Abstract

To quantify the role of land cover during a period of climate change, the runoff response is studied for Plynlimon in Wales, UK. The main objective was two-fold: (i) to create a protocol for modeling water balance on a daily basis; and (ii) to describe the extent to which the impact of land-use changes can be identified and supported by the long-term monitoring data of runoff from two neighboring watersheds with different land covers. The process-oriented CoupModel platform was used to set up the model with a well-defined uncertainty for selected parameters. The behavioral ensembles were applied to simulated daily discharge data for the period of 1992–2010 using subjective criteria to reduce the prior 35,000 candidates with a random uniform distribution of 40 parameters. The accepted ensemble was reduced to 100 candidates by accepting the best root-mean-square error (RMSE) on the accumulated residuals during the simulation period. Similar good performance for the entire period and both watersheds was obtained. The differences in interception evaporation accounted for the most important differences between forest and grassland. The obtained residual demonstrated that changes in the forest cover had an impact on the water balance during the first part of the simulation period.

INTRODUCTION

Land-use changes due to urbanization, agricultural activities, and deforestation or afforestation are the main causal factors of water balance changes (Jansson 1987; Jansson et al. 1999; Wijesekara et al. 2010). Climate change caused by anthropogenic greenhouse gas emissions affects mean global air and ocean temperatures, causing snow and ice to melt and leading to sea level rise (IPCC 2013). The reality of climate change makes it increasingly necessary to predict the multiple impacts of land-use changes and increase the amount and quality of data for doing so. For example, warmer temperatures and periods of drought may induce unpredicted changes in land cover and threaten some vegetation types (Duan et al. 1992). At the same time, researchers have identified climate change to be the ‘symptom’ rather than the ‘illness’, focusing instead on the complex land-use related causes of environmental and hydrological change (cf. Pielke et al. 2002; DeFries & Eshleman 2004; Koutsoyiannis et al. 2009). As Dale writes (1997, p. 766): ‘Because climate-change effects are largely determined by land-cover patterns, land-use practices set the stage on which climate alterations can act’. In order to improve the empirical basis for estimating such land-use related changes, the case has also been made to shift the ontological focus from deterministic predictions to more realistic stochastic models that recognize that ‘change, uncertainty and risk are intrinsic and interrelated properties of this world and are not eliminable, but are quantifiable and manageable’ (Koutsoyiannis 2014).

The main concept of water balance changes refers to the balance between input and output of water, where precipitation can be defined as input and evapotranspiration and ground water recharge and stream flow as output. For instance, forests contribute more heat and moisture to the atmosphere compared to open areas with low vegetation, such as grassland meadows (Bringfelt et al. 1999). This is thought to be a consequence of the higher input of net radiation to the forest. In contrast with forests, grasslands display a higher rate of evapotranspiration during dry summer conditions because of higher transpiration. However, evidence also shows that higher rates of interception evaporation may contribute to a higher total evapotranspiration from forests on a yearly average (Robinson & Dupeyrat 2005).

Trees have the ability to use more water than most other types of vegetation: forested catchments have been found to use larger amounts of water than grasslands (Bosch & Hewlett 1982; Newson 1985; Kirby et al. 1991; Hudson et al. 1997). For example, Kirby et al. (1991) demonstrated that a completely forested catchment would lose an additional 15% of runoff compared with a grassland catchment. On the other hand, with respect to low flow, Robinson & Dupeyrat (2005) provided evidence that forest and grassland catchments do not necessarily have different base-flow characteristics.

The Plynlimon research catchments have been chosen for this case study and lie within the headwaters of the River Severn and the River Wye in the uplands of mid-Wales. Intensive and long-term monitoring within the catchments has supported a wealth of hydrological and hydro-chemical research for nearly 35 years. This case study reviews the long-term water balance results since 1992. The comparison of the forested catchment with the adjacent control grassland catchment are made on an annual and seasonal basis. The data enable the effects of climate to be screened out as well.

Various approaches have been adopted to understand the performance of hydrological models. Still, today, there are many uncertainties in the simulation of runoff, which remains a controversial issue in hydrology (Bloschl & Sivapalan 1995). Nonlinear regression (Vrugt et al. 2003), the fuzzy method, the Bayesian method (Van Oijen et al. 2005), and generalized likelihood uncertainty estimation (GLUE) (Beven & Binley 1992) are a few examples of mentioned methodologies. This study adopts the GLUE framework to estimate the uncertainties in parameters, model assumptions, and measurements. The core of the GLUE method for describing parameter uncertainties is equifinality, which is a set of parameter values that have been shown to produce robust simulations and consider uncertainty (Duan et al. 1992).

The main objective of this study is to identify the impact of land-use changes on hydrological processes in two parallel catchments with different river discharge with the aid of a CoupModel platform (CoupModel 2015) and observation data from the two watersheds. The adopted model is a detailed coupled heat and mass transfer model which uses a continuous Richards' equation (RE) for the soil and has an explicit representation of plant and atmosphere conditions. The model is based on a local-scale hydrological perspective and represents a ‘mixed vegetation–cover approach’, where the land surface is represented by a number of vertically stratified and interacting sub-surfaces (snow, vegetation, intercepted water). The paper also provides an explicit schema for the representation of surface pool and soil surface evaporation, which are important components of the model.

MATERIAL AND METHODS

Study site

The Plynlimon catchments (4°45′W, 52°28′N) are located about 100 km north of Cardiff and 25 km inland from Aberystwyth, and lie in the Cambrian Mountains of mid-Wales (Figure 1). The Plynlimon catchments consist of two watersheds.

