## Abstract

Longwave radiative flux divergence within the lowest 50 m of the atmospheric boundary layer was observed during the Eidgenössische Technische Hochschule (ETH) Greenland Summit experiment. The dataset collected at 72°35′N, 38°30′W, 3203 m MSL is based on longwave radiation measurements at 2 and 48 m that are corrected for the influence of the supporting tower structure. The observations cover all seasons and reveal the magnitude of longwave radiative flux divergence and its incoming and outgoing component under stable and unstable conditions. Longwave radiative flux divergence during winter corresponds to a radiative cooling of −10 K day^{−1}, but values of −30 K day^{−1} can persist for several days. During summer, the mean cooling effect of longwave radiative flux divergence is small (−2 K day^{−1}) but exhibits a strong diurnal cycle. With values ranging from −35 K day^{−1} around midnight to 15 K day^{−1} at noon, the heating rate due to longwave radiative flux divergence is of the same order of magnitude as the observed temperature tendency. However, temperature tendency and longwave radiative flux divergence are out of phase, with temperature tendency leading the longwave radiative flux divergence by 3 h. The vertical variation of the outgoing longwave flux usually dominates the net longwave flux divergence, showing a strong divergence at nighttime and a strong convergence during the day. The divergence of the incoming longwave flux plays a secondary role, showing a slight counteracting effect. Fog is frequently observed during summer nights. Under such conditions, a divergence of both incoming and outgoing fluxes leads to the strongest radiative cooling rates that are observed. Considering all data, a correlation between longwave radiative flux divergence and the temperature difference across the 2–48-m layer is found.

## 1. Introduction

The divergence of the longwave radiative fluxes is an important component of the thermodynamics of the atmospheric boundary layer (Kondratyev 1969; Garratt and Brost 1981). The cooling associated with the divergence of longwave radiation is understood to be essential for the establishment and maintenance of persistent surface inversion layers close to the surface during the polar night (Cerni and Parish 1984). Over large ice sheets, the strong radiative cooling has been found to establish a sloped-inversion pressure gradient force, the primary driving mechanism for katabatic flows (Parish and Bromwich 1986). Other studies have demonstrated the important role of radiative flux divergence for the formation of fog (Fleagle 1953; Kraus 1958; Funk 1962).

From this point of view it is somewhat surprising that for many decades, experimental studies of the stable boundary layers have mainly focused on the turbulent transfer, neglecting the radiative transfer processes. As a matter of fact, measurements of the radiative flux divergence are rare and generally of limited temporal extent.

The first observations of longwave radiative flux divergence were reported by Funk (1960), who recorded nighttime radiative flux divergence above grassland between 0.5 and 1.5 m, corresponding to cooling rates on the order of −120 K day^{−1}. Lieske and Stroschein (1967) reported the first measurements of radiative flux divergence above snow. They found a radiative heating effect of typically 120 K day^{−1} in the stably stratified air between 1 and 5 m at Barrow, Alaska. Observations of radiative flux divergence within the lowest 10 m of the boundary layer covering the entire diurnal cycle and resolving the incoming and outgoing components were first presented by Timanovskaya and Faraponova (1967). Their observations of net longwave radiative flux divergence between 1 and 8 m correspond to peak values of radiative heating of 145 K day^{−1} at noon and of −120 K day^{−1} before sunrise. The nighttime (daytime) divergence (convergence) of the outgoing flux was shown to be the dominating component, compensated slightly by an opposing behavior of the incoming flux. In general, cooling (heating) rates associated with the divergence (convergence) of the longwave radiative flux exceeded the observed temperature tendencies, suggesting that other processes had compensating effects. During the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) experiment, longwave radiative flux divergence was measured within a relatively thick layer, with radiometers installed at 2 and 48 m above ground (Sun et al. 2003). Contrasting the findings of Timanovskaya and Faraponova (1967), radiative flux divergence was found to be largest in the early evening, producing a radiative cooling of approximately −6 K day^{−1}.

