Performance of UK wind power during winter 2013/2014

Headline: The UK fleet of >5000 wind turbines provided 6.6% of peak electrical power requirements this winter.

Winter 2013/14 has been characterized  by strong westerly  gales. The UK has invested heavily in new wind farms resulting in a total fleet of 10GW of installed capacity from over 5000 turbines. Such windy conditions are favorable to higher load capacity. Wind also takes priority over other fuels on the grid.  So how has our fleet of wind farms fared this winter ?

Fuel source meeting peak demand averaged from 21 August 2013 until 15 April 2014

Fuel source meeting peak demand averaged from 21 August 2013 until 15 April 2014

I have been monitoring the national grid statistics for electricity generation every hour from late September 2013. Demand for electricity must be met by supply in real time, so what really matters is the daily peak load on the grid. If demand cannot be met at peak demand then blackouts will occur. For each day over the last 7 months I have calculated the time of peak electricity demand and which fuels were used on the grid to provide the power demand. On average wind provided 6.6% of peak demand.

However, when we look in detail at the daily fluctuations in wind we see a different story to that usually reported by the industry and the media. It is true that wind power records have been  broken this winter during extended windy periods. As a result wind power has occasionally reached up to 14% of UK total demand. What is never reported though is that on other days there has essentially been zero wind power available at peak demand. This fact remains the real show stopper for wind power if we aim  to maintain a modern technological society.


Graph of percentage contribution from wind power to the peak power demands of the UK. Maximum power output of 14% represents 7GW, which is a load factor of 70%. Minimum power output was 0.2GW – load factor of 2%.

This is the unsolved problem with wind power. Without any energy storage solution, wind cannot displace any fossil fuel plants because they are still needed in order to balance the grid. Wind energy produced at night is really paid for by consumers at double peak time rates but is then thrown away. This is the real scandal. Nuclear on the other hand has an inverse problem. Nuclear Power is a continuous process which is  on both night and day. This means that nuclear cannot  be used to balance wind. That is why all motorways have street lighting all night in Belgium, because it costs nothing since  their nuclear energy is essentially free at night. The difference with wind is that nuclear is 100% reliable and we can plan to do something with that power. This makes nuclear a far more important energy source.

Now we look in more detail at the demand and supply this winter. The next graph covers the period from September to March. The fuels used to generate peak electricity are plotted for each day. Wind has priority in that all available power is fed to the grid ahead of other fuels apart from nuclear. The fuel labelled “imported and pumped” is the sum of hydro power and and imported energy from France and Holland via the interconnection links. This winter it has been a one way traffic from them to us. France relies on Nuclear while Holland is building more coal power stations.


Summary of peak daily power requirements and energy sources for the UK from September 2013 until April 2014

The seven day oscillation is of course the variation between weekdays and weekends. Now we look in more detail at the high daily demand period of about 50GW during December and January with a noticeable strong dip over the Christmas break. The next plot is a daily additive stacked bar graph.

It is interesting to note  how the time of day for peak demand changes on Christmas day to lunchtime, whereas normally the peak demand always occurs around 5pm. Presumably this is simply because everyone is indoors cooking Christmas lunch.


Detailed breakdown of Fuel sources for the Christmas period. During this period the UK experienced some severe winter storms and flooding.

There is no doubt that wind energy does make a noticeable contribution to the grid – but one has to ask at what cost and what benefit ? Wind has increased roughly 2% compared to  last winter but on the other hand we are now spending  £6 billion per year in subsidies. The subsidies can only increase with future expansion, similar to those in Germany where annual energy prices are on average costing each household an extra €300 in subsidies. Doubling the number of turbines in the UK would increase the average yield to 12% of peak load, but would still do nothing to improve energy security. That is because sometimes there would still be < 1% of wind energy available at 5pm on the coldest day of the year, so not a single conventional plant could close without the risk of blackouts increasing.

Independent of energy security, there are also serious environmental objections to a massive extension of wind farms in and around our small island.  They are destroying some ancient peat and moorlands. They are ruining some of our best countryside  and seascape views. Meanwhile the renewables lobby are pushing for ever more wind farms partly because they are risk free investments underwritten at our expense.  The only low carbon strategy that makes any sense today  is a rapid expansion of nuclear power, certainly not wind power. Economies of scale say we should instead be building 5 identical Hinkley Point C type stations all in parallel, thereby bringing on line 15GW of new reliable energy  by 2020. Furthermore we could then also recharge everyone’s electric car overnight and light all our motorways for free!  DECC chief scientist David Mackay has suggested instead using future electric car batteries to power the grid when there is no wind . Imagine waking up for work some mornings to find that your car battery is dead after a becalmed night! I somehow expect government cars will be exempted !

Relying on wind energy  is like choosing to sail round the world rather than take the QE2. Sailing is great fun but the journey time is out of your control. You can be becalmed for days on end or be hit by a storm at 3am when you need to sleep.  I am amazed that seemingly intelligent people can be so deluded about “green”  energy. It really is as much a scam to defraud tax payers, than it is a remedy for climate change!


Posted in Energy, nuclear, renewables, Science, Technology, wind farms | Tagged | 5 Comments

The strange case of TCR and ECS

In this post we consider the strange coincidence that the net forcing used by CMIP5 models is essentially the same as CO2 forcing alone. This allows us to derive a value of TCR(Transient Climate Response) just from observational data.  Measuring ECS(EquilibriumClimate Sensitivity) however requires modeling information. We use the average CMIP5 forcing and a model derived “hysteresis” function in order to determine ECS from temperature data. The resulting energy imbalance calculated using these values of ECS and TCR is found to be the same as that derived by other methods.

The net climate forcing is mainly due to changes in anthropogenic GHGs and in aerosols. Something like 20-40% of aerosols are of anthropogenic origin. Aerosols have 3 main effects:

  1. They scatter incoming solar radiation cooling the earth.
  2. They (e.g. black carbon) absorb both incoming solar radiation and surface IR radiation
  3. They help seed clouds formation – net cooling effect.

Energy imbalance Q = F -\lambda\Delta{T}  where \lambda is the aerosol feedback. Models trade off aerosols against Climate Sensitivity to match observed temperatures. Aerosols are essentially the tuning parameter that match GCMs in hindcasts to previous surface temperatures. AR5 admits that they have  “low confidence” in the aerosol-cloud interaction, and the estimated uncertainties are that the net effect of aerosols could even be zero. However, if aerosol forcing is reduced then model sensitivities would be far too high.  I argued in the previous post that climate sensitivity should be defined as the measured temperature change for a measured doubling of CO2. Instead IPCC has defined it as the simulated change in temperature due to CO2 forcing alone, excluding other GHGs and aerosols. The amazing fact however is  that it doesn’t matter! In order for the models to agree with observed temperature rises since 1850 there is a near perfect cancelation between other GHGs and aerosols! Figure 1 shows net CMIP5 forcings compared to a CO2 only forcing.

