Response of sea surface temperature to atmospheric rivers

Domain: earth_science
Published: 2024-06-12
Editorial outcome: major_revision

Abstract
Atmospheric rivers (ARs), responsible for extreme weather conditions, are mid-latitude systems that can cause significant damage to coastal areas. While forecasting ARs beyond two weeks remains a challenge, past research suggests potential benefits may come from properly accounting for the changes in sea surface temperature (SST) through air–sea interactions. In this paper, we investigate the impact of ARs on SST over the North Pacific by analyzing 25 years of ocean reanalysis data using an SST budget equation. We show that in the region of strong ocean modification, ocean dynamics can offset over 100% of the anomalous SST warming that would otherwise arise from atmospheric forcing. Among all ocean processes, ageostrophic advection and vertical mixing (diffusion and entrainment) are the most important factors in modifying the SST tendency response. The SST tendency response to ARs varies spatially. For example, in coastal California, the driver of enhanced SST warming is the reduction in ageostrophic advection due to anomalous southerly winds. Moreover, there is a large region where the SST shows a warming response to ARs due to the overall reduction in the total clouds and subsequent increase in total incoming shortwave radiation.

Introduction
Atmospheric rivers (ARs), characterized by moisture filaments extending thousands of kilometers from the tropics, are responsible for over 90% of meridional water vapor transport from low to mid-latitudes1,2. These events have profound impacts on coastal regions. In California, ARs are responsible for up to 50% of annual rainfall, and 40% to 90% of them are associated with major floods1,3,4, causing more than one billion USD in damage annually5. Past studies have identified predictors of AR activity, such as El Niño Southern Oscillation (ENSO) and Madden–Julian Oscillation6–8. However, the predictability of ARs does not exceed 10–20 days depending on the metric chosen9–11. An important factor contributing to the uncertainty of AR predictions is likely feedbacks associated with their modification of the local sea surface boundary conditions through air–sea interactions12.

The extremes associated with ARs include strong wind, high moisture, intense precipitation, and warm air temperature13. In the upper ocean, ARs perturb sea surface temperature (SST), sea surface height, sea surface current, and mixed layer depth (MLD).

Qualitatively, the physical expectation is that a relatively moist and warm AR heats the surface ocean through increasing downward heat fluxes. Simultaneously, its wind enhances vertical mixing at the base of the mixed layer that cools the surface ocean. ARs’ general impact was first studied by Shinoda et al.14 using five years of composited ARs. They found that ocean entrainment is important in SST cooling, extending downstream from the AR center. In parallel, other evidence shows that air–sea interaction under long-duration AR events can have a signature on synoptic timescales. For example, Sun et al.12 showed that when fixed-SST boundary conditions are replaced with an interactive ocean model, the prediction skill of the integrated water vapor (IWV) improves by 12%, and the prediction skill of integrated vapor transport (IVT) improves by 6% for events associated with stronger cooling periods. However, the studies mentioned above have not quantified the response of SST to ARs in terms of each atmospheric and oceanic process, nor have the studies identified AR spatial dependency, leaving a gap in our understanding of AR impacts on the ocean. This study addresses this gap by using an ocean state estimate with an SST budget equation to diagnose the specific physical processes that govern the SST tendency response to ARs.

Results
In this paper, we focus on Oct–Mar when ARs are the most active in the North Pacific. First, we will show ARs’ general characteristics of water years during 1993–2017 (water year n starts Oct 1 of year n−1). Then, we analyze the SST tendency response to ARs over the North Pacific. Finally, we present the spatial and temporal variability of SST tendency to ARs. We have removed the 15-day-smoothed daily climatology of all variables that will be shown, such that they are all anomalies. Ocean data are obtained from Estimating the Circulation and Climate of the Ocean Version 4 release 4 (ECCOv4)15, and atmospheric data are obtained from ECMWF Reanalysis - Interim (ERA-Interim)16 (see Methods for details).

Climatology of ARs and associated atmospheric forcing

The mean number of AR days during Oct–Mar peaks along latitude 35°N, as shown in Fig. 1a. The interannual variability is concentrated along two pairs of ridges, labeled by dashed and dotted light green lines in Fig. 1a. These two pairs of variability ridges are associated with two leading empirical orthogonal functions (EOFs; shown in Fig. 1b, c. EOF1 and EOF2 roughly represent the shift of AR activity from south to north and west to east, respectively. EOF1 positively correlates with the NINO3.4 SST index (95% confidence interval). This connection arises because ENSO events tend to deepen the Aleutian Low, which controls the location of storm track activity17–20. This result is consistent with Tseng et al.6, who examined this relationship more closely. EOF2 positively correlates with NINO3.4 SST index (80% confidence interval) as well, although the correlation is weaker. These results indicate that ENSO can change ARs’ north-south and east-west frequency. A deeper physical understanding is beyond the scope of this paper and will require future investigations.

To isolate AR impact on SST tendencies, we remove the daily climatology (15-day smoothed) and show only the anomalous component. The composited AR surface forcing is shown in Fig. 1d–f. ARs carry anomalous high IWV and IVT. The anomalous 10-m winds that ARs bring have a latitudinal dependency. Southward of 45°N, ARs accompany anomalous westerly wind, while northward of 45°N, they carry anomalous easterlies. This is consistent with the idea that typical ARs are generated by extending moisture filaments from low latitudes at the southeastern flank of mid-latitude cyclones, and the moisture transport turns northwestward as the counterclockwise airflow advects it14. Northward of 30°N the 10-m wind speed increases, whereas southward of 30°N there is a slight decrease of wind because the anomalous wind opposes the trade wind.

How do ARs modulate SST?

Using the mean mixed layer potential temperature, Θ, as a proxy for SST in the SST budget equation, we can decompose the local SST tendency, Θ_loc = ∂Θ/∂t, into the contributions from shortwave radiation, longwave radiation, sensible heat flux, latent heat flux, dilution effect (rain that enters the surface ocean directly changes the SST), residual velocity (sum of Eulerian and bolus velocity) advection, vertical mixing (diffusion and entrainment), detrainment, and horizontal diffusion. Formally, the tendency is written as

Θ_loc = Θ_sw + Θ_lw + Θ_sen + Θ_lat + Θ_dilu + Θ_adv + Θ_vmix + Θ_det + Θ_hdif (1)

We group terms into the contribution from the surface forcing, Θ_sfc, and the ocean response, Θ_ocn, as indicated by the overbraces. The detailed definition of each term is documented in the Methods Section.

We first want to show that ocean dynamics modulate the anomalous SST tendency. Figure 2a shows the relationship between the anomalous Θ_sfc and anomalous Θ_loc. The slope deviates by 8% from the line Θ_loc = Θ_sfc, meaning Θ_sfc itself cannot fully explain the Θ_loc. Also, anomalous Θ_sfc = 0 implies negative anomalous Θ_loc. Together, these results suggest that other factors, such as wind-induced mixing, might be important, and further investigation is necessary. In Fig. 2b we plot the joint probability distribution between Θ_sfc and Θ_ocn anomalies, effectively removing the slope 1 in 2a. Since the relationship between Θ_sfc and Θ_ocn anomalies is not linear (correlation is only 0.07), we plot the mean and standard error with dotted blue lines and gray shading, respectively, to view Θ_ocn as a nonlinear function of Θ_sfc. Two distinct regimes emerge. The first one is Θ_sfc roughly above 0.2×10−6 K/s, where more positive Θ_sfc induces more negative Θ_ocn, meaning the ocean is opposing the warming forced by the surface fluxes. When Θ_sfc is below roughly 0.2×10−6 K/s, more negative Θ_sfc induces more negative Θ_ocn, implying that the ocean amplifies the cooling forced by surface fluxes.

