Larger variability, better predictability?

Authors

  • Bo Sun,

    Corresponding author
    1. Nansen-Zhu International Research Centre, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
    2. College of Earth Science, Graduate University of Chinese Academy of Sciences, Beijing 100049, China
    3. Climate Change Research Center, Chinese Academy of Sciences, Beijing 100029, China
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  • Huijun Wang

    1. Nansen-Zhu International Research Centre, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
    2. Climate Change Research Center, Chinese Academy of Sciences, Beijing 100029, China
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Bo Sun, Nansen-Zhu International Research Centre, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China. E-mail: sunb@mail.iap.ac.cn

Abstract

The statistical relationship between observed interannual variability and the corresponding predictability of June–July–August mean precipitation is computed and discussed, using hindcasts from the Development of a European Multimodel Ensemble System for Seasonal to Interanuual Prediction (DEMETER) project and reanalysis datasets of the Global Precipitation Climatology Project and Climatic Research Unit. It is found that there exists a globally positive correlation between the variability and predictability, being prominent in the low latitudes and less evident in the high latitudes. Although this correlation varies with modulated verification datasets, multi-model ensembles and temporal periods, all of which are artificial factors, a significant positive correlation is found over East Asia, Australia, South America, Europe and Africa, while a negative correlation for North America, under most circumstances. Moreover, it is also found that different dynamical processes in the climate system seem to have made different contributions to building this ‘larger variability–better predictability’ relationship, possibly through enhancing the predictability over domains where there is a larger contribution to variability by the climate signals, while making an uncertain contribution to the predictability over domains that are less influenced by the signals.

1. Introduction

It is widely recognized that the predictability of climate forecasts is principally determined by the initial conditions, boundary conditions, and model formulations. As Palmer (2000) stated, ‘The predictability of weather and climate forecasts is determined by the projection of uncertainties in both initial conditions and model formulation onto flow-dependent instabilities of the chaotic climate attractor.’

Numerous studies have been dedicated to evaluating climate predictability based on climate models (Goswami and Shukla, 1991; Wang et al., 1997; Koster et al., 2000; Palmer, 2000; Vidale et al., 2003; Hurrell et al., 2006; Koller et al., 2010). It is widely accepted that the long-range predictability of low-frequency climate components is determined by the slowly varying boundary conditions (Shukla, 1981). An early study by Wang et al. (1997) suggested that a possible way to increase model predictability is to improve land surface process modelling and to include interannual variations of land surface conditions. Shukla (1998) found that tropical atmospheric circulation and rainfall patterns are so strongly determined by sea surface temperature that they show little sensitivity to distinct initial atmospheric conditions. Koster et al. (2000) assessed the impact of land surface and ocean boundary conditions on seasonal-to-interannual variability and predictability of precipitation in a coupled modelling system, and concluded that foreknowledge of sea surface temperature contributed significantly to predictability in the tropics, while foreknowledge of land surface moisture state contributes significantly to predictability in transition zones between dry and humid climates. Thus, a better understanding of boundary conditions is crucial for raising the predictability of climate variability. In addition, an improvement of the physical description could also assist a model to perform more appropriately. For instance, Koller et al. (2010) suggested that the simulated Atlantic meridional overturning circulation can be more realistically simulated by simply implementing hydraulic control in the Denmark Strait Overflow. On the other hand, this could probably be realized with an ensemble of models with various formulations. Overall, multi-model ensembles, which involve perturbed initial conditions, changing boundary conditions and various formulations, could be considered as the optimal choice for possibly reliable predictions (Stainforth et al., 2005).

Geographically, the extratropical region has generally low predictability, which could be attributed to the unpredictable internal high-frequency processes, a weak linkage to the El Niño-Southern Oscillation (ENSO) at the interannual scale and the complex mechanisms for its interdecadal climate variability (Wang, 2001, 2002; Goswami and Xavier, 2005; Sun et al., 2011; Zhu et al., 2011). To address this, Wang and Fan (2009) proposed a new, more skilful scheme for improving the seasonal prediction of summer precipitation in East Asia. Fan et al. (2008, 2009, 2009) and Fan and Wang (2009) established a new approach for East Asian summer precipitation prediction by considering the year-to-year increment of both the predictors and the predictand. Lang and Wang (2010) and Liu et al. (2011) tried to improve prediction of summer precipitation in China by merging the information from both the observation and the model.

