Hydrological Modeling - TOPMODEL
Applicability of TOPMODEL in the mountainous catchments in the upper Nysa Kłodzka River basin (SW Poland)
Justyna Jeziorska, Tomasz Niedzielski
Discharge and water level predictions play a crucial role in water management in flood-prone areas. River basins located in the Central Sudetes mountain ranges (SW Poland) demonstrate a high vulnerability to flooding. We have chosen four basins and the corresponding outlets in the upper Nysa Kłodzka River basin in Kłodzko Land (SW Poland) for modeling the streamflow dynamics using TOPMODEL, a physically-based semi-distributed topohydrological model. The model has been calibrated using the Monte Carlo approach – with discharge, rainfall and evapotranspiration data used to estimate the parameters. The overall performance of the model was judged by interpreting the efficiency measures, with the emphasis put on the Nash Sutcliffe Efficiency (NSE). Despite relatively simple structure, TOPMODEL was able to reproduce the main pattern of the hydrograph with acceptable accuracy for two of the investigated catchments. However, it failed to simulate the hydrological response in the remaining two catchments. For the best performing data set – i.e. gauge in Bystrzyca Kłodzka for hydrological year 2011 – we obtained NSE of 0.78. This data set was chosen to conduct a detailed analysis aiming to estimate the optimal time span of input discharge /rainfall /evapotrasporation data for which TOPMODEL performs best. It was found that it is difficult to unequivocally determine such an estimate, however, the longer time span is the better model performance occurs. The best fit was attained for the half-year time span. When winter season was excluded from the analysis the model skill was found to increase, without changing the half-year window.
1. Introduction
Better understanding of watershed dynamics is one of the key factors in solving water-related scientific and practical problems. This role becomes crucial for effective planning and management of water resources (Beven and Freer, 2001a; Bastola et al., 2008) in areas endangered by extreme hydrological events. Key variables influencing the hydrological response of the catchment need to be estimated based on data recorded on gauges, and the limitations occur when data are poor or insufficient. Thus, the hydrological modeling of water cycle components is the essential tool which becomes necessary for extending hydrological data both in space and time (Bastola et al., 2008). Many researchers attempted to develop solutions that would model the complexity of processes and heterogeneity of factors influencing the hydrological system dynamics. The availability of spatial characteristics of the catchment, that rose with the advent of Geographic Information Systems (GIS), shifted the research interests from traditional lumped models towards more complicated, distributed ones. The advantage of the latter is the possibility of having a spatial pattern of the modeling outputs, such as soil moisture or saturation zone extent (Sun and Deng, 2004). In contrast, the lumped models treat the catchment as a single unit and do not account for heterogeneity and spatial variability of catchment components across the whole investigated watershed. Thus, they can provide only spatially averaged values of water cycle elements at the outlet of the catchment. Some parameters of lumped models have no physical meaning (Sun and Deng, 2004; Sigdel et al., 2011), and their estimation requires long-term discharge observations in the stable catchment conditions (Sun and Deng 2004). However, distributed models require much more computational power to produce predictions, and the extended knowledge about the actual hydrological processes is also intrinsic to properly use a distributed model (Yu et al., 2001). Associated with this is usually a need for estimating a large number of parameters (physically measurable attributes of a catchment). One of the semi-distributed and physically-based conceptual models is the TOPography-based hydrological MODEL, known also as TOPMODEL (Beven and Kirkby, 1979; Beven et al., 1995; Beven and Freer, 2001a). It combines the advantages of two above-mentioned approaches. The number of parameters is reduced, but they maintain their physical interpretation. Simplified model structure diminishes the data requirements. Thus, this conceptual model integrates the ability to simulate the spatial distribution of its results at any time step (Choi and Beven, 2007) with the computational efficiency that allows multiple simulations (Peters et al., 2003). These features contribute to the model popularity and successful applications in numerous studies. Furthermore, recent increase of the TOPMODEL application is caused by access to more detailed data describing the watershed characteristics.
According to Beven et al. (1995), the TOPMODEL concept should not be considered as a hydrologic modeling package, but rather as a set of conceptual tools that can describe the catchment behavior. Hence, since its introduction in 1979 (Beven and Kirkby, 1979) many versions have been developed and numerous studies have applied the TOPMODEL approach to a wide range of hydrology-related topics. The research problems investigated with the use of TOPMODEL include: flood frequency analysis (Beven, 1986; Cameron et al., 1999), scaling theory in hydrology (Wood et al., 1988), examination of the influence of the Digital Elevation Model (DEM) resolution on the simulation results (Brasington and Richards, 1998), analysis of climate change scenarios (Romanowicz, 2007), water table estimation (Merot et al., 1995; Moore and Thompson, 1996; Lamb et al., 1997), testing the applicability to water quality problems (Wolock et al., 1990; Robson et al., 1992), and uncertainty analysis (Freer et al., 1996; Choi and Beven, 2007; Bastola et al., 2008; Fisher and Beven, 1996).
