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Monitoring icesheet snowmelt is fundamental to understanding global climate change. A simple and automated snowmelt detection process is critical to the establishment of an icesheet snowmelt monitoring system. However, different icesheet snowmelt detection methods are based on a variety of thresholding schemes using different melt signals for dry and wet snow; these complicate the regular operation of an icesheet snowmelt monitoring. We propose an automated melt signal detection method developed using melt signals derived from the crossgradient polarization ratio snowmelt detection method over Greenland and the wavelet transformationbased snowmelt detection method over Antarctica. Initial results indicate that the proposed method not only increases computational efficiency, practicability and operability but is also more accurate.
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Portions of ice sheets annually experience surface melting. Snowmelt on ice sheets plays an important role in the strength of global vapour circulation, global heat balance and climate change. Huybrechts (
Monitoring the snowmelt characteristics of the ice sheets over large areas and long periods of time is therefore imperative. The high sensitivity of microwave radiometric brightness temperature to changes in the physical characteristics of snow on the ice sheet's surface—for example, the presence of liquid water in the snowpack (Zwally & Gloersen
Icesheet snowmelt detection methods can be grouped into five types. The first is singlechannelbased methods (Mote et al.
The key to icesheet snowmelt detection is the thresholding schemes used to classify wet and dry snow. For the regular operation of icesheet snowmelt detection, the thresholding schemes should have some basic requirements. (1) They must be easy to implement during routine operation. A great deal of parameter input should be avoided. (2) During routine operation, the thresholding schemes must be efficient and the application of in situ measurements must be minimized to reduce costs and work associated with data collection. During regular operation, we can easily just use the crossgradient polarization ratio (XPGR) threshold already derived by Abdalati & Steffen (
This paper is organized into five sections. After describing the data sets, we introduce the basics of a melt signal adaptation method based on a GG model. Then the implementation of two icesheet snowmelt detection methods is described and two modified methods are proposed. These are then analysed and validated. Finally, we present our conclusions.
The test sites we selected in this study are the Antarctic continent and Greenland. The satellite passive microwave data used for this analysis are from the Scanning Multichannel Microwave Radiometer (SMMR) data collected by the US National Aeronautical and Space Administration's Nimbus7 satellite, the Special Sensor Microwave/Imager (SSM/I) data collected by the DMSPF8, F11 and F13 satellites and the Special Sensor Microwave Imager Sounder (SSMIS) data collected by the DMSPF17 satellite. We processed the data spanning from 25 October 1978 to 30 June 2010 in Antarctica, and from 1 July 1988 to 30 June 1995 in Greenland. We employed the 18GHz horizontal polarization channel and 37GHz vertically polarized channel from the SMMR data, and the 19GHz horizontal channel and 37GHz vertically polarized channel from the SSM/I and SSMIS data.
Due to the difference orbital characteristics of the five instruments, the microwave brightness temperatures from these sensors are crossrecalibrated. Using the regression coefficients presented by Liu et al. (
Scatterplots and regression lines for the Antarctic data from 1 January 2009 to 29 April 2009: (a) data from the Special Sensor Microwave/Imager (SSM/I) 19GHz horizontal channel and (b) data from the SSM/I 37GHz vertically polarized channel.
Regression coefficients for data adjustments between different sensors in Antarctica.
Conversion  Slope  Intercept  Correlation coefficient 



SSM/I^{a} F17 37Ghz vertical to SSM/I F8 37Ghz vertical  1.008  −1.17 

SSM/I F17 19Ghz horizontal to SSM/I F8 19Ghz horizontal  1.0286  −3.0094 

^{a}Special Sensor Microwave/Imager.
In addition, to validate the result, the temperature measurements of automatic weather stations (AWSs) in Antarctica and Greenland were also collected. This is explained in more detail later in this paper.
