Hierarchies of Models

With thanks to Inna Polichtchouk.

General circulation models (GCMs) of varying complexity are used in atmospheric and oceanic sciences to study different atmospheric processes and to simulate response of climate to climate change and other forcings.

However, Held (2005) warned the climate community that the gap between understanding and simulating atmospheric and oceanic processes is becoming wider. He stressed the use of model hierarchies for improved understanding of the atmosphere and oceans (Fig. 1). Often at the bottom of the hierarchy lie the well-understood, idealized, one- or two-layer models.  In the middle of the hierarchy lie multi-layer models, which omit certain processes such as land-ocean-atmosphere interactions or moist physics. And finally, at the top of the hierarchy lie fully coupled atmosphere-ocean general circulation models that are used for climate projections. Such model hierarchies are already well developed in other sciences (Held 2005), such as molecular biology, where studying less complex animals (e.g. mice) infers something about the more complex humans (through evolution).

Figure 1: Model hierarchy of midlatitude atmosphere (as used for studying storm tracks). The simplest models are on the left and the most complex models are on the right. Bottom panels show eddy kinetic energy (EKE, contours) and precipitation (shading) with increase in model hierarchy (left-to-right): No precipitation in a dry core model (left), zonally homogeneous EKE and precipitation in an aquaplanet model (middle), and zonally varying EKE and precipitation in the most complex model (right). Source: Shaw et al. (2016), Fig. B2.

Model hierarchies have now become an important research tool to further our understanding of the climate system [see, e.g., Polvani et al. (2017), Jeevanjee et al. (2017), Vallis et al. (2018)]. This approach allows us to delineate most important processes responsible for circulation response to climate change (e.g., mid-latitude storm track shift, widening of tropical belt etc.), to perform hypothesis testing, and to assess robustness of results in different configurations.

In my PhD, I have extensively used the model hierarchies concept to understand mid-latitude tropospheric dynamics (Fig. 1). One-layer barotropic and two-layer quasi-geostrophic models are often used as a first step to understand large-scale dynamics and to establish the importance of barotropic and baroclinic processes (also discussed in my previous blog post). Subsequently, more realistic “dry” non-linear multi-layer models with simple treatment for boundary layer and radiation [the so-called “Held & Suarez” setup, first introduced in Held and Suarez (1994)] can be used to study zonally homogeneous mid-latitude dynamics without complicating the setup with physical parametrisations (e.g. moist processes), or the full range of ocean-land-ice-atmosphere interactions. For example, I have successfully used the Held & Suarez setup to test the robustness of the annular mode variability (see my previous blog post) to different model climatologies (Boljka et al., 2018). I found that baroclinic annular mode timescale and its link to the barotropic annular mode is sensitive to model climatology. This can have an impact on climate variability in a changing climate.

Additional complexity can be introduced to the multi-layer dry models by adding moist processes and physical parametrisations in the so-called “aquaplanet” setup [e.g. Neale and Hoskins (2000)]. The aquaplanet setup allows us to elucidate the role of moist processes and parametrisations on zonally homogeneous dynamics. For example, mid-latitude cyclones tend to be stronger in moist atmospheres.

To study effects of zonal asymmetries on the mid-latitude dynamics, localized heating or topography can be further introduced to the aquaplanet and Held & Suarez setup to force large-scale stationary waves, reproducing the south-west to north-east tilts in the Northern Hemisphere storm tracks (bottom left panel in Fig. 1). This setup has helped me elucidate the differences between the zonally homogeneous and zonally inhomogeneous atmospheres, where the planetary scale (stationary) waves and their interplay with the synoptic eddies (cyclones) become increasingly important for the mid-latitude storm track dynamics and variability on different temporal and spatial scales.

Even further complexity can be achieved by coupling atmospheric models to the dynamic ocean and/or land and ice models (coupled atmosphere-ocean or atmosphere only GCMs, in Fig. 1), all of which bring the model closer to reality. However, interpreting results from such complex models is very difficult without having first studied the hierarchy of models as too many processes are acting simultaneously in such fully coupled models.  Further insights can also be gained by improving the theoretical (mathematical) understanding of the atmospheric processes by using a similar hierarchical approach [see e.g. Boljka and Shepherd (2018)].


Boljka, L. and T.G. Shepherd, 2018: A multiscale asymptotic theory of extratropical wave–mean flow interaction. J. Atmos. Sci., 75, 1833–1852, https://doi.org/10.1175/JAS-D-17-0307.1 .

