LASH hydrological model: An analysis focused on spatial discretization

Catena 173 (2019) 183–193

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LASH hydrological model: An analysis focused on spatial discretization a,⁎

b

c

T

d

Tamara Leitzke Caldeira , Carlos Rogério Mello , Samuel Beskow , Luís Carlos Timm , Marcelo Ribeiro Violab a

Engineering Center, Federal University of Pelotas, Pelotas, RS, Brazil Engineering Department, Federal University of Lavras, Lavras, MG, Brazil Center for Technological Development, Federal University of Pelotas, Pelotas, RS, Brazil d Eliseu Maciel Agronomy Faculty, Federal University of Pelotas, Capão do Leão, RS, Brazil b c

A R T I C LE I N FO

A B S T R A C T

Keywords: Mirim-São Gonçalo basin Water resources management Rainfall-runoff modeling Distributed modeling Semi-distributed modeling

Many of the traditionally used hydrological models have complex formulations and require several input variables over time and space, which are generally scarce and expensive for obtaining, especially in developing countries. In order to overcome these limitations, the Lavras Simulation of Hydrology has been developed and successfully applied to Brazilian basins. The most recent advances of the model address the adaptation of the automatic calibration module considering its distributed and semi-distributed schemes and requiring only a few input variables. In view of this improvement, this study had as main objective to evaluate the performance of the model regarding the estimation of daily hydrograph using two spatial discretization schemes of the basin (distributed and semi-distributed). The hydrographs estimated according to both schemes were compared to the observed hydrograph in the Fragata River basin (FRB), located in Southern Brazil, by using statistical measures. The results indicated that there was effect of the spatial discretization on the quantification of hydrological processes in the studied basin. It was concluded that the distributed scheme outperformed the semi-distributed scheme, although the latter has also provided satisfactory results and can be therefore used for hydrological modeling.

1. Introduction A rainfall-runoff hydrological model quantitatively describes the processes that integrate the water balance in a basin. It can be used for a number of purposes, such as real-time flood forecasts, stream flow frequency estimation, hydrological design of hydraulic structures, reference stream flow analysis and assessment of the impact of climate and land use changes. As a result, this tool has been increasingly used in the management of water resources for decision making (Beskow et al., 2016). Hydrological models require both spatial and temporal input data, whose availability and acquisition, respectively, may be scarce and expensive. The complexity of the model formulation and the spatial discretization scheme used for modeling define how much information is necessary for the application of interest. Some hydrological models can be pointed out with respect to the requirement for more detailed spatial information about the basin and to the high level of parameterization and number of calibration parameters, such as Distributed Hydrology Soil Vegetation Model (DHSVM) (Wigmosta et al., 1994),

Hydrologiska Byrans Vattenbalansavdelning (HBV) (Bergström, 1995), MIKE SHE Systeme Hydrologique European (Abbott et al., 1986) and Soil and Water Assessment Tool (SWAT) (Arnold et al., 1998). Hydrologists commonly have to define a unique set of values representing the calibration parameters for the model of interest, however, this is not an easy task and they need to deal with the equifinality issue. This is an important concept linked to rainfall-runoff models, which means that there might be several acceptable sets of parameters capable of similarly representing different hydrological processes in a basin. According to Beven (2016), there must be parameterizations of the hydrological processes so that hypotheses on them can be assessed in a basin. The level of parameterization is directly related to the model's complexity and equifinality. It should be stressed that the use of a model with greater complexity does not imply in more reliable results, as reported by Grayson et al. (1992). Beven (2016) highlighted that the greater the model's complexity, the greater the number of calibration parameters, but frequently there is no additional data for calibration. Overall, it is important to follow the parsimony principle in hydrological modeling, i.e. the model should represent the behavior of a

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Corresponding author. E-mail addresses: [email protected] (T.L. Caldeira), [email protected]fla.br (C.R. Mello), [email protected] (S. Beskow), [email protected] (L.C. Timm), [email protected]fla.br (M.R. Viola). https://doi.org/10.1016/j.catena.2018.10.009 Received 17 July 2017; Received in revised form 28 August 2018; Accepted 9 October 2018 0341-8162/ © 2018 Elsevier B.V. All rights reserved.

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discretization can exert influence on the representation of parameters and hydrological processes in basins as well as on the calibration and performance of hydrological models. In a 465 km2 basin located in Belgium, El-Nasr et al. (2005) calibrated and validated two hydrological models: a spatially distributed model (MIKE-SHE) and a semi-distributed model (SWAT). The authors found that both models satisfactorily represented the hydrological behavior of the basin, but the distributed model had a slightly better performance. In a basin of 4000 km2, situated in Germany, Singh et al. (2012) analyzed the effect of spatial resolution on the regionalization of parameters of the HBV hydrological model, employing its distributed and semi-distributed versions. The authors concluded that the distributed modeling provided more satisfactory results; also, under the existing data conditions, a better resolution of the model can result in a reasonable description of the processes in ungauged basins. These authors pointed out that the distributed scheme may be more adequate for regionalization due to a more appropriate representation of the processes and greater chance of establishing a better relation between the characteristics of the basin and the model's parameters. Zhang et al. (2013) compared the hydrographs estimated by the BPCC model (distributed scheme) and by the HEC-HMS model (semidistributed scheme) to a hydrograph observed at the basin's outlet (4486 km2), located in a mountain region in China. They concluded that the distributed model presented a better performance. Pignotti et al. (2017) assessed the SWAT model under two spatial discretization schemes in a basin (707 km2) in the USA: based on Hydrologic Response Unit (HRU) and on regular grid cells (SWATgrid). These researchers concluded and recommended that SWATgrid is more indicated for simulation in small watersheds (< 500 km2), as it can take advantage of the detailing and interaction of spatial information. The main objective of this study was to evaluate the effect of two spatial discretization schemes (distributed and semi-distributed) for both representation of input variables and quantification of hydrological processes on the performance of the LASH with respect to the estimation of daily stream flows by using the SCE-UA algorithm for parameter calibration. All the analyses were made taking as reference the Fragata River basin, situated in the south of Rio Grande do Sul State/Brazil.

