Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

hydrograph calculated at 18 km for the Thorthomi Cho GLOF, i.e. the first event. Despite the large size debris flow in the first GLOF event, the  $Q_T$  is much higher in the second

event because the debris flow size reduces gradually after intermittent depositions in the first event but abruptly in the second event. Also, the river storage function was not active as the channel capacity was widen by the first event to pass the debris flow developed along the 4-km initial reach during the second event.

At the 10-km section of the river, almost 30% of the released water volume from the lake passed as a peak flow and the remaining as tail water with long recession time. In all the aforementioned cases, the hydrodynamic routing procedure translated an upstream hydrograph into a subsequent downstream hydrograph. As a result, the recession time in each routed hydrograph is longer but the time that the hydrograph takes to rise is much shorter, which represents a flash flood phenomenon. Multiple peaks appear in each calculated hydrograph. In the second GLOF event, the calculated hydrographs are relatively smoother (Figure 9c) than in the first event (Figure 7f). Further, the temporal change of bed elevation at randomly selected 6-km section (Figure 9d) shows that the GLOF surge eroded the bed at first but the section was deposited later, making the final bed elevation raised by 3.5 m from 4265.2 m.

Likewise, debris flow simulations are performed for the west branch of the Pho Chu river considering the possible breaches of moraine dams at the Lake A and B. The simulated results are summarized in Table 2. Unlikely, the debris flow size in the first GLOF surge (from Lake A) in  $T_{\rm W}$  is not developed well. The maximum sediment


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/9/Figure/2 description: The image displays four line graphs, arranged in a 2x2 grid and labeled (a), (b), (c), and (d).

data/('Prediction and assessment of multiple glacial lake outburst floods scenario in Pho', '.pdf')_extraction.md


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

Graph (a) is titled '6000m'. The y-axis is labeled 'Qs (m³/sec)' and ranges from 0 to 600. The x-axis is labeled 'T (sec)' and ranges from 0 to 1000. The plot shows a sharp peak reaching approximately 600 m³/sec around 250 sec, followed by a smaller peak of about 300 m³/sec, and then several smaller oscillations before returning to near zero after 600 sec.

Graph (b) is titled '10000m'. The y-axis is labeled 'Qs (m³/sec)' and ranges from 0 to 80. The x-axis is labeled 'T (sec)' and ranges from 0 to 1000. The plot shows a peak of about 70 m³/sec around 420 sec, followed by a second peak of about 50 m³/sec. A much smaller, separate peak occurs around 750 sec.

Graph (c) is titled '10000m'. The y-axis is labeled 'QT (m³/sec)' and ranges from 0 to 25000. The x-axis is labeled 'T (sec)' and ranges from 0 to 1000. The shape of this graph is similar to graph (b), with a large peak reaching about 23000 m³/sec around 420 sec, a second peak of about 14000 m³/sec, and a small, separate peak around 750 sec.

Graph (d) is titled '6000m'. The y-axis is labeled 'Bed Elevation (m)' and ranges from 4262 to 4268. The x-axis is labeled 'T (sec)' and ranges from 0 to 1000. The plot shows the bed elevation starting at about 4264.2 m, dropping sharply to about 4262.2 m around 220 sec, then rising sharply to about 4265.5 m. After this, it oscillates and gradually increases to about 4267.5 m by 1000 sec.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 9. Sediment discharge calculated at (a) 6-km and (b) 10-km sections of $T_E$ during the second GLOF event by Lugge Cho Lake, (c) hydrograph of mixture flow $Q_T$ at 10 km and (d) temporal change of bed elevation at 6 km

Figure 9. Sediment discharge calculated at (a) 6-km and (b) 10-km sections of  $T_E$  during the second GLOF event by Lugge Cho Lake, (c) hydrograph of mixture flow  $Q_T$  at 10 km and (d) temporal change of bed elevation at 6 km


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: table
Table: Table II. Peak sediment discharges calculated at different locations due to GLOFs in $T_{\rm W}\,$

| Location A/B |    | 2/2.5 km | 4/4.5 km | 6/6.5 km | 8/8.5 km | 12/12.5 km | 15/15.5 km | 17/17.5 km   |
|--------------|----|----------|----------|----------|----------|------------|------------|--------------|
| 1st GLOF A   | Qs | 500      | 1400     | 650      | 250      | 200        | 220        | 50 $QT=9700$ |
| 2nd GLOF B   |    | 20       | 40       | 10       | 30       | 10         | 10         | 10 $QT=800$  |


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

Values are in cubic metres per second.

discharge reached  $1400 \,\mathrm{m}^3/\mathrm{s}$  at the 4-km section during the first GLOF event but remains at the lowest value at the rest of the downstream sections. Figure 10 shows the riverbed slope distribution, which is relatively steep in the initial 4-km reach but mild in the rest portion. In this event, the erosion and deposition processes are also intermittent phenomenon with no significant sediment transportation because the riverbed profile is very irregular with randomly mixed steep and mild slope reaches. The peak discharge  $(Q_T)$  of the mixture flow during the first GLOF event reached at about  $9000 \,\mathrm{m}^3/\mathrm{s}$  at the 17-km section (Figure 11), where the sediment discharge was reduced to lowest level, i.e.  $50 \,\mathrm{m}^3/\mathrm{s}$  (Table 2). In the second GLOF event from Lake B in  $T_W$ , the sediment discharge remains at the lowest value at

all the sections because the first event stabilized the irregular riverbed profile so no active erosion took place in smoothened mild slope region. Because the debris flow development is not significant in the second GLOF event throughout the river reach, the peak mixture discharge  $(Q_T)$  at 17.5 km (17 km refer to Lake A) remains at  $800\,\mathrm{m}^3/\mathrm{s}$ . This means the first GLOF is destructive than the second one in  $T_W$ , which is different from the case of  $T_E$ , where the second peak was much larger than the first one. The difference also exists because no significant debris flow size was developed within 0.5-km initial reach between Lakes A and B.

Two highest peak hydrographs, one for the Lugge Cho GLOF in  $T_{\rm E}$  calculated at 10 km and the other for the Lake A GLOF in  $T_{\rm W}$  at 17.5 km are then as upstream


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/9/Figure/10 description: A line graph plotting Bed-slope in degrees against Distance in meters. The y-axis, labeled "Bed-slope (degrees)", ranges from 0 to 20. The x-axis, labeled "Distance (m)", ranges from 0 to 18000. The line shows a high and variable bed-slope from 0 to approximately 5000 meters, starting at about 14 degrees and fluctuating roughly between 4 and a peak of over 16 degrees. After 5000 meters, the bed-slope drops significantly and remains low, fluctuating mostly between 0 and 5 degrees for the rest of the distance up to 18000 meters.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 10. Bed slope distribution along TW

Figure 10. Bed slope distribution along TW


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/9/Figure/12 description: A line graph plots Q\_T in cubic meters per second (m^3/sec) versus Time in seconds (sec). The vertical y-axis, labeled 'Q\_T (m^3/sec)', ranges from 0 to 12000, with tick marks every 3000 units. The horizontal x-axis, labeled 'Time (sec)', ranges from 0 to 2000, with tick marks every 500 units. The plotted line is at zero from 0 to approximately 950 seconds. It then spikes sharply to a peak of just under 10000 m^3/sec at around 980 seconds. The value then drops rapidly, has a smaller peak of about 4000 m^3/sec, and then generally decreases with several smaller, sharp peaks occurring between 1300 and 2000 seconds. The text '17000m' is written in the upper right quadrant of the graph.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 11. Total hydrograph ( $Q_T$ ) calculated at 17.0 km in $T_W$

Figure 11. Total hydrograph ( $Q_T$ ) calculated at 17.0 km in  $T_W$


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

boundary conditions for the inundation simulation by HEC-RAS unsteady flow model. Although the exact time of dam breaches and therefore the surge arrival time at mentioned locations is not known, simultaneous loading of surges at the same time from two tributaries is assumed. The result shows that the considered scenario of GLOFs can cause a serious inundation at different locations up to the Bhutan-India border. Although the inundation extent is restricted within the close proximity of the river banks due to the existence of narrow and deep valleys throughout the reach, there are several settlements within such narrow valleys which are found to be highly prone to floodings. Among them, Punakha, Lobeysa and the major portion of Wangdue Phodrang town could be inundated by a few to several metres of flood as shown in Figure 12. The flood depth at some locations reached over 25 m especially in the narrow gorge in mild slope river reach sections of the Pho Chu and Puna Tshang Chu Rivers. The effect of river pooling in many locations causes highest flood depths such as one just downstream to the junction of  $T_E$  and  $T_W$ . On the other hand, shallow depths of flood are also observed in steep river gradient sections. The area bordering India is found to be relatively safe as the effect of the GLOF inundation is small in this area.

The reliability of results discussed in the previous sections greatly depends on the quality of observed data, which is however difficult to maintain for such a difficult terrain. Therefore there are uncertainties in the predicted results, which can however be minimized through additional field surveys and precise and regular monitoring of hydrological conditions including flood discharge measurement. A number of checks for parameter sensitivity may be required to improve the reliability of prediction by numerical model, which may also include the variation in sediment size, sediment type, channel geometry and land uses.

