## 2 Materials and Methods  
### Study Site  
Pakistan has some of the world's largest and longest mid-latitude glaciers due to their numerous high mountains and ample precipitation typical of a monsoon climate. Glacierized land is estimated to occupy 15,000 km\({}^{2}\) (or 37%) of the high mountains [20].  
According to the Intergovernmental Panel on Climate Change report, glaciers in the HKH are melting rapidly [21]. Pakistan has 7253 recognized glaciers [22] and almost all of them are in Gilgit-Baltistan and Khyber Pakhtunkhwa's northern areas. The global average mass balance of glaciers is indisputably negative [23]. The majority of Himalayan glaciers are losing mass at rates comparable to those seen elsewhere [2; 24].  
The sites for the current study include three mountain ranges, namely the Himalaya, Hindukush, and Karakoram ranges. These three sites were chosen to investigate black carbon concentrations in relation to solar radiation reflection (albedo) Figure 1.  
The Karakoram Mountain glaciers account for roughly 3% of the total in recent times [2; 23]. The Passu glacier is located south of the Batura glacier, between 36\({}^{\circ}\)27\({}^{\prime\prime}\) N and 36\({}^{\circ}\)28\({}^{\prime}\) N, and 74\({}^{\circ}\)38\({}^{\prime}\) E and 74\({}^{\circ}\)52\({}^{\prime}\) E. It feeds the Hunza River, which flows west to east through northern Pakistan [25]. The sampling site in Passu glacier is located at 74\({}^{\circ}\)52\({}^{\prime}\)26.94\({}^{\prime\prime}\) E and 36\({}^{\circ}\)27\({}^{\prime\prime}\)20.10\({}^{\prime\prime}\) N at the elevation of 2640 masl (Figure 1). It was discovered that a large volume of water was trapped beneath the ice near the terminus (tongue) of numerous glaciers, including the Passu glacier, which had already caused outbursts. As a result, the massive volume of water that was constantly expanding was not visible, causing catastrophic damage downstream to human lives, towns, and infrastructure [18].  
The Hindukush Range stretches from the Pamir Plateau's western boundary to the Karakoram's western edge. Pakistan, Afghanistan, and China are all separated by it. It contains snow-covered mountains that are traversed by a number of glaciers. Noshak (7369 masl) and Tirich Mir (7690 masl) are the highest peaks in the area. The mountain range is drained into Chitral, Kunar, Punjkora, and Swat rivers [16]. The sampling site in the Meragram glacier is located at 72\({}^{\circ}\)22\({}^{\prime}\)7.56\({}^{\prime\prime}\) E and 36\({}^{\circ}\)15\({}^{\prime}\)11.94\({}^{\prime\prime}\) N at the elevation of 2345 masl (Figure 1).  
The Nanga Parbat massif is the high Himalaya's northwestern limit with the highest height variation ranging from 1030 masl in the Indus Gorge to 8126 masl at the peak of Nanga Parbat. Raikot Glacier, on Nanga Parbat's north flank, is about 15 km long and covers 39 Km\({}^{2}\). Through substantial fluctuations in the steepness of the glacier profile, the ice tongue drops to 3180 masl [26]. The sampling site in the Raikot glacier is located at 74\({}^{\circ}\)35\({}^{\prime}\)31.38\({}^{\prime\prime}\) E and 35\({}^{\circ}\)24\({}^{\prime}\)18.48\({}^{\prime\prime}\) N at the elevation of 2683 masl (Figure 1).  
Figure 1: The study area of observational sites.