Moisture advection to the Arctic 

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Radiosoundings

To validate the characteristics of moisture transport derived from reanalyses, we compared them to observations, namely radiosoundings from the Integrated Global Radiosonde Archive (IGRA, Durre et al. (2006)). For the region north of 60◦N, seventy four sites were active throughout the satellite era from 1979 to 2013 (Figure 1.4). Thirty-nine sites are located on the coast including six on small islands. In Antarctica, there are only ten available sites, all but one on the coast of East Antarctica (Figure 1.5). The observation frequency ranges from once to twice daily, and corresponds to the synoptic times used in operational and retrospective analyses. Measurements are supposed to be available at least on certain standard levels, which are 1000, 850, 700, 500, 400, 300, 250 and 200 hPa in the troposphere.
IGRA does not constitute independent data : finding radiosoundings that are not as-similated in reanalyses is quite a challenge (Francis, 2002). Nevertheless, radiosoundings are important to check the internal consistency of the data assimilation schemes. There may be conflicts between in situ and remote sensing sources as in Grant et al. (2008) or the observations may be overridden by the model. Radiosoundings also have their limitations particularly in dry and supersaturated conditions (Connolley and King, 1993; Miloshevich et al., 2006). In certain cases, the assimilation procedure may be justified in giving them little weight.
Before being archived in IGRA, soundings pass a number of quality control checks. The pressure, temperature and geopotential height variables receive a particular attention. How-ever, the specific humidity and winds, which are of special interest to us, did not undergo climatological checks in IGRA ; thus, we performed additional quality screens on these vari-ables to filter out extremely high values. For this purpose, we used the median as an indicator of central tendency and the interquartile range (IQR) as a measure of spread. Means and standard deviations are overly sensitive to outliers and yield artificially high thresholds. We computed the medians and IQRs for each calendar month to account for the variability due to the annual cycle. After subjective examinations of unnatural shifts and outliers in the time series and vertical profiles, we chose to remove values lying outside the range of ± 4 IQR from the median. Because the IQR of a Gaussian distribution is 1.35 times its stan-dard deviation, our criterion corresponds to approximately 5.4 σ. Although this threshold seems permissive, in the Arctic, it excludes 4.8% of the wind data and 5.5% of the humidity data. Additionally, we required the existence of values on at least five pressure levels before performing linear interpolations of the vertical profiles. Finally, we only considered stations with at least 85% of days with valid soundings over the entire period, which led us to discard 11 sites in the Arctic. Such a threshold would leave us with no data in Antarctica : in Chapter 3, we detail an ad hoc procedure to deal with the gaps in the observation records.
To avoid a sampling bias, we only compared simultaneous observations and reanalysis values. The co-location of reanalysis data with radiosonde sites was performed via bilinear interpolation. In the Arctic, before we averaged a variable over the radiosonde sites, we first grouped the stations in eight 45◦ longitudinal sectors. We averaged the variable within these longitudinal bands after which the averaging was applied over the bands. In this manner, the data-rich regions (such as Europe) are not given an unfair emphasis. We were also concerned that our filters would be biased against intense moisture events because they exclude exceptionally high values of humidity and wind. However, in Table 1.2, the mean meridional moisture fluxes in reanalyses over the radiosonde sites are only slightly reduced by the subsampling.

