AMERICAN METEOROLOGICAL SOCIETY Journal of Atmospheric and Oceanic Technology
EARLY ONLINE RELEASE This is a preliminary PDF of the author-produced manuscript that has been peer-reviewed and accepted for publication. Since it is being posted so soon after acceptance, it has not yet been copyedited, formatted, or processed by AMS Publications. This preliminary version of the manuscript may be downloaded, distributed, and cited, but please be aware that there will be visual differences and possibly some content differences between this version and the final published version. The DOI for this manuscript is doi: 10.1175/2008JTECHA1046.1 The final published version of this manuscript will replace the preliminary version at the above DOI once it is available.
© 2008 American Meteorological Society
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Errors of naturally ventilated air temperature measurements
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in a spatial observation network
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MATTHIAS MAUDER, R. L. DESJARDINS, ZHILING GAO, AND RONALD VAN HAARLEM
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Agriculture and Agri-Food Canada, Research Branch, Ottawa, Ontario, Canada
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Technical Note
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Submitted to Journal of Atmospheric and Oceanic Technology
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2nd Revision
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Corresponding author address: Matthias Mauder, Agriculture and Agri-Food Canada, Research Branch,
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960 Carling Ave., Ottawa, ON, Canada, K1A 0C6.
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Email:
[email protected]
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ABSTRACT
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A spatial network of 25 air temperature sensors was deployed over an area of
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3.5 km x 3.5 km of agricultural land, aiming to calculate the sensible heat flux by spatial
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averaging instead of temporal averaging. Since temperature sensors in naturally
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ventilated solar radiation shields were used for these measurements, a correction for
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radiative heating had to be applied. In this study, the approach of Anderson and
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Baumgartner (1998) was adapted to the cuboidal shaped HOBO Solar Radiation Shields.
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This semi-empirical correction depends on the shield’s area normal to the sun in addition
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to solar radiation and wind speed. The required correction coefficients, which can be
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universally applied for this type of shield, were obtained through comparison with fan-
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aspirated temperature measurements at one site. The root-mean-square error of the
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HOBO temperature measurements was reduced from 0.49 °C to 0.15 °C after applying
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this radiation correction.
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1. Introduction
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Horizontal homogeneity of the air temperature field is considered a prerequisite
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for tower-based micrometeorological techniques to accurately measure the turbulent heat
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exchange between the surface and the atmosphere (Kaimal and Finnigan, 1994). In reality,
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such conditions are probably rarely met. Measuring the spatial distribution of air
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temperature allows checking whether spatial differences are small enough that this basic
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requirement can be assumed. If not, it allows quantifying additional fluxes, such as
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horizontal advection for example. Flux contributions that originate from spatially
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stationary structures also cannot be captured with single-tower measurements and can
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therefore only be measured through spatial Reynolds averaging (Mahrt, 1998; Steinfeld et
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al., 2007). The resulting underestimation of turbulent fluxes is often referred to as the
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energy balance closure problem (e.g. Culf et al., 2004; Mauder and Foken, 2006; Foken,
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2007; Oncley et al., 2007).
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Since evidence of large scale circulations was found through aircraft
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measurements by Mauder et al. (2007), an experiment was designed to measure the
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spatial distribution of air temperature from ground based measurements. A network of
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naturally ventilated air temperature sensors was deployed to obtain the spatial average
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that is required for a spatial eddy covariance calculation. Turbulent fluctuations were
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calculated by subtracting the spatial instead of the temporal average of a scalar.
H=
1 N
30 min
∑ ( w − [ w]) (T − [T ]) , t =0
(1)
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where H is the sensible heat flux, N is the number of samples, w is the vertical wind
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velocity, T is air temperature, and [] denote a spatial average.
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Temperature fluctuations were measured by a sonic anemometer/thermometer.
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Since this instrument is based on a completely different measurement principle, great
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care had to be taken in correcting systematic errors of the spatially averaged temperature
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measurement. The dominant error source of a temperature sensor unit in a multi-plate
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radiation shield is radiative solar heating.
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According to Steinfeld et al. (2007), a number of about 25 measurement sites is
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necessary to obtain a good estimate of the spatially averaged air temperature if they are
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equally distributed over a 10 km x 10 km area at a measurement height of 20 m.
