Status and Progress of Determining the Variability and Controls on Chemical Denudation Rates in Glacierized Basins Around the World

Abstract

Glaciers play a crucial role in shaping global hydrology and biogeochemical cycles, yet their climate-forced dynamic impact on chemical denudation and solute yields remain poorly understood. This study compiled data on 40 well-documented cationic denudation rates (CDR) from glaciers across Northwest America, the Svalbard/Arctic Canada, Iceland, Greenland, Europe, China-Tibet, Antarctica, and the Himalayas, revealing substantial spatial variability. CDRs ranged from 46 to 4160 meq m⁻² yr⁻¹. Northwest American and Himalayan glaciers exhibited the highest CDRs, with the Himalayan denudation rate exceeding the global average by more than fourfold. The exceptionally high mean chemical weathering intensity (CWI) of 801 meq m⁻³ from the Himalayan glaciers indicate a wide range of geochemical and climatic conditions within the region, while Northwest American and Greenland glaciers show comparatively lower mean intensities (273 and 247 meq m⁻³, respectively) suggesting a consistent geochemical regime. Northwest American glaciers had the highest specific discharge rates, while Svalbard/Arctic Canada glaciers had the lowest, reflecting regional disparities influenced by climatic and geological factors. A Bonferroni post hoc test highlighted significant differences in specific discharge between Northwest American glaciers and two other basins, emphasizing their distinct hydrological behavior. Predictive modeling revealed a statistically significant but weak relationship between CDR and specific discharge (R² = 57%), suggesting that much of the variability in CDR cannot be explained by specific discharge alone. A regression coefficient of 382 meq m⁻² yr⁻¹ indicates that CDR increases with glacier discharge, although basin-specific analyses showed minimal variation in this relationship across regions. Svalbard/Arctic Canada, Antarctic, Greenlandic, Icelandic, and European Alpine glaciers displayed lower CDRs, which varied depending on underlying lithology, with higher rates observed in carbonate and basaltic terrains compared to other lithologies. We hypothesize that glacier retreat enhances the downward progression of the weathering reaction front, increasing CDR, particularly in rapidly retreating glaciers.

1. Introduction

Glaciers are important erosive agents on Earth, excavating valleys and transforming landscapes. Understanding glacial denudation dynamics is crucial, as glaciers shape global hydrological systems, regulate Earth’s climate, and play a key role in biogeochemical dynamics and nutrient and metal export to adjacent aquatic environments. Glaciers are an ideal natural laboratory for examining low-temperature geochemistry and the factors regulating glacial biogeochemistry, including the role of microorganisms in accelerating chemical weathering rates in glacial environments [1]. Due to the continued increase in Earth’s surface temperature, glaciers worldwide are retreating rapidly [2,3,4,5], which consequently causes dramatic hydrological changes and has a direct effect on cationic denudation rates (CDR). Understanding CDRs of glacierized basins are crucial to understanding global biogeochemical cycles, glacier hydrology, and global carbon cycles and comparing continental erosion rates across the globe. Cations released through chemical weathering supply tremendous amounts of dissolved loads of ionic species as well as carbon and nutrients, which provide ecological support downstream and maintain a long-term balance of atmospheric CO₂ [6]. Integration of climatic and geological factors is important to gain further insights into CDRs as natural chemical weathering processes help to balance the long-term Earth’s climate and, in combination with physical weathering processes, cause heterogenous erosion of glacial landscapes. However, the impacts of climatic and geological factors on CDRs may be limited by complex interactions and lithological compositions.

The number of studies of glacial biogeochemical processes varies a lot between glacierized regions around the world. Glacial biogeochemistry is well studied in the Svalbard/Arctic Canada region in comparison to other glaciers of the world [1,7]. In contrast, glacial biogeochemistry in regions such as the Southern Alps of New Zealand, Russian Arctic glaciers, glaciers in Central Asia, the Canadian High Arctic, or in South America remain understudied. An important tool to quantify the mobilization of rock-derived ions in glacial rivers is the measurement of sea-salt-corrected cationic denudation rates (CDR). However, there are surprisingly few reports of CDRs from glacierized basins, hampering a regional scale understanding of the chemical component of rock weathering beneath glaciers. Sea-salt correction is a process to separate the marine contributed ions. The contribution of sea-salt derived ions to surface waters can be estimated using the molar ratios of elements found in seawater as documented by various studies earlier from different terrains [8,9,10]. Chloride concentration can be used as a reference species to correct the contribution of sea-salt in surface waters for marine-derived Na, K, Mg, Ca and SO₄ to estimate the non-sea salt or weathered concentration from chemical weathering.

The current scarcity of CDR data is due to the logistical and costly challenges of working near glacier systems. Hydrometric stations, which are used for annual discharge measurements in glacial rivers, are often damaged or destroyed by glacial lake outburst floods (GLOFs) or inundation events induced by intense snowmelt, ice melt, or heavy rainfall. Furthermore, conducting comprehensive meltwater sampling throughout the ablation season requires significant logistics and long-term labor in the field.

However, a few compilations of CDRs are available [7,11,12,13,14], showing a wide variability in reported glacier CDR values that may arise from differences in lithology, glacier area, basal thermal regimes, precipitation levels, discharge measurement methods, sampling duration, sampling proximity to glaciers, and sea-salt correction techniques. CDR reported without sea-salt correction is also a cause for variability as mentioned above. Understanding the relative contribution of these factors is essential for accurately assessing the geochemical dynamics of glacier basins on regional and global scales.

