Introduction
The temperature index melt method exploits the empirical relationship between
near-surface air temperature and ablation rate through the calculation of
positive degree days (PDDs) (Hock, 2003). Within the PDD calculation, the
sigma (σ) parameter is used in the following equation to account for
temperature variations due to the diurnal temperature cycle and random
weather fluctuations:
σ=1N∑i=1NTi-Tm2
where N is the number of temperature observations, Ti is temperature and
Tm is the mean temperature. These temperature fluctuations lead to
short-term positive excursions that cause melt during months when the
average temperature is below 0 ∘C; therefore σ allows the model
to capture melt during these months. Assuming a normal distribution of the
fluctuations around Tm, for Δt days we have PDD=Δt×EPD,
where EPD is the expected positive degree given be Eq. ():
EPD=1σ2π∫0∞Texp-T-Tm22σ2dT
or (after evaluating the integral)
EPD=σβTmσ=σTmσϕTmσ+fTmσ
(Huybrechts and de Wolde, 1999; Janssens and Huybrechts, 2000). Here, the
function β involves the standard normal distribution function φ
and the standard normal density function f.The PDD in a year having the
monthly mean temperatures Tm and constant σ is then
PPD=σ∫YEARβTmσdt.
Equations () and () allow efficient computation of melt in ice-sheet
models by parameterising the effect of diurnal temperature fluctuations and
circumventing the need to resolve them. In this paper, we refer to them as
the PDD parameterisation, and σ as the temperature-variability
parameter.
Numerous GrIS simulations had assumed a constant σ between
∼2.5 and 5.5 ∘C (e.g. Fausto et al., 2009a; Reeh,
1991; Ritz et al., 1997; Huybrechts and de Wolde, 1999; Janssens and
Huybrechts, 2000), with 4.2 ∘C being a typical value (Janssens and
Huybrechts, 2000; Hanna et al., 2011). Recently, however, it is realised that
the choice of σ can significantly affect melt model output, and that
capturing the spatio-temporal variations of σ, notably for the
summer months, may improve estimated of GrIS melt (e.g. Lefebre et al.,
2002; Fausto et al., 2009a, b). This is even though the PDD method is an
empirical index method based on temperature, but in reality surface melt is
a function of energy fluxes at the surface (net long wave, net shortwave,
turbulent heat fluxes) and these fluxes are not a direct function of surface
temperature. The PDD is a quick-and-easy method that is not physically
based, but works well when compared to physically-based methods (and is
elegant to use as it only has three parameters) (Braithwaite, 1995).
For instance, a sensitivity analysis carried out by Fausto et al. (2009a)
showed a 33 % increase in the modelled melt area over the GrIS when using
a summer σ value of 4.5 ∘C instead of 2.53 ∘C. As an
increased summer σ indicates more excursions above 0 ∘C for any
given area on the ice sheet, more melt occurs in areas already experiencing
melt - in addition to expanding the melt area. Fausto et al. (2009a) derived
their lower σ estimate from Eq. () based on observed monthly 2 m air
temperatures from 1996 to 2006. Similarly, Lefebre et al. (2002) derived
July σ values of 2 to 3 ∘C based on 2 m air temperatures
from the European Centre for Medium-Range Weather Forecasts (ECMWF)
re-analysis at the 20 km grid scale for the year 1991. Lefebre et al. (2002)'s results further support the findings of Fausto et al. (2009a), that
σ varies spatially and temporally across the GrIS due to the large
variations in meteorological and climatic conditions experienced across the
ice sheet (Lefebre et al., 2002; Cappelen et al., 2014). It follows that the
approach of using a constant σ in the temperature-index
parameterisation may be invalid, and that introducing spatial and or
temporal variations in σ (e.g. as explored by Fausto et al., 2009a
and Lefebre et al., 2002) is fundamentally a better approach.
