Analysing the source of stressors (flow matrix)

To calculate the source (in terms of regions and sectors) of a certain stressor or impact driven by consumption, one needs to diagonalize this stressor/impact. This section shows how to do this based on the small test mrio included in pymrio. The same procedure can be use for any other MRIO, but keep in mind that diagonalizing a stressor dramatically increases the memory need for the calculations.

Basic example

First we load the test mrio:

[1]:

import pymrio

io = pymrio.load_test()

The test mrio includes several extensions:

[2]:

list(io.get_extensions())

[2]:

['factor_inputs', 'emissions']

For the example here, we use ‘emissions’ - ‘emission_type1’:

[3]:

io.emissions.F

[3]:

	region	reg1								reg2		...	reg5		reg6
	sector	food	mining	manufactoring	electricity	construction	trade	transport	other	food	mining	...	transport	other	food	mining	manufactoring	electricity	construction	trade	transport	other
stressor	compartment
emission_type1	air	1848064.80	986448.090	23613787.00	28139100.00	2584141.80	4132656.3	21766987.0	7842090.6	1697937.30	347378.150	...	42299319	10773826.0	15777996.0	6420955.5	113172450.0	56022534.0	4861838.5	18195621	47046542.0	21632868
emission_type2	water	139250.47	22343.295	763569.18	273981.55	317396.51	1254477.8	1012999.1	2449178.0	204835.44	29463.944	...	4199841	7191006.3	4826108.1	1865625.1	12700193.0	753213.7	2699288.3	13892313	8765784.3	16782553

2 rows × 48 columns

[4]:

et1_diag = io.emissions.diag_stressor(("emission_type1", "air"), name="emtype1_diag")

The parameter name is optional, if not given the name is set to the stressor name + ‘_diag’

The new emission matrix now looks like this:

[5]:

et1_diag.F.head(15)

[5]:

	region	reg1								reg2		...	reg5		reg6
	sector	food	mining	manufactoring	electricity	construction	trade	transport	other	food	mining	...	transport	other	food	mining	manufactoring	electricity	construction	trade	transport	other
region	sector
reg1	food	1848064.8	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	mining	0.0	986448.09	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	manufactoring	0.0	0.00	23613787.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	electricity	0.0	0.00	0.0	28139100.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	construction	0.0	0.00	0.0	0.0	2584141.8	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	trade	0.0	0.00	0.0	0.0	0.0	4132656.3	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	transport	0.0	0.00	0.0	0.0	0.0	0.0	21766987.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	other	0.0	0.00	0.0	0.0	0.0	0.0	0.0	7842090.6	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
reg2	food	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	1697937.3	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	mining	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	347378.15	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	manufactoring	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	electricity	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	construction	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	trade	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	transport	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.00	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

15 rows × 48 columns

And can be connected back to the system with:

[6]:

io.et1_diag = et1_diag

Finally we can calulate the all stressor accounts with:

[7]:

io.calc_all()

[7]:

<pymrio.core.mriosystem.IOSystem at 0x7f9c25d25d30>

This results in a square footprint matrix. In this matrix, every column respresents the amount of stressor occuring in each region - sector driven by the consumption stated in the column header. Conversly, each row states where the stressor impacts occuring in the row are distributed due (from where they are driven).

[8]:

io.et1_diag.D_cba.head(20)

[8]:

	region	reg1								reg2		...	reg5		reg6
	sector	food	mining	manufactoring	electricity	construction	trade	transport	other	food	mining	...	transport	other	food	mining	manufactoring	electricity	construction	trade	transport	other
region	sector
reg1	food	609347.998747	34.963223	1.987631e+05	7.678755e+02	2.873371e+03	5.603158e+04	1.448778e+03	5.225312e+04	4.826852e+04	0.453097	...	74.449012	222.953289	25525.516392	6.557600	1.382548e+05	38.345126	408.937891	4.425472e+04	63.940215	4.876200e+02
	mining	2527.449441	61271.249639	1.232716e+05	5.406781e+04	1.632967e+05	1.459774e+04	4.916876e+03	4.975184e+04	4.311608e+02	288.903690	...	261.326848	829.871069	268.406793	1990.840054	7.400739e+04	6327.871035	299.916699	1.732632e+04	242.874444	4.038056e+03
	manufactoring	1199.041530	38.236679	4.686837e+06	8.108636e+02	1.816229e+04	7.713610e+03	2.825229e+03	1.634290e+04	3.205155e+02	2.886944	...	424.008556	517.344586	145.900439	72.195039	3.424703e+06	94.046696	129.127059	7.826193e+03	241.185186	9.015651e+02
	electricity	148505.091902	12764.784297	1.519466e+06	1.167804e+07	5.265922e+05	1.307806e+06	4.851957e+05	4.308489e+06	1.908031e+04	240.730963	...	9294.381551	28937.569016	7947.002552	476.106897	1.072302e+06	38647.049939	495.159380	9.712017e+05	3850.133826	9.804940e+03
	construction	49.018479	6.053459	4.019302e+02	3.081457e+02	2.568908e+06	7.291250e+02	5.853107e+02	9.718253e+03	4.408230e+00	0.037972	...	1.679791	4.461035	2.211530	0.213951	2.898921e+02	1.682977	12.667370	5.303592e+02	0.988979	3.859558e+00
	trade	138.041355	3.139596	1.880042e+03	8.852940e+01	1.420349e+03	2.390871e+06	4.371531e+02	2.383210e+03	2.637857e+01	0.095853	...	36.433641	50.392051	42.098945	1.141682	1.240785e+03	4.989788	14.192623	1.726377e+06	45.633464	4.276151e+01
	transport	521.216924	122.504968	1.585636e+04	1.428149e+03	6.467383e+03	2.741408e+04	1.018383e+07	4.388313e+04	9.410163e+01	2.099087	...	2854.767892	222.900909	568.393996	55.916912	1.130829e+04	285.596244	127.388007	2.198931e+04	8734.726973	1.309008e+03
	other	537.062679	24.688020	7.752597e+03	1.170368e+03	8.587431e+03	1.322798e+04	4.448616e+03	7.516913e+06	6.837072e+01	0.767113	...	56.726997	435.703359	36.640953	3.856648	5.346664e+03	20.750945	15.152425	1.029493e+04	58.278076	1.356728e+03
reg2	food	234.870108	0.041282	1.213308e+03	3.241119e+00	9.719899e+00	1.004924e+01	4.822982e-01	1.281313e+01	1.694248e+06	0.041642	...	3.026472	0.475024	80.139206	0.025141	2.183449e+02	0.472522	7.011110	1.605455e+02	0.455175	3.092008e+00
	mining	215.562762	1690.186670	5.892279e+04	1.862733e+03	7.746514e+02	7.570607e+02	1.582065e+02	2.302825e+03	1.787512e+03	10287.905967	...	200.678830	58.083367	66.185618	1351.809333	1.430140e+04	2650.008184	42.230072	8.909866e+03	79.981946	3.551366e+03
	manufactoring	75.621346	4.229463	7.185296e+06	6.763336e+01	7.171199e+02	4.429766e+02	1.914508e+02	1.076869e+03	9.941057e+02	5.361056	...	352.701574	125.165588	44.659838	19.157594	1.140699e+06	19.220461	50.982784	3.009360e+03	74.837190	2.460570e+02
	electricity	4.912183	4.392270	6.448813e+03	1.947867e+02	1.552407e+01	2.864877e+01	1.010699e+01	9.682693e+01	1.143809e+03	23.763711	...	225.020323	2.614112	0.740525	3.162466	1.079151e+03	8.601151	0.254639	2.214440e+03	1.186302	1.102287e+01
	construction	0.179274	0.201490	4.711030e+02	8.221412e-01	1.045043e+02	1.884894e+00	1.624084e+00	1.924495e+01	1.001309e+02	1.098256	...	130.390027	4.804088	0.230208	0.152699	7.708346e+01	0.545433	47.750232	3.449526e+02	1.023520	5.208169e+00
	trade	9.487802	0.442851	2.547850e+03	5.931388e+00	3.093165e+01	2.414790e+02	8.294245e+00	5.515915e+01	3.073687e+02	1.313536	...	159.340296	69.421120	25.278297	0.783272	5.438996e+02	2.795486	8.852273	1.174931e+06	20.099409	2.543311e+01
	transport	30.167917	11.691703	1.095783e+04	7.704484e+01	2.369344e+02	1.171461e+03	4.962901e+03	1.299130e+03	9.083313e+02	15.109529	...	789093.398671	117.822465	101.020895	7.816896	2.491430e+03	51.079756	28.609582	8.615321e+03	2234.585845	4.125342e+02
	other	4.710152	0.999656	3.487999e+03	1.504331e+01	6.607788e+01	8.958452e+01	3.266330e+01	1.104173e+03	2.621005e+02	3.670327	...	376.984093	213.700696	7.178914	1.523151	6.818453e+02	7.576198	7.380601	3.072026e+03	37.695142	7.442119e+02
reg3	food	79.487995	0.012420	2.707179e+03	3.212251e-01	1.118965e+00	8.545640e+00	3.848642e-01	2.342262e+01	6.321926e+01	0.001120	...	0.660378	1.095579	96.427089	0.060430	1.350698e+03	0.136524	0.253732	5.444486e+02	0.330214	1.007920e+02
	mining	1.660826	9.283144	2.805174e+03	4.683637e+00	3.721404e+00	1.903501e+01	1.984584e+00	1.130052e+02	1.043411e+00	1.482323	...	1.579297	4.760043	1.028577	9.018513	1.370585e+03	19.208836	0.609243	7.625285e+02	1.234952	6.075141e+02
	manufactoring	256.950787	12.496966	1.951101e+07	1.576456e+02	1.369020e+03	9.774252e+02	4.651207e+02	9.975075e+03	2.274549e+02	2.093210	...	856.521423	1696.838781	304.748914	109.539716	9.493385e+06	71.802017	260.584083	6.010179e+04	587.491671	3.817698e+04
	electricity	346.618944	75.166170	3.907669e+06	8.377082e+03	1.955704e+03	3.618932e+03	1.930657e+03	5.954611e+05	9.697584e+02	33.309324	...	1833.141385	6869.669139	1750.805701	1639.927136	1.908654e+06	44575.821242	628.061059	6.364065e+06	4888.472424	3.661473e+06