It is a fact that the characteristic of flood in the downstream areas is governed by the size of debris flow developed in the upstream areas but not necessarily the amount of water released from the lake. There could be many other possible scenarios, which need to be taken into account seriously for the understanding of GLOFs. For example, depending on the flow characteristics and morphological setting, there is a chance that the second GLOF surge can merge into the first surge as the velocity of second GLOF surge could be faster than the first one. In this study, two different GLOF events for each tributary, which are supposed to be triggered at the same time from the sources, are treated separately to understand how the characteristics of GLOF change with different GLOF surges passing at different times. However, the case treated in this paper could also be one of the worst scenarios. Also, despite the fact that the same dam breach triggering factor could act at the same time, there would be many uncertainties in the breaching process of moraine dams and therefore the timing of breach and water releasing process. The account should also be given to the sediment mass produced by landslides as a result of GLOF, which may add a significant amount of sediment volume in the flow. Besides, accuracy of satellitebased DEM for the derivation of topography and riverbed profile is to be improved for obtaining an applicable result.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: CONCLUSIONS
Type: text

Glacial lake outburst floods and associated risk are widely discussed elsewhere in the literature mainly under the scenario of increasing threats of climate change in high Himalayas. However, the flow dynamics of such outburst floods in highly fragile landscape of the Himalayas is little understood among scientists and engineers and therefore the realization of potential threat due to GLOF is


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: CONCLUSIONS
Type: figure
Figure

Image /page/10/Figure/7 description: A figure containing two maps illustrating flood inundation in a watershed. The map on the left shows the entire watershed with a topographical color scale for elevation, ranging from 52-400 meters (yellow-green) up to 3200-5000 meters (white). A river runs through the valley, and a legend for 'Inundation (m)' shows flood levels from 0-5 m (light blue) to 16-20 m (dark blue). A circular area on this map is highlighted and magnified in the map on the right. The right map is a close-up view showing the 'Inundation Depth (m)' with the same color scale. This map labels several locations, including 'Punakha', 'Lobeysa', 'Wangdue Phodrang', and a specific point marked as 'Fort-Monastery'. The left map has a scale from 0 to 30 kilometers, while the right map has a scale from 0 to 2.5 kilometers.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: CONCLUSIONS
Type: figure
Figure: Figure 12. GLOF inundation map based on 1-D Hydrodynamic computation

Figure 12. GLOF inundation map based on 1-D Hydrodynamic computation


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: CONCLUSIONS
Type: text

unclear. Therefore, an approach is made to evaluate the dynamics of GLOF in a multi-hazard scenario taking an example from the Lunana region in west Bhutan. The upper Pho Chu River basin in Lunana, which is highly seismic sensitive and highly prone to GLOF hazards, is chosen for the study. The breaches of moraine dams at four different glacial lakes namely Thorthormi Cho and Lugge Cho in the east branch and Lakes A and B in the west branch of the Pho Chu River were assumed to develop series of GLOFs. Multiple GLOF surges induced by moraine dam breaches in the tributaries and main reach of the Pho Chu River and then of the Puna Tshang Chu River were reproduced by means of numerical models. Main conclusions from the study are summarized as follows:

- 1. Despite the amount of water released from the lakes, the magnitudes of GLOFs are dependent of the bed slopes and potential erosion depth along the river reach and therefore the debris flow size, which usually reduces in secondary or following surges. This phenomenon is related to the change in riverbed profile associated with the temporal erosion and deposition.
- 2. In the east branch of the Pho Chu River, the amount of sediment discharge during the first GLOF induced by the Thorthormi moraine dam breach is much higher than the amount produced during the second surge of GLOF by Lugge Cho, despite the fact that the properties of both dam breach hydrographs at the lake sites are almost identical. However, at the 10-km section, the magnitude (23 000 m3/s) of the peak flood hydrograph produced by the second GLOF from the Lugge Cho Lake is much higher than the peak (10 000 m3/s) developed during the first GLOF surge from the Thorthormi Lake. This robustness in the second GLOF surge exists due to the increased channel conveyance capacity and minimized hydraulic pooling by channel erosion caused by the first surge from Thorthormi Cho.
- 3. In the west branch of Pho Chu, the characteristic of GLOF is different from the east branch. The total sediment volume produced through erosion is always very small due to the existence of frequently available intermittent mild slope river sections, where sediment deposition takes place immediately after the erosion. Also slopes steeper than 18° in simulation are considered rigid beds and such slopes do not produce sediment budget. The peak flood hydrograph at 17.5 km, where the sediment discharge is at the lowest value, became almost identical with the peak of the dam breach hydrograph at the lake site. Different from east branch, the second GLOF surge from Lake B could not develop a debris flow and the hydrograph attenuates significantly as a normal phenomenon.
- 4. The previously described findings indicate that the GLOF hydrograph characteristic is greatly governed by erosion and deposition processes. In other words, the robustness of the flood peak in downstream area is influenced by the sediment flow dynamics in debris

flow zone. Therefore, GLOF behaviour is greatly influenced by river morphology.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: CONCLUSIONS
Type: text

flood hydrograph at 17 . 5 km , where the sediment discharge is at the lowest value , became almost identical with the peak of the dam breach hydrograph at the lake site . Different from east branch , the second GLOF surge from Lake B could not develop a debris flow and the hydrograph attenuates significantly as a normal phenomenon . - 4 . The previously described findings indicate that the GLOF hydrograph characteristic is greatly governed by erosion and deposition processes . In other words , the robustness of the flood peak in downstream area is influenced by the sediment flow dynamics in debris flow zone . Therefore , GLOF behaviour is greatly influenced by river morphology .

The hydrographs with a peak value of 23 000 m3/s at 10 km in the east branch and 9700 m3/s at 17.5 km in the west branch of the Pho Chu River, which are both considered the worst cases, are used for flood inundation analysis in further downstream areas. The result shows that a serious inundation can occur at different locations up to the Bhutan–India border. Although the inundation extent is restricted within the close proximity of the river banks due to narrow and deep valleys throughout the river reaches, several towns namely Punakha, Lobeysa and the major portion of Wangdue Phodrang are under the biggest threat of GLOF with a potential inundation depth of over 10 m at some locations. The inundation map can be considered as a tool for planning GLOF disaster mitigation projects.

Detail morphological settings, the number of other glacial lakes and socioeconomic conditions need to be taken into account for detail study for GLOF mitigation planning.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: ABSTRACT
Type: text

Thermal stratification plays a key role in lakes' ecosystems. In contrast to deep lakes, the thermal structure of shallow polymictic lakes is characterized by a weak stratification with an apparent diurnal cycle. Long-term changes in stratification are governed by climate change and anthropogenic effects such as water level regulation. We developed a simple and robust model system consisting of an energy balance model to estimate depth-averaged water temperatures and an artificial neural network (ANN) model to predict stratification with high temporal resolution. One novelty of our approach is that instead of directly estimating water temperatures at different depths, we simulated the potential energy anomaly index, the indicator of stratification's strength. The ANN-based model's performance was assessed against a physical-based one-dimensional model (General Ocean Turbulence Model) by modeling a 40-year-long period from 1981 to 2020. The new model accurately predicts a shallow lake's weak stratification and its diurnal cycle. Besides, the model proved reliable on longer time scales, capturing the effect of climate change, anthropogenic water level regulation, and their synergistic interaction on the change of stratification's intensity and duration.

Key words: artificial neural network, climate change, diurnal stratification, potential energy anomaly, shallow lake, weak stratification

data/('Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks', '.pdf')_extraction.md


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: HIGHLIGHTS
Type: text

- A simple energy balance and ANN model system is developed to simulate shallow lakes' stratification and evaluated using a physical-based model.
- Weak stratification is modeled with high temporal resolution to capture its diurnal lifecycle.
- The ANN-based model also reproduces the long-term synergistic impact of climate change and anthropogenic effects.

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: HIGHLIGHTS
Type: figure
Figure

Image /page/1/Figure/1 description: A graphical abstract illustrating a two-part modeling process. Part 1 is titled "Energy balance model" and shows a diagram of a water body with meteorological driving factors. These factors include incoming net shortwave radiation (SW\_net) and outgoing net longwave radiation (LW\_net), sensible heat (H), and latent heat (LE). This model calculates the depth-averaged water temperature (ΔT\_w, T\_w), which is then plotted over time (t) in a graph below, showing temperature fluctuations. Part 2 is titled "ANN model of stratification (φ)". The outputs from the first model (ΔT\_w, T\_w) are used as inputs for this second model. The model is represented by the function φ\_i = f(u\_i, SW\_i, SW\_i-j, H\_i, ..., h\_i, T\_w,i, ΔT\_w,i-j). A diagram of an Artificial Neural Network (ANN) is shown with an input layer (yellow), a hidden layer (blue), and an output layer (pink). The inputs to the network include variables like T\_w,i, ΔT\_w,i-j, and u\_i. The output of the ANN model is the stratification parameter (φ\_i), which is plotted against time (t) in a graph at the bottom.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 1. INTRODUCTION
Type: text

Thermal stratification has a significant role in lakes' ecological status, potentially causing oxygen depletion at the lake's bottom. In deep lakes, when stratification occurs, the water column can be divided into three layers: epilimnion, hypolimnion, and thermocline. Out of these, the hypolimnion plays a crucial role in maintaining stratification, as in typical circumstances, low mixing characterizes this layer, allowing stratification to persist. As a result, oxygen depletion can develop over the bottom, leading to eutrophication through nutrient release (Pettersson *et al.* 2003; Salmaso 2005). In contrast, epilimnion and hypolimnion may not develop in shallow lakes because driving forces of mixing acting at the lake's surface can reach the bottom of the lake, resulting in more frequent mixing periods and shorter stratification durations (Wilhelm & Adrian 2008). The stratification usually lasts for months in deep lakes and ranges from hours to days in shallow lakes. Despite the frequent mixing, oxygen depletion can also develop in the latter case if meteorological conditions are met in such a way that an intermittent – a few days long – but continuous stratification develops, leading to severe ecological problems, such as the record-setting algae bloom in 2019 in Lake Balaton (Istvánovics *et al.* 2022). Thus, stratification can significantly influence the trophic state of shallow lakes (Shinohara *et al.* 2023).