In this study, we present year-round observations of longwave radiative flux divergence between 2 and 48 m. The observations were conducted between June 2001 and July 2002 during the Greenland Summit experiment by Eidgenössische Technische Hochschule (ETH) Zurich. The overall objectives of the experiment were the investigations of the energy balance and the structure of the atmospheric boundary layer in the dry snow zone of Greenland.

At Summit, Greenland, the atmospheric boundary layer is usually characterized by stable stratification. Temperature gradients of up to 40 K (100 m)^{−1} are reached during winter. In summer, however, unstable stratification may develop during daytime close to the surface (underneath the inversion), owing to a positive surface radiation balance. Fog formation within the boundary layer is frequently observed during summer nights. This variety of conditions is considered in presenting the observation.

## 2. Greenland Summit experiment

From June 2001 to July 2002, ETH Zurich carried out an extensive field program at the Greenland Summit Environmental Observatory (72°35′N, 38°30′W, 3203 m MSL) to investigate and monitor the surface energy balance of the dry snow zone of the Greenland ice sheet. The observational program included detailed measurements of the surface radiation balance and a comprehensive investigation of the structure of the atmospheric surface layer and the free atmosphere. Complementing the standard micrometeorological program (profiles of temperature, humidity, wind speed and direction in the lowest 50 m of the atmosphere, direct measurements of turbulent exchange, and temperature profiles in the snow and firn), longwave radiative fluxes were continuously measured at 2 and 48 m above the ground to evaluate the role of longwave radiative flux divergence.

## 3. Method of observation

### a. Instrumentation

Eppley precision infrared radiometers (PIR) were used to continuously measure both incoming and outgoing longwave radiative fluxes at 2 and 48 m above the surface. Measurements taken every 6 s were averaged to minute means and stored on a datalogger. The performance of the instruments was improved by several modifications. The electronic compensation circuit correcting for the instrument’s emission, which leads to systematic errors (Albrecht and Cox 1977), was disabled. Instead, the temperature measured at the cold junction was used to calculate the instrument’s emission. Three additional dome thermistors allowed a more exact correction of the dome’s thermal emission (Philipona et al. 1995). The instruments were ventilated with air heated slightly above ambient temperature to keep the domes free of rime. The pyrgeometer formula by Philipona et al. (1995) was used to infer longwave irradiance from instrument output. At the field site in Greenland, shading experiments were performed under clear-sky conditions to evaluate the degree of shortwave leakage through the PIR domes. The correction factor introduced by Marty (2000) was evaluated from the apparent reduction in longwave radiation measured during the shade period and the simultaneously sampled direct horizontal solar radiation. The two instruments with the least leakage were chosen to measure the incoming longwave flux.

The divergence of the longwave fluxes in units of watts per meter cubed is calculated as the difference between the measured fluxes at 48 and 2 m, divided by the height difference of 46 m. Radiative flux divergence can be expressed as a radiative heating rate in units of kelvin per day,

where *ρ* is the density of air and *c _{p}* is the specific heat of air at constant pressure.

### b. Relative calibration

To obtain radiative flux divergence with a low uncertainty, the uncertainties of the measurement of longwave flux differences must be reduced.

As a first step, all pyrgeometers were calibrated prior to the field campaign in the blackbody radiation source of the Physikalisch-Meteorologisches Observatorium Davos and World Radiation Center (PMOD/WRC) in Davos, Switzerland. The calibration apparatus and procedure has been described by Philipona et al. (1995).

An improvement of longwave flux measurements through field calibrations was demonstrated during the two International Pyrgeometer and Absolute Sky-Scanning Radiometer Comparisons (IPASRC; Philipona et al. 2001; Marty et al. 2003). As a second step, pyrgeometers were therefore subjected to a relative calibration at the field site. The aim of this relative calibration was to reduce the relative difference between the instruments. Calibration data were collected in June and August 2001, during selected days in April 2002, and in May and July 2002. Instruments were calibrated pointing in their designated direction—those reserved for measurements of the incoming flux were calibrated pointing up and those chosen to measure the outgoing flux pointing down. The reference for the relative calibration was derived as the mean of fluxes calculated using the calibration coefficients determined at PMOD/WRC. A robust least squares minimization was used to reevaluate the calibration coefficients in the pyrgeometer formula (Philipona et al. 1995) for the individual pyrgeometers.

