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Reference crop evapotranspiration estimate using high-resolution meteorological network's data

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Adv. Sci. Res., 3, 113–118, 2009www.adv-sci-res.net
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3
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©
Author(s) 2009. This work is distributed underthe Creative Commons Attribution 3.0 License.
Advances inScience andResearch
8 t h E M S A n n u a l M e e t i n g a n d 7 t h E ur o p e a n C o n f er e n c e o nA p p l i e d C l i m a t o l o g y2 0 0 8
Reference crop evapotranspiration estimate usinghigh-resolution meteorological network’s data
C. Lussana
1
and F. Uboldi
21
ARPA Lombardia, Milano, Italy
2
Consultant, Novate Milanese, Italy
Received: 30 December 2008 – Revised: 8 May 2009 – Accepted: 20 May 2009 – Published: 12 October 2009
Abstract.
Water management authorities need detailed information about each component of the hydrolog-ical balance. This document presents a method to estimate the evapotranspiration rate, initialized in order toobtain the reference crop evapotranspiration rate (
ET
0
). By using an Optimal Interpolation (OI) scheme, thehourly observations of several meteorological variables, measured by a high-resolution local meteorologicalnetwork, are interpolated over a regular grid. The analysed meteorological ﬁelds, containing detailed meteoro-logical information, enter a model for turbulent heat ﬂuxes estimation based on Monin-Obukhov surface layersimilarity theory. The obtained
ET
0
ﬁelds are then post-processed and disseminated to the users.
1 Introduction
Lombardia’s public environmental agency (ARPA Lombar-dia) has undertaken a number of projects aimed at improvingknownledge of the water budget in order to support publicauthorities involved in water management. This documentpresents a procedure to estimate
ET
0
, deﬁned by Allen et al.(1998) as the evapotranspiration rate for the hypothetical ref-erence crop (short grass with an ample supply of water).
ET
0
is a climatic parameter computed using meteorolog-ical data only, without considering crop characteristics andsoil factors.The procedure’s outputs are
ET
0
hourly ﬁelds (unitmmh
−
1
). The estimated evapotranspiration rate can be ag-gregated in time and space. Finally, the
ET
0
estimates arepublished in a hydrological bulletin, which is disseminatedto the users.The source of meteorological information is ARPA Lom-bardia’s high-resolution meteorological network. The mete-orological variables used are hourly averaged values of tem-perature, relative humidity, wind components, solar globalradiation and hourly cumulated precipitation values. Theobserving system is composed of about three hundred au-tomated weather stations. The stations spatial distributionpresents strong inhomogeneities, moreover the sensor equip-ment vary from station to station. As an example, Fig. 1
Correspondence to:
C. Lussana(c.lussana@arpalombardia.it)shows the spatial distribution of thermometers and pyra-nometers.The spatial domain of interest consists of the part of Po plain inside Lombardia’s administrative boundaries (seeﬁelds in Figs. 4 and 5). Elevations range from 10m (in the
south-eastern part) to less than 300m (in the northern part).However, all the information available is used in the
ET
0
es-timation procedure in order to reduce border e
ﬀ
ects.Observations from the meteorological network are inter-polated over a regular grid with 1
.
5km of resolution. Forall variables except solar radiation, a statistical interpolationscheme is applied. At present, the interpolation of the hourlyaveragedsolarglobalradiationisperformedwithasimplein-verse distance weighting method, Fig. 4 shows an example.An e
ﬀ
ort is made to prevent observations a
ﬀ
ected by grosserrors from entering the interpolation procedure.It is worthwhile remarking that the grid spatial resolutionaccounts for orographic details, but the interpolated ﬁeldscan correctly reproduce phenomena resolved by the spatialresolution of the observational network, i.e. tenths of kilo-meters.Once obtained the meteorological ﬁelds, a model for tur-bulent heat ﬂuxes estimation is applied at each grid point.The model setup is such that the obtained latent heat ﬂux co-incides with the energetic content associated to
ET
0
.In this document, Sect. 2 describes the statistical interpo-lation scheme, Sect. 3 presents the procedure for turbulentﬂuxes estimation and Sect. 4 describes how the procedure isadapted to estimate
ET
0
.Published by Copernicus Publications.