Boljka, L., T.G. Shepherd, and M. Blackburn, 2018: On the boupling between barotropic and baroclinic modes of extratropical atmospheric variability. J. Atmos. Sci., 75, 1853–1871, https://doi.org/10.1175/JAS-D-17-0370.1 .

Held, I. M., 2005: The gap between simulation and understanding in climate modeling. Bull. Am. Meteorol. Soc., 86, 1609 – 1614.

Held, I. M. and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75, 1825–1830.

Jeevanjee, N., Hassanzadeh, P., Hill, S., Sheshadri, A., 2017: A perspective on climate model hierarchies. JAMES9, 1760-1771.

Neale, R. B., and B. J. Hoskins, 2000: A standard test for AGCMs including their physical parametrizations: I: the proposal. Atmosph. Sci. Lett., 1, 101–107.

Polvani, L. M., A. C. Clement, B. Medeiros, J. J. Benedict, and I. R. Simpson (2017), When less is more: Opening the door to simpler climate models. EOS, 98.

Shaw, T. A., M. Baldwin, E. A. Barnes, R. Caballero, C. I. Garfinkel, Y-T. Hwang, C. Li, P. A. O’Gorman, G. Riviere, I R. Simpson, and A. Voigt, 2016: Storm track processes and the opposing influences of climate change. Nature Geoscience, 9, 656–664.

Vallis, G. K., Colyer, G., Geen, R., Gerber, E., Jucker, M., Maher, P., Paterson, A., Pietschnig, M., Penn, J., and Thomson, S. I., 2018: Isca, v1.0: a framework for the global modelling of the atmospheres of Earth and other planets at varying levels of complexity. Geosci. Model Dev., 11, 843-859.

Oceans in Weather and Climate Course 2018

email: r.frew@pgr.reading.ac.uk

Between the 11th-16th March myself and four other PhDs and post docs attended the Ocean in Weather and Climate (OiWC) course at the Met Office, Exeter. This NERC advanced training course was aimed at PhDs, postdocs and beyond. It provided a great opportunity to spend a week meeting other Oceanography researchers at varying stages of their career, and to expand your understanding of the oceans role in climate beyond the scope of your own work.

The week kicked off with an ice breaker where we had do some ‘Scientific speed dating’, chatting to other participants about: Where are you from? What do you work on? What is your main hobby? What is the biggest question in your field of research? This set the tone for a very interactive week full of interesting discussions between all attendees and speakers alike. Course participants were accommodated at The Globe Inn situated in Topsham, a cute village-sized town full of pastel-coloured houses, cosy pubs, art galleries, and beautiful riverside walks to stretch your legs in the evenings.

The days consisted of four 1.5 hour sessions, split up by caffeine and biscuit breaks to recharge before the next session.

Topics covered in the lecture-style talks included…

  • Dynamical Theory
  • Modelling the Ocean
  • Observations
  • Ocean-atmosphere coupling
  • Air-sea fluxes
  • High Resolution Ocean modelling in coupled forecast systems
  • The Meridional Overturning Circulation
  • The Southern Ocean in climate and climatic change
  • Climate variability on diurnal, seasonal, annual, inter-annual, decadal timescales
  • Climate extremes
  • Climate sensitivity, heat uptake and sea level.
A recurring figure of the week…. taken from Helene Hewitt’s talk on high resolution ocean modelling showing ocean surface currents from HadGEM3-based global coupled models at different resolutions (eddy resolving, eddy permitting and eddy parameterised).


All the talks were very interesting and were followed by some stimulating discussion. Each session provided an overview of each topic and an indication of the current research questions in each area at the moment.

In the post lunch session, there were group practical sessions. These explored observational ARGO float data and model output. The practicals, written in iPython notebooks, were designed to let us play with some data, giving us a series of questions to trigger group discussions to deepen understanding of topics covered that morning.

The course also included some ‘softer’ evening talks, giving research career advice in a more informal manner. Most evenings were spent exploring the lovely riverside walks and restaurants/pubs of Topsham. The final evening was spent all together at the Cosy Club in Exeter, rounding off a very interesting and enjoyable week!

Baroclinic and Barotropic Annular Modes of Variability

Email: l.boljka@pgr.reading.ac.uk

Modes of variability are climatological features that have global effects on regional climate and weather. They are identified through spatial structures and the timeseries associated with them (so-called EOF/PC analysis, which finds the largest variability of a given atmospheric field). Examples of modes of variability include El Niño Southern Oscillation, Madden-Julian Oscillation, North Atlantic Oscillation, Annular modes, etc. The latter are named after the “annulus” (a region bounded by two concentric circles) as they occur in the Earth’s midlatitudes (a band of atmosphere bounded by the polar and tropical regions, Fig. 1), and are the most important modes of midlatitude variability, generally representing 20-30% of the variability in a field.