Figure 1

Plynlimon catchments showing the Severn and the Wye.

Figure 1

Plynlimon catchments showing the Severn and the Wye.

The first catchment contains the source of the River Wye and comprises traditional hill sheep-pastures. The second catchment contains the source of the River Severn and is occupied by the Hafren Forest (∼70% forested with conifer plantations), a Forestry Commission plantation of mixed coniferous species (Forestry Commission 2004). The plantation of coniferous trees in the Severn catchment began in the 1930s. By the mid-1960s, 70% of the total catchment area had been planted by the Forestry Commission. Tree harvesting began in 1993 and by 2000 half of the forest had been felled (Robinson & Dupeyrat 2005). Estimates of the catchment storages have indicated that soil moisture and the shallow groundwater stores may each amount to 120 mm, totaling almost 10% of the average annual precipitation (Hudson 1988; Kirby et al. 1991).

The headwater catchments of the Rivers Wye and Severn are contiguous and lie on the eastern slopes of the Plynlimon upland massif in mid-Wales. Their topography, geology, and soils are similar. The underlying geology for both catchments comprises mudstones, grits, siltstones, and slates that are estimated to make the basins watertight (Robinson & Dupeyrat 2005). The elevation range for the Wye is from 344 to 742 m and for the Severn is 328 to 739 m. The Severn is steeper than the Wye, which may prove important for flow variability. Average annual catchment rainfall (1971–2010) is 2,731 mm for the Wye and 2,708 mm for the Severn. The long-term average annual precipitation for the catchments (1992–2010, which is used as time series in the model) is about 2,600 mm. There is a distinct winter maximum, but every month has an average rainfall greater than 135 mm. Seasonality analysis in Figure 2 shows monthly averages in precipitation, temperature, and runoff from 1992 to 2010. The months October–January have the highest daily precipitation average (more than 8 mm/day), whereas the May–September period has the highest temperature average. Regarding runoff time series (1992–2010), the value recorded in the Severn catchment is lower than that recorded in the Wye catchment, although not markedly (2,185 mm in the Wye and 2,085 mm in the Severn). The main tree species in the Severn watershed is the Sitka spruce (Picea sitchensis), while the Wye catchment has continued to be used as rough pasture for sheep grazing. For both watersheds, a soil depth parameter of 2 m was used in the CoupModel simulations. The value is based on observations by the Institute of Hydrology at the UK Natural Environment Research Council (Bell 2005), which reported the typical thickness of the soil horizon to be 2 m deep. Consequently, consideration of all soil hydraulic property ranges in the models, which consists of water retention and hydraulic conductivity, were limited to 2 m-deep soil.

Figure 2

Monthly mean values changes for the 1992–2010 time-series.

Figure 2

Monthly mean values changes for the 1992–2010 time-series.

Data

Flow data at an hourly interval were provided by the ExpeER (Experimentation in Ecosystem Research) both for Wye and Severn catchments. The climate database was obtained from the Center for Ecology and Hydrology (CEH) hydrometric station in Moorland, near the top of the Hafren catchment. The data (climate and flow) were considered for the time period between 1992 and 2010. The climate data base consists of global radiation, net radiation, air temperature, wind speed, precipitation, and relative humidity.

Observed climatic pattern

The Plynlimon climate is mostly humid and the long-term average annual precipitation for the catchments (1992–2010) is about 2,600 mm. The three years 1998–2000 were the three wettest since records began in 1972 and 2008 was the fifth wettest year, as indicated in Figure 3. The annual rainfall of over 3,000 mm was substantially above the long-term average. Regarding the pattern of measured data in both actual and accumulated values in the model (i.e., global radiation, air temperature, and precipitation), differences were found between the Severn and Wye catchments. The data, which span 30 years, revealed that 1978 and 2005–2008 were the driest years. From a seasonal perspective, October to January are the wettest months, with April to July being the driest months of the year (Figure 2). Potential evaporation (short grass) for the catchment is about 500 mm per year.

Figure 3

Climatic changes in the Plynlimon catchments (1992–2010).

Figure 3

Climatic changes in the Plynlimon catchments (1992–2010).

Catchment water balances are shown in Figure 4. The precipitation is based on the areal network of approximately 30 monthly-reads storage gauges and it is considered in the model simulation as observed data. The report by Grant & Robinson (2009) confirmed that stream flow and weather data were of good quality and mostly without breaks. Long-term trends of climate and weather variables show much year-to-year variability but there is no evidence of a long-term trend with the possible exception of air temperature.

Figure 4

Water balance comparison between the two watersheds (observation data) (1992–2010).

Figure 4

Water balance comparison between the two watersheds (observation data) (1992–2010).

PROCESS DESCRIPTION

Water balance can be divided into two main parts: root zone water balance (Table A1, Equation (A1), available with the online version of this paper) and surface water balance (Table A1, Equation (A2)). Model calibration is a critical phase in the modeling process, and the need for a well-established calibration strategy is obvious. Amount and quality of the available data, applied techniques, and the availability of time and computer power are the main items to achieving successful calibration. In Table 1, a list of parameters for the GLUE calibration is indicated. Different ranges of parameters are considered based on the information obtained from species and land covers.

