Sublimation on the Greenland Ice Sheet from Automated Weather Station Observations

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 1

PDF Version of Accepted Paper (Note some symbol errors may exist, i.e. delta symbol is converted to ?) Sublimation on the Greenland ice sheet from automated weather station observations

Jason E. Box and Konrad Steffen

Cooperative Institute for Research in Environmental Sciences University of Colorado, Boulder, Colorado, USA

Abstract. Greenland Climate Network (GC-Net) surface meteorological observations are used to estimate net surface water vapor flux at ice sheet sites. Results from aerodynamic profile methods are compared with eddy correlation and evaporation pan measurements. Two profile method types are applied to hourly data sets spanning 1995.4 to 2000.4. One method type is shown to accurately gauge sublimation using two humidity and wind speed measurement levels. The other “bulk” method type is shown to underestimate condensation, as it assumes surface saturation. General climate models employ bulk methods and, consequently, underestimate deposition. Loss of water vapor by the surface predominates in summer at lower elevations, where bulk methods agree better with two-level methods. Annual net water vapor flux from the two-level method is as great as -87 ±27 mm at 960 m elevation and -74 ±23 mm at equilibrium line altitude in western Greenland. At an undulation trough site, net deposition is observed (+40 mm ±12). At the adjacent crest site 6 km away and at 50 m higher elevation, net sublimation predominates. At high-elevation sites, the annual water vapor flux is positive, up to +32 ±9 mm at the North Greenland Ice core Project (NGRIP) and +6 ±2 mm at Summit. Sublimation is mapped using trend surface fits to calculated sublimation in terms of elevation and latitude. The resulting ice sheet total sublimation is -0.62 ± 0.25 x 1014 kg yr-1 for the two-level profile method and -1.2 ± 0.65 x 1014 kg yr-1 for the one-level method, indicating 12% or 23% precipitation loss, respectively. Monthly, seasonal, and annual sublimation grids and the mapping functions are available on the internet at http://cires.colorado.edu/steffen.

1. Introduction Determining ice sheet mass balance components is important because major changes in their dimensions affect climate and sea level throughout the world [Patterson, 1994; Oerlemans, 1993]. Variations in sublimation/evaporation on the Greenland ice sheet influence accumulation rates by removing snow and ice and/or by adding mass by deposition/condensation. Thus the mass balance of the ice sheet is sensitive to water vapor fluxes. The magnitude of the net water vapor flux to and from the ice sheet surface, however, is a relatively poorly known component of the mass balance. In situ evaporation studies have spanned too short of periods to derive an annual total sublimation/evaporation flux. As a consequence, only modeling studies have attempted to map Greenland ice sheet sublimation [Ohmura et al., 1999]. Fortunately, sufficient in situ observations now exist from the Greenland Climate Network (GC-Net) [Steffen et al., 1996; Steffen and Box, this issue] to quantify the Greenland ice sheet surface net water vapor flux. Previously, sublimation and evaporation measurements have been made during a succession of spring and summer expeditions on the Greenland ice sheet. Lister [1961] made detailed energy balance and ablation stake measurements in northeast Greenland during the 1953 ablation season. Evaporation rates in late summer were up to 3 mm d-1, accounting for 34% of the available energy for melting. Sublimation was a small quantity in early summer, with increased values during windy periods of active melt. After the melt period, evaporation decreased to a small quantity. Ambach [1977] concluded that no more than 2% of the net ablation results from evaporation in the melt zone of western Greenland. Evaporation calculated by the latent heat flux (QE) used 12% of the total energy available for melt, with radiation being the predominant energy source. The Geological Survey of Greenland (GGU) made ablation measurements on the Nordbogletscher and Qamanarssup Sermia outlet glaciers during 1979-1983 and 1980-1986 [Olesen and Braithwaite, 1989] and Braithwaite and Olesen [1990]

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 2 used the data to calculate ablation by the same approach as Ambach [1977]. They compared their results to stake measurements on the two glaciers. The latent heat flux values were near zero on average, with substantial daily fluctuations between positive and negative flux values (evaporation and condensation, respectively). Surface energy balance measurements were made in southwestern Greenland in the ablation zone from within the tundra to a point 90 km from Sondrestrøm Fjord, near equilibrium line altitude as part of the Dutch Greenland Ice Margin Experiment (GIMEX) [Oerlemans and Vugts, 1993]. On the basis of GIMEX data for a site at equilibrium line altitude in July 1991, it was shown that evaporation absorbs 25% of the energy that would otherwise be available for melting [Henneken et al., 1994, 1997]. At the Swiss Eigendissische Techniche Hochschule (ETH) and University of Colorado (CU) “Swiss Camp,” located at the mean equilibrium line altitude in western Greenland, the magnitude of the latent heat flux (6 W m-2) corresponded to -19 mm of net water vapor flux for the period June 3 to August 13, 1991 [Ohmura et al., 1994]. They state that the latent heat of vaporization of this magnitude corresponds to 140 mm of melt if used exclusively for the melt, which is common on most of the high arctic and alpine glaciers. Therefore evaporation plays an important role in maintaining the ice sheet. Bøggild et al. [1994] measured and modeled the surface energy and mass balance on the Storstrømmen glacier and determined that steeper slopes were where peak sublimation rates occur due to katabatic wind acceleration. At the Swiss Camp, turbulent heat flux measurements throughout the onset of melt indicate that sublimation rates were largest at the onset of melt, with values up to 1 mm d- 1 [Steffen, 1995]. Latent heat flux was recognized as an important sink of sensible heat. In an effort to derive the precipitation rate for Greenland, based on the spatial accumulation distribution, Ohmura et al. [1999] employed high-resolution T106 global climate models ECHAM 3 and ECHAM 4 to estimate sublimation rates above 1500 m elevation with evaporation below 1500 m provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) model. They estimate the annual total evaporation from the Greenland ice sheet to reduce the mass input from precipitation, 590 km3 yr-1 by 74 km3 yr-1, or 12.5%. The Antarctic climate serves as an analogue of the Greenland climate in the context of sublimation. In the strong katabatic wind region of Antarctica at Mizuho Station, sublimation was important to the surface mass balance, according to 1 year of 12-hourly evaporation pan measurements [Fujii and Kusunoki, 1982]. Evaporation pan measurements at Dome Fuji, Antarctica, indicate that sublimation from the atmosphere to the surface is a significant accumulation mechanism [Kameda et al., 1997]. Katabatic winds accelerate greatly as the surface slope angle increases from the ice sheet plateau toward the coast. The divergence of the wind stream promotes the formation of blue ice regions in Antarctica due to sublimation [Bintanja, 1999]. Similar to Ohmura et al. [1999] for Greenland, Van-den-Broeke [1997] used the T106 ECHAM3 general climate model to map Antarctic ice sheet sublimation. Sublimation was recognized as important to surface mass balance near the coast and, in particular, in blue ice zones where low surface albedo values provide more absorbed solar energy to drive sublimation. In a study of blowing snow sublimation, based on an elevation transect of automatic weather station data from Terre Adélie, Antarctica, up to 170 mm yr-1 blowing snow is sublimated in coastal areas [Bintanja, 1998]. On the ice sheet plateau, blowing snow sublimation was negligible to the surface mass balance due to low air temperature and wind speeds. The present study aims to present sublimation rates for locations on the Greenland ice sheet which are representative of different elevation and latitudinal zones, using Greenland Climate Network data. This analysis represents, at most, a 5-year time span, from mid-1995 to mid-2000, and therefore should be taken in that context. Annual statistics are included to illustrate interannual variability. The technique to calculate the latent heat flux in this study is by aerodynamic profile methods. These rely upon accurate measurements and simulation of vertical heat, moisture, and momentum differences and the characterization of turbulent transfer using established theory. Methods of previous studies that have assessed ice sheet sublimation using long-term automatic weather station data sets for Antarctica [Stearns and Weidner, 1993; Bintanja, 1998] are included here. Two types of aerodynamic profile methods are employed in this study. The first method type uses humidity measurements at one level and assumes that the surface is saturated with respect to water vapor, i.e., 100% relative humidity. Evaporation schemes based on a saturated surface are commonly used in general climate simulations for ocean and ice land surface types [Piexoto and Oort, 1992] because model simulations often lack the in situ information to define the vertical humidity profiles in the lowest 10 m of the atmosphere. A second type of profile method is used in this study, one that measures the vertical moisture differences with humidity sensors at two levels above the surface. This study proceeds to show the differences in the resultant sublimation rates from one-level and two-level methods. The two-level methods are shown to represent deposition more accurately, and it becomes

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 3 clear that one-level or two-level methods provide different results for the total ice sheet sublimation estimate. Hence the validity of surface moisture exchange parameterizations over ice sheets by contemporary general climate models is brought into question

2. Data As of mid-2000, the Greenland Climate Network (GC-Net) consists of 20 automatic weather stations (AWS) distributed primarily in the accumulation zone of the ice sheet [Steffen et al., 1996; Steffen and Box, this issue] (Figure 1) (Table 1). More than 50 station-years of hourly data from 16 GC-Net locations spanning mid 1995 to mid 2000 are employed in this study. Instrument heights are between 0.1 and 5 m from the surface, depending on local accumulation rate and tower extensions. GC-Net AWS measurements include temperature, humidity, and wind speed at two levels spaced 1.2 m apart. These and surface height measurements are the primary data employed in this study (Table 2).