Computation of the fluxes

To calculate the moisture budget of a given region we integrate the moisture balance equation (Eq. 1.5). We must resort to finite differences to compute the divergence and this introduces an error, pointed out by Seager and Henderson (2013). ERA Interim happens to provide a vertically integrated moisture convergence product calculated in spectral space on model levels. Over Greenland, it deviates by 0.3% from the finite differences result ; even less over the Arctic Ocean. When we compute the water budget over a polar cap, say the region north of 70◦N, the divergence term simplifies to : ZZ Z div(q~u) ds = − Z Z qv dλ (1.6) φ>70◦ 0 −π 0 where ds is a surface element, φ latitude, λ longitude and v the meridional wind.
Up to now, we have assumed that the transport of water took place exclusively in the gas phase. In the transition from Equation 1.4 to Equation 1.5, we implicitely assumed that the vertical integral of the condensation per unit mass was precipitation. Indeed, the condensed phases, liquid and frozen, only make a fraction of the total column water : 0.9% north of 60◦N and 1.5% south of 60◦S according to ERA-Interim. Few datasets provide the condensed water fraction on model levels and to our knowledge, no study has evaluated their impact on the water transport up to now (Table 1.3).
The condensed water fluxes are extremely variable from one dataset to the next. For the polar cap north of 70◦N, the estimates from JRA 25 and NCEP CFSR vary by a factor of three, over Greenland by fifty. Unlike humidity, the liquid and frozen water fractions are not assimilated by the reanalyses (as far as we know). They are dependent on the forecast model’s individual microphysics schemes. CFSR has the most intense condensed water fluxes : they make for 19.6% of the total water fluxes to Greenland. If moisture advection is used as a proxy for net precipitation on the ice sheet, it is critical to include fluxes of liquid and frozen water as well. The proportion of condensed water fluxes is higher for smaller domains like the Greenland ice sheet or the Antarctic plateau. In larger domains, most of the precipitated water was imported as vapour and condensed later, inside the domain boundaries. To keep the datasets comparable, we only consider water vapour fluxes in the remainder of the manuscript.
Under the hydrostatic approximation, the use of pressure as a vertical coordinate greatly simplifies the equations by removing the density term (e.g. Equation 1.2). However, the numerical models use a different type of vertical coordinate. The conversion from “model levels” to “pressure levels” involves interpolation, a first source of error. What’s more, the sea level pressure during an anticyclone may be higher than the first pressure level, 1000 hPa, hence the near surface information is lost. Conversely, the surface pressure over orography is bound to be lower than 1000 hPa : the pressure levels below the surface must be masked or filled with fictitious values. In Figure 1.8, the blue pressure levels intersect the grey profile of Greenland yet the lowest level does not make it to the sea. At the South Pole Station on the 1st of January, 2010, the surface pressure was approximately 700 hPa : in some datasets, the specific humidity profile was extended to 1000 hPa using different conventions (Figure 1.9).
Whenever possible, it is preferable to make the numerical vertical integrations on model levels. In the forecast models of the first generation reanalyses, the vertical is divided in σ -coordinates. σ is simply the ratio of the pressure at a given level to the surface pressure. In NCEP NCAR R1 and NCEP DOE R2, σ ranges from 0.995 to 0.00273. If the surface pressure is 1000 hPa, this corresponds to 995 hPa for the first level and 2.73 hPa for the last. Whatever the surface elevation or the weather conditions, the σ-coordinates follow the terrain, just like the red curves in Figure 1.8. This ensures that the lowest layers of the atmosphere are properly represented in the model. Unfortunately, σ-coordinates cannot do justice to the stratosphere – which is higly strat-ified as its name suggests – but pressure levels would be ideal. Starting with JRA 25, all the later reanalyses are produced on hybrid σ-pressure levels (so-called η levels), a compromise between the two systems. For any time t and location defined by latitude φ and longitude λ, the kth η level is defined as pk(φ, λ, t) = Ak + Bk ps(φ, λ, t) (Stepaniak, 2008). All the Ak and Bk are constants. The Bk correspond to the σ variable, starting near 1 for the lowest levels and decreasing with altitude, eventually vanishing in the mid-stratosphere (pure pressure levels). The Ak correspond to the pressure increments which are zero near the surface (pure σ -levels) but gradually set the pace as the altitude increases. The JRA 55 archive provides three dimensional data on η levels only : we used the preceding relation to convert it to pressure levels via linear interpolation.