On the basis of the above studies, our concern in this research is what determines the high predictability of climate in certain areas and low predictability in others? Previous work by Manabe and Hahn (1981) showed that the observed geographical distribution of temporal variability of surface pressure and temperature could be approximately reproduced by a model in the middle and high latitudes, where the variability of these characteristics is relatively higher, compared to tropical regions, where their variability is lower. These results imply the possible existence of certain intrinsic relationships between climate variability and predictability, and to clarify these relationships is certainly an important area of research, but one that has received minimal attention to date. Understanding whether variability determines predictability, and to what extent, might further contribute to the improvement of low-quality forecasts.

A pre-estimation of the variability of Global Precipitation Climatology Project (GPCP) precipitation indicates that seasonal mean precipitation generally has a relatively larger interannual variability than annual mean precipitation around the globe, and the interannual variability of seasonal mean precipitation varies spatially within a greater value range than annual means. Hence, it would be more appropriate to use seasonal mean precipitation to examine how the interannual variability of precipitation and its predictability are spatially related. This study focuses on the boreal summer (June–July–August, JJA) precipitation, which accounts for a large part of annual precipitation of Northern Hemisphere. In particular, due to the strong East Asian summer monsoon, the JJA precipitation constitutes about 37% of the annual precipitation of East Asia, where is one of the most important agricultural areas in the world.

In this article, we present primary results from an investigation into the relationship between the variability and predictability of JJA mean precipitation, principally from a statistical viewpoint. Moreover, the roles of climate signals like ENSO in this relationship are examined.

The outline of this article is as follows. Section '2. Data and methods' describes the datasets and methods employed in this study. In Section '3. Interrelationship between predictability and variability', the distribution of predictability versus variability is illustrated and discussed for different latitudes and areas, uncovering a general relationship between predictability and variability. Section '4. Comparison between Combinations 1 and 2' investigates possible impacts of several artificial factors in computation on this relationship to validate its reliability. Roles of climate signals like ENSO in this relationship are further analysed in Section '5. Roles of climate signals' in order to clarify whether or not this relationship is related to physical and dynamical processes in the climate system. Finally, Section '6. Conclusions and discussions' offers some conclusions and discussions.

2. Data and methods

2.1. Data

The DEMETER project was set up for seasonal climate predictions using state-of-the-art global coupled ocean–atmospheric models (Palmer et al., 2004). The seven models used in the DEMETER project are those of CERFACS (European Centre for Research and Advanced Training in Scientific Computation, France), ECMWF (European Centre for Medium-Range Weather Forecasts, International Organization), INGV (Istituto Nazionale de Geofisica e Vulcanologia, Italy), LODYC (Laboratoire d'océanographiehie Dynamique et de Climatologie, France), Météo-France (Centre National de Recherches Météorologiques, Météo-France, France), Met Office (United Kingdom), and MPI (Max-Plank Institue für Meterologie, Germany).

A comprehensive set of hindcasts has been produced by the DEMTER project, based on initial conditions starting from 1 February, 1 May, 1 August, and 1 November, with each hindcast integrated for 6 months and comprising an ensemble of nine members. The hindcasts generated by the seven models respectively cover the periods 1980–2001 (CERFACS), 1958–2001 (ECMWF), 1973–2001 (INGV), 1974–2001 (LODYC), 1958–2001 (Météo-France), 1959–2001 (Met Office), and 1970–2001 (MPI). This study employed the JJA precipitation hindcasts integrated from 1 May, only which integration has been carried out cover through JJA and thus is suitable for assessing the JJA seasonal predictability by DEMETER.

The prediction skill of the DEMETER models has been verified with regards to two datasets as follows. (1) GPCP version 2.2 combined precipitation dataset (2.5° × 2.5°), which consists of monthly means of precipitation derived from satellite and gauge measurements (Adler et al., 2003). (2) Climatic Research Unit (CRU) time series version 3.0 global land precipitation monthly dataset (0.5° × 0.5°) (Mitchell and Jones, 2005). The GPCP and CRU precipitation data respectively cover the periods 1979–2010 and 1901–2006.

