2.1 Purple Crow Lidar (PCL)

The PCL is a Rayleigh–Raman lidar that was located at the Delaware Observatory (42.52^∘ N , 81.23^∘ W) near the University of Western Ontario in London, Canada, from 1992 to 2010 (Argall et al., 2000; Sica et al., 1995, 2000). In 2012, the PCL was moved to the Environmental Sciences Western Field Station (43.07^∘ N, 81.33^∘ W; 275 m of altitude). The PCL has been upgraded over time. Currently, the PCL transmitter is a Nd : YAG laser with a power of 1000 mJ per pulse at 532 nm and a repetition rate of 30 Hz. The PCL receiver is a liquid mercury mirror with a diameter of 2.65 m. From 1994 to 1998, the PCL used a single detection channel (the high-level Rayleigh (HLR) channel) over the range of 30 to 110 km (Sica et al., 1995). In 1999, a low-level Rayleigh (LLR) channel was added, which is nearly linear above 25 km (Sica et al., 2000). This study uses 519 nightly averaged temperature profiles from 1994 to 2013 distributed in time as shown in Tables 1 and 2.

Table 1Number of nightly mean profiles used to calculate the PCL temperature climatology by month between 1994 and 2013.

Download Print Version | Download XLSX

Table 2Number of profiles used to calculate the PCL temperature climatology per year between 1994 and 2013.

Download Print Version | Download XLSX

2.2 Rayleigh-temperature retrieval methods

In this section, we briefly review the OEM and HC methods that have been used in our calculations. Each approach has its own benefits and deficiencies. Both of these methods start with a lidar return proportional to density and then find temperature using the assumption of hydrostatic equilibrium, the ideal gas law, and the lidar equation.

The lidar equation is a mathematical relation between the number of back-scattered photons detected by lidar and the measurable quantities such as altitude, laser power, and scattering cross section. If we consider all atmospheric parameters in the lidar equation to be constant in time, the lidar equation reduces to Eq. (1):

where C is a constant standing for a combination of all the constant properties of the lidar, ψ(z) includes height-dependent parameters like detector nonlinearities or geometric overlap, n(z) is the atmospheric number density as a function of height, and B(z) is the background count due to radiation sources other than the lidar laser, which may or may not be height dependent.

Various lidar system parameters and physical constants affect the photocounts independent of altitude. The combination of these parameters is called the lidar constant and in our definition includes the number of photons emitted by each laser pulse, the optical efficiency, the detection efficiency of the photomultipliers, atmospheric Rayleigh-scatter cross section, and speed of light. Note that most of these quantities are system dependent, and they in fact can change for a specific instrument as hardware changes, such as changing the laser transmitter. We show in the following sections that the OEM method is robust to these changes and that a consistent climatology can be computed using the OEM.

When the pressure gradient of an air parcel in the atmosphere is in balance with its gravitational force, the atmosphere is in hydrostatic equilibrium and is dynamically and thermally stable. The hydrostatic equilibrium equation can be expressed as

where P is the atmospheric pressure, ρ is the density, and g is the acceleration due to gravity.

The mean molecular mass of air is considered to be constant within the 30 to 80 km altitude range. However, the mean molecular mass varies with altitude above 80 km, and this variation affects the temperature retrieval, both through the change in mean molecular mass and the effect of composition changes on the Rayleigh-scatter cross section.

2.2.2 Optimal estimation theory

Sica and Haefele (2015) used a first-principle OEM to retrieve temperature from Rayleigh-scatter lidar measurements. Here first principle means the forward model is the lidar equation and the measurements to the forward model are the raw (level 0) measurements. The OEM (Rodgers, 2011) solves an inverse problem and uses a forward model to estimate the lidar measurements using a set of input parameters usually referred to as state and model parameters. The inversion of the forward model yields the state vector, while the model parameters are known and the measurement is given.