Fig2: Comparison of a pure CO2 GHG forcing and the CMIP5 avergaed forcings used to hindcast past temperature dependency since 1850.

Fig1: Comparison of a pure CO2 GHG forcing and the CMIP5 averaged forcings used to hindcast past temperature dependency since 1850.

So therefore it doesn’t really matter whether we use GCM models to derive a value for TCR or simply fit the temperature data instead. Let’s do that and derive a value for TCR using

DT = \lambda DS and
DS = 5.3ln(C02/290) where 290 is the CO2 value in 1850.
so DT = \lambda *5.3ln(CO2/290)

For CO2 I take the Mauna Loa data smoothly interpolated back to a value of 290 in 1850. We then fit the temperature data to a ln(CO2/290) term. The result is shown below


A fit of the temperature anomaly data to lambda*5.3ln(CO2/290)

This gives a climate response value \lambda = 0.47 degC/Wm2     therefore

TCR = \lambda *3.7 = 1.7C

A  fit to the temperature data which includes a 60 year natural oscillation, possibly linked to AMO (see recent post by Bob Tisdale) , gives a slightly different result.

Fig 3: Overall fit to 164 years of global temperature data (HADCRUT4)

Fig 3: Overall fit to 164 years of global temperature data (HADCRUT4)

A part of the rapid warming from 1970 to 2000 can be seen as potentially due to the upturn in this oscillation. The CO2 component now has a lower climate response with a \lambda  = 0.41 degC/Wm2  and

TCR = \lambda *3.7 = 1.5C

Figure 1 shows that the effective average forcing from all CMIP5 models has essentially been the same as that from CO2 forcing alone. This means we can derive TCR as defined by IPCC through this coincidence. This remains true now even if the ratio of aerosols to other GHGs were to change in the future. These two  analysis essentially measure a value:

TCR = 1.6 ± 0.2 C   where the error is an estimate of the spread in fits.

Equilibrium Climate Response (ECS)

“ECS is defined as the change in global mean temperature, T2x, that results when the climate system, or a climate model, attains a new equilibrium with the forcing change F2x resulting from a doubling of the atmospheric CO2 concentration.” It is the temperature reached after the earth has restored energy balance following a doubling of CO2.  The observed global temperatures since 1850 are instantaneous measurements while the earth is “warming”. The cause of the delay is because the oceans have a huge thermal capacity. One way to estimate ECS is to “measure” the change in heat content of the oceans \Delta{Q} . Then

ECS = \frac{F_{2x}\Delta{T}}{\Delta{F}-\Delta{Q}}

However there is another way to do it by “measuring” instead the response of the earth to a sudden increase in forcing. I used an old GISS model to measure that inertia from a model  run which instantaneously doubles CO2. The temperature response is shown in figure 4 where the red curve is a fit I made to a (1-e^{\frac{t}{\tau}}) term.


Fig 1: Response temperature curve from a pulse doubling of CO2 in 1958 and fit described i the text

Fig 4: Response temperature curve from a pulse doubling of CO2 in 1958 and fit described i the text

T(t) = T_0 + \Delta{T_0}(1-e^\frac{-t}{15})

This provides a method to derive ECS from the temperature data once the net forcing is known.

where \Delta{T}_{0}  is the equilibrium temperature response to a change in forcing \Delta{S}  .

To calculate the CO2 forcing  I take a yearly increment of

\Delta{S} = 5.3 log (\frac{C}{C_0})  ,     where  C and C0 are the values before and after the yearly pulse. All values are calculated from seasonally averaged Mauna Loa data smoothed back to an initial concentration of 280ppm in 1750.

Each pulse is tracked through time and integrated into the overall transient temperature change using:

\Delta{T}(t) = \sum_{k=1}^N (\Delta{T}_{0}(1 - e^\frac{-t}{15}))

\Delta{T}_{0} was calculated based on different values of ECS.  The results are compared to the observed HADCRUT4 anomaly measurements in Figure 4. The publication of AR5 report allows us to update CMIP5 forcings up to 2013 based on this graph.



The data was extended from 2005 to increase forcing and agree with the data – black curve from AR5. The final net forcing in 2013 is 2.2 W/m2. The code that calculates the temperature for different values of ECS  is available here. Figure 4 shows the temperature response calculated from the model using AR5 forcing for different  values of ECS.

Comparison of H4 to ECS values ranging from 1.5-4C. The thinbk black line is the 5 year running average of anomaly data

Comparison of H4 to ECS values ranging from 1.5-4C. The thinck black line is the 5 year running average of anomaly data

Now looking in more detail at recent temperatures where the cumulative effect of past forcing is strongest, we see how unusual the current hiatus in warming appears.

Comparison of ECS with H4 anomalt details since 1960.

Detailed comparison of ECS with H4 temperature anomalies details since 1960. Thick black line is an  FFT smoothing through the temperature anomaly data with a 5 year filter.

Values of ECS > 3 or ECS < 2 are ruled out by the data. The most likely value for ECS consistent with the recent data is apparently slightly less than  2.5C. The longer the hiatus continues the lower the estimate for ECS.

The overall result from this analysis is ECS = 2.3 ± 0.5 C.  The error is really asymmetric so it is more like  +0.5 and -0.3

Let’s see if all this works out as being consistent with the value of TCR that we measured before, and isolate the energy imbalance \Delta{Q}

\frac{ECS}{TCR} = \frac{\Delta{F}}{\Delta{F}-\Delta{Q}}

\Delta{Q} = \Delta{F}(1 - \frac{TCR}{ECS})

= 0.7 ± 0.5 W/m2

This is consistent with other values for \Delta{Q} .

In summary we have shown that there has been a remarkable approximate agreement between pure CO2 forcing and net CMIP5 forcing. This has allowed us to fit the Hadcrut4 temperature anomaly data to derive a value of TCR = 1.6 ±0.2C. The equilibrium climate sensitivity has been measured by using a model derived value for ocean temperature response to forcing of the form \Delta{T}(t) = \sum_{k=1}^N (\Delta{T}_{0}(1 - e^\frac{-t}{15})) . By integrating each annual pulse of  CMIP5 model forcings, we have compared different values for ECS to the Hadcrut4 anomaly data. This hysteresis effect becomes stronger over time so the current hiatus in warming strongly distinguishes between different values of ECS. Values greater than 3C are ruled out as are values < 2C. The best estimate  for ECS based on this method is 2.3 ± 0.5. The values measured values of TCR and ECS are for a total net forcing of 2.2W/m2 with an energy imbalance of 0.7 ± 0.5.



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Is TCR a measurable quantity?

Until yesterday I had assumed that climate sensitivity was the measured temperature rise after a doubling of CO2 in the atmosphere from 280ppm in the pre-industrial era to 560ppm as a result of human activity.