Consequently, several recent studies have attempted to derive variable
σ parameter sets from both automatic weather station (AWS)
temperature records and reanalysis temperature products. Fausto et al. (2009b) used Eq. () and AWS data from the GrIS to calculate the least
squares fit of summer σ from 1996 to 2006 in an observation-based
parameterisation. There is a large altitudinal component to the distribution
of σ, with values of around 5 ∘C in the highest elevation
regions but only around 2 ∘C near the periphery of the ice sheet (Fausto
et al., 2009b). The authors also identified an annual cycle in σ,
with σ values larger in the winter months and smaller during summer
(Fausto et al., 2009b; Lefebre et al., 2002). The low summer values were
largely attributed to the limiting effects of melt on surface temperatures
and therefore near-surface air temperatures during the melt season, which is
absent during other months (Fasuto et al., 2009b). There is also a larger
scatter in σ calculated at lower elevations, which Fausto et al. (2009b) attributed to higher vulnerability to atmospheric variability of the
AWS sites located near the coast.
The validation results of Fausto et al. (2009b) show that σ is
within 1 ∘C of the observations at AWS sites, and increasing accuracy
with elevation. Despite this agreement, Fausto et al. (2009b) suggest that
using just the mean summer σ is not sufficient to model annual
ablation. Including an annual σ distribution more realistically
depicts real temperature variability; however, Fausto et al. (2009b) stated
that the calculation of an “annual distributed cycle” in temperature
variations was limited by data availability.
Several more recent studies have sought to address this data availability
issue using re-analysis products to calculate σ grids for the GrIS.
Sequinot (2013) used ECMWF Interim (ERA-I) reanalysis from 1979 to 2012 in
Eq. () to derive global monthly σ grids; however, daily temperature
averages were taken before calculating σ so the resulting parameter
does not appear to capture variability due to the diurnal cycle. The
resulting σ values range from 0.32 to 12.63 ∘C globally,
and are generally higher in the winter and lower in the summer (Seguinot,
2013). Rogozhina and Rau (2014) used ECMWF ERA-40 reanalysis from 1958 to
2001 to produce a 10km×10km σ gridded dataset for the GrIS. The
resulting monthly σ fields show seasonal cycles, with higher values
in the winter and lower values of 1.1–2 ∘C in summer (July) (Rogozhina
and Rau, 2014). Again, σ is higher in the centre of the ice sheet
and decreases towards the margin (Rogozhina and Rau, 2014). Seguinot and
Rogozhina (2014) further developed this work, by producing long-term σ fields for application to multimillennial ice sheet surface mass balance
(SMB) modelling. Finally, Wake and Marshall (2015) used Greenland Climate
Network (GC-Net) data to determine that the quadratic function of mean
monthly temperature is a better representation of σ than a constant
parameter. Our study presents a further advance in this field, by providing
σ results on the higher resolution 5km×5km grid, using a combination
of ERA-I and Twentieth Century Reanalysis (20CR) reanalysis to extend the
time period from 1870 to 2013 and providing a comprehensive validation of
our results using AWS data for various time periods. Furthermore, trends in
σ over time are discussed here, which, to our knowledge at the time
of submission, has not been carried out before.
Given the range of currently-assumed σ values in the literature, the
potential difference this has on melt area and therefore SMB, together with
the findings of studies like Rogozhina and Rau (2014) where SMB was found
to be highly sensitive to σ, it is clearly vital to better constrain
this parameter. As a result, this study presents an alternative optimised
σ parameter based on calculations using downscaled, corrected ERA-I
and 20CR meteorological reanalysis 2 m air temperatures on a 5km×5km polar
stereographic grid for the GrIS from 1870–2013 inclusive (Compo et al.,
2011; Dee et al., 2011). This is achieved through modification of the
Janssens and Huybrechts (2000) temperature index melt model, to incorporate
monthly varying σ values in the calculation of melt within the
degree-day calculation. The following two sections discuss our method of
calculating the new σ parameter (Sect. 2) and characteristics of the
resulting monthly-varying σ (Sect. 3). Section 4 discusses the
validation and application of this new parameter, including a discussion of
recent temperature variability over the GrIS. The effect of our new σ parameter on the SMB and component outputs from the modified version of
the temperature index melt model will be discussed in a separate paper.