The forward model (F) can be written as

$$\begin{array}{}\text{(5)}& \mathit{y}=F(\mathit{x}\mathbf{,}\mathit{b})+\mathit{ϵ},\end{array}$$

where y is the measurement vector, x is the state vector, b is the model parameter vector, and ϵ is the measurement noise. The state vector is retrieved and contains the temperature profile and some instrument parameters like detector dead time and background. The model parameter vector contains all other parameters needed to represent the measurements. The forward model is the lidar equation (Eq. 1), which is dependent on both the system hardware configuration and atmospheric properties. The measurement noise in lidar measurements implies that the measurements have uncertainties that have a Gaussian distribution of possible values represented by ϵ. The solution of the inverse problem is constrained around an a priori, which can be found in atmospheric models such as the CIRA-86 model or the US Standard model. CIRA-86 can provide the monthly temperatures for use as the a priori. In its most likely state $\widehat{\mathit{x}}$, the solution is a minimum of a cost function:

$$\begin{array}{ll}{\displaystyle }& {\displaystyle }\mathrm{cost}={\left[\mathit{y}-F(\widehat{\mathit{x}}\mathbf{,}\mathit{b})\right]}^T{\mathbf{\text{S}}}_{\mathit{ϵ}}^{-\mathrm{1}}\left[\mathit{y}-F(\widehat{\mathit{x}}\mathbf{,}\mathit{b})\right]\\ \text{(6)}& {\displaystyle }& {\displaystyle }+{\left[\widehat{\mathit{x}}-{\mathit{x}}_{\mathrm{a}}\right]}^T{\mathbf{\text{S}}}_{\mathrm{a}}^{-\mathrm{1}}\left[\widehat{\mathit{x}}-{\mathit{x}}_{\mathrm{a}}\right],\end{array}$$

where S_ϵ is the covariance of the system's state, x_a is the a priori vector, and S_a is the the covariance matrix of the system's state.

Unlike the HC method, the OEM produces a complete uncertainty budget for all parameters in the temperature retrieval process on a profile-by-profile basis. The uncertainty budget includes the uncertainty due to the seed pressure and the other model parameters and measurement noise as well as smoothing. A diagnostic variable of the OEM is the averaging kernel, A, a matrix that describes how the retrieval reacts to a given change in the real atmosphere. A perfect retrieval means the retrieved temperature changes in the same way as the real atmosphere and A is equal to the identity matrix (Rodgers, 2011). However, if the contribution of the a priori increases in the temperature retrieval, A drops to <1 at each point for the altitudes at which the a priori has more influence. If u is a vector with unit elements, Au is the sum along the rows of the averaging kernel and it can be used as a representation of the amount of information coming from the lidar measurements and how much is as a result of the a priori. Therefore, Au was used as the cutoff height reference in the OEM instead of removing one or two scale heights from top of each profile as in the traditional method. Values of Au equal to 0.9 and 0.8 are considered as a cutoff height. These values represent the fractional contribution of the measurements compared to the a priori in the temperature retrieval and are generally recognized in the OEM community as levels above which the effect of the a priori is minimal.

Figure 1(a) Temperature difference between the a priori temperature profiles, US Standard Atmosphere, and CIRA-86 (blue line). (b) Temperature difference between the OEM-retrieved temperature profiles using the a priori profile used in Fig. 1a for 24 May 2012 (red line) and the calculated OEM statistical uncertainty (blue line). The solid black and dashed black lines are the height below which the temperature profile is more than 90 % (0.9) and 80 % (0.8) due to the measurements.

Download

2.3 Methodology to calculate temperature climatology

2.3.1 OEM methodology

The OEM uses the forward model and non-paralyzable dead time correction equation (Sica and Haefele, 2015) (henceforth SH2015) to retrieve the nightly average temperature profiles from the LLR and HLR channels simultaneously. In SH2015 the dead time, background, and temperature were retrieved. They considered the lidar constant as a forward model parameter, but in this study, the lidar constants for LLR and HLR channels were retrieved rather than specified. The OEM uses an estimation of the covariances of the measurements, retrieval, and forward model parameters. The model parameter covariance matrices used in this study are based on SH2015, in which the summary of the values and related uncertainties of the measurements and the retrieval and forward model parameters are presented in Table 3. The data grid is 264 m, and the retrieval grid is 1056 m. Due to the PCL measurements between 1994 and 1998 having only the HLR channel measurements, temperature and background were retrieved but not dead time. Instead, the systematic uncertainty due to the saturation was calculated. The PCL measurements from 1999 to 2011 used the LLR digital channel to get more temperature information, and the dead time of the HLR channel was retrieved using an a priori value of 10 ns (Table 3). The LLR dead time was treated as a model parameter and a standard deviation of 5.7 % was considered. The CIRA-86 model atmosphere was chosen as the temperature a priori with a variance of (35 K)² at all altitudes (Fleming et al., 1988).