Figure 1: Southern Hemisphere midlatitudes (red concentric circles) as annulus, region where annular modes have the largest impacts. Source.

We know two types of annular modes: baroclinic (based on eddy kinetic energy, a proxy for eddy activity and an indicator of storm-track intensity) and barotropic (based on zonal mean zonal wind, representing the north-south shifts of the jet stream) (Fig. 2). The latter are usually referred to as Southern (SAM or Antarctic Oscillation) or Northern (NAM or Arctic Oscillation) Annular Mode (depending on the hemisphere), have generally quasi-barotropic (uniform) vertical structure, and impact the temperature variations, sea-ice distribution, and storm paths in both hemispheres with timescales of about 10 days. The former are referred to as BAM (baroclinic annular mode) and exhibit strong vertical structure associated with strong vertical wind shear (baroclinicity), and their impacts are yet to be determined (e.g. Thompson and Barnes 2014, Marshall et al. 2017). These two modes of variability are linked to the key processes of the midlatitude tropospheric dynamics that are involved in the growth (baroclinic processes) and decay (barotropic processes) of midlatitude storms. The growth stage of the midlatitude storms is conventionally associated with increase in eddy kinetic energy (EKE) and the decay stage with decrease in EKE.

Figure 2: Barotropic annular mode (right), based on zonal wind (contours), associated with eddy momentum flux (shading); Baroclinic annular mode (left), based on eddy kinetic energy (contours), associated with eddy heat flux (shading). Source: Thompson and Woodworth (2014).

However, recent observational studies (e.g. Thompson and Woodworth 2014) have suggested decoupling of baroclinic and barotropic components of atmospheric variability in the Southern Hemisphere (i.e. no correlation between the BAM and SAM) and a simpler formulation of the EKE budget that only depends on eddy heat fluxes and BAM (Thompson et al. 2017). Using cross-spectrum analysis, we empirically test the validity of the suggested relationship between EKE and heat flux at different timescales (Boljka et al. 2018). Two different relationships are identified in Fig. 3: 1) a regime where EKE and eddy heat flux relationship holds well (periods longer than 10 days; intermediate timescale); and 2) a regime where this relationship breaks down (periods shorter than 10 days; synoptic timescale). For the relationship to hold (by construction), the imaginary part of the cross-spectrum must follow the angular frequency line and the real part must be constant. This is only true at the intermediate timescales. Hence, the suggested decoupling of baroclinic and barotropic components found in Thompson and Woodworth (2014) only works at intermediate timescales. This is consistent with our theoretical model (Boljka and Shepherd 2018), which predicts decoupling under synoptic temporal and spatial averaging. At synoptic timescales, processes such as barotropic momentum fluxes (closely related to the latitudinal shifts in the jet stream) contribute to the variability in EKE. This is consistent with the dynamics of storms that occur on timescales shorter than 10 days (e.g. Simmons and Hoskins 1978). This is further discussed in Boljka et al. (2018).

Figure 3: Imaginary (black solid line) and Real (grey solid line) parts of cross-spectrum between EKE and eddy heat flux. Black dashed line shows the angular frequency (if the tested relationship holds, the imaginary part of cross-spectrum follows this line), the red line distinguishes between the two frequency regimes discussed in text. Source: Boljka et al. (2018).


Boljka, L., and T. G. Shepherd, 2018: A multiscale asymptotic theory of extratropical wave, mean-flow interaction. J. Atmos. Sci., in press.

Boljka, L., T. G. Shepherd, and M. Blackburn, 2018: On the coupling between barotropic and baroclinic modes of extratropical atmospheric variability. J. Atmos. Sci., in review.

Marshall, G. J., D. W. J. Thompson, and M. R. van den Broeke, 2017: The signature of Southern Hemisphere atmospheric circulation patterns in Antarctic precipitation. Geophys. Res. Lett., 44, 11,580–11,589.

Simmons, A. J., and B. J. Hoskins, 1978: The life cycles of some nonlinear baroclinic waves. J. Atmos. Sci., 35, 414–432.

Thompson, D. W. J., and E. A. Barnes, 2014: Periodic variability in the large-scale Southern Hemisphere atmospheric circulation. Science, 343, 641–645.

Thompson, D. W. J., B. R. Crow, and E. A. Barnes, 2017: Intraseasonal periodicity in the Southern Hemisphere circulation on regional spatial scales. J. Atmos. Sci., 74, 865–877.

