Archive for the ‘Climate Change’ Category

Why global warming affects the poles more than the equator

May 8, 2022

Friends, welcome to Episode 137 in the occasional series of “Things I really should have known a long time ago, but have somehow only realised just now“.

In this case, the focus of my ignorance is the observation that the warming resulting from our emissions of carbon dioxide affects higher latitudes more than lower latitudes.

This is a feature both of our observations and models. But what I learned this week from reading the 1965 White House Report on Environmental Pollution (link) was the simple reason why.

[Note added after feedback: In this article I am describing an effect that makes the direct effect of increase CO2 levels more important at high latitudes. There are also many feedback effects that amplify the direct effect and some of these are also more  important at high latitudes. Carbon Brief has an excellent article on these feedback effects here, but that is not what I am talking about in this article.


The two gases responsible for majority of greenhouse warming of the Earth’s surface are water vapour and carbon dioxide. But the distribution of these two gases around the planet differs significantly.

  • The concentration of water vapour in the atmosphere depends on the temperature of the liquid surfaces from which the water evaporates. Because the Equator is much hotter than the poles, there is much more water vapour in the atmosphere at the Equator compared with the poles.
  • The concentration of carbon dioxide in the atmosphere is pretty uniform around the globe.

This is illustrated schematically in the figure below.

Click on the image for a larger version. There is more water vapour in the atmosphere in lower latitudes (near the Equator) that at higher latitudes (near the poles). In contrast, carbon dioxide is rather uniformly distributed around the globe.

Of course the truth is a bit more complex than the simplistic figure above might imply.

  • Water vapour from the Equator is transported throughout the atmosphere. But nonetheless, the generality is correct. And the effect is large: the atmosphere above water at 15 °C contains roughly twice as much moisture as the atmosphere above water at 5 °C.
  • Carbon dioxide is mainly emitted in the northern hemisphere, and is then uniformly mixed in the northern hemisphere within a year or so. The mixing with the Southern Hemisphere usually takes two or three years. The variability around the globe is usually within ±2%.

The uniformity of the carbon dioxide distribution can be seen in the figure below from Scripps Institute showing the carbon dioxide concentrations measured at (a) Mauna Loa in the Northern hemisphere, and (b) the South Pole.

Click on the image for a larger version. The carbon dioxide concentrations measured at (a) Mauna Loa in the Northern hemisphere, and (b) the South Pole. Notice that the data from South Pole shows only small seasonal variations and lags behind the Northern Hemisphere data by a couple of years.

Because of this difference in geographical distribution, the greenhouse effect due to carbon dioxide is relatively more important at higher latitudes where the water vapour concentration is low.

And that is why the observed warming at these latitudes is inevitably higher.

Click on the image for a larger version. The observed temperature anomalies shown as a function of location around the Earth for four recent years. Notice the extreme warming at the highest latitudes in the Northern Hemisphere (Source: UEA CRU).

Once I had read this explanation it seemed completely obvious, and yet somehow I had neither figured it out myself nor knowingly read it almost 20 years of study!

2022 to 1965: Looking Back and Looking Forwards

May 7, 2022

Click on the image for a larger version. The front page of a 1965 White House Report.

Friends, last week I wrote about the curious perspective that I gained in reading a Scientific American article on global warming from 1978 (link).

After reading that article, a friend sent me a link to a 1965 White House Report on Environmental  Pollution. You can download a copy here.

The report covered many topics, and tucked away in Appendix Y4 (a sub-appendix of Appendix X6 on “Air Problems”), was an analysis of Atmospheric Carbon Dioxide pollution.

Click on the image for a larger version. The appendices of a 1965 White House Report.

Appendix Y4 begins with a section entitled:

Carbon Dioxide from Fossil Fuels – The Invisible Pollutant

This article is a précis of the report and is followed by a reflection on the document’s conclusions from our perspective in 2022.

Précis#1: How much CO2 are we emitting?

The article begins by outlining the role of CO2 in controlling Earth’s climate. It then goes on to estimate the amount of CO2 in the atmosphere and the rate at which it is increasing from burning of fossil fuels. This exposition is well-written and overall very similar to our modern conception.

The Report goes on to make guesstimates of the likely atmospheric concentration in the years leading up to 2009.

In Table 6, it suggests that if there is no growth in the rate of fossil fuel emission, then in 2009 atmospheric emissions of CO2 would be 31% higher than in 1950. Assuming that 50% of these emissions ended up in the atmosphere (rather than the oceans or the biosphere) then atmospheric CO2 concentration in 2009 would be approximately 346 ppm. This estimate is shown in the figure below.

