Watershed hydrological modelling in data scarce regions; integrating ecohydrology and regionalization for the southern Caspian Sea basin, Iran

Abstract

The aim of this study is to evaluate an alternative approach to indicate how hydrological processes behave in a given watershed, and to test whether this approach can replace traditional calibration, particularly under data deficient conditions. Therefore, a regional calibration method (RC) was adapted to characterize “parameter-based hydrologic processes” as a function of watershed ecologic attributes. The methodological process included (1) temporal phase, (2) correlation analysis and (3) spatial phase. The defined methodology was carried out on a 4160 km² area containing 21 watersheds laying in the southern coastal line of the Caspian Sea, Iran. By implementing the RC, regional models were specified corresponding to each hydrological process defined in the Tank model. Testing the reliability of the transferring process of hydrological parameters was conducted using multi-level accuracy comparison (MAC) benefiting from descriptive statistics, scatter-plots and T-test.

Both temporal and spatial phases have shown acceptable outputs backed by their ecologic significance, but as an alternative approach to traditional calibration, the standalone RC still needs development to achieve a more robust basis covering all the parameters of the hydrologic model. According to the post-processor MAC, the transferability of six out of twelve regional models (height of lower outlet at the first tank, intermediate flow, deep-percolation, infiltration, surface flow, height of outlet at the second tank) was accepted with respect to the given tests. As such, our method outperformed the number of transferable parameters by an outstanding regional model predicting the surface flow in comparison with similar studies.

Although the RC could not achieve total perfection, nevertheless it could still help users by providing more information about the contribution of ecologic variables in the prediction of the hydrological processes of a certain watershed.

Tank model, Rainfall-runoff relationship, Ecohydrological modelling, Regionalization approach, Caspian Sea basin, Donor and recipient watersheds.

1. Introduction

Rainfall-Runoff models (r-r) have been widely used to manage water resources during the past decades. Distributed models are sporadically used in hydrologic response prediction applications due to their long runtime and high volume of input data (Reed et al., 2004; Khakbaz et al., 2012). In contrast, the application of conceptual models in general and the Tank model in particular (which mainly benefits from black-box modelling and a calibration process to retrieve hydrological parameters) have been getting more attention in the prediction of elements of the hydrologic cycle namely streamflow (Ngoc et al., 2016), groundwater (Aqili et al., 2016; Hong et al., 2016) and flood forecasting (Sugiura et al., 2016). For the purpose of overcoming complexities and integrating hydrological processes provided by the conceptual hydrologic models (Patil and Stieglitz, 2014; Haberlandt and Radtke, 2014; Wang et al., 2014), the Tank model was selected as the modelling platform for the current study (Sugawara et al., 1984).

The basic concept of the Tank model was firstly designed by Sugawara et al. (1984) and then has been regionally developed by many researchers. Setiawan et al. (2007) conducted a research using an advanced version of the Tank model entitled GA-Tank. GA-Tank benefits from Genetic Algorithm and far-reaching metrics respectively designed for enabling the use of global searches and providing robust accuracy statement indicators. Podger (2005) completed former achievements by integrating the basic Tank concepts such as initialization and parameter conceptualization, with some sophisticated search algorithms including shuffled complex evolution (SCE) and Rosen-Brock, (RBN) as well as a directory of objective error functions set into an auto-calibration package called e-water.

In the sequence of Tank advancements, Chen and Adams (2006) have coupled the traditional lump Tank with the Neural Network concept by shifting to a semi-distributed form. Chen and Adams’ edition generally modelled the spatial variation of rainfall and watershed heterogeneity with a precision of 0.70–0.90 based on the coefficient of determination. Tank coefficients and parameter variations have widely been studied across different ecohydrological systems by Basri (2013) through a deep literature review. He suggested a set of different Tank models for each ecosystem to bear the right share of landuse and soil class in water balance of the watershed. In terms of environmental application of conceptual hydrologic models, Jabbarian Amiri et al. (2016) implemented a regionalization study over the classic version of the Tank model followed by an uncertainty analysis to determine which combinations of landscape ecological metrics are significantly capable to transfer the given hydrologic processes. Onyutha (2016) carried a research practice to examine the importance of model selection in simulating extreme and moderate flows (as researchers usually do compare model performances under normal conditions) as well as the possible influence of picking goodness-of-fit metrics. In this regard, Cumulative Rank Difference and Non-parametric Anomaly Indicator methods were used to detect sub-trends and variabilities respectively. Based on the results, Tank simulations were moderately above the average with generating no zero-runoff records, and overall the Water-Balance-Based objective function was the most recommendable metric corresponding to the modeling aims. Suryoputro et al. (2017) has implemented a novel approach called rationality runoff coefficient (RRC) to calibrate the Tank surface infiltration parameter. In this study, first the actual imperviousness of the surface was measured through field samplings, and next the RRC-derived surface infiltration metric was estimated based on watershed surface conditions such as landcover, slope and rainfall. Song et al. (2017) have practiced the capabilities of using Simulink in the rainfall-runoff simulation. Owning to the graphical interface provided by Simulink, sophisticated optimization algorithms like SCE-UA could easily be executed. Devising a nested module to calculate the actual evapotranspiration based on coupling crop and soil water stress coefficients, was a significant advancement compared to other studies (mostly considered this parameter as a standalone input). Sheikh Goodarzi et al., 2018, Sheikh Goodarzi et al., 2020 have carried out the research (backed by a preliminary study to explore the comparative performance of conceptual hydrologic models, first) to investigate the robustness of the application of Tank at various spatial scales by applying some catchment hydrologic indicators. The results showed that the given series of hydrological processes in medium to large scale watersheds was satisfactorily projected whereas an unsatisfactory trial applied at small scale watersheds (below 15 k²). Phuong at el (2018) have recruited the Tank model in combination with Cumulative Anomaly and Pettitt-test to address historic runoff variation in Vietnam. In their study, the two storage Tank successfully detected the discharge loss caused by intensive water usage and reservoir constructions in the study areas. Vasconcellos et al. (2020) aimed to explore the reliability of spatially distributed soil water index (SWI) and topographical wetness index (TWI) values in comparison with soil moisture measures. As the flexibility of hydrologic platform is necessary, the D-Tank benefiting from two interconnected tanks was developed based on the distributed concept. Pursuant to technical limitations, an event-based modeling followed by DREAM(ZS) uncertainty analysis was performed and a single set of parameters (averaged by their corresponding uncertainty ranges) was grounded for the runoff generation. Even though the Lump Tank performed slightly better than D-Tank, however SWI and TWI were predicted adequately. Jaiswal et al. (2020) developed a comparative study to evaluate the outcomes of conceptual (TANK, AWBM) and a semi-distributed rainfall-runoff (SWAT) models benefiting differently from the spatial characteristics of the watersheds and climate variables. The results suggested that the Tank performed more appropriately than the others.

