Ocean Cooling Resumes

May Sea Surface Temperatures (SSTs) are now available, and we can see ocean cooling resuming after a short pause from the downward trajectory during the previous 12 months.

HadSST is generally regarded as the best of the global SST data sets, and so the temperature story here comes from that source, the latest version being HadSST3.

The chart below shows the last two years of SST monthly anomalies as reported in HadSST3 including May 2017.

After an upward bump in April 2017 due to the Tropics and NH, the May SSTs show the average declining slightly.  Note the Tropics recorded a rise, but not enough to offset declines in both hemispheres and globally.  SH is now two months into a cooling phase. The present readings compare closely with April 2015, but currently with no indication of an El Nino event any time soon.

Note that higher temps in 2015 and 2016 were first of all due to a sharp rise in Tropical SST, beginning in March 2015, peaking in February 2016, and steadily declining back to its beginning level. Secondly, the Northern Hemisphere added two bumps on the shoulders of Tropical warming, with peaks in August of each year. Also, note that the global release of heat was not dramatic, due to the Southern Hemisphere offsetting the Northern one.

Satellite measures of the air over the oceans give a slightly different result.  The graph below provides UAH vs.6 TLT (lower troposphere temps) over the oceans confirming the general impression from SSTs.

In contrast with SST measurements, air temps in the TLT over the oceans upticked in May with all areas participating in the rise of almost 0.2C.  In the satellite dataset, it is quite noticeable that land air temps rose quite strongly and may have caused air temps in the May TLT over oceans to show higher anomalies than the SSTs.

We have seen lots of claims about the temperature records for 2016 and 2015 proving dangerous man made warming.  At least one senator stated that in a confirmation hearing.  Yet HadSST3 data for the last two years show how obvious is the ocean’s governing of global average temperatures.

USS Pearl Harbor deploys Global Drifter Buoys in Pacific Ocean

The best context for understanding these two years comes from the world’s sea surface temperatures (SST), for several reasons:

  • The ocean covers 71% of the globe and drives average temperatures;
  • SSTs have a constant water content, (unlike air temperatures), so give a better reading of heat content variations;
  • A major El Nino was the dominant climate feature these years.

Solar energy accumulates massively in the ocean and is variably released during circulation events.

 

April Pause in Ocean Cooling

 

Ocean temperature measurements come from a global array of 3,500 Argo floats and other ocean sensors. Credits: Argo Program, Germany/Ifremer

April Sea Surface Temperatures are now available, and we can see a pause in the downward trajectory over the previous 13 months.

HadSST is generally regarded as the best of the global SST data sets, and so the temperature story here comes from that source, the latest version being HadSST3.

The chart below shows the last two years of SST monthly anomalies as reported in HadSST3 including April 2017.

In April 2017, the SH appears to be entering its cooler phase, while both the tropics and NH ticked upward from March, causing the Global anomaly to rise for the fourth month in a row.  The downward momentum has stopped, except now the SH (mostly ocean) has started down from a lower peak than a year ago.  It was the SH that was pulling up the Global average the previous three months.   The Tropics and NH may or may not start a new warming cycle, depending upon the appearance of El Nino.

Note that higher temps in 2015 and 2016 were first of all due to a sharp rise in Tropical SST, beginning in March 2015, peaking in January 2016, and steadily declining back to its beginning level. Secondly, the Northern Hemisphere added two bumps on the shoulders of Tropical warming, with peaks in August of each year. Also, note that the global release of heat was not dramatic, due to the Southern Hemisphere offsetting the Northern one.

Satellite measures of the air over the oceans give a similar result.  The graph below provides UAH vs.6 TLT (lower troposphere temps) over the oceans confirming the impression from SSTs.

Once again it is the Tropical and NH oceans that drove the warming that peaked a year ago.  SH  moderated the Global averages, though the air temps over the oceans are more synchronized than is the case with SSTs. Note how in April all anomalies converged on 0.3C.

We have seen lots of claims about the temperature records for 2016 and 2015 proving dangerous man made warming.  At least one senator stated that in a confirmation hearing.  Yet HadSST3 data for the last two years show how obvious is the ocean’s governing of global average temperatures.

