lstream_v002

Version 2 of HydPy-L-Stream is a computationally more efficient alternative to application model lstream_v001. The higher efficiency is due to not calculating discharges based on channel geometries but based on preprocessed relationships between discharge and storage, similar to the “V/Q-BEZIEHUNG EXTERN” option of LARSIM. An artificial neural network, available as “parameter” VG2QG, serves to describe this relationship. Principally, the neural network can fit any relationship provided by lstream_v001 very accurately. However, high accuracy might require a considerable number of neurons, which also can come with a relevant performance cost.

Integration tests

Note

When new to HydPy, consider reading section How to understand integration tests? first.

main channel flow

The following integration test repeats the main channel flow example of the documentation on application model lstream_v001. The spatial end temporal settings are identical:

>>> from hydpy import pub, Nodes, Element
>>> pub.timegrids = "2000-01-01", "2000-01-05", "30m"
>>> from hydpy.models.lstream_v002 import *
>>> parameterstep("1d")
>>> nodes = Nodes("input1", "input2", "output")
>>> stream = Element("stream",
...                  inlets=["input1", "input2"],
...                  outlets="output")
>>> stream.model = model

We again divide the channel into eight subsections:

>>> gts(8)

Next, we define a relatively small neural network consisting of three neurons in a single hidden layer. This network roughly approximates the discharge calculated by the Gauckler-Manning-Strickler equation on the triple trapezoid profile defined in the main channel flow example:

>>> vg2qg(nmb_inputs=1,
...       nmb_neurons=(3,),
...       nmb_outputs=1,
...       weights_input=[[0.610346, 1.360399, 0.35465]],
...       weights_output=[[432.958081],
...                       [94.674914],
...                       [1778.576841]],
...       intercepts_hidden=[[-2.681908, -2.237483, -3.790469]],
...       intercepts_output=[-78.006394])

In contrast to application model lstream_v001, lstream_v002 uses the stored water volume (VG) as its state variable instead of the water stage (H). Hence, we now must set VG to a value resulting in an initial outflow of 100 m³/s for the defined parameterisation of VG2QG, which holds for 1.570929405 million m³:

>>> from hydpy.core.testtools import IntegrationTest
>>> IntegrationTest.plotting_options.activated = fluxes.qz, fluxes.qa
>>> test = IntegrationTest(stream, inits=[[states.vg, 1.570929405]])

Finally, we define two identical inflow time series:

>>> import numpy
>>> q_base = 100.0
>>> q_peak = 900.0
>>> t_peak = 24.0
>>> β = 16.0
>>> ts = pub.timegrids.init.to_timepoints()
>>> nodes.input1.sequences.sim.series = q_base
>>> nodes.input2.sequences.sim.series = (
...     (q_peak-q_base)*((ts/t_peak)*numpy.exp(1.0-ts/t_peak))**β)

Our approximation of the discharge-storage relationship is far from perfect. Still, it is, at least in the range relevant for the selected event, sufficient to reproduce the original results of application model lstream_v001 with reasonable accuracy (for example, peak flow is 660 m³/s instead of 659 m³/s):