process or a system by using as few parameters as possible. Several researchers have used such principle to build hydrological models with more simplified approaches such that they avoid or minimize overparameterization and reduce uncertainties (Her and Chaubey, 2015). In order to overcome the intrinsic limitations regarding the availability of spatiotemporal information, especially those related to soil, land use and meteorological datasets, hydrological models that require fewer calibration parameters and input variables have been progressively developed. In this sense, a research team from the Federal University of Lavras (Brazil) and Purdue University (USA) began to develop a conceptual rainfall-runoff hydrological model in 2008 and its first version made available two spatial discretization schemes (lumped and semi-distributed). This was applied by Mello et al. (2008) and Viola et al. (2009, 2012, 2013, 2014, 2015), who reported encouraging results in the study regions. Nonetheless, this model did not have an adequate graphical user interface and the calibration of parameters was performed using a general-purpose algorithm (Lasdon et al., 1978) based on a method named as Generalized Reduced Gradient Nonlinear coupled with lumped and semi-distributed modeling schemes. The second version of the model referred to as Lavras Simulation of Hydrology (LASH) was developed in the form of a computer program and included several adaptations and improvements (Beskow, 2009), allowing the spatial discretization by regular grid cells. Furthermore, the developers implemented an automatic calibration module based on a global optimization method termed as Shuffled Complex Evolution – SCE (Duan et al., 1992). This version was successfully applied in the studies of Beskow et al. (2011a,b, 2013, 2016). The third version of the model (Caldeira, 2016) brought significant computational enhancements associated with the temporal and spatial database processing with the aid of specific modules for the semi-distributed scheme. The hydrologic routine and the automatic calibration module with the SCE algorithm (Duan et al., 1992) were fully adapted to deal with such spatial scheme. However, there is no study on LASH performance for its semi-distributed scheme coupled with the automatic calibration of the parameters using the aforementioned optimization algorithm. In addition, the advantages and disadvantages of the distributed scheme of LASH over its semi-distributed scheme have not been evaluated for a basin yet. The spatial discretization scheme, i.e. distributed, semi-distributed or lumped, represents an important way to differentiate hydrological models (Beven, 2004), as it is related to the scale in which the input variables are considered homogeneous and the hydrological processes are quantified. For distributed models, the spatial discretization of the basin is in a regular cell grid; for semi-distributed, the sub-basins are the analysis units; and for lumped models, the basin as a whole is evaluated. The semi-distributed spatial discretization is the most used scheme for hydrological modeling (Wellen et al., 2015). There are evidences in the literature emphasizing that the level of spatial

2. Material and methods 2.1. Study area and data base The state of Rio Grande do Sul, Brazil (Fig. 1) is divided into three hydrographic regions – the Uruguay River, the Guaíba River and Litoral – segmented into 25 basins. One of these is the transboundary MirimSão Gonçalo basin (MSGB), which has a drainage area of 62,250 km2 and occupies the Brazilian and Uruguayan territory. On the Brazilian

Fig. 1. Location of the study area, in the national and state contexts, and the Fragata River basin (FRB). 184

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and root system depth, which are required by LASH for each land use, were the same as those employed by Beskow et al. (2016).

side, the MSGB stands out as the driving force of the state's rice production, playing a unique role within both economic and social sectors. The main water body of the MSGB is the Mirim lagoon, connecting to the Patos lagoon through the São Gonçalo channel, which is a strategic navigable waterway and an important urban public supply source (Alba, 2010). The Fragata River is an important tributary of the São Gonçalo channel. Upstream from its mouth, the National Water Agency (ANA) maintains a water stage monitoring station referred to as “Passo dos Carros”. As the calibration of hydrological models requires stream flow historical series, the Fragata River basin (FRB) was delineated considering such monitoring station as outlet, totaling 132 km2 (Fig. 1). Relative to the meteorological variables (minimum and maximum temperature, wind speed, relative humidity and insolation), their daily historical series were obtained from three public monitoring stations: two of them belong to the Brazilian Agricultural Research Company (EMBRAPA) – MS01 and MS02, while the other is owned by the National Institute of Meteorology (INMET) – 83895. In addition to MS01, MS02 and 83895, a rain gauge owned by ANA (3152016) was also considered to represent rainfall historical series in the FRB. The definition of the stations was based on the Thiessen polygon method (Thiessen, 1911) and took into account MS01 and 3152016 for rainfall historical series and MS01 and MS02 for the remaining meteorological variables, as only these had influence area within FRB. The topographical information was extracted from the cartographic base of Hasenack and Weber (2010), which was prepared for Rio Grande do Sul State on the 1:50,000 scale. This information was used to derive the 30-m spatial resolution Hydrologically Consistent Digital Elevation Model (HCDEM) (Fig. 2a), with the aid of ArcGIS through a tool named as “Topo to Raster”. The spatial distribution of soil classes (Fig. 2b) was obtained from the Soil Survey of the State of Rio Grande do Sul (BRASIL, 1973) on the 1:750,000 scale. The soil classes existing in the FRB are Hapludalf associated with Udorthent (56.95%), Paleudult (34.29%) and Albaqualf (8.76%). The soil attributes required by LASH, i.e. soil depth (Z) and soil water contents at the point of saturation (θS) and at the permanent wilting point (θPMP), had their values established from Aquino (2014) and also adopted by Beskow et al. (2016). The land use map was obtained through interpretation of Landsat satellite images from 2006 using supervised classification according to the Maximum Likelihood method, as recommended by Richards (2013). Fig. 2c illustrates the land uses identified in the FRB, where one can notice that the land use is predominantly agricultural, having the following classes: pasture (45%), native forest (21%), native grassland (13%), annual crop (8%), silviculture (9%) and perennial crop (4%). The values of albedo, leaf area index, plant height, stomatal resistance

