Global snow and ice have been diminishing during the Anthropocene but we still lack a complete mapping of annual minimum exposed snow and ice with a consistent, repeatable algorithm. The Global Land Ice Measurements from Space (GLIMS) project has compiled digital glacier outlines and related metadata for the majority of the world's glaciers but inconsistency among product algorithms and time periods represented precludes the production of a consistently derived global data set. Here we present the MODIS Persistent Ice (MODICE) algorithm that leverages the time series of fractional snow and ice cover from the MODIS Snow Covered Area and Grain size (MODSCAG) algorithm. The end product of MODICE is a consistently derived map of annual minimum exposed snow and ice. Comparisons of MODICE with GLIMS glacier outlines derived from SPOT, ASTER, and Landsat Thematic Mapper show strong agreement with the higher resolution outlines subject to uncertainties with spatial resolution, deep mountain shadows, and GLIMS interpretation errors.
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 Global snow and ice covers have been in general retreat due to several forcings within the Anthropocene, the period of the modern global environment dominated by human activities [Zalasiewicz et al., 2010]. There is now clear evidence that the vast majority of Earth's glaciers have been in retreat during the last 100–150 years [Zemp et al., 2009]. Moreover, snow cover in the Northern Hemisphere has retreated since the late 1970s, consistent with warming and a positive snow-albedo feedback [Déry and Brown, 2007; Flanner et al., 2011]. As with the global record, temperature increases have been reported in the last decades in the mountains of the globe [Pierce et al., 2008; Bhutiyani et al., 2010]. Recent studies show that changes in dust and carbonaceous particles during the last 200 years have been shortening snow cover duration, likely leading to glacier retreat and downwasting [Thompson et al., 2000; Skiles et al., 2012].
 In order to better understand the role of glaciers in the global hydrologic cycle, an effort to complete a global inventory of glaciers was encouraged during the International Geophysical Year (1959) and again during the International Hydrological Decade (1965–1974). Perhaps the simplest method to monitor change of mountain glaciers is by recording the annual location of the glacier terminus. Satellite observations, such as those applied in this study, provide a more enhanced, comprehensive, and systematic approach to monitoring glacier areas at larger scales and higher temporal resolution. Together, in situ glacier measurements and satellite observations provide a wealth of glacier data contained in the archives of both the World Glacier Monitoring Service (WGMS), Zurich, Switzerland, and the National Snow and Ice Data Center (NSIDC), Boulder, USA.
 These archived data include detailed digital glacier outlines and elevations, carefully compiled time series of measurements of glacier termini fluctuations and mass balance, and glacier photograph pairs showing changes through time. Glacier outlines are available through the Global Land Ice Measurements from Space (GLIMS) web site (http://glims.org), now linked with the WGMS website [Raup et al., 2007]. GLIMS ingests snapshot glacier outlines from cooperative scientists who have generated remote sensing data of various spatial resolutions, most commonly from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), the Landsat Enhanced Thematic Mapper Plus (ETM+) or Thematic Mapper, aerial photographs, and topographic maps. As such, these products are generated at relatively fine spatial resolution. While some glaciers have been characterized for two or more well-spaced years [Bolch et al., 2008b; Paul and Andreassen, 2009; Racoviteanu et al., 2010], the vast majority have single representations in GLIMS and as such cannot be evaluated for annual changes in extent.
 While this data collection clearly provides fundamental value to glaciology, the comparative value varies considerably, because the glacier representations derive from a wide range of analysis methods and data sources [Racoviteanu et al., 2010]. Currently a fundamental missing component of the world cryosphere inventory is a single, systematically derived base map of the world's glaciers and annual minimum snow cover, at any scale.
 Here we describe a systematic algorithm for mapping the annual minimum exposed snow and ice extent (SIEmin) across the globe. In this definition, SIEminincludes bare ice in the ablation area of glaciers, as well as snow in the accumulation area, and any remaining seasonal snow that may persist at the end of the ablation season outside the glaciers. The MODICE algorithm is a time-series model that sorts daily fractional snow and ice maps generated by the MODIS Snow Covered Area and Grain size (MODSCAG) model [Painter et al., 2009]. We describe the details of the MODSCAG algorithm that lies at its core, the time-series approach that sorts MODSCAG results into comprehensive MODICE products, validate the algorithm and show its limitations, and finally describe the effort to produce ongoing global products.
2. Algorithm Description
 The MODSCAG snow cover model [Painter et al., 2009] derives from heritage algorithms for retrieving fractional snow cover via multiple endmember spectral mixture analysis [Painter et al., 2003]. This physically based retrieval model inverts the MODIS daily surface reflectance product (MOD09GA/MYD09GA). MODSCAG allows the snow and ice spectral reflectance endmembers to vary by pixel and thereby addresses the spatial heterogeneity that characterizes these surfaces in rough terrain and patchy settings [Painter et al., 2009]. MODSCAG has a fractional cover root mean squared error (RMSE, against higher resolution Landsat Thematic Mapper) of 9.4% [Painter et al., 2009; Rittger et al., 2012]. In detection of snow and ice, MODSCAG has a precision (probability that a pixel identified as snow has snow) of 99.2% and recall (probability of detecting a pixel with snow) of 90.5% across plains, high steppes, and mountain regions without sensitivity to the associated non-snow land cover [Rittger et al., 2012]. MODSCAG details are included in the auxiliary material.