In shallow lakes, meteorological effects can substantially affect stratification, so it is necessary to reveal their influence and their long-term changes (Zhou *et al.* 2023). The dominant driving forces of stratification are the solar radiation, the surface air temperature, and the wind speed. The former two are responsible for building up stratification by warming the water layers with different intensities, while the latter is mainly responsible for breaking it up by current- and wave-induced mixing processes (Torma & Krámer 2017). Just mentioning two examples, as a consequence of climate change, the number of lake heatwaves increases (Wang *et al.* 2023) as well as the intensity of evaporation (Tong *et al.* 2023). In mid-latitude climates, solar radiation, and surface air temperature tend to increase, warming lakes and prolonging stratification periods in the warm seasons (Woolway *et al.* 2020).

In addition to climate change, anthropogenic effects also have a significant impact on the stratification of lakes. Among the effects, those that result in a change in the water level should be highlighted, as the water depth plays a crucial role in the stability of stratification. The higher the depth, the more stable stratification can develop (Kraemer *et al.* 2015). Due to climate change, lake and reservoir water levels may decrease if precipitation and, as a result, runoff rates from the lake's watershed decrease. Consequently, stakeholders try to keep higher water levels to provide a puffer for drought periods. However, more

extended stratified periods can develop by a higher water level, increasing the possibility of oxygen depletion even in shallow, polymictic environments (Istvánovics *et al.* 2022).


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 1. INTRODUCTION
Type: text

highlighted , as the water depth plays a crucial role in the stability of stratification . The higher the depth , the more stable stratification can develop ( Kraemer * et al . * 2015 ) . Due to climate change , lake and reservoir water levels may decrease if precipitation and , as a result , runoff rates from the lake ' s watershed decrease . Consequently , stakeholders try to keep higher water levels to provide a puffer for drought periods . However , more extended stratified periods can develop by a higher water level , increasing the possibility of oxygen depletion even in shallow , polymictic environments ( Istvánovics * et al . * 2022 ) .

In the case of shallow lakes, only weak stratification can develop with a typical diurnal cycle. This means that stratification develops over the day and breaks up due to surface cooling during the nighttime (Torma & Wu 2019). For example, in the very shallow Lake Balaton (Hungary), a stratification that forms over the day (with a maximum temperature difference of 5–6 °C between the surface and the bottom) mostly entirely disappears for the following day. Besides surface cooling, wind can also mix the water column through waves and currents, leading to even shorter stratified periods. Because of the diel cycle, at least hourly measurements are needed to capture the stratification in such environments. Nevertheless, in some cases, neither nighttime cooling nor the wind can mix the whole water column so that a stable stratification can continuously persist near the bottom for a few days. In such cases, anoxic conditions may occur with the consequences mentioned above. Overall, stratification and mixing processes in shallow lakes with a diurnal cycle must be modeled on short time scales of a few hours.

Physical-based models with different dimensions and empirical methods are also available to model stratification (Amorim et al. 2023; Naumenko & Guzivaty 2023). Due to the rapid growth of lake water temperature data, machine learning techniques, as powerful empirical tools, have gained immense potential and have been used more and more widely (Yousefi & Toffolon 2022). In contrast to physics-based models, machine learning techniques lack physical laws and theory; they make predictions based on data alone. One of their drawbacks arises from this, as their inaccuracy can increase if they are forced to make predictions for conditions outside the range used to train the model (Read et al. 2019). Nonetheless, various data-driven techniques, e.g., different artificial neural networks (ANNs), are successfully used to simulate the temperature conditions of lakes.

An ANN model can be a fast way to calculate water temperatures, and it is superior to regression models as they can accurately determine the nonlinear relationships between meteorological driving forces and water temperature changes. Nevertheless, they are usually used for deep lakes and reservoirs and mostly to predict lake water surface temperatures (Kimura *et al.* 2021; Wang *et al.* 2022). Regarding stratification, ANNs were only applied to simulate water temperatures at specific depths instead of directly determining stability conditions (Liu & Chen 2012; Saber *et al.* 2019; Saber *et al.* 2020). In short, based on a literature review, ANNs were not tested for polymictic lakes and for directly predicting stratification, even though they might be quick and reliable methods for these purposes.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 1. INTRODUCTION
Type: text

and water temperature changes . Nevertheless , they are usually used for deep lakes and reservoirs and mostly to predict lake water surface temperatures ( Kimura * et al . * 2021 ; Wang * et al . * 2022 ) . Regarding stratification , ANNs were only applied to simulate water temperatures at specific depths instead of directly determining stability conditions ( Liu & Chen 2012 ; Saber * et al . * 2019 ; Saber * et al . * 2020 ) . In short , based on a literature review , ANNs were not tested for polymictic lakes and for directly predicting stratification , even though they might be quick and reliable methods for these purposes .

The aim of this study is twofold. First, to prove that a simple artificial neural network model can simulate weak diurnal stratification for a shallow lake with high temporal resolution using routine meteorological data alone. Second, to show that an ANN model can quantify the long-term effects of climate change and anthropogenic impacts based on limited observational data.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.1. Study site and data acquisition
Type: text

Lake Balaton is a shallow polymictic lake in Hungary, with a surface area of 596 km2 and a mean depth of 3.2 m (Figure 1). Besides its ecological value, the lake is of great social and economic importance as it is highly populated along the whole shoreline and, after the capital, Hungary's second-most important tourist destination, providing many recreational activities like bathing, sailing, and fishing. It has an elongated shape, and in light of circulation and water quality patterns, it can be divided into four basins (Istvánovics & Honti 2018). The lake's main inflow is the Zala River, which accumulates the runoff from half of the total lake catchment (5.180 km2) and flows into the westernmost basin. The lake has only one outflow in the eastern basin, which is regulated. The mean resident time is more than two years, and the role of throughflow is negligible for stratification, which is, therefore, almost uniquely shaped by meteorological forces.

Hydrometeorological measurements were carried out in the westernmost basin of the lake in the pelagic area in 2019, 2020, and 2022 in the warm season, from late spring to early autumn. The mean depth of this location was around 3.3 m for the three periods. During the measurement campaign, routine meteorological variables and water temperature profiles were recorded with high temporal resolution. The setup was very similar in each year. For 2019, detailed information about the lake, station location, and measurement setup can be found in Lükő *et al.* 2020 and 2022. The wind speed (U) was measured by CSAT3 and Windsonic2D anemometers (Campbell Sci.). The radiation components – incoming and outgoing shortwave ( $SW_{in}$ ,  $SW_{out}$ ) and longwave radiations ( $LW_{in}$ ,  $LW_{out}$ ) – were recorded by a CNR1 net radiometer (Kipp & Zonen). The air temperature ( $T_a$ ) and relative humidity (RH) were measured by a HygroVue10 sensor (Campbell Sci.).

2. MATERIALS AND METHODS
2.1. Study site and data acquisition


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.1. Study site and data acquisition
Type: figure
Figure

Image /page/3/Figure/1 description: A location and bathymetry map of Lake Balaton, labeled as Figure 1. The map shows the depth of the lake using color gradients and contour lines. A legend in the bottom right indicates the depth in meters (m), with colors ranging from dark blue (0 m) to light green and yellow (5 m). The contour lines are labeled with depths such as 2, 2.5, 3, 3.5, 4, and 5. Two measurement sites are marked with white circles. The Zala River (Zala Riv.) is shown flowing into the southwestern end of the lake, and an outlet is marked at the eastern end. The map includes a north arrow and a scale bar in kilometers. Two inset maps in the upper right corner show the location of Hungary in Europe and the location of Lake Balaton within Hungary.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.1. Study site and data acquisition
Type: figure
Figure: Figure 1 | Location and bathymetry map of Lake Balaton. Measurement sites are marked by white circles.

Figure 1 | Location and bathymetry map of Lake Balaton. Measurement sites are marked by white circles.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.1. Study site and data acquisition
Type: text

The water temperature profile was recorded by T107 sensors or a CS225-L thermistor string (both Campbell Sci.) at fixed depths with 0.5 m resolution. A floating sensor attached to a buoy 2 cm below the water surface measured the water surface temperature. During the campaign, both air and underwater instruments were regularly (2 weeks on average) checked, cleaned, and maintained.

In the easternmost basin of the lake, water temperature measurements were carried out by the Hungarian Meteorological Service between 1981 and 2020 near the south shoreline, where the average water depth is around 2.5 m. At this site, daily measurements were taken at a depth of 1 meter below the water surface. The stratification model was set up based on the measurements in the westernmost basin's open water area. In addition, the long-term daily data from the eastern basin was used to check the simulated daily average water temperatures (and thus the energy balance). It can be assumed that this eastern measurement is also representative due to the lake's relatively small thermal inertia and low spatial variability arising from the shallowness. Furthermore, the mean depth of the westernmost basin is around 2.5 m, which is equal to the depth at this eastern measurement location.

The long-term simulations covered a 40-year-long period from 1981 to 2020. For this period, the input meteorological data was gathered from the ECMWF ERA5 reanalysis database, including surface wind speed, wind direction, air temperature, RH, solar radiation, and downward longwave radiation with 1-h time resolution. Comparing the measured and ECMWF meteorological time series, bias correction was needed in the case of U,  $T_a$ , and  $SW_{in}$  variables. It has been performed by matching their cumulative distribution functions employing second-degree polynomials. Daily water level time series, from which monthly mean values were derived, was available from the Hungarian Water Directory.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.2. ANN-based model system
Type: text

For thermal stratification simulations, a simple model system was constructed with two submodules (Figure 2). The first submodule is a zero-dimensional (0D) energy balance model, which calculates the depth-averaged water temperatures ( $T_{zv}$ ) based on routine meteorological data following the energy balance equation:

$$R_n + H + LE = \rho_w \cdot c_{p,w} \cdot \frac{\partial T_w}{\partial t} \cdot h \tag{1}$$

2. MATERIALS AND METHODS
2.2. ANN-based model system


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.2. ANN-based model system
Type: figure
Figure

Image /page/4/Figure/1 description: A flowchart illustrating two parallel modeling approaches originating from a single input labeled "Meteorology". The top path shows meteorological data (SWin, U, Ta, RH, P, cc) being fed into a model labeled "GOTM", which produces an output represented by the symbol Φ in a red circle. The bottom path is more complex. First, a subset of meteorological data (SWin, LWin, U, Ta, RH) is input into a "0D EB model", which outputs "Tw" in a blue circle. This output, along with another subset of meteorological data (SWin, U, Ta, RH), is then fed into an "ANN" model. The ANN model produces an initial output, Φ₀, which then undergoes a "Bias correction" step to produce the final output, Φ. A red double-headed arrow connects the final Φ outputs from both the top (GOTM) and bottom (ANN) paths, indicating a comparison or relationship between them.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.2. ANN-based model system
Type: figure
Figure: Figure 2 | Schematic drawing of the modeling process.

