Papers on diurnal temperature range

This is a list of papers on the diurnal temperature range (daily maximum and minimum temperatures), both global and regional papers are included. The list is not complete, and will most likely be updated in the future in order to make it more thorough and more representative.

Associations of diurnal temperature range change with the leading climate variability modes during the Northern Hemisphere wintertime and their implication on the detection of regional climate trends – Wu (2010) “This study examines associations of diurnal temperature range (DTR) changes in observations at the global, hemispheric, subcontinental, and grid box scales with five leading climate variability modes, including the Arctic Oscillation (AO), hemispheric Pacific–North America (PNA)–like mode, Pacific Decadal Oscillation, El Niño Southern Oscillation (ENSO), and Antarctic Oscillation (AAO) during the Northern Hemisphere winter season (Jan–Mar). Winter DTR variability in most subcontinental regions is significantly related to variations in either the AO, or hemispheric PNA-like mode, or ENSO index in the Northern Hemisphere. In the Southern Hemisphere, the DTR variability appears closely coupled with variations in the ENSO and AAO. From 1951 to 2000, variations in the circulation patterns account for a significant fraction of the DTR increase at all scales although the strength of these associations varies geographically. After removing the linearly congruent component of leading climate variability modes from the total wintertime DTR trends in the observations, statistically significant residual trends in DTR are still found at the global, hemispheric, and most subcontinental regions. Ensemble mean multimodel averaged DTR trends to major anthropogenic and natural forcing are significantly smaller than not only observed total DTR trends but also residual trends at these large scales. The implication of changes in the leading climate variability modes on the detection of regional DTR trends is discussed. We find that the detection of the regional response to combined anthropogenic and natural forcing is robust to the exclusion of trends related to changes of the five modes considered here.” Wu, Q. (2010), J. Geophys. Res., 115, D19101, doi:10.1029/2010JD014026.

Detection and attribution of anthropogenic forcing to diurnal temperature range changes from 1950 to 1999: comparing multi-model simulations with observations – Zhou et al. (2009) “Observations show that the surface diurnal temperature range (DTR) has decreased since 1950s over most global land areas due to a smaller warming in maximum temperatures (T max) than in minimum temperatures (T min). This paper analyzes the trends and variability in T max, T min, and DTR over land in observations and 48 simulations from 12 global coupled atmosphere-ocean general circulation models for the later half of the 20th century. It uses the modeled changes in surface downward solar and longwave radiation to interpret the modeled temperature changes. When anthropogenic and natural forcings are included, the models generally reproduce observed major features of the warming of T max and T min and the reduction of DTR. As expected the greenhouse gases enhanced surface downward longwave radiation (DLW) explains most of the warming of T max and T min while decreased surface downward shortwave radiation (DSW) due to increasing aerosols and water vapor contributes most to the decreases in DTR in the models. When only natural forcings are used, none of the observed trends are simulated. The simulated DTR decreases are much smaller than the observed (mainly due to the small simulated T min trend) but still outside the range of natural internal variability estimated from the models. The much larger observed decrease in DTR suggests the possibility of additional regional effects of anthropogenic forcing that the models can not realistically simulate, likely connected to changes in cloud cover, precipitation, and soil moisture. The small magnitude of the simulated DTR trends may be attributed to the lack of an increasing trend in cloud cover and deficiencies in charactering aerosols and important surface and boundary-layer processes in the models.” Liming Zhou, Robert E. Dickinson, Aiguo Dai and Paul Dirmeyer, Climate Dynamics, Volume 35, Numbers 7-8, 1289-1307, DOI: 10.1007/s00382-009-0644-2. [Full text]