Click on the image for a larger version. The atmospheric concentration of CO2 at the Mauna Loa Observatory – the so-called Keeling Curve. Also shown is the date of the report and two predictions for the atmospheric concentration assuming either no growth in fossil fuel use, or growth at 3.2% p.a.

Table 6 also included predictions for higher growth rates in fossil fuel use (3.2% p.a. and 5.0 % p.a.) that result in predicted concentrations in 2009 of 386 ppm (close to what was observed) and 440 ppm. This latter prediction is just off the chart above, and we will probably reach this concentration in about 2030.

Précis#2: The effect on Earth’s temperature: looking forward.

When considering the likely effect of a 25% increase in atmospheric concentrations the report highlights (then) recent calculations suggesting that the warming would be between 0.6 °C and 4 °C “depending on the behaviour of water vapour“.

The report goes on to point out that there is more water vapour in the atmosphere near the Equator (because it is warmer) than near the poles (where it is colder). In contrast, CO2 is (after a few years of mixing) distributed uniformly around the globe.

Since both water vapour and CO2 are greenhouse gases, the comparative effect of the CO2 (wrt to water vapour) was likely to be more significant at higher latitudes.

However the general conclusion of the report was that more complex calculations were required, and these would likely be complete in the next two to three years i.e. by the end of the 1960’s.

Précis#3: The effect on Earth’s temperature: looking back.

The report also considered the experimental evidence that CO2 emissions of the previous century had already warmed the Earth.

Click on the image for a larger version. The Estimate of Global Average Temperature over the period 1850 to 2018. Also shown is the date of the report. We now know that the rate of warming  over the previous 30 was anomalously stable, but that there had been warming episodes earlier in the Century, and – although they did not know it – profound and ongoing warming was to follow for the following 55 years.

The report noted the work of Callendar (précis here) in 1937 who pointed out (correctly) that the Earth’s temperature had risen since the 1880s, and that the rise in atmospheric CO2 was a likely culprit.

However, they considered that Callendar had likely overestimated the rise in atmospheric CO2, and that the observed world-wide rise in temperature (which they confirmed) probably could not wholly be caused by CO2.

They then noted (correctly) that the Earth’s temperature had not risen substantially in the preceding 30 years (i.e. 1935 to 1965) during which CO2 emissions had risen by 40%.

Overall they concluded that climatic “noise” – intrinsic variability – had masked the warming – which implied that CO2-induced warming was not a significant problem at the present moment.

Précis#4: Other effects.

The report also considered other possible effects of increased concentrations of atmospheric CO2.

  • Melting of the Antarctic Ice Cap
  • Rise of sea level
  • Warming of sea water
  • Increased acidity of fresh water
  • Increase in photosynthesis

All the effects were considered potentially very significant, but at the time there was little evidence of harm in the near term.

It also considered other possible sources of increased concentrations of atmospheric CO2 aside from fossil fuels.

  • Oceanic warming
  • Cement production
  • Soil degradation
  • Ocean organic matter
  • Decline in capture rate of CO2 by the deep ocean
  • Changes in the volume of sea water
  • Volcanoes
  • Balance of dissolution and precipitation of carbonates.

But overwhelmingly they considered (correctly) that fossil fuel burning was the major source of atmospheric CO2 .

Précis#5: Conclusions.

The first few paragraphs of the Report’s conclusions summarise the report with admirable brevity.

Click on the image for a larger version. The first few paragraphs of the conclusions.

This summary contains two key sentences:

The first sentence states that (using gender neutral terminology):

Through worldwide industrial civilisation, humanity is unwittingly conducting a vast geophysical experiment.

Then the last sentence states:

The climatic changes that may be produced by the increased CO2 content could be deleterious from the point of view of human beings.

So having identified a potentially profound  problem what did this committee recommend?

Shockingly, their only comments were on albedo modification – cooling the Earth  by making it more reflective – by adding either white balls to the ocean surface, or seeding cirrus clouds.

And it is this response that I want to conclude on.

What can we learn by looking at this report?

So back in 1965 the brightest and the best – including Dr. Keeling of the Keeling Curve – looked at this issue, and with no strong evidence of the ongoing effect of CO2 (the temperature had not risen noticeably in the previous 30 years) and no ability to calculate the likely effect (such calculations would be 2 or 3 years off) concluded that if this became a problem in later years, all we could do was to alter the albedo of the Earth.

I think this gives us a really profound insight into the zeitgeist of the time. This group considered that there was literally no alternative to burning fossil fuels – it was central to industrial society.

The contrast with what is happening today is stark.