The best context for understanding these two years comes from the world’s sea surface temperatures (SST), for several reasons:

  • The ocean covers 71% of the globe and drives average temperatures;
  • SSTs have a constant water content, (unlike air temperatures), so give a better reading of heat content variations;
  • A major El Nino was the dominant climate feature these years.

Solar energy accumulates massively in the ocean and is variably released during circulation events.

 

Fossil Fuels ≠ Global Warming

Previous posts addressed the claim that fossil fuels are driving global warming. This post updates that analysis with the latest numbers from BP Statistics and compares World Fossil Fuel Consumption (WFFC) with three estimates of Global Mean Temperature (GMT). More on both these variables below.

WFFC

2015 statistics are now available from BP for international consumption of Primary Energy sources. Statistical Review of World Energy.  H/T  Euan Mearns

The reporting categories are:
Oil
Natural Gas
Coal
Nuclear
Hydro
Renewables (other than hydro)

This analysis combines the first three, Oil, Gas, and Coal for total fossil fuel consumption world wide. The chart below shows the patterns for WFFC compared to world consumption of Primary Energy from 1965 through 2015.

The graph shows that Primary Energy consumption has grown continuously for 5 decades. Over that period oil, gas and coal (sometimes termed “Thermal”) averaged 90% of PE consumed, ranging from 94% in 1965 to 86% in 2015.  MToe is millions of tons of oil equivalents.

Global Mean Temperatures

Everyone acknowledges that GMT is a fiction since temperature is an intrinsic property of objects, and varies dramatically over time and over the surface of the earth. No place on earth determines “average” temperature for the globe. Yet for the purpose of detecting change in temperature, major climate data sets estimate GMT and report anomalies from it.

UAH record consists of satellite era global temperature estimates for the lower troposphere, a layer of air from 0 to 4km above the surface. HadSST estimates sea surface temperatures from oceans covering 71% of the planet. HADCRUT combines HadSST estimates with records from land stations whose elevations range up to 6km above sea level.

Both GISS LOTI (land and ocean) and HADCRUT4 (land and ocean) use 14.0 Celsius as the climate normal, so I will add that number back into the anomalies. This is done not claiming any validity other than to achieve a reasonable measure of magnitude regarding the observed fluctuations.

No doubt global sea surface temperatures are typically higher than 14C, more like 17 or 18C, and of course warmer in the tropics and colder at higher latitudes. Likewise, the lapse rate in the atmosphere means that air temperatures both from satellites and elevated land stations will range colder than 14C. Still, that climate normal is a generally accepted indicator of GMT.

Correlations of GMT and WFFC

The first graph compares to GMT estimates over the five decades from 1965 to 2015 from HADCRUT4, which includes HadSST3.

Over the last five decades the increase in fossil fuel consumption is dramatic and monotonic, steadily increasing by 220% from 3.5B to 11.3 B oil equivalent tons.  Meanwhile the GMT record from Hadcrut shows multiple ups and downs with an accumulated rise of 0.9C over 50 years, 6% of the starting value.

The second graph compares to GMT estimates from UAH6, and HadSST3 for the satellite era from 1979 to 2015, a period of 36 years.

In the satellite era WFFC has increased at a compounded rate of nearly 2% per year, for a total increase of 84% since 1979. At the same time, SSTs and  lower troposphere warming amounted to 0.5C, or 3.4% of the starting value.  The temperature rate of change is 0.1% per year, an order of magnitude less.  Even more obvious is the 1998 El Nino peak and flat GMT since.

Summary

The climate alarmist/activist claim is straight forward: Burning fossil fuels makes measured temperatures warmer. The Paris Accord further asserts that by reducing human use of fossil fuels, further warming can be prevented.  Those claims do not bear up under scrutiny.

It is enough for simple minds to see that two time series are both rising and to think that one must be causing the other. But both scientific and legal methods assert causation only when the two variables are both strongly and consistently aligned. The above shows a weak and inconsistent linkage between WFFC and GMT.

In legal terms, as long as there is another equally or more likely explanation for the set of facts, the claimed causation is unproven. The more likely explanation is that global temperatures vary due to oceanic and solar cycles. The proof is clearly and thoroughly set forward in the post Quantifying Natural Climate Change.

Background context for today’s post is at Claim: Fossil Fuels Cause Global Warming.

March Air and Sea Temps

The Pause that Refreshes!