>>> test("lstream_v002_main_channel_flow")
Click to see the table
|                date |         qz |        qza |                                                                                             qg |         qa |                                                                             vg | input1 |     input2 |     output |
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2000-01-01 00:00:00 |      100.0 |      100.0 |      100.0       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |        0.0 |      100.0 |
| 2000-01-01 00:30:00 |      100.0 |      100.0 |      100.0       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |        0.0 |      100.0 |
| 2000-01-01 01:00:00 |      100.0 |      100.0 |      100.0       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |        0.0 |      100.0 |
| 2000-01-01 01:30:00 |      100.0 |      100.0 |      100.0       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |        0.0 |      100.0 |
| 2000-01-01 02:00:00 |      100.0 |      100.0 |      100.0       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |        0.0 |      100.0 |
| 2000-01-01 02:30:00 |      100.0 |      100.0 |      100.0       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |        0.0 |      100.0 |
| 2000-01-01 03:00:00 | 100.000003 | 100.000003 |      100.0       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.000003 |      100.0 |
| 2000-01-01 03:30:00 | 100.000029 | 100.000029 | 100.000003       100.0       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.000029 |      100.0 |
| 2000-01-01 04:00:00 | 100.000175 | 100.000175 | 100.000018  100.000001       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 |  1.57093  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.000175 |      100.0 |
| 2000-01-01 04:30:00 | 100.000826 | 100.000826 | 100.000094  100.000005       100.0       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570931   1.57093  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.000826 |      100.0 |
| 2000-01-01 05:00:00 | 100.003194 | 100.003194 | 100.000392  100.000028  100.000002       100.0       100.0       100.0       100.0       100.0 |      100.0 | 1.570936   1.57093  1.570929  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.003194 |      100.0 |
| 2000-01-01 05:30:00 | 100.010515 | 100.010515 | 100.001392  100.000118  100.000011  100.000001       100.0       100.0       100.0       100.0 |      100.0 | 1.570953  1.570933   1.57093  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.010515 |      100.0 |
| 2000-01-01 06:00:00 | 100.030315 | 100.030315 | 100.004326  100.000423  100.000043  100.000004       100.0       100.0       100.0       100.0 |      100.0 | 1.570999   1.57094   1.57093  1.570929  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.030315 |      100.0 |
| 2000-01-01 06:30:00 | 100.078179 | 100.078179 | 100.011998  100.001333  100.000149  100.000014  100.000001       100.0       100.0       100.0 |      100.0 | 1.571118  1.570959  1.570932   1.57093  1.570929  1.570929  1.570929  1.570929 |  100.0 |   0.078179 |      100.0 |
| 2000-01-01 07:00:00 | 100.183351 | 100.183351 | 100.030196  100.003757  100.000461  100.000049  100.000005       100.0       100.0       100.0 |      100.0 | 1.571394  1.571006  1.570938   1.57093   1.57093  1.570929  1.570929  1.570929 |  100.0 |   0.183351 |      100.0 |
| 2000-01-01 07:30:00 | 100.396214 | 100.396214 | 100.069866  100.009628  100.001287  100.000152  100.000017  100.000002       100.0       100.0 |      100.0 | 1.571982  1.571115  1.570953  1.570933   1.57093  1.570929  1.570929  1.570929 |  100.0 |   0.396214 |      100.0 |
| 2000-01-01 08:00:00 | 100.797305 | 100.797305 | 100.150201  100.022713  100.003292  100.000427  100.000051  100.000006       100.0       100.0 |      100.0 | 1.573146  1.571344  1.570988  1.570938   1.57093   1.57093  1.570929  1.570929 |  100.0 |   0.797305 |      100.0 |
| 2000-01-01 08:30:00 | 101.507032 | 101.507032 | 100.297052  100.054779   100.00835  100.001216   100.00016   100.00002  100.000002       100.0 |      100.0 | 1.575324   1.57178  1.571072  1.570951  1.570932   1.57093  1.570929  1.570929 |  100.0 |   1.507032 |      100.0 |
| 2000-01-01 09:00:00 | 102.694853 | 102.694853 | 100.566876  100.109714  100.018847  100.002973  100.000431  100.000057  100.000007  100.000001 | 100.000001 | 1.579155  1.572603  1.571236  1.570979  1.570937   1.57093   1.57093  1.570929 |  100.0 |   2.694853 | 100.000001 |
| 2000-01-01 09:30:00 | 104.586356 | 104.586356 | 101.026882  100.210142  100.039036  100.006684  100.001052  100.000153  100.000021  100.000003 | 100.000003 | 1.585562  1.574073  1.571543  1.571037  1.570947  1.570932   1.57093  1.570929 |  100.0 |   4.586356 | 100.000003 |
| 2000-01-01 10:00:00 | 107.466641 | 107.466641 | 101.776031  100.384789  100.076246  100.014007  100.002376  100.000373  100.000054  100.000007 | 100.000007 | 1.595805  1.576578  1.572099  1.571149  1.570968  1.570936   1.57093   1.57093 |  100.0 |   7.466641 | 100.000007 |
| 2000-01-01 10:30:00 | 111.678559 | 111.678559 | 102.946883  100.675411  100.141937  100.027735  100.005027  100.000846  100.000133  100.000019 | 100.000019 | 1.611522  1.580666  1.573059  1.571355  1.571009  1.570943  1.570932   1.57093 |  100.0 |  11.678559 | 100.000019 |
| 2000-01-01 11:00:00 | 117.614836 | 117.614836 | 104.710185  101.140371   100.25329   100.05236  100.010071  100.001805  100.000302  100.000047 | 100.000047 |  1.63475  1.587092  1.574656  1.571717  1.571085  1.570958  1.570934   1.57093 |  100.0 |  17.614836 | 100.000047 |
| 2000-01-01 11:30:00 | 125.703736 | 125.703736 | 107.278151  101.858435  100.435142  100.094812  100.019258  100.003654  100.000649  100.000108 | 100.000108 | 1.667916  1.596847  1.577218  1.572329  1.571221  1.570986   1.57094  1.570931 |  100.0 |  25.703736 | 100.000108 |
| 2000-01-01 12:00:00 | 136.388647 | 136.388647 |  110.91141  102.923358   100.72522   100.16599  100.035517  100.007114  100.001336  100.000236 | 100.000236 | 1.713775  1.611226  1.581174  1.573336  1.571456  1.571037   1.57095  1.570933 |  100.0 |  36.388647 | 100.000236 |
| 2000-01-01 12:30:00 | 150.102726 | 150.102726 | 115.896767  104.483442  101.163991  100.280047  100.062884  100.013231  100.002615  100.000486 | 100.000486 | 1.775346   1.63177  1.587149  1.574927  1.571847  1.571127  1.570969  1.570937 |  100.0 |  50.102726 | 100.000486 |
| 2000-01-01 13:00:00 | 167.240349 | 167.240349 | 122.571405  106.692694  101.817703  100.457806  100.107649   100.02373  100.004918  100.000961 | 100.000961 |  1.85575  1.660352  1.595924  1.577375  1.572477  1.571278  1.571003  1.570944 |  100.0 |  67.240349 | 100.000961 |
| 2000-01-01 13:30:00 | 188.127569 | 188.127569 | 131.292887  109.747419  102.766972  100.727721  100.178742  100.041178  100.008926  100.001825 | 100.001825 | 1.958053  1.699133  1.608489  1.581045  1.573465  1.571525  1.571061  1.570957 |  100.0 |  88.127569 | 100.001825 |
| 2000-01-01 14:00:00 | 212.993962 | 212.993962 | 142.425369  113.878332  104.113795   101.12774  100.288703  100.069354  100.015686  100.003349 | 100.003349 | 2.085076  1.750518  1.626065   1.58642  1.574975   1.57192  1.571158  1.570979 |  100.0 | 112.993962 | 100.003349 |
| 2000-01-01 14:30:00 | 241.948195 | 241.948195 | 156.314703  119.348015  105.984474  101.707456  100.454723  100.113673  100.026768  100.005954 | 100.005954 | 2.239216  1.817058   1.65012  1.594119   1.57723  1.572534  1.571314  1.571017 |  100.0 | 141.948195 | 100.005954 |
| 2000-01-01 15:00:00 |  274.95935 |  274.95935 | 173.262326  126.443966  108.531934  102.530462  100.699898  100.181737  100.044472  100.010284 | 100.010284 | 2.422271  1.901331  1.682361  1.604922  1.580525  1.573467  1.571561  1.571078 |  100.0 |  174.95935 | 100.010284 |
| 2000-01-01 15:30:00 | 311.845554 | 311.845554 | 193.508739   135.46699  111.936854  103.676803  101.054675  100.283993  100.072092  100.017303 | 100.017303 | 2.635277  2.005806  1.724716   1.61979  1.585245  1.574854  1.571943  1.571177 |  100.0 | 211.845554 | 100.017303 |
| 2000-01-01 16:00:00 | 352.270855 | 352.270855 | 217.236756  146.716799  116.406984  105.245379  101.558498  100.434542  100.114252  100.028414 | 100.028414 | 2.878339  2.132742  1.779273  1.639881  1.591882  1.576877  1.572519  1.571331 |  100.0 | 252.270855 | 100.028414 |
| 2000-01-01 16:30:00 | 395.750601 | 395.750601 | 244.590445  160.479098  122.174304  107.356088  102.261634  100.652088  100.177319  100.045625 | 100.045625 | 3.150427  2.284143  1.848222  1.666553  1.601052  1.579774  1.573374  1.571568 |  100.0 | 295.750601 | 100.045625 |