2.1. Instrument Accuracy and Calibration GC-Net instruments are factory calibrated. Nonetheless, on-site relative temperature, humidity, and wind speed calibrations are made to increase relative accuracy of profile measurements. The mean deviation from one sensor to the other is reduced using the inverse of the percent mean deviation during a calibration period of 7 to 24 hours. Field calibrations are set to represent the relative bias between the profile instruments over a range of local conditions. It must be noted that the relative accuracy of profile measurements is greater than the absolute accuracy. Corrections based on calibration data are less than 3% in relative humidity and wind speed data and less than 2% for temperature data. Deviations between profile sensors placed at the same height are normally distributed.

2.2. Scaling Humidity Sensors for Subfreezing Temperatures GC-Net AWS employ a Vaisala INTERCAP 50YC temperature/humidity sensor (Vaisala, Oy, Finland). The instrument incorporates the INTERCAP in a capacitance bridge followed by both temperature compensation and linearization circuits to give a final output voltage proportional to relative humidity (RH) over a -40°C to 50°C temperature range. The INTERCAP humidity sensor measures relative humidity scaled with respect to liquid water. For meaningful humidity measurements at temperatures below 0°C, the raw data must be rescaled to reflect saturation with respect to ice. A theory and method to rescale such RH values for saturation with respect to ice is provided by Anderson [1994]. The conversion is made in two steps. The first step is to multiply each RH reading by the ratio of saturation vapor pressure with respect to water over that with respect to ice at a given air temperature. In the second step, the humidity readings are offset with reference to the maximum output of the sensor for temperatures in 1 K intervals. The 98th percentile of each sorted bin is taken as the maximum output of the sensor, since occasional spuriously high readings can occur in the course of 1 year for a given temperature. Makkonen [1996] pointed out that this theory neglects super saturation with respect to ice. Supersaturation is ignored in this analysis, owing to the inability of this instrument to measure supersaturation and the rarity of its occurrence [Anderson, 1996]. During saturation at cold temperatures, i.e., T < -30°C, the range in RH values is no greater than 3%. The same range is taken as the instrument absolute accuracy after rescaling.

2.3. Eddy Flux Correlation Measurements

The eddy flux correlation method (ECM) is a standard technique to directly sample atmospheric turbulent energy and mass fluxes [Stull, 1988]. Wind velocity is measured using speed of sound variations and air density changes with temperature. Air temperature variations are measured using a 0.08 mm chrome-constantan fine wire thermocouple. Humidity variations are measured using the Campbell Scientific KH20 instrument that relates water vapor concentration to its attenuation of ultraviolet radiation from a krypton gas light source. Vertical water vapor mass fluxes are derived from the covariance of vertical and horizontal wind velocity fluctuations (in this case measured by the Campbell Scientific CSAT-3D ultrasonic anemometer) and that of heat or a chemical admixture, e.g., water vapor. The ECM is considered more accurate than techniques that relate averaged temperature, wind speed, and humidity profiles to turbulent heat fluxes [Oke, 1987]. Eddy correlation measurements used in this study have been made at Swiss Camp in 1999 and 2000. These measurements are employed

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 4 as a means of validation of latent heat flux or sublimation and evaporation estimates derived from the GC-Net profile measurements.

2.4. Evaporation Pan Measurements Evaporative mass transfer is directly inferred by measuring weight changes of an isolated volume of snow or solid ice [Kameda et al., 1997]. During May 31 to June 8, 2000, sublimation/evaporation was measured using 190 mm wide x 100 mm deep clear Pyrex glass pans containing snow samples. The pan weights were measured twice daily, primarily during melt conditions and when there was no blowing snow. Wind speed often exceeded 8 m s-1 during the experiment. The air temperature range was -12°C to +0.5°C. One 12-hour measurement of mass gain was associated with nighttime frost deposition. The two daily measurements were set to corresponded with the commonly observed summertime diurnal cycle of water vapor flux, i.e., of mass loss between 0600 to 1800 local time and mass gain 1800 to 0600 local time. Measurements made on this schedule capture the largest mass changes relative to the accuracy of the balance.

2.5. Accumulation Data Sublimation estimates from the GC-Net are compared with accumulation rates derived from ice cores collected at GC-Net sites [Moseley-Thompson et al., this issue] to determine the relative magnitude of sublimation to accumulation. To determine precipitation loss or enhancement by surface water vapor fluxes, sublimation is divided by the “effective precipitation”, i.e., net sublimation plus accumulation. Precipitation estimates based on regional climate modeling [Chen et al., 1997; D. H. Bromwich et al., unpublished data, 2001 (hereinafter referred to as B2001)] are also included in the analysis for a comparison with the implied precipitation rates.

3. Methods To determine sublimation and evaporation rates from profile measurements, the direct relationship between the mass transfer of water vapor (?m) and the amount of latent heat transfer to or from the atmosphere by the phase changes of H2O is employed:

Dm = -QEDt / LrL , (1)

-2 where QE is the latent heat flux (W m ), ?t is the time interval (s), L is the latent heat, either for vaporization (2.501 x 106 J kg-1) when the surface is melting or the latent heat of sublimation, the sum 6 -1 of latent heat of fusion and vaporization (2.834 x 10 J kg ) when the surface is frozen, and ?L is the density of water (1000 kg m-3). ?m is presented in units of millimeters water equivalent depth. The selection of the latent heat of sublimation is made for temperatures below –17.5°C, based on a rough estimate of the availability of ice condensation nuclei [Knight, 1979]. The sensitivity to a random ±7.5 K uncertainty is less than 1% of the mean sublimation, as shown later. Following common convention, energy fluxes in the surface boundary layer are defined with reference to the atmosphere. Upward heat fluxes associated with sublimation are taken as positive. The aerodynamic profile theory has been discussed in a number of text books: Munn [1966], Brutsaert [1982], Oke [1987], Arya, [1988], Monteith and Unsworth [1990], and Garratt [1992], while Patterson [1994] states its application to glaciology. Two profile methods were selected after evaluating five in comparison with eddy flux correlation measurements. The two selected methods fall into two categories, based on whether they employ humidity and wind speed measurements at two levels or at one level. One level methods (1LMs) are commonly used because often only one humidity and wind speed measurement level is available. 1LMs assume that the surface is saturated with respect to ice or water, i.e. 100% relative humidity. 1LMs still require temperature measurements on at least two levels to calculate atmospheric stability and to -4 estimate the surface specific humidity. A surface roughness parameter (z0 » 5 x 10 m) must be assumed by 1LMs to define the wind speed profile. The selected 1LM employs an iterative stability correction based on Lettau [1979] and Stearns and Weidner [1993] and defines the surface temperature by estimating the near-surface sensible heat flux. Estimating the surface temperature in this manner is slightly less uncertain than doing so by an extrapolation of the observed temperature profile, as with other 1LMs evaluated. The two other 1LMs are a bulk drag coefficient method after Brutsaert [1982] and a one humidity level and a two-level wind speed method used by Ishikawa et al., [1992]. The three 1LM results were very similar. The method of Stearns and Weidner [1993] was chosen for discussion

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 5 of Greenland results with Antarctic results. The selected two-level method (2LM) is the so-called “K- theory” formulation described by Munn [1966]. This K theory is a simplified version of the “bulk aerodynamic profile method” [Oke, 1987]. The latter method was evaluated, but performed more erratically than the K theory. In general, 2LMs are believed to be more accurate to calculate net surface sublimation because they sample the in situ vertical moisture differences and do not depend on surface temperature, and surface humidity assumptions of 1LMs. The frequency of condensation, or deposition, occurrences is much greater for 2LMs than for 1LMs, because for the latter method, the lower profile level is forced to be saturated. The 1LMs only detect deposition in extreme temperature inversion cases, when it is possible for specific humidity above the surface to exceed that at a saturated surface. It is commonly assumed that the relative humidity at a snow surface is 100%. This is probably the case for melting. However, in subfreezing conditions, observations indicate that undersaturation of the air near a snow/ice surface occurs [Schmidt, 1982]. Both method types are outlined in detail below. Measurements are made in the “constant flux layer” where diffusion is assumed constant with height. During field experiments at Mizuho Station, Antarctica, momentum flux decreased by only 2% between 2.5 and 30 m [Inoue, 1989]. Turbulence measurements at 2, 10, and 30 m above the surface at the mean equilibrium line altitude in western Greenland, at Swiss Camp, indicate that the similarity assumptions are generally valid for moderately stable conditions [Forrer and Rotach, 1997]. However, within the blowing snow layer near the surface, the assumption of constant fluxes with height may be invalid due to internal sensible and latent heat flux sinks and sources [Bintanja, 2000]. Fortunately, the height range where the majority of the heat flux divergence occurs, i.e., in the lowest 50 cm, where the greatest snow drift concentration occurs, is not within the layer sampled by the AWS profile measurements. The AWS profile is in the height range from 1.5 to 3 m above the surface. The vertical water vapor flux is not sampled unless the moisture passes up or down through the measurement profile. Solid particles in suspension which are transported through the profile will not be accounted for in net surface sublimation estimates. On the basis of the results of four state of the art blowing snow models, the blowing snow sublimation rate above 3 m, once blowing snow is developed, represents only 10% to 20% of the total sublimation from the surface to the 100 m height [Xiao et al., 2000]. In the first minute of blowing snow development, the proportion of sublimation above 3 m is greater. However, the sublimation rates and particle concentration above 3 m in the first simulation minute are much less than at 60 min, when the blowing snow is completely developed. Over the course of the 1-hour averaging of 15 s samples by the AWS, net vertical moisture flux, including that due to blowing snow sublimation passing through the sensor profile, should be captured by the profile measurements. Furthermore, the thickness of the sampled layer is sufficiently small (1.2 m) to assume a constant flux with height.

