Exploring Climate Sensitivity in Hydrological Model Calibration

Abstract

In the context of hydrological model calibration, observational data play a central role in refining and evaluating model performance and uncertainty. Among the critical factors, the length of the data records and the associated climatic conditions are paramount. While there is ample research on data record length selection, the same cannot be said for the selection of data types, particularly when it comes to choosing the climatic conditions for calibration. Conceptual hydrological models inherently simplify the representation of hydrological processes, which can lead to structural limitations, which is particularly evident under specific climatic conditions. In this study, we explore the impact of climatic conditions during the calibration period on model predictive performance and uncertainty. We categorize the inflow data from AnDong Dam and HapCheon Dam in southeastern South Korea from 2001 to 2021 into four climatic conditions (dry years, normal years, wet years, and mixed years) based on the Budyko dryness index. We then use data from periods within the same climatic category to calibrate the hydrological model. Subsequently, we analyze the model’s performance and posterior distribution under various climatic conditions during validation periods. Our findings underscore the substantial influence of the climatic conditions during the calibration period on model performance and uncertainty. We discover that when calibrating the hydrological model using data from periods with wet climatic conditions, achieving comparable predictive performance in validation periods with different climatic conditions remains challenging, even when the calibration period exhibits excellent model performance. Furthermore, when considering model parameters and predicted streamflow uncertainty, it is advantageous to calibrate the hydrological model under dry climatic conditions to achieve more robust results.

1. Introduction

Hydrologists have conducted extensive research on the selection [1], calibration [2,3,4,5], and uncertainty assessment [6,7,8,9,10,11] of hydrological models to obtain optimal information from these models. In the calibration or uncertainty assessment of hydrological models, observational data play a pivotal role, with the critical elements being the length of the data and the climatic conditions (e.g., dry years, normal years, and wet years) to which the data belong [12].

There is a lot of literature related to the length of data [13,14,15,16,17], such as suggesting that a specific period (e.g., 3 to 10 years) may be most suitable for calibration. Moreover, in the context of calibration, the availability of observational data is synonymous with data length. Therefore, there is no doubt that data length is of utmost importance and should be considered a top-priority factor. In contrast, there has been relatively less emphasis on the selection of data types, namely, the choice of climatic conditions for calibration. In particular, conceptual hydrological models, due to their simplified representation of hydrological processes, are inherently prone to structural flaws, which can become evident under specific climatic conditions [18]. While some of these flaws may be partially addressed during the parameter estimation process, it is expected that the values of the estimated parameters will vary depending on the climatic conditions under which the calibration is conducted.

Abebe et al. [19] discovered that parameter estimates can exhibit temporal variations not only due to structural flaws in the model, but also because of the watershed’s nonlinearity in response to climate. Various studies were conducted to evaluate parameter transferability under changing climatic conditions [20,21,22,23,24,25], including research demonstrating that data from years with precipitation levels exceeding the average annual precipitation are the most suitable for calibration [26,27]. In these studies, various unique methods were developed and applied, but they are fundamentally based on the split-sample calibration method proposed by Klemes [28]. In the split-sample calibration method, the calibration and validation periods are selected based on the climatic conditions of the observational data. Subsequently, the calibrated parameters using data from dry or wet periods are validated using data observed during periods with diverse climatic conditions. Wu and Johnston [29] reported better validation performance of parameters calibrated using data from dry climatic conditions compared to parameters calibrated using data from wet or average climatic conditions when experimenting with the Soil and Water Assessment Tool (SWAT). They argued that parameters governing evapotranspiration processes could be better identified during dry periods when evapotranspiration dominates the hydrological cycle. Conversely, Ruelland et al. [30] found that calibration in wet climatic conditions did not result in larger errors compared to calibration in dry conditions. There seem to be no clear guidelines regarding the choice of climatic conditions for calibration, likely due to the fact that different climatic regions can yield highly varied results. Furthermore, except for a few studies [31,32,33], most previous research has primarily focused on model calibration rather than validation. More importantly, it is challenging to find cases where the performance of climate-condition-dependent model calibration, particularly in the context of the Korean Peninsula’s monsoon climate, has been analyzed from the perspectives of model reproducibility and uncertainty. Ahn et al. [34] investigated the impact of calibration methods on climate and hydrological modeling, while Ashu and Lee [35] proposed calibration methods to enhance water balance accuracy in the monsoon watershed. Lee et al. [36] conducted evaluations on evapotranspiration modeling in Korea’s continental and temperate climate zones, whereas Lee et al. [37] examined the variability of Horton indices in East Asia’s monsoon climate and projected vegetation water stress under climate change scenarios. Recent studies have been conducted with the objective of selecting optimal models or improving the accuracy of simulated results. While there has been limited investigation into uncertainties, these efforts primarily focused on enhancing the accuracy of simulations without considering climatic conditions.

