1. Introduction
The FAO definition of ETo for an extensive, well-irrigated grass field and its evaluation through the Penman–Monteith equation, which is derived for idealized horizontally homogeneous and uniform flat terrain, leads to an ambiguity (McMahon et al. 2013; Katerji and Rana 2011, 2014). In practice, irrigation is most relevant in semiarid regions where such idealized fields do not exist. Usually, weather stations are located at fields smaller than 104 m2 and are often surrounded by dry terrain. Under such conditions, processes that can be denoted with the generic name advection will lead to significant inconsistencies between idealized ETo and ETo estimates using ground data (Dingman 1992).
Another, more fundamental drawback of the ETo concept is that it concerns a purely hypothetical grass surface that does not exist in reality, by which experimental validation of any estimation formula for ETo is not really possible. Note that in Allen et al. (1998) there is no chapter dealing with experimental validation of the recommended methodology to calculate ETo, being a version of the Penman–Monteith equation (hereafter PMFAO). Nonetheless, PMFAO is widely used even far outside the goals for which it is developed (irrigation practice). The experimental validations of PMFAO we could find in literature concern (lysimeter) studies mainly in semiarid regions installed in small fields (e.g., Allen et al. 2006). But then local advection cannot be ignored, which contradicts the definition of ETo that refers to extensive grass, therefore suggesting that local advection should be ignored. This has created an ambiguous situation. Moreover, because of the fact that in hydrology and hydrometeorology PMFAO is generally accepted as “the best” to estimate ETo, interest in the physical background has faded. In the last decade, PMFAO has been applied, without further discussion about its validity, outside the field of irrigation, for instance, in climate change studies in which long-term weather records gathered under nonreference conditions are analyzed. We conclude that there is a need to pay attention to actual evapotranspiration of an actual grass field that closely resembles the FAO reference surface.
With this in mind, a model will be presented for actual ET of an existing grass field derived from first physical principles. Our derivation is based on the thermodynamic model by Schmidt (1915) combined with a model for the atmospheric boundary layer. The latter has been used and tested by de Bruin (1983), McNaughton and Spriggs (1986), Jacobs and de Bruin (1992), and, more recently, by van Heerwaarden et al. (2010).
To increase practical applicability, we will deal also with a simple method to estimate net radiation from the incoming solar radiation at the surface (hereafter denoted as global radiation) with the empirical formula of Slob–de Bruin (hereafter SdB; de Bruin 1987; de Bruin and Stricker 2000). And, in a final step, we will apply remotely sensed global radiation as provided by the EUMETSAT Satellite Application Facility on Land Surface Analysis (LSA SAF; Trigo et al. 2011) and by the Surface Insolation under Clear and Cloudy Skies (SICCS) derived from the SEVIRI [a platform on Meteosat Second Generation (MSG)] imagery system of the Royal Netherlands Meteorological Office (Koninklijk Nederlands Meteorologisch Instituut; KNMI) by Greuell at al. (2013) to obtain estimates of ET.
Using the Cabauw Experimental Site for Atmospheric Research (CESAR) database of micrometeorological observations gathered at Cabauw (the Netherlands) over a grass surface that closely resembles the FAO hypothetical reference grass, we will validate our models for actual ET, net radiation, and MSG global radiation against independent measurements.
Finally, we will discuss the operational applicability of our findings in, for example, irrigation practice or in other disciplines, such a climate change studies.