Figure 2 | Schematic drawing of the modeling process.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.2. ANN-based model system
Type: text

where  $R_n$  (W m-2) is the net radiation, H and LE (W m-2) are the turbulent sensible and latent heat fluxes, respectively,  $\rho_w$  (kg m-3) is the density of water,  $c_{p,w}$  (J kg-1 °C-1) is the specific heat of water, t (h) is the time, and t (m) is the water depth. The turbulent heat fluxes were calculated by the following formulas (Lükő et al. 2022):

$$H = \rho_a \cdot c_p \cdot C_H \cdot U_z \cdot (T_a - T_w) \tag{2}$$

$$LE = \rho_a \cdot \lambda \cdot C_q \cdot U_z \cdot (q_z - q_0) \tag{3}$$

where  $\rho_a$  (kg m-3) is the density of air,  $c_p$  (J kg-1 °C-1) is the specific heat of air,  $\lambda$  is the heat of vaporization (J kg-1),  $U_z$  (m s-1) is the wind speed,  $T_a$  (°C) is the air temperature,  $q_z$  (kg kg-1) is the specific humidity of the air, and  $q_0$  (kg kg-1) is the specific humidity at the surface.  $C_h$  and  $C_q$  are transfer coefficients, which were considered constants and calibrated. The 0D model works with hourly resolution

The second module is an ANN model, which uses the water temperature and its temporal change obtained from the 0D model, routine meteorological data  $(U, T_a, RH, SW_{in})$ , and water depth (h) as inputs (Figure 2) and calculates the stratification index called the potential energy anomaly  $(\phi)$  as output (see details in the following subchapter). It also uses the preceding 6-h average of U and  $SW_{in}$  to consider the dominant antecedent meteorological conditions for mixing and stratification, respectively. In the case of water depth, monthly averaged values were used. The model has one hidden layer and consists of six neurons. It is a nonlinear input-output network without using the estimated  $\phi$  from the previous timestep.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.2. ANN-based model system
Type: text

) $ , and water depth ( h ) as inputs ( Figure 2 ) and calculates the stratification index called the potential energy anomaly $ ( \ phi ) $ as output ( see details in the following subchapter ) . It also uses the preceding 6 - h average of U and $ SW_ { in } $ to consider the dominant antecedent meteorological conditions for mixing and stratification , respectively . In the case of water depth , monthly averaged values were used . The model has one hidden layer and consists of six neurons . It is a nonlinear input - output network without using the estimated $ \ phi $ from the previous timestep .

The ANN model was trained for 3 years of data with a Bayesian regularization algorithm. The training and testing were done at 80–20%. Because of the Bayesian regularization, the validation process was unnecessary (Burden & Winkler 2009). The ANN model simulations were performed in the Matlab software environment. For stratification modeling, a 3-h time resolution was used as it was frequent enough to describe the daily cycle of stratification without considering the highly short-term fluctuations. After the training, historical simulations were carried out for four decades, from 1981 to 2020. Each year, the simulations were run from May to September to include the lake's warming up and cooling periods. In the results, only the summer months were examined. After the ANN simulations, a final bias correction was performed to improve the model's performance. A first-order polynomial was used for the correction, whose coefficients were calculated using the measured and trained data in 2019, 2020, and 2022.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.3. Benchmark model
Type: text

The calibrated 1D General Ocean Turbulence Model (GOTM, Burchard *et al.* 1999) was considered as a reference to assess the ANN m'del's reliability for long-term simulations. GOTM is a 1D model that uses a k- $\varepsilon$  turbulence model for vertical mixing, providing stratification results on a physical basis. The model was driven by the same routine meteorological data as the 0D and the ANN model (Table 1). The sensible and latent heat fluxes were calculated by Equations (2) and (3) bulk formulas (Kondo 1975). The GOTM model has one further parameter to calibrate: the light extinction coefficient. In the absence of measurement data, we presumed it to be constant, and following a sensitivity analysis, it was set to  $0.4 \text{ m}^{-1}$ . For water depth, monthly averaged values were used. The water column was divided into 20 layers with an increasing resolution to the water surface and the bottom. The calibration and validation of the model were conducted for the years 2019 and 2022; after that, it was run for the 1981–2020 period with an hourly time resolution.

2. MATERIALS AND METHODS
2.3. Benchmark model


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.3. Benchmark model
Type: table
Table

|               |                    |       | GOTM           | EB | ANN     |
|---------------|--------------------|-------|-----------------------|-----------|----------------|
| Input  | SWin | W m-2 | 1 havg                | 1 havg    | 3 havg, 6 havg |
|               | LWin | W m-2 | -                     | 1 havg    | -              |
|               | U    | m s-1 | 1 havg                | 1 havg    | 3 havg, 6 havg |
|               | Ta   | °C    | 1 havg                | 1 havg    | 3 havg         |
|               | RH   | %     | 1 havg                | 1 havg    | 3 havg         |
|               | P    | hPa   | 1 havg                | 1 havg    | -              |
|               | cc   | -     | 1 havg                | -         | -              |
|               | Tw   | °C    | -                     | -         | 3 havg         |
| Output | Tw   | °C    | 3 havg (in 20 depths) | 3 havg    | -              |


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.3. Benchmark model
Type: text

Table 1 | Input and output variables and their avergaing time for the 0D energy balance, the ANN, and the reference GOTM models


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.4. Evaluation of model performance
Type: text

The intensity and duration of stratification are assessed through the potential energy anomaly index ( $\phi$ , J m-3), which gives the energy needed to fully mix the stratified water column (Wiles *et al.* 2006; Istvánovics *et al.* 2022). The potential energy anomaly can be calculated as follows:

$$\phi = \frac{g}{h} \int_{0}^{h} [\bar{\rho} - \rho(z)] z dz \tag{4}$$

where g (m s-2) is the gravitational acceleration, h (m) is the water depth,  $\rho$  (kg m-3) is the density of the water,  $\bar{\rho}$  (kg m-3) is the mean water density, and z (m) is the vertical coordinate. Figure 3 shows an example of  $\phi$  together with the measured water temperatures at different depths.

The models' performance was evaluated through three statistical indicators: the root mean square error (RMSE), the Nash–Sutcliffe Efficiency (NS), and the relative deviation ( $\Delta_{rel}$ ). They were calculated as follows:

$$RMSE = \sqrt{\sum \frac{(\widehat{y_i} - y_i)^2}{n}}$$
 (5)

$$NS = 1 - \frac{\sum (y_i - \hat{y_i})^2}{\sum (y_i - \overline{y_i})^2}$$
 (6)

$$\Delta_{rel} = \frac{\sum (\hat{y_i} - y_i)}{\sum y_i} \cdot 100 \tag{7}$$

where y and  $\hat{y}$  are the observed and simulated data, while n is the number of observations.

2. MATERIALS AND METHODS
2.4. Evaluation of model performance


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.4. Evaluation of model performance
Type: figure
Figure

Image /page/5/Figure/13 description: An image displaying two stacked line graphs that share a common horizontal axis representing time from July 31 to August 12, with labels for every two days. The top graph plots a variable labeled 'Φ [Jm⁻³]' on the y-axis, which ranges from 0 to 4. The data is shown as a single black line with circular markers, exhibiting a cyclical pattern with peaks mostly between 2 and 3, starting around August 5. The bottom graph plots 'T\_w [°C]' on its y-axis, ranging from 24 to 28. This graph contains multiple overlapping lines in different colors (dark blue, light blue, green, yellow, purple, and red), which also show a daily cyclical fluctuation, with values ranging from approximately 23.5°C to over 28°C. The patterns in both graphs appear to be correlated.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.4. Evaluation of model performance
Type: figure
Figure: Figure 3 | Daily cycle of measured water temperatures at different depths and the corresponding potential energy anomaly (φ) time series.

Figure 3 | Daily cycle of measured water temperatures at different depths and the corresponding potential energy anomaly (φ) time series.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 2. MATERIALS AND METHODS > 2.4. Evaluation of model performance
Type: text

1 havg stands for hourly, 3 havg for three-hourly, and 6 havg for six-hourly averages


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.1. Meteorological and hydrological conditions
Type: text

In the last 40 years, increasing trends have been experienced in the case of wind speed (0.006 m s $^{-1}$ /10 year), incoming short-wave radiation (4.44 W m $^{-2}$ /10 year), and air temperature (0.50 °C/10 year) during the summer months (June-August), which are the main factors of stratification formation and break-up. Along with these, water temperature shows a slightly weaker increasing trend than air temperature, having a warming rate of 0.44 °C/10 year (Figure 4).

