Different rain cap designs were tested for water ingress in a series of laboratory tests (Table : NEON.TIS.4.1615). Figure 1 shows three final rain cap designs: LI-COR's old rain cap (LO) until 2013, part number 9972-054, LI-COR's new rain cap (LN) from 2014, part number 9972-072 and the new NEON rain cap design (NN). Tests were conducted at a mass flow rate (with standard temperature T=20 ∘C and standard pressure p=101.3 kPa) of 23 SLmin-1 (standard liters per minute) to emulate the worst case scenario. This significantly exceeded the minimal recommended volumetric flow rate (at temperature and pressure of measurement location) of 10.5 Lmin-1 (liters per minute) and nominal recommended volumetric flow rate of 15 Lmin-1. The rain caps were sprayed from the top and side with a water hose at rates of 12.1–16.3 Lmin-1, including horizontal spray. Additional tests were conducted at 15 SLmin-1 flow rate to establish whether a downward-oriented tube with 6.4 mm inner diameter (ID) would transport water upwards. Water ingress was observed, and the test concluded that a rain cap would indeed be required for the system to prevent or minimize water ingress. The latter corroborated the results reported for a downward-oriented tube without a rain cap from field tests conducted by ICOS (De Ligne et al., 2014; Aubinet et al., 2016).

Particulate filters aid the upkeep of system performance, but can induce pressure drops exceeding the dynamic range of the IRGA differential pressure sensor (Table : NEON.TIS.4.1618, NEON.TIS.4.1628, NEON.TIS.4.2007). Pressure drops were tested for 15 different filters and for the range of flow rates from 2 to 20 SLmin-1. The overall scheme for these tests included a mass flow controller regulating the flow rate, and pressure measurements upstream and downstream of the filter to measure the pressure drop. One set of tests used the Sierra Mass Flow Controller (C100M-DD-3-OV1, Sierra Instruments, Monterey, CA, USA) and the Dwyer Manometer (Series 477, Dwyer Instruments, Michigan City, IN, USA) in conjunction with compressed air from a cylinder to push air through the filter. Another set of tests used a LI-7200 Flow Module (Model 7200-101, LI-COR Biosciences, Lincoln, NE, USA) as a flow provider and flow controller to pull the air through the filter, and LI-7200 differential pressure measurements to record the pressure drop. Other tests used a vacuum pump (1023-101Q-SG608X, Gast, Benton Harbor, MI, USA) in combination with a ballast chamber (5344R, Scott Specialty Gases, Plumsteadville, PA, USA) and barometer measurements upstream and downstream of the filter (PTB 330, Vaisala, Helsinki, Finland).

This study reports results for the nine filters listed in Table . The ultimately selected FW-2.0 filter (Swagelok, Solon, OH, USA) was tested in several additional experiments, and results are presented as a range of values from all the experiments.

In general, the transfer function FTf of a system is defined as the ratio of its output to its input as a function of the natural frequency f. In an ideal system the transfer function would be unity across all frequencies. In a real system, fluctuations in CO2 or H2O tend to be dampened at higher frequencies. Using power spectra to quantify transfer functions, the output variance or covariance is reduced to 50 % or -3 dB of its input at the half-power frequency f50%. Adding a rain cap, filter and intake tubing to an IRGA essentially acts as a low-pass filter. That is, it attenuates high-frequency fluctuations of H2O and CO2, which subsequently reduces the turbulent flux calculated via correlation with the vertical wind speed measurement. For example, automated high-frequency spectral corrections require excellent frequency response beyond the spectral peak frequency (e.g., Nordbo and Katul, 2012; Table : NEON.TIS.4.1626, NEON.TIS.4.1627).

The transfer function of an IRGA system including the GSS can never be better than the spectral quality of the IRGA itself. Consequently, first the frequency response of the IRGA needs to be quantified. This allows subsequent determination of whether and for which components the GSS optimization can warrant significant frequency response improvements. The LI-7200 optical unit measures CO2 and H2O number density at internal rates exceeding 100 Hz. In combination with minimal inertia thermocouples and pressure transducers for mole fraction conversion, LI-7200 frequency response is likely dominated by volume averaging in the optical cell with a volume of V=16.0 cm3. The volume averaging effect can be quantified by the generalized transfer function of Silverman (1968), in the form of Massman (2004) and Moore (1986): FT(f)=sin⁡2(πfτ)(πfτ)2with the time constantτ,τ=VQv, where π is the number pi, and Qv is the volumetric flow rate in units  cm3s-1. Analogously, Eq. (1) can be used to approximate the along-path (worst case) averaging effect of open-path gas analyzers aligned to within ≈30∘ of being horizontal by determining τ as τ=dlU, with length of the optical path dl (e.g., 12.5 cm for a LI-COR LI-7500) and horizontal wind speed U.