Because of the different temporal coverage of the above hindcasts and verification datasets, this study investigates the relationship between JJA precipitation variability and its predictability (or the prediction skill of the DEMETER models) for two periods of different lengths: (1) 1980–2001—the period for which all the seven DEMETER models have generated hindcasts, and is covered by GPCP data; (2) 1959–2001—covered by the ECMWF, Météo-France, and Met Office models, as well by the CRU data. Therefore, an ensemble of 7 × 9 members (Ensemble 1) and a verification dataset of GPCP are combined for the period 1980–2001 (hereafter Combination 1), while an ensemble of 3 × 9 members (Ensemble 2) and a verification dataset of CRU are combined for the period 1959–2001 (hereafter Combination 2), as shown in Table 1.

Table 1. The two combinations employed for the computation of the relationship between the variability and predictability of JJA mean precipitation
 Combination 1Combination 2
Period1980–20011959–2001
Model ensembleCERFACS, ECMWF, INGV, LODYC, Météo-France, Met Office, MPI (Ensemble 1)ECMWF, Météo-France, Met Office (Ensemble 2)
Verification datasetsGPCP version 2.2 combined precipitationCRU TS 3.0 global land precipitation

Climate signals, which were investigated in terms of their roles in the relationship between variability and predictability, are denoted by the following climate indices: the Nino1 + 2 Index, Nino3 Index, Nino3.4 Index, Nino4 Index, Southern Oscillation (SO) Index, Arctic Oscillation (AO) Index, Antarctic Oscillation (AAO) Index, and the North Atlantic Oscillation (NAO) Index provided by the NOAA Climate Prediction Center (http://www.esrl.noaa.gov/psd/data/climateindices/list/).

2.2. Methods

In the current study, the interannual variability of JJA mean precipitation is denoted by the standard deviation (SD) of GPCP and CRU time series, while its predictability is denoted by the prediction skill of the DEMETER ensembles. For every grid the variability and predictability is computed, and the relationship between variability and predictability in a specified area is evaluated by their pattern correlation coefficients.

The SD is given by:

equation image(1)

where n is the length of time series, x is the time series of observations, and the overbar denotes climatic mean (the same below). With respect to the estimators of predictability, the World Meteorology Organization has been committing to an internationally accepted standardized verification system for long-range forecasts. A series of methodologies has been provided as standard verification tools, such as temporal Anomaly Correlation Coefficients (ACC) and Mean Square Skill Score (MSSS). In this study, the ACC and MSSS are used for evaluating the prediction skill of the DEMETER models. The ACC is given by:

equation image(2)

where f is the time series of hindcasts and c is the climatology. The MSSS is given by:

equation image(3)

where

equation image(4)

and

equation image(5)

Thus, an MSSS approaching 1 denotes a better prediction skill, and vice versa.

Consequently, the relationship between variability and predictability in a specified area could be evaluated by the pattern correlation coefficients between SD and ACC and/or MSSS:

equation image(6)
equation image(7)

Furthermore, the impacts of climate signals on the relationship between predictability and variability are estimated by the following three steps: (1) removing the selected climate signal from the original observations and forecasts; (2) computing the variability and predictability contribution from this climate signal, respectively denoted by ΔSD and ΔACC and/or ΔMSSS; and (3) evaluating the contribution from ΔSD − ΔACC and/or ΔMSSS relationship to the original SD–ACC and/or MSSS relationship. Step (1) is realized by removing the signal covariant with the selected climate index from the original time series, which is given by:

equation image(8)

where ξ* is the original variable, Z is the climate index, cov(ξ*, Z) is the covariance of ξ* with Z, var(Z) is the variance of Z, and ξ is the new variable that has excluded the selected climate signal (An, 2003). In Step (2), the ΔSD, ΔACC, and ΔMSSS are obtained with the SD, ACC, and MSSS for original time series minus those for time series excluding the climate signal.

3. Interrelationship between predictability and variability

Figure 1 shows the SD, ACC, and MSSS of Combinations 1 and 2. For Combination 1, the SD of GPCP time series indicates a prominent high variability in tropical and western Pacific areas (Figure 1(a)), where the prediction skill scores are significantly higher than other areas (Figure 1(c) and (e)). Although not evident, Eurasia, Australia, and South America also present a general agreement between variability and prediction skill. It can be seen that the variability of JJA mean precipitation in mid- and low-latitude monsoonal regions of Asia is generally larger than that of high latitudes of Eurasia; accordingly, so do the scores of ACC and MSSS. In addition, the JJA mean precipitation in eastern Australia and tropical South America are of higher variability and prediction skill relative to central Australia and subtropical South America, respectively. Similar features of the agreement between variability and predictability could also be found for these areas in the results of Combination 2 (Figure 1(b), (d) and (f)), implying that a larger variability tends to be accompanied by a higher predictability. In contrast, the variability in eastern North America is larger than that in the west (Figure 1(a) and (b)); the prediction skills, however, are evidently higher in western North America (Figure 1(c)–(f)). Thus, it can be inferred that the relationship between variability and predictability probably varies depending on the region being considered.