| 2000-01-01 17:00:00 | 441.664962 | 441.664962 | 275.682156  177.018613    129.4901  110.151475  103.227125  100.961053  100.269923  100.071758 | 100.071758 | 3.449196  2.461737  1.933773  1.701363  1.613515  1.583853  1.574618  1.571925 |  100.0 | 341.664962 | 100.071758 |
| 2000-01-01 17:30:00 | 489.279607 | 489.279607 |  310.55212  196.579273  138.618456  113.797651  104.532841  101.392853  100.403562  100.110704 | 100.110704 | 3.770905  2.666888  2.038103   1.74604  1.630192  1.589505  1.576399  1.572452 |  100.0 | 389.279607 | 100.110704 |
| 2000-01-01 18:00:00 |  537.77215 |  537.77215 | 349.076068  219.387366  149.828899    118.4842   106.27352  101.987345   100.59335  100.167754 | 100.167754 | 4.110558  2.900328  2.163308  1.802461  1.652171   1.59722  1.578908  1.573218 |  100.0 |  437.77215 | 100.167754 |
| 2000-01-01 18:30:00 | 586.262607 | 586.262607 | 390.868408  245.647955  163.389138  124.422743  108.562715  102.794439  100.858872  100.249986 | 100.249986 | 4.462268  3.161725  2.311374    1.8726  1.680719  1.607603  1.582392  1.574314 |  100.0 | 486.262607 | 100.249986 |
| 2000-01-01 19:00:00 | 633.846018 | 633.846018 |  435.24892  275.519594  179.558831  131.843834  111.534437  103.875861  101.225204  100.366752 | 100.366752 | 4.819743  3.449237  2.484103  1.958487  1.717276  1.621389  1.587163  1.575859 |  100.0 | 533.846018 | 100.366752 |
| 2000-01-01 19:30:00 | 679.625318 | 679.625318 | 481.302938  309.053185  198.584477  140.992018  115.344235  105.307022  101.724071  100.530248 | 100.530248 | 5.176723  3.759287  2.682947  2.062154  1.763442  1.639456  1.593612  1.578008 |  100.0 | 579.625318 | 100.530248 |
| 2000-01-01 20:00:00 | 722.742733 | 722.742733 |  528.00335  346.101042  220.693309  152.119189  120.169321  107.178937  102.395183  100.756201 | 100.756201 | 5.527254  4.086711  2.908681  2.185587  1.820952  1.662838  1.602223  1.580958 |  100.0 | 622.742733 | 100.756201 |
| 2000-01-01 20:30:00 | 762.408181 | 762.408181 | 574.332042  386.237769  246.080582  165.476907  126.207306  109.600031  103.287721  101.064672 | 101.064672 | 5.865791  4.425281  3.160964  2.330674  1.891637  1.692731  1.613585   1.58496 |  100.0 | 662.408181 | 101.064672 |
| 2000-01-01 21:00:00 | 797.923464 | 797.923464 | 619.355372  428.748227  274.880275  181.308693  133.673153  112.697641  104.461975  101.480999 | 101.480999 | 6.187213  4.768374  3.437926  2.499103  1.977381  1.730487  1.628409  1.590326 |  100.0 | 697.923464 | 101.480999 |
| 2000-01-01 21:30:00 | 828.701418 | 828.701418 | 662.246682  472.702646  307.109452  199.842771  142.794176  116.618889  105.991069  102.036889 | 102.036889 | 6.486832  5.109553  3.735994  2.692183  2.080069  1.777603  1.647539  1.597443 |  100.0 | 728.701418 | 102.036889 |
| 2000-01-01 22:00:00 |  854.27953 |  854.27953 |  702.27674  517.083089  342.592028  221.283824  153.803325  121.530558  107.962696  102.771649 | 102.771649 | 6.760437  5.442902  4.050078  2.910537  2.201534  1.835694  1.671962  1.606787 |  100.0 |  754.27953 | 102.771649 |
| 2000-01-01 22:30:00 | 874.327871 | 874.327871 | 738.798495   560.90094  380.895725  245.799148  166.931431  127.617562  110.480698  103.733579 | 103.733579 |  7.00439  5.763117  4.374087  3.153711  2.343496  1.906459  1.702808  1.618932 |  100.0 | 774.327871 | 103.733579 |
| 2000-01-01 23:00:00 | 888.651531 | 888.651531 | 771.242533  603.265869  421.326778  273.491086  182.399412  135.079699  113.666287  104.981456 | 104.981456 | 7.215726  6.065475  4.701578  3.419815  2.507461  1.991634  1.741352  1.634565 |  100.0 | 788.651531 | 104.981456 |
| 2000-01-01 23:30:00 | 897.187983 | 897.187983 | 799.126157  643.404231  462.998573  304.348272  200.410805  144.126602  117.658598  106.586101 | 106.586101 | 7.392237  6.345775  5.026308  3.705386  2.694548  2.092946  1.788995  1.654495 |  100.0 | 797.187983 | 106.586101 |
| 2000-01-02 00:00:00 |      900.0 |      900.0 | 822.070077  680.648677  504.944768  338.181261  221.143325  154.971161  122.614242  108.631884 | 108.631884 | 7.532511  6.600333  5.342575   4.00556  2.905216  2.212056  1.847237  1.679663 |  100.0 |      800.0 | 108.631884 |
| 2000-01-02 00:30:00 | 897.264896 | 897.264896 | 839.814373  714.423121  546.226532  374.570342  244.735421  167.822108  128.705519  111.218049 | 111.218049 | 7.635922  6.826037  5.645329  4.314541  3.138919    2.3505  1.917647  1.711141 |  100.0 | 797.264896 | 111.218049 |
| 2000-01-02 01:00:00 | 889.260928 | 889.260928 | 852.227698  744.236945  585.999477  412.861994  271.261251  182.876571  136.117041  114.459632 | 114.459632 | 7.702582  7.020421  5.930156  4.626189    3.3938  2.509592  2.001814  1.750124 |  100.0 | 789.260928 | 114.459632 |
| 2000-01-02 01:30:00 | 876.351729 | 876.351729 | 859.307412  769.690509  623.536568  452.228123  300.688566    200.3129  145.040743  118.487709 | 118.487709 | 7.733262  7.181731  6.193233  4.934544  3.666572  2.690268  2.101304   1.79792 |  100.0 | 776.351729 | 118.487709 |
| 2000-01-02 02:00:00 | 858.969595 | 858.969595 | 861.171397  790.486754  658.223704  491.765264  332.824622  220.282548  155.669607  123.448672 | 123.448672 | 7.729298  7.308964  6.431307  5.234169  3.952665  2.892844  2.217607  1.855917 |  100.0 | 758.969595 | 123.448672 |
| 2000-01-02 02:30:00 |   837.5984 |   837.5984 | 858.043758  806.441904  689.547814  530.592242   367.27268   242.89764  168.190686  129.502246 | 129.502246 | 7.692497  7.401847  6.641716  5.520289   4.24664  3.116719   2.35208  1.925556 |  100.0 |   737.5984 | 129.502246 |
| 2000-01-02 03:00:00 | 812.756821 | 812.756821 | 850.236826  817.490209  717.089675  567.915664  403.428655  268.208947  182.778174  136.818079 | 136.818079 | 7.625033  7.460791  6.822437  5.788803  4.542717  3.360115  2.505855  2.008285 |  100.0 | 712.756821 | 136.818079 |
| 2000-01-02 03:30:00 | 784.982427 | 784.982427 | 838.131498  823.680796   740.52434   603.05718  440.530645  296.170244  199.586705   145.57092 |  145.57092 | 7.529365  7.486802  6.972119  6.036243  4.835264  3.619963  2.679705  2.105513 |  100.0 | 684.982427 |  145.57092 |
| 2000-01-02 04:00:00 | 754.817086 | 754.817086 | 822.157419   825.16722  759.625973  635.454347   477.74451   326.59338  218.743875  155.934701 | 155.934701 | 7.408152  7.481384  7.090093  6.259752  5.119142  3.892035  2.873835   2.21857 |  100.0 | 654.817086 | 155.934701 |
| 2000-01-02 04:30:00 |  722.79402 |  722.79402 | 802.774144  822.191729  774.272161  664.651187  514.251842   359.11186  240.339167  168.076088 | 168.076088 | 7.264188  7.446433  7.176348   6.45707  5.389861  4.171287  3.087625  2.348643 |  100.0 |  622.79402 | 168.076088 |
| 2000-01-02 05:00:00 | 689.426711 | 689.426711 | 780.454205  815.066573   784.44387  690.289464  549.313143  393.176751  264.405154  182.148121 | 182.148121 | 7.100338   7.38413  7.231469  6.626548  5.643618  4.452333  3.319414  2.496706 |  100.0 | 589.426711 | 182.148121 |
| 2000-01-02 05:30:00 | 655.199767 | 655.199767 | 755.668881  804.154511  790.219534  712.104484  582.298183   428.09655  290.887933  198.284114 | 198.284114 | 6.919494  7.296856  7.256552  6.767155   5.87727  4.729896   3.56639  2.663393 |  100.0 | 555.199767 | 198.284114 |
| 2000-01-02 06:00:00 | 620.561767 | 620.561767 | 728.877238  789.850222  791.763727  729.924135  612.691172  463.109515  319.610155  216.590965 | 216.590965 | 6.724526  7.187105  7.253108  6.878466  6.088289  4.999143  3.824689  2.848827 |  100.0 | 520.561767 | 216.590965 |
| 2000-01-02 06:30:00 | 585.920022 | 585.920022 | 700.518686  772.563933  789.312071  743.668004  640.083533  497.461733  350.240348   237.13962 |  237.13962 | 6.518248  7.057424  7.222961  6.960626  6.274741  5.255862  4.089687  3.052409 |  100.0 | 485.920022 |  237.13962 |
| 2000-01-02 07:00:00 |  551.63713 |  551.63713 |   671.0088  752.708114  783.154402  753.343914  664.164278  530.467105  382.287485  259.949429 | 259.949429 | 6.303379  6.910365  7.168158  7.014285  6.435264  5.496517   4.35641  3.272617 |  100.0 |  451.63713 | 259.949429 |
| 2000-01-02 07:30:00 | 518.029154 | 518.029154 | 640.737633  730.687694  773.618082    759.0407  684.712521  561.539759  415.131609  284.964028 | 284.964028 | 6.082504  6.748455  7.090883  7.040524  6.569055  5.718228  4.619945  3.506919 |  100.0 | 418.029154 | 284.964028 |
| 2000-01-02 08:00:00 | 485.365238 | 485.365238 | 610.069326  706.893751  761.052888  760.917496   701.59241  590.202951   448.08348  312.021153 | 312.021153 | 5.858037  6.574171  6.993396  7.040768   6.67584  5.918729   4.87576  3.751831 |  100.0 | 385.365238 | 312.021153 |
| 2000-01-02 08:30:00 |  453.86844 |  453.86844 | 579.341696  681.700176  745.818423  759.190714  714.748769  616.084334  480.452752  340.826594 | 340.826594 | 5.632185  6.389925  6.877984  7.016697  6.755836  6.096325  5.119897  4.003158 |  100.0 |  353.86844 | 340.826594 |
