Graphics modeller in QGIS

Question

I am using QGIS 2.6 Brighton.

I am trying to run a Gavrilovic model in the modeller in QGIS. FYI: Gavrilovic model is a set of Imperical equations for sediment yield analysis.

The equations are as follows:

W = T * h * [pi] * sqrt(z^3)      ..1
T = sqrt ( t/10 + 0.1 )           ..2
z = x * y * ( [phi] + sqrt (J) )  ..3

What I have in QGIS ?

I have raster layers of t, h, x, y, [phi], J.

What do I need to do ?

1. Calculate z as in equation 3; I have all required variables as rasters.
2. Calculate T from t as in equation 2.
3. Calculate W.
4. Now I need to change the values of t and h rasters. Lets say for example, the existing values of t need to be first changed by -15%, -10%, -5%, +5%, +10%, +15%. And run the equations again to evaluate what will be the changes in W with respect to change in t. Similar for h.
5. Again I need to evaluate W for -15%, -10%, -5%, +5%, +10%, +15% change in h for each change in t.

To elaborate point no. 4 and 5.
Let us assume each raster has 4 cells. And these be the initial values of t and h.

t =  10,  12,  15, 12
h = 110, 100, 140, 90

Now for the sensitivity test, I need the values of t changed by -15%, -10% , -5%, +5%, +10%, +15%. And similar for h. 6 new t rasters will be created according to the percentage change and the values will be as follows for t.

col A      B      C      D     E     F       G
initial_t -15%   -10%   -5%   +5%    +10%    +15%

   10      8.5     9    9.5   10.5   11      11.5
   12      1.7    1.8   1.9   2.1    2.2     2.3
   15      12.75  13.5  14.25 15.75  16.5    17.25
   12      10.2   10.8  11.4  12.6   13.2    13.8

Similarly 6 new h rasters will be created, as follows:

col  1       2       3        4        5      6      7
initial_h   -15%    -10%     -5%      +5%    +10%   +15%

110         93.5    99       104.5    115.5  121    126.5
100         85      90          95      105  110    115
140         119     126        133      147  154    161
 90         76.5    81        85.5     94.5   99    103.5

Now, I need to run equations 1 to 3 taking t and h in following fashion:

for p = col A to col G {
 for q = col 1 to col 7 {
     run equation 3
     run equation 2
     run equation 1   
 }
}

Note: I've heard changing values of raster and running this algorithm is easier in graphics modeller.
If not, I can create those 6 new rasters for t and h myself. I can use R for that. However if it can be done in QGIS (other than using raster calculator) it would be great if you can share the idea.

I need someone to tell me how can I set up a Graphics modeller 
and perform  these operations.   

I am not familiar with python but I can find my way writing the code.

Answer 1

I'd script this using gdal_calc.py:

Starting with six tiffs:

$ ls *tif
h.tif  j.tif  phi.tif  t.tif  x.tif  y.tif

This script:

# clear intermediates and output
rm -f z.tif bigt.tif W.tif

# z = x * y * ( [phi] + sqrt (J) )  ..3
gdal_calc.py --calc='X*Y*(P+sqrt(J))' -X x.tif -Y y.tif -P phi.tif -J j.tif --outfile=z.tif

# T = sqrt ( t/10 + 0.1 )           ..2
gdal_calc.py --calc='sqrt(T/10 + 0.1)' -T t.tif --outfile=bigt.tif

# W = T * h * [phi] * sqrt(z^3)      ..1
gdal_calc.py --calc='T * H * P * sqrt(Z**3)' -T bigt.tif -H h.tif -P phi.tif -Z z.tif --outfile=W.tif

produces W.tif which (I think) has the final quantity you are computing, alongside the intermediate rasters as well.

Once you've got that running as a shell script at the command line, you can script the process of changing your inputs and collecting the outputs, but the whole thing is a big ask and probably too broad for now, especially if you can do it in R anyway.