Thompson, D. W. J., and J. D. Woodworth, 2014: Barotropic and baroclinic annular variability in the Southern Hemisphere. J. Atmos. Sci., 71, 1480–1493.

Sea ice is complicated, but do sea ice models need to be?

email: r.frew@pgr.reading.ac.uk

Sea ice is complex…

When sea water freezes it forms sea ice, a composite of ice and brine. Sea ice exhibits varying structural, thermodynamic and mechanical properties across a range of length- and time-scales. It can be subcategorised into numerous different types of sea ice depending on where is grows and how old it is.



Different sea ice growth processes and types 1.

However, climate models do not simulate the evolution of floes (they model floes as cylindrical) or the floe size distribution, which has implications for ice melt rates and exchange of heat with the atmosphere and ocean. Sea ice also hosts algae and small organisms within brine channels in the ice, which can be important for nutrient cycles. This is a developing area of earth system modelling.

Schematic of life within brine channels in sea ice 2.

How much complexity do global climate models need to sufficiently model the interactions of sea ice with the ocean and atmosphere?
The representation of sea ice in global climate models is actually very simple, with minimal sea ice types and thickness categories. The main important feature of sea ice for global climate models is its albedo, which is much greater than that of open water, making it important for the surface energy balance. So, it is important to get the correct area of sea ice. Global climate models need sea ice:

  • to get the correct heat exchange with the atmosphere and ocean
  • to get a realistic overturning circulation in the ocean.
  • because salt release during sea ice growth is important for the ocean salinity structure, and therefore important to get the correct amount of sea in/near deep water formation sites.
  • sea ice is not important for sea level projections.

So, do the complex features of sea ice matter, or are simple parameterisations sufficient?

Sea_ice_Drawing_General_features.svg Schematic showing some dynamic features of sea ice 3.

Which leads to a lot more questions…

  • Where does the balance between sufficient complexity and computational cost lie?
  • Does adding extra model complexity actually make it harder to understand what the model is doing and therefore to interpret the results?
  • Do climate models need any further improvements to sea ice in order to better simulate global climate? There is still large uncertainty surrounding other climate model components, such as clouds and ocean eddies, which are believed to explain a lot of the discrepancy between models and observations, particularly in the Southern Ocean.

A lot of these questions depend on the scientific question that is being asked. And the question is not necessarily always ‘how is global climate going to change in the future’. Sea ice is fascinating because of its complexity, and there are still many interesting questions to investigate, hopefully before it all melts!

 Images clockwise from top left: grease ice 4, pancake ice 5, surface melt ponds 6, ice floes 7

The Future Developments in Climate Sea Ice Modelling Workshop

This blog stems from a one day workshop I attended on ‘Future developments in climate sea ice modelling’ at the Isaac Newton Centre as part of a four month programme on the ‘Mathematics of Sea Ice Phenomena’. The format of the day was that three different strands of sea ice researchers gave 40 min talks giving their strand’s point of view of current sea ice developments and what the focus should be for sea ice modelers, each followed by 40 mins of open discussion with the audience.

The three (very good!) talks were:

  1. Dirk Notz: What do climate models need sea ice for? A top-down, system level view of what sea ice models should produce from the perspective of a climate modeller.
  2. Cecilia Bitz: What sea ice physics is missing from models? A bottom-up view of what is missing from current sea ice models from the perspective of a sea ice scientist.
  3. Elizabeth Hunke: What modelling approaches can be used to address the complexity of sea ice and the needs of climate models?


  1. https://nsidc.org/cryosphere/seaice/characteristics/formation.html.
  2. https://www.eduplace.com/science/hmxs/ls/mode/cricket/sect7cc.shtml
  3. https://en.wikipedia.org/wiki/Fast_ice
  4. https://www.travelblog.org/Photos/2101807
  5. http://www.antarctica.gov.au/about-antarctica/environment/icebergs-and-ice/sea-ice
  6. https://en.wikipedia.org/wiki/Sea_ice#/
  7. https://www.shutterstock.com/video/clip-15391768-stock-footage-flying-over-arctic-ice-floes.html

The onset and end of wet seasons over Africa

Email: c.m.dunning@pgr.reading.ac.uk

For many Africans, the timing of the wet season is of crucial importance, especially for those reliant upon subsistence agriculture, who depend on the seasonal rains for crop irrigation. In addition, the wet season recharges lakes, rivers and water storage tanks which constitute the domestic water supply in some areas. The timing of the wet season also affects the availability of energy from hydroelectric schemes, and has impacts upon the prevalence of certain disease carrying vectors, such as mosquitoes.

