2.1. Study Area
 The Himalayas and Tibetan Plateau cover, in various proportions, the countries of Pakistan, Afghanistan, Tajikistan, China, India, Nepal, Myanmar, Bhutan, and Bangladesh (Figure 1). The study area is located between 25.59°N–40.27°N and 69.12°E–105.54°E (Figure 1) and has an estimated area of 5.072 × 106 km2. It extends (in an arc shape) for 2500 km from west to east and 100–400 km from south to north [Muskett, 2008; Mats et al., 2009; Immerzeel et al., 2010]. Although over 80% of the area is in the Tibetan Plateau, it also includes Karakoram, Hindu-Kush, Pamir, Tien Shan, Inner and Outer Himalayas, and several other mountain ranges.
Figure 1. Map showing the geographic location of the study area, national boundaries, drainage, weather monitoring stations, Mount Everest, and the ambient surface elevation.
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 The geophysiographic features in this region are complex and rugged [Bolch et al., 2008], with over 30 of the 110 massif peak elevations above 6000 m [Kaul, 1999; Macintosh, 2005]. The 70 km long Siachen Glacier (on the India-Pakistan border) is the longest of the over 50,000 glaciers in the region [Kaul, 1999; Qiu, 2008]. The mountains are characterized by deep snowcaps, glacial valleys and gorges, and rich ecobiodiversity [Saxena et al. 2005; Harris, 2010]. The mountain valleys, depressions, and canyons provide abundant storage for summer rainwater and meltwater [Ageta et al., 2000]. The tectonic glacial lakes occur at altitudes below 5000 m and generally diminish in size at higher elevations [Thayyen and Gergan, 2009]. Pangong Tso, the largest endorheic lake in the region is ≈134 km long. It spreads across the India-China border at an average altitude of 4350 m [Winiger et al., 2005].
 Of the 519 mm average annual precipitation, 72% falls as summer monsoon rain and 28% as winter snow [Dulal et al., 2006]. Variation in diurnal temperature is large, with a long-term average of 7°С. The coldest (in January) and hottest (in July) average monthly temperatures are 12°С and 16°С, respectively [Shrestha et al., 2000]. Above-16°С summer temperatures are not uncommon on the valley slopes [Dulal et al., 2006]. At elevations over 5000 m, above-zero temperatures only occur during the daytime [Thayyen and Gergan, 2009]. Because of rising temperatures, snow precipitation is increasingly shifting toward rain. Winds generally strengthen at higher altitudes, reaching 120 km/h at 6000 m [Burbank et al., 2003].
 While the western phase of the Himalayas has a generally warm and humid monsoon climate, a typical mountain desert cold climate dominates on the northern slopes and Tibetan Plateau [Goswami et al., 2003]. As Asia's main source of water, the Himalayas and Tibetan Plateau snow and glaciers greatly influence the hydrology, ecology, and livelihoods of millions of people in the subcontinent [Burbank et al., 2003; Qiu, 2008; Thayyen and Gergan, 2009; Immerzeel et al., 2010].
2.2. Hydrologic Mass Balance
 Here storage change Δω [L/T] is the difference between storage anomalies of two successive time steps. A storage anomaly is the residual storage content ω′ [L/T] at a given time with respect to the content at the reference epoch. Reference storage ω′r [L/T] is the mean storage within the time interval for which the temporal mean is computed. Hydrologic mass balance in the Himalayas and Tibetan Plateau study area is mainly driven by storage in snow, glaciers, high-altitude lakes, and permafrost. A glacier mass balance method could therefore be used to estimate the storage change. Studies show that the climate variables with the most impact on glacier dynamics are temperature and precipitation [Meier, 1984; Oerlemans and Fortuin, 1992; Dyurgerov and Meier, 1997; Raper and Braithwaite, 2006; Kaser et al., 2006; Fujita, 2008b; Qiu, 2008]. Using seasonal sensitivity characteristics of temperature and precipitation, Oerlemans and Reighert  conducted glacier mass balance for different climatic regions of the world.