Results
Effect of applying corrections on σ time series
Figure 2 graphically plots the 2 m air temperature series, spread data,
their breakpoints and confidence intervals, clearly showing that the
artificial jumps in the 2 m air temperature series are due to model
artefacts. Table 1 quantifies these inhomogeneities by showing the year of
the break in each monthly series and the correction factor to be applied.
The breakpoint analysis detected breaks in five out of the twelve months. Of
these five months, only one break was detected in the 2 m air temperatures,
each having a corresponding break in the spread series for which the
confidence intervals overlap. These breakpoints are therefore considered
a product of the modelling process and the 20CR 2 m temperature time series
were adjusted for them using the correction factors in Table 1. This altered
the mean temperatures for the time periods before the breakpoints in the
respective time series, as shown in Fig. 3.
Overall, applying the different correction stages to 20CR 2 m air
temperatures brings them into closer agreement with the ERA-I 2 m air
temperatures for the overlap period 1979–2008 for all plots shown in Fig. 3.
The ice sheet average temperature difference between 20CR and ERA-I before
the correction process was 0.59 ∘C compared to 0.05 ∘C thereafter
for the annual data. The residual difference is likely due to the correction
process taking the mean difference in 20CR and ERA-I for the whole period
1979–2008, and applying this to monthly 2 m air temperature. Scaling the 20CR
to ERA-I downscaled and corrected 2 m air temperatures increases the
temperature by an average of 0.6 ∘C for annual, 0.3 ∘C in spring,
1.4 ∘C in summer, 1.1 ∘C in autumn and by 1.5 ∘C in July. Winter
is the only season where scaling to ERA-I reduces the temperature by an
average of 0.4 ∘C (Fig. 3e). Correcting these scaled 20CR 2 m air
temperatures for breakpoints reduces the temperatures again for the early
part of the record before the breakpoints in Table 1 by 0.4 ∘C at the
annual scale, 0.7 ∘C in spring, 0.1 ∘C in summer, 0.5 ∘C in
autumn and 0.1 ∘C in winter on average from 1870–2008. The period after
the breakpoints remains unchanged from the scaled series in all months where
breaks were detected in Table 1. Figure 3a shows that there is still some
disagreement with ERA-I for the overlap period, particularly in the early to
mid-2000s.
Figure 3b shows that for spring, the period before breakpoints were detected
in the 1940s has the largest difference between the corrected and
breakpoints series. From the early 1940s there is good agreement between all
stages of the correction process with small changes at each step. The
breakpoints series is in close agreement with ERA-I with a mean difference
of 0.0004 ∘C for the overlap period. The largest discrepancies between
corrected 20CR and the breakpoints series are shown in Fig. 3c during the
summer, particularly in the early part of the record. The corrected 20CR
series are ∼1–1.5 ∘C lower than the breakpoint series.
There is however, good agreement between the breakpoints series and ERA-I
for the overlap period with an average difference of 0.0002 ∘C. The
different correction stages show less disagreement for autumn (Fig. 3d) with
again good agreement between the breakpoint series and ERA-I series with an
average difference of -0.0004 ∘C for the overlap period. No breakpoints
were detected in any of the winter months (DJF), so the final stage of
correction here was scaling to ERA-I 2 m air temperatures. The two 20CR
series show good agreement throughout (mean difference of 0.38 ∘C from
1870–2008) and with ERA-I (mean difference 0.03 ∘C between scaled and
ERA-I from 1979–2008). Similarly the July series has no breakpoints, with
only August out of the summer months contributing to the breakpoints
correction in Fig. 3c. The scaled series is therefore the final stage of the
correction for July and shows much better agreement with ERA-I with a mean
difference of 0 ∘C from 1979–2008, although there are clear differences
between scaled 20CR and ERA-I for the overlap period, most notably the
systematic bias in 1982, 1983, 1999, 2002 and 2004, when the difference
between the series exceeded ±1 ∘C.