The recent El Nino is cooling down as shown clearly in both sea surface temperatures and lower troposphere air temperatures. The two relevant data sets are UAH v.6 and HadSST v3.1, both now providing averages for the month of March 2017.

The cooling pattern continues in the tropical seas while ocean temperatures in the Northern Hemisphere (NH) are  flat.  Southern Hemisphere (SH) oceans appear to be peaking and pulled the Global SST up a bit, but both are slightly below last March.

Air temperatures in the lower troposphere tell much the same story.  The greater volatility of air temperatures is evident, and we also see that the tropics (20N to 20S) and the NH (0 to 90N) are more closely aligned than are the comparable SSTs.  The downward trajectory of air temps is clear after an upward blip in the NH in February.

Enjoy the pause in warmer temperatures while we watch to see how cool it will get.

Ocean Surface Temps–How Low Will They Go?

 

Ocean temperature measurements come from a global array of 3,500 Argo floats and other ocean sensors. Credits: Argo Program, Germany/Ifremer

We have seen lots of claims about the temperature records for 2016 and 2015 proving dangerous man made warming.  At least one senator stated that in a confirmation hearing.  Now that HadSST3 data is complete through February 2017, let’s see how obvious is the ocean’s governing of global average temperatures.

The best context for understanding these last two years comes from the world’s sea surface temperatures (SST), for several reasons:

  • The ocean covers 71% of the globe and drives average temperatures;
  • SSTs have a constant water content, (unlike air temperatures), so give a better reading of heat content variations;
  • A major El Nino was the dominant climate feature the last two years.

HadSST is generally regarded as the best of the global SST data sets, and so the temperature story here comes from that source, the latest version being HadSST3.

The chart below shows the last two years of SST monthly anomalies as reported in HadSST3, along with the first two months of 2017.

Note that higher temps in 2015 and 2016 are first of all due to a sharp rise in Tropical SST, beginning in March 2015, peaking in February 2016, and steadily declining back to its beginning level. Secondly, the Northern Hemisphere added two bumps on the shoulders of Tropical warming, with peaks in August of each year. Also, note that the global release of heat was not dramatic, due to the Southern Hemisphere offsetting the Northern one.

Finally, the oceans are starting 2017 only slightly lower than a year ago, but this year with much cooler Tropics.  Notice that both the Tropics and also the Northern Hemisphere continue to cool.  The Global average warmed slightly, pulled upward by the Southern Hemisphere which reaches its summer peak at this time.

March may repeat 2016 when NH bottomed and SH peaked, or maybe both will rise or both will drop.  In the latter case, perhaps we will see the long-awaited La Nina.

H/T to Global Warming Policy Forum for adding this informative graphic:
|floatcyclescaled

Much ado has been made of this warming, including claims of human causation, despite the obvious oceanic origin. However, it is unreasonable to claim CO2 functions as a global warming agent, yet the two hemispheres respond so differently.  Moreover, CO2 warming theory expects greater warming in the higher latitudes, while this event was driven by heating in the Tropics, contradicting alarmist warming theory.

Solar energy accumulates massively in the ocean and is variably released during circulation events.

 

Fact: Future Climate Will Be Flatter, not Hotter

Another powerful post by Clive Best on how earth’s surface temperatures change by means of changing meridional heat transfers. Meridional Warming.

The key point for me was seeing how the best geological knowledge proves beyond the shadow of a doubt how the earth’s climate profile shifts over time, as presented in the diagram above.  It comes from esteemed paleoclimatologist Christopher Scotese.  His compete evidence and analysis can be reviewed in his article Some thoughts on Global Climate Change: The Transition from Icehouse to Hothouse (here).

In that essay Scotese shows where we are presently in this cycle between icehouse and hothouse.

As of 2015 earth is showing a GMT of 14.4C, compared to pre-industrial GMT of 13.8C.  According to the best geological evidence from millions of years of earth’s history, that puts us in the category “Severe Icehouse.”  So, thankfully we are warming up, albeit very slowly.

Moreover, and this is Clive Best’s point, progress toward a warming world means flattening the profile at the higher latitudes, especially the Arctic.  Equatorial locations remain at 23C throughout the millennia, while the gradient decreases in a warmer world.