Unfortunately, it can still be challenging to provide data through superseded approaches when performing hydrologic investigations, particularly in ungauged basins whose hydrologic records are confined to local imperfect hydro-climatic networks (Sivapalan et al., 2003). Regional analysis, by which some common information is transferred from one catchment to another within a certain homogenous geographic area, have widely been used in studies to optimize hydrologic models and bring accurate flow prediction in ungauged watersheds as a parallel approach to calibration (Vandewiele et al., 1991; Hundecha Hirpa, 2005). Review of the literature (regional modelling) showed an above average performance for the Structural Similarity (Beck et al., 2016; Bulygina et al., 2009; Li et al., 2009) and Parametric Regression (Jabbarian Amiri et al., 2016, Jabbarian Amiri et al., 2019, 2019; Young, 2006; Boughton and Chiew, 2007; Kim et al., 2016), while Averaging (Zvolensky et al., 2007; Goswami and o’Connor, 2007) and Spatial Proximity (Caballero et al., 2013; Petheram et al., 2011) have shown an acceptable result. The most important issue about Regional Calibration is, the necessity of scenario planning. Accordingly, the Regional Calibration method was effectively employed through a number of studies (Parajka et al., 2006, Parajka et al., 2007, 2007; Hundecha et al., 2008; Samuel et al., 2011; Reichl et al., 2009; Kim and Kaluarachchi, 2008; Oudin et al., 2008).

While application of the concept has begun over three decades ago, the use of ecohydrological features of the landscapes for addressing alterations in different hydrological processes only began in 2010 (Jabbarian Amiri et al., 2016). The evidence has suggested that key attributes of a given landscape can have significant influence on hydrologic responses at watershed scale (Granato, 2012; Jabbarian Amiri et al., 2016). Hence, this approach is still in the early stages of its development. In the framework of parameter regionalization, the following variables have been successfully implemented so far: slope, watershed area, percentage of landuse and landcover, elevation, length of main river, drainage density, topographic indexes, soil and geological classes, electrical conductivity and porosity, extra-terrestrial radiation, temperature and precipitation as well as landscape ecological metrics (Parajka et al., 2013).

Regarding conceptual modelling in data scarce regions, the current study focused on regionalization methods retrieving hydrologic parameters as a function of landscape features (ecological attributes of the watershed) (He et al., 2011; Yokoo et al., 2001; Hundecha and Bardossy, 2004; Hundecha Hirpa, 2005; Jabbarian Amiri et al., 2016). While there are a few studies which have focused on the post-processing of regional models (i.e. Jabbarian Amiri et al., 2019, Jabbarian Amiri et al., 2016), we decided to rather look at the reliability of hydrologic parameter/processes transformation with an emphasis on the multi-level accuracy comparison (MAC). To this end, inspired by the above-mentioned implications, a specific regional calibration (RC) process was devised to be able to answer the following questions: (1) is there any relationship between calibrated parameters of the conceptual rainfall-runoff model and ecologic factors of the catchments? Or (2) to what extent regression-based regional models are reliable using the multi-level accuracy comparison?

It is also worth noting that the following words have been used through the entire article interchangeably; hydrologic parameters (processes), regional models (retrieved regressions equations), landscape features (ecologic attributes of the watersheds), temporal calibration phase (r-r modelling), spatial calibration phase (regionalization) and ecosystem (watershed).

2. Materials and methods

2.1. Case study

The study sites lie in the southern part of the Caspian Sea (which is the most important basin in Iran due to a variety of hydrological processes) with a total coverage of 256,000 square kilometres (see Figure 1). There are nearly a hundred inter-connected watersheds joining the Caspian Sea (Afshin, 1994). According to the Domarten climate index, the study sites are classified under the temperate and humid classes with an annual average precipitation of 1100 mm (Ministry of Energy, 2014). Landuse and landcover (LULC) of the area consist of Settlements, Forest (Fagus, Carpinus, Salix, Alnus, Fraxinus Ulmus, Parrotia Quercus pp), Rangeland, Agricultural areas (orchards, water and dry farming) and Barrenlands with high ecological importance (Sheikh Goodarzi, 2013).

Figure 1.

Distribution of the study areas.

2.2. Input data

2.2.1. Pre-processing

A two-step pre-processing was conducted on the regional calibration input data corresponding to temporal and spatial phases. Hydrometric and climatologic records as well as ecological attributes were acquired from the Iran Water Resources Management Company (www.wrm.ir), the Soil and Water Research Institute of Iran, (swri.ir), the Geological Survey and Mineral Exploration of Iran (www.gsi.ir), the I.R.OF IRAN Meteorological Organization (www.irimo.ir) and the National Cartographic Center of Iran (www.ncc.org.ir) (see Table 1).

Table 1.

Date requirement.

Category	Data layer	Specification
Ecologic variables	- Landuse and Landcover data (LULC)	LULC 2015 in 5 classes: Residential cores, Forest, Rangeland, Agricultural areas and Barrenlands (irimo.ir)
	- Soil data	soil hydrological group namely A, B, C and D representing high to low porosity (swri.ir)
	- Geology data	Geological permeability classes namely N, M and T representing high to low permeability (gis.ir)
Hydro-climatic records	- Precipitation (P)	Daily recorded time-series will be acquired (wrm.ir, irimo.ir)
	- Discharge (Q)
	- Temperature (T min, max)
	- Solar radiation (Sr)
Topology	- Upstream watershed boundary	Vector format (ncc.org.ir)
	- Main-river	Vector format (ncc.org.ir)
	- DEM	Aster global Dem (asterweb.jpl.nasa.gov)

The 3^rd level hydrologic units (watersheds) surrounded by the Mazandaran and Guilan provinces were pre-processed considering at-least 10 years of spatio-temporal compliance between climatologic (precipitation, surface temperature, solar irradiance and evapotranspiration), hydrologic (discharge) and also ecologic attributes (landscape, pedoscape, lithoscape). Missed plots were investigated and time-series were recovered using Multi-year Moving Average method (Sheikh Goodarzi, 2013). Based on the results, only 21 out of hundreds of watersheds were eligible to be used for further investigations. In regard to pre-processing, Forests (coverage area of 46%) and Barrenlands (less than 1%) were respectively the most and less dominant features of the landscape of study watersheds, C (62%) and A (4%) soil types were the most frequent and infrequent elements of the pedoscapes. Meanwhile, N (41%) and M (27%) geological classes were also the most frequent and infrequent categories of the lithoscapes.