Figure 1 illustrates the results of the relative calibration. Distributions of the differences between two up-facing pyrgeometers are shown before (fluxes evaluated using the PMOD/WRC calibration coefficients; Fig1a) and after the relative calibration (Fig. 1b). The distributions refer to a total of 16 690 one-minute averages. Without the relative calibration, a systematic departure of 2.4 W m^{−2} was found, and the standard deviation was 1.2 W m^{−2}. The relative calibration not only eliminated the mean bias but also reduced the standard deviation to 0.84 W m^{−2}. Despite the fact that the latter distribution is not exactly Gaussian, 73.9% of the data points fall within plus/minus one standard deviation. The standard deviation is thus a good measure for the uncertainty of the flux difference measurements.

Analogous to the results for the incoming fluxes, the relative calibration of the down-facing pyrgeometers at the field site reduced the standard deviation of the differences of the outgoing fluxes from 1.64 to 0.63 W m^{−2} and eliminated a mean bias of 3.4 W m^{−2}. The root-mean-square uncertainty in the observed net flux differences is thus ±1.05 W m^{−2}.

Using Eq. (1), and with an air density of 0.9 kg m^{−3} and *c _{p}* of 1005 J kg

^{−1}K

^{−1}, the uncertainty in the observations of net longwave radiative flux divergence expressed in units of heating rate amounts to ±2.19 K day

^{−1}. The uncertainties in the incoming and outgoing components are ±1.31 and ±1.75 K day

^{−1}, respectively.

### c. Correction of the tower’s influence

The pyrgeometers are suspended on horizontal booms of a tower structure. Inevitably the tower is in the field of view of the instruments. An up-facing instrument, for example, will receive radiation emitted by the tower, while a part of the sky radiation is blocked by the tower structure. As the tower structure usually has a higher radiative temperature than the sky, the measured flux is larger than the flux from the sky. A correction for the tower’s influence is thus needed.

The tower is a 49-m-high aluminum structure with a triangular base and a side length of 1.30 m. The two instrument pairs are mounted on horizontal booms, 1.25 m from the main tower structure. A sketch of the side view and top view of the tower is provided in Fig. 2. Seen from an instrument, the azimuthal range *ϕ* between the tower edges is 53°. Within 30% of this azimuthal range, however, the sky is seen through the tower structure. This can be described by a structural density, *ρ*_{tow} of 0.7, which has been determined by photographic means. The effective azimuth *ϕ̃*, product of the structural density *ρ*_{tow} and the azimuth *ϕ*, describes the azimuthal range effectively covered by the tower structure.

The flux measured by an up-facing pyrgeometer at level *i* of the tower can be written as the sum of three contributions, the flux from the unobstructed sky, the tower’s emission, and the flux from the sky reflected from the tower structure,

with *I*_{sky,}* _{i}* as the incoming longwave flux from the sky,

*ε*

_{tow}as the emissivity of tower (very oxidized aluminum) of 0.2 (Sala 1986), and

*I*

_{tow,}

*as the flux emitted by the tower. Assuming all radiation fields to be isotropic, parameter*

_{i}*α*

_{tow,}

*describes the fractional contribution of a radiative flux emerging from that part of the hemisphere effectively covered by the tower structure to the flux from the entire hemisphere. It is calculated as*

_{i}Here, *ζ _{i}*

_{,top}is the zenith angle of the tower top seen from the instrument at level

*i*.

