03-07-2015, 06:32 PM
Renatus wrote, "how does one calculate the course and flow of a minor river 2000 years ago?"
The following passages outline the method I use. The passages come from my earlier essays. I have not cut-n-pasted all the relevant text. Use the links to read more - especially the second link.
I think that will do, don't you?
The following is taken from
Finding_the_site_of_Boudicas_last_battle_Roman_logistics_empowered_the_sword._Steve_Kaye._2013
In outline, the catchment water balance methodology was used in this study for the whole of Britain (Figure 5). This involves calculating the mean flow in rivers by use of rainfall, potential evapotranspiration losses, and catchment characteristics such as area sizes, topographic and geological descriptors and models of the river systems. All these investigations, and other supporting statistical and mathematical calculations, were conducted within SAGA (System for Automated Geoscientific Analyses), a GIS and calculation engine, that contains the key hydrological modules used in this study.
We are interested in river flows in the summer of 60/61AD, especially those within and on the margins of the chalk and limestone uplands of southern Britain. Therefore, the values of the Q95, for the period 1961-2006, have been computed for August and for naturalised catchment and river systems. Essentially these Q95 values - at the height of summer, when rainfall, surface runoff, aquifer discharge and consequently river flows are at a minimum, tells us where these large armies could march and give battle.
It should be made clear that the calculation of low flows is fraught with difficulties and uncertainties, especially when examining flows in the ranges required for this study. The results are imperfect, have unknown error ranges, but are generally representative of the flows the protagonists would have experienced in marching across southern Britain.
It is in part due to these hydrological uncertainties that the numbers of humans and animals was kept low, and the water requirement for humans lowered to 9 litres/man/day rather than use the larger figure from the investigations of the US Army.
The base data used in the aforementioned calculations were:
Shuttle Radar Topography Mission (SRTM), Jarvis A., H.I. Reuter, A. Nelson, E. Guevara, 2006,
Hole-filled seamless SRTM data V3, International Centre for Tropical Agriculture (CIAT), available
from http://srtm.csi.cgiar.org
Rainfall, long term average per month for years 1961-2006 from the Meteorological Office -
http://www.metoffice.gov.uk/climatechang...nthly.html
Evapotranspiration figures from MODIS 16; a NASA/EOS project to estimate global terrestrial
evapotranspiration from the earth land surface by using satellite remote sensing data.
http://www.ntsg.umt.edu/project/MOD16/
Main references to the method are:
Gustard, A., Bullock, A. and Dixon, J, (1992), Report No. 108. Low flow estimation in the United
Kingdom, Institute of Hydrology (NERC).
Gustard, A., Marshall, D., and Sutcliffe, M., (1987), Report No. 101. Low flow estimation in
Scotland, Institute of Hydrology (NERC).
The following is taken from
The_Roman_invasion_of_Britain_43_AD_riverine_wading_and_tidal_studies_as_a_means_of_limiting_the_possible_locations_of_the_invasion-ground_and_the_two
In outline, the task was to determine by calculation the natural channels created by the rivers of SE England in 43 AD and then fill these with the discharge for July 43 AD. This exercise derived discharge rates, depths, widths and velocities for all rivers at the time of the two-day river battle.
The mean annual discharge (a.k.a. average annual discharge) can be used to calculate the bankfull state of a river. The bankfull discharge is that which fills the main channel of a river to capacity; any additional discharge causes over-banking and the flooding of adjacent land. It is generally accepted by most hydrological agencies that the dominant or channel-forming discharge for a dynamically stable channel approximates to the bankfull discharge, i.e. that which determines the gross parameters of the channel, e.g. depth, width, meander sinuosity etc..
Hence, in this study the mean annual discharge (Qannual) for the years 1961-2011 was calculated using the catchment water balance method (Gustard et al, 1992) augmented by calculations of the base flow index (BFI - see definition at http://www.ceh.ac.uk/data/nrfa/data/derived_flow.html) to derive aquifer discharge to rivers. Mean annual precipitation data were taken from the UK Climate Projections study (UKCP09) and mean annual evapotranspiration data from Trabucco and Zomer (2009) for the years 1950-2000.
For this study the derived Qannual value at Teddington on the Thames was 76 m3/s, while at the same location the long-term (1883-1985) measured value is 78.2 m3/s (Beran and Field, 1988). The latter results from point measurements made at Teddington; the former the result of a very large number of individual calculations throughout the drainage basin all accumulating at Teddington: the correspondence between 78 and 76 m3/s suggested the results of the hydrology calculations were plausible.
The bankfull variables depth, width, velocity and discharge for a half-hexagon channel shape were derived in the following manner:
Bankfull depth - derived from a power function of catchment area, (following the findings instigated by Leopold and Maddock, 1953).
Bankfull width - estimation of river widths in Google Earth at 61 points in SE England. Allowance was made for human interference, e.g. averaging the width up and downstream of weirs. These 61 values were regressed against Qannual to give, , R2 of 76.49%. This equation was used to derive bankfull widths for all rivers in SE England.
Bankfull velocity - derived from the Manning velocity formula (a standard hydrological method), where v is the bankfull velocity; k is 1.0 (metric conversion number); n is a roughness coefficient set to 0.07 for rivers of width less than 30 m or 0.065 for greater, e.g. the Thames; R is the hydraulic radius and S is the slope of the channel. The values for n were relatively high compared to values assigned to the same modern-era rivers; this reflected the wider and shallower nature of the ancient rivers and the greater amounts of vegetation bordering and within the river.
