Calibration of Land-Use-Dependent Evaporation Parameters in Distributed Hydrological Models Using MODIS Evaporation Time Series Data

Abstract

The land-use-specific calibration of evapotranspiration parameters in hydrologic modeling is challenging due to the lack of appropriate reference data. We present a MODIS-based calibration approach of vegetation-related evaporation parameters for two mesoscale catchments in western Germany with the physically based distributed hydrological model WaSiM-ETH. Time series of land-use-specific actual evapotranspiration (ETa) patterns were generated from MOD16A2 evapotranspiration and CORINE land-cover data from homogeneous image pixels for the major land-cover types in the region. Manual calibration was then carried out for 1D single-cell models, each representing a specific land-use type based on aggregated 11-year mean ETa values using SKout and PBIAS as objective functions (SKout > 0.8, |PBIAS| < 5%). The spatio-temporal evaluation on the catchment scale was conducted by comparing the simulated ETa pattern to six daily ETa grids derived from LANDSAT data. The results show a clear overall improvement in the SPAEF (spatial efficiency metric) for most land-use types, with some deficiencies for two scenes in spring and late summer due to phenological variation and a particularly dry hydrological system state, respectively. The presented method demonstrates a significant improvement in the simulation of ETa regarding both time and spatial scale.

1. Introduction

Understanding the changes in actual evapotranspiration (ETa) patterns over space and time is crucial for accurately estimating how water balance in catchments is affected by changing climate conditions. Evapotranspiration, which represents the combined processes of water evaporation from soil and water transpiration from plants, plays a critical role in the hydrological cycle and influences the availability of water resources for various applications such as agriculture, water supply, and ecosystem functioning [1]. One of the major challenges in hydrological modeling is the efficient calibration and validation of models, often hindered by the limited availability and quality of in-situ hydro-meteorological datasets [2]. These datasets are crucial for accurately representing local climatic conditions and landscape characteristics, which significantly impact the accuracy of hydrological models [3]. Consequently, researchers have explored alternative data sources to overcome these limitations, leading to the utilization of remote sensing-based data for model calibration and evaluation, particularly in poorly gauged basins [2,4,5,6]. Remote sensing techniques offer a valuable means of obtaining essential hydro-meteorological variables such as ETs over large spatial extents and at frequent intervals. These datasets provide valuable insights into the spatiotemporal dynamics of ETa, which are crucial for understanding the response of catchments to changing climate conditions [7]. For instance, satellite-derived ETa data have been used to identify shifts in ETa patterns, changes in growing seasons, and alterations in vegetation cover that influence water availability and ecosystem dynamics [8,9,10].

However, despite the advantages of using remote sensing-based data, challenges remain in accurately simulating ETa processes in hydrological models due to the complexities associated with land-use- and vegetation-specific parameters. Vegetation characteristics, such as leaf area index (LAI), effective plant height, rooting depth, and stomatal conductance, greatly influence water uptake and transpiration rates, directly impacting the ETa process [11]. Furthermore, variations in vegetation types and land cover introduce spatial heterogeneity in ETa, making it challenging to represent these dynamics accurately in models that rely on coarse-scale data [12]. As pointed out by Dickinson et al. [13], vegetation serves two essential functions in this context: First, plants can extract water from deeper soil layers than bare soil evaporation, making them crucial contributors to ETa processes. Second, during periods of drought stress, plants can reduce ETa rates through stomatal closure, conserving water in the ecosystem. The significance of vegetation-specific parameters is exemplified by the notable difference in aerodynamic resistance between short grass vegetation and forest vegetation. This difference can lead to considerable variations in ETa rates and patterns when simulated in hydrological models [13]. To address these challenges, the need to accurately consider vegetation-specific parameters in hydrological models has been emphasized. Therefore, incorporating feasible vegetation-specific information into the modeling process can lead to more realistic estimates of ETa rates and spatial patterns, thus enhancing the overall efficiency of hydrological models. Perez et al. [14] conducted a comparison of various methods to estimate canopy resistance in a river valley with uniform grass under semi-arid conditions. Their findings revealed that using a constant canopy resistance value could lead to underestimation or overestimation of evapotranspiration, particularly during summer and winter seasons. A study by Kang et al. [15] underscored the crucial role of canopy resistance in influencing evapotranspiration and energy exchange in water-limited environments. It was found that increased canopy resistance during drought conditions led to a shift towards sensible heat flux (H) over latent heat flux (LE) in energy partitioning, resulting in a higher Bowen ratio. In addition to canopy resistance, the leaf area index (LAI) is also a crucial vegetation parameter that directly influences the density and distribution of stomata on the surfaces of leaves. Generally, higher LAI values indicate denser vegetation with more leaves, resulting in a larger number of stomata available for water vapor exchange. Consequently, higher LAI values often lead to lower canopy resistance, meaning that the vegetation allows water vapor to pass through more easily, promoting higher transpiration rates. Nevertheless, LAI displays distinct spatial and temporal patterns. Spatially, it varies in response to the distribution of vegetation biomes across different regions on the Earth’s surface. At a temporal scale, the most significant variation occurs seasonally [16]. This temporal variation corresponds to the phenological phases, particularly leaf unfolding, playing a vital role in accurately parameterizing hydrological models while simulating ETa. By precisely representing phenological phases in hydrological models, we can more accurately identify other linked parameters like LAI and canopy resistance. As a result, the timing and intensity of vegetation’s water use and energy exchange with the atmosphere can be more realistically represented. Remote sensing techniques have proven to be valuable tools for obtaining phenological phases over large spatial areas. These techniques monitor changes in vegetation dynamics, which allows for studying the timing and patterns of phenological events. For instance, Kärgel et al. [17] investigated the long-term development of leaf unfolding in deciduous forests. They devised a method utilizing Landsat time series data to capture both temporal and spatial variations of leaf unfolding in a test area located in Thuringia, Germany. The research showcases the effectiveness of remote sensing techniques in delivering comprehensive phenological information. Dai et al. [18] used MODIS NDVI data for 16 years to investigate changes at the start of the growing season along the elevational gradient for six mountains in northern China with broadleaf deciduous forests.

In this study, we aim to address the connection between a poor model performance in terms of depicting annual evaporation courses and spatial ETa patterns and the lack of reliable parameter ranges for those vegetation parameters that strongly influence evaporation processes, i.e., the albedo, canopy resistance, interception resistance, soil surface evaporation resistance, leaf area index, vegetated cover fraction, root depth and effective vegetation height. As these parameters are often land-use- and catchment-specific, our study addresses model deficiencies for land-use classes for which no reliable parameter value ranges could be retrieved from similar studies or which do not correspond to the site-specific conditions of the catchments under investigation. We demonstrate the effectiveness of the manual calibration of the vegetation parameters mentioned above within realistic parameter ranges [19,20,21]. To attain this objective, in the first step, a series of 1D models were established that represent individual cells on the model grid for all land-use classes within the catchment. In the second step, for each land-use class, simulated ETa time series were calibrated against MODIS-derived 11-year mean ETa time series. In the final step, the catchment model was spatially validated against six cloud-free ETa scenes captured by Landsat-8.