The mean water depth of Lake Balaton for the summer months in the 1980s was 3.21 m, but after some drought periods in the early 2000s – between 2000 and 2003 – it dropped to 2.93 m (Figure 4). The lowest summer water depth was recorded in August 2003, at 2.63 m. After that, water level regulation was made for the lake, and the maximum control water level was increased by 10 cm. It took three years for the lake to reach the new regulation level, so its effect can only be seen starting in 2006. In 2016, due to a new regulation, it has been increased by 10 cm again. Accordingly, the mean water depth for the summer months between 2006 and 2015 was 3.31 m, while from 2016 to 2020, 3.43 m.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: text

The reference GOTM model was calibrated and validated for two parameters –  $T_{w}$  and  $\phi$  – for 2019 and 2022. For depth-averaged water temperature, the model provides good results, with a slight overestimation in the case of sudden cooling periods. In the case of an unstable stratification (resulting in negative  $\phi$  values), the model immediately mixes the water column and couldn't reproduce unstable situations. However, these events are negligible in the summer because they cannot last long and are very weak. Therefore, the rarely occurring negative  $\phi$  values produced by the ANN were also neglected. Overall, the model provided satisfactory results for  $T_{w}$  and  $\phi$ , which made it suitable for further investigations. Table 2 shows the statistical indicators for the calibration and validation periods regarding the two parameters.

The 0D energy balance model was calibrated for 2019, validated for 2020, and then run for the 1981–2020 period. The modeled hourly temperatures were averaged to daily means and compared with the measured ones in the eastern basin. Figure 5 shows the NS and RMSE values for the modeled water temperatures for each year. On average, the NS is above 0.75, and the RMSE is between 1 and 2 °C. There are 4 years of exception (1984, 1985, 1993, and 2001). In these years, the NS and RMSE values are significantly worse. According to the notice obtained from the authority, measurement inaccuracies might have occurred in these years as the temperature sensor likely sank into the sediment.

3. RESULTS
3.2. Calibration and validation


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
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Figure

Image /page/6/Figure/8 description: A figure with four stacked line graphs, each plotting a different variable over time from 1980 to 2020. The caption reads: "Summer averaged values of U, T\_a, T\_w, SW\_in and h between 1981 and 2020 in Hungary."


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: text

The top graph shows wind speed (U) in m/s on the y-axis, ranging from 3 to 4. The data points, marked with blue circles, fluctuate around a horizontal line at approximately 3.4 m/s.

The second graph shows temperature (T) in degrees Celsius on the y-axis, ranging from 18 to 27. It displays two data series: T'a (red squares) and T'w (blue circles). Both series show an increasing trend, indicated by black trend lines. The T'w values are consistently higher than the T'a values.

The third graph shows incoming shortwave radiation (SW\_in) in W/m^2 on the y-axis, ranging from 200 to 260. The data, marked with blue circles, shows a clear increasing trend, highlighted by a black trend line.

The bottom graph shows a variable 'h' in meters on the y-axis, ranging from 2.5 to 3.5. The data, marked with blue circles, fluctuates over the years, with a noticeable dip around the year 2003.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: figure
Figure: Figure 4 | Yearly summer averaged values of U, $T_a$ , $T_w$ , $SW_{in}$ , and h between 1981 and 2020 in Hungary.

**Figure 4** | Yearly summer averaged values of U,  $T_a$ ,  $T_w$ ,  $SW_{in}$ , and h between 1981 and 2020 in Hungary.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: table
Table

| Table 2   Statistical indicators of the calibration and validation periods for the OD energy balance, the | as ANNI and the reference COTM medals |
|------------------------------------------------------------------------------------------------------------------|---------------------------------------|
| Table 2 Established indicators of the cambranon and validation behods for the OD energy balance. If       | ie ann, and the reference GOTM models |


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: table
Table

|       |        | Calibration/Training |      |                | Validation |      |                |
|-------|--------|----------------------|------|----------------|------------|------|----------------|
|       |        | NS                   | RMSE | $\Delta_{rel}$ | NS         | RMSE | $\Delta_{rel}$ |
| 0D EB | Tw     | 0.85                 | 1.07 | 0.15           | 0.78       | 1.51 | 3.3            |
| ANN   | $\phi$ | 0.65                 | 0.54 | 3.99           | -          | -    | -              |
| GOTM  | Tw     | 0.81                 | 1.37 | 0.98           | 0.91       | 0.96 | 0.98           |
|       | $\phi$ | 0.63                 | 0.72 | 0.76           | 0.45       | 0.57 | 0.81           |


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: table
Table

| Axis         | Label     | Values                                               |
|--------------|-----------|------------------------------------------------------|
| Left Y-Axis  | NS [-]    | 1, 0.75, 0.5, 0.25                                   |
| Right Y-Axis | RMSE [°C] | 3, 2, 1, 0                                           |
| X-Axis       | Year      | 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2015, 2020 |


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: figure
Figure: Figure 5 | NS and RMSE values for the 0D m'del's water temperature simulation from 1981 to 2020.

Figure 5 | NS and RMSE values for the 0D m'del's water temperature simulation from 1981 to 2020.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: text

The ANN model was trained and tested for the potential energy anomaly index for 2019, 2020, and 2022. The results were compared with the  $\phi$  values calculated from the field measurements at the western basin and by the GOTM model (Figure 6). It can be seen that the ANN reproduces the measurement well, providing very similar results as the GOTM model and resulting in appropriate goodness-of-fit indices (Table 2). It must be noted that the training/testing period covered a limited range of water depths (60 cm), from 2.98 m to 3.58 m, while monthly mean water depths varied between 2.6 m–3.55 m (92 cm) during the 40-year-long period.

Comparing the measured and simulated potential energy anomaly time series, it was found that both GOTM and ANN can qualitatively follow the course of the diurnal cycle of weak stratification. A representative period is shown in Figure 7. In the case of higher  $\phi$  values, the ANN underestimated the measured ones several times. This was resolved by the bias correction as a final step (Figure 2). Comparing the two models, the ANN model proved to be slightly worse overall, but there have been many periods when ANN's estimations were closer to observations, e.g., on the 5th and 7th of August (Figure 7).


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: figure
Figure

Image /page/7/Figure/7 description: Two scatter plots are displayed side-by-side, comparing model predictions against observed data. Both plots share the same x-axis, labeled "φ\_obs [Jm⁻³]", and have axes ranging from 0 to 6. A diagonal line representing a 1:1 correspondence is drawn on each plot. The left plot shows blue circular data points, with the y-axis labeled "φ\_GOTM [Jm⁻³]". The data points are widely scattered, particularly for observed values below 2 Jm⁻³. The right plot shows red circular data points, with the y-axis labeled "φ\_ANN [Jm⁻³]". The points in this plot are more tightly clustered around the diagonal line compared to the left plot, suggesting a better correlation between the ANN model and the observed data.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: figure
Figure: Figure 6 | Comparison of the measured and simulated φ values. Right: comparing with the GOTM. Left: comparing with the ANN.

Figure 6 | Comparison of the measured and simulated φ values. Right: comparing with the GOTM. Left: comparing with the ANN.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: figure
Figure

Image /page/8/Figure/1 description: A line graph plots three data series over time, from July 31 to August 12. The y-axis, labeled with the symbol Φ and units of [Jm⁻³], ranges from 0 to 4. The x-axis shows dates in two-day increments: Jul 31, Aug 02, Aug 04, Aug 06, Aug 08, Aug 10, and Aug 12. A legend in the top-left corner identifies the three series: 'Observed' is a black line with circular markers, 'GOTM' is a solid blue line, and 'ANN' is a solid red line. All three lines show a cyclical pattern with daily peaks. The 'Observed' data shows significant peaks around August 6 (approx. 2.5), August 9 (approx. 2.4), August 10 (approx. 2.5), and the highest peak on August 12 (approx. 3.5). The 'GOTM' and 'ANN' models attempt to follow the 'Observed' data, generally capturing the timing of the peaks but often underestimating their magnitude, particularly for the larger peaks.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.2. Calibration and validation
Type: figure
Figure: Figure 7 | Measured and simulated $\phi$ time series between 08.01.2019 and 08.13.2019.

**Figure 7** | Measured and simulated  $\phi$  time series between 08.01.2019 and 08.13.2019.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.3. Long-term simulations
Type: text

Along with the meteorological conditions, an increasing trend can also be seen in the strength of the lake's thermal stratification during the summer months over the last 40 years. This was somewhat expected since those meteorological forces  $(T_a, SW_{in})$ , which are responsible for stratification formation, possess more significant growth rates than wind speed, the main driver of mixing. However, the intensity and duration of stability changes were unknown in the absence of long-term observed water temperature profiles. Figure 8 shows the median potential energy anomaly values for the summer periods for each year. IThe whole period was divided into two to separate the effects of climate change and water level regulation. Accordingly, the first period was from 1981 to 2006 - before the water level control could have its effect - while the second one was from 2007 to 2020. In both cases, increasing trends can be observed; however, after the regulation, the steepness of growth increases, meaning that the water depth significantly affects stratification even by a few 10 cm changes. When assessing the long-term impact of climate change and water depth variations, the ANN model demonstrated the same trends as the physics-based one. Regarding the water level periods (1981-2006 and 2007-2020), the trends given by the GOTM are 0.03 and 0.14 J m-3/10 years, while the ANN model resulted in 0.04 and 0.17 J m-3/10 years trends, respectively, which are nearly identical. Looking at the cumulative distribution functions of  $\phi$  for each summer (Figure 9), it could also be concluded that the ANN model tended to overestimate the GOTM-based values at weak stratifications ( $\phi$  < 0.6). Finally, the early 2000s should also be noted, when a three-year-long drought period resulted in extremely low water depths, which were out of the depth range used in the training/testing. However, the ANN model could predict stratification similarly to the GOTM model.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.3. Long-term simulations
Type: figure
Figure

Image /page/8/Figure/5 description: The image displays two line graphs stacked vertically, both plotting data from 1980 to 2020. Each graph compares two models: GOTM, represented by a blue line, and ANN, represented by a red line.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.3. Long-term simulations
Type: text

The top graph shows the 'φ\_median' in units of 'Jm⁻³' on the y-axis, which ranges from 0 to 0.8. Both the GOTM and ANN lines show fluctuating values over the years, with a general increasing trend indicated by superimposed straight trend lines. The trend line for ANN is steeper than that for GOTM.