2. Data and material
a. In situ measurements: Cabauw
Here, we consider data gathered at CESAR for the period 2007–12. The site is located in the western part of the Netherlands (51.971°N, 4.927°E). We used the data collected at the experimental field near the 200-m tower covered with short grass. The soil consists of a 0.7-m-thick clay layer on top of a thick peat layer. The water table is managed by a dense network of ditches, and only rarely. Droughts have reduced evapotranspiration. The terrain around the site also corresponds to grassland, which was free from obstacles up to a few hundred meters in all directions during the whole 2007–12 period. For further details about the CESAR observatory, see Monna and Bosveld (2013). Given its geographical location and local characteristics, the Cabauw resembles closely the hypothetical FAO reference grass for conditions without advection. We extracted the so-called validated and gap-filled meteorological surface data and surface flux files (CESAR Consortium 2013). This concerns 10-min values from which we calculated 24-hourly averages. In particular, we used the actual evaporation that is obtained from the energy budget residual method (Beljaars and Bosveld 1997). Cabauw is located in the midlatitude climate zone where droughts are rare. In the period 2007–12, a limited number of dry spells were detected in the growing season. These were found by comparing measured ET with the reference crop ET evaluated with the formula of Makkink (ETmakkink, see section 5; de Bruin 1987). We ignored days for which the actual ET is less than 0.80 ETmakkink.
The database included net radiometer data as well as separate observations of the four components of net radiation, that is, incoming and reflected shortwave radiation (
The grass site is not irrigated and is surrounded by similar grass. Consequently, under normal conditions advection will be absent. Cabauw evapotranspiration might be affected by advection only when rainfall is distributed in such a way that the site becomes wetter than the surrounding terrain. We found that such rare situations occurred on 27–30 July 2007, 14–15 August 2007, and 24–28 May 2012. Data on these days were also excluded from the main results discussed in this study. On these days the sensible heat flux given by the Extra Large Aperture Scintillometer (XLAS; see Kohsiek et al. 2002), representative for the surrounding area, provides much higher estimates than the locally measured value.
For the selected days, we determined the albedo of the Cabauw site from the ratio of daily mean outgoing and incoming shortwave radiation. The results are plotted in Fig. 1. It appears that the albedo varies from day to day with a standard deviation of 0.018 around the average of 0.23. This is the albedo of the reference grass surface as defined by Allen at al. (1998). Considering the environmental conditions of the Cabauw site regarding, for example, albedo, water stress, and advection, we are confident to state that the Cabauw site resembles fairly closely the hypothetical idealized reference FAO grass surface.
Measured albedo for days of the year 90–275 at Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Measured albedo for days of the year 90–275 at Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Measured albedo for days of the year 90–275 at Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
b. Remote sensing observations: MSG
The SEVIRI instrument on board the geostationary platform MSG provides top-of-the-atmosphere optical measurements every 15 min and with a spatial resolution of up to 3 km.
Several methodologies have been proposed to derive incoming solar radiation at the surface from remote sensing observations. Most rely on the identification of clouds and/or characterization of cloud properties from visible and infrared observations. Moreover, these methods take into account that under cloudy conditions there is a clear link (anticorrelation) between top of the atmosphere reflectances and solar radiation at the surface.
Here we will consider two different remote sensing products, both retrieved from SEVIRI on board MSG and available in near–real time from the LSA SAF (Trigo et al. 2011; Geiger et al. 2008) and from the KNMI SICCS algorithm (Greuell et al. 2013; Deneke et al. 2008). Both LSA SAF and SICCS products are aggregated to daily averages of global radiation. The high temporal frequency of SEVIRI observations (15 min) allows characterizing the diurnal cycle of incoming solar radiation and therefore producing robust daily estimates. The LSA SAF product has been validated against a wide number of in situ observations [including the Baseline Surface Radiation Network (BSRN)], most of which are in Europe, revealing mean errors ranging between around −4 and −7 W m−2 (Ineichen et al. 2009; Carrer et al. 2012). The SICCS product has also been validated against European BSRN measurements, revealing a similar performance with biases between −1 and 13 W m−2 (Greuell et al. 2013).
3. Theory
a. The Schmidt thermodynamic model
b. Parameterization of net radiation
4. Experimental validation
a. Validation using ground observations
A test of Eq. (6) applied to ground measurements taken at Cabauw is depicted in Fig. 2. We recall that this concerns daily values for 2007–12, and 
Latent heat flux estimated according to Eq. (6), that is, using the SdB net radiation formula, plotted against in situ measured values: daily values at Cabauw during 2007–12 except for a limited number of dry and advective days (see text).