3.1. Selection of Input Data A set of input data selection criteria reduced the occurrence of spurious latent heat flux values that would bias monthly means and annual net sublimation. Occasional errors in the profile data occur as the result of rime ice on anemometers, solar overheating of passively aspirated temperature sensors, and electrostatic discharge. Only cases when wind speed increases with height were selected and fluxes are calculated for wind speeds greater than 1 m s-1. Such low wind speeds sometimes are associated with spurious wind speed profile differences that can result in unrealistically large profile-based turbulent flux estimates. Data gaps associated with these cases are interpolated linearly. The extremely small turbulent fluxes that occur at wind speeds less than 1 m s-1 nonetheless have an insignificant influence on monthly to annual net sublimation totals. Times when air temperature exceeded 0.5°C were omitted, as they usually result from overheating of temperature sensors under low wind speed and high solar irradiance. Large spikes in the data caused by electrostatic discharge were removed using a variance threshold of 3 standard deviations from the daily mean of 24-hourly observations. Monthly and annual statistics are generated if at least 90% of data from the time period are available. Temperature, humidity, and wind sensor heights are calculated hourly using the average of the two acoustic instrument surface height measurements. The resultant instrument height changes are validated by instrument height remeasurements made during site maintenance visits. The root-mean-square error of instrument heights was 0.04 m.

3.2. Corrections to Turbulent Heat Fluxes and Atmospheric Stability The surface stability variation has to be known for calculating latent heat flux from aerodynamic profile methods, as the profile theory is derived from neutral stability considerations. When stability is

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 6

either stable or unstable, stability functions for momentum and water vapor (FM and FE) are applied to decrease or increase the vertical flux, respectively. The so-called gradient Richardson number (Ri) is used as a measure of the stability [Garratt, 1992]:

g Dq Dz -1 R = v , (2) i -1 2 q v (DuDz ) where g is gravitational acceleration (9.81 m s-2), is the average virtual potential temperature q v between instrument level 1 and 2 (K), Dqv is the virtual potential temperature difference, level 2 minus level 1 (K), Dz is the difference in profile heights (m), Du is the difference in wind speed (m s-1). When warm air overlies cooler air, buoyant destruction (dq/dz > 0) dominates turbulent shear production (du/dz), and the atmosphere is stable (Ri > 0); that is, the surface layer is resistant to turbulent transfer. Numerous stability function parameters have been derived empirically based on field experiments. Garratt's [1992] text provides a summary of the experimental results to that point in time. Stability functions for stable and unstable conditions have been proposed by Webb [1970] and Dyer and Hicks -1/2 -1/4 [1970], respectively. The stability functions are (1-bRi) and (1-gRi) for unstable and stable conditions, respectively, where g = 16 and b = 5. The parameters g and b vary in the literature [Garratt, 1992]. More recent values from [Högström, 1988] do not differ greatly from earlier values. The observations of Forrer and Rotach [1997] suggest that the use of stability functions from Webb [1970] and Dyer and Hicks [1970] with profile data alone, i.e. no complimentary eddy correlation data, is sufficient to estimate the turbulent surface fluxes to an acceptable accuracy for the general conditions encountered during their 3.5 month spring/summer Greenland ice sheet experiment. In this study, another slightly different form of the stability functions is taken [Steffen and DeMaria, 1996], where g = 18 and b = 5.2. As FM is often not equal to FE [Smeets et al., 1998], Steffen and DeMaria [1996] used FM / 1.3 for extremely unstable cases (Ri < -0.03). The uncertainties associated with extremely unstable and stable conditions do not differ greatly for the majority of AWS sites and conditions encountered on the ice sheet because their frequency of occurrence is generally small (Table 3). The stability characteristics of complete annual records for GC-Net sites are investigated. Stable conditions (Ri > 0) are predominant (Table 3). A greater frequency of stable conditions and extremely stable conditions (Ri > 0.1) is observed at higher-elevation sites (Summit, NGRIP) and for sites on the eastern slope of the ice sheet (NASA-E and NASA-SE). Extremely stable conditions occur at low temperatures and are associated with very small turbulent heat fluxes. In the limit as Ri approaches 0.2, atmospheric turbulence is completely dampened [Garratt, 1992], and turbulent fluxes are effectively zero. Unstable conditions occur in summer due to solar heating of the surface and under low level cloud conditions when longwave sky radiation can heat the surface [Ohmura et al., 1994]. Unstable conditions can also occur for periods of cold air advection. Extremely unstable conditions (Ri < –0.05) occur, in general, between 0% and 4% of the year. Figure 2 shows representative annual stability frequency distributions. The situation at Humboldt illustrates the common predominance of stable conditions for most ice sheet locations. At Tunu-N, at an equivalent elevation and latitude, unstable cases are almost nonexistent. This northeast slope site is colder and has more persistent high pressure and less precipitation [Ohmura et al., 1999; B2001]. The associated clearer skies explain the greater frequency of stable conditions at Tunu-N as compared to Humboldt. At Summit the annual distribution is broader. This may be explained in the context of the weaker winds [Steffen and Box, this issue] at this site as compared to lower elevation sites. A curious stability distribution is found for DYE-2. The annual stability distribution is skewed toward negative values, indicative of frequent unstable conditions. On-site instruments and calibration have been checked and the two pairs of temperature sensors imply that the instability is not instrument related. Solar overheating of the instruments is also not expected to be significant in early spring, when much of the instability is observed. It may be significant that DYE-2 is windier than normal for a site at this elevation and that strong winds amplify Ri calculations.

3.3. Two-Level Profile Method The following two-level profile formulation is based on the familiar Thornthwaite and Holzman [1939] flux-gradient theory, in which a first-order turbulence closure approximation is made. Simplification to the complete formulation is made assuming that the turbulent diffusion is represented sufficiently by the eddy diffusivities of the air [Munn, 1966; Stull, 1988]. This is the so-called K theory.

éæ q - q ö æ u - u öù Q Lu 2 K ç 2 1 ÷ ç 2 1 ÷ , (3) E = -r * êç ÷ ç ÷úF M F E ëè z2 - z1 ø è z2 - z1 øû

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 7

-3 where ? is the air density (kg m ), z1 and z2 are instrument heights increasing upward (m), q is the -1 -1 specific humidity (kg kg ), u is the wind speed (m s ), and FM and FE are stability corrections described above. K is the ratio of eddy diffusivities for momentum and water vapor. There is some experimental evidence to suggest that for neutral conditions, this ratio is equal to 1.35 [Stull, 1988], and, in fact, this constant produces diurnal fluctuation amplitudes that agree with two eddy correlation experiments at Swiss Camp in 1999 and 2000, shown below. Under blowing snow conditions in the Antarctic, Budd et al. [1966] found that the friction velocity -1 -1 (u*, in m s ) was related to the 10 m wind speed (u10, in m s ) according to

u10 , (4) u* = 26.5

Although the use of the observed wind speed profile to determine u* directly would seem to be preferable to the use of an empirical relation, errors in two-level wind speed differences lead to greater u* errors than produced by (4), which is set to only depend on one wind speed level. Wind speed profile errors are caused by rime frost, ice, or obstruction of the wind stream by the tower. Quality control procedures were applied to the data in an effort to remove such errors. However, some errors have persisted. The effect of errors in the wind speed differences is large when input into u* formulations that depend on the wind speed difference between two levels. Using more than two levels leads to smaller errors. Owing to the fact that GC-Net AWS have no more than two wind speed measurement levels, the wind speed at one level was used to determine u*. The wind speed at a reference height (z) is related to the wind speed at a fixed height (z’), 10 m in this case, according to

-m u10 = uz (z / z') , (5) where z is taken as that of profile level 2 and m for aerodynamically smooth surfaces is 1/7 [Arya, 1988]. The results of (4) compare favorably with those derived from three-dimensional (3-D) eddy flux correlation measurements. The one- and two-level method results are compared with 3-D eddy correlation measurements in section 3.5 to asses the profile method accuracy.

3.4. One-Level Profile Method

Lettau [1979] developed wind speed and temperature profile factors, (yz) and (Yz), respectively, to define the departure of the profiles from their neutral form depending on atmospheric stability variations in the Antarctic ice sheet surface boundary layer. Stearns and Weidner [1993] employed an iterative correction based on these formulations to derive latent and sensible heat fluxes for Antarctic -4 AWS sites. Simplifications to the profile theory include a constant roughness length (z0 = 5 x 10 m) required to define the momentum flux given only a single wind speed measurement level. As part of the iterative process, an initial u* estimate is provided on the basis of the parameterization described above (equation (4)). Subsequent u* values are based on the logarithmic wind speed equation and wind speed profile departures from neutral derived by the iteration. Thus the stability correction for momentum is implicit in the final value of u*. The logarithmic wind speed profile is therefore

-1 u(z) = u*k [ln(z / z0 )-y z ], (6) where k is the Von Kármán constant (k @ 0.4) [Arya, 1988]. Lettau [1979] provides the lengthy set of (yz) and (Yz) functions not repeated here. The wind speed profile departure from neutral (yz) is greater than zero for stable conditions and thus reduces the wind speed profile curvature. Values of u* are solved by rearranging (6). In the initial case, yz is zero. To derive the temperature profile curvature (Yz) and ultimately the surface temperature, u* is used to calculate the sensible heat flux (QH).