The bottom graph shows the 'Num. of events' on the y-axis, which ranges from 0 to 15. The x-axis is also the year from 1980 to 2020. Both the GOTM and ANN lines show significant yearly fluctuations in the number of events, with values generally ranging between 2 and 12. The ANN line shows a notable peak close to 14 events around 1997. This graph does not include trend lines.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.3. Long-term simulations
Type: figure
Figure: Figure 8 | Upper: yearly median of summer $\phi$ values between 1981 and 2020. Lower: number of stratification periods between 1981 and 2020, when the stratification lasted at least 24 h, with a threshold of 0.5 J m-3.

**Figure 8** | Upper: yearly median of summer  $\phi$  values between 1981 and 2020. Lower: number of stratification periods between 1981 and 2020, when the stratification lasted at least 24 h, with a threshold of 0.5 J m<sup>-3</sup>.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.3. Long-term simulations
Type: figure
Figure

Image /page/9/Figure/1 description: The image contains four line graphs arranged in a 2x2 grid, each showing cumulative distribution functions. The plots are titled "GOTM", "S0", "S1", and "S3". The y-axis for each plot is labeled "p [-]" and ranges from 0 to 1. The x-axis is labeled "φ [Jm⁻³]" and ranges from 0 to 5. Each graph displays multiple overlapping lines, which are color-coded according to the year. A color bar legend is shown for the S0 and S3 plots, indicating that the colors range from green for 1985, through yellow for 1995 and 2005, to red for 2015. In all four plots, the curves start near the origin, rise steeply, and then level off at a value of p=1.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.3. Long-term simulations
Type: figure
Figure: Figure 9 | Empirical cumulative distribution functions for the GOTM and the ANN training cases between 1981 and 2020.

Figure 9 | Empirical cumulative distribution functions for the GOTM and the ANN training cases between 1981 and 2020.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 3. RESULTS > 3.3. Long-term simulations
Type: text

As mentioned in the Introduction, periods when stratification does not entirely vanish by the next day may be crucial in the lake's ecology. Thus, the number of stratification periods that lasted at least 24 h were looked at using two different thresholds, 0.5 and 1.0 J m-3. In both cases, similar increasing trends experienced. The thresholds were selected to ensure that the stratification would exhibit sufficient strength to be classified as stable. Figure 8 shows how the number of stratified periods evolved in the last 40 years for the 0.5 J/m3 limit.

Both models showed the same tendencies. The GOTM resulted in 5.4 and 7.2 events per year for the two water depth periods, while the ANN gave 4.8 and 7.1 events, respectively. In contrast to the summer median  $\phi$  values, the number of events didn't possess an increasing trend before 2006, meaning that climate change-related intensification of stratification was not strong enough to maintain a stable thermal structure that could survive by the next day. It also has to be mentioned that till 1997, the ANN model suggested a higher variability, having also years without 1-day-long stratification periods. This can be partly explained by the relationship between water depth and light extinction (see Discussion). Overall, the ANN model can assess the same trends for more extended stratification periods as the physics-based GOTM and adequately captures the interactive effect of water depth increase and climate change from 2006.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 4. DISCUSSION > 4.1. The effects of natural and anthropogenic driving forces
Type: text

Lake Balaton's thermal stratification is primarily driven by wind speed, incoming shortwave radiation, and air temperature, which all show an increasing trend (Figure 4).  $SW_{in}$  and  $T_a$  are working in favor of the stratification by increasing vertical water temperature and density differences. In contrast, the U works against it by inducing waves and currents, which make the water column mix and the stratification dissipate. Considering their integrated effect, an increasing trend can be seen in the strength of the lake's thermal stratification (Figure 8), which was captured by the ANN model with a suitable accuracy (Figure 7). Water depth also has a crucial effect on the stratification, as it not only increases its strength but amplifies the impact of climate change. As a result, the observed increasing trend after 2006 is a combined, synergistic effect of the varying climate and the heightened water levels. This interaction increases not just the average stability but also results in longer-lasting stratification, and with this, the 24-h-long events occur more and more often.

Turbidity also greatly affects the lake's stratification. In the case of turbid water, incoming shortwave radiation can penetrate only to a limited depth, warming up only the layers it manages to traverse. This creates a temperature difference between the layers, contributing to the development of stratification. In the other case, when the water is more transparent, solar radiation can penetrate deep and warm up the whole water column, so the temperature difference between the layers will be slighter, resulting in a very weak stratification. Light extinction (or attenuation coefficient), which quantifies the efficiency of water absorbing the incoming light, depends linearly on turbidity (Brown 1984). Turbidity, and thus water transparency, is determined by the concentration of organic and inorganic substances, like phytoplankton and suspended sediments, respectively. As a result, light extinction is a highly variable parameter both on small and large time scales. However, external factors such as meteorology also directly and strongly determine it.

In the case of smaller water depths, sediment resuspension can occur more often as the wind-induced mixing can reach the lake's bottom more quickly and with higher intensity, resulting in more variable water transparency conditions. In the ANN model, this might be indirectly incorporated through nonlinear relationships with wind forcing. Regarding the 1-day-long stratification events, the ANN model showed higher variability for the first period (1981–2006) with lower water levels. In contrast, light attenuation was fixed to a constant in the GOTM model. For example, on the 4th and 5th of August, GOTM underestimated  $\phi$ , and the ANN model provided better results (Figure 7). These two days were preceded by a wind event, likely with sediment resuspension. The suspended fine sediments require quite a long time to settle, and until that, they result in higher turbidity, light attenuation, and stratification, as explained above. This means that in some cases, the ANN may provide better results than the GOTM, even though the latter operates on a physical basis.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 4. DISCUSSION > 4.2. Sensitivity of training parameters
Type: text

Sensitivity analysis was carried out on three main elements of the ANN model setup: (i) the role of the water depth range in the training, (ii) the quantity of the training data, and (iii) the role of antecedent wind and solar radiation conditions. The model was trained using 3 years of data: 2019, 2020 and 2022. This version is referred to as S0. For (i) and (ii), the model was trained with only 2 years of data and then ran it for all the 3 years. The S1 model version was trained for 2019 and 2022, with a wide range of water depths, while the S2 model version was trained for 2019 and 2020 when water levels were significantly higher than in 2022. To assess the differences between the training cases the NS efficiency was used (Table 3).

In 2019 and 2020, the water level was high; the depth varied between 3.55 and 3.30 m at the measurement station, while in 2022, it was between 3.32 and 2.98 m. Due to this difference in water depths, the S2 model had to perform extrapolation for almost the whole of 2022. As a result, the S2 model mostly underestimated  $\phi$  and provided unreliably strong, unstably stratified periods. In the S1 case, the water depth in the training period covered the whole range of the 3-years, so the model did not have to extrapolate. Compared to the accepted S0 version, the NS worsened by less than 5% due to the reduced training data providing fewer possible meteorological states (Table 3). Since the difference between S0 and S1 was not convincing for the three years, both models were run for the 1981–2020 period and compared based on the cumulative distribution functions. The distribution of the S1 case shows a more considerable variability than the one obtained using GOTM or the S0 version (Figure 9). In our case, this means that the S1 version is unreliable and usually overestimates the strength of stratification. However, the three-year dataset proved sufficient to establish reliable connections between meteorological driving factors and thermal structure.

Lastly, a simple sensitivity analysis was made for  $SW_{in}$  and U as the most dominant driving forces of stratification formation and break-up, respectively. In the S0 model, the input data included the mean U and  $SW_{in}$  from the preceding 6 h besides their instantaneous values. Since the NS index declined by only 8% for three years of training, the model was run without

4. DISCUSSION
4.2. Sensitivity of training parameters


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 4. DISCUSSION > 4.2. Sensitivity of training parameters
Type: table
Table: Table 3 | NS values of the different training cases

| Version | Training years       | NS [-] | preceding SWin, U conditions |
|---------|----------------------|--------|------------------------------|
| S0      | 2019, 2020, and 2022 | 0.65   | yes                          |
| S1      | 2019 and 2022        | 0.62   | yes                          |
| S2      | 2019 and 2020        | 0.59   | yes                          |
| S3      | 2019, 2020, and 2022 | 0.60   | no                           |

Version
Training years
NS [-]
preceding SWin, U conditions


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 4. DISCUSSION > 4.2. Sensitivity of training parameters
Type: text

the averaged values for the 1981–2020 period. As a result, the cumulative distribution functions again possess a more significant variability than the physics-based GOTM model. This means that even though the statistical indicators do not clearly support the usage of the 6-h averaged values, they are not negligible because their impacts become pronounced when we consider the long-term changes.


Document: Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks
Section: 5. CONCLUSIONS
Type: text

Machine learning recently became a common and efficient tool for simulating, hindcasting, and predicting lakes' water temperature. A very simple and, thus, robust model has been developed that can simulate shallow lakes' weak stratification and its diurnal cycle with similar accuracy to a complex physics-based 1D model. The presented model system possesses two submodules, both forced by the same routine meteorological variables. The first submodule is a 0D energy balance model, which estimates the depth-averaged water temperature and its temporal change as further inputs for the ANN submodule. As its output, the ANN model calculates the potential energy anomaly index, which characterizes the strength of thermal stratification. The model proved to be reliable both on short and long time scales. Besides capturing the diurnal variation and the intensity of stratification, it was able to explore the effect of climate change, anthropogenic water level regulation, and the synergistic interaction of these two.