\Delta{T_{cr}} = \lambda\Delta{S}   where  \Delta{S} = S_{560} - S_{280}    and    \lambda  is the climate response

The discussion on Ed Hawkins blog concerning Lewis & Croc’s criticism of the AR5 climate sensitivity analysis has highlighted that the official IPCC’s definition of TCR is purely model based and not a directly observable quantity. Piers Foster writes

“Lewis & Crok perform their own evaluation of climate sensitivity, placing more weight on studies using “observational data” than estimates of climate sensitivity based on climate model analysis”. “Here we illustrate the effect of the data quality issues and assumptions made in these “observational” approaches and demonstrate that these methods do not necessarily produce more robust estimates of climate sensitivity.”

The IPCC definition of TCR is : “Transient climate response (TCR) is defined as the average temperature response over a twenty-year period centered at CO2 doubling in a transient simulation with CO2 increasing at 1% per year[Randel et al. 2007]“.

This is a model derived value calculated by drip feeding  CO2 into the atmosphere while keeping all other variables constant. It is only be the temperature rise since pre-industrial times when CO2 levels reach 560 ppm if nothing else changes. Lewis & Croc then try to untangle TCR from the observed temperatures by unfolding  model derived forcings (CO2,NO2,aerosols etc.)  and find that TCR lies in the range 1-2C with a most likely value of 1.35C. They are then criticised for doing this because they “rely” too much on observations !

For a similar reason I am also concerned about the reasoning behind why RCP8.5 emissions scenario results in a forcing of 8.5 W/m2 by 2100. This emission scenario “business as usual” results in CO2 concentrations reaching about 900 ppm by 2100. I assume that models have been used to calculate that this scenario results in a final net forcing of 8.5 W/m2. However those same models implicitly must have built in climate sensitivity in order to derive that forcing. The emission scenario not only covers CO2 but also other anthropogenic GHGs (methane, NCO, CFC)

In other words RCP8.5 has a built in feedback which can be calculated as follows.

1) feedback explicit \Delta{T}_{0} = (\Delta{S_0} + F\Delta{T}_{0})G_{0}

2) no feedback \Delta{T}_{0} = (\Delta{S})G_{0}

In case 1 \Delta{S_0} = 5.3 log (\frac{C}{C_0}) = 6.19
In case 2 \Delta{S} =8.5

Since the temperature rise must be the same in both cases
\frac{\Delta{S_0}}{\Delta{S}} = \frac{3.75}{3.75-F} = \frac{8.5}{6.19}

Therefore F = 1.02 W/m2/deg.C

Or a built in “anthropogenic” booster to the above definition of TCR of about 50%. In fact if you look at the AR5 model forcings you can see that indeed the other GHGs add currently calculated to add ~0.9 W/m2 to the 1.8 W/m2 from increased CO2. However this now introduces model dependent “anthropogenic” feedback.

Radiative Forcings from AR5

Radiative Forcings from AR5

The root of the problem lies in the entanglement of models and  observations in the definition of TCR.  In my opinion it would be much simpler and cleaner to define TCR as a purely measurable quantity rather than one solely based on model simulations.

“Transient climate response (TCR) is defined as the measured average temperature response over a twenty-year period centered on the observed CO2 doubling.”

This definition TCR(E) can be measured by experiment. It is simply the average temperature rise when CO2 levels reach 560ppm. It can also be essentially measured today – see A Fit to Global Temperature Data. This definition removes the non-CO2 anthropogenic effects (CH4, NO2,CFC etc.) and avoids getting trapped by the model centric view. These effects are essentially anthropogenic feedbacks in a sense similar similar to climate feedbacks – e.g. increased H2O.

In all other branches of physics models make predictions and experiments then test the models. Why should climate science be different?

The emission scenarios are based on  socio-economic modeling based on current energy sources. Nearly all of our energy still comes from burning fossil fuels, while farming and transport depend on oil. This is also reflected in the signature of CH4 and NO2 emissions associated with CO2 emissions. Therefore CO2 levels is still a good measure of anthropogenic effects.

Let’s suppose that in the next 50 years there is a breakthrough in zero-carbon energy – say thorium or fusion reactors. CO2 emissions would begin to fall and so too would the balance between other GH gases and CO2. As far as I can see none of this is reflected in the RCP scenarios.

Ed Hawkins says that climate science is an observational science – like astronomy. That seems to be about right. However in astronomy observations are the drivers of progress – for example the discovery of pulsars, dark matter and dark energy. In climate science the modelers are in control and observations play second fiddle. A prime example of this is the definition of TCR.

Posted in AGW, Climate Change, climate science, Science | Tagged , , | 4 Comments

Do clouds control climate?

Clouds have a net average cooling effect on the earth’s climate. Climate models assume that changes in cloud cover are a feedback response to CO2 warming. Is this assumption valid? Following a study with Euan Mearns showing a strong correlation in UK temperatures with clouds, we  looked at the global effects of clouds by developing a combined cloud and CO2 forcing model to sudy how variations in both cloud cover [8] and CO2 [14] data affect global temperature anomalies between 1983 and 2008. The model as described below gives a good fit to HADCRUT4 data with a Transient Climate Response (TCR )= 1.6±0.3°C. The 17-year hiatus in warming can then be explained as resulting from a stabilization in global cloud cover since 1998.  An excel spreadsheet implementing the model as described below can be downloaded from

Best fit  to data with TCR=1.4C

Best fit(Acalc)  to data(H4)  using  TCR=1.4C

A basic uncertainty for climate science is in understanding the net effect of clouds on the radiative balance of the earth [3].  Clouds regulate solar heating by increasing the planet’s albedo while simultaneously absorbing infrared (IR) from the surface. This interplay between albedo and greenhouse effect of clouds is complex and varies with latitude and with season. The net radiative forcing from cloudy regions is So(1-?) –F, where F is the outgoing IR and ? is cloud albedo. On a global scale the Earth Radiation Budget Experiment (ERBE) measurements have shown a net cooling of around -13 watts/m2, which is four times that expected from a doubling of CO2 alone [3].  However, more recent measurements from the Clouds and the Earth’s Radiant Energy System CERES [5] show that the net average cooling effect of clouds is larger (-21 W/m2) (Figure 1b). It is often assumed that changes to cloud cover are a feedback to CO2 forcing rather than an independent phenomenon. A change in climate can induce cloud changes which then feedback into the initial climate change. This effect is built into most Climate models, which then result in a mean cloud feedback of between 0-2 W/m2/°C [6]. Radiative forcing from increasing CO2 levels is rather well understood [7], but its direct impact on cloud cover is unclear. Feedbacks cannot be too large compared to the Planck response as otherwise they soon become unstable \Delta{T} = \frac{\Delta{T_0}}{(1-f)} as f approaches 1.

