# Spatial Patterns in Actual Evapotranspiration Climatologies for Europe

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## Abstract

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## 1. Introduction

^{2}over homogeneous sites. At the same time, ET can vary significantly across short distances, depending on water and energy availability, which, again, depends on soil, vegetation, elevation, incident angle, micro-climate, etc. Essentially, ET remains impossible to measure accurately at high spatial resolutions on large spatial scales, which has turned the focus of such estimations towards satellite remote sensing [3]. Although sensors onboard satellites cannot measure ET directly, satellite data offer the opportunity to measure a range of relevant variables, such as land surface temperature, albedo and vegetation cover. Based on these measurements, several methods, models and algorithms have been developed that estimate ET at the spatial coverage and spatial and temporal resolution of the native satellite data.

## 2. Data and Methodology

^{2}and located below 60°N (Figure 1). The intercomparison of remote-sensing-based ET estimates at a 1 km resolution is conducted on the entire land phase of the domain in Figure 1. Based on the data availability, the aggregation period for the study area is 2002–2014.

#### 2.1. Benchmark Actual Evapotranspiration

#### 2.1.1. Water-Balance ET Approach

#### 2.1.2. Budyko ET Approach

#### 2.2. Remote-Sensing ET Datasets

_{thermal}and TSEB, are in addition to vegetation, based on daily land surface temperature data, which are not readily available for download. PT-JPL

_{thermal}and TSEB require extensive preprocessing, especially on the European scale, since daily cloud masking and corrections for acquisition time is necessary. Moreover, the thermal-based ET methods are limited to clear sky conditions and need to be adjusted before comparison to the other ET estimates, which reflect all weather conditions. This will be elaborated in Section 2.2.5.

#### 2.2.1. MODIS 16 Evapotranspiration (MOD16)

#### 2.2.2. Penman–Monteith–Leuning Evapotranspiration (PML_V2)

#### 2.2.3. Priestly–Taylor Jet Propulsion Lab Thermal Evapotranspiration (PT-JPL_{Thermal})

_{g}) relies on the ratio between absorbed and intercepted PAR while the plant moisture constraint (f

_{M}) estimates the departure of the f

_{APAR}at a given day from the maximum f

_{APAR}within the whole time series.

_{Thermal}method implemented here is based on the model developments described in [11,63], especially adjusted for arid regions. Compared to the original PT-JPL version [64], the PT-JPL

_{Thermal}version implemented here estimates the soil moisture constraint (f

_{sm}) based on the concept of apparent thermal inertia, where the diurnal oscillation of land surface temperature (LST) should scale with the level of surface dryness as well as the surface albedo instead of the atmospheric dryness. This approach has been proven to work better than the original one in water limited and Mediterranean systems [63]. A thermal inertia approach is also now implemented as part of the ECOSTRESS PT-JPL ET product [65].

_{Thermal}model was setup using mainly MODIS-derived input data, such as daytime and nighttime LST, emissivity, NDVI, LAI, albedo and FPAR. Meteorological data was derived from the ECMWF ERA Interim dataset and average daily air temperature was obtained from the E-OBS dataset at 0.25 deg resolution resampled to the MODIS resolution of 1 km. In the result section we will refer to PT-JPL

_{Thermal}simply as PT-JPL in description, figures and tables.

#### 2.2.4. Two-Source Energy Balance Evapotranspiration (TSEB)

_{PT}until the total energy balance is satisfied, meaning that Rn = LE + H + G, while LE

_{soil}and LE

_{canopy}> 0. Our implementation follows the description in [66] and is based on the code provided by the pyTSEB package. The model is run for all days in the period 2002–2014 for all clear-sky pixels across the study domain (Figure 1). The required input data are similar to the PT-JPL

_{Thermal}model described above and include radiative forcings, LST, albedo, LAI, and fraction of green vegetation. The fraction of green vegetation F

_{g}is based on a method proposed in [66], which discriminates between a greening and a senescence phase of the annual vegetation development, where the F

_{g}is higher relative to the NDVI in the greening phase compared to the senescence phase.

