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MASS BALANCE OF GLACIERS IN THE WRANGELL RANGE, ALASKA DETERMINED BY THE PTAA MODEL Wendell Tangborn Preliminary Report (June 2011) Summary The total glacierized area of the Wrangell Mountain Range in Alaska, approximately 4725 km2, is divided into two separate regions of nearly equal area based on north and south orientations of the approximately 30 glaciers in this range. The North Wrangell glacier area is 2418 km2 and the South Wrangell area is 2307 km2. Figure 1 is the area-altitude distribution for the South Wrangell glaciers, and Figure 2 the area-distribution for the North Wrangells. Each of these glacierized regions is divided into 30.5 m (100 feet) elevation intervals by ARC GIS. The purpose of this project is to determine the historical mass balances of the Wrangell Mountain glaciers using the PTAA model. To accomplish this, snow accumulation and snow and ice ablation at each of the 280 elevation intervals is calculated for each day of a 57 year period (1950-2006). These incremental balances are then formed into annual mass balances for each region and for the full period of available weather records. Calibration of the PTAA mass balance model for each glacierized region is accomplished by calculating 9 balance parameters for each day of the summer season (approximately May 15 to September 30) throughout the 1950-2006 period. Linear regressions are run between the calculated balance parameters for each day of the summer season. Daily temperature and precipitation observations at two weather stations are converted to snow accumulation and snow and ice ablation at each AA interval, then totaled for the glacierized areas. (thus each iteration of the simplex optimization procedure requires 3-5 billion calculations). The first 15 iterations are derived from pre-set coefficients, the remaining are automatically computed in the simplex optimizing subroutine. Usually 3-400 iterations are sufficient to close the simplex, which occurs when the optimization function (ERRPC) has reached a designated minimum. It is emphasized that the determination of the coefficients is not restricted in any way and can assume any value as long as the error produced by the balance parameter regressions is minimized. A detailed description of the PTAA model using South Cascade Glacier for its development is provided in Tangborn (1999). Additional applications of the model in Alaska can be found in Tangborn (1997), Bhatt et al (2007), Zang et al (2007a), Zang et al (2007b). The optimization function, ERRPC, is equal to the average root-mean-square plus the complement of the R2 (1-R2) x 100, for the 19 regressions that relate the 9 balance parameters during each day of the summer season (130-150 days), therefore, approximately 2700 linear regressions determine the value of ERRPC for each iteration. Figure 3 demonstrates the optimization error (ERRPC) for each iteration when calibrating the south Wrangell glaciers, and Figure 4 is the results for calibrating the north Wrangells. It should be noted that once the 15 preset coefficients are applied to determine annual balances, the remaining errors are derived solely by simplex optimization. The high value of the optimization error ERRPC (over 40 %) should not be considered significant and is not related to the accuracy of the final balances. The two weather stations used in this example are McKinley Park and Big Delta, located approximately 350 km from Mt. Wrangell. There are closer weather stations; however, no combination of four of them produced a lower ERRPC than these two (that were also found to be optimum for Gulkana Glacier in an earlier study). Calibration for the Wrangell Range glaciers was initiated using Gulkana coefficients, the simplex optimization then produced a new set of coefficients for each of the north and south glacierized areas (Tables 1 and 2). Laser altimetry maps have been constructed for the Kennicott Glacier (1043 km2) in the South Wrangells and the Nabesna Glacier (253 km2) in the North Wrangells. In addition to the 67 north and south facing glaciers in the Wrangell Range, the PTAA model was also run individually on the Nabesna Glacier to represent the north Wrangells and the Kennicott Glacier to represent the South Wrangells. This was done to compare these data to aircraft laser altimetry data collected by the University of Alaska, Fairbanks. These model runs also used the McKinley Park and Big Delta weather stations for the temperature and precipitation data inputs. The Nabesna Glacier PTAA model run covered the time period 1957-2008 and had a total thickness change of -33 meters of ice, or -0.57 m/yr for the 52 year period. The single glacier PTAA model runs for the Nabesna and Kennicott Glaciers show the same patterns as the full area model runs, with the south oriented Kennicott Glacier’s mean annual mass balance (-0.96 m.w.e) being some 40% greater than that for the north facing Nabesna Glacier (-0.57 m.w.e). The mean annual balance for the 1950-2006 period of the North Wrangell glaciers is –0.23 MWE and – 0.66 for the South Wrangell glaciers, corresponding total volume losses of 556 km3 and 1523 km3, respectively. These results predict that mass balances of south facing glaciers are nearly three times more negative (-0.66 to –0.23 mwe) than north facing glaciers, and that the ELA is 200 m higher than the north facing glaciers. Glacier orientation is not included in the model for calculating ablation, but it is noteworthy that the PTAA model apparently incorporates orientation in the calibration process as it produces realistic mass balances using only weather observations from distant stations and a precise calculation of the area-altitude distributions of these glacierized areas. However, unquestionable verification of the model’s accuracy can only be determined using volume changes found by DEM means during a sufficiently long segment of the 1950-2006 period. FRACTION OF TOTAL AREA SOUTH WRANGELL GLACIERS AREA ALTITUDE DISTRIBUTION TOTAL AREA = 2307 KM2 0.025 0.02 0.015 0.01 0.005 45 7 67 1 88 4 10 97 13 11 15 24 17 37 19 51 21 64 23 77 25 91 28 04 30 18 32 31 34 44 36 58 38 71 40 84 42 98 45 11 47 24 49 38 0 ELEVATION (METERS) Figure 1. Area-Altitude distribution of the glaciers of the Southern region of the Wrangell Range, determined for each 30.5 m interval by ARC GIS. NORTH WRANGELL GLACIERS AREA-ALTITUDE DISTRIBUTION TOTAL AREA = 2418 KM2 FRACTION OF TOTAL AREA 0.035 0.03 0.025 0.02 0.015 0.01 0.005 91 4 10 97 12 80 14 63 16 46 18 29 20 12 21 95 23 77 25 60 27 43 29 26 31 09 32 92 34 75 36 58 38 41 40 23 42 06 43 89 45 73 47 55 49 38 0 ELEVATION (METERS) Figure2. Area-Altitude distribution of the northern region of the Wrangell range, determined by ARC GIS. WRANGELL RANGE SOUTH CALIBRATION ERROR VERSUS ITERATION 70 CALIBRATION ERROR - ERRPC (%) 1ST 15 ERRORS DETERMINED FROM PRE-SET COEFFICIENTS 65 60 55 50 45 757 736 715 694 673 652 631 610 589 568 547 526 505 484 463 442 421 400 379 358 337 316 295 274 253 232 211 190 169 148 127 85 106 64 43 22 1 40 ITERATION NUMBER Figure 3. Calibration error (ERRPC) versus iteration of the south Wrangell Range. The first 15 errors are determined by the pre-set coefficients shown in the input file OPT!IN.WRS. WRANGELL RANGE NORTH 110 100 ERRPC (%) 90 80 70 60 50 701 676 651 626 601 576 551 526 501 476 451 426 401 376 351 326 301 276 251 226 201 176 151 126 101 76 51 26 1 40 ITERATION NUMBER Figure 4.. Calibration error (ERRPC) versus iteration of the north Wrangell Range. The first 15 errors are determined by the pre-set coefficients shown in the input file OPT1IN.WRN. The remaining errors resulted from the simplex calibration process WRANGELL RANGE NORTH ANNUAL BALANCE VERSUS CALIBRATION ERROR 2 1.5 MEAN ANNUAL BALANCE (MWE) MEAN BALANCE = -0.23 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 40 50 60 70 80 90 100 110 CALIBRATION ERROR (ERRPC) % Figure 5. The mean annual balance of the north Wrangell glaciers, determined for the 1950-2006 period, versus the calibration error