Climate change is already threatening many vulnerable populations, and changes in the timing or intensity of the wet season, or increasing uncertainty in the timing of the onset, may lead to significant socio-economic impacts. But before we consider future projections or past changes in the seasonality, we need to go back a few steps.

The first step is to find a method for determining when the wet season starts and ends (its ‘onset’ and ‘cessation’). In order to look at large-scale shifts in the timing of the wet season and relate this to wider-scale drivers, this method needs to be applicable across the entirety of continental Africa. Most previous methods for determining the onset focus on the national to regional scale, and are dependent on the exceedance of a certain threshold e.g. the first week with at least 20mm of rainfall, with one rainfall event of more than 10mm, and no dry spell of more than 10 days after the rain event for the next month. While such definitions work well at a national scale they are not applicable at a continental scale where rainfall amounts vary substantially. A threshold suitable for the dry countries at the fringes of the Sahara would not be suitable in the wetter East African highlands.

In addition to a vast range of rainfall amounts, the African continent also spans multiple climatic regimes. The seasonal cycle of precipitation over continental Africa is largely driven by the seasonal progression of the ITCZ and associated rain belts, which follows the maximum incoming solar radiation. In the boreal summer, when the thermal equator sits between the equator and the Tropic of Cancer, the ITCZ sits north of the equator and West Africa and the Sahel experience a wet season. During the boreal autumn the ITCZ moves south, and southern Africa experiences a wet season during the austral summer, followed by the northward return of the ITCZ during the boreal spring. As a consequence of this, central African regions and the Horn of Africa experience two wet seasons per year – one as the ITCZ travels north, and a second as the ITCZ travels south. A method for determining the onset and cessation at the continental scale thus needs to account for regions with multiple wet seasons per year.

In our paper (available here) we propose such a method, based on the method of Liebmann et al (2012). The method has three steps:

  • Firstly, determine the number of seasons experienced per year at the location (or grid point) of interest. This is achieved using harmonic analysis – the amplitude of the first and second harmonic were computed, using the entire timeseries and their ratio compared. If the ratio was greater than 1.0, i.e. the amplitude of the second harmonic was greater than the amplitude of the first harmonic then the grid point was defined as having two wet seasons per year (biannual), if the ratio was less than one then it was defined as having an annual regime. Figure 1 shows the ratio for one African rainfall dataset (TARCATv2). Three regions are identified as biannual regions; the Horn of Africa, an equatorial strip extending from Gabon to Uganda and a small region on the southern West African coastline.

    Figure 1: Location of regions with one and two seasons per year, determined using harmonic analysis. Yellow indicates two seasons per year, while pink/purple indicates one season per year. Computed from TARCATv2 data.
  • Secondly the period of the year when the wet season occurs was determined. This was achieved by looking for minima and maxima in the climatological cumulative daily rainfall anomaly to identify one or two seasons.
  • The third and final stage is to calculate the onset and cessation dates for each year. This is done by looking for the minima and maxima in the cumulative daily rainfall anomaly, calculated for each season.

Figure 2 shows the seasonal progression of the onset and cessation, with the patterns observed in agreement with those expected from the driving physical mechanisms, and continuous progression across the annual/biannual boundaries. Over West Africa and the Sahel, Figure 2a-b shows zonally-contiguous progression patterns with onset following the onset of the long rains and moving north, and cessation moving southward, preceding the end of the short rains. Over southern Africa Figure 2c-d shows the onset over southern Africa starting in the north-west and south-east, following the onset of the short rains, reaching the East African coast last, and cessation starting at the Zimbabwe, Mozambique, South Africa border and spreading out radially into the cessation of the long rains.

As well as testing the method for compatibility with known physical drivers of African rainfall, agreement across multiple satellite-based rainfall estimates was also examined. In general, good agreement was found across the datasets, particularly for regions with an annual regime and over the biannual region of East Africa.

Figure 2: Southward and northward progression of the onset and cessation across the annual/biannual boundaries, computed using GPCP daily rainfall data 1998-2013.

The advantage of having a method that works at the continental scale is the ability to look at the impact of large-scale oscillations on wider-scale variability. One application of this method was to investigate the impact of El Niño upon both the annual rains and short rains (Figure 3). In Figure 3 we see the well-documented dipole in rainfall anomaly, with higher rainfall totals over 0–15°S and the Horn of Africa in El Niño years and the opposite between 15°S and 30°S.  This anomaly is stronger when we use this method compared with using standard meteorological seasons. We can also see that while the lower rainfall to the south is colocated with later onset dates and a consequentially shorter season, the higher rainfall over the Horn of Africa is associated with later cessation of the short rains, with only small differences in onset date.