Numerically evaluating Eqs. (1) and (2) for Qv leads to the perfect linear relationship Qv=f50%× 2.167. The minimum required volumetric flow rate to achieve the most stringent half-power frequency requirement of f50%>4 Hz for the particulate filter can then be determined to be >8.7 Lmin-1. Thus, at larger flow rates, the LI-7200 itself does not limit the objectives of the GSS optimization. For the flow rate set point of 10.8 SLmin-1 (corresponding to ≈13.6 Lmin-1 and ≈16.2 Lmin-1 under laboratory and site conditions, respectively), the LI-7200 operates at f50%=6.3 Hz and f50%=7.5 Hz, respectively. Experimental data by De Ligne et al. (2014) and Aubinet et al. (2016) generally corroborated these calculations, suggesting the nominal frequency response of their test setup of about 7.9 Hz. In comparison to the LI-7200 cell, frequency response due to line-averaging over the 12.5 cm long LI-7500 optical path was variable, with f50%>7.5 Hz for wind speeds exceeding 1.4 ms-1 (i.e., better than the frequency response of the LI-7200 cell at ≈16.2 Lmin-1).

Subsequently, high-frequency attenuation was tested for the IRGA and each separate component of the GSS, as well as for cross-combinations of components, and for the complete system consisting of all listed components (Table 3). Two techniques were used for this purpose: (i) providing a CO2 and H2O change as a singular rising or falling step, and (ii) generating a square wave consisting of a sequence of many rising or falling steps. Based on the assumption of a linear- and time-invariant underlying system mathematical model, the Fourier transform of the time derivative of the measured response to a unit step function is the system transfer function. The differentiate and transform processing approach can be applied directly to the measured responses in (i). This same processing technique can be generalized to the measured responses of (ii), as the square wave input can be treated as an ensemble of rising or falling steps. Underlying principles of these signal processing approaches are described in detail in Lathi (1992), Truax (1999), Kaiser (2004), and Dorf and Bishop (2008). The latter approach was also utilized in a concurrent paper by Aubinet et al., 2016). In all experiments, the solenoid switches were used to rapidly alternate between zero air and predefined concentrations of CO2 or H2O upstream of the tested component. The corresponding change was measured with a LI-7200 downstream of the tested component. In H2O and CO2 experiments the relative humidity (RH) and dry mole fraction varied between 0–90 % and 0–400 ppm, respectively. For H2O specifically, the moist airstream was maintained at RH>90 % to reflect the field environment as well as possible. Nevertheless, for the square wave, the time average over alternating dry and moist airstreams cannot exceed RH=50 %. A dew point generator (for lower flow rates: LI-610, LI-COR Biosciences, Lincoln, NE, USA) or bubbler (for higher flow rates) in combination with a hygrometer (Optisure, Kahn Instruments, Wethersfield, CT, USA) were used to generate, control and record H2O concentrations. Tests were performed for a minimum of 420 s, and LI-7200 variables were recorded at 50 Hz. In these tests, flow rates ranged from 9 to 35 SLmin-1 depending on the experiment's goal, providing fully turbulent tube flow in the vast majority of tests (Reynolds number, Re>4000) or upper range of transient flow in a few tests (Re>3300).

Prior to the power spectra analysis (i) the first 200 s and last 20 s of data were discarded to focus on steady-state periods, (ii) missing values were linearly interpolated (only data sets with < 10 % missing values were further analyzed), (iii) the dry mole fraction time derivative was calculated, (iv) the time derivative was low-pass-filtered with a fifth-order Butterworth filter at 15 Hz half-power frequency to dampen leaking from high frequencies, (v) linear de-trending was applied to minimize bias, and (vi) 5 % of the data at each end of the time series were tapered with a cosine bell to reduce bias and to avoid leaking of peaks at faraway frequencies into other parts of the spectrum. Next, a fast Fourier transform was applied and the unfolded spectral energy was calculated. A recursive circular filter with a Daniell kernel was then used to reduce noise, and the resulting Fourier coefficients were binned into exponentially widening frequency classes using the arithmetic mean. The result for the LI-7200 without additional GSS components Sref(f) corresponds to the reference transfer function of the LI-7200 in combination only with the experimental setup (solenoids, connectors, etc.). The results for the LI-7200 with additional GSS components Stest(f) correspond to the test transfer functions of the LI-7200 in combination with the experimental setup as well as filter, intake tube and rain cap. Transfer functions FT(f) of filter, tube, rain cap as well as their combinations independent of LI-7200 and experimental setup were calculated by division of the individual power spectra (e.g., Foken et al., 2012). For this it is assumed that the mean spectral response between f1=0.01 Hz and f2=0.2 Hz was not attenuated: FT(f)=RNStest(f)Sref(f),with the dimensionless normalization factor RN=∫f1f2Sref(f)df∫f1f2Stest(f)df. Noise was reduced by a circular filtering with a Daniell kernel. In cases where multiple test results were available, ensemble transfer functions and their ranges were calculated. Finally, f50% was determined by inter/extrapolation of the resulting transfer function coefficients using the sigmoidal model of Eugster and Senn (1995): FT(f)=11+ff50%2. Resistor–capacitor theory (e.g., Williams and Taylor, 2006) then allows f50% to be determined for an equivalent first-order system when multiple passive low-pass filters are combined, such as rain cap, filter and tube. An approximation that was found adequate over the range of observations is f50%=1.54f50%′-4.66Hz,with the non-damped half-power frequencyf50%′=fh21n-1,the harmonic frequencyfh=12π∏1nτnnand the time constantτnfor each low-pass filtern:τn=12πf50%,n. The systems' damping coefficients in Eq. (7) were determined from an unweighted least-squares regression (R2=0.92, p value =6.338×10-8); measured f50% for several combinations of rain cap, filter and tube (N=14) were regressed against f50%′ calculated from Eqs. (8)–(10) using the measured f50% for individual components.