for each iteration. The minimum error is reached when the mean balance is –0.23 MWE compared to a mean balance of -0.66 MWE for the south facing glaciers. WRANGELL RANGE SOUTH ANNUAL BALANCE VERSUS CALIBRATION ERROR MEAN ANNUAL BALANCE (1950-2006) MWE 1.5 1 MEAN BALANCE = -0.66 0.5 0 -0.5 -1 -1.5 40 45 50 55 60 65 70 ERROR (ERRPC) % Figure 6. The mean annual balance of the south Wrangell glaciers, determined for the 1950-2006 period, versus the calibration error for each iteration. The minimum calibration error is reached when the mean balance is –0.66 MWE, compared to a mean balance of -0.23 MWE for north facing glaciers. WRANGELL RANGE NORTH ANNUAL BALANCE 0.5 ANNUAL BALANCE (MWE) 0 -0.5 -1 -1.5 -2 04 02 00 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70 68 66 64 62 60 58 56 54 52 06 20 20 20 20 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 50 -2.5 Figure 7. Annual balances for the north Wrangell glaciers for 1950-2006, calculated from the final coefficients determined in the calibration. The mean annual balance for this period of these northerly oriented glaciers is –0.23 mwe. WRANGELL RANGE SOUTH ANNUAL BALANCE 1 ANNUAL BALANCE (MWE) 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 20 04 20 01 19 98 19 95 19 92 19 89 19 86 19 83 19 80 19 77 19 74 19 71 19 68 19 65 19 62 19 59 19 56 19 53 19 50 -3.5 Figure 8. Annual balances for the south Wrangell glaciers for 1950-2006, calculated from the final coefficients determined in the calibration. The mean annual balance for this period for these southerly oriented glaciers is –0.66 mwe. WRANGELL RANGE GLACIER ANNUAL BALANCES 1 SOUTH WRANGELL BALANCE (MWE) 0.5 0 -0.5 -1 y = 1.2987x - 0.2606 R2 = 0.8425 -1.5 -2 -2.5 -3 -3.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 NORTH WRANGELLS BALANCE (MWE) Figure 9. Annual balance of glaciers with southern orientation versus annual balance of northern glaciers WRANGELL RANGE, ALASKA CUMULATIVE ANNUAL BALANCES NORTH AND SOUTH GLACIERS CUMULATIVE ANNUAL BALANCE (MWE) 0 -5 -10 -15 -20 SOUTH WRANGELLS NORTH WRANGELLS -25 -30 20 04 20 01 19 98 19 95 19 92 19 89 19 86 19 83 19 80 19 77 19 74 19 71 19 68 19 65 19 62 19 59 19 56 19 53 19 50 -35 Figure 10. Cumulative annual balances of southerly oriented Wrangell glaciers and northerly oriented glaciers. SOUTH WRANGELL RANGE, ALASKA MEAN ANNUAL, ACCUMULATION AND ABLATION BALANCE VERSUS ELEVATION MEAN BALANCE (1950-2006) MWE . 2 1 0 -1 -2 -3 -4 ANNUAL BALANCE ACCUMULATION BALANCE ABLATION BALANCE -5 -6 -7 48 8 67 0 85 4 10 36 12 20 14 02 15 86 17 68 19 52 21 34 23 18 25 00 26 84 28 66 30 50 32 32 34 16 35 98 37 82 39 64 41 48 43 30 45 14 46 96 48 80 -8 ELEVATION (METERS) Figure 11. Annual, accumulation and ablation balances of south oriented glaciers. Mean ELA is approximately 2040 m elevation. 2 WRANGELL RANGE NORTH, ALASKA MEAN ANNUAL, ACCUMULATION AND ABLATION BALANCE VERSUS ELEVATION 1 BALANCE (MWE) . 0 -1 -2 -3 -4 ANNUAL BALANCE ACCUMULATION BALANCE ABLATION BALANCE -5 94 4 10 97 12 50 14 02 15 54 17 07 18 60 20 12 21 64 23 17 24 70 26 22 27 74 29 27 30 80 32 32 33 84 35 37 36 90 38 42 39 94 41 47 43 00 44 52 46 04 47 57 49 10 -6 ELEVATION (METERS) Figure 12. Annual, accumulation and ablation balances of north oriented glaciers. Mean ELA is approximately 2230 m elevation TABLE 1. SOUTH WRANGELL RANGE FINAL COEFFICIENTS 2.9231002330780029 1 CFF1 PRECIP MULTIPLIER AT MAX ALTITUDE 1.5325336456298828 2 CFF2 PRECIP MULTIPLIER AT TERMINUS 1.9415547847747803 3 CFF3 ALTITUDE OF MAX PRECIP (X 1000) 0.4155697822570801 4 CFF4 PRECIP MIXING FRACTION 0.4223370552062988 5 CFF5 LAPSE-RATE INTERCEPT (> AVG TEMP) 2.4088523387908936 6 CFF6 LAPSE-RATE LINE SLOPE (+2) 0.5889337658882141 7 CFF7 LAPSE-RATE INTERCEPT (< AVG TEMP) 2.1134562492370605 8 CFF8 LAPSE-RATE LINE SLOPE (+2) 13.4472980499267578 9 CFF9 ABLATION FROM TEMP (W/O PRECIP) 11.3437223434448242 10 CFF10 ABLATION FROM TEMP (WITH PRECIP) -0.0121527016162872 11 CFF11 TEMPERATURE THRESHOLD 1.0233986377716064 12 CFF12 ABLATION FROM SOLAR RADIATION 8.0389041900634766 13 CFF13 