(q 2 - q1 ) , (7) QH = -rC p u*k -1 ln z2 / z1 - Y2 + Y1

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 8

-1 -1 where Cp is the specific heat of the air (1005 J kg K ), ?1 and ?2 are the potential temperature (K) at levels z1 and z2, and Y1 and Y2 are the diabatic adjustments to the temperature profile developed from the iteration of QH and surface temperature ?(z0). Y1 and Y2 are not applied in the first iteration. The input parameter for Yz and yz is the Monin-Obukhov nondimensional stability parameter (?z):

3 -1 z z = -gkzQh (rC pTzu* ) , (8) where Tz is the air temperature (K) at height z. As with FM and FE, Lettau's stability corrections vary between stable and unstable conditions, z > 0 and z < 0, respectively. The process to calculate u* and -2 -1 then QH is repeated until the incremental change in QH is less than 0.01 W m . For winds above 6 m s , usually only one iteration is required. As the wind speed decreases to 3 m s-1, up to 10 iterations are required. The iterations serve to decrease (increase) the friction velocity during stable (unstable) conditions, resulting in a decrease (increase) in the latent or sensible heat flux, respectively. The iteration and heat flux was not calculated for cases of extreme stability (z > 0.2) because the iteration resulted in ever increasing sensible heat flux values due to an increase in the stability function in this open limit. The temperature profile is represented by

-1 q (z) -q (z0 ) = -q*k [ln(z / z0 )- Yz ], (9) and the scaling parameter for temperature (q*) is calculated using the sensible heat flux and the friction velocity.

-1 q* = QH (rC pu* ) , (10)

Finally, the surface temperature estimate is given using (9). The surface temperature is used to define the surface saturation vapor pressure and, in turn, the specific humidity needed for the 1LM latent heat flux (QE).

2 -1 QE = -ru* L[qz - q0 ]uz , (11)

-1 where qz and q0 (kg kg ) are the average specific humidities at height z and adjacent to the surface, respectively. The stability correction in (11) is accomplished by the iterative process described above.

3.5. Sensitivity of Profile Calculations

The sensitivity of profile theory based on latent heat flux (QE) calculations to measurement uncertainty is explored using random numbers. Gaussian distributions of 6000 random samples are scaled to represent the instrument uncertainty (e) such that 95% of the samples fall within the assumed uncertainty interval. Absolute instrument uncertainties are quoted from the manufacturer, and the relative accuracy is assessed from on-site calibrations described above. In the case of instrument height or pressure measurements the uncertainty is taken as the absolute accuracy. Simulating uncertainties by this approach allows the isolation of the QE uncertainty due to individual parameters and the estimation of the ensemble uncertainty due to all parameters, including feedbacks. Uncertainty is measured here as 1 standard deviation (s) of the perturbed QE output divided by the mean. In order of rank, the largest sources of uncertainty for the 2LM are relative humidity, temperature, and instrument height (Table 4). The ensemble QE uncertainty for the 2LM is estimated to be 31%. The ensemble uncertainty is 54% for the 1LM, primarily due to the fact that an order of magnitude roughness length uncertainty introduces a 49% 1s uncertainty in QE. Temperature uncertainty alone causes a 31% 1LM uncertainty. Random errors in temperature and instrument height both contribute to a positive skew in QE, while the effect of random errors in other variables is linear. The data in Table 4 represent average conditions associated with sublimation from the surface to the atmosphere. Within the range of expected conditions represented by several uncertainty simulations, it is evident that the uncertainty increases as the temperature, humidity, and wind speed differences decrease. Fortunately, as the sublimation rate decreases with decreasing vertical profile differences, large uncertainties in the two-level method

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 9 during winter, for example when the differences are very small, do not dominate monthly to annual sublimation estimates.

4. Results and Discussion First, the validation of profile methods is discussed. Then the sublimation climate is introduced by the observed characteristics of the vertical specific humidity differences. Sublimation rates derived by the latent heat fluxes are then discussed in the diurnal, monthly, and annual context. Finally, the geographic pattern of sublimation rates is described with results from a method to map sublimation for the entire Greenland ice sheet on an annual time frame. Uncertainties are based on the random error simulation, the assumption that measurement errors have been removed by quality control procedures [Steffen and Box, this issue], and residuals of monthly trend surface regressions discussed below.

4.1. Comparison of Profile Methods With Eddy Correlation and Evaporation Pans

At Swiss Camp, two springtime periods of eddy flux correlation (ECM) latent heat flux (QE) measurements from 1999 and 2000 are compared with QE calculated from the “bulk” one-level (1LM) and two-level (2LM) profile methods. The results of the comparison indicate that the 2LM compares better than the 1LM (Figure 3). The 2LM detects condensation/deposition, while the 1LM rarely indicates condensation/deposition. If the 1LM indicates condensation, it is too small. The means of the 2LM, compared with the eddy correlation, are within a few percent, while the 1LM exhibits a positive bias. Despite the robust nature of the 1LM, its positive bias makes the 2LM more desirable to evaluate the sublimation rates at the Greenland ice sheet surface. The fact that only one site was used to evaluate the accuracy of profile methods for all GC-Net sites is a weakness in this study. Future work will be concerned with making eddy correlation measurements at other sites in order to account for potential elevation or region-dependant parameters in aerodynamic profile methods. 1LM results are still featured throughout the paper to illustrate the effect of underestimating deposition. Furthermore, the result of the 1LM in this study provides a context with which to compare previous studies that employ 1LMs [Stearns and Weidner, 1993] or studies that apply the results of general climate models to ice sheets [Ohmura et al., 1999; Van-den-Broeke, 1997]. Evaporation pan results, compared with net vertical water vapor flux measured by eddy correlation in a spring 2000 experiment at Swiss Camp, verify the ability of eddy correlation to gauge surface evaporation and sublimation (Figure 4). Maximum weight change of -23 ± 4.8 g indicates a maximum 12-hour average latent heat flux of 48 W m-2 (-1.5 mm d-1). Uncertainties due to snow-sampling errors, voids in the sample or compaction of the sample, solar heating of the glass, and reduced snow ventilation due to pan sides, prevent the use of these data for precise absolute calibration of eddy correlation. Uncertainties in pan measurements are shown as the differences in values from two simultaneous side by side pan results. The ECM uncertainties have not been directly addressed in this study as the ECM is only taken here to represent a standard for profile methods.

4.2. Vertical Humidity Gradients The annual variation of monthly vertical water vapor differences indicates a tendency for sublimation from the surface to the atmosphere at midday, when solar radiation is absorbed at the surface. Midday is often characterized by greater water vapor concentration near the surface than at 1.2 m. Relatively small amounts of deposition are favored at night and during winter at sites above equilibrium line altitude by a water vapor difference directed toward the surface due to an increasingly predominant temperature inversion. During summer the vertical humidity differences that favor deposition are not uncommon at high-elevation sites (NGRIP and Summit). Water vapor differences in the ablation zone indicate the tendency for mass loss throughout the year with the exception of deposition cases associated with snowfall.

4.3. Hourly Variations in Sublimation Maximum sublimation from the surface to the atmosphere occurs when temperature and wind speeds are greatest. Furthermore, vertical temperature differences allow vertical specific humidity differences which in turn drive sublimation. Large vertical temperature differences do not persist during high winds without a heat source that provides energy to maintain a vertical temperature differential. Such energy fluctuations include solar radiation absorbed at the surface, radiative cooling, and warm or cold air advection. The largest sublimation occurs when melting reduces the surface albedo, allowing maximum

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 10 solar radiation absorption. In the case of snowfall, warm air advection occurs and a vertical humidity gradient directed toward the surface is set up to drive deposition/condensation. During storms associated with precipitation, there is often an initial water vapor flux to the surface. This is commonly followed by sublimation to the atmosphere as the air mass dries and winds persist. Radiative cooling at nighttime and in winter also leads to deposition. In the majority of daytime cases, the humidity gradient is directed from the surface to the atmosphere, indicative of water vapor transfer from the surface to the atmosphere. Summertime maximum values of hourly latent heat are 100 W m-2 (-0.13 mm h-1 sublimation) for ablation zone sites. The largest hourly latent heat flux from eddy correlation was 93 W m-2 in 1999. Hourly latent heat fluxes are less than 25 W m-2 at sites above 2000 m elevation, with the exception of a handful of cases associated with peak winds. The largest deposition rates, of +0.04 mm h-1 (-35 W m-2), associated with the onset of snowfall are observed at low-elevation sites. Such cases lasted for no more than a few hours. Extended periods of slight deposition (+0.9 to 4.7 mm month-1, -1 to -5 W m-2, respectively) are observed in high-elevation sites in winter. Sublimation rates show a distinct diurnal cycle in summer, during clear-sky conditions, due to surface heating and cooling driven by the cosine effect of diurnal solar elevation angle variations and the associated net irradiance fluctuations. The sensible heat flux responds to net radiation fluctuations. Changes in the sign of vertical temperature difference signals the change in sign of both the sensible and the latent heat fluxes. The latent heat flux is often opposite to the sensible heat flux, as much of the available sensible heat goes into sublimation during the day, especially before melt when much of the absorbed solar radiation goes into heating the surface instead of melting [Steffen, 1995]. At night, as the surface loses radiative energy, the sensible heat flux responds by supplying heat from the atmosphere. In this case, as a result of the temperature inversion, surface deposition is favored. A sensible heat flux from the surface to the atmosphere is occasionally observed under conditions of strong surface heating by solar radiation.

