute to the current discussion in the NAWDEX community.
General and specific comments are listed below to help improving the paper.
As the other reviewer also asked about the forecast quality of the control simulations, we still comment on this aspect here. All control simulations are initialized during the intensification phase of the upstream cyclone, which is typically 2 days prior to blocking onset. The IFS initialization is based on two requirements: (1) LH has to be removed early enough to ensure that its contribution to the ridge amplification is minimal and (2) the control simulation needs to capture the development of a major block, thus the initiation time has to be close to the onset. As an example, for "Thor onset" this is the 30 Sep 2016. This is in contrast to Maddison et al. (2019Maddison et al. ( , 2020, who initiated the ensemble forecast on 27 and 28 Sep 2016, which leads to considerable divergence of the ensemble members at the time of blocking onset. Figure AR1 compares upper-level PV between the control simulation (CNTRL) and the operational analysis fields (ANA) for Thor onset. On 3 October 2016, 3 days into the forecast evolution (Fig. AR1a) the ridge amplification (onset of Thor) is very well represented. By 6 October, 6 days into the forecast, the anticyclonic wave breaking and the intensity and spatial extent of Thor is generally well represented in CNTRL (AR1b). However, there is an eastward shift of the block in CNTRL compared to ANA. Nevertheless, the forecast evolution of the block in CNTRL is similar enough to reality over the time of interest and captures an intense dipole block over Europe, and therefore allows studying the impact of LH on the flow amplification in the IFS sensitivity experiments.

l. 186 what is the APV "index" exactly?
Reply The APV index is the PV anomaly-based blocking index by Schwierz et al., 2004. We improved the explanation in Section 2.3.1.

l. 190 "confirm": is it expected?
Reply We added a reference to the climatological study by Steinfeld and Pfahl (2019), in which we analysed more than 4000 blocking events and showed that a block typically exhibits 2-3 bursts of LH, which are separated by periods of reduced LH contribution.
17. l. 191 why are quasi-adiabatic processes associated with cooling? Reply This is not explicitly shown; however, the quasi-adiabatic trajectories (θ < 2K) are upper-level air masses that travel close to the tropopause and experience week cooling due to long-wave radiation along the flow. Figure AR3 shows the temporal evolution of pressure (a), θ (b) and the temperature tendency from radiation (c) along trajectories from all control simulations that have been separated into heated trajectories (yellow, θ > 2K) and quasi-adiabatic trajectories (blue, θ < 2K). The heated trajectories experience a median heating of ~10K and ascend by about 350hPa in 3 days, while the quasi-adiabatic trajectories are cooled by ~-3K in 3 days. This cooling can be explained by integrating the temperature tendency from radiation along the quasi-adiabatic trajectories, which results in ~-3K in 3 days. a) Pressure b) Potential temperature c) Temperature tendencies from radiation Figure AR3: Temporal evolution of a) pressure, b) θ and c) temperature tendencies from radiation along the heated (yellow, θ > 2K) and quasi-adiabatic (blue, θ < 2K) backwards trajectories initialized in the blocking region (black dot at time 0). Lines show the median with 25-75% range (shaded) for trajectories from all control simulations (Thor onset, Thor maintenance, Canada, Cold spell and Russia). Figure AR5: Probability density distribution of maximum potential temperature change along backward trajectories during three days before their arrival in the blocking region for control (gray line) and NOLH (yellow line) simulations. Percentages of blocking air parcels in the heated flow regimes defined by θ = 2K are given.

Figs. 7 why focus on day 3 here and not on day 2 as above?
Reply There is a temporal lag between the strongest difference in divergent outflow (day 2) and distinct differences in the upper-level PV (day 3). We show the same time step for all Figures in the revised manuscript. We also add a sentence stating the motivation for this selection.

Referee comment
Building upon recent findings related to the importance of tropospheric latent heating on the development of atmospheric blocking, this contribution investigates from a numerical modelling point of view, the extent to which latent heating influences the development of atmospheric blocking and the cause-and-effect relationship involved in this influence. Understanding these processes in the atmosphere is critical due to the important effects that blocking has at the surface and on human activities. Thus, these are without doubt relevant scientific questions within the scope of WCD. For this investigation the researchers performed sensitivity analysis by varying latent heating in ad-hoc regions in numerical simulation of five cases, using the state-of-the-art ECMWF IFS and an advanced methodology based on atmospheric blocking tracking and trajectory analysis. Through their investigation they demonstrate in a convincing manner that atmospheric blocking features such as intensity, spatial extent and lifetime depend strongly on latent heating. However, they also showed that there is a large case-to-case variability. The paper is very well structured and written, and, in my opinion, the description of the methodology is sufficiently complete to allow their reproduction by fellow scientists. Therefore I recommend the article for publication in Weather and Climate Dynamics. I include a list of minor comments that could be considered by the authors to hopefully enhance the paper.