To solve Eq. (2) for the sky radiation, the emission from the tower is needed. Simultaneous measurements of air and tower temperatures at 2 and 35 m in summer 2002 have shown that the temperature of the tower varies with height and that the temperature of the tower exceeds the air temperature when global radiation (total of direct solar radiation and diffuse sky radiation received by a unit of horizontal surface) is high and wind speed is below a critical value of 9.5 m s^{−1}. When wind speed is below this value, the temperature *T*_{tow,}* _{j}* of the tower segment

*j*may be parameterized as a function of air temperature

*T*

_{air,}

*and wind speed*

_{j}*u*at the height of the tower segment and global radiation Gl:

_{j}with an *a* of 0.0084 K (W m^{−2})^{−1} and *b* of 0.0009 K (W m^{−2})^{−1} (m s^{−1})^{−1}.

As the temperature of the tower varies with height, the emission from the tower structure is calculated separately for seven tower segments (Fig. 2) using Stefan–Boltzmann’s law. The flux from the tower at level *i* can be written as the sum of the fluxes emitted from the different tower segments *j*. With *ζ*_{bottom,}_{i}_{,}* _{j}* and

*ζ*

_{top,}

_{i}_{,}

*, the zenith angles of the base and top of each of the tower segments*

_{j}*j*as seen from level

*i*,

*α*

_{i}_{,}

*describes the fractional contribution of each tower segment to the contribution of the entire tower,*

_{j}The flux from the tower structure is now calculated as

Now we can solve Eq. (2) for the sky radiation,

The correction for the outgoing flux is developed accordingly, taking the emission of the tower segments below the measurement level into account.

The magnitude of the correction for the incoming flux varies with the difference of the radiative temperature between the tower and the sky; the correction for the outgoing flux varies with the difference in radiative temperature between tower structure and snow surface. Usually the tower structure seen by the instruments is warmer than the sky and, under stable conditions, warmer than the snow surface. During clear-sky situations, the correction of the incoming flux for the tower influence can reach −2.5 W m^{−2}, while the correction for the (negative) outgoing fluxes usually does not exceed 1 W m^{−2}. Under overcast conditions, the corrections are smaller, because of the warmer cloud base and weaker temperature gradients. Corrections applied to the incoming fluxes are then on the order of −1 W m^{−2}, while the corrections for the outgoing flux range between 0.0 and 0.2 W m^{−2}.

The uncertainty of the correction introduced for the influence of the tower is estimated by varying the temperature and emissivity of the tower. The combination of a higher (lower) tower temperature with a higher (lower) emissivity of the tower leads to the strongest increase (decrease) of the tower influence. Accordingly, the dataset was reevaluated increasing and decreasing the tower temperature and tower emissivity by 0.5°C and 0.05, respectively. The resulting uncertainty in the net longwave radiative heating rate is ±0.45 K day^{−1}, and the uncertainties in the incoming and outgoing longwave radiative heating rates are ±0.27 and ±0.18 K day^{−1}, respectively.

The overall uncertainty in net longwave radiative heating from the uncertainty in the flux difference measurements and the uncertainty in the tower correction can thus be given as ±[(2.19 K day^{−1})^{2} + (0.45 K day^{−1})^{2}]^{1/2} = ±2.3 K day^{−1}. Accordingly, the overall uncertainties of the incoming and outgoing radiative heating rates are 1.8 and 1.4 K day^{−1}. Because these uncertainties are small, and for reasons of clarity, error bars are omitted from the graphs when presenting the results in the following sections.

## 4. Observational results

### a. Annual cycle

The annual cycle of longwave radiative flux divergence is shown in Fig. 3. Time series of 10-day running averages of the components (incoming, outgoing, and net) of longwave radiative flux divergence are shown together with the temperature gradient [°C (100 m)^{−1}] calculated from the temperature difference between 48 and 2 m.

Periods characterized by stronger stabilities are associated with enhanced longwave radiative cooling, which is dominated by the divergence of the outgoing flux. During winter months, values range between −10 K day^{−1} (−0.21 W m^{−3}) and −20 K day^{−1}. In summer, 10-day averages indicate a slight cooling of −2 K day^{−1}, which is dominated by the divergence of the incoming flux, while the outgoing component leads to a slight warming.