2. Materials and Methods

2.1. Study Area

The Altenbamberg and Kellenbach catchments are situated within the Nahe valley in the state of Rhineland-Palatinate located in western Germany. Both catchments exhibit distinct river networks and notable differences in elevation, as shown in Figure 1. The Altenbamberg catchment, covering an expanse of 317.65 km², encompasses an elevation range from 128 m above sea level (m.a.s.l.) in the northern part, ascending to 563 m.a.s.l. on the uplands situated at the central and outer peripheries of the catchment. These areas showcase an average slope gradient of 8.13°, with the steepest slope measuring 33.45°. Conversely, the larger Kellenbach catchment spans 361.82 km² and exhibits an elevation spectrum extending from 220 m.a.s.l. up to 653 m.a.s.l. in the southwest. The average slope gradient here is 4.17°, with a maximum slope gradient of 42.33°.

The hydrometeorological conditions within the study area are characterized by a humid temperate climate (Cfb according to the effective climate classification after Köppen and Geiger [22]). The mean annual precipitation derived from the model’s interpolation of the meteorological input data from the weather stations within the catchments is 686.4 mm/a for the Kellenbach catchment and 664.0 mm/a for the Altenbamberg catchment. The mean annual runoff totals measured at the water gauges are 192.4 mm/a (Kellenbach) and 160.7 mm/a (Altenbamberg). The mean annual ETa sums amount to 494.0 mm/a (Kellenbach) and 503.3 mm/a (Altenbamberg).

Land-use data have been sourced from the CORINE land-cover dataset (CLC 2018). In total, the Altenbamberg catchment comprises 13 distinct land-use classes, while the Kellenbach catchment consists of 12. Within the Altenbamberg catchment, the largest shares of land use are occupied by deciduous forests (22.0%) and arable land (21.6%), followed by grassland (18.3%). In the Kellenbach catchment, coniferous forests (23.0%) take up a larger portion than deciduous forests (19.3%). Arable land (19.7%) and grassland (14.4%) constitute the second and third largest proportions, reflecting similar distribution patterns to those observed in the Altenbamberg catchment (see Figure 2).

2.2. Model Setup and Parameterization

ETa patterns were simulated using the WaSiM-ETH hydrologic model, a distributed and deterministic model following primarily physical principles. The model operates with constant time steps on a grid structure, which can be either regular or irregular in a raster configuration [23]. Comprising several sub-models, the WaSiM-ETH processes each of these sub-models sequentially for every time step across the entire grid (ibid). Within WaSiM-ETH, several sub-models function in a sequential manner for each time step, covering the entirety of the model grid (ibid.). The essential meteorological inputs, including temperature, wind speed, relative humidity, global radiation, and precipitation, were sourced from weather stations situated within the respective catchments. For the acquisition of necessary spatial data, such as slope, sub-catchment structure, flow accumulation, flow directions, and stream geometries, the digital elevation model (DEM) underwent preprocessing using the TANALYS tool within WaSiM-ETH.

Per grid cell, diverse runoff components (overland flow, baseflow, interflow, etc.) and ETa rates were computed. The description of water flow within unsaturated soil is described as one-dimensional with an unsteady flow, according to the principles of the Richards equation [24]. The model depicts soils as layered columns, with each soil layer characterized by specific attributes of water retention curves, which are described by the van Genuchten parameters [25], and saturated hydraulic conductivities [23]. The estimation of van Genuchten soil hydraulic properties was facilitated through the application of pedotransfer functions (PTFs), encompassing soil textural properties, bulk density, soil organic matter, and soil moisture content [26]. To assess the influence of specific PTFs on the spatial distribution of simulated ETa patterns, a series of 11 PTF combinations (refer to

Table 1. PTF combinations to estimate the parameters of van Genuchten (θsat, θres, n) and saturated hydraulic conductivity Ksat.

PTF Combination	van Genuchten Parameters	Soil Hydraulic Conductivity Ksat
1	Wösten et al. (1999) [29]	Ad-Hoc AG Boden (2005) KA5 [27]
2	Renger et al. (2009) [30]	Ad-Hoc AG Boden (2005) KA5
3	Weynants et al. (2009) [31]	Ad-Hoc AG Boden (2005) KA5
4	Zacharias and Wessolek (2007) [32]	Ad-Hoc AG Boden (2005) KA5
5	Teepe et al. (2003) [33]	Ad-Hoc AG Boden (2005) KA5
6	Zhang and Schaap (2017): Rosetta H2w [34]	Ad-Hoc AG Boden (2005) KA5
7	Zhang and Schaap (2017): Rosetta H3w [34]	Ad-Hoc AG Boden (2005) KA5
8	Wösten et al. (1999)	Wösten et al. (1999)
9	Renger et al. (2009)	Renger et al. (2009)
10	Zhang and Schaap (2017): Rosetta H2w	Zhang and Schaap (2017): Rosetta H2w
11	Zhang and Schaap (2017): Rosetta H3w	Zhang and Schaap (2017): Rosetta H3w

) were employed across distinct simulation runs. These combinations determine the values of the van Genuchten parameters (namely θsat, θres, α, n, and m) and the saturated hydraulic conductivity, Ksat. Notably, the PTF combinations numbered 1 to 7 derive Ksat from the Ad-Hoc AG Boden dataset [27]. These PTF combinations diverge in their underlying databases, the quantity of analyzed soil samples, and the predictors utilized within the equations [28].

2.3. MODIS ETa (Dataset for Model Calibration)

To establish a calibration dataset, we utilized continuous satellite-based evapotranspiration time series covering the primary land-cover types within each catchment. These time series spanned the period from 2010 to 2020 and were generated using moderate resolution evapotranspiration estimates, approximately 500 m in scale, derived from the MODIS ETa product (MOD16A2). This product was obtained through the NASA Earth data search interface (https://search.earthdata.nasa.gov/search, accessed on 30 March 2022). The MOD16A2 product [35,36] provides composite net evapotranspiration for 8-day time intervals at 500 m pixel resolution using a modified Penman–Monteith equation with global surface meteorology from the Goddard Earth Observing System (GEOS) and MODIS Collection 6 surface reflectance products as inputs [37].