Specific comments
50. L66: How smooth are the physical temperature tendencies in the native resolution? I fit is not a smooth field, is it properly represented after the interpolation to the 1degree horizontal resolution? Reply We mention now more carefully that the temporal and spatial resolution of the fields are an uncertainty in the trajectory analysis. We attached a Figure AR6, which shows temperature tendencies from cloud microphysics and convection schemes during the intensification phase of the Stalactite cyclone on 2 October 2019. Latent heating indicates the position of the cold front and the bent-back front in the vicinity of the cyclone's low centre. The panels show that there is some variability on small scales in the heating and cooling tendencies. a) Temperature tendencies from cloud microphysics b) Temperature tendencies from convection Figure AR6: Vertically averaged (900 -500hPa) temperature tendencies from (a) cloud microphysics and (b) convection schemes (shading, K in 3h), upper-level 2 pvu contour (black, pvu) and SLP (gray, hPa) at 00 UTC 2 Oct 2016 for the control simulation of Thor onset.
51. L80-81: Please cite the previous studies that the methodology in this study is being contrasted against? In which way is the new methodology different to the one in previous studies? Did they dampened latent heating everywhere in their domain? Reply We explain the novelty of our method more explicitly (modification in predefined box) and refer to previous studies using a similar methodology (but applied in the entire model domain) in the revised manuscript.
52. L105-106: How was the blocking event for which latent heating was reduced and increased chosen? Is the case representative in any way especially after considering that large case-to-case variability reported in this study? Reply See reply to general comment 2 of referee 1. We tried to cover the typical range of different blocking flow configuration (omega versus dipole) with different LH contribution that represent the majority of observed blocking cases in the global ERA-I climatology between 1970 -2016 (Steinfeld and Pfahl, 2019), where 50% of all blocking events had a LH contribution between 35 -55%. However, we agree that there are also blocking cases in the climatological analysis that show no LH contribution (0%) or a contribution above 70%. It is just not possible to cover this entire range with a limited number of case studies.
53. L279-280: Is there any indication of the extent of the influence of initial conditions on the differences after 6 days? How would the differences found here compare to differences between members in an ensemble simulation? This is discussed to a certain extent in Maddison et al. (2020Maddison et al. ( , doi:10.1002, which is in any case a relevant reference that you might want to cite. Reply We include a reference to this important study in the revised manuscript.
Evaluating the sensitivity to LH in ensemble simulations as performed by Maddison et al. (2019; would definitely be interesting, but is beyond the scope of the present study, which focuses on the causal effects of LH and not on predictability aspects. In our simulations, the initiation time was chosen such that the block is well captured in CNTRL, which is in contrast to Maddison et al. (2019;. See also reply to general comment 1 of referee 1. Since the removal of LH in our experiments are very pronounced changes to the simulations (in comparison also to differences in additional conditions and physical parameters between different members in an ensemble forecast), we assume that also the differences between our experiments are larger than typical differences between ensemble members. Note that the differences presented in this study are shown for vertically averaged PV and that differences on a single level (for example PV@320K) are larger in magnitude.

L385-389:
The Russia block is very interesting, and the discussion could be extended. If there is such a limited influence of latent heating in the evolution of the block, what is then the source of the big differences in the evolution of the blocks in the two simulations?
Reply We realized that we did not formulate this sentence carefully enough. The differences are due to changes in LH (since this is the only difference between CNTRL and NOLH). However, in both simulations the block propagates downstream, away from the heating source over the North Atlantic, into a continental region with weak LH contribution. Thus, the dynamics underlying the propagation of the Russia anticyclone after its onset is mostly due to "dry" dynamics and may therefore be understood with the help of the traditional concept of downstream development (Nakamura et al., 1997). We extended the corresponding discussion, also about the other blocking cases (see reply to general comment 2 for referee 1).