Each method derived different melt signals and used different thresholding schemes for classification. The XPGR method determined a melt threshold for the XPGR on the ice sheet by comparing a time series of XPGR values with in situ air temperature data. In contrast, the wavelet transformationbased edge detection approach used the optimal edge threshold based on a biGaussian model to classify the critical values of wet and dry snow. To avoid the complications of using different thresholding schemes, a more efficient method implements only one threshold algorithm, is adaptable for different melt information and remains consistent with the values of the original threshold algorithms.
Generally, snowmelt detection methods involve the problem of classifying melt signals (
The classification precision (determined by the threshold
The function
Determining cost function depends on the probability density function (pdf) of melt signal of dry snow and wet snow. Because different detection methods use different melt signals, the pdfs of melt signals of different methods is likely to be different. For this reason, we considered a model that should be adaptable to the pdfs of different melt signals; that is, it should be capable of spanning a large variety of statistical behaviours. Moreover, for easy implementation during regular operation, it should not require the estimation of an excessively large number of parameters. Among the possible models, the GG distribution is a particularly attractive candidate. The analytical expression of the GG distribution considered in our approach for modelling the two classconditional pdfs is given by (Sharifi & LeonGarcia
where the positive constants
The terms
Under the GG distribution assumption, it can be proved that the cost function is optimized as follows (see the
where:
As shown above, the advantages of the GG model method are: it requires less manual input parameters (the parameters are computed automatically); the classification result is unique (namely, the threshold is unique); and it is capable of spanning a large variety of statistical behaviours.
The melt signal adaptation method can be applicable to many different melt signals in many different snowmelt detection methods, for example the XPGR value in XPGR method, the normalized gradient ratio (GR) value in GR method
Here, we only apply the method to the existing XPGR and wavelet transformationbased icesheet snowmelt detection methods. Further work will focus on the GR method, the
The XPGR method proposed by Abdalati & Steffen (
where
Crossgradient polarization ratio (XPGR) values at the Wilkins Ice Shelf area (from 1978 to 2010).
Crossgradient polarization ratio (XPGR) histogram and optimal threshold at the Wilkins Ice Shelf area (from 1978 to 2010). The red asterisk is the unsupervised XPGR threshold (−0.0293) obtained by the melt signal adaptation method.
Segmentation line of the optimal threshold at the Wilkins Ice Shelf area (from 1978 to 2010). The red line is the unsupervised Crossgradient polarization ratio (XPGR) threshold (−0.0293) obtained by the melt signal adaptation method.
Flowchart of modified crossgradient polarization ratio (XPGR) detection method. Scanning Multichannel Microwave Radiometer is abbreviated to SMMR and Special Sensor Microwave/Imager to SSM/I.
Icesheet snowmelt detection using a wavelet transformationbased method is based on the strong and significant edges in the brightness temperature (Tb) time series curve that signify snow melting and refreezing events (Liu et al.
Liu et al. (
Two optimal thresholds obtained from a bimodal Gaussian distribution model (BG) and a generalized Gaussian model (GG).
Flowchart of the modified icesheet snowmelt detection method based on wavelet transformation. Scanning Multichannel Microwave Radiometer is abbreviated to SMMR and Special Sensor Microwave/Imager to SSM/I.
The difference between the modified XPGR detection method and the XPGR method lies in the method in which the threshold is determined. The XPGR method uses in situ measurements to determine the threshold. The modified XPGR method uses the GG model to automatically seek an optimal threshold. Therefore, the modified XPGR method is solely dependent on the XPGR value. To analyse and compare the results of the method proposed by Abdalati & Steffen (
The threshold determination based on crossgradient polarization ratio (XPGR) value in the Greenland study area. The solid blue line represents the XPGR values from 1988 to 1995, the red line is the XPGR threshold (−0.0158) obtained by Abdalati & Steffen's (
Icesheet snowmelt distribution of the modified crossgradient polarization ratio (XPGR) detection method and the XPGR method on 2 August 1996: (a) the result of the XPGR method; (b) the result of the modified XPGR method.
Analysis and comparison of the modified and original wavelet transformation detection method results are based on the Antarctic SSM/I data from 1978 to 2010.