In this study, the conceptual hydrologic partitioning model (CHPM) developed and validated by Choi et al. [38] and Lee et al. [37] was applied to assess the impact of climatic conditions on the calibration of hydrological models at the AnDong Dam and HapCheon Dam inflows in the southeastern region of the Korean Peninsula. In order to minimize anthropogenic activities, which have a significant impact on the calibration of hydrological models [39,40], a study was conducted on dam watersheds where anthropogenic influences are limited. Daily inflow data for each dam were classified into four climatic conditions (dry years, normal years, wet years, and mixed years) based on the Budyko dryness index. Subsequently, the hydrological model was iteratively calibrated using data from each climatic condition through the Markov Chain Monte Carlo (MCMC) simulation. The model’s predictive performance and uncertainty were evaluated for various validation periods reclassified according to the climatic conditions.

2. Materials and Methods

2.1. Study Area and Data

In this study, the AnDong Dam and HapCheon Dam watersheds within the Nakdong River basin in South Korea were selected as the study areas (Figure 1). The study period spanned from 2001 to 2021. Using daily meteorological data from the Automated Synoptic Observing System (ASOS) operated by the Korea Meteorological Administration, area-averaged daily precipitation and daily potential evapotranspiration data were constructed for the study watersheds using the Thiessen Polygon Network. The weather stations influencing the HapCheon Dam watershed are Hapcheon, Jangsu, Geochang, and Sancheong. For the AnDong Dam watershed, the influencing weather stations are Taebaek, Bonghwa, Uljin, and Andong. Daily potential evapotranspiration was calculated using the Penman–Monteith method based on meteorological data (daily minimum and maximum temperature, daily average wind speed, and daily relative humidity). Additionally, daily streamflow data at the outlets of each dam watershed were obtained from the Water Resources Management Information System (wamis.go.kr, accessed on 5 September 2023) operated by the Korean Ministry of Environment.

2.2. Conceptual Hydrologic Partitioning Model

In this study, a conceptual hydrologic partitioning model (CHPM) is employed, which divides the watershed into surface, soil, and groundwater layers in the vertical direction. In CHPM, precipitation that falls on the watershed is initially partitioned into soil wetting and surface flow. The wetting that infiltrates into the soil then undergoes hydrologic partitioning processes, which include percolation into deeper soil layers or vaporization into the atmosphere [41]. The model applied can be considered a lumped version of the semi-distributed model proposed by Choi et al. [38].

At the surface layer, input rainfall is routed to the maximum surface storage depth, represented as d_s. Any excess rainfall beyond this capacity, denoted as B_t, is then routed to the soil layer. The water retained at the surface layer affects evapotranspiration according to Equation (1).

$$E_t=\mathrm{m}\mathrm{i}\mathrm{n}\left[V_{max,t},d_s\right]$$

(1)

Here, E_t represents the evaporation rate from the surface layer at time t, and V_max,t is the evaporative demand from the atmosphere at t-day. In this study, V_max,t is calculated using the Penman–Monteith method [42,43].