Hodson et al. (2000) [7] identified specific annual discharge as a primary control on CDR, with lithology playing a secondary role. For instance, carbonate and basaltic lithologies exhibit distinct weathering behaviors. Yde et al. (2008) [15] and Stachnik et al. (2016) [16] documented microbially mediated sulfide oxidation coupled with dolomite dissolution as a dominant geochemical process in Svalbard glaciers. Similar processes were observed in the Dokriani Glacier in India and Langtang Lirung Glacier in Nepal within the Himalayas, where pyrite oxidation coupled with carbonate dissolution governs meltwater chemistry [5,10,17,18]. Also, Torres et al. (2017) [19] and Li et al. (2022) [20] reported that chemical weathering beneath glaciers is more intense than in non-glacial basins, underscoring the unique dynamics of glacierized basins. However, despite these and many other studies providing detailed insights into specific chemical weathering processes in glacial basins, there is a need for an updated evaluation focusing on available measurements of CDR.

The objective of this study is to compile data on CDRs from glacier basins worldwide and evaluate the factors influencing CDRs. This synthesis aims to improve our understanding of the variability of global glacial geochemical denudation, with a particular focus on the factors regulating CDRs. The study seeks to address knowledge gaps and contributes to predicting the impacts of glacier retreat on hydrological and geochemical processes, ultimately leading to an increase in CDRs in glacierized basins.

2. Synthesis and Analysis of CDRs Across Global Glacier Basins

2.1. Synthesis of CDR Across Global Glacier Basins

Cationic denudation rates from 50 sites of 40 glacier basins with specific discharge from selected glacier basins worldwide are summarized in Table 1. We separate the data into regions to gain a better overview of the variations in CDR within the region and among other different regions to understand the impacts of possible regulating factors on CDR. In this context, it is important to emphasize that the mean CDR value for a given region is not representative of all glaciers within the region because the currently available dataset is very limited. The addition of one or a few new estimates of CDR would likely have a significant effect on the mean CDR values.

The region “Northwest America” refers to glaciers in the U.S. states of Washington and Alaska and in British Columbia, Canada. The region “Svalbard/Arctic Canada” combines High Arctic glaciers in Svalbard with a single High Arctic glacier located on Baffin Island in Arctic Canada, well knowing that the climate in the two areas differ. We have decided to have the two Low Arctic Greenlandic glaciers in a separate category, but here it is important to keep in mind that Kuannersuit Glacier is a peripheral glacier located on an island, whereas Watson River drains a sector of the Greenland Ice Sheet. The region “Alpine glaciers in Europe” only includes glaciers in Central Europe, as there is currently no data on CDR available from Scandinavian or other European glacierized areas. In Central Asia, we distinguish between “Alpine glaciers in China-Tibet” and “Himalayan glaciers” due to the differences in climate between the monsoon-affected glaciers in the Himalaya mountain range and the glaciers located at a significant distance away from the Himalaya. For “Antarctic glaciers”, CDR is only available for one glacier located on the South Orkney Islands.

Northwest America glaciers: CDR values range from 676 to 1650 meq m⁻² yr⁻¹, with a mean of 1161 meq m⁻² yr⁻¹ [11,21,22,23]. Svalbard/Arctic Canada glaciers: CDR ranges from 94 to 790 meq m⁻² yr⁻¹, with a mean of 512 meq m⁻² yr⁻¹ [7,11,12,15,16,24,25]. Icelandic glaciers: CDR ranges from 630 to 1100 meq m⁻² yr⁻¹, with a mean of 816 meq m⁻² yr⁻¹ [26]. Greenlandic glaciers: CDR values range from 46 to 860 meq m⁻² yr⁻¹, with a mean of 530 meq m⁻² yr⁻¹ [27,28]. Alpine glaciers in Europe: CDR ranges from 478 to 1010 meq m⁻² yr⁻¹, with a mean of 665 meq m⁻² yr⁻¹ [29,30,31,32]. Alpine glaciers in China-Tibet: Three studies report CDR values ranging from 189 to 3108 meq m⁻² yr⁻¹, with a mean of 1485 meq m⁻² yr⁻¹ [14,33,34]. Himalayan glaciers: CDR values range from 462 to 4160 meq m⁻² yr⁻¹, with a mean of 1420 meq m⁻² yr⁻¹ [10,18,35,36,37,38]. Antarctic glaciers: Only one reported CDR value exists, 163 meq m⁻² yr⁻¹, from Tuva Glacier [12].

Low-elevation sites in Nepal Himalaya, such as Trishuli at Betrawati (640 m asl) and Narayani at Narayanghat (169 m asl), report much higher CDR values (1639 to 4032 meq m⁻² yr⁻¹) as documented by Bhatt et al. 2018 [10]. These values are excluded from statistical analysis because discharge was measured far from the glacier region. However, these data are included in Table 1 for the stake of completeness as the water originates from glacier meltwater. The CDR at low-elevation sites is significantly higher than that at high elevations (4032 vs. 746 meq m⁻² yr⁻¹) [10,18].

Global Average CDR: A global average CDR of 390 meq m⁻² yr⁻¹ is included for reference [39].

Table 1. Compilation of cationic denudation rates (CDR) of glacierized basins of the world.