Although the initial TOPMODEL applications concentrated on examining the catchment dynamics in the humid temperate climate zone in the UK (Beven and Kirkby, 1979; Beven et al., 1984; Quinn and Beven, 1993), in the eastern USA (Beven and Wood, 1983; Hornberger et al., 1985), the capability of providing good simulation results have been proven in the variety of environments in basins all over the globe. TOPMODEL has been successfully used in temperate cold climate in Norway (Lamb et al., 1997), as well as in the Alaska tundra (Ostendorf and Reynolds, 1998). Furthermore, the model performance has been investigated in drier Mediterranean regimes (Durand et al., 1992; Piñol et al., 1997), and in the monsoon region of China (Chen and Wu, 2012). The research was also carried out in the humid temperate (Cameron et al., 1999; Bárdossy, 2007; Choi and Beven, 2007; Furusho et al., 2014) and Mediterranean (Gallart et al., 2008) climate zones. TOPMODEL has also been successfully utilized in the tropical climate zone in French Guiana (Molicova et al., 1997) and within the same climate zone, but in its antipodes, in one of the most hydrologically-responsive forested headwater catchments, in Maimai in New Zealand (Freer et al., 2003). Sigdel et al. (2011) applied the model to watersheds in the Bagmati River basin in Nepal. It is worth noting that many researchers focused their studies on the TOPMODEL applications in the Nepal region: Brasington and Richards (1998) applied the TOPMODEL to a small headwater catchment in the Nepal Middle Hills, Shrestha et al. (2007) investigated its performance in different physiographic regions of Nepal, and Bastola et al. (2008) conducted a comparative study of 26 catchments across the globe, including 4 basins in Nepal. The vast majority of the TOPMODEL applications concerns small or medium size catchments (up to several dozen of square kilometers), however, the model demonstrated good performance for: very small basins of 0.75 ha (Lamb et al., 1997) and of 1.57 ha (Molicova et al., 1997) as well as very large basins of over 25 000 km2 (Sun and Deng, 2004; Chen and Wu, 2012). High attention has been paid to the TOPMODEL capability of rainfall-runoff modeling in the mountainous regimes. Holko and Lepistö (1997) applied the model to the Jalovecky Creek catchment in Western Tatra Mountains, Blazkova and Beven (1997) investigated mountain wetlands in the Czech-Moravian highlands and the research area for Nourani and Mano (2007) was watershed located 800–2178 m a.s.l. in the western Iran.
The model has been successfully applied to several catchments in Central Europe. Emphasis should be placed on the above-mentioned research of Holko and Lepistö (1997), focusing on the mountainous watershed in Slovakia, and on the investigation by Bárdossy (2007) into 16 lowland catchments in the German part of the Rhine basin. Even though these studies demonstrated good modeling results, the model performance has never been tested in SW Poland. In order to fill this gap and fulfill a need of detailed analyses of the model in a variety of environments, postulated by Durand et al. (1992), in this study the TOPMODEL is applied to a few medium-size catchments in the flood-prone areas of the Sudety Mountains in SW Poland. Hence, the aim of the modeling experiment was to test the applicability of the TOPMODEL for the purpose of discharge simulation at the outlets of four contributing catchments of Nysa Kłodzka River (gauges: Bystrzyca Kłodzka, Kłodzko, Bardo) and the river of Biała Lądecka (gauge: Żelazno). In addition, we aim to estimate the time span of data (discharge/rainfall/evapotranspiration) for which the TOPMODEL performance is optimal.
The paper is organized as follows: the next section presents a simplified description of the model (its concept and features), based on the extended explanations of TOPMODEL theory given by Beven and Wood (1983) and Beven (1986). The second section also contains overview of methods used for the model assessment. The study area is presented in the third section, followed by the fourth section that focuses on description of data used in the research. The results of land surface parameterization, model calibration, sensitivity analysis and validation of the TOPMODEL for four contributing basins located within the upper Nysa Kłodzka basin (SW Poland) are included in the fifth section. They are concluded in the last section, which also offers an overview of potential future research activities.
2. Methods
2.1. Concept of TOPMODEL
The idea that runoff is primarily a result of overland flow generated by rainfall when infiltration capacity of the soil is exceeded is known as Hortonian theory of infiltration excess overland flow. However, in recent studies it is commonly superseded by the contrary concept that emphasizes the significance of saturation-excess overland flow and subsurface runoff generation. On the contrary to the Hortonian concept, stating that the occurrence of surface overland flow is possible when the soil is not fully saturated, the saturated-excess overland flow theory assumes that the overland flow is generated when the soil is fully saturated to the surface or if subsurface flow returns to the surface in saturated areas (Nourani et al., 2011). Among different applications of this concept in hydrological modeling, one of the most widely used is TOPMODEL (Beven and Kirkby, 1979; Beven, 1997; Beven and Freer, 2001a). The predominant factors influencing the discharge generation in the model are topography of the basin and soil characteristics (Franchini et al., 1996). The topography is quantitatively expressed by the topographic index (also known as Topographic Wetness Index, TWI). Its value is computed from the basin topography using the following expression:
where ai is the upslope contributing area of i-th basin, tan βi is slope of the ground surface of this basin.
Upslope contributing area (Fig. 1) represents the area that can potentially produce runoff to the location of interest, i.e. to the outlet from the contributing basin (Erskine et al., 2006). In the raster representation of the terrain, it should be replaced by the upslope drainage area per unit of contour length (Moore and Wilson, 1992; Moore and Burch, 1986; Desmet and Govers, 1996), which is equivalent to DEM grid cell size (Mitasova et al., 1996). Areas associated with high TWI values tend to saturate first and will therefore constitute potential subsurface or surface contributing areas (Gumindoga and Webster, 2010; Beven, 1997).