Bankfull discharge - derived from the formula, discharge = width*depth*velocity
The following passages outline the method I use. The passages come from my earlier essays. I have not cut-n-pasted all the relevant text. Use the links to read more - especially the second link.
I think that will do, don't you?
The following is taken from
Finding_the_site_of_Boudicas_last_battle_Roman_logistics_empowered_the_sword._Steve_Kaye._2013
In outline, the catchment water balance methodology was used in this study for the whole of Britain (Figure 5). This involves calculating the mean flow in rivers by use of rainfall, potential evapotranspiration losses, and catchment characteristics such as area sizes, topographic and geological descriptors and models of the river systems. All these investigations, and other supporting statistical and mathematical calculations, were conducted within SAGA (System for Automated Geoscientific Analyses), a GIS and calculation engine, that contains the key hydrological modules used in this study.
We are interested in river flows in the summer of 60/61AD, especially those within and on the margins of the chalk and limestone uplands of southern Britain. Therefore, the values of the Q95, for the period 1961-2006, have been computed for August and for naturalised catchment and river systems. Essentially these Q95 values - at the height of summer, when rainfall, surface runoff, aquifer discharge and consequently river flows are at a minimum, tells us where these large armies could march and give battle.
It should be made clear that the calculation of low flows is fraught with difficulties and uncertainties, especially when examining flows in the ranges required for this study. The results are imperfect, have unknown error ranges, but are generally representative of the flows the protagonists would have experienced in marching across southern Britain.
It is in part due to these hydrological uncertainties that the numbers of humans and animals was kept low, and the water requirement for humans lowered to 9 litres/man/day rather than use the larger figure from the investigations of the US Army.
The base data used in the aforementioned calculations were:
Shuttle Radar Topography Mission (SRTM), Jarvis A., H.I. Reuter, A. Nelson, E. Guevara, 2006,
Hole-filled seamless SRTM data V3, International Centre for Tropical Agriculture (CIAT), available
from http://srtm.csi.cgiar.org
Rainfall, long term average per month for years 1961-2006 from the Meteorological Office -
http://www.metoffice.gov.uk/climatechang...nthly.html
Evapotranspiration figures from MODIS 16; a NASA/EOS project to estimate global terrestrial
evapotranspiration from the earth land surface by using satellite remote sensing data.
http://www.ntsg.umt.edu/project/MOD16/
Main references to the method are:
Gustard, A., Bullock, A. and Dixon, J, (1992), Report No. 108. Low flow estimation in the United
Kingdom, Institute of Hydrology (NERC).
Gustard, A., Marshall, D., and Sutcliffe, M., (1987), Report No. 101. Low flow estimation in
Scotland, Institute of Hydrology (NERC).
The following is taken from
The_Roman_invasion_of_Britain_43_AD_riverine_wading_and_tidal_studies_as_a_means_of_limiting_the_possible_locations_of_the_invasion-ground_and_the_two
In outline, the task was to determine by calculation the natural channels created by the rivers of SE England in 43 AD and then fill these with the discharge for July 43 AD. This exercise derived discharge rates, depths, widths and velocities for all rivers at the time of the two-day river battle.
The mean annual discharge (a.k.a. average annual discharge) can be used to calculate the bankfull state of a river. The bankfull discharge is that which fills the main channel of a river to capacity; any additional discharge causes over-banking and the flooding of adjacent land. It is generally accepted by most hydrological agencies that the dominant or channel-forming discharge for a dynamically stable channel approximates to the bankfull discharge, i.e. that which determines the gross parameters of the channel, e.g. depth, width, meander sinuosity etc..
Hence, in this study the mean annual discharge (Qannual) for the years 1961-2011 was calculated using the catchment water balance method (Gustard et al, 1992) augmented by calculations of the base flow index (BFI - see definition at http://www.ceh.ac.uk/data/nrfa/data/derived_flow.html) to derive aquifer discharge to rivers. Mean annual precipitation data were taken from the UK Climate Projections study (UKCP09) and mean annual evapotranspiration data from Trabucco and Zomer (2009) for the years 1950-2000.
For this study the derived Qannual value at Teddington on the Thames was 76 m3/s, while at the same location the long-term (1883-1985) measured value is 78.2 m3/s (Beran and Field, 1988). The latter results from point measurements made at Teddington; the former the result of a very large number of individual calculations throughout the drainage basin all accumulating at Teddington: the correspondence between 78 and 76 m3/s suggested the results of the hydrology calculations were plausible.
The bankfull variables depth, width, velocity and discharge for a half-hexagon channel shape were derived in the following manner:
Bankfull depth - derived from a power function of catchment area, (following the findings instigated by Leopold and Maddock, 1953).
Bankfull width - estimation of river widths in Google Earth at 61 points in SE England. Allowance was made for human interference, e.g. averaging the width up and downstream of weirs. These 61 values were regressed against Qannual to give, , R2 of 76.49%. This equation was used to derive bankfull widths for all rivers in SE England.
Bankfull velocity - derived from the Manning velocity formula (a standard hydrological method), where v is the bankfull velocity; k is 1.0 (metric conversion number); n is a roughness coefficient set to 0.07 for rivers of width less than 30 m or 0.065 for greater, e.g. the Thames; R is the hydraulic radius and S is the slope of the channel. The values for n were relatively high compared to values assigned to the same modern-era rivers; this reflected the wider and shallower nature of the ancient rivers and the greater amounts of vegetation bordering and within the river.
Bankfull discharge - derived from the formula, discharge = width*depth*velocity