2.2.2. Temporal processing

Considering the Tank model inputs, hydrologic and climatological data including precipitation (P), actual evapotranspiration (ET_A) and surface discharge (Q) were provided on a daily basis. Evaluating the given data prior to r-r modelling, a preliminary assessment containing unit conversion (i.e. standardizing m³/s to mm/d) and ET_A calculation (from ET₀) was conducted (FAO, 1998; Allen et al., 1998; Heryansyah, 2001; Verstraeten et al., 2005; Jabbarian Amiri et al., 2016).

2.2.3. Spatial processing

Based on the reviewed literature, ecological variables were selected to be used in the intended regionalization process. The major dynamic and static factors are: main LULC types (Agriculture, Rangeland, Forest, Barrenland and Urban areas), soil hydrological groups (A, B, C and D represent high to low porosity) and geological permeability classes (T, M and N classes where permeability increases from T to N) (USDA, 2007; Wolock et al., 2004). A simple and terse landscape metric, PLAND (which refers to the percentage of coverage of any type of feature classes within the landscape) is used to quantify the study watersheds (McGarigal and Marks, 1995).

In this step, the landscape features of well-calibrated watersheds were collected to be implemented in further processing. Ecohydrological characteristics of the study sites are illustrated in Figure (2) and Table (2). It should be noted that Statistical analyses were all completed using SPSS for Windows Release 11.5 and hydrologic calculations were done under the Tank optimizer package developed by Setiawan et al. (2007).

Figure 2.

Ecological attributes of the study sites; A) Landuse type, B) Soil hydrological group and C) Geological permeability class; where B, R, F, U and A respectively represent for Barrenlands, Rangeland, Forest, Urban areas and Agriculture; Soil hydrologic A, B, C and D represent for high to low porosity; Geological class N, M and T represent for high to low permeability.

Table 2.

Hydrological specification of watersheds.

Descriptive Statistics	Area (KM)	Built	Elevation (M)	Record duration	P	Et	Q
Average	198	1968	358	9.43	5.72	0.76	1.83
Median	135	1967	300	10	0.00	0.46	1.13
Max	752	2002	1380	10	98.00	11.05	110.85
Min	9	1949	-14	5	0.00	0.00	0.00
SD	204	-	424	1.43	7.11	0.65	3.55

2.3. Hydrological platform (tank model)

Tank is a well-known lumped hydrologic model with simple calculations and strong ability for prediction of hydrological processes especially in large watersheds with varied hydro-climatologic conditions (World Meteorological Organization, 1975; Franchini and Pacciani, 1991). Now, after many years of application, it has become a competing platform in comparison with its semi-sophisticated rivals (Jaiswal et al., 2020; Sheikh Goodarzi et al., 2018).

Fundamentals of the Tank concepts were based on the associated reservoirs complex (ARC), which means that all watershed processes are conceived as a standalone ARC with vertically connected reservoirs. Tank model calculates water balance components (WBCs) from differences in the values of rainfall, evapotranspiration, and runoff (see Eqs. (1) and (2)).

$$\frac{d{h}_A}{dt}=R_T-E_T-Q_T$$ Eq. (1)

$$Q_T=\left(Y_{A1}+Y_{A2}+Y_{B1}+Y_{C1}+Y_{D1}\right)$$ Eq. (2)

Where R, E, Q, and Y are respectively standing for rainfall, evapotranspiration, runoff and its lateral flows.

As illustrated in Figure (3) and Table (3), the Tank model contains a main body (twelve general parameters) and many side components (such as Tank volumes H_a, H_b, H_c and H_d) associated with the discharge. In this regard, vertical movements are formed by P₃, P₄, P₈ and P₁₁ which range from 1 to 100. These parameters are respectively responsible for “height of outlet in the lower part of the first tank”, “height of outlet in the upper part of the first tank”, “height of outlet in the second tank” and “height of outlet in the third tank”. Furthermore, P₁, P₆ and P₉ coefficients, ranging from 0 to 1, modulate the whole penetration process (infiltration to second tank, percolation to third tank and deep-percolation to forth tank) through the ecosystem of the watersheds. Horizontal movements are also formed by P₅, P₂, P₇, P₁₀ and P₁₂ which vary from 0 to 1. The aforementioned parameters are respectively responsible for “surface flow”, “sub-surface flow”, “intermediate flow”, “sub-base flow” and “base flow” (Podger, 2005; Sheikh Goodarzi, 2017).

Figure 3.

Tank model structure (Sheikh Goodarzi et al., 2020); where P_i stands for a given hydrologic process in the watershed; P3, P4, P8 and P11 are responsible for “height of outlet in the lower part of the first tank”, “height of outlet in the upper part of the first tank”, “height of outlet in the second tank” and “height of outlet in the third tank”; P1, P6 and P9 are responsible for “infiltration to second tank”, “percolation to third tank” and “deep-percolation to forth tank”; P5, P2, P7, P10 and P12 are responsible for “surface flow”, “sub-surface flow”, “intermediate flow”, “sub-base flow” and “base flow”.

Table 3.

Tank hydrological parameters and components (modified after Sheikh Goodarzi, 2017).

No.	Program	Initial	Min	Max	Unit	Description
1	R	-	-	-	mm/d	Rainfall
2	ET	-	-	-	mm/d	Evapotranspiration
3	QO	-	-	-	mm/d	Observed discharge
4	QM	-	-	-	mm/d	Calculated discharge
5	t	-	-	-	day	Time interval
6	(P2) YA1	0.2	0	1	mm/d	Lateral water flow from outlet 1 in Tank A
7	(P5) YA2	0.2	0	1	mm/d	Lateral water flow from outlet 2 in Tank A
8	(P7) YB1	0.2	0	1	mm/d	Lateral water flow from outlet 1 in Tank B
9	(P10) YC1	0.2	0	1	mm/d	Lateral water flow from outlet 1 in Tank C
10	(P12) YD0 or D1	0.2	0	1	mm/d	Lateral water flow from outlet 1 in Tank D
11	(P3) HA1	1	1	100	mm	Height of outlet 1 in Tank A
12	(P4) HA2	1	1	100	mm	Height of outlet 2 in Tank A
13	(P8) HB1	1	1	100	mm	Height of outlet in Tank B
14	(P11) HC1	1	1	100	mm	Height of outlet in Tank C
15	HD1	1	1	100	mm	Height of outlet in Tank D
16	A0,A1,A2,B0,B1,C0,C1,D0	0.1	0	1	-	Discharge Coefficient
17	(P1) YA0	0.2	0	1	mm/d	Vertical water flow in Tank A
18	(P6) YB0	0.2	0	1	mm/d	Vertical water flow in Tank B
19	(P9) YC0	0.2	0	1	mm/d	Vertical water flow in Tank C
20	hA	-	-	-	mm	Water level in Tank A
21	hB	-	-	-	mm	Water level in Tank B
22	hC	-	-	-	mm	Water level in Tank C
23	hD	-	-	-	mm	Water level in Tank D