Surface flow Q is calculated according to Equations (2) and (3), based on the method of [44], using the wetting W stored in the soil layer from excess rainfall B_t on the surface layer.

$$W_t=\frac{B_{t}n{Z}_r\left(1-s_t\right)}{B_t+n{Z}_r\left(1-s_t\right)}$$

(2)

$$Q_t=B_t-W_t$$

(3)

Here, nZ_r represents the effective depth of the soil layer, and s_t is the normalized soil moisture ranging from 0 to 1. The modeled vaporization V of the storage water in the soil layer is calculated according to Equation (4).

$$\begin{array}{c}{V}_t=\left(V_{max,t}-E_t\right)\frac{s_t}{s^{*}},for0\le s_t\le s^{*}\\ \hspace{0.17em}\hspace{0.17em}=\left(V_{max,t}-E_t\right),for{s}^{*}<s_t\le 1\end{array}$$

(4)

When the current soil moisture is less than the critical soil moisture threshold s*, vaporization decreases proportionally with soil moisture. However, when the soil moisture is greater than s*, vaporization occurs at the rate demanded by the atmosphere.

The amount of water percolating from the soil layer to the groundwater layer is calculated as a function of the soil moisture in the soil layer, using the saturated hydraulic conductivity coefficient K_s and the percolation exponent $\beta$. The calculation is expressed as in Equation (5).

$$K_t=K_S{s_t}^{\beta }$$

(5)

The base flow G from the groundwater layer is modeled proportionally to the water height R accumulated in the groundwater layer. The modeling is expressed as in Equation (6).

$$G_t={\alpha R}_t$$

(6)

Here, α represents the base flow coefficient. Therefore, streamflow y is composed of the sum of Q and G.

Therefore, the CHPM used in this study consists of six parameters (nZ_r, s*, K_s, $\beta$, $\alpha$, d_s), and it requires input data for precipitation and atmospheric demand for vaporization. The calculation time interval is set to a daily basis. The prior distributions for the parameters for the Markov Chain Monte Carlo (MCMC) technique [45,46], as described later, are configured as shown in

Table 1. CHPM parameters and prescribed bounds for uniform parameter distributions.

Parameter	Unit	Lower Bound	Upper Bound
nZr	mm	5	2000
s*	-	0.01	0.99
Ks	mm/day	15	500
$\beta$	-	1	20
$\alpha$	-	0.01	0.99
ds	mm	1	20

.

2.3. Parameter Estimation Using Markov Chain Monte Carlo (MCMC) Technique

The six parameters of the CHPM were estimated using the Metropolis–Hastings (MH) algorithm, which is one of the algorithms used for MCMC sampling. The MH algorithm, a general form of MCMC (Markov Chain Monte Carlo), has been a compelling choice for generating samples from posterior distribution and has proven successful in many instances [47]. The MH algorithm starts with an initial parameter value ${\theta }_0$. Then, a sequence of N + M (total number of iterative extractions) parameter values, denoted as ${\theta }_i,i=1,\cdots ,N+M$, is generated following the procedure described below:

(1)

A candidate parameter ${\theta }^{*}$ is sampled from the proposal distribution $q\left({\theta }^{*}|{\theta }_{i-1}\right)$

(2)

The adoption threshold value, T_c, is calculated.

$$T_c=\frac{\pi \left(Y|{\theta }^{*}\right)q\left({\theta }_{i-1}|{\theta }^{*}\right)}{\pi \left(Y|{\theta }_{i-1}\right)q\left({\theta }^{*}|{\theta }_{i-1}\right)}$$

(7)

Here, $\pi \left(Y|{\theta }^{*}\right)$ and $\pi \left(Y|{\theta }_{i-1}\right)$ are defined as the likelihood values at parameters ${\theta }^{*}$ and ${\theta }_{i-1}$, respectively.

$$\pi \left(Y|\theta \right)={\prod }_{i=1}^n{e}^{-\frac{B\left[{Y_i}^o\right]-B\left[{Y_i}^s\right]}{2{{\sigma }_o}^2}}$$

(8)

Here, Y^o represents the observed streamflow, Y^s is the simulated streamflow using the parameter $\theta$, n is the number of observed streamflow data, and ${{\sigma }_o}^2$ is the variance of the observed streamflow data. B[*] indicates that the streamflow data have been subjected to a Box–Cox transformation [48,49]. In this study, a Box–Cox transformation coefficient of λ = 0.5 was applied. The reason for applying a Box–Cox transformation to the streamflow data is to prevent biased sampling, as the posterior distribution tends to be skewed towards high flows.