Figure 3: a-c) Composite of onset, cessation and wet season rainfall in El Niño years for annual rains and short rains, minus the mean over 1982-2013, computed using CHIRPS data d) Oct-Feb rainfall anomaly in  years (CHIRPS).

In addition to using this method for research purposes, its application within an operational setting is also being explored. Hopefully, the method will be included within the Rainwatch platform, which will be able to provide users with a probabilistic estimate of whether or not the season has started, based on the rainfall experienced so far that year, and historical rainfall data.

For more details, please see the paper detailing this work:

Dunning, C.M., E Black, and R.P. Allan (2016) The onset and cessation of seasonal rainfall over Africa, Journal of Geophysical Research: Atmospheres, 121 11,405-11,424, doi: 10.1002/2016JD025428


Liebmann, B., I. Bladé, G. N. Kiladis, L. M. Carvalho, G. B. Senay, D. Allured, S. Leroux, and C. Funk (2012), Seasonality of African precipitation from 1996 to 2009, J. Clim.25(12), 4304–4322.

Understanding our climate with tiny satellites

Gristey, J. J., J. C. Chiu, R. J. Gurney, S.-C. Han, and C. J. Morcrette (2017), Determination of global Earth outgoing radiation at high temporal resolution using a theoretical constellation of satellites, J. Geophys. Res. Atmos., 122, doi:10.1002/2016JD025514.

Email: J.Gristey@pgr.reading.ac.uk          Web: http://www.met.reading.ac.uk/~fn008822/

The surface of our planet has warmed at an unprecedented rate since the mid-19th century and there is no sign that the rate of warming is slowing down. The last three decades have all been successively warmer than any preceding decade since 1850, and 16 of the 17 warmest years on record have all occurred since 2001. The latest science now tells us that it is extremely likely that human influence has been the dominant cause of the observed warming1, mainly due to the release of carbon dioxide and other greenhouse gases into our atmosphere. These greenhouse gases trap heat energy that would otherwise escape to space, which disrupts the balance of energy flows at the top of the atmosphere (Fig. 1). The current value of the resulting energy imbalance is approximately 0.6 W m–2, which is more than 17 times larger than all of the energy consumed by humans2! In fact, observing the changes in these energy flows at the top of the atmosphere can help us to gauge how much the Earth is likely to warm in the future and, perhaps more importantly, observations with sufficient spatial coverage, frequency and accuracy can help us to understand the processes that are causing this warming.

Figure 1. The Earth’s top-of-atmosphere energy budget. In equilibrium, the incoming sunlight is balanced by the reflected sunlight and emitted heat energy. Greenhouse gases can reduce the emitted heat energy by trapping heat in the Earth system leading to an energy imbalance at the top of the atmosphere.

Observations of energy flows at the top of the atmosphere have traditionally been made by large and expensive satellites that may be similar in size to a large car3, making it impractical to launch multiple satellites at once. Although such observations have led to many advancements in climate science, the fundamental sampling restrictions from a limited number of satellites makes it impossible to fully resolve the variability in the energy flows at the top of atmosphere. Only recently, due to advancements in small satellite technology and sensor miniaturisation, has a novel, viable and sustainable sampling strategy from a constellation of satellites become possible. Importantly, a constellation of small satellites (Fig. 2a), each the size of a shoe-box (Fig. 2b), could provide both the spatial coverage and frequency of sampling to properly resolve the top of atmosphere energy flows for the first time. Despite the promise of the constellation approach, its scientific potential for measuring energy flows at the top of the atmosphere has not been fully explored.

Figure 2. (a) A constellation of 36 small satellites orbiting the Earth. (b) One of the small “CubeSat” satellites hosting a miniaturised radiation sensor that could be used [edited from earthzine article].
To explore this potential, several experiments have been performed that simulate measurements from the theoretical constellation of satellites shown in Fig 2a. The results show that just 1 hour of measurements can be used to reconstruct accurate global maps of reflected sunlight and emitted heat energy (Fig. 3). These maps are reconstructed using a series of mathematical functions known as “spherical harmonics”, which extract the information from overlapping samples to enhance the spatial resolution by around a factor of 6 when compared with individual measurement footprints. After producing these maps every hour during one day, the uncertainty in the global-average hourly energy flows is 0.16 ± 0.45 W m–2 for reflected sunlight and 0.13 ± 0.15 W m–2 for emitted heat energy. Observations with these uncertainties would be capable of determining the sign of the 0.6 W m–2 energy imbalance directly from space4, even at very short timescales.