Fleming et al. (1988)McPeters et al. (2007)Griggs (1968)Mulaire (2000)Nicolet (1984)

Table 3Values and associated uncertainties of the measurements and the a priori, retrieval, and forward model parameters

Download Print Version | Download XLSX

2.4 Effect of a priori on the retrieval temperature profiles in the OEM

A retrieved temperature profile using the CIRA and the US Standard Atmosphere as the a priori for a sample PCL night (24 May 2012) was plotted in order to demonstrate the contribution of the a priori temperature profiles in the retrieval results and the temperature difference between the a priori temperature profiles (Fig. 1). The temperature difference between the a priori profiles is shown in Fig. 1a. The temperature difference around 94 km, which is below the OEM cutoff heights, is about 20 K. In Fig. 1b, the red profile is the temperature difference due to the a priori and the blue profile is the statistical uncertainty calculated by the OEM. The 0.9 and 0.8 value lines in the Au are the cutoff heights for the OEM and are shown with solid and dashed lines, respectively. It can be seen that the choice of a priori has little effect (1.5 K below the 0.9 line and less than 2 K below the 0.8 line) on the retrieved temperature and that the difference between the retrieved temperatures from each choice is much less than the statistical uncertainty (10 K below the 0.9 line and 12 K below the 0.8 line) at the top of the profiles.

3.1 Uncertainty budget and vertical resolution

The lidar measurements include both systematic and random uncertainty. Systematic uncertainties originate in the forward model from uncertainties due to model parameters. One of the advantages of the OEM is that it provides systematic uncertainties for all retrieved parameters, as well as the random uncertainties. The systematic uncertainties calculated in the PCL OEM technique (Table 3) are based on the following model parameters:

1. knowledge of the HLR dead time (1994–1998 only);

2. determination of the Rayleigh-scatter cross section for air;

3. Rayleigh cross section variation with composition in the mesosphere and thermosphere;

4. air number density influence effect on Rayleigh extinction;

5. ozone absorption cross section;

6. ozone concentration effect on transmission;

7. seed (tie-on) pressure;

8. acceleration due to gravity; and

9. mean molecular mass variations with height above 80 km.

3.1.1 Uncertainty budget for the PCL climatology

A typical case for the temperature statistical and systematic uncertainties for a nightly average retrieval is shown in Fig. 5. The temperature uncertainty due to the seed pressure has the highest contribution among all of the systematic uncertainties at the altitudes above the mesopause. However, temperature uncertainties related to ozone, including the ozone absorption cross section, have the largest effect below 40 km. The uncertainty contribution for the gravity model is almost constant with height and is of the order of 0.002 K.

Figure 5A typical night's systematic and random uncertainties for the OEM temperature retrieval.

Download

The nightly OEM statistical uncertainty profiles were used to form the statistical temperature uncertainty of the PCL temperature climatology (Fig. 6) using the procedure described in AS2007. The statistical uncertainty below 75 km is less than 1 K and gradually increases with height until it reaches 0.9 Au at which it is less than 10 K. The monthly average minimum, maximum, and median of temperature uncertainties related to the systematic uncertainties for all months are plotted in Fig. 7.

Figure 6Statistical temperature uncertainty of the temperature climatology. The white lines are the height below which the temperature climatology is more than 90 % (0.9) and 80 % (0.8) due to the measurements.

Download

An improvement of the OEM over the HC method is its ability to yield the vertical resolution at each height (Fig. 8). The vertical resolution is 1056 m below 95 km and is equal to the retrieval grid. It is 3000 m below the 0.9 cutoff height; however, it increases rapidly to 5000 m around the 0.8 cutoff line. Leblanc et al. (2016b) recommended two standardized definitions for a temperature profile vertical resolution. In order to compare the retrieved temperature profiles using the OEM and the HC method, the two vertical resolution definitions given by Leblanc et al. (2016b) were used to find the best bin size for the HC method so it would have an identical vertical resolution to the OEM retrieval. We found that 264 m co-added bins and a “3's and 5's” filter gave a vertical resolution of 1008 m, close to the OEM temperature retrieval grid (1056 m).