The resulting spliced 2 m air temperature series, shown in Fig. 4, takes 20CR
from 1870–1978, i.e. to the beginning of the ERA-I record together with the
full available ERA-I series from 1979–2013. There is a clear narrowing of
the difference between the spliced and unspliced series through time from
0.56 ∘C in 1870 to 0.46 ∘C in 2008, with the gap closing completely
in the 1960s, after the last breakpoint in 1966 (Table 1), then a slight
widening again after 1979 when the ERA-I is introduced.
Spatio-temporal variation in σ
Figure 5 shows an overall increase in σ from 1870–2013 for all
seasons, annual and July plots, with relatively low σ until the
1930s, followed by a period of increasing σ until the 1960s, then
a slight decrease to the 1980s plateauing since then but little apparent
overall change, particularly in summer and July. Before the 1930s, annual,
spring, autumn and winter σ all appear to fluctuate around or close
to the assumed value of 4.2 ∘C. Since 1930, σ increased in these
series to between 5 and 7 ∘C. The summer and July plots in Fig. 5
show that σ was lower than 4.2 ∘C pre-1930, rising to just below
4.2 ∘C from the 1940s before falling again in the 1980s to between
2.5 and 3.5 ∘C, with an ice sheet average σ of
∼3.2 ∘C for the whole study period in summer.
In Fig. 6 the annual, seasonal and July mean σ plots show that
σ increases with elevation, reaching up to 10 ∘C around Summit
(above 3000 m elevation) in winter. The range of σ values varies
between seasons and individual months. During summer, lower values from
1 ∘C at the periphery to 6 ∘C in the middle of the ice sheet
dominate, showing areas where σ is currently under- and
over-estimated by the constant-σ parameter. July shows the same
range but with lower values extending further into the ice sheet to around
2000 m elevation, as opposed to 1500 m for summer. During spring and autumn,
σ ranges from 1 to 9 ∘C, again with higher values at
elevations above 2000 m.
Figure 7 shows that when spatial variations are averaged out a clear
seasonal cycle in σ emerges, with lower mean values in the summer
months (2.6 ∘C for July), as discussed above, and higher mean values in
the winter (5.9 ∘C for January). The interquartile ranges show that over
50 % of the data lie within ±2 standard deviations of the monthly
mean, with only one point in June falling outside the error bars for summer.
The rest of the data fall within the monthly maximum and minimum lines,
showing the presence of relatively high and low outliers in all months
except July and August. During June and July the interquartile ranges are
narrower, indicating less variability about the mean during these months.
σ validation
The comparison of modelled (σ calculated from ERA-I and 20CR) and
observed (calculated from observed AWS 2 m-air temperature) σ in
Fig. 8 shows the strongest correlation with the annual data, which is
a highly significant (p<0.01) positive relationship between the
observations and modelled σ when averaged over the year. Despite
being weaker, the summer and July correlations are still highly significant
(p<0.01) positive relationships between the observed and modelled
σ. Overall there is statistically significant agreement between the
observed and modelled σ calculated from reanalysis data to those
data points on the ice sheet for the periods where validation data are
available.
There is a systematic bias in the sign of the offset between observed and
modelled σ when plotted against elevation (Fig. 9). The new modelled
σ parameter overestimates the observed σ in the ablation
zone below the equilibrium line altitude (ELA), which lies at
∼1500 m. There is a shift in the sign of the difference in the
accumulation zone where the model parameter underestimates σ
compared to the observations. The annual, summer and July correlations in
Fig. 9 indicate highly significant negative relationships, with σ
decreasing with elevation.
Figure 10 shows weak negative correlations between the difference in observed
and modelled σ, and latitude. Despite these correlations being
relatively weak compared with those in Fig. 9, the R values indicate all
three correlations are highly significant: annual and summer at the 99 %
level and July at the 95 % level: this is due to the large number of data
points (pixels) on the ice sheet. The trend lines indicate the bias shifts
further northwards, with positive differences in the south between 60
and 65∘ N, shifting to more negative differences further north. This
indicates that the new parameter underestimates σ by 0.06
(0.82) ∘C in the south (north) on average. There is however,
considerable scatter around the trend lines; therefore this effect is hard
to compensate for by further correcting the σ data.
