Multiple Regression Analysis of the JRA-25 Monthly Temperature
Junichi Tsutsui1 and Shinji Kadokura111

Central Research Institute of Electric Power Industry, JapanCorrespondence: tsutsui@criepi.denken.or.jp

INTRODUCTION

Long-term global reanalysis of atmospheric observations generates a high-quality homogeneous climate
data set using a ﬁxed modern data assimilation system and quality-controlled comprehensive observations. Reanalysis products have been used for a wide variety of climate studies and applications. Despite this reanalysis
concept and usefulness, the quality of current reanalysis products is generally not adequate for the detection andattribution of low-frequency climate variability mainly due to historical changes in observation systems. Unexpected defective procedure and fragmented computation streams during production processes may also result inerroneous changes in reanalysis products. Recent growing concerns about anthropogenic climate change lead toneed for improvement of reanalysis quality regarding not only general climatology but also long-term variability. This study investigates temporal variability of JRA-25 (Onogi et al., 2007), the latest reanalysis producedjointly by the Japan Meteorological Agency and the Central Research Institute of Electric Power Industry, toprovide basic information about its climate quality.
The motivation of this study also arises from the study by Crooks and Gray (2005), in which they foundsigniﬁcant signals to the 11-year solar cycle using ERA-40 (Uppala et al., 2005) from the surface to the lower
mesosphere. Solar signals from reanalysis were also investigated by Haigh (2003) using NCEP R-1 (Kalnayet al., 1996). Because the vertical domain of JRA-25 covers the whole range of the stratosphere, it can becompared with ERA-40 in view of how well climate signals are detected in the stratosphere. As reviewed
by Gray et al. (2005), empirical studies based on various observations have shown a variety of atmospheric
responses to the solar cycle with increasing conﬁdence. Detected signals, however, show some diﬀerences in
the amplitudes and geographical and altitudinal patterns depending on observation sources. This study discusses
robustness of the detection and attribution of climate signals focusing on the solar cycle.
2METHODOLOGYThis study applies multiple regression analysis to zonally-averaged monthly temperature anomalies fromJRA-25 and compares results with those from ERA-40 and NCEP R-1 to discuss spatial structures of climate
signals. Temperature data used in this study cover 1979–2004, the whole period of JRA-25, (or 1979–2001
for ERA-40) at reference pressure levels with 2.5-degree lat/lon resolution from 1000 hPa to 1 hPa (or 10 hPa
for the top level of NCEP R-1). Although native reanalysis grid has a higher spatial resolution, it has been
conﬁrmed for JRA-25 that reduced resolution does not much aﬀect results described below.
Explanatory variables include linear trend, the cold tongue index (Deser and Wallace, 1990) associatedwith El Niño and Southern Oscillation (ENSO), Arctic Oscillation (AO) index by Climate Prediction Center1 ,10.7-cm solar radio ﬂux2 as a proxy of solar activity, stratospheric aerosol optical depth (Sato et al., 1993)
to represent volcanic eruptions, an orthogonal pair of quasi-biennial oscillation (QBO) indexes, and a unit step
function to explain a major discontinuity of reanalysis. The QBO indexes are the ﬁrst two principal components
to represent equatorial zonal wind variations in the stratosphere derived from JRA-25. These QBO indexes arealmost equivalent to indexes derived from ERA-40. The set of explanatory variables is similar to that used inCrooks and Gray (2005) and Haigh (2003), but they consider North Atlantic Oscillation instead of AO and use
additional indexes to represent annual and semi-annual cycles.
As shown in Figure 1, JRA-25 temperatures include several discontinuities in the stratosphere associatedwith satellite transitions. The step function for JRA-25 is used to explain the major discontinuity at the end ofOctober 1998 associated with TOVS-ATOVS3 transition. No other step function is used to avoid ambiguity of1

http://www.cpc.noaa.gov/products/precip/CWlink/
http://www.ngdc.noaa.gov/stp/SOLAR/ftpsolarradio.html
3
TOVS: TIROS (Television and Infrared Observational Satellite) Operational Vertical Sounder, ATOVS: Advanced TOVS
2