Icesheet snowmelt distribution during 2007–08 derived from the two optimal thresholds: (a) the bimodal Gaussian distribution model optimal threshold; (b) the generalized Gaussian model automatic threshold.
Icesheet snowmelt detection results obtained from the modified wavelet transformation method in Antarctica, 2007–08: (a) melt onset; (b) melt end; (c) melt duration.
This comparison shows that the optimal threshold based on the GG model is almost the same as those based on the BG model. However, the melt signal adaptation method increases threshold determination efficiency, has higher accuracy and is independent of estimation and initial value.
In addition to comparing the results of the modified and original methods, we have performed quantitative validations on the effectiveness and precision of the modified icesheet snowmelt detection method.
We use in situ data to validate the daily snowmelt detection results of each method. In general, surface melting occurrence spatially corresponds to the spatial pattern of temperature. Therefore, we validate the snowmelt detection results derived from two methods with the corresponding surface air temperature acquired by AWSs. An AWS cannot cover the same area observed by largescale remote sensing and can therefore not completely reflect largescale climate. However, to minimize the influence of the environment, we choose AWSs in those areas where the spatial gradients are relatively simple because the temperature data collected on these stations can reflect average temperature of large areas to some degree. Based on the Radarsat Antarctic Mapping Project Digital Elevation Model, we use the 1km data to calculate the minimum height, maximum height and standard deviation of height in the 625 km^{2} area around the AWS. We use those parameters as a standard of evaluation of spatial complexity. We choose the AWS in the area where the standard deviation of height and difference between the extreme values of height and elevation of AWS are smallest.
Because of the limited temperature records and strong fluctuations in surface melt on the Ross Ice Shelf, on the RonneFilchner Ice Shelf and in Marie Byrd Land AWSs were not chosen in those regions. The AWSs on Butler Island, at Bonaparte Point, on Larsen Shelf and at Amery G3 were chosen (
Automatic weather stations.
Station name  Latitude/longitude  Elev.  Dates  Days  Min.  Max.  SD 



Larsen Ice Shelf  66.90S/60.60W  50 m  07/02/83–01/01/86  2390  36.46 m  49.78 m  1.6874 
66.97S/60.55W  01/01/86–01/02/99  
–  66.949S/60.897W  –  01/02/99–02/01/04  –  –  –  – 
67.012S/61.550W  02/01/04–01/01/07  
67.012S/61.550W  01/01/07–  
Butler Island  72.20S/60.34W  91 m  01/03/86–25/01/89  2449  −14.80 m  95.36 m  16.83 
72.21S/60.16W  25/01/89–11/01/97  
72.21S/60.17W  11/01/97–11/01/00  
–  72.207S/60.160W  –  11/01/00–22/12/03  –  –  –  – 
72.206S/60.170W  02/02/05–02/02/11  
72.206S/60.170W  02/02/11–  
Bonaparte Point  64.78S/63.06W  8 m  05/01/92–09/03/94  1761  −35.10 m  311.72 m  77.97 
64.78S/63.07W  09/03/94–23/12/96  
–  64.778S/63.067W  –  23/12/96–14/03/08  –  –  –  – 
64.778S/63.067W  14/03/08–20/11/09  
64.778S/63.067W  20/11/09–  
Amery G3  70°53′31′′S/69°52′21′′E  84 m  1999–  1931  95.20 m  104.08 m  1.84 
The daily mean air temperature data together with the corresponding daily detection results of each modified snowmelt detection method were used to quantitatively validate the snowmelt detection results of each method. For processing the AWS data, we chose the daily mean air temperature data from the summer months (November–March) in Antarctica. The total number of days
True positives (TP): the number of melt days that were correctly detected, and
False positives (FP): the number of nonmelt days that were incorrectly detected as “melt” (also known as false alarms), and
True negatives (TN): the number of nonmelt days that were correctly detected, and
False negatives (FN): the number of melt days that were incorrectly detected as “nonmelt” (also known as miss detections), and
Based on these four quantities, three assessment indices are proposed to evaluate the snowmelt detection result of the proposed method. The three assessment indices are as follows: Correct Detection Rate (CDR), Priori True Positives Rate (Priori TPR) and Posterior True Positives Rate (Posterior TPR). CDR is the ratio between the number of correctly detection results and the total number of detection results (or the total number of temperature data); Priori TPR is the ratio between the number of correctly detected “melt” results and the number of temperature data above 0°C; Posterior TPR is the ratio between the number of correctly detected “melt” results and the number of detected “melt” results:
The statistical analysis results are shown in
Quantitative snowmelt detection results (in %), applying two methods in four areas.
