Processes: Scale, Complexity and Emergence

Norman H. Crawford


In early work on transport and fate of agricultural pesticides from the land surface at the EPA Laboratory in Athens , Georgia two approaches were used. Small watersheds in the range from five to twenty-five were monitored, and some very small plots were instrumented. Runoff and sediment transport were sampled and, for the small watersheds, pesticide concentrations in water and on sediments were sampled.


The philosophy was - to understand small watershed processes responsible for pesticide movement it would be necessary to extrapolate from the small plots which were approximately 8 by 12 feet. Precipitation, wind and humidity at several elevations above the plots, and soil moisture at several depths in the plots were measured on time intervals down to 10 seconds. A minicomputer logged data from the sensors and a 2400 ft. magnetic tape of data was recorded every day.


After about a year of data collection the small plots were abandoned and the data that were collected, I suspect, no longer exist. The small watershed measurements together with process modeling based on earlier work at Stanford led to the Agricultural Runoff Model that became part of HSPF.


The field work in Georgia , done in the 1970s, is history but the philosophy that prompted the two approaches remains very current. Some argue that, “to calculate or understand marco scale phenomena in watersheds we must first measure and analyze processes on a micro scale”. The contrary argument is, “macro scale phenomena are ‘emergent’, and micro scale data and analysis is irrelevant”: Emergent is ‘arising unexpectedly’. In “A Different Universe” (Basic Books, Perseus Book Group) Robert Laughlin writes that Newton ’s Laws are emergent, a consequence of aggregation of quantum matter – but they vanish into nothingness is examined too closely (on quantum scales).


The same philosophical argument is happening in physics. In 1972 in Science, P. W. Anderson wrote,


“the great majority of active scientists I think accept without question the ‘reductionism’ hypothesis (the assumption that the sum of the parts is equal to the whole). It seems inevitable – at first sight – that if everything obeys the same fundamental laws, the only scientists who are studying anything really fundamental are those who are working on those laws. The main fallacy of the reductionist  hypothesis is – it does not imply a constructionist one. The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.


The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity – at each level of complexity new properties appear – the whole becomes not only more than the sum of, but very different from the sum of the parts . . .”


  In hydrology is “the sum of the parts equal to the whole?” I believe this is true (we don’t deal with quantum effects), but there are problems of scale and complexity that are overlooked if a constructionist philosophy is casually accepted. Processes take place on all scales. It is useful to study and understand processes that take place at a point in a vertical soil column, but processes that take place at a point are not sufficient to understand all watershed processes. Analysis of the smallest scale only does not provide information on processes that take place on larger scales.


  In the experimental plots and small watersheds in Georgia it was not at all clear how or if the plot measurements were related to the watershed measurements. Sediment from the plots was highly variable – plots side by side gave sediment yields that were an order of magnitude different in the same storm. In the small watersheds sediment erosion and deposition could be seen within distances of a few feet. Runoff from the small watersheds would react to high rainfall intensities over one to three minutes within a storm, but not to tens second intensities – the ten second intensities were most likely non-uniform over the small watersheds.


  A Précis on Processes and Scale for Runoff and Hydrograph Shape


  What then does matter? Topography? Rainfall intensity? Soils? Vegetation? Stream channel characteristics? An unsatisfactory answer is that all of these things matter depending on circumstances. To attempt to be more specific, the following are generalizations, and in hydrology there are always exceptions.





  Forecasting the volume and timing of runoff from lands based on current watershed conditions and rainfall is very difficult. Runoff is a difference between rainfall (or water the snow pack when snow is present) and infiltration or ‘losses’. Often runoff is a small difference between large numbers.


  Infiltration into the soil profile varies in both time and space, even if rainfall intensity is uniform over an area. Water may pond on uneven land surfaces and infiltrate latter, and flow occurs on flow paths that have dramatically different timing; surface runoff may enter streams in minutes and groundwater may enter streams months after rainfall occurs.


  Infiltration and flow in the vadose zone is extraordinarily complex. In many watersheds runoff volume and timing is strongly influenced preferential flow processes. The program for a 2006 conference on preferential flow in Ascona , Switzerland states, preferential flow has shown to be more the rule than the exception at many study sites.


 Conceptual Models of Flow and Transport in the Fractured Vadose Zone’ by the National Academies Press contains field observations and  conceptual approaches to modeling the vadose zone. This book can be read on-line. The executive summary includes statements that;


·        The current state of knowledge is not adequate to determine which processes are likely to control unsaturated flow and transport at a given field site.

·        Research is needed to understand the spatial variability in vadose zone properties, and to develop upscaling methods.

·        Spatial variability is a key cause of model uncertainty


At Stanford in the 1960s, in work with continuous simulation models for surficial runoff, it was immediately clear that existing infiltration approaches would not reproduce observed runoff into stream channels – concepts were needed that would include both time and spatial variability of key processes like infiltration, and variability in soil moisture storage characteristics. Necessity gave birth to the ‘cumulative distributions of infiltration capacity’ and ‘nominal soil moisture capacities’ in Stanford Model IV. Nominal soil moisture capacities are discussed in Fuzzy Sets. Uncertainty about processes on the land was much greater than that for channel flow hydraulics – the hydraulics of flow in channels was well developed.


It is not clear if Interflow and Preferential Flow are synonymous; definitions of these terms vary. It is clear that preferential flow contributes to the delayed runoff traditionally known as interflow. It is equally clear that scale and complexity in surficial hydrologic process are challenging and that moving from micro scale analysis to ‘land segment’ macro scale analysis is perilous. Perhaps spatial variability of hydrologic processes like infiltration is ‘emergent’ and cannot be anticipated with micro scale analysis.



Hydrograph Shape


   Hydrograph shape, peak flows: The determinants of hydrograph shape and peak flows depend on the ratio of flow time for the overland flow to the flow time in stream channels. Overland flow times in natural watersheds are +/- 10 minutes. If channel flow times are 3 minutes – say or 700 feet at about 4 feet/second – hydrograph shape will be dominated by surficial flow paths on the watershed. In a watershed of this scale and channel flow times (10 to 15 acres) channel characteristics will not be relevant.

  In larger watersheds with longer channel flow times the overland flow hydrograph will be attenuated and hydrograph shaped becomes dependent on channel characteristics. Figure 1 shows runoff from a land segment entering a stream channel (outflow from overland flow plus interflow and groundwater), but is not representative of all of the runoff in the watershed – there are about 300 land segments.



Figure 1


  Figure 2 illustrates the effects of routing in stream channels for Clearwater Creek, an 18.5 sq. mi. tributary to the Middle Fork. The figure shows total inflow to the channel network and the routed streamflow at the gage.

  The Clearwater has high channel gradients and no extensive overbank flows so hydrograph shape is primarily dependent on inflows to the channel network.




Figure 2


Figure 3 shows channel network inflow and streamflow at the gage on Dry Creek nr. Modesto . Dry Creek is larger (193 sq. mi.) than Clearwater Creek (18.5 sq. mi.) and has lower chanel gradients so routing in channel significantly attenuates inflows from the land.



Figure 3


Since Clearwater Creek is has greater sensitive to channel inflows peak flows are more dependent on rainfall intensities over 15 minute to hourly intervals. Dry Creek peak flows are more dependent on channel characteristics; channel inflow timing coming from the land surface could change without changing the hydrograph peak flow or shape at the gage.



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