Geography 327      Hydrology

PRECIPITATION

• transfer of solid and liquid water from the atmosphere to the earth's surface
• a climatic parameter and thus a subject of hydrometeorology; however whereas climatologists as primarily concerned with the amount and variability of precipitation as at place, hydrologists are interested in precipitation as the input of water to the hydrological cycle and therefore
  
  
  1. the type of precipitation
  2. measurement of precipitation and especially the underestimation of point observations
  3. areal extrapolation and interpretation of the measured data
  4. variation of precipitation in time and space

Types of Precipitation

according to its appearance

1. liquid precipitation
   
   
   1. rain: drops of liquid water; most begins as snow
   2. drizzle: droplets (<0.5 mm in diameter)
   3. dew: condensation of water vapour onto a cool surface
   4. fog-drip (occult precipitation): accumulation of fog droplets on vegetation and other obstacles (horizontal interception)

   
   

2. solid precipitation
   
   
   1. snow grains: small crystals of ice; solid equivalent of drizzle
   2. snow flakes: agglomeration of grains; solid equivalent of rain
   3. sleet: frozen rain
   4. graupel: pellets of ice 2-5 mm in diameter formed by collision of snow crystals and rain drops when cloud temperatures are near the freezing point
   5. hoar frost: solid equivalent of dew; formed by sublimation of water vapour onto cold surfaces as feature-like crystals
   6. rime (occult precipitation): freezing of water droplets from fog onto cold surfaces; includes artificial snow; crystals tend to be larger than in snow
   7. hail: spherical lumps of ice composed of concentric layers; distinct from other forms of solid precipitation because it form in the warmest season and thus begins to melt immediately upon contact with the ground

according to its place of origin

1. adjacent to cold ground: dew, fog-drip, rime and frost
   
   
2. above the condensation level in the atmosphere, where water vapour, in air below the dew point temperature, condenses onto hygroscopic nuclei or sublimates to form ice crystals

• outside the tropics, most precipitation begins as ice crystals which melt as they fall through warmer air
• cirrus clouds composed of ice crystals often precede a storm
• sun dogs are light refracted by ice crystals
• ice crystals grow at the expense of water droplets because the colder air next to the ice has low vapour pressure (hold less water) and thus supercooled water droplets freeze to the ice crystals
• whereas dew point temperatures are achieved near the ground by radiative cooling, they occur at higher altitudes during the rising, expansion and adiabatic cooling of moist air; therefore precipitation from above the condensation level can be further classified by mode of uplift:
  
  
  • convergence of tropical and subtropical air masses (hurricanes)
  • mid-latitude frontal (cyclonic) precipitation where warmer air is diaplced along fronts between air masses (tornados)
  • differential heating of the earth and therefore thermal convection lower atmosphere (thunderstorms)
  • orographic: rise of air masses over mountains (Figures 4-11 in Dingman shows mean annual precipitation and topography across southern B.C.)

  
  

• these mechanisms are superimposed on one another (e.g. monsoons (convergent precipitation) rising over northern India (Himilaya) to produce highest annual precipitation in the world, 10800 mm)
• precipitation requires cooling of air to the dew point temperature, condensation on nuclei, coalescence of droplets to form rain drops, and a continuous source of vapour to sustain the process
• prior to the 1940's, the source of water vapour was thought to be local and this notion was the basis for proposals to modify land use to ameliorate the dust bowl
• however, Holzman (1937) and subsequent studies have shown that most precipitation comes from maritime air masses and most water evapotranspiring from land into continental air masses moves off the continent (see maps on pp. 78-79 in Dingman)
• thus little precipitation falls where the water originates, except over large evaporating surface (e.g. Amazon basin, northern wetlands, great lakes)

Measurement of precipitation

purpose

point estimation of the depth of precipitated water within the area surrounding the gauge

method

intercepting precipitation over a defined area bounded by the precipitation gauge rim

assumption

that the depth of water intercepted by the gauge is representative of the depth of water falling over a large area around the gauge

types of gauges

non-recording

a cylinder that is manually observed on a regular basis

• standard Canadian rain gauge
  • 
    
  • 91 mm in diameter (formerly 4 in) with the orifice 305 mm above ground and no shield
  • the rainwater is funneled into a smaller cylinder, i.e. about 0.1 of the diameter of the gauge opening
  • the recording cylinder is calibrated and graduated to reflect this ratio, so that one unit of rainfall into the gauge actually fills the small cylinder to a depth of 10 units

recording

a continuous record of rainfall consisting of marks are holes punched on a tape as a bucket fills and tips or is weighed

measurement errors

• the distribution of global precipitation reflects both geographic variability of precipitation and differences in instrumental procedures among countries
• all point observations of rainfall are underestimates, measured errors have ranged from 5-15% and 3-30% for long-term totals (e.g. annual data) with larger error (up to 75%) for individual storms and especially for snow
• errors of similar magnitude may apply to other components of the hydrological cycle, even so it is desirable to minimize the error in precipitation estimate caused by