We can break down Θ_ocn into ocean processes as shown in Fig. 3a by using the decomposition Equation (1). When the surface forcing anomalously cools the SST, Θ_sfc < 0, the mixed layer deepens anomalously as shown in the anomalous ∂(h−η)/∂t ≈ ∂h/∂t in Fig. 3b (h is the mixed layer thickness, and η is the surface height anomaly from the mean ocean depth). Usually, mixed layer deepening induces SST cooling, with exceptions occurring in barrier layers when salinity dominates the stratification such that there is little temperature gradient at the base of the mixed layer. As the mixed layer deepens, the even cooler deeper ocean water results in a larger vertical temperature gradient (Fig. 3c), therefore producing stronger vertical mixing cooling. When the surface forcing anomalously warms the SST, Θ_sfc > 0, the mixed layer anomalously shoals. The shoaling induces detrainment that leads to an increase in the vertically averaged mixed layer potential temperature Θ. Since detrainment does not change SST, the increase is because the SST, slightly warmer than the water below, has a greater impact when computing Θ with shallower MLD. The anomalously reduced MLD also results in a weaker vertical temperature gradient at the base of the mixed layer ∂Θ/∂z (Fig. 3c). However, weaker ∂Θ/∂z does not lead to weaker vertical mixing Θ_vmix (Fig. 3a). This shows that the turbulent wind work is strong such that the turbulent kinetic energy in the oceanic boundary layer remains vigorous. Therefore, the downward transport of the turbulent kinetic energy extends the high vertical diffusivity Kv out of the shoaled mixed layer and maintains a strong SST cooling. This is consistent with the fact the cooling of Θ_vmix grows linearly as Θ_sfc increases. Even when Θ_sfc is zero, anomalous vertical mixing Θ_vmix can still happen due to the increased anomalous wind (Fig. 3d) that generates turbulent kinetic energy and thus higher Kv. The anomalous advection Θ_adv produces strongest cooling when the anomalous Θ_sfc is near zero, where Θ_adv is dominated by ageostrophic advection. The ageostrophic contribution here can be attributed to Ekman advection because its cooling strength aligns with the anomalous zonal 10-m wind u_10m (solid line in Fig. 3d). For large positive anomalous Θ_sfc > 0.5×10−6 K/s, the cooling due to anomalous ageostrophic advection −v_ag · ∇_z Θ is strong while the overall anomalous cooling due to advection Θ_adv is weak. This is a consequence of the cancellation of Ekman advection cooling by the bolus velocity-driven advection, eddy, and entrainment as detailed in Equation (13) (see Section Methods). This strong anomalous Θ_sfc is located in the strong marine warming region (15°N, 25°N × 120°W, 135°W). As we will see later, this region has a very different SST tendency response due to the pre-existing stratocumulus clouds.

We now want to better understand AR forcing over the AR-active region, where ocean dynamics can have a large impact. In Fig. 4, we plot a bar chart of SST tendency decomposition at 35°N, 151°W, marked with a red cross in Fig. 1a. ARs cause strong anomalous SST warming, and ocean dynamics overall offset over 100% of this anomalous warming that would have otherwise increased SST (Fig. 4a). Warming due to surface forcing comes from reduced evaporation, surface sensible heat loss, and longwave radiation (Fig. 4b). On the other hand, cooling is due to reduced incoming shortwave radiation (Fig. 4b). These anomalous forcing terms are opposite in sign to their climatological values (Fig. S1b). In the ocean, anomalous cooling is due to cold advection and vertical mixing (Fig. 4c).

Finally, the anomalous SST tendency response has seasonality, which can be due to the seasonality of the MLD. Since the MLD is shallower in October and reaches its maximum by March, the anomalous SST tendencies, Θ_sfc and Θ_ocn, are generally the strongest in October and weakest in March. In Feb–Mar, the strengths of detrainment Θ_det and vertical mixing Θ_vmix are comparable, and the anomalous SST tendency (Fig. 4a) is comparable to climatology (Fig. S1a). It shows that the role of air–sea interaction becomes important in early spring because the total surface heat flux is important in the evolution of MLD21,22. Overall, the strong cancellation between surface fluxes and ocean response makes the local SST tendency Θ_loc a non-trivial function of time and space. Later, we will discuss the seasonality in greater detail.

Spatial distribution of anomalous SST tendency response to ARs

For a more comprehensive understanding, the analysis in the previous subsection can be extended to every 2°×2° grid box over the North Pacific. Figure 5 shows the anomalous daily SST tendency response to ARs in the extratropical northern Pacific during Oct–Mar, with auxiliary variables shown in Fig. 6 to clarify the results. The local SST tendency response Θ_loc (Fig. 5a) is decomposed into the contribution of surface forcing Θ_sfc (Fig. 5f) and ocean dynamics Θ_ocn (Fig. 5b). The local anomalous SST tendency Θ_loc shows a warming response roughly northward of 30°N and cooling southward. This pattern is driven by the surface forcing Θ_sfc, while the oceanic response Θ_ocn opposes it. The warming signal comes from the increased longwave radiation, sensible heat flux, and latent heat flux (Fig. 5h–j). Cooling is generated by a reduction in shortwave radiation forcing Θ_sw (Fig. 5g) because of the increased total cloud cover that blocks sunlight (Fig. 6a). The response in the region (120°W, 135°W × 15°N, 25°N) is different from other regions, as here the anomalous SST tendency exceeds 0.3 K/day. Henceforth, we refer to this as the strong marine warming region, which will be discussed separately below.

The ocean dynamics component Θ_ocn (Fig. 5b) shows the strongest SST cooling along the northwestern coastal region, which is dominated by the vertical mixing Θ_vmix (Fig. 5d). From 20°–50°N, ARs bring anomalous westerlies (Fig. 1f), which produce strong advective cooling Θ_adv (Fig. 5c) that is mostly southward Ekman advection (Fig. 6d). In most of the domain, the increased heat fluxes outcompete the wind work and shoal the mixed layer (Fig. 6e). Therefore, they induce anomalous detrainment Θ_det (Fig. 5e) that increases the mixed layer potential temperature Θ. The effect of detrainment is strongest along the Kuroshio Extension, a region rich in SST mesoscale eddies. We do not investigate further because ECCOv4’s 1° resolution is not ideal for understanding oceanic eddies. Another location with strong detrainment is the strong marine warming region, which will be discussed below.

Along the California coast, there is a strong anomalous warming response due to anomalous Ekman advection (Figs. 5c and 6d) driven by the anomalous southerly winds (Fig. 1f). This warming is opposed by anomalous vertical mixing Θ_vmix (Fig. 5d). Because there is no notable change in MLD and ∂Θ/∂z (Fig. 6e and f) and their patterns do not match Θ_vmix, we rule out the possibility of a change in vertical thermal structure. Rather, this evidence shows that there is generation of turbulent kinetic energy, associated with the anomalous Ekman advection, which is transported downward and extends high vertical diffusivity Kv beyond the mixed layer, therefore increasing the cooling due to vertical diffusion Θ_vmix.

The interannual variability of anomalous SST tendency response is mostly located at the Kuroshio Extension and in the strong marine warming region, indicated by the contours in Fig. 5a. The ocean response Θ_ocn (Fig. 5b) contributes more variability in the Kuroshio Extension region than the surface fluxes Θ_sfc (Fig. 5f), highlighting the role of mesoscale eddies as they enhance the air–sea fluxes when AR passes from above23. Along 40°N this variability is attributed to advection Θ_adv and vertical mixing Θ_vmix (Fig. 5c, d), whereas the contribution of vertical mixing is restricted to the Pacific Ocean near Japan.

Seasonality of anomalous SST tendency response to ARs

While the qualitative roles of different processes do not change, the anomalous SST tendency has a notable seasonality. There is a strong cancellation between surface fluxes and ocean modification in Oct–Nov and Feb–Mar (Figs. S2 and S3). The warming of atmospheric forcing decays as the months progress. The location of the strongest warming follows the latitudinal position of the strongest meridional SST gradient, which is also the stormtrack location. The advective cooling Θ_adv consequently shows a similar progression in time and latitudinal location (Fig. S3). In the meanwhile, cooling due to the vertical mixing Θ_vmix is strong in Oct–Nov, but almost muted in Dec–Jan. This is because the mixed layer is seasonally thinner in fall and thicker in spring, and the vertical temperature gradient at the base of the mixed layer is stronger in fall and weaker in later months (Fig. S4). On the other hand, in Feb–Mar, there is a modest cooling due to vertical mixing. This is likely because in early spring, AR forcing is compatible with seasonal forcing such that AR-induced anomalous surface fluxes Θ_sfc have stronger control over the MLD. Therefore, when an AR arrives, the warming can effectively reduce the MLD (Fig. S4) and in turn enhance cooling due to vertical mixing.