Trends in σ
All trends in Fig. 11 are positive from 1870–2013, implying that temperature
has become more variable over the study period. The largest trends in
σ are in the southern and north-western parts of the ice sheet,
indicating that temperature has become relatively more variable over time
here than anywhere else. The smallest rates of change in σ are
consistently found at high elevations in the centre of the ice sheet. This
area displays trends ranging from 0.0–0.3 ∘C decade-1, equivalent
to an increased temperature variability of ∼0.0–4.3 ∘C
over the whole 144 year period. σ is therefore still becoming more
variable in the centre but less so than in more peripheral regions. The
centre of the ice sheet is also the only region which shows
non-statistically significant results for spring and winter, indicating that
these weaker trends could occur by chance. In Fig. 11a the annual rate of
change in σ for each 5km×5km grid cell is positive from 1870–2013,
showing that overall temperature variability has increased. Figure 11b
indicates that all p values lie between 0 and 0.006, so we interpret these
long-term trends in annual σ to be statistically significant.
The spring plots show a similar spatial pattern in trend to the annual plot,
with smaller values around Summit at higher elevations of the ice sheet. The
range in values is greater, from ∼0.7 ∘C in the centre to
∼5.8 ∘C in the north-west periphery of the ice sheet over
the whole 144 year period. There is an area around Summit in the centre of
the ice sheet where these trends are not significant: p values exceed 0.05
here, indicated by blue, purple and black tones. The rest of the ice sheet
shows the trends are statistically significant. The summer trends in Fig. 11g
show lower values for the ice sheet as a whole than spring or annual trends.
The lowest values are on the west coast and the highest in the south and
north-west, indicating areas of weaker and stronger trends respectively, but
all are statistically significant (Fig. 11h). Autumn σ trends range
from ∼0.7 ∘C on the eastern periphery to ∼6.5 ∘C in the north-west over the 144 year period. The p values range
from 0 to 0.005 making these trends statistically significant across the ice
sheet. The winter trends have the same range as autumn but a different
spatial pattern. The lowest values are again in the centre of the ice sheet
at the highest elevations, with high values of ∼7.2 ∘C in
the south-west and up to ∼6.5 ∘C in the north-west over
the 144 year period. The trends in the centre of the ice sheet are not
significant at the 95 % level with p values over 0.05 in blues and
purples, and in excess of 0.09 in black.
Some negative trends are evident over the shorter period 1990–2013 (Fig. 12)
and they show greater spatial variation than for the full time series. They
are strongest in the south for the annual time series with values of -0.4 ∘C decade-1 and in the northwest in July with values down to -0.3 ∘C decade-1. Strong positive trends of 0.4 ∘C
decade-1 are apparent in the north at the annual timescale and during
the summer (Fig. 12a and b), as well as in the south at higher elevations
in July (Fig. 12c). The trend plots show small areas of statistically
significant positive trends in the southern region at the annual scale and
in the northwest in July.