The previous post explained what is wrong with averaging temperature anomalies.  See Temperature Misunderstandings

Conclusion:

We have many, many centuries to go before the earth can warm up to the “Greenhouse” profile, let alone get to “Hothouse.”  Regional and local climates at higher latitudes will see slightly warming temperatures and smaller differences from equatorial climates.  These are facts based on solid geological evidence, not opinions or estimates from computer models.

It is still a very cold world, but we are moving in the right direction.  Stay the course.

Meanwhile, keep firing away Clive.

damaged-ship3

 

Temperature Misunderstandings

Clive Best provides this animation of recent monthly temperature anomalies which demonstrates how most variability in anomalies occur over northern continents.

Beyond the issues with the measurements and the questionable adjustments, there is a more fundamental misconception about air temperatures in relation to “climate change.” Clive Best does a fine job explaining why Global Mean Temperature anomalies do not mean what people think. Below is my synopsis of his recent essay entitled Do Global Temperatures make sense? (link)

Background: Earth’s Heat Imbalance

ERBE measurements of radiative imbalance.

The earth’s temperature at any location is never in equilibrium. It changes daily, seasonally and annually. Incoming solar radiation varies enormously especially near the poles which receive more energy per day in summer than the equator.

The earth cools primarily by moving heat from hot tropical regions towards high latitudes where net IR radiation loss cools the planet, thus maintaining a certain temperature profile.

Key Point: Heat Distribution Changes, not Global Temperatures

Rising CO2 levels modify that radiation imbalance profile slightly. Surface temperatures in the tropics are not really warming at all. Any excess heat induces more clouds and more convection while surface temperatures remain constant. What really happens is that the meridional radiation profile changes. Slightly more heat is transported polewards so that hot places are shifting more heat to cold places which are doing the warming. If CO2 levels stop rising then a new temperature and radiation profile would rather quickly be reached. This is then called ‘climate change’ but any such changes are concentrated in colder regions of the world. The global ‘temperature’ itself is not changing, but instead the global distribution of temperature is changing.

Key Point: More Atmospheric Heat means Warming in the Coldest Places

Temperatures at the poles during 6 months of darkness would fall well below -150C if there was no atmosphere, similar to the moon. Instead heat is constantly being transported from lower latitudes by the atmosphere and ocean and so that temperatures never fall much below -43C. If more heat is transported northwards than previously, then minimum temperatures must rise, and this is what we observe in individual measurements.

Key Point: GMT Anomalies Are Dominated by the Highest Latitudes

The main problem with all the existing observational datasets is that they don’t actually measure the global temperature at all. Instead they measure the global average temperature ‘anomaly’. . .The use of anomalies introduces a new bias because they are now dominated by the larger ‘anomalies’ occurring at cold places in high latitudes. The reason for this is obvious, because all extreme seasonal variations in temperature occur in northern continents, with the exception of Antarctica. Increases in anomalies are mainly due to an increase in the minimum winter temperatures, especially near the arctic circle. 

To take an extreme example here is the monthly temperature data and calculated anomalies for Verkoyhansk in Siberia. Annual temperatures vary from -50C in winter to +20C in summer. That is a seasonal range of 70C each year, and a year to year anomaly variation of ~8C is normal. The only global warming effect evident is a slight increase in the minimum winter temperatures since 1900. That is not due to any localised enhanced greenhouse effect but rather to an enhanced meridional heat transport. Temperatures in equatorial regions meanwhile have only ~4C seasonal variations, and show essentially no warming trend.

Long term changes in temperature anomalies occur mainly in northern continents in winter months. This is not because the earth as a whole is warming up but rather that meridional heat transport from the equator to the poles has increased and the largest effect on ‘anomalies occurs in winter. The average absolute temperature of the earth’s surface is unknown. Basing the evidence for climate change on the 150 year trend in global averaged temperature anomalies still biases the result towards higher latitudes where most of the stations are located.

Summary

When heat is released into the atmosphere from the oceans, it is transported toward the poles to dissipate into space. Places in higher latitudes are warmed, not by radiative effects of greenhouse gases in those locales, but by the incursion of warmer air from the equator.

What happens if more CO2 is added into the atmosphere? No one knows, but there are many opinions, a popular one being that more heat is retained in the atmosphere. But in that case, that additional heat will be shed by the planet in exactly the same manner: transport to the poles with slightly less extremely cold air at the higher latitudes.

Why in the world would we pay anything to prevent a little bit of warming in the world’s coldest places?