It is important to emphasize that all high-frequency attenuation experiments suffered from the intrinsic inability to produce a perfect step change or a perfect square wave under real-life conditions. Response time of the laboratory setup (solenoids, effects of connectors and other physical mixing volumes upstream of a tested component) attenuate the step change itself. This resulted in an apparent reduction in frequency response of a tested component. A remedy was to normalize the results of the LI-7200 in combination with GSS components to the LI-7200 alone. Such a procedure not only allowed the unveiling of the individual transfer functions of each GSS component, but also compensated for setup differences and enabled cross-comparison and aggregation of the results from the numerous different experiments.

In addition to physical laboratory tests, high-frequency attenuation processes were also modeled using computational fluid dynamics (CFD) software (ANSYS, Canonsburg, PA, USA). To corroborate the experimental results, turbulent flow simulations of cases with well-mixed and plug-flow assumptions were performed. The CFD results consistently showed lower attenuation by the components than experimental data, indicating that a perfect step change or a perfect square wave is not achievable in real-life settings.

A variety of additional aspects need to be considered and warrant testing when optimizing an IRGA-GSS. Of these, heating of the tube, filter and other components are addressed by the field experiments in this study (Sects. , ), and by Fratini et al. (2015). Other tests are outside the scope of this paper, such as optimization of tube length, tube material and flow rates, which have been covered both conceptually and experimentally by Runkle et al. (2012); Burba et al. (2010, 2012); Fratini et al. (2012); Clement et al. (2009); Massman and Ibrom (2008); Rannik et al. (1997).

US-NR1 is located in the Rocky Mountains, Colorado, USA (40∘1′58′′ N, 105∘32′47′′ W; 3050 m elevation), where measurements began in November 1998 (Monson et al., 2002; Turnipseed et al., 2002, 2003). The forest near the tower is around 110 years old, and primarily composed of subalpine fir (Abies lasiocarpa var. bifolia), lodgepole pine (Pinus contorta) and Englemann spruce (Picea engelmannii). The tree density is around 0.4 treesm-2 with a leaf area index of 3.8–4.2 m2 m-2, tree heights of 12–13 m (Monson et al., 2010; Turnipseed et al., 2002) and an approximate displacement height of 7.8 m.

Table 4 provides descriptive statistics of temperatures and humidities for all time periods utilized in this study. The median ambient temperature and relative humidity varied in a range of 11.7–15.1 ∘C and 46.1–68.7 % among periods, respectively. Specifically, the LO-0 Watt period without intake tube heating was driest with RHa=46.1 %, making it difficult to find periods of high relative humidity for intercomparison. The LO-6 Watt period with 6 W of intake tube heating was the most humid with RHa=68.7 %.

All instrumentation used in the field tests was deployed on the US-NR1 tower at 21.5 m above ground, equivalent to 13.7 m above the displacement height (Fig. 2). The companion study by Burns et al. (2014) provides an in-depth description of the sensor deployments. They are described as follows in short.

A Vaisala HMP35-D platinum resistance thermometer and capacitive hygrometer (Vaisala, Helsinki, Finland) was sampled at 1 Hz and was used in this study as reference for ambient air temperature (Ta) and relative humidity (RHa), respectively.

A CSAT3 sonic anemometer (Campbell Scientific, Logan, UT, USA, S/N 0254, firmware v4) was used to measure the turbulent wind components. The measurements were performed in single-measurement mode at 10 Hz sampling rate, collected using the Campbell Scientific Synchronous Devices for Measurement protocol, and synchronized with variables from other sensors using Network Time Protocol (NTP). From the CSAT3, the along-axis, cross-axis and vertical-axis wind components as well as sensor health information (from the CSAT3 diagnostic word) were used in this study.

Infrared gas analyzers were used to measure the turbulent fluctuations of H2O and CO2. A LI-7500 open-path IRGA (LI-COR Biosciences, Lincoln, NE, USA, S/N 75H-0084, firmware v2.0.4) was used as a reference for high-frequency response. The LI-7500 optical path was vertically centered with the CSAT3 sonic path, and laterally separated by 30 cm until 8 October 2013 and ≈90 cm thereafter. Data were collected at 10 Hz sample rate and 20 Hz bandwidth settings without observed aliasing, and synchronized with variables from other sensors using NTP. From the LI-7500, H2O and CO2 number densities were used in this study. A LI-7200-enclosed IRGA (LI-COR Biosciences, Lincoln, NE, USA, S/N 72H-0192 until 2 November 2013, S/N 72H-0479 thereafter, both firmware v6.5.2) was used to study the impact of GSS intake tube heating and rain cap on high-frequency response. The LI-7200 rain cap was vertically centered with the CSAT3 sonic path, and laterally separated by 30 cm until 12 November 2013 and 22 cm thereafter. The measurements were performed with a flow rate setting of 10.8 SLmin-1. At the ambient air density this resulted in approximately 16.2 Lmin-1 volumetric flow rate, or a ≈16 Hz renewal rate of the 16.0 cm3 LI-7200 optical cell assuming plug flow. Data were collected at a 20 Hz sample rate and 10 Hz bandwidth settings using the LI-7550 analyzer interface, and synchronized with variables from other sensors using the Precision Time Protocol. From the LI-7200, H2O and CO2 number densities, inlet, outlet and block temperatures of the optical cell (Tin, Tout, Tblock, respectively), as well as sensor health information were used in this study.