TWI refers to variable source area concept of runoff generation (Hewlett and Hibbert, 1967) and is based on the following three simplifying assumptions regarding the hydrologic system (Nourani et al., 2011; Gumindoga and Webster, 2010; Brasington and Richards, 1998; Beven et al., 1995; Holko and Lepistö, 1997):
dynamics of the saturated zone can be approximated by successive steady-state representations;
hydraulic gradient of the saturated zone can be approximated by the local surface topographic slope (tan βi), thus the groundwater table and saturated flow are parallel to the local surface slope;
distribution of downslope transmissivity with depth is an exponential function of storage deficit or depth to the water table.
This approach implies that all points with the same value of TWI respond in the same way (Fisher and Beven, 1996). Calculations need to be performed only for representative values of the index, what greatly simplifies the procedure and reduces the computational cost while maintaining the capability of the identification of water table levels and soil moisture within the catchment (Chairat and Delleur, 1993; Fisher and Beven, 1996). The results may be mapped back into space using knowledge of the pattern of TWI derived from a topographic analysis (Beven, 1997).
Sigdel et al. (2011) pointed out that the above assumptions may be valid for small and medium catchments, with shallow soils and moderate topography, which do not experience excessively long dry periods. The quasi-steady state dynamics concept has been criticized (Barling et al., 1994; Beven, 1997; Peters et al., 2003), and it cannot be always safely accepted (Beven, 1997).
The extended interpretation of the TOPMODEL theory is given by Beven and Wood (1983) and Beven (1986).
2.2. Key features of TOPMODEL
According to the TOPMODEL concept, there are two main factors that account for runoff generation, namely the catchment topography and the transmissivity that diminishes with depth (Beven and Kirkby, 1979). A soil column in TOPMODEL is defined as a set of three stores: root zone, unsaturated zone and saturated zone. They behave like three interdependent repositories (Fig. 1). Rainfall infiltrates the superior layer, root zone, until its storage capacity is reached. An additional component, the interception storage, needs to be added, where the surface is covered by the forest canopy. The root zone can be depleted at the linear rate by the actual evapotranspiration from the surface, described by the following formula (Sigdel et al., 2011):
where Ea is actual evapotranspiration, Ep is potential evapotranspiration, Srmax is maximum root zone deficit and Srz is root zone deficit.
After infiltration, the excess water reaches the unsaturated zone with a delay, fills this reservoir and recharges the saturated zone – the water table rises, reducing the distance
between ground and the saturation zone. According to the first TOPMODEL assumption, the local water table depth is represented by local storage deficit _ , which can be calculated for the each TWI class using the following formula (Wu et al., 2007):
where Di is mean storage deficit (catchment average water table depth), __
is average TWI, and m is scaling parameter.
The water table touches the ground surface when the storage deficit _ = 0. Thus, the value of average TWI for which Di = 0 constitutes the threshold for maximum storage capacity and each point that has greater TWI value is considered to be in the saturated condition. Any further rainfall falling onto these saturated surfaces cannot infiltrate and the excess water is directly transferred into saturated overland runoff.
The other process that accounts for the total surface flow Qs is the infiltration excess flow fex that is generated when the precipitation intensity exceeds the infiltration capacity (Taschner, 2003), and Qs and fex are interrelated in the following way:
for which
where q0 is overland runoff, P0 is precipitation per unit width, Pi is precipitation infiltrated into the soil in the i-th unit, Suz is local water storage in the unsaturated zone.
The water storage deficit is reduced by the recharge water flux from the unsaturated zone to groundwater, and its rate can be calculated using the formula (Sun and Deng, 2004):
where Di is the local storage deficit (local water table depth), Td is the mean residence time in the Suz.
Hence, the total recharge rate Qv is expressed as the sum of all values of qv multiplied by the upslope area Ai representing a set of hydrologically homogenous points, associated with topographic index class of the i-th location (Peters et al., 2003), namely the following expression holds:
where Qv is total flux, _ is the flux of water entering the water table locally (per unit area), Ai is area associated with topographic index class.
The base flow Qb is represented as the subsurface saturated zone flux qs, and can be defined by:
where Q0 is the hydrological flux for the entire catchment area when _ = 0. Both above described components – surface flow Qs and base flow Qb account for the total discharge.
Thus, following the TOPMODEL concept, the total runoff at the river outlet of the catchment, expressed as the sum of surface and base flow, can be calculated for each time step.
The downslope transmissivity T, according to the third TOPMODEL assumption, diminishes with depth following the negative exponential law versus saturation deficit _ with m being a recession parameter (Sigdel et al., 2011):
where T0 is the local saturated transmissivity.
2.3. Model performance measures
Assessment of the efficiency of the hydrological model is necessary not only for the estimation of its ability to reproduce catchment behavior, but also for modifying model structure. Apart from the subjective visual inspection of the simulated and observed hydrographs, there are numerous statistical measures which can be used for hydrological model assessment (Krause et al., 2005). In this study, three model performance measures have been chosen: Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Nash Sutcliffe Efficiency (NSE). The latter was created specifically to assess hydrological models (Nash and Sutcliffe, 1970) and can be calculated using the formula:
where Qobst is observed discharge, Qsimt is simulated discharge at time step t, and N is number of observations/simulations.