For this study, the daily ETa values for each of the land-use classes from the MOD16A2 and the MYD16A2 products were aggregated to the 8-day ETa average over 11 years (2010–2021).

Time series of average 8-day ETa were generated for each major land-use class within the study catchments based on the CORINE land-cover layer. The coarse ~500 m MODIS-scale pixels were first screened for land-cover homogeneity to minimize mixed pixel effects in the resulting time series. For each MODIS pixel, we then calculated the majority CORINE land-cover class share within the 500 m² cell and classified pixels with less than 80% majority cover share as heterogeneous. These mixed pixels were subsequently filtered out and the remaining homogeneous MODIS ETa data cells were averaged by CORINE land-cover class to create the final ETa time series. The evaluation of the water balance at the Kellenbach gauge showed that to close the water balance, a correction factor of 0.904 had to be applied to the MODIS ETa time series using:

$$\mathrm{S}\mathrm{u}\mathrm{m}\left(\mathrm{E}\mathrm{T}{\mathrm{a}}_{\mathrm{M}\mathrm{O}\mathrm{D}\mathrm{I}\mathrm{S}}\right) \mathrm{\ast } 0.904=\mathrm{S}\mathrm{u}\mathrm{m}\left(\mathrm{E}\mathrm{T}\mathrm{a}\right)=\mathrm{S}\mathrm{u}\mathrm{m}\left(\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\right)-\mathrm{S}\mathrm{u}\mathrm{m}\left(\mathrm{r}\mathrm{u}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{f}\right)$$

(1)

2.4. Landsat ETa (Dataset for Model Validation)

For the validation of the model’s performance, a selection of six dates (15 April 2015, 29 June 2019, 4 July 2015, 23 August 2016, 19 September 2020 and 24 September 2016) was made. These dates were carefully chosen to represent diverse system moisture states that encompass the annual course of vegetation development and span the entire spectrum from wet to dry conditions. The validation dataset utilized Landsat-8 scenes that covered the geographical extent of the study region. These scenes were acquired via the USGS Earth Explorer application (https://earthexplorer.usgs.gov accessed on 30 March 2022) and consisted of atmospherically corrected surface reflectance and land surface temperature data from Landsat Collection 2 Level-2 science products. The spatial resolution of these datasets was nominally set at 30 m. Landsat surface reflectance data were generated using the Land Surface Reflectance Code (LaSRC) at the Earth Resources Observation and Science (EROS) Center. These data provide an estimate of the surface spectral reflectance at ground level, effectively eliminating atmospheric effects like scattering and absorption [38]. Corresponding Landsat surface temperature products were generated at the Earth Resources Observation and Science (EROS) Center using the Landsat Collection 2 Level-1 thermal infrared bands with a single-channel algorithm. This algorithm incorporated a range of auxiliary data fields to account for factors such as land surface reflectance, emissivity, vegetation cover, and atmospheric conditions [39].

Actual evapotranspiration (ETa) estimates, offering high spatial resolution (~50 m), were derived through the Operational Simplified Surface Energy Balance (SSEB) model [7,40]. The SSEB model leverages a linear relationship between sensible heat flux and land surface temperature (LST) within a remote sensing scene to estimate ETa. This estimation involves scaling a reference evapotranspiration (ET0) between two extreme points—termed hot and cold pixels—within the image. The hot pixel signifies minimal evapotranspiration due to the absence of evaporative cooling, while the cold pixel represents maximal evapotranspiration (equal to ET0). For all other pixels, ETa is scaled proportionally to their LST relative to the hot and cold pixels, resulting in the dimensionless evaporative fraction (ETf):

$${ET}_f=\frac{{LST}_H-{LST}_i}{{LST}_H-{LST}_C}$$

(2)

where LST_H is the LST at the hot pixel, LST_C is the LST at the cold pixel and LSTi is the LST of any image pixel. The hot (LST_H) and cold pixels (LST_C) for a given scene are selected using the scenes LST–NDVI feature space with hot pixels corresponding to dry, barren fields with low NDVI and high LST and cold pixels corresponding to fully-vegetated, well-watered plots. The ETa for each pixel in the study area can then calculated by:

$${ET}_a={ET}_f\times {ET}_0$$

(3)

where ET_a is the actual evapotranspiration [mm], ET_f is the evaporative fraction and ET₀ is the reference evapotranspiration [mm]. Reference evapotranspiration ET₀ was calculated with standard meteorological station data using the Penman–Monteith equation for a shortgrass crop (FAO-56). We used the gridded INTERMET meteorological station data for Rhineland-Palatinate [41] as meteorological data inputs.

Since our study area was characterized by mixed landscapes and considerable topography, we applied a suggested adaption of the SSEB model for more complex landscapes [42], which further integrates digital elevation (DEM) and vegetation index (VI) data to adjust LST and ET_f, respectively:

$${LST}_{DEM}=LST+L\times DEM$$

(4)

where LST_DEM is the elevation-adjusted LST [°K] that replaces the regular LST for ET_f calculations, L is the atmospheric lapse rate [0.0065 °K/m] and DEM is the terrain elevation [m];

$${ET}_{f,VI}=(0.35\times \frac{NDVI}{0.7}+0.65)\times {ET}_f$$

(5)

where ET_f,VI is the vegetation index-adjusted evaporative fraction.

2.5. Land-Use-Specific Calibration Process Using MODIS Data

To systematically calibrate the hydrological model based on land-use characteristics and vegetation-specific parameters with the aim of enhancing the simulation of spatial ETa patterns in the catchment, the following approach has been implemented.

(i)

Setup of 1D models for land-use-specific calibration:

One-dimensional models were established to represent individual cells on the model grid, specifically tailored for distinct land-use classes in both catchments. The selection process involved identifying pixels that were exclusively covered by a particular land-use class, minimizing the inclusion of mixed signatures through the inherent attributes of the selected raster cells, such as coordinates, elevation, and soil data, which were extracted from chosen raster cells to serve as input parameters for the model.