1. small diameter gauges
   
   
   • not good for snow
   • more difficult to calibrate since relative error in diameter opening is larger
   • a larger proportion of water adheres to walls
   • more water loss (evaporation) since water heats more quickly in a smaller chamber

   
   

2. wind as a function of gauge height
   
   
   • largest source of error
   • gauges projecting into wind create eddies around the opening the deflect snow flakes and small rain drops
   • gauges can be shielded with sheet metal or plastic baffles
   • the best solution is pit gauges where the opening is near ground level, but this generally is not practical because a pit would have to dug for each existing gauge with protection from splash (slope ground around gauge, use fibre mats or egg-crate structure)
   • snow gauges have to be above the snow surface and thus conventional and pit gauge data are not comparable

   
   

3. obstructions
   
   
   • the best gauge location is within a clearing surrounding by trees or other objects to reduce wind
   • but there should be a 45 degree (angle from the vertical) conical space above the gauge and no objects closer than twice (preferably four times) its height above the gauge

   
   

4. splash and evaporation
   
   
   • water may spashs into a gauge if it is full or near ground
   • water loss by evaporation is prevented by draining the precipitation to a closed vesell or by introducing a nonvolatile immiscible oil, (i.e. does not vapourize or mix with water)

   
   

5. instrument errors
   
   
   • usually confined to recording gauges where mechanical and electrical deterioration and failure occur
   • systematic (poor calibration) or gross (malfunction) errors

   
   

6. observer error
   
   

   random

   unavoidable, but over- and under-estimates should offset one another
   
   

   systematic

   consistent under or over-estimation is the most problematic source of error
   
   

   gross

   blunders which can be detected by comparing precipitation records to those from nearby stations to other weather data (e.g. description of storm) or to stream flow records

   
   

7. variation in observation time
   
   
   • gauges usually are observed daily
   • ideally this would be a midnight (end of the day), but rarely is this the case
   • thus, storm precipitation can be assigned to either to the current day or to the following day depending when it occurs relative to the time of observation
   • when storms occur on the last day of the month the precipitation could actually be assigned to the next month (or to the next year, in the case of December 31)

   
   

8. occult precipitation
   
   
   • fog-drip and rime are not recorded by gauges
   • this requires special techniques, especially at high elevations and coasts
   • for example, fog drip accounted for about 30% of the annual precipitation in a Douglas fir forest in Oregon and 100% in the cloud forest of the rainless Atacama desert of Peru
   • rime contributes up to 50 mm per year in the Cascade mountains of Washington State

   
   

9. low intensity rain
   
   
   • a trace of precipitation is a fraction of a mm, that is, not perceptible in a gauge
   • on the north slope of Alaska, trace precipitation accounts for 10% to 1/3 of annual precipitation

double-mass curve

• a plot of cumulative annual precipitation for one station versus a group of stations in the same area, for checking for consistency among point measurements
• a single mass curve is cumulative annual data against time (e.g. for stream discharge)
• if a single station is consistent with the others, the curve should be a straight line with a slope of about one
• changes in slope can reflect errors in gauge observation, climatic change or changes in the immediate surroundings of the gauge in question
• usually the break in slope must persist for five or more years to be considered significant, since there can be anomalous years at one station
• data from before the change in slope can be adjusted by multiplying them by the ratio of the new slope to the old slope of the double-mass curve

Estimation of areal precipitation

• statistical methods are extensively applied to hydrologic data because this is the branch of mathematics for the analysis of samples
• water data represent samples from infinite populations (potential observations)

1. arithmetic mean (average)
   
   
   • theoretically appropriate only where precipitation gauges are randomly distributed and the terrain is uniform, as precipitation varies with elevation

   
   

2. area-weighted average: Thiessen polygons
   
   
   • accounts for uneven distribution of gauges and for data from nearby stations in adjacent areas (basins)
   • on a map, straight lines are drawn between gauges; perpendicular bisectors of these lines are the sides of irregular polygons that define the area of land corresponding to each gauge
   • thus the various sizes of the polygons reflect the distribution of the gauges
   • precipitation on each component polygon is the product of the depth of precipitation measured at the gauge and the ratio of the area of the polygon (or portion in the basin) to the basin area
   • total precipitation is the sum of the precipitation on each polygon

   
   

3. elevation-weighted average
   
   
   • accounts for both the spacing of gauges and differences in their elevations
   • the polygon sides perpendicularly intersect the lines joining stations, but at the midpoint elevation
   • or the midpoint elevations are joined with lines creating triangles and the angles of theses new triangles are then bisected to form the elevation-weighted polygons
   • thus the largest polygon will correspond to the gauge which is most isolated both horizontally and vertically

   
   

4. isohyetal methods
   
   
   • isos (gr.): equal     hyeto: rain
   • mean precipitation between isohyets is weighted by the area or according to the lengths of the isohyets

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   Dimensions of Point Precipitation