Although its value has been questioned (Criss and Winston, 2008), it is still most widely used criterion for evaluating TOPMODEL performance (Beven and Binley, 1992). The main critic relates to its sensitivity to extreme values and, since the hydrological data often contain outliers, the measure can be misleading. Values of NSE vary from –∞ (strong misfit) to 1 (perfect fit), and the situation NSE = 0 occurs when model predictive skills are similar to performance of extrapolated mean of observations.
3. Study area
The TOPMODEL performance was investigated using data from four gauges located in the Sudety Mountains in upper Nysa Kłodzka basin (SW Poland and the border region of Czech Republic). The following reasons led to the choice of the study area.
The present research is associated with the HydroProg system (Niedzielski et al., 2014) in which TOPMODEL is used for predicting river stages in real time.
Rainfall and water level data sets are available, and the access to date is courtesy of the authorities of Kłodzko County, the owner of the Local System for Flood Monitoring (Lokalny System Osłony Przeciwpowodziowej, LSOP).
TOPMODEL has not been applied in the upper Nysa Kłodzka basin so far.
TOPMODEL has been already shown to work well in small mountainous catchments in different parts of the world (i.e. Bastola et al., 2008; Cameron et al., 1999).
The Sudety Mountains are a medium-high mountain range spread along the Polish-Czech boundary in Central Europe. A maximum elevation of the mountains is equal to 1603 m a.s.l. Sudety Mountains are an example of fault-block mountains which are characterized by fault-generated mountain fronts and structural basins attributed to up- and downfaulting in the late Cenozoic (Migoń and Placek, 2014). Diverse tectonic structure is additionally enhanced by the lithological complexity. Highly complex and diversified landscape is a result of the mosaic of underlying geology and its polygenetic origin (Wieczorek and Migoń, 2014). The structure has also significant impact on extreme events: meteorological, hydrological and geomorphological ones (Migoń, 2010). Large elevation differences strengthen foehn effects and reinforce orographic rainfall that can lead to flood wave formation in mountainous steep-slope streams (Migoń, 2010).
The main river of the study area is Nysa Kłodzka, the left tributary of the Odra River. It is characterized by rapid water supplies in the spring and summer as the result of concentric arrangement of numerous tributaries, which are mostly mountain streams. Tab. 1 juxtaposes main characteristics of the studied basins, along with mean discharges measured at four outlets under study. Three of the investigated basins have outlet located along Nysa Kłodzka. The largest one, with the area of 1744 km2, is the contributing basin above the gauge in Bardo. Further southward, 16 km upstream, located is the Kłodzko gauge which closes the second biggest of the investigated basins. The smallest one, still located along Nysa Kłodzka, is the basin above the gauge in Bystrzyca Kłodzka, with the area of nearly 260 km2. However, the Żelazno gauge is located along Biała Lądecka which is the longest right tributary of Nysa Kłodzka in the study area. The contributing basin above Żelazno is a subcatchment of Bardo and Kłodzko basins.
The study area belongs almost entirely to Poland, only the NW parts of the Bardo catchment belongs to Czech Republic. That division makes the data related to geographical characteristics of the entire investigated area (i.e. soil cover, land use) not compatible due to different national classification criteria. Thus, the detailed statistical data, that can be assumed as representative for the study area, are available for Kłodzko County which is the administrational unit covering 84.17% of the area of interest.
The topography of the research area, i.e. Kłodzko Valley and the upper Nysa Kłodzka basin surrounded by mountain ranges, is responsible for its distinct microclimate. Although the investigated catchments, as the entire Sudety Mountains, are located in the cool temperate climate zone with marked maritime influences (Schmuck, 1969), diversity between the main climate components is noticeable. Average annual air temperature calculated for the entire area of Kłodzko County is 6.3ºC (Geographic Characteristic of Counties, 2004). Allowing for the temperature drop with altitude, it is lower than 1ºC at the summits (Waroszewski et al., 2013). In contrast, in Kłodzko Valley (most of Bystrzyca Kłodzka and Żelazno subcatchments) the annual average temperature rises to approximately 7.4ºC (Schmuck, 1969). The altitude influence is also clearly seen in the annual precipitation sums, which vary from 590 mm in the lower parts of Kłodzko Valley to about 1500 mm at the summits (Godek et al., 2015). The mean annual precipitation rate calculated for the entire county is 803 mm (Geographic Characteristic of Counties, 2004), distributed evenly throughout the year (Latocha and Migoń, 2006). While the storms with rainfall intensity 20–50 mm are not considered to be abnormal (Piasecki, 1996), catastrophic rainfall episodes with daily precipitation exceeding 50 mm are observed rarely – a few times per decade (Pawlik et al., 2013).
In the river valleys of Nysa Kłodzka, Biała Lądecka, Ścinawka and lower reach of Bystrzyca Dusznicka, the groundwater level does not exceed 2 m (Geographic Characteristic of Counties, 2004). It changes with the distance from the river, and 2–6 km from the channel it deepens to 10 m. The lowest water levels occur within the mountain massifs and can reach depth of several tens of meters.