55
. L411: I've got a bit confused with this description, in which the authors talk about a median heating of 3 K (dashed curves in Fig. 10a,b). What I can see is cooling in those curves? I'm sure I'm missing something. Can you clarify? Reply We are sorry for the confusion. The median heating of 3K is calculated for the entire blocking life cycle and only for those trajectories, which are classified as heating trajectories (θ > 2K). The dashed curves in Fig. 10a,b show the temporal evolution of the median for all trajectories (quasi-adiabatic and heating trajectories). We improve the explanation of the changes in Theta along the trajectories in the revised manuscript (see also our reply to comment 31 of referee 1).
56. L435-436: Should the statement that the Thor onset and Cold spell block amplify without the contribution of LH be qualified? The LH was eliminated only between 900 -500hPa, and as the authors acknowledge in Section 2 there are diabatic processes active above that layer.
Reply We agree that this statement is misleading. LH contribution is reduced, but it is not zero (see dashed curves in Fig 10a). We now discuss the limitation of the box and that diabatic processes still occur outside of the box in the NOLH simulations.

L123
: Spatial extent is among the set of blocking characteristics calculated for each blocking event. Even though the method to identify blocking considers an atmosphere's layer rather than a single level, the extent referred to here is horizontal extent rather than a three-dimensional size. Is this so? It would be useful to add details on the layer considered for the blocking identification. Is it the 'upper-level' layer, i.e. 500 -150hPa? Is it possible to compute details on the vertical extent of the blocking region? Reply Yes, the blocking index uses vertically averaged (500 -150hPa) PV as 2d field, which tracks negative PV anomalies that have a quasi-barotropic structure in the vertical. The spatial extent is then calculated as the horizontal extent of this 2d field.
62. L230 and 241: There are references to Fig. 3e,g, but I cannot see those panels.
Reply Thanks for spotting the mistake.
63. L220-221: Where are the trajectories emanating from in the vertical direction? Are they initially located between 500 hPa and 150 hPa? Or at a particular level? Reply Yes, trajectories are started between 500 hPa and 150 hPa every 50 hPa, with the additional criterion that PV must be smaller than 1 pvu (to exclude points located in the stratosphere). We make this clearer in the revised manuscript.

64.
L269: Are the divergent wind speeds quoted averages over a region? Please, specify.
Reply The quoted wind speeds are the average over 9 grid cells centred around the strongest divergent wind found at the western flank of the block. We make sure this is clear in the revised text. Note that we changed the discussion on divergent wind and PV advection by the divergent wind (see reply to comment 41).

Introduction
The formation and maintenance of prolonged anticyclonic circulation anomalies, denoted as atmospheric blocking, represents an important and challenging aspect of mid-latitude weather variability. Atmospheric blocking leads to persistent changes in the large-scale circulation and blocks the westerly flow (Rex, 1950;Woollings et al., 2018), often causing anomalous, sometimes 20 extreme weather (Green, 1977) in a situation of increased forecast uncertainty in weather models (Pelly and Hoskins, 2003;Rodwell et al., 2013).
The sensitivity experiments are presented as follows. Section 2 describes the methodology, while section 3 exemplarily 65 introduces one blocking event :: as :: an :::::::: example with a synoptic overview. The results of the sensitivity experiments are presented in section 4 and our conclusions are summarized and discussed in section 5.
3-hourly output fields, including physical temperature tendencies, are interpolated to a regular grid at 1 • horizontal resolution.

80
Following a series of seminal numerical sensitivity studies that investigated the role of LH in cyclone dynamics (e.g., Kuo et al., 1990; Stoeli , the total ::: The :::::: causal effect of cloud-diabatic heating on atmospheric blocking is investigated with sensitivity experiments by comparing the full-physics control simulation including LH (hereafter referred to as CNTRL) to the corresponding simulation without LH (NOLH). LH is artificially turned off by multiplying the instantaneous temperature tendencies due to parameterized cloud and convection processes with a factor α = 0.0, but still allowing for moisture changes due to cloud and precipitation 85 formation. Other non-conservative processes, such as radiative heating and turbulent mixing, which can also modify PV Attinger et al., 2019), are not altered.
The box has a vertical extent between 900 -500 hPa and a horizontal extent which is adjusted for each blocking case (see Table   1). To define the heating region objectively, location and time of strongest latent heat release are determined along backward 100 trajectories initiated in the upper-tropospheric blocking in the CNTRL simulation (cf. Steinfeld and Pfahl, 2019). It should be kept in mind that other microphysical processes, such as ice-phase microphysics close to the outflow level, can also contribute to the heating and PV modification along the WCB (Joos and Wernli, 2012). As these processes also occur above 500 hPa, our approach does not fully remove all cloud-related LH, and there is still moderate heating/cooling outside of the box. Near the edges of the box (in a zone of 5 • horizontally and 50 hPa in the vertical), the temperature tendency multiplying factor alpha is 105 interpolated linearly to obtain a smooth transition from α = 0.0 to 1.0.

