(a) What is deep percolation in the context of
L'vovich's water balance? (b) What is its average value on a global
basis? (c) Why is deep percolation usually neglected in practice?
(a) Deep percolation is the amount of aquifer percolation which
reaches deep enough to avoid the return
to the surface waters by way of baseflow.
(b) On a global basis,
an average value of deep percolation is less than 1.5% of precipitation.
(c) In practice, deep percolation is usually neglected because
of the inability to estimate its value with enough precision.
What is the difference
between the psychrometric constants used in the Penman and Penman-Monteith
evaporation methods?
Unlike the psychrometric constant γ used in the Penman method,
in the Penman-Monteith method the psychrometric constant γ*
is also a function
of the aerodynamic resistance ra
and the stomatal resistance rs, as follows:
γ* = γ [ 1 + (rs / ra)]
(a) Describe
Mockus' explanation
of how he arrived at his rainfall-runoff
relation.
(b) What other sources of variability
are implicitly included in the Antecedent Moisture Condition (AMC),
other than soil type, land use, and hydrologic
condition?
(a) Mockus said that he arrived at the equation
(P- Q) / S
= Q / P
one evening after dinner, seeing that it fitted the data very well,
and after having tried many other alternative relations.
(b) Other sources of variability implicitly included in the concept of AMC
are:
(i) spatial variability of storm and watershed properties;
(ii) temporal variability of the storm, i.e.,
changes in rainfall intensity within the storm; and
(iii) quality of the measured data.
(a) In catchment flow,
what is the
difference between: (a) superconcentrated and concentrated flow?
(b) concentrated and subconcentrated flow?
Explain the differences in terms of the
shape of the runoff hydrograph and the
associated peak flow.
(a) Superconcentrated flow features a flat hydrograph peak, while
concentrated flow features a singular value of peak flow.
The peak flow for both superconcentrated and concentrated catchment flow
hydrographs is: Qp = Ie A,
in which Ie =
effective rainfall intensity, and A = catchment area.
(a) Concentrated flow features a singular
value of peak flow, equal to
Qp = Ie A, while
subconcentrated catchment flow features a flat peak,
of value which is less than the maximum peak flow
for full concentration. Effectively,
the flow did not concentrate, i.e., attain its maximum possible value,
because the rainfall duration is less than the
time of concentration.
(a)
Explain how a tropical rainforest such as the Amazon
is better able to
recycle rainfall than a semiarid forest. (b) What demonstrable fact reveals
that humid regions recyle moisture more effectively than arid regions?
(a) Tropical rainforests feature a characteristically low albedo,
tipically around 7%, and therefore,
are subject to substantial amounts of cooling, by thermal lifting,
of the
lower atmosphere. This effect results in a relatively
high recycling coefficient Kc of about 0.3.
(b) The ratio of atmospheric moisture content between humid to arid regions
is low, approximately 3. However, the ratio of mean annual precipitation
between humid and arid regions may be quite large, often more than
100. This marked difference between atmospheric moisture
content and precipitation flux
is due to the greater
precipitation recycling capacity prevalent in humid regions.
(a) What is the value
of the (mean) annual global terrestrial precipitation Pagt
used in the conceptual model of drougnt intensity-duration-frequency
across the climatic spectrum? (b) How is it determined?
(a) The value is 800 mm.
(b) A mean value of global terrestrial
atmospheric moisture is estimated to be 25 mm, the average of a
range of 2 mm (dry) to 50 mm (wet).
The atmospheric moisture recycles every 11 days on the average,
for a total of 33 cycles per year. The total average global
terrestrial flux (precipitation) is: 25 × 33 = 825 mm.
A round number of Pagt = 800 mm may be adopted for convenience.
Why
is the determination
of regional aquifer parameters using baseflow recession data
likely to be more accurate
than conventional hydrogeologic determinations based of pumping tests?
Determinations of aquifer parameters based on baseflow recession data
comprise the entire aquifer, providing values which represent
the totality of the
aquifer. On the other hand, determinations based on pumping
tests are perforce of local nature.
(a) When using a linear
reservoir in unit hydrograph determinations, why is the Courant number
C
limited to values less than or equal to 2? (b) Why does C = 2 effectively
result in a hydrograph resembling the rational method?
(a) For values of C > 2,
the temporal interval Δt exceeds twice the time
of storage K,
resulting in negative diffusion,
i.e., a numerical amplification effect,
which renders the
model unstable.
(b) For C = 2, the outlow hydrograph of the linear reservoir
has zero runoff diffusion; thus, it has
the shape of an isosceles triangle, featuring
equal rising and receding limbs.
This hydrograph shape
mimics the outflow hydrograph of the rational method,
which ostensibly features only runoff convection, with zero runoff diffusion.
What condition is necessary for the
Muskingum-Cunge (M-C) method to improve
on the classical Muskingum method?
(b) What value of Courant number C assures numerical accuracy in the M-C method? Why?
(a) The Muskingum-Cunge method will improve on the Muskingum method
when the discrete geometric cross-sectional data
on which to base the computation of the routing
parameters is truly representative of the channel reach under consideration.
(b) For Courant number C = 1, the Muskingum-Cunge method assures
numerical accuracy and grid independence. This is due to the fact that for
C = 1, the method
minimizes numerical dispersion (third-order error).
What is the reason
for the documented
increase in the number of glacial lakes in the
White Range of Peru in the past 50 years?
In the past 50 years,
the documented increase in the number of glacial lakes
in the White Range
has been due to the global-climate-change induced
increase in glacial melt in the presence of glacial till (moraine)
geomorphology. The conjunction of glacial melt and glacial till
is conducive to
the formation of glacial lakes.
Why do the Muskingum and Muskingum-Cunge
methods become unstable and break down for values of X > 0.5?
Because according to Cunge's portrait analysis,
in the range X > 0.5, the R1
amplitude portrait becomes greater than 1 for all
values of Courant number and spatial
resolution. This fact produces a strong tendency for numerical instability.
Why is the general dimensionless unit
hydrograph (GDUH) better suited for unit hydrograph analysis than
the conventional NRCS and Snyder unit hydrographs?
Because unlike the NRCS and Snyder models, which are empirically based
on regional data,
the GDUH has a distinct conceptual basis and, it is, therefore, of global applicability.
(Extra bonus question) (a) What is runoff
diffusion in the context of modeling surface-water hydrology?
(b) What physical parameter quantifies
runoff diffusion? (c) How has this parameter evolved in the past sixty years of
research in the modeling of surface-water hydrology?
(a) Runoff diffusion entails the determination (calculation) of wave diffusion
in surface-water flow in open channels and catchments.
(b) The amount of runoff diffusion is quantified by the hydraulic diffusivity of
Hayami (1951),
which states that the diffusion coefficient is:
ν = qo / (2So), in which
qo =
unit-width discharge, and So = bottom slope.
(c) Recent research has shown that a more complete
theoretical expression for hydraulic diffuxivity is:
ν = ( 1 - V2 ) qo / (2So),
wherein V = Vedernikov number.