understanding regression results. The step function for ERA-40 is used to explain the discontinuity at the endof March 1986, as shown in Figure 2. Although NCEP R-1 possibly includes spurious changes associated withsatellite transition, such as negative anomalies in the upper troposphere from the late 1990s, no step function isused considering its rather continuous behavior.
Figure 3 shows normalized time series of the ENSO, AO, solar, volcanic, and QBO indexes. Note thatthese explanatory variables have some relations to each other. For example, two peaks of the volcanic index,
El Chichón and Mt. Pinatubo eruptions, correspond to a similar declining phase of the ﬁrst and second solarcycles, respectively. Besides such an accidental relation, some of the indexes are possibly aﬀected by non-linear
interaction involving multiple factors. For example, the frequency of QBO varies systematically with the solarcycle (Salby and Callaghan, 2006), which makes diﬃculties in the attribution of climate signals in the tropicallower stratosphere.
The regression model used in this study incorporates auto-regression (AR) terms, considering that elementsof residual time series are generally not independent of each other for climate variables. The model is formulated as follows:∑Yt =xt j β j + Wt , Wt − φ1 Wt−1 − · · · − φ p Wt−p = Zt ,(1)jwhere Y, x, W, and Z are time series of temperature, explanatory variables, regression residual, and AR residualthat is supposed to be white noise; β and φ are regression coeﬃcient and AR coeﬃcient; subscript t, j, and p aretime index, explanatory variable index, and AR order. Regression coeﬃcients are estimated by the generalized
least-squares method considering covariance matrix of W according to Brockwell and Davis (2002). AR orderand coeﬃcients are basically estimated by likelihood maximization. Regression coeﬃcients and AR coeﬃcientsare determined iteratively.
As an example, Figure 4 shows regression coeﬃcients for JRA-25 temperature at 70 hPa, 10N by thegeneralized least-squares method in comparison with those by the ordinary least-squares method. While themagnitude of regression coeﬃcients are not much diﬀerent between the two method, conﬁdence intervals aresubstantially larger in the generalized least-squares method, which is acceptable because residual dependency isappropriately incorporated in computing variance of regression coeﬃcients. The ordinary least-squares method
would overestimate climate signals.
3RESULTS

Figure 5 to 9 compare the three reanalyses with regard to vertical-meridional distributions of regression
coeﬃcients for ENSO, AO, solar, and volcanic signals in units of kelvin per standard deviation and linear trend
in units of kelvin per decade. Regression coeﬃcients for QBO signals and the step function are also shown in
Figure 10 for JRA-25. Although zonal averaging may result in reduced signals for zonally asymmetric phenomena like ENSO, spatial structures of climate signals represented by the regression coeﬃcients are basicallyconsistent with previous studies.
ENSO signals are characterized by tropospheric warming in the tropics and compensating cooling above(Reid, 1994). The warming signal indicates vertical propagation in the Northern Hemisphere, which is consistent with the fact that ENSO usually peaks in boreal winter when signal propagation is allowed in backgroundwesterlies in the Northern Hemisphere (Garcı́a-Herrera et al., 2006).
AO signals show well-known dipole structure in northern mid to high latitudes throughout the troposphere.
The cooling signal centered at the north pole extends to the lower stratosphere with increasing magnitude,
and the surrounding warming signal in the extratropics appears to extend to the Southern Hemisphere toward
the lower stratosphere, both of which are consistent with ﬁndings by Baldwin and Dunkerton (1999). Upper
stratospheric AO signals comprise another dipole structure with those in lower altitudes and suggest changes in
the polar night jet, leading to AO through the downward propagation mechanism (Kodera and Kuroda, 2000).
Although inﬂuences of the solar variability on the Earth’s climate are not fully understood, some of thesigniﬁcant solar signals shown in the regression results are well documented in previous literature. Positivesignals in the tropical upper stratosphere are likely due to direct solar ultraviolet (UV) heating. Because theFigure 1: Assimilated periods of TOVS/ATOVS satellites in comparison with pressure-time cross section of
globally-averaged temperatures from JRA-25.

Figure 2: Pressure-time cross sections of globallyaveraged temperatures from ERA-40 and NCEP R-1.

Figure 3: Normalized time-series of ENSO, AO,solar, volcanic, and QBO indexes.

Figure 4: Regression coeﬃcients for JRA-25 temperature at 70 hPa, 10N. Red/blue bar indicates results from generalized/ordinary least-squares with
95% conﬁdence interval.

total solar irradiance is less variable than the UV irradiance, signiﬁcant signals in the troposphere and the lower
stratosphere are considered to be indirect solar inﬂuences. In comparison with Crooks and Gray (2005), thedirect signal in the tropical upper stratosphere in this study is less clear; the peak response to the solar cycle,
deﬁned as 120-unit change in the 10.7 cm ﬂux, is about 0.7 K and 0.9 K (values in Figure 7 are multipliedby 2.34) for JRA-25 and ERA-40, respectively, which are substantially smaller than 1.75 K found by Crooks
and Gray (2005). Diﬀerences are also noticed for the lower stratospheric signal; Figure 7 indicates positive
responses throughout low latitudes while Crooks and Gray (2005) detected a pair of positive responses centeredabout 25N and 25S and not signiﬁcant equatorial region. Presumably, these diﬀerences are due to methodology
diﬀerences in the multiple regression procedure, which remains a matter of debate in particular for the nonlinear interaction between solar and QBO signals.
Compared to ENSO and AO signals, diﬀerences among the three reanalyses are noticeable for solar signals.
Parts of signiﬁcant regions in the stratosphere from JRA-25 and ERA-40 are not necessarily consistent witheach other. The vertical extent of positive signal in the tropical lower stratosphere is more conﬁned in JRA25. Mid-latitude troposphere signals are more clearly identiﬁed in NCEP R-1. These inter-product diﬀerences
provide a measure of robustness of speciﬁc climate signals.
Volcanic signals are characterized by warming in the lower stratosphere due to enhanced absorption ofshort-wave radiation and resulting cooling in the troposphere. The lower-stratospheric warming distributes

