Defining alternative climatologies:why, what for and how

overview:

1) why?

2) what for?

3) how?

– problems with current climatologies

– applications

– discrete process convolution models

1) why?

Traditional climatologies, such as Levitus climatologies of ocean temperature and salinity, use Objective Analysis Techniques.

firstguess(lat,lon,dep)=zonal meanFor pass=1 to 3

For all lat, lon and depnewguess(lat,lon,dep)= firstguess(lat,lon,dep) + weighted sumwithin a radius(pass) of differences between observed and firstguess means

NextFor all lat, lon and dep

Run a median smoother and/or another type of spatial smootheron newguess

NextFor all lat, lon and dep

firstguess(lat,lon,dep)=newguess(lat,lon,dep)Next

Next

firstguess observations newguesssmoothednewguess

+

Pass 1º ¼º

1 892 km 321 km

2 669 km 267 km

3 446 km 214 km

Radii sizes in Levitus 1º and ¼º climatologies

Although termed an objective method, several subjective choices must be made:

a) number of passes

b) weighting function

c) radii sizes

d) type of smoother and associated parameters

The whole process is purely mathematical, and corrections to meet physical assumptions (e.g., stability of the water column) must be performed a posteriori.

Example of weighting function

Example of a linear smoother

1) why?

But the most important problem is that sampling errors are not taken into consideration with the Objective Analysis Technique.

(a sampling error is an error that derives from not obtaining a representative sample)

World Ocean Database – used by Levitus et al.

1) why?

In each region, one particular decade has more observations than the others; this decade is not the same for all regions.

1) why?

Impacts of sampling errors:

Since temperature and salinity change from one decade to the next, the climatology may be unrealistic, i.e., it may present inexistent gradients (1) and/or lose others that exist (2).

(1)

(2)

1) why?

Impacts of sampling errors:

2) what for?

Alternative climatological fields, specifically designed for the region of interest, will allow:

1) a better characterization of the hydrodynamic circulation, including upwelling, countercurrents and undercurrents;

2) more reliable estimates to be coupled with other circulation models (e.g., MM5), as well as biological models;

3) more reliable time-series of anomalies that will be used to investigate climate change and relationships between properties (e.g., coastal temperature and winds, coastal chlorophyll-a and winds)

4) freedom for MOHID users to customize the climatology

From: The MOHID Portugal/Galicia Regional model – first numerical experiments

With a statistical-based approach that allows the data to dictate the amount of spatial smoothing that seems appropriate and can also accommodate the temporal component of the data.

This will lead to time averaged spatial field estimates that are not biased towards any particular decade.

E.g.: yearly anomaly fields yearly climatology

3) how?

Discrete process convolution models (DPCMs)

Example of a 1D standard process convolution with a Gaussian kernel

3) how?

A DPCM requires:

1) a kernel

2) a discount factor

3) a lattice

The discount factor is the component of the DPCM that determines the amount of information lost from one time instant to the next.

Choosing the lattice, the discount factor and the kernel’s shape determines the quality of the fit. These choices are initially subjective but may be optimized with Markov chain Monte Carlo methods.

Discrete process convolution models (DPCMs)3) how?

Examples of lattices

Different kernel shapes for different regions

summary on “Defining alternative climatologies”

why? – current climatologies derive from subjective mathematical procedures that require posterior corrections; also they do not take sampling errors into consideration.

what for? – to provide reliable products for many people

how? – with discrete process convolution models, coupled with MCMC methods to increase the goodness-of-fit and reduce the subjectivity.