The soil pattern is homogenous in the studied catchments. The soils types of the region are mainly Brown Earths and Podzoles. The river valleys are covered with Fluvisoles (Geographic Characteristic of Counties, 2004).
4. Data
The data which become inputs to TOPMODEL can be divided into two groups, i.e. hydrometeorological time series (temporal variability) and terrain characteristics (spatial variability). The next two subsections correspond to this classification. For the purpose of the experiment, we selected three consecutive hydrologic years, abbreviated hereinafter as HYs (note that in Poland hydrologic year begins on 1 November and finishes on 31 October). These HYs are: 2010, 2011, 2012. We focus only on four contributing basins which are mentioned and characterized above.
4.1 Hydrometeorological time series
In order to calibrate TOPMODEL we need time series of discharge, rainfall and potential evapotranspiration. They all should be calculated in m/m2 per time step. The observed riverflow and precipitation data, sampled every 15 minutes, are obtained from the above-mentioned Local System for Flood Monitoring, known also as LSOP, courtesy of Kłodzko County. However, potential evapotranspiraion is modelled empirically, and the same 15-minute time step is kept.
Since LSOP observes only water level, and thus no discharge is measured, there is a need to use rating curves to calculate discharge time series. This has been done using the tabulated rating curves for four gauges under study, obtained courtesy of the Institute of Meteorology and Water Management – National Research Institute (Instytut Meteorologii i Gospodarki Wodnej – Państwowy Instytut Badawczy, IMGW–PIB). The tabulated rating curves, after applying the square-root transformation to the discharge data, have been approximated with high-order polynomials which have been fitted using the least-squares method. Attention has been paid to the uniqueness of the model solution, specifically for low flows. The models have used to compute discharge time series, expressed in m3/s, for four sites under scrutiny, and sampling every 15 minutes have been inherited from river stages. Since discharge data should be expressed in m/m2 per time step, for each gauge we multiplied so calculated discharge by 15 × 60 (15 minutes between consecutive discharge data times 60 seconds in a minute) and divided it by basin area (expressed in m2).
Rainfall is measured in LSOP at 13 automatic weather stations, and hourly precipitation rate is recorded every 15 minutes. The data have been recalculated to fit the 15-minute time step, and millimeters of rainfall have been converted to m/m2 per time step. Since no continuous information on precipitation field is provided, we applied the Thyssen polygons to relate rainfall to a given contributing basin.
Potential evapotranspiration has been computed empirically, i.e. we constructed an averaged time series which is assumed to be valid for every year. In our exercise, the evapotranspiration data set is a combination (sum) of: the daily averaged potential evapotranspiration data for the entire year (computed for each day of year as a mean potential evapotranpiration on the corresponding days in many years) and the diurnal harmonic variation computed on the basis of the true sunrise and sunset times.
Due to the fact that the daily evapotranspiration data are not available for Kłodzko Land, we utilized the daily potential evapotranspiration data for the nearest German site of Goerlitz, computed using the Turc-Wendling method in frame of the NEYMO project. Since Goerlitz is located approximately 140 km from the centre of Kłodzko Land, we proposed a scaling approach to account for change in evapotranspiration between Goerlitz and the considered sites in Kłodzko Land. We thus multiplied the daily averaged evapotranspiration data for Goerlitz by a constant number which was a ratio of: (1) mean annual potential evapotranspiration between 1966 and 1995 in a single site in Kłodzko Land (499 mm for Bystrzyca Kłodzka as well as 516 mm for Kłodzko, Bardo and Żelazno) and (2) mean annual potential evapotranspiration between 1966 and 1995 in Zgorzelec which is equal to 570 mm (Zgorzelec is a Polish town that forms an entity with German town of Goerlitz). The resulting ratios, computed using values published by Drabiński et al. (2006), led to the calculation of daily averaged potential evapotranspiration data for basins above gauges in Bystrzyca Kłodzka, Kłodzko, Bardo and Żelazno.
Diurnal harmonic variation was simulated on a basis of true sunrise and sunset times. It was assumed that evapotranspiration is equal to zero in the night and starts growing non-linearly after the sunrise, reaches the daily maximum and declines to zero at sunset. In this paper, the day segment was modelled with a sinusoid and replicated many times to reveal the same length as the above-mentioned daily evapotranspiration data. The similar, but not entirely identical approach, was applied by Liu et al. (2005). In our exercise, the mean value of the diurnal components was subtracted, and such a procedure prevented extra evapotranspiration values to occur when integration over time was performed.
Subsequently, the data-based daily averaged potential evapotranspiration data was added to the mean-corrected diurnal evapotranspiration component, leading to the ultimate estimate of potential evapotranspiration.
4.2 Terrain characteristics
Topography of the investigated watersheds, as a major factor influencing the TOPMODEL performance, was in this study a subject of close scrutiny. Based on the flow accumulation maps generated using GIS tools, the TWI value was assigned to each raster cell in the digital elevation models of the watersheds. The classification of the values into 16 classes was performed in order to reduce the computation time, thus the calculations were carried out for the topographic index class instead of each individual value. Fig. 3 shows the frequency and the spatial distribution of the TWI values. It is clearly seen that the highest values – which indicate potential subsurface or surface contributing areas (Beven, 1997) – are associated with the bases of slopes and the stream valleys. These areas are characterized by large contributing areas and relatively flat slopes. The mean TWI for the watersheds varies from 6.34 for Bystrzyca Kłodzka catchment, through 6.81 and 6.91 for Żelazno and Kłodzko respectively, to the highest mean value of 7.37 obtained for the Bardo catchment.