### b. Summer days

In summer, longwave radiative flux divergence within the lowest 48 m of the boundary layer shows a distinct diurnal cycle. The 5-day period from 30 June to 5 July 2001, which was dominated by mostly clear-sky conditions, is selected to present the diurnal variation of longwave radiative flux divergence (Fig. 4). On 30 June, a low stratocumulus cloud cover started to dissolve in late afternoon and reduced to one-tenth at 1900 local standard time (LST = UTC − 3 h). The following days, 1–3 July, were cloud-free days. During the nights, however, the formation of fog was observed. At all of the 0000 LST synoptic observations, fog reduced the horizontal visibility to between 0.5 and 1.5 km. The vertical extent and the density of the fog varied from night to night. In the early mornings of 2 and 4 July, the fog layer was denser (lower horizontal visibility) than on 1 and 3 July. On 3 July, the fog layer was very shallow, with its top below the 48-m level. On 4 July, a cirrus cover developed, covering one-tenth of the sky at 0900 LST and six-tenths at 1800 LST.

The time series of the longwave radiative heating rate and its in- and outgoing components between 2 and 48 m are shown together with the temperature stratification within this layer in Fig. 4. Hatched areas of the plot indicate times when fog reduced the horizontal visibility. In addition to the synoptic observations, a diffuse radiation threshold method based on the clear-sky detection algorithm by Long and Ackerman (2000) was used to detect times with fog.

The diurnal cycle of longwave radiative flux divergence correlates well with the diurnal variation of stability within the 2–48-m air layer. A longwave radiative cooling results during stable conditions, while longwave radiative heating is observed when stratification is unstable. Daytime (0900–1700 LST) longwave radiative heating ranges from 5 to 15 K day^{−1}; nighttime (2100–0500 LST) longwave radiative cooling ranges from −10 to −30 K day^{−1}.

The net longwave radiative flux divergence is dominated by the outgoing flux component. For most of the time, the divergence of the incoming flux plays only a secondary role. During daytime, a cooling due to the divergence of the incoming flux reduces the heating due to the (negative) outgoing flux divergence slightly; in the beginning of the night, radiative heating due to the convergence of the incoming flux opposes the divergence of the outgoing flux. In the middle of the night, however, a divergence of both the outgoing and incoming longwave flux is observed. Then, the incoming component contributes a considerable part to the resulting net longwave radiative cooling. These observations, when both components lead to a cooling, coincide with the occurrence of fog (Fig. 4).

A mean summer (15 May–15 August) diurnal cycle of longwave radiative flux divergence is presented in Fig. 5. The variation of the divergence of the outgoing flux clearly dominates the diurnal cycle, while the divergence of the incoming flux remains constant (−4 K day^{−1}) throughout the day. The contribution of the divergence of the incoming flux leads, however, to a daily mean longwave radiative cooling.

The diurnal variation of the observed temperature tendency (change of temperature with time or “full” heating rate) and the contribution of longwave radiative flux divergence in the air layer between 2 and 48 m during the summer months (15 May–15 August) are presented in Fig. 6. The observed temperature tendency is calculated as the rate of change with time of the weighted mean temperature between 2 and 48 m, based on the temperature measurements at 2, 5, 10, 20, 35, and 48 m. A lag of approximately 3 h is seen between the observed temperature tendency and longwave radiative flux divergence. The contribution of longwave radiative flux divergence to the overall temperature change is symmetric around 1300 LST, with a maximum heating of 4 K day^{−1} at midday and a maximum cooling of −10 K day^{−1} at midnight. The observed temperature tendency shows the maximum heating between 0900 and 1000 LST (13 K day^{−1}), and the strongest cooling at 2100 LST (−12 K day^{−1}).