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Although the size of the observation area and the measurement height were different for
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our set-up, we decided to follow this recommendation and deployed 25 HOBO 12-Bit
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Smart Sensors (Onset Computer Corporation, Bourne, Massachusetts, part # S-TMB-
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M002) in combination with HOBO Solar Radiation Shields (Onset, part # M-RSA) as a
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practical and economical solution. These HOBO systems are an improved version of the
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temperature datalogger HOBO H8 Pro, which has been evaluated by Whiteman et al.
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(2000). It has been shown that these sensors are durable, compact, easy to maintain, and
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very low in power consumption. Nakamura and Mahrt (2005, NM05 in the following)
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have developed a correction for the radiative error of the HOBO M-RSA radiation shield.
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However, this correction is not sufficient for the purpose of this experiment, i.e.
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determining the sensible heat flux by replacing the temporal average with a spatial
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average when computing turbulent air temperature fluctuations. Turbulent temperature
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fluctuations are usually on the order of 1.0 °C (standard deviation of sonic temperature),
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and the measurement error of the HOBO sensors should preferably be one order of
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magnitude less.
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Therefore, our goal is to reduce the measurement error of the HOBO systems as
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much as possible. In this study, an improved correction for the radiative heating error of
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naturally ventilated HOBO radiation shields is presented. This correction is able to
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provide better results than the approach of NM05 because it considers the shield’s
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geometry. The approach of NM05 uses wind speed and the shortwave radiation normal to
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the earth’s surface only. It does not consider the shield’s area normal to the sun and is
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therefore not as effective. The method presented in this paper uses an adaptation of the
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correction developed by Anderson and Baumgartner (1998, AB98 in the following) for
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cylindrical shaped shields to the cuboidal shaped HOBO shields.
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2. Model for the radiative heating error
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Since our correction for radiative heating is based on the work by AB98, we will
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briefly summarize this method and point out necessary modifications for its application to
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the HOBO shield. Sensor and shield are considered as one unit. The three major effects
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that influence the temperature of this system are
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•
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radiative heating, meaning primarily the incoming shortwave solar radiation that hits the shield’s surface,
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natural convection, meaning the heat transfer by fluid circulation or
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movement solely due to the natural forces of buoyancy at zero wind speed;
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this process is called “conductive cooling” by AB98, and
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•
forced convection, meaning the heat transfer due to movement of the fluid
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with the mean wind, which is called “convective cooling” by AB98.
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According to AB98, the incoming shortwave radiation is the dominant term in the
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radiation budget, at least during daytime. In comparison the longwave radiation balance
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is small and the reflected shortwave radiation is linked to the incoming shortwave
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radiation through a relatively constant factor, the albedo. This means that only the
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measurement of the incoming shortwave radiation is required for a radiation correction of
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temperature measurements. The error due to longwave radiation was determined by
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NM05 during nocturnal conditions and these measurements showed a nighttime error of
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less than 0.1 °C on average. This effect was neglected for the correction presented in this
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paper. As a result of the three processes listed above, the measured temperature in the
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shield is usually greater than or equal to the actual air temperature during daytime. The
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heat budget of this system can be written as
α s Rs As = L + S ,
(2)
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where radiative heating term is the product of an absorption coefficient αs, the shortwave
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flux density Rs, and the area normal to the incident solar radiation As. L and S are the heat
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transfer terms for forced and natural convection. In accordance with AB98, Rs can be
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described as Rs =
SW ↓ , rd + (1 − rd ) sin θ
(3)
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where θ is the sun’s elevation angle, and SW↓ is the flux density of shortwave radiation
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normal to the surface. Here, a constant ratio rd of diffuse radiation to total downward
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radiation of 0.1 is assumed. The justification is that the largest radiative heating occurs
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under clear skies rather than under cloudy conditions (AB98).
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The calculation of the area normal to the sun As has to be adapted for the HOBO
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shield. Its geometry can be described with a cuboid of 0.213 m length l, 0.188 m depth d,
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and 0.152 m height h. The contribution of the top area Atop of the cuboid to As is a
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function of θ.
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Atop = l ⋅ d ⋅ sin θ .
(4)
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The contribution of the sides of the cuboid Asides to the total area As is a function of θ, the
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sun’s azimuth α, and the orientation of the HOBO shield ϕ. It can be written as the sum
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of the contribution from the longer side Al and the contribution from the shorter side Ad.
Asides = Al + Ad = h ⋅ cos θ ⋅ l ⋅ sin (α − ϕ ) + h ⋅ cos θ ⋅ d ⋅ cos (α − ϕ ) .