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Latent heat flux estimated according to Eq. (6), that is, using the SdB net radiation formula, plotted against in situ measured values: daily values at Cabauw during 2007–12 except for a limited number of dry and advective days (see text).
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Latent heat flux estimated according to Eq. (6), that is, using the SdB net radiation formula, plotted against in situ measured values: daily values at Cabauw during 2007–12 except for a limited number of dry and advective days (see text).
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
For the same selected days, a separate test of the SdB formula for daily net radiation applied to ground data is given in Fig. 3, using 
Test net radiation formula of SdB at Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Test net radiation formula of SdB at Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Test net radiation formula of SdB at Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
b. MSG-derived solar and net radiation
Figure 4 shows scatterplots of LSA SAF and SICCS global radiation estimated from MSG SEVIRI satellite observations against in situ observations at Cabauw, for the 2010–12 period. The points in Fig. 4 assume the following conditions concerning the quality indicators provided when both products are verified simultaneously: (i) the missing SEVIRI observations in the case of the LSA SAF are less than 5% and (ii) quality flag above 0.5 in the case of SICCS. The two solar radiation products reveal comparable behavior, with nearly the same scatter around the observations (the standard deviation of this difference is about 12 W m−2). In this case, SICCS has a negligible bias, while the LSA SAF underestimates the observations by 6 W m−2. These results are fairly in line with the other validation exercises mentioned above and suggest the two products are of similar quality.
Scatterplots of daily solar radiation estimates from SEVIRI MSG (W m−2) against in situ observations in Cabauw considering (a) LSA SAF and (b) SICCS products. The mean (bias) and standard deviation of differences are also displayed.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Scatterplots of daily solar radiation estimates from SEVIRI MSG (W m−2) against in situ observations in Cabauw considering (a) LSA SAF and (b) SICCS products. The mean (bias) and standard deviation of differences are also displayed.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Scatterplots of daily solar radiation estimates from SEVIRI MSG (W m−2) against in situ observations in Cabauw considering (a) LSA SAF and (b) SICCS products. The mean (bias) and standard deviation of differences are also displayed.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
The SICCS product has also been validated against European BSRN measurements, revealing a similar performance with biases between −1 and 13 W m−2 (Greuell et al. 2013). Differences between the LSA SAF and SICCS solar radiation products are intrinsically linked to the respective algorithms and underlying assumptions. Estimates are particularly sensitive under cloudy conditions. In this case SICCS relies on the retrieval of cloud properties (optical thickness, effective radius), while the LSA SAF assumes the pixel to be covered by a homogeneous cloud layer, where cloud transmittance is inferred from cloud albedo.
To demonstrate the skill of using remotely sensed estimations of solar fluxes to model net radiation, we compare the output of the SdB formula using the MSG SICCS global radiation with ground measurements (Fig. 5). These results reveal the suitability of the MSG-derived products for practical application. The bias (1.6 W m−2) is small and the standard deviation of this difference (11.7 W m−2) is slightly greater than that found for global solar radiation.
As in Fig. 3, but for SEVIRI MSG global radiation according the SICCS algorithm.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
As in Fig. 3, but for SEVIRI MSG global radiation according the SICCS algorithm.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
As in Fig. 3, but for SEVIRI MSG global radiation according the SICCS algorithm.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
When the net radiation estimates are used to obtain evapotranspiration, that is, through the use of Eq. (6), we do not get any significant degradation of the results obtained from Eq. (6) fed with in situ measurements only (shown in Fig. 2). The comparison with daily evapotranspiration values corresponding to eddy covariance observations (Fig. 6) reveals a bias of 2.8 W m−2 and the standard deviation of this difference is 7.7 W m−2.