Our study provides at least two main novelties. First, it proves that a simple ANN model can simulate a delicate environment with rapidly changing and weak stratification conditions. Of course, to train the model, it is required to have a suitably long and high-frequency time series, including both temperature profiles and meteorological variables. In our case, the time series from three summer seasons proved sufficient. Second, instead of directly estimating water temperature in different depths, the potential energy anomaly index was simulated that adequately describes a shallow lake's stratification. Water temperatures are estimated based on the energy balance equation, which requires only routine meteorological data, and its calibration is also straightforward. This method also has the advantage that water temperature estimates satisfy the energy conservation in contrast to temperatures estimated by machine learning techniques.

The ANN model's predictivity can be improved in the future. Firstly, the hydrometeorological measurements have continued in Lake Balaton, so the training dataset can be extended with further seasons. Secondly, the most simple ANN structure was used for the modeling. It is conjectured that the ANN model's accuracy will increase by including estimated  $\phi$  values from previous time steps in the inputs. Similarly, real-time in-situ measurements can be easily introduced to such a system, making it suitable for nowcasting purposes. Finally, if turbidity or light extinction data are also available, a more complex system would be worth establishing that estimates turbidity conditions first and stratification in a second step. The simultaneous availability of these two parameters would also be fruitful for simulating habitat conditions.

The proposed model system offers an efficient tool for examining several changes in shallow lake environments in the long term. The ANN model can capture intra-daily stratification and its alteration by slowly varying climate change-driven meteorological forces and by much faster human interventions like water level regulation, incorporating their synergistic effect, too. Since the system includes an energy balance submodule, evaporation changes can also be tracked. Evaporation plays a crucial role in the lake's water resource as it is the main loss component of the water balance. For water resources management, accounting for the changes in stratification and evaporation is inevitable, and this model system offers a simple and fast method for their joint calculation. In light of these changes, stakeholders can make informed decisions to ensure sustainable management of the lake's environment.


Document: Refining lake volume estimation and critical depth identification
Type: text

Abstract. Climate change leads to changes in glacier mass balance, including steady advancements and surges that reposition the glacier snouts. Glacier advancement can dam proglacial meltwater lakes. Within the Karakoram and surrounding regions, the positive feedback of climate change has resulted in more frequent ice-dammed glacial lake outburst floods (GLOFs), often facilitated by englacial conduits. However, the complex and multi-factor processes of conduit development are difficult to measure. Determining the lake depths that might trigger GLOFs and the numerical model specifications for breaching is challenging. Empirical estimates of lake volumes, along with field-based monitoring of lake levels and depths and the assessment of GLOF hazards, enable warnings and damage mitigation. Using historical data, remote sensing techniques, high-resolution imagery, cross-correlation feature tracking, and field-based data, we identified the processes of lake formation, drainage timing, and triggering depth. We developed empirical approaches to determine lake volume and trigger water pressure leading to a GLOF. A correlation, albeit a weak one, between glacier surge velocity and lake volume reveals that glacier surge may play a crucial role in lake formation and thus controls the size and volume of the lake. Lake volume estimation involves geometric considerations of the lake basin shape. A GLOF becomes likely when the lake's normalized depth (n') exceeds

0.60, equivalent to a typical water pressure on the dam face of 510 kPa. These field and remotely sensed findings not only offer valuable insights for early warning procedures in the Karakoram but also suggest that similar approaches might be effectively applied to other mountain environments worldwide where GLOFs pose a hazard.

data/('Refining lake volume estimation and critical depth identification', '.pdf')_extraction.md


Document: 1 Introduction
Section: 1 Introduction
Type: text

Globally, glacier shrinkage is a strikingly visible sign of climate change, as is an apparent increase in the number of glacier hazards such as avalanches (Byers et al., 2023; Kääb and Girod, 2023; Li et al., 2024; You and Xu, 2022) and glacial lake outburst floods (GLOFs) (Bazai et al., 2021; Bhambri et al., 2019; Emmer, 2017; Zheng et al., 2021). However, within high-mountain Asia (HMA), particularly the Karakoram, Kunlun Shan, and eastern Pamir, the glaciers have gained mass since 1970 (Berthier and Brun, 2019; Gardelle et al., 2012; Kääb et al., 2015; Minora et al., 2013; Yao et al., 2012). This positive response to climate change may now be over (Jackson et al., 2023), with many glaciers more recently displaying stability (Ali et al., 2021) or retreat (Singh et al., 2023). Nonetheless, the mass gain has influenced glacier dynamic behaviors, with the Karakoram

<sup>1Key Laboratory of Mountain Hazards and Earth Surface Process/Institute of Mountain Hazards and Environment, Chinese Academy of Sciences (CAS), Chengdu, China

<sup>2China-Pakistan Joint Research Center on Earth Sciences, Chinese Academy of Sciences and HEC, Islamabad, Pakistan

<sup>3School of Geography and Environmental Science, University of Southampton, Southampton, SO17 1BJ, UK

<sup>4Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China

<sup>5Earth Surface Process Modelling, German Research Centre for Geosciences (GFZ), Potsdam, Germany

<sup>6National Disaster Reduction Centre of China, Ministry of Emergency Management, Beijing, China

<sup>7DTU Space, Technical University of Denmark, 2800 Kongens Lyngby, Denmark


Document: 1 Introduction
Section: 1 Introduction
Type: text

sup > 4 < / sup > Institute of Geographic Sciences and Natural Resources Research , Chinese Academy of Sciences , Beijing , China < sup > & < / sup > lt ; sup > 5 < / sup > Earth Surface Process Modelling , German Research Centre for Geosciences ( GFZ ) , Potsdam , Germany < sup > & < / sup > lt ; sup > 6 < / sup > National Disaster Reduction Centre of China , Ministry of Emergency Management , Beijing , China < sup > & < / sup > lt ; sup > 7 < / sup > DTU Space , Technical University of Denmark , 2800 Kongens Lyngby , Denmark

glaciers thickening, increasing glacier surges (Bazai et al., 2021, 2022; Mu et al., 2024) and advancing glacier termini throughout the region (Bhambri et al., 2013; Bolch et al., 2017). This behavior contrasts that found in neighboring regions with more sustained negative glacier mass budgets, such as the Himalaya, Hindu Kush, and Tibet (Bazai et al., 2021; Bolch et al., 2011; Frey et al., 2014). In the latter areas, glaciers continue to shrink, thin, and reduce in volume, showing no significant glacier advance (Dehecq et al., 2019; Farinotti et al., 2020; Yao et al., 2012). As a result, the increase in moraine lake formation has increased the number of GLOFs in the glacier-retreating regions (Nie et al., 2017). However, in regions where ice mass has increased, glacier advance has prompted the rapid formation of ice-dammed lakes accompanied by sudden releases of meltwater originating from these lakes (Zhang et. al., 1990; Hewitt, 1982, 1998; Hewitt and Liu, 2010; Singh et al., 2023). Although the number and size of GLOFs may decrease with progressive deglaciation (Veh et al., 2023), ice-dammed lake floods currently represent the dominant hazard in cryospheric regions (Veh et al., 2022), comprising 70 % of GLOFs through recorded history (Carrivick and Tweed, 2016). In contrast, moraine-dammed lakes contribute only 9 % (with the remaining 16 %, 3 %, and 2 % associated with unknown dam types, volcanic activity, and bedrock failure, respectively) (Carrivick and Tweed, 2016). Specific details of the GLOF hazard for HMA have been compiled by Shrestha et al. (2023).


Document: 1 Introduction
Section: 1 Introduction
Type: text

GLOFs may decrease with progressive deglaciation ( Veh et al . , 2023 ) , ice - dammed lake floods currently represent the dominant hazard in cryospheric regions ( Veh et al . , 2022 ) , comprising 70 % of GLOFs through recorded history ( Carrivick and Tweed , 2016 ) . In contrast , moraine - dammed lakes contribute only 9 % ( with the remaining 16 % , 3 % , and 2 % associated with unknown dam types , volcanic activity , and bedrock failure , respectively ) ( Carrivick and Tweed , 2016 ) . Specific details of the GLOF hazard for HMA have been compiled by Shrestha et al . ( 2023 ) .

Herein, the focus is upon ice-dammed lakes. The mechanisms and frequency of dam-related GLOFs remain poorly understood, hindering accurate prediction (Bazai et al., 2021; Cook et al., 2016; Harrison et al., 2018; Richardson and Reynolds, 2000). Recent studies have investigated changes in frequency due to climate change (Rick et al., 2023; Veh et al., 2023), and there are regional assessments of flood volume and hazards (Rick et al., 2023). Despite these efforts, understanding the drainage and predicting flood events from icedammed lakes remain challenging. Nonetheless, anticipating the risks associated with these events is crucial due to their potential to have devastating impacts on human lives and livelihoods, ecosystems, infrastructure (e.g., roads, bridges, hydropower systems), and river channel stability and to have effects on agriculture and fisheries (Carrivick and Tweed, 2016; Cook et al., 2016; Emmer, 2017; Clague et al., 2000; Neupane et al., 2019; Zhang et al., 2022). GLOFs have been recorded up to 500 km from ice-dammed lakes (Hewitt and Liu, 2010), resulting in hundreds of human fatalities and the other impacts noted above (Carrivick and Tweed, 2016; Cui et al., 2014, 2015; Kreutzmann, 1994; Mason, 1929; Stuart-Smith et al., 2021; Zhang et al., 1990; Zheng et al., 2021).

Whilst progress has been made in understanding the breaching mechanisms of moraine lake outburst floods, triggered by ice or debris falls, strong earthquake shaking, internal piping, or overtopping waves that exceed the shear resistance of the dam (Emmer and Vilímek, 2013; Richardson and Reynolds, 2000), understanding the mechanisms of ice-

dammed lake outburst floods remains a challenge (Werder et al., 2010), making prediction using numerical modeling currently impossible. Therefore, there is an urgent need for simplified approaches to GLOF prediction to mitigate downstream impacts.