114 C. Lussana and F. Uboldi: Reference crop evapotranspiration estimate
Figure 1.
Orography and station locations in the Lombardia do-main. Triangles: thermometers. Circles: pyranometers. The boldblack line is the administrative boundary. The inset shows the geo-graphical location of Lombardia, longitude 8
.
5 to 11
.
5
◦
E
, latitude44
.
6 to 45
.
7
◦
N
2 Statistical interpolation
The statistical interpolation scheme is an implementation of the Optimal Interpolation (OI; Gandin, 1963). OI produces
the best (in the sense of minimum analysis error variance),linear, unbiased estimate of the atmospheric ﬁeld. The sta-tistical interpolation scheme is applied to hourly averagedvalues of temperature, relative humidity, wind and to hourlycumulated precipitation values. OI ﬁlters out the unresolvedspatial scales. OI schemes often use a model-derived ﬁrstguess, but the implementation reported here uses a back-ground ﬁeld built by observations detrending, thus the pre-sented OI implementations are model-independent. Figure 2shows temperature and relative humidity ﬁelds.The description of the OI implementation for temperatureand relative humidity can be found in Uboldi et al. (2008)while in Lussana et al. (2009) the application to other vari-
ables is discussed and several test cases are reported. Atpresent, with respect to that work, here the OI implemen-tation for precipitation uses raingauges measurements only,without the integration of radar-derived precipitation esti-
Figure 2.
28 July 2006, 18:00UTC
+
1. Top: temperature (
◦
C).Bottom: relative humidity (%).
mates. The background ﬁeld is set to zero everywhere andthe OI parameters maintain the analysis ﬁeld as close as pos-sible to the observations: an example is shown in Fig. 3. Theprecipitation analysis plays an important role in the
ET
0
es-timation procedure, but only as a trigger: where the analyzedﬁeld of precipitation has a value greater than 1mmh
−
1
the
ET
0
value is not computed. In the future, the integrationof raingauges with radar-derived precipitation estimates willallow a better deﬁnition of the portion of the domain not in-terested by precipitation.Adv. Sci. Res., 3, 113–118, 2009 www.adv-sci-res.net
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C. Lussana and F. Uboldi: Reference crop evapotranspiration estimate 115
Figure 3.
28 July 2006, 18:00UTC
+
1. Precipitation rate (mmh
−
1
).The observed values are reported at station locations.
Figure 4.
28 July 2006, 18:00UTC
+
1. Solar global radiation(Wm
−
2
).
3 Turbulent ﬂuxes estimation
This Section presents a procedure to determine the surfacemoisture ﬂux, using single-level meteorological data only.The moisture ﬂux is intended as representative of an arearather than of a single roughness element. Due to the three-dimensional nature of turbulent vortices, the assumption of
Figure 5.
28 July 2006. Daily cumulated
ET
0
ﬁeld (mmday
−
1
) forthe spatial domain of interest.
horizontalrepresentativenessalsoimposesaconstraintontheheight above the ground where ﬂuxes must be evaluated.In fact, from the general Atmospheric Boundary Layer(ABL) theory, the Surface Layer (SL) (about 10% of theABL vertical extension) can be divided in Roughness Sub-Layer (RSL) and Inertial Sub-Layer (ISL) (Garratt, 1994).The RSL – the lower portion of the SL – contains the canopylayer. On the one hand, turbulence in the RSL is inﬂu-enced by individual roughness elements and the turbulence-related variables exhibit strong gradients in the vertical di-rection. On the other hand, turbulence in the ISL is inﬂu-enced by the integrated e
ﬀ
