### 1. Introduction

### 2. Methods and Materials

### 2.1. Study Area

^{2}. The watershed area compared to the water surface area (36.5 km

^{2}) is very large and the average depth of the lake is around 6.5 m. The residence time is very short, comparatively, such that it seems to be a stream-like reservoir.

### 2.2. Analysis of Air and Water Temperature Trends at Lake Paldang Using the Mann-Kendall Test

##### (1)

$${S}_{g}=\sum _{i=1}^{n-1}\sum _{j=i+1}^{n}sgn\left({X}_{jg}-{X}_{ig}\right),\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}g=1,2,\dots \mathrm{..},m,$$##### (2)

$$sgn(x)=\{\begin{array}{c}1\hspace{0.17em}if\hspace{0.17em}x>0\\ 0\hspace{0.17em}if\hspace{0.17em}x=0\\ -1\hspace{0.17em}if\hspace{0.17em}x<0\end{array}.$$*S*is E[S]=0 and the variance σ

^{2}is:

##### (3)

$${\mathrm{\sigma}}^{2}=1/18\hspace{0.17em}\left\{n(n-1)(2n+5)-\sum _{j=1}^{p}{t}_{j}({t}_{j}-1)(2{t}_{j}+5)\right\},$$*p*is the number of the tied groups in the data set and

*t*

*is the number of data points in the*

_{j}*j*th tied group. The statistic

*S*is approximately normally distributed, provided that the following Z-transformation is employed:

##### (4)

$$\text{Z}=\{\begin{array}{cc}\frac{S-1}{\sigma}& if\hspace{0.17em}S>0\\ 0& if\hspace{0.17em}S=0\\ \frac{S+1}{\sigma}& if\hspace{0.17em}S<0\end{array}.$$##### (6)

$$D={\left[\frac{1}{2}n(n-1)-\frac{1}{2}\sum _{j=1}^{p}{t}_{j}({t}_{j}-1)\right]}^{1/2}\hspace{0.17em}{\left[\frac{1}{2}n(n-1)\right]}^{1/2}.$$*Ŝ*, for the entire series is calculated according to

*i*<

*j*≤

*n*), where

*d*is the slope,

*X*denotes the variable, n is the number of data points, and

*i*and

*j*are the indices. Sen’s slope is then calculated as the median from all slopes;

*b*=Median

*d*

*. The intercepts are computed for each timestep*

_{k}*t*, as given by:

*(x*

_{ij}*, x*

_{ik}*)*pair,

*i*= 1,2,…,

*m*, where 1 ≤

*k*≤

*j*≤

*n*

*and*

_{i}*n*

*is the number of known values in the*

_{i}*i*th season. The seasonal slope estimator is the median of the

*d*

*values. A p-value of < 0.5 at 95% confidence indicates a statistical trend. A positive value for the Kendall statistic (S) indicates an increasing trend, and a negative value indicates a decreasing trend. To investigate the extent of trends in relation to the Mann-Kendall test, the Sen’s slope and the seasonal Sen’s slope (the seasonal Kendall slope estimator) were obtained [42, 46, 47]. Data were constructed by month and the analyses were performed using the statistical program R (ver.3.6.1).*

_{ijk}### 2.3. Measurement of Air and Water Temperature in the Influent Stream of Lake Paldang

### 2.4. Measurement of Surface Water Temperature at Lake Paldang

### 2.5. Water Temperature Hysteresis at Lake Paldang Using a Numerical Model

### 3. Results and Discussion

### 3.1. Analysis of air and water temperature trends at Lake Paldang

#### 3.1.1. Long-term air temperature trends

#### 3.1.2. Comparison of air and water temperature trends at Lake Paldang

### 3.2. Changes in air and water temperature in influent streams to Lake Paldang

#### 3.2.1. Relationship between air temperature and water temperature

#### 3.2.2. Water temperature hysteresis in the influent rivers to Lake Paldang

^{2}using multiple regression analysis representing increasing flow volume and thermal capacity that give rise to reduced water temperatures. This is consistent with previous multivariate analysis of river temperatures [55].