Appendix Y4 of the report is essentially an early version of the current IPCC report. Except that:

  • Now we have climate models that allow us to understand the role of CO2 in exceptional – but still not perfect – detail.
  • Now we have data that allow us to understand the role of the CO2 in affecting our climate over decades, centuries and millennia
  • Now we would suggest fossil-fuel demand reduction strategies: insulation of homes and targets for improved mileage on motor vehicles.
  • Now we would suggest increased use of solar and wind power – the cheapest and fastest growing technologies for electricity generation.
  • Now we would suggest increased use of internet-enabled grid-scale batteries which can stabilise the grid over seconds, minutes and hours.
  • Now we would  suggest development of longer term storage options to keep the grid operational over hours, days and weeks.
  • Now we would suggest increased nuclear power.
  • Now we would suggest a switch to electrically-powered vehicles.

In short, now we have access to technologies that did not exist in 1965, and which did not exist at a global scale until just a few years ago.

So although it would have been better to have started earlier, as I have written previously – I don’t think we are as far behind the optimal curve as it may seem.

2022 to 1978: Looking Back and Looking Forwards

May 3, 2022

Friends, it’s been two years since I retired, and since leaving the chaos and bullying at NPL, retirement has felt like the gift of a new life.

I now devote myself to pastimes befitting a man of my advanced years:

  • Drinking coffee and eating Lebanese pastries for breakfast.
  • Frequenting Folk Clubs
  • Proselytising about the need for action on Climate Change
  • Properly disposing of the 99% of my possessions that will have no meaning to my children or my wife after I die.

It was while engaged in this latter activity, that I came across some old copies of Scientific American magazine.

Last year I abandoned my 40 year subscription to the magazine because it had become almost content free. But in its day, Scientific American occupied a unique niche that allowed enthusiasts in science and engineering to read detailed articles by authors at the forefront of their fields.

In the January Edition for 1978 there were a number of fascinating articles:

  • The Surgical Replacement of the Human Knee Joint
  • How Bacteria Stick
  • The Efficiency of Algorithms
  • Roman Carthage
  • The Visual Characteristics of Words


  • The Carbon Dioxide Question

You can read a scanned pdf copy of the article here.

This article was written by George M Woodwell a pioneer ecologist. The particular carbon dioxide question he asked was this:

Will enough carbon be stored in forests and the ocean to avert a major change in climate?

The article did not definitively answer this question. Instead it highlighted the uncertainties in our understanding of the some of the key processes required to answer the question.

In 1978 the use of satellite analysis to assess the rate of loss of forests was in its infancy. And there were large uncertainties in estimates of the difference in storage capacity between native forests, and managed forests and croplands.

The article drew up a global ‘balance sheet’ for carbon, and concluded that there were major uncertainties in our understanding of many of the physical processes by which carbon and carbon dioxide was captured (or cycled through) Earth’s systems.

Some uncertainty still remains in these areas, but the basic picture has become clearer in the subsequent 44 years of intense study.

So what can we learn from this ‘out of date’ paper?

Three things struck me.


Firstly, from a 2022 perspective, I noticed that there are important things missing from the article!

In considering likely future carbon dioxide emissions, the author viewed the choices as being simply between coal and nuclear power.

Elsewhere in the magazine, the Science and the Citizen column discusses electricity generation by coal with no mention of CO2 emissions. Instead the article simply laments that coal will be in short supply and concludes that:

“There is no question… coal will supply a large part of the nation’s energy future. The required trade-offs will be costly however, particularly in terms of human life and disease.

Neither article mentions generation of electricity by gas turbines. And neither makes any mention of either wind or solar power generation – now the cheapest and fastest growing sources of electricity generation.

From this I note that in it it’s specific details, the future is very hard to see.


Despite the difficulties, the author did make predictions and it is fascinating from the perspective of 2022 to look back and see how those predictions from 1978 have worked out!

The article included predictions for 

  • The atmospheric concentration of CO2
  • CO2 emissions from Fossil Fuels

Click on image for a larger version. Figure from the 1978 article by George Woodwell. The curves in green (to be read against the right-hand axis) shows two predictions for atmospheric concentration of CO2. The curves in black (to be read against the left-hand axis) shows two predictions for fossil fuel emissions of CO2. In each case, the difference between the two curves represents the uncertainty caused by changes in the way CO2 would be cycled through (or captured by) the oceans and forests. See the article for a detailed rubric.

The current atmospheric concentration of carbon dioxide is roughly 420 ppm and the lowest projection from 1978 is very close.

The fossil fuel emissions estimates are given in terms of the equivalent change in atmospheric CO2, and I am not exactly sure how to interpret this correctly.