2.4. Regional calibration strategy

2.4.1. Temporal phase (rainfall-runoff modelling)

Our calibration strategy includes two steps, a temporal and a spatial phase. The temporal phase mainly focuses on r-r modelling in all study sites to produce calibrated hydrologic parameters. The statistical database which at least covers a wet and a dry period (3652 days) was split into trial (70%) and test (30%) sections in advance of the r-r modelling. In the meantime, the first 10% of each part was excluded from further analysis in order to warm the process up.

2.4.2. Correlation analysis (screening)

The Regional Calibration generally needs to discover ecologic significance of the relationship between watershed attributes and the calibrated hydrological parameters, derived from the former step, using the Pierson coefficient of correlation (r) prior to the spatial phase. Ergo, a cross-correlation analysis was applied in order to investigate the inter-intra relationships within and between each group of parameter-landscape attributes. Having provided a robust basis for the following steps, the most indicative variables were selected. In other words, the correlation analysis is applied, to some extent, to screen the outputs of the temporal phase (well-calibrated watersheds) which is then used as the input for the spatial phase. As a result, overlapped and counter-intuitive modelling outcomes will be prevented from further contributions.

2.4.3. Spatial phase (regionalization)

The spatial step focuses on regionalization, which is aimed to assess the possibility of transferring hydrologic processes from donor to recipient basins. The spatial phase is basically fed by the hydrologic parameters of well-calibrated watersheds (r-r modelling outputs) and distinguishing ecologic attributes (correlation analysis outputs). Therefore, 6 out of 21 watersheds and their respective results were excluded from further calculations regarding the imperfect r-r modelling performances. Accordingly, the rest of the sample watersheds were split into training (10) and testing (5) groups. In this study, the regionalization is featured through the following steps:

2.4.3.1. Training phase

Regionalization mainly benefits from tentative operations such as multiple linear regressions. A set of stepwise-based linear models was formed to retrieve regression Betas (β) and constant coefficients built on training watersheds (the given 10 watersheds).

2.4.3.2. Testing phase

Applying testing watershed attributes (the given 5 watersheds) into the retrieved regression equations, the regionalized parameters have been generated. The following equations (Eqs. (3), (4), (5), and (6)) clearly exemplify how the spatial phase of the regional calibration works (how the calibrated and the regionalized hydrologic parameters are obtained and contrasted for further interpretations) (Sheikh Goodarzi, 2017).

Regress (P_{iCalibrated (Training)}, X_TTraining) ⇒ b_i Eq. (3)

b_i × X_TTraining ⇒ P_{iRegionalized (Training)} Eq. (4)

b_i × X_TTesting ⇒ P_{iRegionalized (Testing)} Eq. (5)

P_{iCalibrated (Training, Testing)} VS. P_{iRegionalized (Training, Testing)} Eq. (6)

In this module, P_i, X_T and b correspondingly refer to the Tank hydrologic parameters (dependent variables), watershed ecologic attributes (independent variables) and the coefficient of regressions (b_i).

2.4.4. Accuracy assessment

Evaluating the performance of the r-r modelling process (temporal phase) and the developed regional models (spatial phase), was assessed by the implementation of objective error functions (OEFs) including RMSE, Nash–Sutcliffe model efficiency coefficient (NSE), r² and p-value (Nash and Sutcliffe, 1970; Gooijer and Hyndman, 2006; Motovilov et al., 1999).

NSE values range from -∞ to +1 which implies the quality of modelling procedure. Thus, the NSE quantity reflects the modelling perfection. Values greater than 0.35 are commonly appreciated in natural sciences, however values greater than 0.50 (or even 0.75 in particular cases) are more satisfactory in universal modelling. RMSE values are reversely associated with modelling performance, which means that lower amounts, will lead to better modelling specification. Values below 5 or ideally, quantities lower than 1 are most acknowledged with reference to the literature reviewed. Another way to assess the values of RMSE might be expressing it as a fraction of standard deviation of the given database (values between 0.50 to 1 are considered small). R squared which is better known as the coefficient of determination, is the proportion of the variance in a dependent variable that is predictable from independent variables. Probability value (p-value) is also telling us about the level of modelling specification, ranging from 0 to 1 (values below 0.05 or even 0.01 signify on the well-specified models) (Moriasi et al., 2007).

2.4.4.1. Post-processing

Finally, to examine the statistical reliability of the Regional Calibration in hydrologic model parameter transformation, a multi-level accuracy comparison (MAC) benefiting from descriptive Statistics, scatter-plots and T-test was adopted. Practically, the MAC aims to provide a cornerstone for comparing calibrated and regionalized hydrologic parameters (corresponding to given hydrologic processes) for the possible use of beneficiaries. The research methodology is illustrated in Figure (4) in depth.

Figure 4.

Methodological concept used in the study.

3. Results

The feasibility of hydrological process transformation was assessed under the applied regional calibration procedure. The calibration results are demonstrated in detail below.

3.1. Temporal phase

In this step, the r-r modelling procedure was conducted to retrieve the calibrated hydrologic parameters. Accordingly, the optimization procedure was built on initial parameter space definition, training (choosing the best parameter sets), and testing simulated discharge series through objective error functions. On this basis, the best optimized parameter sets were extracted for each given watershed (training), and the corresponding discharges were afterward simulated using the testing records (as shown in Figure 5 and Table 4). Due to the temporal calibration results, the watersheds of Shalmanroud (16-061), Sefid-roud (17-057), Ghale-roudkhan (18-003), Sardab-roud (16-023), Neka (13-006) and Tajan (13-019) which failed to pass the acceptable criteria, were excluded from further processing. Thus, the simulations exceeding the objective function thresholds (RMSE above 5 and NSE 0.25), neither can be a decent representation for regionalization in general, nor for the r-r nexus modelling in particular.