As in Fig. 2, but for SEVIRI MSG global radiation (SICCS) as input.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
As in Fig. 2, but for SEVIRI MSG global radiation (SICCS) as input.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
As in Fig. 2, but for SEVIRI MSG global radiation (SICCS) as input.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
5. Discussion
This work is focused on a model for actual ET of actual grass that is close to hypothetical FAO grass, accepting that the interpretation of the FAO definition “extensive field” excludes advection. The methodology is based on the thermodynamic model by Schmidt (1915), published 100 years ago. Furthermore, we argue that air above well-watered grass is never saturated because after sunrise warm and dry air is entrained into the ABL, explaining the need for a correction factor 
Measured 
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Measured
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Measured
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
When the measured 
The use of a single site for validating the approach described here may be a limiting factor. However, the analysis of other sites, such as those within the well-known EUROFLUX network (e.g., Hu et al. 2015; see also Valentini 2003), did not reveal any other with the characteristics of Cabauw, where measurements are provided within a wide green nonstresses grass area. Nevertheless, we argue that, since the formulation described above is fairly based on fundamental physical principles, our model is applicable for all similar grass sites. The readers are invited to test our models against other independent data. For the time being, we conclude that, because our formulas are based on first physical principles, our model is applicable for all similar grass sites.
Furthermore, the fact that for Cabauw site actual ET appears to be determined primarily by global radiation and air temperature was found earlier by de Bruin (1987), who tested the revised Makkink Eq. (7) for an older dataset. A test of this approach is shown in Fig. 8. It is seen that the revised Makkink tends to overestimate slightly at high values, but the overall performance is very suitable for most practical applications.
Test of the revised Makkink Eq. (7) as proposed by de Bruin (1987). Daily values are for Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Test of the revised Makkink Eq. (7) as proposed by de Bruin (1987). Daily values are for Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Test of the revised Makkink Eq. (7) as proposed by de Bruin (1987). Daily values are for Cabauw during 2007–12.
Citation: Journal of Hydrometeorology 17, 5; 10.1175/JHM-D-15-0006.1
Our model can be applicable in other areas; for example, in lumped rainfall–runoff models it can be applied to estimate the so-called potential evapotranspiration (see, e.g., Oudin et al. 2005). Furthermore, the approach described here can be applicable in climate change studies such as those carried out by van der Schrier et al. (2006) and Sheffield et al. (2012).
Note that our Eq. (4) in a slightly different form was tested earlier by de Bruin and Holtslag (1997). It has been applied in practical studies on air pollution in which estimates of the evolution of the convective boundary height are needed (van Ulden and Holtslag 1985; Holtslag and van Ulden 1983; Pechinger et al. 1997; Beljaars and Bosveld 1997; de Rooy and Holtslag 1999). Note that Beljaars and Bosveld (1997) found that the Penman–Monteith equation with a fixed surface resistance did not work for Cabauw, that is, they obtained a diurnal variation for the mean surface resistance [as reported by Allen et al. (2006)]. Nowadays, such land parameterization schemes are implemented in weather forecast models (van den Hurk et al. 2000; Ek and Holtslag 2004).
Recently, Kleidon and Renner (2013) and Kleidon et al. (2014) considered the thermodynamic limitations of the hydrological cycle and arrived at a very similar finding to that by Schmidt (1915) and by us.
A by-product of this study is that the SdB parameterization for net radiation over well-watered grass appears to work very well. It has the advantage that it requires global radiation as input only. This confirms the earlier finding by de Bruin (1987), but this was for the same Cabauw site. The question arises whether the constant 
We successfully applied the SdB formula using satellite-derived global radiation. Note that Dong et al. (1992) describe satellite-derived net radiation.
It should be stressed that the SdB formula is developed for well-watered grass. De Bruin (1987) showed that “surface dryness” may significantly affect outgoing longwave radiation. See, for instance, de Bruin et al. (2012), who analyzed measured net radiation data gathered in Burkina Faso over bare soil. In the dry season, net radiation is much smaller than that given by SdB or the net radiation estimate given in FAO-56 (Allen et al. 1998).
Another aspect of the present study is that the revised approach for ET estimation yields reasonable results for all seasons. Note that de Bruin and Holtslag (1982) considered the growing season only, when net radiation is relatively high. This is an interesting result, since in wintertime solar radiation is no longer the dominant energy source and actual evapotranspiration can exceed net radiation because of mesoscale advection of sensible heat (Pielke 2013). Further study would still be needed to fully understand the seasonal variability of mechanisms involved in ET over nonstressed grass surfaces. In any case, the growing season is most relevant for agriculture, and solar radiation is then the most significant energy source for evapotranspiration.
