The sensitivity of snowpack sublimation estimates to instrument and measurement uncertainty perturbed in a Monte Carlo framework

doi:10.1007/s11707-018-0721-0

Front. Earth Sci.

2018, Vol. 12

Issue (4) : 728-738 https://doi.org/10.1007/s11707-018-0721-0

RESEARCH ARTICLE

The sensitivity of snowpack sublimation estimates to instrument and measurement uncertainty perturbed in a Monte Carlo framework

D.M. HULTSTRAND¹, S.R. FASSNACHT^2,^3,^4,⁵(

)

¹. EASC-Watershed Science, Colorado State University, Fort Collins, CO 80523-1482, USA
². ESS-Watershed Science, Colorado State University, Fort Collins, CO 80523-1476, USA
³. Cooperative Institute for Research in the Atmosphere, Fort Collins, CO 80523-1375, USA
⁴. Geographisches Institut, Abt. Kartographie, GIS & Fernerkundung, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
⁵. Natural Resources Ecology Laboratory, Fort Collins, CO 80523-1499, USA

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Abstract

The bulk aerodynamic flux equation is often used to estimate snowpack sublimation since it requires meteorological measurements at only one height above the snow surface. However, to date the uncertainty of these estimates and the individual input variables and input parameters uncertainty have not been quantified. We modeled sublimation for three (average snowpack in 2005, deep snowpack in 2011, and shallow snowpack in 2012) different water years (October 1 to September 30) at West Glacier Lake watershed within the Glacier Lakes Ecosystem Experiments Site in Wyoming. We performed a Monte Carlo analysis to evaluate the sensitivity of modeled sublimation to uncertainties of the input variables and parameters from the bulk aerodynamic flux equation. Input variable time series were uniformly adjusted by a normally distributed random variable with a standard deviation given as follows: 1) the manufacturer’s stated instrument accuracy of 0.3°C for temperature (T), 0.3 m/s for wind speed (U_z), 2% for relative humidity (RH), and 1 mb for pressure (P); 2) 0.0093 m for the aerodynamic roughness length (z₀) based on z₀ profiles calculations from multiple heights; and 3) 0.08 m for measurement height (z). Often z is held constant; here we used a constant z compared to the ground surface, and subsequently altered z to account for the change in snow depth (d_s). The most important source of uncertainty was z₀, then RH. Accounting for measurement height as it changed due to snowpack accumulation/ablation was also relevant for deeper snow. Snow surface sublimation uncertainties, from this study, are in the range of 1% to 29% for individual input parameter perturbations. The mean cumulative uncertainty was 41% for the three water years with 55%, 37%, and 32% occurring for the wet, average, and low water years. The top three variables (z varying with d_s, z₀, and RH) accounted for 74% to 84% of the cumulative sublimation uncertainty.

Keywords snow sublimation uncertainty aerodynamic methods

Corresponding Author(s): S.R. FASSNACHT

Just Accepted Date: 02 July 2018 Online First Date: 03 August 2018 Issue Date: 20 November 2018

Cite this article:

D.M. HULTSTRAND,S.R. FASSNACHT. The sensitivity of snowpack sublimation estimates to instrument and measurement uncertainty perturbed in a Monte Carlo framework[J]. Front. Earth Sci., 2018, 12(4): 728-738.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-018-0721-0
https://academic.hep.com.cn/fesci/EN/Y2018/V12/I4/728

Fig.1 Topographic map of West Glacier Lake watershed, located in the Snowy Range of the Medicine Bow Mountains of southern Wyoming. Contour interval is 15 m. Solid dot shows location of lake outlet. The star shows the location of GLEES meteorological station used in this study. Data from the GLEES tower were used in the study.

Fig.2 Brooklyn Lake SNOTEL (a) snow depth and (b) snow water equivalent, and (c) the calculated unperturbed and range of perturbed cumulative sublimation for water year 2005, 2011, and 2012. The median d_s (2004 to 2017) and SWE (1981–2017) are included. In Fig. 2(c), the shaded zones are the upper and lower limits of the perturbed computations.

Variable/parameter	WY2005	WY2011	WY2012
Temperature T/°C	–4.78	–6.18	–4.82
Relative humidity RH/%	67.8	72.3	62.4
Wind speed U_z/(m·s^–1)	4.99	5.42	5.28
Saturation vapor pressure e_s/mb	4.71	4.36	4.85
Station pressure P/mb	684	685	687
Vapour pressure e/mb	2.92	2.89	2.66
Momentum stability function; $ϕ m$	0.94	1.01	0.98
Water vapour stability function; $ϕ v$	0.99	1.05	1.01
Total precipitation/mm	777	1303	671
Peak snow water equivalent SWE/mm	521	1087	450
Snow cover period/days	234	249	220
Unperturbed sublimation/mm	290	276	350

Tab.1 Snowpack and mean meteorological conditions for October–May, the period when temperatures are below 0°C and conducive for sublimation, plus the unperturbed sublimation estimated from the BF method

Tab.2 Summary of the seven numerical tests that were performed in the sensitivity analysis for sublimation calculations. The mean and standard deviation used in the perturbations for the variables and parameters is listed

Fig.3 Histogram of 1000 modeled sublimation simulations for z₀ perturbations for water year 2005 (unperturbed 290 mm), 2011 (unperturbed 276 mm), and 2012 (unperturbed 350 mm).

Fig.4 Sensitivity statistics by water year (a) 2005, (b) 2011, and (c) 2012 for the Monte Carlo simulation from uniformly perturbing input sublimation variables and parameters (see Table 2). The unperturbed sublimation is shown as a dotted line for each water year.

Tab.3 Uncertainty summary statistics by Water Year based on Monte Carlo simulation from uniformly perturbing input sublimation variables/parameters: T is air temperature, RH is relative humidity, U_z is wind speed, z₀ is the aerodynamic roughness length, z = 3, is a constant measurement height of 3.0 m, and z is the height of the instrumentation above the snow surface that varies as a function of the snow depth. The variable z was not perturbed (Table 2) so no range is available. The P perturbations are not included as they did not impact the calculated sublimation

Tab.4 The amount of sublimation for the minimum, base and maximum computed values compared to peak SWE and annual total precipitation, given as a percent

Fig.5 Comparison of the estimated cumulative sublimation using dewpoint temperature as the surface temperature (T_s) versus the base case, using air temperature to estimate T_s for the study winters of 2005, 2011, and 2012.

Fig.6 Mean hourly computed sublimation for the base case with air temperature (see x-axis in Fig. 5) and using the dewpoint temperature (see y-axis in Fig. 5).

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