Strong marine warming region over the East Pacific

The strong marine warming region (15°N, 25°N × 120°W, 135°W) (Fig. 5a) responds differently from other parts of the ocean. In this region, AR conditions increase the shortwave radiation (Fig. 5g) and slightly decrease the longwave radiation (Fig. 5h), which together warm the SST and shoal the MLD (Fig. 6e). The shoaling of the mixed layer increases the mixed layer potential temperature Θ through detrainment (Fig. 5e).

The reason for this anomalous behavior is that this region is often covered with stratocumulus clouds24–26, characterized by low cloud cover that reflects sunlight. The marine stratocumulus is supported by the large-scale subsidence-induced capped-inversion26–29. Our composite shows that when ARs arrive, the SST is anomalously high (0.2–0.4 K), which weakens the capped-inversion. Meanwhile, the AR brings in a low-pressure system that creates ascending motion and further reduces subsidence. Therefore, the stratocumulus is much reduced (Fig. S5d, low cloud cover). On the other hand, the arrival of the AR increases mid and high cloud covers (Fig. S5b, c). Altogether, there is a net decrease in the total cloud cover, which in turn introduces sunlight (Fig. 5g). The shortwave radiation stratifies the surface ocean and shoals the MLD (Fig. 6e). In this case, the anomalous high SST produces anomalous cooling by increasing upward longwave radiation, which can be offset by the greenhouse effect due to high IWV30. Even more complicated, the high pre-existing SST is likely associated with ENSO, which increases the AR activity projected as EOF1 (also EOF2, but the mechanism is unclear). Our analysis aligns with Park and Leovy31, who found a negative correlation between the ENSO index and stratocumulus cloud frequency over the strong marine warming region. They argued that the reduction in stratiform cloud cover during ENSO is due to the increased SST, warm advection, and increased storm frequency.

One should not mistake strong marine warming events for marine heatwaves. There are at least two differences between marine heatwaves and strong marine warming events that we identify here. First, strong marine warming events refer to extreme SST tendencies, whereas marine heatwaves are typically defined through extreme SST episodes. Second, marine heatwaves require extreme SST to persist for over five days, which is much longer than the local lifetime of a typical AR event32.

Methods
Datasets and AR condition
We obtain ocean potential temperature, salinity, and surface fluxes from Estimating the Circulation and Climate of the Ocean Version 4 release 4 (ECCOv4)15,38, which uses a 1° resolution MIT general circulation model (MITgcm)39 and reconstructs ocean states by assimilating observational data and forcing the ocean with adjusted ERA-interim air–sea fluxes. The ECCOv4 assimilation procedure does not nudge the model’s internal ocean state, meaning that the heat budget is exactly closed, and diagnostic terms needed to analyze this budget are made available by NASA Jet Propulsion Laboratory Physical Oceanography Distributed Active Archive Center (NASA JPL PODAAC).

The ECCOv4 data extend from 1992 Jan 1 to 2018 Jan 1. This limits our target time interval to water years 1993–2017 (water year n starts Oct 1 of year n−1).

To compute IWV and IVT, we use the ECMWF Reanalysis–Interim (ERA-Interim)16, which has 60 vertical layers and a horizontal resolution of 79 km. We follow widely used definitions12,40–42 to compute these quantities as

IWV = 1/g ∫_{p=ps}^{200hPa} q dp (2a)

IVT = 1/g ∫_{p=ps}^{200hPa} vq dp (2b)

where q is the specific humidity, ps is the surface pressure, and v is the horizontal wind speed vector. To test the sensitivity, we have also used ECMWF Reanalysis v5 (ERA5)43, which has a horizontal resolution of 30 km and 137 vertical levels, to compute IWV and IVT. The outcome is almost identical to that of ERA-Interim. To detect ARs, we identify so-called AR objects. We adopt the definition from Guan and Waliser [44, hereafter GW15]. A valid AR object satisfies the following seven criteria: (1) Connected area where IVT is greater than a threshold. The threshold for a given day and location is defined as 100 kg/m/s or 85th percentile IVT of daily mean IVT within 15 days (i.e., previous 7 days, the given day, and post 7 days) using all 25 years, whichever is greater. (2) The length of the AR object, defined as the maximum great circle distance of the grids within the AR object, has to exceed 2000 km. This is a more selective criterion than GW15 used, but easier to define. (3) The overall orientation, defined as the great circle that measures the AR object length, cannot deviate more than 45° from the mean IVT vector of the AR object. (4) No more than 50% of the grid cells in the AR object can have IVT deviating 45° from the mean IVT. (5) The aspect ratio, defined as the square of the AR length divided by the area of the AR object, must be greater than 2. This is a stronger criterion than GW15 because the AR length we define is always greater than that defined by GW15. (6) AR objects cannot straddle the equator. (7) The IVT must be greater than 250 kg/m/s. Overall, we adopted the AR detection algorithm that is more selective than GW15. We label a particular day for a given location as an AR day if an AR object covers the location.

In this study, we focus on the North Pacific (10°N, 60°N × 120°E, 120°W). Since the ECCOv4 and ERA-Interim grids do not coincide, we regrid both datasets by taking the cosine-latitude-weighted-average of the data points that are within a common 2°×2° box. Since we linearly regrid the data, and we compute the SST budget analysis using only the ECCOv4 data, regridding does not affect the closure of the SST budget.

Mixed-layer diagnoses
The mixed layer is a well-mixed surface layer characterized by a low vertical potential density gradient. The MLD is defined as the shallowest depth at which the potential density exceeds the surface potential density by 0.03 kg m−3 45. The potential density is computed using the nonlinear parameterization of Millero and Poisson46, which is consistent with ECCOv415,47.

We briefly introduce how we obtain the SST budget equation for nonlinear free-surface formulation. In the MITgcm, the potential temperature tendency equation is39,48

∂Θ/∂t = −∇_z · (vΘ) − 1/ρ_0 ∂F/∂z + ∂/∂z (Kv ∂Θ/∂z) + ∇_z · (KH ∇_z Θ) (3)

where vectors are denoted in bold, Θ is the ocean potential temperature, ρ_0 is the reference seawater density, (v, w) = (v_Eu, w_Eu) + (vb, wb) is the residual ocean velocity as the sum of Eulerian and eddy-parametrizing bolus velocity, ∇_z is horizontal divergence (or gradient) operator with z held fixed, Kv and KH are the vertical and horizontal diffusivity of potential temperature. In ECCOv4, Kv is determined using the Gaspar-Grégoris-Lefevre (GGL) turbulent kinetic energy parameterization scheme49. The surface flux F = F_sw + F_lw + F_sen + F_lat is the sum of shortwave radiation, longwave radiation, sensible heat flux, and latent heat flux (upward positive). The terms on the right-hand side of Equation (3) are external forcing, three-dimensional advective flux convergence, vertical diffusion, and horizontal diffusion.

