Jökull - 01.01.2005, Page 141

Mass balance of Vatnajökull outlet glaciersreconstructed back to 1958
Table 1: Difference in mean balance component from glacier 4 (m w.e.) over common period (n years). Stan-
dard deviation σ (m w.e.) and correlation (percent r) between components over full period of record of obser-
vations (N in Table 3.). Boldface r significant at 99 percent, italic at 95 percent. – icelandic
Glacier n ∆bw ∆bs ∆bn σw σs rnw rns rws
1 Tungnaárjökull 7 -0.17 -0.61 -0.79 0.37 0.47 93 96 78
2 Köldukvíslarjökull 8 -0.24 -0.02 -0.26 0.27 0.42 83 93 57
3 Dyngjujökull 6 -0.13 +0.24 +0.11 0.29 0.65 93 99 86
4 Brúarjökull 0.22 0.53 80 97 63
5 Eyjabakkajökull 6 +0.15 -0.83 -0.68 0.50 0.48 79 76 22
Here f is termed the snow flux, T (z1) is inter-
polated between the 1000 and 850-hPa levels in the
NCEP-NCAR Reanalysis data, and T ′ = +2◦C is
the rain-snow discriminator (Oerlemans, 1993; Ras-
mussen and others, 2000). Physical basis for using
+2◦C is that precipitation forming at high altitude as
snow requires a layer of air with T > 0◦C to change
to rain; at the average wet adiabatic lapse rate of
≈6◦C/km, +2◦C corresponds to a layer thickness of
≈300 m.
Table 2: Glacier to glacier correlation (percent r) of
observed winter balance bw (above the diagonal) and
summer balance bs (below the diagonal) over com-
mon period of record (n in Table 1.) Boldface r sig-
nificant at 99 percent, italic at 95 percent. – icelandic
Glacier 1 2 3 4 5
1 Tungnaárjökull 78 75 71 -13
2 Köldukvíslarjökull 90 84 10 -14
3 Dyngjujökull 93 96 86 95
4 Brúarjökull 78 87 99 90
5 Eyjabakkajökull 32 56 75 84
The model estimates winter balance b∗
w
by
b∗
w
= αwfw + γw (4)
Coefficients αw and γw are obtained by the linear re-
gression of observed winter balance bw and fw, which
is the October-April average of f. Because RH is di-
mensionless, both F and f have the same units as U ,
meters per second, so αw has units to convert to me-
ters water equivalent.
The model estimates summer balance b∗
s
by
b∗
s
= αsfs + βsT + γs (5)
in which the May-September average of f is f
s
,
and that of temperature interpolated at altitude z2 =
1200 m between the 1000 and 850-hPa levels, consid-
ering only T > 0◦C, is T . Coefficients βs and γs are
obtained by the linear regression of observed summer
balance bs with fs and T . The coefficient αs is set
to bw/fw where bw is the mean of bw and fw is the
mean of f
w
over the period of record.
For the Vatnajökull outlet glaciers, both b∗w and
b∗s are estimated from upper-air conditions at the
NCEP-NCAR Reanalysis gridpoint at 65◦N, 17.5◦W.
Mean winter conditions over 1958–2003 are shown in
Figure 2. Critical direction φ′ (Table 3) and the regres-
sion coefficients in Equations (4) and (5) are found
separately for each glacier.
MODEL RESULTS
Model estimates of seasonal components, both of
which are identified by the calendar year in which the
balance year ends, are illustrated in Figure 3. Good-
ness of fit is expressed by the coefficient of determi-
nation
r2 = 1 −
( rms
σ
)2
(6)
JÖKULL No. 55 141