Table 1

Parameters selected for the stochastic optimization in CoupModel and their initial value and uncertainty ranges

Parameters Unit Symbol Equation Prior
 
Appendix Min Max 
Transpiration and interception 
 Leaf area index (LAI) m2/m2 A1 (13) 
 Conduct max m s−1 gmax (7) 0.005 0.05 
 Water capacity per LAI mm/m2 iLAI (14) 0.1 0.5 
 CritThesholdDry (Response function to water soil potential) cm water ψ– 10 1 × 104 
 Canopy height HP – 20 
 Maximal cover – cmax – 0.5 
 Max cover m2/m2 pcmax – 0.5 
 Root depth – – −2 −0.01 
 Conduct VPD Pa gvpd (7) 100 4 × 103 
 Conduct Ris J/m2/day gris (7) 1 × 104 1 × 107 
 Windless Exchange Snow. Minimum turbulent exchange coefficient over bare soil s−1 ra,max,snow−1 – 0.001 0.1 
Soil evaporation and snow process 
 EquilAdjustPsi (Vapor pressure at the soil surface) – ψeg – 
 MeltCoefAirTemp (Temperature coefficient in the empirical snow melt function) kg ◦C−1 m−2 day−1 m– 
 MeltCoefGlobRad (Global radiation coefficient in the empirical snow melt function) kg J−1 mRmin – 1 × 10−7 3 × 10−6 
 OnlySnowPrecTemp. Below this temperature all precipitation is snow °C TSnowL – −4 
 MeltCoefAir kg °C−1m−2 day−1 mT – 
 RoughLBareSoilMom z0M – 0.001 1 × 107 
Soil water flow 
 SurfCoef 1/day asurf – 0.1 
 AScale sorption –  – 0.1 10 
Drainage and deep percolation 
 Drain level z(16), (17) −2 −0.3 
 Drain spacing dp (16), (17) 10 1 × 104 
Soil water process 
 n Tortuosity (1)–(3) – n – −1 
 Lambda (1)–(3) – λ (15) 0.1 0.4 
 Air entry (1)–(3) cm water ψa (15) 0.1 0.4 
Parameters Unit Symbol Equation Prior
 
Appendix Min Max 
Transpiration and interception 
 Leaf area index (LAI) m2/m2 A1 (13) 
 Conduct max m s−1 gmax (7) 0.005 0.05 
 Water capacity per LAI mm/m2 iLAI (14) 0.1 0.5 
 CritThesholdDry (Response function to water soil potential) cm water ψ– 10 1 × 104 
 Canopy height HP – 20 
 Maximal cover – cmax – 0.5 
 Max cover m2/m2 pcmax – 0.5 
 Root depth – – −2 −0.01 
 Conduct VPD Pa gvpd (7) 100 4 × 103 
 Conduct Ris J/m2/day gris (7) 1 × 104 1 × 107 
 Windless Exchange Snow. Minimum turbulent exchange coefficient over bare soil s−1 ra,max,snow−1 – 0.001 0.1 
Soil evaporation and snow process 
 EquilAdjustPsi (Vapor pressure at the soil surface) – ψeg – 
 MeltCoefAirTemp (Temperature coefficient in the empirical snow melt function) kg ◦C−1 m−2 day−1 m– 
 MeltCoefGlobRad (Global radiation coefficient in the empirical snow melt function) kg J−1 mRmin – 1 × 10−7 3 × 10−6 
 OnlySnowPrecTemp. Below this temperature all precipitation is snow °C TSnowL – −4 
 MeltCoefAir kg °C−1m−2 day−1 mT – 
 RoughLBareSoilMom z0M – 0.001 1 × 107 
Soil water flow 
 SurfCoef 1/day asurf – 0.1 
 AScale sorption –  – 0.1 10 
Drainage and deep percolation 
 Drain level z(16), (17) −2 −0.3 
 Drain spacing dp (16), (17) 10 1 × 104 
Soil water process 
 n Tortuosity (1)–(3) – n – −1 
 Lambda (1)–(3) – λ (15) 0.1 0.4 
 Air entry (1)–(3) cm water ψa (15) 0.1 0.4 

An index of 1 or 2 or 3 within brackets means that the parameter represents the characteristics of forest and grassland layers or understorey layers by the respective value of the index.

Parameters governing the canopy surface resistance, actual root water uptake, within-canopy aerodynamic resistances for interception evaporation, snow evaporation, and bare soil evaporation, were all chosen according to their expected impact and ability to represent the differences in response of the vegetation cover and major soil properties. Seasonal development of leaf area index and canopy height, potential transpiration, interception, and water uptake were used but no long-term trends were assumed in the characteristic of vegetation.

Soil evaporation and snow process

Soil evaporation is often lumped together with plant transpiration as total evapotranspiration, which forms the second or third largest term in the water balance equation when applied to the climate zone of the study case (Trautz et al. 2012). However, here we represented soil evaporation, interception evaporation, and transpiration as separate components. An iterative physical based energy balance approach was applied for both soil evaporation and snow evaporation (Table A1, Equation (A3)).

Transpiration

The potential transpiration, Etp, is calculated from the Penman combination equation in the form given by Monteith (1965) which is mentioned in Table A1, Equation (A4). Actual transpiration is calculated in two steps. The first step is to account for the possible compensatory uptake of water by roots in layers with no water stress, if there are roots in other layers that are exposed to water stress (Table A1, Equation (A5)). The second step is to calculate the water uptake without any account of compensatory uptake (Eta*), which is expressed as the reduction in potential transpiration (Etp*) by reducing interception evaporation (Table A1, Equation (A6)).

Surface resistance is a function of leaf area index and stomatal conductance (Table A1, Equations (A7) and (A8)). Stomatal conductance was constrained by global radiation, vapor pressure deficit (VPD), and maximal stomatal conductance, as expressed by the Lohammar equation (Lohammar et al. 1980) (Table A1, Equation (A8)).