Figure 1.

The SD (unit: mm d−1, the same below), ACC, and MSSS of Combination 1 (left panel) and Combination 2 (right panel)

To verify this agreement between variability and predictability, the prediction skill scores for global grids were plotted against the corresponding variability. As shown in Figure 2(a) and (d), both the ACC and MSSS scores of Combination 1 present an evident ascending trend as the SD increases, with a value of 0.43 for both CCa and CCb, significant exceeding the 99% confidence level. This is indicative of a significant positive correlation between the variability and predictability of JJA mean precipitation around the globe. However, when only land grids are considered (Figure 2(b) and (e)), the CCa and CCb are leveled down to 0.29 and 0.35, respectively signifying that this relationship tends to be less significant over land areas than ocean areas. The remarkably high variability and predictability along the tropical Pacific should have largely added the agreement of the two for ocean areas, while such high values could hardly be found in land areas. Furthermore, the relatively high positive correlation between variability and predictability resulting from Combination 1 seems to be less significant when it comes to Combination 2. It can be seen in Figure 2(c) and (f) that in spite of a slight ascending trend, the ACC and MSSS scores do not increase with SD as rapidly as those in Figure 2(b) and (e). The corresponding CCa and CCb are 0.17 and 0.20, respectively; however, still significant at the 99% confidence level. This distinction between Combinations 1 and 2 will be discussed in Section '4. Comparison between Combinations 1 and 2'. In the main, a general positive correlation between variability and predictability could be drawn from both combinations. Nevertheless, it should be noted that this correlation is more evident in the higher variability belts than lower variability belts. For instance, in the belts of SD > 1.0 mm d−1, the prediction skill scores would present a relatively notable growing tendency as SD increases, while being much more disorderly in the lower variability belts. As a matter of fact, the variability of JJA mean precipitation is generally larger in lower latitudes than higher latitudes. This, presumably, implies a varying correlation between variability and predictability with latitudes.

Figure 2.

Scatterplot of ACC and MSSS versus SD for global grids of Combination 1 (left panel), only land grids of Combination 1 (middle panel) and Combination 2 (right panel). A small number of grids with extreme low MSSS (here, lower than − 1.0) were omitted, which may mislead the result of CCb (the same below)

Taking that into account, the CCa and CCb for global latitudinal belts were computed using Combinations 1 and 2, respectively, as shown in Figure 3. As a result, the CCa and CCb of Combination 1 are around 0.40 in the range of 30°S–30°N, and decline notably poleward to around zero, especially in the Northern Hemisphere. The poleward declining of CCa and CCb of Combination 2 could also be identified in the Northern Hemisphere, while not evident in the Southern Hemisphere, probably due to the fact that only sparse land grids having been used for the computation in the Southern Hemisphere, which also leads to a number of less confident values. In particular, the minimums of CCa and CCb appear in 50–70°N, indicating a weak interrelationship between variability and predictability in this belt. With respect to polar latitudes, both positive and negative values of CCa and CCb were obtained. Hence, there exists a considerable uncertainty in qualifying the relationship between variability and predictability of JJA mean precipitation in polar latitudes.

Figure 3.

CCa and CCb for nine latitudinal belts: 90–70°S, 70–50°S, 50–30°S, 30–10°S, 10°S–10°N, 10–30°N, 30–50°N, 50–70°N and 70–90°N, all with a longitudinal range of 0–360°E. The hollow bars are significant below the 99% confidence level. The high values of CCa and CCb of Combination 2 in the 70–50°S belt are not significant because of the very few land grids used for computation

Therefore, a ‘larger variability–better predictability’ proposition for JJA mean precipitation is verified to be generally tenable in low and mid latitudes, while remaining more suspect in high latitudes. However, as mentioned previously, this relationship might possibly vary from region to region, even those in the same latitudes.