Figure 5.

Rainfall-runoff simulated series for aggregated period; all study areas at glance (bigger panel) and chosen watersheds (Zilaki-roud, Kour-koursar, Navroud, Ghezel-ozan and Samoush watersheds).

Table 4.

Calibrated hydrologic parameters.

Parameter	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	RMSE (training)	NSE (training)	RMSE (testing)	NSE (testing)
Average	0.03	0.13	57.2	38.2	0.37	0.58	0.5	43.3	0.4	0.36	55.1	0.03	2.17	0.54	3.04	0.29
Median	0.02	0.04	54	37.5	0.25	0.6	0.56	40	0.35	0.35	59.5	0.02	1.60	0.55	2.58	0.26
Max	0.08	0.6	96	79	0.92	0.96	0.98	80	0.8	0.97	92	0.08	4.79	0.94	4.86	0.66
Min	0	0	6	2	0.01	0.17	0.02	17	0.09	0.06	12	0	0.88	0.22	1.36	0.09
SD	0.03	0.19	31.72	28.6	0.33	0.27	0.34	21.24	0.23	0.27	27.33	0.03	1.08	0.21	1.16	0.15

Probability Fitness: P₁Log-Pearson 3 (α = 3.30, β = -0.65, ϒ = -1.49);P₂Fatigue Life (α = 1.82, β = -0.06, ϒ = 0.00);P₃Johnson SB (ϒ = -41, δ = 0.71, λ = 117.94, ξ = -8.61);P₄Beta (α1 = 0.39, α2 = 0.62, a = 2, b = 84);P₅Beta (α1 = 0.59, α2 = 0.59, a = 0.01, b = 0.98);P₆Johnson SB (ϒ = -0.31, δ = 0.81, λ = 1.07, ξ = 0.03);P₇Gen. Pareto (k = -0.73, σ = 0.85, μ = -0.05);P₈Error (k = -100, σ = 23.83, μ = 47.95);P₉Log-Pearson 3 (α = 4.90, β = -.42, ϒ = 0.89);P₁₀Hypersecant (σ = 0.21, μ = 0.33);P_{1 1}Gen. Extreme Value (k = -0.65, σ = 33.08, μ = 54.83);P₁₁₂Gen. Extreme Value (k = -0.76, σ = 0.02, μ = 0.01).

The average RMSE values were 2.17 and 3.04 respectively for training and testing steps. Also, the minimum and maximum RMSE values were 0.88 (Chaloos watershed) and 5.93 (Ghale-roudkhan watershed) for the training step, and 1.36 (Chaloos watershed) and 6.65 (Sefid-roud watershed) for the testing step. Consequently, it seems that RMSE values were generally acceptable when compared to the figures in similar studies (e.g. Moriasi et al., 2007; Jaiswal et al., 2020; Sheikh Goodarzi et al., 2020). Based on the NSE results, 0.54 and 0.29 were respectively obtained as average values for the entirety of training and testing steps. The minimum and maximum values for the training step were -2.77 (Neka watershed) and 0.94 (Kourkoursar watershed), and also -2.84 (Neka watershed) and 0.66 (Kourkoursar watershed) for the testing step. Having looked at the attributes of the worst performing watersheds, revealed the fact that their hydrographs were most simulated, containing too many gaps.

3.2. Correlation analysis

Correlation analysis is a process during which the direction and magnitude of any significant relationships between paired variables are quantified. Variables, where significant inter-relationship was above 0.10, were recognized and chosen as indicative factors for the spatial phase (regionalization), based on Pearson's coefficient of correlation. In this regard, each detected connection between pairs of dependent-independent variables was ecologically interpreted to provide a robust ground and avoid fallacious regression modelling. According to the results, the reverse relationship was strongly confirmed between “P₁₂-Urban areas” referring to base flow, “P₆-Dsoil” referring to the percolation to third tank, “P₇-Tgeo” referring to intermediate flow, “P₃-Mgeo” referring to the height of outlet in the lower part of the first tank, “P₅-Mgeo” referring to the surface flow. Meanwhile, the direct relevance was identified among “P₂-Dsoil” referring to sub-surface flow, “P₉-Ngeo” referring to deep-percolation to forth tank, “P₈-Ngeo” referring to height of outlet in the second tank, “P₁₀-Ngeo” and “P₁₀-Mgeo” referring to sub-base flow (see Table 5).

Table 5.

Cross-correlation between pair variables.

Cross-correlation	P12	P11	P10	P9	P8	P7	P6	P5	P4	P3	P2	P1
Land_A	.247	.113	-.160	.091	-.480	-.280	.181	-.227	-.466	-.244	-.013	.127
Land_U	-.552	.046	-.084	-.296	-.179	-.253	-.206	.275	-.337	.026	.310	.308
Land_F	-.087	.143	.112	.122	.191	.242	.292	.432	.382	.277	-.414	.313
Land_R	-.127	-.218	-.014	-.236	.248	-.026	-.433	-.243	.002	-.048	.438	-.449
Land_B	-.128	-.322	.341	.443	-.426	.154	-.201	-.387	-.003	-.450	-.017	-.028
Soil_A	.056	-.325	-.385	-.357	.267	.149	-.160	.303	-.308	.406	.166	.382
Soil_B	-.226	.085	-.066	.581∗	-.413	-.417	.180	-.135	-.034	-.327	-.318	-.144
Soil_C	.189	.213	.231	-.282	.341	.069	.247	.114	.005	-.102	-.176	.040
Soil_D	-.039	-.273	-.049	-.105	-.174	.377	-.574∗	-.202	.242	.373	.644∗∗	-.115
Geo_T	.174	.466	-.091	.221	-.522∗	-.622∗	.214	.492	.087	.217	.064	.435
Geo_N	.034	-.046	-.577∗	-.609∗	.643∗∗	.437	-.220	.070	-.234	.443	.190	-.213
Geo_M	-.210	-.426	.676∗∗	.391	-.120	.190	.004	-.570∗	.148	-.667∗∗	-.256	-.226

The bold values are show their significance correspondingly at the levels of 0.10, 0.05 (with an astrisk) and 0.01 (with a dubble astrisk).

3.3. Spatial phase

A stepwise-based regression analysis which is the main part of the spatial phase, was conducted to compile the calibration-derived hydrologic parameters and their corresponding ecologic attributes using training data. The prime outputs of the regression analysis include the retrieved linear equation for each of the hydrologic processes (twelve Tank model parameters) (as shown in Eqs. 3-1 to 3-12).