4.4. Sublimation Climatology Annual cycles of monthly mean latent heat flux and the corresponding sublimation rates are featured for representative sites (Figure 5). This graph illustrates interannual variability that is associated with temperature and wind speed anomalies. Relatively windy and warmer years result in greater sublimation from the surface to the atmosphere. Relatively calm years exhibit greater deposition rates, as stronger temperature inversions are observed and weak katabatic winds are unable to mix as much warm air from the temperature inversion to the surface to drive sublimation. Relatively large sublimation rates are observed at lower latitudes, resulting from longer and more intense ablation periods, while at the northern sites annual latent heat fluxes are small (Table 5). Monthly mean latent heat fluxes are as great as 17.0 W m-2 (-16 mm month-1) for June at the mean equilibrium line altitude at Swiss Camp. Down glacier from Swiss Camp, at JAR1, the June mean latent heat flux in 2000 was 35 W m-2 (-33 mm month-1). In other years, monthly fluxes are around 15 W m-2 (-12 mm month-1). At DYE-2 where substantial instability is observed, monthly mean fluxes peak in excess of 40 W m-2 (-41 mm month-1). At Summit and NGRIP, high on the ice sheet plateau where surface melting is effectively nonexistent, monthly fluxes are all less than 15 W m-2 (-14 mm month-1). At 2631 m, high on the eastern plateau at NASA-E, the annual range of latent heat fluxes is the smallest for the GC-Net with monthly values always less than 3 W m-2. At NGRIP and to a more limited extent at Summit, monthly latent heat fluxes are indicative of deposition, not only in winter but also occasionally in summer (Table 5, Figure 5). Summertime deposition is not observed for all years. On the basis of personal observation from both authors, it is apparent that small amounts of condensation occurring each day may add up to a significant contribution to the accumulation at Summit and NGRIP. The mass input from sublimation to the surface accounts for roughly 4 and 15% of the accumulation at NGRIP and Summit, respectively. The results from NGRIP and Summit are consistent with those from snow stake and evaporation pan measurements at Dome Fuji, Antarctica, also located at a topographic peak on the ice sheet (3810 m) [Kameda et al., 1997]. Net annual deposition is also evident at high- elevation sites in the north, Humboldt and Tunu-N, where deposition contributes approximately 4 and 28% to the accumulation, respectively. The large value at Tunu-N is the result of relative large deposition values promoted by a strong temperature inversion in winter and a low average accumulation rate of roughly 100 mm yr-1 [Moseley-Thompson et al., this issue]. To derive average annual sublimation mass fluxes based on profile methods, the annual variation of monthly mean latent heat fluxes and their resulting equivalent sublimation for all available data are integrated (Table 6). The largest annual sublimation rates are calculated to occur at DYE-2 (-181 mm yr-1). DYE-2 is located 300 km south of JAR1 and JAR2 and thus receives more intense solar radiation.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 11

The annual average wind speed is 6.6 m s-1 at DYE-2, second only to Swiss Camp (7.1 m s-1) and JAR1 (7.0 m s-1), both more than 1000 m lower in elevation [Steffen and Box, this issue]. The lowest elevation GC-Net sites, JAR1 and JAR2 also exhibit large net annual sublimation, in excess of -80 mm yr-1. Comparisons with Antarctic results from Dalrymple et al. [1966], Stearns and Weidner [1993], Van den Broeke [1997], and Kameda et al. [1997] indicate a similar regional and temporal pattern of sublimation to the Greenland ice sheet. Maximum Antarctic monthly mean latent heat fluxes based on -2 -2 the 1LM are between 10 and 30 W m . The largest negative monthly mean QE is reported as -5 W m [Stearns and Weidner, 1993]. However, larger negative QE would probably be detected using the two- level method of this study. The annual cycle of latent heat fluxes, exhibiting a summer sublimation peak and the tendency for a small net deposition throughout winter, is equivalent to Antarctic results. As with GC-Net sites, sublimation increases toward lower elevations and latitudes, particularly during summer, due primarily to elevation-temperature relationships, as temperature is an important driver for sublimation. Maximum annual sublimation was estimated to be -70 mm water equivalent on the Ross Ice Shelf at AWS Elaine [Stearns and Weidner, 1993]. Latent heat flux measurements from the 1958 South Pole micrometeorological program, by a two-level profile technique, indicate 2.5 mm deposition to the surface from autumn through spring [Dalrymple et al., 1966]. This study does not, however, include midsummer estimates which may have reduced the net annual deposition, as sublimation to the atmosphere is likely to occur in summer. Cumulative sublimation for 1986 from the South Pole AWS data for an 11-month period, using the one-level method followed in this study, was –33 mm [Stearns and Weidner, 1993]. The difference is largely attributed to the use of the 1LM which neglects the bulk deposition amount. Using the output of a 1.1° horizontal resolution general circulation model (ECHAM-3 T106), the annual cycle in sublimation is well reproduced in comparison with this 1LM AWS-based data [Van den Broeke, 1997]. However, deposition in the model is underestimated in winter as compared to the 1LM results. It should be restated that daily to annual sublimation estimates based on the 1LM are probably too high because of its inherent neglect of deposition. The ECHAM results suggest that 10-15% of the annual precipitation over Antarctica is lost through sublimation, an equivalent result to that of Ohmura et al. [1999] for Greenland. Van den Broeke [1997] notes that the ECHAM-3 model seems to underestimate deposition. The blowing snow sublimation parameterization in Bintanja [1998] yields -180 mm yr-1 at GC-Net site JAR1, for 1997 and 190 mm yr-1 in 1998. These totals are similar to the sum of 2LM profile method negative water vapor transfers, i.e., positive latent heat fluxes only. At other sites higher on the Greenland ice sheet, the parameterization values are much greater than the GC-Net profile-based estimates. It must be clarified that the parameterization gauges blowing snow sublimation loss only, while a profile method such as the 2LM measures the net sublimation, i.e., including the effect of water vapor pressure simultaneously directed toward and away from the surface. The strength of the water vapor gradient component directed toward the surface increases toward higher elevations due to a generally more developed temperature inversion at high-elevation sites. Thus these two techniques cannot be directly compared as they measure different quantities. An estimate of precipitation is made for sites without runoff by summing the net sublimation and the observed accumulation. At sites where sublimation augments accumulation, the sublimation value is subtracted from the accumulation to estimate the precipitation. Greenland precipitation, from the diagnostic model of Chen et al. [1997], is, on average, about 15% smaller than the precipitation rate estimated from the sublimation calculated from profile methods and accumulation from ice core date at GC-Net sites [Moseley-Thompson et al., this issue]. In a recent reanalysis, using the same diagnostic model, but with a more accurate topographic dataset [B2001], the modeled precipitation rates for Greenland sites have generally increased. The difference between estimated and modeled precipitation is now much smaller (5%). It should be noted, however, that snow redistribution by the wind may also be a source of accumulation in ice core data which is neglected by this comparison. The only site where blowing snow is certainly thought to contribute to accumulation is discussed in section 4.5.

4.5. Undulation Scale Sublimation Variability Sublimation rates vary substantially from one undulation crest site to its adjacent trough, AWS CP1 and CP2, respectively. CP2 is 40 m lower in elevation and 6 km up the flow line. CP1 is approximately 45° to the left of the prevailing wind flow from CP2. At the undulation trough, monthly latent heat fluxes based on the two-level method, more often indicate sublimation from the atmosphere to the surface, while at the undulation crest, the latent heat fluxes are more often indicative of net water vapor flux from the surface to the atmosphere. Some of the largest negative hourly latent heat fluxes, in the GC-Net data, -55 W m-2, are observed in January at CP2. The January 1998 average is –7.6 W m-2

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 12

(+ 7.2 mm). Surface height measurements and snow pits show that accumulation rates are roughly 40% greater at the trough site when compared to the crest site. The difference in annual sublimation explains roughly 18% of the 192 mm difference in accumulation between the two sites. The remaining difference in accumulation is thought to result from snow drift deposition into the undulation trough. These results raise an important issue in the placement of point measurements such as AWS and ice cores, given that large-scale representativity is sought. Consulting a high-resolution elevation map for prior knowledge of local slope angles may be a useful approach in determining representative sites.