2.2. Spatial discretization LASH is mainly intended to estimate daily stream flows at the basin's outlet or at subbasins' outlets. In addition, it also makes available temporal series of other variables corresponding to various hydrological processes (e.g. evapotranspiration, direct surface runoff, etc.) according to different spatial discretization schemes. From the temporal series of daily stream flows at the outlet (or outlets) of interest and of other processes in the basin, the modeler can afford to use information according to his/her needs. In order to evaluate the impacts of the spatial discretization of the hydrological processes and the LASH's parameterization on the daily hydrograph estimation, two spatial discretization schemes were outlined (Fig. 3): distributed scheme (setup 1) and semi-distributed scheme (setup 2). It is important to mention that the same data bases associated with relief, soil, land use and meteorological and hydrological variables, were used for both setups as previously discussed (see Section 2.1 Study area and data base). Before differentiating the two setups, it should be stressed that the water balance equation (Eq. (1)) is the central concept behind LASH independently of the level of spatial discretization. The soil water storage at time t (At) is the dependent variable, while the independent ones are rainfall (P), capillary rise (DCR), real evapotranspiration (ETR), base flow (DB), subsurface flow (DSS), direct surface runoff (DS) and the soil water storage in the immediate preceding time (At-1). All elements are given in depth (mm). The variable Δt is related to the simulation time step, indicating the time interval in which each process will be quantified.

At = At − 1 + (P + DCR − ETR − DB − DSS − DS)·∆t

(1)

The soil water storage is an essential variable for hydrological simulation, as it exerts influence on the evapotranspiration and on the generation of direct surface runoff, subsurface runoff and base flow. For this study, such variable was calculated from the water balance (Eq. (1)) considering all the other components. Each component listed on the right hand of the Eq. (1) (except At−1) has a specific hydrological routine implemented in the LASH, however, the description of the methodology for estimation of these components is out of the scope of this article. Further details on the formulation of the different hydrological processes simulated by LASH can be found in other studies, as those of Mello et al. (2008), Beskow et al. (2011a) and Caldeira (2016). In this article, LASH was evaluated using a daily time and spatial discretization according to two schemes (setups).

Fig. 2. Hydrologically Consistent Digital Elevation Model (a), soil classes in FRB according to the Soil Survey of the State of Rio Grande do Sul (BRASIL, 1973), and land use classes in the FRB (c). 185

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Fig. 3. Spatial discretization for quantification of the hydrological processes used in the LASH, considering the basin divided into a regular cell grid (setup 1) and subbasins (setup 2).

in the basin. This processing resulted in raster maps corresponding to the soil attributes required by the model, which were directly employed for setup 1 (distributed approach) by Beskow et al. (2016). On the other hand, the average values of Z, θS and θPMP were taken for each subbasin in the setup 2 based on the respective raster map. The 30-m land-use map was used as basis for setup 1 and setup 2 to feed the model with the following vegetation-related parameters: albedo, leaf area index, plant height, stomatal resistance and root system depth. This land-use map along with the values recommended by Beskow et al. (2016) made it possible to generate a raster map for each aforementioned vegetation-related parameter. Such parameters are used in the LASH to model different hydrological processes (e.g. evapotranspiration and interception by land cover), therefore, the way that these parameters are considered might exert considerable impact on the water balance in the basin. All these raster maps containing vegetation information were directly used by Beskow et al. (2016) for the distributed approach (setup 1). For the setup 2, the average value of each parameter was calculated from the corresponding raster map for each sub-basin.

For setup 1, named in this study as distributed scheme, each component in Eq. (1) was quantified on a cell basis within a regular grid covering the basin. In the case of the setup 2 – referred to as semidistributed scheme, the components of Eq. (1) were computed for each sub-basin. It should be pointed out that all the components were updated every day in each grid cell (setup 1) or in each sub-basin (setup 2). This is essential because the model is able to compute the variation of At over space and time and, consequently, to better represent the spatial and temporal behavior of ETR, DS, DSS, DB and DCR. In addition, the routing of surface, subsurface and groundwater flows through the different reservoirs was also conducted with basis on grid cells and subbasins for setup 1 and setup 2, respectively. Briefly, the main difference between setups 1 and 2 is the level of detailing at which the independent variables of Eq. (1) are quantified to determine the dependent variable. In other words, the hydrological processes that occur in the basin are substantially more detailed when they are discretized according to setup 1 (distributed scheme), provided that the area of each cell is smaller than that of the sub-basins (setup 2). This is true in the study case used in this article because the basin was divided into 527 cells of 500 × 500 m (0.25 km2) for setup 1, while 23 sub-basins were delineated with drainage areas ranging from 1.5 to 19.3 km2 in the case of setup 2. With respect to the data bases used for modeling, input information associated with daily historical series of meteorological variables and with relief, soil and vegetation-related variables, were taken for each grid cell (setup 1) or for each sub-basin (setup 2). The Thiessen polygon method (Thiessen, 1911) was the procedure used to define the influence area of each meteorological station within the entire basin. Therefore, the delineation of the influence areas was taken into account to determine the daily mean values for rainfall, maximum temperature, minimum temperature, relative humidity, wind speed and insolation, for each grid cell (setup 1) or sub-basin (setup 2). The HCDEM was used for both spatial discretization schemes to derive values of altitude, which are required by the model for determination of evapotranspiration, however, the use of such values was variable between the schemes. In setup 1, LASH takes the altitude for each grid cell, whereas, the mean altitude is computed in each subbasin considering the values of all the grid cells encompassed by it for setup 2. HCDEM also exerts influence on the time of concentration, which in turn might have impact over routing of surface and subsurface runoff through grid cells and sub-basins. The methodological interpretation for determination of time of concentration in each scheme is analogous to that described for altitudes. Although the information source on soil was identical for both spatial discretization schemes, the extraction of values for the soil attributes required by LASH was particular for each scheme. Soil depth (Z) and soil water contents at the point of saturation (θS) and at the permanent wilting point (θPMP) had their values initially established from the map of soil classes (Fig. 2b) combined with information obtained by Aquino (2014) for these soil attributes under field conditions

2.3. Model calibration and validation For setup 1, we adopted the parameterization of Beskow et al. (2016). The calibration of setup 2 was performed following the same strategy as Beskow et al. (2016): 7 parameters (Table 1) were calibrated in a lumped manner by replacing absolute values and considering the root mean square error (Eq. (2)) as the objective function of the SCE-UA algorithm (Duan et al., 1992). The same methodology for parameter calibration was used to minimize the effect of external sources other than spatial discretization.

