Models Methods Software

Dan Hughes

Testing Energy Balance and Budget

In this previous post, I mentioned the energy budget / balance for the Earth’s systems. Specifically, the fundamental hypothesis for AGW is that human activities have created an imbalance in the radiative-energy transport budget and that an increase in temperature will be obtained in order to return to some kind of, but practically undefined, equilibrium state. A true state of energy in-come = energy out-go is never attained for the Earth’s systems. The daily and yearly cyclic variations are observed easily by direct experience and instrumental means. Especially, neither the out-going infrared energy or the in-coming ultra-violet energy are constant, and are not monotonically increasing or decreasing.

As I noted in that post, many of the important phenomena and processes that can change the amounts of energy in-coming to and out-going from the Earth’s systems are independent of the radiative-energy states of the systems. There are no inherent natural physical phenomena and processes acting so as to maintain a state of radiative-energy balance for the Earth’s systems. Natural events, both external from and internal to, the Earth’s systems are free to cause changes in the state of the systems such that either an increase or a decrease in the amount of energy results; in-come. Natural events can also act to both increase or decrease the amount of energy leaving the systems; out-go. Very likely, the grand-time-and-space-average albedo is changing all the time and thus changing the in-coming energy. So are the mechanisms that effect loss of infrared energy and changes in the out-going energy.

The occurrence of the natural events, and the outcome relative to the associated radiative-energy transport properties, cannot be known until after the fact. Many human activities including CO2 emissions can also change conditions that affect the radiative-energy transport properties of the Earth’s systems. The perturbations due to human activities on the radiative-energy balance are reported to be small; a few W/m^2.

Testing the Models and Methods
Additional consideration of this situation has led me to think about how testing of GCM model results might better be reported. It seems to me that models and methods are better tested if results of calculations are compared with information more nearly directly related to the basic premise of a problem and its investigations. If the temperature is changing, there should be corresponding changes in the outgoing long-wave radiative energy. The interactions between water vapor in the atmosphere for both UV and IR radiative transport are of first-order importance.

Because it results in an amplification of the effects of increasing concentrations of CO2, an increase in the water-vapor content of the atmosphere has been determined to be an important consequence of an increasing temperature at the Earth’s surface. The physical phenomena and processes that are critical parts of this interaction are tightly coupled to the temperature distribution, primarily in the vertical direction, in the atmosphere. Accurate calculation of the response will require accurate calculation of the temperature distribution.

The several radiative-energy transport aspects of clouds, almost all represented by parameterizations, are critically important. Clouds are the primary contributor to the numerical value of the albedo. Water vapor is not transparent to radiative-energy transport for infrared energy. Such mundane aspects as representation of the variation of the vapor pressure of water with respect to temperature are also importance. Let’s ignore other aspects of the solid and liquid phases of water in the atmosphere and all the other suspended particulate matter.

None of these critically important first-order phenomena and processes can be calculated from first principles and instead are handled with empirical data and / or parameterizations.

As these are the critical aspects of the AGW hypotheses, calculated results should be compared with data measured for the these phenomena and processes. While the data might not be of the highest quality due to the enormous temporal and spatial scales for the problem, comparisons with these directly related aspects are preferable over comparisons with the usual much more indirect aspects. To note the direct relationship to the AGW hypotheses, if the temperature is increasing, the OLR must be increasing as a reflection of the increasing temperature.

WGI SPM Contribution
I have looked at the WGI contribution to the SPM. I don’t see any discussions of these aspects of the problem and I don’t find comparisons of calculations with data for these processes. I consider this to be an important shortcoming. Direct testing of hypotheses is critical to increasing confidence in both the hypotheses and the models and methods developed to investigate these.

Energy Balance and Budget and Models
There are other important related issues relative to the models and calculations. What level of accuracy in the basically empirical models of the first-order interactions described above will be necessary to accurately resolve the relatively small changes in the radiative-energy balance. Specifically, can the temporal-averge, whole-Earth albedo be determined to the required degree of fidelity. Can the effects of water vapor and clouds, on both ultra-violet and infrared energy, be determined to the required degree of fidelity. Can the estimated change in the Earth’s response due to increasing CO2 concentrations even be detected in the measured data?

The calculations with GCMs are known to use a relatively course spatial resolution. Has the spatial resolution that is necessary to accurately resolve the temperature distribution and its associated effects through water vapor and clouds, of the radiative-energy balance been determined.

The estimates of the magnitude of the perturbations in the energy balance of the Earth’s systems due to all the changes in the systems made by humans is small; a few ( maybe 5 ) Watts per square meter. I think the documentation that is available in the open literature for the GCMs is not sufficiently detailed to determine the degree to which accurate accounting of the mass and energy equations is attained. Additionally, the fidelity of the model is equally affected by the treatment of the model’s equations beyond the continuous-equation stage.

The calculated initial energy content of the Earth’s systems, for example, will be a function of the spatial resolution used at run time. Conservation of that initial energy, plus accurate accounting for the gains and losses, especially in the inter-systems transfer of sensible energy and the inter-phase transfer for those processes that involve phase change, is critically dependent on the several aspects of the numerical solution methods. Ensuring that the discrete approximations conserve energy and careful attention to the time-level at which the various terms are evaluated are critically important. Different time levels for the temperatures of materials that exchange sensible energy, for example, introduces numerical non-conservation of energy. As do the time levels for processes associated with phase change. As do the time levels for all discrete approximations that model driving gradients.