4.6. Sublimation Mapping The observed latitude and elevation patterns of monthly net sublimation are used to construct seasonal and annual sublimation maps to quantify the Greenland ice sheet total and regional net water vapor mass transfer at the surface. Linear trend surface fits of monthly sublimation versus elevation and latitude were derived (Table 7). Monthly and annual mapping functions are given for 2LMs and 1LMs. Monthly sublimation residuals are as large as 9 mm month-1 in summer when sublimation is greatest. The GC-Net distribution is insufficient in the east to justify incorporating the longitude component to resolve any east-west slope differences. The Danish mapping center Kort and Matrikelstyrelsen (KMS) Greenland digital elevation model (DEM) [Ekholm, 1996; Bamber et al., this issue] and ice sheet mask are used as the input data set for sublimation mapping. A 13.7 km x 13.7 km equal area grid was interpolated from a latitude-longitude grid, using a distance-weighted average of elevation data that fell into a 15 km search radius. Sublimation values for sites below 560 m (5% of the ice sheet area and 13% of the net sublimation) are extrapolations. Seasonal and annual sublimation estimates are then totaled from the grid (Table 8) and annual maps are provided, based on the sum of monthly grids (Figure 6). Uncertainties in the grid data are based on the random uncertainty analysis of hourly latent heat flux calculations described above, plus a general 10% uncertainty based on the residuals of the trend surface fit. Thus the uncertainty of 2LM-based map results is 41 and 54% for 1LM maps. Note the underestimation of deposition for the 1LM map as compared to the 2LM map. The results for the lower elevations are in general agreement, within the mapping uncertainty, because deposition rates are much smaller at the lower elevations. Mass transfers in elevation bands and in facial zones can also be presented using this grid (Figure 7). Mapping functions imply that the annual maximum sublimation occurs near 64.1° N, 40.0° W, 120 m elevation, at the southern tip of Greenland, while maximum deposition occurs near 72.8° N, 37.4° W, 3250 m elevation (Table 8). On the basis of the annual 2LM map, there is a region of zero net sublimation at 2300 m elevation, near 82° N and 3000 m, near 71° N. South of 71° N, net annual sublimation is from the surface to the atmosphere at all sites on the Greenland ice sheet. The annual total ice sheet net sublimation is -0.62 ± 0.25 x 1014 kg yr-1 based on the trend surface fits to the two-level profile results and -1.2 ± 0.65 x 1014 kg yr-1 for the one-level results. The factor of 2 difference in the annual flux is due to the fact that about 87% of the ice sheet area lies above 1500 m, where water vapor deposition greatly influences the sublimation total. Monthly, seasonal, and annual 13.7 km sublimation/evaporation grids and the mapping functions are available online at http:// cires.colorado.edu/steffen. The net sublimation for Greenland in this study, according to the two-level method, agrees with the ice sheet total “evaporation” result from Ohmura et al. [1999]. However, the spatial distribution of sublimation in the two maps is quite different. Greater sublimation rates are found below 1000 m in the 2LM map, as compared to the Ohmura et al. [1999] map. The evaporation map based on the ECMWF reanalysis and the ECHAM 3 in the work of Ohmura et al. [1999], however, does not exhibit a region of net deposition, a result that is consistent with a conclusion of Van-den-Broeke [1997] that the ECHAM-3 model underestimates deposition for Antarctica, even when compared to the 1LM Antarctic results from Stearns and Weidner [1993], which probably also underestimate deposition, according to the 2LM results in this study. Sublimation values below about 500 m may be lower than featured in the maps because of greater cloud amount near the ice margin associated with marine cloudiness of the adjacent seas. Increasing cloudiness toward lower elevations is the case for the largest ice cap in Iceland [Oerlemans et al., 1999]. Furthermore, the katabatic wind may become decoupled from the surface at the lowest elevations on the ice sheet, as it does in East Antarctica [Bintanja, 1998]. Thus the sublimation at lower elevations may be overestimated by this mapping procedure and this in turn the total ice sheet sublimation value may be overestimated. This potential error will affect about 13% of the bulk estimate for 5% of the ice sheet area that exists below 560 m elevation.

5. Conclusions

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Over 50 station years of Greenland Climate Network automatic weather station data are used to estimate sublimation rates on the Greenland ice sheet. Results are presented for point locations and in the form of ice sheet sublimation maps. The maps are used to estimate the total net water vapor mass flux for the Greenland ice sheet surface. Methods that employ one or two humidity measurements levels are validated using eddy correlation measurements and evaporation pans. Methods that employ only one humidity measurement level underestimate deposition and have greater uncertainty than two- level methods, 54% and 31%, respectively. One level methods are consistent with that used in global and regional climate simulations. Therefore the climate models are susceptible to a similar bias and uncertainty. Sublimation rates are greatest in summer at low elevation sites. In winter, small amounts of deposition association with large surface temperature inversions are observed, particularly at high- elevation sites. Winter storm activity leads to substantial variability in sublimation rates for low- elevation sites. The diurnal cycle of sublimation is similar to the annual cycle. During midday, sublimation rates are at their maximum as a result of increasing vertical temperature and specific humidity differences. At night, deposition is favored, as the surface cools radiatively and a near-surface temperature inversion develops, driving a sensible heat flux from the atmosphere to the surface. A surface net flux of sensible heat or radiation creates the potential for net surface water vapor exchanges. During periods of melt, absorbed solar radiation provides the energy necessary to drive sublimation or evaporation from the surface to the atmosphere, while the katabatic wind provides turbulent mixing. Sublimation losses are greatest in summer and toward lower elevations and latitudes of the Greenland ice sheet. Annual net sublimation at GC-Net sites, according to the two-level method is as great as –87 ±27 mm water equivalent at 960 m elevation, in the Jakobshavn ablation region, -74 ±23 mm up glacier at equilibrium line altitude (1150 m), and from +40 ±12 mm to –82 ±25 mm in the zone between 1150 and 2200 m. On the ice sheet plateau, above 2200 m, annual net water vapor flux is often toward the surface, with a maximum value of +18 ±6 mm found at Summit. Sublimation rates are greater at an undulation crest AWS site relative to an adjacent trough site. At the undulation trough, monthly latent heat fluxes indicate condensation, while at the undulation crest, sublimation to the atmosphere is predominant. Surface height measurements show that accumulation rates are 40% greater at the trough site when compared to the crest site [Steffen and Box, this issue]. The difference in sublimation explains approximately 18% of the difference, while the remainder is thought to result from snow drift deposition into the undulation trough. These results raise an important issue in the placement of AWS and ice cores. Monthly elevation and latitude trend surfaces of sublimation are used to construct sublimation maps for the entire ice sheet to derive total annual and seasonal surface water vapor fluxes. The Greenland ice sheet total net sublimation is -0.62 ± 0.25 x 1014 kg yr-1 for the two-level profile method and is -1.2 ± 0.65 x 1014 kg yr-1 for the one-level method. With the ice sheet accumulation total of 5.16 x 1014 kg yr-1 [Ohmura et al. 1999], ice sheet precipitation loss by sublimation is 12 and 23%, respectively. The net sublimation for Greenland in this study, according to the two-level method, agrees with the result from Ohmura et al. [1999]. However, the spatial distribution of sublimation in the two maps is quite different. Greater sublimation rates are found below 1000 m in the two-level maps as compared to the Ohmura et al. [1999] map. Monthly, seasonal, and annual 13.7 km sublimation grids and the mapping functions are available on line at http:// cires.colorado.edu /steffen. Uncertainties associated with hourly 1LM and 2LM results are substantial, 41 and 31%, respectively. Longer-term figures, such as monthly means and annual sublimation totals, should suffer less from instantaneous uncertainties. The weakest link of our preferred method, the two-level method is the assumption of the ratio of the eddy diffusivities. We use the comparison of 2LM latent heat fluxes with eddy correlation to establish the skill of this method in measuring sublimation (Figure 3). One-level methods are shown to underestimate deposition, while 2LMs yield a more realistic result. More sophisticated simulations of blowing snow sublimation that separate surface and blowing snow sublimation as separate quantities should offer more insight into the problem. The relative proportion of sublimation that occurs in situ, at the surface versus beneath the snow surface, aloft during blowing snow, and that which is imported from air upstream needs to be addressed in future research.

Acknowledgments. We acknowledge NASA Polar Oceans Division for funding the GC-Net AWS for the past 5 years. NSF OPP has sponsored two AWS sites in the north of Greenland. The Summit, NGRIP, and DYE-2, GITS, and NASA-U sites were accessible with NSF supported flights from the 109th ANG LC-130H, Scotia, NY, USA. Thanks to PICO and VECO staff and NGRIP personnel for logistics support. N. Cullen maintained eddy correlation measurements in 1999 and 2000. Personal communication with P. Calanca, and critical insight from the reviewers, is greatly appreciated.

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Ohmura, A., T. Konzelmann, M. Rotach, J. Forrer, M. Wild, A. Abe-Ouchi, and H. Toritani, Energy balance for the Greenland ice sheet by observation and model computation, in IAHS Publ., Snow and Ice Covers: Interaction With the Atmosphere and Ecosystems, edited by H. Jones, T. Davies, A. Ohmura, and E. Morris, 223, 85-94, Int. Assoc. of Hydrol. Sci., Gentbrugge, Belgium, 1994. Ohmura, A., P. Calanca, M. Wild, and M. Anklin, Precipitation, accumulation, and mass balance of the Greenland ice sheet, Z. Gletsch. Glazialgeol., 35(1), 1-20, 1999. Oke, T., R., Boundary Layer Climates, 435 pp., Methuen, New York, 1987. Olesen, O. B., and R. J. Braithwaite, Field stations for glacier climate research, West Greenland, in Glacier Fluctuations and Climate Change, edited by J. Oerlemans, pp. 219-233, Kluwer Acad., Norwell, Mass., 1989. Patterson, W. S. B., The Physics of Glaciers, 480 pp., Pergamon, New York, 1994. Piexoto, J. P., and A. H. Oort, Physics of Climate, 520 pp., Am. Inst. of Phys., College Park, Md., 1992. Schmidt, R. A., Vertical profiles of wind speed, snow concentration, and humidity in blowing snow, Boundary Layer Meteorol., 23, 223-246, 1982. Smeets, C. J. P. P., P. G. Duynkerke, and H. F. Vugts, Turbulence characteristics of the stable boundary layer over a mid-latitude glacier, part I, A combination of katabatic and large-scale forcing, Boundary Layer Meteorol., 87(1), 117-145, 1998. Stearns, C. R., and G. A. Weidner, Sensible and Latent heat flux estimates in Antarctica, in Antarctic Meteorology and Climatology: Studies Based on Automatic Weather Stations, Antarct. Res. Ser., 61, edited by D. H. Bromwich and C. R. Stearns, 109-138, AGU, Washington, D.C., 1993. Steffen, K., Surface energy exchange at the equilibrium line on the Greenland ice sheet during onset of melt, Ann. Glaciol., 21,13-18, 1995. Steffen, K., and J. Box, Surface climatology of the Greenland ice sheet: Greenland Climate Network 1995-1999, J. Geophys. Res., this issue. Steffen, K., and T. DeMaria, Surface energy fluxes of arctic winter sea ice in Barrow Strait, J. Appl. Meteorol., 35(11), 2067-2079, 1996. Steffen, K., J. Box, and W. Abdalati, Greenland climate network: GC-Net, CRREL, pp. 98-103, Cold Reg. Res. and Eng. Lab., Hanover, N. H., 1996. Stull, R. B., An Introduction to Boundary Layer Meteorology, 666 pp., Kluwer Acad., Norwell, Mass., 1988. Thornthwaite, C. W., and B. Holzman, The Determination of evaporation from land and water surfaces, Mon. Weather. Rev., 67, 4-11, 1939. Van den Broeke, M. R., Spatial and temporal variation of sublimation on Antarctica: Results of a high-resolution general circulation model, J Geophys. Res., 102, 29,765-29,777, 1997. Webb, E. K., Profile relationships: The log-linear range, and extension to strong stability, Q. J. R. Meteorol. Soc., 96, 67-90, 1970. Xiao, J., R. Bintanja, S. J. Déry, G. W. Mann, and P. A. Taylor, An intercomparison among four models of blowing snow, Boundary Layer. Meteorol., 97(1), 109-135, 2000.