20 rows × 48 columns

The total footprints of a region - sector are given by summing the footprints along rows:

[9]:

io.et1_diag.D_cba.sum(axis=0).reg1

[9]:

sector
food             2.056183e+06
mining           1.794235e+05
manufactoring    9.749300e+07
electricity      1.188759e+07
construction     3.342906e+06
trade            3.885884e+06
transport        1.075027e+07
other            1.582152e+07
dtype: float64

[10]:

io.emissions.D_cba.reg1

[10]:

	sector	food	mining	manufactoring	electricity	construction	trade	transport	other
stressor	compartment
emission_type1	air	2.056183e+06	179423.535893	9.749300e+07	1.188759e+07	3.342906e+06	3.885884e+06	1.075027e+07	1.582152e+07
emission_type2	water	2.423103e+05	25278.192086	1.671240e+07	1.371303e+05	3.468292e+05	7.766205e+05	4.999628e+05	8.480505e+06

The total stressor in a sector corresponds to the sum of the columns:

[11]:

io.et1_diag.D_cba.sum(axis=1).reg1

[11]:

sector
food              1848064.80
mining             986448.09
manufactoring    23613787.00
electricity      28139100.00
construction      2584141.80
trade             4132656.30
transport        21766987.00
other             7842090.60
dtype: float64

[12]:

io.emissions.F.reg1

[12]:

	sector	food	mining	manufactoring	electricity	construction	trade	transport	other
stressor	compartment
emission_type1	air	1848064.80	986448.090	23613787.00	28139100.00	2584141.80	4132656.3	21766987.0	7842090.6
emission_type2	water	139250.47	22343.295	763569.18	273981.55	317396.51	1254477.8	1012999.1	2449178.0

Aggregation of source footprints

If only one specific aspect of the source is of interest for the analysis, the footprint matrix can easily be aggregated with the standard pandas groupby function.