Figure 5: ENSO signal in zonally-averaged monthly temperature anomalies from JRA-25 (left), ERA-40 (center), and NCEP R-1 (right) represented by regression coeﬃcients in units of kelvin per standard deviation of theENSO index. Orange/blue shading indicates positive/negative values with 0.05 signiﬁcance level. Thick/dashedcontours denote zero/negative values.

Figure 6: Same as Figure 5, except for AO signal.

Figure 7: Same as Figure 5, except for solar signal.

Figure 8: Same as Figure 5, except for volcanic signal.

Figure 9: Same as Figure 5, except for linear trend in units of kelvin per decade.

Figure 10: QBO signals (left and center) and discontinuities explained by the step function (right) in zonallyaveraged monthly temperature anomalies from JRA-25 represented by regression coeﬃcients in units of kelvinper standard deviation for QBO or kelvin for the step function. Contour properties are the same as in Figure 5.
over broader latitudes than that for the solar signal. Signiﬁcant signals in the upper stratosphere are possibly
indirect responses related to diﬀerential heating between sunlit areas and the polar night. As in the case of solar
signals, the signiﬁcant positive region in the lower stratosphere is more conﬁned in JRA-25, and diﬀerences
between JRA-25 and ERA-40 are relatively large in the upper stratosphere.
Linear trends basically indicate tropospheric warming and stratospheric cooling as an evidence of anthropogenic climate change due to increasing long-lived greenhouse gases and depleting ozone. One major exception is spurious cooling in the southern mid-latitude troposphere of JRA-25. In the stratosphere, the step
function applied to JRA-25 reasonably explains TOVS-ATOVS diﬀerences and results in rather homogeneoustrends. The satellite transition impacts are marginal in the troposphere, which has been conﬁrmed from anexperimental regression analysis excluding the step function variable. Regarding ERA-40, however, regression
coeﬃcients for the step function (not shown) indicate some signiﬁcant values in the troposphere, which seems
to add erroneous trend signals in the tropics.
Details in the tropical troposphere display some discrepancies among the three reanalyses, implying insufﬁcient climate quality of current reanalysis as well as its source observations (e.g., Sterin et al., 2008). JRA-25
trends are about 0.1 K/decade (not signiﬁcant) and around a lower bound of independent estimations summarized in the latest report of Working Group I of the International Panel on Climate Change. The ampliﬁcationof upper tropospheric warming, which is theoretically predicted considering the moist adiabatic response togreenhouse-gas forcing, is vague in JRA-25, or extremely exaggerated in ERA-40 partly due to the side eﬀectof the step function. NCEP R-1 trends are not statistically signiﬁcant and partly negative at mid to upper levels. By contrast, greater amplitude in the upper troposphere is noticeable for ENSO signals from JRA-25 andERA-40.
QBO signals (shown for JRA-25 only) clearly illustrate staggered structure around the tropical stratosphereand surrounding regions corresponding to the orthogonal pair of the QBO indexes. This structure is understood

as a response related to thermal wind balance in the lower stratosphere, and signals in higher latitudes come fromthe winter hemisphere (e.g., Randel et al., 1999). Three-cell structure in the vertical alignment of signiﬁcantregions has been recognized by Pascoe et al. (2005) from ERA-40.
4

CONCLUSION

Temporal variability of zonally-averaged upper-air temperatures is reasonably detected from reanalysis
products using the multiple regression analysis with AR terms. Spatial structures of long-term trend andother component variability from JRA-25 are generally consistent with current scientiﬁc understanding. Intercomparison using multiple reanalysis products provides useful information about reanalysis quality and robustness of climate signals.
Further investigation is needed to ensure sensitivity to the choice of explanatory variables and to illustrate
more complete structure of climate signals including other meteorological elements. Because of the limitation of regression analysis, comparison with climate model experiments would be helpful to isolate relevant
components to a speciﬁc signal and to understand their non-linear interaction.
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