# The role of cyclones in moisture advection

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## 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 70N, the divergence term simplifies to : ZZ >70 Zps 0 div(q~u)dp g ds = − Z − Zps 0 qv dp g   (1.6).
where ds is a surface element, latitude, 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 caps north of 60N, 70N, the Arctic
Ocean defined in Serreze et al. (2006) and the Greenland ice sheet defined in Cullather and Bosilovich (2011). caps south of 60S, 70S, the Antarctic ice sheet (smoothed boundary in red, excludes ice shelves) and plateau (elevation 2250 m), as in Palerme et al. (2014).
60N and 1.5% south of 60S 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 70N, 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.

### Long-term moisture budgets

Table 2.1 and Figure 2.5 present the terms of the moisture budget in the different datasets for four regions : north of 70N, north of 60N, the Arctic Ocean and the Greenland ice sheet. The mean moisture convergence through 70N is remarkably consistent between the seven reanalyses studied because they are constrained by common observations despite different model settings and resolutions. The minimum value (187 mm year−1) is given by JRA 25 and the maximum (203 mm year−1) by MERRA. In line with our findings in the previous section, the fluxes derived from radiosondes (Serreze et al., 1995) or computed from satellite data (Groves and Francis, 2002) tend to be lower than the reanalysis values. Estimates of precipitation and evaporation are more scattered among datasets ; net precipitation computed from model physics ranges from 95 mm year−1 (NCEP DOE R2) to 244 mm year−1 (NCEP CFSR). The interdataset standard deviation for net precipitation is 45 mm year−1 compared to 5.1 mm year−1 for transport.
Predictably, no reanalysis succeeds in closing the moisture budget, with the largest mismatch found in NCEP DOE R2, where the moisture convergence exceeds net precipitation by 52%. This mismatch is smaller in the other datasets (although still 34% for MERRA). CFSR exhibits the most intense water cycle. Net precipitation is higher than the moisture convergence only in CFSR and JRA 55.
For the polar cap north of 60N, the results of Bengtsson et al. (2004a) using ERA-Interim from 1989 to 2005 are congruent with our estimates from 1979 to 2013 for evaporation and transport but not precipitation (7% relative difference). Our precipitation estimates were computed as accumulated values by the numerical weather prediction model between the initialisation and the first twelve hours of forecast. Bengtsson et al. (2004a) preferred a time window shifted 18 hours from the analysis to avoid the model spin-up effects. At such lead times, net precipitation (physics output method) overshoots the transport estimates (aerological method).
We performed a similar budget analysis for the Arctic Ocean and the Greenland ice sheet. Atmospheric moisture convergence represents an important source term in the Arctic freshwater budget impacting ocean stratification, convection, the intensity of the thermohaline circulation and the formation of sea ice (Serreze et al., 2006). For Greenland, net precipitation along with meltwater runnoff and blowing snow determine the surface mass balance of the ice sheet (Ettema et al., 2009; Burgess et al., 2010). Despite the warnings from Bengtsson et al. (2011), integrating fluxes on pressure levels has only a moderate impact on the results even over these complex domains (Table 1.4). The maximum relative error (3.8%) is found in MERRA over the Arctic Ocean. Even when applying the same time window (1979-2005), we were unable to reconcile our estimate of the moisture convergence over the Greenland ice sheet using MERRA (393 mm year−1) with that of Cullather and Bosilovich (2011) (459 mm year−1). This mismatch does not apply to precipitation and evaporation.