______J. E. Box and K. Steffen, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO, 80309-0216, USA. ([email protected]; [email protected]).

(Received July 31, 2000; revised April 25, 2001; accepted May 1, 2001.)

Paper number 2001JD900219. 0148-0227/01/2001JD900219$09.00

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 16

Figure 1. Greenland Climate Network (GC-Net) locations referred to in the text.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 17

Humboldt Tunu-N ] % [

y c n e u q e r F

Summit DYE-2 ] % [

y c n e u q e r F

Ri [dimensionless] Ri [dimensionless] Figure 2. Annual histograms of stability (Ri) at representative GC-Net sites for 1998. Values beyond dashed lines from zero indicate cases for which stability functions are not well defined.

Figure 2. Annual histograms of stability (Ri) at representative GC-Net sites for 1998. Values beyond dashed lines from zero indicate cases for which stability functions are not well defined.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 18

1LM 1999

2LM 1999 ] 2 - m

W [

) E Q (

x u

l May 25 May 27 May 29 May 31 June 02 June 04 F

a 1LM 2000 e H

t n e t a L

2LM 2000

May 21 May 23 May 25 May 27 May 29 May 31 June 02 June04 Eddy Correlation Profile Methods

Figure 3. Latent heat flux from profile methods and eddy correlation.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 19

1.0 Pan A: 0.5 Pan B: ] 1 - d

m 0 m [

n o i t a

l -0.5 e r r o C

y -1.0 d d E -1.5

-2.0 -1.5 -1.0 -0.5 0 0.5 1.0 -1 Evaporation Pan [mm d]

Figure 4. Comparison of 12-hourly evaporation pan results with eddy correlation measurements at Swiss Camp (69° 34’ 06” N, 49° 18’ 57” W, 1149 m), May 31 to June 8, 2000.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 20

1995 1996 1997 1998 1999 X 2000

Swiss Camp Humboldt ] 1 - h t ] n 2 - CP1 Summit o m m

W m [

) m E [

Q n (

o i x t i u s l o F

JAR1 CP2 p t e a e D / H n

t o i n t e a t a m i L l b

Saddle NGRIP u S

Figure 5. Annual cycle of monthly mean latent heat fluxes and sublimation representative sites based on the two-level profile method. The dotted line indicates ± 1 standard deviation of hourly data in the monthly mean.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 21

1-level Annual Method Sublimation 80 N 72 W

76 N

16 W

60 W 72 N 20 W

24 W 68 N 28 W

56 W 32 W

36 W

40 W

52 W

48 W 44 W 2-level Annual Method Sublimation 80 N 72 W

76 N

16 W

60 W 72 N 20 W

24 W 68 N 28 W

56 W 32 W

36 W

40 W

52 W 48 W 44 W

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 22

Figure 6. Greenland sublimation maps based on two types of aerodynamic profile calculations applied to the Greenland Climate Network data set.

1LM 2LM ] 1 - a

g k [

n o i t a m i l b u S

t e N

Elevation [m] Figure 7. Sublimation versus elevation for the Greenland ice sheet based on one-level and two-level aerodynamic profile methods. The dotted line indicates the 54 and 41% uncertainty, respectively.

Figure 7. Sublimation versus elevation for the Greenland ice sheet based on one-level and two-level aerodynamic profile methods. The dotted line indicates the 54 and 41% uncertainty, respectively.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 23

Table 1. GC-Net Site Information Station Latitude and Longitude Elevation Installation Number of Number of (m) Date Yearsa Yearsb Swiss Camp 69° 34’ 06” N, 49° 18’ 57” W 1149 1995.38 3.3 3.3 CP1 69° 52’ 47” N, 46° 59’ 12” W 2022 1995.39 2.1 3.2 NASA-U 73° 50’ 31” N, 49°, 29’ 54” W 2369 1995.41 3.1 3.9 GITS 77° 08’ 16” N, 61° 02’ 28” W 1887 1995.43 2.5 2.5 Humboldt 78° 31’ 36” N, 56° 49’ 50” W 1995 1995.47 3.3 4.3 Summit 72° 34’ 47” N, 38° 30’ 16” W 3254 1996.37 2.3 2.8 Tunu-N 78° 01’ 00” N, 33° 59’ 38” W 2113 1996.38 1.9 3.5 DYE-2 66° 28’ 48” N, 46° 16’ 44” W 2165 1996.4 3.8 4.2 JAR1 69° 29’ 54” N, 49° 40’ 54” W 962 1996.47 4.1 4.1 Saddle 66° 00’ 02” N, 44° 30’ 05” W 2559 1997.3 3.0 3.0 South Dome 63° 08’ 56” N, 44° 49’ 00” W 2922 1997.31 0.5 1.6 NASA-E 75° 00’ 00” N, 29° 59’ 59” W 2631 1997.34 1.8 2.0 CP2 69° 54’ 48” N, 46° 51’ 17” W 1990 1997.36 0.9 2.5 NGRIP 75° 05’ 59”N, 42° 19’ 57” W 2950 1997.52 2.0 2.0 NASA-SE 66° 28’ 52” N, 42° 19’ 20” W 2425 1998.3 1.8 1.8 JAR2 69° 25’ 12” N, 50° 03’ 27” W 568 1999.4 1.3 1.3 a refers to data availability for two-level method and b to the one-level method.

Table 2. GC-Net Instruments Employed in this Study Parameter Instrument Instrument Accuracy Sampling Interval Air Temperature Vaisala 50YC 0.1 °C 60 s (Campbell Sci. CS-500) Air Temperature Type-E Thermocouple 0.1 °C. 15 s Relative humidity Vaisala INTERCAP or 5% < 90% RH 60 s Vaisala HUMICAP 180 3% > 90% RH -1 Wind speed* RM Young 05103 0.1 m s 60 s*, 15 s Station pressure Vaisala PTB101B 0.1 hPa 60 min Surface height change Campbell Sci. SR-50 1 mm 10 min Multiplexer Campbell Sci. AM-25T - - Data logger Campbell Sci. CR-10/10X - - * sampling interval changed to 15 s in 1999.

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Table 3. Annual Stability Characteristics at GC-Net Sites for Complete Years R > 0 R < 0 |R | < 0.001 R > 0.1 R < -0.05 Site Year i i i i i % % % % % Swiss Camp 1999 74 22 16 2 3 CP1 1999 72 23 31 1 1 NASA-U 1998 64 33 5 3 7 GITS 1996 52 46 5 3 6 Humboldt 1997 82 16 5 3 2 Humboldt 1998 78 21 3 4 4 Humboldt 1999 91 8 2 6 2 Summit 1999 83 17 1 20 5 Tunu-N 1997 97 3 1 11 1 Tunu-N 1998 89 10 5 5 1 Tunu-N 1999 75 23 7 2 3 DYE-2 1997 77 22 5 6 5 DYE-2 1998 41 57 4 3 22 DYE-2 1999 28 70 5 2 18 JAR1 1997 80 15 5 1 1 JAR1 1998 91 8 16 0 1 JAR1 1999 75 23 10 1 3 Saddle 1999 61 32 8 7 3 South Dome 1998 72 25 22 9 2 NASA-E 1998 76 21 10 18 4 CP2 1998 79 19 2 3 2 NGRIP 1998 85 14 11 18 7 NGRIP 1999 78 22 1 9 7 NASA-SE 1999 64 32 5 12 7

Table 4. Standard Deviations of Latent Heat Flux Calculations Based on Random Errors 1LM 2LM 1s 1s Parameter Q Q Relative uncertainty Absolute uncertainty E QE E QE Control 20.6 0 23.8 0 0 0 Temperature 20.4 6.3 24.4 4.7 ±0.1K 1K Relative humidity 21.5 3.5 19.1 4.6 ±2% 3% Wind speed 20.6 1.5 22 3.8 ±0.2 m s-1 1 m s-1 Instrument height 20.8 0.6 23.2 3.4 ±0.03 m ±0.05 m Pressure 20.6 > 0.1 23.8 > 0.1 N/A ±1 hPa Roughness length 21.2 10.4 N/A N/A ±0.005 m ±0.05 m Stability corrections 22 4.9 19.2 2.4 f(T,u,q,P) f(T,u,q,P) Latent heat 20.8 0.2 24 0.3 N/A ±7.5°C Using e of all parameters 22.1 12 23.7 7.3 N/A N/A