RMSE =

1 N

N

∑ (Qobst − Qestt )2

(2)

t=1 3 −1

where Qobst is the stream flow (m ·s ) observed at time t, Qestt is the stream flow (m3·s−1) estimated at time t and N is the number of time steps. As there are uncertainties related to the lack of information on the hydrological conditions at the beginning of the simulation, especially Table 1 Calibration parameters of LASH used in this study.

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Parameter

Description

λ KB KSS KCAP CS CSS CB

Initial abstraction coefficient (dimensionless) Shallow saturated zone hydraulic conductivity (mm·d−1) Subsurface hydraulic conductivity (mm·d−1) Maximum flow returning to soil by capillary rise (mm·d−1) Surface storage response time parameter (dimensionless) Subsurface storage response time parameter (dimensionless) Baseflow recession time (d)

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Fig. 4. Hydrograph observed at the FRB's outlet and hydrographs estimated by the LASH model based on the spatial discretization for setups 1 (Beskow et al., 2016) and 2, considering the calibration period (a) and validation period (b). N

regarding soil moisture, the year of 1994 was used to warm up the model, as also employed by Beskow et al. (2016). The periods considered in this study were 01/01/1995 to 31/12/2000 and 01/01/2001 to 31/12/2008 for calibration and validation, respectively. This study considered the same periods as those defined by Beskow et al. (2016) in order to allow comparisons between the two studies. The authors of the prior study decided to choose these periods because when the study was conducted (2013–2014), the historical series necessary as input in the model – temperature, relative humidity, wind speed, insolation, and rainfall – had no gaps. The validation scheme was based on the Split sample test (Klemeš, 1986), which was proposed for validation of hydrological models for application of stationary processes with calibration and simulation in the same watershed. The Split sample test requires the division of the period in two intervals: one for model calibration and the other for model performance on independent data.

CNS = 1 −

∑t = 1 (Q obst − Q estt )2 N

∑t = 1 (Q obst − Qobs )2

(3)

N

CNS log(Q) = 1 − N

∆Q =

∑t = 1 (log(Q obst) − log(Q obst ))2 N

∑t = 1 (log(Q obst) − (logQ obs ))2

(4)

N

∑t = 1 Q estt − ∑t = 1 Q obst N ∑t = 1 Q obst

·100 (5) 3 −1

where Qobst refers to the stream flow (m ·s ) observed at time t, Qestt is the stream flow (m3·s−1) estimated at time t, Qobs corresponds to the mean observed stream flow (m3·s−1), and N is the historical series length. The CNS (Nash and Sutcliffe, 1970) reflects the efficiency of the model for more accurate estimates when very high stream flows are observed, while the CNS log(Q) reflects the model's ability to estimate stream flows during droughts (Guilhon et al., 2007). The CNS values can range from −∞ to 1, and Motovilov et al. (1999) indicate good adjustment for values > 0.75 and a satisfactory adjustment for values ranging between 0.36 and 0.75. The ΔQ (Eq. (5)) allows analyzing if the model overestimates or underestimates the observed stream flows, such that negative values correspond to underestimations, positive values indicate overestimations and “0” means a perfect fit. According to Van Liew et al. (2003), ΔQ values < 10% represent a very good fit, between 10 and 15%, a good fit, between 15 and 25%, satisfactory, and over 25%

2.4. Analysis of the influence of spatial discretization on stream flow estimation The effect of both the spatial discretization of the hydrological processes and LASH parameterization on the estimation of daily hydrographs was evaluated in this study by means of a comparative analysis between the estimated data and those observed at the FRB's outlet. This analysis included three statistical measures: Nash-Sutcliffe coefficient (CNS) (Eq. (3)) and its version for logarithmized values (CNS log(Q)) (Eq. (4)), and percentage relative error of stream flow estimates (ΔQ) (Eq. (5)). 187

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hydraulic conductivity of the subsurface and groundwater reservoirs, respectively, and are related to the soil type. Their calibrated values (Table 3) differ in magnitude between the setups 1 and 2, especially KSS. Representing the maximum flow returning to soil by capillary rise, the parameter KCAP also varied between the setups (Table 3), depending on the spatial discretization used to quantify the hydrological processes. Its calibrated values were 2.67 mm·h−1 and 0.971 mm·h−1 for setups 1 and 2, respectively. The parameters CS and CSS are related to the time of concentration, reflecting the lag time of each reservoir considered in the model's structure. It is expected that the magnitude of their values varies as the scale is changed. In other words, it is plausible that the values of the time of concentration tend to be smaller when using representation of cells with 0.25 km2 (setup 1) compared to sub-basins with drainage areas ranging from 1.5 km2 to 19.3 km2 (setup 2). Relative to the parameter CB, which corresponds to the lag time of the groundwater reservoir and is particularly important to understand the baseflow behavior, the model calibration for FRB resulted in a value of 49.9 days for setup 1 and 43.07 days for setup 2.

Table 2 Statistical measures for evaluation of the LASH performance considering setups 1 and 2 with respect to spatial discretization. Statistical measure

Nash-Sutcliffe coefficient (CNS) Logarithm of Nash-Sutcliffe coefficient (CNS log(Q)) Estimated stream flow relative error ΔQ (%)

Calibration

Validation

Setup 1a

Setup 2b

Setup 1a

Setup 2b

0.81 0.69

0.74 0.63

0.72 0.83

0.54 0.75

−0.01

−11.48

0.03

−7.39

a Distributed approach in which the input variables and the hydrological processes are quantified in a regular cell grid (Beskow et al., 2016). b Semi-distributed approach in which the input variables and the hydrological processes are quantified in sub-basins.

represent inappropriateness for estimation. These statistical measures were chosen because they allow an analysis wider and more robust on the modeling objectives when applying LASH. In other words, the combination of these statistics enables the modelers to assess the overall representation of the long-term hydrograph, potential for estimation of mean, maximum and minimum stream flows, and under- / overestimation of daily stream flows.