(3)

If the uniform random number u between 0 and 1 satisfies the min(1, T_c) > u, it becomes ${\theta }_i={\theta }^{*}$; otherwise, it becomes ${\theta }_i={\theta }_{i-1}$.

The Markov Chain, formed after the initial N iterations, converges to a chain that contains parameters randomly sampled from the posterior distribution $\pi \left(\theta |Y\right)$. Parameters extracted before the initial N iterations are discarded.

Before employing the MH algorithm, it is necessary to establish initial parameters ${\theta }_0$, the proposal distribution $q\left({\theta }^{*}|{\theta }_{i-1}\right)$, the initial number of iterations N, and the total number of iterations N + M. The choice of the initial value ${\theta }_0$ is typically not very sensitive to the results, but the selection of the proposal distribution $q\left({\theta }^{*}|{\theta }_{i-1}\right)$ is crucial. A common approach is to use a truncated normal distribution with a mean of ${\theta }_{i-1}$ and a constant covariance matrix $\sum$, where the truncation is determined by the upper and lower bounds of the parameters. It is recommended to choose $\sum$ in such a way that the acceptance rate of (min(1, T_c) > u) falls within the range of 30–40%. The number of discarded iterations N is known to be sufficient when it is at least 20% of M. It is also necessary to ensure an adequate number of samples M to allow the chain to progress and converge to the mean values of the parameter posterior distribution, which can be monitored as the chain advances [50].

From the generated samples, the characteristics of the parameter posterior distribution can be quantified. Typically, the final estimated parameter set $\overline{\theta }$ is calculated as follows:

$$\overline{\theta }=\frac{1}{M}{\sum }_{i=N+1}^M{\theta }_i$$

(9)

In addition to this, the variance of the estimated parameters can also be calculated from the generated samples.

2.4. Model Predictive Performance Evaluation and Uncertainty Analysis

The evaluation of model predictive performance is performed using four statistics (R², NSE, KGE, pBias). R² represents the coefficient of determination obtained from the linear regression analysis between the observed and modeled data. If it is greater than or equal to 0.6, the model’s predictive performance (i.e., agreement with observed data) is considered satisfactory [51]. NSE is the Nash–Sutcliffe model efficiency coefficient [52], shown in Equation (10). Generally, when KGE is closer to 1, it signifies that the model is more accurate. A threshold value equal to or greater than 0.5 is recommended to indicate a model of sufficient quality [53].

$$NSE=1-\frac{{\sum _{i=1}^n\left({Y_i}^s-{Y_i}^o\right)}^2}{{\sum _{i=1}^n\left({Y_i}^o-\overline{Y^o}\right)}^2}$$

(10)

Here, ${Y_i}^s$, ${Y_i}^o$, and $\overline{Y^o}$ represent the simulated time series, observed time series, and mean of the observed time series, respectively. KGE (Kling–Gupta Efficiency) is a coefficient proposed by Gupta et al. [54] and is calculated through Equation (11).

$$KGE=1-\sqrt{{\left({\gamma }^{\prime }-1\right)}^2+{\left({\alpha }^{\prime }-1\right)}^2+{\left({\beta }^{\prime }-1\right)}^2}$$

(11)

In the Equations mentioned above, ${\gamma }^{\prime }$ represents the linear correlation coefficient between the observed and simulated values, ${\alpha }^{\prime }$ represents the ratio of the standard deviation of the simulated values to the standard deviation of the observed values, and ${\beta }^{\prime }$ represents the ratio of the mean of the simulated values to the mean of the observed values. When KGE is close to 1, it indicates that the simulated data closely replicate the observed data at a high level. Patil and Stieglitz [55] suggested that KGE values of 0.6 or higher can be considered sufficiently satisfactory for modeling results. pBias, as a coefficient, measures the average tendency of the simulated values to be greater or smaller than the observed values, as defined below [56].

