Modeling recession curve of karstic springs – parallel or serial reservoirs? Alon Rimmer, Israel Oceanographic and Limnological Research, The Yigal Allon Kinneret Limnological Laboratory, Israel. e-mail: alon@ocean.org.il Observations Objective To gain a better understanding of the baseflow from the karstic region of Mt. Hermon – the origin of the main three tributaries (Dan, Senir, Hermon) of the Jordan River. The linear reservoir concept The hydrograph of a spring during dry season that follows a rainy period will decay following an exponential curve, or the sum of several exponentials. In traditional hydrology this trend is mathematically equivalent to a model of spring flow recession with one reservoir, or several parallel reservoirs. In this case recession process will start at the very end of the rainy season. Analysis of measured spring discharges in the karstic Hermon region (North Israel) reveals a clear diversity of recession curves during the dry season. While the recession of two large springs are fast during the beginning of the dry season and slow during the end (exponential decay?), the recession of the third spring is rather slow (or sometimes increases) after the beginning of the dry season and becomes faster towards the end of this season. Moreover, following a low precipitation season, the recession of this spring is faster than the recession following a high precipitation season. It is proposed that the appropriate modeling approach for each spring in this karstic region includes two serial reservoirs, where the upper one stands for the vadose zone, and the lower represents the groundwater. Our analysis showed that by using only one linear reservoir model, the recession constant K appears to be too large, and may fluctuate from one value to another, depending on the period we selected for the recession analysis. However, if we use a model with two serial reservoirs for the same purpose, the spring discharge will always be a function of constant recession parameters K 1 and K 2 , and the initial conditions (Q 01 and Q 02 ) for each reservoir. The predictions of the spring flow will therefore be independent of the selected period of recession, and, the entire system will be more physically based. 9During a hydrological year the precipitation on the Hermon region are restricted to the wet season from October to April. 9Analysis of measured discharge reveals a clear diversity of the recession curves during the dry season. 9The recession of springs that recharge the Hermon and Snir streams are fast during the beginning of the dry season and slow during the end (exponential decay?). 9The recession of the Dan stream is rather slow during the beginning, and increases during the end of the dry season. 9Following a low precipitation season, the recession of the Dan Spring is faster than the recession following a high precipitation season. The hydrograph of a spring (or stream) during dry season that follows a rainy period will decay following an exponential curve, or the sum of several exponentials. In traditional hydrology this trend is mathematically equivalent to a model of spring flow recession with one reservoir, or several parallel reservoirs. In this case recession process will start at the very end of the rainy season. Model type Abstract Mt. Hermon watershed-location map Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Snir Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Hermon Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Dan Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Sde Nehemya Senir Hermon Dan ( ) () () t Q t Q dt t dV out in − = K represents the natural inner structure of the reservoir, and should not change from one season to another. h Surface area =A (volume) V=A ⋅ h(t) (outflux) Q out =V/K Q out Q in A ( ) 0 t Q in = ( ) ( ) K t Q dt t dQ out out − = () ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = K t exp Q t Q 0 out ( ) ( ) t Q K t V out × = () ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = 2 02 1 01 out K t exp Q K t exp Q t Q days K 1 =50 Q 01 =480 K 2 =1000 Q 02 =110 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Discharge (1000 m 3 ) measured LR 2 LR 1 Total dry season dry season precipitation Monitoring station h 1 h 2 Two parallel linear reservoirs 200 400 600 800 Hermon 200 400 600 800 Senir Oct1993 Oct1994 Oct1995 Oct1996 Oct1997 Oct1998 Oct1999 400 600 800 Dan date Discharge (1000 m 3 ) FNF BFS