| 2000-01-02 09:00:00 | 423.717566 | 423.717566 | 548.864793  655.462387  728.274463  754.120194  724.201675  638.906481  511.604077  370.947274 | 370.947274 |  5.40692   6.19805  6.746922  6.970175  6.809689  6.249856  5.349041   4.25634 |  100.0 | 323.717566 | 370.947274 |
| 2000-01-02 09:30:00 | 395.049792 | 395.049792 | 518.918002  628.516968  708.774195  745.995862  730.039026  658.477672  540.990819  401.833364 | 401.833364 | 5.183957  6.000772  6.602459  6.903176  6.838411  6.378667  5.560518  4.506824 |  100.0 | 295.049792 | 401.833364 |
| 2000-01-02 10:00:00 | 367.963873 | 367.963873 | 489.746062  601.181099  687.659953  735.125905  732.407105  674.684366  568.167408   432.86615 |  432.86615 | 4.964749  5.800189  6.446797  6.817737  6.843305  6.482568  5.752248  4.750366 |  100.0 | 267.963873 |  432.86615 |
| 2000-01-02 10:30:00 | 342.523746 | 342.523746 | 461.554942  573.750945  665.260736  721.826989  731.499827  687.484765  592.787545    463.4165 |   463.4165 | 4.750493  5.598236  6.282079  6.715918  6.825894  6.561795  5.922703  4.983234 |  100.0 | 242.523746 |   463.4165 |
| 2000-01-02 11:00:00 | 318.762374 | 318.762374 |  434.50873  546.498683  641.890721  706.416699  727.547582   696.90236  614.595923  492.896592 | 492.896592 |  4.54215  5.396654  6.110374  6.599771  6.787859  6.616956  6.070855  5.202293 |  100.0 | 218.762374 | 492.896592 |
| 2000-01-02 11:30:00 |  296.68568 |  296.68568 | 408.728472  519.668437  617.847968  689.208015  720.806566  703.018666  633.418624  520.794264 | 520.794264 | 4.340473  5.196962   5.93365  6.471323  6.730981  6.648974  6.196135  5.405016 |  100.0 |  196.68568 | 520.794264 |
| 2000-01-02 12:00:00 | 276.276442 | 276.276442 | 384.293438  493.471882  593.412715  670.505444  711.549248  705.964973  649.154375  546.688554 | 546.688554 | 4.146042  5.000441  5.753757  6.332556  6.657102  6.659026  6.298394  5.589455 |  100.0 | 176.276442 | 546.688554 |
| 2000-01-02 12:30:00 | 257.498082 | 257.498082 | 361.244738  468.084509  568.844967  650.602299  700.056323  705.913379  661.766941  570.251174 | 570.251174 | 3.959298  4.808129  5.572388  6.185393  6.568085  6.648483  6.377858  5.754183 |  100.0 | 157.498082 | 570.251174 |
| 2000-01-02 13:00:00 | 240.298231 | 240.298231 | 339.590802  443.643488  544.381428  629.778595  686.610246  703.067639  671.278073  591.240255 | 591.240255 | 3.780571  4.620834   5.39106  6.031678  6.465788   6.61886  6.435079  5.898251 |  100.0 | 140.298231 | 591.240255 |
| 2000-01-02 13:30:00 | 224.612057 | 224.612057 | 319.314005  420.247662  520.232165  608.299119  671.490234  697.654395  677.760412  609.491325 | 609.491325 | 3.610108  4.439154  5.211088  5.873158  6.352044  6.571765  6.470888  6.021136 |  100.0 | 124.612057 | 609.491325 |
| 2000-01-02 14:00:00 | 210.365288 | 210.365288 | 300.377677  397.959795  496.577591  586.411392  654.968464  689.915212  681.330078  624.908252 | 624.908252 | 3.448085  4.263506  5.033576  5.711457  6.228641   6.50886  6.486341  6.122695 |  100.0 | 110.365288 | 624.908252 |
| 2000-01-02 14:30:00 |  197.47692 |  197.47692 |  282.73276  376.810719  473.566392  564.343402  637.307164  680.099684  682.138961  637.455041 | 637.455041 | 3.294625  4.094166  4.859416  5.548058  6.097307  6.431834   6.48267  6.203126 |  100.0 |   97.47692 | 637.455041 |
| 2000-01-02 15:00:00 | 185.861607 | 185.861607 | 266.323572  356.804787  451.314849  542.301248  618.756263  668.459716  680.366999  647.148425 | 647.148425 | 3.149793  3.931299  4.689297  5.384283  5.959688  6.342368  6.461237  6.262919 |  100.0 |  85.861607 | 647.148425 |
| 2000-01-02 15:30:00 | 175.431719 | 175.431719 | 251.092244  337.925893  429.907745  520.466922  599.551351  655.244912  676.214759   654.05085 |  654.05085 | 3.013605  3.774999   4.52373  5.221276  5.817336  6.242119  6.423492  6.302814 |  100.0 |  75.431719 |  654.05085 |
| 2000-01-02 16:00:00 | 166.099094 | 166.099094 |  236.98167  320.143444  409.400784  498.996583  579.911775  640.698926  669.896632  658.263599 | 658.263599 | 2.886016  3.625308  4.363067  5.060004  5.671688  6.132702  6.370936  6.323754 |  100.0 |  66.099094 | 658.263599 |
| 2000-01-02 16:30:00 | 157.776495 | 157.776495 | 223.937004  303.417733  389.824172  478.019629  560.038822  625.056582  661.634835  659.919937 | 659.919937 | 2.766927  3.482242  4.207535  4.901252  5.524054   6.01567  6.305095  6.326841 |  100.0 |  57.776495 | 659.919937 |
| 2000-01-02 17:00:00 | 150.378786 | 150.378786 | 211.905958  287.704424  371.186927  457.638756  540.114049  608.541548  651.654307  659.178404 | 659.178404 | 2.656178  3.345805  4.057267  4.745639  5.375598  5.892501  6.227492  6.313297 |  100.0 |  50.378786 | 659.178404 |
| 2000-01-02 17:30:00 | 143.823868 | 143.823868 | 200.838292  272.957968  353.481451  437.931067  520.297882    591.3644  640.178495  656.216395 | 656.216395 | 2.553552   3.21599  3.912324  4.593629  5.227338  5.764581  6.139627  6.284429 |  100.0 |  43.823868 | 656.216395 |
| 2000-01-02 18:00:00 | 138.033385 | 138.033385 | 190.684932  259.133947  336.687963  418.950124  500.728668  573.720967  627.425939  651.224256 | 651.224256 | 2.458779  3.092781  3.772727  4.445558  5.080137  5.633195  6.042958  6.241592 |  100.0 |  38.033385 | 651.224256 |
| 2000-01-02 18:30:00 | 132.933235 | 132.933235 | 181.397097  246.190422  320.778512  400.728723  481.522314  555.790883  613.607536  644.400006 | 644.400006 | 2.371544  2.976153  3.638469  4.301647  4.934708  5.499512  5.938888  6.186166 |  100.0 |  32.933235 | 644.400006 |
| 2000-01-02 19:00:00 | 128.453911 | 128.453911 | 172.925686  234.088439  305.720374  383.282113  462.772606  537.736385  598.924336  635.944785 | 635.944785 | 2.291495   2.86606  3.509531  4.162036  4.791625  5.364577  5.828749  6.119529 |  100.0 |  28.453911 | 635.944785 |
| 2000-01-02 19:30:00 | 124.530701 | 124.530701 | 165.221042  222.791892  291.478775   366.61138  444.552229    519.7014  583.565759   626.05902 |  626.05902 | 2.218253  2.762433  3.385895  4.026797  4.651332  5.229308  5.713793  6.043041 |  100.0 |  24.530701 |  626.05902 |
| 2000-01-02 20:00:00 | 121.103761 | 121.103761 | 158.233068  212.266948  278.018906  350.706755  426.914384  501.810994  567.708135  614.939268 | 614.939268 |  2.15142  2.665172  3.267541  3.895959  4.514158  5.094494  5.595179  5.958025 |  100.0 |  21.103761 | 614.939268 |
| 2000-01-02 20:30:00 | 118.118088 | 118.118088 | 151.911611  202.481266  265.307298  335.550663  409.894906  484.171277  551.513518   602.77566 |  602.77566 | 2.090591  2.574147  3.154454  3.769521  4.380338  4.960797  5.473963  5.865753 |  100.0 |  18.118088 |  602.77566 |
| 2000-01-02 21:00:00 | 115.523427 | 115.523427 | 146.207009  193.403192  253.312612  321.120382  393.514675  466.869773  535.128758  589.749838 | 589.749838 | 2.035361  2.489193  3.046617  3.647467  4.250029  4.828758  5.351096  5.767435 |  100.0 |  15.523427 | 589.749838 |
| 2000-01-02 21:30:00 | 113.274094 | 113.274094 | 141.070659  185.001082  242.005932  307.390271   377.78216  449.976276  518.684856  576.033305 | 576.033305 | 1.985327  2.410119  2.944009  3.529775  4.123323  4.698808  5.227421  5.664208 |  100.0 |  13.274094 | 576.033305 |
| 2000-01-02 22:00:00 | 111.328777 | 111.328777 | 136.461306  177.240521  231.360436  294.332346  362.695202  433.543186  502.294084  561.781496 | 561.781496 | 1.940089  2.336716  2.846593  3.416426   4.00027  4.571282  5.103669  5.557131 |  100.0 |  11.328777 | 561.781496 |
| 2000-01-02 22:30:00 | 109.650285 | 109.650285 | 132.320953  170.095174  221.352002  281.922564   348.24623  417.611102  486.060973  547.152255 | 547.152255 | 1.899281  2.268722  2.754331  3.307399  3.880887  4.446425   4.98046  5.447166 |  100.0 |   9.650285 | 547.152255 |
| 2000-01-02 23:00:00 | 108.205287 | 108.205287 | 128.614683  163.526887  211.957568  270.133977  334.420361  402.204236  470.064722   532.27419 |  532.27419 | 1.862545  2.205881  2.667155  3.202681  3.765172  4.324414  4.858311  5.335189 |  100.0 |   8.205287 |  532.27419 |
| 2000-01-02 23:30:00 | 106.964036 | 106.964036 | 125.302473  157.501969   203.15477  258.942673  321.199735  387.337102  454.372995  517.267835 | 517.267835 | 1.829535  2.147921   2.58498  3.102263  3.653109  4.205367  4.737646  5.221979 |  100.0 |   6.964036 | 517.267835 |
| 2000-01-03 00:00:00 | 105.900084 | 105.900084 | 122.347031  151.986541  194.921648  248.326575  308.564478  373.015122  439.039334  502.239752 | 502.239752 | 1.799931   2.09457  2.507697  3.006134  3.544681  4.089356  4.618803  5.108218 |  100.0 |   5.900084 | 502.239752 |