$$pBias=\frac{\sum _{i=1}^n\left({Y_i}^s-{Y_i}^o\right)}{\sum _{i=1}^n{Y_i}^o}\times 100$$

(12)

Uncertainty was analyzed from two perspectives. The first perspective concerns the uncertainty of the estimated parameters. Parameter uncertainty was quantified using the coefficient of variation PCV_p for each parameter, as expressed in Equation (13).

$${PCV}_p=\frac{{\sigma }_p}{\widehat{{\theta }_p}}$$

(13)

Here, ${\sigma }_p$ represents the standard deviation of the ensemble of the parameter p simulated via MCMC, and $\widehat{{\theta }_p}$ is the estimated value of parameter p (i.e., the ensemble mean). The uncertainty of the simulated streamflow can be quantified by the mean coefficient of variation (MCV). MCV reflects the degree of variability in the ensemble of streamflow simulated via MCMC and is calculated as shown in Equation (14).

$$MCV=\frac{1}{n}{\sum }_{i=1}^n\left(\frac{{\sigma }_{Y,i}}{\widehat{Y_i}}\right)$$

(14)

Here, ${\sigma }_{Y,i}$ represents the standard deviation of the ensemble corresponding to the i-th observed data, and $Y_i$ is the model prediction (i.e., the ensemble mean) corresponding to the i-th observed data.

3. Results and Discussion

3.1. Segmentation of Hydrological Model Calibration and Validation Periods Based on Climatic Conditions

The core concept of the split-sample calibration method involves dividing the available streamflow data into multiple periods, conducting calibration, and performing validation under different climatic conditions. In this study, the determination of whether a specific year is a dry year, a normal year, or a wet year was accomplished using the Budyko dryness index [57]. The dryness index DI, represented by Equation (15), reflects the competition between energy and water in the watershed. Years with high dryness index values are characterized by water limitations (i.e., high vaporization demand), while years with low dryness index values are primarily dominated by precipitation, resulting in limited energy availability in the environment.

$${DI}_y=\frac{A{E}_{o,y}}{A{P}_y}$$

(15)

Here, $A{E}_o$ represents the annual atmospheric vaporization demand in a specific year (mm/year), and AP represents the annual precipitation in a specific year (mm/year). Based on the dryness index, 7 years with the highest dryness index values and 7 years with the lowest dryness index values were classified as wet years and dry years, respectively, among the 21 years of data, with the remaining years designated as normal years. Figure 2 displays the annual precipitation in the AnDong Dam and HapCheon Dam watersheds. It is worth noting that the AnDong Dam watershed is one of the regions in the South Korea with relatively low precipitation, while the HapCheon Dam watershed is one of the regions with high precipitation.

Table 2. Classification of selected years (std: standard deviation).

		Mean	Std (Standard Deviation)	Min	Max	Dry Year (2015)	Normal Year (2005)	Wet Year (2003)
AnDong Dam watershed	Annual Precipitation (mm)	1175	254	684	1707	684	1097	1707
	Annual Potential Evapotranspiration (mm)	993	39.5	923	1050	1044	967	929
	Dryness Index	0.889	0.224	0.545	1.53	1.53	0.882	0.545
HapCheon Dam watershed	Annual Precipitation (mm)	1318	332	633	1947	633	1240	1947
	Annual Evapotranspiration (mm)	1060	36.7	958	1127	1112	1085	958
	Dryness Index	0.870	0.292	0.492	1.76	1.76	0.874	0.492

provides information on the climate characteristics in the study area and details for three different years with varying climatic conditions. During the calibration phase, the initial year was designated as a warming-up period, and calibration and validation data were prepared based on four climatic conditions, dry years, normal years, wet years, and mixed years, with a reference period of three years. Taking AnDong Dam as an example, calibration for dry years was performed using data from the years 2008, 2014, and 2015, while calibration for normal years utilized data from 2009, 2010, and 2012. Calibration for wet years was based on data from 2003, 2004, and 2006, and calibration for mixed years was carried out using data from 2007 to 2009. The estimated parameters for each climatic condition were validated using data from dry years (2016, 2017, 2019), normal years (2013, 2018, 2021), wet years (2007, 2011, 2020), and mixed years (2019 to 2021). The mixed years period consisted of one year from each of the dry, normal, and wet years for both the calibration and validation phases.