Atmospheric concentration of CO2 is currently rising at approximately 2.5 ppm per year, and roughly 56% of fossil fuel emissions end up in the atmosphere. So the annual emissions predicted for 2022 are around 2.5/0.56 ~ 4.5 ppm /year, which is rather lower than the lowest prediction of around 6 ppm/year.

The article also predicts that this will be the peak in annual emissions, but that has yet to be seen.

The predictions did not cover the warming effect of carbon dioxide emissions, the science of which was in the process of being formulated. ‘Modern’ predictions can be dated to 1981, when James Hansen and colleagues published a landmark paper in Science (Climate Impact of Increasing Atmospheric Carbon Dioxide) which predicted:

A 2 °C global warming is exceeded in the 21st century in all the CO2 scenarios we considered, except no growth and coal phaseout.

This is the path we are still on.

From this I note that the worst predictions don’t always happen, but sometimes they do.


The final observation concerns the prescience of the author’s conclusion in spite of his ignorance of the details.

Click on the image for a larger version. This is the author’s final conclusion in 1978

His last two sentences could not be truer:

There is almost no aspect of national or international policy that can remain unaffected by the prospect of global climatic change.

Carbon dioxide, until now an apparently innocuous trace gas in the atmosphere may be moving rapidly toward a central role as a major threat to the present world order.


First Winter with a Heat Pump

April 27, 2022

Friends, our first winter with a heat pump is over.

Last week:

  • I switched off the space heating, and…
  • I changed the heating cycle for domestic hot water (DHW) from night-time (using cheap-rate electricity) to day-time (using free solar electricity).

From now until the end of July, I am hopeful that we will be substantially off-grid.

Let me explain…

No Space Heating 

The figure below shows the temperatures relevant to our heating system for the week commencing Saturday 9th April.

The week started cold, with overnight temperatures close to 0 °C and daytime temperatures peaking at 12 °C.

But the week ended with much warmer temperatures, and even in the absence of any heating flow, the household temperature rose above 21 °C. At this point I decided to switch off the space heating. You can see this on the monitoring data below.

Up to the 15th April, the heat pump would operate each evening – you can see this because radiator temperatures oscillated overnight as the heating circuit struggled to deliver a very low heating power.

From the 16th April – with the space-heating off – you can see the radiator temperatures simply fell after the DHW water heating cycle.

Click image for a larger version. Graph showing four temperatures during the week beginning 9th April 2022. The upper graph shows the temperature of radiator flow and the domestic hot water (DHW). The lower graph shows the internal and external temperatures. In the colder weather at the start of the week, the radiator flow temperatures cycled on and off. In the warmer temperatures at the end of the week, heating stopped automatically. On 16th April I switched the space heating circuit off.

Heating DHW during the day 

The next graph shows the same data for the following week. Now there is no space-heating in the house, but the insulation is good enough that household temperature does not fall very much overnight.

On the 20th April I switched from heating the domestic hot water at night (using cheap rate electricity) to heating during the afternoon (using electricity generated using solar PV).

My plan was that by 2:00 p.m., the battery would be substantially re-charged, and heating the hot water at that time would:

  1. Minimise exports to the grid and maximise self-use of solar-generated electricity.
  2. Heat the domestic hot water using air that was ~ 10 °C hotter than it would be at night – improving the efficiency of the heat pump.

Click image for a larger version. Graph showing four temperatures during the week beginning 16th April 2022. The upper graph shows the temperature of radiator flow and the domestic hot water (DHW). The lower graph shows the internal and external temperatures. The radiator flow was switched off. On 20th April I switched from heating the domestic hot water at night to heating during the day.

One can see that household temperature has fallen a little during the week, but only to around 19 °C, which feels quite ‘spring-like’ in the sunshine.

The big picture 

The graph below shows:

  1. The amount of electricity used by the household
  2. The amount of electricity drawn from the grid

It covers the whole of 2021 and the start of 2022 up to today (almost) the end of April. The graphs show running averages over ± 2 weeks.

Click image for a larger version. Graph showing the amount of electricity used by the household each day (kWh/day) and the amount of electricity drawn from the grid each day (kWh/day). Over the 8 months of the winter heating season, 27% was supplied by solar generated electricity.

The 4 kWp solar PV system was installed in November 2020 and was just beginning to make a noticeable difference to our electricity consumption in the spring of 2021.

In March 2021 we installed the Powerwall and immediately dropped off the grid for just over 2 months! In mid-summer we had a run of very poor solar days and we began to draw from the grid again.

In July 2021 we installed a heat pump and this extra load (for DHW) coupled with the decline in solar generation caused us to need to draw a few kWh from the grid each day.