March 16, 2010 - Posted by | Uncategorized | ,


  1. Speaking of energy balances and budgets, suppose we take all the energy from burning fossil fuels and dump it into the atmosphere. According to my back-of-the-envelope calculations, this could account for about 6 times the observed warming. Do any of these climate models account for the sensible heat addition to the atmosphere from burning fossil fuels?


    Back of the envelope calculation:

    Mass of earth’s atmosphere = =5.148*10^18 kilograms (reference's_atmosphere )

    Specific heat of air = 1.0035 kJ / kg K (reference )

    Total energy used in 2004 = 5E+20 Joules (reference = )

    so total temperature rise = Energy/Mass/Specific heat
    = 0.097 deg C

    Observed temperature rise (picked off a chart at =
    0.3 deg C over 20 years or

    = 0.015 deg C

    In other words, the observed temperature rise is only about 15% of what is actually observed (which might well be due to the fact that the oceans and land also heat up, not only the air).

    As I see it from my simple-minded view, the amount of energy we are dumping into the earth’s air, water, and land is more than enough to account for the observed warming without all the fancy greenhouse gas modeling.

    Detailed calculations will be provided in spreadsheet form on request . . . it is likely I may have screwed something up.

    Comment by Bob White | March 16, 2010 | Reply

  2. Different time levels for the temperatures of materials that exchange sensible energy, for example, introduces numerical non-conservation of energy. As do the time levels for processes associated with phase change. As do the time levels for all discrete approximations that model driving gradients.
    The Community Climate model seems to use an operator splitting approach; you’re right, if they aren’t careful this sort of coupling can lead to worse than first order accuracy (which generally means you aren’t conserving). This is similar to the problems that the fluid-structure interaction guys have, if you don’t couple things to at least first order accuracy then you end up adding energy and momentum into the flow because of numerical errors. Operator splitting can get 2nd order accuracy…if you do it right. Where’s the verification test-suite results? Haven’t found those on the site yet. The claim [pdf] is that each component is conservative:
    The CCSM3 system includes new versions of all the component models. The atmosphere is CAM version 3.0 (Collins et al. 2004, 2005b), the land surface is CLM version 3.0 (Oleson et al. 2004; Dickinson et al. 2005), the sea ice is CSIM version 5.0 (Briegleb et al. 2004), and the ocean is based upon POP version 1.4.3 (Smith and Gent 2002). New features in each of these components are described below. Each component is designed to conserve energy, mass, total water, and fresh water in concert with the other components.
    Here’s some more detail on the coupling methodology:
    The physical component models of CCSM3 communicate through the coupler, an exec- utive program that governs the execution and time evolution of the entire system (Craig et al. 2005; Drake et al. 2005). CCSM3 is comprised of five independent programs, one for each of the physical models and one for the coupler. The physical models execute and communicate via the coupler in a completely asynchronous manner. The coupler links the components by providing flux boundary conditions and, where necessary, physical state information to each model. The coupler monitors and enforces flux conservation for all the fluxes that it exchanges among the components. The coupler can exchange flux and state information among components with different grid and time steps. Both of these capabil- ities are used in the standard configurations of CCSM3. State data is exchanged between different grids using a bilinear interpolation scheme, while fluxes are exchanged using a second-order conservative remapping scheme. The basic state information exchanged by the coupler includes temperature, salinity, velocity, pressure, humidity, and air density at the model interfaces. The basic fluxes include fluxes of momentum, water, heat, and salt across the model interfaces.
    It sounds closely-coupled, but it’s actually rather loosely-coupled:
    In the standard T85 1 configuration, the atmosphere, land, and sea ice exchange fluxes and state information with the coupler every hour, while the ocean exchanges these data once per day. The internal time steps for the land, atmosphere, ocean, and sea ice components are ten minutes, twenty minutes, one hour, and one hour, respectively.

    Comment by jstults | March 17, 2010 | Reply

  3. Conserving Energy, something you may want to consider:
    In the future, we may consider using the total energy as a transported prognostic variable so that the total energy could be automatically conserved.
    Finite Volume Dynamical Core

    Oh, that pesky first law, we’ll get to it eventually…

    Comment by jstults | March 17, 2010 | Reply

  4. Josh

    This post has references to papers that address some aspects of energy conservation for models and codes, and verification.

    Here are two recent papers addressing verification The Ocean–Land–Atmosphere Model (OLAM). Part I: Shallow-Water Tests and The Ocean–Land–Atmosphere Model (OLAM). Part II: Formulation and Tests of the Nonhydrostatic Dynamic Core. Maybe the necessary work is finally getting started.

    I remain astounded that for a problem in which a small number is absolutely critically important, that conservation of the quantity controlling that number seems to seldom be properly considered. When you’re looking for small numbers, fidelity of the model equations to the real world applications of interest, and accurate numerical solutions are vital; no shortcuts can be taken.

    BTW, I’ve seen numerical solution methods destroy mass and energy conservation at the very last procedure in a time-step by how the algebraic Equation of State is solved. The EOS is a straightforward cell-by-cell problem potentially well-suited for parallelization. After all the computationally expensive aspects have been solved, attempts to save a few CPU cycles screws up two fundamental aspects of the physics. The two most critically important aspects, in my opinion.

    Many in the GCM business continue to say that the models, methods, and software cannot be verified. I know that the major components can be verified using a standalone approach; we’ve done it. Coupling issues can be investigated by using a theoretical approach that isolates the problem on a smaller scale and use a few calculations to demonstrate that the coupling has been correctly handled.

    Comment by Dan Hughes | March 18, 2010 | Reply

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