The selected years for calibration and validation are not consecutive, and as shown in Figure 3, non-consecutive years may be included in the calibration and validation periods. However, the selection of non-consecutive periods applies only to the data chosen for calibration and validation. The hydrological model was always run for the entire 21-year period. In Figure 3, DC represents the calibration period for dry years, DV is the validation period for dry years, NC is the calibration period for normal years, NV is the validation period for normal years. Similarly, WC is the calibration period for wet years, WV is the validation period for wet years, MC is the calibration period for mixed years, and MV is the validation period for mixed years. Regarding the colors of the years, dry years are denoted in orange, normal years in green, and wet years in light blue.

3.2. Calibration Results by Climatic Condition and Discussion

The results for the calibration using data from different climatic conditions (DC, NC, WC, and MC) are presented in

Table 3. Results of calibration performance criteria for four different 3-year calibrations at AnDong Dam watershed.

Calibration Condition	Parameter		PCV	R2	NSE	KGE	MCV
Dry	nZr	478	0.583	0.743	0.729	0.706	0.663
	s*	0.586	0.444
	Ks	307	0.338
	β	3.55	0.445
	α	0.713	0.280
	ds	8.50	0.554
Normal	nZr	364	0.504	0.632	0.603	0.757	0.527
	s*	0.607	0.407
	Ks	346	0.312
	β	3.53	0.461
	α	0.759	0.228
	ds	9.45	0.488
Wet	nZr	469	0.754	0.603	0.565	0.480	1.40
	s*	0.628	0.422
	Ks	300	0.421
	β	5.98	0.787
	α	0.650	0.354
	ds	9.14	0.569
Mixed	nZr	386	0.666	0.734	0.729	0.741	0.969
	s*	0.599	0.436
	Ks	316	0.379
	β	4.45	0.583
	α	0.680	0.323
	ds	9.95	0.528

and

Table 4. Results of calibration performance criteria for four different 3-year calibrations at HapCheon Dam watershed.

Calibration Condition	Parameter		PCV	R2	NSE	KGE	MCV
Dry	nZr	526	0.519	0.795	0.793	0.809	1.11
	s*	0.623	0.376
	Ks	250	0.548
	β	4.47	0.386
	α	0.648	0.357
	ds	8.42	0.626
Normal	nZr	589	0.587	0.780	0.755	0.679	1.17
	s*	0.672	0.366
	Ks	274	0.499
	β	5.80	0.619
	α	0.643	0.373
	ds	9.15	0.593
Wet	nZr	651	0.586	0.736	0.731	0.775	2.48
	s*	0.646	0.403
	Ks	285	0.466
	β	8.28	0.594
	α	0.660	0.345
	ds	9.40	0.576
Mixed	nZr	561	0.597	0.756	0.748	0.735	0.832
	s*	0.665	0.371
	Ks	270	0.513
	β	5.37	0.605
	α	0.646	0.373
	ds	8.52	0.599

. The first point to mention from the results in Table 3 and Table 4 is the ensemble mean values of the parameters (i.e., the final estimated parameter values). For each of the four calibration climatic conditions, different parameter values were estimated. Parameters s*, K_s, $\alpha$, and d_s were estimated with relatively minor differences across the calibration climatic conditions, while parameters nZ_r and $\beta$ showed sensitivity to the calibration climatic conditions. In particular, for calibration under WC, four or more of the estimated values among the six parameters were either the highest or lowest compared to the values estimated under different calibration climatic conditions. Notably, parameters estimated for the relatively humid HapCheon Dam watershed appeared to be more responsive to the climatic conditions of the calibration. In the case of the HapCheon Dam watershed, five of the six parameters, excluding s*, were estimated to be the highest under WC and the lowest under DC, with the exception of parameter $\alpha$.