Clive Best takes the analysis further and relates to work by Christopher Scotese in a later post Fact: Future Climate Will Be Flatter, not Hotter

Footnote 1:  Polar temperatures are well below freezing most of the year, so polar air is dry.  Dry air heat capacity is about 1/3 that of humid air, so polar air temps are more volatile, both in warming and cooling.

For more on arctic amplification and enthalpy, see Arctic Amplification?

Footnote 2: Scott Pruitt provides a concise synopsis of the issues in measuring global surface temperatures.  From his responses to Senators’ questions during confirmation hearings:

Senator Merkley:

Are you aware that each of the past three decades has been warmer than the one before, and warmer than all the previous decades since record keeping began in the 1880s? This trend is based on actual temperature measurements. Do you believe that there is uncertainty in this warming trend that has been directly measured? If so, please explain.

Nominee Pruitt:

I am aware of a diverse range of conclusions regarding global temperatures, including that over the past two decades satellite data indicates there has been a leveling off of warming, which some scientists refer to as the “hiatus.”
I am also aware that the discrepancy between land-based temperature stations and satellite temperature stations can be attributed to expansive urbanization within in our country where artificial substances such as asphalt can interfere with the accuracy of land-based temperature stations and that the agencies charged with keeping the data do not accurately account for this type of interference.
I am also aware that ‘warmest year ever’ claims from NASA and NOAA are based on minimal temperature differences that fall within the margin of error.
Finally, I am aware that temperatures have been changing for millions of years that predate the relatively short modern record keeping efforts that began in 1880.

More Q&A is at Running the Climate Gauntlet

More explanation at The Climate Water Wheel

Oceans Make 2015 & 2016 Climate

 

Ocean temperature measurements come from a global array of 3,500 Argo floats and other ocean sensors. Credits: Argo Program, Germany/Ifremer

We are seeing lots of claims about the temperature records for 2016 and 2015 proving dangerous man made warming.  At least one senator stated that in a confirmation hearing.  Now that HadSST3 data is complete for last year, let’s see how obvious is the ocean’s governing of global average temperatures.

The best context for understanding these two years comes from the world’s sea surface temperatures (SST), for several reasons:

  • The ocean covers 71% of the globe and drives average temperatures;
  • SSTs have a constant water content, (unlike air temperatures), so give a better reading of heat content variations;
  • A major El Nino was the dominant climate feature these years.

HadSST is generally regarded as the best of the global SST data sets, and so the temperature story here comes from that source, the latest version being HadSST3.

The chart below shows the last two years of SST monthly anomalies as reported in HadSST3.

hadsst3-2015-2016all

Note that higher temps in 2015 and 2016 are first of all due to a sharp rise in Tropical SST, beginning in March 2015, peaking in January 2016, and steadily declining back to its beginning level. Secondly, the Northern Hemisphere added two bumps on the shoulders of Tropical warming, with peaks in August of each year. Also, note that the global release of heat was not dramatic, due to the Southern Hemisphere offsetting the Northern one.

Finally, the oceans are entering 2017 at the same temperature level as 2015, only now with downward momentum.

Much ado will be made of this warming, including claims of human causation, despite the obvious oceanic origin. However, it is unreasonable to claim CO2 functions as a global warming agent, yet the two hemispheres respond so differently.  Moreover, CO2 warming theory expects greater warming in the higher latitudes, while this event was driven by heating in the Tropics, contradicting alarmist warming theory.

Solar energy accumulates massively in the ocean and is variably released during circulation events.

 

Anatomy of the Hottest Years Ever

 

Ocean temperature measurements come from a global array of 3,500 Argo floats and other ocean sensors. Credits: Argo Program, Germany/Ifremer

With the year end, media climate attack dogs are going after the Trump administration, throwing whatever they can (hoping for anything to stick). One thing they will surely trumpet is the temperature records for 2016 and 2015 as proof of dangerous man made warming.

Now the best context for understanding these two years comes from the world’s sea surface temperatures (SST), for several reasons:

  • The ocean covers 71% of the globe and drives average temperatures;
  • SSTs have a constant water content, (unlike air temperatures), so give a better reading of heat content variations;
  • A major El Nino was the dominant climate feature these years.

HadSST is generally regarded as the best of the global SST data sets, and so the temperature story here comes from that source, the latest version being HadSST3.