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Table 5. Monthly Latent Heat Fluxes at GC-Net Sites Based on Two-Level Profile Method Site W m-2 Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Net, Year mm Swiss mean 0.5 -1.6 4.1 0.5 15.5 17.0 7.7 7.7 6.9 0.5 7.3 9.0 1997 -74 Camp sd 7.4 2.0 5.4 10.4 20.5 13.2 10.5 9.8 8.8 5.2 11.3 13.7 CP1 mean -6.7 -1.6 -3.5 -1.0 -3.4 10.3 7.3 3.4 3.5 -1.2 -3.6 -8.7 1997.5- 5 sd 8.9 5.8 8.2 12.4 19.4 12.9 13.8 12.4 9.6 5.9 5.8 8.9 1998.4 NASA-U mean -0.1 -0.5 0.4 9.8 16.7 18.9 17.1 11.1 7.5 0.0 -0.9 -2.7 1998 -73 sd 3.8 1.5 3.4 17.7 23.0 21.6 18.6 16.1 13.4 3.4 6.5 3.1 GITS mean 1.8 -1.0 3.2 1.7 11.3 19.9 14.0 21.0 2.4 0.0 0.7 0.0 1996 -71 sd 5.2 5.4 6.0 5.4 16.3 18.3 17.8 37.2 6.8 5.9 6.4 12.3 Humboldt mean -1.0 -1.1 -0.2 0.4 0.2 4.9 4.0 -1.3 -1.4 -1.3 -1.7 -1.9 1998 0 sd 6.8 1.2 2.6 12.9 4.4 10.7 9.5 7.3 11.5 5.9 7.2 2.6 Summit mean -4.2 -1.4 -1.8 -1.1 3.1 2.2 2.8 -0.1 -0.2 -0.4 -3.6 -1.4 1996.4- 6 sd 8.0 2.3 3.8 4.7 12.7 7.1 9.1 4.6 3.0 1.4 6.9 3.5 1999.5 Tunu-N mean -1.6 -0.9 -0.7 -3.8 -2.8 4.3 6.5 0.0 -9.0 -5.7 -2.8 -4.7 1997- 20 sd 5.6 1.0 0.7 3.8 4.7 9.4 11.0 6.9 17.3 6.9 4.0 4.7 1998 DYE-2 mean -6.0 -1.7 2.2 4.2 10.0 47.5 17.8 10.2 9.3 0.9 -2.7 -4.5 1997 -82 sd 16.2 1.6 9.5 14.5 10.1 36.6 29.2 27.2 18.9 10.9 8.4 10.2 JAR1 mean 11.6 3.1 10.1 4.3 10.4 5.0 1.6 4.0 5.6 4.8 14.3 11.1 1997 -82 sd 29.9 8.3 19.0 9.2 10.5 5.7 3.0 6.7 12.3 10.2 25.3 23.1 JAR1 mean 15.5 2.1 3.5 16.7 8.7 5.3 4.5 1.0 9.1 3.1 11.2 10.1 1998 -87 sd 30.1 6.9 6.9 21.5 10.5 5.7 9.2 6.5 13.1 10.7 18.6 18.2 Saddle mean -6.4 -2.7 -1.7 5.0 17.0 13.1 8.4 13.2 6.6 0.4 0.8 2.6 1998 -53 sd 5.8 3.5 7.4 19.9 26.4 22.2 24.3 26.7 16.8 3.8 2.7 5.6 Saddle mean 1.5 1.9 3.4 2.2 11.3 13.4 24.5 16.4 0.6 -0.7 -1.2 -1.1 1999 -68 sd 3.1 4.9 8.2 7.4 20.8 18.5 28.1 21.5 9.7 3.4 2.3 1.8 South mean 12.6 7.2 -7.8 6.6 -1.4 7.0 1999 * * * * * * * Dome sd 23.9 22.5 24.8 29.1 13.4 12.3 NASA-E mean -0.3 -0.1 0.3 -0.8 -0.6 2.4 0.6 -2.7 -1.8 -1.0 -0.5 -1.7 1997.4- 6 sd 0.3 0.2 1.1 0.4 2.5 6.9 5.2 11.5 3.2 2.4 0.5 2.6 1998.5 CP2 mean -7.6 -3.6 -3.0 -2.5 0.6 1.6 4.6 0.6 -4.0 -7.6 -11.4 -9.9 1997.4- 40 sd 12.7 6.0 7.7 23.2 18.5 19.0 17.2 15.6 21.1 14.3 22.2 13.0 1998.5 NGRIP mean -2.4 -0.7 -0.1 -4.1 -4.1 -6.7 -4.0 -5.4 -2.3 -1.2 -0.8 -1.9 1998 32 sd 3.7 1.2 0.5 4.3 3.7 6.8 4.6 6.5 4.0 2.5 3.2 3.7 NASA- mean -3.3 -3.1 -0.8 -3.9 -7.5 -4.5 3.6 4.5 1.1 -0.3 -1.1 -1.1 1999 15 SE sd 8.0 6.2 4.5 8.3 15.7 15.3 14.3 18.8 9.9 3.6 6.0 1.4 JAR2 mean 1.7 1.5 1.5 4.1 3.4 23.0 3.2 6.8 7.3 4.3 1.4 3.2 1999.8- -61 sd 4.7 6.8 6.4 10.4 8.3 21.4 5.7 9.3 12.3 8.7 6.7 8.7 2000.7 * insufficient data.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 26

Table 6. Net Annual Sublimation at GC-Net Sites Based on All Available Data 1995-2000 1LM 2LM Site -1 -1 (mm w e yr ) (mm w e yr ) Swiss Camp -89 ±36 -64 ±20 CP1 -48 ±19 -60 ±19 NASA-U -35 ±14 -29 ±9 GITS -29 ±12 -59 ±18 Humboldt -18 ±7 5 ±2 Summit -10 ±4 18 ±6 Tunu-N -21 ±8 28 ±9 DYE-2 -63 ±25 -186 ±58 JAR1 -138 ±55 -114 ±35 Saddle -28 ±11 -31 ±10 South Dome -35 ±14 * NASA-E -16 ±6 5 ±2 CP2 -75 ±30 38 ±12 NGRIP -8 ±3 8 ±2 NASA-SE -30 ±12 9 ±3 JAR2 -166 ±66 -50 ±16 * insufficient data.

BOX AND STEFFEN: SUBLIMATION ON THE GREENLAND ICE SHEET 27

Table 7. Latitude and Elevation Gradients of Sublimation From Profile Methods Month Latitude Intercept r2 Elevation intercept r2 Gradient [mm] Gradient [mm] [mm deg-1] [mm km-1] 1LM Jan 0.101 -8.131 0.04 2.33 -4.87 0.59 Feb 0.091 -7.307 0.05 2.14 -4.47 0.64 Mar 0.095 -7.695 0.06 2.11 -4.41 0.73 Apr 0.498 -39.783 0.17 6.22 -12.99 0.75 May 0.386 -33.462 0.19 4.53 -9.46 0.79 Jun 0.629 -56.64 0.13 10.22 -21.33 0.91 Jul 0.477 -44.455 0.13 7.67 -16 0.92 Aug 0.35 -31.231 0.14 5.29 -11.04 0.89 Sep 0.434 -35.588 0.12 6.8 -14.19 0.82 Oct 0.169 -13.725 0.05 3.87 -8.07 0.7 Nov 0.121 -9.876 0.04 2.93 -6.12 0.61 Dec 0.144 -11.573 0.05 3.37 -7.04 0.66 Annual 0.291 -24.956 0.10 4.79 -9.998 0.75

2LM Jan 0.013 -1.529 0.07 3.23 -8.3 0.51 Feb 0.113 -9.937 0.10 1.22 -3.92 0.52 Mar 0.033 -16.869 0.11 1.63 -2.97 0.53 April 0.204 -32.964 0.06 3.21 -9.63 0.68 May 0.651 -62.249 0.14 5.19 -4.03 0.62 June 0.388 -74.677 0.11 7.43 -25.14 0.73 July 0.137 -45.122 0.08 4.26 -16.2 0.62 Aug 0.548 -73.022 0.28 2.91 -10.58 0.62 Sept. 0.338 -51.976 0.16 3.71 -11.59 0.69 Oct. 0.339 -38.063 0.26 1.59 -5.09 0.66 Nov. 0.233 -22.246 0.05 2.89 -7.68 0.59 Dec. 0.281 -25.064 0.11 2.88 -7.31 0.55 Annual 0.273 -37.81 0.13 3.36 -9.37 0.61

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Table 8. Seasonal And Annual Total Greenland Ice Sheet Evaporative Mass Transfer Time Period Profile Net Total Mass Transfer Grid Maximum Net Grid Maximum Net Method (x 1012 kg yr-1) Sublimation (mm) Deposition (mm) Winter (DJF) 2LM -0.7 -16.8 9.7 Spring (MAM) 2LM -17.2 -33.7 5.6 Summer (JJA) 2LM -38.3 -53.1 1.8 Autumn (SON) 2LM -5.7 -25.8 8.6

Winter (DJF) 1LM -8.5 -20.8 6.6 Spring (MAM) 1LM -26.1 -43.5 5.2 Summer (JJA) 1LM -65.7 -84.6 0.5 Autumn (SON) 1LM -19.4 -39.5 9.4

Annual 2LM -61.8 -128.4 25.6 Annual 1LM -119.7 -188.4 21.8