In light of this, six continental areas were selected to extend a comparative insight into this issue, which were: East Asia (10–60°N, 70–140°E); Australia (40–10°S, 110–155°E); North America (30–70°N, 130–60°W); South America (60°S–10°N, 80–35°W); Europe (30–70°N, 30°W–45°E); and Africa (35°S–30°N, 20°W–50°E), as shown in Figure 4. These domains were all selected in rectangles, covering basically the whole Australia, South America, and Africa, while although not whole but the main parts of North America, Europe, and East Asia, which should be appropriate enough to capture the main features under investigation.

Figure 4.

The six continental areas: East Asia (10–60°N, 70–140°E); Australia (40–10°S, 110–155°E); North America (30–70°N, 130–60°W); South America (60°S–10°N, 80–35°W); Europe (30–70°N, 30°W–45°E); and Africa (35°S–30°N, 20°W–50°E)

Figure 5 provides the CCa and CCb for the six areas obtained from Combinations 1 and 2, only land grids were used for both combinations. As can be seen, the CCa and CCb of both combinations are uniformly positive for East Asia, Australia, South America, Europe, and Africa, most significant at the 99% confidence level, and thus supporting the ‘larger variability–better predictability’ proposition. On the contrary, the values of CCa and CCb for North America indicate a negative correlation between the variability and predictability of its JJA mean precipitation. In addition, although it shows uniformly positive values of CCa and CCb for those five areas mentioned above, their magnitudes and the corresponding confidence levels seem to be uneven. Thus, the relationship between variability and predictability are indeed distinct for different domains. The reasons for this distinction will be discussed in Section '5. Roles of climate signals'.

Figure 5.

CCa and CCb for six continental areas: East Asia (10–60°N, 70–140°E); Australia (40–10°S, 110–155°E); North America (30–70°N, 130–60°W); South America (60°S–10°N, 80–35°W); Europe (30–70°N, 30°W–45°E); and Africa (35°S–30°N, 20°W–50°E). The hollow bars are significant below the 99% confidence level. Only land grids were used for computation

Before that, another basic question needs to be clarified, which relates to the alarming result that the CCa and CCb of Combination 2 are generally smaller than those of Combination 1, as depicted in Figures 3 and 4. For instance, the CCa and CCb for East Asia are equal or above 0.20 when using Combination 1, while they are both below 0.20 and less significant when using Combination 2. In particular, those for South America are above 0.40 and significant exceeding the 99% confidence level when using Combination 1; however, they are just above 0.10 and not significant when using Combination 2. This may cause confusion and reduce the reliability of the above findings. Therefore, it is quite necessary to make it clear what leads to this discrepancy and to what extent it would influence the reliability of our findings. These aspects will be discussed in the following section.

4. Comparison between Combinations 1 and 2

The differences of the variability–predictability relationships between those obtained from Combinations 1 and 2 are substantially caused by the distinctions between the two combinations. The two combinations differ from each other mainly in three aspects, which respectively are the different periods, the different model ensembles, and the different verification datasets. With that in mind, three computations and comparisons were carried out to understand the impacts of these three artificial factors on the relationship between variability and predictability, and thus examine the reliability of the above findings. Considering the CRU precipitation contains only land data, the six continental areas are taken into account for a qualified comparison.

To evaluate the sensitivity of the interrelationships between variability and predictability to different periods, the CCa and CCb were computed for the period 1980–2001 using Ensemble 2 and the verification datasets of CRU, in contrast to those for period 1959–2001 using Combination 2. As can be seen in Figure 6(a), the differences of CCa and/or CCb between the two periods are mostly below or near the 95% confidence level. In particular, the CCa and CCb of Africa for 1980–2001 are nearly equal to those for 1959–2001. Compared to 1959–2001, the CCa and CCb of East Asia and Europe are lower for 1980–2001, while those of Australia and South America are higher. In addition, the negative CCa and CCb of North America are greater for 1980–2001. However, these differences between the two periods are most significant for South America, the CCa and CCb of which are both above 0.30 for 1980–2001 but below 0.20 for 1959–2001. Moreover, the CCa of North America, CCb of Europe, and CCa of Australia appear to differ significantly between the two periods, at the 95% confidence level. Thus, it can be inferred that there may be a significant interdecadal distinction of the interrelationship between variability and predictability for South America, while less prominent for the other areas. Whereas, it should be noted that this inference is merely as far as these two periods are concerned, and might be different for other periods.