115
LH in extratropical cyclones is coupled to and interacts with other processes, and hence, its artificial removal can affect many aspects of the flow, such as the cyclone intensification and its baroclinic coupling to the upper-level trough (e.g. Hoskins et al., 1985) :::::::::::::::::::::::::::::::::::::::::: (e.g., Hoskins et al., 1985;Ahmadi-Givi et al., 2004). The role of LH in explosively developing cyclones has been studied in great detail, and thus, we focus on the evolution and structure of upper-level blocking here. However, to better understand such non-linear interactions and their effect on the large-scale flow, we additionally conduct sensitivity 120 experiments with reduced LH (α = 0.5) and increased LH (α = 1.5) for one specific blocking event.

2.3 Diagnostic methods
A combination of Eulerian and Lagrangian diagnostics is applied to study :: and :::::::: quantify the processes involved in the development of blocking, and in particular the role of latent heat release in ascending airstreams. The term "upper-level" is used hereafter to describe the vertically averaged flow between 500 and 150 hPa. and temporally smoothed with a 2-day running mean filter. Different thresholds for intensity, persistence and quasi-stationary have been tested in order to track and compare upper-level negative PV anomalies in both CNTRL and NOLH simulations. In 130 all simulations, blocks are identified with a threshold of -1 pvu and a spatial overlap of 80 % between two consecutive time steps. No persistence criterion is applied. The reason for this is that the tracked negative PV anomalies in the NOLH simulations are weak (see below) and would not be classified as persistent blocks (see also Croci-Maspoli et al., 2007). Nevertheless, all blocking events investigated here also fulfill the stricter blocking criteria used, e.g., by Steinfeld and Pfahl (2019) in the CNTRL simulation. The advantage of the PV-anomaly-based (APV) index is that it objectively captures the core of the anomalous 135 anticyclonic circulation and thus directly allows for an investigation of the origin and evolution of individual blocks and the associated air masses. A number of relevant blocking characteristics and their evolution are calculated during the blocking life cycle, such as location :: of ::: the ::::::: blocking :::::: center (center of mass)and track, spatial extent, blocking intensity (area-averaged upper-level negative PV anomaly) and lifetime. The calculated quantities are area-weighted with the cosine of latitude.

Effects of latent heating 140
To capture the full three-dimensional complexity of LH in ascending airstreams and to quantify its effect on blocking dynamics, a combined Eulerian and Lagrangian perspective is adapted. The effects of LH on the upper-tropospheric PV distribution are quantified as follows: -Backward trajectories: To estimate the relative contributions of dry (adiabatic :::::::::::: quasi-adiabatic transport of mass) and moist (cross-isentropic transport of mass) processes to upper-level negative PV anomalies that characterize blocking, we 145 compute kinematic 3-day backward air-parcel trajectories based on the three-dimensional wind using the Lagrangian Analysis tool LAGRANTO (Wernli and Davies, 1997;Sprenger and Wernli, 2015). The trajectories are started from an equidistant grid (∆x = 100 km horizontally and ∆p = 50 hPa vertically between 500 and 150 hPa) in a :: the : blocking region every three hours, with the additional criterion that PV must be smaller than 1 pvu to exclude points located in the stratosphere. Since both PV and potential temperature θ are conserved for adiabatic and frictionless motion, changes in 150 these variables between two time steps along a trajectory are attributed to diabatic processes, such as cloud formation, radiation and friction. Following the method of Pfahl et al. (2015) and Steinfeld and Pfahl (2019), the effect of LH is quantified by the percentage of blocking trajectories with a maximum heating (Lagrangian change of θ) of ∆θ > 2 K during the three days prior to reaching the blocking region (in the following denoted as LH contribution).