| 2000-01-03 00:30:00 |  104.99001 |  104.99001 | 119.713819  146.946901  187.236176  238.265441  296.493918  359.236502  424.104399  487.282557 | 487.282557 | 1.773428  2.045551  2.435176  2.914282   3.43987  3.976419   4.50204  4.994497 |  100.0 |    4.99001 | 487.282557 |
| 2000-01-03 01:00:00 | 104.213141 | 104.213141 |  117.37102  142.349906  180.075942  228.740673  284.967511  345.993966  409.597403  472.475217 | 472.475217 | 1.749744  2.000589   2.36727  2.826685  3.338661  3.866572  4.387554  4.881317 |  100.0 |   4.213141 | 472.475217 |
| 2000-01-03 01:30:00 | 103.551298 | 103.551298 | 115.289448  138.163306  173.417969  219.734996  273.965495  333.276294  395.537628  457.883613 | 457.883613 | 1.728615  1.959416  2.303811  2.743314  3.241047  3.759812  4.275484  4.769094 |  100.0 |   3.551298 | 457.883613 |
| 2000-01-03 02:00:00 | 102.988541 | 102.988541 | 113.442426  134.356023  167.238694  211.232062  263.469306  321.069642   381.93598  443.561327 | 443.561327 | 1.709798  1.921771  2.244622  2.664126   3.14702  3.656131  4.165924  4.658169 |  100.0 |   2.988541 | 443.561327 |
| 2000-01-03 02:30:00 |  102.51094 |  102.51094 | 111.805648  130.898372  161.514049  203.216038  253.461786  309.358651  368.796495  429.550623 | 429.550623 | 1.693068  1.887404  2.189514  2.589063  3.056577  3.555517  4.058936  4.548811 |  100.0 |    2.51094 | 429.550623 |
| 2000-01-03 03:00:00 | 102.106358 | 102.106358 | 110.357028  127.762211  156.219638  195.671239  243.927215  298.127329  356.117758  415.883572 | 415.883572 | 1.678216  1.856075  2.138291   2.51805  2.969716  3.457957  3.954553  4.441233 |  100.0 |   2.106358 | 415.883572 |
| 2000-01-03 03:30:00 | 101.764251 | 101.764251 | 109.076541  124.921026  151.330958  188.581815  234.851207  287.359734  343.894195   402.58326 |  402.58326 | 1.665054  1.827555  2.090753  2.450998  2.886431  3.363442  3.852791  4.335592 |  100.0 |   1.764251 |  402.58326 |
| 2000-01-03 04:00:00 |  101.47548 |  101.47548 | 107.946073   122.34998  146.823636  181.931539  226.220507  277.040468  332.117213  389.665032 | 389.665032 | 1.653407  1.801628    2.0467  2.387804  2.806711  3.271966  3.753653  4.232006 |  100.0 |    1.47548 | 389.665032 |
| 2000-01-03 04:30:00 | 101.232151 | 101.232151 | 106.949265  120.025909  142.673664   175.70368  218.022721  267.155009  320.776183  377.137719 | 377.137719 | 1.643116   1.77809  2.005934   2.32835  2.730537  3.183528  3.657135  4.130556 |  100.0 |   1.232151 | 377.137719 |
| 2000-01-03 05:00:00 | 101.027458 | 101.027458 | 106.071374  117.927292  138.857605  169.880974  210.246024  257.689884  309.859262  365.004811 | 365.004811 | 1.634037  1.756749   1.96826  2.272508   2.65788  3.098129   3.56323  4.031294 |  100.0 |   1.027458 | 365.004811 |
| 2000-01-03 05:30:00 | 100.855551 | 100.855551 | 105.299136  116.034197  135.352771  164.445671  202.878864  248.632733  299.354061  353.265548 | 353.265548 | 1.626039  1.737426  1.933486  2.220141    2.5887  3.015772  3.471932  3.934253 |  100.0 |   0.855551 | 353.265548 |
| 2000-01-03 06:00:00 | 100.711411 | 100.711411 | 104.620632  114.328217  132.137357  159.379637  195.909698  239.972259   289.24816  341.915902 | 341.915902 | 1.619002  1.719953   1.90143  2.171105  2.522946  2.936459  3.383235  3.839451 |  100.0 |   0.711411 | 341.915902 |
| 2000-01-03 06:30:00 | 100.590745 | 100.590745 | 104.025177  112.792384  129.190547    154.6645  189.326782  231.698108    279.5295   330.94945 |  330.94945 |  1.61282  1.704172  1.871913  2.125252  2.460554  2.860191  3.297139  3.746895 |  100.0 |   0.590745 |  330.94945 |
| 2000-01-03 07:00:00 | 100.489885 | 100.489885 | 103.503201  111.411093  126.492575  150.281807  183.118014  223.800686  270.186645  320.358121 | 320.358121 | 1.607396  1.689937  1.844767  2.082431  2.401449  2.786962  3.213644  3.656586 |  100.0 |   0.489885 | 320.358121 |
| 2000-01-03 07:30:00 | 100.405708 | 100.405708 |  103.04615  110.170014  124.024767  146.213196  177.270845   216.27095  261.208944  310.132826 | 310.132826 | 1.602644  1.677115  1.819828  2.042492  2.345545  2.716762  3.132756  3.568523 |  100.0 |   0.405708 | 310.132826 |
| 2000-01-03 08:00:00 |  100.33556 |  100.33556 | 102.646388  109.056006  121.769545  142.440546   171.77225  209.100189  252.586598  300.263973 | 300.263973 | 1.598484  1.665577  1.796944  2.005284  2.292748  2.649571   3.05448  3.482704 |  100.0 |    0.33556 | 300.263973 |
| 2000-01-03 08:30:00 | 100.277186 | 100.277186 | 102.297111  108.057036  119.710424  138.946123  166.608754  202.279806  244.310652  290.741875 | 290.741875 | 1.594848  1.655209  1.775968   1.97066  2.242955  2.585363  2.978825  3.399128 |  100.0 |   0.277186 | 290.741875 |
| 2000-01-03 09:00:00 | 100.228681 | 100.228681 | 101.992265  107.162099  117.831985  135.712693  161.766498   195.80113   236.37292  281.557064 | 281.557064 | 1.591674  1.645904  1.756762  1.938475  2.196058  2.524101  2.905795  3.317797 |  100.0 |   0.228681 | 281.557064 |
| 2000-01-03 09:30:00 | 100.188431 | 100.188431 | 101.726473  106.361141  116.119844  132.723618  157.231334  189.655269  228.765872  272.700507 | 272.700507 | 1.588905  1.637561  1.739196  1.908588  2.151945  2.465738  2.835396  3.238714 |  100.0 |   0.188431 | 272.700507 |
| 2000-01-03 10:00:00 | 100.155078 | 100.155078 | 101.494962  105.644991  114.560604  129.962928  152.988943  183.832989  221.482483  264.163748 | 264.163748 | 1.586494  1.630091  1.723148  1.880864  2.110498  2.410219  2.767627  3.161888 |  100.0 |   0.155078 | 264.163748 |
| 2000-01-03 10:30:00 | 100.127477 | 100.127477 | 101.293509  105.005287  113.141816  127.415366   149.02495  178.324658  214.516066  255.938985 | 255.938985 | 1.584395   1.62341  1.708502  1.855171    2.0716  2.357479  2.702483  3.087327 |  100.0 |   0.127477 | 255.938985 |
| 2000-01-03 11:00:00 | 100.104666 | 100.104666 | 101.118378  104.434421  111.851922  125.066422  145.325047  173.120217  207.860109  248.019077 | 248.019077 |  1.58257  1.617441  1.695151  1.831385  2.035135  2.307448  2.639951  3.015041 |  100.0 |   0.104666 | 248.019077 |
| 2000-01-03 11:30:00 | 100.085838 | 100.085838 | 100.966269  103.925471  110.680208  122.902346  141.875101  168.209195  201.508112  240.397508 | 240.397508 | 1.580985  1.612115  1.682992  1.809385  2.000984  2.260047  2.580013   2.94504 |  100.0 |   0.085838 | 240.397508 |
| 2000-01-03 12:00:00 | 100.070317 | 100.070317 | 100.834274  103.472154  109.616755  120.910146  138.661253   163.58076  195.453452  233.068316 | 233.068316 |  1.57961  1.607366  1.671932  1.789057  1.969032  2.215191  2.522642  2.877333 |  100.0 |   0.070317 | 233.068316 |
| 2000-01-03 12:30:00 | 100.057539 | 100.057539 | 100.719833  103.068767  108.652385  119.077579  135.669998  159.223778  189.689272  226.025984 | 226.025984 | 1.578418  1.603138  1.661881  1.770292  1.939166  2.172795  2.467804  2.811927 |  100.0 |   0.057539 | 226.025984 |
| 2000-01-03 13:00:00 | 100.047032 | 100.047032 | 100.620693  102.710144   107.77862  117.393137  132.888255  155.126904  184.208398  219.265319 | 219.265319 | 1.577385  1.599377  1.652758  1.752986  1.911274  2.132765  2.415457  2.748824 |  100.0 |   0.047032 | 219.265319 |
| 2000-01-03 13:30:00 | 100.038402 | 100.038402 | 100.534879  102.391612   106.98763  115.846017  130.303413  151.278669  179.003291  212.781327 | 212.781327 | 1.576492  1.596035  1.644485  1.737041  1.885251   2.09501  2.365553  2.688024 |  100.0 |   0.038402 | 212.781327 |
| 2000-01-03 14:00:00 | 100.031322 | 100.031322 | 100.460657  102.108944  106.272193  114.426097  127.903373   147.66757  174.066033  206.569081 | 206.569081 | 1.575719  1.593068  1.636991  1.722363  1.860992  2.059434  2.318036  2.629518 |  100.0 |   0.031322 | 206.569081 |
| 2000-01-03 14:30:00 | 100.025521 | 100.025521 |  100.39651  101.858325  105.625656  113.123907   125.67657  144.282159  169.388332  200.623601 | 200.623601 | 1.575051  1.590437   1.63021  1.708867  1.838397  2.025944  2.272845  2.573295 |  100.0 |   0.025521 | 200.623601 |
| 2000-01-03 15:00:00 | 100.020773 | 100.020773 | 100.341109  101.636317   105.04189  111.930594  123.611982  141.111122  164.961558  194.939755 | 194.939755 | 1.574475  1.588106   1.62408  1.696467  1.817371  1.994446  2.229914  2.519334 |  100.0 |   0.020773 | 194.939755 |
| 2000-01-03 15:30:00 | 100.016892 | 100.016892 | 100.293296  101.439823  104.515259  110.837893  121.699139  138.143349  160.776792  189.512176 | 189.512176 | 1.573977  1.586042  1.618544  1.685086   1.79782  1.964846  2.189174   2.46761 |  100.0 |   0.016892 | 189.512176 |
| 2000-01-03 16:00:00 | 100.013722 | 100.013722 | 100.252059  101.266058  104.040583  109.838093  119.928119  135.367995  156.824888  184.335201 | 184.335201 | 1.573548  1.584217   1.61355  1.674651  1.779658  1.937054  2.150551  2.418092 |  100.0 |   0.013722 | 184.335201 |