The chart below shows the last two years of SST monthly anomalies as reported in HadSST3.

hadsst3-2015-2016

Note that higher temps in 2015 and 2016 are first of all due to a sharp rise in Tropical SST, beginning in March 2015, peaking in January 2016, and steadily declining back to its beginning level. Secondly, the Northern Hemisphere added two bumps on the shoulders of Tropical warming, with peaks in August of each year. Finally, note that the global release of heat was not dramatic, due to the Southern Hemisphere offsetting the Northern one.

Much ado will be made of this warming, including claims of human causation, despite the obvious oceanic origin. Further, it is curious that CO2 functions as a warming agent so unevenly around the world, and that the Tropics drove this event, contradicting global warming theory.

Solar energy accumulates massively in the ocean and is variably released during circulation events.

 

On Warming Holes (Global Warming Gaps)

 

Animation showing the 25-year and 40-year trends in surface air temperature in the Cowtan and Way v2.0 dataset, with plots to the right showing the fraction of the earth surface in a cooling trend (the blue areas in maps).

Ed Hawkins at his blog provides above the display of variability of warming and cooling across the globe. The post is entitled Regional Temperatures This Century (here).

We found that some regions experience periods of cooling at this timeframe even when global temperature is increasing rapidly. Cooling periods of 25 years duration occurred in 13 to 74 % of the earth surface through the observed record, and cooling periods of 40 years occurred in 6 to 71% of the earth surface, including in the most recent decades. Cooling periods are more prevalent where the long-term trend is low such as in the Southern Ocean, and/or where decadal variability is high such as Pacific Ocean regions influenced by the Inter-Decadal Pacific Oscillation (IPO). However, there are cases where low trend or high variability due to the IPO (or Atlantic Multi-decadal Oscillation) are not the only factors, and there may be a role for forcings and other regional effects. These cases include the well-known ‘warming hole’ in the south east US through the last half of the 20th Century (noting this ‘hole’ has an important seasonal aspect to it) and the recent cooling in northern Australia linked to increasing cloud and rainfall.

He refers to the cooling regions as “warming holes”. Since there are periods where cooling dominates globally, we could also refer to exceptional regions as “warm spots.” This shows dynamically how regional climate trends differ over time. For example, over the last century in the continental US, about a third of land stations showed cooling trends contrary to the slightly warming average overall.

Cautionary note regarding the Cowtan and Way 2.0 Dataset

This dataset is controversial in its use of “krieging” to spread temperature readings from a handful of land stations across the full extent of the Arctic (and Antarctic) including surfaces of ocean, ice and mixtures of the two. As the charts show, this results in extra warming in the Arctic, double the trend shown by UAH (satellite) dataset.

Another example of the inconsistency of “global warming” is provided by NOAA’s presentation of continental temperatures. (here) The table below is for October 2016, and shows not only variability, but also how land temperatures are falling following El Nino’s disappearance.

CONTINENT ANOMALY (1910-2000) TREND (1910-2016) RANK
(OUT OF 107 YEARS)
RECORDS
°C °F °C °F YEAR(S) °C °F
North America +1.33 +2.39 +0.05 +0.09 Warmest 7ᵗʰ 1963 +2.16 +3.89
Coolest 101ˢᵗ 1919 -1.94 -3.49
South America +0.85 +1.53 +0.17 +0.30 Warmest 15ᵗʰ 2014 +1.60 +2.88
Coolest 92ⁿᵈ 1922 -1.04 -1.87
Ties: 1994
Europe +0.40 +0.72 +0.11 +0.20 Warmest 41ˢᵗ 2006, 2001 +1.96 +3.53
Coolest 67ᵗʰ 1912 -1.99 -3.58
Africa +1.35 +2.43 +0.09 +0.16 Warmest 2ⁿᵈ 2015 +1.59 +2.86
Coolest 106ᵗʰ 1910 -0.65 -1.17
Asia -0.15 -0.27 +0.10 +0.18 Warmest 69ᵗʰ 2011 +1.76 +3.17
Coolest 39ᵗʰ 1912 -2.22 -4.00
Oceania +0.21 +0.38 +0.13 +0.23 Warmest 44ᵗʰ 2015 +2.71 +4.88
Coolest 64ᵗʰ 1910 -1.15 -2.07