Over the 8 month heating season from the start of August to the end of April, the household used 4,226 kWh of electricity for all the normal activities (~ 2,200 kWh) plus heating using the heat pump (~2,000 kWh). Over this period the heat pump delivered just over 7,000 kWh of heat for a seasonally averaged COP of around 3.5.

However, even in this winter season, only 3,067 kWh were drawn from the grid – mostly at low cost. The balance (27%) was solar generated.

Summer and Winter Settings

The optimal strategy for the Powerwall is now becoming clear.

In the Winter season, daily consumption can reach 25 kWh/day and solar generation is only ~ 2 kWh day. So in this season:

  • We operate the household from the grid during the off-peak hours.
  • We time heavy loads (dishwashing, tumble drying and DHW heating) to take place in the off peak hours.
  • We buy electricity from the grid to fill the battery (13.5 kWh) with cheap rate electricity – and then run the household from the battery for as long as possible. Typically we would need to draw full price electricity from the grid only late in the day.

Click image for a larger version. Images showing the time of day that we have drawn power from the grid (kW) in half-hour periods through the day. Each image shows the average for one month. The graph was assembled using data from the fabulous Powershaper software (link).

In the ‘summer’ season, daily household consumption is ~11 kWh and average solar generation is typically 15 kWh/day. So given that the battery has 13.5 kWh of storage, we can still stay ‘off-grid’ even during a periods of two or three dull days.

So during this period

  • We switch the battery from ‘time-based’ mode to ‘self-powered’ mode.
  • We time heavy loads (dishwashing, tumble drying and DHW heating) to take place in the afternoon.

This year and last year 

Last year (2021), as soon as we installed the Tesla Powerwall battery, we dropped off-grid within days.

But this year (2022) we have an additional daily electrical load. Now we are heating DHW electrically with a heat pump which requires ~ 1.5 kWh/day.

Nonetheless, I hope it will be possible to remain substantially ‘off-grid’ for the next few months. Time will tell.

I’ve been interviewed for a Podcast!

April 25, 2022

I’m on a Podcast! (Link)

Friends, I have been relatively quiet lately because I have been indulging some of my other retirement enthusiasms.

Some of these are a source of delight – such as singing and recording songs – and others are not so delightful – such as trying to clear out the detritus of my life. Throwing things out is hard.

I have been writing blog articles, but somehow the simple topics I have chosen to write about have become more complicated as I have written the articles. This is another of example of the fact that I am not writing to record what I think: I am writing to discover what I think!

But my previous articles about heat pump sizing (1, 2, 3, 4) and the summary ‘Rule of Thumb’ video have been catching people’s attention! As I write 394 people have watched the summary video – more than all the other videos on the channel put together!

Part of that popularity is because Nathan Gambling, the mastermind behind the BetaTeach initiative, asked me if I would take part in a podcast.

Nathan is from a family of heating engineers and runs BetaTeach to encourage heating engineers to adopt a ‘systems approach’ that enables them to install heat pumps in all kinds of homes.

His approach contrasts with many training programs which tend to focus on how to install the products of a particular company.

I was honoured to be asked to be his guest on his BetaTalk podcast and you can hear the results of our Zoom chat here:

It is 64 minutes of truly random chat, with a vague theme linking to temperature and heat. At times I lost my way in the interview, but hopefully you won’t.

If the above link doesn’t work, then search Google for “Betatalk – the Renewable Energy and Low Carbon Heating Podcast

Could you heat your house with a hairdryer?

April 12, 2022

Click the image for a larger version. The graph shows the average electrical power (in kW) used by our heat pump to keep the 164 square metres of Podesta Towers at approximately 20.5 °C throughout the winter.  Also shown is the typical power used by a hairdryer on typical high, medium and low powers.

Friends, a chance remark on the internet intrigued me.

Someone commented that their heat pump was heating their house using less power than a hairdryer. Could that really be true?

Looking it up (link), I found that a hair dryer actually uses rather more power than I had supposed: somewhere between 850 watts (0.85 kW) and 1850 watts (1.85 kW) depending on its power setting.

I then looked up week-by-week data for our heat pump at Podesta Towers.

And slightly to my surprise I found that even in the coldest weeks, the average electrical power used by the heat pump was less than 800 watts (0.8 kW) i.e. we were heating our house with less electricity than it takes to run a hairdryer – on its lowest setting! And that includes re-heating the hot water tank each day!

So why didn’t I just buy a hairdryer?

Why? Because a hairdryer – even on full power – could not heat my house.