(ii)

Soil parameterization and land-use transformation:

For the parameterization of soil-related properties, we selected PTF combination 1 to estimate the key soil parameters required for the modeling process. To integrate land-use specifics, initial land-use classes from the CORINE land-cover data (as described in Section 2.1) were transformed into comprehensive land-use tables. These tables were integrated into the model’s control files to incorporate land-use-specific vegetation and ETa parameters. One example for the land-use table of arable land is shown in

Table 2. Calibrated vegetation parameters in the WaSiM model for arable land (CLC 211).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.200	0.200	0.200	0.200	0.200	0.200	0.210	0.250	0.220	0.200	0.200	0.200
rsc	100	100	105	105	60	55	110	135	100	100	100	100
rs_interception	50	50	50	50	50	50	50	50	50	50	50	50
rs_evaporation	200	225	240	245	160	150	200	260	205	150	150	180
LAI	0.900	0.900	0.900	0.900	3.800	4.900	1.700	0.900	0.900	0.900	0.900	0.900
z0	0.500	0.500	0.500	0.500	1.000	1.000	0.900	0.400	0.500	0.500	0.500	0.50
vcf	0.500	0.500	0.500	0.500	0.600	0.660	0.450	0.300	0.500	0.500	0.500	0.50
root depth	0.400	0.400	0.400	0.400	1.100	1.200	1.000	0.400	0.400	0.400	0.400	0.40

; the other land-use tables are included in the Appendix A (

Table A1. Calibrated vegetation parameters in the WaSiM model for settlement (CLC 112).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.150	0.150	0.150	0.150	0.150	0.150	0.150	0.150	0.150	0.150	0.150	0.150
rsc	100	100	100	110	110	100	150	150	130	100	100	100
rs_interception	50	50	50	50	50	50	60	65	65	50	50	50
rs_evaporation	200	200	220	250	200	240	330	360	290	200	200	200
LAI	0.800	0.900	1.000	1.100	1.900	2.000	1.400	1.250	1.250	1.225	1.100	0.800
z0	1.000	1.000	1.200	1.300	1.300	1.300	1.300	1.300	1.300	1.200	1.000	1.000
vcf	0.260	0.268	0.270	0.280	0.460	0.500	0.350	0.330	0.320	0.300	0.274	0.260
root depth	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

,

Table A2. Calibrated vegetation parameters in the WaSiM model for mine (CLC 131).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.200	0.200	0.200	0.200	0.200	0.200	0.200	0.200	0.200	0.200	0.200	0.200
rsc	100	100	100	100	90	110	135	130	100	100	100	100
rs_interception	50	50	50	50	50	55	70	65	50	50	50	50
rs_evaporation	215	215	220	250	190	250	265	260	200	200	200	250
LAI	0.800	1.000	1.100	1.200	2.500	2.350	1.600	1.600	1.600	1.300	1.000	0.800
z0	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300
vcf	0.260	0.270	0.270	0.270	0.500	0.500	0.450	0.450	0.450	0.400	0.350	0.260
root depth	0.500	0.500	0.500	0.500	0.500	0.500	0.500	0.500	0.500	0.500	0.500	0.500

,

Table A3. Calibrated vegetation parameters in the WaSiM model for viticulture (CLC 221).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.145	0.145	0.145	0.180	0.190	0.190	0.190	0.190	0.190	0.190	0.150	0.150
rsc	100	100	100	110	90	85	135	140	115	100	100	100
rs_interception	50	50	50	50	50	45	65	65	50	50	50	50
rs_evaporation	260	250	250	275	265	260	280	290	270	200	220	260
LAI	1.000	1.000	1.100	1.100	2.000	2.250	1.200	1.250	1.550	1.800	1.300	1.000
z0	1.800	1.800	1.800	1.800	2.000	2.100	2.000	2.000	2.000	2.000	1.900	1.900
vcf	0.500	0.500	0.525	0.450	0.600	0.600	0.500	0.500	0.550	0.550	0.550	0.500
root depth	2.000	2.000	2.000	2.000	2.000	2.000	2.000	2.000	2.000	2.000	2.000	2.000

,

Table A4. Calibrated vegetation parameters in the WaSiM model for grassland (CLC 231).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.193	0.193	0.197	0.197	0.197	0.197	0.197	0.197	0.193	0.193	0.193	0.193
rsc	100	125	125	125	80	80	120	115	100	100	100	100
rs_interception	50	60	60	60	50	40	50	60	50	50	50	50
rs_evaporation	200	350	350	350	310	260	300	300	200	200	200	200
LAI	1.900	1.900	1.900	1.900	4.000	4.000	4.000	3.500	3.500	3.250	2.000	1.600
z0	0.100	0.100	0.130	0.200	0.500	0.500	0.200	0.200	0.200	0.150	0.130	0.100
vcf	0.750	0.750	0.750	0.750	0.950	0.950	0.750	0.700	0.750	0.750	0.750	0.750
root depth	0.400	0.400	0.400	0.400	0.450	0.450	0.450	0.400	0.400	0.400	0.400	0.400

,

Table A5. Calibrated vegetation parameters in the WaSiM model for scrubland (CLC 324).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.160	0.160	0.160	0.180	0.180	0.180	0.180	0.180	0.180	0.17	0.17	0.160
rsc	100	100	100	100	100	95	160	160	100	100	100	100
rs_interception	50	50	50	60	50	50	60	60	50	50	50	50
rs_evaporation	280	280	300	400	400	400	400	400	380	280	280	290
LAI	1.000	1.000	1.300	1.800	4.000	4.200	3.200	2.900	2.400	1.800	1.000	1.000
z0	1.000	1.000	2.000	2.500	3.500	3.500	3.200	3.000	3.000	2.500	2.000	1.000
vcf	0.400	0.400	0.500	0.550	0.850	0.900	0.800	0.750	0.700	0.650	0.500	0.400
root depth	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300	1.300

,

Table A6. Calibrated vegetation parameters in the WaSiM model for coniferous forest (CLC 312).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.125	0.125	0.124	0.120	0.118	0.112	0.105	0.105	0.105	0.110	0.110	0.120
rsc	130	130	130	130	110	100	160	160	90	100	100	100
rs_interception	60	60	60	60	50	50	60	70	45	50	50	50
rs_evaporation	900	900	900	900	800	800	850	900	700	800	800	800
LAI	4.000	3.900	3.900	4.400	5.900	5.900	5.900	5.800	5.800	5.500	5.000	4.500
z0	10.00	10.00	10.00	10.00	10.00	10.00	10.00	10.00	10.00	10.00	10.00	10.00
vcf	0.700	0.700	0.710	0.740	0.830	0.850	0.830	0.820	0.820	0.750	0.750	0.700
root depth	1.500	1.500	1.500	1.500	1.500	1.500	1.500	1.500	1.500	1.500	1.500	1.500

and

Table A7. Calibrated vegetation parameters in the WaSiM model for mixed forest (CLC 313).