Site No	Field Area/Basin	Geology/Mineralogy	CDR (meq m−2 yr−1)	Specific Discharge (m yr−1)	References
	Northwest America
1	South Cascade, USA *	Plutonic Metamorphic	930	3.28	[21]
2	South Cascade, USA *	Plutonic Metamorphic	676	3.9	[23]
3	Berendon, Canada	Conglomerate/siltstone	1650	3.7	[22]
4	Berendon, Canada	Granodiorite/volcanic	947	3.7	[22]
5	Worthington, USA	Plutonic Metamorphic	1600	7.68	[11]
	Svalbard/Arctic Canada
6	Longyearbreen, Svalbard	Sedimentary rocks	322	0.3	[15]
7	Austre Brøggerbreen, Svalbard	Sedimentary mix	240–260	0.8–1.3	[12]
8	Bayelva, Svalbard	Metamorphic rocks	470–574	0.82–0.88	[7]
9	Brøggerbreane, Svalbard	Carbonate-rich	480–510	0.8–1.0	[12]
10	Hannabreen, Svalbard	Sedimentary mix	320	0.8	[7]
11	Erikbreen, Svalbard	Sedimentary mix	320	0.5	[7]
12	Erdmannbreen, Svalbard	Sedimentary mix	190	0.8	[7]
13	Finsterwalderbreen, Svalbard	Metamorphic rocks	210–440	0.35–0.84	[7]
14	Scoot Turnerbreen, Svalbard *	Shale-rich	160	0.52	[24]
15	Scoot Turnerbreen, Svalbard	Shale-rich	350	0.5	[12]
16	Werenskioldbreen, Svalbard	Metamorphic rocks	1601–1762	1.83–1.83	[16]
17	Finsterwalserbreen, Svalbard	Shale-rich	790	1.1	[25]
18	Rieperbreen, Svalbard	Shale-rich	292	0.4	[12]
19	Midtre Lovénbreen, Svalbard	Plutonic Metamorphic	450–560	1.3–1.5	[7]
20	Lewis River, Barnes Ice Cap, Canada	Plutonic Metamorphic	94	0.71	[11]
	Iceland
21	Tungufljot *	Basalt	718	2.1	[26]
22	Hvita-S	Basalt	1100	2.1	[26]
23	Hvita-W	Basalt	630	1.8	[26]
	Greenland
24	Kuannersuit Glacier	Basalt-rich	683–860	2.5–2.5	[27]
25	Watson River	Plutonic Metamorphic	46	0.373	[28]
	Europe/Alpine
26	Haut Glacier d’Arolla, Switzerland *	Plutonic Metamorphic	640–685	1.71–2.31	[32]
27	Gornergletschler, Switzerland	Plutonic Metamorphic	1010	1.38	[30]
28	Gornergletschler, Switzerland	Plutonic Metamorphic	478.1	1.35	[29]
29	Tsidjiore Nouve, Switzerland	Plutonic Metamorphic	510	1.2	[31]
	China-Tibet/Alpine
30	Urumi Glacier No. 1, China	Schist-Granodiorite	577–703	1.12–0.96	[33]
31	Dongkemadi Glacier, Tibet	Metamorphic	189	0.98	[34]
32	Hailuogou Glacier, Tibet	Metamorphic	2850–3108	4.37–4.63	[14]
	Antarctica
33	Tuva Glacier	Plutonic Metamorphic	163	0.53	[12]
	Himalaya
34	Batura Glacier, Pakistan	Carbonate-rich	1460	1.95	[36]
35	Batura Glacier, Pakistan	Carbonate-rich	1600	1.6	[38]
36	Chhota-Shigri, India	Plutonic Metamorphic	750	3.5	[35]
37	Dokriani Glacier (Bamak), India	Plutonic Metamorphic	462	1.12	[37]
38	Dokriani Glacier, India	Plutonic Metamorphic	4160	6.5	[17]
39	Lirung Glacier, Nepal	Plutonic Metamorphic	746	0.567	[18]
40	Langtang Glacier, Nepal *	Plutonic Metamorphic	764	0.60	[10]
41	Trishuli River, Nepal *	Plutonic Metamorphic	1639	1.27	[10]
42	Narayani River, Nepal *	Plutonic Metamorphic	4032	1.45	[10]
43	Global Average	Mixed	390	nd	[39]

Note(s): * Corrected for atmospheric inputs. Trishuli River (at Betrawati, 640 m asl) and Narayani River (at Narayanght, 169 m asl) are glacial meltwaters originating from the Langtang Glacier, and both Langtang and Annapurna Glaciers, respectively. These two basins are not used for analysis as they are far from actual glaciers but included just for comparison with other glacierized basins in the Himalayas and with the global average. nd = no data.

Table 1. Compilation of cationic denudation rates (CDR) of glacierized basins of the world.

Site No	Field Area/Basin	Geology/Mineralogy	CDR (meq m−2 yr−1)	Specific Discharge (m yr−1)	References
	Northwest America
1	South Cascade, USA *	Plutonic Metamorphic	930	3.28	[21]
2	South Cascade, USA *	Plutonic Metamorphic	676	3.9	[23]
3	Berendon, Canada	Conglomerate/siltstone	1650	3.7	[22]
4	Berendon, Canada	Granodiorite/volcanic	947	3.7	[22]
5	Worthington, USA	Plutonic Metamorphic	1600	7.68	[11]
	Svalbard/Arctic Canada
6	Longyearbreen, Svalbard	Sedimentary rocks	322	0.3	[15]
7	Austre Brøggerbreen, Svalbard	Sedimentary mix	240–260	0.8–1.3	[12]
8	Bayelva, Svalbard	Metamorphic rocks	470–574	0.82–0.88	[7]
9	Brøggerbreane, Svalbard	Carbonate-rich	480–510	0.8–1.0	[12]
10	Hannabreen, Svalbard	Sedimentary mix	320	0.8	[7]
11	Erikbreen, Svalbard	Sedimentary mix	320	0.5	[7]
12	Erdmannbreen, Svalbard	Sedimentary mix	190	0.8	[7]
13	Finsterwalderbreen, Svalbard	Metamorphic rocks	210–440	0.35–0.84	[7]
14	Scoot Turnerbreen, Svalbard *	Shale-rich	160	0.52	[24]
15	Scoot Turnerbreen, Svalbard	Shale-rich	350	0.5	[12]
16	Werenskioldbreen, Svalbard	Metamorphic rocks	1601–1762	1.83–1.83	[16]
17	Finsterwalserbreen, Svalbard	Shale-rich	790	1.1	[25]
18	Rieperbreen, Svalbard	Shale-rich	292	0.4	[12]
19	Midtre Lovénbreen, Svalbard	Plutonic Metamorphic	450–560	1.3–1.5	[7]
20	Lewis River, Barnes Ice Cap, Canada	Plutonic Metamorphic	94	0.71	[11]
	Iceland
21	Tungufljot *	Basalt	718	2.1	[26]
22	Hvita-S	Basalt	1100	2.1	[26]
23	Hvita-W	Basalt	630	1.8	[26]
	Greenland
24	Kuannersuit Glacier	Basalt-rich	683–860	2.5–2.5	[27]
25	Watson River	Plutonic Metamorphic	46	0.373	[28]
	Europe/Alpine
26	Haut Glacier d’Arolla, Switzerland *	Plutonic Metamorphic	640–685	1.71–2.31	[32]
27	Gornergletschler, Switzerland	Plutonic Metamorphic	1010	1.38	[30]
28	Gornergletschler, Switzerland	Plutonic Metamorphic	478.1	1.35	[29]
29	Tsidjiore Nouve, Switzerland	Plutonic Metamorphic	510	1.2	[31]
	China-Tibet/Alpine
30	Urumi Glacier No. 1, China	Schist-Granodiorite	577–703	1.12–0.96	[33]
31	Dongkemadi Glacier, Tibet	Metamorphic	189	0.98	[34]
32	Hailuogou Glacier, Tibet	Metamorphic	2850–3108	4.37–4.63	[14]
	Antarctica
33	Tuva Glacier	Plutonic Metamorphic	163	0.53	[12]
	Himalaya
34	Batura Glacier, Pakistan	Carbonate-rich	1460	1.95	[36]
35	Batura Glacier, Pakistan	Carbonate-rich	1600	1.6	[38]
36	Chhota-Shigri, India	Plutonic Metamorphic	750	3.5	[35]
37	Dokriani Glacier (Bamak), India	Plutonic Metamorphic	462	1.12	[37]
38	Dokriani Glacier, India	Plutonic Metamorphic	4160	6.5	[17]
39	Lirung Glacier, Nepal	Plutonic Metamorphic	746	0.567	[18]
40	Langtang Glacier, Nepal *	Plutonic Metamorphic	764	0.60	[10]
41	Trishuli River, Nepal *	Plutonic Metamorphic	1639	1.27	[10]
42	Narayani River, Nepal *	Plutonic Metamorphic	4032	1.45	[10]
43	Global Average	Mixed	390	nd	[39]