The thickness of an η level is obtained using half levels, designated by half-integer indices : Δpk = pk+.5 − pk−.5. k ranges from 1 (the highest level) to K (closest to the surface). The vertical integral of any variable f(p) is then approximated by : Z ps f(p)dp ≈ N f(p)(Ak+.5 − Ak−.5 + (Bk+.5 − Bk−.5) • ps) (1.7)
Ideally, the numerical vertical integrations should be made on model levels. For NCEP NCAR R1, NCEP DOE R2, NCEP CFSR and JRA 25, we only had specific humidities and winds on pressure levels, from p0 = 1000 hPa to pN = 200 hPa (300 hPa for NCEP NCAR R1) ; above these levels, moisture concentrations become negligible. The value of the variable on the lowest pressure level above the ground was taken to be the value of the variable at the surface. Let pn0 be that level. The vertical integral of any variable f(p) was approximated following the trapezoidal rule :
ps N−1 1 (f(pn+1) + f(pn))(pn − pn+1) + f(pn0 )(ps − pn0 ) (1.8)
Z0 f(p)dp ≈ n=n0 2
Fluxes on model levels are available in ERA Interim, MERRA and JRA 55 and can be compared with the pressure level estimates. In all four regions considered, the relative differences in mean moisture convergence are below 4% and as low as 2% for the polar cap north of 70◦N. The effects of the various numerical approximations are summarised in Table 1.4.
We reorganise Equation 1.8 to make the weight given to each level more apparent.  ps f(p)dp ≈ f(pN ) pN−1 − pN n=0
To avoid the influence of fictitious underground values, we use these weights in our temporal and spatial averages, as in : 1 R t2 p , t w t ) d t q(pn) = t1 q(t2 nw )(t)nd(t (1.10) where pn is a given pressure level and the overbar signals a temporal average between times t1 and t2.
To elucidate which time scales contribute most to the net moisture imports, we decom-pose the winds and humidity into mean and fluctuation (denoted by primes) using monthly averages to filter the synoptic transients as in Peixóto and Oort (1992). For a given loca-tion and altitude, the mean moisture flux breaks down into two terms, one due to transient eddies, the other to the mean flow : qv = q,v, + q¯v¯ (1.11)
Other applications of the Reynolds decomposition to the atmospheric moisture transport to the polar regions can be found in Groves and Francis (2002), Oshima and Yamazaki (2006), Newman et al. (2012), Tsukernik and Lynch (2013) and Liu and Barnes (2015a), on individual datasets. Following Peixóto and Oort (1992), we introduce additional notations to refer to the zonal mean, [q], and the vertical mean on pressure levels, {q}, and the deviations therefrom, q◦ and q∗. After vertical and zonal averaging of the meridional flux, we further decompose the mean flow term :
{[ qv¯]} = {[q,v,]} + {[¯q∗v¯∗]}
(1.12)
+{[¯q]◦[¯v]◦} + {[¯q]}{[¯v]}
The first term on the right hand side groups the contribution of small-scale, short-lived, “transient eddies,” including extratropical cyclones. The second term is the product of the zonal anomalies of the mean humidity and wind fields which are designated as “stationary eddies.” For instance, in the North Atlantic at 70◦N, the air is particularly moist and the meridional wind is particularly strong compared to other longitudes. The third term on the right-hand side corresponds to the product of vertical anomalies in the zonally symmetric time mean humidity and wind fields, known as “vertical cells” by reference to the overturning circulations of the Hadley, Ferrel and polar cells. The fourth and last term should be zero because there is no net mass flux into a closed region on yearly time scales. We will test this assumption shortly.
Equation 1.12 involves the meridional wind averaged along time, longitude and over the full height of the atmosphere. For most reanalyses, our wind data is limited to an altitude of pN = 200 hPa, i.e. four fifths of the mass of the atmosphere. To cover the last fifth, we would need three times the current amount of vertical levels. Indeed, as shown in Table 1.1, we only use one third of the available levels, at least for the modern reanalyses. We can circumvent this problem by invoking the conservation of mass. We integrate Equation 1.2 over the polar cap north of latitude φ0 on the horizontal, and between the top of the atmosphere (0 hPa) and pN on the vertical.

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Table of contents :

Introduction 
1 Data and methods 
1.1 Reanalyses
1.2 Radiosoundings
1.3 Computation of the fluxes
2 Moisture advection to the Arctic 
2.1 Spatial structure
2.2 Long-term moisture budgets
2.3 Role of the mean flow and transient eddies
2.4 Seasonal variability
2.5 Interannual variability
3 Moisture advection to Antarctica 
3.1 Spatial variability
3.2 Long-term moisture budgets
3.3 Role of the mean flow and transient eddies
3.4 Seasonal variability
3.5 Interannual variability
4 The role of cyclones in moisture advection 
4.1 Temporal scale decompositions
4.2 Contribution of individual cyclones
4.3 Contribution of all cyclones
Conclusions 
Bibliography 
List of Figures
Appendix

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