Parameters representing the response to the atmospheric demand related to VPD was included since we can expect a difference between forest and grassland. High values of the ‘Conduct VPD’ parameter describe a small response to high VPD values whereas small values correspond to a strong response by lowering the demand when actual VPD will be high. The maximal conductance of fully open stomata (Conduct max) and vapor pressure deficit (Conduct VPD) are the parameters related to transpiration in the calibration procedure (Table A1, Equation (A9)).

Interception

Interception evaporation was calculated from the Penman combination equation, assuming a surface resistance, which represents the resistance to the single source point of the whole canopy (Table A1, Equation (A10)). The potential interception evaporation rate will be decreased if the water on the leaves does not cover the entire leaf (Table A1, Equation (A11)). Actual evaporation from the canopy is limited either by the potential interception evaporation rate or by the interception storage (Table A1, Equation (A12)).

The parameters considered for calibration representing interception are: (i) water capacity per leaf area index, which is defined as interception water storage capacity per LAI unit (Table A1, Equations (A13) and (A14)); and (ii) maximal cover, which is the surface cover function for different plants. As a consequence, in areas in Plynlimon where the canopy is wet for most of the year, interception loss is expected to be the largest component of the total evaporation.

Surface, soil water and drainage process

Two different soil hydraulic properties, the water retention curve and the unsaturated conductivity function, need to be determined in order to solve the water balance equation. In both catchments the water retention function was determined by Brooks & Corey (1964) (Table A1, Equation (A15)). When the groundwater level was above an assumed drain level (representing equilibrium with zero flow rate), the drainage rate was estimated by a linear response equation (Table A1, Equation (A16)) also assuming a spacing between virtual drainage pipes that represent an assumed drainage efficiently in a landscape. The unsaturated conductivity was estimated from an assumed saturated value and coefficient in the Brooks and Corey's function (Table A1, Equation (A17)).

MODEL STRUCTURES

The model approach selected for the purpose of this study is focusing on the hydrological component of the CoupModel (Figure 5).

Figure 5

A conceptual diagram of the CoupModel with water flow, where, zp is the lower depth of the drainage pipe, i.e., the drainage level, zsat is the simulated depth of the ground water table, and dp is a characteristic distance between drainage pipes.

Figure 5

A conceptual diagram of the CoupModel with water flow, where, zp is the lower depth of the drainage pipe, i.e., the drainage level, zsat is the simulated depth of the ground water table, and dp is a characteristic distance between drainage pipes.

The CoupModel is a platform compounded by multiple modules (Jansson & Moon 2001) and represents research with various focuses during the latest 30 years, with many developments to understanding also uncertainty in modeling studies (Jansson 2012). The platform has its origins in the SOIL model initially designed to simulate water and heat fluxes in soil, focusing on soil physics, and based on a coupling of RE for water flow and Fourier equation for heat flows in a 1D domain (Jansson & Halldin 1979). The SOIL model was then expanded to include the turnover of nitrogen in soils, leading to the SOILN model (Johnsson et al. 1987). Over the years, additional components and sub-models have been successively integrated into the platform, and the CoupModel has been refined on a continuous basis (for a more detailed account of the development of the CoupModel, refer to CoupModel (2016)).

The model represents a coupling between soil, vegetation, and atmospheric processes (i.e., soil evaporation, surface runoff, snow-melt, interception of precipitation, and evapotranspiration). Two coupled differential equations for water and heat flow represent the central part of the model. These equations are solved with an explicit numerical method, where a vertical soil profile is discretized into horizontal layers. The basic assumptions behind these equations are as follows:

  1. The law of conservation of mass and energy.

  2. Flows occur as a result of gradients in water potential (Darcy's law) or temperature (Fourier's law).

Dynamic inputs to the model are classified as driving variables. Time-series of variables define the important boundaries between ecosystems like soil and atmosphere, and plant and atmosphere. Precipitation and air temperature but also air humidity, wind speed, and cloudiness are of special interest as driving variables.

The calculations of water and heat flows are based on soil properties, such as: the water retention curve; functions for unsaturated and saturated hydraulic conductivity; the heat capacity including the latent heat at thawing/melting; and functions for the thermal conductivity. The most important plant properties are: development of vertical root distributions; the surface resistance for water flow between plant and atmosphere during periods with a non-limiting water storage in the soil; how the plants regulate water uptake from the soil and transpiration when stress occurs; how plant cover influences both aerodynamic conditions in the atmosphere and the radiation balance at the soil surface.

Different numerical methods are used to solve the surface energy balance for plants, snow, and bare soil. The dynamic coupling between surface temperature, heat fluxes, and net radiation is only used for the bare soil surface and for the snow surface. Evaporation from the soil surface is normally calculated using an iterative energy balance approach (Alvenäs & Jansson 1997), whereas the transpiration and interception evaporation is obtained using the Penman–Monteith big leaf approach to represent evaporation. The sensible heat flux from the big leaf and the corresponding surface temperature of the vegetation are calculated based on the residual term of the energy balance for the vegetation. The most important equations which are linked to the water balance and selected parameters in this study are listed in the Appendix (available with the online version of this paper).

MODEL SETUP

Period of simulation

The model was run with daily meteorological data and was evaluated based on the 18-year datasets from Climate Plynlimon (January 1992–December 2010). The model was run with 35,000 runs. Initial values were obtained by simulating the 18 preceding years starting with climatological air temperature, net radiation, global radiation, wind speed, precipitation, and relative humidity. Daily average values of observed runoff in both Severn and Wye catchments were used as validation data.