Julian Days	15	46	74	105	135	166	196	227	258	288	319	349
albedo	0.140	0.139	0.137	0.136	0.136	0.138	0.135	0.132	0.135	0.135	0.130	0.130
rsc	115	115	115	115	105	97.5	152.5	152.5	105	112.5	100	100
rs_interception	55	55	55	60	50	50	60	65	47.5	50	50	50
rs_evaporation	590	590	600	650	650	600	620	645.5	595	540	540	545
LAI	2.500	2.450	2.300	3.450	6.950	6.950	6.750	6.700	6.700	4.500	3.000	2.750
z0	5.50	5.50	5.75	6.00	10.00	10.00	10.00	10.00	10.00	6.50	5.75	5.50
vcf	0.550	0.550	0.600	0.650	0.840	0.870	0.830	0.830	0.830	0.700	0.610	0.550
root depth	1.710	1.710	1.710	1.710	1.710	1.710	1.710	1.710	1.710	1.710	1.710	1.710

).

(iii)

Manual Calibration of Vegetation Parameters and Phenological Patterns:

For the calibration of the 1D models, a range of vegetation parameters within the land-use tables was adjusted manually using three efficiency metrics (PBIAS, RMSE and SKout), as described in Section 2.6. The calibrated parameters included albedo, canopy resistance (rsc) in s/m, interception resistance (rs_interception) in s/m, soil surface evaporation resistance (rs_evaporation) in s/m, leaf area index (LAI), vegetated cover fraction (vcf), root depth in m, and effective vegetation height (z0) in m. In the WaSiM model, z0 represents the effective vegetation height—computed as the difference between canopy height and the zero-plane displacement height (d) [23].

The calibration process was guided by feasible value ranges derived from the existing literature on phenological parameters. Notably, LAI value ranges and annual courses were based on a study conducted in the southwest of Germany [19]. It was observed, in line with Sakai et al. (1997) [20], that the initial rise in LAI during spring correlated often with an increase in albedo and a decrease in canopy resistance (rsc). Subsequently, during leaf senescence, transpiration and photosynthesis became less effective, leading to a reduction in LAI and a corresponding increase in canopy resistance and albedo. The static parameterization of the land-use tables in the WaSiM model does not allow for the depiction of dynamic phenology. Instead, the vegetation parameters are calibrated for 12 dates specified as Julian days covering all phenological cycles during the year. Thus, the variability of parameters such as the LAI can only be depicted within the years, but not between different years of the dataset, which might result from shifts in the phenological cycle due to changing hydrometeorological conditions or varying harvest dates. An example of the calibrated vegetation parameters for the land-use class arable land is given in Table 2. In accordance with the LAI value ranges given by Hung et al. [19], the LAI for the arable land was adjusted between 0.9 in winter and early spring when there is no or little vegetation and 4.9 when the crops are fully developed and the roots reach deeper. Accordingly, the canopy resistance (rsc), which was initially set to 100 s/m, was reduced for the months with increasing LAI values and root depths (Julian days 135 and 166).

2.6. Performance Metrics for Model Analysis

The assessment of the conformity between the ETa curves originating from the 1D-model outputs and the MODIS ETa curves was accomplished using three distinct efficiency metrics: the percent bias (PBIAS), root-mean-squared error (RMSE), and skill score (SKout). Additionally, to evaluate the congruence of ETa spatial patterns derived from the model in relation to those observed through remote sensing, a spatial efficiency metric formulated by Demirel et al. (2018) was employed.

The percent bias quantifies the dissimilarity between the simulated and observed values. According to Gupta et al. (1999), it is calculated by deducting the sum of the observed values (sum_obs) from the sum of the simulated values (sum_sim) and then dividing this result by the sum of the observed values and subsequently multiplying by 100%:

$$PBIAS=\frac{{sum}_{sim}-{sum}_{obs}}{{sum}_{obs}\times 100 \%}$$

(6)

The root-mean-squared error represents the square root of the mean squared error within the dataset (Hodson 2022):

$$RMSE=\sqrt{MSE}$$

(7)

The skill score (SKout) is an efficiency measure similar to the Nash-Sutcliffe Efficiency, where a value closer to one indicates better model prediction. It is defined as one minus the RMSE divided by the standard deviation (std_obs) of the observed data (Burkey, 2023):

$$SKout=1-\frac{RMSE}{{std}_{obs}}$$

(8)

To facilitate comparative analysis across various conditions over the years, the “system state”, denoted as the “potential mean daily ETa” in mm per day was computed. For each day of the simulation, the system state was stored and used as initialization for a 1-day simulation of ETa with uniform meteorological input, characterized by warm, dry, and high solar radiation conditions. This was done for all 11 pedotransfer function (PTF) configurations.

For the final validation of the catchment model, six cloud-free ETa scenes were used. They were distributed across the period from April to September during the years 2015 to 2021. To compare these scenes to the simulated ETa, we applied the so-called spatial efficiency metric (SPAEF), which is an innovative and bias-insensitive spatial performance metric that has been developed based on the Kling–Gupta efficiency (KGE) [43]. Unlike the KGE, which includes the standard deviation term, this metric substitutes the latter with the coefficient of variation. Moreover, instead of using bias, it incorporates a histogram comparison index, signifying the intersection between the observed and simulated patterns [44].

The SPAEF is mathematically expressed by the following equation:

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

(9)

where:

$$\alpha =\mathit{\rho }\left(\mathit{A},\mathit{B}\right); \mathit{\beta }=\left(\frac{{\mathit{\sigma }}_{\mathit{A}}}{{\mathit{\mu }}_{\mathit{A}}}\right)/\left(\frac{{\mathit{\sigma }}_{\mathit{B}}}{{\mathit{\mu }}_{\mathit{B}}}\right); \mathit{\gamma }=\frac{\sum _{\mathit{j}=1}^{\mathit{n}}\mathbf{min}\left({\mathit{K}}_{\mathit{j}},{\mathit{L}}_{\mathit{j}}\right)}{\sum _{\mathit{j}=1}^{\mathit{n}}{\mathit{K}}_{\mathit{j}}}$$

α represents the Pearson correlation coefficient between the observed data (A) and the simulated data (B), while β denotes the fraction of the coefficient of variations. Additionally, γ signifies the percentage of the histogram overlap. The SPAEF is rescaled to range between −∞ and 1. Positive values indicate a pattern alignment, with values approaching 1 indicating a higher similarity between the observed and simulated patterns [44].