Finally, the results discussed here reveal that the global radiation MSG products, operationally delivered by the EUMETSAT LSA SAF and by the KNMI SICCS systems, are accurate enough for practical application to estimate our advection-free reference crop in midlatitude climate regions from geostationary satellite imagery.
Despite the fact that installation and maintenance of a ground-based network of standard meteorological (FAO) stations is increasingly expensive and labor intensive, the availability of remote sensing data covering wide areas with high spatial and temporal samplings is increasing. As such, it is shown that actual ET of extensive well-watered grass fields can be reliably estimated from geostationary satellite data, in line with what was proposed in other similar studies such as Choudhury and de Bruin (1995), Bois et al. (2008), Hart et al. (2009), de Bruin et al. (2010, 2012), and Cammalleri and Ciraolo (2013), who explored satellite-derived information for estimation of (crop reference) evapotranspiration.
6. Conclusions
Starting with the 100-yr-old thermodynamic approach by Schmidt (1915) and considering more recent insight into the planetary boundary layer process of entrainment, a simple formula is derived for daily actual evapotranspiration of a well-watered grass field that closely resembles FAO reference grass. In addition, it is found that the empirical SdB formula for daily net radiation of well-watered grass, as proposed by de Bruin (1987), performs well. Combining these findings yields an approximation of daily actual ET, requiring global radiation and air temperature as input only. This was tested against in situ observations at Cabauw for 2007–12, using (i) in situ measured input and (ii) global radiation obtained from MSG imagery. A fair agreement was found, that is, a bias of 3 W m−2 and an error (standard deviation of estimate minus measured) of 7.6 W m−2. Separately, we tested two algorithms for MSG-derived global radiation, notably, the LSA SAF and SICCS schemes, and found a bias and the standard deviation of this difference of −5.9 and 12.7 W m−2 for LSA SAF and 0.9 and 11.9 W m−2 for SICCS.
It is recalled that our study is confined to cases without local advection. The question of whether or not our new simple approach to estimate actual ET can be applied to determine the FAO reference crop evapotranspiration ETo could not be answered because of the ambiguity in the definition regarding accounting for local advection effects. If one interprets the definition such that local advection is excluded, our approach can be applied.
If local advection should be included, then the rationale of Schmidt (1915) is still applicable, but then an additional parameterization of the term Qadv in Eq. (8) should be included.
Acknowledgments
Isabel Trigo was supported by the Satellite Application Facility (SAF) on Land Surface Analysis (LSA), a project funded by EUMETSAT. Jan Fokke Meirink was supported by the EUMETSAT SAF on Climate Monitoring.
REFERENCES
Allen, R. G., Pereira L. S. , Raes D. , and Smith M. , 1998: Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56, 300 pp. [Available online at www.fao.org/docrep/X0490E/X0490E00.htm.]
Allen, R. G., and Coauthors, 2006: A recommendation on standardized surface resistance for hourly calculation of reference ETo by the FAO56 Penman–Monteith method. Agric. Water Manage., 81, 1–22, doi:10.1016/j.agwat.2005.03.007.
Beljaars, A. C. M., and Bosveld F. C. , 1997: Cabauw data for the validation of land surface parameterization schemes. J. Climate, 10, 1172–1193, doi:10.1175/1520-0442(1997)010<1172:CDFTVO>2.0.CO;2.
Berengena, J., and Gavilán P. , 2005: Reference evapotranspiration estimation in a highly advective semiarid environment. J. Irrig. Drain. Eng., 131, 147–163, doi:10.1061/(ASCE)0733-9437(2005)131:2(147).
Bois, B., Pieria P. , van Leeuwen C. , Wald L. , Huard F. , Gaudillere J.-P. , and Saur E. , 2008: Using remotely sensed solar radiation data for reference evapotranspiration estimation at a daily time step. Agric. For. Meteor., 148, 619–630, doi:10.1016/j.agrformet.2007.11.005.