Global cloud cover variations measured by a number of satellites under the guidance of the International Satellite Cloud Climatology Project (ISCCP) are subject to uncertainty linked to data acquisition methods [10], and viewing biases [11]. However, we have found previously [12] that using sunshine hours at surface as an inverse-proxy for cloud cover confirms the ISCCP results over the UK. In private correspondence, NASA have also provided assurance that data acquisition and corrections are now reliable and that the ISCCP data are therefore robust.

Figure showing the ISCCP global averaged monthly cloud cover from July 1983 to Dec 2008 over-laid in blue with Hadcrut4 monthly anomaly data. The fall in cloud cover coincides with a rapid rise in temperatures from 1983-1999. Thereafter the temperature and cloud trends have both flattened. The CO2 forcing from 1998 to 2008 increases by a further ~0.3 W/m2 which is evidence that changes in clouds are not a direct feedback to CO2 forcing.

Figure 1a showing the ISCCP global averaged monthly cloud cover from July 1983 to Dec 2008 over-laid in blue with Hadcrut4 monthly anomaly data. The fall in cloud cover coincides with a rapid rise in temperatures from 1983-1999. Thereafter the temperature and cloud trends have both flattened. The CO2 forcing from 1998 to 2008 increases by a further ~0.3 W/m2 which is evidence that changes in clouds are not a direct feedback to CO2 forcing.

CERES measured data on global cloud forcing. Reflected short wave radiation reduces surface heating by ~44 watts/m2 which is offset by cloud absorption of outgoing IR therefby increasing the greenhouse effect from clouds by ~26watts/m2. This results in a net cooling effect from cloudy skies globally of -22 watts/m2. This figure is used to define the NCF = 0.91. [5]

Fig 1b: CERES measured data on global cloud forcing. Reflected short wave radiation reduces surface heating by ~44 watts/m2 which is offset by cloud absorption of outgoing IR therefby increasing the greenhouse effect from clouds by ~26watts/m2. This results in a net cooling effect from cloudy skies globally of -22 watts/m2. This figure is used to define the NCF = 0.91. [5]

Figure 1a shows the ISCCP global averaged cloud cover [8] compared to Hadcrut 4 global temperature anomalies [4]. Until 1998 cloud cover decreased in line with increasing CO2 levels, which may support the existence of a CO2 feedback. However, since 1998 both cloud cover and temperatures have remained flat while CO2 forcing has continued to rise. This is evidence that cloud cover does not depend simply on CO2 forcing alone and may itself be a major natural driver for climate change. There is no direct evidence that cloud cover varies in response to CO2 and the ISCCP data discussed here is cyclic in nature which cannot be explained by unidirectional CO2 forcing. We have therefore developed a model that treats clouds and CO2 forcing independently and separately. Mearns and Best [10] have reported evidence that changes in cloud cover can explain approximately 40% of the UK surface temperature changes since 1956 especially during summer months (June, July, August)[10]. We now apply essentially the same model on a global scale using data from the ISCCP [9] that we downloaded from the US National Oceanic and Atmospheric Administration (NOAA) web site [ref] since the NASA web site has been disabled [ref] referenced to measured surface temperature data from CRU-Hadley (HADCRUT4)[8]. ISCCP cloud data is available beyond 2008 but is not yet in the public domain.

 Cloud forcing model. We define the net cloud-forcing factor (NCF) as the resultant balance between albedo and Green House (GH) effects for clouds. In effect NCF is used to describe the ratio of the combined forcing (cloud transmissibility and GH effect) of clouds relative to that for clear skies. Effectively (1-NCF) is the net cooling factor of clouds with respect to clear skies. Radiative energy balance is then given by

(1-CC)\times{S_0} + CC\times{NCF}\times{S_0} = \epsilon \sigma\ T^4

where, S0 for clear skies is taken as a global average 240 W/m2 [13]. Therefore for each month, m, the incoming net insolation is

S(m) = (1-CC(m))S_0 + CC(m) \times NCF \times S_0

The calculated temperature change for Tcalc (m) is then given by

\Delta{T(m)} = \frac{(S(m)-S(m-1))}{3.5}

where 3.5 Wm-1°C-1 is the Planck response  DS/DT for 288K and is the increase in IR radiation for a 1oC rise in surface temperature. We initialize the model by normalising the first data point Tcalc(July 1983) = Thcrut(July 1983) and then calculate all subsequent  monthly temperatures based only on the measured changes in ISCCP Cloud Cover (CC).

T_{calc}(m) = T_0(m-1) + \Delta{T(m)}

We fix NCF = 0.91 as measured by the CERES for global net cloud forcing.

The CO2 radiative forcing model: The change in CO2 forcing for month (m) is calculated using the formula [7]

S(m) = CS \times 5.3\ln(\frac{CO_2(m)}{CO_2(m-1)})

where ?S  is the monthly change in radiative forcing,CO2(y)/ is the concentration of CO2 in the atmosphere for month y, and CS is a factor representing climate sensitivity. CO2 values are the measured monthly Mauna-Loa data [14]. The model with CS=1.0 then corresponds to an equilibrium climate sensitivity (ECS) of 1.1°C. However, when the model is applied to contemporaneous temperature data, CS corresponds instead to the transient climate response (TCR). Climate models with net positive feedbacks yield larger values of ECS of between 2 to 5°C [15].  The model value of CS is to be determined empirically from the data.

We apply the model to calculate global temperature anomalies from variance in global cloud cover after normalising the start point (July 1983) to the measured global average temperature and then compare model output to measurements of actual temperature variance as recorded by HadCRUT4. Our criterion for goodness of fit between the model and HadCRUT4 is based on the use of ?2 per degree of freedom (?2/df). For ?2 we take a measurement error of 0.1°C for the monthly anomalies.  The ?2 results found by varying CS values with NCF fixed at 0.91 are shown in Figure 2b. A minimum in ?2 is found for CS = 1.45 corresponding to TCR = 1.6 °C.  The error on CS is determined by how much variation is needed to shift  ?2/df by 1 ?.


Fig 2 a) Results of the model calculations (Tcalc) for the best fit value of CS =1.45 (TCR=1.6 °C) compared to monthly Hadcrut4 anomaly data.
b) Variation of ?2 per degree of freedom calculated between the predicted and the measured anomalies calculated for different CS values taking NCF=0.91 as measured by CERES.

Clouds and CO2 alone cannot explain all the variations in monthly global temperatures. It is known that explosive volcanic eruptions and ENSO[E1]  also have transient effects on global temperatures, and for this reason it is no surprise that the minimum ?2/df > 1.0. However the main trend is well reproduced by the model as shown in Figure 2a which compares the best-fit value of CS to the real measured data. The general warming trend until 1998 can mostly be explained by the fall in cloud cover during that period. The flattening off in temperature since 1998 coincides with a leveling off in global cloud cover. To explain observed warming over the full period by a CO2 dependent term alone with clear skies (NCF=1) would require TCR = 2.2 °C resulting in an approximate linear increase of 0.7 °C over this time period. Examining the yearly change in cloud forcing shows that it increased from 225.5 W/m2 in 1984 to 262.2 W/m2 in 1999, or an increase in forcing of ~0.7 watts/m2. CO2 forcing with TCR = 1.6 °C increased by 0.54 W/m2 over the same time period.  This result demonstrates that more than half of the rapid warming observed in the 1980s and 1990s can be explained by a decrease in cloud cover. Since 1999 net cloud forcing has remained approximately constant (-0.2 W/m2), while CO2 forcing has increased by a further 0.58 W/m2.