#### 2.2.5. Adjustments to Improve Comparability between RS-ET Estimates

^{2}at 13 h are converted to daily LE (MJ/m

^{2}/day) and subsequently to ET (mm/day). The conversion is based on dependencies on latitude, day of year and time of day according to the formulations by [67].

#### 2.3. ET Spatial Pattern Evaluations

#### 2.3.1. Spatial Efficiency Metric SPAEF

#### 2.3.2. Estimation of Correlation Structures Using the Copula Approach

#### 2.3.3. Hierarchical Cluster Analysis

## 3. Results

#### 3.1. Spatial Patterns of Benchmark ET

#### 3.2. Spatial Patterns of Remote-Sensing ET

#### 3.3. Benchmark ET Compared with Remote-Sensing ET

#### 3.4. ET Evaluation Using Budyko Curve Analysis

#### 3.5. Copula-Based Dependence Structures of ET Products

#### 3.6. Similarity Assessment Using Cluster Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The study area showing the distributions of 23 selected catchments and 30 FLUXNET sites with the underlying topography across Europe.

**Figure 2.**The water-balance ET approach components at a 25 km spatial resolution: (

**a**) E-Obs precipitation and (

**b**) E-Run surface runoff, both for the period of 2002–2014.

**Figure 3.**The Budyko curve representing the energy-limit (ET = PET) and the water-limit (ET = P) lines.

**Figure 4.**The Budyko ET approach components at a 25 km spatial resolution: (

**a**) potential evapotranspiration and (

**b**) distributed n parameter values derived from NDVI, both for the period of 2002–2012.

**Figure 5.**The long-term monthly mean (2002–2014) latent heat flux (LE) during all days and sunny days for 30 FLUXNET stations across Europe. See Figure 1 for the spatial distribution of the EC sites.

**Figure 6.**The grid-based (25 km) annual mean benchmark ET spatial patterns over the period of 2002–2014: (

**a**) water-balance WB-ET and (

**b**) Budyko ET. The catchments boundaries (N: 23) are overlaid on the ET maps. See Figure 1 for detailed descriptions.

**Figure 7.**The grid-based (1 km) annual mean RS-ET spatial patterns over the period of 2002–2014: (

**a**) MOD16, (

**b**) PML_V2, (

**c**) PT-JPL, and (

**d**) TSEB. The catchments boundaries (N: 23) are overlaid on the RS-ET maps. See Figure 1 for detailed descriptions.

**Figure 8.**The catchment-based SPAEF calculation between the RS-ET products with a 1 km spatial resolution over the period of 2002–2014. The catchments are shown in y-axis (rows) and the RS-ET datasets are displayed in x-axis (columns).

**Figure 9.**The normalized (each ET map was divided by its mean value) catchment-based annual mean ET spatial patterns with a 25 km spatial resolution over the period of 2002–2014: (

**a**) WB-ET, (

**b**) Budyko ET, (

**c**) MODIS16 ET, (

**d**) PML_V2 ET, (

**e**) PT-JPL ET and (

**f**) TSEB ET.

**Figure 10.**(

**a**) Evaluation of the long-term (2002–2014) estimated WB-ET and derived RS-ET products using the Budyko curve; (

**b**) geographical location of the catchments corresponding to the color of points in panels a. The red (blue) box represents catchments with the highest (lowest) aridity index, which fall in the water-limited (energy-limited) environment.

**Figure 11.**The empirical Copula densities (1 km grid at full-domain) amongst the satellite RS-ET products. (

**a**–

**c**) MODIS16 vs. other RS-ET estimates (

**d**,

**e**) PML_V2 vs. other RS-ET estimates, and (

**f**) PTJPL vs. TSEB. The sample size is 2,247,522 data tuples for the ET datasets.

**Figure 12.**The empirical Copula densities (25 km grid at catchment-scale): (

**a**–

**d**) WB-ET and (

**e**–

**h**) Budyko ET against RS-ET datasets, and (

**i**) WB-ET against Budyko ET. The sample size is 3413 data tuples for the ET datasets.

**Figure 13.**The hierarchical cluster analysis for the annual mean (2002–2014) normalized ET datasets in a 25 km grid, representing the overall similarity ranking among the ET products for each of the catchments across the study area. See Figure 1 for the locations of the catchments.