Discussion
We first consider the improvements made by the pre-processing of the 20CR
2 m air temperature series. The three step correction process of the
original 20CR 2 m air temperature series in spring and winter shows that the
uncorrected 20CR series appears to be biased towards higher temperatures,
systematically overestimating temperatures relative to ERA-I. Conversely in
summer and autumn, the inverse occurs, where 20CR is biased towards lower
temperatures. These 20CR temperature biases would result in, respectively,
over- and under-estimated melt in the PDD-based melt-model calculation. As
the process of correcting the 20CR temperature time series does not alter
the variation within the dataset, the standard deviation of temperature is
not affected and therefore is not deemed essential for the derivation of the
new σ parameter. However, while the correction would not affect the
σ calculation, both the 3 hourly and monthly 2 m air temperatures
are fed into the degree-day model for calculating SMB, and are thus
essential for better quantifying mass balance. Although the correction
process brings 20CR temperatures more in line with ERA-I for the overlap
period, there are some discrepancies in absolute values between the fully
corrected 20CR and ERA-I series. This suggests that the fully corrected 20CR
series in Fig. 3 still does not capture all of the 2 m air temperature
variation and underestimates (overestimates) temperatures in 92 (88) out of
180 cases compared to ERA-I. It is unclear why such a large difference of
over ±1 ∘C between 20CR and ERA-I occurs in some years, but this
could partly be due to the aftermath of climatically-significant volcanic
eruptions, e.g. in 1982 and 1983 where 20CR over or under-estimates the
volcanic effect on Greenland temperatures compared to ERA-I. The ERA-I
reanalysis is assumed to be more accurate than 20CR as the reanalysis
product is more sophisticated/higher-resolution and involves the
assimilation of far more observations including upper air and satellite
data, while the 20CR relies on observed synoptic surface pressures and sea
surface temperature boundary conditions prescribed from HadISST1 (Wake et al., 2009; Hanna et al., 2011; Compo et al., 2006, 2011; Dee et al., 2011). The
20CR temperature fluctuations are smaller in magnitude compared to ERA-I,
possibly due to the lower spatial resolution of 20CR (2∘×2∘)
compared to ERA-I (∼0.75×0.75∘), which could lead to
artificially small σ values from 20CR, assuming ERA-I to be the more
accurate series.
Residual differences after 1979 between the spliced and un-spliced series,
when the ERA-I is incorporated into the spliced series, may be attributable
to resolution differences present in the original datasets before
downscaling as this latter part of the series is not affected by
breakpoints. The notable convergence of temperatures after 1930 in Fig. 4 is
synchronous with an increasing σ from around 1930. This increase in
σ may be partly attributable to more temperature observations being
assimilated by 20CR into the model – which may well improve the calculations
of both absolute temperature and its variability – with decreasing accuracy
and artificially smooth temperature variability inherent before 1930.
Summer is the dominant season in the melt calculation as this is when most
melting takes place. Moreover, the higher σ values above the ELA are
generally of little consequence as these are in line with the constant
σ values previously used. It is therefore values below the ELA
during the melt season that will have most effect on the melt calculation.
As the summer (especially July) σ values are consistently lower than
4.2 ∘C, this has implications for the modelled melt and therefore SMB of
the GrIS for the study period. As previously discussed, lower constant
σ values yield a decreased modelled melt area and a higher SMB
(Fausto et al., 2009a). However, the variable parameter will likely affect
the total melt volume rather than melt area as lower σ values are
evident largely below the ELA during the melt season. Our results give
a mean 1870–2013 summer σ value averaged across the entire ice sheet
of ∼3.2 ∘C, which is ∼1–2 ∘C lower
than in many studies. Indeed some values around the ice sheet periphery are
at least five times smaller than some constant parameters discussed in
Rogozhina and Rau (2014). Our summer σ values range from 0–5 ∘C
over the whole ice sheet and 0–4 ∘C in the ablation zone. These values
are overall higher than the 1–2.5 ∘C that Rogozhina and Rau (2014)
obtained for summer σ based on ERA-40 reanalysis from 1958–2001.
Their shorter time series, different model used and lower spatial resolution
(10km×10km compared to our 5km×5km), which tends to smear the edges of the ice
sheet, are likely to account for some of the differences in calculated
σ.
The statistically significant increases in σ through time over the
study period in Fig. 11 would predict that the melt area has increased on
average for the last 144 years. This would result in a downward trend in SMB
from 1870–2013, in line with the results of Rogozhina and Rau (2014) to be
investigated in a planned study into SMB of the GrIS using our variable
σ. Part of this trend may, however, be due to an increasing number
of weather stations assimilated into the 20CR series capturing more surface
air temperature variability during the second half of the reanalysis period.