The wonder and fascination of heat pumps is that they don’t just squander the electricity they consume: they use it to scavenge heat from the outside air and even on the coldest days they can deliver many times more heat energy into the house than the electrical energy they consume.

The ratio of the heat energy they deliver to the electrical energy they consume is called the Coefficient of Performance (COP) and for my heat pump the average COP since installation is 3.6.

In other words the heat pump has delivered more energy than two hairdryers on full power while consuming less energy a single hair dryer on low power.


The graph below shows the COP evaluated week-by-week and the average value since August 2021.

Click the image for a larger version. The graph shows the average coefficient of performance (COP) week-by-week since installation in August 2021. Also shown in the average coefficient of performance (COP) since installation, also known as the Seasonal Coefficient of Performance (SCOP).

The low average values in the autumn are because the heat pump is only delivering domestic hot water at 55 °C and is not heating the house at all.

During this time, the 20 watts of electrical power that the heat pump’s computer consumes (0.5 kWh/day) represents a significant fraction of the energy delivered.

In contrast, in winter the heat pump is delivering more than 20 kWh of heat energy per day and the consumption by the heat pumps’ control circuitry is less than 3% of the heat energy delivered.


I found this juxtaposition intriguing. 

A hair dryer is a simple device – a hand-held fan heater – and a heat pump is a much more complex machine.

But comparing them just by their electrical consumption highlights the awesome power of heat pumps.

March 2022

April 8, 2022

Friends, Spring is springing, and our first winter with a heat pump is ending.

Overall, it has been phenomenally successful. All the parts of our refurbishment have played their part.

  • The triple-glazing and external wall insulation have reduced the heating power required to heat the house.
  • The solar panels continued to deliver ~5% of our electricity requirements even in December.
  • The battery (a 13.5 kWh Tesla Powerwall) allowed us to download cheap electricity at night and use it to heat the house during the day.
  • The heat pump kept the house warm and delivered hot water, with an average Coefficient of Performance of around 3.5.

In this article I will be looking at figures for the month of March 2022.

When the heating season is a little more over than it is at present, I will write about the winter as a whole.

Solar PV and Battery

Click image for a larger version. This is on the notice board outside my house.

I have put a notice on the front of the house to advertise how little we are spending on heating and running the house. Excluding the standing charges, we spent just £14.34 heating the house and running all the electrical items in the house.

In honesty, I am embarrassed to disclose how little I am spending on fuel bills. I am embarrassed because of the suffering and anxiety that so many people will be feeling now as prices rise.

Nonetheless, when it comes to communicating the wonder of a well-insulated home powered by solar, talking about money is one way to communicate more viscerally than using kilowatt-hours and kilograms of carbon dioxide.

Energy Flows

Click image for a larger version. This graphic shows my best estimate of the energy flows around my house. There are two sources of electricity: the grid and the solar PV system. During the hours when grid electricity is cheap, the grid supplies the house directly and charges the battery. Solar PV supplies the house directly, then if household demand is met, it charges the battery, and if the battery is full, it exports electricity. My analysis suggests that the battery is only 87% efficient i.e. 13% of the energy is lost in the process of charging and discharging the battery.

The graphic above describes the energy flows in the house.

On a typical day:

  • Between 00:30 and 04:30 the house runs on cheap grid electricity, and we time the dishwasher and hot water heating to run over this period. The grid also charges the battery.
  • After 04:30 the battery runs the household and is then re-charged during daylight hours by whatever solar PV is available.
    • If the battery charge reaches 100%, then solar PV is exported.
    • If the battery discharges to 0%, then we run off full price grid electricity.

Analysing the data from the Tesla App, it looks like the battery returns 87% of the charge delivered to it. The system is specified to have a charge/discharge efficiency of 90%. I suspect that extra losses arise from the energy the battery uses to maintain its own condition.

The figure below shows the average pattern of grid use during the month. The majority of electricity is used during the cheap rate period and only a small fraction of full-price electricity is required on days when solar PV generation is insufficient to keep the battery topped up.

Click image for a larger version. This graphic shows the time of day at which the house drew electricity from the grid in March 2022. The vast majority of the electricity was consumed at night to (a) charge the battery and (b) directly operate timed loads such as the dishwasher, washing machine, and heat pump domestic hot water cycle.

Heat Pump

Click image for a larger version. Graph showing internal and external temperatures, and the temperature of water flowing in the radiators during the month of March. Data were collected every 2 minutes. The radiator flow temperature data has been smoothed. It is clear the system operates well to keep the internal temperature constant even as the external temperature varies

The average external temperature was 9.3 °C, but the month started very cold, and then later there were some exceptionally warm days (with cold nights).