Results for the summer cloud analysis for a) Northern Hemisphere with model TCR=1.0C and NCF=0.9 and b) Southern Hemisphere with model TCR = 1.65C and NCF=0.91. The Hadcrut4 data and the model data for each year are the averaged results for June, July and August in case a) and for December, January and February for case b). In the latter case the year is assigned to that of December. There is a clear difference in dependence with CS for the Northern and Southern Hemispheres. Changes in cloud cover have a greater impact in the northern hemisphere than in the southern hemisphere. This affects the best fit values for CS for each hemisphere.

Results for the summer cloud analysis for a) Northern Hemisphere with model TCR=1.0C and NCF=0.9 and b) Southern Hemisphere with model TCR = 1.65C and NCF=0.91. The Hadcrut4 data and the model data for each year are the averaged results for June, July and August in case a) and for December, January and February for case b). In the latter case the year is assigned to that of December. There is a clear difference in dependence with CS for the Northern and Southern Hemispheres. Changes in cloud cover have a greater impact in the northern hemisphere than in the southern hemisphere. This affects the best fit values for CS for each hemisphere.

There are marked seasonal variations in cloud cover for each hemisphere – particularly in the southern hemisphere. In order to isolate differences between the long-term effects of clouds in each hemisphere we have made summer averages of temperature and cloud cover (June, July, August (JJA) for Northern Hemisphere (NH) and December, January, February (DJF) for Southern Hemisphere (SH)) and then compared the model with the hemispheric HadCRUT4 anomaly data. For the average summer hemispheric insolation we take a value of S0=312 W/m2 which is 240 W/ m2 corrected for the angle of the sun for summer months. The results of this analysis are shown in Figure 3.  There is a clear difference between the northern hemisphere and southern hemisphere. The response to cloud forcing in the northern hemisphere is stronger with fixed NCF=0.91, and leads to a lower c2 fitted value for CS (TCR = 1.0 ± 0.3°C). The southern hemisphere shows a smaller cloud forcing response with correspondingly larger values for CS (TCR = 1.65 ± 0.3°C). This difference is most likely due to dominance of oceans in the southern hemisphere. By studying each hemisphere separately and by eliminating as far as possible seasonal effects, the global result is confirmed. These results demonstrate that over half the warming observed between 1983 and 1999 is due to a reduction in cloud cover mainly effecting the northern hemisphere. The apparent slowdown in warming observed since 1999 coincides with a stabilization of global cloud cover. In an analysis of cloud and temperature variance in the UK, Mearns and Best [12] reach a similar conclusion which is that approximately 50% of net warming since 1956 is due to a net reduction in cloud cover. However, in that study NCF was estimated empirically to be 0.54, significantly lower than the CERES value of 0.91 used here. A lower NCF factor means that clouds are having a larger effect and the difference between the global and UK results may reflect latitude and the fact that UK data are land based only.

In conclusion, natural cyclic change in global cloud cover has a greater impact on global average temperatures than CO2. There is little evidence of a direct feedback relationship between clouds and CO2. Based on satellite measurements of cloud cover (ISCCP), net cloud forcing (CERES) and CO2 levels (KEELING) we developed a model for predicting global temperatures. This results in a best-fit value for TCR = 1.4 ± 0.3. Summer cloud forcing has a larger effect in the northern hemisphere resulting in a lower TCR = 1.0 ± 0.3. Natural phenomena must influence clouds although the details remain unclear, although the CLOUD experiment has given hints that increased fluxes of cosmic rays may increase cloud seeding [19].  In conclusion, the gradual reduction in net cloud cover explains over 50% of global warming observed during the 80s and 90s, and the hiatus in warming since 1998 coincides with a stabilization of cloud forcing.


1. Randall, D. A. Cloud Feedbacks. Frontiers in the Science of Climate Modeling (2006).

2. Randall, D. A. & Wood, R. A. Climate Models and Their Evaluation. (Cambridge Univ. Press: Cambridge [u.a.], 2007).

3. V. Ramanathan, R.DCess, E.F. Harrison, P.Minnis, B.R. Barkstrom, E. Ahmad, D. Hartmann, Cloud-Radiative Forcing and Climate: Results from the Earth Radiation Budget Experiment, Science, Vol 243, P 57, 1989

4. Jones, P. D., D. H. Lister, T. J. Osborn, C. Harpham, M. Salmon, and C. P. Morice (2012), Hemispheric and large-scale land surface air temperature variations: An extensive revision and an update to 2010, J. Geophys. Res., 117, D05127,

5. Richard P. Allan, Combining satellite data and models to estimate cloud radiative effects at the surface and in the atmosphere, RMetS Meteorol. Appl. 18: 324–333, 2011

6. Bony, S. et al. How Well Do We Understand and Evaluate Climate Change Feedback Processes? Journal of Climate 19, 3445–3482 (2006).

7. Myhre, G., E.J. Highwood, K.P.Shine,, F.Stordal, New Estimate of Radiative ForcingDur to Well Mixed Greenhouse Gases, Geophys. Ress. Lett. 25, 2715-2718, 1998

8. Monthly averaged ISCCP cloud data Data derived from file, Catalog. (2009)

9. Morice, C. P., J. J. Kennedy, N. A. Rayner, and P. D. Jones (2012), Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: The HadCRUT4 dataset, J. Geophys. Res., 117,

10. Rossow, W. B. & Schiffer, R. A. Advances in Understanding Clouds from ISCCP. Bulletin of the American Meteorological Society 80, 2261–2287 (1999).

11. Evan, A. T.; A. K. Heidinger, and D. J. Vimont (2007). Arguments against a physical long-term trend in global ISCCP cloud amounts. Geophy. Ress. Lett 34 (L04701)

12. E.W. Mearns, C.H. Best, Strong coherence between cloud cover and surface temperature variance in the UK

13. K.E. Trenberth, J.T. Fasullo & J. Kiehl, Earth’s Global Energy Budget, Bulletin of the American Meteorological Society (2009)

14. Keeling, C. D. et al. Atmospheric carbon dioxide variations at Mauna Loa Observatory, Hawaii. Tellus 28, 538–551 (1976).

15. Solomon, S. et al. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. (Cambridge Univ. Press: Cambridge [u.a.], 2007).

16. J. Kirby et al. Role of sulphuric acid, ammonia and galactic cosmic rays in atmospheric aerosol nucleation, Nature 476, 429–433 (2011).