3.3. Influence of the spatial characterization of the basin on the LASH performance for estimation of stream flow indicators The influence of the spatial discretization level on both the representation of the input variables and quantification of the hydrological processes can also be verified by indicators that reflect the hydrological behavior of the basin, such as maximum, average and minimum annual stream flows, water yield and flow-duration curve. With regard to the maximum, average and minimum annual stream flows, it was found that the estimated values for these indicators had good agreement with the observed data (Fig. 5), as they tended to concentrate around the 1:1 line and between the dispersion thresholds represented by the standard deviation. The estimation of average stream flows is of great importance for water resources management. The long-term average stream flow is an indicator commonly associated with water availability that represents the average amount of water available to meet the demand from human activities and preserve the ecosystem (Caldeira, 2016). On evaluating all the period (calibration and validation), the observed water yield in the FRB was 21.8 L·s−1·km−2; whereas, LASH resulted in estimated values of 22 L·s−1·km−2 and 19.7 L·s−1·km−2 for setups 1 and 2, respectively. Fig. 6 illustrates the flow-duration curves considering observed average daily stream flows and values estimated by LASH for FRB based on the two setups of spatial discretization. From the flow-duration curves, it is possible to infer on the stream flows associated with different exceedance frequencies. Also, ΔQ statistic can be derived from estimated and observed stream flows, enabling a better evaluation regarding the fitting of the estimated flowduration curves. Based on these values and the classification indicated by Van Liew et al. (2003), setup 1 had a “very good” fit for quantiles from 10 to 80% and “unsatisfactory” for 90 and 95%, while for setup 2, the adjustment was “very good” for the quantiles of 30 and 40%, “good” for 10 to 20%, “suitable” for 50, 60, 80 and 90%, and “unsatisfactory” for 70 and 95%.

3. Results 3.1. Model performance based on precision statistics The observed and estimated hydrographs for setups 1 (Beskow et al., 2016) and 2 (this study), addressing calibration and validation periods, are depicted in Fig. 4. A visual analysis enables to infer that the LASH was able to capture in both setups the general behavior of the observed hydrograph, which is also confirmed when the statistics presented in Table 2 are analyzed. Considering setup 1, the CNS values were 0.81 and 0.72 for the calibration and validation periods, respectively, whereas these values were 0.74 and 0.54 for setup 2. Estimated stream flow relative errors were substantially lower for setup 1 for both periods. Overall, the statistical measures indicated that the model had superior performance for setup 1 (distributed scheme). 3.2. Parameter calibration considering the setups 1 and 2 The influence of the spatial discretization level of the input variables and hydrological processes is also verified on the values of the LASH's calibrated parameters, which can be analyzed for both setups in Table 3. The calibrated λ values in the FRB were 0.147 and 0.039 for setup 1 and setup 2, respectively. The KSS and KB parameters represent the Table 3 Values optimized by the SCE-UA algorithm for the calibration parameters of the LASH. Parameter

Setup 1a

Setup 2b

λ KB (mm·d−1) KSS (mm·d−1) KCAP (mm·d−1) CS CSS CB (d)

0.147 0.192 2.080 2.670 3389.200 28,216.400 49.900

0.039 0.476 10.777 0.971 43.406 355.047 43.075

3.4. Runoff partitioning It is of great relevance that a hydrological model presents satisfactory performance in accordance with appropriate statistical measures, guaranteeing reliability to the results obtained for a given basin. Nevertheless, the estimation and understanding of the behavior of different runoff components in the basin is as important as an acceptable overall model performance (Beskow et al., 2011b). A summary of the results generated by LASH for FRB is depicted in Fig. 7, demonstrating the performance of the LASH in estimating runoff components when considering setups 1 and 2 for representation of

a

Distributed approach in which the input variables and the hydrological processes were quantified taking as reference a regular cell grid (Beskow et al., 2016). b Semi-distributed approach in which the input variables and the hydrological processes were quantified by sub-basins. 188

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Fig. 5. Maximum, average and minimum annual stream flows observed at the basin's outlet and estimated by the LASH model using setups 1 (Beskow et al., 2016) and 2.

the calibration for setup 1 and “satisfactory” fit for both calibration of setup 2 and validation of setups 1 and 2. According to Mello et al. (2016), the first discussion of LASH's structure led to the conclusion that the major challenge would be to elaborate a model compatible with the reality of developing countries. Brazil can be taken as example, with a coverage of public meteorological and hydrological variables monitoring network commonly insufficient. In addition, soil databases available for some regions in Brazil provide neither a desirable scale nor attributes necessary for the purpose of hydrological modeling. Several studies on the application of hydrological models have employed CNS to evaluate the accuracy of the results. On calibrating and validating SWAT model on a monthly basis for a basin located in the Argentine Pampa region, Havrylenko et al. (2016) obtained CNS values of 0.59 and 0.76, respectively. Fukunaga et al. (2015) found a

input variables and quantification of the hydrological processes. In general, it can be noticed that the estimated stream flows were dominated by direct surface runoff over the years in FRB, corresponding on average to 75% of the runoff when estimated from setup 1, and 76% for setup 2. The base flow and subsurface flow represented on average, respectively, 8 and 17% (setup 1), and 14 and 10% (setup 2). 4. Discussion 4.1. Model performance based on precision statistics According to the classification proposed by Motovilov et al. (1999), the CNS results in both setups (Table 2) suggest that LASH can be used for hydrological modeling in the FRB, since it provided a “good” fit in

Fig. 6. Flow-duration curves observed at the FRB's outlet and estimated by the LASH model using setups 1 (Beskow et al., 2016) and 2. 189

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Fig. 7. Percentage of the runoff components (direct surface runoff, subsurface flow and base flow) over the years used in the calibration and validation of LASH model, considering the setups 1 (Beskow et al., 2016) and 2.