DEM was also used for the estimation of the delay function which represents the time for a particle of water to travel to the outlet. Based on the flow length map, each watershed was divided into 5 zones, grouping the similar values of the function. The simple matrix was prepared for the further computations, with the first column indicating average distance to the outlet and the second column representing relative cumulative area of each zone.
5. Results
5.1 Parameter estimation
Although the TOPMODEL assumptions require relatively small number of parameters that need to be estimated, the difficulty of the calibration is caused by the uncertainty of the parameters (Kuczera and Mroczkowski, 1998). Additionally, as Beven and Freer (2001b) stress out, a diverse set of possible parameter values can produce a similar modeling results.
The Monte Carlo procedure, that has been proven to be particularly useful for hydrological studies (Romanowicz and Beven, 2003), was carried out to estimate a set of parameters that offer the best model performance. In this paper, the Monte Carlo approach is used in association with the uniform distribution, i.e. random sampling across the specified parameter range is performed, assuming the same probability of sampling each element. Tab. 2 shows the ranges applied for each parameter based on the previous studies and manual calibration. The ranges of the parameters were kept wider than the expected possible values for the catchment (Freer et al., 1996). In order to enhance the certainty, the number of simulations was set to 10 000. Further increase of this number did not improve the final result and required a more time-consuming computation. The procedure was carried out for all above-mentioned catchments, in each case study for the period of one hydrological year, and the data from HY 2010, HY 2011 and HY 2012 were taken as an input. Tab. 2 confirms the statement that constraining the perfect parameter set is not possible and the modeling needs to rely on the best performing, not necessary actual, values.
Each parameter is equally important during the Monte Carlo sampling, although the manual calibration showed, that four of the parameters – m, lnTe, SrMAX and vch – are more meaningful, i.e. variation in their values influences the model performance and the shape of the simulated hydrograph most significantly. The highest sensitivity is associated with m parameter, which represents the change in the saturate hydraulic conductivity with depth. Small values of m imply the quick flow and insignificant subsurface runoff, while large values indicate that more rainfall can infiltrate the soil, thus less water reaches the outlet via surface route (Sigdel et al., 2011). For the investigated catchments m parameter range was kept wide, assuming that the well vegetated, deep seated catchments of the study area can be well characterized by the large values of m. The next highly sensitive parameter, lnTe, influences directly the shape of hydrograph. The quick recession is associated with small values of the lnTe parameter, while low values result in gradual fall of the hydrograph limb after the peak, as a result of increasing saturated transmissibility that may cause runoff delay. This parameter draws a special attention in this study, since the shape of the recession limb in the modelled hydrographs often did not resemble the observed ones. Constrained allowable range for this parameter was set to be between –2 and 1, and its value for the most efficient runs vary from –1.37 (Bystrzyca Kłodzka catchment, simulation for 2011) to 0.99 (Żelazno catchment, simulation for 2012). The third parameter that was found to be sensitive, although not as much as the previous ones, is the maximum root zone deficit Srmax. The value of this parameter indicates the influence of evapotranspiration on the hydrological behavior of the catchment. Small root zone deficit (low Srmax value) allows less water to be stored in the root zone and hence available for evapotranspiration (Sigdel et al., 2011) what can lead to the increased runoff. An extended knowledge of the catchment vegetation is necessary for the Srmax calculation. The difference of the water contents at field capacity and the permanent wilting point needs to be multiplied by the rooting depth of the soil (Beven and Freer, 2001a). Due to the lack of such detailed data, Srmax parameter ranges were very wide (0–3 m). The best performing parameter sets for the simulations for different HY in the same catchment contained Srmax parameters with various values, and the estimation of the right span was difficult. Constraining the ranges for the last highly sensitive parameter did not cause such problems, since channel flow velocity can be estimated by dividing the observed discharge by the cross-sectional area of the stream. The channel velocity varies along the stream, but for all the investigated catchments the best performed parameter sets were generated when the each parameter range was set to 800–1000 m/s.
There final parameter values ranges presented in Tab. 3 yielded the best overall fit of the model when executed for entire hydrograph for a HY.
5.2 Model performance
The calibration of the model was performed on all 4 watersheds for HY 2010, HY 2011 and HY 2012. The rainfall, discharge and evapotranspiration data were converted to 15-minute time steps, and the Monte Carlo procedure was performed to generate the best performing parameters set out of 10000 individual sets. Tab. 3 shows the modeling results and the calibrated parameter values. Obtained efficiency statistics as well as the parameter ranges are not consistent for all catchments and all simulation periods. For all of the catchments, TOPMODEL achieved the best fit modeling the discharge in HY 2011. The topography, land use, soils and other characteristics of terrain influencing the runoff generation were relatively steady, but model efficiency statistics varied between the modeling time periods, which proves that the model performance measures are strongly dependent on weather conditions.