### c. Persistent winter inversion

The 4-day period between 19 and 23 January 2002 is chosen to present the wintertime behavior of the incoming, outgoing, and net components of longwave radiative flux divergence within the lowest 48 m of the boundary layer. On 19 January, stratus clouds covered the sky and temperature at 2 m was about −40°C. The following days were cloud-free, and a steady temperature decrease to −48°C was observed. The temperature gradient between 2 and 48 m reached 40°C (100 m)^{−1} by the end of 21 January. This stable period ended at around 2000 LST on 2100 January, when a sudden temperature rise of 10 K was observed in relation to a change in synoptic conditions. Figure 7 presents the longwave radiative heating rate, its incoming and outgoing components, and the temperature stratification between 48 and 2 m.

A strong and persistent cooling due to the divergence of the net longwave flux is observed. As in the case of fog-free periods of summer nights with stable stratification, the strong cooling due to the divergence of the outgoing flux dominates over a weak heating caused by the convergence of the incoming flux component. Longwave radiative cooling rates of −30 K day^{−1} are reached on 21 January. The heating due to the convergence of the incoming flux amounts to 10 K day^{−1}, while the cooling due to the outgoing flux divergence reaches values close to −45 K day^{−1}. The reduction in stability seen around 20 UTC on 21 January is associated with a reduction of both the divergence of the outgoing and the convergence of the incoming flux. A correlation is seen between the divergence of the net longwave radiation and the vertical temperature gradient.

### d. Longwave radiative flux divergence and temperature gradient

Our measurements indicate a relationship between longwave radiative flux divergence and temperature gradient expressed as the temperature difference across the 2–48-m layer. This relationship has been observed in the annual cycle as well as during the diurnal variations in summer and during persistent inversions in winter. Figure 8 shows this relationship for the incoming, outgoing, and net component of longwave radiative flux divergence, based on 6930 hourly observations collected throughout the 14-month field experiment. The incoming longwave flux shows a convergence (radiative heating) under increasingly stable conditions. The relationship for the outgoing flux component shows the opposite behavior—an increasing divergence (radiative cooling) with growing temperature gradient. The latter relationship is stronger; therefore, a stronger divergence of the longwave net flux (cooling) under increasingly stable conditions results. The coefficients of determination *R*^{2} for the linear fit describing the relationship between incoming, outgoing, and net longwave radiative flux divergence and temperature difference across the 2–48-m layer are 0.15, 0.74, and 0.34, respectively; the standard errors of estimates are 7.2, 5.6, and 9 K day^{−1}, respectively.

## 5. Discussion

Longwave radiative flux divergence between 2 and 48 m and its in- and outgoing components were measured continuously for 14 months at the Greenland Summit Environmental Observatory. A relative calibration of the pyrgeometers reduces the uncertainty of the observations to ±2.3 K day^{−1}.

In section 3c we develop a correction for the tower effects on the longwave radiative flux measurements. It is particularly important when determining the bulk divergence from measurements carried out on the top and base of the tower structure, as typically the tower is in the field of view of mainly one of the instruments (the bottom one in respect to the incoming flux, the top one with respect to the outgoing flux). The correction expressed as a heating rate amounts to typically 3 K day^{−1} under clear-sky summer conditions. Under average summer conditions, neglecting the tower’s influence on the measurements would lead to an underestimation of the net longwave radiative heating at noon by 30% and to an overestimation of the peak longwave radiative cooling around midnight by 10%. The uncertainty of the correction of the tower’s influence is about one order of magnitude less than the correction itself. It is estimated by varying the tower structure temperature by ±0.5 K and the emissivity of the tower by ±0.05 and amounts to ±0.45 K day^{−1}.

For the first time, longwave radiative flux divergence in the atmospheric boundary layer is presented for an entire year. Throughout the year, the vertical gradient of the net longwave flux introduces a cooling in the lowest 50 m above the surface. During the summer months the effect is small (−2 K day^{−1}), but in winter a mean cooling rate of −11 K day^{−1} results.