4.2. Parameter calibration considering the setups 1 and 2

CNS value of 0.75 for validation period using the SWAT model on a daily time step for simulation in a Brazilian tropical basin. In the calibration and validation of the DHSVM model in a headwater Brazilian basin, Alvarenga et al. (2016) obtained CNS values of 0.52 for both calibration and validation when evaluating the model on a daily basis; the modeling with monthly time step resulted in CNS of 0.63 and 0.77 for calibration and validation, respectively. In all the aforementioned situations, it was concluded that the models provided good accuracy and could be applied for hydrological simulation in the respective regions, as also indicated by the results obtained for both setups analyzed in this study. Analyzing the CNS log(Q) statistic (Table 2), the classification by Motovilov et al. (1999) indicates a “satisfactory” fit for the calibration and “good” fit for the validation of both spatial discretizations (setups 1 and 2). Such statistic is greatly influenced by recession periods of the hydrographs due to the reduction in amplitude caused by the scale (Viola et al., 2009). Based on this assumption, it can be inferred that LASH: (i) was capable of adequately capturing the hydrological behavior in dry periods for both setups; and (ii) has potential to be used for estimation of minimum stream flows, which are fundamental for water resources management. The ΔQ values (Table 2), analyzed along with the classification of Van Liew et al. (2003), indicate a “very good” fit for setup 1, whereas, setup 2 resulted in fits framed as “good” and “very good” in the calibration and validation, respectively. Although the statistics presented in Table 2 indicate good fits between the hydrographs estimated according to setups 1 and 2 and the observed hydrograph, one can clearly notice that LASH presented better performance when the input variables and hydrological processes were quantified according to setup 1. The same behavior was observed by ElNasr et al. (2005), Singh et al. (2012) and Zhang et al. (2013), when contrasting distributed and semi-distributed spatial discretization schemes through MIKE-SHE, HBV, and HEC-HMS and BPCC, respectively. This behavior might be attributed to the level of spatial discretization and can be elucidated by taking sub-basin 1 as an example: LASH represented all the input variables and estimated each component of the water balance (Eq. (1)) on a daily basis considering a homogeneous area of 18.3 km2. This means that each input variable (soil moisture at saturation and permanent wilting points, leaf area index, meteorological variables, etc.) and each component of the water balance (soil water storage, capillary rise, real evapotranspiration, etc.) was represented by a unique value in this area. In the distributed approach, the same sub-basin was represented by 70 cells of 500 × 500 m (0.25 km2), that is, 70 times more detailed when compared to the semidistributed scheme.

Parameter λ corresponds to the initial abstraction coefficient used in the Modified Curve Number method (Mishra et al., 2006) to estimate direct surface runoff – portion of the runoff yielded by rainfall excess that flows on the ground, responsible for the rapid stream flow increase in rivers. This parameter is directly related to water losses that occur before the generation of direct surface runoff. SCS (1971) recommends that λ = 0.2, which implies that the initial abstractions are equivalent to 20% of the potential maximum retention (S parameter). However, λ values can be variable depending on the basin to be assessed, especially because of the differences in climate, rainfall pattern and soil moisture conditions (Mishra et al., 2003), thereby justifying its calibration. Based on the calibrated values (Table 3), the beginning of direct surface runoff was delayed for setup 1 when compared to setup 2 because of the greater value found for the former setup, leading to greater initial abstraction values. The difference between KSS and KB found for the studied setups (Table 3) seems to be small when compared to the results reported by Beskow et al. (2011b). These authors evaluated the distributed modeling scheme of LASH for hydrological modeling in a basin of 32 km2 with the predominance of Latosols, and found calibrated values of 182.15 mm·day−1 and 3.18 mm·day−1 for KSS and KB, respectively. To better illustrate this issue, the hydrological classification of Brazilian soils (Sartori et al., 2005) can be taken into account, allowing classifying the basin analyzed by Beskow et al. (2011b) as groups A or B. This categorization (A or B groups) represents low to moderate direct surface runoff potential, while FRB is framed as D group, in other words, its soils have high direct surface runoff potential and very low infiltration rate. Additionally, it should be highlighted an analysis of soil saturated hydraulic conductivity (KSAT) in the two basins: Alvarenga et al. (2011) obtained KSAT values ranging between 61 and 146 mm·h−1 for the basin analyzed by Beskow et al. (2011b), while Aquino (2014) found a mean value of 18 mm·h−1 for FRB. Based on the classification of KSAT values for Brazilian soils proposed by Pruski et al. (1997), FRB is classified as a basin with below average infiltration capacity, having potential to generate above average direct surface runoff. Although the KSS values were not the same for setups 1 and 2 (Table 3), the calibration reflected a very similar hydrological behavior, with no effect of the spatial discretization on the hydrological processes. It should be stressed that a soil map (Fig. 2b) on 1:750,000 scale was used in this study for both setups associated with LASH. It is expected that the use of a soil map with higher spatial resolution will result in more pronounced differences regarding representation of the input variables, quantification of the hydrological processes and calibration parameters between the two spatial discretization approaches. This is a 190

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difficulties related to computational restrictions. Furthermore, the calibration of distributed parameters is a time consuming task and preferably should make use of observed data within the basin, which are generally scarce (Ajami et al., 2004), as identified in the present study. The authors consider that the calibration scheme for LASH is an important issue that should be addressed and has therefore a broad field for investigation in future studies.