Temporal resolution

A daily time step was chosen for the model simulation. This time step could appear too coarse given the usually quick response of the current areas to rainfall events. However, the objective of the present study was not to accurately simulate the response to specific events. Rather, the objective was to perform long-term continuous simulations and survey the seasonality, focusing only on the hydrological regime and long-term water balance variables such as the seasonal variations of runoff, evapotranspiration, or soil moisture. These components of the hydrological balance can be efficiently assessed at larger time scales and using a coarser time step, as the dominant processes involved have intrinsically large time scales (Bloschl & Sivapalan 1995).

Model parameterization

Regarding the main concept of the model, the selected parameter values were based on water balance concern and determining the main differences between two watersheds, one forest and the other grassland. The model simulation adopted the RE approach. In this case, soil profile and soil physical properties, forest surface properties, grassland surface properties, forest plant cover, and grassland plant cover were considered in the model. In total, 40 parameters were selected for calibration, some of which are listed in Table 1. A total of 35,000 simulations were made using the Monte Carlo random uniform (random number using linear scale between min and max value) sampling of the parameter ranges. The statistical performance indicators were calculated based on: (1) the actual daily data (Actual value); (2) accumulation of daily values since the start of each year (Yearly accumulated); and (3) accumulation of daily data since the start of the entire simulation period (Accumulated value). This was performed to quantify the importance of the short time behavior in relation to the seasonal behavior or the long-term behavior of the models. Actual data (1) are making the conventional approach and all single events are counted independent of each others. Transformation number (2) and (3) are creating a memory which allows compensating by nearby events to smooth out and ignore individual events. The timing will be of smaller importance but the contribution to the seasonality of the between years variability will be emphasized depending on (2) or (3).

The accepted ensembles of 200 behavior simulations were selected by accepting the mean error (ME) criteria. Finally, the accepted ensemble was reduced to 100 candidates by accepting the best root-mean-square error (RMSE) on the accumulated residuals during the simulation period as calculated from the three transformations of the data results.

RESULTS

In general, the performance of the calibrated runoff in the ME and RMSE evaluation demonstrated good agreement with both dynamic and yearly results, based on the statistics of 100 behavioral model simulations. Table 2 indicates the model statistics performance which focuses on RMSE in three considered value variables (actual, yearly accumulated, and whole accumulated) and indicates posterior model parameters. Regarding statistical performance, the ensembles of the equal good runs were identified after defining the acceptance criteria for the individual runs. The maximum values of RMSE with respect to runoff in both catchments were low and mean error was close to zero.

Table 2

Performance statistics obtained on calibration for actual, whole accumulated, and yearly accumulated values variables on the 35,000 (prior) behavioral simulations and 100 accepted simulations (posterior)

Calibrated variable RMSE
 
Actual value (mm/day)
 
Yearly accumulated (mm)
 
Whole accumulated (mm)
 
Min Max Mean Min Max Mean Min Max Mean 
CoupModel Severn 3.78 5.38 4.51 95.6 120.81 111.2 198.5 271.3 241.96 
CoupModel Wye 4.01 5.43 4.7 90.19 109.16 101.15 208.7 268.7 245.78 
Calibrated variable RMSE
 
Actual value (mm/day)
 
Yearly accumulated (mm)
 
Whole accumulated (mm)
 
Min Max Mean Min Max Mean Min Max Mean 
CoupModel Severn 3.78 5.38 4.51 95.6 120.81 111.2 198.5 271.3 241.96 
CoupModel Wye 4.01 5.43 4.7 90.19 109.16 101.15 208.7 268.7 245.78 

The criteria started with ME and then RMSE controller limited the range to 100 for all.

The posterior distributions were constrained to relatively low mean value for the entire period for both watersheds. The performance was improved by using accumulation for the entire period and minimizing the mean value of the accumulated residuals. Surprisingly, the value for the Severn was generally larger than for the corresponding value obtained for the Wye watershed (Table 2). The long-term patterns of the accumulated residuals demonstrated that both systems had the same general pattern (Figure 6). The general pattern is probably due to the model structure error related to the long-term response of the climate system. The general pattern may also be related to various measurement errors.

Figure 6

Mean of the residual (difference between simulated and measured runoff) ensemble of the RE approach cumulated values for the Severn (bottom line) and Wye (top line), from 1992 until 2010, based on one accepted ensemble of 100 runs.

Figure 6

Mean of the residual (difference between simulated and measured runoff) ensemble of the RE approach cumulated values for the Severn (bottom line) and Wye (top line), from 1992 until 2010, based on one accepted ensemble of 100 runs.

Parameter values

The model showed clear differences in the posterior distribution for a number of parameters that were constrained by the common applied criteria. The RE approach (Figure 7), showed a similar tendency for plant height and leaf area index. It also attributed most of the differences between the two watersheds to evaporation from the soil surface, in turn explaining the less pronounced impact of the canopy properties.

Figure 7

Constraints of parameters in the Severn (forest site) and Wye (grassland) watersheds, and the parameters which showed a tendency to be constrained by the data by accumulated values and criteria (RMSE and mean value). Canopy height, conduct max, leaf area index, surface runoff, drainage spacing are the parameters which were sensitive to criteria in RE approach: left, Severn; right, Wye.

Figure 7

Constraints of parameters in the Severn (forest site) and Wye (grassland) watersheds, and the parameters which showed a tendency to be constrained by the data by accumulated values and criteria (RMSE and mean value). Canopy height, conduct max, leaf area index, surface runoff, drainage spacing are the parameters which were sensitive to criteria in RE approach: left, Severn; right, Wye.

