mLM Milestone 4: Scalable Lake Module

The most simple and convenient situation with lakes would be a large lake encompassing many L1 (L11) cells. However, in reality there will be intricate cases depending on lake size, numbers and L1 resolution. Inevitably situation will arise where either there are multiple lakes in a single L1 cell or that a lake lies completely within a L1 cell.
Thus as a generalised solution, the lake routing was conceptualised to be comprised of two cases - large lake case and small lake case.
A small lake is the one which doesn't lie in the main stream of mRM. For such lakes, the inflow is conceptualised as the area weighted fraction of mHM flow. The area weighted fraction is calculated using overlap of L1 cell/s with the catchment of the lake. For this an array (L0 into lake) stores lakeIds/ lakeIndex at L0 in call cells that comprise the catchment area of small lakes.
The large lake is the one through which the main stream of mRM passes through. Thus, the large lake has stream inflow as well as the side inflows. The catchment of the large lake is the catchment of main stream + the side inflow catchment. In L0 into lake, the large lake's Id/ Index is stored in the cells of the side inflow catchment. The side inflow will again be the area weighted fraction of mHM flow as for small lakes. Whereas L0 into lake will contain 0 for L0 cells in the main stream catchment denoting that these cells have already been taken into account in the main stream routing.
Thus in this manner, instead of lake class at L1 being dened from the lake fraction coverage and harshly classifying the cell as inflow, lake cell and outflow cell, it would be better for the model to do the analysis (via stream network and catchment area concepts) at sub-grid level for the mRM-lake-mRM connections.
This approach will give better chances of keeping mHM scalable with lakes as every lake will get its inflow no matter the category of lakes (large or small) in which it falls according to the L1 resolution. Also, the assumption that keeps the mHM routing simplistic i.e. the travel time effect of the minor streams are negligible compared to the mainstream, is also maintained.

In above figure, water flows across four l1 level cells i, j, k, l. Each l1 cell has numerous l0 level cells i.e. subgrids.
In this case, cell l has four lakes. The darker cells are lakes while the corresponding lighter colored cells are catchment/ partial catchment of each lake.
Out of the four lakes, only lake 4 lies in the main stream of mRM (Blue line). Thus by previous definition lake 4 is the large lake while 1, 2, 3 are small lakes. The small lakes are connected via the Gray line which is not included in the mRM.
Since only lake 4 lies in the mRM network, it will get the routed flow as inflow to the lake. Without subgrid processing, all cell discharge will be fed into lake 4 and the small lakes will be omitted. In order to include them the resolution of computation ( l1 ) needs to be refined which will incur greater computational expense. But more significantly lakes will appear or disappear in mHM system based on scale i.e. mLM becomes a scale dependent module.
As a different approach, subgrid processing is introduced. In this method, each l0 cell in mHM is either part of the lake catchment or the main stream catchment or belong to lake/s / main stream catchment of the surrounding cells.
Once the catchment map is prepared, the cell generated discharge (Qcell) is split among the lakes and main stream based on their catchment area. Thus, even the small lakes will now get some inflow into them (w/o routing).
For this particular case in cell l, the fraction of Ql cell based on catchment of lake 1 is the inflow to lake 1. Similar is the case for lake 3 but it additionally get some more in flow as fraction of Qcell from surrounding cells i, j and k. Since lake 2 is d/s of lake 3 it gets outflow from lake 3 (direct, w/o routing) and fraction of Qcell from cells l and i. Then, lake 4 inflow comprises of the main stream routed flow, outflows from lakes 1 and 2 (direct, w/o routing) and fraction of Ql cell based on its side catchment. Finally, the water is routed to next l1 cell which is the sum of outflow from lake 4 and any remaining fraction of Ql cell based on the catchment of the main stream within cell l.
In this way, all the lakes are included in the module irrespective of the model resolution.This approach is expected to minimize the discrepancy of model output across model scales thus improving the chances of mLM in becoming a scale independent module.