The second point to consider is the performance in reproducing the observed streamflow obtained using the estimated parameters, specifically, R², NSE, and KGE. The scenario with the best performance in reproducing streamflow based on the observed data used for calibration was DC. Next in line were NC and MC, with WC performing the least favorably. For the AnDong Dam watershed, MC and DC showed superior calibration performance, with WC performing the least favorably. In the HapCheon Dam watershed, DC and NC exhibited superior performance, while MC had the least favorable results. Generally, considering that these three indicators are widely used to assess model accuracy during hydrological model calibration, these results suggest that it is advisable to formulate a strategy that adequately combines normal years and wet years, with a focus on dry years, for model parameter estimation. This implies that a calibration strategy using only the wet years data is not valid. However, it is essential to recognize that the streamflow performance based on the four calibration strategies in Table 3 and Table 4 is generally acceptable for the AnDong Dam watershed, except for WC. This is because R², NSE, and KGE exceed a minimum threshold, indicating that they achieve satisfactory performance regardless of the calibration strategy.

However, when examining the uncertainty of the parameters using PCV, it was observed that parameters estimated under WC exhibited the highest uncertainty. In the AnDong Dam watershed, all parameters except s* displayed the highest uncertainty under WC. Additionally, in the AnDong Dam watershed, all parameters except $\beta$ exhibited the least uncertainty under NC, with $\beta$ being the most reliable under DC. For the HapCheon Dam watershed, the difference in parameter uncertainty based on the climatic conditions used for calibration was not substantial.

The range of parameter ensembles sampled using data from each climatic condition is presented in Figure 4 and Figure 5. In the case of DC, the ranges of parameters nZ_r and $\beta$ were smaller than those corresponding to parameters under different calibration climatic conditions, with NC also displaying a range of uncertainty similar to DC.

The uncertainty in streamflow as examined using the MCV was larger than that of the parameters (see Table 3 and Table 4). This means that the uncertainty in parameters not only influences the uncertainty in the model’s predicted streamflow, but also amplifies it. The predicted streamflow uncertainty was highest under WC. These results indicate that even if calibration under WC demonstrates satisfactory streamflow reproducibility, the high uncertainty in both parameters and streamflow may render it less appropriate in terms of model reliability. In other words, estimating model parameters using data from wet years can introduce significant uncertainty into predictions of critical dry years’ streamflow, which can have significant implications for water resource supply planning. It can also raise issues about the reliability of streamflow projects when devising water resource supply strategies for dry future scenarios due to climate change.

3.3. Validation Results by Climatic Condition and Discussion

In this section, we validate the model’s prediction accuracy under various climatic conditions using parameter ensembles obtained from calibration for each climatic condition (see Figure 6, Figure 7, Figure 8 and Figure 9). The shaded area highlighted in yellow represents the 90% confidence interval (CI). Figure 6, Figure 7, Figure 8 and Figure 9 display the model’s performance under various climatic conditions (DV, NV, WV, and MV) using the estimated parameters for each climatic condition. Monthly streamflow data were aggregated to visualize the differences between climatic conditions. Calibration under NC yielded good validation results not only for dry years but also for normal and wet years (Figure 6). However, calibration under WC exhibited good validation results for wet years but less satisfactory results for dry and normal years (Figure 7). Especially considering that the streamflow reproducibility under WC for the HapCheon Dam watershed was similar to that under DC and NC, these results suggest a need for more detailed analysis. Given the satisfactory streamflow reproducibility under WC but the high uncertainty in estimated parameters and predicted streamflow, these results emphasize the importance of not only assessing reproducibility performance metrics like R², NSE, and KGE, but also considering the associated uncertainty in prediction when evaluating the suitability of calibration.