 MODICE determines annual minimum exposed snow and ice cover by searching each pixel's time series of MODSCAG retrievals for a snow-free date. For any pixel that meets the metrics for view geometry and clear sky (described below), if MODSCAG indicates that the snow or ice covered area equals 0, that pixel is then considered not persistent exposed snow or ice in that year. The remaining pixels in the region are those for which a snow-free date is never found and, unless they are never “seen” according to the metrics described below, they are considered minimum exposed snow and ice for that year. Note that the remaining snow cover may lie either on or off glacier surfaces.
 Pre-filtering the MODSCAG data according to limited view zenith angles and clear skies is required in order to assure higher quality, near-native resolution retrievals. While Terra MODIS and Aqua MODIS each image the vast majority of the globe on a daily basis, this is accomplished at the expense of spatial resolution. MODIS scans with a nominal range of ±55° and at-nadir spatial resolution of 463 m. However, at the edge of the scan, the ground instantaneous field-of-view is double in the along-track (1.003 km) direction and 5 times in the cross-track (2.417 km) direction [Dozier et al., 2008]. Therefore, MODICE only includes MODSCAG retrievals for those pixels for which the sensor zenith angle is less than or equal to 25°. This angular threshold was selected to keep the utilized MODIS pixels to those with at most 10% deviation from nominal area at nadir.
 Once we determine whether a pixel has the adequate spatial resolution, we then filter for clear skies using the cloud flag in the MOD10A1 product to maintain consistency with viewable snow cover in comparisons. While it is possible to detect snow cover through optically thin clouds such as cirrus, fractional retrievals are less reliable. Therefore, we conservatively choose to mask out any area for which there is indication of cloud, whether optically thick or thin.
 The MODICE persistence processing initializes the scene to 100% snow/ice in each pixel. Each pixel in the MODSCAG snow/ice fraction images is examined sequentially. When a pixel meets the three criteria: 1) acceptable sensor zenith angle ≤25°, 2) cloud-free, and 3) is snow/ice free, then the pixel maintains a value of 0.0 thereafter for that year. For those that meet the sensor geometry and cloud cover criteria, but have non-zero snow/ice fractional area that is lower than the saved value, then the pixel is assigned the new, lower value. Over the period of observation, this persistence approach ensures that the final scene includes the lowest reliably observed snow/ice fraction for each pixel. Any pixel that survives the persistence processing with non-zero snow/ice fraction greater than the 15% snow/ice fraction detectability threshold of MODSCAG (below which snow/ice is not mapped) is considered to be annual minimum exposed snow or ice.
 The final MODICE products are a raster image of fractional snow/ice coverage at the native 463 m spatial resolution and a vector representation of the perimeter (external and internal) of annual minimum snow and ice cover. Both are saved in the native SIN projection and can be mapped into other projections. The MODICE processing is described in flow chart form in Figure S1and visually through a multi-panel animation inAnimation S1.
 Presently, the biggest challenge in validating MODICE is the lack of a data set with complete temporal coverage during the period from 2000 to present, at higher spatial resolution than MODICE. Additionally, MODICE retrieves annual minimum exposed snow and ice, whereas GLIMS interprets for glacier extent in a composite of automated and manual techniques and as a single snapshot in time. Nevertheless, in order to best understand uncertainties with MODICE, we compare MODICE with those outlines from GLIMS that we consider to be highest quality interpretations.
 We use glacier data sets from two glacierized areas, derived from medium-resolution imagery (10–30 m): Cordillera Blanca, Peru (CB - 2003 ASTER and 2005 SPOT5 images) and Langtang, Nepal (LAN - 2003 ASTER). All scenes were acquired near the end of the ablation season (July–Aug for CB; Oct-Nov for LAN). The SPOT5 scenes (CB) were cloud-free and snow-free; the ASTER scenes (LAN) had minimal snow and clouds. In addition, the ASTER scenes were acquired using GLIMS gains, which provided higher contrast over snow and ice [Raup et al., 2007]. Bare ice was delineated using semi-automated methods (ASTER or SPOT band ratios) described in detail inRacoviteanu et al. [2008a, 2008b, 2010] and the auxiliary material.
 At the end of the ablation season, in some areas of the world such as the eastern Himalaya where one of our study areas is situated (Langtang), snowfall can still occur after the ablation season, and it may persist outside the glacier boundaries. It is important to note that such persistent seasonal snow, remaining at the end of the ablation season outside the glacier boundaries, is removed subjectively from glacier outlines in this methodology. Debris covered tongues cannot be discriminated using multi-spectral analysis in the visible and near infrared (VNIR) due to the similar spectral signature of supra-glacial debris to surrounding lateral moraines. Thus, our validation data sets do not include debris-covered tongues. In contrast, recall that MODICE retrieves annual minimum exposed ice and any remaining seasonal snow.