ect of many roughness elements,thus the turbulence-related variables are representative of alarger area and the values of the turbulent ﬂuxes are assumedto be constant with height. Most of Lombardia’s automaticstations are located within the ISL (in practice, only urbanstations lie within the RSL). The meteorological ﬁelds enter-ing the procedure presented in the current session refer thento the ISL.Based on the outlined structure of the SL, the evapotran-spiration rate is deﬁned as the net rate of passage of watervapor across a horizontal reference plane inside the ISL.Turbulence is the most e
ﬃ
cient mechanism to exchangemomentum, energy and mass inside the ABL. In the frame-work of turbulence theory it is more convenient to deal withthe energetic content associated to the moisture ﬂux: the tur-bulent latent heat ﬂux
H
e
(Wm
−
2
). The evaporation rate
E
(mmh
−
1
) can be obtained by using:
E
∝
H
e
λρ
w
(1)www.adv-sci-res.net
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Adv. Sci. Res., 3, 113–118, 2009
116 C. Lussana and F. Uboldi: Reference crop evapotranspiration estimatewhere
λ
is the latent heat of evaporation and
ρ
w
is the densityof water.The main assumptions taken for this work are summarizedin the following.In order to make turbulence more tractable, without loos-ing its main features, it is customary to assume that, locally,the ergodic condition applies (horizontal homogeneity andstationarity for the averaged values of the meteorologicalvariables). Furthermore, it is assumed that the wind vanishat the aerodynamic roughness length
z
0
– the bottom RSLboundary – as prescribed by the no-slip condition. Espe-cially in case of tall canopies, also the zero-plane displace-ment height
d
must be introduced. Finally, the presence of ice and liquid water is not considered, then phase transitionsare not taken into account.The two turbulent heat ﬂuxes, latent,
H
e
, and sensible,
H
0
,are related to the meteorological variables using the so-calledscaling parameters:
H
0
=
−
ρ
c
p
u
∗
T
∗
(2)
H
e
=
−
ρλ
u
∗
q
∗
(3)Where
ρ
is the air density,
c
p
is the speciﬁc heat at con-stant pressure;
u
∗
,
T
∗
and
q
∗
are the scaling parameters formomentum, temperature and speciﬁc humidity, respectively.These last three parameters are (vertically) constant throughall the ISL.In analogy with Zdunkowski and Bott (2003), the Monin-Obukhov Similarity Theory (MOST) for the SL allows com-putingthescalingparametersthroughtheiterativeprocedure:
u
=
u
(
n
)
∗
k
ln
z
−
d z
0
−
Ψ
M
z
−
d L
(
n
−
1)
∗
+Ψ
M
z
0
L
(
n
−
1)
∗
(4)
T
−
T
0
=
T
(
n
)
∗
k
ln
z
−
d z
0
−
Ψ
H
z
−
d L
(
n
−
1)
∗
+Ψ
H
z
0
L
(
n
−
1)
∗
(5)
q
−
q
0
=
q
(
n
)
∗
k
ln
z
−
d z
0
−
Ψ
H
z
−
d L
(
n
−
1)
∗
+Ψ
H
z
0
L
(
n
−
1)
∗
(6)
L
(
n
−
1)
∗
=
T gk
u
2
∗
T
∗
(
n
−
1)
,
L
(0)
∗
=
∞
(7)Here
u
,
T
and
q
are the wind velocity, temperature andspeciﬁc humidity, referred to the height above the ground
z
(in the ISL);
k
is the von Karman constant;
L
∗
is the Monin-Obukhov length scale;
n
is the iteration index. The itera-tion stops when a prescribed accuracy for the
L
∗
estimate isreached. The functions
Ψ
are the characteristic functions formomentum (
M
) and heat (
H
) (Beljaars and Holtslag, 1991).
The unknown temperature and speciﬁc humidity
T
0
and
q
0
are formally assigned to
z
0
, but they must be intended as twoparameters characterizing the whole RSL.In order to evaluate Eqs. (4)–(7),
T
0
and
q
0
are needed.To obtain their values, a number of approximations must bemade. The most relevant is the hypothesis of proportional-ity between ISL’s turbulent ﬂuxes and the di
ﬀ
erence betweenRSL and ISL values for the correspondent meteorologicalvariables:
H
0
=
ρ
c
p
T
0
−
T r
H
(8)
H
e
=
ρλ
q
s
(
T
0
)
−
qr
V
(9)The resistances
r
H
and
r
V
have the physical units of sm
−
1
.Both Eqs. (8) and (9) implicitly assume steady conditions.