During the field tests, the LI-7200 GSS consisting of a rain cap, connected to a FW-2.0 filter and a stainless steel tube was tested. Until 7 January 2014, the LO rain cap (Fig. 1) was used in combination with a 70 cm long 4.8 mm ID tube. Thereafter, a prototype of the LN rain cap was used in combination with an 80 cm long 5.3 mm ID tube. Both tube and filter were uniformly covered by a Watlow 010300C1 100 Ohm heating element rated at 120 V and 150 W (Watlow Electric, St. Louis, MO, USA). A tight fit and thermal contact was ensured by plastic spiralling, followed by AP/Armaflex closed-cell elastomeric thermal insulation with 12.7 mm ID and 9.5 mm wall thickness (Armacell International, Capellen, Grand Duchy of Luxembourg) and white heat shrink, minimizing the impact of wind speed on thermal dissipation. For a 4 W heater setting, heat release within 0.5 m of the sonic anemometer was determined to ≤0.5 W. The corresponding inflow sector was excluded from analysis to avoid potential impacts on energy budget and Bowen ratio estimates. A Tenma 72–7705 power supply rated at 60 V and 6 A (Tenma Test Equipment, Washington, OH, USA) was used to test different heating power settings.

An analysis package developed in GNU R version 3.1.3 (R Development Core Team, 2012) was used for data processing. This package, described in detail in Metzger et al. (2012, 2013a), has been verified against other turbulence processors (e.g., Mauder and Foken, 2011). All data were prepared by first regularizing to evenly spaced time increments, which are exactly 1 s for HMP35, 0.1 s for CSAT3 and LI-7500 and 0.05 s for LI-7200, respectively. Next, observations with invalid sensor health information were discarded, thresholds for physically feasible value ranges were applied and spikes were removed using the median filter method by Brock (1986). Thereafter, the wind components were rotated into the 14 month average aerodynamic plane using the planar fit rotation (Wilczak et al., 2001), and all slow-sample variables (1, 10 Hz) were linearly interpolated to 20 Hz with zero gap tolerance. Finally, lag times resulting from lateral separation and gas transport in the GSS were determined via cross correlation in a 1 s window over high-pass filtered data (4-pole Butterworth filter with half-power frequency at 0.5 Hz) and shifted on a 30 min basis. Intake tube heating power was interpolated between site visits with R2>0.99 and 0.38 K residual standard error using the difference between Tin and Tout as well as a unique identifier for each tube as predictors.

Prior to power spectra analysis on a 30 min basis, missing values were linearly interpolated (only data sets with < 10 % missing values were further analyzed). Linear de-trending was applied and 5 % of the data at each end of the time series were tapered with a cosine bell. Next, a fast Fourier transform was applied, and unfolded spectral energy and cospectra were calculated. Where indicated, a recursive circular filter with a Daniell kernel was used to reduce variance for graphical presentation. The resulting Fourier coefficients were binned into exponentially widening frequency classes using the median operator. Transfer functions were derived following Eqs. (4) and (5) by dividing the H2O and CO2 number density power spectra from the LI-7200 by those from the LI-7500, and normalizing to the same spectral power between 0.005 and 0.05 Hz. While the LI-7500 measured the full effect of temperature fluctuations on density, these were dampened in the case of the LI-7200. In particular for H2O these effects were comparatively small (< 10 %), and the resulting transfer function was dominated by the attenuation of the dry mole fraction itself. Since LI-7200 and LI-7500 rely on a quasi-identical sampling cell, the effect of the sampling cell itself is offset analogously to the laboratory tests, and both types of tests characterize the GSS only. The determination of the half-power frequency was then automated in the following way: (i) determining the frequency >0.5 Hz for which the transfer function reaches its first minimum, (ii) recasting the transfer function Eq. (6) and solving for half-power frequency. Lastly, the spectral correction factors for the corresponding EC fluxes were determined by applying the transfer functions to the cospectra of H2O and CO2 dry mole fraction and the vertical wind speed.

Before calculating the ensemble power spectra, all available periods were screened for (i) recorded maintenance activities and interruptions, and >90 % raw data coverage (78 % half hours remained), (ii) non-zero lag correction with a correlation maximum > 0.01 (70 % half hours remained), (iii) undisturbed inflow sector (65 % half hours remained) and (iv) measured variations in H2O and CO2 number density in excess of 5:1 signal-to-noise (instrument resolution) ratio (Lenschow and Sun, 2007, 46 % half hours remained).

At the given measurement height of 13.7 m above displacement height, the amplitude of fluctuations at frequencies >1 Hz can approach the detection limit of an enclosed IRGA, resulting in the latter 19 % data loss. It should also be mentioned that the July 2014 period (LN rain cap) was not only drier than the July 2013 period (LO rain cap), but also the H2O fluctuations and flux were ≈1/3 lower in 2014 compared to 2013 (not shown). As a result, the July 2014 power spectra began to display noise at lower frequencies. This also moves the minimum of the transfer function, and hence the base for calculating the half-power frequencies, towards lower frequencies for the GSS with the LN rain cap.