Given an MLD, h = h(x, y, t), and the surface height anomaly, η = η(x, y, t), we define

s(·) := 1/h ∫_{η−h}^{η} (·) dz (4)

as the vertical averaging operator within the mixed layer. In the rest of the paper, we will use the mixed layer potential temperature Θ as a proxy for SST. Applying the averaging operator to (3), as shown in Supplementary Note 1, one may derive a mixed layer potential temperature tendency as

Θ_loc = Θ_sw + Θ_lw + Θ_sen + Θ_lat + Θ_dilu + Θ_adv + Θ_vmix + Θ_det + Θ_hdif (5)

where Θ_loc = ∂Θ/∂t is the local tendency of mixed layer potential temperature,

Θ_sw = −1/(ρ_0 h) ∂F_sw/∂z (6)

Θ_lw = −1/(ρ_0 h) ∂F_lw/∂z (7)

Θ_sen = −1/(ρ_0 h) ∂F_sen/∂z (8)

Θ_lat = −1/(ρ_0 h) ∂F_lat/∂z (9)

are the tendency due to the denoted surface heat fluxes, and

Θ_dilu = (P − E)/(ρ_0 h) (Θ_η − Θ) (10)

is the tendency due to the dilution effect of surface freshwater (P − E stands for precipitation minus evaporation mass flux in units of m/s, Θ_η is evaluated as the P − E potential temperature). The dilution term only tracks the flux of freshwater and does not account for the latent heat involved. In general, the dilution term is weak compared to other major contributions. The tendency of vertical mixing,

Θ_vmix = (Kv ∂Θ/∂z)|_{η−h} / h + (∂(h − η)/∂t) (Θ_η−h − Θ) / h (11)

includes vertical diffusion and the tendency due to the deepening of the mixed layer. Although these two terms look different, they are meant to capture the vertical mixing due to entrainment (the turbulent vertical flux at the bottom of the mixed layer). The entrainment is captured in the first term for schemes parameterizing entrainment as enhanced Kv, such as the GGL scheme49 used in ECCOv4 or the K-profile parameterization scheme21,50 used in many climate models. On the other hand, the entrainment is captured in the second term for schemes that directly solve for ∂(h − η)/∂t, such as the Niiler-Kraus bulk formulation22,51. The tendency due to horizontal diffusion is

Θ_hdif = ∇_z · (KH ∇_z Θ) (12)

The tendency due to advection,

Θ_adv = −v · ∇_z Θ + v_0 · ∇_z Θ_0 + (w_η−h / h) (Θ_η−h − Θ) − v · ∇_z (h − η) (Θ_η−h − Θ) / h (13)

includes the effects of mean flow advection, eddies (prime term (·)0 = (·) − (·) is the departure from the vertical mean), and entrainment at the bottom of mixed layer due to residual velocities. The last term,

Θ_det = (∂(h − η)/∂t) (Θ_η−h − Θ) / h (14)

is the tendency due to detrainment, and it generally increases Θ (because typically ∂Θ/∂z > 0). Notice that detrainment does not change SST. The awkward Θ_det ≠ 0 is a construct due to the definition of vertical averaging. For convenience, we define

Θ_sfc = Θ_sw + Θ_lw + Θ_sen + Θ_lat + Θ_dilu (15)

Θ_ocn = Θ_adv + Θ_vmix + Θ_det + Θ_hdif (16)

as the overall tendency due to surface fluxes and ocean dynamics such that

Θ_loc = Θ_sfc + Θ_ocn (17)