Diurnal temperature range over Europe between 1950 and 2005 – Makowski et al. (2008) “It has been widely accepted that diurnal temperature range (DTR) decreased on a global scale during the second half of the twentieth century. Here we show however, that the long-term trend of annual DTR has reversed from a decrease to an increase during the 1970s in Western Europe and during the 1980s in Eastern Europe. The analysis is based on the high-quality dataset of the European Climate Assessment and Dataset Project, from which we selected approximately 200 stations covering the area bordered by Iceland, Algeria, Turkey and Russia for the period 1950 to 2005. We investigate national and regional annual means as well as the pan-European mean with respect to trends and reversal periods. 17 of the 24 investigated regions including the pan-European mean show a statistical significant increase of DTR since 1990 at the latest. Of the remaining 7 regions, two show a non-significant increase, three a significant decrease and two no significant trend. Changes in DTR are affected by both surface shortwave and longwave radiation, the former of which has undergone a change from dimming to brightening in the period considered. Consequently, we discuss the connections between DTR, shortwave radiation and sulfur emissions which are thought to be amongst the most important factors influencing the incoming solar radiation through the primary and secondary aerosol effect. We find reasonable agreement between trends in SO2 emissions, radiation and DTR in areas affected by high pollution. Consequently, we conclude that the trends in DTR could be mostly determined by changes in emissions and the associated changes in incoming solar radiation.” Makowski, K., Wild, M., and Ohmura, A., Atmos. Chem. Phys., 8, 6483-6498, doi:10.5194/acp-8-6483-2008, 2008. [Full text]

Impact of global dimming and brightening on global warming – Wild et al. (2007) “Speculations on the impact of variations in surface solar radiation on global warming range from concerns that solar dimming has largely masked the full magnitude of greenhouse warming, to claims that the recent reversal from solar dimming to brightening rather than the greenhouse effect was responsible for the observed warming. To disentangle surface solar and greenhouse influences on global warming, trends in diurnal temperature range are analyzed. They suggest that solar dimming was effective in masking greenhouse warming, but only up to the 1980s, when dimming gradually transformed into brightening. Since then, the uncovered greenhouse effect has revealed its full dimension, as manifested in a rapid temperature rise (+0.38°C/decade over land since mid-1980s). Recent solar brightening cannot supersede the greenhouse effect as main cause of global warming, since land temperatures increased by 0.8°C from 1960 to 2000, even though solar brightening did not fully outweigh solar dimming within this period.” Wild, M., A. Ohmura, and K. Makowski (2007), Geophys. Res. Lett., 34, L04702, doi:10.1029/2006GL028031. [Full text]

Maximum and minimum temperature trends for the globe: An update through 2004 – Vose et al. (2005) “New data acquisitions are used to examine recent global trends in maximum temperature, minimum temperature, and the diurnal temperature range (DTR). On average, the analysis covers the equivalent of 71% of the total global land area, 17% more than in previous studies. Consistent with the IPCC Third Assessment Report, minimum temperature increased more rapidly than maximum temperature (0.204 vs. 0.141°C dec⁻¹) from 1950–2004, resulting in a significant DTR decrease (−0.066°C dec⁻¹). In contrast, there were comparable increases in minimum and maximum temperature (0.295 vs. 0.287°C dec⁻¹) from 1979–2004, muting recent DTR trends (−0.001°C dec⁻¹). Minimum and maximum temperature increased in almost all parts of the globe during both periods, whereas a widespread decrease in the DTR was only evident from 1950–1980.” Vose, R. S., D. R. Easterling, and B. Gleason (2005), Maximum and minimum temperature trends for the globe: An update through 2004, Geophys. Res. Lett., 32, L23822, doi:10.1029/2005GL024379. [Short version of the article]

Diurnal temperature range as an index of global climate change during the twentieth century – Braganza et al. (2004) “The usefulness of global-average diurnal temperature range (DTR) as an index of climate change and variability is evaluated using observations and climate model simulations representing unforced climate variability and anthropogenic climate change. On decadal timescales, modelled and observed intrinsic variability of DTR compare well and are independent of variations in global mean temperature. Observed reductions in DTR over the last century are large and unlikely to be due to natural variability alone. Comparison of observed and anthropogenic-forced model changes in DTR over the last 50 years show much less reduction in DTR in the model simulations due to greater warming of maximum temperatures in the models than observed. This difference is likely attributed to increases in cloud cover that are observed over the same period and are absent in model simulations.” Braganza, K., D. J. Karoly, and J. M. Arblaster (2004), Geophys. Res. Lett., 31, L13217, doi:10.1029/2004GL019998. [Full text]