175
which develop under different environmental conditions (different seasons, geographical locations and LH contribution), as summarized in Table 1. Blocks are selected from the main blocking regions over the North Atlantic and North Pacific, but also from a secondary region over Russia. Some of those blocks are associated with extreme weather events: the 2010 summer heat wave in western Russia, the devastating wildfires in :::::: Alberta, : Canada in May 2016 and the cold spell in Europe in February 2018.
One of these cases, Thor (onset and maintenance) in the year 2016, is used hereafter to introduce our method. Therefore, its evolution is described in detail in the following section.
6 and Downstream Impact Experiment (NAWDEX; Schäfler et al., 2018). The onset of Thor was associated with large forecast uncertainty, in particular the predictability of the upstream cyclone and its diabatic outflow was low (Maddison et al., 2019).
Thor shows typically observed blocking characteristics (e.g., Dole, 1986), such as the rapid onset (fast increase in intensity and spatial extent, Fig. 2) on time scales consistent with synoptic-scale phenomena (2-4 October) and the fluctuation in intensity and size during the blocking lifetime (mature phase: 5-17 October) until its decay (19 October). The episodic nature of the 220 LH contribution and the mean diabatic heating confirm that ::::::: highlight : the importance of LH changes throughout the life cycle, alternating between times when either moist-diabatic (heating) processes or quasi-adiabatic (cooling ::::: mostly :::: due :: to ::::::::: long-wave ::::::: radiation) processes dominate: the LH contribution is generally largest during onset (70 %) and then declines to the lowest value (almost 0 %) when the block decays. However, there are multiple bursts of LH (local maxima of LH) during the life cycle, which are followed by fluctuations in intensity and size. The block exhibits its most rapid amplification during such LH bursts, 225 suggesting that there is a linkage between moist-diabatic processes and the development of the block. Averaged over the entire lifetime (onset and maintenance), Thor has a LH contribution of 41 %, that is almost half of the blocking air masses have been diabatically heated by more than 2 K.
Given the changes in LH contribution and diabatic heating along the blocking trajectories, we now focus on the impact of upper-level divergent windand mid-level : , :::: SLP ::: and :::::::::: lower-level : cloud-diabatic heating from the NOLH ::::::::: simulations : to the corresponding results from the CNTRL simulations. Note that the differences between CNTRL and NOLH are initially weak (after 2 days in the Thor onset and Thor maintenance simulations), but become more pronounced with lead time. Nevertheless, these initial time steps highlight ::: the :::: early :::::::: evolution :::::::: highlights : the critical phase when the two simulations start to deviate.

Thor maintenance
To better understand the role of LH for the persistence of a blocking, we now focus on the Thor maintenance simulation. Both 365 CNTRL and NOLH simulations start with a well established dipole block ::: over ::::::: Europe and a large-scale deformation flow field over Europe ::::::: diffluent :::: flow :::: field ::::::: upstream ::::::: (visible :: in ::: the ::::: Z500 :::::::: contours), where a large region with low upper-level PV values covers most of Scandinavia on day 2 ( ::: R2 :: in Fig. 4a,b). However, first pronounced differences in the divergent outflow strength and the upper-level PV structure occur in the region of upstream ridge R4 to the east of trough T4. In the absence of LH, ridge R4 and consequently the PV streamer T3 are not as strongly extended in the meridional direction as they are in CNTRL, despite 370 being subject to a strong diffluent flow, suggesting that the (dry) eddy straining mechanism (Shutts, 1983) does not fully explain the amplification of the incoming upstream waves. As a consequence, R4 in NOLH does not replace the initial negative PV anomaly R2 over Scandinavia (cf. Fig. 4c,d). Without the :::::: diabatic : contribution of 'fresh' low-PV air, and facilitated by the radiative decay (cooling :: and ::: net ::: PV :::::::: increase along upper-level trajectories) of the remaining air masses recirculating inside the block (Fig. 5d : ,f), Thor weakens in the NOLH simulation and is no longer captured by the APV blocking index on 15 October 375 (day 5). In contrast, the CNTRL block persists for another 4 days, also due to the additional absorption of anticyclonic air masses in R5 on day 6 ( Fig. 3 : 4c,d).