The model showed minor differences between the watersheds with respect to the obtained values of the differences in the parameters for soil and runoff. However, the surface runoff coefficient and the drain spacing values also showed differences between the two watersheds (Figure 7).

Model performance for specific periods

The simulated ensemble results after consideration of the ME and RMSE criteria indicated in Figure 8 for the period January–June and July–December 2003, respectively, show the simulated and uncertainty ranges in the model. The year 2003 was considered among the 30-year available simulated time-series because of availability of data; it had the highest mean temperature, was the driest year, and had less precipitation. The results were divided into two parts: periods from January 2003 until June 2003 and from July 2003 until December 2003. Selected ensembles showed the hydrological response in different land uses and land covers. The uncertainty band of runoff was narrow in the model, which reflects the tendency to constrain its performance. Simulated runoff showed a tendency toward overestimation in the period from July to December 2003 for the Severn and Wye catchments, especially for the summer period. A small uncertainty in simulated range was observed during the time-series in the spring period. The results for other years showed a similar degree of performance.

Figure 8

Measured runoff compared with observation data and mean of accepted run in the Severn and Wye watershed: January–June 2003 in top figures; July–December 2003 in the lower panels.

Figure 8

Measured runoff compared with observation data and mean of accepted run in the Severn and Wye watershed: January–June 2003 in top figures; July–December 2003 in the lower panels.

Long-term behavior of the models

In line with the first evaluation, the correlation between the variables for the 100 behavioral models is calculated for the secondary and third evaluations. Regarding the three transformation types, actual value variables give the highest variability. In contrast, all accumulated values give the lowest variability between the chosen time series values. There is no doubt that all the accumulated values minimize the deviation for the whole period of simulation. Although the deviation between the values is relatively small, the comparison of the accumulated values for the whole period provides the best result because the residual result is close to zero.

Regarding RMSE and ME criteria, the long-term accumulated residual based on actual values was considered and is indicated in Figure 6 for both catchments. Table 3 lists the parameters for the GLUE calibration regarding the accumulated value criteria.

Table 3

Parameter distributions for 26 calibrated parameters

Parametersa CoupModel Severn (Forest)
 
Posterior distribution CoupModel Wye (Grassland)
 
Posterior
 
Posterior
 
Mean Post St.D CVb Mean Post St.D CV 
Transpiration 
 Conduct max 0.060 0.024 0.41 U 0.057 0.027 0.48 
 WindLessExchangeCanopy 0.028 0.025 0.92 U 0.026 0.031 1.19 
 Conduct VPD 1.013 991.3 0.97 U 927.2 1.01 1.09 
 Conduct Ris 5.22 2.49 0.47 U 5.44 2.60 0.47 
 CritThesholdDry 4.83 2.79 0.57 U 4.71 2.73 0.58 
 Canopy height 15.65 3.25 0.20 U 13.48 3.91 0.29 
Interception 
 Maximal canopy cover 0.72 0.145 0.20 U 0.72 0.14 0.20 
 Max cover (Surface canopy cover) 0.724 0.14 0.20 U 0.71 0.14 0.20 
 Root depth −0.94 0.59 0.63 U −0.87 0.53 0.61 
 Leaf area index (LAI) 3.98 1.69 0.42 U 3.70 1.76 0.47 
 Water capacity per LAI. (Interception water storage capacity per LAI unit) 0.33 0.10 0.30 U 0.31 0.12 0.38 
Soil evaporation and snow process 
 EquilAdjustPsi (Vapor pressure at the soil surface) 1.25 0.67 0.53 U 1.27 0.79 0.62 
 RoughLBareSoilMom (Bare soil evaporation) 0.0096 0.01 1.10 U 0.012 0.012 0.95 
 MeltCoefAirTemp (Temperature coefficient in the empirical snow melt function) 2.416 0.86 0.35 U 2.60 0.94 0.36 
 MeltCoefGlobRad (Global radiation coefficient in the empirical snow melt function) 8.9 × 10−7 8.2 × 10−8 0.92 LN 6.89 6.2 × 10−8 0.90 
 OnlySnowPrecTemp (Below this temperature all precipitation is snow) −1.54 1.56 1.01 U −1.49 1.34 0.89 
 OnlyRainPrecTemp (Above this temperature all precipitation is rain) 3.05 1.14 0.37 U 3.10 1.25 0.40 
Soil water flow 
 Surface runoffCoef 2.0 1.11 0.55 U 2.15 1.145 0.53 
 AScale sorption (Sorption scaling coefficient for flow in the matric pore domain) 4.80 2.86 0.59 U 4.89 2.47 0.506 
Drainage and deep percolation 
 DrainLevel −1.20 0.45 0.37 U −1.25 0.47 0.38 
 DrainSpacing 1.194 2.01 1.68 U 1.49 2.41 1.61 
Soil water process 
 Total conductivity (1)–(2) 1.41 × 107 2 × 105 1.80 LN 7.81 × 106 1.3 × 105 1.71 
 Total conductivity (3) 5.68 2.53 0.44 Re 5.24 2.40 0.45 
 Tortuosity (1)–(3) 0.37 0.923 2.49 U 0.57 0.83 1.46 
 Lambda (1)–(3) 0.26 0.081 0.30 U 0.27 0.084 0.31 
 Air entry (1)–(3) 7.18 1.43 0.19 U 7.25 1.53 0.21 
Parametersa CoupModel Severn (Forest)
 
Posterior distribution CoupModel Wye (Grassland)
 