Cammalleri, C., and Ciraolo G. , 2013: A simple method to directly retrieve reference evapotranspiration from geostationary satellite images. Int. J. Appl. Earth Obs. Geoinf., 21, 149–158, doi:10.1016/j.jag.2012.08.008.
Carrer, D., Lafont S. , Roujean J.-L. , Calvet J.-C. , Meurey C. , Le Moigne P. , and Trigo I. F. , 2012: Incoming solar and infrared radiation derived from METEOSAT: Impact on the modeled land water and energy budget over France. J. Hydrometeor., 13, 504–520, doi:10.1175/JHM-D-11-059.1.
CESAR Consortium, 2013: Datasets cesar_surface_meteo_lc1_t10_v10 and cesar_surface_flux_lc1_t10_v10. Subset used 2007–2012, accessed 2013. [Available online at http://www.cesar-database.nl/.]
Choudhury, B. J., and de Bruin H. A. R. , 1995: First order approach for estimation unstressed transpiration from meteorological satellite data. Adv. Space Res., 16, 167–176, doi:10.1016/0273-1177(95)00398-X.
de Bruin, H. A. R., 1983: A model for the Priestley–Taylor parameter α. J. Appl. Meteor., 22, 572–578, doi:10.1175/1520-0450(1983)022<0572:AMFTPT>2.0.CO;2.
de Bruin, H. A. R., 1987: From Penman to Makkink. Proceedings and Information: TNO Committee on Hydrological Research No. 39, J. C. Hooghart, Ed., Netherlands Organization for Applied Scientific Research, 5–30.
de Bruin, H. A. R., and Holtslag A. A. M. , 1982: A simple parameterization of the surface fluxes of sensible and latent heat during daytime compared with the Penman–Monteith concept. J. Appl. Meteor., 21, 1610–1621, doi:10.1175/1520-0450(1982)021<1610:ASPOTS>2.0.CO;2.
de Bruin, H. A. R., and Stricker J. N. M. , 2000: Evaporation of grass under non-restricted soil moisture conditions. Hydrol. Sci. J., 45, 391–406, doi:10.1080/02626660009492337.
de Bruin, H. A. R., Trigo I. F. , Jitan M. A. , Temesgen Enku N. , van der Tol C. , and Gieske A. S. M. , 2010: Reference crop evapotranspiration derived from geo-stationary satellite imagery. A case study for the Fogera flood plain, NW-Ethiopia and the Jordan Valley, Jordan. Hydrol. Earth Syst. Sci., 14, 2219–2228, doi:10.5194/hess-14-2219-2010.
de Bruin, H. A. R., Trigo I. F. , Galivan P. , Martinez A. , and Gonzales M. P. , 2012: Reference crop evapotranspiration estimated from geostationary satellite imagery. IAHS Publ., 352, 111–114.
Deneke, H. M., Feijt A. J. , and Roebeling R. A. , 2008: Estimating surface solar irradiance from METEOSAT SEVIRI-derived cloud properties. Remote Sens. Environ., 112, 3131–3141, doi:10.1016/j.rse.2008.03.012.
de Rooy, W. C., and Holtslag A. A. M. , 1999: Estimation of surface radiation and energy flux densities from single-level weather. J. Appl. Meteor., 38, 526–540, doi:10.1175/1520-0450(1999)038<0526:EOSRAE>2.0.CO;2.
Dingman, S. L., 1992: Physical Hydrology. Prentice Hall, 575 pp.
Dong, A., Grattan S. , Carroll J. , and Prashar C. , 1992: Estimation of daytime net radiation over well-watered grass. J. Irrig. Drain. Eng., 118, 466–479, doi:10.1061/(ASCE)0733-9437(1992)118:3(466).
Doorenbos, J., and Pruitt W. O. , 1975: Guidelines for predicting crop water requirements. FAO Irrigation and Drainage Paper 24, Food and Agriculture Organization, 179 pp. [Available online at http://www.fao.org/3/a-f2430e.pdf.]