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#### Role of the mean flow and transient eddies

We now turn to the analysis of the moisture transport into the Arctic using the decomposition given by Equation 1.11. Figure 2.6 shows the climatological mean moisture transport due to the mean flow and transient eddies as represented in ERA Interim. Driven by the westerly winds, the mean flow is largely responsible for the zonal component of the total transport.
The transient eddy flux is one order of magnitude weaker but is nearly exclusively meridional suggesting its dominant contribution to the poleward advection of moisture. However, the mean flow flux is not consistently zonal ; it has relatively small meridional components.
Given the large magnitude of the mean flux, it also contributes to the moisture advection toward or away from the Arctic. For example, approximately half of the total northward flux over the storm tracks is due to the mean flow component.
Over the Canadian archipelago and Strait of Denmark, the mean flow transport imparts a southward direction to the total transport, offsetting the effect of the transients. The explanation is found in Peixóto and Oort (1992) and the standing wave pattern the authors identified in the mean tropopause winds. One of the two troughs is located East of the American continent implying southward winds over Canada and northward winds over the Baffin Bay and the Greenland Sea. Over Canada, these southward winds extend to the surface, so the mean flow flux in this region is also southward. Over the Strait of Denmark, the high northward winds advect a small amount of moisture compared to the southward surface winds associated with the Icelandic low, because the air is more humid near the surface. As a result, the vertically integrated mean flow flux is directed south between Greenland and Iceland.

Long-term moisture budgets

With fewer observations to constrain the analysed fields, we cannot expect to find a similar agreement between datasets in the Antarctic as in the Arctic. On the other hand, the analysis increment should be reduced due to the smaller amount of new information to accomodate. This is indeed what the figures in Table 3.1 suggest. Unlike the Arctic, precipitation is generally higher than evaporation plus advection, but only by 25% in the worst case (JRA 25 over the Antarctic Plateau). This can be be seen in Figure 3.6 by comparing the left and right bar of each reanalysis. The evaporation in NCEP NCAR R1 is unrealistically large (Hines et al., 1999) and still excessive in NCEP DOE R2 (Bromwich et al., 2011). In the latest reanalyses, it is barely positive, with net sublimation in JRA 55.
The 60S latitude circle covers only ocean ; the Antarctic Plateau covers only land. The 70S parallel briefly crosses the Antarctic Peninsula and intersects large swaths of East Antarctica so it could count as “piecewise homogeneous” terrain. On the boundaries of the ice sheet however, the moisture fluxes experience substantial changes of magnitude and direction over short distances. This translates in the ratio of the inter-dataset standard deviation to the inter-dataset mean : 4 % at 60S, 3% at 70S, 11% for the ice sheet and 7% for the plateau despite its radical climate. CloudSat does not reach latitudes south of 82S, which justified a separate table, adapted from Palerme et al. (2014). The different variables are close to one another over the whole ice sheet. The difference between net precipitation and atmospheric water convergence is of the same order of magnitude as the liquid precipitation ( 10 mm year−1).

Temporal scale decompositions

The two previous chapters have shown the predominant contribution of transient eddies to the moisture transport to the high latitudes : 90-92% at 70N, 84-145% to the (smoothed) Antarctic ice sheet. Now we would like to delve deeper into the meaning of this statistic. How dependent is it on the choice of a temporal threshold ? How does it compare to spectral methods ?
Our original purpose was to identify the mechanisms responsible for moisture advection : we wanted to know which time scales contributed the most to the transports. Let [0,A] be the period of study, in our case 35 years and qv the mean moisture flux at a given location and altitude. a = A/N is a shorter time scale e.g. a month, and N the number of months in period A. What is the contribution of time scales shorter than a to qv ?
By analogy with fluid mechanics, the Reynolds decomposition lends itself to the study of turbulence on synoptic scales. For a given month n 2 J0,NK, we divide any variable, say q, into its monthly mean and monthly anomaly : q = hqin + q, where hqin = 1 a Z (n+1)a na q dt and q, = q − hqin (4.1) Since q and v are correlated, the mean of their product is not the product of their means but hqvin = hqinhvin + hq,v,in. The remaining term is the “eddy” flux : hq,v,in = 1 a Z (n+1)a na (q − hqin)(v − hvin) dt.

Introduction
1 Data and methods
1.1 Reanalyses
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
3.1 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
Bibliography

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