3. Results

3.1. System State Analysis

The initial evaluation of the uncalibrated model revealed a substantial mismatch between the MODIS curves and the model output for the 1D simulations, resulting in partially inverted patterns with negatively correlated SPAEF values for the six selected LANDSAT dates (15 April 2015; 4 July 2015; 29 June 2019; 23 August 2016; 19 September 2020 and 24 September 2016). To investigate the influence of the different moisture conditions of the catchment system (dry or wet), the scenes were categorized based on their system state, as depicted in Figure 3. Notably, the date 15 April 2015 (A) represented the wettest condition in the dataset, serving as an average of the system state (the white dots in Figure 3). Conversely, the date 19 September 2020 (E) portrayed the driest system state in the simulation for all PTFs. Interestingly, even under these dry conditions, PTF combinations No. 4 and 5 exhibited higher water availability compared to other PTFs, as evidenced by their elevated ETa values. The four other scenes (B, C, D, F) lie in between and represent well the decreasing soil moisture (compared to April) and the changing vegetation status during the growing season. The second September scene (F) is much wetter than the dry September scene, which allows for a detailed evaluation of water-holding capacity in the model.

3.2. Land-Use-Specific Calibration of Single-Cell Models

Since the calibration process was guided by reasonable value ranges derived from scientific experience including the literature on phenological parameters, all vegetation-specific parameters were manually adjusted.

Table 3. Calibrated vegetation parameters in the WaSiM model for deciduous forest (CLC 311).

Julian Days	15	46	74	105	135	166	196	227	268	298	319	349
albedo	0.150	0.150	0.150	0.180	0.180	0.180	0.180	0.170	0.170	0.170	0.170	0.160
rsc	100	100	100	100	100	95	145	145	120	120	100	100
rs_interception	50	50	50	60	50	50	60	60	50	50	50	50
rs_evaporation	280	280	300	400	400	400	390	390	280	280	280	290
LAI	1.000	1.000	1.500	2.500	8.000	8.000	7.500	7.500	7.500	3.600	1.000	1.000
z0	1.000	1.000	1.500	2.000	10.00	10.00	10.00	10.00	10.00	3.000	1.500	1.000
vcf	0.400	0.400	0.500	0.550	0.850	0.900	0.840	0.840	0.840	0.650	0.500	0.400
root depth	2.200	2.200	2.200	2.200	2.300	2.300	2.300	2.200	2.200	2.200	2.200	2.200

gives an example of the final vegetation parameters for deciduous forests (CLC 311). Here, we find a fast increase in LAI in May and June and a drop during October when leaves are falling. Canopy resistance (rsc) is close to 100 s/m during phases of sufficient water availability, and between July and October, rsc increases, representing the stomatal reaction of the trees to (temporal) water limitation. Effective vegetation height (z0) follows the LAI because leaves increase the aerial resistance of the tree. The calibrated vegetation parameters of the remaining land-use types, which show the highest alignment between simulated and measured ETa, are shown in the Appendix A. The tables only contain the vegetation parameters that were manually calibrated in this study. All other parameters contained in the model’s land-use tables have been adopted from Rieger [45] and Teschemacher [46], except for the altitude dependence, which was set to a constant value of zero for all land-use types.

Upon conducting land-use-specific calibration for the single-cell models by adjusting the vegetation parameters as outlined in the example of the deciduous forest, a noticeable enhancement in model performance for all land-use classes was observed across various efficiency metrics, as outlined in

Table 4. Efficiency of the 1D models before and after the land-use-specific manual calibration.

Land Use	PBIAS		RMSE		SKout
	Before	After cal.	Before	After cal.	Before	After cal.
112: Settlement	17.32	1.21	2.77	0.77	0.50	0.86
121: Commercial	17.36	1.40	2.73	0.87	0.54	0.85
131: Mine	4.00	−0.08	1.36	0.80	0.75	0.85
132: Landfill	4.35	2.73	2.41	1.14	0.64	0.83
142: Sports areas	−15.08	−4.87	3.60	1.66	0.59	0.81
211: Arable land	−12.60	1.86	3.55	0.73	0.55	0.91
221: Viticulture	50.57	0.32	5.20	0.77	0.10	0.87
231: Grassland	−8.23	0.79	2.89	0.77	0.66	0.91
242: Complex arable land	−5.39	0.82	2.47	0.81	0.69	0.90
243: Arable land (natural)	20.90	1.22	4.02	1.08	0.56	0.88
311: Deciduous forest	12.84	−0.11	3.00	1.20	0.69	0.88
312: Coniferous forest	36.51	2.12	4.77	1.17	0.42	0.86
313: Mixed forest	27.07	1.01	4.24	1.20	0.53	0.87
322: Moorland	26.39	9.67	3.88	1.64	0.35	0.72
324: Shrubland	31.16	1.99	4.25	0.98	0.51	0.89

. Particularly remarkable improvements were achieved for specific land-use classes, including 243 (arable land (natural)), 211 (arable land), and the deciduous, coniferous, and mixed forests (CLC 311, 312, and 313). For instance, the initially highly negative percent bias (PBIAS) of −12.60% for arable land transformed to a small positive value of 1.86. Concurrently, the root-mean-square error (RMSE) decreased from 3.55 to 0.73, and SKout improved to 0.91 (see Table 4). Similar improvements were noted for the deciduous forest, which saw a shift from a large PBIAS (12.84%) to a near-neutral value (−0.11), alongside reduced RMSE (from 3.00 to 1.20) and improved SKout (from 0.69 to 0.90). The fitting of vegetation parameters for land-use classes with high variability in surface properties or a very small percentage of the area (landfill, sports areas, moorland) was less effective. Vegetation parameters for settlements including commercial areas remain catchment-specific since the vegetated fraction of the surface is highly variable in those areas.

The effectiveness of this calibration process is illustrated in Figure 4 for the land-use classes with the highest areal share of the catchments. The MODIS 8-day-sum ETa curves (red) and the calibrated simulated 8-day-sum ETa curves (blue) show a good alignment. However, some deviations are evident for certain times of the year. For instance, the arable land (CLC 211) shows a small misfit between the simulated and the measured ETa in late summer and autumn. On the other hand, the simulated ETa of the deciduous forest (CLC 311) exhibits a visible misfit between June and September. The coniferous forest (CLC 312) shows the highest misfit in April. The misfits for the deciduous and the coniferous forest are both visible in the plotted ETa curves of the mixed forest (CLC 313). The mixed forest has been parameterized by a simple averaging of all vegetation parameters of deciduous and coniferous forests.

3.3. Spatial Pattern Analysis Based on SPAEF

The catchment-wide validation of simulated ETa with the LANDSAT scenes showed a clear improvement of SPAEF for most PTFs and most of the dates after the calibration of vegetation parameters. Figure 5 shows a good matching pattern. The SPAEF is 0.49, whereas the correlation is 0.74, and the variance ratio is 0.91. The histogram overlap is a bit smaller (0.57) because the absolute values of ETa differ. The ETa pattern is correctly simulated for all main vegetation units, and the simulation reproduces even small topographic features like (wetter) valleys.