Posterior
 
Posterior
 
Mean Post St.D CVb Mean Post St.D CV 
Transpiration 
 Conduct max 0.060 0.024 0.41 U 0.057 0.027 0.48 
 WindLessExchangeCanopy 0.028 0.025 0.92 U 0.026 0.031 1.19 
 Conduct VPD 1.013 991.3 0.97 U 927.2 1.01 1.09 
 Conduct Ris 5.22 2.49 0.47 U 5.44 2.60 0.47 
 CritThesholdDry 4.83 2.79 0.57 U 4.71 2.73 0.58 
 Canopy height 15.65 3.25 0.20 U 13.48 3.91 0.29 
Interception 
 Maximal canopy cover 0.72 0.145 0.20 U 0.72 0.14 0.20 
 Max cover (Surface canopy cover) 0.724 0.14 0.20 U 0.71 0.14 0.20 
 Root depth −0.94 0.59 0.63 U −0.87 0.53 0.61 
 Leaf area index (LAI) 3.98 1.69 0.42 U 3.70 1.76 0.47 
 Water capacity per LAI. (Interception water storage capacity per LAI unit) 0.33 0.10 0.30 U 0.31 0.12 0.38 
Soil evaporation and snow process 
 EquilAdjustPsi (Vapor pressure at the soil surface) 1.25 0.67 0.53 U 1.27 0.79 0.62 
 RoughLBareSoilMom (Bare soil evaporation) 0.0096 0.01 1.10 U 0.012 0.012 0.95 
 MeltCoefAirTemp (Temperature coefficient in the empirical snow melt function) 2.416 0.86 0.35 U 2.60 0.94 0.36 
 MeltCoefGlobRad (Global radiation coefficient in the empirical snow melt function) 8.9 × 10−7 8.2 × 10−8 0.92 LN 6.89 6.2 × 10−8 0.90 
 OnlySnowPrecTemp (Below this temperature all precipitation is snow) −1.54 1.56 1.01 U −1.49 1.34 0.89 
 OnlyRainPrecTemp (Above this temperature all precipitation is rain) 3.05 1.14 0.37 U 3.10 1.25 0.40 
Soil water flow 
 Surface runoffCoef 2.0 1.11 0.55 U 2.15 1.145 0.53 
 AScale sorption (Sorption scaling coefficient for flow in the matric pore domain) 4.80 2.86 0.59 U 4.89 2.47 0.506 
Drainage and deep percolation 
 DrainLevel −1.20 0.45 0.37 U −1.25 0.47 0.38 
 DrainSpacing 1.194 2.01 1.68 U 1.49 2.41 1.61 
Soil water process 
 Total conductivity (1)–(2) 1.41 × 107 2 × 105 1.80 LN 7.81 × 106 1.3 × 105 1.71 
 Total conductivity (3) 5.68 2.53 0.44 Re 5.24 2.40 0.45 
 Tortuosity (1)–(3) 0.37 0.923 2.49 U 0.57 0.83 1.46 
 Lambda (1)–(3) 0.26 0.081 0.30 U 0.27 0.084 0.31 
 Air entry (1)–(3) 7.18 1.43 0.19 U 7.25 1.53 0.21 

CV = coefficient of variance. Post St.D = standard deviation divided by the mean value. U = uniform distribution and LN = log normal distributions in posterior (100 accepted simulations) parameter distributions. The detailed meanings of each parameter can be found in the Appendix (available with the online version of this paper).

aParameter number within brackets.

bCV means coefficient of variation (=standard deviation divided by the mean) and PDF is the probability distribution function, including uniform (U), normal (N), and log-normal (LN) distributions, (Re) related to top layers.

Table 4

Water balance table after model calibration based on long-term accumulated values (1992–2009) for the Wye and Severn watersheds simulated by RE equation (COUP)

Water balance Severn catchment Wye catchment 
Soil evaporation (mm) 112.48 132.15 
Transpiration (mm) 251.62 208.42 
Interception (mm) 265.33 193.25 
Total evapotranspiration (mm) 629.53 533.72 
Runoff (mm) 2,085 2,185 
Water balance Severn catchment Wye catchment 
Soil evaporation (mm) 112.48 132.15 
Transpiration (mm) 251.62 208.42 
Interception (mm) 265.33 193.25 
Total evapotranspiration (mm) 629.53 533.72 
Runoff (mm) 2,085 2,185 

The patterns in the first 10 years (1992–2002) showed the largest deviations. The observed deviations are probably due to actual changes in land cover that possibly influenced evaporation, namely, a more rapid transition of forest recovery from 1992 to 1999, following clearcutting in the beginning of the 1990s (personal communication Bridget Emmett, CEH).

For the beginning of the monitored time period, the model matches real-world conditions quite accurately. However, discrepancies become apparent in the 1995–1997 period, featuring overestimation, and then in the 1998–2000 period, characterized by underestimation of actual conditions.

Regarding the three peaks in both forested and grassland graphs in Figure 6 from 1999 until 2009, there are no changes in the main compounds of the catchment water balance, for example, air temperature, precipitation, and stream flow. One would assume that forest and grassland are the same in the model as they are in the observed climate data and geology of the two catchments (Figures 2 and 4). The climate for all years shows variations, which fact will generate different real-life responses in terms of vegetation. For example, favorable climatic conditions may induce greater than average tree or grassland growth in the Severn and Wye catchments, respectively. However, the model may not account for such yearly climate-induced variations in the extent of vegetation. Instead, the model can display overestimations in, for example, runoff and evaporation, in contrast to actual occurrences in the two catchments. The model reflects an excess of runoff that does not decrease with evaporation. The selected range of evaporation parameter values in the multi-run set up should probably be increased so as to account for differences in the climatic pattern. Periodic climatic variations will therefore provide an explanation for the periodic variations in land cover, such as in the Severn catchment, an expanding forest in the first time period (1992–1997), and relatively similar changes in the second time period (1998–2001). It is worth mentioning for the second period, a process of clearcutting was simultaneous with forest recovery in the form of new planted trees, leading to an overall reduction in evaporation losses. A receding forest cover in the third time period (last 10 years) is also obvious.