 The validation is quantified according to the following metrics. Accuracyis the probability a pixel is correctly classified, but this statistic can mislead where comparison areas have large snow-free areas.Precision is the probability that a pixel identified with snow/ice indeed has snow/ice. Recallis the probability of detection of a snow/ice-covered pixel.
 The large regional image included here (Figure 1) shows the 2001 MODICE SIEmin for the mountains of High Asia – including the Tien Shan, Hindu Kush, Karakoram, Pamirs, and Himalaya. We calculate the area of annual minimum exposed snow and ice for this region in 2001 at 154,063 km2. The annually-resolved mapping presented at this scale is unprecedented.
 In the Langtang region of Nepal, MODICE SIEmin has accuracy of 0.93, precision of 0.75, and recall 0.81 when compared with the GLIMS glacier outlines from the 2003 ASTER base scene (Figure 2). This figure shows that MODICE represents well the spatial distribution of snow and ice as interpreted by GLIMS. Analysis of the MOD09GA spectral reflectance data indicate that deep shadows can cause omission by MODICE (in western half of the basin) and that some of the errors of omission (such as those in the eastern half of the basin) are due to erroneous delineation of glaciers in the GLIMS retrieval.
 In the Cordillera Blanca of Peru, comparing MODICE SIEmin with GLIMS glacier outlines from SPOT (2003) (Figure 3) gives accuracy at 0.98, precision at 0.86, and recall at 0.76. In 2005, GLIMS glaciers from ASTER (2005) are 0.98 accuracy, 0.84 precision, and 0.77 recall. In both comparisons, all Cordillera Blanca massifs identified using semi-automated GLIMS techniques are well represented and captured by MODICE.
 The annual resolution of the MODICE SIEmin retrieval facilitates analysis of time series across the MODIS record, such as those for the Upper Indus (UI), the Cordillera Blanca (CB), and the Alaskan Panhandle (AP) shown in Figure 4 (MODICE SIEmin maps for UI and AP are given in Figures S2 and S3). SIEmin in the UI was relatively stable for the period 2000–2010, whereas both of the CB and AP subregions experienced significant reductions in annual minimum snow and ice exposure.
 The UI and AP results are not inconsistent with the mass changes presented in Jacob et al.  whereas the negative trend in the CB region is inconsistent with the lack of significant trend for their region 16 (South America excluding Patagonia). The relationship between snow/ice extent and mass change is highly uncertain, however, particularly across a time span as short as those shown in our work here and Jacob et al. .
 MODICE results compare well to glacier outlines derived from GLIMS techniques in the regions presented here. MODICE omission differences are primarily at perimeters of glacial and snow-covered massifs in linear features and in some cirques with deep shadowing (Figure 3). MODSCAG detects fractional cover of snow and ice but it cannot detect ice beneath debris cover. Some differences may also result from spatially incomplete GLIMS processing, GLIMS analyst inconsistencies due to available image quality, and/or different observation dates.
 While the GLIMS glacier mapping techniques and MODSCAG base imagery both have errors of omission and commission, the difference in spatial resolution between the higher resolution sensors and MODIS would result in apparent errors even if both mapping techniques were perfect. Moreover, while the daily product from MODIS could have larger errors than the product derived from higher spatial resolution data, the much higher temporal resolution product makes new science possible via enabling time series analysis. Indeed, the comprehensive coverage of MODICE can be used to refine and improve GLIMS analysis, by highlighting regions of disagreement that result from the inadequate temporal GLIMS range.
 The tiled MOD09GA surface reflectance product has geolocation uncertainties of ∼0.5 pixels near nadir from where we select MODICE data. Therefore, across the distribution of geolocations for each pixel in the time series, perimeters of snow/ice next to bare ground will have a circularly fuzzy boundary (if there is no bias in the geolocation uncertainty). Given the unforgiving nature of the MODICE algorithm, once a pixel is deemed snow/ice-free, it is locked as such. This geolocation uncertainty then necessarily injects a negative bias to the MODICE product.
 MODICE allows mapping of minimum exposed snow and ice for each year across the globe, whereas other snow and ice inventories have been hobbled by infrequent acquisitions. At time of writing, we have completed ablation-season processing that encompasses the snow and ice of the globe for 2001, and for the period 2000–2010 for High Asia, the Cordillera Blanca and Alaska. These products and the rest of the globe for 2000–2012 will be made available via FTP server at NSIDC and the JPL Snow Data Server (http://snow.jpl.nasa.gov/).
 Funding for this work came from the Cryospheric Sciences program of NASA. A. Racoviteanu's current work is supported by the Centre National d'Études Spatiales (CNES), France. We acknowledge Ken Knowles for his original idea for MODICE persistence and his initial implementation. We also thank S. McKenzie Skiles, Karl Rittger, and the Snow Data System team at JPL for assistance with GIS and comparisons. Thanks also to Bruce Raup at the NSIDC GLIMS archive and to the French IRD for providing access to SPOT imagery. Part of this work was performed at the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.