Chapter 4, Section 4.3.2, defines a method to quantify the quality of a climate record by the time required to detect climate change trends. The time to detect trends decreases as quality increases, thereby increasing the science value and societal value of the observation. This appendix applies the equations defined in Section 4.3.2 to a range of current climate data records to demonstrate examples of the quality metric Q2, both with and without continuity (Table B.1). Appendix C is also an example of applying the Q metric to a full quantified objective example, but for the shortwave cloud forcing data record.
Many climate data records (surface or satellite) have multiple versions usually developed and analyzed by different research groups. For the quality metric examples shown below the primary quantity controlling the time to detect climate change is the natural variability level in the record and its magnitude relative to long term trends, and to uncertainty analysis of the climate record. Interannual to decade scale natural variability tends to be large for most climate records and the differences in climate data records do not significantly change the natural variability estimate from the record. Examples of this are shown in Figure B.3 for two versions of middle tropospheric temperature, and Figure B.2 for global total ozone. For such cases, the Q metric tends to depend minimally on the climate data record version used.
The climate records analyzed are shown in Figures B.1 to B.4; each is a time series of annual average values, with the time unit in years. For all cases the confidence internal is 95 percent (s = 2) and the length of the satellite mission is 10 years (τunc= 10). The selection of s = 2 for the confidence interval is arbitrary and is made for purpose of illustration; the value of s will likely vary depending on the significance of the trend and the required accuracy for testing key climate change hypotheses. Except for total solar irradiance (TSI), for which directly measured TSI observations are used, the quantities are evaluated using deseasonalized anomalies obtained by removing the annually repeating seasonal variations. Long-term trends are estimated statistically, by fitting a line (Figure B.1), polynomial (Figure B.4) or from multiple regression analysis of the measurements (Figures B.2 and B.3; Lean, 2014).
The trends shown in the figures have two-fold importance: firstly, they allow direct comparisons of different versions of a climate data record, whereby trend differences quantify the (lack of) repeatability, and secondly the removal of the trend quantifies the (residual) “natural” variability of the measurement, against which the trend magnitude is then compared. The upper panels in Figures B.1-B.4 show the annual mean (deseasonalized in Figures B.2 to B.4) climate data records, including their trends (green lines), and the lower panels show the residual “natural” variability obtained by removing the trends from the deasonalized annual mean values. Note that detecting
TABLE B.1 Existing Climate Records and Estimated Parameters for their Quality Expressions
|Climate Record||Total Solar Irradiance||Global Total Ozone Anomaly||Microwave Sounding Unit Mid-troposphere Global Temperature Anomaly||Arctic Sea Ice Area||Global Sea Level Anomaly|
|nominal||1361.5 W m−1||294 DU||−17.5°C||12 ´ 106 km2||0 mm|
|L||35 years||35 years||35 years||35 years||23 years|
|m||0.015 W m−2 yr−1||0.1 DU yr−1||0.01°C yr−1||0.3 ´ 106 km2 yr−1||1 mm yr−1|
|σunc||0.5 W m−2||3 DU||0.2°C||0.5 ´ 106 km2||0.4 mm yr−1|
|σrep||0.02 W m−2 yr−1||0.3 DU yr−1||0.01°C yr−1||0.01 ´ 106 km2 yr−1||2 mm yr−1|
|σvar||0.5 W m−2||2.5 DU||0.14°C||0.17 ´ 106 km2 yr−1||2.3 mm|
|ΔtP||75.2 years||39.1 yrs||21.1 years||2.8 years||8.0 years|
|ΔtC||75.3 years||40.1 years||21.5 years||2.8 years||8.56 years|
|ΔtNC||98.6 years||78.9 years||58.6 years||11.1 years||17.6 years|
|Q2 with continuity||1.00||0.97||0.99||1.00||0.98|
|Q2 without continuity||0.22||0.00||0.00||0.72||0.68|
L is the length of the currently available satellite climate record used to provide the examples in Appendix B.
m is the magnitude of the climate trend detection level required to meet the quantified objective
σunc is the instrument calibration uncertainty relative to international physical standards.
σrep is the instrument repeatability (often called stability).
τunc, τrep are the time scales of typical instrument lifetime in orbit.
σvar is the standard deviation of climate system natural variability.
τvar is the time scale of climate system natural variability.
ΔtP is the time scale to detect a trend of magnitude m at 95% confidence for a perfect observing system (zero uncertainty in the observation, limited only by natural variability).
ΔtC is the time scale to detect a trend of magnitude m at 95% confidence for an observing system with calibration uncertainties of σunc, σrep, τunc, τrep that achieves continuity of the observations.