Equation (9) takes into account the evaporation srcinatingfrom saturated surfaces in the RSL; the speciﬁc humidity dif-ference in Eq. (9) can be rewritten as a linearized function of temperature:
q
s
(
T
0
)
−
q
= ∆
(
T
0
−
T
)
+
δ
q
(10)Where
∆
≡
∂
q
s
/∂
T
is evaluated at a reference temperaturebetween
T
0
and
T
. Moreover,
δ
q
≡
q
s
(
T
)
−
q
.Referring to Monteith (1981), the resistance
r
H
in Eq. (8)isestimatedbytheaerodynamicresistance,
r
H
r
a
, governingthe di
ﬀ
usion of energy and masses between RSL and ISL.
r
V
in Eq. (9) is estimated as
r
V
r
a
+
r
s
, where the surface resis-tance
r
s
is introduced to account for the evaporation and tran-spiration processes in the RSL. In this work the “big-leaf”model is used: the canopy is treated as a plane located at thelower boundary of the RSL and the latent heat ﬂux is deter-mined by the evaporation of liquid water from the “big-leaf”.With these assumptions, Eq. (9) is replaced by:
H
e
=
ρλδ
q
0
r
s
(11)where
δ
q
0
≡
q
s
(
T
0
)
−
q
0
.A further relation between the turbulent heat ﬂuxes can beobtained from the overall surface energy balance. By meansof the prognostic equation for entalphy applied to the earthsurface, the energy balance can be written as (Zdunkowskiand Bott, 2003):
R
n
−
G
=
H
0
+
H
e
(12)Where
R
n
is the net radiation and
G
is the heat ﬂux storedin the soil. The left-hand side deﬁnes the available energy.Equation (12) is strictly valid for atmosphere-surface inter-face in case of bare soil. Nevertheless, Eq. (12) is intendedas the energy balance equation at the canopy top because thehorizontal ﬂux of energy due to advection and the rate of en-ergy storage per unit area in the canopy layer are neglected.Therefore, the turbulent heat ﬂuxes in Eq. (12) are assumedto be ﬂuxes in the ISL and are interpreted as surface ﬂuxes.The net radiation is estimated using the Net All-wave Ra-diation Parameterization model (NARP; O
ﬀ
erle et al., 2003)while for
G
the expression
G
=
β
R
n
is used (
β
=
0
.
1 for daytimeand
β
=
0
.
5 nighttime).Adv. Sci. Res., 3, 113–118, 2009 www.adv-sci-res.net
/
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/
C. Lussana and F. Uboldi: Reference crop evapotranspiration estimate 117By making use of Eqs. (8)–(12), the turbulent heat ﬂuxes
are computed as (deRooy and Holtslag, 1999):
H
e
= ∆∆+
γ
(
R
n
−
G
)
+
ρ
c
p
(
∆+
γ
)
r
a
(
δ
q
−
δ
q
0
) (13)
H
0
=
γ
∆+
γ
(
R
n
−
G
)
−
ρ
c
p
(
∆+
γ
)
r
a
(
δ
q
−
δ
q
0
) (14)Where
γ
=
c
p
/λ
is the psychrometric constant. Equations (13)and (14) are used to overcome the problem of eliminating
T
0
and
q
0
inside the iterative procedure of Eqs. (4)–(7). The
iterative procedure is then rewritten as:
u
=
u
(
n
)
∗
k
ln
z
−
d z
0
−
Ψ
M
z
−
d L
(
n
−
1)
∗
+Ψ
M
z
0
L
(
n
−
1)
∗
(15)
r
(
n
)
a
=
1
ku
(
n
)
∗
ln
z
−
d z
0
−
Ψ
H
z
−
d L
(
n
−
1)
∗
+Ψ
H
z
0
L
(
n
−
1)
∗
(16)
δ
q
(
n
)0
=
∆∆+
γ
(
R
n
−
G
)
+
ρ
c
p
(
∆+
γ
)
r
(
n
)
a
δ
q
ρλ
r
s
+
ρ
c
p
(
∆+
γ
)
r
(
n
)
a
(17)
H
(
n
)0
=
γ
∆+
γ
(
R
n
−
G
)
−
ρ
c
p
(
∆+
γ
)
r
(
n
)
a
δ
q
−
δ
q
(
n
)0
(18)
T
(
n
)
∗
=
−
H
(
n
)0
ρ
c
p
u
(
n
)
∗
(19)
L
(
n
−
1)
∗
=
T gk
u
2
∗
T
∗
(
n
−
1)
,
L
(0)
∗
=
∞
(20)For the iterative procedure, the three parameters
z
0
,
d
and
r
s
need to be speciﬁed. Moreover, the albedo of the surface isrequired by the NARP model.
