## 1. Introduction

The scintillometry method is based on atmospheric refraction. For optical waves, the refraction is dominated by atmospheric temperature fluctuations, so one can confidently obtain the structure parameter of temperature

The derivation of

While scintillometry has been widely applied over grassland and cropland, and some of those studies have been over heterogeneous terrain (e.g., Schüttemeyer et al. 2006; Ezzahar et al. 2007; Ward et al. 2011), only few scintillometry studies have been performed over cities (Kanda et al. 2002; Lagouarde et al. 2006; Roth et al. 2006; Masson et al. 2008; Pauscher 2010; Salmond et al. 2012; Zieliński et al. 2012; Wood et al. 2013b). Cities cause difficulties in the interpretation of scintillometer data, given the possible heterogeneous surface below the path—in particular, the difficulty in determining effective height (including knowledge of the zero-plane displacement height). Furthermore, all studies over cities have been conducted in midlatitude cities. Therefore, our aim is to understand

In the future, if a model–measurement intercomparison is to be done, then one desires a purely measured quantity to compare with a purely modeled one. For the case of scintillometer-derived fluxes, one compares a flux derived with MOST using experimental values of a stability parameter with a flux derived with MOST using a modeled stability parameter. It would be desirable to compare measured

In this paper, we report (i) the first results from many months' data from two scintillometers and compare them with data from two sonic anemometers over Helsinki, Finland, and (ii) the evaluation of an algorithm for obtaining

## 2. Materials and methods

### a. Instrumentation and site description

Two large-aperture scintillometers (BLS900, Scintec AG, Germany) and two sonic anemometers (USA-1, Metek GmbH, Germany) have been part of a suite of equipment installed across the city of Helsinki, Finland, on the coast of the Gulf of Finland (Fig. 1; Table 1). They are a part of the Helsinki Urban Boundary-Layer Atmosphere Network (URBAN; http://urban.fmi.fi; Wood et al. 2013a), with increasing activity in observing the urban boundary layer in particular since 2004. The site is characterized by the vicinity of the sea and the strong seasonality in climate, caused by the high latitude (>60°N) and semicontinental climate. Downtown Helsinki is located in a peninsula protruding southward (Fig. 1a), including the sites of Torni, Sitra, and Elisa. Most of the land area on the map is 5–15 m above mean sea level (MSL), with some hills up to about 30 m.

Instrument positions (see also Fig. 1). Effective heights are as per Eq. (14) for scintillometers using data in Figs. 1b and 1d, and directionally averaged *z*–*z _{d}* for sonic anemometers.

It is desirable to have near-horizontal scintillometer paths, given that

The 10-Hz sonic-anemometer time series, of the three components of wind and sonic temperature (i.e., virtual temperature), were used to calculate turbulent fluxes: friction velocity

### b. Obtaining structure parameter from scintillometers

From 500-Hz light intensity measurements, 1-min averages of the structure parameter of the refractive index of air

^{−5}K hPa

^{−1}(Scintec 2011). Atmospheric pressure measurements from SMEAR III–Kumpula (HMP243, Vaisala Oyj, Vantaa, Finland) were used for both scintillometers. Air temperature measurements were from the Elisa mast (HMP45D, Vaisala Oyj) for the downtown scintillometer, and an average temperature of Elisa and SMEAR III–Kumpula (homemade platinum resistance thermometer Pt-100) masts for the city-scale scintillometer.

### c. Obtaining structure parameter from sonic anemometers

We estimate the structure parameter of temperature from time series of virtual temperature (i.e., uncorrected 10-Hz temperature data directly from the sonic anemometer) by fitting the parameters of model high-frequency spectra proposed by Kouznetsov and Kallistratova (2010). Because that reference is not permanent, we provide further details here.

*T*), one can write a power spectral density in the temporal domain aswhere

_{υ}^{−1}) and

For practical calculations of the spectra, we used a one-size-fits-all approach: a fixed segment length of about 10 s (128 data points at 10 Hz), which was generally well within the inertial subrange of turbulence for the heights of several tens of meters. The calculations with the data used for this study have shown small dependence (<20%–30%) of the resulting structure parameters on the segment length within a range from 32 to 1024 points. Too-small segments lead to the decrease of the structure parameter accuracy at low values, when the spectrum is strongly affected by measurement uncertainties. This effect was most pronounced for low values of the temperature structure parameters. If segments are too long, then the signal from beyond the inertial subrange appears in the estimated spectrum. This results in a degradation of fitting performance of the model spectrum [Eq. (6)] and a corresponding increase in chi square. The choice of a segment length could be performed with some approximation of turbulent spectra (Kaimal et al. 1972); however, a simpler way is to choose a fixed segment length and then discard the resulting structure parameters that do not meet the quality criteria for the accuracy and goodness of fit.

Unlike the earlier methods (Greenhut and Mastrantonio 1989; Beyrich et al. 2005), the model spectrum [Eq. (6)] does not require any procedure to select the high-frequency limit of the inertial subrange in measured spectra, but it can use the spectra up to the Nyquist frequency. Attenuation of spectra, due to insufficient sensor response at high frequencies, was not observed; however, it can be incorporated into the model spectrum. Were this attenuation to become substantial, it would be detected with the chi-square test.