Note: I have posting this only now because after a long review process the paper was finally rejected. I am beginning to despair of any outsider ever getting anything published in a climate science journal!

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Tidal effects in polar regions

The tidal force acting on the oceans generates tidal currents due to the tractional component parallel to the surface. This is because horizontally there is no net gravitational force acting to counteract motion. This tractional force reaches a maximum at around 45 degrees to the central tidal bulge. Chiefio has a nice article describing how the declination of the moon during spring tides can effect induced currents in the polar regions.


Fig 1: Diagram showing how the tractional tidal component at the poles depends strongly on the lunar declination angle.

I have been using the JPL ephemeris and the French INPOP10 ephemeris to investigate how this has varied over the last 2000 years. I calculate the maximum net annual tide based on the positions of the sun and moon, the maximum tractional component at 65N (arctic circle) and what I call the ‘melting index’. The melting index is meant to represent an extra ice melt influence of tidal motion working with summer insolation. It is zero during the arctic winter and proportional to average daily insolation times tidal acceleration in summer.

Recent daily tidal components. The lunar tide is shown in blue, the solar tide in red. Green shows the tractional acceleration at 65N.

Fig 2: Recent daily tidal components. The lunar tide is shown in blue, the solar tide in red. Green shows the tractional acceleration at 65N.

The tractional component at 65N typically varies between zero and half the net tidal force. The daily variations in tides show a rich structure of spring and neap tides enhanced by perihelion of the earth and lunar orbits. However are there long term changes in these cycles affecting climate?

Next I looked at the long term dependence by calculating for each year the maximum for each tidal component. Figure 3 shows the annual maximum tides and  their tractional component at 65N. There is a regular oscillation of ~8.8 years in the tractional force with the precession of the lunar orbit.


Maximum annual tides and their tractional force exerted at 65N

Fig 3: Maximum annual tides and their tractional force exerted at 65N

However if we instead find the maxima of the tractional component at 65N independently to the maximum annual tide then there is a far more stable dependency. The following plot shows  the maximum tide and the maximum tractional acceleration calculated independently for each year. Superimposed in red is what I call the ‘melt index’ which is defined as the tractional acceleration weighted by its offset (in days) from midsummer maximum insolation (June 21).

MI = 1.0 – ABS(date-June21)/(April1-June21)

If date < April  or date > August  MI=0

The black curve shows the annual maximum tide. The blue curve shows independently the maximum tractional tide at 65N. Both are essentially constant with time. However the melt index shown in red shows a regular ~40 year cycle showing coincidence of maximum tide and high summer insolation.

Fig 4: The black curve shows the annual maximum tide. The blue curve shows independently the maximum tractional tide at 65N. Both are essentially constant with time. However the melt index shown in red shows a regular ~40 year cycle showing coincidence of maximum tide and high summer insolation.

The maximum traction at the poles is now also nearly constant but there is a definite cyclical effect on the timing with the seasons in they occur in as picked up by the melt index. If we assume that large tides combined with high insolation enhances the arctic ice summer melting then this follows a roughly 40 year cycle.

Zoom in of last 500 years

Fig 5: Zoom in of last 500 years

This graph is a zoom in on the last of the period 1600 – 2100.  If the tides influence the summer melt then we would expect to see a roughly 40 year regular variation  in ice extent.

Conclusions. I find no evidence for  variations in inter-annual variations in the maximum  tides on earth  over  a 2000 year period using either JPL ephemeris or INPOP10. The maximum tides however show an 8.8 year variation in their tractional forces at the arctic circle (65N). However if instead we calculate the maximum tractional force independently then I also find no long term variation.  The only variation which may effect polar climates is  seen in the timing of the tractional force with the seasons. The occurrence of maximum tides  in the arctic coincident with maximum solar insolation does  have a ~40 years cycle. The tidal currents thereby induced may effect the summer melting of sea ice.

Next I will look at far longer timescales into the influence of Milankovitch  cycles on the earth’s orbital eccentricity which directly affects tides.

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Understanding Tides

There has been a long animated discussion about tides at Wattsupwiththat which highlighted a confusion about both the causes of tides and their strength. Several people are adamant that tides are a universal phenomena experienced by any object near a large gravitational source. They argue that tides are caused by the gradient of the 1/r^2 field.

While an extended object falling into a star  or black hole will experience a transient  tidal force, it is only bodies in orbit around each other that experience long term tidal forces acting on the surface. The earth is in orbit about the earth-moon barycenter. It is not in an inertial frame. It is in an accelerating frame of reference, similar to the way that the rotation of the earth about its axis causes a reduction in g at the equator.

So what is the real cause of tides on earth and why is the lunar tide larger than the solar tide ? Here is my derivation for  the formulae for tides.

For 2 bodies in orbit the “centrifugal force” must balance the gravitational force. The centrifugal force is constant within a solid body in the same way that it is for a plate spinning on a stick.

Fig 1

Fig 1


\frac{GMm}{r^2} = M\omega^2d

Therefore the centrifugal acceleration on body M is \omega^2d = \frac{Gm}{r^2}

Now consider the net force per unit mass acting on point a). Assuming that \phi = 0 we get

\frac{Gm}{(r-R \cos \theta)^2}  - \frac{Gm}{r^2}

= \frac{Gm}{r^2}( (1 - \frac{R}{r \cos \theta})^{-2} - 1)

assuming that r>>R we can do a binomial expansion to get

= \frac{Gm}{r^2}(1 +\frac{2R}{r}\cos \theta - 1)

= \frac{2GmR \cos \theta}{r^3}

This derives the approximate formula for the tidal force. There are two bulges centered on \theta = 0 (and) \theta =\pi

Now we can do the full calculation where the angle \phi is no longer zero and thereby identify how the tidal force acquires a vertical component.

Calculation of the angle phi. Distance a-m is the hypotomuse

Calculation of the angle phi. Distance a-m is the hypotomuse

The distance a-m is by Pythagorus

\sqrt{R^2 \sin^2 \theta + (r - R \cos \theta)^2}

= \sqrt{R^2 +r^2 -2rR \cos \theta}

Gravity acting on point a) is therefore =  \frac{Gm}{R^2 + r^2 -2rR \cos \theta}

Net tidal force now has 2 components

Fx = Gm( \frac{ \cos \phi}{R^2 + r^2 - 2rR \cos \theta} - \frac{1}{r^2})

Fy = \frac{ -Gm \sin \phi}{R^2 + r^2 - 2rR \cos \theta}


\cos \phi = \frac{r-R \cos \theta}{\sqrt{R^2 + r^2 - 2rR \cos \theta}}


\sin \phi = \frac{R \sin \theta}{\sqrt{R^2 + r^2 - 2rR \cos \theta}}

Now let’s compare the two solutions by calculating the effective tidal acceleration. Figure 3 shows the approximate formula in red and the two components of the exact result in blue.