Figure 7PCL temperature systematic uncertainty due to the (a) saturation function (1994 to 1998 only), (b) Rayleigh extinction cross section, (c) Rayleigh cross section variation with height, (d) air density affect on Rayleigh extinction, (e) ozone absorption cross section (f) ozone concentration, (g) seed (tie-on) pressure, (h) gravity model, and (i) mean molecular mass variation with height. In each figure, red, blue, and black lines are the minimum, maximum, and median between all months, respectively.

Download

3.1.2 Comparison with uncertainty budget of the traditional method

Leblanc et al. (2016b), hereafter NDACC2016, used a Monte Carlo method to calculate the statistical and systematic uncertainties for the temperature retrieval. We have compared our results with his ND : YAG 532 nm lidar results. NDACC2016 and our climatology give the temperature uncertainties for several of the same parameters (Table 3), including the statistical uncertainty (detection noise), the Rayleigh cross section, air number density, ozone absorption cross section, ozone number density, and the gravity model. NDACC2016 calculated the temperature uncertainty due to each parameter per 1 % uncertainty. In order to compare NDACC2016 results with the PCL uncertainties using the OEM, we need to scale NDACC2016 simulations to the PCL as recommended by Leblanc et al. (2016b). For example, if the temperature uncertainty due to air number density is per 1 % uncertainty in NDACC2016, then we must multiply NDACC2016 uncertainties by a factor of 5 because we assume an air number density uncertainty of 5 % (recommended by NDACC2016) in the PCL forward model (Table 3). We have compared our results with the statistical and systematic uncertainties presented in Figs. 1 to 9 in NDACC2016 for the case of a 532 nm laser beam with a 1 MHz count rate at 45 km, a height resolution of 300 m, and an integration time of 2 h (Fig. 9).

The statistical uncertainty comparison between the PCL and NDACC2016 is shown in dark blue in Fig. 9. It can be seen that the NDACC2016 statistical uncertainty almost equals the scaled PCL statistical uncertainty above the stratopause. However, there is a difference at altitudes below 50 km. The statistical uncertainty difference in the lower altitudes is due to using the two Rayleigh channel measurements (HLR and LLR) to calculate the temperature in the lower altitudes. The uncertainties at these altitudes are then a combination of the LLR and HLR uncertainties.

The temperature uncertainty due to the uncertainty in the Rayleigh cross section in NDACC2016 for each 1 % at two sample altitudes, 30 and 38 km, is of the order of 0.001 K (NDACC2016, Fig. 4). The temperature uncertainty due to the Rayleigh cross section in the OEM is presented per 0.2 %; therefore, the scaled cross section uncertainty for NDACC2016 is 1 order of magnitude smaller than the PCL Rayleigh cross section uncertainty. However, this temperature uncertainty is very small.

The uncertainty due to air number density as an input quantity per 1 % is shown in NDACC2016 (their Fig. 5 left panel). The NDACC2016 scaled temperature uncertainty due to air number density is of the same order of magnitude as the OEM-derived uncertainty for the PCL (Fig. 9).

The standard deviation for the ozone cross section in the OEM forward model is 2 %. Therefore, the NDACC2016 ozone cross section temperature uncertainties should be doubled to compare them with the PCL. The temperature uncertainty due to the ozone cross section uncertainty in NDACC2016 (their Fig. 6a) after scaling is about 4 times smaller. The other temperature uncertainty due to ozone is the ozone number density. The temperature uncertainty due to ozone number density uncertainty for the NDACC (their Fig. 7a), after scaling by a factor of 0.25 (as the PCL a priori assumes 4 % uncertainty), is almost twice that of the PCL's. The uncertainties due to ozone number density are so small above 45 km that they have not been listed in the total uncertainty budget in NDACC2016's final results.

The temperature uncertainty due to the choice of pressure at the highest altitude (seed pressure) is called the tie-on uncertainty in NDACC2016. The tie-on uncertainties are in the same range and the small differences between the PCL and NDACC2016 (their Fig. 8) are related to the fact that the seed pressure altitude is at 99 km for NDACC2016 and at 110 km for the PCL.