Lastly, in order to attribute the effect of intake tubes with different length dl and inner diameter did, we solved the transfer function proposed by Philip (1963) in the form of Massman (1991) for half-power frequency: f50%=-ln⁡0.5U2Λ(Re)dldid22π, with the longitudinal mean flow velocity in the tube U, and a linear interpolation of tabulated values (Table 1 in Massman, 1991) for the attenuation coefficient Λ (Re) (Lee and Gill, 1977, 1980).

An important part of optimizing an enclosed IRGA EC system is determining which arrangement provides the best frequency response of the entire system. This could obviously be achieved by using a very short tube in the absence of any filter or rain cap. However, for the practical reason of preventing precipitation from entering the filter and sampling cell, most experimental sites would benefit from using a rain cap. The rain cap is a mixing volume, so focus of the optimization was to determine which rain cap design provided the least frequency attenuation, while still preventing water ingress into the tube, filter and sampling cell.

Numerous rain cap designs have been tested conceptually using the CFD software to minimize sample mixing in the rain cap. Several designs have been selected, built and tested for water ingress in the laboratory experiments. The caps that ingested liquid water when sprayed horizontally while operating at 23 SLmin-1 flow were rejected. In addition, tests found that adding a slight downward tilt to the intake tube (≈10∘ from horizontal) helped prevent water ingress during the field tests (Sect. ), which included periods of heavy precipitation. The remaining three designs were then tested in the laboratory for frequency response following Eqs. (4) and (5). Figure 3 (top left panel) shows good frequency performance for LN and NN rain caps, with f50%≥14.3 Hz and f50%≥11.8 Hz, respectively (Table 5 provides an overview for all system components). Both newer rain caps considerably exceeded the performance of the older LO rain cap (f50%≥2.4 Hz), and NEON.TIS.4.1615 (Table ) was fulfilled. However, both designs were still more limiting to high-frequency response compared to the filters with the best frequency response tested in Sect. .

ICOS conducted field tests of several additional rain caps for their LI-7200-based flux systems (De Ligne et al., 2014; Aubinet et al., 2016): (i) LI-COR's rain cap before 2013, part number 9972-043, which is a previous version of the LO rain cap, (ii) a modification of this rain cap with tubing extending all the way to the screen, (iii) a custom-built rain cap with lateral insertion and small volume were tested alongside (iv) a downward-oriented tube without a rain cap and (v) the LN rain cap. The range of results when used with the FW-2.0 filter (1.36≤f50%≤7.9 Hz) was similar to our tests but slightly lower. Differences may be attributed to differing gas injection design in the laboratory, different experiment settings required for the field testing and possible filter contamination. The conclusion was that the frequency response of the LN rain cap assembly was second only to the downward-oriented tube, and the latter was found to provide insufficient water ingress protection. The experiments of De Ligne et al. (2014) and Aubinet et al. (2016) also concluded that the rain cap critically contributed to overall system frequency response.

Similar to the rain cap component, the highest frequency response of an enclosed IRGA EC system would be achieved without using a particulate filter. Such configurations are possible for a system based on the LI-7200 analyzer, and have previously been used in the field (Burba et al., 2010, 2012; Clement et al., 2009). However, they would require frequent cleaning of the sampling cell in dusty environments or during high-contamination periods (e.g., harvest, pollination). To reduce the demand for manual cleaning, an intake particulate filter can be used. The important trade-off when optimizing the filter is to determine which models provide the least frequency attenuation with the smallest pressure drop and still provide a pore size small enough to filter out most of the ambient particulate contaminants. Figure 4 shows results from multiple laboratory experiments for such an optimization. Out of nine tested filters, the Swagelok FW-2.0 filter (Table  provides detailed filter specifications) had the lowest pressure drop (0.2 kPa at 10 SLmin-1), reasonably small high-frequency attenuation (f50%≥14.9 Hz), and still delivered 2.0 µm particulate filtering. The ZenPure PF-0.1 filter was a close second in terms of pressure drop (0.6 kPa at 10 SLmin-1), but its frequency attenuation for CO2 was much worse than the FW-2.0 at the high-frequency range (f50%≥8.3 Hz), and its attenuation for H2O was unacceptable (f50%≥1.4 Hz). The PF-0.1 was followed by PolyPro filter models PP-5.0 and PP-2.5, which provided higher pressure drops (2.9 and 4.9 kPa at 10 Lmin-1 respectively) while offering less filtering capacity. Other tested filters had even larger pressure drop, ranging from 5 to 25 kPa at 10 Lmin-1, which is undesirable for high-quality dry mole fraction computation, and unnecessarily increases the power consumption and wear on the system.