SEASONAL SNOWLINE RISE MULTIPLIER 1.3465770483016968 14 CFF14 TEMPORARY SNOWLINE RISE MULTIPLIER 0.8375621438026428 15 CFF15 INTERNAL ACCUMULATION MULTIPLIER TABLE 2. NORTH WRANGELL RANGE FINAL COEFFICIENTS 2.3887887001037598 1 CFF1 PRECIP MULTIPLIER AT MAX ALTITUDE 1.4978747367858887 2 CFF2 PRECIP MULTIPLIER AT TERMINUS 1.8936026096343994 3 CFF3 ALTITUDE OF MAX PRECIP (X 1000) 0.4049295783042908 4 CFF4 PRECIP MIXING FRACTION 0.3593062758445740 5 CFF5 LAPSE-RATE INTERCEPT (> AVG TEMP) 2.3861336708068848 6 CFF6 LAPSE-RATE LINE SLOPE (+2) 0.5852508544921875 7 CFF7 LAPSE-RATE INTERCEPT (< AVG TEMP) 2.1820788383483887 8 CFF8 LAPSE-RATE LINE SLOPE (+2) 13.8239889144897461 9 CFF9 ABLATION FROM TEMP (W/O PRECIP) 10.9378795623779297 10 CFF10 ABLATION FROM TEMP (WITH PRECIP) 0.0039875274524093 11 CFF11 TEMPERATURE THRESHOLD 0.8797739744186401 12 CFF12 ABLATION FROM SOLAR RADIATION 8.5338897705078125 13 CFF13 SEASONAL SNOWLINE RISE MULTIPLIER 1.3889465332031250 14 CFF14 TEMPORARY SNOWLINE RISE MULTIPLIER 0.8865205049514771 15 CFF15 INTERNAL ACCUMULATION MULTIPLIER Conclusions The PTAA model apparently generates realistic mass balances using only low-altitude weather observations because the glacier has retained a memory of the past climate. Over the thousands of years of its existence, erosion produced by the sliding glacier has carved its climatic history in the underlying bedrock. The surface configuration of the glacier (its area-altitude distribution) reflects both the undulations of its bed and ice flow of the glacier, thus by combining current weather observations with the current AA distribution, which is embedded with the past climate, the current mass balance (snow accumulation minus snow and ice ablation) can be calculated. The surface configuration of these glaciers influence the timing, distribution and amount of snow accumulation and ablation. Orientation of the surface strongly affects ablation, and to some extent accumulation, and the Wrangell mass balances determined by the model show that south-facing glaciers have 3 times the ablation rate as north-facing glaciers. Therefore, the model appears to have sensed from the AA profiles of the north and south facing glaciers that ablation would be much greater for the south-facing glaciers Surface orientation is not an input to the model, also, the same weather stations were used for both north and south glaciers. Theoretically, it should be possible to reconstruct the climate of this region for the past several hundred years based only on how these glaciers respond to the current climate. Acknowledgements The area-altitude distributions were calculated by Indrani Das using ARC DIS. Funding for the Wrangell project is provided by HyMet Inc References Zhang, J., U. S. Bhatt, W. V. Tangborn, and C. S. Lingle, 2007: Climate downscaling for estimating glacier mass balances in northwestern North America: Validation with a USGS benchmark glacier, Geophysical Research Letters, 34, L21505, doi:10.1029/2007GL031139. pdf version . Bhatt U.S., J. Zhang, W.V. Tangborn, and C.S. Lingle, L. Phillips, 2007: Examining Glacier Mass Balances with a Hierarchical Modeling Approach, Computing in Science and Engineering, 9 (2), 61-67. pdf version. Zhang J. , U.S. Bhatt, W. V. Tangborn, C.S. Lingle, 2007: Response of Glaciers in Northwestern North America to Future Climate Change: an Atmosphere/Glacier Hierarchical Modeling Approach, Annals of Glaciology, Vol. 46, 283 – 290. pdf version. Tangborn, W.V., A Mass Balance Model that Uses Low-altitude Meteorological Observations and the Area–Altitude Distribution of a Glacier , Geografiska Annaler: Series A, Physical Geography Volume 81, Issue 4, December 1999, Pages: 753–765, Tangborn, W.V., Using low-altitude meteorological observations to calculate the mass balance of Alaska’s Columbia Glacier and relate it to calving and speed. Report of a Workshop, February 28 – March 2, 1997, Byrd Polar Research Center, Report No. 15 Article first published online : 15 DEC 2003, DOI: 10.1111/1468-0459.00103