The best performance of TOPMODEL was found for Bystrzyca Kłodzka catchment in HY 2011, with NSE = 0.78 and the correlation between observed and simulated discharge of 0.89 (Fig. 4). Slightly less skillful was TOPMODEL in Kłodzko catchment, with values of the above-mentioned statistics of 0.66 and 0.83, respectively. The model performance expressed by NSE > 0.6 is considered as satisfactory, also named as behavioral (Beven and Freer, 2001b). For two remaining catchments, Bardo and Żelazno, TOPMODEL was unable to simulate the hydrograph with fair accuracy. In Bardo basin, the modelled discharge was for each time period less accurate as the mean of the observed data (NSE < 0). For Żelazno catchment this situation occurred for the HY 2012 data, and the results for the remaining modeling periods, HY 2010 and HY 2011, were also not satisfactory, with NSE = 0.31 and 0.42, respectively.
Based on the results of calibration using the yearly data, the watersheds were categorized into three categories: “good” – all obtained NSE > 0, “acceptable” – all obtained NSE ≥ 0 and “unacceptable” – some obtained NSE < 0 (Blazkova et al., 2002). The thirdcategory, containing two watersheds – Żelazno and Bardo – was excluded from further analysis and we focused on finding the underlying causes of model bad performance in these basins.
Bardo is the biggest of the investigated catchments (Fig. 2) and includes the basin of the left Nysa Kłodzka River tributary – i.e. Ścinawka. Within this watershed there is only one meteorological station with rain gauge. Hence, due to numerous local anomalies in the precipitation field in the study area (orographic precipitation, rain shadows) the precipitation measurements weighted by Thiessen polygons are imprecise representation of real spatial variability of rainfall. Both dense distribution of measurements in the mountainous areas and relatively small number of stations located on the plains and in the NW part of Bardo watershed lead to the difficulty in adjusting model parameters and, as result, in accurate simulating discharge. Żelazno is a watershed with the most diverse topography, hence the local anomalies in precipitation occur more frequently and have greater impact on model misrepresentation of the spatial rain pattern. It is also considered that the soil properties in this forested watershed (forests composes over 63% of land use) can exhibit seasonal variability which is more significant than in remaining watersheds. Further investigation into the latter problem is needed because Polish digital soil maps provide information about soil properties only for agricultural land (Drzewiecki et al., 2014), thus there is no data for forested areas.
For Bystrzyca Kłodzka and Kłodzko watersheds, TOPMODEL performed better in predicting discharge than the observed mean. The only exception is associated with Kłodzko watershed in HY 2010, for which the model predictions were exactly as accurate as the mean observed discharge (NSE = 0.03). In the watershed where TOPMODEL performance was superior over the remaining basins, i.e. Bystrzyca Kłodzka, the model obtained the highest efficiency for HY 2011, what is consistent with other watersheds investigated in HY 2011. We may hypothesize that meteorological conditions in this HY differed significantly from the remaining calibration HYs, and the processes involved in these conditions can be better represented by the model. This may be confirmed by the analysis of rainfall and discharge patterns in Kłodzko station (Tab. 4).
The primary difference in the shapes of hydrographs for HYs 2010-2012 is the existence of a large mid-summer peak as a result of major storm event occurring on 24/07/2011. The peak was reconstructed well by the model – its underestimation by over 20% is acceptable taking into account the magnitude of the event. The well-fitted parts of the hydrograph include also recession curve after the main peak, and modelling such situations is perceived as one of the most problematic responses to be reconstructed by the TOPMODEL (Sigdel et al., 2011). The model was able to predict smaller peaks after the event and the estimation of the base flow also improved after the main peak. The biggest discrepancies between observed and simulated runoff occur in the winter season. This is due to the limitation of this simple version of TOPMODEL which does not account for the water accumulated in snow cover. Because the model uses the same parameters to estimate the discharge during the whole simulation period, its values need to be calibrated to produce the smallest overall prediction error, for different hydrological settings. In such a case, the model seems to provide superior fit to the large peaks rather than to other hydrological situations. The evaluation of model performance on a basis of NSE itself can be misleading due to the inclination of this measure to place emphasis on the larger errors, while the smaller ones tend to be neglected. The acceptable performance of the model during one extreme event contributes to good statistical performance for entire hydrograph and poor results in the representation of the base flow. Although this discrepancy occurs during long periods of simulation for low flows, its impact on the overall efficiency measure is rather small. The model parameters estimated with support of this criterion produce a hydrograph that recreates peaks with reasonable accuracy, but fails to match the observed hydrograph during low flows.
In 2011, despite the high 0.78 NSE, the model underestimated the mean discharge by over 40%, similar to the HY 2012 with much lower NSE of 0.29.
The same pattern can be observed in Kłodzko catchment. In this case the recession curve was not reproduced as accurately and the overall model performance is lower (NSE=0.66) than in Bystrzyca Kłodzka catchment (Fig. 5). The model does not provide a good representation of hydrograph during the winter season, when discharge is impacted by snow melt and water can be stored in snow cover. Similar situation was detected also on other hydrographs for all the catchments, i.e. simulations for period December–April were found to be inaccurate. This leads to the conclusion that snow component should be included in the model structure in order to properly reconstruct the hydrological behavior of the investigated catchments in winter seasons. In order to confirm the impact of this misrepresentation of the hydrograph, the model was tested on the shorter periods and the following section contains the results of this simulations.