typical problem found by modelers in which the level of detailing for several parameters is commonly not compatible with their application in the hydrological modeling (Grayson et al., 1992). CB parameter can be calibrated or derived from the analysis of a recession period of the observed hydrograph, as employed by Beskow et al. (2011b) and Viola et al. (2013). Nonetheless, CB may present high variability due to the used recession period. Values of CB were calculated from different recession periods identified in the historical series at the FRB's outlet, allowing concluding that the longest recession period culminated in CB equal to 35 days. Given that this value greatly depends on the experience of the hydrologist regarding the recession period that will be used, the calibration of this parameter can reduce likely uncertainties, as the model considers the entire observed data period, tending to minimize the error. Thus, it can be stated that the small difference between the values calibrated according to setups 1 and 2 (Table 3) suggests a similar hydrological behavior. As LASH employs an optimization algorithm to seek for ideal values for the calibration parameters, it is necessary to mention that rainfallrunoff hydrological models do not provide a unique solution capable of satisfying the modelers in terms of accuracy in simulation. This issue is referred in the literature as to equifinality, as previously discussed. Detailed studies on sensitivity and uncertainty analysis of the LASH have indicated the use of six (Beskow et al., 2011a) or seven parameters (Viola et al., 2013) for the model calibration. The present study followed the guidelines recommended in the cited studies for parameter calibration. As LASH has a lower number of both calibration parameters (Table 1) and input variables, and less complexity than other hydrological models (Mello et al., 2016), it is hoped that the model will be less subject to the equifinality issue. Furthermore, this tends to minimize over-parameterization and reduce uncertainties, as pointed out by Her and Chaubey (2015). It is worthwhile to discuss about the calibration strategy adopted in this study in relation to what has been found in a broader literature. According to Ajami et al. (2004), rainfall-runoff models with distributed approaches have a substantial increase in the number of parameters to be estimated through calibration when compared to those with lumped schemes. Even though distributed models consider parameters in a distributed manner over the basin, Beven and Binley (1992) reported that the over-parameterization due to the great amount of distributed information, along with limitations of data sets, might result in inadequate solutions. Furthermore, Ajami et al. (2004) highlighted that the use of distributed parameters does not necessarily reflect in the improvement of the model performance, especially if there is not additional observed stream flow data in other sites inside the basin to be used for calibration. A lumped calibration strategy was applied in the present study for distributed and semi-distributed spatial discretization schemes. Thus, the better results for setup 1 (Table 2) cannot be attributed to the calibration strategy, i.e. this occurred due to the more detailed representation of the basin through input variables and their interaction, thereby making the estimation of the components of the water balance more accurate over time. The semi-distributed scheme (setup 2) allows a distributed calibration of unknown parameters, that is, different values are assigned to the parameters taking the sub-basin as reference for analysis. Setup 2 would result in the optimization of 161 parameters (7 parameters × 23 sub-basins), but the authors considered that this would be an inappropriate option as it would demand a high computational effort to the calibration algorithm. In the case of the distributed scheme (setup 1), this calibration strategy tends to be computationally infeasible. This discussion on calibration schemes goes along with the findings of Pignotti et al. (2017), who evaluated the SWAT model through its distributed and HRU schemes. These authors concluded that given computational constraints for the distributed scheme, SWATgrid currently does not enable direct calibration. Instead, Rathjens and Oppelt (2012) suggested another calibration strategy for SWATgrid based on the transference of parameters from HRU scheme in order to minimize

4.3. Influence of the spatial characterization of the basin on the LASH performance for estimation of stream flow indicators Analyzing the annual minimum stream flows (Fig. 5), 2/3 of the estimated values from setup 2 (semi-distributed scheme) were closer to those observed when compared to the estimated values from setup 1 (distributed scheme). This trend was not noticed in the case of average and maximum annual stream flows (Fig. 5), as these indicators were closer to those observed for setup 1. It should be highlighted that there were many years in which minimum stream flow in the distributed modeling scheme significantly exceeded the value corresponding to the semi-distributed scheme. This behavior may be partially attributed to the calibration process because RMSE is an objective function that guides the search in calibration for sets of parameters that are more important for a satisfactory estimation of mean and high stream flows. Nonetheless, the influence of the objective function on the hydrological modeling with LASH is out of the scope of this article. The results associated with estimation of water yield corroborate the statistics presented in Table 2, since the hydrograph estimated based on setup 1 (Fig. 4) presented more accuracy. Nevertheless, when the ΔQ statistic was analyzed, both setups had a “very good” fit because the difference between the observed and estimated water yield was < 10%. The flow-duration curve estimated by LASH from the setup 2 was underestimated for calibration and validation periods (Fig. 6). However, there was overestimation of the quantiles > 90% and 82% for calibration and validation, respectively, as well as in the observed maximum stream flow for the validation period. On the other hand, the flow-duration curve estimated by the LASH for setup 1 was closer to that observed, but overestimates were also identified in the low stream flows and in the maximum observed stream flows for the validation period. LASH has been evaluated in the southeastern Brazil regarding its accuracy in generating the flow-duration curve (Viola et al., 2009, 2013; Beskow et al., 2013). These researchers also reported an acceptable accuracy for estimating this important hydrological function, employing the semi-distributed scheme in the first two studies and the distributed scheme in the third study. On comparing the two spatial schemes in the present study (Fig. 3), it was found that the distributed modeling culminated in slightly more satisfactory results, except for low reference stream flows (Q90% and Q95%), which were better estimated by the semi-distributed modeling scheme. 4.4. Runoff partitioning A great potential for generating direct surface runoff was observed in this study for FRB (Fig. 7), which is supported by the hydrological behavior of the Brazilian soils (Sartori et al., 2005). This may be attributed to a combination of low soil saturated hydraulic conductivity (KSAT), predominance of pasture in the basin and of frontal rainfall events (Beskow et al., 2016). It is also important to emphasize the considerable portion of subsurface flow (Fig. 7). According to Beskow et al. (2011b), this component may be negligible in many basins, but it can be critical when evaluating forested basins, headwater basins and basins with soils of contrasting textures between A and B horizons (soils with Bt horizon). The results found for this runoff component corroborate the conclusions of Beskow et al. (2011b), since FRB has a forested area of approximately 191

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it is important to highlight that the LASH was applied to other basins under different geomorphological characteristics, such as soil type, relief, land use and climate, and it provided satisfactory performance for distributed and sub-basin schemes. Nevertheless, these spatial discretization schemes have not been evaluated for the same basin yet. Future insights about LASH are encouraged towards different spatial scales, such as a calibration based on Hydrologic Units (combination of soils, topography and land-uses) seeking to better represent the parameters over space. This will not be a simple task, however, it could be an important novelty, especially for LASH which is based on a fewer number of parameters than other models available in the literature.