The gravity temperature uncertainties for both NDACC2016 and the scaled PCL are consistent and are roughly 0.002 K. NDACC2016 states that the temperature uncertainty due to the molecular mass is negligible below 85 km and is of the order of 0.05 K and above 85 km can increase up to 1 K (NDACC2016, Table 3). The OEM shows that the PCL molecular mass temperature uncertainty at 85 km is 0.06 K. The PCL molecular mass temperature uncertainties from 90 to 100 km are between 0.1 and 0.6 K. However, the semi-empirical mean molecular mass variation of the US Standard model is considerably different from the variation assumed by NDACC2016, accounting for the differences in the calculated uncertainties.

Figure 8The OEM vertical resolution. The vertical resolution below 80 km is 1056 m; that is, it is equal to the retrieval grid spacing (not shown). The white lines are the height below which the temperature climatology is more than 90 % (0.9) and 80 % (0.8) due to the measurements.

Download

4.1 Comparison between the PCL climatology using the OEM and HC methods

AS2007 used PCL measurements between 1994 and 2004 to calculate a PCL temperature climatology (henceforth, 2004 PCL climatology) using the HC method. The top 10 km of all temperature profiles was removed from the 2004 PCL climatology in order to reduce the effect of seed pressure and the same procedure was followed in the HC calculations for the updated PCL climatology (between 1994 and 2013). The temperature differences between the OEM and updated HC PCL temperature climatologies are shown in Fig. 10. The white space in the upper part of Fig. 10 is due to removing 10 km from the top of each profile for the updated HC PCL climatology. In addition, the lines corresponding to the 10 and 15 km cutoff for the HC method and the 0.9 cutoff line for the OEM are superimposed onto Fig. 10.

Figure 9Comparison of the PCL statistical and systematic uncertainties with scaled uncertainties from Leblanc et al. (2016b) as described in the text. The solid lines are the uncertainties due to the PCL and the dashed lines are uncertainties due to NDACC2016.

Download

The OEM temperature climatology is 0.55±0.23 K warmer than the updated HC climatology average from 40 to 60 km. Although the difference is within the statistical uncertainty of the measurements (Fig. 5), there is a warm bias. The bias due to differences in ozone profile between the two climatologies is only +0.05 K. The OEM used measurements from two Rayleigh channels (HLR and LLR) after 1999 to calculate the OEM climatology, while only the HLR channel measurements were used for the HC method and the OEM before 1999. The effective LLR signal is up to about 60 km of altitude. The temperature difference in the bottom range (between 40 and 60 km) of measurements is because of using a two-channel retrieval in the OEM and comparing it with a one-channel (HLR) retrieval in the HC method. The two-channel OEM method retrieves the dead time for each profile, while the dead time in the HC method was an empirically determined constant based on count measurements using a pulsed LED source. In order to compare the OEM with HC temperature climatology, we could have merged the calculated LLR and HLR temperature profiles in the HC method. However, the temperature uncertainty induced by the merging will be more than the ±0.05 K temperature difference between the OEM and HC climatology (Jalali, 2014).

The OEM temperature above 80 km up to the 10 and 15 km cutoffs is colder than the temperatures obtained using the HC method. The temperature differences above 80 km are mostly due to the sensitivity of the model seed pressure in the HC method. Figure 10 shows that the OEM temperature climatology reaches 5 to 10 km higher in altitude than the HC temperature climatology. The differences between the OEM and HLR are not calculated below 40 km due to the lack of HLR data in some time periods.

Finally, in order to evaluate the effect of the a priori on the temperature differences, the same temperature climatologies were calculated using the OEM with the US Standard model as the a priori temperature profile and the same differences as discussed above were obtained, again demonstrating that the results show little sensitivity to the choice of any reasonable a priori profile.

Figure 10PCL temperature climatology difference between the OEM and HC method (OEM minus HC) using seed pressure. The blue lines show the height below which the OEM temperature climatology is more than 90 % (0.9) and 80 % (0.8) due to the measurements. The red lines are the 10 and 15 km cutoff height for the HC method.