Figure 3. (top) “Truth” and (bottom) recovered enhanced-resolution maps of top of atmosphere energy flows for (left) reflected sunlight and (right) emitted heat energy, valid for 00-01 UTC on 29th August 2010.

Also investigated are potential issues that could restrict similar uncertainties being achieved in reality such as instrument calibration and a reduced number of satellites due to limited resources. Not surprisingly, the success of the approach will rely on calibration that ensures low systematic instrument biases, and on a sufficient number of satellites that ensures dense hourly sampling of the globe. Development and demonstration of miniaturised satellites and sensors is currently underway to ensure these criteria are met. Provided good calibration and sufficient satellites, this study demonstrates that the constellation concept would enable an unprecedented sampling capability and has a clear potential for improving observations of Earth’s energy flows.

This work was supported by the NERC SCENARIO DTP grant NE/L002566/1 and co-sponsored by the Met Office.


1 This statement is quoted from the latest Intergovernmental Panel on Climate Change assessment report. Note that these reports are produced approximately every 5 years and the statements concerning human influence on the climate have increased in confidence in every report.

2 Total energy consumed by humans in 2014 was 13805 Mtoe = 160552.15 TWh. This is an average power consumption of 160552.15 TWh  / 8760 hours in a year = 18.33 TW

Rate of energy imbalance per square metre at top of atmosphere is = 0.6 W m–2. Surface area of “top of atmosphere” at 80 km is 4 * pi * ((6371+80)*103 m)2 = 5.23*1014 m2. Rate of energy imbalance for entire Earth = 0.6 W m–2 * 5.23*1014 m2 = 3.14*1014 W = 314 TW

Multiples of energy consumed by humans = 314 TW / 18.33 TW = 17

3 The satellites currently carrying instruments that observe the top of atmosphere energy flows (eg. MeteoSat 8, Aqua) will typically also be hosting a suite of other instruments, which adds to the size of the satellite. However, even the individual instruments are still much larger that the satellite shown in Fig. 2b.

4 Currently, the single most accurate way to determine the top-of-atmosphere energy imbalance is to infer it from changes in ocean heat uptake. The reasoning is that the oceans contain over 90% of the heat capacity of the climate system, so it is assumed on multi-year time scales that excess energy accumulating at the top of the atmosphere goes into heating the oceans. The stated value of 0.6 W m–2 is calculated from a combination of ocean heat uptake and satellite observations.


Allan et al. (2014), Changes in global net radiative imbalance 1985–2012, Geophys. Res. Lett., 41, 5588–5597, doi:10.1002/2014GL060962.

Barnhart et al. (2009), Satellite miniaturization techniques for space sensor networks, Journal of Spacecraft and Rockets46(2), 469–472, doi:10.2514/1.41639.

IPCC (2013), Climate Change 2013: The Physical Science Basis, available online at https://www.ipcc.ch/report/ar5/wg1/.

NASA (2016), NASA, NOAA Data Show 2016 Warmest Year on Record Globally, available online at https://www.nasa.gov/press-release/nasa-noaa-data-show-2016-warmest-year-on-record-globally.

Sandau et al. (2010), Small satellites for global coverage: Potential and limits, ISPRS J. Photogramm., 65, 492–504, doi:10.1016/j.isprsjprs.2010.09.003.

Swartz et al. (2013), Measuring Earth’s Radiation Imbalance with RAVAN: A CubeSat Mission to Measure the Driver of Global Climate Change, available online at https://earthzine.org/2013/12/02/measuring-earths-radiation-imbalance-with-ravan-a-cubesat-mission-to-measure-the-driver-of-global-climate-change/.

Swartz et al. (2016), The Radiometer Assessment using Vertically Aligned Nanotubes (RAVAN) CubeSat Mission: A Pathfinder for a New Measurement of Earth’s Radiation Budget. Proceedings of the AIAA/USU Conference on Small Satellites, SSC16-XII-03

Geoengineering – how could we detect its cooling effect?

Detecting sulphate aerosol geoengineering with different methods
Lo, Y. T. E. et al. Detecting sulphate aerosol geoengineering with different methods. Sci. Rep. 6, 39169; doi: 10.1038/srep39169 (2016).