Figure 6.

(a) The CCa and CCb for the period 1959–2001 versus those for the period 1980–2001, using the same ensemble (Ensemble 2) and verification datasets (CRU). (b) The CCa and CCb using Ensemble 1 versus those using Ensemble 2, for the same period (1980–2001) and verification datasets (GPCP). (c) The CCa and CCb with verification datasets of CRU versus those of GPCP, for the same period (1980–2001) and ensemble (Ensemble 2). Symbols outside the grey shaded areas indicate the differences caused by modulated (a) periods, (b) model ensembles, (c) verification datasets are significant above the 95% confidence level (Brandner, 1933). Since the number of grids for the six areas differs, which is an influencing factor for the test of significance, the 95% confidence area (outside of grey areas) is given as the intersection of those for the six areas

Second, the impact of different ensembles is evaluated by contrasting the CCa and CCb obtained using Ensemble 1 with that using Ensemble 2, based on the same period (1980–2001) and verification datasets (GPCP). As shown in Figure 6(b), both the CCa and CCb for East Asia, Australia, and Europe are higher when using Ensemble 1 than Ensemble 2, implying that the interrelationship between variability and predictability tends to be closer for these areas when using Ensemble 1. On the other hand, the CCa for North America, the CCb for Africa, and both CCa and CCb for South America are slightly lower when using Ensemble 1. Generally, an ensemble containing a larger number of members would lead to an improved prediction skill. Here, it seems this is also conducive to a tightened connection between variability and predictability, for most domains. However, these discrepancies of CCa and/or CCb caused by different ensembles are fairly small, nearly all below the 95% significance level, except the CCb of Europe. Thus, it appears that modulated ensembles would have a rather weak impact on the correlation between variability and predictability in this regard, in spite of the fact that this correlation tends to be more evident for most areas when using a larger ensemble.

Finally, the impact due to different verification datasets on the correlation between variability and predictability is estimated. Figure 6(c) shows the CCa and CCb with verification datasets of CRU versus those of GPCP, both using Ensemble 2 for the period 1980–2001. It can be seen that nearly all the magnitudes of CCa and CCb are greater when using GPCP precipitation as verification datasets than using CRU precipitation, except the CCa of Australia. This discrepancy resulting from different verification datasets is prominent for East Asia and South America, significant at the 95% confidence level. In particular, the CCb for Europe is reaching 0.40 when GPCP precipitation is used as verification datasets, but below 0.10 when CRU precipitation is used instead. Thus, the differences between GPCP and CRU precipitation might have been a key factor that caused the discrepancies of CCa and/or CCb between Combinations 1 and 2. These two datasets differ in several respects. The CRU precipitation is constructed based on global meteorological station records, while the GPCP precipitation also incorporates precipitation estimates from satellite data. In addition, different algorithms for interpolation of station records into grid data have been utilized for the two datasets, with a resolution of 0.5° × 0.5° and 2.5° × 2.5° for CRU and GPCP precipitation, respectively. It is hard to say which one of the two datasets is more realistic. Nonetheless, the positive correlation between variability and predictability for most areas and the negative correlation for North America remain basic facts.

Therefore, the strength of the interrelationship between JJA mean precipitation variability and predictability is influenced by the above three artificial factors in varying ways and to different degrees. On the whole, the discrepancies caused by varying periods, ensembles and verification datasets are mostly within acceptable small ranges. Specifically, the great discrepancy of CCa and CCb for South America between Combinations 1 and 2 (shown in Figure 5) could be principally attributed to the different temporal periods. It could be inferred that, for a specified period, the prediction skills of a larger multi-model ensemble would probably have a tighter connection with the observed variability, possibly more significant when it is verified with respect to GPCP precipitation. However, it depends on circumstances. Moreover, it would be useful in future work to make it clear which out of the CRU and GPCP precipitation datasets is more realistic with respect to a given period and region. This calls for further studies.

5. Roles of climate signals

It is quite important to clarify whether or not this interrelationship between variability and predictability is independent of dynamical processes in the climate system, which could be denoted by climate signals like ENSO or NAO. This is because, if it is, a simple empirical relationship between variability and predictability could be built for a specified domain, as an empirical reference for improving forecasts, unconcerned with physical processes; if not, this relationship should be reconsidered to be more complicated than it appears, involved in a three-way relationship between variability, dynamics, and predictability.

