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<title>About</title>
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<link rel="icon" type="image/png" href="favicon-32x32.png" sizes="32x32"><title>About adJULES</title></head>


<body><img src="test1.png" alt="JULES logo" width="100%" align="middle">


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<h2>About.</h2>

<p>JULES has over a hundred internal parameters representing the
environmental sensitivities of the various land-surface types and PFTs
within the model. In general these parameters are chosen to represent
measurable “realworld” quantities (e.g. aerodynamic roughness length,
surface albedo, plant root depth).
</p><p>
Data assimilation is the act of incorprating observations into a model.
By changing the internal parameters of the model, the model output can
be made to more closely resemble the observed time-series. The optimal
set of parameters is one that minimises the difference between the model
 output and the observed time-series the most. In order to minimse this
difference, the 'adjoint' of JULES is used. This is a complex piece of
code, derived by automatic differentiation, which enables efficient and
objective calibration against observations. The adjoint is central to
the adJULES parameter estimation system, hence the name.
</p><p>
</p><h4>Example</h4>
These figures show the time-series of latent heat (left) and a
photosynthesis flux called GPP (right) at a measurement site in Denmark
(DK-Sor). The observations (black) are compared to JULES runs using
default parameters (orange) and optimised parameters (blue). The
optimised run can be seen to be much closer to the observations than the
 default JULES run.
<div style="text-align: center"><img src="DK-Sor_single_0_LE_2.png" width="35%" align="middle"><img src="DK-Sor_single_0_GPP_2.png" width="35%" align="middle"></div>

<h3> Theoretical Background</h3>
<div>
<p>
</p><p>
For a given subset of internal parameters ($\mathbf{z}$), JULES
generates a modelled time-series. A misfit or cost function which
measures the mismatch between this time-series and the observations is
created. The function also includes a term which measures the mismatch
between the parameter values ($\mathbf{z}$) and the initial parameter
values ($\mathbf{z}_0$). Finally the function is weighted by the prior
error covariance matrixes on observations $\mathbf{R}$ and paramters
$\mathbf{B}$. This function is minimised with respect to the parameters
in order to find the best fit.

$$J(\mathbf{z};\mathbf{z}_0) = \frac{1}{2}\left[\sum_t
(\mathbf{m}_{t}(\mathbf{z})-\mathbf{o}_{t})^{T}\mathbf{R}^{-1}
(\mathbf{m}_{t}(\mathbf{z})-\mathbf{o}_{t}) +
(\mathbf{z}-\mathbf{z}_{0})^{T}\mathbf{B}^{-1}(\mathbf{z}-\mathbf{z}_0)\right]$$


There
 are several ways this cost function could be minimised. The adJULES
system uses what is called a gradient descent method. Gradient descent
methods utilise the first-derivative of the cost to identicate which
direction in parameter shape minimises the function. The
second-derivative of the cost (called the Hessian) can also be used to
map the curvature of parameter space and therefore show which direction
minimises the function the fastest. Gradient descent methods iteratively
 minimise the cost function using this information until the optimimum
(i.e. gradient $\approx$ 0) is reached or the bounds of the function are
 hit. The iterative algorthim currently used in the adJULES system is
call the <a hre="https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm">BFGS</a>.
</p><p>
The first and second derivative of the cost function are calculated
analytically using the adjoint of the JULES model. This information can
also be used at the optimum to generate uncertainties associated to each
 parameter. If curvature of parameter space at the optimum has steep
sides, there is low uncertainty associated to the parameter as moving it
 will significantly increase the cost. If the sides are flat, there is
high uncertainty associated to the parameter.
</p></div>


<div style="text-align: center"><img src="diagram_simple.png" alt="JULES logo" width="80%" align="middle"></div>

For more technical details and results please read papers listed in the <a href="publications.html">publications</a>.
<h3> Data </h3>

<a href="https://daac.ornl.gov/cgi-bin/dataset_lister.pl?p=9">FluxNet</a>
 data are currently integrated in the adJULES distribution. These
provide driving data for JULES and observations against which to
calibrate the model.

<div style="text-align: center"><img src="FLUXNET_locations.png" width="60%" align="middle"></div>
<p>
Currently, the adJULES system uses in situ data from individual or
multiple sites to calibrate these parameters. New data sources such as
satellite products are expected to be integrated into the system soon.


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<div class="note" align="center">© 2014 — 2017, developed by N.M. Raoult, maintained by the adJULES team at University of Exeter</div>
<div class="block-content content" align="center"> Funded by the UK Natural Environment Research Council (<a href="https://www.nerc.ac.uk/" style="color: rgb(0,163, 204)">NERC</a>) through the National Centre for Earth Observation (<a href="https://www.nceo.ac.uk/" style="color: rgb(0,163, 204)" "="">NCEO</a>)</div>
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