Note(s): * Corrected for atmospheric inputs. Trishuli River (at Betrawati, 640 m asl) and Narayani River (at Narayanght, 169 m asl) are glacial meltwaters originating from the Langtang Glacier, and both Langtang and Annapurna Glaciers, respectively. These two basins are not used for analysis as they are far from actual glaciers but included just for comparison with other glacierized basins in the Himalayas and with the global average. nd = no data.

2.2. Descriptive Statistics of Global Glaciers for CDR

The summary of descriptive statistics of CDR across glaciers in different regions worldwide is presented in Table 2. Key statistics include the sample size (n), mean CDR, standard deviation (SD), 95% confidence intervals (CI) for the mean (Lower B, Upper B), and the observed minimum and maximum CDR values for each region. The data reveals considerable regional variability, with Himalayan glaciers exhibiting the highest mean CDR and Svalbard/Arctic Canada glaciers the lowest. The overall glacier mean CDR is 835 meq m⁻² yr⁻¹ with a wide range of values across all glaciers.

Table 2. Regional estimations of CDR (in meq m⁻² yr⁻¹).

Region	N	Mean	SD	Min	Max	95% CI for Mean
						Lower B	Upper B
Northwest America	5	1161	438	676	1650	617	1704
Svalbard/Arctic Canada	20	512	431	94	1762	310	414
Iceland	3	816	250	630	1100	195	1437
Greenland	3	530	428	46	860	−534	1593
Alpine-Europe	5	665	212	478	1010	478	1010
Alpine-China-Tibet	5	1485	1380	189	3108	−228	3198
Himalaya	7	1420	1278	462	4160	239	2602
Antarctica	1	163	-	-	-	-	-
Total	49	835	796	46	4160	607	1064

2.2.1. ANOVA Test for H₀₁: Equality of Average CDR Across Seven Global Glacierized Regions

An ANOVA was conducted to test the null hypothesis (H₀₁) that the average CDRs are equal across the six glacierized basins. The test yielded Fisher’s F-statistic of 2.305 with degrees of freedom (df) of 6 and 41, and a p-value of 0.052. This result indicates that H₀₁ cannot be rejected, confirming that the average CDRs do not significantly differ among the seven basins. Note that Antarctica was excluded from the analysis as it only has a single data point.

The mean regional CDRs of glacierized regions arranged in decreasing order of magnitude are shown as in Figure 1.

Figure 1. Mean regional cationic denudation rates (CDR) ordered by magnitude.

2.2.2. Trends in Cationic Denudation Rate

Figure 2 shows the strong regional variations in CDR among the different glacierized regions. Northwest America glaciers display the highest median CDR with a relatively narrower range and no visible outliers, implying more consistency in CDR values. The Himalayan basin exhibits the 2nd highest median CDR, with a wider range and a notable outlier, indicating substantial variability in its cationic denudation rates. The Alpine-China-Tibet basin shows a markedly higher CDR median, with an extremely wide range, suggesting substantial variability in its cationic denudation rates. Iceland basins have moderate CDR median value within a compact range, reflecting more uniform rates. Greenland glaciers present a narrow CDR range, indicating highly uniform rates, with their median positioned among the lower values. The Alpine-Europe glaciers show slightly lower variability, with a median and range comparable to those of the Iceland glaciers. The Svalbard/Arctic Canada glaciers exhibit the lowest median CDR, with minimal variability but two outliers observed. This plot underscores the considerable regional differences in CDR, with the Northwest America and Svalbard/Arctic Canada basins representing the extremes of the spectrum.

Figure 2. Box plot of CDRs of the glacierized basins. NB: O = Outlier, * = Extreme outlier.