(5)
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The sun’s angles θ and α were computed according to a parameterization
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(http://www.jgiesen.de/SME/tk/index.htm). The orientation angle ϕ is defined as the
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direction, where the mounting plate on the longer side of the cuboid is facing.
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The sum of the cooling terms L and S is a function of the shield surface temperature T and the ambient air temperature Ta. It is written as L + S = hu (T − Ta ) Ac + ho (T − Ta ) Ac ,
(6)
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where Ac is the surface area of the shield, which is the actual heat exchange area; hu and
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ho are the heat transfer coefficients for forced convective and natural convective cooling.
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The coefficient ho is a constant, because natural convection is defined for zero wind and it
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is solely based on buoyancy. The unit of ho is W m−2 °C−1. The heat transfer coefficient
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for forced convection hu is usually described by an empirical model (Incropera and
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DeWitt, 1985). In accordance with AB98, hu can be expressed as a function of wind
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speed V and two empirical parameters C and m. hu = CV m ,
(7)
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where m is a non-dimensional constant and the coefficient C incorporates another non-
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dimensional constant C ′ , the thermal conductivity k, the viscosity of the air ν, and the
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Prandtl number Pr.
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C=
C ′ Pr k . ν
(8)
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It is assumed that all the parameters in Eq. (8) are constant over the observed air
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temperature range. Thus, the unit of C is J m−3 °C-1. Combining Eqs. (1), (5), and (6) and
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dividing by αs, the sum of both heat transfer coefficients, δ, is
δ = CV m + ho =
Rs As . (T − Ta ) Ac
(9)
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Ta can be substituted by the reference (aspirated) temperature measurements, while T is
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the shielded HOBO temperature. Here, we assume that the shield surface temperature can
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be substituted by the temperature measured inside the shield by the HOBO sensor. All the
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variables on the right-hand-side of Eq. (7) and wind speed V are available, which allows
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determining the three empirical constants C, m, and ho from a regression analysis as
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described in AB98. The corrected ambient air temperature measurement in the naturally
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ventilated shield then becomes
Tc = T −
Rs As . δ Ac
(10)
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3. Experimental Set-up
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The HOBO 12-Bit Smart Sensor is a thermistor with a built-in A/D converter. Its
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digital output was recorded on HOBO Micro Station dataloggers (Onset, part # H21-002).
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The sensor was placed inside the HOBO Solar Radiation Shield, which was mounted on a
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3-Meter Tripod (Onset, part # M-TPB). The measurement height of the temperature
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sensor was 2.60 m above ground level. The accuracy of the sensor itself is ±0.2 °C
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according to the manufacturer (Table 1). The response time specification of < 2 min is
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approximately confirmed by the findings of Whiteman et al. (2000) and NM05. This is
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adequate for measuring horizontal temperature gradients to calculate advective fluxes.
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We also do not expect the spatial mean to change at a faster rate over our study area of
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3.5 km x 3.5 km, because the spatial averaging acts a low-pass filter.
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The measurements were carried out over farmland in southwest Ottawa, Ontario,
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Canada (45°18’13” N, 75°46’12” W, 88 m a.s.l.). The observation period was from 17
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May 2007 to 20 June 2007. Wheat, corn, soybean, grass and alfalfa were cultivated on
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this land. 25 HOBO sensors were distributed over the 3.5 km x 3.5 km area in a regular 5
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x 5 grid. The orientation of the HOBO shields ϕ was 54° for all the 25 sensors of our set-
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up. The central site of that grid was located on a 700 m x 300 m large grassland area. In
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addition to the HOBO sensor datalogger combination, this site was equipped with a high-
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precision temperature sensor of type 063 (MetOne Instruments Inc., Grants Pass, Oregon)
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in a radiation shield of type 076B, also produced by MetOne. This system served as
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reference for determining the correction coefficients ho, C, and m, since its fan-aspirated
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shield reduces the radiative error to < 0.03 °C according to the manufacturer (MetOne
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Instruments, 1997). This extremely low error is safeguarded though the shield’s
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construction including a large umbrella-shaped cover plate of 51 cm in diameter, triple-
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sided walls, double-cross mask bottoms towards the ground, and a relatively large flow
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rate of 37.7 l s-1.