4
ET
0
estimation
The general method presented in Sect. 3 allows estimatingthe turbulent heat ﬂuxes from single-level meteorologicaldata. In order to obtain
ET
0
, the parameters in the proce-dure must be properly initialized. In Allen et al. (1998) thereference crop is deﬁned as grass with height
h
=
0
.
12m andalbedo equals to 0.23. Furthermore, the relation for the sur-face roughness parameters are indicated as
z
0
=
0
.
123
h
and
d
=
2
/
3
h
. With respect to the
r
s
value, in a review of the FAOmethod for hourly period Allen et al. (2006) suggest using
r
s
=
50sm
−
1
during daytime and
r
s
=
200sm
−
1
during night-time. The
ET
0
value is not computed for grid points wherethe hourly precipitation rate is greater than 1mmh
−
1
becausein case of rain the assumptions made in Sect. 3 are not justi-ﬁed. Figure 5 shows a ﬁeld of daily cumulated
ET
0
, obtainedby summing up the hourly
ET
0
estimates.
5 Conclusions
The presented procedure for
ET
0
estimation relies on theavailability of interpolated meteorological ﬁelds and com-bines these ﬁelds with a model for turbulent ﬂuxes estimationnear the ground, properly initialized.The amount of information that contribute to the produc-tion of a
ET
0
hourly ﬁeld is remarkable, in consideration of the domain extension. In fact, about one thousand of mete-orological observations are used every hour. The quality of the input meteorological ﬁelds is of crucial importance. TheOI implementations for the meteorological variables providereliable and detailed meteorological ﬁelds. However, the es-timate of solar global radiation over the domain must be im-proved.The outputs of the turbulent ﬂuxes estimation model mustbe compared with experimental data. Nevertheless, prelimi-nary qualitative evaluations are very encouraging.In principle, the turbulent ﬂuxes estimation procedurecould be set up to obtain the real evapotranspiration rate forthe actual crop. This would imply a more complex treatmentof both the available geographical information and the veg-etation behaviour, as a consequence several complementaryparameters would need to be tuned. It would be thus possi-ble to compare hourly estimates with the evapotranspirationestimates obtained using, for example, the approach of Allenet al. (2006), then possibly obtain some insights about crop
coe
ﬃ
cient values.
Edited by: E. KochReviewed by: two anonymous referees
References
Allen, R. G., Pereira, L. S., Raes, D., and Smith, M.: Crop evap-otranspiration – Guidelines for computing crop water require-ments – FAO Irrigation and drainage paper 56, FAO – Food andAgriculture Organization of the United Nations, 1998.Allen, R. G., Pruitt, W. O., Wright, J. L., Howell, T. A., Ventura, F.,Snyder, R., Itenﬁsu, D., Steduto, P., Berengena, J., Yrisarry, J. B.,Smith, M., Pereira, L. S., Raes, D., Perrier, A., Alves, I., Walter,I., and Elliott, R.: A recommendation on standardized surfaceresistance for hourly calculation of reference ETo by the FAO56Penman-Monteith method, Agricultural Water Management, 81,1–22, 2006.Beljaars, A. and Holtslag, A.: Flux parameterization over land sur-faces for atmospheric models, J. Appl. Meteorol., 30, 327–341,1991.deRooy, W. C. and Holtslag, A.: Estimation of Surface Radiationand Energy Flux Densities from Single-Level Weather Data, J.Appl. Meteorol., 38, 526–540, 1999.Gandin, L. S.: Objective Analysis of Meteorological Fields,Gidromet, Leningrad. English translation by Israeli Program forScientiﬁc Translations, Jerusalem, 1963.Garratt, J.: The atmospheric boundary layer, Cambridge UniversityPress, 1994.Lussana, C., Salvati, M. R., Pellegrini, U., and Uboldi, F.: E
ﬃ
cienthigh-resolution 3-D interpolation of meteorological variables foroperational use, Adv. Sci. Res., 3, 105–112, 2009.Monteith, J.: Evaporation and surface temperature, Q. J. Roy. Me-teorol. Soc., 107, 1–27, 1981.
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