++ Lemon Creek *

Figure 1.  Lemon Creek glacier. Photo by L. Bernier, 2007


The historical Net, Ablation and Accumulation daily balances and runoff of the Lemon Creek Glacier, Alaska are  determined for the 1951-2011 period with the PTAA (precipitation-temperature-area-altitude) model, using daily precipitation and temperature observations collected at the Juneau weather station, together with the area-altitude distribution of the glacier.  The mean annual balance for this 61-year period is  -0.4 mwe, the accumulation balance is +1.3 and the ablation balance is - 1.7 mwe.  Comparison of PTAA balances with manual measurements provided by the Juneau Icefield Research Program for the 1953-2011 period show nearly equal  average mass losses (-0.44 mwe for PTAA versus -0.41 mwe for manual measurements).  However, the R2 for a regression fit of annual balances  is only 0.20 indicating large annual balance differences between the two methods.


The Lemon Creek glacier is one of the nine North American glaciers selected for a global monitoring program  during the International Geophysical year, 1957/58. Annual balance measurements on the Lemon Creek Glacier,  Alaska conducted by the Juneau  Icefield  Research Program (JIRP) from 1953 through 2011 provide a continuous 59 year record of mass balance (Miller and Pelto, 1999).  Balance data have been collected primarily by employing consistent ground methods (snow pits and ablation stakes), conducted on similar annual dates and calculated using comparable methodology (known as the Glaciological Method).

Mass Balance Results

The PTAA mass balance  (precipitation-temperature-area-altitude) model is applied to the glacier's area-altitude distribution shown in Figure 2, using as input the daily temperature and precipitation observations at  Juneau, Alaska, located approximately  12 km. SE of the glacier terminus, and at an elevation  of 5 meters.  The mean annual balance for the Lemon Creek Glacier averaged for 61 years (1951-2011) is -0.4  mwe) (Figure 3). Total thinning averaged over the glacier surface for 61 years is 26 meters of ice or 0.4  meters of ice per year (Figure 4). The mean Accumulation Balance is +1.3 mwe and the Ablation Balance is -1.7 mwe (Figure 5).  Mass balance terminology used in this report deviates slightly from that proposed by the IACS Working Group of Mass Balance Terminology and Methods  (Cogley et al, 2011). The main variables that determine mass balance, such as precipitation, temperature, lapse rates and snowfall, are directly dependent on elevation. Glacier
balance models are constructed by applying relationships between these variables.  For example, precipitation  and temperature are both dependent on elevation but for different reasons.   Depicting elevation as being dependent on mass balance as is suggested in the IACS report may be misleading.  Therefore, in this report, balance and other variables are all shown to be dependent on elevation.

In addition, the terms Accumulation Balance and Ablation Balance are preferred over Winter Balance and Summer Balance  that are used in the IACS report. For most Alaskan glaciers, snow accumulation at higher elevations occurs throughout the year and can be especially heavy in August and September. For many Himalayan
Range glaciers, snow accumulation is greatest during the Monsoon season, from June through September, and at lower elevations ablation often occurs during the winter months.

Figure 2.  Area-altitude distribution of the Lemon Creek Glacier. The total area of the glacier is 9.56 km2 and there are 72 altitude intervals spaced at 10 m, ranging from 665 to 1365 meters in elevation.  Latitude 58.390 N,  Longitude -134.349 W.

Figure 3.  Annual balance of the Lemon Creek Glacier for the 1951-2011 period. The average annual balance is -0.6 mwe.  The minimum balance for the period (-3.0 mwe) occurred in 2004.

Figure 4.  Cumulative balance of the Lemon Creek  Glacier.  Total thinning during this 61 year period is 27 meters or 0.4 m of ice per year. 

Figure 5.  Accumulation and Ablation Balances for the 1951-2011 period. The average annual accumulation balance for this period  is +1.3 and the average ablation balance is -1.7 (mwe).  Maximum ablation (-4.3 mwe)  occurred in 2004.

Balance versus Elevation

The Net, Accumulation and Ablation balances as a function of elevation are shown in Figure 6a, averaged for the 1951-2011 period, and in Figure 6b for the 2004 balance year. The contrast between b(z) curves in Figures 6a and 6b demonstrate how ablation and the ELA of Lemon Creek Glacier were affected by the above normal temperatures during the 2004 summer. Ablation at the terminus increased from 5 to 8 mwe and the ELA moved up 160 m, from 1120 m average elevation to 1280 m in 2004. The annual balance in 2004 (-3.0 mwe) is the most
negative for the 1951-2011 period of record.

Figure 6a.  Net, Accumulation and Ablation balances of the Lemon Creek Glacier  as a function of elevation, averaged for the 1951-2011 period. The ELA  (1120  meters) is defined as the point at which the Net balance crosses the zero balance line.

Figure 6b.  Net, Accumulation and Ablation balances of the Lemon Creek Glacier as a function of elevation, averaged for the 2004 period. The ELA is 1280  meters, 160 meters above average. The balance at the  terminus (-8 mwe) is nearly 1.5 times as negative as on a normal year.