**Table 1.**Characteristics of remote-sensing ET products. P-M: Penman–Monteith; GPP: Gross Primary Production; P-T: Priestly–Taylor; FPAR: Fraction of Photosynthetically Active Radiation; GMAO: Global Modeling and Assimilation Office; and GLDAS: Global Land Data Assimilation System.

Product | Spatial Resolution | Temporal Resolution | ET Algorithm | Input Data Sources | References |
---|---|---|---|---|---|

MODIS16 | 1 km | 8-day | PM | MODIS (land cover type2, FPAR/LAI, albedo) and flux towers /GMAO (forcing data) | [13] |

PML_V2 | 500 m | 8-day | PML ^{1} | MODIS (LAI, albedo, emissivity) and GLDAS (forcing data) | [14] |

PT-JPL_{Thermal} | 1 km | Daily | PT | MODIS (LST, emissivity, albedo, LAI, FPAR, NDVI), E-OBS (air temperature) ERA-Interim reanalysis (forcing data) | [11] |

TSEB | 1 km | daily | TSEB (based on PT) | MODIS (LST, albedo, LAI) and ERA-Interim reanalysis (forcing data) | [9] |

^{1}ET and GPP coupled through surface conductance in PM.

**Table 2.**The SPAEF calculation between the RS-ET products with a 1 km spatial resolution at full domain.

ET Products | SPAEF | ET Products | SPAEF |
---|---|---|---|

[PML_V2, MODIS16] | 0.12 | [TSEB, MODIS16] | 0.28 |

[PTJPL, PML_V2] | 0.20 | [TSEB, PML_V2] | 0.11 |

[PTJPL, MODIS16] | 0.50 | [TSEB, PTJPL] | 0.67 |

**Table 3.**The SPAEF calculation between the ET products with a 25 km spatial resolution across catchments.

Data | SPAEF | Data | SPAEF |
---|---|---|---|

[WB, Budyko] | 0.26 | ||

[WB, MODIS16] | 0.17 | [Budyko, MODIS16] | 0.43 |

[WB, PML_V2] | 0.03 | [Budyko, PML_V2] | 0.15 |

[WB, PT-JPL] | 0.07 | [Budyko, PT-JPL] | 0.40 |

[WB, TSEB] | −0.11 | [Budyko, TSEB] | 0.25 |

[TSEB, MODIS16] | 0.25 | [MODIS16, PT-JPL] | 0.53 |

[TSEB, PML_V2] | 0.03 | [MODIS16, PML_V2] | 0.05 |

[TSEB, PT-JPL] | 0.61 | [PT-JPL, PML_V2] | 0.24 |

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**MDPI and ACS Style**

Stisen, S.; Soltani, M.; Mendiguren, G.; Langkilde, H.; Garcia, M.; Koch, J.
Spatial Patterns in Actual Evapotranspiration Climatologies for Europe. *Remote Sens.* **2021**, *13*, 2410.
https://doi.org/10.3390/rs13122410

**AMA Style**

Stisen S, Soltani M, Mendiguren G, Langkilde H, Garcia M, Koch J.
Spatial Patterns in Actual Evapotranspiration Climatologies for Europe. *Remote Sensing*. 2021; 13(12):2410.
https://doi.org/10.3390/rs13122410

**Chicago/Turabian Style**

Stisen, Simon, Mohsen Soltani, Gorka Mendiguren, Henrik Langkilde, Monica Garcia, and Julian Koch.
2021. "Spatial Patterns in Actual Evapotranspiration Climatologies for Europe" *Remote Sensing* 13, no. 12: 2410.
https://doi.org/10.3390/rs13122410