Variance inflation factor (VIF) was also calculated to ensure a satisfactory range of collinearity (across the finalized regression models parameters). In this regard, VIF values higher than 5 imply lack of the collinearity among independent variables or in other words, indicate that the collinearity between a given group of variables is in an acceptable range (Chatterjee et al., 2000). Henceforth, the rest of the data were substituted into the retrieved regression equations to generate the regionalized parameter sets. Tables 6 and 7 indicate the equations including their respective coefficients and ecologic attributes.

P₁=0.3921 – (Land_A∗0.0042) – (Land_F∗0.0036) – (Land_R∗0.0039) + (Soil_A∗0.0068) Eq. (3-1)

P₂=0.0207 + (Soil_A∗0.0312) + (Soil_D∗0.0049) Eq. (3-2)

P₃=21.0312 + (Land_F∗0.5737) + (Soil_A∗3.9503) + (Soil_D∗0.7966) – (Geo_M∗0.4088) Eq. (3-3)

P₄=49.8954 – (Land_A∗0.5688) Eq. (3-4)

P₅=1.2735 – (Land_B∗0.0052) – (Geo_N∗0.0080) – (Geo_M∗0.0108) Eq. (3-5)

P₆=13.0910 – (Land_B∗-0.1040)–(Soil_B∗0.1108)–(Soil_C∗0.1198)–(Soil_D∗0.1211)–(Geo_T∗0.0153)–(Geo_N∗0.0074) Eq. (3-6)

P₇=11.708 – (Land_A∗0.1158)–(Land_F∗0.1057)–(Land_R∗0.1129)–(Geo_T∗0.0106)–(Geo_M∗0.0099) Eq. (3-7)

P₈=21.3489 – (Soil_D∗0.4115) + (Geo_N∗0.5768) Eq. (3-8)

P₉=0.7883 – (Soil_A∗0.0584) – (Geo_N∗0.0063) Eq. (3-9)

P₁₀=0.6996 – (Soil_B∗0.0030) – (Geo_N∗0.0056) Eq. (3-10)

P₁₁=44.7509 – (Geo_T∗0.4761) Eq. (3-11)

P₁₂=0.0254 + (Land_U∗0.0255) Eq. (3-12)

Table 6.

Specification of regional models.

Parameter Variable	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12
RMSE	0.01	0.09	11.88	26.72	0.27	0.14	0.23	10.87	0.15	0.19	30.23	0.04
r2	0.79	0.78	0.89	0.24	0.58	0.85	0.74	0.80	0.74	0.51	0.21	0.31
p-Value	0.01	0.00	0.00	0.10	0.06	0.05	0.08	0.00	0.00	0.03	0.08	0.03

Table 7.

Regionalized hydrologic parameters.

Phase	Catchment ID	File ID	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12
Training	16–059	1	0.0804	0.2752	96	50	1.0000+	0.7844	0.1926	38	0.1312	0.5352	79	0.0254
	17–033	3	0.0112	0.0207	21	49	0.3325	0.7434	0.1655	50	0.4756	0.4141	45	0.0254
	17–051	4	0.0455	0.0357	37	49	0.1970	0.7387	0.4978	21	0.7828	0.6946	45	0.0254
	18–027	7	0.0344	0.0207	64	50	0.3734	0.6345	0.7818	58	0.3829	0.3294	45	0.0254
	18–028	8	0.0264	0.0207	46	50	0.3409	0.7211	0.5026	52	0.4566	0.3967	45	0.0254
	18–035	9	0.0232	0.0207	60	50	0.4726	0.3704	0.9075	79	0.1581	0.1242	45	0.0254
	13–005	10	0.0000-	0.0207	42	14	0.2894	0.9384	0.0610	55	0.4190	0.0675	64	0.0254
	14–021	11	0.0260	0.2036	90	47	0.4613	0.4010	0.7941	54	0.2718	0.2279	46	0.0254
	15–013	12	0.0081	0.5136	91	48	0.4323	0.1384	0.4372	24	0.3173	0.2696	46	0.0288
	15–017	13	0.0318	0.1245	18	11	0.0299	0.3685	0.6161	13	0.7840	0.4638	55	0.0430
Testing	16–011	14	0.0344	0.0207	78	50	0.7588	0.4757	0.0732	21	0.7883	0.4047	92	0.0254
	16–021	15	0.0202	0.0207	40	50	0.5052	0.4534	0.4987	57	0.3935	0.3391	51	0.0485
	16–157	17	0.5015	1.0000+	100+	50	0.4298	1.0000+	0.9828	58	0.0000+	0.2127	45	0.0254
	14–017	20	0.0667	0.2667	76	19	0.8924	0.9393	0.3415	44	0.0802	0.4348	73	0.1214
	16–159	21	0.0230	0.0207	16	50	0.3716	0.7581	0.2946	38	0.6030	0.5304	49	0.1005

Variable-wise, the regional models of “height of outlet in the upper part of first tank P₄”, “height of outlet in the third tank P₁₁” and “base flow P₁₂” were meaningful by only one variable, whereas the regional models of “percolation to third tank P₆“ and “intermediate flow P₇” were formed respectively by six and five variables.

Performance-wise, the best model specifications were seen in the regional models of “infiltration to second tank P₁”, “sub-surface flow P₂”, “deep-percolation to forth tank P₉” and “sub-base flow P₁₀” due to a combination of p-value, RMSE and r² metrics. The most significant models (proven by p-values) were observed in “infiltration to second tank P₁”, “sub-surface flow P₂”, “height of outlet in the lower part of first tank P₃”, “height of outlet in the second tank P₈” and “deep-percolation to forth tank P₉”. The best RMSE values were calculated for “infiltration to second tank P₁” and “base flow P₁₂”. In the meantime, the best figures of r² were seen in “infiltration to second tank P₁”, “sub-surface flow P₂”, “height of outlet in the lower part of first tank P₃”, “percolation to third tank P₆”, “intermediate flow P₇”, “height of outlet in the second tank P₈” and “deep-percolation to forth tank P₉”.