ICOS conducted field tests of several additional filters for their LI-7200-based flux systems (De Ligne et al., 2014; Aubinet et al., 2016). A Pall open-face 2 µm filter (Pall Corporation, Port Washington, NY, USA) was tested for pressure drop alongside the FW-2.0 and AC-1.0. The AC-1.0 pressure drop was found unacceptable, and Pall 2 µm open-face filter was found to be less effective in contamination prevention as compared to the FW-2.0 filter. The pressure drop for the FW-2.0 filter in the De Ligne et al. (2014) and Aubinet et al. (2016) experiments was small, on the order of 0.9 kPa for 10 Lmin-1 at approximately sea level, but still 4–5 times the pressure drop found in our study. De Ligne et al. (2014) do not present half-power frequencies for individual GSS components, but state that addition of one of those filters did not significantly reduce LI-7200 system frequency response. Aubinet et al. (2016; Table 2) presented half-power frequencies for the entire system for a number of cases with multiple filters and caps, including cases not covered in this study. They also found the combination of lowest pressure drop and best system response when using FW-2.0 filter. Overall the conclusion from all three studies was similar suggesting the FW-2.0 filter to be optimal out of all tested models, and fulfilling NEON.TIS.4.1618, NEON.TIS.4.1627, NEON.TIS.4.1628 and NEON.TIS.4.2007 (Table ).

Depending on the interaction of the system components reflected by Eq. (7), the total frequency response of the system may differ from a superposition of all components according to Eqs. (8)–(10). Hence, experiments were conducted to determine the actual effect of combining various system components on the total frequency response of the system, i.e., to parameterize Eq. (7). Figure 3 (top right and bottom panels) shows the results of such experiments for three main practical combinations of the components: (i) tube and filter, (ii) tube and rain cap and (iii) combination of tube, filter and rain cap deployed altogether. Table 5 summarizes these and other results of laboratory experiments for various filters, rain caps and their combinations.

Combining the tube and the FW-2.0 filter leads to a very minor effect on CO2 frequency response as expected from the small volume of the filter and turbulent tube flow (11.9 Hz ≤f50%≤15.4 Hz, Fig. 3 top right panel and Table 5). The H2O response was affected more than CO2, although still to a relatively small degree (11.2 Hz ≤f50%≤11.6 Hz). Such a reduction in H2O frequency response is expected because both the filter and the tube have large surface areas in relation to the sample volume and flow. The dipolar nature of the water molecule and surface adsorption/desorption rates related to relative humidity lead to a “sticky” behavior of water vapor at the tube and filter surfaces. Such a phenomenon was studied, modeled and corrected for in a number of studies (e.g., Fratini et al., 2012; Massman and Ibrom, 2008; Rannik et al., 1997; Runkle et al., 2012). It can be remedied to a large extend by heating the elements to reduce the relative humidity at the wall surface below 50–60 %. Below this threshold, H2O behaves principally similar to CO2 and theoretical corrections can be used to compensate for the frequency losses (Kaimal et al., 1972; Moncrieff et al., 1997). In the absence of heating, semi-empirical corrections progressive with relative humidity can also be used (e.g., Fratini et al., 2012; Massman and Ibrom, 2008; Runkle et al., 2012).

Combining the tube and rain cap led to a larger reduction in frequency response than combining the tube and filter for both CO2 and H2O (1.9 Hz ≤f50%≤14.6 Hz, Fig. 3 bottom left panel and Table 5). In fact, out of all elements in the system, the rain cap appeared to have the largest effect on the GSS frequency response. The importance of the rain cap choice was somewhat a surprise given that traditional closed-path GSSs utilize various custom-made rain caps with volumes exceeding several times those shown in Fig. 1. However, recent analyses by NEON (Metzger et al., 2014) and ICOS (De Ligne et al., 2014; Aubinet et al., 2016) corroborated the importance of the rain cap size and design as a critically sensitive component affecting EC system frequency response. The CFD simulations (data not shown) corroborated that even small rain caps may experience vortices mixing the samples. In result the residence time of the sample in the rain cap increases, and may significantly exceed the time computed by simply dividing the rain cap volume by the flow rate assuming plug flow.

The frequency response of the combination of all GSS elements is shown in Fig. 3 (bottom right panel). The worst response was observed for the combination of the tube, FW-2.0 filter and the LO rain cap. This response was primarily driven by the effects of the rain cap (Fig. 3, top left panel) and yielded f50%≥2.0 Hz for the entire GSS for both CO2 and H2O (Table 5). Using the new, smaller rain caps significantly improved GSS system response, with half-power frequencies 2–6 times higher than with the LO rain cap. Differences among the GSS with the NN (f50%≥9.3 Hz) and LN (f50%≥4.3 Hz) rain caps were noticeable for both CO2 and H2O, but overall, both rain caps were much closer to each other compared to the LO rain cap. Also, these differences may be biased due to different sampling techniques, levels of relative humidity and by how a step change or a square wave were generated in the laboratories. These tolerances were also apparent from a slightly better frequency response for the combination of tube, FW-2.0 filter and NN rain cap (f50%=12.0 Hz) compared to the setup omitting the FW-2.0 filter (f50%=11.9 Hz). Moreover, the laboratory tests of the NN rain cap did not include any dead volume potentially created by the rain caps' outer lip and leaking into the sample flow. While this lip adds rain protection and is vertically offset, it might increase air residence time in the vicinity of the rain cap, thus potentially providing a better response in the laboratory than might be attainable under field conditions.