Non-linear effects of latent heating
In order to exemplify the non-linearity of the relationship between LH and blocking, Fig. 6 shows the 2 pvu tropopause at day 2 : 3 : and day 6 of Thor onset with and without LH, and also with reduced LH (α = 0.5) and increased LH (α = 1.5). The 380 evolution of the tropopause shows a crucial sensitivity to changes in LH with a non-monotonic behaviour of blocking to LH.
In the following, we have ::: take a closer look at the individual cases. In Thor onset (Fig. 8a), negative PV differences inside the block and positive differences south of it indicate the anticyclonic wrap-up :::: wrap :: up : of low-over high-PV air and the formation of a dipole block with easterly winds in CNTRL, while in NOLH the negative PV anomaly is detached further north above Svalbard as a tropospheric cut-off.
In Thor maintenance (Fig. 8b), the block is still present in CNTRL while it is already too weak to be detected in NOLH. The poleward elongation of the CNTRL block is reflected in the negative PV difference  with an anticyclonic flow centered over Iceland. In NOLH, the decaying blocking ridge over Europe and the cut-off PV anomaly east of Greenland 455 do not merge . ::: (see ::::::::: discussion :::::: above). : For the case Canada (Fig. 8c), the omega-shaped structure of the block with tilted upstream and downstream troughs is not reproduced without LH, and the NOLH block develops as an open ridge embedded in a Rossby wave with a weak anticyclonic circulation over western Canada.
In the case of Russia (Fig. 8e), the initial PV differences over western Europe have propagated eastward and reach values of 460 -5 pvu :::::: further :::::::::: downstream over western Russia at day 6, with a strong anticyclonic flow only present when LH is included.
In contrast to the other cases, the PV values inside the block's core are similar in CNTRL and NOLH for the Cold spell case (Fig. 8d). Largest negative PV differences are found along the edge of the block, i.e. the block is smaller in spatial extent in NOLH, and further south over the Azores, where the NOLH block detaches from the tropospheric reservoir.

510
The episodic nature of LH contribution and diabatic heating (Fig. 10a,b) during the blocking life cycle in the different CNTRL simulations :::: (solid ::::: lines) : is associated with the passage of synoptic cyclones and the associated cross-isentropic transport of low-PV air in WCBs. LH bursts (local maxima of LH contribution and diabatic heating) typically indicate the time of strongest interaction between the block and the approaching upstream cyclones (see also Steinfeld and Pfahl, 2019).

615
A key finding of the numerical sensitivity experiments is that the intensity, spatial extent and lifetime of all simulated blocking events depends strongly on latent heating. In some cases (in 4 of 5 cases), the presence of LH even determines whether or not blocking (according to the blocking index of Schwierz et al. (2004a)) occurs at all. Consistent with the findings of previous studies (Davis et al., 1993;Stoelinga, 1996;Pauley and Smith, 1988;Pomroy and Thorpe, 2000), the primary effects of latent heating on the tropopause arise from the diabatic reduction of PV and the associated enhancement of the divergent outflow 620 aloft. Latent heating enhances ::::::::: accelerates the vertical motion and divergent outflow on the western flank of the block, locally by a factor : of : 4, and the succeeding interaction with the upper-level PV distribution modifies the amplification and propagation of ::::::::: upper-level :::::: waves ::: and blocking compared to the simulations without latent heating. These processes act to slow down the eastward propagation and amplify the intensity and extent of the negative PV anomaly in all cases.
A comparison between the five cases reveals a large case-to-case variability of the effect of latent heating on blocking, which 625 depends strongly on the phase of the blocking life cycle and the state of the background flow. During the early growth phase, latent heating contributes to the initial ridge amplification and facilitates a faster growth of the incipient ridge. During the mature phase, on the other hand, the large-scale flow can further amplify also without the contribution of LH and thus appears to be less sensitive to changes in LH. This amplification is related to the state of the background flow: In the cases with a more meridional flow and a pre-existing large-scale ridge, a block also develops in the absence of latent heating, though weaker and 630 less extended. The presence of this pre-existing ridge induces large-scale upper-level deformation (diffluent flow) :::::: diffluent :::: flow, which supports the meridional amplification of arriving synoptic-scale waves (eddy straining mechanism Shutts, 1983;Mullen, 1987) and the poleward quasi-adiabatic transport of low-PV air from lower latitudes ahead of baroclinic disturbances (e.g., Colucci, 1985). Nevertheless, as demonstrated in the case study of the maintenance of block Thor, the absence of latent heating can also lead to a more rapid decay of blocking. In this case, the dry-adiabatic forcing due to eddy straining in the diffluent 635 region upstream of the block is not strong enough to sustain the system against dissipation.