The derivation of each tendency term from MITgcm is documented in Supplementary Note 2.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Summary and major comments:\nIn “Response of Sea Surface Temperature to Atmospheric Rivers”, the authors seek toward exploring the\natmospheric river (AR)-induced impacts on sea surface temperatures (SSTs) over the North Pacific and\ntheir interacfions with ocean dynamics. They idenfify some key oceanic processes under the AR\ninfluence that play the most important roles in modulafing the SST tendency. These include ageostrophic\nadvecfion, verfical diffusion, and entrainment.\nThe study focuses on the mixed-layer depth diagnoses based on a 25-year dataset and a decomposifion\nof the local SST tendency. The authors present an interesfing work in which they compare and explore\nvarious potenfial contribufions of ARs to the development of SST anomalies. Their effort is fimely and\nhas potenfial to fill the gap in our understanding of AR feedback to oceanic forcing. However, there are\nsome major issues that prevent me from suggesfing an immediate publicafion. These include a) the AR\ndefinifion used in this study is not appropriate, and b) the links between some oceanic processes and\nARs are not well explained. My recommendafion is that the manuscript be returned for a major revision.\nMinor comments and suggesfions:\nAbstract: In the first sentence, ARs are responsible for SOME (not all) extreme weather condifions. In the\nsentence “Among all ocean processes, ageostrophic advecfion, verfical diffusion, and entrainment are\nthe most important in modulafing the SST tendency response”, what are the contribufions of ARs to\nthese processes? In the sentence “For example …, sunlight”, you could replace “marine warming region\nwhose SST warming” with “marine region where SST warming”; how the disappearance of\nstratocumulus is related to AR acfivity? In the last sentence, consider replacing “the reducfion” with “the\nAR-induced reducfion”.\nL11: The two-week limit applies to the determinisfic numerical weather predicfion (NWP) methods\nthanks to the chaofic nature of the atmosphere. Some probabilisfic forecast skill beyond this\ndeterminisfic limit into the subseasonal-to-seasonal fime scales (3 to 5 weeks) could be obtained by\nusing ensemble NWP methods or through knowledge of some prominent air-sea oscillafions, such as the\nMadden-Julian oscillafion (Baggeft et al. 2017; Lin et al. 2019).\nL14-L16: Here, could you briefly menfion the main mechanisms through which ARs insert their impacts\non the oceans?\nL28: Using daily climatology could include large day-to-day variability in your analysis. A 5-day or 10-day\nrunning climatology would be more appropriate.\nL33: Consider replacing “two ridges” with “two variability ridges” or “two standard deviafion ridges”.\nL35-36: What is your definifion of moderate correlafion? The stafisfical significance of the correlafion\ncoefficient depends on the length of the data series N. |r| = 0.30 has different significance levels\nbetween N = 25 and N = 50. With only 25-year data, you should consider the AR correlafion with ENSO,\nwhich is an interannual (5 to 7 years) oscillafion, rather than with PDO, which is a decadal (or mulfi-\ndecadal) oscillafion. By the way, PDO has an ENSO-like paftern in SST.\nL38-L40: EOF1 and EOF2 are supposed to be two independent modes. Do you use one physical\nmechanism to explain two independent modes?\nL42: High IWV anomalies with ARs are not obvious in Fig. 1d.\nL139: Could you explain briefly here why (how) AR condifions in this region would reduce the low cloud\ncover? And how about the AR-induced cloudiness?\nL143-L148: Mo et al. (2022) invesfigated some AR-induced mechanisms for land heat waves, which could\npartly apply to the marine heat waves.\nL149-L167: Could you include a remark about the implicafion of climate change on your findings? A\nwarmer climate will certainly produce more and stronger ARs. Will it lead to larger SST anomalies?\nL171: By “reduced shortwave radiafion”, do you mean downward or upward?\nL175: Is “incoastal” a typo?\nL180-L195: You need to menfion the period (1993-2017) of your study in this dataset descripfion. You\nmay also need to jusfify why this 25-year period is selected. Is it long enough to address decadal\noscillafion problem?\nL185-L188: Atmospheric river can be generally defined as a long, narrow, and transient corridor of strong\nhorizontal water vapor transport (hftps://glossary.ametsoc.org/wiki/Atmospheric_river). Specifically,\nmost studies have a length requirement of 2000 km or at least 1500 km (Rutz et al. 2014; Guan &\nWaliser 2015; Mo et al. 2022). The AR definifion used in this study is too simple. The minimum length of\n500 km is too short, and without a requirement for an appropriate length/width rafio (e.g., > 2 in Guan &\nWaliser, 2015), some typhoons could be mis-idenfified as ARs. You need to either sharpen your AR\ndefinifion or use one of the AR catalogues published by ARTMIP (Shields et al. 2018).\nReferences:\nBaggeft, C. F., Barnes, E. A., Maloney, E. D., and Mundhenk, B. D., 2017: Advancing atmospheric river\nforecasts into subseasonal-to-seasonal fime scales. Geophys. Res. Left., 44, 7528–7536,\nhftps://doi.org/10.1002/2017GL074434.\nGuan, B., and Waliser, D. E., 2015: Detecfion of atmospheric rivers: Evaluafion and applicafion of an\nalgorithm for global studies. J. Geophys. Res. Atmos., 120, 12514–12535,\nhftps://doi.org/10.1002/2015JD024257.\nLin, H., Mo, R., Vitart, F., and Stan, C., 2019: Eastern Canada Flooding 2017 and its subseasonal\npredicfions. Atmosphere-Ocean, 57, 195–207, hftps://doi.org/10.1080/07055900.2018.1547679.\nMo, R., Lin, H., and Vitart, F., 2022: An anomalous warm-season trans-Pacific atmospheric river linked to\nthe 2021 western North America heatwave. Commun. Earth Environ., 3, 127,\nhftps://doi.org/10.1038/s43247-022-00459-w.\nRutz, J. J., Steenburgh, W. J., and Ralph, F. M., 2014: Climatological characterisfics of atmospheric rivers\nand their inland penetrafion over the western United States. Mon. Wea. Rev., 142, 905–921,\nhftps://doi.org/10.1175/MWR-D-13-00168.1.\nShields, C. A., and Coauthors, 2018: Atmospheric River Tracking Method Intercomparison Project\n(ARTMIP): project goals and experimental design. Geosci. Model Dev., 11, 2455–2474,\nhftps://doi.org/10.5194/gmd-11-2455-2018.\nRuping Mo\nEnvironment Climate Change Canada, Vancouver, BC, Canada\nruping.mo@ec.gc.ca", "reviewer_2": "Summary: In this study the authors use 25 years of ocean reanalysis data to discern how ARs affect SSTs\nover the North Pacific. They found that ARs have an overall warming effect on SSTs through reduced\nshortwave radiafion and enhanced downward longwave radiafion/sensible heat flux. This warming is\noffset up to 70% by ocean dynamics, namely ageostrophic advecfion and verfical mixing. The authors\nalso showed that these SST responses to both surface and ocean forcing are not uniform throughout the\nNorth Pacific and also has some seasonal variability driven primarily by variafions in the mixed layer\ndepth as the cool season progresses. Shedding light on how ARs have a significant effect on SSTs and\nhighlighfing the need for interacfive ocean models for subseasonal AR predicfion is an invaluable\ncontribufion to the scienfific community. Overall the paper is well wriften and structured and the\nauthor’s asserfions are supported by the figures and text, however, some further clarificafion is needed\nregarding the AR detecfion methodology used. In the opinion of this reviewer, this study adds to the\nexisfing body of scienfific work in a tangible way and is worthy of publicafion with the\nrevisions/comments outlined below.\nMajor Comments:\n1. AR Detecfion Methodology - Please clarify what you mean by “interior points.” Addifionally, are your\nresults sensifive to AR length? 500km is very short, most AR studies require a standard length of at least\n1500km for an anomalously high IVT/IWV region to be considered an AR.\nReference: Shields, Chrisfine A., et al. \"Atmospheric river tracking method intercomparison project\n(ARTMIP): project goals and experimental design.\" Geoscienfific Model Development 11.6 (2018): 2455-\n2474.\nAddifionally, have you checked how AR detecfion frequency/locafion in ERA-Interim differs from AR\ndetecfion frequency/locafion in ERA5?\n2. Figure 4: How was the 10 day threshold chosen as a “valid year?” Are results sensifive to this\nthreshold? I also don’t understand how only 5 of the 25 years used in this study had 10 AR days over a\nvery acfive region throughout Feb-Mar.\n3. Line 128: May be worth expanding on this a bit more. Yes, the anomalous local SST tendency does\npeak in Dec-Jan, but only because ocean damping is much weaker than the surface forcing. However,\nanomalous local SST tendencies forced by the surface and ocean components both peak in Oct-Nov.\nBecause the ocean damping is much stronger in Oct-Nov than Dec-Jan it weakens the surface forcing\nmore, giving the appearance of a peak in anomalous local SST tendency in Dec-Jan. The same\nconclusions can be drawn from Figure 4b and should be noted there as well around lines 92-93.\nMinor Comments:\n1. Instances where references are italicized should be changed to regular text (lines 18, 150, 199).\n2. Figure 1: Need to denote what the dots in (d)-(f) indicate.\n3. Lines 86-87: I don’t believe the argument can be made that there is warming due to dilufion. Dilufion\nactually looks mostly negligible or negafive throughout Figure 4d and, by extension, 5g. 4. According to\nFigure 4 the warming is instead primarily due to increased sensible heafing, longwave radiafion and\nlatent heafing. Latent heafing should be included in this sentence.\n5. Figure 6: Panel d appears to only show the ageostrophic advecfion. Why is geostrophic advecfion\nmenfioned in the capfion? Should there be an addifional panel showing geostrophic advecfion? If not\nplease remove reference to geostrophic advecfion.\n6. Line 115: Do you mean 6d instead of 6b?\n7. Line 171: Sfill not sure reduced evaporafion does much other than actually causing a cooling\nas shown by figures 4d and 5g. Would omit “reduced evaporafion” from sentence.