The tests found that possible choices of filters (f50%≥1.4 Hz) and rain caps (f50%≥2.4 Hz) limit system frequency response compared to the LI-7200 sampling cell (f50%≥6.3 Hz at 13.6Lmin-1) and a short and thin intake tube (f50%≥15.9 Hz). In order to better understand cross-sensitivity, we utilized Eqs. (7)–(10) and determined the frequency responses for all possible combinations of filters and rain caps, including those not explicitly tested (Fig. 5). It can be seen that for H2O, the NN and LN rain caps provided similar frequency response, up to Δf50%=5 Hz better compared to the LO rain cap. Yet, for both of these ”good” caps, the filter choice was critical, as some filters could decrease system frequency response by as much as 6 Hz. For the already limiting LO rain cap, the effect of the filter choice was less pronounced.

To summarize, laboratory tests have shown that the order of priority for optimizing GSS components should be as follows:

rain cap, with focus on frequency response and water ingress;

The optimal performance was achieved by the combination of an NN or LN rain cap and the FW-2.0 filter together with a thin and short stainless steel tube. Such a combination provided the best and most comparable frequency response for both H2O and CO2, out of all tested combinations of the components.

Figure 6 shows the meteorological conditions and the effect of filter and intake tube heater settings for July 2013 with the LO rain cap. It can be seen that the LI-7200 sampling cell inlet temperature (Tin) increased above the ambient air temperature (Ta) due to heating, and generally followed the heater power setting. The initial 4 W of heating power increased the sampling cell inlet temperature by about 6–8 ∘C above ambient, and after the heating was switched off on 7 July 2013, this difference (Tin-Ta) decreased to 0–3 ∘C. During both settings, the temperature gradient in the sampling cell (Tin-Tout) did not exceed 5 ∘C, and the temperature difference between the sampling cell inlet and block (Tin-Tblock) was well below 15 ∘C. However, during the 5 and 6 W settings, the temperature gradient in the sampling cell exceeded 5 ∘C. Consequently, NEON.TIS.4.1667, NEON.TIS.4.1668 and NEON.TIS.4.2017 (Table ) were only fulfilled for the 4 W heater setting. At a given power setting, the increase in sampling cell inlet temperature above ambient (Tin-Ta) was correlated with the ambient temperature. For example, during the 4 W heating period, the sampling cell inlet temperature increased by 1.26 ∘C per 1 ∘C rise in ambient temperature (r>0.7). Similar behavior was found without heating (1.29 ∘C per 1 ∘C, r>0.7). Consequently, the heating circuit does not exhibit a feedback with ambient temperature, thus avoiding the risk of superimposing artificial correlations. After water ingress on 14 July 2013, the intake tube was changed from horizontal to slightly downward tilted (≈10∘) alignment, which prevented any future ingress. The new tube was deployed with identical heating power setting. Yet, it is apparent that the replacement tube generated more heat than the previous tube, likely indicating an impact of variable manufacturing tolerances.

In order to avoid sensor offsets, relative humidity in the LI-7200 cell (RHcell) was calculated from the ambient relative humidity (RHa) taking into account temperature and pressure differences. Compared to RHa, RHcell was reduced by ≈10, ≈20, ≈25 and ≈30 % during the 0, 4, 5 and 6 W heating periods, respectively. However, none of the tested heater settings was capable of continuously reducing RHcell below 60 %, and therefore NEON.TIS.4.1666 (Table ) could not be fulfilled at this time. Nevertheless, 4 W of heating was sufficient to decrease the number of events where RHa>60 % resulted in RHcell>60 % by ≈50 %.

Spectral analysis as described in Sect.  was performed on the field data, and Fig. 7 shows ensemble transfer functions of LI-7200-measured H2O number density relative to the LI-7500. In all cases, heating improved the high-frequency response. For RHa<60 %, the half-power frequency of the LO rain cap in combination with unheated filter and intake tube was f50%≈2 Hz, which reflects the laboratory results well.

Filter and intake tube heating marginally increased f50% to ≈2.5 Hz. For RHa>60 %, f50% of the LO rain cap in combination with the unheated filter and intake tube decreased to ≈1 Hz. This is about half of the f50% observed in the laboratory, but the latter could not actually be conducted at such a high average relative humidity. Also, it should be noted that the sample size of the LO-0 Watt control period was extremely small for RHa>60 % (here, N=3, due to the generally low relative humidity in this period, median 46.1 %). Filter and intake tube heating increased f50% to ≈1.5–2 Hz, and the 4 and 5 W heating power settings yielded a slightly higher f50% compared to the 6 W setting, which was likely a result of the higher ambient relative humidity during the LO-6 Watt period.

Overall, no obvious improvement of H2O frequency response was found for increasing heating power beyond 4 W. The resulting 8 ∘C temperature increase above ambient appeared to be sufficient, and the remaining field tests will focus on this heater setting, which is the only setting that also fulfills NEON.TIS.4.1667, NEON.TIS.4.1668, NEON.TIS.4.2017 (Table ). It thus results in the largest possible reduction of relative humidity, without impacting the performance of the underlying measurement principle. While the tests presented have been performed at a single site, Fratini et al. (2015) have found similar results under quite different conditions, indicating applicability across environments.