The longer time-series of data presented here showed interesting changes in the water balance over the forest cycle. An increase in stream flow can be considered as a consequence of felling, such that less evaporation is to be expected. On the other hand, an important issue which must be considered here is related to the evaporation loss before the reduction in forest land cover: evaporation losses were reducing before felling commenced. The age of trees and the effects of an older forest crop can decline through time, which is partly due to forest felling and restructuring, as well as a decrease in water use with forest aging (Hudson et al. 1997). Another reason can be related to criteria consideration in the residual cumulative value evaluation, of which focus was, in general, sharp to zero at the end of the data series (last 10 years), leading one to expect fewer differences within the years. Changes are therefore related to possible dynamic vegetation. A possible explanation that can justify the mentioned changes in the catchments is linked to the extent of vegetation and evaporation which are related to changes in climate and land cover patterns from 1992 to 2009, which in turn, impact on stream water differences in the Wye and Severn.

DISCUSSION

The grassland (Wye) showed higher runoff and lower evapotranspiration compared to the forested watershed (Severn) although differences are not very high as annual losses are 546 mm for the Wye and 640 for the Severn catchment. These results are in line with Marc & Robinson (2007), who identified increasing runoff along with a decline in vegetation cover. Good performance was obtained with respect to the dynamics and mean values. Differences in the obtained parameter distributions suggested that differences between the watersheds were with respect to both plant cover and soil-related factors. However, the plant cover was most important and covariances between plant and soil-related parameters were normally small Table 4.

The actual evaporation was regulated by the water availability and root distribution in the root zone in the RE model. Canopy height, conduct max, and leaf area index showed a tendency to be constrained by the data in the model. Height of canopy was optionally used to estimate roughness length by using the equation originating from Shaw & Pereira (1982). Conduct max is the maximal conductance of fully open stomata, which is related to the surface resistance for water flow between plant and atmosphere to regulate water uptake from the soil and transpiration when stress occurs. Leaf area index is the dimensionless quantity that characterizes plant canopies.

The discrepancies between the simulated and measured values showed similar tendencies with respect to time period for both watersheds. The suggested explanation for the lower runoff from the forested watershed depends, to a large extent, on the model used and the assumptions made for the criteria. Similar differences in the water balance could be suggested by actual evaporation, declining markedly in both main and sub-catchments.

Result comparisons between the RMSE on cumulated data showed robust behavior, both within year dynamics and the long-term trends for the sites. Due to particular climatic conditions (e.g., with the canopy remaining wet for most parts of the year), forest total evapotranspiration in the Plynlimon area was greater than in the grassland. The simulated and observed discharge from the forest catchment (Severn) showed a higher rate of evapotranspiration compared to the grassland (Wye) with model simulation.

In the first evaluation, which was based on actual values of residuals, similar differences between the watersheds were observed. However, the use of accumulated residuals instead of actual values of residuals puts more focus on the long-term response. Accumulated values smooth out the short-term timing problems without deviating from the seasonal and long-term water balance.

In general, efforts to calibrate watershed properties by using only runoff and climate data are doubtful and tricky. The high quality and the long-term data for Plynlimon were useful for testing both calibration procedures and comparison of model structure errors with parameter value errors.

CONCLUSION

The Plynlimon catchments indicate that evapotranspiration losses from forests are greater than those from grassland, as indicated by climatic trends and model results. Land-use, typified by different vegetation patterns, resulted in differences in the water balance, as indicated by increased surface runoff and river discharge due to changes in evaporation. The main explanation suggested by the data and the model was that interception evaporation accounted for the major difference in the water balance between the forested and grassland watersheds. Due to the particular climatic conditions in the forest canopy environment, which are wet for much of the year, evaporation losses can be twice as great as in grassland. The obtained performance evaluation by RMSE on cumulated data was generally within an acceptable range and contributes to the constraining of water balance-related parameters. The differences in interception evaporation accounted for the most important differences between forest and grassland. The obtained residuals demonstrated that changes in the forest cover had an impact on the water balance during the first part of the simulation period. The forest catchment showed more unexplained variability both within and between years considering the same climatic pattern as in the observed monitoring data. Such unexplained variability can be accounted for in terms of a period of forest regrowth following clearcutting, as well as aging trees, as suggested in the Results section. However, the most important pattern of residuals was common for both forest and grassland. The results of the study point to possible model improvements that could better account for climate-induced changes in vegetation and achieve a more accurate description of excess runoff in the model. For example, a reiteration of the range of evaporation parameter values in the multi-run set up should be considered and increased. With this consideration, the model would produce results closer to the observed data than were obtained in this study. Further research currently being considered with the constructed CoupModel in the Plynlimon massif concerns the modeling of ecosystem fluxes in carbon and heat for both Severn and Wye catchments.

ACKNOWLEDGEMENTS

Thanks to Professor Jack Cosby, CEH, who provided the measured data and Bridget Emmet who gave valuable background information on forestry in the Severn area. Erik MirHadi Madani calibrated the model and analyzed the results. Per Erik guided the use of model and results during the entire project. Note that the data and the setup for running the model are also available from a tutorial for the CoupModel.

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Supplementary data