Figure 10 presents the numerical results of model performance validation under various climatic conditions using calibrated parameters from different climatic conditions. In the case of the AnDong Dam watershed, NC exhibited the best validation performance, with DC and MC showing similar performance. WC performed particularly poorly in dry and normal years. For the HapCheon Dam watershed, DC, MC, and NC showed relatively better validation performance, with no significant performance differences among them. However, WC, as in the case of AnDong Dam, had notably poor validation performance in dry and normal years. This implies that if model calibration is primarily based on wet years, it may not ensure good model performance in drier years. Therefore, this suggests that a calibration strategy incorporating as many dry years as possible may be more advantageous for ensuring the accuracy of predicted streamflow. In other words, simply dividing the available data into two periods for calibration and validation may not be reasonable. As Figure 3 shows, wet years were predominant until 2012, and dry years have been more frequent since. Using only data before 2012 for model calibration, and then, simulating streamflow for a planning period of 30–100 years may have limitations in accurately modeling drier years’ streamflow. This characteristic can also have a significant impact when forecasting future streamflow. Using a hydrological model calibrated with data from unspecified past years to predict streamflow in the highly likely occurrence of dry years may not be appropriate. Particularly when constructing a hydrological model for use in planning related to water supply and ecology, careful selection of the appropriate calibration climatic condition is necessary, depending on the purpose.

As discussed earlier in the context of calibration results, the uncertainty in parameter estimates is amplified and reflected in the uncertainty of predicted streamflow. This characteristic becomes more pronounced in the validation climatic conditions. Figure 11 illustrates the uncertainty of predicted streamflow under various climatic conditions, using calibrated parameters from different climatic conditions. In Figure 11, PC represents the width of the 90% confidence interval of the ensemble of predicted streamflow, with larger PC values indicating higher uncertainty. If the PC becomes 1, it means that all observations have crossed the confidence interval, indicating high uncertainty. The parameter uncertainty, which depends on the calibration climatic conditions, is magnified and propagated into the streamflow uncertainty under the validation climatic conditions, as observed in Figure 4 and Figure 5. Calibration with DC results in the smallest propagation of uncertainty in the predicted streamflow under different climatic conditions, while calibration with WC leads to the most significant amplification of uncertainty in the predicted streamflow. In particular, as evident in the MCV results, WC calibration greatly amplifies the uncertainty in the predicted streamflow in dry years. Consequently, it is challenging to claim that streamflow derived from a hydrological model calibrated with data primarily from wet years is reliable. These findings emphasize the need for careful consideration of the uncertainty in predicted streamflow, especially when forecasting streamflow under drier climatic conditions in the future.

4. Conclusions

The selection of data periods for hydrological model calibration and validation is often subjective, and there are no clear, objective guidelines to determine the most reliable calibration period for obtaining accurate predictions. This study investigated the impact of selecting calibration and validation data on parameter estimation and streamflow prediction performance.

The study focused on the Nakdong River basin in the southeastern part of South Korea, specifically, the AnDong and HapCheon Dam watersheds. Historical hydrological and meteorological records covering 21 years were used in the analysis. The data were classified into three different climatic conditions: dry years, normal years, and wet years. Four calibration climatic conditions were then constructed based on the climatic conditions: dry years, normal years, wet years, and mixed years. A conceptual hydrologic partitioning model was calibrated using Markov Chain Monte Carlo simulations for each calibration climatic condition. Subsequently, the calibrated models for each calibration climatic condition were validated under four different validation climatic conditions.

The study revealed that the climatic conditions of the data used for calibration significantly influenced the estimated model parameters and simulated streamflow. While most of the models met the minimum performance standard for streamflow calibration, it was observed that good calibration performance did not necessarily guarantee similar performance during validation. From this study, it can be suggested that conducting calibration during wet years may result in reduced accuracy and increased uncertainty when predicting streamflow during dry years or normal years. However, these findings could be generalized after conducting research in various watersheds with diverse climates in different regions worldwide.

The approach taken in this study could serve as a starting point for future research involving diverse climates, different types of watersheds, and more complex hydrological models. Additionally, investigating the relationship between data length and climatic conditions is an interesting topic for future research.