5.3 Optimal time span for simulations
The best performing watershed – Bystrzyca Kłodzka – was chosen to conduct a detailed analysis of the model ability to reproduce hydrological response during periods of different lengths. It was assumed, based on the shape of the simulated hydrograph for entire year in relation to the observed one, that the model performance during the winter season will exhibit the lowest accuracy expressed by the NSE. In order to determine the most optimal time span for the model simulations the periods of 1 week, 2 weeks, 3 weeks, 1 month, 2 months, 3 months and 6 months were taken into account. Tab. 5. shows the results for HY 2011, where a given time span (e.g. one week of data) was iteratively moved forward by 1 day (which corresponds to 96 observations) to rerun simulations and get a set of statistics. Fig. 6 depicts the variability in achieved NSE values for two-week, one-month and six-month periods.
The overall performance of a model for particular time period was judged subjectively by comparing the efficiency measures obtained by each simulation independently. In order to shorten the time consuming calculations, the number of simulations in the Monte Carlo procedure has been reduced from 10000 to 1000. It was impossible to find the timespan that would give satisfactory results for all hydrological settings, and this is clearly seen when analyzing winter seasons. The mean NSE, calculated for a window of a given length moved in a stepwise way through the entire year, is severely impacted by the low values representing the periods in winter season. Most sensitive to this effect, and thus producing dispersed values, were shorter periods – standard deviation of NSE for the 1-week period exceeds 2 m3/s. The NSE of the best-fitted parameter set in all periods is very high, namely of 0.95–0.97, but these values relate mostly to the time spans when the discharge rate is stable and this stability is expressed properly by the model. In order to avoid the positive bias, percentage of the parameter sets that can be considered behavioral (NSE>0.6) and percentage of the parameter sets that perform better than the mean of observed values (NSE>0) have been calculated. The variability of the mean NSE among the investigated periods is high, but the ratio of behavioral parameter sets and especially parameter sets with NSE>0 is much more stable. The NSE decreases rapidly after each peak caused by the snowmelt as indicated on Fig. 6. Another major dip corresponds to the storm from 24 July 2011, when the underestimation of the main peak flow affects the NSE value. The best performance of the model was noticed for the 6 months period. Just after the winter season the NSE values rise gradually and reach a plateau of NSE>0.9 beginning with the simulations starting at the end of March. It has been noticed that for the longer time spans, the model was able to simulate the major peak from 24 July 2011 with higher accuracy.
6. Conclusions
TOPMODEL was successfully applied to four subcatchments of the upper Nysa
Kłodzka river basin. The conclusions are the following.
TOPMODEL was able to reproduce the main pattern of the hydrograph with acceptable accuracy only for two of investigated catchments.
Poor performance of the model can have variety of reasons, including input data error, calibration inaccuracy, parameter uncertainty and model structure. The most probable cause of misrepresentation of hydrograph lies in the snow-melt component that is not included in this basic version of TOPMODEL. A more sophisticated structure of the response function needs to be used in order to improve the TOPMODEL performance in all of the investigated watersheds. Low accuracy of the model can also be effect of the model inability to represent distributed rainfall pattern.
Complicated environment and lack of soil data makes the calibration of parameters challenging. The Monte Carlo simulation produces the most suitable parameter sets, but they may not correspond to the actual conditions in the watershed.
We have found that the goodness-of-fit increases along with time span of data used for TOPMODEL calibration, and among the studied periods the half-year solution produces the best agreement between data and model simulations. However, such estimates cannot be treated as global ones, since they are highly dependent on hydrological settings and weather conditions.
Simulations that do not include winter season provided promising results, the NSE for nearly half of the simulations using 6-month time span of data for Bystrzyca Kłodzka catchment are higher than 0.6.
Acknowledgments
The research has been financed by the National Science Centre (Poland), research project no. 2011/01/D/ST10/04171 under leadership of Dr hab. Tomasz Niedzielski, Professor at the University of Wrocław (Poland). The authors thank the authorities of the County Office in Kłodzko for productive partnership and providing us with the data of the Local Flood Monitoring System (Lokalny System Osłony Przeciwpowodziowej – LSOP). The tabulated rating curves have been acquired from the Institute of Meteorology and Water Management, National Research Institute (Poland). Sincere gratitude needs to be expressed to Prof. Renata Romanowicz for the guidance and support in clarifying the model concepts and nuances. Further thanks go to Prof. Helena Mitasova who provided comments and valuable suggestions during the last stage of project. We also thank Dr Wouter Buytaert for unveiling the details of the source code. The daily evapotranspiration data for Goerlitz was obtained courtesy of the KLAPS/NEYMO projects, and we wish to thank Mr. Andreas Völlings, Sächsisches Landesamt für Umwelt, Landwirtschaft und Geologie (Germany), for his approval for use of the aforementioned data set. We are also grateful to Mrs. Magdalena Stec for preparing evapotranspiration time series. We are also indebted to Dr Danuta Trojan for discussions on LSOP and on water management problems in Kłodzko County. We thank Dr hab. Mariusz Szymanowski, Dr Małgorzata Wieczorek and Dr Waldemar Spallek for preparing the Digital Elevation Model that has been used in this study. Last but not least we express our thanks to Mr. Bartłomiej Miziński who kindly helped to verify the rating curve models.
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