Email: y.t.e.lo@pgr.reading.ac.uk

Sulphate aerosol injection (SAI) is one of the geoengineering proposals that aim to reduce future surface temperature rise in case ambitious carbon dioxide mitigation targets cannot be met.  Climate model simulations suggest that by injecting 5 teragrams (Tg) of sulphur dioxide gas (SO2) into the stratosphere every year, global surface cooling would be observed within a few years of implementation.  This injection rate is equivalent to 5 million tonnes of SOper year, or one Mount Pinatubo eruption every 4 years (large volcanic eruptions naturally inject SOinto the stratosphere; the Mount Pinatubo eruption in 1991 led to ~0.5 °C global surface cooling in the 2 years that followed (Self et al., 1993)).  However, temperature fluctuations occur naturally in the climate system too.  How could we detect the cooling signal of SAI amidst internal climate variability and temperature changes driven by other external forcings?

The answer to this is optimal fingerprinting (Allen and Stott, 2003), a technique which has been extensively used to detect and attribute climate warming to human activities.  Assuming a scenario (G4, Kravitz et al., 2011) in which 5 Tg yr-1 of SO2 is injected into the stratosphere on top of a mid-range warming scenario called RCP4.5 from 2020-2070, we first estimate the climate system’s internal variability and the temperature ‘fingerprints’ of the geoengineering aerosols and greenhouse gases separately, and then compare observations to these fingerprints using total least squares regression.  Since there are no real-world observations of geoengineering, we cross-compare simulations from different climate models in this research.  This gives us 44 comparisons in total, and the number of years that would be needed to robustly detect the cooling signal of SAI in global-mean near-surface air temperature is estimated for each of them.

Figure 1(a) shows the distribution of the estimated time horizon over which the SAI cooling signal would be detected at the 10% significance level in these 44 comparisons.  In 29 of them, the cooling signal would be detected during the first 10 years of SAI implementation.  This means we would not only be able to separate the cooling effect of SAI from the climate system’s internal variability and temperature changes driven by greenhouse gases, but we would also be able to achieve this early into SAI deployment.

Figure 1: Distribution of the estimated detection horizons of the SAI fingerprint using (a) the conventional two-fingerprint detection method and (b) the new, non-stationary detection method.

The above results are tested by applying a variant of optimal fingerprinting to the same problem.  This new method assumes a non-stationary background climate that is mainly forced by greenhouse gases, and attempts to detect the cooling effect of SAI against the warming background using regression (Bürger and Cubasch, 2015).  Figure 1(b) shows the distribution of the detection horizons estimated by using the new method in the same 44 comparisons: 35 comparisons would require 10 years or fewer for the cooling signal to be robustly detected.  This shows a slight improvement from the results found with the conventional method, but the two distributions are very similar.

To conclude, we would be able to separate and thus, detect the cooling signal of sulphate aerosol geoengineering from internal climate variability and greenhouse gas driven warming in global-mean temperature within 10 years of SAI deployment in a future 5 Tg yr-1 SAI scenario.  This could be achieved with either the conventional optimal fingerprinting method or a new, non-stationary detection method, provided that the climate data are adequately filtered.  Research on the effects of different data filtering techniques on geoengineering detectability is not included in this blog post, please refer to the article cited at the top for more details.

This work has been funded by the University of Reading.  Support has also been provided by the UK Met Office.

Note: So how feasible is a 5 Tg yr-1 SO2 injection scenario?  Robock et al. (2009) estimated the cost of lofting 1 Tg yr-1 SO2 into the stratosphere with existing aircrafts to be several billion U.S. dollars per year. Scaling this to 5 Tg yr-1 is still not a lot compared to the gross world product. There are practical issues to be addressed even if existing aircrafts were to be used for SAI, but the deciding factor of whether to implement sulphate aerosol geoengineering or not would likely be its potential benefits and side effects, both on the climate system and the society. 



Self, Stephen, et al. “The atmospheric impact of the 1991 Mount Pinatubo eruption.” (1993).

Allen, M. R., and P. A. Stott. “Estimating signal amplitudes in optimal fingerprinting, Part I: Theory.” Climate Dynamics 21.5-6 (2003): 477-491.

Kravitz, Ben, et al. “The geoengineering model intercomparison project (GeoMIP).” Atmospheric Science Letters 12.2 (2011): 162-167.

Bürger, Gerd, and Ulrich Cubasch. “The detectability of climate engineering.” Journal of Geophysical Research: Atmospheres 120.22 (2015).

Robock, Alan, et al. “Benefits, risks, and costs of stratospheric geoengineering.” Geophysical Research Letters 36.19 (2009).