2.3. Descriptive Statistics of Discharge for Glaciers

Discharge of glacier basins refers to the bulk volume of water released from glaciers, typically measured over a specified area and time. It represents the contribution of glacier meltwater to rivers, lakes, fjords, or oceans, and is an important component of the hydrological cycle. The unit, m yr⁻¹, indicates the average depth of water, measured in meters, which is exported from the glacier per year, normalized over the basin’s area.

Table 3 presents summary statistics and 95% confidence intervals for the average discharge rates (m yr⁻¹) across global glacierized basins. Northwest American glaciers exhibit the highest mean discharge (4.45 m yr⁻¹) with a broad range (3.28–7.68 m yr⁻¹). Svalbard/Arctic Canada glaciers have the lowest mean (0.92 m yr⁻¹) among multi-sample regions, with relatively low variability. Iceland, Greenland, Alpine-Europe, Alpine-China-Tibet, and the Himalaya show moderate discharge means ranging from 1.59 to 2.41 m yr⁻¹, though Greenland and Himalaya display higher variability. The newly included Alpine-China-Tibet region has a mean of 2.41 m yr⁻¹, with a wide confidence interval (0.04–4.78). Antarctica, represented by a single observation, shows the lowest discharge (0.53 m yr⁻¹). Overall, the global mean discharge is 1.80 m yr⁻¹, spanning from 0.30 to 7.68 m yr⁻¹.

Table 3. Estimations of global glaciers for discharge rates (m yr⁻¹).

Region	n	Mean	SD	Min	Max	95% CI for Mean
						Lower B	Upper B
Northwest America	5	4.45	1.82	3.28	7.68	2.19	6.71
Svalbard/Arctic Canada	20	0.92	0.45	0.30	1.83	0.71	1.13
Iceland	3	2.00	0.17	1.80	2.10	1.57	2.43
Greenland	3	1.79	1.23	0.37	2.50	−1.26	4.84
Alpine-Europe	5	1.59	0.44	1.20	2.31	1.04	2.14
Alpine-China-Tibet	5	2.41	1.91	0.96	4.63	0.04	4.78
Himalaya	7	2.26	2.12	0.57	6.50	0.30	4.22
Antarctica	1	0.53	-	-	-	-	-
Total	49	1.80	1.57	0.30	7.68	1.35	2.26

2.3.1. ANOVA Test for H₀₂: Equality of Average Discharge or Runoff Across Seven Global Glacierized Regions

An ANOVA was conducted to test the null hypothesis (H₀₂) that the average discharges are equal across the six glacierized basins. The test yielded Fisher’s F-statistic of 5.955 with degrees of freedom (df) of 6 and 41, and a p-value < 0.001. This result indicates that H₀₂ can be rejected, confirming that the average discharge significantly differs among the seven basins. Note that Antarctica was excluded from the analysis as it only has a single data point.

Bonferroni post hoc test results: After rejecting the null hypothesis (H₀₂) that the average discharge rates are equal across the six regions, we performed a Bonferroni post hoc test to identify specific pairs of regions with significantly different average discharge values. The Bonferroni post hoc test results in Table 4 reveal significant differences in mean discharge values (m yr⁻¹) between several regions.

Table 4. The results of the Bonferroni post hoc test for H₀₂. The asterisk (*) indicates significant difference in the means.

(I) Region	(J) Region	Mean Difference (I − J)	p-Value
Northwest America	Svalbard/Arctic Canada	3.53	<0.001 *
	Iceland	2.45	0.200
	Greenland	2.66	0.109
	Alpine-Europe	2.86 *	0.015 *
	Alpine-China-Tibet	2.04	0.261
	Himalaya	2.19	0.088
Svalbard/Arctic Canada	Northwest America	−3.53 *	<0.001 *
	Iceland	−1.08	1.000
	Greenland	−0.87	1.000
	Alpine-Europe	−0.67	1.000
	Alpine-China-Tibet	−1.49	0.419
	Himalaya	−1.34	0.363
Iceland	Northwest America	−2.45	0.200
	Svalbard/Arctic Canada	1.08	1.000
	Greenland	0.21	1.000
	Alpine-Europe	0.41	1.000
	Alpine-China-Tibet	−0.41	1.000
	Himalaya	−0.26	1.000
Greenland	Northwest America	−2.66	0.109
	Svalbard/Arctic Canada	0.87	1.000
	Iceland	−0.21	1.000
	Alpine-Europe	0.20	1.000
	Alpine-China-Tibet	−0.62	1.000
	Himalaya	−0.47	1.000
Alpine-Europe	Northwest America	−2.86 *	0.015 *
	Svalbard/Arctic Canada	0.67	1.000
	Iceland	−0.41	1.000
	Greenland	−0.20	1.000
	Alpine-China-Tibet	−0.82	1.000
	Himalaya	−0.67	1.000
Alpine-China-Tibet	Northwest America	−2.04	0.26
	Svalbard/Arctic Canada	1.49	0.419
	Iceland	0.41	1.000
	Greenland	0.62	1.000
	Alpine-Europe	0.82	1.000
	Himalaya	0.15	1.000
Himalaya	Northwest America	−2.19	0.088
	Svalbard/Arctic Canada	1.34	0.363
	Iceland	0.26	1.000
	Greenland	0.47	1.000
	Alpine-Europe	0.67	1.000
	Alpine-China-Tibet	−0.15	1.000

Note(s): * = The mean difference is statistically significant at the 5% level of significant.

Table 4 summarizes the results of Bonferroni-adjusted pairwise comparisons of average discharge rates among glacierized regions. The only statistically significant difference (p-value < 0.05) is observed between glaciers in Northwest America and Alpine-Europe, with Northwest America showing a significantly higher mean discharge (mean difference = 2.86 m yr⁻¹, p-value = 0.015). Although Northwest American glaciers also have higher mean specific discharges compared to other regions, these differences are not statistically significant after adjustment. No other pairwise comparisons yielded significant differences, suggesting a substantial overlap in average discharge rates among the remaining regions.