The weather compensation adjusted the flow temperature in the radiators to keep the internal temperature at a comfortable average of 21.1 °C

The monthly averaged Coefficient of Performance was 3.75 which is rather more than I had hoped for.


When we installed the battery in March 2021, we immediately dropped of the grid for 90 days: this felt astonishing. But back then then our heating was with gas.

Now our heating and hot water systems are electrical and this adds to the daily load.

As the year progresses, Solar PV generation is growing and heating demand is falling. At some point I hope we will again be able to reduce grid use to zero for an extended period – but it will definitely not be as long as last year.

It was interesting to arrive at a figure for the battery storage efficiency. The figure of 87% was lower than I had hoped for, but since the battery is saving us so much money, it seems churlish to complain!



What Size Heat Pump Do I Need? A Rule of Thumb

April 5, 2022

Friends, a few weeks ago I wrote four articles about using the idea of Heating Degree Days to make simple calculations about heat losses from one’s home.

  • Article 1 was an introduction to the idea of Heating Degree Days as a general measure of the heating demand from a dwelling.
  • Article 2 explained how and why the idea of Heating Degree Days works.
  • Article 3 looked at the variability of Heating Degree Days across the UK, at locations around London, and from year to year.
  • Article 4 introduced some rules of thumb for estimating the Heat Transfer Coefficient for a dwelling and the size of heat pump it requires.

The Rule of Thumb for Heat Pump Sizing is dramatically simple:

The video above is about using these ‘Rules of Thumb’.

I feel these rules could be helpful to both heat pump installers and their clients.

The Powerpoint slides (.pptx) I use in the presentation can be found here.






Analysis of 16 years of Solar PV data.

March 16, 2022

A friend from North London kindly allowed me to analyse the data they had collected on the performance of their solar PV installation over the last 16 years.

What an opportunity to discover how solar PV panels behave over the long term!

Let me tell you what I found:

The System

Installed in July 2006, the system consisted of 16 Sanyo PV panels, each 0.88 m x 1.32 m with a nominal peak output of 210 W. This implies the panels output was initially ~180 watts per square metre.

They were installed on two adjacent roofs with a tilt of about 30° and facing 25° East of South and with no nearby trees or shading structures on the horizon other than their neighbour’s house.

The data set consisted of roughly 700 readings of the solar generation meter, most of them taken weekly but with a couple of gaps for a few months, and few points that were clearly in error. Rather than try to be sophisticated, I simply omitted points that were obviously in error.

Click image for a larger version. The ‘cleaned up’ data set.

Annual Analysis

One of things I was most anxious to search for was evidence of a year-on-year decline. The annual results are shown below:

Click image for a larger version. Graph of the Annual Output (kWh) of a North London PV system from 2006 to 2021. The dotted line is a linear fit to the data showing a systematic year-on-year decline in output.

It’s clear that there is a systematic year-on-year decline. If we re-plot the data to express this as a percentage we can compare it with what we might expect.

Click image for a larger version. The same data as in the previous graph but expressed as a fraction of the average output over the years 2007 and 2008. The dotted line is a linear fit to the data showing a systematic year-on-year decline in output.

This decline is – sadly – inevitable, arising as I understand it from atomic defects created in the silicon cells by exposure to the UV radiation in sunlight. These defects trap electrons which would otherwise reach an external contact if the crystal had been undamaged.

A decline of 6.1% per decade (0.61% per year) is quite competitive. Older panels showed higher declines (link) and more modern cells claim better performance, but not much better.

For example a 2020 Q-Cells Duo panel (link) specifies 0.54%/year decline for up to 10 years,  i.e. 5.4% per decade.

Click image for a larger version. Extract from a Q-cells data sheet showing expected decline in panel output over 25 years.


In addition to a linear decline in output the data also shows significant year-to-year variability. I wondered whether this variability arose from the natural variability of available sunshine, or some other factor.

To check this I exploited the EU Photovoltaic Geographical Information System (a.k.a. a ‘Sunshine Database’) which allows the calculation of the output of PV cells at any point in Europe or Africa over the period 2005 to 2016.

I had previously used this database to model the year-to-year variability of sunshine in West London when I was planning a battery installation.

To see if this was the cause of the year-to-year variability I plotted two quantities on the same graph:

  • The so-called ‘residuals’ of the fit to the data in the second graph above.
  • The variability of EU-database data.

The results are shown below.

Click image for a larger version. The variability of the North London PV data and the natural variability of sunshine as retro-dicted by the EU sunshine database

It is clear that in the years for which the two datasets overlap they agree well, suggesting that the variability observed is not due to some other poorly understood factor.