Download

The HC method usually uses a seed pressure value at the highest point of the profile. However, the seed pressure can be substituted by temperature and density and is called the seed temperature (Gardner et al., 1989, Eq. 86). When a seed temperature is used, the temperature is obtained from the CIRA-86 model, and the measured relative density profile is normalized (typically by a model) to obtain a seed pressure to use in the HC retrieval. The temperature differences between the OEM climatology and the updated HC climatology using the seed temperature (instead of seed pressure) are shown in Fig. 11. Comparing Figs. 10 and 11 reveals that the temperature difference above 80 km between the OEM and the updated HC using seed temperatures is larger than the differences between the OEM and the updated HC using seed pressures. However, the differences below 80 km are identical and the small temperature differences between the OEM and HC method are due to the tie-on temperature or pressure value. The difference between the HC climatologies calculated by these two methods highlights the sensitivity to seed pressure at the greatest heights in this method.

Figure 11PCL temperature climatology difference using the OEM and HC method (OEM minus HC) using seed temperature. The blue lines show the height below which the OEM temperature climatology is more than 90 % (0.9) and 80 % (0.8) due to the measurements. The black lines are the 10 and 15 km cutoff height for the HC method.

Download

Gerding et al. (2008) used coincident Rayleigh and sodium resonance lidar temperature measurements to minimize the seed pressure. For altitudes below the sodium layer, Rayleigh lidar measurements are used to determine the temperature. While having this combination of a Rayleigh and resonance temperature lidar is ideal, most Rayleigh-temperature lidar systems are not colocated with a resonance temperature lidar, and hence the effect of seed pressure is the largest systematic uncertainty at the upper range of the temperature profile determined.

Figure 12PCL temperature climatology difference from the URB sodium lidar climatology (PCL minus URB). The horizontal black lines are the height below which the temperature climatology is more than 90 % (0.9) and 80 % (0.8) due to the measurements.

Download

4.2 Comparison with sodium lidar climatologies

The comparison between the PCL Rayleigh-temperature climatology using the HC method with sodium lidars was done by AS2007. Their results showed that the average temperature between 83 and 95 km measured by the PCL was between 7 and 7.4 K colder than CSU and URB climatologies, respectively. Using the OEM to extend the PCL Rayleigh lidar temperature climatology to above 100 km provides the opportunity to validate the PCL results against sodium lidar climatologies, which have their highest signal-to-noise ratio in a few kilometer-wide regions between about 90 and 95 km of altitude, and obtain sufficient high-quality measurements to calculate climatologies from 85 to 105 km. Sodium lidars directly measure the kinetic temperature without assuming hydrostatic equilibrium or requiring the knowledge of mean molecular mass and molecular cross section variations with height and can be configured to obtain temperatures during both the day and night. She et al. (2000), Yuan et al. (2008), and States and Gardner (2000a) have published sodium temperature lidar climatologies in the same latitude range as PCL. Both sites are west of the PCL, but in the case of URB the separation in longitude is less than 8^∘. The URB and CSU climatologies are among the best datasets for validation of upper-mesosphere and lower-thermosphere temperatures, plus they allow for a direct comparison between our new climatology and AS2007. The upgraded CSU (Yuan et al., 2008) provides additional years of overlap with our new climatology for validation of our OEM-derived temperatures. The nighttime URB and upgraded CSU temperature climatologies were compared with the PCL temperature climatology.

Figure 13PCL temperature climatology difference from the CSU (1990–1999) sodium lidar climatology (PCL minus CSU). The horizontal black lines are the height below which the temperature climatology is more than 90 % (0.9) and 80 % (0.8) due to the measurements.

Download

The PCL temperature climatology differences using the OEM compared with the sodium lidars are presented in Figs.  12, 13, and 14. The absolute value of the average differences in 5 km height bins between the sodium lidar temperature climatologies and the PCL climatology using the OEM and the HC method are given in Table 4. The absolute value is used to avoid differences canceling each other. The bottom part of the table is important, as it gives the differences between the sodium lidars themselves. The differences between the sodium lidars are taken as the level of difference defining the agreement between the PCL lidar and the sodium systems. The PCL HC climatology in general does not agree with the sodium lidar climatologies to the same extent to which they agree with each other, while the PCL OEM climatology typically does agree with the sodium lidar climatologies to the level at which they agree with each other. The temperature differences between the PCL OEM and sodium lidar climatologies for the entire range of altitudes (80 to 105 km) are smaller than the temperature difference between the PCL HC climatology and the sodium lidar climatologies in the range of 80 to 95 km for which PCL HC temperatures are available. There is a temperature difference at the winter mesopause between the PCL climatology and CSU climatology, but this difference has decreased in the upgraded nighttime CSU climatology compared to that determined by AS2007. The large temperature differences between the PCL (OEM) and URB temperature climatology during summertime below 85 km existed in AS2007 and may be in part due to the signal-to-noise ratio of the sodium lidar measurements rapidly decreasing below 85 km.