Daily maximum and minimum temperature trends in a climate model – Stone & Weaver (2003) “The recent observed global warming trend over land has been characterised by a faster warming at night, leading to a considerable decrease in the diurnal temperature range (DTR). Analysis of simulations of a climate model including observed increases in greenhouse gases and sulphate aerosols reveals a similar trend in the DTR of −0.2°C per century, albeit of smaller magnitude than the observed −0.8°C per century. This trend in the model simulations is related to changes in cloud cover and soil moisture. These results indicate that the observed decrease in the DTR could be a signal of anthropogenic forcing of recent climate change.” Stone, D. A., and A. J. Weaver (2002), Geophys. Res. Lett., 29(9), 1356, doi:10.1029/2001GL014556. [Full text]

Effects of Clouds, Soil Moisture, Precipitation, and Water Vapor on Diurnal Temperature Range – Dai et al. (1999) “The diurnal range of surface air temperature (DTR) has decreased worldwide during the last 4–5 decades and changes in cloud cover are often cited as one of the likely causes. To determine how clouds and moisture affect DTR physically on daily bases, the authors analyze the 30-min averaged data of surface meteorological variables and energy fluxes from the the First International Satellite Land Surface Climatology Project Field Experiment and the synoptic weather reports of 1980–1991 from about 6500 stations worldwide. The statistical relationships are also examined more thoroughly in the historical monthly records of DTR, cloud cover, precipitation, and streamflow of this century. It is found that clouds, combined with secondary damping effects from soil moisture and precipitation, can reduce DTR by 25%–50% compared with clear-sky days over most land areas; while atmospheric water vapor increases both nighttime and daytime temperatures and has small effects on DTR. Clouds, which largely determine the geographic patterns of DTR, greatly reduce DTR by sharply decreasing surface solar radiation while soil moisture decreases DTR by increasing daytime surface evaporative cooling. Clouds with low bases are most efficient in reducing the daytime maximum temperature and DTR mainly because they are very effective in reflecting the sunlight, while middle and high clouds have only moderate damping effects on DTR. The DTR reduction by clouds is largest in warm and dry seasons such as autumn over northern midlatitudes when latent heat release is limited by the soil moisture content. The net effects of clouds on the nighttime minimum temperature is small except in the winter high latitudes where the greenhouse warming effect of clouds exceeds their solar cooling effect. The historical records of DTR of the twentieth century covary inversely with cloud cover and precipitation on interannual to multidecadal timescales over the United States, Australia, midlatitude Canada, and former U.S.S.R., and up to 80% of the DTR variance can be explained by the cloud and precipitation records. Given the strong damping effect of clouds on the daytime maximum temperature and DTR, the well-established worldwide asymmetric trends of the daytime and nighttime temperatures and the DTR decreases during the last 4–5 decades are consistent with the reported increasing trends in cloud cover and precipitation over many land areas and support the notion that the hydrologic cycle has intensified.” Dai, Aiguo, Kevin E. Trenberth, Thomas R. Karl, 1999: Effects of Clouds, Soil Moisture, Precipitation, and Water Vapor on Diurnal Temperature Range. J. Climate, 12, 2451–2473, doi: 10.1175/1520-0442(1999)0122.0.CO;2. [Full text]

Maximum and Minimum Temperature Trends for the Globe – Easterling et al. (1997) “Analysis of the global mean surface air temperature has shown that its increase is due, at least in part, to differential changes in daily maximum and minimum temperatures, resulting in a narrowing of the diurnal temperature range (DTR). The analysis, using station metadata and improved areal coverage for much of the Southern Hemisphere landmass, indicates that the DTR is continuing to decrease in most parts of the world, that urban effects on globally and hemispherically averaged time series are negligible, and that circulation variations in parts of the Northern Hemisphere appear to be related to the DTR. Atmospheric aerosol loading in the Southern Hemisphere is much less than that in the Northern Hemisphere, suggesting that there are likely a number of factors, such as increases in cloudiness, contributing to the decreases in DTR.” David R. Easterling, Briony Horton, Philip D. Jones, Thomas C. Peterson, Thomas R. Karl, David E. Parker, M. James Salinger, Vyacheslav Razuvayev, Neil Plummer, Paul Jamason and Christopher K. Folland, Science 18 July 1997, Vol. 277 no. 5324 pp. 364-367, DOI: 10.1126/science.277.5324.364. [Full text]