Document: 1 Introduction
Section: 1 Introduction
Type: text

2021 ; Zhang et al . , 1990 ; Zheng et al . , 2021 ) . Whilst progress has been made in understanding the breaching mechanisms of moraine lake outburst floods , triggered by ice or debris falls , strong earthquake shaking , internal piping , or overtopping waves that exceed the shear resistance of the dam ( Emmer and Vilímek , 2013 ; Richardson and Reynolds , 2000 ) , understanding the mechanisms of ice - dammed lake outburst floods remains a challenge ( Werder et al . , 2010 ) , making prediction using numerical modeling currently impossible . Therefore , there is an urgent need for simplified approaches to GLOF prediction to mitigate downstream impacts .

Despite the uncertainty related to the details of GLOF initiation, sudden glacier advances during surge cycles have a prominent role in the formation of ice-dammed lakes by creating an ice barrier in the valleys, particularly in narrow valley floor sections and at confluences (Bazai et al., 2021; Bhambri et al., 2019), that dams rivers (Singh et al., 2023). Glacier surges have resulted in the formation of icedammed lakes in the Swiss Alps (Haeberli, 1983), northern Norway (Xu et al., 2015), Argentinian Patagonia (Vandekerkhove, 2021), Alaska (Trabant et al., 2003), Karakoram, and the Pamir (Bazai et al., 2021; Hewitt and Liu, 2010) and Tian Shan regions (Ng et al., 2007; Shangguan et al., 2017). Recent studies have revealed that the draining processes of ice-dammed lakes potentially involve one or more mechanisms: subglacial breaching, overspill, rapid ice mass instability, and slow deformation of subglacial cavities (Björnsson, 2003; Haemmig et al., 2014; Round et al., 2017). Several attempts have been made to explore the drainage behavior of ice-dammed lake outburst floods (Hewitt and Liu, 2010). However, due to the remoteness, danger, and inhospitable terrain where such lakes can be found, real-time data are few, and significant gaps remain in our knowledge of these pro-


Document: 1 Introduction
Section: 1 Introduction
Type: text

) . Recent studies have revealed that the draining processes of ice - dammed lakes potentially involve one or more mechanisms : subglacial breaching , overspill , rapid ice mass instability , and slow deformation of subglacial cavities ( Björnsson , 2003 ; Haemmig et al . , 2014 ; Round et al . , 2017 ) . Several attempts have been made to explore the drainage behavior of ice - dammed lake outburst floods ( Hewitt and Liu , 2010 ) . However , due to the remoteness , danger , and inhospitable terrain where such lakes can be found , real - time data are few , and significant gaps remain in our knowledge of these pro -

In the Karakoram, ice-dammed lakes are found in five major valleys, three of which are densely populated and highly vulnerable to unexpected GLOFs. Recent advances in understanding have been made (Bazai et al., 2021) concerning the formation of episodic ice-dammed lakes, which, due to ice mass transfer variations, are linked to changes in the glacier surface velocity and ice thickness (Singh et al., 2023) and fluctuations in the crevasse density during the surge cycle (Rea and Evans, 2011; Sharp, 1985). Consequently, herein, we explore two main hypotheses: (1) that lake volume is related to glacier velocity and (2) that there is a critical lake depth associated with ensuing GLOFs (Thoraninsson, 1939). As lake volume can dictate the characteristics of a GLOF, a third secondary hypothesis was addressed: (3) that icedammed lakes can exhibit geometries similar to regular geometric shapes such that, in the absence of detailed lake volume data, lake volumes might be estimated from geometric consideration. Despite advancements in knowledge globally, the techniques for measuring and estimating both the volume of the lake before an outburst and the critical depth (for GLOF release), as well as for the timely prediction of GLOFs, remain largely unexplored or unidentified (Round et al., 2017; Shangguan et al., 2016; Steiner et al., 2018). Very few ice-dammed lake volume data are available. These icedammed lake volumes were measured while the lake basin was either empty (after a GLOF event) or partially filled and thus shallow (Round et al., 2017; Shangguan et al., 2016; Steiner et al., 2018). Given that their potential full volumes are unknown, the downstream threat from such lakes remains high. To measure the flood volume and flood magnitude for a deep and potentially full lake, the lake volume measurement is recognized as a critical variable that needs to be accurately calculated or at least well-estimated (Bazai et al., 2021, 2022). An accurate estimate of lake volume will also help in exploring the GLOF timing, triggering depth of the lake, and frequency of ice-dammed lake outburst floods in relation to surge cycles. Timing information can be approximated by correlating glacier velocities and GLOF occurrences (Bazai et al., 2021, 2022), which should assist in timely hazard assessment. Herein, the primary objective of this study is to enhance predictive capabilities regarding GLOF event timing by refining empirical lake volume estimation and identifying critical depths for future hazard and risk reduction. We seek to achieve the objective within a framework of adjustment of lake volume to glacier surge speed, which has implications for changes in the depth of lakes relative to the heights of the ice barriers that impound the lakes.


Document: 1 Introduction
Section: 2 Study area
Type: text

The Karakoram Range in HMA is known for its complex geology, climatic variability, and denudation processes, including debris flows, mudflows, landslides, rockfalls, avalanches, and GLOFs. As was noted in the preceding section, changes in glacier dynamics, increasing glacier surges, and a trend of increases in GLOF-related disasters characterize this region. These hazards are responsible for substantial economic losses, including the destruction of residences, infrastructure such as roads and bridges, and agricultural areas, as well as blockages of transportation routes like the Karakoram Highway and other expressways (Shrestha et al., 2023).

Glacier surges in the region have been recorded since the 15th century (Bazai et al., 2021). Since the application of remote sensing to the monitoring of the glaciers from 1970 to 2020, an increasing occurrence of glacier surges has been recorded since the 1990s, with some glacier surges being linked to the formation of ice-dammed lakes and subsequent GLOFs. Some lakes persist only seasonally, forming in the winter when temperatures are very low and draining slowly in the spring or summer. Other lakes are more persistent (Bhambri et al., 2019; Hewitt and Liu, 2010) and have the potential for catastrophic outbursts. The most frequent glacier surges and formation of lakes leading to outburst floods in the Karakoram region occur for the Khurdopin, Kyagar, and Shishper glaciers. For example, Round et al. (2017) concluded that surges were the main factor controlling the formation of ice-dammed lakes associated with the Kyagar Glacier, with the volumes of the lakes reaching a maximum 3 years after the surge period (Li et al., 2023). Similarly, Bazai et al. (2022) concluded that surge velocities have a significant effect on lake formation related to the Khurdopin Glacier.

Although the foreland of the Kyagar Glacier, situated in the Shaksgam Valley, is uninhabited, GLOFs have caused damage and losses further downstream. Conversely, GLOFs from the Khurdopin and Shishper glaciers, located in the densely populated Hunza area, have resulted in casualties and substantial economic losses. Consequently, these glaciers and their lakes are selected for study. The focus of the broader investigation is to obtain the data necessary to understand the complex behavior of the glaciers and their drainage systems with a view to anticipating when the occurrence of GLOFs is imminent. Therefore, there is an urgent need to identify triggering factors for GLOFs to provide downstream warnings in a timely fashion. A better understanding of the complex process behaviors should eventually lead to improved prediction of such events, not only within the Karakoram but also worldwide.


Document: 1 Introduction
Section: 3 Data and methods > 3.1 Remote sensing data
Type: text

The identification and mapping of the Khurdopin, Kyagar, and Shishper ice-dammed lakes were accomplished using open and commercial satellite imagery sources from 1970 to 2022. The datasets include 590 images from Landsat 2– Landsat 5 and Landsat 7-Landsat 9 and 45 images from Sentinel-2, downloaded from the United States Geological Survey (USGS) website (http://earthexplorer.usgs.gov/, last access: 12 December 2023) (Table S1 in the Supplement). The commercial high-resolution images consisted of 35 images from Gaofen-1 (GF-1) and Gaofen-2 (GF-2), 11 images from SPOT 6 and SPOT 7, and 5 images from CRESDA (https://www.cresda.com/zgzywxyyzxeng/ cooperation/odatad/list/odatad\_1.html, last access: 20 July 2022; https://earth.esa.int/eogateway, last access: 23 July 2022; and https://www.planet.com/products/planet-imagery, last access: 10 August 2022, respectively). The following DEM datasets have been used to estimate lake volume, depth, and dam height: the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and the Phased Array type L-band Synthetic Aperture Radar (PALSAR) DEM data scenes from the National Aeronautics and Space Administration (NASA) Earthdata website (https://search.earthdata. nasa.gov/, last access: 10 December 2022) and KH-9 and Shuttle Radar Topography Mission (SRTM) data downloaded from http://earthexplorer.usgs.gov/ (last access: 12 December 2022) (Table S2 in the Supplement). Field surveys were conducted of the Shishper Glacier lakes in 2019, 2021, and 2022 and of the Khurdopin Glacier lakes in 2017 and 2018 using handheld GPS devices and uncrewed aerial vehicles (UAVs) (see Sect. 3.2) to determine annual lake extents, lake depths, glacier altitudes and thickness, terminus positions, and glacier surface displacements. The purpose of the field campaigns was to obtain (i) data on processes that could not be derived from remote sensing and (ii) field data to calibrate and validate remote-sensing-derived data. The glacier outlines were obtained from the Randolph Glacier Inventory (RGI 6.0) (RGI Consortium, 2017) and modified according to surge movements with time (https://www.planet.com/products/planet-imagery/, last access: 10 October 2022).

3 Data and methods
3.1 Remote sensing data