Mean discharge from glacierized basins decreases in magnitude, with Northwest America has the highest whereas Antarctica has the lowest discharge (Figure 3).

Figure 3. Regional mean discharges of glaciers ordered by magnitude.

2.3.2. Variations in Discharge of Glaciers

Figure 4 illustrates the variation in discharge rates across glacierized regions globally. Northwest American glaciers display the highest median discharge and the smallest range of variability among all glacier basins. Outliers are evident, with one extreme value significantly above the upper whisker, highlighting a potential anomaly or unique glacier behavior. Alpine-China-Tibet glaciers stand out with the highest variability—evidenced by a wide interquartile range (IQR). Himalayan glaciers show moderate discharge with notable variability and a wide IQR, indicating diverse meltwater contributions across this region. The upper whisker extends substantially, capturing a wider spread of discharge values.

Figure 4. Box plots of global glaciers for discharge rates. NB: O = Outlier, * = Extreme outlier.

Icelandic glaciers demonstrate the most consistent discharge rates, with both a narrow IQR and minimal deviation from the median. Greenlandic glaciers display moderately higher discharge levels with greater spread and a lower whisker extending close to zero, suggesting substantial variability across the region. Alpine-European glaciers also show low median discharge with limited variability, aside from one mild outlier. Finally, Svalbard/Arctic Canada glaciers exhibit low median discharge with a compact IQR, indicating consistent and low variability. Overall, the figure highlights regional contrasts in glacier melt behavior, with Icelandic and Svalbard/Arctic Canada glaciers exhibiting the most stable discharge, while Alpine-China-Tibet and Himalayan glaciers show considerable variability. The presence of outliers in Northwest America, Himalayan, and Alpine-Europe regions suggest potential localized factors affecting melt intensity, meriting further investigation.

2.4. Descriptive Statistics of Chemical Weathering Intensity (CWI)

We present the Chemical Weathering Intensity (CWI) = CDR/Specific Discharge from global glaciers in Table 5. The CWI of glacier basins refers to the amount of chemical weathering products (such as ions released from mineral dissolution) exported per unit volume of meltwater. It quantifies the intensity of chemical weathering relative to water flux, offering insights into geochemical processes occurring within glacial environments. The unit, meq m⁻³, indicates the concentration of weathering-derived solutes in meltwater per unit volume.

Table 5. Estimations of global glaciers for CWI (meq m⁻³).

Region	n	Mean	SD	Min	Max	95% CI for Mean
						Lower B	Upper B
Northwest America	5	273	105	173	446	143	404
Svalbard/Arctic Canada	20	557	252	132	1073	439	676
Iceland	3	405	103	342	524	150	661
Greenland	3	247	113	123	344	−33	527
Alpine-Europe	5	436	172	297	732	223	650
Alpine-China-Tibet	5	553	216	193	732	284	821
Himalaya	7	801	419	214	1316	414	1188
Antarctica	1	308	-	-	-	-	-
Total	49	517	285	123	1316	435	599

Table 5 summarizes the CWI across glacierized regions of the world, highlighting substantial geographic variability in mean values and dispersion. Among the 50 CWI values from 40 glaciers analyzed, the Himalaya exhibits the highest mean CWI (801 meq m⁻³), with wide variability (SD = 419), reflecting diverse hydrochemical and climatic conditions within the region. In contrast, Northwest America and Greenlandic glaciers show comparatively lower mean intensities (273 and 247 meq m⁻³, respectively), with narrower confidence intervals, suggesting more consistent geochemical regimes. The Svalbard/Arctic Canada and Alpine-China-Tibet glaciers display relatively high means (557 and 553 meq m⁻³, respectively) with moderate to high variability, while Iceland and Alpine-Europe fall within mid-range values. Notably, the data from Antarctica is limited to a single observation, precluding statistical inference. Overall, the global mean CWI across all sampled glaciers is 517 meq m⁻³, with a 95% confidence interval ranging from 435 to 599 meq m⁻³. These findings underscore the complex interplay of climatic, lithological, and hydrological factors that influence chemical weathering processes across glacierized environments.

2.4.1. ANOVA Test for H₀₃: Equality of Average CWI Across Regions

An ANOVA was conducted to test the null hypothesis (H₀₃) that the average CWI are equal across the seven regions. The test yielded Fisher’s F-statistic of 3.051 with degrees of freedom (df) of 6 and 41 and a p-value of 0.015. This result indicates that H₀₃ can be rejected, confirming that the average CWI significantly differs among the seven basins. Note that Antarctica was excluded from the analysis as it only has a single data point.

Multiple Comparisons: Bonferroni Post Hoc Test Results: After rejecting the null hypothesis (H₀₃) that the average CWI rates are equal across the seven glacierized basins, we performed a Bonferroni post hoc test to identify specific pairs of basins with significantly different average CWI values. The Bonferroni post hoc test results in Table 6 reveal significant differences in mean CWI values (meq m⁻³) between several glacier basin pairs. Specifically:

Table 6. The results of the Bonferroni post hoc test results for H₀₃.