| 2000-01-03 16:30:00 | 100.011136 | 100.011136 | 100.216516  101.112519  103.613106  108.924008  118.289533  132.774526  153.096544  179.402836 | 179.402836 | 1.573178  1.582604  1.609049  1.665091    1.7628  1.910981  2.113972  2.370741 |  100.0 |   0.011136 | 179.402836 |
| 2000-01-03 17:00:00 | 100.009028 | 100.009028 |   100.1859  100.976962  103.228467  108.088944  116.774519  130.352757   149.58237  174.708744 | 174.708744 |  1.57286   1.58118  1.604997  1.656342  1.747166   1.88654  2.079358  2.325513 |  100.0 |   0.009028 | 174.708744 |
| 2000-01-03 17:30:00 | 100.007313 | 100.007313 | 100.159544  100.857376  102.882668  107.326673  115.374718  128.092882  146.272961  170.246251 | 170.246251 | 1.572586  1.579924  1.601351  1.648343   1.73268  1.863648  2.046634  2.282361 |  100.0 |   0.007313 | 170.246251 |
| 2000-01-03 18:00:00 | 100.005918 | 100.005918 | 100.136867  100.751961  102.572052  106.631402  114.082262  125.985489  143.158961  166.008373 | 166.008373 |  1.57235  1.578817  1.598075  1.641036  1.719268  1.842222  2.015722  2.241232 |  100.0 |   0.005918 | 166.008373 |
| 2000-01-03 18:30:00 | 100.004785 | 100.004785 | 100.117366  100.659108  102.293273   105.99775  112.889746  124.021572   140.23112  161.987853 | 161.987853 | 1.572148  1.577842  1.595133  1.634368  1.706863  1.822185  1.986545   2.20207 |  100.0 |   0.004785 | 161.987853 |
| 2000-01-03 19:00:00 | 100.003865 | 100.003865 | 100.100606   100.57738  102.043278   105.42072  111.790211  122.192539  137.480351   158.17721 |  158.17721 | 1.571973  1.576983  1.592495  1.628289  1.695398   1.80346  1.959027  2.164816 |  100.0 |   0.003865 |  158.17721 |
| 2000-01-03 19:30:00 | 100.003119 | 100.003119 | 100.086208  100.505495  101.819278  104.895675  110.777126  120.490206  134.897767  154.568791 | 154.568791 | 1.571824  1.576229   1.59013  1.622751  1.684811  1.785977  1.933093  2.129408 |  100.0 |   0.003119 | 154.568791 |
| 2000-01-03 20:00:00 | 100.002515 | 100.002515 | 100.073845  100.442313  101.618735  104.418318  109.844358  118.906796  132.474722  151.154832 | 151.154832 | 1.571695  1.575565  1.588012  1.617712  1.675044  1.769664  1.908671  2.095784 |  100.0 |   0.002515 | 151.154832 |
| 2000-01-03 20:30:00 | 100.002026 | 100.002026 | 100.063234  100.386818  101.439336  103.984667   108.98616  117.434928  130.202836  147.927508 | 147.927508 | 1.571585  1.574983  1.586118   1.61313  1.666042  1.754457  1.885689  2.063879 |  100.0 |   0.002026 | 147.927508 |
| 2000-01-03 21:00:00 | 100.001631 | 100.001631 | 100.054131  100.338106  101.278979   103.59104  108.197145  116.067609   128.07402  144.878992 | 144.878992 | 1.571491  1.574472  1.584424  1.608969  1.657751   1.74029  1.864077   2.03363 |  100.0 |   0.001631 | 144.878992 |
| 2000-01-03 21:30:00 | 100.001312 | 100.001312 | 100.046325  100.295377  101.135755  103.234029  107.472268  114.798219  126.080482  142.001505 | 142.001505 |  1.57141  1.574023  1.582912  1.605192  1.650122  1.727103  1.843769  2.004973 |  100.0 |   0.001312 | 142.001505 |
| 2000-01-03 22:00:00 | 100.001054 | 100.001054 | 100.039633  100.257919   101.00793  102.910488   106.80681  113.620498  124.214748  139.287354 | 139.287354 |  1.57134  1.573631  1.581562  1.601767  1.643108  1.714838  1.824699  1.977842 |  100.0 |   0.001054 | 139.287354 |
| 2000-01-03 22:30:00 | 100.000846 | 100.000846 | 100.033899  100.225101  100.893936  102.617515  106.196356  112.528533  122.469654  136.728979 | 136.728979 | 1.571281  1.573286  1.580358  1.598665  1.636666  1.703441  1.806805  1.952175 |  100.0 |   0.000846 | 136.728979 |
| 2000-01-03 23:00:00 | 100.000679 | 100.000679 | 100.028988  100.196366  100.792352  102.352431   105.63678   111.51674  120.838357   134.31898 |  134.31898 |  1.57123  1.572985  1.579285  1.595857  1.630755  1.692857  1.790026   1.92791 |  100.0 |   0.000679 |  134.31898 |
| 2000-01-03 23:30:00 | 100.000544 | 100.000544 | 100.024782  100.171221  100.701891  102.112771   105.12423  110.579852  119.314325  132.050147 | 132.050147 | 1.571186  1.572722   1.57833  1.593317  1.625334  1.683037  1.774304  1.904985 |  100.0 |   0.000544 | 132.050147 |
| 2000-01-04 00:00:00 | 100.000436 | 100.000436 | 100.021181  100.149229  100.621394  101.896267   104.65511  109.712903  117.891335   129.91548 |  129.91548 | 1.571149  1.572491   1.57748  1.591022  1.620368  1.673933  1.759583  1.883342 |  100.0 |   0.000436 |  129.91548 |
| 2000-01-04 00:30:00 | 100.000349 | 100.000349 |   100.0181  100.130005  100.549813  101.700831  104.226066  108.911216  116.563468  127.908202 | 127.908202 | 1.571117   1.57229  1.576724   1.58895  1.615823  1.665499  1.745809  1.862921 |  100.0 |   0.000349 | 127.908202 |
| 2000-01-04 01:00:00 | 100.000279 | 100.000279 | 100.015463   100.11321  100.486205  101.524551  103.833974  108.170385  115.325094  126.021778 | 126.021778 |  1.57109  1.572114  1.576053  1.587081  1.611666  1.657694  1.732931  1.843667 |  100.0 |   0.000279 | 126.021778 |
| 2000-01-04 01:30:00 | 100.000223 | 100.000223 | 100.013209  100.098544  100.429719  101.365668  103.475923  107.486262   114.17087  124.249912 | 124.249912 | 1.571066   1.57196  1.575457  1.585397  1.607867  1.650475  1.720898  1.825525 |  100.0 |   0.000223 | 124.249912 |
| 2000-01-04 02:00:00 | 100.000178 | 100.000178 | 100.011281  100.085744   100.37959  101.222573  103.149209  106.854947  113.095723  122.586562 | 122.586562 | 1.571046  1.571826  1.574928  1.583879  1.604399  1.643805  1.709665  1.808442 |  100.0 |   0.000178 | 122.586562 |
| 2000-01-04 02:30:00 | 100.000142 | 100.000142 | 100.009632  100.074578  100.335133  101.093794  102.851314  106.272774  112.094846   121.02593 |  121.02593 | 1.571029  1.571709  1.574459  1.582514  1.601236  1.637646  1.699185  1.792366 |  100.0 |   0.000142 |  121.02593 |
| 2000-01-04 03:00:00 | 100.000113 | 100.000113 | 100.008224  100.064842  100.295729  100.977981  102.579903  105.736299  111.163682  119.562469 | 119.562469 | 1.571015  1.571607  1.574043  1.581286  1.598352  1.631965  1.689416  1.777248 |  100.0 |   0.000113 | 119.562469 |
| 2000-01-04 03:30:00 |  100.00009 |  100.00009 |  100.00702  100.056356  100.260827  100.873906  102.332807  105.242287  110.297915  118.190876 | 118.190876 | 1.571002  1.571518  1.573675  1.580182  1.595726  1.626728  1.680316  1.763041 |  100.0 |    0.00009 | 118.190876 |
| 2000-01-04 04:00:00 | 100.000072 | 100.000072 | 100.005992  100.048963   100.22993  100.780444  102.108017  104.787703  109.493462  116.906087 | 116.906087 | 1.570991  1.571441  1.573349  1.579191  1.593337  1.621904  1.671845  1.749698 |  100.0 |   0.000072 | 116.906087 |
| 2000-01-04 04:30:00 | 100.000057 | 100.000057 | 100.005113  100.042526  100.202596  100.696572  101.903672  104.369702  108.746457  115.703271 | 115.703271 | 1.570982  1.571374  1.573061  1.578302  1.591164  1.617465  1.663967  1.737176 |  100.0 |   0.000057 | 115.703271 |
| 2000-01-04 05:00:00 | 100.000046 | 100.000046 | 100.004363  100.036922  100.178426  100.621358  101.718049  103.985618  108.053248  114.577825 | 114.577825 | 1.570975  1.571315  1.572806  1.577505   1.58919  1.613384  1.656646  1.725431 |  100.0 |   0.000046 | 114.577825 |
| 2000-01-04 05:30:00 | 100.000036 | 100.000036 | 100.003722  100.032047  100.157067  100.553953  101.549558  103.632954   107.41038  113.525365 | 113.525365 | 1.570968  1.571264  1.572581   1.57679  1.587398  1.609634  1.649846  1.714424 |  100.0 |   0.000036 | 113.525365 |
| 2000-01-04 06:00:00 | 100.000029 | 100.000029 | 100.003175  100.027806  100.138203  100.493587  101.396727  103.309375  106.814593  112.541718 | 112.541718 | 1.570962   1.57122  1.572383  1.576151  1.585772  1.606191  1.643537  1.704116 |  100.0 |   0.000029 | 112.541718 |
| 2000-01-04 06:30:00 | 100.000023 | 100.000023 | 100.002709  100.024119   100.12155  100.439561  101.258203  103.012696  106.262807  111.622917 | 111.622917 | 1.570957  1.571181  1.572207  1.575578  1.584299  1.603033  1.637687  1.694467 |  100.0 |   0.000023 | 111.622917 |
| 2000-01-04 07:00:00 | 100.000018 | 100.000018 |  100.00231  100.020915  100.106857  100.391239  101.132734  102.740879  105.752116  110.765189 | 110.765189 | 1.570953  1.571148  1.572053  1.575066  1.582964  1.600138  1.632266  1.685444 |  100.0 |   0.000018 | 110.765189 |
| 2000-01-04 07:30:00 | 100.000014 | 100.000014 |  100.00197  100.018131  100.093901  100.348047  101.019171   102.49202   105.27978   109.96495 |  109.96495 |  1.57095  1.571119  1.571916  1.574609  1.581756  1.597487  1.627248   1.67701 |  100.0 |   0.000014 |  109.96495 |
| 2000-01-04 08:00:00 | 100.000011 | 100.000011 |  100.00168  100.015713  100.082482  100.309464  100.916455  102.264343  104.843216  109.218794 | 109.218794 | 1.570947  1.571093  1.571796    1.5742  1.580663  1.595061  1.622606  1.669134 |  100.0 |   0.000011 | 109.218794 |