Landuse-wise, the contribution of each category of the landuse was assessed based on their frequency of appearance in the regional models. In this regard, urban areas (U-land) and very low porous soil (Csoil) minimally associated (in just one model) whereas highly permeable geology class (Ngeo) appeared in five different models. Controlling horizontal water movements (P₂, P₅, P₇, P₁₀, P₁₂) throughout the watershed is dominantly based on moderate to highly permeable geology classes (Ngeo, Mgeo), which is the most frequent variable among the horizontal movement models. Moreover, vertical water movements (P₁, P₆, P₉) are mainly predicted by highly permeable geology class (Ngeo) and highly porous soil class (Asoil) which are the most common variables in vertical movement models. More interestingly, there was no common ecologic variable among reservoir related models (the heights of the outlets: P₃, P₄, P₈, P₁₁).

3.4. Accuracy assessment

The possibility of transforming hydrological processes from donor to recipient stations has been investigated by coupling r-r modelling and parameter regionalization. The MAC test was also specifically devised to post-process the efficiency of the proposed methodology (as illustrated in Table 8 and Figure 6). In this procedure, the calibrated vs. the regionalized hydrologic parameter sets (respectively derived from r-r modelling and regionalization) were cross-compared and interpreted by T-test, scatter-plots and descriptive statistics as elements of the MAC test.

Table 8.

Multi-level accuracy comparison of the regional calibration.

Regional models			P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12
MAC	Descriptive statistics	Training	✓	✓	✓	-	✓	✓	✓	✓	✓	✓	-	-
		Testing	×	×	✓	-	✓	×	✓	×	✓	×	-	-
	Scatter plot	Training	✓	✓	✓	-	✓	✓	✓	✓	✓	✓	-	-
		Testing	✓	×	✓	-	✓	×	✓	✓	✓	✓	-	-
	T-test	Training	✓	✓	✓	-	✓	✓	✓	✓	✓	✓	-	-
		Testing	✓	✓	✓	-	×	✓	✓	✓	✓	×	-	-
Final Decision			✓	×	✓✓	-	✓	×	✓✓	✓	✓✓	×	-	-

Where double (✓✓) and single (✓) tick-marks are respectively implying on crucial and moderate model satisfactions.

Figure 6.

The regionalized vs. calibrated parameter sets; A) Training Phase P1–P12 and B) Testing Phase P1–P12.

According to the descriptive statistics and particularly the cross-correlation coefficient among the regionalized and the calibrated parameters, fair to loose connections were obtained between “height of outlet in the upper part of first tank”, “height of outlet in the third tank” and “base flow” (for training phase), and ” infiltration to second tank”, ” surface flow”, ” height of outlet in the upper part of first tank”, ” percolation to third tank”, ” height of outlet in the second tank”, ” sub-base flow”, “height of outlet in the third tank” and “base flow” (for testing phase). Likewise, an ascending trend is evident from training to testing phase, with regard to the range of variance, skewness and kurtosis. In the following step, the investigation of conformity among each parameter set was also conducted using scatter-plot and T-test as well. According to the results, there was no significant differentiation among pair parameter sets (in training phase) but to “sub-surface flow” (p-value 0.02) and “sub-base flow” (p-value 0.07), which have shown notable differences in testing phase. It is noteworthy that “height of outlet in the upper part of first tank”, “height of outlet in the third tank” and “base flow” were excluded from further processing, due to their imperfect model specifications.

4. Discussion

This research has focused on watershed hydrological modelling in data deficient conditions by integrating ecohydrology and regionalization approaches. In other words, our aim was to characterize the contribution of watershed ecologic attributes into the rainfall-runoff modelling towards building an alternative approach to the traditional calibration. Our work aimed to address the shortcomings and deficiencies of the Iranian national hydrologic database as well as the importance of providing the robust hydrologic predictions for ungauged watersheds. Therefore, we have utilized a regional calibration method benefiting from a temporal phase, correlation analysis and spatial phase backed by a multi-level accuracy comparison test. Our goal was to investigate to what extent the approach of parameter-based regionalization can be reliable in the southern part of the Caspian Sea basin, Iran (whose relic ecosystems which are second to none, still are in urgent demand of conservational measures followed by a thorough understanding of the current hydrologic conditions).

4.1. Temporal phase

Despite selecting a variety of watersheds spanning across the southern part of the Caspian Sea basin, few of them were chosen to be put through further analyses according to having a 10-year spatio-temporal compliance. The cumulative area of the study watersheds is about 4160 square kilometres (with an average and standard deviation about 200 km²) mostly covered by forest landscapes (46%) and moderately-low porous soils (62%) as well as highly permeable geological substrate. Since 6 out of 21 watersheds failed processing to the r-r modelling, we went through the underpinning factors of the failure, and have found that the malfunction mostly resulted by the statistical gaps among the datasets (rainfall and discharge) and insufficient coverage of a 10-year period. Having considered the above discussed issue as one increasing emphasis on the necessity of conducting the current study since our basic aim is to implement an alternative approach for hydrological modelling in ungauged watersheds where the insufficiency of hydro-climatic records is deterministic.

According to the results of r-r modelling, runoff generations were satisfactory at least in 15 out of 21 chosen watersheds based on error criteria. The performance of the Tank hydrologic model can be evaluated under different flows. Even though applying some watershed signature metrics could be indicative, nonetheless the accuracy of the model in predicting low to normal flows and high flows can be visually interpreted. As such, the former (low to moderate flow) was successfully predicted but there is some noise in high flows needing to be further assessed (which is respectively in contrast and in compliance with the results of Phuong at el., 2018 and Jaiswal et al., 2020). The results are also in concordance with Sheikh Goodarzi et al. (2020) implying the capability of the Tank model in predicting at various spatial scales.

4.2. Correlation analysis

The correlation analysis was basically applied to screen and check the ecological significance between each pair of calibrated parameters and ecologic attributes of the study watersheds. The pathway showed 9 sets of strongly meaningful correlations (including 5 negatively and 4 positively correlated ways) for each of the hydrologic processes specified in the Tank model with the exception of P₁, P₄ and P₁₁. It means that there would be no solid ecologic base for the regionalization of surface infiltration, height of lower outlet at first tank as well as height of outlet at third tank. For instance, the negative relation among baseflow-urban areas can be interpreted in the way that the denser residential areas are, the less baseflow is penetrated through the ecosystem body. We can reach other similar conclusions in terms of percolation-Dsoil and intermediate flow-Tgeo relations respectively signifying that the less the porous soil groups are available, the less percolation rate occurs, and the more the permeable geology classes are, the less side flow is discharged. On the other hand, there are some positive correlations among sub-surface flow-Dsoil, deep percolation-Ngeo (as the most permeable geology class) and sub-base flow-Ngeo.