Model Calibration

The PTAA model is calibrated by calculating the daily balance for each altitude interval and for each day of the 1951-2011 period, using 15 coefficients and a Simplex optimizing procedure (Nelder and Mead, 1962).  The annual balance is found by integrating daily balances over one year.  The coefficients convert observed precipitation and temperature at two low-altitude weather stations to daily snow accumulation and snow and ice ablation. Physical explanations for each coefficient are provided in Tangborn (1999).

The initial 15 coefficient values are random estimates, based on a reasonable range of potential values for each parameter.  For example, the coefficient that converts gauge precipitation to basin precipitation is assigned 15 different values that vary from 0.107 to 0.288.   The final value after 350 iterations and the calibration is completed is 0.2007.  Similar estimates are made for initial values of the other 14 coefficients.  The annual balances shown for each iteration in Figure 7a are based on the initial estimates  of  the 15 coefficients.  The first 15 balances vary from approximately -5.0 to +3.0 mwe corresponding to the initial, pre-set coefficient values.  As the calibration proceeds, coefficient values are determined automatically by the Simplex.

One iteration of the Simplex determines for each elevation level the daily and annual balances for the period of record, and calculates the average error that occurs when multiple balance parameters are regressed against each other. The average root-mean-square-error resulting from these regressions is minimized to obtain the optimum coefficients.   The size of the error automatically determines the minute adjustment that is made to each coefficient for the next iteration.  After approximately 350 iterations, the calibration error reaches a minimum (in this case about 35 %), and the mean annual balance is an optimum value (about -0.4 mwe).

Figure  7a.  Mean annual balance versus iteration number of the optimizing Simplex. Balances  1-15 are derived from preset coefficients.  Balances 16-380 are calculated automatically from coefficients determined by the Simplex optimizing process.   When the calibration error reaches a minimum, the average annual balance is -0.4 mwe.

The scatter plot in Figure 7b shows the mean annual balance versus the corresponding error for each iteration.  When the calibration error is a minimum at 35 %, the mean annual balance is -0.40 mwe

Figure 7b.  Mean annual balance versus calibration error.  When the calibration error reached a minimum of  about 35%,  the average annual balance is -0.4 mwe. Each point represents the mean annual balance based on 61 years daily balance determinations.

Real-time Glacier Balances

One goal of the PTAAGMB project is to continuously monitor all 200 glaciers in the project and display the current mass balance of each one, in real-time, if up-to-date weather observations are available, or near real-time if weather observations are delayed.  The daily balances for the 2011 balance year shown in Figure 8 demonstrates how real-time mass balances for the Lemon Creek Glacier will be displayed in future years. 

On September 30, 2011, the Lemon Creek Net Balance is - 1.7 mwe, the Accumlation Balance, 1.0 mwe, and the Ablation Balance, -2.7 mwe. Analysis of the daily balances of a large number of glaciers simultaneously will be applied to produce an improved understanding of glacier/climate relationships.   Historical and current mass balance results for other glaciers worldwide (including others in Alaska) are shown elsewhere on this site.

Figure 8.  Daily balances of Lemon Creek Glacier during the 2011 balance year. The final net balance for 2011 on September 30 equals  -0.1 mwe, the Accumulation Balance is 1.3 and the Ablation balance is  -1.2 mwe.  Note that snow accumulation on the Lemon Creek Glacier begins on approximately July 1 each year, thus "winter" balance is a misnomer for this glacier.

Comparison of PTAA with Measured Balances

The annual balance of the Lemon Creek Glacier has been measured annually since 1953 using the Glaciological Method by the Juneau Icefield Project.  Comparisons of Measured versus PTAA balances are shown in Figure 9a (line plot of annual balances), and 9b (scatter plot of Measured versus PTAA annual balances.   The average Measured balance is  -0.44 for the 1953-2011 period compared to an average of - 0.41 for the PTAA model. Therefore, the volume losses for the 1953-2011 period for the two methods closely agree.

The R2 for a regression fit between Measured and PTAA annual balances is 0.20, which is significantly lower than that shown in balance comparisons for other glaciers, such as the Gulkana, Wolverine and Vernagtferner.  The cause of the greater variability shown for the Lemon Creek glacier is unknown. Both measured and PTAA balance errors contribute to the variability shown in 9a and 9b, although the relative contribution of each method is also unknown.

Figure 9a.  Measured and PTAA annual balances of the Lemon Creek glacier from 1953-2011.  The average measured balance is  -0.44 for the 1953-2011 period compared to an average of - 0.41 for the PTAA model.

Figure 9b.  Measured versus PTAA balances from 1953-2011. The R2 for this sample is 0.20


Annual balances of Lemon Creek glacier for the 1953-2011 period is calculated with the PTAA model using Juneau weather observations and the area-altitude distribution of the glacier, however the agreement with measured balances is poor (R2 = 0.20).  If the model versus measured balance comparison is made for the period after 1977 (1978-2011) the R2 increases to 0.40, which suggests the measured balances before 1977 are in error.


Wendell Tangborn


January 03, 2013


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Beedle, Matthew , www.GlacierChange.org
A new website that chronicles the rapid changes in the world's glaciers and the impact these changes are having on the lives of all living creatures

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The Lemon Creek area-altitude distribution was provided by Matthew Beedle.  Funding for the project was provided by HyMet Inc.