The Influence of Land Use/Land Cover on Climatological Values of the Diurnal Temperature Range – Gallo et al. (1996) “The diurnal temperature range (DTR) at weather observation stations that make up the U.S. Historical Climatology Network was evaluated with respect to the predominant land use/land cover associated with the stations within three radii intervals (100, 1000, and 10 000 m) of the stations. Those stations that were associated with predominantly rural land use/land cover (LULC) usually displayed the greatest observed DTR, whereas those associated with urban related land use or land cover displayed the least observed DTR. The results of this study suggest that significant differences in the climatological DTR were observed and could be attributed to the predominant LULC associated with the observation stations. The results also suggest that changes in the predominant LULC conditions, within as great as a 10 000 m radius of an observation station, could significantly influence the climatological DTR. Future changes in the predominant LULC associated with observation sites should be monitored similar to the current practice of monitoring changes in instruments or time of observation at the observations sites.” Gallo, Kevin P., David R. Easterling, Thomas C. Peterson, 1996, J. Climate, 9, 2941–2944. [Full text]

Southwest Pacific temperatures: trends in maximum and minimum temperatures – Salinger (1995) “Diurnal temperature trends are described for newly homogenised climate data sets for a large area of the South Pacific. The diurnal trends differ from those documented for Northern Hemisphere land areas, where decreases are observed in the diurnal temperature range as a result of increases principally in minimum temperature. The Southwest Pacific divides into four regions that share coherent diurnal temperature trends over the past five decades. Two regions southwest of the South Pacific Convergence Zone (SPCZ) display steady warming in mean temperature. The other two regions, located northeast of the SPCZ, cooled in the 1970’s and warmed in the 1980’s. The warming in three of the four regions can be attributed to increases in both mean daily maximum (mostly daytime) and mean daily minimum (mostly night time) temperature, with little change in the diurnal temperature range. In New Zealand, modification of the regional temperature trend occurs as atmospheric circulation interacts with the high orography, producing different local behaviour in trends of maximum and minimum temperature and diurnal temperature range. The present results come from sites where there can be no question of any urban influence. Most of the Southwest Pacific sites provide a very good climate monitoring platform for the surrounding oceans because of their island location.” M. J. Salinger, Atmospheric Research, Volume 37, Issues 1-3, July 1995, Pages 87-99, doi:10.1016/0169-8095(94)00071-K. [Full text]

Recent variations in mean temperature and the diurnal temperature range in the Antarctic – Jones (1995) “Monthly mean surface temperature data are available from nearly twenty stations for the period since the International Geophysical Year 1957. All but three stations show an increase in mean temperatures over this time, amounting in the average to 0.57°C over 1957 to 1994. All of this warming occurred before the early 1970s. Since then, there has been no change. The warming has been greatest in the Antarctic Peninsula. Analyses of the less‐widely available diurnal temperature range (DTR) (maximum‐minimum) data show regions of increase and decrease over Antarctica. An average continental DTR series shows no trend over 1957 to 1992. Analyses for six mid‐to‐high latitude Southern Ocean islands show increases in mean temperature over 1961–90. Given the low year‐to‐year variability in these data, these trends are more significant than for any of the stations on the Antarctic continent. The marked decrease in mean temperatures over Antarctica during 1993 and 1994 seems unrelated to sea‐ice variations which show little change since the early 1980s.” Jones, P. D. (1995), Geophys. Res. Lett., 22(11), 1345–1348, doi:10.1029/95GL01198.

Asymmetric diurnal temperature change in the Alpine Region – Weber et al. (1994) “By now there is general agreement that the annual mean temperature of earth’s surface has increased during the last century. Recently, it has become obvious that this warming is quite inhomogeneous in various respects. Besides the spatial and seasonal variability of the temperature trend a diurnal asymmetry of increase has been observed. In large continental regions the annual mean of the daily minimum temperature has increased noticeably faster than the annual mean of the daily maximum. The same behaviour is found in the present study for low‐lying stations in Central Europe. However, data from mountain top stations show a similar increase for both minimum and maximum of daily temperatures. No diurnal asymmetry was observed for these stations. The good agreement of the time series from different mountain stations leads us to believe that the observed trends of minimum and maximum temperature are not caused by particular local influences or observation errors. An analysis of monthly and seasonal means shows that most of the warming took place in fall.” Weber, R. O., P. Talkner, and G. Stefanicki (1994), Geophys. Res. Lett., 21(8), 673–676, doi:10.1029/94GL00774. [Full text]

Nighttime warming and the greenhouse effect – Kukla & Karl (1993) No abstract.