My North London friend had one final question. Would they avoid more carbon dioxide emissions if they upgraded to modern panels?

To answer this I made two models:

  • The first model assumed that they did not upgrade and the existing panels were used to out to 2050.
  • The second model assumed they were replaced in 2022 with panels which operated with an efficiency of around 200 W/m^2 at peak illumination. This is about 20% more than the panels currently generate.

I assumed that the new panels would embody around 2 tonnes of CO2 emissions because Q-cells suggest their latest panels embody 400 kgCO2 per kWp.

I then assumed that 50% of the generated electricity was exported and 50% used domestically. As the grid currently functions:

  • Exported electricity reduces gas-fired generation which emits 450 gCO2/kWhe.
  • Domestic use avoids consumption of grid electricity with a carbon intensity of around 220 gCO2/kWhe in 2022.

Based on these assumptions, there is small advantage to replacing the panels, but this would not be realised until 2035.

Click image for a larger version. Does it make carbon-sense to replace existing PV cells with new more efficient cells?

One can model variations of these parameters, but the basic result is not affected: the carbon advantage is marginal.

My friend would help the climate more effectively by allocating his capital expenditure to something which might have more impact on CO2 emissions, perhaps buying shares in a wind farm?

But the result that really struck me from this modelling was how great the solar panels were in the first place!

Installed in 2006 and given minimal maintenance, it looks like the existing cells will avoid almost 30 tonnes of CO2 emissions by 2050. Not many technologies can achieve results like that as easily as that.

Heating Degree Days:4:Three numbers you need to know about your home

March 15, 2022

Friends, after the previous three posts (1, 2, 3) about Heating Degree Days, you may be wondering:

  • Is Michael OK? He seems to be obsessed with Heating Degree Days?
  • Hasn’t he been keeping an eye on the COVID figures?

Well, I have indeed been focussed on Heating Degree Days, and in this short (!) article I would like to summarise why.

The Heating Degree Day (HDD) concept enables two calculations for numbers you really should know about your dwelling:

  • It’s thermal leakiness: technically its heat transfer coefficient (HTC)
  • The size of heat pump your dwelling requires.

When combined with an estimate for how good the insulation is, you will be in a great position to make rational choices about improving the thermal performance of your dwelling.

Here are the three calculations:

#1:Heat Transfer Coefficient.

How much does heating power does it take to make your dwelling 1 °C warmer?

The answer to this question is known as the Heat Transfer Coefficient (HTC) for a dwelling.

A first estimate of your HTC can be made by dividing your annual gas consumption (in kWh) by 57.3:

Note: This formula was revised on 21/3/2022 due to a typo in the original text.

This assumes your dwelling (flat or house) is in the southern half of the UK (i.e. South of Manchester) and that you set your thermostat to 20 °C.

  • If you live between Manchester and Edinburgh, reduce your estimate of HTC by 10%.
  • For each 1 °C above 20 °C that you set your thermostat, reduce the first estimate of HTC by 10%.
  • For each 1 °C below 20 °C that you set your thermostat, increase the first estimate of HTC by 10%.

#2:Heat Pump Size.

How big a heat pump do I need?

It’s the question everyone wants an answer to!

A first estimate of the size of heat pump you require can be made by dividing your annual gas consumption (in kWh) by 2,900.

This assumes your dwelling (flat or house) is in the southern half of the UK (i.e. South of Manchester) and that you set your thermostat to 20 °C.

  • If you live between Manchester and Edinburgh, increase your estimate of heat pump power by 10%.
  • For each 1 °C above 20 °C that you set your thermostat, increase your estimate of heat pump power by 10%.


Do I need more insulation?

If your home is a house (rather than a flat), then you can assess how good your home is compared to the best possible as follows.

Divide your annual gas consumption (in kWh) by the floor area of all the floors in your home that live in i.e. include the loft if its part of the domestic space but not if it’s just used for storage.

  • The best possible is < 15 kWh/m^2/year: this is the Passivhaus standard
  • The best possible retrofit is < 25 kWh/m^2/year: this is the Enerphit retrofit standard
  • The AECB retrofit standard is < 50 kWh/m^2/year.

My house was ~ 90 kWh/m^2/year before external wall insulation and triple-glazing reduced it to around 45 kWh/m^2/year. The only way to significantly improve on this would be with underfloor insulation and air-tightness work.

If the figure for your home is very much above 100 kWh/m^2/year then I would suggest you consider insulation work.


If you know these numbers – even approximately – for your home, then you will be in a position to make reasonable choices about what to do next.

Please bear in mind that all the figures are approximate. I can see ways in which they could be wrong by 10%, but I would be surprised if they were 20% wrong.

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