A strong diurnal variation of longwave radiative flux divergence is observed in summer. The heating rates due to the divergence of the longwave flux reach values between −30 and 15 K day^{−1}, which is on the same order of magnitude as the observed temperature tendency (the observed change of the bulk air temperature between 2 and 48 m). This stresses the important role of longwave radiative flux divergence for the thermodynamics of the atmospheric boundary layer over the Greenland ice sheet.

A phase shift of approximately 3 h is observed between longwave radiative flux divergence and the observed temperature tendency (total heating rate) within the 2–48-m layer (Fig. 6). Maximum longwave radiative heating is observed at 1300 LST, while the greatest heating occurs between 0900 and 1000 LST. Accordingly, the observed strong cooling in the evening (2100 LST) precedes the maximum longwave radiative cooling observed at midnight. This emphasizes the importance of cooling contributions from other processes, such as the divergence of the sensible heat flux in the initial evening cooling.

Our observations support the findings of Timanovskaya and Faraponova (1967), who report the same diurnal pattern of radiative flux divergence, with a radiative heating during daytime and a radiative cooling during the night, and a dominant role of the divergence of the outgoing flux component. However, their observations were made in a shallower layer (1–8 m) and correspond to longwave radiative heating rates one order of magnitude larger than our results.

The more recent observations by Sun et al. (2003), however, show a different diurnal pattern. They report a maximum of longwave radiative cooling in the early evening, while our observations indicate the maximum in longwave radiative flux divergence in the middle of the night. The observations of Sun et al. (2003) are limited to times between 1530 and 0730 LST. Nevertheless, a sign change from a longwave radiative heating during the day to a longwave radiative cooling during the night can be inferred from their Fig. 12. Opposing behaviors of the incoming and outgoing flux divergence are also seen in their Figs. 5 and 13, which agree well with our observations and those of Timanovskaya and Faraponova (1967).

Our observations show a strong influence of fog on longwave radiative flux divergence, especially on the incoming component. Under stable conditions, a change from a negative incoming flux divergence to a divergence is observed when fog forms (Fig. 4). This change reflects the different absorption characteristics of clear air and of air suspending fog droplets. The radiative energy exchange between fog-free air layers takes place in the strong absorption bands of water vapor and carbon dioxide. Under stable conditions, a radiative heating is caused by a negative divergence of the incoming longwave flux (Figs. 4, 7). Fog droplets, however, act as gray bodies and introduce an additional energy exchange in the atmospheric window region. In this region a cooling is introduced, which overcompensated for the heating within the strong absorption bands of water vapor and carbon dioxide. Fog formation is frequently observed during summer nights. This is reflected in the mean diurnal cycle of longwave radiative cooling (Fig. 5). A cooling contribution of the incoming component is seen during the mean summer night. During summer, the strongest longwave radiative cooling rates are observed under fog conditions, reaching values of −35 K day^{−1} and below.

During winter, our measurements indicate that the bulk temperature between 2 and 48 m remains more or less constant over prolonged periods despite the continuous cooling due to longwave radiative flux divergence. From the point of view of the thermodynamic energy equation, the latter must be compensated by processes such as warm air advection, subsidence, or possibly by a negative divergence of the sensible heat flux. Our data do not allow us to quantify these other processes, but we can nevertheless formulate a few hypotheses. Let us consider the period between 20 and 22 January 2002 (Fig. 7). Greenland was under the influence of a high pressure ridge. Under such conditions the establishment of subsidence is likely. The gradient of potential temperature at 48 m estimated from the temperature difference between the measurements at 35 and 48 m amounts to 0.08 K m^{−1}. A downward airflow on the order of 0.5 cm s^{−1} would be required to maintain a heating rate of 30 K day^{−1} to compensate for the longwave radiative cooling, which seems to be a realistic estimate.