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Further, a CSAT3 sonic anemometer (Campbell Scientific Inc., Logan, Utah) and
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a CMA6 first-class albedometer (Kipp&Zonen, Delft, The Netherlands) were deployed at
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this site. All these sensors were collocated in an area of 20 m x 20 m. The sonic data were
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recorded on a Campbell CR23X datalogger at a sampling rate of 20 Hz. All slow-
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response sensors were recorded at 30 s intervals.
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4. Field intercomparison
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In order to estimate the precision of the HOBO systems under field conditions, a
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side-by-side intercomparison was conducted before the actual deployment in the main
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experiment. All 25 HOBO sensors were set-up together with the aspirated MetOne sensor
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over grassland on the Central Experimental Farm of Agriculture and Agri-Food Canada
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in Ottawa, Ontario. The 25 HOBO sensors were set-up in a 5 x 5 grid in an area of 10 m
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x 10 m. The MetOne sensor was located 2 m beside this grid (Fig. 1). To ensure
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comparable conditions to the later deployment in the main experiment, all sensors were
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mounted at a height of 2.60 m above ground level facing the same direction, and the
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sampling interval was set to 30 s.
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The systems recorded air temperature on 2 May and 3 May 2007. Temperatures
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ranged from 9.5 °C to 16 °C during this period. Root-mean-square errors (RMSE) were
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calculated for all HOBOs sensors choosing one of them randomly as a reference. The
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RMSE values ranged between 0.05 °C and 0.14 °C with a median of 0.09 °C. However,
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the maximum deviation of the HOBO measurements from the fan-aspirated MetOne
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temperature was +1.54 °C. This clearly shows the need for a radiation correction.
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Fortunately, it is possible to use the same radiation correction for all 25 sensors because
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of the good precision of the HOBO units and because all shields were oriented in the
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same direction. However, it has to be assumed that the incoming shortwave radiation and
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the wind speed were similar over the entire study area, and that possible differences
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cancel out when calculating the spatial average from the 25 sensors. The topography of
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the measurement domain is generally flat with elevation changes of only a few meters
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over the entire area. The assumption of a constant V is therefore reasonable.
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5. Results and discussion
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Wind speeds V and δ values were calculated as 30-min averages in order to
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determine the empirical coefficients for the radiation correction. A dependency of δ on
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either wind direction or the sun’s azimuth, as found by AB98, could not be detected for
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our measurements. Therefore, it was not necessary to apply wind blocking or shading
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adjustments. From an analysis of nighttime data, an offset of +0.32 °C was found for the
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HOBO sensor compared to the MetOne system. This was probably related to the
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characteristics of the sensor/data acquisition system and was therefore generally
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subtracted from the HOBO readings. After discarding data from periods with rain, 593
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pairs of V and δ values remained from the six-week observation period. These samples
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were classified into 30 equal sample size bins of ascending wind speed. The wind speed
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range was 0.04 to 6.36 m s−1. A nonlinear regression analysis was conducted, which
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resulted in the coefficients ho = 242.24 W m−2 °C−1, C = 44.87 J m−3 °C-1, and m = 2.05
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(nondimensional).
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Fig. 2 shows examples of magnitude of the correction term (Tc − T) as a function
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of wind speed V for various combinations of Rs and As. For calm wind, the correction
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term reaches up to −1.2 °C for Rs = 1000 W m−2 and As = 0.06 m2, which are both at the
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upper limit of the range of values that occurred during this experiment. The correction
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term decreases rapidly for wind speeds larger than 1 m s−1. At 3 m s−1 the correction term
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is 0.5 °C for the highest product of Rs and As values. For wind speeds larger than 5 m s−1
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the correction term is generally less than 0.2 °C. For radiative heating term of 500 W m−2,
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which corresponds to the midday conditions on an overcast day in summer, the maximum
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correction term is 0.6 °C for calm winds.
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In theory, the parameters ho, C, and m can be universally applied for this type of
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HOBO radiation shields over similar surfaces. However, the exposure of the sensors
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during this experiment in May and June of 2007 was limited and only a selection of all
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possible meteorological conditions was covered. Thus, these parameters are only valid
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for daytime conditions as long as wind speed, solar radiation, and solar angles are within
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the range of the observations during this experiment (V < 6.36 m s−1; SW↓ < 1008 W m−2 ;
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θ < 68.1°). This correction cannot be applied for periods of precipitation and when the
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shields surface characteristics are altered, e.g. through adherent water or snow. A site
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with a different albedo than grass (≈ 0.2), which formed the reflecting surface during this
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experiment, would also require a recalibration of the correction parameters. Regular
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weather stations mostly use measurement heights of 1.5 m or 2.0 m. The HOBO sensors
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in our set-up were located at a height of 2.6 m. We do not expect that the radiative error
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of the HOBO shields would be significantly different between these heights.