In the Kellenbach catchment, there are still negatively correlated SPAEF values, which even experienced a further reduction across all PTFs after the calibration for April 2015, as depicted in Figure 6. Furthermore, for the driest month within the time series (19 September 2020), only PTFs 4 and 5 displayed positive SPAEF values even before calibration. While the calibration led to a clear improvement in SPAEF for PTF 5 during the dry September of 2020, PTF 4 exhibited a slight drop in SPAEF after the calibration, while still maintaining a positive SPAEF value. Among the remaining PTFs (6, 7, 10, and 11), the calibration induced SPAEF improvements for the September date, but definitive remarkable shifts were witnessed only in PTFs 6 and 7. Notably, the calibration consistently yielded a visible overall SPAEF improvement across all PTFs for the remaining dates (29 June 2019, 4 July 2017, 23 August 2016, and 24 September 2016).

A similar trend emerged in the Altenbamberg catchment. The calibration consistently elevated SPAEF values across all dates and PTFs, as highlighted in Figure 7. Nevertheless, similar to the Kellenbach catchment, certain dates continued to exhibit negative SPAEF values post-calibration, particularly notable in April 2015 and September 2020. However, in contrast to the Kellenbach catchment, the SPAEF for April 2015 improved for all PTFs but remained negative or near zero. For the dry September 2020, PTFs 4 and 5 again show the best model performance in terms of SPAEF values. Whereas in the Kellenbach catchment, the behavior of the PTFs for September 2020 is heterogenous with some PTFs that result in increasing and others in decreasing SPAEF values post calibration, in the Altenbamberg catchment, all PTFs show an improvement in terms of SPAEF for September 2020.

Zooming out to gain a broader temporal perspective, we obtained compelling dynamics through an examination of the distribution of MODIS-derived 8-day evaporation sum from 2010 to 2020. These dynamics highlight the remarkable contrast in ETa variability between distinct timeframes, notably exemplified by the cases of 15 April 2015 and 19 September 2020. The ETa variability around the mean value (represented by the dark blue line in Figure 8) is much larger for 15 April 2015 than for 19 September 2020, as indicated by the red arrows in Figure 8. Moreover, we observe a general trend of heightened ETa variability during the summer months in contrast to the relatively stable pattern with lower fluctuations during the winter season, as depicted by the grey lines symbolizing the standard deviation in Figure 8.

4. Discussion

An initial evaluation of the uncalibrated model revealed a substantial mismatch between the model’s predictions and observed MODIS data, resulting in partially inverted patterns of ETa and negative SPAEF values. Examining the broader temporal patterns, the distribution of MODIS-derived 8-day ETa sum from 2010 to 2020 highlighted substantial ETa variability, notably between 15 April 2015 and 19 September 2020. This variability, in general, was more pronounced during summer months compared to the relatively stable winter pattern. The land-use-specific MODIS-based calibration of vegetation parameters significantly improved the model’s performance, particularly for arable land and deciduous forests (i.e., evident through the overall improvements in various efficiency measures shown in Table 4, where negative biases shifted to positive or near-neutral values, RMSE decreased, and SKout improved).

Moreover, during model validation using LANDSAT data after the calibration of vegetation parameters, we observed a distinct and consistent enhancement in SPAEF values (i.e., that primarily focused on patterns rather than specific values) across most of the six available dates. However, some challenges remain, particularly the negative SPAEF values observed in April 2015 and in the dry September of 2020. Our calibration strategy was to linearly scale canopy resistance and other ETa-related vegetation parameters based on the literature values [19,20,21] and assumed phenological cycles (e.g., canopy resistance was set to values around 100 s/m and then calibrated within a range between 55 and 160 s/m). This strategy proved to be applicable to the conditions within our catchments. To further investigate dependencies on moisture conditions, we categorized six selected LANDSAT dates based on the catchment’s moisture conditions (wet vs. dry). The validation process using six selected LANDSAT dates revealed that the system state, whether wet or dry, significantly influences the efficiency of manual land-use-specific model calibration, as indicated by the SPAEF values. This aligns with the findings of Sakai et al. [20], who observed a linear relationship between canopy resistance (rc), surface resistance (rs), and LAI during the growing season (i.e., rc ≈ rs/LAI). This suggests that under wet conditions, forests transpire as much as LAI allows, even during leaf senescence. However, this relationship becomes invalid under dry conditions. Further insights come from Lin et al. [47], who noted the coupling of canopy resistance and water vapor fluxes with meteorological conditions. The behavior of canopy resistance in different seasons and under varying conditions plays a crucial role in modulating ETa patterns. For example, if canopy resistance exceeds 200 s/m, the Penman–Monteith equation becomes less sensitive to rc changes, but this sensitivity increases when rc falls below 100 s/m.

The variation of MODIS-driven ETa between 2010 and 2020 (depicted in Figure 8) shows that ETa estimates represent different values in different years (be they wet or dry), with the highest variability in April among all 11 years. This implies that ETa estimates for seasons and months within the years are not static, and, for example, for April, we see a high variability between different years (deviation from the mean value). These segments of high variation coincide with changes in the phenological status of vegetation cover, such as the start of the growing season in April and harvest dates in late summer and autumn. This dynamic interaction highlights that the fluctuations in vegetation behavior—driven by the changing seasons and phenological transitions—play a dominant role in shaping the characteristics of key vegetation parameters, e.g., canopy resistance. As a result, this leads to substantial spatial, intra-annual, and inter-annual variability in ETa rates [13,48]. This phenomenon exerts an even more pronounced impact in terms of estimating divergent ETa values and varying the timing of events like harvesting within a single land-use class—albeit in different catchments, during distinct seasons, and across various years—compared to the influence that variations in land-cover types (e.g., between arable lands and different forests) have on adjusting vegetation parameters.