Convergence of the sensible heat flux may also be considered, although the common view (Caughey et al. 1979; Nieuwstadt 1984; Stull 1988) is that in stable stratification the downward heat flux decreases in magnitude with height, ruling out this possibility. Previous measurements carried out on the Greenland ice sheet (Forrer and Rotach 1997), however, have shown that a local increase of the heat flux with height is possible. In any case, the quantitative aspects of the thermodynamics of the stable boundary layer need to be further investigated.

A general correlation is found between the divergence of the net longwave flux and the temperature difference across the 2–48-m layer throughout the year. Under stable conditions, the divergence of the net longwave flux leads to a radiative cooling, while a radiative heating effect is observed during unstable conditions. This relationship between longwave radiative flux divergence and temperature gradient is dominated by the divergence of the outgoing flux, while the divergence of the incoming flux tends to be increasingly negative under stable conditions. One should keep in mind, however, that fog formation has a strong impact on longwave radiative flux divergence, especially on the incoming component.

The present study focuses on the divergence of the longwave radiative flux in the relatively thick bulk layer between 2 and 48 m. With the exception of Sun et al. (2003), previous studies have analyzed longwave radiative flux divergence in thinner layers located closer to the surface. This makes a comparison of the results difficult, as longwave radiative flux divergence may vary with height. From the available observations, a trend to stronger heating or cooling rates closer to the surface is suggested. In the lowest 10 m above the surface, for example, the observations by Timanovskaya and Faraponova (1967) and Funk (1960) show longwave radiative flux divergence one order of magnitude higher than our observations or those by Sun et al. (2003) in the 2–48-m layer. Under the assumption that the correlation between temperature gradient and longwave radiative flux divergence is applicable as well for the more shallow layers closer to the surface, a decrease of longwave radiative flux divergence with height becomes perspicuous, as temperature gradients are expected to be stronger closer to the surface. The shape of the profile of radiative flux divergence, however, needs to be investigated in more detail and is subject to further research.

## 6. Conclusions

Year-round observations of longwave radiative flux divergence were made within the lowest 48 m above the firn at Summit, Greenland. Under stable (unstable) conditions, a divergence (convergence) of the longwave flux is observed within the 2–48-m layer. The divergence (convergence) of the outgoing flux dominates over a weaker but opposing convergence (divergence) of the incoming flux. Under stable conditions with fog, the sign of the incoming component changes, and an additional longwave radiative cooling results. Longwave radiative flux divergence plays an important role for the thermodynamics within the lowest 50 m of the boundary layer, reaching the same order of magnitude as the observed temperature tendency. During summer, nighttime longwave radiative cooling reaches typically −10 K day^{−1}, but values of −35 K day^{−1} are observed under fog conditions. Daytime longwave radiative heating reaches, on average, 4 K day^{−1}, but heating rates exceeding 15 K day^{−1} have been observed. A phase shift is observed between the temperature tendency and longwave radiative flux divergence. The longwave radiative heating rate lags behind the observed temperature tendency by approximately 3 h. This indicates the importance of additional processes such as sensible heat flux divergence for the evening cooling. During winter, longwave radiative cooling rates of −30 K day^{−1} may persist for several days. This cooling must be compensated by subsidence heating, advection, and/or the convergence of the sensible heat flux. Comparisons with previous studies in more shallow layers suggest a decrease of longwave radiative cooling with height, but the detailed vertical structure of radiative flux divergence is subject to further investigation.

## Acknowledgments

This work was financed by the Swiss National Science Foundation, Grants 21-57249 and 20-66760. We thank Dr. C. Peter Schelander, Dr. C. Saskia Bourgeois, Karl Schroff, and Hans-Jörg Frei for their contributions to the Greenland Summit experiment. We thank VECO Polar Resources for the logistic support in Greenland.

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## Footnotes

* Current affiliation: Department of Meteorology, University of Utah, Salt Lake City, Utah

*Corresponding author address:* S. Hoch, Department of Meteorology, University of Utah, 135 S. 1450 E., Rm. 819, Salt Lake City, UT 84112. Email: sebastian.hoch@utah.edu