There is considerable variation in the spatial distribution of σ on
both the inter- and intra-annual timescales for the period of study. Banding
with elevation is evident in all seasons, in agreement with the findings of
Fausto et al. (2009b), but is less evident in the summer months. Higher
σ values in the centre of the ice sheet in Fig. 6 can be attributed to
the effects of continentality and dominant more stable weather patterns with
predominantly clearer skies further inland (Taurisano et al., 2004). The
lower σ values in coastal areas may be attributed to temperature
inversions and greater cloud cover (suppressing the diurnal temperature
range) for much of the year (Cappelen et al., 2001; Mernild and Liston,
2010). The south-west of the GrIS also tends to have higher σ values
due to transient low-pressure systems moving eastwards from the Labrador Sea,
especially in summer. Winter σ values tend to be larger (Fig. 6) due
to the intense cold that often dominates the centre of the ice sheet during
these months, which is sometimes interrupted by the intrusion of transient
weather systems, especially in the south and south east, thus leading to
large shifts in temperature (Box, 2002; Hanna et al., 2012). The banding with
elevation is less noticeable during the summer months due to the limiting
effect of melt on near-surface temperatures, as discussed previously.
The spatial and temporal variations in σ across the GrIS underscore
the importance of including a variable parameter in the temperature-index
method. As Fausto et al. (2009a) found a 33 % difference in melt area with
a ∼2 ∘C variation in a spatially and temporally constant
σ, following their results the ∼1 ∘C lower summer
σ found here could reduce the melt area by over 15 %. The impact
of this change in melt area on the SMB, particularly during summer months:
will be quantified using our updated version of the Janssens and Huybrechts
(2000) PDD model. The effect of increased σ in other months and
seasons also needs to be investigated to determine whether this compensates
in part for the effect of lower summer σ or has little impact on the
melt calculation. This will be presented elsewhere.
Validation of the new σ parameter is difficult due to the limited
spatial and temporal coverage of in situ surface air temperature
observational data available for Greenland. There is inevitably more data
available for areas around and surrounding the ice-sheet margin, which may
introduce bias into the validation, alongside some issues concerning the
independence of the validation and reanalysis meteorological datasets. As
the AWS temperatures are fed into the σ parameter, either directly
through least-squares fit or more indirectly through reanalysis products,
this may affect the validation results by producing stronger correlations
than would be the case for entirely independent datasets (Compo et al., 2011;
Dee et al., 2011; Fausto et al., 2009b). On the other hand, the ice-sheet
margin areas are where most melt occurs, and many of the weather stations
are in relatively close proximity to this region.
Data gaps are inherent in the DMI, GC-Net and PROMICE AWS data used here,
which can limit the validation and introduce errors. To mitigate this issue,
only stations with over two thirds complete data were included in the
validation. The time period of available data also varies by station, so
care was taken to ensure that the same time period was selected for the
modelled σ as was available for the corresponding station, limiting
errors and making the full use of available observations. For a full
description of errors in the validation data, we refer the reader to DMI TR
11–16 (DMI), van As et al. (2011) (PROMICE) and Steffen and Box (2001)
(GC-Net). The point-to-pixel comparison carried out in this study will
inevitably also introduce some errors into the validation. Comparing
a 5km×5km pixel with a single AWS point introduces issues of scale
incompatibility; however, this technique has been used in previous studies,
including those of Hanna and Valdes (2001) and Radić and Hock (2006).
Some 81 % of σam, 62 % σjjam and 57 %
σjm are within ±1 ∘C of σ calculated from
observations (Tables 2, 3 and 4). These percentages are lower than those of
Fausto et al. (2009b) where 93 % of summer σ were within 1 ∘C
of observations (Table 1), and Fausto et al. (2011) where 93 % of annual
and 96 % of July σ values were within 1 ∘C of the observations
(Table 2). There is also an increase in accuracy with elevation up to the
ELA (∼1500 m), with a decrease thereafter in our study. This
may be due to a combination of using more validation sites, which encompass
areas where the model struggles to capture the observations, and differences
in the nature of the calculation between these two studies – with Fausto
using AWS data to carry out least-squares fit on observed σ rather
than using (as here) downscaled, corrected reanalysis data.