For example, to aggregate to the source region of stressor, do:

[13]:

io.et1_diag.D_cba.groupby(level="region", axis=0).sum()

[13]:

region	reg1								reg2		...	reg5		reg6
sector	food	mining	manufactoring	electricity	construction	trade	transport	other	food	mining	...	transport	other	food	mining	manufactoring	electricity	construction	trade	transport	other
region
reg1	7.628249e+05	74265.619882	6.554229e+06	1.173668e+07	3.296308e+06	3.818391e+06	1.068369e+07	1.199973e+07	6.829377e+04	535.974719	...	1.300377e+04	3.122120e+04	3.453617e+04	2.606829e+03	4.727453e+06	4.542033e+04	1.502541e+03	2.799800e+06	1.323776e+04	1.794454e+04
reg2	5.755115e+02	1712.185384	7.269345e+06	2.227236e+03	1.955463e+03	2.743145e+03	5.365729e+03	5.967041e+03	1.699751e+06	10338.264024	...	7.905415e+05	5.920865e+02	3.254335e+02	1.384431e+03	1.160092e+06	2.740299e+03	1.930713e+02	1.201258e+06	2.449865e+03	4.998925e+03
reg3	1.054578e+03	215.654591	2.382082e+07	9.500254e+03	7.044809e+03	1.285847e+04	2.265449e+04	2.844767e+06	1.740953e+03	54.246936	...	2.026441e+04	3.336623e+04	5.910854e+03	2.129253e+03	1.160211e+07	4.640647e+04	2.506927e+03	2.295789e+07	4.824482e+04	1.756144e+07
reg4	1.147382e+03	2323.792084	1.219510e+07	3.931814e+03	6.717898e+03	2.272241e+03	2.088695e+03	1.054927e+04	8.986664e+02	5812.809417	...	1.818417e+03	1.930517e+03	2.402317e+03	1.257375e+06	8.856003e+06	7.878447e+03	2.121123e+03	6.469320e+06	5.546359e+03	1.756339e+04
reg5	1.283812e+06	6596.713907	1.588478e+07	1.642030e+04	1.234768e+04	1.598377e+04	2.387931e+04	2.906402e+04	1.828518e+04	1121.255607	...	4.126106e+07	1.129572e+07	4.599517e+04	7.759982e+03	1.519859e+07	1.879346e+04	8.076635e+03	7.701012e+06	4.094084e+04	2.125918e+04
reg6	6.769053e+03	94309.570045	3.176873e+07	1.188346e+05	1.853198e+04	3.363451e+04	1.259087e+04	9.314423e+05	4.368062e+03	1283.054207	...	8.360619e+03	2.378125e+04	1.508319e+07	7.406276e+04	2.990651e+07	3.671043e+07	1.822296e+06	1.286404e+06	4.794367e+07	1.839977e+07

6 rows × 48 columns

In addition, the aggregation function of pymrio also work on the diagonalized footprints. Here as example together with the country converter coco:

[14]:

import country_converter as coco

io.aggregate(
    region_agg=coco.agg_conc(
        original_countries=io.get_regions(),
        aggregates={
            "reg1": "World Region A",
            "reg2": "World Region A",
            "reg3": "World Region A",
        },
        missing_countries="World Region B",
    )
)

[14]:

<pymrio.core.mriosystem.IOSystem at 0x7f9c25d25d30>

[15]:

io.et1_diag.D_cba

[15]:

	region	World Region A								World Region B
	sector	food	mining	manufactoring	electricity	construction	trade	transport	other	food	mining	manufactoring	electricity	construction	trade	transport	other
region	sector
World Region A	food	6.413682e+06	5.952471e+01	6.070321e+05	9.326086e+02	3.306995e+03	5.987980e+04	3.514385e+03	5.762977e+04	3.437446e+04	7.789050e+00	3.648174e+05	6.373523e+01	1.339737e+03	4.505792e+04	1.557188e+02	1.163124e+03
	mining	6.832129e+03	2.421509e+06	4.487266e+05	1.936672e+05	1.984123e+05	2.126768e+04	1.676197e+04	7.595762e+04	4.373682e+02	3.805693e+03	2.419141e+05	1.079248e+04	1.073022e+04	2.708989e+04	8.090257e+02	1.908491e+04
	manufactoring	1.575255e+04	4.337974e+03	5.857218e+07	5.217160e+03	1.108166e+05	1.787260e+04	4.264953e+04	8.572782e+04	1.196817e+03	2.389005e+02	5.612155e+07	1.442696e+03	6.427781e+03	7.159629e+04	3.128223e+03	9.631846e+04
	electricity	1.148908e+06	8.329886e+05	1.095357e+07	5.960881e+07	1.529502e+06	1.771262e+06	3.062426e+06	9.812779e+06	1.717518e+04	2.384122e+03	1.167721e+07	3.179723e+05	1.151092e+04	7.346021e+06	2.360035e+04	8.544805e+06
	construction	1.287094e+03	3.530581e+03	7.855368e+03	4.364648e+03	1.082799e+07	1.811093e+03	1.193404e+04	4.796826e+04	8.117404e+00	1.278994e+00	9.064738e+03	2.977577e+01	1.183350e+03	1.057865e+04	1.704971e+02	5.278625e+04
	trade	1.302177e+04	3.358650e+03	1.320568e+05	5.581957e+03	7.080932e+04	4.827615e+06	3.359931e+04	6.189364e+04	1.772741e+03	3.095513e+01	1.747324e+05	5.736669e+02	2.618051e+03	1.843441e+07	4.414173e+03	9.440231e+04
	transport	1.661673e+04	1.013917e+04	2.026243e+05	1.186026e+04	9.463786e+04	6.605838e+04	6.900978e+07	2.981319e+05	3.570924e+03	2.342901e+02	2.223755e+05	2.064082e+03	4.978304e+03	3.583977e+05	8.792139e+05	3.666801e+05
	other	4.973365e+04	5.119490e+04	4.157135e+05	3.141636e+04	2.451423e+05	7.347058e+04	3.463245e+05	3.192544e+07	1.468825e+03	2.988605e+02	5.284564e+05	3.388346e+03	7.111777e+03	6.871237e+05	8.921976e+03	3.158392e+07
World Region B	food	1.331074e+06	5.840707e+01	1.158034e+06	7.157090e+02	2.277605e+03	2.977910e+04	1.009061e+03	6.741954e+03	2.366136e+07	1.599984e+02	7.393735e+05	3.069128e+03	2.404678e+04	1.717301e+05	3.012820e+04	7.478749e+04
	mining	1.120813e+04	1.223669e+05	6.244537e+06	3.478494e+05	3.383509e+04	1.050007e+05	3.107988e+04	1.118387e+05	3.852121e+04	1.612039e+06	6.627586e+06	1.172268e+06	5.475534e+05	1.556577e+05	8.352660e+04	2.849191e+05
	manufactoring	1.165415e+04	1.112145e+03	1.403366e+08	4.253396e+03	1.644812e+04	4.518924e+04	1.350120e+04	3.504348e+04	7.406372e+04	3.204186e+03	1.254308e+08	3.173150e+04	2.217880e+05	8.865177e+04	1.225773e+05	1.739262e+05
	electricity	6.624049e+03	2.433130e+04	5.205461e+06	1.790907e+05	1.709844e+04	2.343087e+06	1.540263e+04	8.184191e+05	7.886875e+05	2.316855e+04	6.039318e+06	1.225545e+08	4.700901e+05	2.298746e+05	1.006105e+06	2.680870e+06
	construction	2.441345e+03	3.338858e+02	6.498032e+04	1.067936e+03	2.843476e+04	1.094280e+04	2.562950e+03	1.372537e+04	1.229142e+04	2.193007e+03	4.813644e+04	3.446390e+04	1.097151e+07	3.431794e+04	6.586141e+04	3.153222e+05
	trade	7.186649e+02	1.172395e+02	8.340493e+04	3.915868e+02	7.298241e+02	1.845264e+07	1.527523e+03	1.037099e+04	1.802717e+04	4.401980e+02	9.207769e+04	4.792922e+03	3.300157e+04	1.960537e+07	4.424292e+04	4.933951e+04
	transport	1.118710e+04	1.051599e+03	3.382896e+05	3.512873e+03	4.336422e+03	6.536434e+04	3.522339e+06	2.451637e+04	3.616496e+04	2.977747e+03	2.337329e+05	3.716876e+04	9.823204e+04	2.505787e+05	1.102146e+08	2.615115e+05
	other	4.082899e+02	1.690002e+02	4.761138e+04	5.086643e+02	7.504197e+02	2.293492e+04	2.199852e+03	4.906621e+06	5.528324e+03	8.635489e+02	4.987069e+04	8.685131e+03	2.601768e+04	3.556939e+04	3.218539e+04	4.074021e+07