A New Perspective on Recent Global Warming: Asymmetric Trends of Daily Maximum and Minimum Temperature – Karl et al. (1993) “Monthly mean maximum and minimum temperatures for over 50% (10%) of the Northern (Southern) Hemisphere landmass, accounting for 37% of the global landmass, indicate that the rise of the minimum temperature has occurred at a rate three times that of the maximum temperature during the period 1951–90 (0.84°C versus 0.28°C). The decrease of the diurnal temperature range is approximately equal to the increase of mean temperature. The asymmetry is detectable in all seasons and in most of the regions studied. The decrease in the daily temperature range is partially related to increases in cloud cover. Furthermore, a large number of atmospheric and surface boundary conditions are shown to differentially affect the maximum and minimum temperature. Linkages of the observed changes in the diurnal temperature range to large-scale climate forcings, such as anthropogenic increases in sulfate aerosols, greenhouse gases, or biomass burning (smoke), remain tentative. Nonetheless, the observed decrease of the diurnal temperature range is clearly important, both scientifically and practically.” Karl, Thomas R., and Coauthors, 1993, Bull. Amer. Meteor. Soc., 74, 1007–1023. [Full text]

Southwest Pacific temperatures: Diurnal and seasonal trends – Salinger et al. (1993) “Temperature trends are presented for a large part of the southwest Pacific. The trends differ from those documented for Northern Hemisphere land areas, where warming has occurred mainly through increases in minimum temperature. The New Zealand patterns are derived from recently completed analyses of monthly and annual mean maximum and minimum surface temperature records for a newly homogenised historical climate data series for New Zealand and outlying islands. They indicate that the warming in the New Zealand region over the past five decades can be attributed to increases in both mean maximum (mostly daytime) and mean minimum (mostly night time) temperature. All seasons show a temperature increase, with the largest occurring in summer (DJF). Northern Hemisphere evidence suggests that changes in cloud cover and the presence of sulfate aerosols plays a direct role. The present results imply that, while the observed warming in a large portion of the Northern Hemisphere landmass may be significantly affected by both these factors, sulfate aerosol effects may be less important in the Southern Hemisphere.” Salinger, M. J., J. Hay, R. McGann, and B. Fitzharris (1993), Geophys. Res. Lett., 20(10), 935–938, doi:10.1029/93GL01113.

Global warming: Evidence for asymmetric diurnal temperature change – Karl et al. (1990) “Analyses of the year‐month mean maximum and minimum surface thermometric record have now been updated and expanded to cover three large countries in the Northern Hemisphere (the contiguous United States, the Soviet Union, and the People’s Republic of China). They indicate that most of the warming which has occurred in these regions over the past four decades can be attributed to an increase of mean minimum (mostly nighttime) temperatures. Mean maximum (mostly daytime) temperatures display little or no warming. In the USA and the USSR (no access to data in China) similar characteristics are also reflected in the changes of extreme seasonal temperatures, e.g., increase of extreme minimum temperatures and little or no change in extreme maximum temperatures. The continuation of increasing minimum temperatures and little overall change of the maximum leads to a decrease of the mean (and extreme) temperature range, an important measure of climate variability. The cause(s) of the asymmetric diurnal changes are uncertain, but there is some evidence to suggest that changes in cloud cover plays a direct role (where increases in cloudiness result in reduced maximum and higher minimum temperatures). Regardless of the exact cause(s), these results imply that either: (1) climate model projections considering the expected change in the diurnal temperature range with increased levels of the greenhouse gases are underestimating (overestimating) the rise of the daily minimum (maximum) relative to the maximum (minimum), or (2) the observed warming in a considerable portion of the Northern Hemisphere landmass is significantly affected by factors unrelated to an enhanced anthropogenically‐induced greenhouse effect.” Karl, T. R., G. Kukla, V. N. Razuvayev, M. J. Changery, R. G. Quayle, R. R. Heim Jr., D. R. Easterling, and C. B. Fu (1991), Geophys. Res. Lett., 18(12), 2253–2256, doi:10.1029/91GL02900.