| 2000-01-04 08:30:00 | 100.000009 | 100.000009 | 100.001433  100.013614  100.072422  100.275019  100.823615  102.056194  104.439992  108.523491 | 108.523491 | 1.570944  1.571071   1.57169  1.573836  1.579676  1.592842  1.618316  1.661784 |  100.0 |   0.000009 | 108.523491 |
| 2000-01-04 09:00:00 | 100.000007 | 100.000007 | 100.001221  100.011792  100.063564  100.244286  100.739757  101.866035  104.067818  107.875974 | 107.875974 | 1.570942  1.571052  1.571597   1.57351  1.578784  1.590815  1.614352  1.654929 |  100.0 |   0.000007 | 107.875974 |
| 2000-01-04 09:30:00 | 100.000006 | 100.000006 | 100.001041  100.010212  100.055767  100.216882  100.664064  101.692434   103.72454  107.273336 | 107.273336 |  1.57094  1.571036  1.571515   1.57322  1.577979  1.588964  1.610695  1.648542 |  100.0 |   0.000006 | 107.273336 |
| 2000-01-04 10:00:00 | 100.000004 | 100.000004 | 100.000888  100.008841  100.048908   100.19246  100.595786  101.534059  103.408133  106.712818 | 106.712818 | 1.570939  1.571022  1.571443  1.572962  1.577253  1.587275  1.607321  1.642593 |  100.0 |   0.000004 | 106.712818 |
| 2000-01-04 10:30:00 | 100.000004 | 100.000004 | 100.000757  100.007652  100.042877  100.170708  100.534236  101.389677  103.116696  106.191808 | 106.191808 | 1.570937  1.571009   1.57138  1.572732  1.576599  1.585735  1.604213  1.637058 |  100.0 |   0.000004 | 106.191808 |
| 2000-01-04 11:00:00 | 100.000003 | 100.000003 | 100.000645  100.006621  100.037576  100.151345  100.478787  101.258143  102.848444  105.707833 | 105.707833 | 1.570936  1.570998  1.571324  1.572527  1.576009  1.584332   1.60135  1.631911 |  100.0 |   0.000003 | 105.707833 |
| 2000-01-04 11:30:00 | 100.000002 | 100.000002 |  100.00055  100.005728  100.032919  100.134117  100.428866  101.138394  102.601704  105.258551 | 105.258551 | 1.570935  1.570989  1.571275  1.572345  1.575479  1.583055  1.598716  1.627129 |  100.0 |   0.000002 | 105.258551 |
| 2000-01-04 12:00:00 | 100.000002 | 100.000002 | 100.000469  100.004954  100.028829  100.118797  100.383949   101.02945  102.374906  104.841747 | 104.841747 | 1.570934  1.570981  1.571232  1.572183  1.575001  1.581893  1.596294  1.622688 |  100.0 |   0.000002 | 104.841747 |
| 2000-01-04 12:30:00 | 100.000001 | 100.000001 | 100.000399  100.004284  100.025239  100.105182  100.343561  100.930402  102.166583  104.455325 | 104.455325 | 1.570934  1.570974  1.571194  1.572039  1.574572  1.580837  1.594069  1.618569 |  100.0 |   0.000001 | 104.455325 |
| 2000-01-04 13:00:00 | 100.000001 | 100.000001 |  100.00034  100.003704  100.022088  100.093087  100.307265  100.840411  101.975361  104.097307 | 104.097307 | 1.570933  1.570968  1.571161  1.571911  1.574187  1.579877  1.592026  1.614749 |  100.0 |   0.000001 | 104.097307 |
| 2000-01-04 13:30:00 | 100.000001 | 100.000001 |  100.00029  100.003201  100.019324  100.082348  100.274668  100.758702  101.799955  103.765824 | 103.765824 | 1.570932  1.570963  1.571132  1.571798  1.573841  1.579006  1.590152  1.611211 |  100.0 |   0.000001 | 103.765824 |
| 2000-01-04 14:00:00 | 100.000001 | 100.000001 | 100.000247  100.002767  100.016901  100.072818  100.245408  100.684561  101.639167  103.459113 | 103.459113 | 1.570932  1.570958  1.571107  1.571697   1.57353  1.578215  1.588434  1.607935 |  100.0 |   0.000001 | 103.459113 |
| 2000-01-04 14:30:00 | 100.000001 | 100.000001 | 100.000211   100.00239  100.014777  100.064365   100.21916  100.617332  101.491878   103.17551 |  103.17551 | 1.570932  1.570954  1.571084  1.571608  1.573251  1.577499   1.58686  1.604904 |  100.0 |   0.000001 |  103.17551 |
| 2000-01-04 15:00:00 |      100.0 |      100.0 |  100.00018  100.002065  100.012916  100.056871  100.195627  100.556407  101.357044  102.913449 | 102.913449 | 1.570931  1.570951  1.571065  1.571529  1.573002  1.576849  1.585418  1.602103 |  100.0 |        0.0 | 102.913449 |
| 2000-01-04 15:30:00 |      100.0 |      100.0 | 100.000153  100.001783  100.011286   100.05023  100.174539  100.501231  101.233696  102.671453 | 102.671453 | 1.570931  1.570948  1.571048  1.571459  1.572778  1.576261    1.5841  1.599515 |  100.0 |        0.0 | 102.671453 |
| 2000-01-04 16:00:00 |      100.0 |      100.0 |  100.00013   100.00154  100.009859  100.044347  100.155653  100.451291  101.120927  102.448135 | 102.448135 | 1.570931  1.570945  1.571033  1.571397  1.572578  1.575729  1.582895  1.597126 |  100.0 |        0.0 | 102.448135 |
| 2000-01-04 16:30:00 |      100.0 |      100.0 | 100.000111   100.00133   100.00861  100.039138  100.138748  100.406118    101.0179  102.242189 | 102.242189 | 1.570931  1.570943   1.57102  1.571342  1.572398  1.575248  1.581793  1.594922 |  100.0 |        0.0 | 102.242189 |
| 2000-01-04 17:00:00 |      100.0 |      100.0 | 100.000094  100.001143  100.007492  100.034435  100.123343  100.364596  100.922409  102.049826 | 102.049826 |  1.57093  1.570941  1.571008  1.571293  1.572238  1.574814  1.580789  1.592893 |  100.0 |        0.0 | 102.049826 |
| 2000-01-04 17:30:00 |      100.0 |      100.0 |  100.00008  100.000987  100.006542  100.030378  100.109876  100.327827  100.836807  101.875381 | 101.875381 |  1.57093   1.57094  1.570998   1.57125  1.572095  1.574421  1.579873  1.591023 |  100.0 |        0.0 | 101.875381 |
| 2000-01-04 18:00:00 |      100.0 |      100.0 | 100.000068  100.000853  100.005711   100.02679  100.097839  100.294624  100.758745  101.714821 | 101.714821 |  1.57093  1.570938  1.570989  1.571212  1.571967  1.574067  1.579038  1.589302 |  100.0 |        0.0 | 101.714821 |
| 2000-01-04 18:30:00 |      100.0 |      100.0 | 100.000058  100.000736  100.004984  100.023618  100.087084  100.264657  100.687603  101.567135 | 101.567135 |  1.57093  1.570937  1.570982  1.571179  1.571853  1.573747  1.578276  1.587719 |  100.0 |        0.0 | 101.567135 |
| 2000-01-04 19:00:00 |      100.0 |      100.0 |  100.00005  100.000635  100.004349  100.020814   100.07748  100.237626  100.622807  101.431378 | 101.431378 |  1.57093  1.570936  1.570975  1.571149  1.571751  1.573459  1.577583  1.586264 |  100.0 |        0.0 | 101.431378 |
| 2000-01-04 19:30:00 |      100.0 |      100.0 | 100.000042  100.000548  100.003793  100.018337  100.068907  100.213257  100.563828  101.306666 | 101.306666 |  1.57093  1.570935  1.570969  1.571123   1.57166  1.573199  1.576952  1.584927 |  100.0 |        0.0 | 101.306666 |
| 2000-01-04 20:00:00 |      100.0 |      100.0 | 100.000036  100.000473  100.003308   100.01615  100.061258    100.1913  100.510174  101.192173 | 101.192173 |  1.57093  1.570934  1.570964    1.5711  1.571579  1.572965  1.576378  1.583699 |  100.0 |        0.0 | 101.192173 |
| 2000-01-04 20:30:00 |      100.0 |      100.0 | 100.000031  100.000408  100.002884  100.014219  100.054438  100.171526  100.461395  101.087128 | 101.087128 |  1.57093  1.570934   1.57096  1.571079  1.571506  1.572754  1.575856  1.582573 |  100.0 |        0.0 | 101.087128 |
| 2000-01-04 21:00:00 |      100.0 |      100.0 | 100.000026  100.000352  100.002514  100.012515  100.048358  100.153728  100.417073  100.990812 | 100.990812 |  1.57093  1.570933  1.570956  1.571061  1.571442  1.572565  1.575382   1.58154 |  100.0 |        0.0 | 100.990812 |
| 2000-01-04 21:30:00 |      100.0 |      100.0 | 100.000022  100.000304  100.002191  100.011012  100.042941  100.137716  100.376825  100.902553 | 100.902553 |  1.57093  1.570933  1.570952  1.571046  1.571384  1.572394  1.574952  1.580594 |  100.0 |        0.0 | 100.902553 |
| 2000-01-04 22:00:00 |      100.0 |      100.0 | 100.000019  100.000262  100.001909  100.009686  100.038117  100.123319  100.340296  100.821727 | 100.821727 |  1.57093  1.570932  1.570949  1.571032  1.571333  1.572241  1.574561  1.579727 |  100.0 |        0.0 | 100.821727 |
| 2000-01-04 22:30:00 |      100.0 |      100.0 | 100.000016  100.000226  100.001663  100.008518  100.033823  100.110381  100.307162  100.747753 | 100.747753 |  1.57093  1.570932  1.570947  1.571019  1.571288  1.572103  1.574207  1.578934 |  100.0 |        0.0 | 100.747753 |
| 2000-01-04 23:00:00 |      100.0 |      100.0 | 100.000014  100.000195  100.001448  100.007488  100.030001  100.098758  100.277124   100.68009 |  100.68009 |  1.57093  1.570931  1.570945  1.571008  1.571247  1.571979  1.573886  1.578209 |  100.0 |        0.0 |  100.68009 |
| 2000-01-04 23:30:00 |      100.0 |      100.0 | 100.000012  100.000168  100.001261  100.006581  100.026602  100.088323  100.249907  100.618238 | 100.618238 |  1.57093  1.570931  1.570943  1.570999  1.571211  1.571868  1.573595  1.577546 |  100.0 |        0.0 | 100.618238 |
Click to see the graph