ΔtNC is the time scale to detect a trend of magnitude m at 95% confidence for an observing system with calibration uncertainties of σunc, σrep, τunc, τrep that fails to achieve continuity of the observations.
XC is the ratio of ΔtC/ΔtP and provides the fractional increase in time to observe a climate system trend using an observing system with continuity relative to that of a perfect observing system. Note that XC is independent of the assumed value of m.
XNC is analogous to XC, but for an observing system without continuity.
Q2 is an example quality metric (Eq. 3 of Section 4.3.2) that converts delay in the time to detect climate trends versus a perfect observing system (Δt − ΔtP) into a quality metric scale of 0 to 1 for use in the value framework.
such trends as shown in the upper panels of the figures is a scientific objective of the measurements. The statistical metrics of the residual “natural” variability given in the lower panels of the figures are directly incorporated into the quality metric: the square of the standard deviation of the residuals (given by sdev in the figures) provides an estimate of the variance, σvar2, in Equation 1 and the autocorrelation at the first (1 year) lag (given by acf1 in the figures) allows for estimation of the autocorrelation time scale τvar = (1 + acf1)/(1 - acf1).
FIGURE B.1 Total solar irradiance. Shown in the top panels are annual mean values of total solar irradiance according to two different composite records, PMOD (Physikalisch-Meteorologisches Observatorium Davos) and ACRIM (Active Cavity Radiometer Irradiance Monitor), each constructed using different combinations of individual observations (from the total solar irradiance [TSI] database show in Chapter 2), and corrections for bias calibration and drift. The lines, which are linear fits to the annual mean values, have different slopes which indicate that the repeatability of the 35-year TSI record is no better than 0.01 W m−2 per year. Shown in the bottom panels are the residuals of the two time series in the upper panel from the linear trends, which indicate “natural” TSI solar cycle variations in the two records. That the 1s values of the residuals (given by sdev in the figures) of the PMOD and ACRIM composites differ, indicates disagreement in their respective characterizations of the 11-year solar cycle signal, against which possible long-term irradiance trends must be detected. SOURCE: Courtesy of Judith L. Lean, Naval Research Laboratory.
Lean, J.L. 2014. Evolution of total atmospheric ozone from 1900 to 2100 estimated with statistical models. Journal of Atmospheric Science 71:1956-1984.
FIGURE B.2 Global total ozone. Shown in the upper panels are annual mean values of global total ozone anomalies (deseasonalized by removing an average annual cycle) according to two different composite records, MOD V8 and MOD V8.8, constructed from, respectively, the TOMS (Total Ozone Mapping Spectrometer) and SBUV (Solar Backscatter UltraViolet) observations, with different techniques for assessing long-term changes in each of multiple instruments flown on a sequence of satellites. The smooth curves through the annual mean values are estimates of the combined influence of anthropogenic chlorofluorcarbons and greenhouse gases, derived from statistical regression models of the monthly ozone data sets (Lean, 2014). The residuals of the annual global total ozone from the trends, shown in the bottom panel, are indicative of “natural” variability in ozone, due to various influences, including solar irradiance changes, volcanic eruptions, and the Quasi-Biennial Oscillation. The magnitude of this variability, estimated by the 1s standard deviations of the residuals (given by sdev in the figures), indicates the “noise” of ozone natural variability, against which anthropogenic changes, including ozone recovery following the Montreal Protocol must be detected. SOURCE: Courtesy of Judith L. Lean, Naval Research Laboratory.
FIGURE B.3 Global middle troposphere temperature. Shown in the top panel are annual mean values of global middle troposphere temperature anomalies (at about 5 km, deseasonalized by removing an average annual cycle), according to two different analyses of observations made by a series of MSU/AMSU (Microwave Sounding Unit/Advanced Microwave Sounding Unit) instruments flown on a sequence of satellites (as discussed in Chapter 2). The smooth curves through the annual mean values are estimates of the trends. The residuals of the annual global middle troposphere temperature from the trends, shown in the bottom panel, are indicative of “natural” variability due to various influences including solar irradiance changes, volcanic eruptions and El Niño southern oscillation. The magnitude of this variability, estimated by the 1s standard deviations of the residuals (given by sdev in the figures), indicates the “noise” of middle troposphere natural variability, against which anthropogenic changes must be detected. SOURCE: Courtesy of Judith L. Lean, Naval Research Laboratory.
FIGURE B.4 (A) Arctic sea ice area and (B) global sea level. Shown in the upper panels are annual mean values of deseasonalized Arctic Sea Ice area (left) and global sea level (right). The smooth curves indicate long-term trends (estimated by polynomials), from which the residuals of the annual mean values are shown in the lower panels, as indicators of natural variability in these two climate change records. SOURCE: Courtesy of Judith L. Lean, Naval Research Laboratory.