(I) Region	(J) Region	Mean Difference (I – J)	p-Value
Northwest America	Svalbard/Arctic Canada	−284	0.655
	Iceland	−132	1.000
	Greenland	27	1.000
	Alpine-Europe	−163	1.000
	Alpine-China-Tibet	−279	1.000
	Himalaya	−527	0.021 *
Svalbard/Arctic Canada	Northwest America	284	0.655
	Iceland	152	1.000
	Greenland	311	1.000
	Alpine-Europe	121	1.000
	Alpine-China-Tibet	5	1.000
	Himalaya	−243	0.745
Iceland	Northwest America	132	1.000
	Svalbard/Arctic Canada	−152	1.000
	Greenland	158	1.000
	Alpine-Europe	−31	1.000
	Alpine-China-Tibet	−148	1.000
	Himalaya	−395	0.627
Greenland	Northwest America	−27	1.000
	Svalbard/Arctic Canada	−311	1.000
	Iceland	−158	1.000
	Alpine-Europe	−190	1.000
	Alpine-China-Tibet	−306	1.000
	Himalaya	−554	0.064
Alpine-Europe	Northwest America	163	1.000
	Svalbard/Arctic Canada	−121	1.000
	Iceland	31	1.000
	Greenland	190	1.000
	Alpine-China-Tibet	−116	1.000
	Himalaya	−364	0.398
Alpine-China-Tibet	Northwest America	279	1.000
	Svalbard/Arctic Canada	−5	1.000
	Iceland	148	1.000
	Greenland	306	1.000
	Alpine-Europe	116	1.000
	Himalaya	−248	1.000
Himalaya	Northwest America	527	0.021 *
	Svalbard/Arctic Canada	243	0.745
	Iceland	395	0.627
	Greenland	558	0.064
	Alpine-Europe	364	0.398
	Alpine-China-Tibet	248	1.000

Note(s): * = The mean difference is statistically significant at the 5% level of significant.

Table 6 presents the results of Bonferroni post hoc comparisons of mean CWI among glacier regions. While most pairwise differences are not statistically significant (p-value > 0.05), a significant difference is observed between the Himalaya and Northwest American glaciers (mean difference = 527 meq m⁻³, p-value = 0.021), indicating substantially higher weathering intensity in the Himalaya. All other regional comparisons yielded non-significant results, suggesting that, despite observable differences in means, variability within regions limits the detection of statistically significant differences across most pairs. When mean CWI of glacierized basins are arranged in decreasing order of magnitude, the Himalaya shows the highest mean CWI of 801 meq m⁻³, while the Greenland exhibits the lowest, with a mean CWI of 247 meq m⁻³ (Figure 5).

Figure 5. Regional mean CWI ordered by magnitude.

2.4.2. Variations in CWI

Figure 6 illustrates the distribution of CWI across seven glacierized regions. The Himalaya region exhibits the highest median CWI and the widest range, indicating both intense and variable chemical weathering activity. In contrast, Greenland shows the lowest median CWI values (247 meq m⁻³) (Figure 5). The Svalbard/Arctic Canada and Alpine-China-Tibet regions display moderate to high median values, but the Svalbard/Arctic Canada shows the greatest spread and variability, as evidenced by its wide box and extended whiskers. Outliers are present in several regions, including the Northwest America, Alpine-Europe, and Alpine-China-Tibet, highlighting localized deviations from regional trends. Overall, the plot reveals significant regional variability in CWI, with the Himalaya standing out as a hotspot of intense chemical weathering among the regions.

Figure 6. Box plots of regional CWI. NB: O = Outlier, * = Extreme outlier.

3. Predictive Modeling of CDR over Glacier Specific Discharge

To analyze the relationship between CDR and glacier specific discharge, we tested the null hypothesis H₀₄: There is no regression relationship between CDR and glacier specific discharge.

Statistical Analysis: The ANOVA results revealed a significant regression model, with Fisher’s statistic F = 21.5, degrees of freedom (1, 42), and p-value < 0.001. This led to the rejection of H₀₄, confirming that CDR is significantly associated with glacier specific discharge. Despite the statistical significance, the model’s R² value was only 57%, indicating that a substantial 43% of the variation in CDR remains unexplained by specific discharge. This limitation reduces the model’s predictive utility. Regression coefficient of 382 suggests that for every 1 m yr⁻¹ increase in discharge, the CDR increases by 382 meq m⁻² yr⁻¹ (Figure 7). A separate regression analysis was conducted for each region. However, the results were almost consistent across all regions, indicating a similar relationship between CDR and specific discharge regardless of location. This analysis highlights a significant but modest predictive relationship, warranting further investigation into additional factors influencing CDR variability.

Figure 7. The relationship between CDR and glacier specific discharge.

4. Summary of Research Findings

This study investigated the variations and interrelationships among three key variables associated with global glaciers: CDR, specific discharge, and the predictive modeling of CDR based on discharge. Through statistical analyses, including descriptive statistics, comparative tests, and regression modeling, the research provided valuable insights into the dynamics of regional glacial weathering systems. The findings are summarized below, categorized by each type of analysis.

4.1. Variations in CDR

The analysis of the sparsely available CDR across global glacierized basins revealed significant variability in chemical weathering rates on a regional scale. Himalayan glaciers exhibited the highest mean CDR values, indicating a potentially greater contribution to chemical denudation processes in this region (Figure 2). In contrast, Svalbard/Arctic Canada and Antarctic glaciers showed markedly lower CDR values, suggesting limited chemical weathering activity in these colder regions. Statistical tests confirmed significant differences in CDR values among various glacier basins worldwide. The Bonferroni post hoc test identified notable contrasts, particularly between Himalayan and Northwest American glaciers and those in the Svalbard/Arctic Canada, Iceland, and Alpine regions. These findings highlight the diverse environmental and climatic conditions influencing CDR across global glaciers. Overall, the variations in CDR suggest that region-specific factors such as climatic conditions (primarily temperature and precipitation) and discharge, glacier dynamics, and the geochemical characteristics of the underlying bedrock play critical roles in determining chemical weathering regime.

4.2. Variations in Glacier Discharge

Discharge displayed significant variations across glacier basins. Northwest American glaciers exhibited the highest discharge rates, while Svalbard/Arctic Canada glaciers had the lowest. Other regions, including Alpine, Iceland, and Himalayan glaciers, showed moderate discharge values. These variations underscore the diverse contributions of glacier meltwater, shaped by factors such as temperature, precipitation, and glacier size. Boxplot analysis revealed substantial variability within certain basins, such as Greenland, where discharge values spanned a wide range (Figure 4). Conversely, basins like the Iceland glaciers demonstrated relatively narrow discharge ranges, indicating more uniform meltwater behavior. Statistical tests further validated significant differences in discharge between Northwest American glaciers and other basins, reflecting trends observed in CDR values.