In this section, the potential contribution of ENSO and some other climate signals to this relationship is assessed, which could be either positive or negative. Their contribution to the variability is denoted by ΔSD that is given by the original SD minus that after exclusion of the signals, and the contribution to predictability is denoted by ΔACC and/or ΔMSSS given in the same way. Hence, the corresponding contribution to the interrelationship between variability and predictability can be preliminarily assessed with a view to the pattern correlation coefficients between ΔSD and ΔACC and/or ΔMSSS, given by:

equation image(9)
equation image(10)

The ENSO signal was fully excluded through successively eliminating signals of Nino1 + 2, Nino3, Nino3.4, Nino4, and SO indices of the prior winter, spring, and concurrent summer from the original Combinations 1 and 2.

Results of variability (not shown) indicate that ENSO has made a remarkable contribution to global JJA precipitation variability, with a significant contribution in the tropical Pacific region and the maritime continent. It has also contributed notably to the variability over the western Pacific and monsoonal regions of East Asia.

The contribution to predictability was assessed by the ΔACC and ΔMSSS caused by ENSO. It was found that ENSO has made a significant contribution to the predictability in the tropical Pacific region and the maritime continent, indicating that ENSO is a key contributor for these areas to remain high predictability in terms of JJA precipitation. In addition, the predictability of JJA precipitation in a large part of East Asia, western North America and East Australia has also been enhanced due to ENSO, represented by a positive ΔACC and/or ΔMSSS. On the other hand, the predictability has been reduced in several domains due to ENSO, including coastal East China, Central Australia, and eastern North America, represented by a negative ΔACC and/or ΔMSSS. These indicate that the ENSO signal has both positive and negative contribution to the prediction skills of JJA precipitation around the globe, varying from region to region. However, it has been found that ENSO has made a uniformly positive contribution to the interannual variability of JJA precipitation on a global scale, to various extents. In light of this, it appears to not support the hypothesis that ENSO contributes to the positive correlation between variability and predictability. Nevertheless, further analysis would show that ENSO probably plays an important role in constructing this interrelationship between variability and predictability.

Figure 7 shows the ΔACC and ΔMSSS versus the ΔSD due to ENSO obtained from Combinations 1 and 2. As can be seen, for the ΔACC and ΔMSSS of both combinations, there is a dense mass of positive and negative values scattered in the lower ΔSD belts, from which it can be inferred that there is a strong uncertainty regarding ENSO's contribution to the predictability in areas where ENSO makes little contribution to the variability. However, as the ΔSD increases, the ΔACC and/or ΔMSSS presents an ascending trend to be above zero, nearly all values of which are positive in the higher ΔSD belts. This indicates that ENSO tends to make a positive contribution to the predictability in areas where it makes a greater contribution to the variability. The corresponding CCa and CCb for Combination 1 are 0.38 and 0.49, respectively (Figure 7(a) and (d)), while those for Combination 2 are both 0.27 (Figure 7(c) and (f)), all significant at the 99% confidence level, indicating a good agreement between the variability contribution and predictability contribution made by ENSO. In addition, when only land grids are considered (Figure 7(b) and (e)), the CCa and CCb of Combination 1 remain a high value of 0.33 and 0.46, respectively, a little lower than those when both ocean and land grids are considered, implying that ENSO exerts a nearly equivalent influence on the variability–predictability relationship over ocean and land areas.

Figure 7.

Scatterplot of ΔACC and/or ΔMSSS versus ΔSD due to ENSO

Therefore, it seems that ENSO contributes to building a ‘larger variability–better predictability’ relationship by enhancing, relatively, the predictability of JJA precipitation where its variability is prominently influenced by ENSO, while it makes an uncertain contribution to the predictability in those areas less influenced by ENSO. Furthermore, it is found that signals like the AO and NAO probably contribute to this interrelationship between variability and predictability in a similar way. However, as domains around the globe are influenced by varying signals to varying extents, presumably a distinct contribution should have been made by different signals to different domains.