4.3. Spatial phase

The significance level and robustness of the regression equations retrieved during the spatial phase, has been checked using p-value, RMSE and r² measures. As we first discuss the transferability of the retrieved regional models here, exploring the contribution of independent variables into the models is further discussed. Having conducted an investigation in the regionalization process, although the totality of the results was satisfactory, there are a few out-band records shown in Samoush (16-059), Nozarabad (13-005) and Simroud (16-157) watersheds. Irrespective of being considered as training or testing step failure, the specification of the regional models can be promoted by enlisting some non-linear regression forms for producing a better match of the predictor and descriptor variables. As for post-processing of the adapted methodology (regional calibration), the MAC test was devised and performed. According to the results, the transferability of half of the Tank oriented hydrological processes was approved based on six acceptable parameters (P₁, P₅, P₈, P₃, P₇, P₉).

As we have earlier discussed the significant and comprehendible pathways between ecologic predictors and hydrological processes of the watershed (in section 4.2), in this section we just focus on the evaluation of how the regional models benefited from those ineligible relationships. Based on the results, the majority of the models used at least one of the above referenced relations in their linear equation coupled with other justifying variables with the exception of those recognized without having any revealed direct correlation (P₁, P₄ and P₁₁). It is worth noting that P₁ was the only parameter with its regionalization justifiably successful (without benefiting from any of the proven ecologic pathways).

Having reviewed the literature in terms of using the Tank model (either selected as the main or in combination with other forms to model the water balance of ecosystems), we reach to the below discussed conclusion. As researchers have always been seeking for the platforms that enable them to simulate the hydrological processes with less effort and more performance, many have adapted a series of lumped to distributed forms of Tank to advance the hydrologic predictions based on the local data availability and model flexibility (Chen and Adams, 2006; Basri, 2013; Onyutha, 2016; Jabbarian Amiri et al., 2016; Suryoputro et al., 2017; Song et al., 2017; Sheikh Goodarzi et al., 2018, 2020; Phuong et al., 2018; Jaiswal et al., 2020; Vasconcellos et al., 2020).

Data-wise, evapotranspiration, which is one of the key factors in the rainfall-runoff modeling process, has been calculated by different methods ranging from lysimeter-based field measurements, Penman modified (Vasconcellos et al., 2020) to Hargreaves (Jabbarian Amiri et al., 2016). As for indirect methods we need the actual evapotranspiration to be estimated based on the growing crops. Our study and Jabbarian Amiri et al. use an average status of the crops and landuse over the course of a year, however Song et al. (2017) used an innovated way benefiting from conjugated application of crops and water stress coefficients.

However, different aims of the clients and developers have led to employing various time steps, namely single events (Vasconcellos et al., 2020), daily (Song et al., 2017 and current study) or monthly (Phuong et al., 2018). As a matter of defining calibration strategy, researchers have equipped Neural Network (Chen and Adams, 2006), global search optimization methods such as Genetic Algorithms and Shuffled Complex Evaluation (Sheikh Goodarzi et al., 2018; Song et al., 2017) and different sets of objective functions (NSE and RMSE) to calibrate their hydrologic platforms. For example, applying dimensionless error metrics in line with an absolute error measure such as MAE will depict more analytic error space (Moriasi et al., 2007).

Following the use of ancillary variables to get an added value in r-r modeling, some preferred to integrate watershed features (such as slope and physical indexes) and ecologic attributes (such as landuse, soil properties and geology) under the framework of regionalization which recently has become popular among researchers certainly in the conditions of data scarcity. In this regard, Basri (2013) focused on the concept of sub-watershed modeling proposing a variety of ecosystem-based schemes for the involvement of soil and landuse conditions to project discharge and infiltration more accurately (double tank for residential areas, tripled tank for paddy and agricultural areas, quad fold tank for forests). Others aimed to predict the hydrological processes through the parameter regionalization (i. e. estimating surface infiltration P₁ based on rationality runoff coefficient by Suryoputro et al., 2017; successfully transferring of infiltration P₁, height of sub-base flow P₃, intermediate flow P₇ and height of intermediate flow P₈ by Jabbarian Amiri et al., 2016). As an advancement to the latter study, we enhanced their achievements and increased the number of successfully transferred parameters to 6 processes (surface flow P₅ and deep-percolation P₉ alongside the above-mentioned regional models). The key output from our study is the successful transformation of surface flow and we still see a possibility for improving the parameter regionalization of hydrological processes through the application of a wider variety of predictors and regression-based methods.

Basic and comparative studies have shown that the Tank model can be used as a robust alternative to its conceptual (such as AWBM) and even distributed rivals (such as SWAT) (Jaiswal et al., 2020) based on the performance results. However, some limitations should be taken into account when applying the Tank model to different spatial scales, particularly to small watersheds (Sheikh Goodarzi et al., 2020). As such, some researchers aimed to post-process the modeling results (Vasconcellos et al., 2020 and Jabbarian Amiri et al., 2016 validated their outputs with an uncertainty analysis). The MAC test applied in this study can also be recommended to ensure that the modeling outputs are reliable enough or (in case of regionalization) transferable.

5. Conclusion

With respect to the methodology adapted, both temporal and spatial phases have shown acceptable outputs in general (backed by their ecologic significance), but as an alternative approach to traditional calibration, standalone RC and resulting regionalized models still need development to achieve more robust basis covering all of the hydrologic processes defined in the Tank model. According to the post-processor MAC test, the transferability of six out of twelve regional models was ratified in a range of acceptable parameters, according to the applied tests. In this respect, lower height of outlet in the first tank (P₃), intermediate flow (P₇), deep-percolation (P₉) crucially and infiltration (P₁), surface flow (P₅), height of outlet in the second tank (P₈) were successfully ratified. Comparing with the recent regionalization studies, we have increased the number of transferable parameters by the outstanding regional model predicting the surface flow. Although RC could not achieve total perfection, nevertheless it could still help stakeholders by providing more elaboration on the contribution of landscape, pedoscape and lithoscape in predicting the hydrological processes under the scale of watershed. Additionally, considering a broad range of composition, configuration and connectivity metrics is highly recommended in future.

Declarations

Author contribution statement

Mehdi Sheikh Goodarzi: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Bahman Jabbarian Amiri: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data.

Hossein Azarnivand: Conceived and designed the experiments; Performed the experiments.

István Waltner: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

István Waltner's contribution was supported by the Higher Education Institutional Excellence Program (NKFIH-1159- 6/2019) awarded by the Ministry for Innovation and Technology within the framework of water-related research of Szent István University.

Data availability statement

Data will be made available on request.

Declaration of interests statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.