Fig 3: Comparison of the exact solution for tides with the approximation. There is now a significant vertical (y) component to the tidal force.

Fig 3: Comparison of the exact solution for tides with the approximation. There is now a significant vertical (y) component to the tidal force.

On earth the gravitational acceleration ‘g’ = 9.8 m/s^2  This can be compared with the above “tidal” accelerations of ~ 10^-6 m/s^2. So the moon’s tidal force is 10 million times less than the earth’s gravitational force at the surface.  This is not going to do any direct heavy lifting of the oceans! Instead it is the tractional component of the tidal force parallel to the surface which moves vast quantities of ocean.  Now with the addition of the vertical component Fy the vector diagrams of tidal forces looks more like this:

Fig 4: Vector diagram showing resultant tidal force (fx,Fy)

Fig 4: Vector diagram showing resultant tidal force (fx,Fy)

Note that the largest tractional forces are at larger theta angles. This drag of water currents throughout the depth of the ocean results in both tidal bulges. Figure 5 shows the tractional north-south force parallel to the earth’s surface which is unaffected by the earth’s gravity and therefore moves water from outside the bulge towards the centre.

Fig 5: The tractional force moving vast quantities of water in the oceans to cause the tides.

Fig 5: The tractional force moving vast quantities of water in the oceans to cause the tides.

The position and strength of these tractional forces is constantly changing during the lunar month, during the 18.6 year precession cycle and during longer time scale astronomical cycles. So the way I like to understand tides is that both the moon and the sun exert a horizontal drag force on the oceans and atmosphere. Twice a month we get spring tides when the sun and moon line up at  new moon and the full moon, whose strength depends on the coincidence with both orbital perigees.  Long term astronomical variations must have an effect on  climate as orbital parameters slowly change increasing or decreasing ocean mixing and atmospheric dynamics.


There is a new argument about whether centrifugal forces play any role at all in tides. In some sense both sides in this argument are correct. You don’t need to use the centrifugal force to derive the formula for tides. This is because there is a perfect balance between the centrifugal force and the gravitational force at the center of the earth when in orbit around the earth-moon barycenter. This balance also determines the strength of tides on earth. When in doubt see what Feynman says.

What do we mean by “balanced”? What balances? If the moon pulls the whole earth toward it, why doesn’t the earth fall right “up” to the moon? Because the earth does the same trick as the moon, it goes in a circle around a point which is inside the earth but not at its center. The moon does not just go around the earth, the earth and the moon both go around a central position, each falling toward this common position. This motion around the common center is what balances the fall of each. So the earth is not going in a straight line either; it travels in a circle. The water on the far side is “unbalanced” because the moon’s attraction there is weaker than it is at the center of the earth, where it just balances the “centrifugal force.” The result of this imbalance is that the water rises up, away from the center of the earth. On the near side, the attraction from the moon is stronger, and the imbalance is in the opposite direction in space, but again away from the center of the earth. The net result is that we get two tidal bulges.

A body in free fall into the sun experiences ever increasing tidal forces until it is torn apart. A body in orbit eperiences varying tidal forces depending on the eccentricity of the orbit. So on a purely logical basis Willis and Greg are correct because centrifugal forces don’t enter into the formula for tides. However in order to calculate the variations of tides on earth you need to include orbital dynamics because they change the earth-moon distance.

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The AR5 Attribution Statement

The following conclusion of AR5 undoubtably had the most political impact.

“It is extremely likely that human activities caused more than half of the observed increase in GMST from 1951 to 2010.”

Humans cause  global warming with 95% confidence thereby confirming that tough action is needed to enforce carbon targets in Europe and elsewhere. Skeptics have been proved wrong etc.

Fig 10.5 from AR5. ANT is the net anthropogenic forcing. I do not understand how the ANT errors get smaller after adding GHG and OA together !

Fig 10.5 from AR5. ANT is the net anthropogenic forcing. Natural forcings (AMO/PDO) are essentially considered to be zero , as are natural (random) variations.  However, I still do not understand how the ANT errors get to be  smaller after adding GHG and OA together ! I am assured this is because modeling  errors rather than observational errors are relevant. ( see:  realclimate post )

Pretty convincing eh!

Well now just 4 months later we have a new claim that the 17 year hiatus in warming has instead been caused by an increase in trade winds over the western pacific – part of the Pacific Decadel Oscillation (PDO). A Met Office report on the storms and flooding now affecting parts of the UK says that perturbations to the  Jet stream has been driven in part by “persistent rainfall over Indonesia and the tropical West Pacific”.

What they don’t point out though is that this explanation is totally at odds with the explanation given in the AR5 chapter 10 which defined  the above attribution statement. Peter Stott of the Met Office was the lead author of this chapter. If explanations for the pause in warming  can change so fast so that now PDO is the dominant effect then surely also the attribution statement needs itself to be revised.

AR5 writes:

The observed recent warming hiatus, defined as the reduction in GMST trend during 1998–2012 as compared to the trend during 1951–2012, is attributable in roughly equal measure to a cooling contribution from internal variability and a reduced trend in external forcing (expert judgement, medium confidence).The forcing trend reduction is primarily due to a negative forcing trend from both volcanic eruptions and the downward phase of the solar cycle. However, there is low confidence in quantifying the role of forcing trend in causing the hiatus because of uncertainty in the magnitude of the volcanic forcing trends and low confidence in the aerosol forcing trend. Many factors, in addition to GHGs, including changes in tropospheric and stratospheric aerosols, stratospheric water vapour, and solar output, as well as internal modes of variability, contribute to the year-to-year and decade- to-decade variability of GMST.

The Atlantic Multi-decadal Oscillation (AMO) could be a confounding influence but studies that find a significant role for the AMO show that this does not project strongly onto 1951–2010 temperature trends.

They go on to write

Zhou and Tung (2013a) show that GMST are consistent with a linear anthropogenic trend, enhanced variability due to an approximately 70-year Atlantic Meridional Oscillation (AMO) and shorter-term variability. If, however, there are physical grounds to expect a nonlinear anthropogenic trend (see Box 10.1 Figure 1a), the assumption of a linear trend can itself enhance the variance assigned to a low-frequency oscillation. The fact that the AMO index is estimated from detrended historical temperature observations further increases the risk that its variance may be overestimated, because regressors and regressands are not independent. Folland et al. (2013), using a physically based estimate of the anthropogenic trend, find a smaller role for the AMO in recent warming. To summarize, recent studies using spatial features of observed temperature variations to separate AMO variability from externally forced changes find that detection of external influence on global temperatures is not compromised by accounting for AMO-congruent variability (high confidence). There remains some uncertainty about how much decadal variability of GMST that is attributed to AMO in some studies is actually related to forcing, notably from aerosols. There is agreement among studies that the contribution of the AMO to global warming since 1951 is very small (considerably less than 0.1°C; see also Figure 10.6) and given that observed warming since 1951 is very large compared to climate model estimates of internal variability (Section, which are assessed to be adequate at global scale (Section, we conclude that it is virtually certain that internal variability alone cannot account for the observed global warming since 1951.</blockquote>

There is no mention at all of the PDO in this chapter. But  suddenly just a few months later it is now the PDO that is responsible for the global warming hiatus and seemingly the Met Office is confirming this. If that is the case then the whole basis behind Fig 10.5 where  both natural forcing and natural variation were reduced to  just  0.0± 0.1C disappears.