\n8. In either the methods or results secfion please elaborate on why the study focuses only on Oct-Mar as\nopposed to the enfire year.\n9. Line 175: Add a space between “in” and “coastal”.\n10. Equafions 2a/b: Integral is backwards, p=ps should be on the boftom and 200 hPa should be on the\ntop since it’s an atmospheric variable.\n11. Lines 204 and 209: Please define GGL and KPP before using their acronyms.\n12. Equafions 6-9: Should there be negafives here? There are no negafives for these terms in equafion 3\nor supplemental informafion equafion 8.\n13. Supplemental Figures: Should note in the figure capfion that it’s the decomposifion of the\nresponse of SST tendency to ARs broken down by 2 month periods.\n14. Supplemental Figure 1: Note in figure capfion that the blue contours indicate wind direcfion.\n15. Supplemental Figure 3: Missing that row 4 is detrainment in figure capfion, while horizontal\ndiffusion should be noted as row 5.", "reviewer_3": "Review of “Response of Sea Surface Temperature to Atmospheric Rivers”\nThis manuscript analyzes the oceanic response to atmospheric rivers (AR) in the North Pacific region\nusing an ocean reanalysis dataset. The main result is that ocean dynamics generally acts to damp the\nwarming effect of ARs on SSTs north of 25N. Different terms in the mixed layer heat budget are analyzed\nto understand the oceanic response, which shows significant geographical variafion.\nThe issue of oceanic response during AR events is important because the sea surface temperature (SST)\nresponse can act as a feedback that affects the subsequent atmospheric evolufion of the weather system\nthat drives the AR event. This manuscript makes a useful contribufion to this topic and I would\nrecommend publicafion after addressing the comments below.\nComments\nLine 49: How well do the different terms in the SST budget balance? Is there a large residual term?\nUnlike in a model simulafion, where all terms will balance, the reanalysis procedure may create spurious\nheat sources/sinks associated with adjustment of temperatures. Is this a significant effect?\nLine 57-60: The slope of the relafionship between Theta_ocn and Theta_sfc is quite small. Doesn’t this\nmean that this explains only a small fracfion of the overall variance?\nFig. 4: There is too much detail in this figure. It would be befter to perhaps omit some of the informafion\nthat is not relevant. Even for some other figures (e.g., Fig. 5), some the details are quite hard to read. The\nlarge version of the figures included at the end of the manuscript are helpful, but when the paper is\nprinted, the small version of the figures may obscure the details."}, "author_response": "Reply to Reviewer 1’s Comments on\n“Response of Sea Surface Temperature\nto Atmospheric Rivers”\nDear reviewer,\nThank you for your thorough review of our manuscript. Your feedback has been valuable in\nrefining the content. In this revision, we have changed the dataset used to compute IVT from\nERA5 to ERA-interim, and we also now use a widely accepted AR detection method. We will first\nelaborate on these changes, and then address each of your comments.\nUse ERA-interim instead of ERA5 to compute IVT\nIn the original manuscript, we used ERA5 to compute IVT, while ECCOv4 uses ERA-interim to\nconstruct the reanalysis. Because this choice was questioned by some reviewers and is indeed\na less ideal choice, in the revision, we recomputed IVT using ERA-interim data. We found little\ndifference in IVT between these two datasets. Thus, although we have updated our reanalysis\nproduct, we have also concluded the IVT is not sensitive to the choice of datasets between\nERA5 and ERA-interim.\nAn update on AR detection algorithm\nReviewers also raised concerns about our AR detection algorithm, specifically about the\nthreshold of the size of ARs. In our original manuscript, we used 1000km as the length threshold\n(500km was a typo), which is smaller than the typical choice of 1500 to 2000km.\nGiven this concern from the reviewers, in this revision, we have updated the AR detection\nalgorithm to approximately follow that of Guan & Waliser (2015) (GW15 afterwards):\n1. IVT anomaly threshold is 85th monthly percentile IVT [15-day smoothed] or 100 kg m/s,\nwhichever is greater.\n2. The AR size (length) >= 2000km. Here, we define the length as the great arc of farthest\npoints in the AR object. In GW15, they track the AR length on top of the great arc,\nmeaning for the same given AR object, AR length defined in GW15 will always be\ngreater than length defined by us. Therefore, we have a stricter criterion.\n3. Aspect ratio length / width = length^2 / area > 2. Because our AR size is always equal or\nsmaller than GW15’s AR length, for the same AR object, our algorithm gives an equal or\nsmaller aspect ratio. This effectively makes this criterion stricter than GW15.\n4. Direction check, meaning more than half of the grid points have an IVT vector that\ndeviates less than 45 degrees from the mean IVT vector.\n5. AR objects that straddle the equator are discarded, and\n6. ARs whose poleward meridional IVT < 50 kg/m/s are discarded.\nThe change of AR detection results in fewer ARs detected in the middle of the Pacific but more\nalong the coastline. Additionally, the revised AR detection removes ARs in low latitudes. EOF1\nremains similar. The change in the second mode is that the new EOF2 has more emphasis over\nJapan and Eastern Pacific. This second mode better captures AR events that originate from the\nEastern Pacific and influence the west coast America.\nOld AR detection New AR detection\nThe change also affects the analysis in cases with negative surface forcing (AR cools the SST),\nas can be seen as follows\nOld AR detection New AR detection\nReviewer #1 (Remarks to the Author):\nSummary and major comments:\nIn “Response of Sea Surface Temperature to Atmospheric Rivers”, the authors seek toward\nexploring the atmospheric river (AR)-induced impacts on sea surface temperatures (SSTs) over\nthe North Pacific and their interactions with ocean dynamics. They identify some key oceanic\nprocesses under the AR influence that play the most important roles in modulating the SST\ntendency. These include ageostrophic advection, vertical diffusion, and entrainment.\nThe study focuses on the mixed-layer depth diagnoses based on a 25-year dataset and a\ndecomposition of the local SST tendency. The authors present an interesting work in which they\ncompare and explore various potential contributions of ARs to the development of SST\nanomalies. Their effort is timely and has potential to fill the gap in our understanding of AR\nfeedback to oceanic forcing. However, there are some major issues that prevent me from\nsuggesting an immediate publication. These include a) the AR definition used in this study is not\nappropriate, and b) the links between some oceanic processes and ARs are not well explained.\nMy recommendation is that the manuscript be returned for a major revision.\nReply: We address the AR-detection issue above.\nMinor comments and suggestions:\nAbstract: In the first sentence, ARs are responsible for SOME (not all) extreme weather\nconditions. In the sentence “Among all ocean processes, ageostrophic advection, vertical\ndiffusion, and entrainment are the most important in modulating the SST tendency response”,\nwhat are the contributions of ARs to these processes? In the sentence “For example …,\nsunlight”, you could replace “marine warming region whose SST warming” with “marine region\nwhere SST warming”; how the disappearance of stratocumulus is related to AR activity? In the\nlast sentence, consider replacing “the reduction” with “the AR-induced reduction”.\nL11: The two-week limit applies to the deterministic numerical weather prediction (NWP)\nmethods thanks to the chaotic nature of the atmosphere. Some probabilistic forecast skill\nbeyond this deterministic limit into the subseasonal-to-seasonal time scales (3 to 5 weeks) could\nbe obtained by using ensemble NWP methods or through knowledge of some prominent air-sea\noscillations, such as the Madden-Julian oscillation (Baggett et al. 2017; Lin et al. 2019).\nReply:\nThank you for pointing this out. After some research, we found that the 10-14 day prediction skill\nseems to be documented by DeFlorio et al. (2018), who use “AR hits” as the metric.\nIncorporating this information, we have updated the text as follows:\n“Past studies have identified predictors of AR activity, such as El Niño Southern Oscillation\n(ENSO) and Madden--Julian Oscillation [cite: Tseng et al. (2021), Lin et al. (2019), Baggett et al.\n(2017)]. However, skillful AR predictions do not exceed 10-20 days depending on the metric\nchosen [cite: DeFlorio et al. (2018), DeFlorio et al. (2019), Wick et al. (2013)].”\nReference:\nDeFlorio, Michael J., et al. \"Global assessment of atmospheric river prediction skill.\" Journal of\nHydrometeorology 19.2 (2018): 409-426.\nL14-L16: Here, could you briefly mention the main mechanisms through which ARs insert their\nimpacts on the oceans?\nReply: We added the text to address this comment as follows: “Qualitatively, the physical\nexpectation is that a relatively moist and warm AR heats the surface ocean through increasing\ndownward heat fluxes. Simultaneously, its wind enhances vertical mixing at the base of the\nmixed layer that cools the surface ocean.”\nL28: Using daily climatology could include large day-to-day variability in your analysis. A 5-day\nor 10-day running climatology would be more appropriate.\nReply: As mentioned above, we changed the AR detection method. In this method, we obtain a\nmonthly 85 percentile IVT field of 25 years using 15-day smoothing centered at each target date\n(i.e. 85 percentile of 25*15=375 samplings). This process removes large day-to-day variability.\nL33: Consider replacing “two ridges” with “two variability ridges” or “two standard deviation\nridges”.\nReply: We have revised the language. Also, after updating the AR detection algorithm we now\nfind four variability ridges, and these spatially match the locations of bigger amplitudes in EOF1\nand EOF2.