30% (native and silviculture) and soils predominantly with Bt horizon. Although the results depicted in Fig. 7 cannot be assessed for accuracy – as there is no measured data for each runoff component in the FRB – it should be verified whether they are consistent with the characteristics of the basin. Analyzing the values of the calibration parameters for the LASH (Table 3), runoff partitioning and basin characteristics, especially the soil type and land use, it can be inferred that the model had potential to represent the hydrological behavior of the FRB. 4.5. Spatial discretization scheme in the LASH – distributed versus semidistributed

5. Conclusions

The best performance of the LASH was generally observed when the input variables and hydrological processes were quantified in a distributed manner (Table 2), however, the choice of a specific type of spatial discretization depends on the modeling purposes. This finding regarding spatial discretization goes along with that of other researchers who assessed different hydrological models (El-Nasr et al., 2005; Pignotti et al., 2017; Singh et al., 2012; Zhang et al., 2013). One of the strengths of the LASH under its distributed scheme (setup 1) over the semi-distributed scheme (setup 2) is the way in which the input variables are represented in the basin and how these variables interact with each other. According to Zhang et al. (2013), distributed schemes allow for the models to better understand the spatial variation of meteorological variables and physical parameters. Pignotti et al. (2017) mentioned that distributed approaches are especially useful for hydrological simulation in small watersheds where the detailing and interaction of spatial information can be further investigated due to the higher level of detailing for the quantification of the hydrological processes (Beven, 1985). It should be taken into account that distributed approaches demand more computational cost (Arnold et al., 2010). In the case of this study with LASH, 527 grid cells were considered for representation of the basin in setup 1 against 23 sub-basins in setup 2; therefore, the computational cost of the setup 1 was approximately 23 times as much as that for setup 2. Nonetheless, Zhang et al. (2013) stress that models with distributed approaches do not necessarily result in better performance for simulation of hydrological processes than those with semi-distributed approaches. Because of the aforementioned discussion, the semi-distributed modeling scheme is the most used for hydrological modeling (Wellen et al., 2015). It is known that semi-distributed models (setup 2) might not adequately represent the real basin conditions because they consider average values within each sub-basin for parameters associated with land cover and soil type (Zhang et al., 2013). Koren et al. (2004) emphasized that semi-distributed schemes have potential to improve the estimation of hydrographs at the basin outlet. In addition, these authors stressed that another advantage of such scheme is that it enables estimations of hydrographs at other sites (e.g. tributaries) within the basin where observed historical series are not available. This advantage also applies to the LASH through its semi-distributed scheme (setup 2), as it allows estimation of the hydrograph for each sub-basin. It is greatly pertinent for hydrologists to analyze these hydrographs due to the lack of stream flow data in the sites of interest, mainly in small basins, thereby making it possible to estimate stream flows for upstream tributaries. From the point of view of water resources management and hydraulic structure designs, the semi-distributed scheme would be a suitable alternative in this case in spite of not having provided results as satisfactory as the distributed scheme. Considering the rainfall-runoff model used in this study, as well as the methodology and interpretation and discussion of results, some limitations should be listed: (i) the simulations and analyses were conducted for just one basin; (ii) the scale of some input information, especially the coarse scale of the soil map and small number of meteorological monitoring stations available for the basin; and (iii) calibration schemes evaluated for the model. Relative to the first limitation,

This study pioneered the assessment of the influence of two spatial discretization schemes – distributed (setup 1) and semi-distributed (setup 2) – for representation of input variables and quantification of hydrological processes on the performance of the LASH to estimate daily hydrographs. The main conclusions are: i) Both setups had the model's parameters calibrated by the same global genetic optimization algorithm in accordance with a lumped approach. Based on statistical measures for appraisal of the main hydrological indicators, the best results were obtained for the setup 1. However, the setup 2 resulted in satisfactory results, meaning that this spatial discretization scheme can also be employed by LASH users; ii) LASH (both setups) was able to adequately estimate daily stream flows, minimum, average and maximum annual stream flows, flowduration curve and water yield. On assessing the values for the calibration parameters for both setups, especially those related to soil type and land use, and the runoff components, it is possible to conclude that the model presented potential to suitably represent the hydrological behavior of the studied basin; iii) A better performance of the LASH through its distributed scheme can be especially attributed to the spatial discretization of input variables and quantification of hydrological processes, which were more detailed. It is expected that the application of a more refined soil map will imply in greater differences between the setups with respect to the representation of input variables, quantification of hydrological processes, calibration parameters and model performance; iv) A more simplified approach of LASH provided results as accurate as other models reported in the literature, which have more complex structurations. Furthermore, LASH is less prone to the equifinality, resulting in the minimization of over-parameterization and reduction of uncertainties; v) Although the distributed scheme of the LASH has outperformed its semi-distributed scheme, it should be taken into account that the former demands more computational cost, i.e. setup 1 demanded computational cost 23 times as much as setup 2. This difference can be increased depending on the delineation of sub-basins, definition of cell size and the basin area.

Acknowledgements The authors wish to thank Coordination for the Improvement of Higher Education Personnel - Brazil (CAPES) - Finance Code 001 for scholarship to the first author, to National Council for Scientific and Technological Development (CNPq) for scholarships to the second (301556/2017-2), third (308645/2017-0), fourth (305820/2015-0) and fifth (305854/2015-1) authors, and to Foundation for Research Support of Rio Grande do Sul State (FAPERGS)/CNPq (16/2551-0000 247-9) for research grant to the third author. 192

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