Ek, M. B., and Holtslag A. A. M. , 2004: Influence of soil moisture on boundary layer cloud development. J. Hydrometeor., 5, 86–99, doi:10.1175/1525-7541(2004)005<0086:IOSMOB>2.0.CO;2.
Geiger, B., Meurey C. , Lajas D. , Franchistéguy L. , Carrer D. , and Roujean J.-L. , 2008: Near real-time provision of downwelling shortwave radiation estimates derived from satellite observations. Meteor. Appl., 15, 411–420, doi:10.1002/met.84.
Greuell, W., Meirink J. F. , and Wang P. , 2013: Retrieval and validation of global, direct, and diffuse irradiance derived from SEVIRI satellite observations. J. Geophys. Res. Atmos., 118, 2340–2361, doi:10.1002/jgrd.50194.
Hart, Q., Brugnach M. , Temesgen B. , Rueda C. , Ustin S. , and Frame K. , 2009: Daily reference evapotranspiration for California using satellite imagery and weather station measurement interpolation. Civ. Eng. Environ. Syst., 26, 19–33, doi:10.1080/10286600802003500.
Holtslag, A. A. M., and van Ulden A. P. , 1983: A simple scheme for daytime estimates of the surface fluxes from routine weather data. Climate Appl. Meteor., 22, 517–529, doi:10.1175/1520-0450(1983)022<0517:ASSFDE>2.0.CO;2.
Hu, G., Jia L. , and Menenti M. , 2015: Comparison of MOD16 and LSA-SAF MSG evapotranspiration products over Europe for 2011. Remote Sens. Environ., 156, 510–526, doi:10.1016/j.rse.2014.10.017.
Ineichen, P., Barroso C. , Geiger B. , Hollmann R. , Marsouin A. , and Mueller R. , 2009: Satellite application facilities irradiance products: Hourly time step comparison and validation over Europe. Int. J. Remote Sens., 30, 5549–5571, doi:10.1080/01431160802680560.
Jacobs, C. M. J., and de Bruin H. A. R. , 1992: The sensitivity of regional transpiration to land-surface characteristics: Significance of feedback. J. Climate, 5, 683–698, doi:10.1175/1520-0442(1992)005<0683:TSORTT>2.0.CO;2.
Katerji, N., and Rana G. , 2011: Crop reference evapotranspiration: A discussion of the concept, analysis of the process and validation. Water Resour. Manage., 25, 1581–1600, doi:10.1007/s11269-010-9762-1.
Katerji, N., and Rana G. , 2014: FAO-56 methodology for determining water requirement of irrigated crops: Critical examination of the concepts, alternative proposals and validation in Mediterranean region. Theor. Appl. Climatol., 116, 515–536, doi:10.1007/s00704-013-0972-3.
Kleidon, A., and Renner M. , 2013: Thermodynamic limits of hydrologic cycling within the Earth system: Concepts, estimates and implications. Hydrol. Earth Syst. Sci., 17, 2873–2892, doi:10.5194/hess-17-2873-2013.
Kleidon, A., Renner M. , and Porada P. , 2014: Estimates of the climatological land surface energy and water balance derived from maximum convective power. Hydrol. Earth Syst. Sci., 18, 2201–2218, doi:10.5194/hess-18-2201-2014.
Kohsiek, W., Meijninger W. M. L. , Moene A. F. , Heusinkveld B. G. , Hartogensis O. K. , Hillen W. C. A. M. , and De Bruin H. A. R. , 2002: An extra large aperture scintillometer for long range applications. Bound.-Layer Meteor., 105, 119–127, doi:10.1023/A:1019600908144.
McMahon, T. A., Peel M. C. , Lowe L. , Srikanthan R. , and McVicar T. R. , 2013: Estimating actual, potential, reference crop and pan evaporation using standard meteorological data: A pragmatic synthesis. Hydrol. Earth Syst. Sci., 17, 1331–1363, doi:10.5194/hess-17-1331-2013.