Therefore, the poor performance of the WaSiM model in depicting the spatial patterns of ETa during April and September, as indicated by the SPAEF values (Figure 6 and Figure 7), can be attributed to a fundamental limitation of the model. Specifically, the WaSiM model employs a static parameterization that struggles to account for the dynamic inter-annual variations in plant development, particularly during these critical months (Figure 8). Hence, the ETa pattern dissimilarities in April are due to a model deficiency in the adjustment of phenological patterns across different land-use types. April marks the start of the growing season in temperate climates, characterized by significant changes in vegetation, including bud burst and leaf development [49]. However, the exact timing of these events can vary from year to year due to climate change and other environmental factors. For instance, in years with extended winters, vegetation may still experience frozen days in April, delaying its growth cycle. Conversely, in milder years, growth initiation might occur earlier [50]. The static consideration of a fixed date for processes like leaf development in the model overlooks these phenological adjustments. Another major model deficiency becomes apparent in September, during the harvesting period for various land-use types and within distinct catchments. Successful calibration demands an understanding of the multifaceted variables influencing crop growth, including water availability, sunshine duration, and temperature. These factors differ not only across catchments but also in various agricultural practices and land-use types. Optimal harvesting times vary for each catchment based on local agricultural practices and environmental conditions. When the model fails to capture variations in crop growth rates and optimal harvesting times unique to each catchment’s land-use classes, it cannot adjust for dynamic changes in soil moisture and water stress periods accurately. Consequently, the error observed in September is related to the model’s inability to represent the complex interplay of these factors accurately and consider the role of crop sensitivity to water stress in estimating ETa [51]. To effectively tackle these identified limitations, a phenology-driven model—one capable of accurately representing inter-annual variations in vegetation development—might enhance model performance. By dynamically adjusting to the evolving phenological patterns, the model can better account for the actual timing of growth stages for various vegetation types. Furthermore, a targeted approach could involve categorizing crops based on their unique planting times. Boegh et al. [52] suggested a more efficient approach involving the classification of crops into separate categories based on their planting times, distinguishing between early- and late-spring sowing. Implementing such a strategy in our specific case might contribute to improved SPAEF values, especially for the April 2015 timeframe. Moreover, soil-specific analysis could further explain how soil properties interact with ETa patterns and model behavior and consequently improve the ETa estimations in September [53].

Divergent ETa patterns between different catchments under the same climatic conditions can be attributed to several key factors [2,54], where in our specific case of the Altenbamberg and Kellenbach catchments, we find pronounced differences. They exhibit variations in phenology related to vegetation growth stages and soil characteristics, modified by varying elevations above sea level. Elevation influences the annual phenological cycle via temperature and precipitation values and thus determines the timing of agricultural practices, leading to variable and specifically different harvest dates between the two catchments [50]. In addition, when considering land use in forested areas, it is essential to account for local conditions that can introduce variability. Factors like tree age and nutrient levels may significantly differ between the two investigated catchments and play a substantial role in generating these variabilities [6].

Given these existing disparities, it becomes evident that employing a uniform calibration approach based on the mean ETa estimations of both catchments obtained from MODIS data is insufficient, and it is regarded as another potential explanation for the suboptimal pattern performance in terms of SPAEF values. Research by Becker et al. [55] highlights that calibrating a model to the mean values of remotely sensed ETa data can pose challenges, particularly in small-scale agricultural regions. This challenge becomes apparent during seasons characterized by highly diverse crop patterns, where the spatial variability of ETa cannot be adequately represented.

The other factor significantly affecting the spatial patterns of simulated ETa was the variability in the PTF combinations used. The choice of PTFs emerges as a key determinant, showcasing distinct behaviors in terms of SPAEF values across the catchments. Since PTFs are grounded in soil characteristics [26], the disparities in the spatial patterns of simulated ETa and those obtained from remote sensing can be also attributed to the contrasting soil compositions within the two catchments [56]. Specifically, the Kellenbach catchment predominantly features sandy loams and clays, while the Altenbamberg catchment is characterized by sandy soils [57]. This contrast in soil characteristics significantly influences the behavior of the PTFs [58] and, consequently, the simulation outcomes [28,53,56]. To gain a deeper understanding of these variations, conducting a soil-specific analysis of spatial patterns, utilizing the SPAEF measure is imperative. Such an analysis would provide valuable insights into how soil properties elaborately shape model behavior, particularly in the context of interactions between the unsaturated zone and ETa patterns. Soil properties, such as moisture retention capacity and hydraulic conductivity, are fundamental aspects that govern subsurface interactions (i.e., water movements), particularly within the unsaturated zone. These interactions encompass processes such as infiltration, soil moisture dynamics, and groundwater recharge, and as a result, they can alter the availability and timing of water for plants and therefore, evapotranspiration-related processes [59,60]. Interestingly, even under the most arid conditions, characterized by a dry system state, specific combinations of PTFs (4 and 5) consistently maintained elevated ETa levels, demonstrating a high capacity to sustain soil water availability. PTF combination 5 outperformed other combinations in this regard. Consequently, the optimal model performance for both catchments is achieved when employing PTFs 4 and 5. This observation is consistent with findings from a previous study [56], which also highlighted the effectiveness of using PTF combination 5 for accurately representing spatial patterns of dominant runoff processes.

5. Conclusions and Outlook

It has been shown that the proposed land-use-specific manual calibration approach of ETa-related vegetation parameters provides satisfying results for land-use types for which reliable parameter ranges were retrieved from existing field studies in catchments with similar natural and climatic conditions. The main deficiencies in terms of model performance are related to:

(1)

The lack of information on reasonable vegetation parameters for certain land-use types like moorland and industrial areas or land-use classes that only constitute a very small aerial share within the catchments.

(2)

Catchment-specific conditions such as elevation, soil moisture states, and harvest times, which influence annual phenological courses and inter-annual shifts in evaporation patterns.

(3)

The inherent uncertainty in the MODIS dataset due to the remaining mixed signatures resulting from the rather coarse resolution.

Despite these deficiencies, our study suggests several promising future research directions. It shows that a good model performance in terms of PBIAS, RMSE, SKout, and SPAEF can be achieved by combining the MODIS ETa as a calibration dataset with the LANDSAT validation dataset. As the latter provides a higher resolution, it allows for a detailed analysis considering topographic features and different moisture conditions (“system state”). In this context, the different PTF combinations strongly influence spatial ETa patterns due to their differences in terms of water-holding capacity. PTF combination 5 [33] has been found to provide the highest spatial efficiency for the dry September, which was less effectively depicted by the remaining PTF combinations. In this regard, the SPAEF metric proved to be an effective tool within our evaluation framework. It facilitated a distinct analysis of simulated spatial patterns of ETa, allowing for a comprehensive assessment of how well the WaSiM model represents the observed spatial distributions over a wide range of PTFs and different moisture states. The availability of different PTF combinations that differ in their ability to reproduce the annual soil moisture course allows for a soil-specific calibration.

Nevertheless, our approach highlights the critical necessity of establishing reliable value ranges for land-use and catchment-specific vegetation parameters. A reliable site-specific vegetation parameter set is the first step towards effectively depicting ETa patterns. If it is then combined with pedotransfer functions matching the catchment’s soil characteristics and moisture states, the proposed calibration and validation approach using MODIS and LANDSAT ETa datasets is expected to increase model performance in terms of all applied efficiency measures. In addition, the 11-year MODIS record contains information on the phenological development in wet and dry years and colder and warmer years. This could also allow for the calibration of a dynamic phenology model instead of a static phenology model, as used in our study.