Is Recent Climate Change Across the United States Related to Rising Levels of Anthropogenic Greenhouse Gases? – Plantico et al. (1990) “Global warming as a result of rising concentrations of anthropogenic greenhouse gases is predicted by current climate models. During the period 1948–1987, the concentration of anthropogenic greenhouse gases increased by more than 30%, and the mean annual temperature of the northern hemisphere increased by about 0.15°C. The mean annual temperature of the contiguous United States, however, does not show any significant trend. To gain a better understanding of why the United States’ temperature record does not reflect the anticipated greenhouse warming, we studied the inter-relationships between trends of temperature, cloudiness, sunshine and precipitation. Both the seasonal and annual trends for 23 geographic regions covering the United States were analyzed using Monte Carlo field significance tests. Several seasonal and regional differences were noted. While winters and autumns cooled, springs and summers warmed. Annually, cooling has occurred across the eastern half of the country, while warming dominates in the West. The largest changes in maximum temperature, daily temperature range, cloud amount, percent of possible sunshine and precipitation occur during autumn. Autumn also has the most significant correlations between trends. We found that the recent decrease of the maximum temperature and daily temperature range in autumn is statistically associated with increasing cloud amount and precipitation, and with decreasing sunshine. The widespread reduction in the temperature range is a result of decreased maximum and increased minimum temperatures. Cloud amount increased over most of the country during all seasons except spring. During spring the cloud amount remained fairly constant even though precipitation increased. Interestingly, no significant correlation was found between trends of mean temperature and cloud amount. Although several features of the recent climate change across the United States agree qualitatively with the model-predicted impact of increasing anthropogenic greenhouse gases, the regional and seasonal distribution of the observed trends do not appear in line with the model results. We conclude that either the recent changes of temperature, cloud amount, sunshine and precipitation over the United States are as yet unrelated to the increasing anthropogenic greenhouse gases, or that the transient response of regional climates to the greenhouse effect is not proportional to the modeled difference between the 1 × CO2 and 2 × CO2 equilibrium climates.” Plantico, M. S., T. R. Karl, G. Kukla, and J. Gavin (1990), J. Geophys. Res., 95(D10), 16,617–16,637, doi:10.1029/JD095iD10p16617.

Relationship between Decreased Temperature Range and Precipitation Trends in the United States and Canada, 1941–80 – Karl et al. (1986) “Previous work has shown significant decreases of the diurnal temperature range (1941–80) across a network of 130 stations in the United States and Canada. In the present study, changes in monthly total precipitation at these same stations were related to the decrease in temperature range using various Monte Carlo. These tests indicate that factors other than those related to precipitation contributed to the decrease of daily temperature range. Further study of the mechanisms responsible for the decreased temperature range is warranted, based on these results. The decreased range may be one of the few pieces of evidence available in North America that is consistent with potential impacts of increased greenhouse gases and/or anthropogenic aerosols.” Karl, Thomas R., George Kukla, Joyce Gavin, 1986, J. Climate Appl. Meteor., 25, 1878–1886. [Full text]

Decreasing Diurnal Temperature Range in the United States and Canada from 1941 through 1980 – Karl et al. (1984) “An appreciable number of nonurban stations in the United States and Canada have been identified with statistically significant (at the 90% level) decreasing trends in the monthly mean diurnal temperature range between 1941–80. The percentage of stations in the network showing the decrease is higher than expected due to chance throughout the year, with a maximum reached during late summer and early autumn and a minimum in December. Monte Carlo tests indicate that during five months the field significance of the decreasing range is above the 99% level, and in 12 months above the 95% level. There is a negligible probability that such a result is due to chance. In contrast, trends of increasing or decreasing monthly mean maximum or minimum temperatures have at most only two months with field significance at or above the 90% level. This is related to the tendency toward increasing temperature in the western portions of North America and decreasing temperature in the east. The physical mechanism responsible for the observed decrease in the diurnal range is not known. Possible explanations include greenhouse effects such as changes in cloudiness, aerosol loading, atmospheric water vapor content, or carbon dioxide. Change in circulation is also a possibility, but it will be difficult to isolate since the patterns of the decreased diurnal temperature range have high field significance throughout much of the year, relatively low spatial coherence, and occur at many stations where individual trends in the maximum and minimum temperature are not statistically significant. Our data show that the trends in the maximum and minimum temperatures may differ considerably from trends in the mean.” Karl, T. R., G. Kukla, J. Gavin, 1984, J. Climate Appl. Meteor., 23, 1489–1504. [Full text]