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The effect of the consideration of the cuboidal HOBO geometry on the solar
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heating term is shown in Fig. 3 for three very different consecutive days. The first day, 19
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May 2007, was cloudless with a maximum incoming solar radiation of 970 W m−2 and
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low wind speeds between 0.1 m s−1 and 2.5 m s−1. The second day was overcast, and the
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maximum incoming solar radiation was 444 W m−2. Wind speeds were much higher
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ranging between 2.3 m s-1 and 6.0 m s-1. The third day was cloudless in the morning
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before some cumulus clouds developed in the afternoon. Incoming shortwave radiation
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was undisturbed from clouds at solar noon and reached 984 W m−2. Wind speeds were
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between 3.1 m s−1 and 6.0 m s−1.
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The shield’s area normal to the sun As had a trimodal diurnal course. On the clear
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sky day, 19 May 2007, the highest maximum was at 0842 local solar time (LST), a
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secondary maximum at 1615 LST, and a tertiary maximum at 1220 LST. In comparison,
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the diurnal course of RsAs for a cylindrical shaped shield is bimodal with a distinct
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minimum at solar noon (AB98). The geometry factor As modulated the incoming
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shortwave radiation in such a way that the largest radiative heating of the HOBO shield
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RsAs occurred at 0855 LST. The maximum radiation correction on 19 May 2007 was
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1.17 °C. This maximum was reached twice on that day, firstly between 0830 LST and
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0900 LST when the RsAs term had its absolute maximum, and secondly between
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1130 LST and 1200 LST when wind speeds were lowest. On 20 May 2007, the maximum
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temperature correction was only 0.30 °C at maximum. The radiative heating was lower
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and wind speeds were higher compared to the previous day. On 21 May 2007, the
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radiation conditions were similar to 19 May 2007 in the morning when the radiative
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heating is usually largest. However due to higher wind speeds, the maximum temperature
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correction was only 0.37 °C.
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The overall improvement of the HOBO temperature measurements through the
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radiation correction is shown in Fig. 4. Without this correction, the HOBO temperature
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measurements were sometimes up to 1.2 °C higher. The differences between the
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uncorrected HOBO temperature T and the aspirated temperature Ta scattered around an
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average of +0.42 °C with a standard deviation of 0.27 °C. The median was +0.38 °C.
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After applying the radiation correction, the HOBO temperatures Tc and Ta were almost
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identical on average with significantly less scatter. The mean difference between Tc and
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Ta was +0.01 °C with a standard deviation of 0.15 °C and a median of +0.02 °C. The
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root-mean-square difference between the HOBO temperature measurements and the fan-
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aspirated reference measurements was reduced from 0.49 °C to 0.15 °C. The remaining
295
error is only slightly larger than the precision of the HOBO sensor-shield combinations
296
themselves.
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6. Conclusions
300 301
The principle of AB98’s correction for radiative heating of naturally ventilated
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shields was successfully adapted to the cuboidal geometry of the HOBO Solar Radiation
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Shields. This modified correction method makes it possible to deploy a network of many
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relatively low-cost and low-maintenance temperature sensors in naturally ventilated
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shields with a data quality close to aspirated systems, provided wind and radiation
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measurements are available for at least one of sites over the entire measurement period.
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The study area also must be small enough that similar conditions for incoming shortwave
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radiation and wind can be assumed. At many weather stations, shortwave radiation and
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wind speed belong to the standard set of measured variables, so that this radiation
310
correction can be applied for the temperature measurements in HOBO Solar Radiation
311
Shields. An aspirated temperature sensor was deployed over a 35-day period in May and
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June 2007, in order to obtain estimates for the three empirical correction coefficients
313
required. These parameters may be generally applied for clean and dry HOBO Solar
314
Radiation Shields of type M-RSA during daytime periods over surfaces with similar
315
radiative properties. Further measurements are needed to validate these parameters for
316
meteorological conditions that are not covered by the field observations presented here.