McNaughton, K. G., and Spriggs T. W. , 1986: A mixed-layer model for regional evaporation. Bound.-Layer Meteor., 34, 243–262, doi:10.1007/BF00122381.
Monna, W., and Bosveld F. , 2013: In higher spheres: 40 years of observations at the Cabauw Site. KNMI-Publication 232, KNMI, 56 pp. [Available online at http://www.cesar-observatory.nl/publications/reports/knmipub232.pdf.]
Oudin, L., Hervieu F. , Michel C. , Perrin C. , Andreassian V. , Anctil F. , and Loumagne C. , 2005: Which potential evapotranspiration input for a lumped rainfall–runoff model? Part 2—Towards a simple and efficient potential evapotranspiration model for rainfall–runoff modelling. J. Hydrol., 303, 290–306, doi:10.1016/j.jhydrol.2004.08.026.
Ouwersloot, H. G., and Vilà-Guerau de Arellano J. , 2013: Analytical solution for the convectively-mixed atmospheric boundary layer. Bound.-Layer Meteor., 148, 557–583, doi:10.1007/s10546-013-9816-z.
Pechinger, U., Erbes G. , Johansson P.-E. , Karppinen A. , Musson-Genon L. , Omstedt G. , and Tercier Ph. , 1997: Surface energy balance. Cost Action 710—Final report: Harmonization of pre-processing of meteorological data for atmospheric dispersion models, European Commission, EUR 18195 EN, 3–94.
Pielke, R. A., Sr., 2013: Mesoscale Meteorological Modeling. 3rd ed., Academic Press, 720 pp.
Raupach, M. R., 2001: Combination theory and equilibrium evaporation. Quart. J. Roy. Meteor. Soc., 127, 1149–1181, doi:10.1002/qj.49712757402.
Schmidt, W., 1915: Strahlung und Verdunstung an freien Wasserflächen; ein Beitrag zum Wärmehaushalt des Weltmeers und zum Wasserhaushalt der Erde (Radiation and evaporation over open water surfaces; a contribution to the heat budget of the world ocean and to the water budget of the earth). Ann. Hydro. Maritimen Meteor., 43, 111–124, 169–178.
Sheffield, J., Wood E. F. , and Roderick M. L. , 2012: Little change in global drought over the past 60 years. Nature, 491, 435–438, doi:10.1038/nature11575.
Trigo, I. F., and Coauthors, 2011: The satellite application facility on land surface analysis. Int. J. Remote Sens., 32, 2725–2744, doi:10.1080/01431161003743199.
Valentini, R., 2003: EUROFLUX: An integrated network for studying the long-term responses of biosphere exchanges of carbon, water, and energy of European forests. Fluxes of Carbon, Water and Energy of European Forests, R. Valentini, Ed., Ecological Studies, Vol. 163, Springer, 1–8, doi:10.1007/978-3-662-05171-9_1.
van den Hurk, B. J. J. M., Viterbo P. , and Beljaars A. C. M. , and Betts A. K. , 2000: Offline validation of the ERA40 surface scheme. ECMWF Tech Memo. 295, ECMWF, 42 pp. [Available online at http://www.ecmwf.int/sites/default/files/elibrary/2000/12900-offline-validation-era40-surface-scheme.pdf.]
van der Schrier, G., Briffa K. R. , Jones P. D. , and Osborn T. J. , 2006: Summer moisture variability across Europe. J. Climate, 19, 2818–2834, doi:10.1175/JCLI3734.1.
van Heerwaarden, C. C., Vilà-Guerau de Arellano J. , Gounou A. , Guichard F. , and Couvreux F. , 2010: Understanding the daily cycle of evapotranspiration: A method to quantify the influence of forcings and feedbacks. J. Hydrometeor., 11, 1405–1422, doi:10.1175/2010JHM1272.1.
van Ulden, A. P., and Holtslag A. A. M. , 1985: Estimation of atmospheric boundary layer parameters for diffusion applications. J. Climate Appl. Meteor., 24, 1196–1207, doi:10.1175/1520-0450(1985)024<1196:EOABLP>2.0.CO;2.