Automatic weather station  Snowmelt detection method 




CDR^{e}  Priori TPR^{f}  Posterior TPR^{g} 



Bonaparte Point  Wavelet  55.03  4.49  12.66  27.83  67.69  66.42  92.46 
XPGR^{h}  32.14  3.35  13.80  50.71  45.94  38.79  90.56  
Butler Island  Wavelet  6.7  15.03  71.87  6.41  78.56  51.09  30.83 
XPGR  4.08  14.56  72.02  9.34  76.09  30.38  21.87  
Larsen Ice Shelf  Wavelet  22.51  13.14  51.38  12.97  73.89  63.44  63.15 
XPGR  26.16  20.81  45.59  7.44  71.75  77.86  55.70  
Amery G3  Wavelet  4.97  9.01  83.43  2.59  88.40  65.75  35.56 
XPGR  5.58  20.42  71.90  2.09  77.49  72.73  21.48 
^{a}The number of melt days that were correctly detected.
^{b}The number of nonmelt days that were incorrectly detected as “melt” days.
^{c}The number of nonmelt days that were correctly detected.
^{d}The number of melt days that were incorrectly detected as “nonmelt” days.
^{e}Correct detection rate, the ratio between the number of correct detection results and the total number of detection results.
^{f}Priori true positives rate, the ratio between the number of correctly detected “melt” results and the number of temperature data above 0°C.
^{g}Posterior true positives rate, the ratio between the number of correctly detected “melt” results and the number of detected “melt” results.
^{h}Crossgradient polarization ratio.
However, we were primarily concerned with Priori TPR and Posterior TPR. Although the comparative statistics with in situ data were collected at the Bonaparte Point AWS and the Larsen Ice Shelf AWS, the result values of both methods show relatively high probabilities, except the XPGR methods in the area around the Bonaparte Point AWS. Moreover, the Posterior TPR of both methods are over 90%. For the Amery G3 AWS, the Priori TPR of both methods are over 65%; however, the Posterior TPR show relatively low probabilities. For the Butler Island AWS, both methods have low Priori TPR and low Posterior TPR. This is because the Butler Island AWS is very close to the seaside, so it does not reflect the average temperature of a large adjacent inland area.
Using temperature data to validate the snowmelt detection results of the modified XPGR detection method and the modified wavelet transformationbased method shows that they have relatively high precision.
This paper reports the results of an icesheet snowmelt detection study using microwave radiometer data sets. We proposed a melt signal adaptation method to automate melt signal detection, based on a GG model, for a variety of melt signals derived from two different icesheet snowmelt detection methods. We proposed a modified XPGR snowmelt method and a modified snowmelt detection method based on wavelet transformation edge detection. By comparing the two methods and validating them with temperature data from AWSs, we found that the methods not only ensure computational efficiency, practicability and operability due to independence from in situ measurement, but also—to some extent—improve icesheet snowmelt detection accuracy over the original methods. The two proposed methods can be used to efficaciously determine the threshold for various snowmelt detection methods in different ice sheets. Most importantly, the method can be adapted to different kinds of melt information. The signal melt adaptation method provides methodological support for an icesheet snowmelt monitoring system.
This research was supported by the National Natural Science Foundation of China (General Programme, no. 41076129) and the National Hightech R&D Program of China (Programme 863, no. 2008AA121702)