Figure 13 shows high correlation coefficients of 0.73, 0.76, 0.79 and 0.82
for annual, spring, autumn and winter respectively. These correlation
coefficients are all statistically significant showing a strong positive
significant relationship between temperature variability calculated from
20CR and ERA-I for the overlap period 1979–2008. The summer and July plots
however, show weaker correlations between 20CR and ERA-I, with a positive
bias in 20CR compared to ERA-I of ∼0.76 ∘C in summer and
0.7 ∘C in July for the overlap period. These correlations are still
statistically significant, showing there is a significant relationship
between 20CR and ERA-I σ from 1979–2008, despite the spread about
the trend line.
A unique aspect of the present work is the assessment of trends in σ
over the last 144 years for each 5km×5km pixel on the ice sheet. The
significant trends in σ across the ice sheet shown in all plots
(with the two previously-highlighted exceptions) indicate that σ has
increased from 1870–2013 and therefore temperatures have become more
variable across the ice sheet over the last 144 years. This increase is
especially prominent in the southern region for all plots, and also in the
north-west for all seasons. Other studies (e.g. Hall et al., 2013) have found
the greatest increase in temperatures in these regions of the GrIS,
indicating that not only are these regions becoming warmer, but they have
also experienced increased high-frequency (sub-monthly) temperature
variability. This is unsurprising given the extent of recent warming with
accompanying more frequent and extreme warm air/melt episodes over Greenland
(Hanna et al., 2008, 2014; Overland et al., 2012, 2015), and stronger
Greenland high-pressure blocking coupled with increasingly variable winter
NAO over the last 100 years (Hanna et al., 2013, 2015). Also the assimilation
of more weather stations into 20CR during the latter half of the 1870–2013
period is likely to have had an adverse effect of increasing variability in
temperatures because this enhances the effective spatial resolution and
sensitivity of the reanalysis. On the other hand, given the positive bias in
20CR σ shown in Fig. 13, the 1870–2013 trend may be an underestimate
if ERA-I is assumed to be the more accurate re-analysis and therefore 20CR
is overestimating variability. The balance of these various effects will
influence the observed trend.
However, when the more recent period (1990–2013) is examined separately, the
trends become more complex with fewer areas of statistical significance than
for the 144 year trend. The presence of negative trends in all these plots
for the shorter/recent timescale suggests that temperatures became less
variable across large parts of the ice sheet during this period.
Interestingly, in the north-west in July there is a statistically
significant area of reduced σ, indicating reduced temperature
variability here since 1990. This could be due to more widespread, intense
and longer-lasting summer melt suppressing near-surface air temperatures at
around freezing for longer in summer. This was coincident with a time of
more negative summer NAO, leading to more southerly warm air advection and
amplified Greenland warming in the last 1–2 decades (Hanna et al., 2015; Overland et al., 2012, 2014).
Figure 14 shows correlations between σ and NAOI/GBI for summer for
different time periods. The GBI-v.-σ plot for 1990–2013 shows
significant negative correlations (<-0.4) along parts of the
western margin, going slightly inland, and in extreme north-west Greenland.
Temperature variability is less in these regions with high GBI, due to more
stable prevailing weather conditions under high pressure. There is an
opposite, negative correlation along the southeast Greenland coast due to
this being on the other side of the high pressure block and therefore more
subject to associated vagaries in weather conditions, e.g. sometimes
affected by strong cold northerly winds flowing south along the Denmark
Strait due to changes in the position/intensity of the High. The pattern of
GBI-σ correlations for 1948–2013 is similar but somewhat muted (but
is broadly similar as significance levels are then lower). The
NAO-v.-σ 1899–2013 plot shows modest but significant positive
correlations over most of the GrIS, which are associated with less blocking
and more variable temperatures under a high NAO regime. The NAO-σ
plot for 1990–2013 shows an area of significant negative correlation in
inland southeast Greenland, which rather resembles the area of opposite
correlation in the GBI-σ plot for the same time period.