class hydpy.models.lstream_v002.Model

Bases: hydpy.models.lstream.lstream_model.Model

Version 3 of HydPy-L-Stream.

The following “inlet update methods” are called in the given sequence at the beginning of each simulation step:

• Pick_Q_V1 Query the current inflow from all inlet nodes.

The following methods define the relevant components of a system of ODE equations (e.g. direct runoff):

• Calc_QZA_V1 Calculate the current inflow into the channel.

• Calc_QG_V2 Determine the discharge of each the total cross-section based on an artificial neural network describing the relationship between water storage in the total channel and discharge.

• Calc_QA_V1 Query the actual outflow.

The following methods define the complete equations of an ODE system (e.g. change in storage of fast water due to effective precipitation and direct runoff):

• Update_VG_V1 Update the water volume.

The following “outlet update methods” are called in the given sequence at the end of each simulation step:

• Pass_Q_V1 Pass the outflow to the outlet node.

numconsts: hydpy.core.modeltools.NumConstsELS

numvars: hydpy.core.modeltools.NumVarsELS

element: Optional[‘devicetools.Element’]

cymodel: Optional[typingtools.CyModelProtocol]

parameters: parametertools.Parameters

sequences: sequencetools.Sequences

masks: masktools.Masks

class hydpy.models.lstream_v002.ControlParameters(master: hydpy.core.parametertools.Parameters, cls_fastaccess: Optional[Type[hydpy.core.parametertools.FastAccessParameter]] = None, cymodel: Optional[hydpy.core.typingtools.CyModelProtocol] = None)

Bases: hydpy.core.variabletools.SubVariables[hydpy.core.parametertools.Parameters, Parameter, hydpy.core.parametertools.FastAccessParameter]

Control parameters of model lstream_v002.

The following classes are selected:

• GTS() Anzahl Gewässerteilstrecken (number of channel subsections) [-].

• VG2QG() Künstliches Neuronales Netz zur Abbildung der Abhängigkeit des Abflusses einer Gewässerteilstrecke von deren aktuller Wasserspeicherung (artificial neural network describing the relationship between total discharge and water storage of individual channel subsections [-].

class hydpy.models.lstream_v002.DerivedParameters(master: hydpy.core.parametertools.Parameters, cls_fastaccess: Optional[Type[hydpy.core.parametertools.FastAccessParameter]] = None, cymodel: Optional[hydpy.core.typingtools.CyModelProtocol] = None)

Bases: hydpy.core.variabletools.SubVariables[hydpy.core.parametertools.Parameters, Parameter, hydpy.core.parametertools.FastAccessParameter]

Derived parameters of model lstream_v002.

The following classes are selected:

• Sek() Sekunden im Simulationszeitschritt (Number of seconds of the selected simulation time step) [s].

class hydpy.models.lstream_v002.FluxSequences(master: hydpy.core.sequencetools.Sequences, cls_fastaccess: Optional[Type[FastAccessType]] = None, cymodel: Optional[hydpy.core.typingtools.CyModelProtocol] = None)

Bases: hydpy.core.sequencetools.OutputSequences[FluxSequence]

Flux sequences of model lstream_v002.

The following classes are selected:

• QZ() Mittlerer Zufluss in Gerinnestrecke (average inflow into the channel) [m³/s].

• QZA() Aktueller Zufluss in Gerinnestrecke (current inflow into the channel) [m³/s].

• QG() Durchfluss gesamt (total discharge) [m³/s].

• QA() Abfluss aus Gerinnestrecke (outflow out of the channel) [m³/s].

class hydpy.models.lstream_v002.InletSequences(master: hydpy.core.sequencetools.Sequences, cls_fastaccess: Optional[Type[FastAccessType]] = None, cymodel: Optional[hydpy.core.typingtools.CyModelProtocol] = None)

Bases: hydpy.core.sequencetools.LinkSequences[InletSequence]

Inlet sequences of model lstream_v002.

The following classes are selected:

• Q() Abfluss (runoff) [m³/s].

class hydpy.models.lstream_v002.OutletSequences(master: hydpy.core.sequencetools.Sequences, cls_fastaccess: Optional[Type[FastAccessType]] = None, cymodel: Optional[hydpy.core.typingtools.CyModelProtocol] = None)

Bases: hydpy.core.sequencetools.LinkSequences[OutletSequence]

Outlet sequences of model lstream_v002.

The following classes are selected:

• Q() Abfluss (runoff) [m³/s].

class hydpy.models.lstream_v002.SolverParameters(master: hydpy.core.parametertools.Parameters, cls_fastaccess: Optional[Type[hydpy.core.parametertools.FastAccessParameter]] = None, cymodel: Optional[hydpy.core.typingtools.CyModelProtocol] = None)

Bases: hydpy.core.variabletools.SubVariables[hydpy.core.parametertools.Parameters, Parameter, hydpy.core.parametertools.FastAccessParameter]

Solver parameters of model lstream_v002.

The following classes are selected:

• AbsErrorMax() Absolute numerical error tolerance [m3/s].

• RelErrorMax() Relative numerical error tolerance [-].

• RelDTMin() Smallest relative integration time step size allowed [-].

• RelDTMax() Largest relative integration time step size allowed [-].

class hydpy.models.lstream_v002.StateSequences(master: hydpy.core.sequencetools.Sequences, cls_fastaccess: Optional[Type[FastAccessType]] = None, cymodel: Optional[hydpy.core.typingtools.CyModelProtocol] = None)

Bases: hydpy.core.sequencetools.OutputSequences[StateSequence]

State sequences of model lstream_v002.

The following classes are selected:

• VG() Wasservolumen (water volume) [million m³].