As a matter of fact, ENSO and NAO are among the most prominent signals in the Earth's climate system, which respectively occur over the Pacific and Atlantic oceans, and both have a wide influence on the global climate. To make a comparison between the contribution made by ENSO and NAO on this issue, the CCa and CCb with respect to ΔSD and ΔACC and/or ΔMSSS were computed for both signals. As shown in Figure 8, the CCa and/or CCb of ENSO are fairly high for Australia, South America, and Europe, followed by East Asia and Africa (Figure 8(a)), while those of NAO are relatively lower and less significant (Figure 8(b)), implying that ENSO might have more to do with the ‘larger variability–better predictability’ relationship in these areas than NAO. In contrast, the CCa and CCb of NAO for North America, especially those obtained from Combination 2, are negative and significant, while those of ENSO are mostly non-significant small positive values. This could be indicative of a relatively tighter connection between NAO and the unusually negative correlation of variability and predictability for North America, rather than ENSO. In addition, it is noteworthy that although the CCa and CCb of NAO are generally smaller than those of ENSO for Europe, South America, and Australia, the NAO signal seems to also play an important role in this very relationship for these three domains, but has less to do with East Asia and Africa.

Figure 8.

CCa and/or CCb between ΔSD and ΔACC and/or ΔMSSS for (a) ENSO and (b) NAO for East Asia (10–60°N, 70–140°E); Australia (40–10°S, 110–155°E); North America (30–70°N, 130–60°W); South America (60°S–10°N, 80–35°W); Europe (30–70°N, 30°W–45°E); and Africa (35°S–30°N, 20°W–50°E). The ENSO and NAO signals of the prior winter, spring and concurrent summer were excluded for the computation of corresponding ΔSD, ΔACC and ΔMSSS

Furthermore, the contribution of some other signals that have relationships with interannual variability of global climate, such as AAO, was also evaluated and compared. It was learned that distinct signals seem to make different contributions to this interrelationship for different areas. Nonetheless, it remains an open question as to why North America, as well as the corresponding contribution by NAO for this area, is so different from other areas on this issue. This needs further investigation to yield a deeper insight.

6. Conclusions and discussions

The statistical interrelationship between the variability and predictability of JJA mean precipitation has been estimated in this study. It was found that there exists a globally positive correlation between the two, which is more marked in low latitudes and less evident in high latitudes. Although this correlation varies with the verification datasets, multi-model ensembles, and temporal periods, a significantly positive correlation between variability and predictability was found for East Asia, Australia, South America, Europe, and Africa, while significantly negative for North America, under most circumstances.

Dynamical processes denoted by climate signals seem to have made their own contribution to building this ‘larger variability–better predictability’ relationship. Generally, this is possibly done through enhancing, relatively, the predictability in areas where there is a larger contribution by the climate signals to variability, while the contribution to predictability is of great uncertainty for those areas with a smaller contribution to variability by climate signals. On a global scale, ENSO, the largest signal in interannual climate variation (Wang et al., 1999), tends to be an important contributor to this relationship for Australia, South America, Europe, East Asia, and Africa; and, there is a good possibility that NAO has a closer connection with that of North America. Hence, such physical factors (e.g. ENSO, NAO, AO, AAO, and many others) exerting influences upon the interannual variability of global climate seem to be important for the construction of this relationship, and would affect that of various domains differently.

However, it should be noted that this varying relationship is of great uncertainty with respect to domains of the regional scale. For example, the interannual variability of JJA mean precipitation in Southeast China is prominent, but the corresponding predictability there is relatively low. Therefore, it is better to understand this ‘larger variability–better predictability’ relationship in view of probability, especially when the regional scale is concerned.

In addition, all the results above are focused on the boreal summer precipitation. A further investigation concerning other seasons and the relevant seasonal variation of this relationship is under way. The preliminary results have shown similar features of other seasons on the global scale as in this article, but the significance of this relationship for specified areas and the corresponding contribution of climate signals seem to differ evidently among seasons.

Above all, this finding is promising to provide an empirical reference for estimating the reliability of forecasts, and might further be taken into account for improving simulated forecasts by statistical means. Moreover, a deeper insight into the nature of the three-way relationship between variability, climate signals, and predictability could be important for improvements in climate models. Goswami and Xavier (2005) argued that the interannual variability governed by unpredictable internal processes is an important reason of poor predictability, while the interannual variability depending on external boundary forcing is generally related with high predictability. This signifies that there might be different relationships between predictability and variability from different origins, which maybe originated from internal process or external forcing. These all call for further research to be carried out.

Acknowledgements

This research was supported by the National Basic Research Program of China (Grant No. 2010CB950304) and the Special Fund for Public Welfare Industry (meteorology) (GYHY200906018).

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