\nL35-36: What is your definition of moderate correlation? The statistical significance of the\ncorrelation coefficient depends on the length of the data series N. |r| = 0.30 has different\nsignificance levels between N = 25 and N = 50. With only 25-year data, you should consider the\nAR correlation with ENSO, which is an interannual (5 to 7 years) oscillation, rather than with\nPDO, which is a decadal (or multi-decadal) oscillation. By the way, PDO has an ENSO-like\npattern in SST.\nSee the next comment.\nL38-L40: EOF1 and EOF2 are supposed to be two independent modes. Do you use one\nphysical mechanism to explain two independent modes?\nReply: No, our intent was only to make connections between ENSO and EOF1 & EOF2. And we\nshould not use one mechanism to explain both EOFs since they are temporally independent.\nWe have rewritten the text in L37-45 as\n“EOF1 and EOF2 roughly represent the shift of AR activity south to north and west to east,\nrespectively. EOF1 positively correlates with the NINO3.4 SST index (95% confidence interval).\nThis connection arises because ENSO events tend to deepen the Aleutian Low, which controls\nthe location of stormtrack activity [citation]. This result is consistent with Tseng et al. (2021) who\nexamined this relationship more closely. EOF2 positively correlates with NINO3.4 SST index\n(80% confidence interval) as well, although the correlation is weaker. These results indicate that\nENSO can change ARs' north-south and east-west frequency. A deeper physical understanding\nis beyond the scope of this paper and will require future investigations.”\nL42: High IWV anomalies with ARs are not obvious in Fig. 1d.\nReply: We were showing the composited total IWV. Now we have changed it to show\ncomposited anomalous IWV.\nOriginal Manuscript Revision\nL139: Could you explain briefly here why (how) AR conditions in this region would reduce the\nlow cloud cover? And how about the AR-induced cloudiness?\nReply:\nWe think that ARs are typically in the vicinity of low-pressure systems that bring in large-scale\nconvergence. The large-scale convergence removes the capping inversion, which does not\nfavor the formation of marine stratocumulus (Lily 1968, Kuo and Schubert 1988). Also, the\ncomposited SST shows that the SST is on average 0.2K~0.4K warmer than climatology. This is\nan indication of ENSO. Therefore, the reduction of subsidence can also be partially due to large-\nscale warm SST. The reduced subsidence does not favor marine stratocumulus, and thus it is\nreduced. The mid and high clouds brought in by ARs cannot fully compensate the loss of low\ncloud, and there is a net reduction of total cloud cover.\nHowever, the story is complicated by ENSO increasing AR frequency over the eastern Pacific. It\nwill take a separate study to explore air-sea interaction in this region.\nWe have rewritten the text in L158-169.\nL143-L148: Mo et al. (2022) investigated some AR-induced mechanisms for land heat waves,\nwhich could partly apply to the marine heat waves.\nReply: We have added some text that mentions the possible greenhouse effect due to high\nIWV, which might reduce the longwave cooling.\nL149-L167: Could you include a remark about the implication of climate change on your\nfindings? A warmer climate will certainly produce more and stronger ARs. Will it lead to larger\nSST anomalies?\nReply: We added the text as follows (bold font below; in L184-186 of the paper)\n“…This effect will be important in the case of multiple AR occurrences, known as atmospheric\nfamily events [cite Fish et al. (2022), Fish et al. (2019)] where the later ARs will interact with\nthe SST anomalies induced by the earlier ARs. Moreover, an emerging consensus\nprojects that ongoing global warming will lead to more frequent AR activity [cite Payne et\nal. 2020], making AR impact on SST even more influential in the future.”\nL171: By “reduced shortwave radiation”, do you mean downward or upward?\nReply: We mean downward. In this revision, we have added “downward” to make it clearer.\nL175: Is “incoastal” a typo?\nReply: Yes it is a typo. We corrected it to “... response in coastal California…”\nL180-L195: You need to mention the period (1993-2017) of your study in this dataset\ndescription. You may also need to justify why this 25-year period is selected. Is it long enough to\naddress decadal oscillation problem?\nReply: The ECCOv4 data spans from 1992 Jan 1 to 2018 Jan 1. This limits our target time\ninterval down to water years 1993-2017 (water year 𝑛 starts Oct 1 of year 𝑛−1). We have\nadded this information to the Method section.\nAlso, we agree that it is a stretch to relate a 25-year record to the PDO, and we now focus on\ntheir relationship to ENSO as explained in the previous comments.\nL185-L188: Atmospheric river can be generally defined as a long, narrow, and transient corridor\nof strong horizontal water vapor transport (https://glossary.ametsoc.org/wiki/Atmospheric_river).\nSpecifically, most studies have a length requirement of 2000 km or at least 1500 km (Rutz et al.\n2014; Guan & Waliser 2015; Mo et al. 2022). The AR definition used in this study is too simple.\nThe minimum length of 500 km is too short, and without a requirement for an appropriate\nlength/width ratio (e.g., > 2 in Guan & Waliser, 2015), some typhoons could be mis-identified as\nARs. You need to either sharpen your AR definition or use one of the AR catalogues published\nby ARTMIP (Shields et al. 2018).\nReply: We have updated the AR detection method as explained in the beginning of this\ndocument.\nReferences:\nBaggett, C. F., Barnes, E. A., Maloney, E. D., and Mundhenk, B. D., 2017: Advancing\natmospheric river forecasts into subseasonal-to-seasonal time scales. Geophys. Res. Lett., 44,\n7528–7536, https://doi.org/10.1002/2017GL074434.\nGuan, B., and Waliser, D. E., 2015: Detection of atmospheric rivers: Evaluation and application\nof an algorithm for global studies. J. Geophys. Res. Atmos., 120, 12514–12535,\nhttps://doi.org/10.1002/2015JD024257.\nLin, H., Mo, R., Vitart, F., and Stan, C., 2019: Eastern Canada Flooding 2017 and its\nsubseasonal predictions. Atmosphere-Ocean, 57, 195–207,\nhttps://doi.org/10.1080/07055900.2018.1547679.\nMo, R., Lin, H., and Vitart, F., 2022: An anomalous warm-season trans-Pacific atmospheric river\nlinked to the 2021 western North America heatwave. Commun. Earth Environ., 3, 127,\nhttps://doi.org/10.1038/s43247-022-00459-w.\nRutz, J. J., Steenburgh, W. J., and Ralph, F. M., 2014: Climatological characteristics of\natmospheric rivers and their inland penetration over the western United States. Mon. Wea. Rev.,\n142, 905–921, https://doi.org/10.1175/MWR-D-13-00168.1.\nShields, C. A., and Coauthors, 2018: Atmospheric River Tracking Method Intercomparison\nProject (ARTMIP): project goals and experimental design. Geosci. Model Dev., 11, 2455–2474,\nhttps://doi.org/10.5194/gmd-11-2455-2018.\nReviewer #2 (Remarks to the Author):\nSummary: In this study the authors use 25 years of ocean reanalysis data to discern how ARs\naffect SSTs over the North Pacific. They found that ARs have an overall warming effect on\nSSTs through reduced shortwave radiation and enhanced downward longwave\nradiation/sensible heat flux. This warming is offset up to 70% by ocean dynamics, namely\nageostrophic advection and vertical mixing. The authors also showed that these SST responses\nto both surface and ocean forcing are not uniform throughout the North Pacific and also has\nsome seasonal variability driven primarily by variations in the mixed layer depth as the cool\nseason progresses. Shedding light on how ARs have a significant effect on SSTs and\nhighlight the need for interactive ocean models for subseasonal AR prediction is an\ninvaluable contribution to the scientific community. Overall the paper is well written and\nstructured and the author’s assertions are supported by the figures and text, however, some\nfurther clarification is needed regarding the AR detection methodology used. In the opinion of\nthis reviewer, this study adds to the existing body of scientific work in a tangible way and is\nworthy of publication with the revisions/comments outlined below.\nMajor Comments:\n1. AR Detection Methodology - Please clarify what you mean by “interior points.” Additionally,\nare your results sensitive to AR length? 500km is very short, most AR studies require a\nstandard length of at least 1500km for an anomalously high IVT/IWV region to be considered an\nAR.\nReference: Shields, Christine A., et al. \"Atmospheric river tracking method intercomparison\nproject (ARTMIP): project goals and experimental design.\" Geoscientific Model Development\n11.6 (2018): 2455-2474.\nAdditionally, have you checked how AR detection frequency/location in ERA-Interim differs from\nAR detection frequency/location in ERA5?\nReply: We have addressed this comment above.\n2. Figure 4: How was the 10 day threshold chosen as a “valid year?” Are results sensitive to\nthis threshold? I also don’t understand how only 5 of the 25 years used in this study had 10 AR\ndays over a very active region throughout Feb-Mar.\nReply:\nBecause we changed the AR detection algorithm, which shifted the average AR position, we\nhave changed the point location for the analysis in Figure 4. We picked the new location at\n[35N, 155W] where the ocean’s modification can be better demonstrated. As for the threshold\nsensitivity, our tests show that there is an insignificant difference between 3, 5 and 10 AR-days,\nwhile 15 AR-days greatly reduces the sampling size, such that the outcome is meaningless. In\nthis revision, we picked 5 days to include most of the wateryears, and we have updated the text\nto address the sensitivity. Finally, we show these sensitivity tests here for your reference.