In addition the logic behind the SPM attribution statement must also need revisiting.



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Lunar madness

I had  hoped to calculate from the JPL ephemeris how the regular 100,000 and 400,000 cycle  in the eccentricity of the earth-moon orbit around the sun  would also effect the moon-earth orbital eccentricity. Such variations could dramatically change the tidal forces acting on earth and play a leading role in triggering interglacials.

The seminal work on solar system dynamics has been done over decades by the French group at Observatoire de Paris. The latest paper La2010: A new orbital solution for the long term motion of the Earth gives the most accurate orbital parameters for the earth over the last 20 million years. However it also shows just how difficult it is to disentangle the moon’s orbit around the earth from their barycentre orbit around the sun, making it almost impossible to predict any long term changes in tides. Their quoted  error in calculating the moon’s eccentricity the last 1 Mya is ±0.03 compared to ±0.00000005 for the earth eccentricity around the sun!


So it is indeed quite possible that major changes in the moon’s orbital parameters will occur as the eccentricity of the Earth-Moon barycentre increases every 100,000 years. However it is almost impossible to calculate how large is the effect.

LA2010 also published some very accurate eccentricity values for the earth over the last 20 million years and into the future. I plotted these out and could not help but notice that the earth’s next 400 y cycle looks almost exactly the same as that which occurred roughly 3 million years ago. That was during an when  glaciations followed the 41,000 year obliquity cycle. Exactly the same eccentricity cycle is observed nearly 5 million years ago. There is therefore a larger 2.8 million year super-cycle in the earth’s eccentricity .

LA2010 calclations of the earth's eccentricity over a 4 million year period spanning the present day.

LA2010 calcluations of the earth’s eccentricity over a 4 million year period spanning the present day.

The graph below shows  the L04 stack sediment data from 3 million years  ago (colder is larger dO18). The larger the obliquity the larger are the extremes between the seasons. For large eccentricity the precession term then introduces a significant north-south asymmetry which depends on which particular northern/southern hemispheric season aligns with perihelion.

Combined fits compared to data 900-1500 ya

Combined fits compared to data 3 million to 1 million years ago

I am proposing that it was only when the obliquity cycle became insufficient to trigger an interglacial 800,000 years ago that the moon’s resonant tidal effect was needed to complete the job. This was the cause of the switch in phase to a 100,000 year glacial cycle.

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Tidal variations

Finally I have a working program which calculates the strength of tides based on the relative positions of the moon and the sun. This is based on the JPL ephemeris which is the most accurate available and is also used for space probes. The calculation is based on the relative distances of the moon and sun from the earth at any day over the last 60 years. The net tidal force is the vector sum of both components during their respective orbits. To sum these I take the dot product of the position vectors and apply a factor Mass/R^3 to both terms. Twice a month the earth experiences spring tides corresponding to the new moon and the full moon.  This is because the sun’s tidal force aligns more or less in the same direction to the moon’s tide at new moon and again slightly less at full moon. This is then amplified when the new moon coincides with perihelion of the earth’s orbit around the sun. These are perihelion spring tides and up to 4 times the strength of neap tides.

Fig 1. The net effect of the solar and lunar tides are reinforced  when they align  in the same plane. Maxima occur when the relative distances are minimised. Every 18000 y they coincide in a perfect plane with all distances minimised.

Fig 1. The net effect of the solar and lunar tides are reinforced when they align in the same plane. Maxima occur when the relative distances are minimised. Every 18000 y they coincide in a perfect plane with all distances minimised.

Now look carefully at just how much the earth’s eccentricity modulates the net tidal forces. This is because the sun’s mass is 27 million times larger than the moon and small changes in earth-sun distance can have large effects. Currently the eccentricity is 0.0167 and can reach as high as 0.057 during Milankovitch cycles leading to a rough doubling of the direct solar tide. This then must also amplify  the net vector lunar-solar tide as indicated  above significantly. Small changes in sun-earth distance are amplified with respect to those of the moon by a mass ratio of 2.7*10^7 caused by the  1/R^3 dependence of tidal forces.

Now consider the coastal flooding this winter which has mainly effected  western coastal regions of the  UK. The main reason for this are the unusually strong spring tides rather than global warming. These storms have tended to coincide with unusually extreme tides. Next winter such flooding is unlikely to re-occur. 

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The Moon’s eccentric orbit

As far as I can tell no long term study of lunar eccentricity has been done, so  I decided to begin investigating this myself, even though I am a complete novice in astronomical calculations. The key resource for all planetary motions in the solar system is the JPL ephemeris, and the easiest way to access it is through their Horizon web interface. Initially I ran a simulation of the lunar orbit relative to the earth-moon barycentre over a 10 year period beginning in december 2000.

I was amazed  to discover that the moon’s orbit around the earth is anything but simple and the quoted parameters are just approximations. The eccentricity of the orbit is changing almost on a daily basis due to complex variations in gravitational  effects depending on the relative positions of the sun and the earth, and also Jupiter and Venus. Figure 1 plots the eccentricity from Dec 12 2000 until October 12 2010 on a daily basis. The eccentricity varies in total between the extreme values of  0.026 and 0.077. This is a huge range which can alone  change the strength of lunar tides up to a maximum of 20%.

Figure 1: Variations in eccentricity of the moon's orbit around the Earth-Moon barycentre.

Figure 1: Variations in eccentricity of the moon’s orbit around the Earth-Moon barycentre. The blue curve is a fit to two oscilations with time periods 31.8 days and 205.9 days. Click to expand.

There are at least 2 regular resonances which at first sight seems odd because neither coincide with the orbital period of the moon (27.32days) nor that of the earth (365.25 days). There are also beats in the amplitude. Following this german article, I made a least squares fit shown as the blue curve which reproduces almost perfectly the signal .

eccentricity(d) = 0.55 + 0.014cos(0.198*d + 2.148) + 0.0085cos(0.0305*d +10.565)

This variation in eccentricity changes the perihelion distance from the earth significantly causing  large variations in the strength of spring tides on a yearly basis. The eccentricity becomes a maximum when the semi-major axis of the orbit lines up with the sun. This happens every 205.9 days – more than half a year due to the precession of the orbit every 18.6 years.  The 31.8 day variation is I think  the regular orbital change in distance from the sun.

Horizons only goes back as far as 8000 BC, so in order to investigate paleoclimate effects of eccentricity of lunar orbit around the time of the last interglacial we now need to find another tool.


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