 In this study, the method of Oerlemans and Reighert  is modified to estimate water storage change in the Himalayas and Tibetan Plateau region. To achieve this, it is assumed that the time derivative of the residual storage anomaly ω′ [L/T] with respect to the initial time of the water storage ω [L/T] is a nonlinear function of temperature T (K) and precipitation P [L]; i.e., ω′ = f(T, P). A linearization of this function at the vicinity of the reference temperature Tr (K) and reference precipitation Pr [L] yields
with the residual storage change Δω′ = ω′ − ω′r [L/T], reference storage ω′r = f(Tr, Pr) [L/T], temperature coefficient CT = ∂f/∂T [L/K], and precipitation coefficient CP = ∂f/∂P (dimensionless). The integration of the linearized relationship, after discretization, gives
The index k is the time step (annual, seasonal, monthly, or other time scales) associated with the reference temperature Tr and precipitation Pr of the reference mass balance ω′r (preferably zero). The temperature coefficient CT,k [L/K] and precipitation coefficient CP,k (dimensionless) in equation (2) are the so-called climate sensitivity characteristics (CSC) of the mass balance [Fujita, 2008b]. The CT,k and CP,k of the mass balance are quantified as
This can be determined by any simple or complex degree-day or energy balance model that computes the cumulative mass balance through the year [Oerlemans and Reighert, 2000].
 As this study focuses on the entire snow and glacier system of the Himalayas and Tibetan Plateau, a bulk CSC value is calculated using the energy–mass balance model described by Fujita [2008b]. Because of the great size, apparently all glacier types exist in this region. This allows the use of average values and eliminates the need for different sets of parameters for individual glaciers. The areas of the glaciers in the region are therefore added together and treated as a seamless glacier. Most of the model input parameters (including glacier and ice extent, albedo, etc.) are derived from Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat thematic mapper data [König et al., 2001]. The energy fraction of the model is balanced on glacier surface daily heat, radiation, sensible and latent turbulent heat, and conductive heat into the glacier mass. The mass fraction of the model is balanced on accumulated snow and refrozen meltwater and on snowmelt and evaporation [Fujita, 2008a, 2008b]. The model gains mass via solid precipitation and loses it via ablation. Conductive heat into the glacier system and the amount of water at the snow-glacier interface are used to estimate meltwater refreeze [Fujita and Ageta, 2000]. Snow surface albedo (which declines with glacier depth and melt season duration) is calculated in relation to surface snow density (which changes with compaction). This preserves climate feedback effects on the snow and glacier regimes. The model has been validated on selected glaciers in the Himalayas and Tibetan Plateau region. Further details of the model, including validation analyses, are documented by Fujita and Ageta , Fujita et al. , and Fujita [2008a, 2008b].
 In calculating CSC, the calibrated model is rerun for the reference state Δω′ = 0 by adjusting annual mean air temperature within ±2 K. Next, systematic monthly perturbations in temperature (±0.5 K) and in precipitation (±10%) are induced to derive the CT,k and CP,k in equation (3), respectively. Further details, including the rationale of this procedure, are explained by Oerlemans and Reighert . The results of the CSC analysis are depicted in Figure 2a.
Figure 2. (a) Graphic illustration of climate sensitivity characteristics in the Himalayas and Tibetan Plateau snow and glacier, along with (b) annual temperature sensitivity index, (c) annual precipitation sensitivity index, (d) average annual field-measured versus GLDAS Noah-estimated temperature, and (e) average annual field-measured versus GLDAS Noah-estimated precipitation for 2003–2008.
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 One distinctive feature of glaciers is the length of period for which perturbations in temperature or precipitation affect their annual mass balances [Oerlemans and Reighert, 2000]. The stability of the average Himalaya glacier system is relatable to climate change and global warming, which are mainly driven by summer climate trends. Hence, a sensitivity index (SI) that shows the average behavior of the glaciers through the year is used to quantify perturbations in temperature (SITy) and precipitation (SIPy) as
where y is the year and 6, 7, and 8 denote June, July, and August, respectively. The SI is related to average yearly temperatures and precipitation for 2003–2008 in Figure 2. The power fits in Figures 2a and 2c show strong correlations between SI and temperature (R2 = 0.91) and precipitation (R2 = 0.86); all are significant at p < 0.01. Figure 2 suggests that snow and glacier vulnerability in the region increases with increasing temperature and precipitation. Of course, rising temperatures favor rain precipitation (Figure 3), which in turn increases glacier vulnerability [Oerlemans and Reighert, 2000].
Figure 3. Time series of monthly and seasonal anomalies in (a) snowfall, (b) rainfall, (c) precipitation, (d) temperature, and (e) GRACE total water storage (TWSA) for the period 2003–2008 in the Himalayas and Tibetan Plateau study area.
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 The CSC so computed is used in the ECM model to estimate storage change in the study area. In GRACE, the steady state portion of water storage is highly correlated with static gravity fields. It is difficult to separate the steady state portion of the water storage from the static gravity estimates. Hence, what GRACE provides is not total terrestrial water content but its anomaly field. Raw GRACE monthly solutions contain information about water storage anomaly in relation to the reference storage. In other words, GRACE is indirectly sensitive to total water storage signal. In this study, water storage change estimated independently by the ECM model in equation (1) is compared with that derived from the GRACE satellite gravity data.