   Depth

   • standard dimension for expressing point precipitation
   • up to 1500 mm (5 feet) in single storms in equatorial regions, i.e., monsoon (convergent precipitation) over mountains
   • trace of precipitation (< 0.5 mm or < 0.2 mm) is insignificant in terms of water budgets has important ecological and human effects (e.g., freezing rain, cooling of desert pants, latent heat of vaporization)
   • expressions of variability

   • range = maximum – minimum for a given period and place
   • standard deviation, the square root of the sum of the average squared deviations from the mean: (sum (p_i-P)²/n-1)^1/2, where p_i is the individual precipitation observation, P is the mean precipitation and n is the number of observations
   • interquartile range (dispersion about the median) between the 75% and 25% positions in a ranked series, i.e., between the upper and lower quartiles
   • coefficient of variation: standard deviation / mean; low for humid environments, highest for dry climates
   • inter-annual variation: sum | p_i-1 – p_i | / n-1 * 100; a measure of average variation among years expressed as a percentage; highest for direst climates (e.g., rebate on snow blower if snowfall is less than average by a certain amount, but then most people live in humid climates where the IAV is low)

   Intensity

   • rate of precipitation; depth / duration (e.g., mm per hour)
   • measured directly buy recording rain gauges
   • there is a negative exponential relationship between intensity and duration; i.e., decreasing decrease in intensity with increasing duration; short duration storms (usually convective) have the highest intensities
   • the shape of the intensity – duration curve varies geographically according to the relative amounts of convective versus cyclonic precipitation (steeper curve with more convective storms)
   • with individual storms, the depth of precipitation climbs sharply early in the storm and then levels off, whereas cyclonic precipitation shows an almost constant increase in depth (i.e., more or less constant intensity)
   • whereas rainfalls of maximum depths (e.g., 187 cm in 24 hours at Réunion Island off Madagascar during March, 1952) have intensities in the range of 4-8 mm per hour, the most intense (convective) storms have intensities of > 25 mm per hours (e.g., Buffalo Gap, SK: about 250 mm of rainfall in about one hour
   • significance of intensity:

   • soil erosion: raindrop impact, rainsplash and sheet erosion
   • local flooding
   • visibility
   • snow removal
   • nature of the hydrological cycle and thus landscape (bursts versus sustained input of similar annual amounts)

   Areal extent

   • determines whether the effects are local or regional, for example, whether flooding is local or delayed with ultimately larger but more extensive increase in streamflow

   Temporal extent (duration)

   • depends on the areal extent and rate of movement of a storm
   • thus typical durations for a place depend on the relative amounts of convective versus cyclonic precipitation

   Frequency

   • how often precipitation of certain magnitude reoccurs
   • expressions of frequency:

   • # of events of a specific magnitude / specific period of time (e.g., once in ten years)
   • probability: # of events of a specific magnitude / total # of events (e.g., 3 events / 300 storms = 0.01; or 2 monthly totals > 50 cm out of 60 months = 0.033)
   • recurrence interval (return period): average time period during which precipitation of a specific magnitude will reoccur (e.g., 100 year flood occurs on average once in 100 years)

   • return period and probability are inversely related; i.e., there is a small probability of a storm with a long return period
   • return period (years) = (n+1) / r, where n is the # of observations and r is the rank of a particular magnitude
   • thus the highest precipitation event or total (r = 1), will occur only once during the period record (n) and thus will have a return period of n+1

   • intensity – frequency – depth

   • described by straight lines or shallow curves on semi-log scale (log – frequency)
   • decrease in frequency with increasing intensity and depth

   • precipitation probabilities are established from

   • existing records which are sufficiently large (although records can be too long by encompassing climate change: a moving mean)
   • theoretical frequency distribution if a precipitation record can be assumed to approximate a known frequency distribution (e.g., log normal or Weibull)
   • probabilities are extrapolated assuming that the distribution of storm size and intensity will remain the same (probably invalid with global warming)
   • probabilities periodically be adjusted (e.g., after extreme events)

   N.B.: probabilities indicate nothing about the timing of events!! (just long term probability); thus two hundred year storms could occur in consecutive years, but their long-term probability still remains 0.01

   Engineering Structure	Probability of storm that exceeds it's capacity
   urban storm sewers, airports, expressways	0.2 (5 year storm); inconvenience but small threat to life or property
   protection of rural land (e.g., levees)	0.1 (10 year storm); more severe consequences than above
   protection of urban land	0.4 (25-year) storm; more population than rural land
   spillways (reservoir drainage)
   farm land downstream	0.04 < p < 0.01 (25-100 year storm)
   settlement downstream	probable maximum precipitation*

   * PMP is the depth of precipitation for a given location and duration that can be reached but not exceeded under imperfectly known meteorological conditions

   • theoretically determined from knowledge of maximum humidities, rates of advection and proportion of precipitable vapour at a given place
   • empirically determined from statistical analysis of extreme rainfalls
   • if the estimated PMP is too low, it will be exceeded; if it's too high, it can be adjusted as knowledge of meteorological processes improves

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