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Acknowledgements. We are grateful to Doug Glowenlock, manager of the Canadian Food
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Inspection Agency research farm in Ottawa, and Bert Moore, manager of the Greenbelt
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research farm in Ottawa, for their cooperation during the realization of the presented
322
measurements.
323 324
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REFERENCES
326 327
Anderson, S. P. and M. F. Baumgartner, 1998: Radiative heating errors in naturally
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ventilated air temperature measurements made from buoys. J. Atmos. Oceanic Technol.,
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Culf, A. D., T. Foken, and J. H. C. Gash, 2004: The energy balance closure problem.
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Vegetation, Water, Humans and the Climate. A New Perspective on an Interactive System,
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P. Kabat and M. Claussen, Eds., Springer, 159-166.
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Foken, T., 2007: The energy balance closure problem - an overview. Ecological
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Applications, accepted.
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Incropera, F. P. and D. P. DeWitt, 1985: Fundamentals of Heat Transfer. 2nd revised
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edition ed. John Wiley and Sons, 802 pp.
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Kaimal, J. C. and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their
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Structure and Measurement. Oxford University Press, 289 pp.
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Mahrt, L., 1998: Flux sampling errors for aircraft and towers. J. Atmos. Oceanic Technol.,
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15, 416-429.
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Mauder, M. and T. Foken, 2006: Impact of post-field data processing on eddy covariance
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flux estimates and energy balance closure. Meteor. Z., 15, 597-609.
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Mauder, M., R. L. Desjardins, and J. I. MacPherson, 2007: Scale analysis of airborne flux
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measurements over heterogeneous terrain in a boreal ecosystem. J. Geophys. Res., 112,
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D13112, doi: 10.1029/2006JD008133.
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MetOne Instruments, Inc., 1997: Fan Aspirated Radiation Shield. [Available online from
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http://www.metone.com/documents/076BShieldDSTemp.pdf.]
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Nakamura, R. and L. Mahrt, 2005: Air temperature measurement errors in naturally
349
ventilated radiation shields. J. Atmos. Oceanic Technol., 22, 1046-1058.
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Oncley, S. P., T. Foken, R. Vogt, W. Kohsiek, H. de Bruin, C. Bernhofer, A. Christen, D.
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Grantz, E. Lehner, C. Liebethal, H. Liu, M. Mauder, A. Pitacco, L. Ribeiro, and T.
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Weidinger, 2007: The Energy Balance Experiment EBEX-2000. Part I: Overview and
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Steinfeld, G., M. O. Letzel, S. Raasch, M. Kanda, and A. Inagaki, 2007: Spatial
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representativeness of single tower measurements on the imbalance problem with eddy-
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covariance fluxes: results of a large-eddy simulation study. Bound.-Layer Meteor., 123,
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Whiteman, C. D., J. M. Hubbe, and W. J. Shaw, 2000: Evaluation of an inexpensive
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FIGURE CAPTIONS
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Fig. 1: Intercomparison pre-experiment of the 25 naturally ventilated HOBO sensors and one aspirated MetOne reference sensor (on the right side). Fig. 2: Difference between corrected and measured HOBO temperature (Tc − T) as a function of wind speed V for various combinations Rs and As values. Fig. 3: Shield area normal to the sun (As) and radiative heating term (RsAs) for three selected days in May 2007. Fig. 4: Histograms of the difference between the HOBO temperature and the aspirated temperature before and after applying the radiation correction.
373 374
18
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Table 1: Selected specifications of the HOBO 12-Bit Smart Sensor
Specifications Measurement range
−40 °C to +100 °C
Accuracy
< ±0.2 °C from 0 °C to 50 °C
Resolution
< 0.03 °C from 0 °C to 50 °C
Drift
< 0.1 per year
Response time
< 2 min (in 2 m s−1 moving air flow)
375 376
19
376 377 378
Fig. 1: Intercomparison pre-experiment of the 25 naturally ventilated HOBO sensors and one aspirated MetOne reference sensor (on the right side).
379
20
379 380 381
Fig. 2: Difference between corrected and measured HOBO temperature (Tc − T) as a function of wind speed V for various combinations Rs and As values.
382
21
383 384 385
Fig. 3: Shield area normal to the sun (As) and radiative heating term (RsAs) for three selected days in May 2007.
386
22
387 388 389
Fig. 4: Histograms of the difference between the HOBO temperature and the aspirated temperature before and after applying the radiation correction.
390
23