In this study, the sonic-derived structure parameter data were rejected primarily based on the chi-square test. The main reason for the test failure is too-low wind speed that invalidates the Taylor hypothesis for temperature fluctuations. The rejected fractions are 7.6% and 14.2% of all 30-min-average values for the SMEAR III–Kumpula and downtown (Torni) sites, respectively.

### d. Estimating sensible heat flux from structure parameter

^{−2}is acceleration due to gravity,

^{−3}) and

^{−1}kg

^{−1}). Different expressions for

*H*, for example, as is used in situations where EC data are not available (e.g., Hartogensis et al. 2003).

*u*is along-beam distance) to represent different conditions along the beam. However, in the calculation of

*H*, one single height is needed to be representative of the single value of

*H*for unstable stratification. The scintillometer effective height takes into account the spatial averaging and the stability dependence. The effective height as defined in the eddy-covariance community is simply the difference between the sonic-anemometer height and the zero-plane displacement height in the flux footprint.

Estimates of sensible heat flux are subject to some uncertainty. For greater certainty a source-area-model technique (Kormann and Meixner 2001) could be performed to estimate the zero-plane displacement height from morphological techniques (Grimmond and Oke 1999) for different upwind sectors and stabilities (and thus different

## 3. Results

### a. Structure parameter from the scintillometers

The variability of ^{−3} to 10^{−1} K^{2} m^{−2/3}) occurred during daytime unstable conditions. But also, there were a few high values during November, January, and February nights, consistent with the large occurrence of negative sensible heat fluxes over Helsinki. Indeed, the sonic-derived sensible heat fluxes were negative for 45% of the time in those particular studied months, partly driven by the long nights and snow cover (Wood et al. 2013a). The lowest

Comparing

### b. Comparison of structure parameter from sonic and scintillometer

The ratios

The ratio of

A comparison between sonic and scintillometer downtown (Figs. 5a,b) for many days of data shows a good agreement for *r* = 0.85). This corroborates the usability of the spectral method to calculate

Two case days demonstrate the time evolution of

### c. Relationship with sensible heat flux

It is not possible to estimate

The quality of *H* from the sonic than the

These sensible heat flux comparisons are only slightly worse than other scintillometer studies (Lagouarde et al. 2006; Roth et al. 2006; Zieliński et al. 2012)—that is, giving high correlation coefficients of 0.85–0.95, but also rms errors of 20–100 W m^{−2}. Note, however, that the absolute scatter in Figs. 5c–f is mostly caused by larger values of

## 4. Summary

Measurements were performed in the city of Helsinki using two large-aperture scintillometers (Scintec BLS900) and two sonic anemometers (Metek USA-1). One scintillometer has been installed in relatively homogeneous terrain downtown with a 1.8-km path; the other one has a longer city-scale path and more heterogeneity underneath. Sonics were installed at the end points of the city-scale scintillometer path (ideal points near the center of scintillometer beams were not possible because of practical constraints in finding available measurement locations in cities). The values of

A robust method to derive

The challenges in estimating sensible heat flux from ^{−2}.

The climate conditions in Helsinki represent a challenge for scintillometry, given the urban surface and the high-latitude location giving rise to negative sensible heat fluxes even above an urban surface. The values of sensible heat flux are typically small, which poses a problem to MOST-based methods. Moreover, shallow boundary layers of a few tens of meters that often occur over Helsinki can invalidate the surface layer scaling, which is a prerequisite of MOST. In such cases, a surface layer might not exist.

A challenge now presents itself: how do we make best use of

## Acknowledgments

This work has been supported by the EC FP7 ERC Grant 227915 “Atmospheric planetary boundary layers: Physics, modelling and role in earth system,” Academy of Finland (Projects 138328, 1118615, and ICOS-Finland 263149), and the Russian Foundation for Basic Research (Project 13-05-00846). Kari Riikonen, Erkki Siivola, Petri Keronen, and Sami Haapanala provided technical support. We are grateful to the reviewers for their valuable comments and to Timo Vesala, Sylvain Joffre, Ari Karppinen, Lukas Pauscher, Helen Ward, Oscar Hartogensis, Daniëlle van Dinther, and Sue Grimmond for the fruitful discussions. The results and conclusions in this study were made at specific locations and with specific equipment configurations. They should not be used to judge the general performance of instruments or particular manufacturers.

## APPENDIX

### Saturation of the Scintillometers

To quantify the effect of saturation (Kohsiek et al. 2006) for our scintillometers, the histograms of ^{−2} K^{2} m^{−2/3} for the longer path with a very pronounced transition and (ii) at about 3 × 10^{−2} K^{2} m^{−2/3} for the shorter path with a less-pronounced transition. The Scintec manual (Scintec 2011) states that the maximum measurable values of ^{2} m^{−2/3} for 2- and 5-km paths, respectively. The manual's limit values are well above the values for which we observed saturation in our instruments. Note that only the data reported valid by the Scintec SRun 1.09 software are used for the histograms. Such behavior is likely caused by the inability of the implemented correction (Clifford et al. 1974) to correct all the data affected by saturation. It is not clear if this is an implementation problem or a problem of the correction itself. Most values of ^{−2} K^{2} m^{−2/3}, and for them the downtown histograms coincide quite well. We thus consider those data reliable.

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