4.3. Predictive Modeling of CDR Based on Specific Discharge

To investigate the relationship between CDR and specific discharge, a regression analysis was conducted. The null hypothesis (H₀₂): There is no regression relationship between CDR and specific discharge was tested using ANOVA. The results indicated a statistically significant relationship and consequently, the null hypothesis was rejected, confirming that specific discharge plays a role in predicting CDR. However, the regression model explained only 57% of the variability in CDR, leaving a substantial portion unexplained.

While specific discharge is a significant predictor of CDR, additional factors such as temperature, bedrock composition, and hydrological processes likely contribute to the unexplained variance. The regression coefficient of 382 suggests that for every 1 m yr⁻¹ increase in discharge, the CDR increases by 382 meq m⁻² yr⁻¹, reinforcing the positive association between these variables which supports the previous finding of Hodson et al. (2000) [7] in glacierized basins and other largest river basins of the world [10]. A separate regression analysis conducted for individual glacier basins yielded consistent results, indicating that the relationship between specific discharge and CDR is robust across different geographic regions. However, the low values for these basin-specific models highlight the need for further investigation into region-specific factors influencing CDR.

4.4. Integrating of Findings

The combined analysis of CDR, specific discharge, and their predictive relationship highlights a significant but modest association, warranting further investigation into additional factors such as glacier dynamics, climate, and lithology that may influence CDR variability. Significant regional variations in both CDR and discharge underscore the influence of local environmental and climatic conditions on glacier behavior. The observed correlation between discharge and CDR, while statistically significant, emphasizes the complexity of chemical weathering processes in glacier systems, as a large portion of the variability remains unexplained by discharge alone. These findings have important implications for understanding the role of glaciers in global biogeochemical cycles. High CDR in the Himalaya glaciers could be due to exposure of fresh reactive minerals surfaces due to intense tectonic activities in the region and high glacier retreat rate which enhances the downward movement of reaction front and hence accelerate the weathering rates. High CDR and discharge values in Northwest American glaciers, for example, suggest these systems may contribute disproportionately to chemical weathering rates and nutrient fluxes into downstream ecosystems. Conversely, the low values observed in Svalbard/Arctic Canada and Antarctic glaciers highlight the reduced weathering potential in polar regions. The Himalayan glacier shows the highest mean CWI among the documented glacier systems in the world suggesting high extent of chemical weathering.

In summary, this review and analysis of CDR in glacierized basins highlights the dynamic interplay between glacier discharge and chemical weathering processes. While the study provides valuable insights, it also points to the need for further research to uncover additional factors influencing CDR and to improve the predictive capabilities of regression models. By integrating discharge with other environmental variables, future studies can enhance our understanding of the complex mechanisms driving chemical denudation in glacier systems.

5. Future Research

Several avenues remain open for future exploration to deepen our understanding and address the limitations of the current study. Below are some key directions for future research.

5.1. Enhanced Data Collection and Granularity

To improve the robustness and applicability of predictive models, future research should focus on gathering more extensive and high-resolution datasets for both CDR and discharge. Despite glacial hydrochemistry research that has been conducted for several decades, available data on CDR is surprisingly sparse. A key issue is the logistics and funding involved in establishing hydrometric stations and maintaining long-term discharge measurement series in highly dynamic rivers close to glacier portals. Incorporating additional basins, particularly those currently underrepresented (e.g., glaciers from Antarctica, the Canadian High Arctic, Russian Arctic, central Asia, the south Alps of New Zealand, and South America), could yield a more comprehensive global perspective. Longitudinal data capturing seasonal and interannual variability in CDR and discharge would also enhance the precision of modeling efforts.

5.2. Integration of Climate and Geological Factors

While this study primarily examined the relationship between discharge and CDR, future research could incorporate climatic variables (e.g., temperature, precipitation, and glacier mass balance) and geological characteristics (e.g., rock type, sediment load) to explore their influence on chemical denudation. Including such factors could help explain the unexplained variance observed in the current predictive models and provide a more holistic understanding of the drivers of CDR in glacierized basins.

5.3. Basin-Specific Modeling

Although this study suggests that the relationship between discharge and CDR is relatively consistent across glacierized basins, future research could explore basin-specific characteristics that may enhance predictive models. Local environmental factors such as hydrology, anthropogenic impacts, and nutrient fluxes could create unique patterns not fully captured by a generalized model. Developing regionally tailored models could offer more precise insights for specific basins.

5.4. Impacts of Climate Change

The ongoing effects of climate change on glaciers and hydrological systems represent a critical area for future exploration. Researchers could investigate how changing glacier size and melt rates influence both discharge and CDR over time. Modeling future scenarios under different climate trajectories would provide valuable insights for anticipating and mitigating the impacts of global warming on water quality and availability. The step of coupling among glacier discharge modelling, CDR and solute export is still missing.

5.5. Broader Environmental Impacts

Future studies could examine the downstream effects of CDR on ecosystems, such as nutrient cycling and aquatic biodiversity. Understanding how variations in CDR affect riverine and coastal ecosystems could have important implications for environmental management and conservation effort. Additionally, exploring the role of CDR in carbon sequestration and its potential feedback loops within the global carbon cycle could contribute to broader climate research.

5.6. Comparative Studies

Finally, comparative studies between glacierized basins and non-glacierized regions could highlight the unique contributions of glaciers to global chemical denudation processes. Such comparisons would help contextualize the findings of this study within a broader environmental framework and elucidate the distinct roles glaciers play in Earth’s biogeochemical cycles.

In conclusion, while this research has provided a foundational understanding of the relationship between discharge and CDR in glacierized basins, these suggested avenues for future research can build upon this foundation to address existing gaps, enhance predictive models, and offer actionable insights for environmental management and climate adaptation strategies.