\nThreshold = 3 AR-days\nThreshold = 5 AR-days\nThreshold = 10 AR-days\nThreshold = 15 AR-days\n3. Line 128: May be worth expanding on this a bit more. Yes, the anomalous local SST\ntendency does peak in Dec-Jan, but only because ocean damping is much weaker than the\nsurface forcing. However, anomalous local SST tendencies forced by the surface and ocean\ncomponents both peak in Oct-Nov. Because the ocean damping is much stronger in Oct-Nov\nthan Dec-Jan it weakens the surface forcing more, giving the appearance of a peak in\nanomalous local SST tendency in Dec-Jan. The same conclusions can be drawn from Figure 4b\nand should be noted there as well around lines 92-93.\nReply: We have rewritten and expanded the discussion on seasonality.\nMinor Comments:\n1. Instances where references are italicized should be changed to regular text (lines 18, 150,\n199).\nReply: Updated as suggested.\n2. Figure 1: Need to denote what the dots in (d)-(f) indicate.\nReply: We have added this information.\n3. Lines 86-87: I don’t believe the argument can be made that there is warming due to dilution.\nDilution actually looks mostly negligible or negative throughout Figure 4d and, by extension, 5g.\n4. According to Figure 4 the warming is instead primarily due to increased sensible heating,\nlongwave radiation and latent heating. Latent heating should be included in this sentence.\nReply to 3 and 4: We do not argue that dilution plays an important role in SST warming. We only\npresent the dilution effect in the figure for completeness.\n5. Figure 6: Panel d appears to only show the ageostrophic advection. Why is geostrophic\nadvection mentioned in the caption? Should there be an additional panel showing geostrophic\nadvection? If not please remove reference to geostrophic advection.\nReply: This is a typo. Geostrophic response is too weak to be shown. We have fixed the\ncaption.\n6. Line 115: Do you mean 6d instead of 6b?\nReply: This is a typo. We have fixed the text.\n7. Line 171: Still not sure reduced evaporation does much other than actually causing a cooling\nas shown by figures 4d and 5g. Would omit “reduced evaporation” from sentence.\nReply: The titles of the subfigures might have confused the reviewers. In the previous version of\nthe manuscript he 5g was a dilution effect, which is negligible. (We have dropped it in the\nrevision.) The new Figure 5j shows the strong anomalous warming due to latent heating.\nBecause latent heating only involves evaporation, the explanation can only be reduced\nevaporation.\n8. In either the methods or results section please elaborate on why the study focuses only on\nOct-Mar as opposed to the entire year.\nReply: We add in the text at the beginning of result section: “In this paper, we focus on Oct--Mar\nwhen ARs are the most active in the North Pacific.”\n9. Line 175: Add a space between “in” and “coastal”.\nReply: We have fixed the text as suggested.\n10. Equations 2a/b: Integral is backwards, p=ps should be on the bottom and 200 hPa should\nbe on the top since it’s an atmospheric variable.\nReply: We change the integral bounds as follows.\n200hPa\ng\np=ps\nand\n200hPa\ng\np=ps\nWhich is the same mathematical form as ARTMIP whitepaper (Christian et al. 2018).\n11. Lines 204 and 209: Please define GGL and KPP before using their acronyms.\nReply: Updated as suggested.\n12. Equations 6-9: Should there be negatives here? There are no negatives for these terms in\nequation 3 or supplemental information equation 8.\nReply: Yes. We have fixed the equation and noted these fluxes are upward positive.\n13. Supplemental Figures: Should note in the figure caption that it’s the decomposition of the\nresponse of SST tendency to ARs broken down by 2 month periods.\nReply: We have added this information.\n14. Supplemental Figure 1: Note in figure caption that the blue contours indicate wind\ndirection.\nReply: We have added this information.\n15. Supplemental Figure 3: Missing that row 4 is detrainment in figure caption, while horizontal\ndiffusion should be noted as row 5.\nReply: We have added this information.\nReviewer #3 (Remarks to the Author):\nReview of “Response of Sea Surface Temperature to\nAtmospheric Rivers”\nThis manuscript analyzes the oceanic response to atmospheric rivers (AR) in the North Pacific\nregion using an ocean reanalysis dataset. The main result is that ocean dynamics generally acts\nto damp the warming effect of ARs on SSTs north of 25N. Different terms in the mixed layer\nheat budget are analyzed to understand the oceanic response, which shows significant\ngeographical variation.\nThe issue of oceanic response during AR events is important because the sea surface\ntemperature (SST) response can act as a feedback that affects the subsequent atmospheric\nevolution of the weather system that drives the AR event. This manuscript makes a useful\ncontribution to this topic and I would recommend publication after addressing the comments\nbelow.\nComments\nLine 49: How well do the different terms in the SST budget balance? Is there a large residual\nterm? Unlike in a model simulation, where all terms will balance, the reanalysis procedure may\ncreate spurious heat sources/sinks associated with adjustment of temperatures. Is this a\nsignificant effect?\nReply: There is no residual. Compared to other reanalyses, ECCOv4 is unique in that the 4D-\nvariational data assimilation occurs over a single assimilation period. The 1992 initial conditions\nare adjusted, as are the atmospheric state and mixing parameters, but there is no nudging\nthroughout the ~30-year window. All terms to close the budget to machine precision are\navailable via PO.DAAC (https://podaac.jpl.nasa.gov/ECCO). We have noted this in the text by\nadding the sentence, “The ECCOv4 assimilation procedure does not nudge the model internal\nocean state, meaning that the heat budget is exactly closed, and all budget terms needed to\nclose this budget are available from the NASA Jet Propulsion Laboratory Physical\nOceanography Distributed Active Archive Center (NASA JPL PODAAC).”\nFinally, to avoid confusion, we have changed the abbreviation “ECCO” to “ECCOv4” in this\npaper.\nLine 57-60: The slope of the relationship between Theta_ocn and Theta_sfc is quite small.\nDoesn’t this mean that this explains only a small fraction of the overall variance?\nReply: Our intent is to show that their relationship is nonlinear by computing a linear fit and\nshowing its low R value. We additionally include a bin-averaged dotted blue line to roughly show\ṅ\na non-linear relationship with two regimes split by Θ = 0.\nsfc\nFig. 4: There is too much detail in this figure. It would be better to perhaps omit some of the\ninformation that is not relevant. Even for some other figures (e.g., Fig. 5), some the details are\nquite hard to read. The large version of the figures included at the end of the manuscript are\nhelpful, but when the paper is printed, the small version of the figures may obscure the details.\nReply: In this revision, we split the figure by rows: climatology (upper row) and AR forcing\n(anomaly, lower row). We retain the resulting AR-forcing figure in the main article and include\nthe climatology in supplementary.\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors have addressed all of my concerns with the original manuscript. The revised manuscript\nrepresents a significant improvement and is ready for publicafion.\nReviewer #2 (Remarks to the Author):\nThe authors have sufficiently addressed all of my comments and concerns. Upon review of the revision I\njust have a couple minor points to add:\n1) Lines 135-136: The authors note that the surface and ocean fluxes contribute to the variability in the\nKuroshio Extension region equally, however, from Figure 5 this does not appear to be the case. While a\nvery small 0.6 contour is found in the KE region in Figure 5f, the contours around the KE region in 5b are\ngreater in magnitude and cover a much larger areal extent. As far as I can tell from Figure 5, KE variability\n(i.e. variability along 40N) is dominated by advecfion and verfical mixing, which is menfioned in the next\nsentence.\n2) Figure 6a-c: The labels in the figure capfion do not match the labels on the figure itself. Please fix.\n3) Line 144: There is a typo where \"due\" is wriften as \"du.\"\n4) Make sure the supplementary figures are numbered in the order they are referred to. Both Figures S3\nand S4 are menfioned before S2.\nReply to Reviewer 2’s Comments on\n“Response of Sea Surface Temperature to\nAtmospheric Rivers”\nDear reviewer,\nThank you for your additional comments and review of our manuscript. Your feedback helps refine the\ncontent. In this revision, we have addressed your comments on the variability as shown below. And we\nthank you for pointing out formatting problems in detail as well.\nReviewer #2 (Remarks to the Author):\nThe authors have sufficiently addressed all of my comments and concerns. Upon review of the revision I\njust have a couple minor points to add:\n1) Lines 135-136: The authors note that the surface and ocean fluxes contribute to the variability in the\nKuroshio Extension region equally, however, from Figure 5 this does not appear to be the case. While a\nvery small 0.6 contour is found in the KE region in Figure 5f, the contours around the KE region in 5b are\ngreater in magnitude and cover a much larger areal extent. As far as I can tell from Figure 5, KE\nvariability (i.e. variability along 40N) is dominated by advection and vertical mixing, which is mentioned\nin the next sentence.\nReply: Yes, the ocean contributes to the variability more than the atmosphere (although does not\ndominate the overall variability). We have rewritten the sentence as follows: “The ocean response\n(Figure 5b) contributes more variability in the Kuroshio Extension region than the surface fluxes (Figure\n5f), highlighting the role of mesoscale eddies as they enhance the air-sea fluxes when AR passes above\n[citation Liu et al. 2021].”\n2) Figure 6a-c: The labels in the figure caption do not match the labels on the figure itself. Please fix.\nReply: We have fixed this issue.\n3) Line 144: There is a typo where \"due\" is written as \"du.\"\nReply: We have fixed the typo.\n4) Make sure the supplementary figures are numbered in the order they are referred to. Both Figures\nS3 and S4 are mentioned before S2.\nReply: We have put the correct order now."}]

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