Since the rain cap has been identified as a design priority in Sect. , we expected that decreasing the rain cap mixing volume would further improve frequency response for H2O. However, for the 4 W heating setting, the LN rain cap did not appear to outperform the LO rain cap. This contradicts our laboratory findings, which suggest f50%>4 Hz for the combination of LN rain cap with filter and tube. Also, during the LN rain cap period, filter and tube heating was actually 0.3±0.9 W higher and RHa was -13.1±35.5 % lower compared to the corresponding LO rain cap period, which should have given the LN rain cap a slight advantage.

For the LN rain cap, CO2 frequency response was found to be unattenuated at frequencies ≤1 Hz under all RH conditions. A difference between the frequency response under heated and unheated conditions appeared only for RH >60 % and was not systematic (data not shown). NEON.TIS.4.1626 (Table ) was thus fulfilled for CO2.

In order to further investigate the impact of relative humidity on frequency response, we determined the half-power frequencies as described in Sect.  individually for each half-hour period. The results for the different GSSs and heating strategies are shown in Fig. 8 as a function of relative humidity. In general, 4 W of heating increased f50% by 0.5–1 Hz. For RHa<40 %, the heated GSS with LN rain cap yielded f50%>3 Hz, approaching the laboratory results of f50%>4 Hz. At higher relative humidities, the heated GSS with LO rain cap outperformed the heated GSS with LN rain cap, contradicting our laboratory findings.

Together with the change from the LO to the LN rain cap, however, the intake tube length was also changed from 70 to 80 cm, and the ID from 4.8 to 5.3 mm. For the given flow rate set point of 10.8 SLmin-1 (or ≈16.2 Lmin-1 at site conditions), this led to a reduction of the Reynolds number in the tube of -9.4 % from Re≈3470 to Re≈3150. Following Eq. (11) the half-power frequency of the tube was thus reduced by -32.9 % from 17.1 to 11.5 Hz. For the given volumetric flow rate, the LI-7200 cell by itself yielded f50%=7.5 Hz due to volume averaging in Eq. (1). Combining LI-7200 cell and the tube according to Eqs. (7)–(10) yielded a half-power frequency reduction of -30.8 % from 6.5 to 4.5 Hz due to the change in intake tube. This effect alone approximately offsets the gain in half-power frequency for changing from LO to LN rain cap as observed in the laboratory (Table 5, from 2.0 Hz to 4.3–6.1 Hz). In addition, not only did the tube inner volume increase by 42 % from 12.4 to 17.7 cm3, but also the inner surface area increased by 28 % from 104.5 to 133.2 cm2. As a result, the surface heating from the heater into the tube effectively decreased from 363.8±19.1 Wm-2 to 307.8±52.6 Wm-2. The combined effects resulting from changes in the tube ID and length increased the residence time in the tube, decreased turbulence in the tube, promoted surface adsorption of H2O and thus reduced the frequency response in particular under high relative humidity conditions. This explains that for a given 4 W heater setting, the GSS with LN rain cap performed similarly to the GSS with LO rain cap for RHa<60 %, but the performance was worse for RHa>60 %.

Applying Eqs. (7)–(10) to the half-power frequencies for the LI-7200 (f50%=7.5 Hz), 80 cm tube with 5.3 mm ID (f50%=11.5 Hz), filter FW-2.0 (f50%=17.4 Hz) and LN rain cap (f50%=12.05 Hz) yielded a system half-power frequency of f50%=3.1 Hz. This matched the field results in Fig. 8 at 35 % relative humidity. Substituting in Eqs. (7)–(10) the 80 cm tube with 5.3 mm ID by the 70 cm tube with 4.8 mm ID (f50%=17.1 Hz), the half-power frequency for a theoretically improved system was estimated to be f50%=3.9 Hz at 35 % relative humidity. The average decrease of Δf50%=0.36 Hz per 10 % RH for the observed heated GSS with LO rain cap was utilized to extrapolate f50%=2.1 Hz for the improved system at 85 % relative humidity. This compares to the observed f50%=0.6 Hz and f50%=0.9 Hz for the heated GSS with LN and LO rain caps, respectively. Using Eq. (6), the signal attenuation at 1 Hz for RHa=85 % can now be determined to 74, 55 and 19 % for the original heated GSS with LN and LO rain cap, and the theoretically improved GSS, respectively. While even the theoretically improved GSS did not fulfill NEON.TIS.4.1626 (Table ), attenuation rapidly decreased to <5 % at 0.5 Hz. This still warrants the application of automated spectral correction procedures (e.g., Nordbo and Katul, 2012) for NEON towers with a minimum measurement height of 6 m, which was the objective underlying the requirement.

Ultimately, the GSS optimization aimed to minimize the need for cospectral correction of the EC fluxes. We found that for the unheated GSS with LO rain cap, the H2O correction is in excess of 5 % for RHa>60 %, and that 4 W of heating reduces the cospectral correction by almost a similar amount (data not shown). For the GSS with LN rain cap and 4 W of heating, the cospectral correction never exceeded ≈3 %, even at very high relative humidity. For CO2, heated and unheated GSS with LO rain caps required marginal cospectral corrections, while practically no cospectral correction was required for the heated GSS with LN rain cap.