Table 4Absolute value of the average PCL temperature differences with sodium lidars and the temperature difference between sodium lidars. The HC method does not provide the temperature above 95 km; therefore, the columns with an altitude range greater than 95 km are shown as “–”.

Download Print Version | Download XLSX

Overall comparisons between the PCL climatologies and sodium lidar climatologies (Table 4) show that in the 85–90 km and 90–95 km height ranges, at which both the Rayleigh and Na methods have good measurement signal-to-noise ratio, the OEM-calculated temperatures show 20 % better agreement with the sodium lidars than the HC method temperatures: that is, 5.0 K versus 6.3 K on average. The variability of the temperature difference between the sodium lidars themselves is around 4.5 K. The difference among the sodium lidars is approximately the same as the differences with the OEM-derived temperatures, meaning the temperatures derived using the OEM retrieval are approximately the same as those from the sodium lidars; this is contrary to the AS2007 comparison, which showed significant differences between the two techniques. Furthermore, the OEM temperature retrievals allow valid retrievals to be obtained in the 95–100 km altitude region, where the systematic uncertainty of the tie-on pressure of the HC-derived temperatures is too large for the temperatures to be useful. Possible sources of these differences were addressed in AS2007, but they did not have the uncertainty budget now available to assess systematic uncertainties. These differences could include the following factors.

Figure 14PCL temperature climatology difference from the upgraded CSU (2002–2006) sodium lidar climatology (PCL minus upgraded CSU). The horizontal black lines are the height below which the temperature climatology is more than 90 % (0.9) and 80 % (0.8) due to the measurements.

Download

1. The assumption of a seed pressure can introduce uncertainty in the PCL temperature retrievals. Using an OEM allows us to calculate the effect of this assumption quantitatively (Fig. 7). In the altitude range of 80 to 95 km, it is less than 1.5 K, increasing to a maximum of 3.5 K at 100 km.

2. The effects of Rayleigh-scatter cross section, Rayleigh-scatter density, and mean molecular mass were mentioned in AS2007 as possible reasons for discrepancies with the sodium lidar temperatures. Figure 7 shows a quantitative determination of the magnitude of these effects. The uncertainties for the Rayleigh-scatter cross section and Rayleigh-scatter density are much less than the temperature differences between the two measurement techniques. Mean molecular mass uncertainty is larger than the other two parameters, but its maximum value is less than 0.7 K at 105 km.

3. The other significant contribution to the temperature uncertainty budget at higher altitudes is ozone cross section, whose uncertainty increases with altitude due to increasing measurement uncertainty (as do many of the retrieval uncertainties due to the model parameters). The uncertainty on the retrieved temperatures due to ozone reaches a maximum of 1 K at 100 km.

4. Geographic location could be another possible cause. The PCL is about 3^∘ north of the sodium lidars and, while relatively close to URB in longitude, the PCL is 24^∘ east of CSU. Hence, tides and planetary waves could be the primary cause of the temperature differences between the PCL, URB, and CSU lidars. Gravity waves could also contribute, although the effect of gravity waves is minimized by averaging temperature over several hours and using common days in different years to calculate the composite climatology. Sica and Argall (2007) have shown that the seasonal gravity wave activity over London, Canada, is large and highly variable and is possibly related to London's proximity to both Lake Ontario to the west and Lake Erie to the east. The effect of solar tides on the sodium lidar temperature is discussed in States and Gardner (2000b) and Yuan et al. (2006). The upgraded CSU is capable of continuous observation during day and night. Yuan et al. (2008) removed tidal signals from the mean values and calculated diurnal mean monthly temperatures. They show that the amplitude of the diurnal tide is around 5 K at night between 84 and 95 km, increasing to 8 K at 100 km. Hence, we conclude that large-scale waves cause many of the discrepancies between locations.

The comparison with sodium lidars shows that the PCL Rayleigh-temperature climatology using the OEM in general agrees as well with the sodium lidar climatologies as the sodium climatologies agree with one another, validating the PCL OEM height-extended climatology.